Fundamental Physical Constants Mohr, P.; Taylor, B. 5 by Marco Acuña

Table of the Isotopes

11-134 Elem. or Isot. 158 159

160 161

Gd Gd

Natural Abundance (Atom %) 24.84(7)

21.86(19)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

157.924104 158.926389

18.6 h

β- 0.971

159.927054 160.929669

> 1.9 × 1019 y 3.66 m

β- ββ- /1.956

162

161.930985

8.4 m

β- /1.39

163

162.9340

1.13 m

β- /3.1

Gd Gd 166 Gd 167 Gd 168 Gd 169 Gd

163.9359 164.9394 165.942 166.946 167.948 168.953

45. s 10 s ~ 4.8 s

β- /2.3 β-

164 165

158.92535(2)

Tb Tb 139 Tb

137.9532 138.9483

135 138

0.9 ms

2.4 s

β+, EC/11

Tb Tb 142m Tb 142 Tb 143 Tb 144m Tb 144 Tb 145m Tb

140.9415

3.5 s 25 μs 0.30 s 0.60 s 12. s 4.1 s < 1.5 s 30. s

β+, EC/~ 8.3

Tb Tb

144.9293

Tb Tb

145.92725

146.92405

142m2

145

146m

146

147m

147

148m

487_S11.indb 134

141.9387 142.9351 143.93305

0+ 3/2-

1.56/85

0+ 5/2-

1.0/

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b) -0.44

γ-Energy / Intensity (MeV/%) Tb k x-ray 0.36351 0.058-0.855 Tb k x-ray 0.1023 0.3149 0.3609 0.4030 0.4421 0.2868 0.214 1.685

0+ 0+

(0.040-1.015)

p/1.179

1.6 s

139.946

141

0.971/58 0.913/29 0.607/12

Spin (h/2 π)

140

Particle Energy/ Intensity (MeV/%)

0.109 0.120 0.329 0.355–0.740

β+, EC/ β+, EC/10. β+, EC/7.4 IT β+, EC/8.4 β+, EC/~ 6.6

40+ 11/251+ 11/2-

β+, EC/6.5 β+ /76 / EC/24 /

½+ (5-)

~ 8. s 1.8 m

β+ /8.1 β+ /35 / EC/65 /

1+ 11/2-

1.6 h

β+ /42 /4.61 EC/58 /

5/2+

2.3 m

β+ /25 / EC/75 /

23. s

ann.rad./ 0.2577 0.5370 0.9876 ann.rad./ Gd k x-ray 1.0789 1.5795

+1.70

ann.rad./ Gd k x-ray 1.3977 1.7978 ann.rad./ Gd k x-ray 0.6944 1.1522 (0.120–3.318) ann.rad./ Gd k x-ray 0.3945 0.6319 0.7845

4/17/06 11:00:06 AM

Table of the Isotopes Elem. or Isot. 148

Natural Abundance (Atom %)

Atomic Mass or Weight 147.92427

149m

149

148.923246

150m

150

149.92366

151m

151

150.923103

152m

11-135 Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV) β+, EC/5.69

4.16 m

EC/88 / β+ /12 /

11/2-

4.13 h

β+ /4 /3.636 α/16/

6.0 m

β+ /17 / EC/83 /

3.3 h

β+, EC/4.66

-0.90

25. s

I.T./95 / β+, EC/7 /

11/2-

17.61 h

β+/1 /2.565 EC/99 /

4.3 m

I.T./79 /0.5018 EC/21 /4.35

17.5 h

β+ /20 /3.99 EC/80 /

153

152.923435

2.34 d

154

487_S11.indb 135

153.92468

-1.75

+1.35

151.92407

1.8/ 3.97/

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

½+

154m1

Spin (h/2 π)

1.00 h

152

154m2

Particle Energy/ Intensity (MeV/%)

0.70/

1/2+

-0.3

+0.92

(8+)

2.5/ 2.8/

-0.58

+0.3

EC/1.570

5/2+

+3.44

+1.1

23.1 h

EC/98 / I.T./2 /

(7-)

0.9

9. h

β+ /78 / I.T./22 /

(3-)

1.7

21.5 h

EC/99 /3.56 β+ /1 /

1.86/ 2.45

+3.

γ-Energy / Intensity (MeV/%) 0.8824 ann.rad./ Gd k x-ray 0.4888 0.7845 (0.14–3.8) ann.rad./ Gd k x-ray 0.1650 0.7960 Gd k x-ray 0.1650 0.3522 0.3886 (0.1–3.2) ann.rad./ Gd k x-ray 0.4384 0.6380 0.6504 0.8275 ann.rad./ 0.4963 0.6380 (0.3–4.29) 0.0229 0.0495 0.3797 0.8305 Gd k x-ray 0.1083 0.2517 0.2870 (0.1–1.8) Tb k x-ray Gd k x-ray 0.2833 0.3443 0.4111 ann.rad./ Gd k x-ray 0.3443 (0.2–2.88) Gd k x-ray 0.2119 (0.05–1.1) Gd k x-ray 0.1231 0.2479 0.3467 1.4199 Gd k x-ray 0.1231 0.2479 0.5401 (0.12–2.57) Gd k x-ray 0.1231 1.2744 2.1872

4/17/06 11:00:07 AM

Table of the Isotopes

11-136 Elem. or Isot. 155

Natural Abundance (Atom %)

Atomic Mass or Weight 154.92351

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

5.3 d

EC/0.82

3/2+

1.02 d

I.T./

(7-)

5.3 h

I.T./0.0884

(0+)

156m2

156m1

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b) +2.01

+1.41

156

155.924747

5.3 d

EC/2.444

~ 1.7

+2.

157

156.924025

1.1 × 102 y

EC/0.0601

3/2+

+2.01

+1.4

10.5 s

I.T./0.11

157.925413

1.8 × 102 y

EC/80 /1.220 β- /20 /0.937

+1.76

+2.7

158.925347 159.927168

72.3 d

β- /1.835

0.57/47 0.86/27

3/2+ 3-

+2.014 +1.79

+1.43 3.8

2.2

+1.2

158m

158

159

Tb Tb

160

100.

161

160.927570

6.91 d

β- /0.593

0.46/23 0.52/66 0.6/10

3/2+

162

161.92949

7.6 m

β- /2.51

1.4

(1/2-)

163

162.930648

19.5 m

β- /1.785

0.80/

3/2+

164

163.9334

3.0 m

β- /3.9

1.7/

(5+)

165

164.9349

2.1 m

β- /3.0

166

Tb Tb

165.9380 166.9401

26 s 19 s

β-/

167.944 168.946 169.950 170.953

167

Tb Tb 170 Tb 171 Tb 168 169

162.500(1)

138.960

139

487_S11.indb 136

0.6 s

3/2+

γ-Energy / Intensity (MeV/%) (0.12–3.14) Gd k x-ray 0.08654 0.10530 Tb k x-ray 0.0496 Tb k x-ray 0.0884 Gd k x-ray 0.08896 0.19921 0.53435 1.22245 Gd k x-ray 0.0545 Gd k x-ray 0.0110 Gd k x-ray 0.0795 0.9442 0.9621 Dy k x-ray 0.08678 0.29857 0.87936 0.96615 Dy k x-ray 0.02565 0.04892 0.07458 Dy k x-ray 0.2600 0.8075 0.8882 Dy k x-ray 0.3511 0.3897 0.4945 Dy k x-ray 0.1689 0.2157 0.6110 0.6885 0.7548 0.5389 1.1785 1.2920 1.6648 0.057 0.070 0.075–0.227

β+, p

4/17/06 11:00:09 AM

Table of the Isotopes Elem. or Isot. Dy Dy 142 Dy 143 Dy 144 Dy 145m Dy 146m Dy 146 Dy 147m Dy 140

Natural Abundance (Atom %)

141

Atomic Mass or Weight 139.954 140.9514 141.9464 142.9438 143.93925 144.9365 145.93285

11-137 Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

0.9 s 2.3 s 3.9 s 9.1 s 14. s 0.15 s 30. s 56. s

EC, β+ /9. EC, β+ /7.1 EC, β+ /~ 8.8 EC, β+ /~ 6.2 EC, β+ I.T. EC, β+ /5.2 I.T./40 / β+, EC/60 /

147

146.93109

75. s

EC, β+ /6.37

148

147.92715

3.1 m

β+ /4 /2.68 EC/96 /

149

148.92731

4.2 m

β+, EC/3.81

150

149.925585

7.18 m

150.926185

17. m

β+, EC/67 /1.79 α/33 / β+ /5 /2.871 EC/89 / α /6 /

151

152

153

154 155

156 157

158 159

151.92472

2.37 h

152.925765

6.3 h

Dy Dy

3. × 106 y 9.9 h

α/2.95 β+ /2 /2.095 EC/98 /

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

1.2/

0+ 11/210+ 0+ (11/2-)

-0.66

½+

-0.92

(7/2-)

4.233/

+0.7

-0.12

-0.62

-0.95

-0.30

(7/2-)

-0.78

~-0.15

0+ 3/2-

-0.385

+1.04

Tb k x-ray 0.0655 0.2269

0+ 7/2-

4.067/

3.63/ 0.89/

3.46/

2.87/ 0.845/

Dy k x-ray 0.072 0.6787 ann.rad./ 0.1007 0.2534 0.3653 ann.rad./ Tb k x-ray 0.6202 ann.rad./ 0.1008 0.1063 0.2534 0.6536 0.7894 1.7765 1.8062 Tb k x-ray 0.3967 Tb k x-ray 0.1764 0.3030 0.3861 0.5463 (0.16–2.09) Tb k x-ray 0.2569 Tb k x-ray 0.0807 0.0997 0.2137 (0.08–1.66)

0.056(3)

155.92428 156.92547

8.1 h

EC/1.34

0+ 3/2-

-0.301

+1.30

Dy Dy

0.095(3)

157.924409 158.925739

144. d

EC/0.366

0+ 3/2-

Tb k x-ray (0.0609–1.319)

-0.354

+1.37

2.329(18) 18.889(42) 25.475(36) 24.896(42) 28.260(54)

159.925198 160.926933 161.926798 162.928731 163.929175

Tb k x-ray 0.3262

-0.480

+2.51

+0.673

+2.65

Dy Dy 162 Dy 163 Dy 164 Dy 165m Dy 161

487_S11.indb 137

153.92442 154.92575

Spin (h/2 π)

Dy Dy

160

165

EC/0.60 α/ β+ /1 /2.171 EC/99 / α /0.01 /

Particle Energy/ Intensity (MeV/%)

164.931703

1.26 m

I.T./98 /0.108 β- /2 /

2.33 h

β- /1.286

0+ 5/2+ 0+ 5/20+ 1/2-

1.29/

7/2+

-0.52

+3.5

Dy k x-ray 0.1082 0.5155 Ho k x-ray

4/17/06 11:00:10 AM

Table of the Isotopes

11-138 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

166

165.932807

3.400 d

β- /0.486

0.40/

167

166.9357

6.2 m

β- /~ 2.35

1.78

(1/2-)

168

167.9371

8.5 m

β- /1.6

Dy Dy 171 Dy 172 Dy 173 Dy

168.9403 169.9424 170.9462 171.9488 172.953

~ 39. s

β- /3.2

169 170

Ho Ho 141 Ho 142 Ho 143 Ho 144 Ho 145 Ho 146 Ho 147 Ho 148m Ho 148 Ho 140

141m

139.969 140.963 141.960 142.9546 143.9515 144.9472 145.9446 146.94006 147.9377

6 ms 8 μs 4.2 ms 0.4 s > 0.2 μs 0.7 s 2.4 s 3.3 s 5.8 s 9. s 2. s

p/ p/ β+, p EC/β+, p

p/1.09 p/1.23 p/1.71

β+, EC/12 β+ β+, EC/10.7 β+, EC/8.2 β+, EC/ β+, EC/9.4

(10+) 11/241+

21. s

β+, EC/

11/2-

1/2+ (9+)

> 30. s 25. s

β+, EC/6.01 β+, EC/

149.93350

1.3 m

β+, EC/6.6

47. s

β+, EC/87 / α/13

4.605/

35.2 s

β+, EC/80/5.13 α/20 /

4.519/

50. s

β+, EC/90/ α/10/

4.453/

152m

487_S11.indb 138

148.93378

151m

151

Ho Ho

150m

150

γ-Energy / Intensity (MeV/%) 0.09468/3.8 Ho k x-ray 0.0282 0.0825 Ho k x-ray 0.2593 0.3103 0.5697 (0.06–1.4) Ho k x-ray 0.1925 0.4867

164.93032(2)

149m

149

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

150.93169

0.307

(9+)

ann.rad./ ann.rad./ ann.rad./ ann.rad./ 0.6615 1.6883 ann.rad./ 1.0733 1.0911

+5.9

-1.

ann.rad./ 0.3939 0.5511 0.6534 0.8034 ann.rad./ 0.5913 0.6534 0.8034 ann.rad./ 0.2102 0.4889 0.6948 0.7762 ann.rad./ 0.3522 0.5274 0.9676 1.0471 ann.rad./ 0.4929 0.6138 0.6474

4/17/06 11:00:11 AM

Table of the Isotopes Elem. or Isot. 152

Natural Abundance (Atom %)

Atomic Mass or Weight 151.93171

153m

153

152.93020

154m

11-139 Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

2.4 m

β+, EC/88/6.47 α/12/

9.3 m

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(3+)

-1.02

β+, EC/99+/4.12 α/ 4.01/

5/2

+1.19

2.0 m

β+, EC/99+/4.13 α/ 3.91/

11/2-

+6.8

-1.1

3.3 m

β+, EC/

(8+)

5.7

-1.0

4.387/

+0.1

154

153.93060

12. m

β+, EC/5.75

-0.64

+0.2

155

154.92910

48. m

β+/6/3.10 EC/94 /

(5/2+)

+3.51

+1.5

5.8 m

I.T./0.0352 β+ /25 / EC/75 /

+2.99

+2.3

7/2-

+4.35

+3.0

+2.44

+1.6

+3.77

+4.1

156m

1.8/ 2.9/

156

155.92984

56. m

β+, EC/4.4

157

156.92826

12.6 m

β+/5/2.54 EC/95/

28. m

I.T./44/ EC/56/

21. m

β+, EC/

(9+)

11.3 m

β+/8/4.24 EC/92/

158m2

158m1

158

487_S11.indb 139

157.92894

(5+)

1.18/

1.30/

γ-Energy / Intensity (MeV/%) 0.6835 ann.rad./ 0.6140 0.6476 ann.rad./ 0.0905 0.1089 0.1618 0.2302 0.2707 0.3659 0.4565 ann.rad./ 0.2958 0.3346 0.4381 0.6383 ann.rad./ 0.3346 0.4124 0.4771 ann.rad./ Dy k x-ray 0.3346 0.5700 0.8734 ann.rad./ Dy k x-ray 0.0474 0.1363 0.3254 (0.06–2.24) ann.rad./ Dy k x-ray 0.1378 0.2666 (0.28–2.9) ann.rad./ 0.1378 0.2665 ann.rad./ Dy k x-ray 0.2800 0.3411 ann.rad./ Dy k x-ray 0.0989 0.2182 ann.rad./ 0.0981 0.1664 0.2182 0.3205 0.4062 0.9774 1.0532 0.4846 ann.rad./ Dy k x-ray 0.0989

4/17/06 11:00:13 AM

Table of the Isotopes

11-140 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

159m

159

158.927712

Ho Ho

160m

159.92873

161m

161

160.927855

162m

162

161.929096

163m

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

IT/0.206

1/2+

33.0 m

EC/1.838

7/2-

+4.28

+3.2

1+ 2-

+2.52

+1.8

+3.71

+4.0

IT/67/0.060 EC/33/3.35

25.6 m

β+, EC/3.29

0.57/

6.8 s

IT/0.211

2.48 h

EC/0.859

7/2-

+4.25

+3.2

1.12 h

IT/61/ EC/39/

+3.60

+4.

15. m

EC/96 /0.295 β+ /4 /

1.09 s

I.T./0.298

(1/2+) +4.23

+3.6

+4.17 3.6

+3.49 -3.

Ho Ho

162.928734

4.57 × 103 y 38. m

EC/0.00258 I.T./0.140

7/2(6-)

164

163.930234

29. m

EC/58 /0.987 β- /42 /0.963

165

Ho Ho

1.2 × 103 y

β- /

163

164m

166m

100.

164.930322

7/27-

166

165.932284

1.117 d

β- /1.855

1.776/48 1.855/51

167

166.93313

3.1 h

β- /1.007

0.31/43 0.61/21

(7/2-)

487_S11.indb 140

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

8.3 s

3. s 5.0 h

160m2

160

Half-life/ Resonance Width (MeV)

γ-Energy / Intensity (MeV/%) 0.2182 0.9488 Ho k x-ray 0.1660 0.2059 Dy k x-ray 0.1210 0.1320 0.2529 0.3096 (0.06–1.2) 0.0868 0.1970 0.6464 0.7281 0.8791 0.9619 0.9658 See Ho[166m] 0.7282 0.8794 Ho k x-ray 0.2112 Dy k x-ray 0.0256 0.0592 0.0774 0.1031 Dy k x-ray Ho k x-ray 0.0807 0.1850 0.2828 0.9372 1.2200 Dy k x-ray 0.0807 1.3196 1.3728 Ho k x-ray 0.2798 Dy M x-rays Ho k x-ray 0.0373 0.0566 0.0940 Dy k x-ray 0.0734 0.0914 Er k x-ray 0.18407 0.71169 0.81031 Er k x-ray 0.08057 1.37943 Er k x-ray 0.0793

4/17/06 11:00:14 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

169

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

2.2 m 3.0 m

I.T./ β- /2.91

168.93687

4.7 m

β- /2.12

43. s

β- /

170

169.93962

2.8 m

β- /3.87

171

Ho Ho

170.941 171.9448

53 s 25. s

β- / β- /

Ho Ho 175 Ho

172.9473 173.951 174.954

173 174

143.9604 144.9574 145.9520 146.9495 147.9446 148.94231 149.93791

> 0.2 μs 0.9 s ~ 1.7 s 2.5 s 4.5 s 10. s 10.7 s 18. s

Er Er

150.93745 151.93505

23. s 10.2 s

153

152.935063

37.1 s

154

153.93278

3.7 m

155

154.93321

5.3 m

156

155.93107

20. m

145

152

487_S11.indb 141

2.0/

1.2/ 2.0/

(7/2-)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.0835 0.2379 0.3213 0.3465 Er k x-ray 0.7413 0.8159 0.8211 (0.08–2.34) 0.1496 0.7610 0.7784 0.7884 0.8529 0.0787 0.8123 1.8940 1.9726 Er k x-ray 0.1816 0.2582 0.8902 0.9321 0.9414 1.1387 Er k x-ray (0.077–1.186)

167.259(3)

Er Er 146 Er 147 Er 148 Er 149m Er 149 Er 150 Er 144

151

Spin (h/2 π)

167.93552

170m

172

Particle Energy/ Intensity (MeV/%) 0.96/15 0.97/15

Ho Ho

168m 168

11-141

β+ β+ E.C, β+ /~ 9.1 β+, EC/6.8 IT ECβ+ /8.1 β+ /36 /4.11 EC/64 / β+, EC/5.2 β+, EC/10/3.11 α/90/ α/ β+, EC/47/4.56 β+, EC/99+/2.03 α/0.5/ β+, EC/47/3.84 EC/53 /

β+, EC/1.7

0+ 0+ 11/2½+ 0+

4.804/ 4.674 4.35/ 4.166/

ann.rad./ Ho k x-ray 0.4758 ann.rad./ ann.rad./

7/20+ -0.934

-0.42

0.351 (0.0945–1.700) ann.rad./

-0.669

-0.27

ann.rad./ Ho k x-ray 0.1101 0.2415 ann.rad./ 0.0298 0.0352 0.0522 0.1336

0+ (7/2-)

4/17/06 11:00:16 AM

Table of the Isotopes

11-142 Elem. or Isot.

156.93192

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 25. m β+, EC/3.5

157.92989

2.2 h

EC/99.5 /1.78 β+ /0.5 /

158.930684

36. m

β+ /7 /2.769 EC/93 /

3/2-

159.92908

1.191 d

EC/0.33

160.93000

3.21 h

EC/2.00

3/2-

1.25 h

EC/1.210

0+ 5/2-

10.36 h

EC/0.376

2.27 s

I.T./0.208

0+ 5/20+ ½7/2+ 0+ ½-

+0.485

0+ 5/2-

0.66

157

Natural Abundance (Atom %)

158

159

160

161

Atomic Mass or Weight

Particle Energy/ Intensity (MeV/%)

0.74/

Spin (h/2 π) 3/2-

Er Er

0.139(5)

161.928778 162.93003

Er Er 166 Er 167m Er

1.601(3)

163.929200 164.930726 165.930293

Er Er 169 Er

22.869(9) 26.978(18)

166.932048 167.932370 168.934590

9.40 d

β- /0.351

Er Er

14.910(36)

169.935464 170.938030

7.52 h

β- /1.491

171.939356

2.05 d

β-/0.891

172.9424

1.4 m

β- /2.6

(7/2-)

174

173.9442

3.1 m

β- /1.8

Er Er 177 Er

174.9478 175.9501 176.954

1.2 m

β-

~ 1.9 μs 3.1 μs

p p// ~ 10

162 163

164 165

167 168

170 171

172

173

175 176

33.503(36)

168.93421(2)

Tm Tm

144.9701

144 145

487_S11.indb 142

0.35/~ 100

0.28/48 0.36/46

Nuclear Elect. γ-Energy / Magnetic Quadr. Intensity Mom. (nm) Mom. (b) (MeV/%) -0.412 +0.92 ann.rad./ 0.117 0.385 1.320 1.660 1.820 2.000 Ho k x-ray 0.0719 0.2486 0.3868 -0.304 +1.17 ann.rad./ Ho k x-ray 0.6245 0.6493 (0.07–2.5) Ho k x-ray (0.05–0.96) -0.37 +1.36 Ho k x-ray 0.8265 (0.07–1.74) +0.557

+2.55

Ho k x-ray 0.4361 0.4399 1.1135

+0.643

+2.71

Ho k x-ray

-0.5639

+3.57

Er k x-ray 0.2078

Tm k x-ray 0.1098 0.1182 2.9

Tm k x-ray 0.11160 0.29591 0.30832 (0.08–1.4) Tm k x-ray 0.0597 0.4073 0.6101 Tm k x-ray 0.1928 0.1992 0.8952 Tm k x-ray (0.100–0.152) (0.0765–1.168)

1.70, 1.43 1.73/91

4/17/06 11:00:19 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-143 Atomic Mass or Weight

146m

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

0.198 s

β+, p

145.9664

0.08 s

β+/14. p

147

Tm Tm

146.9610

0.4 ms 0.56 s

Tm Tm 149 Tm 150 Tm 151 Tm 152m Tm 152 Tm 153 Tm

147.9578

0.7 s

β+, p EC, β+/85 p/15/ β+, EC/12.

148.9527 149.9500 150.94548

0.9 s 2.3 s 4. s 8. s 5. s 1.6 s

146

147m

148m 148

151.9444 152.94201

3.3 s

154m

154.93920

30. s

Tm Tm

155.93898

19. s 1.40 m

α/ β+, EC/7.6 α/

4.23/

156.93697

3.6 m

β+, EC/4.5 α/

2.6 3.97/

157.93698

4.0 m

158.93498

Tm Tm

159.93526

156

157

158

159

160m 160

(0.1007–2.177) ann.rad./ ann.rad./ ann.rad./ ann.rad./ 0.4605–0.7960 ann.rad./ 0.0315 0.0638 0.0881 0.2268 0.5320 0.6067

4.46/

γ-Energy / Intensity (MeV/%)

ann.rad./

5.109/ α/5.031/100 4.84/0.24 α/4.956/100 4.83/0.45

8.1 s

156m

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

153.94157

155

Spin (h/2 π)

11/26-

154

487_S11.indb 143

β+, EC/~ 9.2 β+, EC/~ 11.5 β+, EC/7.5 β+, EC/ β+, EC/8.8 β+, EC/10 /6.46 α/90 / β+, EC/15 / α/ β+, EC/56 /7.4 α/44 / β+, EC/5.58 α/

Particle Energy/ Intensity (MeV/%) 1.4/9 p/1.118/100 1.01/ 0.89/8 p/1.19/100 1.01/28 0.94/22 p/1.115 ~ 10.7 1.052/

+0.40

-0.5

+0.48

β+, EC/74 /6.5 EC/26 /

(2-)

+0.04

+0.7

9.1 m

β+/23 /3.9 EC/77 /

5/2+

+3.42

+1.9

1.24 m 9.4 m

IT β+/15 /5.9 EC/85 /

(5) 1-

+0.16

+0.58

ann.rad./ 0.3446 0.4529 0.5860 ann.rad./ 0.1104 0.3484 0.3855 0.4550 (0.1–1.58) ann.rad./ Er k x-ray 0.1921 0.3351 0.6280 1.1498 (0.18–2.81) ann.rad./ Er k x-ray 0.0591 0.0848 0.2713 (0.05–1.27) ann.rad./ Er k x-ray 0.1264 0.2642 0.7285 0.8544

4/17/06 11:00:20 AM

Table of the Isotopes

11-144 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

160.93355

161

162m

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

31. m

β+, EC/3.2

7/2+

24. s

I.T./90 / β+, EC/10 /

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

+2.40

+2.9

+0.69

161.93400

21.7 m

β+ /8 /4.81 EC/92 /

+0.07

162.93265

1.81 h

EC/98 /2.439 β+ /1 /

½+

-0.082

5.1 m

I.T./80 / β+, EC/20 /

162

163

164m

163.93356

2.0 m

β+ /36 /3.96 EC/64 /

+2.38

164.932435

1.253 d

EC/1.593

½+

-0.139

165.93355

7.70 h

EC/98 /3.04 β+ /2 /

+0.092

166.932852

9.24 d

EC/0.748

½+

-0.197

167.934173

93.1 d

EC/1.679

+0.23

+3.2

168.934213 169.935801

128.6 d

½+ 1-

-0.232 +0.247

-1.2 +0.74

170.936429

1.92 y

β- /99.8/0.968 EC/0.2 /0.314 β- /0.096

½+

-0.230

171.93840

2.65 d

β- /1.88

172.939604

8.2 h

β- /1.298

164

165

166

167

168

Tm Tm

169 170

171

172

173

487_S11.indb 144

Half-life/ Resonance Width (MeV)

100

2.94/

0.883/24 0.968/76 0.03/2 0.096/98 1.79/36 1.88/29

0.80/21

½+

+0.71

+2.14

γ-Energy / Intensity (MeV/%) 0.8614 1.3685 ann.rad./ Er k x-ray 0.0595 0.0844 1.6481 (0.04–2.15) Tm k x-ray Er k x-ray 0.0669 0.8115 0.9003 ann.rad./ Er k x-ray 0.1020 0.7987 (0.1–3.75) Er k x-ray 0.0692 0.1043 0.2414 0.0914 0.1394 0.2081 0.2405 0.3149 ann.rad./ Er k x-ray 0.0914 Er k x-ray 0.0472 0.0544 0.29728 0.80636 Er k x-ray 0.0806 0.1844 0.7789 1.2734 2.0524 Er k x-ray 0.0571 0.20778 Er k x-ray 0.19825 0.4475 0.81595 Yb k x-ray 0.08425 0.06674 Yb k x-ray 0.07879 1.38722 1.46601 1.52982 1.60861 Yb k x-ray

4/17/06 11:00:21 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-145 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%) 0.86/71

Spin (h/2 π)

Tm Tm

173.94217

2.29 s 5.4 m

β- /3.08

0.70/14 1.20/83

(4-)

174.94384

15.2 m

β- /2.39

0.9/36 1.9/23

(1/2+)

176

175.9470

1.9 m

β-/4.2

2.0/ 1.2/

(4+)

Tm Tm 179 Tm

176.9490 177.9526 178.955

1.4 m

β-

173.04(3)

Yb Yb 150 Yb 151 Yb 152 Yb 153 Yb 154 Yb

147.967 148.964 149.9584 150.9554 151.9503 152.9495 153.94639

0.7 s > 0.2 μs 1.6 s 3.2 s 4. s 0.40 s

β+, p

154.9458

1.7 s

155.94282

26. s

156.94263

39. s

157.93987

1.5 m

β+, EC/1.9

158.94005

1.4 m

EC, β+/5.1

159.93755

4.8 m

β+, EC/2.0

160.93790

4.2 m

β+, EC/3.9

3/2-

161.93577

18.9 m

β+, EC/1.7

174m 174

175

177 178

148 149

155

156

157

158

159

160

161

162

487_S11.indb 145

β+ /8.5 β+ EC/5.5 β+ EC/6.7 β+ EC/7 /4.49 α/93 / β+, EC/16 /6.0 α/84 / β+, EC/21/3.57 α/79 / β+, EC/99+/5.5 α/0.5/

p/2.5–6.4/

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.3988 0.4613 Yb k x-ray 0.07664 0.17669 0.27332 0.3666 0.99205 (0.08–1.6) Yb k x-ray 0.36396 0.51487 0.94125 0.98247 Yb k x-ray 0.1898 0.3819 1.0691

0.647

0+ 0+

5.32/ 5.19/ 4.69/

ann.rad./ -0.8

-1.

ann.rad./ -0.64

4.69/

ann.rad./

-0.37

-.022

-0.33

+1.03

ann.rad./ 0.231 (0.035–0.670) ann.rad./ 0.0741 0.2526 Tm k x-ray 0.1661 0.1772 0.3297 0.3903 ann.rad./ 0.1404 0.1737 0.2158 ann.rad./ Tm k x-ray 0.0782 0.5999 0.6315 ann.rad./ Tm k x-ray 0.1188

4/17/06 11:00:23 AM

Table of the Isotopes

11-146 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

162.93633

11.1 m

β+ /26 /3.4

163.93449

1.26 h

EC/1.0

164.93528

9.9 m

β+ /10 /2.76 EC/90 /

165.93388

2.363 d

EC/0.30

166.934950

17.5 m

β+ /0.5 /1.954 EC/99.5 /

46. s

I.T./0.0242

0+ 1/2-

32.02 d

EC/0.909

7/2+

4.19 d

β- /0.470

0+ 1/20+ 5/20+ 7/2-

11.4 s

I.T./1.051

175.942572

1026 y 6.41 s

β-βI.T./0.3315

176.945261

1.9 h

β- /1.399

1.40

9/2+

178

177.94665

1.23 h

β- /0.65

0.25/

Yb Yb 181 Yb

178.9502 179.9523 180.9562

8. m 2. m

β- /2.4 β-

163

164

165

166

167

Yb Yb

168

169m

0.13(1)

168.935190

169

Yb Yb 172 Yb 173 Yb 174 Yb 175 Yb 170 171

167.933897

3.04(15) 14.28(57) 21.83(67) 16.13(27) 31.83(92)

169.934762 170.936326 171.936382 172.938211 173.938862 174.941277

176m

Yb Yb

176

177m

177

179 180

487_S11.indb 146

12.76(41)

1.4/

Spin (h/2 π) 3/2-

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b) -0.37

+1.24

+0.48

+2.48

+0.62

+2.70

1.58/

(5/2-)

0.639/

0.466/73 0.071/21 0.353/6.2

5/2-

(8-)

0+ 1/2-

-0.63

+3.5

γ-Energy / Intensity (MeV/%) 0.1635 ann.rad./ Tm k x-ray 0.0636 0.8603 (0.06 –1.9) Tm k x-ray 0.0914 0.6752 ann.rad./ Tm k x-ray 0.0801 1.0903 Tm k x-ray 0.0828 0.1844 0.7789 1.2734 2.0524 Tm k x-ray 0.06296 0.10616 0.11337 0.17633 Yb L x-ray 0.0242 0.1979/35.9 0.3078/10.05 0.0207–0.2611

+0.49367 -0.67989 0.77

+2.80 Lu k x-ray 0.3963/13 (0.114–0.28) Yb k x-ray 0.0961 0.1901 0.2929 0.3897 Yb k x-ray 0.1131 0.2084 Lu k x-ray 0.1504 0.1415 0.3246 0.3516 0.3815 0.6125 0.1028–0.4423

174.967(1)

4/17/06 11:00:25 AM

Table of the Isotopes Elem. or Isot.

154.95432

Half-life/ Resonance Width (MeV) 0.045 ms 43. ms 16 μs 0.08 s 0.7 s 0.9 s 1.0 s 2.6 ms 0.07 s

155.9530

0.20 s ~ 0.5 s

Lu Lu

156.95010

~ 9.6 s 4.8 s

157.94931

10.4 s

158.94663

12.3 s

β+, EC/6.0

159.9460

36.1 s

β+, EC/7.3

160.94357

1.2 m

β+, EC/5.3

Lu Lu

161.9433

~ 1.5 m 1.37 m

EC/ β+, EC/6.9

162.94118

4.1 m

β+, EC/4.6

163.94134

3.14 m

β+, EC/6.3

1.6/ 3.8/

164.93941

10.7 m

β+, EC/3.9

2.06/

2.1 m

β+ /35 / EC/65 /

Lu Lu 151m Lu 151 Lu 152 Lu 153 Lu 154 Lu 155m Lu 155 Lu 150m 150

Lu 156 Lu

Natural Abundance (Atom %)

11-147 Atomic Mass or Weight

149.973 150.9676 151.9641 152.9588 153.9575

156m

157m 157

158

159

160

161

162m 162

163

164

165

166m2

487_S11.indb 147

Decay Mode/ Energy (/MeV) p/1.29 p p/1.31 p/1.231

β+, EC/10.8 α/7.41 EC/8.0 α/ α/ β+, EC/9.5 α/ α β+, EC/94 /6.93 α/ β+, EC/99 /8.0 α/

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

5.66/90 5.57/

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

ann.rad./

5.45/ 4.925/

ann.rad./

5.00/ 4.67/

41-

1/2+

(0-)

ann.rad./ 0.3682 0.4770 ann.rad./ 0.1505 0.1875 0.3693 ann.rad./ 0.2434 0.3957 0.5773 ann.rad./ 0.0437 0.0671 0.1003 0.1108 0.1562 0.2562 ann.rad./ 0.1666 0.6314 ann.rad./ 0.0539 0.0581 0.1504 0.1631 0.3717 0.1238 0.2621 0.7404 0.8639 0.8804 ann.rad./ 0.1206 0.1324 0.1742 0.2036 (0.04–2.0) ann.rad./ Yb k x-ray 1.0673 1.2566 2.0986

4/17/06 11:00:26 AM

Table of the Isotopes

11-148 Elem. or Isot. Lu

166m1

Natural Abundance (Atom %)

Atomic Mass or Weight

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π) (3-)

165.93986

2.8 m

β+ /25 /5.5 EC/75 /

166.93827

52. m

β+ /2 /3.1 EC/98 /

6.7 m

β+ /12 / EC/88 / IT/<0.8

5.5 m

β+ /6 /4.5 EC/94 /

2.7 m

I.T./0.0290

1.419 d

EC/2.293

0.7 s

I.T./0.0929

2.01 d

EC/3.46

1.31 m

I.T./0.0711

8.24 d

EC/1.479

3.7 m

I.T./0.0419

166

167

168m

168

167.93874

169m

169

168.93765

170m

170

169.93848

171m

171

170.937913

172m

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(6-)

2.1/

7/2+

1.2/

(6-)

1/21.271/

7/2+

2.30

3.5

2.30

3.42

2.44/

1/20.362/

7/2+

171.939086

6.64 d

EC/2.519

2.90

3.80

172.938931

1.37 y

EC/0.671

7/2+

2.28

3.63

142. d

IT/99.3/ EC/0.7 /

1.50

172

173

174m

487_S11.indb 148

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 1.4 m β+, EC/58 / I.T./42 /0.0344

0.17086

γ-Energy / Intensity (MeV/%) ann.rad./ 0.1024 0.2281 0.2861 0.8119 0.8301 ann.rad./ Yb k x-ray 0.1024 0.2281 0.3375 0.3679 Yb k x-ray 0.0297 0.2392 (0.03–2.0) ann.rad./ Yb k x-ray 0.1988/190 0.8960/100 0.9792/128 0.018–2.65 ann.rad./ Yb k x-ray 0.1114 0.1124 0.2286 0.3483 1.4836 Lu L x-ray 0.0290 Yb k x-ray 0.19121 0.9606 (0.08–2.1) Lu L x-ray 0.04449 0.0484 Yb k x-ray 0.58711 0.5908 1.28029 (0.1–3.38) Lu k x-ray 0.07119 Yb k x-ray 0.01939 0.66744 (0.02–1.3) Lu L x-rays 0.04186 Yb k x-ray 0.18156 1.09367 (0.07–2.2) Yb k x-ray 0.07860 0.27198 Lu k x-ray 0.067055

4/17/06 11:00:27 AM

Table of the Isotopes Elem. or Isot. Lu

174

Natural Abundance (Atom %)

11-149 Atomic Mass or Weight

173.940338

Lu Lu

97.41(2)

174.940772

2.59(2)

175.942686

175

176m

176

Lu Lu

177m2 177m

177

176.943758

178m

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 3.3 y EC/1.374

3.66 h

β- /1.315

3.73 × 1010 y

β- /1.192 β+/ < 0.9

6. m 160.7 d

βIT/22/0.9702 β- /78

6.65 d

β- /0.498

23.1 m

β- /

Particle Energy/ Intensity (MeV/%)

1.229/ 1.317/

Spin (h/2 π) 1-

7/2+ 17-

39/223/2-

0.497/

7/2+ (9-)

177.945955

28.5 m

β-/2.099

2.03/

178.94733

4.6 h

β- /1.405

1.35/

7/2+

179.9499

5.7 m

β- /3.1

1.49/

180.9520

3.5 m

β- /2.5

181.9550

2.0 m

β- /~ 4.1

Lu Lu

182.9576 183.9609

58. s 20 s

β- / β-

7/2+

178.49(2)

Hf Hf 155 Hf 156 Hf 157 Hf 158 Hf

152.971 153.965 154.9634 155.9594 156.9584 157.95480

> 0.2 μs 2. s 0.9 s 25. ms 0.11 s 2.9 s

158.95400

5.6 s

159.95068

~ 12. s

Hf Hf

160.95028 161.94721

17. s 38. s

EC, β+/~ 6.7 EC, β+/8. α/ α/ EC/54 /5.1 α/46 / β+, EC/88 /6.9 α/12 / β+, EC/97 /4.9 α/4.78 α/ β+, EC/3.7

162.94709

40. s

β+, EC/5.5

178

179

180

181

182

183 184

153 154

159

160

161 162

163

487_S11.indb 149

(7/2+)

Nuclear Elect. γ-Energy / Magnetic Quadr. Intensity Mom. (nm) Mom. (b) (MeV/%) 1.9 Yb k x-ray 0.07664 1.2419 +2.2327 +3.49 +0.318 -1.47 Hf k x-ray 0.088372 +3.169 +4.92 Hf k x-ray 0.20187 0.30691 0.089 2.33 5.4 Lu k x-ray Hf k x-ray 0.11295 0.20836 0.37850 0.41853 +2.239 +3.39 0.11295 0.20836 0.2166 0.3317 Hf k x-ray 0.0932 1.3099 1.3408 (0.09–1.7) 0.2143 0.3377 0.40795/50. (0.07–1.9) 0.0458 0.2059 0.5749 0.0978 0.7208 0.8182

5.27/ 5.09/

4.60/

0+ ann.rad./ 0+

ann.rad./

ann.rad./ 0.1739 0.1963 0.4101 ann.rad./ 0.0454 0.0621 0.0710

4/17/06 11:00:29 AM

Table of the Isotopes

11-150 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Hf Hf 166 Hf

163.94438 164.94457 165.94218

2.8 m 1.32 m 6.8 m

EC, β+/3.0 EC/4.6 EC/93 /2.3 β+ /7 /

0+ 11/20+

166.94260

2.0 m

β+ /40 /4.0 EC/60 /

(5/2-)

167.94057

25.9 m

β+, EC/1.8

168.94126

3.25 m

EC/85 /3.3 β+ /15 /

(5/2-)

169.93961

16.0 h

EC/1.1

Hf Hf

170.94049

30. s 12.2 h

EC, β+ /2.4

(1/2-) 7/2+

171.93945

1.87 y

EC/0.35

172.94051

23.6 h

EC/1.6

½-

2.0 × 1015 y 71. d

EC/0.686

0+ 5/2-

51.4 m

I.T./2.740

0+ 37/2-

1.1 s

I.T./

23/2+

31. y

I.T./

7/216+

4.0 s

I.T./

164 165

167

168

169

170

171m 171

172

173

Hf Hf

0.16(1)

173.940046 174.941509

Hf Hf

5.26(7)

175.941409

174 175

176

177m2

177m1

Hf Hf

177

178m2

178m1

487_S11.indb 150

18.60(9)

176.943221

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.6882

ann.rad./ Lu k x-ray 0.0788 ann.rad./ Lu k x-ray 0.1754 0.3152 ann.rad./ (0.0144–1.311) ann.rad./ Lu k x-ray 0.3695 0.4929 Lu k x-ray 0.0985 0.1202 0.1647 0.5729 0.6207

+0.53 -0.67

+3.46

ann.rad./ Lu k x-ray 0.1221 0.6620 1.0714 Lu k x-ray 0.02399 0.12582 (0.0818–0.123) Lu k x-ray 0.12367 0.13963 0.29697 0.31124 (0.1–2.1)

-0.60

+2.7

Lu k x-ray 0.08936 0.34340

+0.7935 +8.16

+0.337 +6.00

Hf k x-ray 0.2140 0.2951 0.3115 0.3267 Hf k x-ray 0.20836 0.22847 0.37851 Hf k x-ray 0.32555 0.42635 0.089–0.574 Hf k x-ray 0.21342 0.32555

4/17/06 11:00:30 AM

Table of the Isotopes Elem. or Isot. Hf Hf

178

179m2

Natural Abundance (Atom %) 27.28(7)

11-151 Atomic Mass or Weight

177.943699

179m1

Hf Hf

179

180m

Hf Hf 181 Hf 180

181m

13.62(2)

178.945816

35.08(16)

179.946550 180.949101

182m

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

25.1 d

I.T./1.1057

0+ 25/2-

18.7 s

I.T./0.375

½-

5.52 h

I.T./1.1416

9/2+ 8-

1.5 ms 42.4 d

/1.738 β- /1.027

0.408/

0+ 25/21/2-

62. m

β- /54 /1.60 IT/46 /1.173

0.49/43 0.95/10

181.95055

8.9 × 106 y

β- /0.37

182.95353

1.07 h

β- /2.01

1.18/68 1.54/25

3/2-

184

183.95545

4.1 h

β- /1.34

0.74/38 0.85/16 1.10/46

Hf Hf 187 Hf 188 Hf

184.9588 185.9609 186.9646 187.967

~ 3.5 m ~ 2.6 m > 0.3 μs > 0.3 μs

β- /

p/1.77 β+ /~ 11.6 p/ α/ p/ α/

182

183

185 186

180.94788(2)

Ta Ta

154.975 155.9723

12 μs 0.11 s

156.9682

10 ms

157.9667

37. ms

158.96302

0.6 s

159.9615

1.4 s

160.9584

3.16 s

161.9573

4. s

155 156

157

158

159

160

161

162

487_S11.indb 151

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.42635

7.4

Hf k x-ray 0.1227 0.1461 0.3626 0.4537 Hf k x-ray 0.1607 0.2141

-0.641 +9.

+3.79 +4.6

Hf k x-ray 0.2152 0.3323 0.4432

Ta k x-ray 0.13294/54 0.48200/100 0.3459/20 Hf k x-ray 0.0509 0.2244 0.3441 0.4558 0.5066 0.9428 Ta k x-ray 0.2704/79 (0.098-0.270) Ta k x-ray 0.0732 0.4591 0.7837 Ta k x-ray 0.0414 0.1391 0.3449 0.165 0.738

β+, EC/20 /8.5 α/80 / β+, EC/10.1 α β+, EC/7.5 α/ EC/8.6

1.02/~ 100 6.117 0.927/3.4 6.05/100 5.97/100 α/5.52/34 5.60/55 5.41/ 5.15

ann.rad./ ann.rad./ ann.rad./

4/17/06 11:00:32 AM

Table of the Isotopes

11-152 Elem. or Isot. Ta Ta

163 164

Natural Abundance (Atom %)

Atomic Mass or Weight 162.95433 163.95353

Particle Energy/ Intensity (MeV/%)

4.62/

Spin (h/2 π)

164.95077 165.95051

31. s 34. s

ECβ+/5.9 β+ /82 /7.7 EC/18 /

Ta Ta

166.94809 167.94805

1.4 m 2.4 m

β+, EC/5.6 β+ /77 /6.7 EC/23 /

168.94601

4.9 m

β+, EC/4.4

169.94618

6.8 m

β +/70 /6.0 EC/35 /

(3+)

170.94448

23.3 m

β+, EC/3.7

(5/2-)

171.94490

36.8 m

β+ /25 /4.9 EC/75 /

(3-)

172.94375

3.6 h

β+ /24 /3.7 EC/76 /

(5/2-)

173.94445

1.12 h

β+ /27 /3.8 EC/73 /

(3+)

174.94374

10.5 h

EC/2.0

7/2+

175.94486

8.1 h

EC/3.1

176.944472

2.356 d

EC/1.166

7/2+

2.4 h

EC/

(7-)

9.29 m

EC/99 /1.9 β+ /1 /

166

167 168

169

170

171

172

173

174

175

176

177

178m

178

177.94578

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

Ta Ta

165

487_S11.indb 152

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 10.6 s EC/6.8 14.2 s β+ /8.5 α/

γ-Energy / Intensity (MeV/%) ann.rad./ 0.2110 0.3768

1.70

-1.9

2.27

+3.7

2.25

+2.74

+0.65

ann.rad./ Hf k x-ray 0.1587 0.3117 0.8101 ann.rad./ ann.rad./ Hf k x-ray 0.1239 0.2615 0.7502 ann.rad./ 0.0288 0.1535 0.1924 ann.rad./ Hf k x-ray 0.1008 0.2212 0.0496 0.5018 0.5064 (0.05–1.02) ann.rad./ Hf k x-ray 0.21396 1.10923 (0.09 –3.8) ann.rad./ Hf k x-ray 0.06972 0.17219 (0.06 –2.7) ann.rad./ Hf k x-ray 0.09089 0.20638 (0.09–3.64) Hf k x-ray 0.2077 0.2671 0.3487 Hf k x-ray 0.08837 1.15735 Hf k x-ray 0.11295 (0.07–1.06) Hf k x-ray 0.08886 0.21342 0.32555 0.42635 ann.rad./ Hf k x-ray

4/17/06 11:00:33 AM

Table of the Isotopes Elem. or Isot. Ta Ta 180 Ta

Natural Abundance (Atom %)

179

180m

Ta Ta

181

182m

0.0120(2)

99.9880(2)

11-153 Atomic Mass or Weight

178.945930 179.947465

180.947996

Half-life/ Resonance Width (MeV) 1.8 y >1.2 × 1015 y 8.15 h

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

EC/0.110 EC/87 /0.854 β- /13 /0.708

15.8 m

I.T./0.5198

0.61/3 0.71/10

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

7/2+ (9-) 1+

2.29 4.82

3.37

7/2+ 10-

+2.370

+3.3

+2.6

181.950152

114.43 d

β- /1.814

0.25/30 0.44/20 0.52/40

+3.02

182.951373

5.1 d

β- /1.070

0.45/5 0.62/91

7/2+

+2.36

183.95401

8.7 h

β- /2.87

1.11/15 1.17/81

(5-)

184.95556

49. m

β- /1.99

1.21/5 1.77/81

(7/2+)

186

185.9586

10.5 m

β- /3.9

2.2/

(3-)

Ta Ta 189 Ta

186.9605 187.9637 188.9658

> 0.3 μs 5 μs > 0.3 μs

183.84(1)

W W 159 W 160 W 161 W

157.975 158.9729 159.9685 160.9674

0.14 ms 1.3 ms 7. ms 0.08 s 0.41 s

161.9635

1.39 s

163

162.9625

2.8 s

164

163.95895

6. s

164.95828

5.1 s

165.95503

16. s

W W

166.95482 167.95181

20. s 53. s

182

183

184

185

187 188

158m 158

162

165

166

167 168

487_S11.indb 153

γ-Energy / Intensity (MeV/%) 0.09316 Hf k x-ray Hf k x-ray W k x-ray 0.09333 0.10340 Ta k x-ray 0.14678 0.17157 W k x-ray 1.12127/100 1.22138/79 0.085–1.289 W k x-ray 0.0847 0.0991 0.1079 0.2461 0.3540 W k x-ray 0.2528/44. 0.4140/74. (0.09–1.4) W k x-ray 0.0697 0.1739 0.1776 W k x-ray 0.1979 0.2149 0.5106 (0.09–1.5) 0.292

α α/ α/ α/ β+, EC/18 /8.1 α/82 / β+, EC/54 /5.8 α/46 / β+, EC/59 /7.5 α/41 / β+, EC/97 /5.0 α/3 / β+, EC/99 /7.0 α/1 / β+, EC/99 /4.2 α/1 / EC/5.6 EC/3.8 α/10-5/

8.28(3)/ 6.433/96

5.92/

5.78/ 5.54/ 5.38/ 5.15/ 4.91/ 4.74/

4.40(1)

ann.rad./ ann.rad./

ann.rad./

ann.rad./ Ta k x-ray 0.1755

4/17/06 11:00:35 AM

Table of the Isotopes

11-154 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

169

168.95178

1.3 m

EC/5.4

170

169.94923

2.4 m

EC/2.2

171

170.94945

2.4 m

EC/4.6

172

171.94729

6.6 m

β+, EC/2.5

173

172.94769

6.3 m

EC/4.0

174

173.94608

35. m

EC/1.9

175

W W

174.94672 175.94563

35. m 2.5 h

EC/2.9 β+, EC/0.8

½0+

177

176.94664

2.21 h

EC/2.0

(1/2-)

178

W W

177.94588

21.6 d 6.4 m

0+ (1/2-)

179

178.94707

38. m

EC/0.091 IT/99.7/0.222 EC/0.3/ EC/1.06

180

W W

0.12(1)

179.946704 180.948197

1.8 × 1018 y 121.1 d

α/ EC/0.188

0+ 9/2+

W W

26.50(16)

181.948204

> 7.7 × 1021 y 5.15 s

α/ I.T./

0+ (11/2+)

14.31(4) 30.64(2)

182.950223 183.950931

> 4.1 × 1021 y > 8.9 × 1021 y 1.6 m

α/ α/ I.T./0.1974

½0+ 11/2+

28.43(19)

184.953419 185.954364

74.8 d > 8.2 × 1021 y 1.6 μs 23.9 h

β- /0.433 α/ IT β- /1.311

176

179m

181

182

183m

W W 185m W 183 184

W W 187m W 187 W 185 186

487_S11.indb 154

186.957161

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(7/2-)

0.433/99.9 0.411 0.624/66

3/20+ 11/2+ 3/2-

γ-Energy / Intensity (MeV/%) (0.037–0.573) ann.rad./ Ta k x-ray 0.123 (0.097–0.699) ann.rad./ Ta k x-ray 0.3162 (0.060–0.144) ann.rad./ Ta k x-ray 0.1842 (0.052–0.479) ann.rad./ Ta k x-ray 0.0389 (0.034–0.674) ann.rad./ Ta k x-ray 0.4576 (0.035–0.623) ann.rad./ Ta k x-ray 0.3287 0.4288 (0.056–0.429) (0.015–0.27) 0.03358 0.06129 0.09487 0.10020 Ta k x-ray 0.15505 0.18569 0.42694 Ta k x-ray W k x-ray 0.2220 Ta k x-ray 0.0307 Ta k x-ray 0.13617 0.15221

+0.1177848

W k x-ray 0.0465 0.0526 0.0991 0.1605

W k x-ray 0.0659 0.1315 0.1737 0.12536

0.62

(0.014-0.287) Re k x-ray

4/17/06 11:00:36 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-155 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%) 1.315/16 0.081–1.18 0.349/99

Spin (h/2 π)

188

187.958489

69.78 d

β- /0.349

189

188.9619

9.7 m

β- /2.5

(3/2-)

W W

189.9632

~ 0.06 ms 30. m

1.4/ 2.5/

β- /1.3

0.95/

W W

190.9666 191.968

> 0.3 μs > 0.3 μs

186.207(1)

159.9821

0.7 ms

160.9776

14 ms

161.9760

0.10 s

162.97208

0.26 s

163.9703

0.9 s

Re 165 Re

164.96709

~ 2.37 s 2.6 s

165.9658

2.5 s

Re 167 Re

166.9626

6.2 s 3.4 s

167.96157

4.4 s

190m 190

191 192

160

161

162

163

164

165m

166

167m

168

169m

8.1 s

β+, EC/9.0 α/ β+, EC/10.7 α/ α/ β+, EC/87 /8.1 α/ β+, EC/9.4 α/ α, EC/ β+, EC/7.4 α/ β+, EC/9.1 α/ α

16. s 9.2 s

β+, EC/9.0

Re Re

170.95572

15.2 s 55. s

EC/~ 5.7 β+, EC/

171.9554

15. s

β+, EC/7.3

Re Re

172.95324 173.95312

2.0 m 2.4 m

EC/~ 3.9 β+, EC/5.6

Re Re

174.95138 175.95162

5.8 m 5.3 m

β+, EC/4.3 β+, EC/5.6

176.95033

14. m

EC/78 /3.4 β+ /22 /

171

172m

172

173 174

175 176

177

487_S11.indb 155

p/ α/ α/ p α/

168.95879 169.95822

170

γ-Energy / Intensity (MeV/%) 0.68572/33 0.134–0.773 0.0636 0.2271 0.2907 0.2604 (0.1262-1.466) (0.0585-0.694) Re k x-ray 0.1576 0.1621

Re Re

169

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

1.261(6)/91 6.54/ 6.24 1.35 6.12/94 6.09/94 α/5.87/32 5.92/66 5.78/ 5.502/ 5.49/ < 5. 5.50/

5.015/ 0.1117

4.833/ 4.70/ 4.87/

0.1560 0.3055 0.4125 (2)

(3+)

(5/2-)

ann.rad./ 0.1234 0.2537 0.3504 ann.rad./ 0.1234 0.2537 ann.rad./ ann.rad./ 0.1119 0.2430 ann.rad./ ann.rad./ 0.1089 0.2406 ann.rad./ W k x-ray

4/17/06 11:00:38 AM

Table of the Isotopes

11-156 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

177.95099

13.2 m

Re Re

178.94999

0.47 ms 19.7 m

179.95079

180.95007

178

179m 179

180

181

182m

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.0797 0.0843 0.1968 ann.rad./ W k x-ray 0.1059 0.2373 0.9391 W k x-ray 0.1199 0.2900 0.4154 0.4302 1.6803 ann.rad./ W k x-ray 0.1036 0.9028 (0.07–2.2) W k x-ray 0.3607 0.3655 0.6390 W k x-ray 0.0677 1.1214 1.2215 (0.06–2.2) W k x-ray 0.0678 0.2293 1.1213 1.2214 W k x-ray 0.16232 Re k x-ray 0.1047 0.2165 0.92093 (0.10–1.1) W k x-ray 0.79207 0.90328 (0.1–1.4)

β+ /11 /4.7 EC/89 /

3.3/

(3+)

EC/99 /2.71 β+ /1 /

0.95/

(5/2+)

2.8

2.45 m

EC/92 /3.80 β+ /8 /

1.76/

1.6

20. h

EC /1.74

5/2+

3.19

12.7 h

EC/

3.3

+1.8

0.55/ 1.74/

181.9512

2.67 d

EC/2.8

(7+)

2.8

+4.1

182.95082

70. d

EC/0.56

(5/2+)

+3.17

+2.3

165. d

I.T./75 /0.188 EC/25 /

+2.9

38. d

EC/1.48

+2.53

+2.8

2.0 × 105 y

I.T./0.150

5/2+ 8+

+3.1871

+2.18

185.954986

3.718 d

β- /92 /1.070 EC/8 /0.582

0.973/21 1.07/71

+1.739

+0.62

186.955753

4.2 × 1010 y 18.6 m

β- /0.00266 I.T./0.172

0.0025/

5/2+ (6-)

+3.2197

+2.07

187.958114

17.00 h

β- /2.120

1.962/20 2.118/79

+1.788

+0.57

188.95923

24. h

β- /1.01

1.01/

(5/2+)

182

183

184m

183.952521

184

Re Re

185

186m

37.40(2)

186

Re Re

187

188m

188

189

487_S11.indb 156

Half-life/ Resonance Width (MeV)

62.60(2)

184.952955

Re k x-ray 0.0590 W k x-ray 0.1227/0.6 0.1372/9.5 (0.63–0.77) Re k x-ray 0.0925 0.1059 Os k x-ray 0.15502 0.309–2.022 0.1471

4/17/06 11:00:43 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-157 Atomic Mass or Weight

190m

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

3.0 h

β- /51 / I.T./49 /

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

(6-)

190

189.9618

3.0 m

β- /3.2

1.8/

Re Re 192 Re 193m Re 193 Re 194 Re

190.96313

9.7 m ~ 0.12 ms 16. s ~ 0.08 ms > 0.3 μs > 0.3 μs

β- /2.05

1.8/

β- /4.2

~ 2.5/

190.23(3)

Os Os 164 Os 165 Os 166 Os

161.984 162.9827 163.9780 164.9768 165.97269

1.8 ms 5.5 ms 0.04 s 0.07 s 0.18 s

6.60 6.51

166.9716

0.7 s

167.96780

2.2 s

168.96702

3.3 s

α/ α/ α α β+, EC/28 /6.3 α/72 / β+, EC/76 /8.2 α/24 / β+, EC/51 /5.7 α/49 / β+, EC/89 /7.7 α/13 /

169.96358

7.1 s

170.96319

8.4 s

171.96002

19. s

172.95981

16. s

173.95706

44. s

174.95695

1.4 m

β+, EC/5.3

175.95481

3.6 m

β+, EC/3.2

176.95497

2.8 m

β+, EC/4.5

(1/2-)

177.95325

5.0 m

β+, EC/2.3

191

192m

162 163

167

168

169

170

171

172

173

174

175

176

177

178

487_S11.indb 157

191.9660 192.9675 193.9704

β+, EC/5.0 α/ β+, EC/98 /7.1 α/19 / β+, EC/99 /4.5 α/1.1/ β+, EC/6.3 α/0.4 / β+, EC/3.9 α/0.02 /

6.27/ 5.98/ 5.84/

5.57/80 5.51/12 5.54/8 5.40/ α/5.24/93.5 5.17/6.5 5.10/ 4.94/ 4.76/

(2-)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.2167 0.2194 0.2451 Re k x-ray 0.1191 0.2238 0.6731 (0.1–1.79) Os k x-ray 0.1867 0.5580 0.6051 (0.0606-0.146) (0.2–0.75) (0.061-0.146)

0+ 0+ 0+

ann. rad./ ann.rad./

ann.rad./ (0.162–0.216) ann.rad./ 0.190–0.705 ann.rad./ (0.063–1.120) ann.rad./ 0.142–0.299 0.118 0.138 / 0.001 0.158 0.325 0.125 0.181 0.248 0.8155 0.7758 0.8573 1.2093 1.2909 0.0848 0.1958 0.3002 1.2686 ann.rad./ 0.5946

4/17/06 11:00:45 AM

Table of the Isotopes

11-158 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

178.95382

7. m

β+, EC/3.7

179.95238

21.5 m

β+, EC/1.5

1.75 h

EC/

(1/2-)

179

180

181m

180.95324

2.7 m

EC/2.9

(7/2-)

181.95211

21.5 h

EC/0.9

9.9 h

EC/84 / I.T./16 /

½-

182.95313

13. h

EC/2.1

9/2+

93.6 d

EC/1.013

0+ ½-

2. × 1015 y

α/

5.8 h

I.T./0.0308

0+ ½0+ 9/2-

9.9 m

I.T./1.705

3/2+ 10-

13.1 h

I.T./0.0744

0+ 3/2-

15.4 d

β- /0.314

6.0 s

I.T./2.0154

191.961481 192.964152

30.5 h

β- /1.141

1.04/20

193.965182

6.0 y

β- /0.097

Os Os

194.968 195.96964

6.5 m 34.9 m

β- /2.0 β- /1.16

0.054/33 0.096/67 2.0/ 0.84/

181

182

183m

183

Os Os

0.02(1)

183.952489 184.954042

Os Os 188 Os 189m Os

1.59(3) 1.96(2) 13.24(8)

185.953838 186.955750 187.955838

Os Os

16.15(5)

188.958148

Os Os

26.26(2)

189.958447

184 185

186 187

189

190m

190

191m

190.960930

191

192m

Os Os

192 193

194

195 196

487_S11.indb 158

Half-life/ Resonance Width (MeV)

40.78(19)

~ 2.75/

0.140/100

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

-0.79

+3.1

Re k x-ray 0.6461 0.8748 0.8805 +0.0646519

+0.65993 -0.6

9/2-

+0.86

+2.5

(10-)

0+ 3/2-

γ-Energy / Intensity (MeV/%) 0.6850 0.9687 1.3311 ann.rad./ 0.0654 0.2186 0.5938 Re k x-ray 0.0202–0.7174 ann.rad./ 0.0489 ann.rad./ 0.11794 0.23868 0.8267 (0.07–2.64) Re k x-ray 0.1802 0.5100 Os k x-ray Re k x-ray 1.1020 1.1080 Re k x-ray 0.1144 0.3818

+0.730

+0.47

Os L x-ray 0.0308 Os k x-ray 0.1867 0.3611 0.5026 0.6161 Os k x-ray 0.0744 Ir k x-ray 0.1294 Os k x-ray 0.2058/65.9 0.5692/70 (0.201–1.000) Ir k x-ray 0.1389 0.4605 Ir L x-ray 0.0429 0.1262/5 0.4079/5.9

4/17/06 11:00:47 AM

Table of the Isotopes Elem. or Isot. Os

197

Natural Abundance (Atom %)

11-159 Atomic Mass or Weight

192.217(3)

Ir Ir

163.9922 164.9875

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 2.8 m β-

167

166.98167

32. ms

Ir Ir 169 Ir 170 Ir 171 Ir 172 Ir

167.9799 168.97630 169.9750 170.97163 171.9705

0.16 s 280. ms 353. ms 0.43 s 1.3 s 2.1 s

p p/87 α/13 α/98.2 p/1.8 α/93 p/6.9 α/48, β+ p/32 α/80, β+ p/0.4 α/82 α/ α/ α/ α/ α/

172.96750

3.0 s

α/

5.665/

173.96686

4. s

α/

5.478/

Ir Ir

174.96411 175.96365

~ 4.5 s 8. s

5.393/

176.96130

30. s

177.96108

12. s

α/ EC, β+/80 α/3.2/ EC, β+/5.7 α/0.06/ β+, EC/6.3

178.95912

4. m

EC/4.9

179.95923

1.5 m

EC/6.4

180.95763

4.9 m

β+, EC/4.1

181.95808

15. m

β+ /44 /5.6 EC/56 /

182.95685

57. m

β+, EC/3.5

183.95748

3.0 h

β+ /12 /4.6 EC/88 /

184.95670

14. h

β+ /3 /2.4 EC/97 /

164 165

14.3 ms

166m

166

165.9858

169m

173

174

175 176

177

178

179

180

181

182

183

184

185

487_S11.indb 159

0.010 s 26. ms

167m

168

0.06 ms 0.3 ms

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.2239 (0.0412-0.406)

1.78 1.71 6.72 6.545 1.32 6.56 1.15 6.39/90 1.25/0.42 6.35/48 1.06/39.3 6.12/59 5.99/42 6.03/ 5.91/ 5.811/

0.228 (0.379–0.475) 0.0493 (0.092–0.296) 0.1587 (0.276–1.33) 0.1056 0.260 (0.135–0.415) 0.184 (0.062–0.194)

5.118/ 5.011/

(7/2+)

2.3/ 2.9/

0.70

+2.41

(5/2-)

2.60

-2.1

0.1320 0.2667 0.3633 0.0975 (0.045–0.220) 0.2765 ((0.132–1.106) ann.rad./ 0.1076 (0.0196–1.715) ann.rad./ Os k x-ray 0.1273 0.2370 ann.rad./ 0.0877 0.2285 0.2824 ann.rad./ Os k x-ray 0.11968 0.2640 0.3904 ann.rad./ Os k x-ray 0.2543 1.8288

4/17/06 11:00:48 AM

Table of the Isotopes

11-160 Elem. or Isot.

185.95795

15.7 h

EC/98 /3.83 β+ /2 /

(5+)

186.95736

10.5 h

EC/1.50

3/2+

187.95885

1.72 d

β+ /2.81 EC/99+ /

188.95872

13.2 d

EC/0.53

3/2+

3.09 h

(11-)

1.12 h 11.8 d

β+, EC/95 / I.T./5 / I.T. /0.0263 EC/2.0

Nuclear Elect. γ-Energy / Magnetic Quadr. Intensity Mom. (nm) Mom. (b) (MeV/%) 0.64 +1.46 Os k x-ray 0.1371 0.7675 3.9 -2.55 Os k x-ray 0.1372 0.2968 0.4348 (0.13–3.0) +0.94 Os k x-ray 0.0743 0.4009 0.4271 0.6109 0.9128 0.30 +0.48 Os k x-ray 0.1550 0.4780 0.6330 2.2146 0.13 +0.88 Os k x-ray 0.2449 0.376

7+ (4+)

0.04

4.93 s

I.T./0.1714

11/2-

+0.603

241. y 1.44 m

I.T./0.161 I.T./0.0580

3/2+ (9+) (1+)

+0.151

+0.82

73.83 d

β- /1.460

(4-)

+1.92

+2.15

10.53 d

I.T./0.0802

11/2-

170. d

β- /

3/2+ 11

+0.164

+0.75

19.3 h

β-/2.247

1.92/9 2.25/86

+0.39

+0.34

3.9 h

β- /

0.41/ 0.97/

(11/2-)

2.8 h

β- /1.120

(3/2+)

1.40 h

β-/

1.0/80 1.11/13 1.16/

186m

Natural Abundance (Atom %)

186

187

188

189

Atomic Mass or Weight

190m2

190m1

190

189.960546

191m

191

Ir 192m1 Ir 192m2

37.3(2)

190.960594

191.962605

192

193m

Ir Ir

193

194m

194

62.7(2)

192.962926

193.965078

195m

195

196m

487_S11.indb 160

194.965980

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 1.7 h EC /

Particle Energy/ Intensity (MeV/%)

1.13/ 1.64/

Spin (h/2 π) (2-)

(2-)

+2.8

Ir L x-ray Os k x-ray 0.1867 0.4072 0.5186 0.5580 0.6051 (0.2–1.4) Ir k x-ray 0.1294 Ir k x-ray Ir L x-ray 0.0580 0.3165 Pt k x-ray 0.31649/83. 0.46806/48. Ir L x-ray 0.0803 Pt k x-ray 0.3284 0.4829 0.5624 0.2935 0.3284 0.6451 (0.1–2.2) Pt k x-ray 0.3199/9.6 0.3649/9.5 0.4329/9.6 0.6849/9.6 Pt k x-ray 0.0989/9.7 Pt k x-ray

4/17/06 11:00:50 AM

Table of the Isotopes Elem. or Isot.

196

Natural Abundance (Atom %)

11-161 Atomic Mass or Weight

195.96840

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

52. s

β- /3.21

8.9 m

196.96965

5.8 m

β- / I.T./ β- /2.16

197.9723

8. s

β- /4.1

198.97380

195.084(9)

Pt Pt 168 Pt

165.995 166.930 167.9882

0.3 ms 0.9 ms 2.1 ms

Pt Pt

168.9867 169.98250

197m

2.1/15 3.2/80

Spin (h/2 π)

(11/2-) (3/2+)

α/ α/ α

7.11/ 6.98/ 6.82

7.0 ms 14.0 ms

α α

6.69 6.55

170.9812

0.05 s

6.45

Pt Pt

171.97735 172.9764

0.10 s 0.36 s

173.97282

0.89 s

6.31/94 6.23 6.20/

174.97242

2.5 s

α/ β+, EC/8.2 α/ β+, EC/17 /5.6 α/83 / β+, EC/65 /7.6 α/35 /

175.96895

6.3 s

β+, EC/60 /5.1 α/40 /

176.96847

11. s

EC/91 /6.8 α/9 /

177.96565

21. s

EC/93 /4.5 α/7 /

178.96536

33. s

179.96303

52. s

Pt Pt

180.96310 181.96117

51. s 2.7 m

β+, EC/5.7 α/ 5.16/ β+, EC/99.7 /3.7 0+ 5.140/ α/0.3 / β+, EC/5.2 β+, EC/2.9

198

199

166 167

169 170

171

172 173

174

175

176

177

178

179

180

181 182

183m

43. s

β+, EC/ I.T./

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

1.5/ 2.0/

197

487_S11.indb 161

Particle Energy/ Intensity (MeV/%)

6.040/ 5.831/5 5.96/54 6.038/ 5.528/0.6 5.750/41 5.53/ 5.485/3 5.525/6 5.286/0.2 5.442/7

γ-Energy / Intensity (MeV/%) 0.3557 0.3935 0.4471 0.5214 0.6473 0.3329 0.3557 0.7796 0.3465 see Ir[197] 0.0531 0.1351 0.4306 0.4697 0.4074 0.5070

0.582/69 0.594/69 0.725/62

0.509/100 0.662/86 0.214–0.726 0.4450 (0.1564-1.208)

0+ 0.0774 0.1354 0.2128 0+

ann.rad./ 0.2277 0.0908

+0.43

(7/2-)

+0.48

+0.78

+3.4

ann.rad./ 0.1360 0.1460 0.2100 ann.rad./ 0.3132/26

4/17/06 11:00:51 AM

Table of the Isotopes

11-162 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

182.96160

7. m

β+, EC/4.6

183.95992

17.3 m

β+, EC/2.3

Pt Pt

184.96062

33. m 1.18 h

β+, EC/ β+, EC/3.8

½(9/2+)

185.95935

2.0 h

β+, EC/1.38

186.96059

2.35 h

β+, EC/3.1

3/2-

187.95940

10.2 d

EC/0.51

188.96083

10.9 h

β+, EC/1.97

4.5 × 1011 y 2.86 d

183

184

185m 185

186

187

188

189

Pt Pt

0.014(1)

189.95993 190.961677

Pt Pt

0.782(7)

191.961038

32.967(99)

192.962988 193.962680

33.832(10) 25.242(41)

194.964791 195.964952

190 191

192

193m

Pt Pt 195m Pt 193 194

Pt Pt 197m Pt 195 196

196.967340

197

Pt Pt

198

199m

199

487_S11.indb 162

Half-life/ Resonance Width (MeV)

7.163(55)

197.967893

198.970593

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

+0.50

+0.5 -0.75

+3.7

-0.41

-1.1

3/2-

-0.43

-1.2

EC/1.02

0+ (3/2-)

-0.50

-0.9

4.33 d

I.T./0.1498

0+ 13/2+

-0.75

60. y

EC/0.0566

4.01 d

I.T./0.2952

(1/2-) 0+ 13/2+

+0.60

1/20+ 13/2+

+0.6095

0.51

1.590 h

I.T./97 / β- /3 /

19.9 h

β- /0.719

1/2-

13.6 s

I.T./0.424

0+ 13/2+

30.8 m

β- /1.70

0.90/18

(5/2-)

-0.61

γ-Energy / Intensity (MeV/%) 0.3164/59 0.6296/100 0.058–1.75 ann.rad./ 0.119/100 0.307/93 0.260/90 0.058–1.377 ann.rad./ 0.1549 0.1919 0.5484 ann.rad./ 0.1353 0.1974 0.2296 0.2551 ann.rad./ 0.6115 0.6892 ann.rad./ Ir k x-ray 0.1064 0.1100 0.2015 0.2849 0.7092 Ir k x-ray 0.1876 0.1951 Ir k x-ray 0.0943 0.6076 0.7214 (0.09–1.47) Ir k x-ray 0.3599 0.4094 0.5389 Pt k x-ray 0.1355 Ir k x-rays

+1.4

Pt k x-ray 0.0989

Pt k x-ray 0.0530 0.3465 Au k x-ray 0.1914 0.2688 Pt k x-ray 0.3919 0.3170/3.88

4/17/06 11:00:53 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-163 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Spin (h/2 π)

199.971441

12.5 h

β- /~ 0.66

200.97451

2.5 m

β- /2.66

(5/2-)

Pt Pt

201.9757

0.3 ms 1.8 d

196.966569(4)

200

201

202m 202

0.62 ms

170m

170

169.9961

0.30 ms 1.09 ms

171m

p/58 α/42 p/89 α/11 α/66 p/34 p/100

1.74/ 7.11/ 1.46/ 7.00/ 6.995 1.694 1.437 6.86 6.732 6.672 6.54

170.99188

0.022 ms

Au Au 173 Au 174 Au 175 Au 176 Au

171.9900 172.98624 173.9848 174.98127 175.9801

4 ms 15 ms 0.02 s 0.14 s 0.15 s 0.9 s

α/7.02 α/92 α/94 α α β+, EC/10.5 α/

177

176.97687

1.2 s

α/

Au Au 180 Au

177.9760 178.97321 179.97252

2.6 s 7.5 s 8.1 s

α/ α/ EC/8.6 α/

180.97008

11.4 s

181.96962

21. s

EC/97.5/6.3 α/2.7/ β+, EC/6.9 α/0.13/

182.96759

42. s

EC/5.5 α/0.8/

Au Au

183.96745

48 s 21. s

I.T. EC, β+/7.1 α/0.013/ β+, EC/ I.T./0.145 β+, EC/4.71 α/0.26/ β+, EC/ β+, EC/6.0

172

173m

178 179

181

182

183

184m 184

6.8 m

185m

184.96579

4.3 m

Au Au

185.96595

< 2. m 10.7 m

185

186m 186

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

171

487_S11.indb 163

Particle Energy/ Intensity (MeV/%) 1.14/14

6.260/80 6.290/20 6.115/ 6.150/ 5.920/ 5.85/ 5.65 5.61 5.50

γ-Energy / Intensity (MeV/%) 0.49375/4.47 0.5430/11.7 (0.055–1.293) Au k x-ray 0.13590 0.22747 0.24371 0.070 0.152 0.222 1.760 (0.535-0.719) 0.440

0.1522 0.2564 0.5242 0.6765 0.8084 0.8597

5.482/

+1.97

ann.rad./ 0.1549 0.2649 (0.13–1.4) 0.1630 0.2730 0.3625 0.069(IT)

(2+) (5+)

+1.44 +2.07

+1.9 +4.7

(5/2-)

+2.17

-1.1

ann.rad./

-1.26

+3.1

0.1915 ann.rad./

4/17/06 11:00:55 AM

Table of the Isotopes

11-164 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Decay Mode/ Energy (/MeV) α/8(10)-4/

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.1915 0.2988 ann.rad./ 0.9152 1.2668 1.3321 1.4081 ann.rad./ 0.2660 0.3404 0.6061 0.1667 ann.rad./ Pt k x-ray 0.4478 0.7133 0.8128 ann.rad./ Pt k x-ray 0.2958 0.3018 0.5977 Au k x-ray 0.2414 0.2526 Pt k x-ray 0.5864/16 (0.088–1.30) ann.rad./ Pt k x-ray 0.2959 0.3165 Au k x-ray 0.2580 Pt k x-ray 0.1862 0.2556 ann.rad./ Pt k x-ray 0.2935 0.3284/61 Au k x-ray 0.2617 Pt k x-ray Au k x-ray 0.1478 0.1883 0.0847 Pt k x-ray Au k x-ray 0.1302 0.2790

Au Au

186.96457

2.3 s 8.3 m

IT β+, EC/3.60

9/21/2+

+0.54

187.96532

8.8 m

β+, EC/5.3

(1-)

-0.07

Au Au

188.96395

4.6 m 28.7 m

β+, EC/ EC/96 /3.2 β+ /4 /

11/21/2+

+6.19 +0.49

189.96470

43. m

β+ /2 /4.44 EC/98 /

-0.07

0.9 s

I.T./0.2663

(11/2-)

6.6

3/2+

+0.137

+0.72

-0.011

-0.23

187m 187

188

189m 189

190

191m

190.96370

3.2 h

EC/1.83

191.96481

4.9 h

β+ /5 /3.52 EC/95 /

3.9 s

I.T./0.2901

11/2-

6.2

+1.98

3/2+

+0.140

+0.66

+0.076

-0.24

191

192

193m

2.19/ 2.49/

192.96415

17.6 h

EC/1.07

193.96537

1.64 d

β+ /3 /2.49 EC/97 /

30.5 s

I.T./0.3186

11/2-

6.2

+1.9

186.10 d 9.7 h

EC/0.227 I.T./0.5954

3/2+ 12-

+0.149 5.7

+0.61

8.1 s 6.17 d 7.8 s

I.T./0.0846 EC/92 /1.506 I.T./0.4094 β- /8 /0.686

8+ 211/2-

+0.591 +6.0

0.81 +1.7

2.30 d

I.T./0.812

3/2+ (12-)

+0.14575

+0.55

2.695 d

β- /1.372

+0.5934

+0.64

193

194

195m

Au Au

194.965035

195

196m2

Au Au 197m Au 196m1

195.966570

196

Au Au

197

198m

198

487_S11.indb 164

Half-life/ Resonance Width (MeV)

100.

196.966569

197.968242

1.49/

0.290/1 0.961/99

Au k x-ray 0.0972 0.1803 0.2419 Hg k x-ray 0.411794

4/17/06 11:00:57 AM

Table of the Isotopes Elem. or Isot. Au

199

Natural Abundance (Atom %)

11-165 Atomic Mass or Weight

198.968765

200m

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 3.14 d β- /0.453

18.7 h

β- /84 /1.0 I.T./16 /

Particle Energy/ Intensity (MeV/%) 0.25/22 0.292/72 0.462/6 0.56/

Spin (h/2 π) 3/2+

12-

200

199.97073

48.4 m

β- /2.24

0.7/15 2.2/77

Au Au 203 Au 204 Au

200.971657 201.9738 202.975155 203.9777

26. m 29. s 1.0 m 40. s

β- /1.28 β- /3.0 β- /2.14 β- /4.5

1.27/82

3/2+ (1-) 3/2+ (2-)

204.9799

31. s

β- /

200.59(2)

Hg Hg 173 Hg 174 Hg 175 Hg 176 Hg 177m Hg 177 Hg 178 Hg

171.0038 171.9988 172.9972 173.99286 174.9914 175.98736 176.9863 177.98248

0.06 ms 0.3 ms 0.8 ms 1.9 ms 0.02 s 21 ms 1.5 μs 0.13 s 0.26 s

178.98183

1.05 s

179.97827

2.6 s

α α α α α α IT α EC/50 /6.1 α/50 / EC/8.0 α/ EC/5.5 α/

180.97782

3.6 s

β+ EC/76 /~ 7.3 α/24 /

181.97469

10.8 s

β+, EC/85/5.0 α/15/

182.97445

9. s

β+, EC/77/6.3 α/

183.97171

30.9 s

β+, EC/99/4.1 α/1/

21. s

β+, EC, IT, α/

184.97190 185.96936

51. s 1.4 m

186.96981

1.7 m 2.4 m

β+, EC/95/5.8 β+, EC/3.3 α β+, EC/ β+, EC/4.9

201 202

205

171 172

179

180

181

182

183

184

185m

Hg Hg

185 186

Hg 187 Hg 187m

487_S11.indb 165

~ 1.9/

7.49 7.36 7.20 7.07 6.74/94 6.58 6.43/ 6.29/ 6.12/33 5.69/.03

5.87/8.6 5.45/0.03 5.83/ 5.91/ 5.54/1.3 5.07/0.002 5.37/

5.09/0.02

Nuclear Elect. γ-Energy / Magnetic Quadr. Intensity Mom. (nm) Mom. (b) (MeV/%) +0.2715 +0.51 Hg k x-ray 0.15837 0.20820 5.9 Au k x-ray 0.2559/71 0.3680/77 0.4978/73 0.5793/72 0.084–0.904) 0.3679/19 1.2254/10.6 (0.077–1.570) (0.027–0.732) 0.4396 (0.04–0.37) 0.4366 1.5113 (0.38–1.33)

0+ 0+ 0+

0.246

(1/2-)

+0.507

½-

+0.524

13/2+

-1.02

½0+

+0.509

13/2+ 3/2-

-1.04 -0.594

+0.2

+0.5 -0.8

0.1250 0.3005 0.3812 0.0663 0.0811 0.0924 0.1474 0.1587 0.2142 0.2398 0.129/122 0.2176/66 0.0256–0.543 0.0714 0.0874 0.1538 0.1565/102 0.2367/100 0.2384/18 (0.018-0.4227) 0.211 0.292 0.02–0.55 0.1119 0.2518 see Hg187 0.1034/32

4/17/06 11:00:59 AM

Table of the Isotopes

11-166 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

187.96758

188

189m

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

3.2 m

β+, EC/2.3 α

8.6 m

EC/

13/2+

-1.06

+0.7

-0.6086

-0.8

4.61

188.96819

7.6 m

EC/4.2

3/2-

189.96632

20.0 m

EC/1.5

51. m

β+ /6 / EC/94 /

13/2+

-1.07

+0.6

-0.62

-0.8

189

190

191m

190.96716

50. m

β+, EC/3.2

(3/2-)

191.96563

5.0 h

EC/~ 0.5

11.8 h

β+, EC/91 / I.T./9 /0.2901

13/2+

-1.05843

+0.92

191

192

193m

192.96667

3.8 h

EC, B+/2.34

3/2-

-0.6276

-0.7

Hg Hg

193.96544

520. y 1.67 d

EC/0.04 I.T./(54)/0.3186 EC/(46)/

0+ 13/2+

-1.04465

+1.1

194.96672

10.5 h

EC/1.51

1/2-

+0.541475

195.965833

>2.5 × 1018 y 23.8 h

I.T./(93)/0.2989

0+ 13/2+

-1.02768

196.967213

2.69 d

EC/0.600

1/2-

+0.527374

193

194

195m

195

Hg Hg

196

197m

0.15(1)

197

198

487_S11.indb 166

Half-life/ Resonance Width (MeV)

9.97(20)

197.9667690

+1.2

γ-Energy / Intensity (MeV/%) 0.2334/100 0.2403/33 0.27151/31 0.3763/38 0.5254/30 0.10–2.18 0.0988 0.1148 0.1424 0.1900 0.0780 0.3210 0.4345 0.5655 (0.08–2.170) 0.2005 0.2038 0.2386 0.2485 0.1296 0.1426 ann.rad./ Au k x-ray 0.2741 0.4203 0.5787 (0.07–1.9) 0.1963 0.2247 0.2524 Au k x-ray 0.1572 0.2748 0.3065 Hg k x-ray 0.1866 0.2580 0.4076 0.5733 0.9324 (0.1–1.96) 0.1866 0.2580 0.8611 Au L x-rays Hg k x-ray Au k x-ray 0.2617 0.5603 0.7798 Au k x-ray 0.0614 0.7798 Hg k x-ray Au k x-ray 0.13398 Au k x-ray 0.07735

4/17/06 11:01:00 AM

Table of the Isotopes Elem. or Isot. Hg

199m

Hg Hg 201 Hg 202 Hg 203 Hg

Natural Abundance (Atom %)

11-167 Atomic Mass or Weight

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 42.7 m I.T./0.532

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π) 13/2+

16.87(22) 23.10(19) 13.18(9) 29.86(26)

198.9682799 199.9683260 200.970302 201.970643 202.972873

46.61 d

β- /0.492

0.213/100

1/20+ 3/20+ 5/2-

6.87(15)

203.9734939 204.976073

5.2 m

β- /1.531

1.33/4

0+ 1/2-

206

205.97751

8.2 m

β- /1.31

0.935/34 1.3/63

Hg Hg 209 Hg 210 Hg

206.9826 207.9859 208.9910 209.9945

2.9 m 41. m 36 s > 0.3 μs

β- /4.8 βββ-

p p/51 α/49 α/73 p/27 α/

199 200

Hg Hg

204 205

207 208

204.3833(2)

Tl Tl

176.0006

5 ms 0.23 ms

176.99643

0.017 s

177.9949

0.25 s

176

177m

177

178

1.7 ms

Tl Tl

178.99109 179.9899

0.3 s 1.5 s

α α α α//8

Tl Tl 182 Tl

180.98626 181.9857

1.4 ms 3.2 ms 3. s

α α/ < 10 β+, EC/10.9

53. ms

5. s 11. s

β+, EC/7.7 β+, EC/(98)/9.2 α/(2)/

1.8 s 20. s 4. s 28. s

I.T./0.453 α/5.97 EC/β+/6.6 I.T./0.374 β+, EC/7.5

15.6 s 50. s 1.18 m

I.T./~ 0.33 β+, EC/6.0 β+, EC/

179m

179 180

181m 181

183m

Tl Tl

183 184

182.98219 183.98187

185m

Tl Tl 186 Tl 185

186m

Tl Tl 188m Tl

184.9788 185.9783

187m 187

487_S11.indb 167

186.97591

Nuclear Elect. γ-Energy / Magnetic Quadr. Intensity Mom. (nm) Mom. (b) (MeV/%) -1.014703 +1.2 Hg k x-ray 0.15841 +0.505885 -0.560226

+0.39

+0.8489

+0.34

+0.6010

Tl k x-ray 0.279188 0.20378 (0.2–1.4) Tl k x-ray 0.3052 0.6502

(9/2+) 0+

0.474 0.324

1.26/~ 100 1.95 7.48

6.704 6.785 6.62 6.859 /7.21/80 /7.10/20 6.57/ 6.28/30 6.36/30 6.21/18 6.56/15 6.47/7 6.58/100 6.19/100

6.33/80 6.38/16 6.46/4

0.351 (0.26–0.41) 0.0618 (0.046-0.0894)

9/2-

½+

0.208 0.2868 0.3399 0.3667 0.1688 0.2840

6.16/

6.01

(9/2-)

(9/2+) ½+ (7+)

+3.8 1.6

-2.4

0.3738 0.3567 0.4026 0.4053 0.2995 Hg k x-ray 0.4129

4/17/06 11:01:02 AM

Table of the Isotopes

11-168 Elem. or Isot.

188

Natural Abundance (Atom %)

Atomic Mass or Weight

187.97601

189m

189

188.97359

190m

190

189.97388

191m

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

1.2 m

β+, EC/7.8

(2-)

+0.48

+0.13

1.4 m

β+, EC/

(9/2-)

+3.878

-2.29

2.3 m

β+, EC/5.2

(1/2+)

3.7 m

β+, EC/

4.2/

(7+)

+0.495

+0.29

2.6 m

β+, EC/7.0

5.7/

(2-)

+0.25

-0.33

5.2 m

β+, EC/(98)/

(9/2+)

+3.903

-2.3

10.8 m

β+, EC/

(1/2) (7+)

1.59 +0.518

0.46

Tl Tl

190.97179

191.97223

9.6 m

β+, EC/6.4

(2-)

+0.20

-0.33

Tl Tl

192.9707

2.1 m 22. m

I.T./(75)/ β+, EC/3.6

(9/2-) (1/2+)

+3.948 +1.591

-2.2

32.8 m

β+ /(20)/~ 0.30 EC/(80)/

(7+)

+0.540

+0.61

33.0 m

β+, EC/5.3

0.140

-0.28

3.6 s

I.T./0.483

9/2-

1.16 h

EC/97/2.8 β+ /(3)/

1/2+

+1.58

1.41 h

β+, EC/95/4.9

(7+)

0.55

191

192m

192

193m 193

194m

194

193.9712

195m

195

196m

487_S11.indb 168

Half-life/ Resonance Width (MeV)

194.96977

+0.76

γ-Energy / Intensity (MeV/%) 0.5043 0.5921 see Tl[188m] 0.4129 0.2156 0.2284 0.3175 0.4452 0.3337 0.4510 0.5223 0.9422 0.1968 0.4164 0.7311 0.4164 0.6254 0.6838 1.0999 0.2157 0.2647 0.3256 0.3359 0.1740 0.4228 0.6348 0.7863 0.7455 0.3975 0.4228 0.6908 0.3650 0.2077 0.3244 0.3440 0.6761 1.0447 1.5793 ann.rad./ Hg k x-ray 0.4282 0.6363 0.7490 0.4279/75.2 0.6452/10.8 (0.395-1.623) Tl k x-ray 0.0990 0.3836 ann.rad./ Hg k x-ray 0.2422 0.5635 0.8845 1.3639 (0.13–2.5) 0.0840 0.4261 0.6353

4/17/06 11:01:03 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-169 Atomic Mass or Weight

195.97048

196

197m

196.96958

197

198m

Decay Mode/ Energy (/MeV)

0.54 s

IT/53/0.608 β+, EC/47/

9/2-

2.83 h

β+ /(1)/2.18 EC/(99)/

1/2+

+1.58

1.87 h

β+, EC/(53)/ IT/47/0.5347

+0.64

EC, β+ /(1)/3.5

198.96988

7.4 h

EC/1.4

199.97096

1.087 d

EC/2.46

200.97082

3.038 d

201.97211

201

202

Tl Tl

29.524(14)

202.972344 203.973864

Tl Tl

70.476(14)

204.974428

203 204

205

206m

206

205.976110

207m

1.4/ 2.1/ 2.4/

1/2-

+1.60

0.04

EC/0.48

1/2+

+1.605

12.47 d

EC/1.36

0.06

3.78 y

β- /97/0.7637 EC/(3)/0.347

1/2+ 2-

+1.622258 0.09

3.76 m

I.T./2.644

1/2+ 12-

+1.638215

4.20 m

β- /1.533

1.3 s

I.T./1.350

1.07/ 1.44/

0.763/97

1.53/99.9

011/2-

206.97742 207.982019

4.77 m 3.053 m

β- /1.423 β- /5.001

1.43/99.8 1.28/23 1.52/22 1.796/51

1/2+ (5+)

208.98536

2.16 m

β-/3.98

1.8 /100

(1/2+)

208

209

+0.072

Tl Tl

207

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

5.3 h

200

Spin (h/2 π)

β+ /(15)/4.4 EC/(85)/

197.9405

199

Particle Energy/ Intensity (MeV/%)

1.84 h

198

487_S11.indb 169

Half-life/ Resonance Width (MeV)

+1.88 +0.29

-0.18

γ-Energy / Intensity (MeV/%) 0.6954 (0.08–1.0) ann.rad./ Hg k x-ray 0.4257 0.6105 (0.03–2.4) Tl k x-ray 0.2262 0.4118 0.5872 0.6367 Hg k x-ray 0.1522/8.2 0.4258 Hg k x-ray Tl k x-ray 0.4118 0.5872 0.6367 Hg k x-ray 0.4118 0.6367 0.6759 (0.23–2.8) Hg k x-ray 0.2082 0.2473 0.4555 Hg k x-ray 0.36799 1.2057 (0.11–2.3) Hg k x-ray 0.13528 0.16740/10.0 Hg k x-ray 0.43957 Hg k x-ray

Tl k x-ray 0.2166 0.2661 0.4534 0.6866 1.0219 Pb k x-ray 0.80313 Tl k x-ray 0.3501 1.0000 0.89723 Pb k x-ray 0.27728 0.51061 0.58302 2.61448 Pb k x-ray

4/17/06 11:01:05 AM

Table of the Isotopes

11-170 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

209.99007

1.30 m

β- /5.48

Tl Tl

210.9935 211.9982

> 0.3 μs > 0.3 μs

ββ-

207.2(1)

210

211 212

Pb Pb 180 Pb 181 Pb 182 Pb 183m Pb

178.00383 179.0022 179.99792 180.9966 181.99267

183

178 179

Particle Energy/ Intensity (MeV/%)

1.3/25 1.9/56

~ 0.2 ms α/ α/ α α

182.99187

0.54 s

α/

Pb Pb 185 Pb

183.98814 184.98761

0.48 s 4.3 s 6.3 s

α/~ 80 α α/

185.98424

5. s

β+, EC/95/5.5 α/(5)/

15.2 s

β+, EC/ α/12

6.32/ 6.34/<100 6.01/<0.2 5.99/ 6.19/

6.08/

185m

186

187m

186.98392

18.3 s

EC/7.2 α/7

187.98087

23. s

EC/(78)/4.8 α/(22)/

188.98081

51. s

189.97808

1.2 m

EC/6.1 α/ β+ (13)/4.1 EC/(86)/ α/(0.9)/

187

188

189

190

191m

β+, EC/

190.97827

1.3 m

β+, EC/5.5

191.97579

3.5 m

β+, EC/~ 3.4 α/.006/

192

487_S11.indb 170

2.2 m

191

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(5+)

γ-Energy / Intensity (MeV/%) 1.5670/100 0.4651/95 (0.12–1.33) Pb k x-ray 0.081 0.2981 0.79788

5 ms 0.05 s 55 ms 0.42 s

184

Spin (h/2 π)

7.25 7.07 6.90 6.70/82.7 6.86/1.9 6.57/4.3 6.78/11.0 6.63/ 6.41/100 6.29/56 6.49/44 6.55/<1.4

5.98/<10 5.61/<0.1 5.58/

0+ 0+ 13/2+ (3/2-) 0+ 13/2+ 3/2-

-1.2 -1.1

0.205 0.269

(1/2-)

0.0674 0.2080 0.2755 0.2995 0.4487 0.7477 0.1930 0.3314 0.3435 0.3934 0.1850 0.7582

13/2+

5.58/

13/2+

5.11

-1.17

+0.085

ann.rad./ Tl k x-ray 0.1415 0.1512 0.9422 ann.rad./ 0.3871 0.6135 0.7122 ann.rad./ 0.9368 ann.rad./ 0.1675 0.6082 1.1954

4/17/06 11:01:07 AM

Table of the Isotopes Elem. or Isot. Pb

193m

Pb Pb

193 194

Natural Abundance (Atom %)

11-171 Atomic Mass or Weight

192.97617 193.97401

~ 2. m 10. m 15. m

195m

EC/5.2 β+, EC/2.7 α β+ /(8)/ EC/(92)/

Particle Energy/ Intensity (MeV/%)

4.64

Spin (h/2 π) 13/2+

3/2 (-) 0+ 13/2+

Nuclear Elect. γ-Energy / Magnetic Quadr. Intensity Mom. (nm) Mom. (b) (MeV/%) -1.15 +0.19 ann.rad./ 0.3650 0.3922

-1.132

+0.30

194.97454

~ 15. m

β+, EC/5.8

195.97277

37. m

β+, EC/2.1

43. m

EC/79/ β+ /2/ IT/19/0.3193

13/2+

-1.104

+0.38

-1.075

-0.08

-1.074

+0.08

195

196

197m

196.97343

~ 8. m

EC/97/3.6 β+ /3/

(3/2-)

197.97203

2.4 h

EC/1.4

12.2 m

IT/93/0.4248 β+, EC/(7)/ EC/(99)/2.9 β+ /(1)/

13/2+

197

198

199m

198.97292

1.5 h

199.97183

21.5 h

EC/0.81

1.02 m

I.T./0.6291

13/2+

9.33 h

EC/1.90

5/2-

+0.675

-0.009

3.53 h

IT/90/2.170 β+ /10/

-0.228

+0.58

+0.686

+0.10

199

200

201m

201

200.97289

202m

5/2-

Pb Pb

201.97216

5.3 × 104 y 6.2 s

EC/0.05 I.T./0.8252

0+ 13/2+

202.97339

2.163 d

EC/0.98

5/2-

1.13 h

I.T./2.185

202

203m

203

204m

487_S11.indb 171

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 5.8 m β+, EC/

ann.rad./ 0.2036 ann.rad./ Tl k x-ray 0.3836 0.3942 0.8784 ann.rad./ 0.3836 0.3937 0.7776 Tl k x-ray 0.2531 0.5021 Tl k x-ray 0.3079 0.3877 0.7743 (0.2–2.2) Tl k x-ray 0.3755 0.3858 0.7611 Tl k x-ray 0.1734 0.2903 0.3654 Pb k x-ray 0.4255 Tl k x-ray 0.3534 0.7202 1.1350 (0.22–2.4) Tl k x-ray 0.14763 Pb k x-ray 0.6288 Tl k x-ray 0.33120 0.36131 (0.11–1.8) Pb k x-ray Tl k x-ray 0.42219 0.78700 0.96271 Tl L x-ray Pb k x-ray 0.8203 0.8252 Tl k x-ray 0.279188 Pb k x-ray 0.37481 0.89922

4/17/06 11:01:08 AM

Table of the Isotopes

11-172 Elem. or Isot.

Natural Abundance (Atom %)

Pb Pb 206 Pb 207m Pb

1.4(1)

Pb Pb 209 Pb 210 Pb

22.1(1) 52.4(1)

Atomic Mass or Weight

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.91175

+0.712

Tl L x-ray

1.51 × 107 y

EC/0.0512

0.80 s

I.T./1.632

0+ 5/20+ 13/2+

206.975897 207.976652 208.981090 209.984189

> 2 × 1019 y 3.25 h 22.6 y

sf β- /0.644 β- /0.0635

1/20+ 9/2+ 0+

+0.59258 -1.474

-0.3

210.988737

36.1 m

α β- /1.37

(9/2+)

-1.404

+0.09

211.991898

10.64 h

β- /0.574

Pb Pb

212.99658 213.999805

10.2 m 26.9 m

β- /2.1 β- /1.0

215.0048

36 s

208.98040(1)

Bi Bi 185 Bi

184.0011 184.9976

204 205

207 208

211

212

213 214

215

24.1(1)

203.973044 204.974482 205.974465

Half-life/ Resonance Width (MeV)

185.9966

9.8 ms

α α p/90 α/10 α p/<0.5 α

187

Bi Bi

186.99316

~ 8. ms 32. ms

α/12 α/7

Bi Bi 189 Bi 190m Bi

187.99227

0.271 s 7.0 ms 0.68 s 5.7 s

α α α α/90

189.9883

~ 5.9 s

Bi Bi

190.98579

0.12 ms 12.4 s

191.98546

40. s

β+, EC/(30)/8.7 α/70 α/ β+, EC/(60)/7.3 α/(40)/ β+, EC/(80)/9.0 α/(20)/ β+, EC/ α/ β+, EC/40/7.1 α/(60)/ β+, EC/99.9/8.2 α/0.1/

184m 184

15. ms

186m

186

187m

188

189m

190

188.9892

191m 191

192

3.2 s

193m

192.98296

1.11 m

193.98283

1.8 m

193

194

487_S11.indb 172

0.007 s 13. ms 60. μs

0.645/100 0.017/81 0.061/19 3.72 0.57/5 1.36/92

0.28/83 0.57/12

0.67/48 0.73/42

(7.22-7.85)

+0.23

Pb k x-ray 0.56915 1.06310

0.40486 0.42700 0.83186 (0.09–1.27) Bi k x-ray 0.23858 Bi k x-ray 0.24192 0.29509 0.35187

0.449 0.124

1.55 8.03 7.07-7.23

(0.087-0.520)

7.26 7.37

0.1085

7.00/88.3 7.61/8.0 7.37/3.7 6.81 7.30

(0.071-0.320)

6.43 (6.23-6.72) α/6.45 (6.39-6.82) 6.87/100

(0.105-0.314) (0.089-0.374)

6.31 6.06/ 6.48/ 5.91/

1/2+ 9/2+ (10-)

0.1661 0.1740 0.2802 0.421

4/17/06 11:01:10 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-173 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

1.45 m

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

194.98065

2.9 m

196

195.98067

5. m

β+, EC/(94)/ α/(6)/ β+, EC/99.8/5.8 α/(0.2) EC/~ 7.4

Bi Bi 198 Bi

196.97886 197.97921

5. m 7.7 s 11.8 m

β+, EC/5.2 I.T./0.2485 β+, EC/6.6

1/2+ (10-) (7+)

198.97767

24.7 m 27. m

β+, EC/ β+, EC/4.3

9/2-

31. m

β+, EC/

(2+)

36. m

EC/(90)/5.9 β+ /(10)/

59.1 m

I.T./0.846 β+, EC/ EC/3.84

(1/2+)

195m

195

197

198m

Bi Bi

199m 199

200m

200

199.97813

201m

200.97701

1.8 h

201.97774

1.72 h

β+ /(3)/5.16 EC/(97)/

202.97688

11.8 h

EC/99.8/3.25 β+ /(0.2)/

203.97781

11.2 h

204.97739

205.97850

201

202

203

204

205

206

487_S11.indb 173

6.11/ 5.45/

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

3/20.1376 0.3720 0.6880 1.0486

4.6

9/2-

4.8

+4.26

-0.72

9/2-

+4.02

-0.69

EC/4.44

+4.32

-0.43

15.31 d

EC/2.71

9/2-

+4.07

-0.59

6.243 d

EC/3.76

+4.36

-0.39

1.35/

γ-Energy / Intensity (MeV/%) 0.5754 0.9650

0.2485 0.0900 0.1976 0.5624 1.0635 ann.rad./ 0.7203 0.8374 0.8417 0.9460 1.0528 1.3056 (0.12–3.2) 0.2453 0.4198 0.4624 1.0265 ann.rad./ Pb k x-ray 0.4198 0.4623 1.0265 Bi k x-ray 0.8464 Pb k x-ray 0.6288 0.9357 1.0138 (0.13–2.4) ann.rad./ Pb k x-ray 0.57860 0.92734 (0.08–3.5) Pb k x-ray 0.1865 0.8203 0.8969 1.8475 (0.1–2.9) Pb k x-ray 0.37481 0.89922 0.98409 Pb k x-ray 0.70347 1.76435 Pb k x-ray 0.51619

4/17/06 11:01:11 AM

Table of the Isotopes

11-174 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

206.978471

31.55 y

EC/2.399

9/2-

4.08

-0.6

207.979742

3.68 × 105 y

EC/2.880

4.63

-0.64

208.980399

1.9 × 1019 y 3.0 × 106 y

α α/

9/29-

+4.111 +2.73

-0.37 -0.47

209.984120

5.01 d

β- /1.163

3.13 4.420(3)/0.29 4.569(3)/3.9 4.584(3)/1.4 4.908(4)/39 4.946(3)/55 1.16/99

-0.0445

+0.136

210.98727

2.14 m

α/(99.7)/ β- /(0.3)/0.58 β- / α/(93)/ β- /(7)/

6.279/16 6.623/84

9/2-

207

208

Bi Bi

209

210m

210

211

100.

Bi Bi

7. m 25.0 m

212m2 212m1

211.991286

1.009 h

β- /(64)/2.254 α/(36)/

212.994385

45.6 m

β- /(98)/1.43 α/(2)/

213.99871

19.7 m

β- /3.27

Bi Bi

215.00177

37. s 7.7 m

β β- /2.3

216.00631

2.3 m

β-/4.0

217.0095

98 s

β/

218.0143

33. s

β-

187.99942

0.27 ms

188.99848

5 ms

189.99510

2.4 ms

α/

93. ms

212

213

214

215m 215

216

217

218

6.300/40 6.340/53

(15-) (9-)

(1-)

+0.32

+0.1

1.02/31 1.42/66 5.549/0.16 5.869/2.0

9/2-

+3.72

-0.60

7.91/80 7.320 7.532/8 7.259/80 7.309/12 7.53/96.4 7.01/3.3 7.376/50 6.888/46

6.051/25 6.090/9.6

γ-Energy / Intensity (MeV/%) 0.80313 0.88100 Pb k x-ray 0.56915 1.06310 Pb k x-ray 2.61435 Tl k x-ray 0.2661 0.3052 0.6502 0.2661 0.3.52 Tl k x-ray 0.3501 0.120 0.233 0.275 0.404 0.727 Tl k x-ray Po k x-ray 0.2881 0.72725 0.78551 1.62066 Po k x-ray 0.4404 (0.15–1.328) 1.10006 0.60931 1.12027 1.76449 (0.19–3.2) (0.158-0.498) 0.2937/35.2 (0.271–1.399) 0.5498 0.4192 0.2646/100 (0.254-1.017) 0.5097/134 0.3857/100 (0.174-0.703)

188

189

190

191m

487_S11.indb 174

4/17/06 11:01:12 AM

Table of the Isotopes Elem. or Isot.

190.99457

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 22 ms α/

191.99134

32. ms

α/8.5

Po Po 194 Po

192.99103 193.98819

~ 0.07 s 0.45 s 0.2 s

α/ α/ α/

Po Po 196 Po

194.98811 195.98554

~ 2.8 s ~ 3.9 s 5. s

α/ α/ α/(95)/ β+, EC/(5)/~4.6 α/(84)/ β+, EC/(16)/ α/(44)/ β+, EC/(56)/6.2 α/(70)/ β+, EC/(30)/4.0 β+, EC/(51)/ α/(39)/

191

192

Natural Abundance (Atom %)

11-175 Atomic Mass or Weight

193m 193

195m 195

25.8 s

197m

196.98566

53. s

197.98339

1.76 m

197

198

199m

4.2 m

β+, EC/(88)/7. α/(12)/

5.952/7.5

199.981780

11.5 m

β+, EC/85/3.4 α/(15)/

5.863/11.1

8.9 m

β+, EC/(57)/ IT/40/0.418 α/(3)/

5.786/~ 3.

201m

0+ 13/2+

5.2 m

13/2+

1.00

3/2-

0.94

200.98226

15.3 m

β+, EC/98/4.9 α/(2)/

5.683(3)/1.1

201.98076

45. m

β+, EC/98/2.8 α/(2)/

5.588/1.9

1.2 m

IT/96/0.6414 β-EC/(4)/

13/2+

5/2-

202

203m

202.98142

35. m

β+, EC/4.2

203.98032

3.53 h

EC/2.34 α

204.98120

1.7 h

β+, EC/3.53

203

204

205

5.377/0.66

0.99

(3/2-)

201

γ-Energy / Intensity (MeV/%)

6.18/57 5.27/7.6 × 10-4 6.059/24

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(3/2-)

198.98367

200

Spin (h/2 π)

6.282(4)/76

199

487_S11.indb 175

Particle Energy/ Intensity (MeV/%) 7.334/77 6.97/8 7.17/98.6 6.59/1.4 7.00 6.95 6.84/93 6.19/0.22 6.70/ 6.62/ 6.53/94 5.77/0.02 6.385(3)/55

+0.74

5/2-

+0.76

+0.17

ann.rad./ 0.2745 0.4998 1.0020 Bi k x-ray 0.1877 0.3616 1.0214 1.0344 0.14748 0.32792 0.6176 0.6709 Bi k x-ray Po k x-ray 0.2726 0.4123 0.4179 0.9670 Bi k x-ray 0.2056 0.2250 0.8483 0.9048 0.0410 0.1656 0.3158 0.6884 Bi k x-ray Po k x-ray 0.6414 0.17516 0.21477 0.89350 0.90863 1.09095 Bi k x-ray 0.2702 0.8844 1.0162 (0.11–1.9) Bi k x-ray

4/17/06 11:01:14 AM

Table of the Isotopes

11-176 Elem. or Isot.

206

Natural Abundance (Atom %)

Atomic Mass or Weight

205.98048

207m

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

EC/(95)/1.85 α/(5)/

2.8 s

I.T./1.383

19/2-

5/2-

206.98159

5.80 h

EC, β+/2.91

207.981246

2.898 y

α/5.213

208.982430

102. y

α/4.976

209.982874

138.4 d

α/5.407

25.2 s

α/

0.516 s

α/7.594

45. s

α/

208

209

210

211m

211

210.986653

212m

Po Po

211.988868 212.992857

0.298 μs 3.7 μs

α/8.953 α/8.537

213.995201

163.7 μs

α/7.833

214.999420

1.780 ms

α/7.526

216.001915

0.145 s

α/6.906

Po Po

217.00634 218.008973

1.53 s 3.04 m

α/6.662 α/6.114

Po Po

219.0137 220.0166

~2m > 0.3 μs

212 213

214

215

216

217 218

219 220

Spin (h/2 π)

8.8 d

207

Particle Energy/ Intensity (MeV/%)

5.223/5.5

4.233/0.0002 5.1158/100 4.624/0.56 4.879/99.2 4.516/0.001 5.304/100 7.273/91 7.994/1.7 8.316/0.25 8.875/7.0 6.570/0.54 6.892/0.55 7.450/98.9 8.514/2.0 9.086/1.0 11.650/97 8.784/100 7.614/0.003 8.375/100 6.904/0.01 7.686/99.99 6.950/0.02 6.957/0.03 7.386/100 5.895/0.002 6.778/99.99 6.539/ 6.003/99.999 5.181/0.11

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

+0.79

0+ 1/20+ 25/2+

9/2+

~ +0.77

+0.28

γ-Energy / Intensity (MeV/%) 0.83681 0.84983 0.87241 1.00124 (0.12–2.7) Bi k x-ray 0.28644 0.31156 0.51134 0.80737 1.03228 (0.11–1.5) Po k x-ray 0.2682 0.30074 0.81448 Bi k x-ray 0.74263 0.91176 0.99225

0.26049 0.8964 0.80313 Pb k x-ray 0.32808 0.56915 0.89723 1.06310 0.56915 0.89723

16+

0+ 9/2+ 0+ (9/2+)

0.7995 0.298

191m

At At

191

193m

487_S11.indb 176

2.1 ms

~ 1.7 ms 21 ms

α α

7.65/98 7.72/2 7.55/100 7.33/98 7.42/2

4/17/06 11:01:16 AM

Table of the Isotopes Elem. or Isot. At At 195m At 195 At 196m At 196 At 197m At 197 At 193 194

Natural Abundance (Atom %)

11-177 Atomic Mass or Weight

192.9998 193.9987 194.99627 195.9958 196.99319

1.0 s

198m

At 199 At 198

197.99284 198.99053

At At

4.1 s 6.9 s 47. s 3.5 s

200m2 200m

Decay Mode/ Energy (/MeV) α/ α/ α α/ α/ α β+, EC/7.8 α/ β+, EC/(75)/ α/(25)/ α/ β+, EC/8/5.6 α/(92)/ α β+, EC/(80) α/(20)/ β+, EC/65/~ 8.0 α/(35)/

Particle Energy/ Intensity (MeV/%) 7.24/100

7.05/ 6.707 6.960/ 6.856/86 6.755/94 6.643/ 6.411/ 6.538/12

199.99035

43. s

200.98842

1.48 m

At At

201.98863

0.46 s 3.02 m

202.98694

7.4 m

β+, EC/69/5.1 α/(31)/6.210

6.088/

203.98725

9.1 m

β+, EC/95/6.5 α/(5)/

5.951/

204.98607

26. m

β+, EC/90/4.54 α/(10)/6.020

5.902/

205.98667

29.4 m

β+, EC/99/5.72 α/(1)/5.881

5.703/

206.98578

1.81 h

β+, EC/90/3.91 α/(10)/5.873

5.758/

207.98650

1.63 h

β+, EC/99/4.97 α/(1)/5.752

208.98617

5.4 h

β+, EC/96/3.49 α/(4)/5.757

201

202m 202

203

204

205

206

207

208

209

β+, EC/29/5.9 α/(71)/6.474 I.T./0.391 β+, EC/88/7.2 α/(12)/

Spin (h/2 π)

7.07-7.22 6.95

200

487_S11.indb 177

Half-life/ Resonance Width (MeV) 28 ms 40 ms 147 ms 0.33 s 8 μs 0.39 s 2.0 s 0.39 s

6.412/44 6.465/57 6.344/

6.135/7.7 6.225/4.3

5.626/0.01 5.641/0.53

5.647/4.1

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

0.158 (1/2+) (9/2-)

9/2-

105+

9/2-

(5+)

(9/2-)

9/2-

(6+)

ann.rad./ 0.4413 0.5697 0.6753 0.1458 0.2459 0.6414 1.0020 1.0340 Po k x-ray 0.3271 0.4254 0.5156 0.6837 Po k x-ray 0.1543 0.6696 0.7194 Po k x-ray 0.20186 0.39561 0.47716 0.70071 Po k x-ray 0.16801 0.58842 0.81448 Po k x-ray 0.1770 0.2060 0.6601 0.6852 0.8450 1.0281 Po k x-ray 0.10422 0.54503

4/17/06 11:01:17 AM

Table of the Isotopes

11-178 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

209.98715

8.1 h

EC/99.8/3.98 α/(0.2)/5.632

210.987496

7.21 h

EC/(58)/0.787 α/(42)/5.980

0.119 s

α/

210

211

212m

Particle Energy/ Intensity (MeV/%)

5.361/0.05 5.442/0.05

5.211/0.004 5.868/42 7.837/65 7.897/33 7.058/0.4 7.088/0.6 7.618/15 7.681/84 9.080/

Spin (h/2 π)

9/2-

(9-)

212

211.99075

0.314 s

α/7.828

At At 214 At 215 At

212.992937 213.996372 214.99865

0.11 μs 0.76 μs 0.56 μs 0.10 ms

α/9.254 α/8.762 α/8.987 α/8.178

216.002423

0.30 ms

α/7.947

217.004719

32. ms

α/7.202

218

218.00869

1.6 s

α/6.883

At At 221 At 222 At 223 At

219.011162 220.0154 221.0181 222.0223 223.0252

50. s 3.71 m 2.3 m 0.9 m 50. s

α/6.390 β- /3.7 β β β

5 ms 6 ms 4. ms 0.02 s 0.07 s 64. ms 0.32 s 0.62 s 1.06 s

α α α/ α α/ α α α/ α/(98)/ EC/(2)/5. EC/(10)/ α/(90)/ α/(80)/ EC/(20)/

7.56 7.54 7.46 7.36 7.26 7.205 7.060 6.989 6.901/

α/(12)/ EC/(88)/ α/

6.641/

6.551

13/2+

213

214m

216

217

219 220

8.819/100 7.626/0.045 8.023/99.9 7.595/0.2 7.697/2.1 7.800/97 6.812/0.06 7.067/99.9

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.78189 0.79020 (0.1–2.6) Po k x-ray 0.24535 0.52758 1.18143 1.43678 1.48335 (0.04–2.4) Po k x-ray 0.66956 0.6870 0.74263

(1-)

9/2(9-) (1-) (9/2-)

0.40486

(1-)

(9/2-)

0.2595 0.3345 0.5940

6.654/6 6.695/90 6.748/4 6.275/

(0.24–0.70)

Rn Rn 196 Rn 197m Rn 197 Rn 198 Rn 199m Rn 199 Rn 200 Rn 195m 195

195.00544 196.00212 197.0016 197.99868 198.9984 199.99570

3.8 s

201m

200.9956

7.0 s

201.99326

9.9 s

201

202

203m

487_S11.indb 178

28. s

6.773/ 6.725/ α/6.778

0+ (13/2+) 3/20+

0.4329 0.5043

13/2+ (3/2-)

-0.96

+1.3

0.5695 0.2876–0.6255

4/17/06 11:01:19 AM

Table of the Isotopes Elem. or Isot. Rn

203

Natural Abundance (Atom %)

11-179 Atomic Mass or Weight

202.99339

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 45. s α/(66)/6.629 EC/(34)/~ 7.4 1.24 m α/(68)/ EC/(32)/3.8 2.8 m α/(23)/6.390 EC/(77)/5.2

Particle Energy/ Intensity (MeV/%) 6.499/

3/2-

6.420/

6.123(3)/0.02 6.262(3)/23

(5/2-)

6.258(3)/

203.99143

204.99172

205.99021

5.7 m

α/(68)/6.384 EC/(32)/3.3

206.99073

9.3 m

β+, EC/77/4.6 α/(23)/6.252

207.98964

24.3 m

208.99042

29. m

α/(60)/6.260 EC/(40)/2.85 β+ /(83)/3.93 α/(17)/

5.469(2)/0.003 6.140(2)/60 2.16/2.3 5.887(3)/0.04 5.898(3)/0.02 6.039(2)/16.9

209.98970

2.4 h

α/(96)/6.157 EC/(4)/2.37

5.351(2)/0.005 6.039(2)/96

210.99060

14.6 h

β+, EC/74/2.89 α/(26)/5.964

211.990704

24. m

α/6.385

213

212.99388

19. ms

α/8.243

Rn Rn 216 Rn 217 Rn

213.99536 214.99875 216.00027 217.003928

0.27 μs 2.3 μs 45. μs 0.6 ms

α/9.209 α/8.840 α α/7.885

218.005601

35. ms

α/7.267

219.009480

3.96 s

α/6.946(1)

204

205

206

207

208

209

210

211

212

214 215

218

219

487_S11.indb 179

5.995(4)/0.02 6.068(3)/0.15 6.126(3)/22.8

5.619(1)/0.7 5.784(1)/16.4 5.851(1)/8.8

5.587(4)/0.05 6.260(4)/99.95 7.552(8)/1.0 8.087(8)/98.2 7.254/0.8 9.037(9)/ 8.674(8)/ 7.500/0.1 7.742(4)/100 6.534(1)/0.16 7.133(1)/99.8 6.3130(5)/0.05

Spin (h/2 π)

5/2-

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

+0.80

+0.06

+0.82

+0.22

+0.8388

+0.31

0+ 5/2-

1/2-

+0.60

0+ 9/2+

γ-Energy / Intensity (MeV/%)

0.2652 0.3553 0.4648 0.6205 0.6753 0.7300 0.06170 0.0968 0.3245 0.3862 0.4822 0.4973 0.7728 At k x-ray 0.32947 0.34455 0.36767 0.40267 0.74723 (0.18–1.4)

At k x-ray 0.27933 0.33753 0.40841 0.68942 0.74594 (0.18–3.2) At k x-ray 0.19625 0.45824 0.57104 0.64868 (0.14–1.7) At k x-ray 0.16877 0.25022 0.37049 0.67412 0.67839 1.36298 (0.11–2.7)

0.540

0+ (9/2+) 0+ 9/2+ 0+ (5/2+)

-0.44

+0.93

0.6093 0.6653 Po k x-ray

4/17/06 11:01:20 AM

Table of the Isotopes

11-180 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

220.011394

55.6 s

α/6.404

221.01554

25. m

α/(22)/6.148 β- /(78)/1.2

222.017578

3.823 d

α/5.590

Rn Rn

223.0218 224.0241

23. m 1.8 h

β- / β- /

Rn Rn 227 Rn 228 Rn

225.0284 226.0309 227.0354 228.0380

4.5 m 7.4 m 2. s 65. s

β- / β- / β- / β- /

Fr Fr 201m Fr 201 Fr 202m Fr 202 Fr 203 Fr 204m2 Fr 204m1 Fr 204 Fr

199.00726 200.0066

12 s 49 ms ~ 0.02 s ~ 60 ms 0.29 s 0.30 s 0.54 s 0.8 s 2. s 1.8 s

α α α/ α/ α α/7.590 α/7.280 α α α/

Fr Fr 206 Fr 207 Fr 208 Fr

204.99859 205.99867 206.99695 207.99714

3.9 s 0.7 s 16.0 s 14.8 s 59.1 s

208.99595

50.0 s

209.99641

3.2 m

α/7.050 α/ α/7.416 α/6.900 α/(77)/6.770 EC/(23)/6.99 α/(89)/5.1 EC/(11)/5.16 α/6.670/71 EC/6.26

210.99554

3.10 m

211.99620

212.99619

220

221

222

223 224

225 226

Particle Energy/ Intensity (MeV/%) 6.425(3)/7.5 6.5309(4)/0.12 6.5531(3)/12.2 6.8193(3)/81 5.7486(5)/0.07 6.2883(1)/99.9 5.778(3)/1.8 5.788(3)/2.2 6.037(3)/18

4.987(1)/0.08 5.4897(3)/99.9

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.13057 0.27113 0.40170 (0.1–1.05)

-0.020

-0.38

Fr L x-ray 0.07384 0.08323 0.0610 0.18639 0.510

-0.78

+0.80

-0.70

+0.84

0+ 7/2+

7/20+

0.1085 0.2601 0.2655

199 200

205

206m

209

210

211

212

213

487_S11.indb 180

201.0039 202.00337 203.00093

204.00065

7.66 7.47 7.454 7.36/ 7.236/ 7.24/100 7.132(5)/ 7.01 6.97 7.03/96 6.97/90 7.01/74 6.914(5)/ 6.93 6.792(5)/84 6.766(5)/ 6.636(5)/

9/27+

+3.9 -4.8

-0.16 +0.004

6.646(3)/

9/2-

+3.9

-0.24

6.543(5)/99.87 (5.90-6.42)

+4.4

+0.19

α/6.660/87 EC/4.61

6.534(5)/99.94 (5.87-6.20)

9/2-

+4.0

-0.19

20. m

EC/(57)/5.12 α/(43)/6.529

(5+)

+4.6

-0.10

34.6 s

α/6.905

6.261(1)/16 6.335(1)/4 6.335(1)/4 6.343(1)/1.3 6.383(1)/10 6.406(1)/9.5 6.08–6.18 8.476(4)/51

9/2-

+4.0

-0.14

(9/2-)

0.531(IT)

0.7978 (0.1103–1.384) 0.2030 0.6438 0.8175 0.9008 0.220 0.2799 0.5389 0.9169 Rn x-ray 0.08107 0.08378 0.2277 1.1856 1.2748 0.014–1.178 (0.408-0.577)

4/17/06 11:01:22 AM

Table of the Isotopes Elem. or Isot. Fr

214m

Natural Abundance (Atom %)

11-181 Atomic Mass or Weight

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 3.4 ms α/

214

213.99897

5.0 ms

α/8.587

Fr Fr 217 Fr 218m Fr 218 Fr

215.00034 216.00320 217.00463 218.007578

0.12 μs 0.70 μs 0.016 ms 22. ms 1. ms

α/9.537 α/9.175 α/8.471 α α/8.014

219.00925

21. ms

α/8.132

220.012327

27.4 s

α/6.800

221.014255

4.8 m

α/6.457

222.01755

14.3 m

223.019736

22.0 m

β- /2.03 α/5.850 β- /1.149 α//0.006

224.02325

3.0 m

β- /2.82

Fr Fr

225.02557 226.0294

3.9 m 49. s

Fr Fr 229 Fr 230 Fr 231 Fr 232 Fr

227.0318 228.0357 229.03845 230.0425 231.0454 232.050

215 216

219

220

221

222

223

224

225 226

227 228

Particle Energy/ Intensity (MeV/%) 8.547(4)/46 6.775–8.046 7.409(3)/0.3 7.605(8)/1.0 7.940(3)/1.0 8.355(3)/4.7 8.427(3)/93 9.360(8)/ 9.005(10)/95 8.315(8)/ 7.384(10)/0.5 7.542(15)/1.0 7.572(10)/5 7.732(10)/0.5 7.867(2)/93 6.802(2)/0.25 6.967(2)/0.6 7.146(2)/0.25 7.313(2)/99 6.582(1)/10 6.630(2)/6 6.641(1)/12 6.686(1)/61 6.39–6.58 5.9393(7)/0.17 5.9797(7)/0.49 6.0751(7)/0.15 6.1270(7)/ 6.2433(3)/1.3 6.3410(7)/83.4 1.78/

Spin (h/2 π) 9-

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(1-)

(0.073-0.966)

(9/2-)

(0.045–0.160)

(9/2-) (1-)

(9/2-)

-0.67

+0.47

(5/2-)

+1.58

-1.0

+0.63

+0.51

(3/2+)

+1.17

+0.40

+0.517

β- /1.87 β- /3.6

3/2 1

+1.07 +0.071

+1.3 -1.35

2.48 m 39. s 50. s 19. s 17. s 5. s

β- /2.5 β- /~ 3.5 β- / β- / β- / β- /

1/2 2-

+1.50 -0.76

+2.4

~ 1.6 ms ~ 0.02 ms 24 ms ~ 31 ms 0.06 s ~ 0.17 s 0.22 s 0.4 s

α α α α α

7.91/ 7.74 7.61 7.59 7.48

α α/7.416

7.34 7.272(5)/

α/5.291 5.314 5.403

γ-Energy / Intensity (MeV/%)

0.0450 0.061 0.1060 0.1539 0.1617 At k x-ray 0.0995 0.21798 0.4091

0.1509 0.0589 0.1453 0.13150 0.21575 0.8367 (0.1–2.21) 0.18606 0.25373

(3) (0.0545-0.721)

Ra Ra 203m Ra 203 Ra 204 Ra 205m Ra 205 Ra 206 Ra 201 202

487_S11.indb 181

202.0099 203.0093 204.0065 205.0063 206.00383

4/17/06 11:01:23 AM

Table of the Isotopes

11-182 Elem. or Isot. Ra Ra 209 Ra 210m Ra 210 Ra 211m Ra 211 Ra 207 208

Natural Abundance (Atom %)

Atomic Mass or Weight 207.0038 208.00184 209.00199 210.00050 211.00090

Half-life/ Resonance Width (MeV) 1.3 s 1.4 s 4.6 s 2.4 μs 3.7 s 3.9 μs 13. s

Decay Mode/ Energy (/MeV) α/7.270 α/7.273 α/7.150

Particle Energy/ Intensity (MeV/%) 7.133(5)/ 7.133(5)/ (6.50-7.14)

Spin (h/2 π) 0+ 5/2-

α/7.610

7.020(5)/

α/7.046 EC/5.0

6.907/99. (6.26-6.79)

(5/2-)

α/7.033 IT

6.901(2)/

Ra 212 Ra 213m Ra

211.99979

8.3 μs 13.0 s 2.1 ms

213.00038

2.7 m

Ra Ra

214.00011

> 0.015 ms 2.46 s

α/7.272

Ra Ra

215

215.00272

7.6 μs 1.64 ms

7.14/99.8/ 6.51/0.2

α/8.864

(9/2+)

Ra Ra 218 Ra 219 Ra

216.00353 217.00632 218.00714 219.01009

0.18 μs 1.6 μs 26. μs 0.010 s

α/9.526 α/9.161 α/8.547 α/8.132

220.01103

18. ms

α/7.593

221.013917

29. s

α/6.879

222.015375

36.2 s

α/5.590

223.018502

11.43 d

α/5.979

224.020212

3.66 d

α/5.789

225.023612

14.9 d

β- /0.36 α

226.025410

1599. y > 4 × 1018 y

α/4.870 sf/4 × 10-14

7.883(6)/2.8 8.171(3)/1.4 8.700(3)/95.9 9.349(8)/ 8.992(8)/ 8.390(8)/ 7.680(10)/65 7.982(9)/35 7.39/5 7.45/95 6.254(10)/0.7 6.578(5)/3 6.585(3)/8 6.608(3)/35 6.669(3)/21 6.758(3)/31 6.237(2)/3.0 6.556(2)/97 5.287(1)/0.15 5.338(1)/0.13 5.365(1)/0.13 5.433(5)/2.3 5.502(1)/1.0 5.540(1)/9.2 5.607(3)/24 5.716(3)/52 5.747(1)/9 5.857(1)/0.32 5.872(1)/0.85 5.034(10)/0.003 5.047(1)/0.007 5.164(5)/0.007 5.449(2)/4.9 5.685(2)/95 0.32/100 5.01 × 10-5 4.98 × 10-6 4.194(1)/0.001 4.343(1)/0.006 4.601(1)/6.16

212m

213

214m 214

215m

216 217

220

221

222

223

224

225

226

487_S11.indb 182

EC/(20)/3.88 α/(80)/6.860

6.521(3)/4.8 6.622(3)/39 6.730(3)/36

(1/2-)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

+0.87

+0.40

+0.878

+0.48

(0.196-1.048) 0.773/100 0.852/74 0.055–1.048

0.465 -0.180

+1.9

0+ +0.271

(3/2+)

(0.120-0.665) (0.440-0.824)

(0.181-1.382) 0.642

(3/2+)

(0.387-0.634) (0.0967-0.775) 574.9 (0.396-0.802)

(0.160-1.061) 0.1024 0.11010 0.2125

+0.613

0+ 9/20+

5/2+

γ-Energy / Intensity (MeV/%)

+1.25

0.324 0.1448–0.8402 Rn k x-ray 0.12231 0.14418 0.15418 0.15859 0.26939 0.32388 0.33328 0.44494 (0.10–0.7) Rn k x-ray 0.2407 0.4093 0.6501

-0.734

Ac k x-ray 0.0434 Rn k x-ray 0.1861/3.64 0.2624

4/17/06 11:01:25 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-183 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

227.029178

42. m

β- /1.325

228.031070

5.76 y

β- /0.046

Ra Ra

229.03496 230.03706

4.0 m 1.5 h

β- /1.76 β- /1.0

231.0412 232.0436 233.0481 234.051

1.7 m 4. m 30. s ~ 30. s

ββββ-/

208.0116 209.00949 210.0094 211.0077 212.0078 213.0066 214.00690

0.04 s ~ 26 ms 27 ms ~ 25. ms ~ 0.1 s ~ 0.10 s 0.34 s 0.20 s 0.9 s 0.73 s 8.2 s

α α α/ α/ α/ α/ α/7.610 α/7.620 α/7.520 α/7.500 α/(86)/7.350 EC/(14)/6.34

215.00645

0.17 s

α/7.750

0.44 ms

α/

227

228

229 230

Ra Ra 233 Ra 234 Ra 231 232

Particle Energy/ Intensity (MeV/%) 4.784(1)/93.8 1.03/ 1.30/ 0.039/50 0.014/30 0.026/20 1.76/ 0.7/

Spin (h/2 π) (3/2+)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b) -0.404

+1.5

+0.503

+3.1

(3/2+) 0+

γ-Energy / Intensity (MeV/%) 0.053–2.448 Ac L x-ray Ac k x-ray 0.02739 0.0135 (0.006–0.0306) 0.0145–0.1715 0.0631 0.0720 0.2028 0.4698 0.4787

0+ 0+

Ac Ac 207 Ac 208m Ac 208 Ac 209 Ac 210 Ac 211 Ac 212 Ac 213 Ac 214 Ac 206m 206

215

206.0145 207.0120

216m

216.00872

44. ms

α/9.241

Ac Ac 218 Ac 219 Ac 220 Ac

217.00935 218.01164 219.01242 220.01476

0.7 μs 0.07 μs 1.1 μs 0.012 ms 26. ms

α/ α/9.832 α/9.380 α/8.830 α/8.350

221.01559

52. ms

α/7.790

63. s

α/(>89)/

216

217m 217

221

222m

487_S11.indb 183

7.79 7.75 7.69 7.72 7.62 7.58 7.462(8)/ 7.480(8)/ 7.379(8)/ 7.364(8)/ 7.215/54 7.081/42 (6.48-7.15) 7.60/99.57 7.21/0.46 7.03/0.20 6.96/0.14 8.198(8)/1.7 8.283(8)/2.5 9.028(5)/49 9.106(5)/46 8.990(2)/10 9.070(8)/90 10.540/100 9.650(10)/100 9.205(15)/ 8.664(10)/ 7.610(20)/23 4.680(20)/21 7.790(10)/13 7.850(10)/24 7.985(10)/4 8.005(10)/5 8.060(10)/6 8.195(10)/3 7.170(10)/2 7.375(10)/10 7.440(15)/20 7.645(10)/70 6.710(20)/7

(9/2-) (5+)

(0.0626-0.754)

(9/2-)

0.399 0.582 0.654

(9-)

(0.0826-1.375)

(1-)

9/2(9/2-)

4/17/06 11:01:27 AM

Table of the Isotopes

11-184 Elem. or Isot.

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV) EC/(1)/ I.T./(<10)/

222.01784

5. s

α/7.141

223.01914

2.1 m

α/(99)/6.783 EC/(1)/0.59

224.021723

2.7 h

EC/(90)/1.403 α/(10)/6.323

225.023230

10.0 d

α/5.935

226.026098

1.224 d

EC/(17)/0.640 β- /(83)/1.116 α/(0.006)/5.51

222

223

224

225

226

227.027752

21.77 y

β- /98.6/0.045 α/(1.4)/5.043

228.031021

6.15 h

β- /2.127

227

228

487_S11.indb 184

Natural Abundance (Atom %)

Particle Energy/ Intensity (MeV/%) 6.750(20)/13 6.810(20)/24 6.840(20)/9 6.890(20)/13 6.970(20)/7 7.000(20)/13 6.967(10)/6 7.013(2)/94 6.131(2)/0.12 6.177(2)/0.94 6.293(1)/0.47 6.326(1)/0.3 6.332(2)/0.14 6.360(1)/0.22 6.397(1)/0.13 6.448(1)/0.2 6.473(1)/3.1 6.523(2)/0.6 6.528(1)/3.1 6.563(1)/13.6 6.582(3)/0.3 6.646(1)/44 6.661(1)/31 5.841(1)/0.5 5.860(1)/0.75 5.875(1)/1.7 5.941(1)/4.4 6.000(1)/6.7 6.013(1)/1.4 6.056(1)/22 6.138(1)/26 6.154(1)/1.0 6.204(1)/12 6.210(1)/20 5.286(1)/0.2 5.444(3)/0.1 5.554(1)/0.1 5.608(1)/1.1 5.636(1)/4.5 5.681(1)/1.4 5.722(1)/2.9 5.731(1)/10 5.791(1)/9 5.793(1)/18

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

1(5/2-)

0.0725 0.0839 0.0927 0.0990 0.1917 0.2158 0.3588 0.4768

Ra L x-ray Ra k x-ray 0.08426 0.13150 0.1571 0.21575 0.2619 (0.03–0.3)

3/2

Fr k x-ray 0.06296/0.48 0.09982/1.36 0.1084 0.1116 0.1451 0.150.02/0.691 0.15724 0.18795/0.54 0.0075–0.8085 Ra k x-ray Th k x-ray 0.07218 0.15816 0.23034 0.0838/23. 0.0811/14. 0.2696/13. (0.044–1.27) Th L x-ray Th k x-ray 0.12903 0.33842 0.91116 0.96897 (0.2–1.96)

(1-)

5.399(5)/0.006

0.045/54 4.869(1)/0.09 4.938(1)/0.52 4.951(1)/0.65 1.11/32 1.85/12 2.18/11

γ-Energy / Intensity (MeV/%)

(3/2-)

(3+)

+1.1

+1.7

4/17/06 11:01:28 AM

Table of the Isotopes Elem. or Isot.

229.03302

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 1.04 h β- /1.10

Particle Energy/ Intensity (MeV/%) 1.1/

230.0363

2.03 m

β- /2.7 β-, sf

1.4/ /0.000119

231

231.0386

7.5 m

β- /2.1

2.1/100

(1/2+)

Ac Ac 234 Ac

232.0420 233.0446 234.0484

2.0 m 2.4 m 40. s

β- /3.7 β- / β- /

~ 0.01 s ~ 9 ms 0.04 s ~ 30. ms 0.14 s 0.10 s 1.2 s

α α α α/ α/7.840 α/7.825 α/7.660

0.14 ms

229

230

232 233

Natural Abundance (Atom %)

11-185 Atomic Mass or Weight

232.03806(2)

Th Th 211 Th 212 Th 213 Th 214 Th 215 Th

209.0177 210.0158 211.0149 212.01298 213.0130 214.01150 215.01173

209 210

216m

216.01106

27. ms

α/8.071

217

217.01311

0.25 ms

α/9.424

Th Th 220 Th 221 Th

218.01328 219.01554 220.01575 221.01818

0.11 μs 1.05 μs 10. μs 2. ms

α/9.847 α/9.510 α/8.953 α/8.628

222.01847

2.24 ms

α/8.129

223.02081

0.60 s

α/7.454

224.02147

1.05 s

α/7.305

225.023951

8.72 m

EC/(10)/0.68 α/(90)/6.920

226.024903

30.83 m

α/6.454

216

218 219

222

223

224

225

226

487_S11.indb 185

Spin (h/2 π) (3/2+)

(2-) (1/2+) (1+)

8.08 7.90 7.79 7.80/ 7.692(10)/ 7.677(10)/ 7.33(10)/8 7.395(8)/52 7.524(8)/40 9.93/74 8.00, 9.31 7.92/99.46 7.30/0.54 9.27/94.6 8.46/3.8 8.73/1.6 9.665(10)/ 9.340(20)/ 8.790(20)/ 7.732/7 8.142/72 8.469/21 7.980/97.7 7.599/2.3 7.29(1)/41(5) 7.32(1)/29(5) 7.350(15)/20(5) 7.390(15)/10(4) 6.768(5)/1.2 6.997(5)/19 7.170(5)/7 6.441(2)/15 6.479(2)/43 6.501(3)/14 6.627(3)/3 6.650(5)/3 6.700(5)/2 6.743(3)/7 6.796(2)/9 6.026(1)/0.2

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.09335/2.43 0.16451/2.61 0.56916/2.24 0.0111–0.898 Th k x-ray 0.45497 0.50820 (0.12–2.5) 0.14379 0.18574 0.22140 0.28250 0.3070

0+ 0+ 0+ (1/2-)

0.134 0.192 (0.069-0.295) (0.0905-1.478) 0.628 (0.546-0.822)

0+ 0+

(3/2+)

Ra k x-ray

4/17/06 11:01:29 AM

Table of the Isotopes

11-186 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

227.027704

18.72 d

α/6.146

228.028741

1.913 y

α/5.520

Th Th

229.031762

13.9 h 7.9 × 103 y

α α/5.168

230.033134

7.54 × 104 y

α/4.771

> 2 × 1018 y

sf/< 4 × 10-12

231.036304

1.063 d

β- /0.390

232.038055

1.40 × 1010 y 1.2 × 1021 y

α/4.081 sf/1.1 × 10-9

233.041582

22.3 m

β-/1.245

234.043601

24.10 d

β- /0.273

235.04751

7.2 m

β- /1.9

236.0499

37.5 m

β- /~ 1.0

Th Th

237.0539 238.0565

5.0 m 9.4 m

β-

231.03588(2)

Pa Pa 214 Pa 215 Pa 216 Pa

212.0232 213.0211 214.0209 215.0192 216.0191

~ 5 ms 7 ms 17 ms 15. ms 0.19 s

α α α α α/

227

228

229m 229

230

231

232

233

234

235

236

237 238

212 213

487_S11.indb 186

100.

Particle Energy/ Intensity (MeV/%) 6.041(1)/0.19 6.098(1)/1.3 6.2283(4)/23 6.3375(4)/75

5.1770(2)/0.18 5.2114(1)/0.4 5.3405(1)/26.7 5.4233(1)/73 4.83-5.08 4.814/9.3 4.845(5)/56 4.9008(5)/10.2 4.689–5.077 4.4383(6)/0.03 4.4798(6)/0.12 4.6211(6)/23.4 4.6876(6)/76.3 0.138/22 0.218/20 0.305/52

3.830(10)/0.2 3.952(5)/23 4.010(5)/77 1.245/

0.102/20 0.198/72

Spin (h/2 π)

γ-Energy / Intensity (MeV/%) 0.1112 0.2421 0.1310 0.1733–0.9295 Ra L x-ray Ra k x-ray 0.05014 0.23597 0.25624 (0.02–1.0)

+0.46

0.1935/4.3 0.21089/277 0.13697/1.21 0.0111–0.6036 0.0677/0.46 0.1439/0.078

(3/2+)

5/2+

½+

8.27 8.24 8.12 8.08/100 7.95/51 7.82/45 7.79/4

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

+4.

Pa L x-ray Pa k x-ray 0.02564 0.084203/ (0.02–0.3) 0.0590 0.124 Pa L x-ray Pa k x-ray 0.02938 0.08653 0.45930 (0.02–1.2) Pa L x-ray 0.06329/4.1 0.09235/2.4 0.09278/2.4 0.4162 0.6594 0.7272 0.747 0.9318 Pa k x-ray 0.1107 0.0890

0.134

4/17/06 11:01:31 AM

Table of the Isotopes Elem. or Isot. Pa

217m

Natural Abundance (Atom %)

11-187 Atomic Mass or Weight

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 1.08 ms α/

217.0183

3.8 ms

α/8.490

218

218.02004

0.12 ms

α/

Pa Pa 221 Pa 222 Pa

219.0199 220.0219 221.0219 222.0237

0.05 μs 0.8 μs 6. μs ~ 4.3 ms

α α α α/8.700

223.0240

~ 6.5 ms

α/8.340

224.02563

0.84 s

α/7.630

225.0261

1.8 s

α/7.380

226.02795

1.8 m

α/(74)/6.987 EC/(26)/2.83

227.02881

38.3 m

α/(85)/6.582 EC/(15)/1.02

228.031051

22. h

EC/(98)/2.111 α/(2)

229.032097

1.5 d

EC/(99.8)/0.32 α/(0.2)/5.836

230.034541

17.4 d

EC/(90)/1.310 β-/(10)/0.563

231.035884

3.25 × 104 y

α/5.148

> 2 × 1017 y

sf/< 1.6 × 10-15

217

219 220

223

224

225

226

227

228

229

230

231

487_S11.indb 187

Particle Energy/ Intensity (MeV/%) 10.16/72 8.306/11 9.55/6 9.69/2 8.337/99 7.873/0.4 7.728/0.3 7.710/0.3 9.54/31 9.61/69

9.08(3) 8.180/50 8.330/20 8.540/30 8.006(10)/55 8.196(10)/45 7.555(10)/75(3) 7.46(1)/25(3) 7.195(10)/30 7.245(10)/70 6.728(10)/0.7 6.823(10)/35 6.863(10)/39 6.357(4)/7 6.376(10)/2.2 6.401(4)/8 6.416(4)/13 6.423(10)/10 6.465(4)/43 5.779/0.23 5.805/0.15 6.078/0.4 6.105/0.25 6.118/0.22

5.536(2)/0.02 5.579(2)/0.09 5.668(2)/0.05 0.51/

4.6781(5)/1.5 4.7102(5)/1.0 4.7343(5)/8.4 4.8513(5)/1.4 4.9339(5)/3 4.9505(5)/22.8 4.9858(5)/1.4 5.0131(5)/25.4 5.0292(5)/20 5.0318(5)/2.5

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) 0.4504–0.8208

0.0466–0.634

0.092

0.1945 (0.028–0.412)

(5/2-)

(3+)

0.0649 0.0669 0.1100

+3.5

Th k x-ray 0.409/100 0.4631/222 0.91116/242 0.96464/120 0.96897/149 0.058–1.96 0.04244 (0.024–0.18)

(2-)

2.0

3/2-

2.01

Th L x-ray Th k x-ray 0.4437 0.45477 0.89876 0.91856 0.95199 (0.053–1.07) Ac L x-ray Ac k x-ray 0.01899 0.027396 0.03823 0.04639 0.25586 0.26029 0.28367 0.30007

(5/2+)

-1.7

4/17/06 11:01:32 AM

Table of the Isotopes

11-188 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

232.03859

1.31 d

β- /1.34

233.040247

27.0 d

β-/0.571

1.17 m

β- /99.9/2.29 IT/0.13/

233

234m

Particle Energy/ Intensity (MeV/%) 5.0587(5)/11

Spin (h/2 π)

0.15/40 0.256/60

3/2-

(0-)

234.043308

6.69 h

β- /2.197

0.51/

(4+)

Pa Pa

235.04544 236.0487

24.4 m 9.1 m

β- /1.41 β- /2.9

1.4/97 1.1/40 2.0/50 3.1/10

(3/2-) (1-)

237.0512

8.7 m

β- /2.3

1.1/60 1.6/30 2.3/10

(1/2+)

238.0545

2.3 m

β- /3.5

1.2/ 1.7/

(3-)

239.0573

1.8 h

238.02891(3) α α α α α α/ α/ α/

8.02 10.68 8.61 9.68(4)/

α/7.560

235 236

237

238

239

U U 218 U 219 U 222 U 223 U 224 U 225 U

217.0244 218.02354 219.0249 222.0261 223.0277 224.02761 225.02939

~ 0.2 ms ~ 0.56 ms 0.5 ms ~ 0.08 ms ~ 1.μs 0.02 s ~ 1. ms 84. ms

226.02934

0.26 s

217

218m

226

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(2-)

234

487_S11.indb 188

Decay Mode/ Energy (/MeV)

232

Half-life/ Resonance Width (MeV)

8.78(4)/ 8.46/100 7.87/83 7.82/15 7.63/2 7.56/86 7.38/14

+4.0

-3.0

γ-Energy / Intensity (MeV/%) 0.30264 0.33007 (0.02–0.61) U k x-ray 0.10900 0.15009 0.89439 0.96934 (0.10–1.17) U L x-ray U k x-ray 0.30017 0.31201/38.4 (0.0286-0.456) U k x-ray 0.25818/0.07 0.76641/0.32 1.0009/0.86 (0.06–1.96) U L x-ray U k x-ray 0.1312/0.03 0.5695/0.02 0.9256/0.02 (0.02–1.99) 0.0308–0.65893 U k x-ray 0.64235 0.68759 1.7630 (0.04–2.18) 0.4986 0.5293 0.5407 0.8536 0.8650 (0.04–1.4) 0.10350 0.1785 0.4484 0.6350 0.6800 1.01446 (0.04–2.5)

0+ 0+ 0+

4/17/06 11:01:34 AM

Table of the Isotopes Elem. or Isot. 227 228

U U

Natural Abundance (Atom %)

11-189 Atomic Mass or Weight

227.03116 228.03137

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 1.1 m α/7.200 9.1 m α/6.803

229

229.03351

58. m

EC/(80)/1.31 α/(20)/6.473

230

230.033940

20.8 d > 4 × 1010 y

α/5.992 sf/< 10-10

231

231.036294

4.2 d

EC/0.36 α/(10-3)

232

232.037156

70. y 2.6 × 1015 y

α/5.414 sf/2.7 × 10-12

233

233.039635

1.592 × 105 y > 2.7 × 1017 y

α/4.909 sf/6 × 10-11

234

0.0054(5)

234.040952

2.455 × 105 y 1.5 × 1016 y

α/4.856 sf/1.6 × 10-9

U U

0.7204(6)

235.043930

26. m 7.04 × 108 y 1.0 × 1019 y

IT/0.0007 α/4.6793 sf/7 × 10-9

235m 235

Particle Energy/ Intensity (MeV/%) 6.870/ 6.404(6)/0.6 6.440(5)/0.7 6.589(5)/29 6.681(6)/70 6.223/3 6.297(3)/11 6.332(3)/20 6.360(3)/64 5.5866(3)/0.01 5.6624(3)/0.26 5.6663(3)/0.38 5.8178(3)/32 5.8887(3)/67 5.46/1.6 × 10-3 5.47/1.4 × 10-3 5.40/1. × 10-3 4.9979(1)/0.003 5.1367(1)/0.3 5.2635(1)/31 5.3203(1)/69 4.7830(8)/13.2 4.8247(8)/84.4 4.510–4.804 4.604(1)/0.24 4.7231(1)/27.5 4.776(1)/72.5 4.1525(9)/0.9 4.2157(9)/6. 4.3237(9)/4.6 4.3641(9)/19. 4.370(4)/6 4.3952(9)/57. 4.4144(9)/2.1 4.5025(9)/1.7 4.5558(9)/4.2 4.5970(9)/4.8 4.332(8)/0.26 4.445(5)/26 4.494(3)/74

Spin (h/2 π) 0+

+0.59

3.66

Th L x-ray 0.04244 0.09714 (0.0252–1.119) 0.05323/0.156 0.12091

-0.38

4.9

Th L x-ray Th k x-ray 0.10917 0.14378 0.16338 0.18574 0.20213 0.20533 0.22140 (0.03–0.79) Th L x-ray 0.04946/100 0.11279/24.1 0.17115/0.080 Np L x-ray Np k x-ray 0.05953 0.20801 Th L x-ray 0.04955/.06 0.1135/.01 (0.522–0.681)

1/2+ 7/2-

236.045568

2.342 × 107 y 2.5 × 1016 y

α/4.569 sf/9 × 10-8

237

237.048730

6.75 d

β- /0.519

0.24/ 0.25/

1/2+

238

238.050788

4.47 × 109 y 8.2 × 1015y

α sf/5 × 10-5

239

239.054293

23.5 m

β- /1.265

240

240.05659

14.1 h

β- /0.39

4.0395/0.23 4.147(5)/23 4.196(5)/77 1.2/ 1.3/ 0.36/

242

242.0629

16.8 m

β- /~ 1.2

487_S11.indb 189

Th L x-ray 0.07218 0.15421 0.23034 (0.081–0.8565) Pa L x-ray Pa k x-ray 0.02564 0.08420

(5/2-)

5/2+

5/2+ 0+

γ-Energy / Intensity (MeV/%) 0.095 0.152 0.187 0.246

(3/2+)

236

99.2742(10)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

Np L x-ray 0.04410 0.05558 0.06760

4/17/06 11:01:35 AM

Table of the Isotopes

11-190 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

Np Np 227 Np

225.0339 226.0352 227.0350

> 2 μs 0.03 s 0.51 s

228.0362

61. s

Np Np

229.0363 230.0378

4.0 m 4.6 m

231.03825

48.8 m

232.0401

14.7 m

EC/99 /2.7

(4-)

233.04074

36.2 m

EC/1.2

(5/2+)

234.04290

4.4 d

β+, EC/1.81

235.044063

1.085 y

EC/99.9 /0.124 α/0.001/5.191 EC/52 / β- /48 /

5/2+

(6-)

225 226

228

229 230

231

232

233

234

235

22.5 h

236m

EC/60(7)/ α/40(7)/, sf α/7.010 EC/97 /3.6 α/3 EC/98 /1.8 α/2 /6.368

8.04(2)/ 7.65(2)/ 7.68(1)/

6.890(20) 6.660(20) 6.280/2

0.79/

5/2

(1-)

236.04657

1.55 × 105 y

EC/91 /0.94 β- /9 /0.49

237.048173

2.14 × 106 y 1 × 1018 y

α/4.957 sf/2.1 × 10-10

238.050946

2.117 d

β- /1.292

239.052939

2.355 d

β- /0.722

0.341/30 0.438/48

5/2+

7.22 m

β- /99.9 / IT/0.1 /

2.18/

(1+)

237

238

239

240m

0.2629 0.3475 0.3703 U L x-ray U k x-ray 0.3268 0.81925 0.86683 U L x-ray U k x-ray 0.29887 0.31201 U L x-ray U k x-ray 1.5272 1.5587 1.6022 U k x-ray

(0+)

236

487_S11.indb 190

α/ α/

4.6395(5)/6.5 4.766(5)/9.7 4.7715(5)/22.7 4.7884(5)/47.8 4.558–4.873 1.2/

5/2+

+3.14

+3.89

U L x-ray Pu L x-ray U k x-ray 0.64235 0.68759 U L x-ray U k x-ray 0.10423 0.16031 Pa L x-ray Pa k x-ray 0.029378/15 0.08653/12 (0.03–0.28) Pu L x-ray Pu k x-ray 0.98447/25.2 1.02855/18.3 (.044–1.026) Pu L x-ray Pu k x-ray 0.10613 0.228186/11 0.27760/15 (0.04–0.50) 0.25143 0.26333 0.55454 0.59735

4/17/06 11:01:37 AM

Table of the Isotopes Elem. or Isot. Np

240

241

Natural Abundance (Atom %)

11-191 Atomic Mass or Weight

240.05616

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 1.032 h β- /2.20

Particle Energy/ Intensity (MeV/%) 0.89/

241.0583

13.9 m

β- /1.3

1.3/

5/2+

2.2 m

β- /

β- /2.7

2.7/

7.81(2)/ 7.46/ 7.06/81 7.00/19

242m

242.0616

5.5 m

Np Np

243.06428 244.0679

1.9 m 2.3 m

Pu Pu 230 Pu

228.03874 229.0402 230.03965

~ 1.1 s ~ 1.5 m 1.7 m

α/ α/ α/

231.04110

8.6 m

232.04119

34. m

EC/90 α/10 EC/>80/1.1 α/<20/6.716

233.04300

20.9 m

EC(99.9)/1.9 α/0.1 /6.416

234.04332

8.8 h

EC/94 /0.39 α/6 /6.310

235.04529

25.3 m

Pu Pu

236.046058

1.2 μs 2.87 y 1.5 × 109 y

EC/99+ /1.2 α/0.003/5.957

237.048410

45.7 d

EC/99.9 /0.220 α/0.003 /5.747

238.049560

87.7 y 4.75 × 1010 y

α/5.593 sf/1.8 × 10-7

239.052163

2.410 × 104 y 8. × 1015 y

α/5.244 sf/3 × 10-10

242

243 244

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(1+)

γ-Energy / Intensity (MeV/%) 0.1471/ 0.5664 0.6008 0.1330/ 0.1740 0.280 0.15910 0.2651/ 0.78570 0.9448/ 0.6209 0.73620 0.78074 1.47340 (0.04–2.37)

228 229

231

232

233

234

235

236m 236

237

238

239

487_S11.indb 191

α/5.867 sf/1.9 × 10-7

6.72 6.542(10)/38 6.600(10)/62

0.1503 0.1804 0.2353 0.5002 0.5346/ 1.0352/

6.300(20)/0.1

6.035(3)/0.024 6.149(3)/1.9 6.200(3)/4. 5.850(20)/0.003 5.611/0.21 5.7210/30.5 5.7677(1)/69.3 5.334(4)/0.0015 5.356(4)/0.0006 5.650(4)/0.0007

5.3583(1)/0.10 5.465(1)/28.3 5.4992(1)/71.6 5.055/0.047 5.076/0.078 5.106/11.9 5.144/17.1 5.157/70.8 (4.74 –5.03)

(5/2+)

7/2-

1/2+

+0.203

0.0476/0.07 0.109/0.02 (0.17–0.97) Np L x-ray Np k x-ray 0.026344 0.03319 0.05954 (0.03–0.5) U k x-ray 0.04347 (0.04–1.1) U k x-ray 0.05162 0.05682 0.12928 0.37502 0.41369

4/17/06 11:01:38 AM

Table of the Isotopes

11-192 Elem. or Isot. Pu

240

Natural Abundance (Atom %)

Atomic Mass or Weight 240.053814

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 6.56 × 103 y α/5.255 sf/5.7 × 10-6 1.14 × 1011 y

Particle Energy/ Intensity (MeV/%) 5.0212(1)/0.07 5.1237(1)/26.4 5.1681(1)/73.5

Spin (h/2 π)

4.853/3 × 10-4 4.897/0.002

5/2+

4.7546(7)/0.098 4.8564(7)/22.4 4.9006(7)/78 0.49/21 0.58/60

241.056852

14.3 y

242.058743

< 6 × 1016 y 3.75 × 105 y 6.77 × 1010 y

β-/99+/0.0208 α/0.002 /5.139 sf/> 2.4 × 10-14 α/4.983 sf/5.5 × 10-4

243.062003

4.956 h

β- /0.582

244.064204 245.06775

α/99.9/4.665 sf/0.12 β- /1.21

4.546(1)/19.4 4.589(1)/80.5 0.93/57 1.21/11

8.00 × 107 y 6.6 × 1010 y 10.5 h

246.07021

10.85 d

β- /0.40

0.150/85 0.35/10

247.0741

2.3 d

Am Am 234 Am 235 Am

232.0466 233.0464 234.0478 235.0480

0.9 m ~ 3.2 m 2.3 m 10.3 m

Am Am 237 Am

236.0496 237.0500

2.9 m 3.6 m 1.22 h

238.05198

241

242

243

244

245

246

247

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

-0.683

+6.

γ-Energy / Intensity (MeV/%) U L x-ray 0.04524 0.10423 (0.04–0.97) 0.14854 0.1600 U L x-ray 0.04491 0.10350 Am L x-ray 0.0417 0.0839 U L x-ray 0.0439 Am L x-ray Am k x-ray 0.2804 / 0.30832 0.32752 0.56014 (0.03–1.2) Am L x-ray Am k x-ray 0.04379 0.22371

7/2+

(9/2-)

232 233

236m

6.78

6.46/0.4

EC EC/99.98 /1.7 α/0.02 /6.20

6.042(5)/0.02

1.63 h

EC/2.26 α/0.0001 /6.04

5.940/0.0001

239.053025

11.9 h

EC/99.99/0.803 α/0.01/5.924

240.05530

2.12 d

EC/1.38 α/5.592

241.056829

432.7 y 1.2 × 1014 y

α/5.637 sf/3.6 × 10-10

236

238

239

240

241

487_S11.indb 192

EC/~ 5.0 α EC/4.2 EC α

5.734(2)/0.001 5.776(2)/0.008

5.378(1)/16 × 10-4

5.2443(1)/0.002 5.3221(1)/0.015 5.3884(1)/1.4 5.4431(1)/12.8

(1-) (5-) (5/2-)

5/2-

(3-)

5/2-

+1.58

+3.1

Pu K x-ray 0.291/100 (0.170-0.828) (0.583-0.713) (0.158-1.038) Pu k x-ray 0.14559 0.28026 0.43845 Pu L x-ray Pu k x-ray 0.91870 0.96278 Pu L x-ray Pu k x-ray 0.18172 0.22818 0.27760 Pu L x-ray Pu k x-ray 0.88878 0.98764 (0.1–1.3) Np L x-ray 0.02634 /.024 0.03319/.00126 0.05954/0.359

4/17/06 11:01:40 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-193 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

141. y

242m

> 3 × 1012 y

Decay Mode/ Energy (/MeV)

IT/99.5/0.048 α/0.5/5.62 sf/< 4.7 × 10-9

Particle Energy/ Intensity (MeV/%) 5.4857(1)/85.2 5.5116(1)/0.20 5.5442(1)/0.34 5.141(4)/0.026 5.2070(2)/0.4

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) (0.03–1.128)

+1.0

+6.5

Am L x-ray 0.04863 0.08648 0.10944 0.16304 Pu L x-ray Cm L x-ray Pu k x-ray 0.0422 0.04453 0.04354 0.07467 0.08657 0.11770 0.14197 0.0429 Am L x-ray Cm k x-ray 0.7460 0.9000 Cm L x-ray Cm k x-ray 0.25299 Cm L x-ray Cm k x-ray 0.27002 0.79881 1.06201 1.07885 (0.04–2.29) Cm L x-ray Cm k x-ray 0.1529 0.2046 0.6786 Cm L x-ray Cm k x-ray 0.2267 / 0.2853 /

242.059549

16.02 h

β- /83 /0.665 EC/17 /0.750

0.63/46 0.67/37

+0.388

-2.4

243.061381

7.37 × 103 y 2. × 1014 y

α/5.438 sf/3.7 × 10-9

5/2-

+1.5

+2.9

Am Am

244.064285

~ 26. m 10.1 h

β- /1.498 β- /1.428

5.1798(5)/1.1 5.2343(5)/11 5.2766(5)/88 5.394(5)/0.12 5.3500(5)/0.16

245.066452

2.05 h

β- /0.894

0.65/19 0.90/77

(5/2+)

25.0 m

β- /

1.3/79. 1.60/14 2.1/7

1.2/

(7-)

7.34/ 7.24/

242

243

244m 244

245

246m

246.06978

39. m

β- /2.38

247.0721

22. m

β- /1.7

~ 51. s

α/ α

246

247

(1-)

Cm Cm 235 Cm 236 Cm 237 Cm 238 Cm 233 234

239.0550

~ 3. h

EC/1.7 EC/2.5 EC/>90 /0.97 α/<10 /6.632 EC/1.7

240.055530

27. d

α/6.397

1.9 × 106 y

sf/3.9 × 10-6

239

240

487_S11.indb 193

233.0508 234.05016 235.0514 236.0514 237.0529 238.05303

2.4 h

6.520(50)/<10

5.989/0.014 6.147/0.05 6.2478(6) /28.8 6.2906(6) /70.6

0.0407 0.1466 0.1874

4/17/06 11:01:41 AM

Table of the Isotopes

11-194 Elem. or Isot. Cm

241

242

243

244

245

Natural Abundance (Atom %)

Atomic Mass or Weight 241.057653

242.058836

243.061389

244.062753

245.065491

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 32.8 d EC/99 /0.768 α/1 /6.184

162.8 d

α/6.216

7.0 × 106 y

sf/6.4 × 10-6

29.1 y

α/6.167

5.5 × 1011 y

sf/5.3 × 10-9

18.1 y

α/5.902

1.32 × 107 y

sf/1.4 × 10-4

8.48 × 103 y

α/5.623

1.4 × 1012 y

sf/6.1 × 10-7

α/5.476 sf/0.026 α/5.352

246.067224

247.070354

4.76 × 103 y 1.8 × 107 y 1.56 × 107 y

248.072349

3.48 × 105 y

α/99.92 /5.162

249.075953

4.15 × 106 y 64.15 m

sf/8.38 β- /0.900

250.07836

~ 9.7 × 103 y

251.08229

16.8 m

sf/85.8 α/5.27 β- /1.42

252.0849

<2d

238.0583 239.0583 240.0598 241.0602 242.0620 243.063008

2.4 m

EC/5.0

~ 4.8 m 4.6 m 7.0 m 4.5 h

EC EC/3.0 EC/99.8 /1.508

246

247

248

249

250

251

252

Particle Energy/ Intensity (MeV/%) 5.8842(4)/0.12 5.9291(4)/0.18 5.9389(4)/0.69

Spin (h/2 π) 1/2+

5.9694(1)/0.035 6.069(1)/25 6.1129(1)/74

5.6815(5) /0.2 5.6856(5)/1.6 5.7420(5)/10.6 5.7859(5)/73.3 5.9922(5)/6.5 6.0103(5)/1.0 6.0589(5)/5 6.0666(5)/1.5

5/2+

5.6656/0.02 5.7528/23 5.8050/77 5.515/0.004 5.235(10)/0.3 5.3038(10)/5.0 5.3620(7)/93 5.4927(11)/0.8 5.5331(11)/0.6

5.343(3)/21 5.386(3)/79 4.818(4)/4.7 4.8690(20)/71 4.941(4)/1.6 4.9820(20)/2.0 5.1436(20)/1.2 5.2104(20)/5.7 5.2659(20)/13.8 4.931(5)/0.07 5.0349(2)/16.5 5.0784(2)/(75)/1 0.9/

7/2+

9/2-

0.41

0.5

0.37

γ-Energy / Intensity (MeV/%) Am k x-ray 0.13241 0.16505 0.18028 0.43063 0.47181 Pu L x-ray 0.04408 0.10189 (0.04–1.2) Pu L x-ray Pu k x-ray 0.10612 0.20975 0.22819 0.27760 0.28546 0.33431 (0.04–0.7) Pu L x-ray 0.04282 0.09885 0.15262 Pu L x-ray Pu k x-ray 0.04195 0.13299 0.13606 0.17494 Pu L x-ray 0.04453 Pu k x-ray 0.2792 0.2886 0.3471 0.4035

1/2+

0+ 0.90/16

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(1/2+)

Bk k x-ray 0.56039/0.84 0.63431/1.5 (0.085-0.653)

0.3896 / 0.5299 0.5425

Bk Bk 240 Bk 241 Bk 242 Bk 243 Bk 238 239

487_S11.indb 194

(0.152-0.262) 6.542(4)/0.03

(3/2-)

0.1466

4/17/06 11:01:43 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-195 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV) α/0.15 /6.871

244.06518

4.4 h

EC/99.99 /2.26 α/0.01 /6.778

245.066362

4.94 d

EC/99.9 /0.810 α/0.1 /6.453

246.0687

1.80 d

EC/1.35

247.07031

1.4 × 103 y

α/5.889

248.07310

23.7 h

β- /70 /0.87 EC/30 /0.72

249.074987

320. d

250.078317

1.8 × 109 y 3.217 h

β- /0.125 α/0.001 /5.525 sf/4.9 × 10-8 β- /1.780

251.08076

56. m

β- /1.09

252.0843

1.8 m

Cf Cf

237.062 238.0614

2.1 s 21 ms

Cf Cf

239.0624 240.0623

~ 0.7 m 1.1 m

241.0637

4. m

242.06370

3.5 m

243.0654

11. m

244.066001

20. m

244

245

246

247

248

249

250

251

252

Particle Energy/ Intensity (MeV/%) 6.5738(2)/0.04 6.7180(22)/0.02 6.7581(20)/0.02

6.625(4)/0.003 6.667(4)/0.003

5.8851(5)/0.03 6.1176(9)/0.01 6.1467(5)/0.02 6.3087(5)/0.014 6.3492(5)/0.018

5.465(5)/1.5 5.501(5)/7 5.532(5)/45 5.6535(20)/5.5 5.678(2)/13 5.712(2)/17 5.753(2)/4.3 5.794(2)/5.5 0.86/

0.125/100 5.390(1)/0.0002 5.4174(6)/0.001 0.74/

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(4-)

3/2-

(2-)

Cm L x-ray Cm k x-ray 0.79881 1.08142 0.04175 0.0839 0.268

(3/2-)

(1-)

7/2+

(3/2-)

γ-Energy / Intensity (MeV/%) 0.1874 0.755 0.840 0.946 0.1445 0.1876 0.2176 0.9815 0.9215/ Cm L x-ray Cm k x-ray 0.25299 0.3809 0.3851

2.0

Cm L x-ray Cf L x-ray Cm k x-ray Cf k x-ray 0.5507 0.327/10-5 0.308/10-6 Cf L x-ray Cf k x-ray 0.98912 1.03184 (0.04–1.6) 0.02481 0.1528 0.1776

237 238

239 240

241

242

243

244

487_S11.indb 195

α, sf/10 sf/~ 100 α/~ 0.2 α α/7.719 sf/ ~ 2.1 EC/3.3 α/7.60 α/7.509 sf/<0.014 EC/86 /2.2 α/14 /7.40 α/7.328

7.590(10)/

7.335(5)/ 7.351(6)/20 7.385(4)/80 7.060(6)/20 7.170/4 7.168(5)/25

0+ (1/2+) 0+

4/17/06 11:01:44 AM

Table of the Isotopes

11-196 Elem. or Isot. Cf

245.068049

44. m

α/36 /7.255 EC/64 /1.569

246.068805

1.49 d

α/6.869

1.8 × 103 y

sf/2.3 × 10-4

Particle Energy/ Intensity (MeV/%) 7.210(5)/75 7.14/91.7 6.983/0.31 7.09/7 7.065/0.68 6.6156(10)/0.18 6.7086(7)/21.8 6.7501(7)/78.0

6.301(5)/

245

246

Natural Abundance (Atom %)

Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

247.07100

3.11 h

EC/99.96 /0.65 α/0.04 /6.55

248.07219

249.074854

334. d 3.2 × 104 y 351. y

α/6.369 sf/0.0029 α/6.295

8. × 1010 y

sf/4.4 × 10-7

13.1 y 1.7 × 104 y

α/6.129 sf/0.077

26.3 μs 9.0 × 102 y

α/6.172

247

248

249

250.076406

Cf Cf

251.079587

252.081626

2.65 y 86. y

α/96.9 /6.217 sf/3.1/

253.08513

17.8 d

254.08732

60.5 d

β- /99.7 /0.29 α/0.3 /6.126 sf/99.7/ α/0.3/5.930

Cf Cf

255.0911 256.0934

1.4 h 12. m

β- /0.7 sf

Es Es 243 Es

241.0685 242.0698 243.0696

~8s 16 s 21. s

244.0709

37. s

245.0713

1.3 m

246.0729

7.7 m

247.07366

4.8 m

α α α/>30 / EC/<70 /4.0 EC/76 /4.6 α/4 / α/40 /7.858 EC/60 /3.1 EC/90 /3.9 α/10 / EC/93 /2.48 α/7 /

250

251m 251

252

253

254

255 256

6.220(5)/17 6.262(5)/83 5.758/3.7 5.812/85.7 5.8488(2)/1.0 5.9029(2)/2.8 5.9451(2)/4.0 6.1401(2)/1.1 6.1940(2)/2.2 5.8913(4)/0.3 5.9889(4)/15 6.0310(4)/84.5 5.56448(7)/1.5 5.632(1)/4.5 5.648(1)/3.5 5.6773(6)/35 5.762(3)/3.8 5.7937(7)/2.0 5.8124(8)/4.2 5.8514(6)/27 6.0140(7)/11.6 6.0744(7)/2.7 5.7977(1)/0.23 6.0756(4)/15.2 6.1184(4)/81.6 0.27/100 5.921(5)/0.02 5.792(5)/0.05 5.834(5)/0.26

Spin (h/2 π)

7/2+

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%) Cm K x-ray 0.5709 0.6014 0.6163 Cm L x-ray 0.04221 0.0945 0.147 Bk k x-ray 0.2941 0.4778

9/2-

Cm L x-ray Cm k x-ray 0.25299/2.5 0.33351/13.6 0.38832/63.6 (0.0376–1.103)

Cm L x-ray 0.04285

1/2+

0.109/19.8 0.1775/17.3 (0.0385-0.354)

Cm L x-ray 0.04339 0.1002

(7/2+) 0+

241 242

244

245

246

247

487_S11.indb 196

8.11 7.92 7.89/>30

7.57/4 7.74

7.35 7.32

4/17/06 11:01:46 AM

Table of the Isotopes Elem. or Isot. Es

248

249

Natural Abundance (Atom %)

11-197 Atomic Mass or Weight

248.0755 249.07641

250m

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 26. m EC/99.7 /3.1 α/0.3 / 1.70 h EC/99.4 /1.45 α/0.6 / 2.2 h EC/ β+

250.0786

8.6 h

EC/2.1

251.07999

1.38 d

EC/99.5 /0.38 α/0.5 /

252.08298

1.29 y

253.084825

20.47 d 6.3 × 105 y

α/76 / EC/24 /1.26 α/ sf/8.9 × 10-6

250

251

252

253

1.64 d

6.87 6.77

Spin (h/2 π)

(6+)

6.462/0.05 6.492/0.4 6.632/61.0 6.562/10.3 6.633/89.8 6.5916/6.6

(3/2-)

(5-) 7/2+

+4.10

2.9

3.7

2+ 2+

6.429

(7+)

2.6 × 103 y 7.6 h

α/ sf/< 3 × 10-6 β- /92 /0.29 α/8 / sf/0.0042 β- /

256.0936 257.0960

25. m 7.7 d

β-/1.7 β-

Fm Fm

242.0734 243.0744

0.8 ms 0.2 s

Fm Fm

244.0741 245.0754

3.3 ms 4. s

246.07530

1.2 s

Fm Fm

247.0769

4.3 s 29. s

248.07720

33. s

249.0790

1.6 m

sf/> 96 α/ sf/< 0.4 sf/> 97 α/ sf/<0.1 α/85/ sf/15/ α/ α/8.20 EC/2.9 α/99.9 /8.001 sf/0.1/ EC/2.4 α/ IT/ sf/<8 × 10-5 α/ EC/0.8 sf/0.007 EC/98 /1.47 α/2 /

254.088022

255.09027

254

256m

Es Es

256 257

276. d > 2.5 × 107 y 40. d

6.26 6.300

γ-Energy / Intensity (MeV/%)

0.3795 0.8132 Cf L x-ray Cf k x-ray 0.9891 1.0319 Cf L x-ray Cf k x-ray 0.30339 0.34948 0.82883

(1-)

0.475 6.382

> 10. y

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

(7/2+)

β- /99.6 / α/0.3 /6.67 sf/0.045

254m

255

Particle Energy/ Intensity (MeV/%)

0.04180/5.6 0.3892/2.7 (0.0309-1.106) Fm L x-ray Fm k x-ray 0.6488 0.6938 0.064

(7/2+)

(8+)

(1+)

0.218 0.232 0.862

100 242 243

244 245

246

247m 247

248

249

1.8 s

250m

250

250.07952

30. m

251.08158

5.3 h

251

487_S11.indb 197

8.55

8.15/ 8.24/ 8.17/ 7.87/70 7.93/30 7.83/20 7.87/80 7.57

7.43/

6.833

0+ (7/2+)

(9/2-)

4/17/06 11:01:47 AM

Table of the Isotopes

11-198 Elem. or Isot.

253.085185

254.086854

255.089962

256.09177

257

257.09511

Fm Fm 260 Fm

258.0971 259.1006 260.103

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 1.058 d α/7.154 sf/0.0023 3.0 d EC/88/0.333 α/12 / 3.240 h α/ sf/0.059 20.1 h α/ sf/2.3 × 10-5 1.0 × 104 y 2.63 h sf/91 α/19 100.5 d α/99.79 sf/0.21 0.37 ms sf/ 1.5 s sf/ ~ 4 ms sf/

Md Md 246 Md

245.0808 246.0819

~ 0.4 s 0.9 ms 1.0 s

α sf α

Md Md 248 Md

247.0816 248.0828

~ 0.2 s 3. s 7. s

249.0830

24. s

250.0844

50. s

251.0848

4.0 m

252

252.0866

2. m

Md 254m Md 254 Md 255 Md

253.0873 254.0897 255.09108

~6m 30. m 10. m 27. m

sf/ α EC/80 /5.3 α/20 / sf/<0.05 EC>/<80 /3.7 α/>20 /8.46 EC/94 /4.6 α/6 /8.25 EC/>94 /3.1 α/<6 / EC/>50 /3.9 α/<50 / EC/2.0 EC/ EC/2.7 EC/92 /1.04 α/8 / sf/< 0.15

256.0941

1.30 h

EC/89 /2.13 α/11 / sf/< 2.6

257.095541

5.5 h

252

253

254

255

256

258 259

Natural Abundance (Atom %)

Atomic Mass or Weight 252.08247

Particle Energy/ Intensity (MeV/%) 6.998/15 7.039/85 6.676/ 6.943/ 7.150 7.192 6.9635(5)/5.0 7.0225(5)/93.4

8.64, 8.68

6.92/ 6.519

Spin (h/2 π) 0+ ½+ 0+ 7/2+ 0+ (9/2+) 0+

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

Es k x-ray 0.2719

0.08148/1. (0.041-0.900)

0.1794 0.2410

101

245m 245

247m 247

249

250

251

253

256

258.098431

51.5 d

259.1005

1.64 h

260.1037

~ 27.8 d

EC/85 /0.41 α/15, sf/< 1 EC/ sf/< 30 α/7.40 sf/< 0.003 sf/>98.7 α/<1.3 sf/ 73–100

248.0866

< 1.0 μs

257

57. m

258m

258

259

260

8.74 8.50–8.56 8.43 8.32/15 8.36/5

8.030(20)/ 7.75/4 7.83/2 7.55/ 7.73/

α/7.33/93 7.27/5 7.75/1 7.71/1 7.21/71 7.14/22 7.68/2.5 7.25/2.5 7.64/2.1

(7/2-)

7.074 7.014

(7/2-)

6.718(2)/ 6.763(4)/

(1-) (8-) 7/2+

0.121/100 0.115/65 0.136/35 0.141–0.453 Fm k x-ray 0.121/409 0.115/266 0.136/143 0.634/119 0.141–1.37 Fm k x-ray (0.181–0.389) Fm k x-ray 0.3678 0.057–0.448

102

248

487_S11.indb 198

4/17/06 11:01:49 AM

Table of the Isotopes Elem. or Isot. No

249

Natural Abundance (Atom %)

11-199 Atomic Mass or Weight

249.0878

250.0875

No No

251.0890

252.08898

253.0907

250

251m 251

252

253

254m

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 0.05 ms sf α/ < 20 6. μs sf/ α/ < 10 0.9 s α 0.78 s α/91 sf/0.26 2.44 s α/75/8.551 sf/24/ EC, β+/<1.6 1.7 m α/ EC/3.2 0.28 s I.T./ sf/< .2 49. s α/ EC/1.1 sf/0.17 3.1 m α/62 / EC/38/2.01

254.09096

255.09324

256.09428

2.9 s

257.09688

24.5 s

No No

258.0982 259.1010

~ 1.2 ms 58. m

No No

260.1026 262.1073

0.11 s ~ 8. ms

251.0944 252.0954

39 m ~ 0.36 s

254

255

256

257

258 259

260 262

α/ sf/0.5 α/ sf/<1.5 sf/ α/78 /7.794 EC/22/0.5 sf/<9.7 sf/ sf/

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

0+ 8.67 8.62/96 8.58/4 8.42 8.37

8.00

(9/2-)

0.222/100 (0.151-0.280)

8.09

0.102 0.152

8.12/ 7.93 8.08 8.43

½+

0.187

8.222/83 8.27 8.323/17

(7/2+)

7.52 7.55

0+ (9/2+)

0.0770 0.1018 0.1241

0+ 0+

103

Lr Lr

251 252

~ 0.57 s

253m

253.0952

1.5 s

254.0965

13. s

255.09669

22. s

256.0986

27. s

257.0996

0.65 s

258.1018

3.9 s

259.1029

6.1 s

260.1055

3. m

253

254

255

256

257

258

259

260

487_S11.indb 199

sf α sf/<1 α sf/1.3 α/ sf/8 α/ EC/5.2 sf/<0.1 α/ EC/3.2 sf/< 0.1 α/99.7 /8.554 EC/4.2 sf/< 0.03 α/ EC/2.5 sf/< 0.03 α/ EC/3.4 sf/< 5 α/80 sf/20 α/

9.02/73 8.97/27 8.79 8.72 8.45

8.37/60 8.43/40 8.43/ 8.39 8.80

7/2+

8.60/46 8.62/25 8.56/20 8.65/9 8.44(1) 8.03

4/17/06 11:01:50 AM

Table of the Isotopes

11-200 Elem. or Isot. Lr Lr

261 262

Natural Abundance (Atom %)

Atomic Mass or Weight 261.1069 262.1096

Half-life/ Decay Mode/ Resonance Energy (/MeV) Width (MeV) 40. m sf 3.6 h EC/2. sf/<10

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

104

253.1007

~ 48. μs

254.1002

23. μs

255.1013

1.6 s

256.10117

6.2 ms

257.1030

4.7 s

258.1035

12. ms

259

259.1056

3.4 s

Rf Rf 261 Rf 262 Rf 263 Rf 265 Rf 267 Rf

260.1064 261.10877 262.1099 263.1126 265.1167 267.122

20. ms 1.3 m 5. s 2.1 s 10. m ~ 13 h ~ 0.1 d

255.1074

~ 1.5 s

256.1081

1.6 s

253

254

255

256

257

258

260

261m

sf α/<10 sf/>98.5 α/<1.5 α sf/52

sf/99.68 α/0.32 α/9.22 EC/11 sf/<1.4 sf/87 α/13 α/9.09/93 sf/7 sf/ α α/60, sf/40 sf/>99.2 sf, α α sf

0+ 8.72/<0.05 8.77/94 8.67/<0.05 8.58/<0.05 8.92/<0.05 8.81 8.77 9.01 8.95 8.62

8.77(2)/ 8.86/ 8.28 8.52/

0.203 0.142

0+ 0.117

105 255

256

0.8 s

257m

257.1077

1.5 s

258.1092

4.2 s

259.1096

~ 0.51 s

Db 260 Db

260.1113

0.3 m 1.5 s

261.1121

1.8 s

262.1141

0.5 m

257

258

259

260m

261

262

487_S11.indb 200

α, sf/~ 20 α/64 EC/35 sf/0.05 α sf/<13 α/ sf/<6

α/ EC/5.3 sf/<33 sf/ α/ α/ sf/<9.6 α/ sf/<18 sf/<33

9.02/67 8.89/11 9.08/11 9.12/11 9.16 8.97/33 9.07/38 9.12/5.5 8.94/9 9.02/9 8.89/5.5 9.30/ 9.17/ 9.08/ 9.47/ 9.05/ 9.08/ 9.13/ 8.93/

4/17/06 11:01:51 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-201 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV) α/

263.1150

~ 0.45 m

Db Db

267.1224 268.125

1.2 h 1.2 d

258.1132

~ 2.9 ms

259.1145

0.5 s

260.11442

4. ms

α/50 sf/50

Sg Sg

261.1161 262.1164

0.3 s 0.007 s

Sg Sg

263.1183

0.3 s 0.8 s

265.1211

8. s

α, sf/<10 sf α/<22 α α sf/<30 α/>65 sf/<35

266.1221

~ 21. s

271.133

~ 0.04 h

260.122 261.1217

12. ms

263

267 268

sf/57 α/41 EC/3 sf sf, EC

Particle Energy/ Intensity (MeV/%) 8.45/ 8.53/ 8.67/ 8.36/ 8.41/

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

106 258

259

260

261 262

263m 263

265

266

271

sf α/<20 α/ sf/<20

α/ sf/<82 α/50 sf/50

0+ 9.62 9.35 9.03 9.76 9.72 9.81 9.56

9.2 9.06 9.25 8.84/46 8.76/23 8.94/23 8.69/8 8.77/66 8.52/33 8.53

107

Bh Bh

260 261

8. ms

262m

α α/, sf <10

α/ sf/<12 α/ sf/<12

262.1229

0.10 s

264

264.1246

1.0 s

Bh Bh 267 Bh

265.1252 266.1269 267.1277

0.9 s ~2s ~ 17 s

α/ sf/ α α α

~ 0.08 ms ~ 0.75 ms

α/ α/, sf/~ 50 α

262

265 266

10.40 10.10 10.03 10.37 10.24 10.06 9.91 9.74 9.3 – 9.8 9.24 9.08 8.83

108

Hs Hs 265m Hs

263.1286 264.12839

265.1301

263 264

265

487_S11.indb 201

2.0 ms

α/ sf/<1

11.0 10.57/63 10.73 10.52 10.34 10.30/90 10.43 10.37

4/17/06 11:01:53 AM

Table of the Isotopes

11-202 Elem. or Isot.

Natural Abundance (Atom %)

Atomic Mass or Weight

Hs Hs 267 Hs

266.1301

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%) 10.25 10.2

267.1318

~ 2.3 ms ~ 0.8 s 0.05 s

269

269.1341

~ 14 s

Hs Hs 277 Hs

270.1347 275.146 277.150

~ 3.6 s ~ 0.15 s ~ 11 m

α α sf

266.1373 267.137 268.1387 270.141 275.149 276.151

~ 1.2 ms ~ 0.7 ms 19 ms ~ 0.03 s 5 ms 0.01 s ~ 0.7 s

α α α α/>68 α α α

10.46–10.81 10.48–11.31

11.6 11.11 10.95 11.15 12.15 11.03 9.9 10.8 11.8 9.73

266

267m

270 275

α/>88

9.88 9.83 9.75 9.23 9.18 9.16 9.3

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

109

Mt Mt 267 Mt 268 Mt 270 Mt 275 Mt 276 Mt 266m 266

10.3 - 10.8 10.0 10.3 9.7

110

Ds Ds 270m Ds

267.1443 269.1451

~ 3 μs 0.17 ms ~ 6 ms

α/>32 α/>75 α

Ds Ds 271 Ds 273m Ds 273 Ds 279 Ds

270.1447

0.1 ms 0.07 s 1.6 ms 0.076 ms 118 ms 0.18 s

Ds 281 Ds 282 Ds

280.160 281.162

~ 7.6 s 10. s 0.5 ms

α α α α α/ sf/90 α/10 sf/ sf sf

272.1536 274.156 279.162 280.164

~ 2 ms ~ 65 ms ~ 0.17 s ~ 3.6 s

α/>68 α α α

10.82 11.2 10.4 ~ 9.75

112

277.1639

~ 0.24 ms

283

112

283.172

~ 4. s

112 285 112

284.172 285.174

0.10 s ~ 34. s

sf/< 10 α/~ 100 sf α

11.45 11.65

283.176 284.178

0.24 ms ~ 0.1 s ~ 0.5 s

α α α

267 269

270

271m

280

271.1461 273.1489 279.159

9.7

111

Rg Rg 279 Rg 280 Rg 272 274

112

112 277

284

9.5 9.16

113

113 113 284 113 278 283

487_S11.indb 202

11.7 10.1 10.0

4/17/06 11:01:54 AM

Table of the Isotopes Elem. or Isot.

Natural Abundance (Atom %)

11-203 Atomic Mass or Weight

Half-life/ Resonance Width (MeV)

Decay Mode/ Energy (/MeV)

Particle Energy/ Intensity (MeV/%)

Spin (h/2 π)

Nuclear Elect. Magnetic Quadr. Mom. (nm) Mom. (b)

γ-Energy / Intensity (MeV/%)

114

114 286

114

286.184

0.16 s

114 114 289 114

287.186 288.186 289.187

287 288

10.2

0.5 s 0.8 s ~ 2.7 s

α/40 sf/60 α α α

287.191 288.192

~ 0.03 s ~ 0.09 s

α α

10.6 10.5

290.199 291.200 292.200

~ 15 ms ~ 6. ms ~ 18. ms ~ 0.05 s

α α α α

10.9 ~ 10.74 ~ 10.66 10.5

~ 2.0 ms

11.7

10.0 9.95 9.82

115

115 115

287 288

116

116 116 292 116 293 116 290 291

118

294

487_S11.indb 203

4/17/06 11:01:55 AM

NEUTRON SCATTERING AND ABSORPTION PROPERTIES Norman E. Holden This table presents an evaluated set of values for experimental quantities that characterize the properties for scattering and absorption of neutrons. The neutron cross section is given for room temperature neutrons, 20.43°C, corresponding to a thermal neutron energy of 0.0253 electron volts (eV) or a neutron velocity of 2200 meters/second. The neutron resonance integral is defined over the energy range from 0.5 eV to 0.1×106 eV, or 0.1 MeV.

Bound neutron scattering lengths and neutron cross sections averaged over a Maxwellian spectrum at 30 keV for astrophysical applications are also presented. A list of the major references used is given below. The literature cutoff date is January 2003. Uncertainties are given in parentheses. Parentheses with two or more numbers indicate values to the excited state(s) and to the ground state of the product nucleus.

Table Layout Column Number Column Title 1 Isotope/Element 2 3

Isotopic Abundance Half-life

Thermal Neutron Cross Sections

Neutron Resonance Integrals

Neutron Scattering Lengths

Maxwellian Averaged Cross Section

Description For elements, atomic number and chemical symbol are listed. For nuclides, mass number and chemical symbol are listed. Isomers are indicated by the addition of m, m1, or m2. in atom percent Half-life in decimal notation. µs = microsecond; ms = millisecond; s = second; m = minute; h = hour; d = day; y = year. Cross sections for neutron capture reactions in units of barns (10-24 cm2) or millibarns (mb). Proton, alpha production and fission reactions are designated by σp, σα, σf , respectively. Separate values are listed for isomeric production. Resonance integrals for neutron capture reactions in barns (10 -24 cm2) or millibarns (mb). Proton, alpha production and fission reactions are designated by R.I.p, R.I.α, R.I.f, respectively. Separate values are listed for isomeric production. Bound coherent scattering lengths for neutron scattering reactions in units of femtometers (fm), which is equal to fermis (10-13 cm). Astrophysical Cross Sections, averaged over a stellar neutron maxwellian spectrum characterized by a thermal energy of 30 keV, expressed in barns (10-24 cm2), millibarns (mb) or microbarns (µb).

General Nuclear Data References The following references represent the major sources of the nuclear data presented: Mughabghab, S.F., Divadeenam, M., Holden, N.E.; Neutron Cross Sections, Vol. 1 Neutron Resonance Parameters and Thermal Cross Sections, Part A, Z = 1-60. Academic Press Inc., New York, New York (1981); Mughabghab, S.F.; Part B, Z = 61-100. Academic Press Inc., Orlando, Florida (1984). Holden, N.E.; Fifty Years with Nuclear Fission Conference, Wash., D.C., Gaithersburg, Md. April 26-29, 1989, p. 946. American Nuclear Society, LaGrange Park, Illinois (1989).

Elem. or Isot. 1H 1H 2H 3H 2He 3He 4

He Li Li

3 6

Natural Abundance (%) 99.9885(70) 0.0115(70)

Half-Life >2.8×1023 y 12.33 y

0.000134(3)

Tuli, J.K.; Nuclear Wallet Cards , Brookhaven National Laboratory (Jan. 2000). Holden, N.E.; Half-lives of Selected Nuclides , Pure & Applied Chemistry 62, 941 (1990). Holden, N.E., Hoffman, D.C.; Spontaneous Fission Half-lives for Ground State Nuclides, Pure & Applied Chemistry 72, 1525 (2000). Koester, L., Rauch, H., Seymann, E.; Neutron Scattering Lengths: A Survey of Experimental Data and Methods, Atomic Data Nuclear Data Tables 49, 65 (1991). Sears, V.F.; Neutron Scattering Lengths and Cross Sections, Neutron News 3, (3), 26 (1992). Bao, Z.Y., Beer, H., Käppeler, F., Voss, F., Wisshak, K., Raucher,T.; Neutron Cross Sections for Nucleo-synthesis Studies, Atomic Data Nuclear Data Tables 76, 70 (2000).

Thermal Neut. Cross-Section (barns) 0.332(2) 0.332(2) 0.51(1)mb < 6. µb < 0.05 σp = 5.33(1)×103 0.05(1) mb

Resonance Integral (barns) 0.149(1) 0.149(1) 0.23(2) mb

71.(2) σt = 9.4(1)×102

32.(1) RIt = 422.(4)

RIp = 2.39(1)×103

99.999867(3) 7.59(4)

Coh. Scat. σ (30 keV) Maxw. Length (fm) Avg. (barns) -3.739(1) - 3.741(1) 0.25(2) mb* 6.671(4) 2.1(4) µb 4.79(3) 3.26(3) 5.74(7) 8.(1) µb* 3.26(3) - 1.90(2) 2.0(1) σt ≈ 1.

*Extrapolated value.

11-185

11-186 Elem. or Isot. 7

Neutron Scattering and Absorption Properties Natural Abundance (%)

Li Li 4Be 7Be

92.41(4)

Be Be 5B 10B

100.

80.1(7)

53.28 d

1.52¥106 y 19.9(7)

98.93(8) 1.07(8) 5715. y 99.636(20)

N O 8 16O 17O

0.364(20)

0.205(14)

O 9F 19F 10Ne 20Ne 21Ne 22

99.757(16) 0.038(1)

100. 90.48(3) 0.27(1)

Ne 11Na 22Na

9.25(3)

100.

Na Mg 12 24Mg 25Mg 26Mg 27Mg 13Al 26Al 27

Al Si Si 29Si 30Si 31Si 32Si 15P 31P 16S 32S 14 28

Thermal Neut. Cross-Section (barns) 39.(5) mb 45.(5) mb

Resonance Integral (barns) 17.(2) mb 20.(2) mb

Coh. Scat. Length (fm)

8.8(4) mb sp = 3.9(1)¥104 sa ≈ 0.1 8.8(4) mb <1. mb 7.6(1)¥102 sa = 38.4(1)¥102 0.3(1) sp = 7.(1) mb st = 8.(2) mb 5.(3) mb 3.5(1) mb 3.5(1) mb 1.4(1) mb <1.4 mb 2.00(6) sp = 1.93(5) 0.080(1) 0.04(1) mb 0.29(1) mb 0.19(1) mb sa = 0.257(10) 0.54(7) mb 0.16(1) mb 9.5(1) mb 9.5(1) mb 42.(5) mb 39.(5) mb 0.7(1) sa = 0.18(9) mb 51.(5) mb 0.53(2) sp = 2.8(3)¥104 sa = 2.6(4)¥102 sm = 0.43(3) 66.(6) mb 0.053(6) 0.20(1) 0.038(1) 0.07(2) 0.230(2) sp = 1.97(10) sa = 0.34(1) 0.230(2) 0.166(9) 0.17(1) 0.12(1) 0.107(3) 73.(6) mb < 0.5 0.17(1) 0.17(1) 0.54(2) 0.55(5) sa < 0.5 mb

3.9(2) mb RIp = 1.75(5)¥104

7.79(1)

3.9(2) mb

7.79(1)

3.4(1)¥102 RIa = 17.3(1)¥102 0.13(4)

5.30(4) - 0.1(3)

2.(1) mb 1.6(1) mb 1.6(1) mb 1.7(2) mb

6.65(4) 6.646(1) 6.651(2) 6.19(9)

0.90(3) RIp = 0.87(3) 0.034(1) 0.11(3) mb 0.40(4) mb 0.36(4) mb 0.11(1) 0.39(5) mb 0.81(4) mb 21.(3) mb 21.(3) mb 19.(3) mb 18.(3) mb 0.31(5)

9.36(2) 9.37(2)

- 2.22(2)

0.84 s

B C 6 12C 13C 14C 7N 14N

Half-Life

2.605 y

78.99(4) 10.00(1) 11.01(3) 9.45 m 7.1¥105 y 100. 92.223(19) 4.685(8) 3.092(11) 2.62 h 1.6¥102 y 100. 94.93(31)

*Extrapolated value.

23.(3) mb 0.32(2) RIp< 2.¥105 RIa = 1.2(2) x 102 RIm = 0.30(6) 38.(5) mb 32.(4) mb 98.(15) mb 25.(2) mb 0.03(1) 0.17(1)

s (30 keV) Maxw. Avg. (barns) 0.06(1) mb* 42.(3) mb < ≈ 5.5 mb sp = 16(4)*

6.44(3) 5.805(4) 5.805(5) 5.8(2) 5.84(7) 5.65(1) 5.65(1) 4.566(6) 4.631(6) 6.7(2)

16.(1) mb* 0.021(4) mb 3.(1) mb* sp = 1.8(2) mb* 0.04(1) mb 6.(1) mb* 34.(4) mb sa = 3.9(5) mb* 9.(1) mb* 6.(1) mb 6.(1) mb 0.12(1) mb ≈ 1.5 mb

3.87(1) 3.63(2)

58.(4) mb* 2.1(2) mb

3.63(2) 5.375(4) 5.7(2) 3.6(2) 4.9(2)

2.1(2) mb 3.3(4) mb 6.4(4) mb 0.13(1) mb*

3.45(1) 0.14(2)

0.17(1) 0.12(2) 0.11(2) 0.08(2) 0.62(6) 33.(3) mb

3.45(1) 4.15(1) 4.11(1) 4.7(1) 4.61(1)

0.08(1) 0.08(1) 0.24(2) 0.25(2)

5.13(1) 5.13(1) 2.847(1) 2.804(2)

2.9(3) mb 2.9(3) mb 7.9(9) mb 3.2(3) mb*

1.7(1) mb 4.1(2) mb

Neutron Scattering and Absorption Properties Elem. or Isot. 33S

S S 17Cl 35Cl 36

Cl 18Ar 36Ar

Ar Ar

Ar Ar 19K 39K

75.78(4)

3.01¥105 y

24.22(4) 0.3365(30)

35.0 d 0.0632(5) 268. y 99.6003(30)

20 40

1.82 h 93.2581(44)

0.0117(1)

K Ca Ca

6.7302(44)

Ca Ca 44Ca 45Ca 46Ca 48Ca 21Sc 45Sc 46Sc 22Ti 44Ti 43

Ti Ti 48Ti 49Ti 50Ti 23V 50V 47

1.26¥109 y

96.941(156) 1.02¥105 y

Half-Life

4.29(28) 0.02(1)

Natural Abundance (%) 0.76(2)

0.647(23) 0.135(10) 2.086(110) 0.004(3) 0.187(21)

162.7 d >4¥1015 y 4.3¥1019 y

100. 83.81 d 60 y 8.25(3) 7.44(2) 73.72(3) 5.41(2) 5.18(2) 0.250(4)

*Extrapolated value.

1.4¥1017 y

Thermal Neut. Cross-Section (barns) 0.46(3) sa = 0.12(1) sp = 2. mb 0.25(1) 0.24(2) 33.6(3) 43.7(4) sp = 0.44(1) sa≈ 0.08 mb sp = 46.(2) mb <10. sa = 0.59(7) mb (0.05 + 0.38) 0.66(3) 5.(1) sa = 5.4(3) mb sp < 1.5 mb sa = 1.08(8)¥103 sp = 37.(4) 0.8(2) 6.(2)¥102 sa <0.29 0.64(3) 0.5(1) 2.1(1) 2.1(2) sa = 4.3(5) mb sp < 0.05 mb 30.(8) sp = 4.4(4) sa = 0.42(8) 1.46(3) 0.43(2) 0.41(3) sa = 0.13(4) mb ≈ 4. sa = 0.18(3) s p = 7.(2) mb 0.65(10) 6.(1) 0.8(2) ≈ 15. 0.70(3) 1.0(1) 27.2(2) (10.+17.) 8.(1) 6.1(1) 1.1(2) sp<0.2 0.6(2) 1.6(2) 7.9(9) 1.9(5) 0.179(3) 5.0(2) 21.(4) sp = 0.7(4) mb

11-187 Resonance Integral (barns) 0.21(2) RIa = 0.05(1) 0.13 0.26(3) 15.(2) 20.(2) RIp = 0.2

Coh. Scat. s (30 keV) Maxw. Length (fm) Avg. (barns) 4.7(2) 7.4(15) mb sa = 0.18(1) 3.48(3) 9.58(1) 11.7(1)

RIa = 900. RIp = 31. 0.4(1)

0.41(5) 0.2(1) 1.0(1) 0.9(1)

9.4(3) mb sp = 1.7(2) mb* sp = 91.(8) mb

RIp = 0.02

(0.04+0.26) 0.42(5) 2.(1)

0.23(1) mb 0.17(1) mb*

3.1(1) 1.91(1) 24.9(1)

sa = 0.9(2) mb 2.0(2) mb

sa ≈ 1.3 sp ≈ 0.04 3.5(35)

1.83(1)

2.5(3) mb

3.67(2) 3.74(2)

11.8(4) mb

sp = 7.(1) mb sa = 40.(6) mb

13.(4) 2.0(2) 1.4(2) 0.23(2) 0.22(4)

2.69(8) 4.70(2) 4.80(2)

22.(1) mb 6.7(7) mb

0.39(4) 3.9(2) 0.56(1)

3.4(1) - 1.56(9) 1.42(6)

16.(2) mb 51.(6) mb 9.(1) mb

0.9(1) 0.5(1) 12.(1) (5.6+6.4) 3.6(5) 2.8(2)

3.6(2) 0.39(9) 12.3(1) 12.3(1)

5.3(5) mb* 0.8(1) mb*

- 3.438(2)

0.4(1) 1.6(2) 3.6(2) 1.2(2) 0.12(2) 2.8(1) 50.(20)

4.93(6) 3.63(1) - 6.09(2) 1.04(5) 6.18(8) - 0.382(1) 7.6(6)

69.(5) mb

27.(3) mb 64.(8) mb 32.(5) mb 22.(2) mb 3.6(4) mb

11-188 Elem. or Isot. 51V 24Cr 50Cr 51Cr 52Cr 53Cr 54Cr 25Mn 53Mn 54Mn 55Mn 26Fe 54Fe 55

Natural Abundance (%) 99.750(4) 4.345(13)

Fe Fe 58Fe 59Fe 27Co 58mCo 58Co 59Co 60mCo 60Co 28Ni 58Ni 57

Ni Ni

Ni Ni 64Ni 65Ni 29Cu 63Cu 64Cu 65Cu 66Cu 30Zn 64Zn

Half-Life

>1.8¥1017 y 27.70 d

83.789(18) 9.501(17) 2.365(7) 3.7¥106 y 312.1 d 100. 5.845(35)

Neutron Scattering and Absorption Properties

2.73 y 91.754(36) 2.119(10) 0.282(4) 44.51 d 9.1 h 70.88 d 100. 10.47 m 5.271 y 68.0769(89)

>4¥1019 y ≈ 7.6¥104 y

26.2231(77) 1.1399(6) 3.6345(17)

100. y 0.9256(9) 2.517 h 69.15(15) 12.701 h 30.85(15) 5.09 m 48.27(32)

27.977(77)

4.102(21)

19.02(12)

Zn Ga

0.631(9)

>2.3¥1018 y

243.8 d

*Extrapolated value.

Thermal Neut. Cross-Section (barns) 4.9(1) 3.0(2) 15.(1) < 10. 0.8(1) 18.(2) 0.36(4) 13.3(1) 70.(10) < 10. 13.3(1) 2.7(1) 2.3(2) sa = 10. mb 13.(2) sa = 0.01 2.8(3) 1.4(2) 1.3(1) 13.(3) 37.19(8) 1.4(1)¥105 1.9(2)¥103 (20.7+16.5) 58.(3) 2.0(2) 4.5(2) 4.6(4) sa < 0.03 mb sabs = 92.(4) sa = 14.(2) sp = 2.(1) 2.9(3) 2.5(5) sa = 0.03 mb 15.(1) 20.(5) 1.6(1) 22.(2) 3.8(1) 4.5(2) ≈ 270. 2.17(3) 1.4(1)¥102 1.1(2) 0.74(5) sp < 12. mb sa = 11.(3) mb 66.(8) sa = 2.0(2) 0.9(3) sa < 0.02 mb 6.9(1.4) sa = 0.4 mb (0.072 + 0.8) sa <0.02 mb (8.1+83.) mb 2.9(1)

Resonance Integral (barns) 2.7(2) 1.7(1) 8.(1)

Coh. Scat. s (30 keV) Maxw. Length (fm) Avg. (barns) - 0.402(2) 38.(4) mb 3.635(7) - 4.5(1) 0.05(1)

0.6(2) 9.(1) 0.25(5) 14.0(3) 32.(5)

4.91(2) - 4.2(1) 4.6(1) - 3.75(2)

8.8(4) mb 0.06(1) 7.(2) mb

14.0(3) 1.4(2) 1.3(2) RIa = 1.1(1) mb 6.(1)

- 3.75(2) 9.45(2) 4.2(1)

40.(3) mb

1.4(2) 0.8(4) 1.3(2) 6.(1) 74.(2) 2.5(10)¥105 7.(1)¥103 (39.+35.) 230.(50) 4.3(10) 2.3(2) 2.3(2)

9.93(3) 2.3(1) 15.(7)

11.7(5) mb 40.(4) mb 12.(1) mb

29.(2) mb

2.49(2)

10.3(1) 14.4(1)

38.(4) mb

41.(2) mb

RIabs = 1.4(1)¥102

1.5(2) 1.5(4)

2.8(1) 7.60(6)

25.(1) mb 82.(8) mb

6.8(3) 9.(2) 1.2(2) 10.(1) 4.1(4) 5.(1)

- 8.7(2)

13.(4) mb

- 0.37(7)

9.(1) mb

2.2(1) 60.(20) 2.8(4) 1.4(3)

10.61(19)

41.(5) mb

5.680(5) 5.23(4)

59.(5) mb

1.8(2)

5.98(5)

35.(3) mb

25.(5)

7.58(8)

0.15(2)

(0.2 + 2.9)

6.04(3)

0.9(2) 22.(3)

19.(2) mb sm = 3.(1) mb 0.02(1)

7.288(2)

7.718(4) 6.43(15)

0.09(1)

30.(4)

Neutron Scattering and Absorption Properties Elem. or Isot. 69Ga 71Ga Ge Ge 70Ge 72Ge 73Ge 74Ge 76Ge 33As 75As 34Se 74Se 75Se 76Se 77Se

Natural Abundance (%) 60.108(9) 39.892(9)

32 68

Se Se 82Se 35Br 76Br 79Br 80

Br Kr 36 78Kr 80Kr 82Kr 83Kr 84Kr Kr Kr 37Rb 84Rb 85Rb 86Rb 87Rb 88Rb 38Sr 84Sr 86Sr 87Sr 88Sr 89Sr 90Sr 39Y 89Y 90Y 91Y 40Zr 90

Zr Zr 92Zr 93Zr 91

>2.4¥1026 y

270.8 d 20.370(89) 27.380(60) 7.759(78) 36.656(80) 7.835(81)

>1.8¥1023 y 1.6¥1021 y

100. 0.89(4) 119.78 d 9.37(29) 7.63(16) 23.77(28) 49.61(41) 8.73(22)

≈ 1¥1020 y 16.0 h

50.69(7) 49.31(7) 0.353(3) 2.286(10) 11.593(3) 11.500(19) 56.987(15)

85 86

Half-Life

>2.3¥1020 y

10.73 y 17.279(41) 32.9 d 72.17(2) 27.83(2)

18.65 d 4.88¥1010 y 17.7 m

0.56(1) 9.86(1) 7.00(1) 82.58(1) 50.52 d 29.1 y 100. 2.67 d 58.5 d

51.45(40) 11.22(5) 17.15(8)

*Extrapolated value.

1.5¥106 y

Thermal Neut. Cross-Section (barns) 1.68(7) 4.7(2) sm = 0.15(5) 2.2(1) 1.0(5) (0.3 + 2.7) 0.9(2) 15.(1) (0.14 + 0.28) (0.09 + 0.06) 4.0(4) 4.0(4) 12.(1) 50.(2) 3.3(10)¥102 (22. + 63.) 42.(4) sa = 0.97(3) mb sm = 0.38(2) (0.05+0.54) (39.+ 5.2) mb 6.8(2) 224.(42) (2.5+8.3) (2.4+0.24) 24.(1) (0.17+6.) (4.6+7.) (14.+7.) 183.(30) (sm+ sg) = 0.11 sm = 0.09 1.7(2) 3.(2) mb 0.39(4) sp = 12.(2) (0.06+0.38) <20. 0.10(1) 1.2(3) 1.2(1) (0.6+0.2) sm = 0.81(4) 16.(3) 5.8(4) mb 0.42(4) 10.(1) mb 1.25(5) (0.001+1.25) <6.5 1.4(3) 0.19(1) sa <0.1 mb ≈ 0.014 1.2(3) 0.2(1) <4.

11-189 Resonance Integral (barns) 16.(2) 31.(3) 6.(2)

Coh. Scat. s (30 keV) Maxw. Length (fm) Avg. (barns) 7.88(4) 0.14(1) 6.40(3) 0.12(1) 8.19(2)

2.3(1) 0.8(3) 66.(20) (0.4+0.5) (1.3+0.6) 61.(5) 61.(5) 14.(3) 520(50)

10.0(1) 8.5(1) 5.02(4) 7.6(1) 8.2(15) 6.58(1) 6.58(1) 7.970(9) 0.8(3)

88.(5) mb 0.07(2) 0.3(1) 53.(7) mb 0.03(2)

(9.+31.) 30.(5)

12.2(1) 8.25(8)

0.16(1) 0.3(1)

0.57(4) 0.2(1)

RIm = 4.3(4) (0.15+0.85) 39.(4) mb 92.(8)

8.24(9) 7.48(3) 6.34(8) 6.79(2)

0.1 42.(3) mb 0.04(2)

(36.+96.)

6.79(7)

51.(5) 39.(6) 20.(1) 57.(6) 130.(13) 183.(20) 2.4(3)

6.78(7) 7.81(2)

0.63(4) sm = 0.08(1) 0.31(2) (0.11+0.19) (0.09+0.18) 90.(6) mb 0.24(2) (16.+33.) mb

1.8(10) ≈ 1. mb 6.(3)

8.1(3) 7.08(2)

(0.7+7.)

7.0(1)

0.24(1)

2.3(4) 0.5(1) 10.(1) (9.+1.) RIm = 4.(1) 118.(30) 0.07(3) 0.2 0.10(2) 1.0(1) (0.006+1.0)

7.3(1)

16.(1) mb

5.68(5) 7.41(7) 7.16(6)

0.4(1) (48.+22.) mb 97.(5) mb 6.0(2) mb

7.75(2) 7.75(2)

19.(1) mb

0.6(1) 0.95(9)

7.16(3)

0.2(1) 5.(2) 0.6(2) 16.(5)

0.07(2) 3.2(4) mb

7.02(2)

6.4(1) 8.8(1) 7.5(2)

21.(2) mb 60.(8) mb 33.(4) mb 0.10(1)

11-190 Elem. or Isot. 94Zr 96Zr 41Nb

Neutron Scattering and Absorption Properties Natural Abundance (%) 17.38(28) 2.80(9)

Half-Life >1017 y >1.7¥1018 y

2.4¥104 y

Nb Mo

34.97 d

100.

95 42

14.77(31)

Mo Mo

9.226(99) 15.900(85)

Mo Mo

16.674(12) 9.560(50)

Mo Mo 43Tc 98Tc 99Tc 44Ru 96Ru 98Ru 99Ru 100Ru 101Ru

24.20(25) 9.67(20)

96 97

100

102

Ru Ru 104Ru 105Ru 106Ru 45Rh 103Rh 104mRh 104Rh 105Rh 46Pd 102Pd 104Pd 105Pd Pd Pd 108Pd 110Pd 47Ag 107Ag 109Ag 110mAg 111Ag 48Cd 106Cd 108Cd

≈ 1¥1019 y ≈ 6.6¥106 y 2.13¥105 y

5.54(14) 1.87(3) 12.76(14) 12.60(7) 17.06(2)

>3.1¥1016 y

31.55(14)

103

106

>3¥1017 y

39.27 d 18.62(27) 4.44 h 1.020 y 100. 4.36 m 42.3 s 35.4 h 1.02(1) 11.14(8) 22.33(8) 27.33(3)

107

6.5¥106 y 26.46(9) 11.72(9) 51.839(8) 48.161(8) 249.8 d 7.47 d 1.25(6) 0.89(3)

*Extrapolated value.

>2.6¥1017 y >4.1¥1017 y

Thermal Neut. Cross-Section (barns) 0.049(6) 0.020(3) 1.11(1) sa <0.1 mb 1.1 sm = 0.86 (sm+ sg) = 15.(1) sm = 0.6(1) <7. 2.5(1) sa <0.1 mb 0.06 sm = 0.2 mb 0.02 13.4(3) sa = 30.(4) mb 0.5 2.5(2) sa = 0.4(2) mb 0.14(1) 0.19(1) sm = 0.9(2) 23.(2) 2.6 (1) 0.23(4) < 8. 4.(1) 5.8(6) 5.(1) sa <0.15 mb 1.2(1) <20. 0.49(2) 0.29(3) 0.15(4) 145.(2) (11.+ 134.) 800.(100) 40.(30) 1.1(3)¥104 7.(1) 3.2(10) 22.(2) sa = 0.5(2) mb (0.013+0.28) 1.8(2) (0.19+8.5) (0.033+0.7) 62.(1) (1.+35.) (4.1 + 87.) 82.(11) 3.(2) 2.52(5)¥103 0.20(3) 1.

Resonance Integral (barns) 0.25(3) 5.0(5) 8.5(6) (6.3+2.2)

Coh. Scat. s (30 keV) Maxw. Length (fm) Avg. (barns) 8.3(2) 26.(1) mb 5.5(1) 11.(1) mb 7.14(3) 7.14(3)

266.(5) mb

126.(13) <200. 26.(5)

6.72(2)

≈ 0.8

6.93(8)

0.07(1)

≈ 0.8 109.(5)

6.82(7) 6.93(6)

0.10(2) 0.29(1)

17.(3) 14.(3)

6.22(6) 7.26(8)

0.11(1) 0.34(1)

7.2(7) 3.6(3)

6.60(7) 6.75(7)

0.10(1) 0.11(1)

4.0(4)¥102 48.(5) 7.(2)

6.8(3) 7.03(3)

0.93(5) 0.21(1) 0.3(1) 1.2(3) 0.21(1) 1.00(4)

195.(20) 11.(2) 1.1(3)¥102 4.3(5) ≈ 30. 6.(2) 0.13(1) 2.0(6) 1.2(1)¥103 (0.08+1.1)¥103

1.7(4)¥104 82.(8) 10.(2) 16.(2) 60.(20) (0.2+5.5) 108.(4) (2.+240.) (0.7+8.) 767.(60) (3.+105.) (0.7+14.1)¥102 20.(4) 105.(20) 73.(8) 4.(1) 14.(3)

0.15(1) 0.15(1)

5.88(4) 5.88(4)

0.81(1)

5.91(6)

5.5(3) 6.4(4) 4.1(3) 5.922(7) 7.56(1) 4.17(1)

0.3(1) 0.29(3) 1.20(6) 0.25(3) 1.34(6) 0.20(2) 0.15(2) 0.80(3) 0.79(3)

4.87(5) 5.4(1)

0.30(2) 0.20(1)

Neutron Scattering and Absorption Properties Elem. or Isot. 109Cd 110

Natural Abundance (%)

Half-Life 462.0 d

Cd Cd 112Cd 113Cd

12.49(18) 12.80(12) 24.13(21) 12.22(12)

7.7¥1015 y

114

28.73(42) 7.49(18)

3.8¥1019 y

4.29(5) 95.71(5)

4.4¥1014 y

111

Cd Cd 49In 113In 115In 50Sn 112Sn 113Sn 114Sn 115Sn 116Sn 117Sn 118Sn 119Sn 120Sn 122Sn 124Sn 51Sb 121Sb 123Sb 124Sb 52Te 120Te 122Te 123Te

116

124

Te Te 126Te 128Te 130Te 53I 125I 127I 128I 129I 130I 131I 54Xe 124Xe 125Xe 126Xe 127Xe 128Xe 129Xe 130Xe 131Xe 132Xe 133Xe 134Xe 135Xe 125

0.97(1) 115.1 d 0.66(1) 0.34(1) 14.54(9) 7.68(7) 24.22(9) 8.59(4) 32.58(9) 4.63(3) 5.79(5)

>2.2¥1018 y

57.21(5) 42.79(5) 60.20 d 0.09(1) 2.55(12) 0.89(3) 4.74(14) 7.07(15) 18.84(25) 31.74(8) 34.08(62)

>5.3¥1016 y

2.2¥1024 y 8.¥1020 y 59.4 d

100. 25.00 m 1.7¥107 y 12.36 h 8.021 d 0.0953(27)

>1017 y 17.1 h

0.0890(14) 36.34 d 1.910(22) 26.40(18) 4.071(53) 21.233(62) 26.9087(680) 10.436(29)

*Extrapolated value.

5.243 d >1.1¥1016 y 9.10 h

Thermal Neut. Cross-Section (barns) ≈ 180. sa <0.05 (0.06+11.) 3.5(20) (0.012+2.2) 2.06(4)¥104 sa <1. mb (0.04+0.29) (26.+52.) mb 197.(4) (3.1+5.0+3.9) (88.+73.+44.) 0.61(3) (0.15+0.40) ≈ 9. ≈ 0.12 sa = 0.06 mb (0.006+0.14) 1.1(1) sm = 4. mb 2.(1) (0.001+0.13) (0.15+0.001) (0.13+0.004) 5.2(2) (0.4+5.8) (0.02+0.04+4.0) 17.(3) 4.2(1) (1.+5.) (0.4+3.) 370.(40) sa = 0.05 mb (1.+6.) 1.1(2) (0.12+0.8) (0.03+0.2) (0.01+0.19) 6.2(1) 900.(100) 6.2(1) 22.(4) (20.7+10.3) 18.(3) ≈ 0.7 25.(1) (28.+137.) sa < 0.03 (0.45+3.) sa ≤ 0.01 sm = 0.48 22.(5) sm = 0.45 90.(10) (0.05+0.4) 190.(90) (0.003 + 0.26) 2.65(11)¥106

11-191 Resonance Integral (barns) 6.7(12)¥103

Coh. Scat. Length (fm)

(6.+34.) 51.(6) 15. 390.(40)

5.9(1) 6.5(1) 6.4(1) - 8.0(2)

16.(7) 1.2 3.3(2)¥103 (220.+90.) (1.5+1.2+0.7)¥103 8.(2) (8.+19.) 210.(50) 5.(1) 29.(6) (0.5+11.) 16.(5) 4.7(5) 2.9(5) 1.2(3) 0.81(4) (8.0+0.08) 169.(20) (13.+192.) (1.+119.) ≈ 8. 47.(3) ≈ 1. (5.+75.) 4.5(3)¥103 (1.4+4.) 21.(4) (0.6+7.4) (0.2+1.6) (0.03+0.3) 1.5(1)¥102 1.4(2)¥104 1.5(1)¥102 ≈ 10. 36.(4) ≈ 8. 8.(4) 263.(50) (0.6+3.0)¥103

7.5(1) 6.3(1) 4.07(2) 5.39(6) 4.01(2) 6.225(2)

s (30 keV) Maxw. Avg. (barns)

(0.01+0.22) 0.75(1) 0.19(1) 0.67(1) (0.01+0.12) (12.+47.) mb (0.48+0.31) (0.69+0.02) 0.21(1)

6.2(3) 5.93(5) 6.48(5) 6.07(5) 6.12(5) 6.49(5) 5.74(5) 5.97(5) 5.57(3) 5.71(6) 5.38(7) 5.80(3) 5.3(5) 3.8(2) - 0.05

134.(3) mb 0.34(1) 91.(2) mb 319.(7) mb 62.(1) mb 0.18(1) (0.5+36.) mb (18.+4.) mb 12.(2) mb 0.53(2) 0.30(1)

0.4(1) 295.(3) mb 0.83(1)

8.0(1) 5.02(8) 5.56(7) 5.89(7) 6.02(7) 5.28(2)

155.(2) mb 431.(4) mb (28.+53.) mb (3.+41.) mb (4.+11.) mb

5.28(2)

0.64(3) 0.44(2)

4.92(3) (0.13+0.51)

(8.+52.)

(0.04+0.32)

RIm = 38.(10) 250.(50) RIm = 16.(4) 9.(1)¥102 (0.9+3.7)

0.26(1) 0.62(2) 0.132(3) 0.45(8) (5.+60.) mb

0.40(4) 7.6(5)¥103

20.(2) mb

11-192 Elem. or Isot. 136Xe 55Cs 132Cs 133Cs 134Cs 135Cs 137Cs 56Ba 130Ba 132Ba 133Ba 134Ba 135Ba 136Ba 137Ba 138Ba 139Ba 140Ba 57La 138La 139La 140La 58Ce 136Ce 138Ce 140Ce 141Ce 142Ce 143Ce 144Ce 59Pr 141Pr 142Pr 143Pr 60Nd 142Nd 143Nd 144 145

146

Nd Nd

Nd Nd 148Nd 150Nd 61Pm 146Pm 147Pm 148mPm 148Pm 149Pm 151Pm 62Sm 144Sm 145Sm 147Sm 148Sm 149Sm

Neutron Scattering and Absorption Properties Natural Abundance (%) 8.858(33)

Half-Life >8¥1020 y 6.48 d

100. 2.065 y 2.3¥106 y 30.2 y 0.106(1) 0.101(1)

2.2¥1021 y 1.3¥1021 y 10.53 y

2.417(18) 6.592(12) 7.854(24) 11.232(24) 71.698(42) 1.396 h 12.75 d 0.090(1) 99.910(1)

1.06¥1011 y 1.678 d

0.185(2) 0.251(2) 88.450(51) 11.114(51)

32.50 d >1.6¥1017 y 1.38 d 284.6 d

100. 19.12 h 13.57 d 27.2(5) 12.2(2) 23.8(3) 8.3(1)

2.1¥1015 y

17.2(3)

147

10.98 d 5.7(1) 5.6(2)

≈ 1¥1019 y 5.53 y 2.623 y 41.3 d 5.37 d 2.212 d 1.183 d

3.07(7) 14.99(18) 11.24(10) 13.82(7)

*Extrapolated value.

340. d 1.06¥1011 y 7¥1015 y 1016 y

Thermal Neut. Cross-Section (barns) 0.26(2) 30.4(8) sa < 0.15 (2.7+27.3) 140.(10) 8.3(3) (0.20+0.07) 1.3(2) (1.+8.) (0.84+9.7) 4.(1) (0.1+1.3) (0.014+5.8) (0.010+0.44) 5.(1) 0.41(2) 5.(1) 1.6(3) 9.2(2) 57.(6) 9.2(2) 2.7(3) 0.64(4) (1.0+6.5) (0.025+1.0) 0.58(4) 29.(3) 0.97(3) 6.1(7) 1.0(1) 11.5(4) (4.+7.5) 20.(3) 90.(10) 51.(2) 19.(1) 330.(10) sa = 17. mb 3.6(3) 47.(6) sa = 12. mb 1.5(2) 440.(150) 2.4(1) 1.0(1) 8.4(1.7)¥103 (84.+96.) 10600.(800) ≈ 103 1400.(200) ≈ 150. 5.6(1)¥103 1.6(1) 280.(20) 56.(4), sa = 0.6 mb 2.4(6) 4.01(6)¥104, sa = 31. mb

Resonance Integral (barns) 0.7(2) 422.(50) (32.+360.) 54.(9) 38.(3) 0.36(7) 10.(2) (25.+200.) (4.7+24.) 85.(30) (5.6+18.) (0.47+131.) (0.1+1.5) 4.(1) 0.4(1) 2.2(5) 14.(1) 12.(1) 4.1(9)¥102 12.(1) 69.(4) 0.71(6) 58.(12) (1.5+5.2) 0.50(5) 13.(2) 1.3(3) 2.7(3) 2.6(3) 14.(3) 14.(3) 9.(1) 190.(25) 49.(5) 34.(11) 128.(30)

Coh. Scat. Length (fm)

s (30 keV) Maxw. Avg. (barns) 0.9(1) mb

5.42(2) 5.42(2)

5.07(3) - 3.6(6) 7.8(3) 5.7(1) 4.7(1) 4.91(8) 6.8(1) 4.84(8)

(0.04+0.47)

0.76(11) 0.6(1) 0.18(1) 0.46(2) 61.(2) mb 76.(3) mb 4.0(2) mb

8.24(4) 8.24(4)

38.(3) mb

4.84(2) 5.80(9) 6.70(9) 4.84(9)

(0.028+0.3) 179.(5) mb 11.0(4) mb

4.75(9)

28.(1) mb

4.58(5) 4.58(5)

111.(2) mb

7.69(5) 7.7(3)

35.(1) mb 0.24(1)

3.9(5) 260.(40)

2.8(3)

81.(2) mb 0.42(1)

3.0(4) 200. 13.(2) 14.(2)

8.7(2)

91.(1) mb

5.7(3) 5.3(2)

147.(2) mb 0.16(1)

(1000.+1280.)

12.6(4)

2.(1)

2.6(2.4)¥103

1.4(2)¥103 2.4(3) 600.(90) 710.(50) 27.(14) 3.1(5)¥103

92.(6) mb 14.(3)

0.97(1) 241.(2) mb 1.82(2)

Neutron Scattering and Absorption Properties Elem. or Isot. 150Sm 151Sm 152Sm 153Sm 154Sm 63Eu 151Eu

Natural Abundance (%) 7.38(1)

90. y 26.75(16) 1.929 d 22.75(29) 47.81(6)

152m1

Eu Eu 153Eu 154Eu 155Eu 64Gd 148Gd 152Gd 153Gd 154Gd 155Gd 156Gd 157Gd 158Gd 160Gd 161Gd 65Tb 159Tb 160Tb 66Dy 156Dy 158Dy 159Dy 160Dy 161Dy 162Dy 163Dy 164Dy 165mDy 165Dy 67Ho 163Ho 165Ho 166mHo 68Er 162Er 164Er 166Er 167Er 168Er 170Er 171Er 69Tm 169Tm 170Tm 171Tm 70Yb 168Yb 169Yb 170Yb

Half-Life

9.30 h 13.5 y

152

52.19(6) 8.59 y 4.76 y

0.20(1) 2.18(3) 14.80(12) 20.47(9) 15.65(2) 24.84(7) 21.86(19)

75. y 1.1¥1014 y 240. d

>1.9¥1019 y 3.66 m

100. 72.3 d 0.056(3) 0.095(3) 144. d 2.39(18) 18.889(42) 25.475(36) 24.896(42) 28.260(54) 1.26 m 2.33 h

Thermal Neut. Cross-Section (barns) 102.(5) 1.52(3)¥104 206.(15) 420.(180) 7.5(3) 4570.(100) (4.+3150.+6000.) sa = 8.7(3) mb 6.8(15)¥104 1.1(2)¥104 300.(20), sa <1. mb 1.5(3)¥103 3.9(2)¥103 48.8(6)¥103 1.40(14)¥104 700.(200), sa <7. mb 2.(1)¥104, sa = 0.03 (0.035+60.) 61.(1)¥103, sa = .08 mb ≈ 2.0 2.54(3)¥105, sa <0.05 2.3(3) 1.5(7) 2.0(6)¥104 23.2(5) 23.2(5) 570.(110) 9.5(2)¥102 33.(3), sa < 9. mb 43.(6), sa < 6. mb 8.(2)¥103 60.(10), sa < 0.3 mb 600.(50), sa < 1. mb 170.(20) 120.(10), sa < 20. mb (1.7+1.0)¥103 2.0(6)¥103 3.5(3)¥103 61.(2)

11-193 Resonance Integral (barns) 290.(30) 3520.(60) 3.0(3)¥103 32.(6) 3.8(5)¥103 (2.+4.)¥103 < 105 1.6(2)¥103 1.8(4)¥103 1.6(2)¥103 1.6(2)¥104 400.(10)

Coh. Scat. s (30 keV) Maxw. Length (fm) Avg. (barns) 14.(3) 422.(4) mb 2.(1) - 5.0(6) 473.(4) mb 9.(1) 5.3(3)

(1.6+2.2)

8.2(1)

1.2¥103 y 0.139(5) 1.601(3) 33.503(36) 22.869(9) 26.978(18) 14.910(36) 7.52 h 100 128.6 d 1.92 y 0.13(1) 32.02 d 3.04(15)

*Extrapolated value.

(3.1+58.), sa < 20. mb 3.1(8)¥103 1.5(2)¥102 19.(3), sa < 11. mb 13.(3), sa < 1.2 mb (3.+14.), sa < 70. mb 6.5(8)¥102, sa = 3. mb 2.3(3), sa = 0.09 mb 8.(2) 370.(40) 108.(4) (8.+100.) 100.(20) ≈ 160. 52.(10) 2.4(2)¥103, sa < 0.1 mb 3.6(3)¥103 12.(2), sa < 10. mb

5.(2) 2.8(1) 4.4(7) 1.3(1)

9.5(2)

700.(200)

1.05(2)

230.(50) 1540.(100) 104.(15) 800.(100) 73.(7) 6.(1)

9.(2) 9.15(5)

1.03(1) 2.65(3) 615.(5) mb 1.37(2) 324.(3) mb 0.15(2)

7.34(2) 7.34(2)

1.6(2)

420.(50) 420.(50)

6.3(4)

1.5(2)¥103 1000.(100) 120.(10)

16.9(3)

1100.(200) 1100.(100) 2755.(300) 1600.(400) (4.+2.)¥102

6.7(4) 10.3(4) - 1.4(5) 5.0(4) 49.4(2)

2.2(3)¥104 670.(40)

6.1(5)

(?+670.) 10.(3)¥103 730.(10) 480.(50) 105.(10) 96.(12) 2970.(70) 37.(5) 26.(4) 170.(20) 1.5(2)¥103 1.5(2)¥103 460.(50) 118.(6) 1.7(2)¥102 2.0(5)¥104 5200.(500) 320.(30)

1.6(2) 0.8(2) 0.89(1) 1.96(2) 446.(4) mb 1.11(1) 212.(3) mb

8.01(8)

4.57¥103 y 100.

0.21(1)

8.01(8)

(0.4+1.7) (0.8+0.5)

7.79(2) 8.8(2) 8.2(2) 10.6(2) 3.0(3) 7.4(4) 9.6(5)

1.6(1) 1.08(5) 0.56(6) 1.4(2) 0.34(4) 0.17(1)

7.07(3) 7.07(3)

1.13(6)

12.43(3) -4.07(2)

0.7(4)

6.8(1)

0.77(1)

11-194 Elem. or Isot. 171Yb 172Yb 173Yb 174Yb 176Yb 71Lu 175Lu 176Lu 177mLu 177Lu 72Hf 174Hf 176Hf 177Hf 178m2Hf 178Hf 179Hf 180Hf 181Hf 73Ta 179Ta 180mTa 181Ta 182Ta 74W 180W 182W 183W 184W 185W 186W 187W 188W 75Re 185Re 187Re 76Os 184Os 186Os 187Os 188Os 189Os 190Os 191Os 192Os 193Os 77Ir 191Ir 192Ir 193Ir 194Ir 78Pt 190Pt 192Pt 194Pt 195Pt 196Pt 198Pt

Neutron Scattering and Absorption Properties Natural Abundance (%) 14.28(57) 21.83(67) 16.13(27) 31.83(92) 12.76(41) 97.41(2) 2.59(2)

0.16(1) 5.26(7) 18.60(9)

Half-Life

3.73¥1010 y 160.7 d 6.65 d 15

2.0¥10 y

31. y 27.28(7) 13.62(2) 35.08(16) 42.4 d

0.012(2) 99.988(2)

1.8 y > 1.2¥1015 y 114.43 d

0.12(1) 26.50(16) 14.31(4) 30.64(2) 28.43(19)

37.40(2) 62.60(2) 0.02(1) 1.59(3) 1.96(2) 13.24(8) 16.15(5) 26.26(2)

7.4¥1016 y 8.3¥1018 y 1.9¥1018 y 4.0¥1018 y 74.8 d 6.5¥1018 y 23.9 h 69.78 h

4.2¥1010 y >5.6¥1013 y 2.¥1015 y

15.4 d 40.78(19) 30.5 h 37.3(2) 73.83 d 62.7(2) 19.3 h 0.014(1) 0.782(7) 32.967(99) 33.832(10) 25.242(41) 7.163(55)

*Extrapolated value.

4.5¥1011 y

Thermal Neut. Cross-Section (barns) 53.(5), sa < 1.5 mb ≈ 1.3, sa < 1. mb 16.(2), sa < 1. mb (46.+17.), sa < 0.02 mb 3.1(2), sa < 1. mb 78.(7) (16.+8.) (2.+2100.) 3.2(3) 1000.(300) 106.(3) 600.(50) 23.(4) (1.+375.), sa < 20. mb sm2 = 45.(5) (54.+32.) (0.43+46.) 13.0(5), sa < 13. mb 30.(25) 20.(1) 9.3(6)¥102 ≈ 560. (0.012 + 20.), sa <1. mb 8200.(600) 18.(1) ≈ 4. 20.(1) 10.5(3) (0.002 + 2.0) ≈ 3.3 37.(2) 70.(10) 12.(1) 90.(4) (0.33+110.) (2.+72.) 17.(1) 3.3(3)¥103, sa <10. mb ≈ 80., sa < 0.1 mb 2.(1)¥102, sa < 0.1 mb ≈ 5., sa < 30. mb (0.00026+40.),sa<10. mb (9.+4.), sa < 20. mb 3.8(6)¥102 3.(1), sa < 10. mb 2.5(5)¥102 4.2(1)¥102 (0.14+660.+260.) 1.4(3)¥103 (0.04+6.+109.) 1.6(3)¥103 10.(1) 1.5(1)¥102, sa < 8. mb (2.0+6.), sa < 0.2 mb (0.1+1.1), sa < 5. mb 28.(1), sa < 5. mb (0.045+0.55) (0.3+3.1)

Resonance Integral (barns) 315.(30) 25.(3) 380.(30) (13.+16.) 8.(2) 8.3(7)¥102 (550.+270.) (3.+930.) 1.4(2) 19.7(5)¥102 400.(50) 700.(100) 7170.(200) RIm2 = 8(1)¥102 (0.9+1.0)¥103 (6.8+620.) 32.(1) 650(20.) 1.22(7)¥103 1350.(100) (0.4+650.) 900.(90) 3.6(3)¥102 210.(30) 600.(90) 340.(50) 15.(2) 300.(50) 510.(50) 2760.(550) 8.4(2)¥102 1700.(50) (9.+310.) 1.5(1)¥102 1.4(1)¥103 3.8(9)¥102 5.0(7)¥102 1.5(2)¥102 (0.013+670.) (22.+8.) 1.7(3)¥102 7.(1) 1.1(2)¥102 2.8(4)¥103 (1.0+4.2)¥103 4.8(7)¥103 1.4(2)¥103 7.(2)¥102 1.3(1)¥102 70.(10) 115.(20) (4.+?) 365.(50) 7.(2) (5.+53.)

Coh. Scat. Length (fm) 9.7(1) 9.4(1) 9.56(7) 19.3(1) 8.7(1) 7.21(3) 7.24(3) 6.1(2)

7.8(1) 11.(1) 6.6(2)

5.9(2) 7.5(2) 13.2(3)

s (30 keV) Maxw. Avg. (barns) 1.21(1) 0.34(1) 0.75(1) 151.(2) mb 116.(2) mb (1.04+0.11) 1.53(7)

0.8(2) 0.46(2) 1.5(1) 0.31(1) (0.01+0.95) 179.(5) mb

6.91(7)

0.77(2)

4.86(2) 6.97(4) 6.53(4) 7.48(6)

0.54(6) 274.(8) mb 0.52(2) 0.22(1)

- 0.72(4)

176.(5) mb

9.2(3) 9.0(3) 9.3(3) 10.7(2)

1.54(6) 1.16(6)

7.6(3) 10.7(3) 11.0(3)

0.4(2) 0.42(2) 0.90(3) 0.40(2) 1.17(5) 0.30(5)

11.5(4)

0.31(5)

12(2)

10.6(3) 1.35(4) 0.99(7) 9.60(1) 9.(1) 9.9(5) 10.55(8) 8.8(1) 9.89(8) 7.8(1)

0.7(2) 0.6(1) (0.03+0.34) 0.9(2) (0.01+0.19) (3.+79.) mb

Neutron Scattering and Absorption Properties Elem. or Isot. 199Pt 79Au 197Au

Natural Abundance (%)

100.

198

Au Au Hg 80 196Hg 198Hg 199Hg 200Hg 201Hg 202Hg 204Hg 81Tl

2.695 d 3.14 d

199

203

Tl Tl 205Tl 82Pb 204Pb 205Pb 206Pb 207Pb 208Pb 210Pb 83Bi 209Bi 210mBi 84Po 210Po

Half-Life 30.8 m

0.15(1) 9.97(8) 16.87(10) 23.10(16) 13.18(8) 29.86(20) 6.87(4)

>2.5¥1018 y

29.524(14)

204

3.78 y 70.476(14) 1.4(1) 1.51¥107 y 24.1(1) 22.1(1) 52.4(1)

>2¥1019 y 22.6 y

100. 3.0¥106 y

At Rn Rn 222Rn 88Ra 223Ra 224Ra 226Ra 228Ra 89Ac 227Ac 90Th 227Th 228Th 229Th

Thermal Neut. Cross-Section (barns) ≈ 15. 98.7(1) sm+g = 98.7(1) sm = 8.(2) mb 26.5(15)¥103 ≈ 30. 3.7(1)¥102 (105.+3000.) (0.017+2.) 2.1(2)¥103 ≈ 1. ≈ 8. 4.9(5) 0.4(1) 3.3(1) 11.(1), sa < 0.3 mb 22.(2) 0.11(2) 0.172(2) 0.68(7) ≈ 5. 0.027(1) 0.61(3) 0.23(1) mb, sa < 8. mb < 0.5 0.034(1) (11.+23.) mb,sa<0.3 mb 54.(4) mb

138.4 d

sm<0.5 mb, sa < 2. mb sg<30. mb, sf< 0.1

55.6 s 3.823 d

<0.2 0.74(5)

11.43 d 3.66 d 1599. y 5.76 y

1.3(2)¥102, sf< 0.7 12.0(5) ≈ 13., sf< 7. mb 36.(5), sf< 2.

21.77 y

8.8(7)¥102, sf< 0.35 mb 7.4 sf = 2.0(2)¥102 1.2(2)¥102, sf<0.3 ≈ 60. sf = 30.(3) 23.4(5) sf < 0.5 mb 7.37(4) sf = 3.(1) mb sa < 1. mb 1.5(1)¥103 sf = 15.(2) 1.8(5) sf < 0.01

11-195 Resonance Integral (barns) ≈ 7. 1.55(3)¥103 RIm+g = 1.55(3)¥103 RIm = 0.06(2) ≈ 4.¥104

Coh. Scat. Length (fm) 7.63(6) 7.63(6)

87.(5) (53.+410.) (1.7+70.) 435(20) 2.1(5) 30.(3) 4.5(2) 0.8(2) 12.5(8)

12.69(2) 30.(1)

41.(2) 90.(20) 0.6(2) 0.14(4) 2.0(2) ≈ 2. 0.10(1) 0.38(1) 2.0(2) mb

7.0(2)

0.19(2) 0.19(2) 0.20(3)

16.9(4)

11.(1)

18.72 d 1.913 y 7.9¥103 y

230

7.54¥104 y

232

233

22.3 m

234

24.10 d

100.

*Extrapolated value.

1.40¥1010 y

9.52(7) 9.402(2) 10.9(1)

124.(8) mb 0.14(5) 54.(4) mb

9.23(5) 9.28(2) 9.50(3) 8.532(2) 8.532(2)

2.7(5) mb

10.(1)

1.5(4)¥103 85.(3)

10.31(3)

1014.(400) 1.0(2)¥103 RIf = 466.(75) 1.0(1)¥103

4.(1)¥102

0.4(2) 0.17(2) 0.37(2) 0.12(1) 0.26(1) 74.(6) mb 42.(4) mb

90.(6) mb 0.06(1) 16.(1) mb 10.(1) mb 0.36(4) mb

280.(50)

85.(3)

582.(9) mb

8.776(5)

86 220

s (30 keV) Maxw. Avg. (barns)

10.31(3)

11-196

Neutron Scattering and Absorption Properties

Elem. or Isot. 91Pa 230Pa 231Pa 232

Natural Abundance (%)

Half-Life 17.4 d 3.25¥104 y

1.31 d

233

27.0 d

U U 231U 232U

20.8 d 4.2 d 70. y

92 230

233

1.592¥105 y

234

0.0054(5)

2.455¥105 y

235

0.7204(6)

7.04¥108 y

236

2.342¥107 y

237

6.75 d

238

239

99.2742(10)

Np Np 235Np 236mNp 236Np 237Np 93 234

238

Np Np

239

Pu Pu 237Pu 238Pu 94 236

4.47¥109 y

23.5 m

4.4 d 1.085 y 22.5 h 1.55¥105 y 2.14¥106 y 2.117 d 2.355 d

2.87 y 45.7 d 87.7 y

239

2.410 x 104 y

240

6.56¥103 y

241

14.4 y

242

3.75 x 105 y

243

4.956 h

*Extrapolated value.

Thermal Neut. Cross-Section (barns) 1.5(3)¥103 2.0(1)¥102 sf = 20.(1) mb 4.6(10)¥102 sf = 1.5(5)¥103 39.(2) sm = 20.(4) sg = 19.(3) sf < 0.1 3.4(3); sf = 4.2(1) sf ≈ 25. sf ≈ 250. 73.(2) sf = 74.(8) 47.(2) sf = 5.3(1)¥102 sa < 0.2 mb 96.(2) sf = 0.07(2) 95.(5) sf = 586.(2) sa < 0.1 mb 5.1(3) sf < 1.3 mb ≈ 102 sf < 0.35 2.7(1) sf ≈ 3. mb sa = 1.4(5) mb 22.(2) sf = 15.(3) sf = 9.(3)¥102 1.6(1)¥102 sf = 2.7(2)¥103 sf = 3.0(2)¥103 1.7(1)¥102 sf = 20.(1) mb sf = 2.6(3)¥103 (32.+19.) sf < 1. sf = 1.6(3)¥102 sf = 2.3(3)¥103 5.1(2)¥102 sf = 17.(1) 2.7(1)¥102 sf = 752.(3) sa ≤ 0.3 mb 2.9(1)¥102 sf ≈ 59. mb 3.7(1)¥102, sa <0.2 mb sf = 1.01(1)¥103 19.(1) sf<0.2 <100. sf = 2.0(2)¥102

Resonance Integral (barns)

Coh. Scat. Length (fm)

750.(80) RIf = 0.05(1) 300.(70) RIf = 1.0(1)¥103 (460.+440.)

9.1(3)

280.(20),RIf = 2.0

8.417(5)

280.(15) RIf = 350.(30) 137.(6) RIf = 760.(17) 660.(70) RIf = 6.5 144.(6) RIf = 275(5)

10.1(2)

12.(4) 10.47(4)

360.(15) RIf = 4.38(50) 1200.(200) 277.(3) 1.54(15) mb

7.(4)¥102 1.35(30)¥103 6.5(3)¥102 RIf = 4.7 1.4(3)¥103

8.402(5)

10.6(1)

1000.(60) 1.6(2)¥102 RIf = 26.(2) 2.0(2)¥102 3.0(1)¥102

14.1(5)

8.4(3)¥103 RIf = 3.2 1.6(1)¥102 5.7(4)¥102 1.1(1)¥103 RIf = 0.23

3.5(1)

7.7(1)

8.1(1)

s (30 keV) Maxw. Avg. (barns)

Neutron Scattering and Absorption Properties Elem. or Isot. 244Pu 245Pu 95Am 241Am 242m

Natural Abundance (%)

Half-Life 8.00¥107 y 10.5 h 432.7 y

141. y

242

16.02 h

243

7.37¥103 y

244m

Am Am 96Cm 242Cm

≈ 26. m 10.1 h

243

29.1 y

244

162.8 d

244

18.1 y

245

8.48¥103 y

246

4.76¥103 y

247

1.56¥107 y

248

3.48¥105 y

249

Cm Cm 97Bk 249Bk

64.15 m ≈ 9.7¥103 y

250

Bk Cf 98 249Cf

3.217 h

250

13.1 y

251

9.0¥102 y

250

320. d

351. y

252

2.65 y

253

17.8 d

254

Cf Es 99 253Es 254mEs 254Es

60.5 d

255 100 255

257

20.47 d 1.64 d 276. d

Es Fm Fm

20.1 h

100.5 d

*Extrapolated value.

40. d

11-197

Thermal Neut. Cross-Section (barns) 1.7(1) 1.5(3)¥102

Resonance Integral (barns) 41.(3) 220.(40)

(0.6+6.4)¥102 sf = 3.15(10) 1.7(4)¥103 sf = 5.9(3)¥103 sf = 2.1(2)¥103 3.3(5)¥102 (75.+5.) sf = 79.(2) mb sf = 1.6(3)¥103 sf = 2.2(3)¥103

(1.+14.)¥102 14.(1) ≈ 200. RIf = 1.8(1)¥103 RIf = < 300. ≈ 1.5¥102 (17.1+1.0)¥102 RIf = 0.056

≈ 20. sf ≈ 5. 1.3(1)¥102 sf = 6.2(2)¥102 15.(1) sf = 1.1(2) 3.5(2)¥102 sf = 2.1(1)¥103 1.2(2) sf = 0.16(7) 60.(30) sf = 82.(5) 2.6(3) sf = 0.36(7) ≈ 1.6 ≈ 80.

120.(50) 214.(20) RIf = 1.6(1)¥103 640.(50) RIf = 10.8(8) 110.(10) RIf = 8.(1)¥102 120.(10) 13.(2) 5.(1)¥102 7.3(7)¥102 270.(30) 13.(2)

7.(1)¥102 sf ≈ 0.1 sf = 1.0(2)¥103

9.(1)¥102

5.0(3)¥102 sf = 1.7(1)¥103 2.0(2)¥103 sf = 110.(90) 2.9(2)¥103 sf = 4.5(5)¥103 20.(2) sf = 32.(4) 18.(2) sf = 1.3(2)¥103 4.5(10)

7.7(4)¥102 RIf = 2.1(3)¥103 12.(2)¥103 RIf = 160.(40) 1.6(1)¥103 RIf = 5.5(3)¥103 43.(3) RIf = 1.1(3)¥102 8.(1) 2.

(180.+5.8) sf = 1.8(1)¥103 28.(3) sf = 1.8(2)¥103 ≈ 55.

(37.5+1.1)¥102

26.(3) sf = 3.3(2)¥103 sf = 3.0(2)¥103

14.(2)

18.(2) RIf = 1.2(3)¥103

Coh. Scat. Length (fm)

8.3(2)

9.5(3)

9.3(2)

7.7(2)

s (30 keV) Maxw. Avg. (barns)

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TECHNIQUES FOR MATERIALS CHARACTERIZATION Experimental Techniques Used to Determine the Composition, Structure, and Energy States of Solids and Liquids H.P.R. Frederikse The many experimental methods, originally designed to study the chemical and physical behavior of solids and liquids, have grown into a new field known as Materials Characterization (or Materials Analysis). During the past 30 years a host of techniques aimed at the study of surfaces and thin films has been added to the many tools for the analysis of bulk samples. The field has benefitted particularly from the development of computers and microprocessors, which have vastly increased the speed and accuracy of the measuring devices and the recording of their output. Materials characterization was and is a very important tool in the search for new physical and chemical phenomena. It plays an essential role in new applications of solids and liquids in industry, communications, and medicine. Many of its techniques are used in quality control, in safety regulations, and in the fight against pollution. In most Materials Characterization experiments the sample is subjected to some kind of radiation: electromagnetic, acoustic, thermal, or particles (electrons, ions, neutrons, etc.). The surface Technique

Sample

analysis techniques usually require a high vacuum. As a result of interactions between the solid (or liquid) and the incoming radiation a beam of a similar (or a different) nature will emerge from the sample. Measurement of the physical and/or chemical attributes of this emerging radiation will yield qualitative, and often quantitative, information about the composition and the properties of the material being probed. The modern tendency of describing practically everything in this world by a combination of a few letters (acronyms) has also penetrated the field of Materials Characterization. The table below gives the meaning of the acronym for every technique listed, the form and size of the required sample (bulk, surface, film, liquid, powder, etc.), the nature of the incoming and of the emerging radiation, the depth and the lateral spatial resolution that can be probed, and the information obtained from the experiment. The last column lists one or two major references to the technique described. Out

Lateral resolution

Depth

Information obtained

Ref.

Optical and Mass Spectroscopies for Chemical Analysis 1. 2.

8. 9.

10.

AAS Atomic Absorption Spectroscopy ICP-AES Induct. Coupled Plasma – Atomic Emission Spectroscopy Dynamic SIMS Dynamic Secondary Ion Mass Spectroscopy Static SIMS Static Secondary Ion Mass Spectroscopy SNMS Sputtered Neutral Mass Spectroscopy SALI Surface Analysis by Laser Ionization LIMS Laser Ionization Mass Spectroscopy

Atomize (flame, electro, thermal, etc.) Atomize (flame, electro, thermal, ICP, etc.)

Light e.g., glow discharge –

Surface

Ion beam (1–20 keV)

Surface

Ion beam (0.5–20 keV)

Surface, bulk

Plasma discharge; noble gases: 0.5–20 keV e-beam, ion-beam, or laser for sputtering

Surface, bulk

u.v. laser (ns pulses)

SSMS Spark Source Mass Spectroscopy GDMS Glow Discharge Mass Spectroscopy

Sample in the form of two electrodes Sample forms the cathode for a D.C. glow discharge Liquid-dissolved sample carried by gas stream into R.F. induction coil

High voltage R.F. spark produces ions Sputtered atoms ionized in plasma

ICPMS Induct. Coupled Plasma Mass Spectroscopy

Surface

Ions produced in argon plasma

Absorption spectrum

–

Emission spectrum

–

Secondary ions; analysis with mass spectrometer Secondary ions, analysis with mass spectrometer Sputtered atoms ionized by atoms or electrons; then mass analyzed Sputtered atoms ionized by laser; then mass analyzed Ionized species; analyzed with mass spectrometer Ions – analyzed in mass spectrometer Ions – analyzed in mass spectrometer

2 nm–1 µm (or deeper: ion milling) 0.1–0.5 nm

0.50 nm

0.1–0.5 nm (or deeper: ion milling) 0.1–0.5 nm up to 3 µm in milling mode 50–150 nm

1 cm

60 nm

Surface analysis; depth profiling 7

5 µm–1 mm

Elemental (micro)analysis; detection limits: 1–100 ppm

1–5 µm

–

0.1–100 µm

3–4 mm

Survey of trace elements; detection limit: 0.01–0.05 ppm (Bulk) trace element analysis; detection limit: sub-ppb

Ions – analyzed in quadrupole mass spectrometer

–

High sensitivity analysis of trace 11 elements

Electronic transitions (mainly in semiconductors and superconductors); vibrational modes (in crystals and molecules) Spectra obtained at higher speed and resolution

10 µm

Concentration of atomic species 1,2 (quantitative, using standards) Concentration of atomic species 3 (quantitative, using standards) Elemental and isotopic analysis; depth profile (all elements); detection limits: ppb-ppm Elemental analysis of surface layers; molecular analysis; detection limits: ppb-ppm Elemental analysis Z ≥ 3; depth profile; detection limit: ppm

4,6

9,10

Photons — Absorption, Reflection and Electron Emission 11.

IRS Infrared Spectroscopy

Thin crystal, glass, liquid

I.R. light (W-filament, globar, Hg-arc)

I.R. spectrum

–

12.

FTIR Fourier Transform I.R. Spectroscopy

White light (all frequencies)

–

ATR Attenuated Total Reflection (µ)-RS (Micro-) Raman Spectroscopy

–

Fourier Transform of spectrum (interferometer) –

–

13.

Solid, liquid; transmission or reflection Surface or thin crystal

µm’s

–

Solid, liquid (1 µm–1 cm)

Laser beam, e.g., Arline, YAG-line

Raman spectra

0.5 µm

14.

12,13,14

Atomic or molecular spectra of 16 surfaces and films Molecular and crystal vibrations 12,14,17

12-1

Section 12.indb 1

4/28/05 1:53:49 PM

Techniques for Materials Characterization

12-2 Technique 15.

16. 17.

18.

CARS Coherent Anti-Stokes Raman Spectroscopy Ellipsometry UPS Ultraviolet Photo-electron Spectroscopy PSD Photon Stimulated Desorption

Sample

Out

Lateral resolution

Depth

Information obtained

Ref.

Solid, liquid (50 µm–3 cm)

Pump beam (ω0)+ probe beam (ωs)

Anti-Stokes spectrum

–

High resolution Raman spectra

Transparent films, crystals, adsorbed layers Surfaces, adsorbed layers

Polarized light

Change in polarization

18,19

Electrons

25 µm (or sample thickness) 0.1–10 nm

Refractive index and absorption

u.v. light, 10–100 eV; 200 eV (synchrotron)

0.05 nm–5 µm 0.2–10 nm

Energies of electronic states of surfaces and free molecules

20,21

Surfaces with adsorbed species

Far u.v. light E > 10 eV

Ions – analyzed with mass spectrometer

0.1–2 nm

–

Structure and desorption kinetics of adsorbed atoms and molecules

Identification of crystallographic structures; all elements (low Z difficult) Elemental analysis; all elements except H, He, Li – (EDS also used in XRD, SEM, TEM and EPMA) Local atomic structure: order/ disorder in vicinity of absorbing atom (Quantitative) identification of all elements in surface layer or film

23,24

Energy levels of impurities and point defects Identification of surface species

X-Rays 19.

XRD X-Ray Diffraction

Single crystals, powders films

X-rays: λ = 0.05–0.2 nm (6–17 keV)

Diffracted X-ray beam

1–1000 µm

0.1–10 mm

20.

XRF/EDS X-Ray Fluorescence/Energy Dispersive Spectroscopy

Thin films, single layer

Prim. X-ray beam λ = 0.02–0.1 nm 12–80 keV

Fluorescent X-rays

1–100 µm

10 mm

21.

EXAFS Extended X-Ray Absorption Fine Structure XPS/ESCA X-Ray Photo-electron Spectroscopy/ Electron Spect. for Chemical Analysis

Films, foils

High intensity X-rays (synchrotron)

Spectrum near absorption edge

nm–µm

–

Surfaces, thin films (≈20 atomic layers)

Soft X-rays (1–20 keV)

Core electrons; valence electrons

0.5–10 nm

5 nm–50 µm

CL Cathode Luminescence APS Appearance Potential Spectroscopy

Insulators, semiconductors Surface (≈20 atomic layers)

Electrons 5–50 keV

Photons 0.1–5 eV

1 nm–2 µn

1 or 2 µm

Electrons (energy scan) 50–2000 eV

–

25.

AES Auger Electron Spectroscopy

Thin films, surfaces

Electrons 3–10 keV

X-rays to pinpoint electron energy threshold Auger electrons 20– 2000 eV

0.3–3 nm

≈30 nm

26.

EELS Electron Energy Loss Spectroscopy

Very thin samples (<200 nm)

Electrons (100–400 keV)

(Retarded) electrons; minus 1–1000 eV

<200 nm

1–100 nm

27.

EXELFS Extended Electron Energy Loss Fine Structure ESD Electron Stimulated Desorption

Thin films

Electrons (100–400 keV)

Electrons energies 0–30 eV above edge

<200 nm

1–100 nm

Adsorbed species

Electrons E > 10 eV

Ions – analyzed with mass spectrometer

–

ESDIAD ESD-Ion Angular Distribution EPMA Electron Probe (X-Ray) Micro Analysis LEED Low Energy Electron Diffraction

(See ESD)

–

Solid conductors and insulators <1 cm thick

Electrons 5–30 keV

Directional dependence of emitted ions Characteristic X-ray 0.1–15 keV

100 nm–5 µm

1 µm

Surface

Mono-energetic electron beam 10– 1000 eV Electron beam at grazing angle 5–50 keV High energy electrons usually ~30 keV

Diffracted electrons

0.4–2 nm

<5 µm

Crystallographic structure of surface; resolution: 0.01 nm

Reflected electrons

0.2–10 nm

<5 µm

Surface symmetry

36,37

Secondary and backscattered electrons

1 nm–5 µm

1–20 nm

33,34

Transmitted and diffracted electrons

(Sample thickness)

2–20 nm

≈0.5 nm

10–100 nm

Surface image, defect structure; resolution 5–15 nm; magnification 300,000× (Defect) structure of cryst. solids; microchemistry; high resol.: 0.2 nm Surface image, crystallographic structure

1–5 nm

2–10 nm

1–100 nm

0.5–5 nm

0.2–130 nm

22.

25,26

28,29

Electrons 23. 24.

28.

29. 30.

31.

32.

RHEED Reflection High Energy Electron Diffraction SEM Scanning Electron Microscopy

Surface

(S)TEM (Scanning) Transmission Electron Microscopy FEM Field Emission Microscopy

Thin specimen – <200 nm

High energy electrons typically 300 keV

Metals, alloys (sharp point)

–

36.

STM Scanning Tunneling Microscopy

Polished or cleaved surface (conducting)

37.

SPM Scanned Probe Microscopy

Very flat surface

38.

AFM Atomic Force Microscopy

Very flat surface

33.

34.

35.

Section 12.indb 2

Bulk, films (conducting)

Electron emission (with appl. electric field – 50 kV) Tunneling current controls distance between sample and very sharp tip Any field: e.g. mechan. vibration recorded with laser probe; same with magnetic, electric or thermal field Similar to STM; force measured with cantilever spring

Elemental composition of surface (except H, He); detection limit 0.1–1% Local elemental concentration; electronic structure, chem. bonding; interatomic distances Density of states of valence electrons (above Fermi level)

21, see also C 28,29

27,32

Structure and desorption 22 properties of adsorbed atoms and molecules Geometries of adsorbed species 22 (atoms or molecules) Elemental analysis, Z ≤ 4, major, 33,34 minor and trace amounts

Atomic-scale relief map of surface; resolution: vert. 0.002 nm, hor. 0.2 nm Surface-magnetic field, surfacethermal conductivity, etc.

Surface topography with atomic resolution; interatomic force

39a

4/28/05 1:53:51 PM

Techniques for Materials Characterization Technique

Sample

12-3 In

Out

Lateral resolution

Depth

Information obtained

Ref.

Ions and Neutrons 39.

ISS (or LEIS) Ion Scattering Spectroscopy (Low Energy Ion Scattering) FIM Field Ion Microscopy RBS Rutherford Back Scattering

Surface

Ion beam He+ or Ne+ <3 keV

Sputtered ions (energy analysis)

0.1–0.5 nm

1–100 µm

Surface: metals, alloys; very sharp tip Solids, thin films

He ions + high electric field produce image Backscattered ions

≈0.1 nm

0.1–2 nm

10 nm–1 µm

1 mm

Element identification (Li to U) detection limit: 0.01–1%

42.

NRA Nuclear Reaction Analysis

Solids, thin films

Protons, deuterons 3He, 0.1–5 µm α-particles, γ-rays

10 µm–10 mm

Element identification (all) detection limit: 10–12–10–2

43.

PIXE Particle Induced X-ray Emission

Thin films, surface layers

(He gas above sample) Mono-energetic ions (H+ or He++) 0.5–3 MeV Mono-energetic ions (Li, Be, B, etc.) 200 keV–6 MeV High energy ions (H+ or He++)

Characteristic X-rays

<10 µm

1 µm–2 mm

44.

INS Ion Neutralization Spectroscopy NAA Neutron Activation Analysis

Surface

He-ions (≈5 eV)

Electrons

–

Trace impurities: Z >3 detection limit: 0.1–100 ppm (depending on sample thickness) Energies of valence electrons

Bulk, >0.5 g

Thermal neutrons

Characteristic γ-rays, (≈1 MeV)

Bulk

–

N(P)D Neutron (Powder) Diffraction SANS Small Angle Neutron Scattering

Crystalline solids

Diffracted neutrons

Bulk

–

Scattered neutrons

1–25 mm

–

Trace concentrations (of isotopes) of elements: trans. metals, Pt-group; detection limit: 108–1014 atoms/cm3 Crystallographic structure; porosity, particle size Average size of inhomogeneities; range: 1 nm– 1 mm

Reflected acoustic wave

µm–cm

0.1–20 mm

Defect structure; thickness measurement

40. 41.

45.

46. 47.

Thermal neutrons E ≈0.0025 eV Inhomogeneous solids; Thermal neutrons 2 θ powders; porous samples = 10–2–10–4

Elemental analysis (better for low Z) detection limits: 0.01– 1% Atomic structure of surface

34,42

44 45

Acoustic 48.

SLAM Scanning Laser Acoustic Microscopy

Bulk, film

Acoustic wave produced by laser 1 MHz–1 GHz

Thermal 49. 50.

51.

DTA Differential Thermal Analysis DSC Differential Scanning Calorimetry

Specimen and reference Uniform heating sample Specimen and ref. sample Controlled heating

Temperature difference

Bulk

–

Phase transitions, crystallization 51

Measure heat required for equal temperature

Bulk

–

TGA Thermo Gravimetric Analysis

Bulk, 1–100 g

Controlled heating

Weight as function of temperature (and time)

Bulk

–

Phase transitions, crystallization; activation energies Decomposition, nonstoichiometry, kinetics of reaction

Local environment of paramagnetic ion; concentration of paramagnetic, species; detection limit: 1011 spins/cm3 Electronic energy bands, effective masses

53,54

Resonance 52.

EPR (ESR) Electron Paramagnetic (Spin) Resonance

Paramagnetic solids or liquids

Microwave radiation in magnetic field 3– 300 GHz; 1–100 kG

Microwave absorption (at resonance)

Bulk

–

53.

ECR Electron Cyclotron Resonance

Bulk

–

Mössbauer Effect

Microwave radiation in magnetic field 10– 30 GHz; 5–10 kG Mono-energetic γrays: 5–100 keV

Microwave absorption (at resonance)

54.

Semiconductors, metals; free electrons (low temperature) Source and absorber

Mössbauer spectrum (Doppler shifted (lines)

50 m

1 cm

55.

NMR (MRI) Nuclear Magnetic Resonance (Magnetic Resonance Imaging)

Solids, liquids

<1 cm

1 cm

56.

ENDOR Electron Nuclear Double Resonance

Solids, liquids

–

Hyperfine interaction → local atomic structure

57.

NQR Nuclear Quadrupole Resonance

Solids

R.F. absorption R.F. radiation + magnetic field; e.g. for protons: 60 MHz, 14 kG Microwave absorption R.F. + microwave radiation in magn. field. R.F. absorption R.F. radiation 0.5– 1000 MHz

–

Asymmetry of the charge distribution at the nucleus

55,59

–

Surface area measurement

Interaction between nucleus and 56 its environment (local electric, magnetic fields; bonds; valency; diffusion, etc.) Quant. analysis; local magnetic 58 environment; diffusion; imaging

Other 58.

Section 12.indb 3

BET Brunauer-Emmett-Teller

(Large) surface area 1–20 Adsorbed gas (e.g., N2 at low temp.) as function m2/g of pressure (monolayer coverage)

4/28/05 1:53:52 PM

Techniques for Materials Characterization

12-4

References General References A. Wachtman, J. B., Characterization of Materials, ButterworthHeinemann, Boston, 1993. B. Brundle, C. R., Evans, C. A., and Wilson, S., Eds., Encyclopedia of Materials, Butterworth-Heinemann, Boston, 1992. C. Woodruff, D. P. and Delchar, T. A., Modern Techniques of Surface Science, Cambridge University Press, Cambridge, 1986. D. Metals Handbook, 9th Edition, Vol. 10, Materials Characterization, Whan, R. E., Coordinator, American Society for Metals, Metals Park, OH, 1986. Specific References 1. Slavin, M., Atomic Absorption Spectroscopy, 2nd Edition, John Wiley & Sons, New York, 1978. 2. Schrenk, W. G., Analytical Atomic Spectroscopy, Plenum Press, New York, 1975. 3. Dean, J. A. and Rains, T. E., Flame Emission and Atomic Absorption Spectroscopy, Vols. 1–3, Marcel Dekker, New York, 1969. 4. Benninghoven, A., Rudenauer, F. G., and Werner, H. W., Secondary Ion Mass Spectroscopy, John Wiley & Sons, New York, 1987. 5. Bird, J. R. and Williams, J. S., Eds., in Ion Beams for Materials Analysis, Academic Press, New York, 1989, pp. 515–537. 6. Smith, G. C., Quantitative Surface Analysis for Materials Science, The Institute of Metals, London, 1991. 7. Becker, E. H., in Ion Spectroscopies for Surface Analysis, Czanderna, A. W. and Hercules, D. M., Eds., Plenum Press, New York, 1991, p. 273. 8. Simons, D. S., Int. J. Mass Spectrometry and Ion Processes, 55, 15, 1983. 9. White, F. A. and Wood, G. M., Mass Spectrometry: Applications in Science and Engineering, John Wiley & Sons, New York, 1986. 10. Harrison, W. W. and Bentz, B. L., Prog. Anal. Spectrometry, 11, 53, 1988. 11. Bowmans, P. W. J. M., Inductively Coupled Plasma Emission Spectroscopy, Parts I and II, John Wiley & Sons, New York, 1987. 12. Brame, Jr., E. G. and Grasselli, J., Infrared and Raman Spectroscopy, Practical Spectroscopy Series, Vol. I, Marcel Dekker, New York, 1976. 13. Hollas, J. M., Modern Spectroscopy, John Wiley & Sons, New York, 1987. 14. Turrell, G., Infrared and Raman Spectroscopy of Crystals, Academic Press, New York and London, 1972. 15. Griffith, P. R. and Haseth, J. A., Fourier Transform Infrared Spectroscopy, John Wiley & Sons, New York, 1986. 16. Barnowski, M. K., Fundamentals of Optical Fiber Communications, Academic Press, New York, 1976. 17. Long, D. A., Raman Spectroscopy, McGraw-Hill, New York, 1977. 18. Azzam, R. M. A., Ellipsometry and Polarized Light, Elsevier-North Holland, Amsterdam, 1977. 19. Hecht, E., Optics, 2nd Edition, Addison-Wesley, Reading MA, 1987. 20. Brundle, C. R., in Molecular Spectroscopy, West, A. R., Ed., Heyden, London, 1976. 21. Park, R. L., in Experimental Methods in Catalytic Research, Vol. III, Anderson, R. B. and Dawson, P. T., Academic Press, New York, 1976, pp. 1–39. 22. Madey, T. E. and Stockbauer, R., in Solid State Physics: Surfaces, Vol. 22 of Methods of Experimental Physics, Park, R.L. and Lagally, M. G., Eds., Academic Press, New York, 1985. 23. Cullity, B. D., Elements of X-Ray Diffraction, 2nd Edition, AddisonWesley, Reading, MA, 1978. 24. Schwartz, L. H. and Cohen, J. B., Diffraction from Materials, Springer Verlag, Berlin, 1987. 25. deBoer, D. K. G., in Advances in X-Ray Analysis, Vol. 34, Barrett, C. S. et. al., Eds., Plenum Press, New York, 1991. 26. Birks, L. S., X-Ray Spectrochemical Analysis, 2nd Edition, John Wiley & Sons, New York, 1969. 27. Bonnelle, C. and Mande, C., Advances in X-Ray Spectroscopy, Pergamon Press, Oxford, 1982.

Section 12.indb 4

28. Practical Surface Analysis by Auger and X-Ray Photo-Electric Spectroscopy, Briggs, D. and Seah, M. P., Eds., John Wiley & Sons, New York, 1983. 29. Powell, C. J. and Seah, M. P., J. Vac. Sci. Technol. A, Vol. 8, 735, 1990. 30. Yacobi, G. G. and Holt, D. B., Cathodeluminescence Microscopy of Inorganic Solids, Plenum Press, New York, 1990. 31. Egerton, R. F., Electron Energy Loss Spectroscopy in the Electron Microscope, Plenum Press, New York, 1986. 32. Disko, M. M., Krivanek, O. L., and Rez, P., Phys. Rev., B25, 4252, 1982. 33. Goldstein, J. I., et. al., Scanning Electron Microscopy and X-Ray Microanalysis, 2nd Edition, Plenum Press, New York, 1986. 34. Murr, L. E., Electron and Ion Microscopy and Microanalysis, Marcel Dekker, New York, 1982. 35. Armstrong, R. A., in Experimental Methods in Catalytic Research, Vol. III, Anderson, R. B., and Dawson, P. T., Eds., Academic Press, New York, 1976. 36. Dobson, P. J. et. al., Vacuum, 33, 593, 1983. 37. Rymer, T. B., Electron Diffraction, Methuen, London, 1970. 38. Reimer, L., Transmission Election Microscopy, Springer-Verlag, Berlin, 1984. 39. Scanning Tunneling Microscopy and Related Methods, Behm, R. J., Garcia, N., and Rohrer, H., Eds., Kluwer Academic Publishers, Norwell, MA, 1990. 39a. Wikramasinghe, H.K., Scientific American, Vol. 261, No. 4, pp. 98– 105, Oct. 1989. 40. Rugar, D. and Hansma, P., Physics Today, 43(10), pp. 23–30, 1990. 41. Feldman, C. C. and Mayer, J. W., Fundamentals of Surface and Thin Film Analysis, North-Holland, Amsterdam, 1986. 42. Muller, E. W. and Tsong, T. T., Field Ion Microscopy, Elsevier, Amsterdam, 1969. 43. Amiel, S., Nondestructive Activation Analysis, Elsevier, Amsterdam, 1981. 44. Bacon, G. E., Neutron Diffraction, 3rd Edition, Clarendon Press, Oxford, 1975. 45. Neutron Scattering, Part A., in Methods of Experimental Physics, Vol. 23, Skold, K. and Price, D. L., Eds., Academic Press, New York, 1986. 46. Chu, W. K., Mayer, J. W., and Nicolet, M. A., Backscattering Spectroscopy, Academic Press, New York, 1987. 47. Rickey, F. A., in High Energy and Heavy Ion Beams in Materials Analysis, Tesmer, J. R., et. al., Eds., MRS, 1990, pp. 3–26. 48. Johansson, S. A. E. and Campbell, J. L., PIXE: A Novel Technique for Elemental Analysis, John Wiley & Sons, New York, 1988. 49. Hagstrum, H. D., in Inelastic Ion-Surface Collisions, Tolk, N. H. et. al., Eds., Academic Press, New York, 1977, pp. 1–46. 50. Nikoonahad, M., in Research Techniques in Nondestructive Testing, Vol. VI, Sharpe, R.S., Ed., Academic Press, New York, 1984, pp. 217– 257. 51. Gallagher, P. K., Characterization of Materials by Thermoanalytical Techniques, MRS - Bulletin, Vol. 13, No. 7, pp. 23–27, 1988. 52. Earnest, C. M., Compositional Analysis by Thermogravimetry, ASTM Special Technical Publication 997, 1988. 53. Poole, C. P., Electron Spin Resonance – A Comprehensive Treatise on Experimental Techniques, 2nd Edition, John Wiley & Sons, New York, 1983. 54. Atherton, N. M., Principles of Electron Spin Resonance, Ellis Horwood Ltd., Chichester, U.K., 1993. 55. Kittel, C., Introduction to Solid State Physics, 6th Edition, John Wiley & Sons, New York, 1986, p. 196. 56. Gibb, T. C., Principles of Mössbauer Spectroscopy, Chapman & Hall, London, 1976. 57. Slichter, C. P., Principles of Magnetic Resonance, 3rd Edition, SpringerVerlag, Berlin, 1990. 58. NMR Spectroscopy Techniques, Dybrowski, C. and Lichter, R. L., Eds., Marcel Dekker, New York, 1987. 59. Das, T. P. and Hahn, E. L., Nuclear Quadrupole Resonance Spectroscopy, Academic Press, New York, 1958. 60. Somorjai, G. A., Principles of Surface Chemistry, Prentice-Hall, Englewood Cliffs, NJ, 1972, p. 216

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SYMMETRY OF CRYSTALS L. I. Berger The ability of a body to coincide with itself in its different positions regarding a coordinate system is called its symmetry. This property reveals itself in iteration of the parts of the body in space. The iteration may be done by reflection in mirror planes, rotation about certain axes, inversions and translations. These actions are called the symmetry operations. The planes, axes, points, etc., are known as symmetry elements. Essentially, mirror reflection is the only truly primitive symmetry operation. All other operations may be done by a sequence of reflections in certain mirror planes. Hence, the mirror plane is the only true basic symmetry element. But for clarity, it is convenient to use the other symmetry operations, and accordingly, the other aforementioned symmetry elements. The symmetry elements and operations are presented in Table 1. The entire set of symmetry elements of a body is called its symmetry class. There are thirty-two symmetry classes that describe all crystals which have ever been noted in mineralogy or been synthesized (more than 150,000). The denominations and symbols of the symmetry classes are presented in Table 2. There are several known approaches to classification of individual crystals in accordance with their symmetry and crystallochemistry. The particles which form a crystal are distributed in certain points in space. These points are separated by certain distances (translations) equal to each other in any chosen direction in the crystal. Crystal lattice is a diagram that describes the location of particles (individual or groups) in a crystal. The lattice parameters

are three non-coplanar translations that form the crystal lattice. Three basic translations form the unit cell of a crystal. August Bravais (1848) has shown that all possible crystal lattice structures belong to one or another of fourteen lattice types (Bravais lattices). The Bravais lattices, both primitive and non-primitive, are the contents of Table 3. Among the three-dimensional figures, there is a group of polyhedrons that are called regular, which have all faces of the same shape and all edges of the same size (regular polygons). It has been shown that there are only five regular polyhedrons. Because of their importance in crystallography and solid state physics, a brief description of these polyhedrons is included in Table 4. The systematic description of crystal structures is presented primarily in the well known Structurbericht. The classification of crystals by the Structurbericht does not reflect their crystal class, the Bravais lattice, but is based on the crystallochemical type. This makes it inconvenient to use the Structurbericht categories for comparison of some individual crystals. Thus, there have been several attempts to provide a more convenient classification of crystals. Table 5 presents a compilation of different classifications which allows the reader to correlate the Structurbericht type with the international and Schoenflies point and space groups and with Pearson’s symbols, based on the Bravais lattice and chemical composition of the class prototype. The information included in Table 5 has been chosen as an introduction to a more detailed crystallophysical and crystallochemical description of solids.

TABLE 1. Symmetry Operations and Elements Symmetry element Symbol Presentation on the stereographic projection International Schoenflies Parallel Perpendicular (Hermann-Mauguin)

Symmetry operation

Name

Reflection in a plane

Plane

Rotation by angle α = 360°/n about an axis

Axis

n = 1, 2, 3, 4 or 6

n=2

n=3

n=4

n=6

n = 3, 4, 6

Cni

n = 3

C3i

n = 4

C4i

Rotation about an axis and inversion in a symmetry center lying on the axis

Inversion (improper) axis

12-5

Section 12.indb 5

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Symmetry of Crystals

12-6

Symmetry operation

Name

Inversion in a point Parallel translation Reflection in a plane and translation parallel to the plane Rotation about an axis and translation parallel to the axis Rotation about an axis and reflection in a plane perpendicular to the axis

Crystal symbol Triclinic Monoclinic Orthorhombic Trigonal Tetragonal Hexagonal Cubic a

TABLE 1. Symmetry Operations and Elements Symmetry element Symbol Presentation on the stereographic projection International Schoenflies Parallel Perpendicular (Hermann-Mauguin)

Primitive

n = 6

C6i

Center

1

Translation    vector a, b, c Glide–plane

a, b, c, n, d

Screw axis

nm (m = 1, 2, .., n – 1) ñ ñ = 1, 2, 3, 4, 6

Rotatoryreflection axis

TABLE 2. The Thirty-Two Symmetry Classes Class namea Planal Axial Plane-axial Inversion primitive and its symbol – International (Int) and Schoenflies (Sch) Int Sch Int Sch Int Sch Int Sch

Central

Int 1

Sch C1

Int 1

Sch Ci

3 4 6 23

C3 C4 C6 T

3 4/m 6/m m3

C3i C4h C6h Th

m mm2

Cs C2v

2 222

C2 D2

2/m mmm

C2h D2h

3m 4mm 6mm 43m

C3v C4v C6v Td

32 422 622 432

D3 D4 D6 O

3m

C3d D4h D6h Oh

Per Fedorov Institute of Crystallography, USSR Academy of Sciences, nomenclature.

4/mmm 6/mmm m3m

4 6

S4 C3h

Inversion-planal Int

Sch

42m 6m2

D2d D3h

TABLE 3. The Fourteen Possible Space Lattices (Bravais Lattices)

Crystal system

Metric category of the system

No. of different lattices in the system

+ +

Triclinic Monoclinic Orthorhombic Trigonal

Trimetric Trimetric Trimetric Dimetric

1 2 4 1

+ + +

(rhombohedral) Tetragonal Hexagonal Isometric (cubic)

Dimetric Dimetric Monometric

2 1 3

+ + +

Section 12.indb 6

α≡(b,c), β≡(a,c), γ≡(a,b)

+ + + +

+ + +

+ +

1 1 or 2 1, 2 or 4 1

a ≠ b ≠ c, α ≠ β ≠ γ a ≠ b ≠ c, α = γ = 90° ≠ β a ≠ b ≠ c, α = β = γ = 90° a = b = c, 120° > α = β = γ ≠ 90°

1 2/m mmm 3m

C C2h D2h D3d

1 or 2 1 1, 2 or 4

+ + +

a = b ≠ c, α = β = γ = 90° a = b ≠ c, α = β = 90°, γ = 120° a = b = c, α = β = γ = 90°

4/mmm 6/mmm m3m

D4h D6h Oh

Lattice typea (marked by +) P

+ +

Description of characteristic parameters a⊂X, b⊂Y, c⊂Z

No. of identipoints per unit cell

Characteristic parameters (marked by +)

+ + +

Symmetry of the lattice Int

Sch

Designations of the space-lattice types: P – primitive, C – side-centered (base-centered), I – body-centered, F – face-centered, R – rhombohedral.

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Symmetry of Crystals

12-7 TABLE 4. The Five Possible Regular Polyhedrons

Polyhedron Tetrahedron

Symmetry (Schoenflies) Class Elements T 4C33C2

Cube (hexahedron) Octahedron

O O

3C44C36C2 3C44C36C2

Pentagonal dodecahedron Icosahedron

J J

6C510C315C2 6C510C315C2

Per formula by Leonhard Euler: F + V – E = 2

Form of faces Equilateral triangle Square Equilateral triangle Regular pentagon Equilateral triangle

Faces (F) 4

Number ofa Edges (E) 6

Vertices (V) 4

6 8

12 12

8 6

12 20

30 30

20 12

TABLE 5. Classification of Crystals Strukturbericht symbol 1 A1 A2 A3 A4 A5 A6 A7 A8 A10 A11 A12 A13 A15 A20 B1 B2 B3 B4 B81 B82 B9 B10 B11 B13 B16 B17 B18 B19 B20 B27 B31 B32 B34 B35 B37 Be Bf (B33) Bg Bh Bi C1 C1b C2

Section 12.indb 7

Structure name 2 Cu W Mg C Sn In As Se Hg Ga α-Mn β-Mn OW3 α-U ClNa ClCs SZn SZn AsNi InNi2 HgS OPb γ-CuTi NiS GeS PtS CuS AuCd FeSi BFe MnP NaTl Pds CoSn SeTl CdSb ξ-BCr BMo CW γ´CMo (AsTi) CaF2 AgAsMg FeS2

Symmetry group International Schoenflies 3 4 Fm3m O4h Im3m O9h P63/mmc D46h O7h Fd3m D194h If1/amd I4/mmm D174h R3m D53d P3121 or P3221 D43 (D63) D53d R3m Cmca D182h I43m T3d O7 P4132 Pm3n O3h Cmcm D172h Fm3m O5h Pm3m O1h F43m T2d P63mc C46v P63/mmc D46h P63/mmc D46h D43 or D63 P3121 or P3221 P4/nmm D74h P4/nmm D74h D53d R3m Pnma D162h D94h P42/mmc P63/mmc D46h Pmma D52h P213 T4 Pnma D162h Pnma D162h Fd3m O7h P42/m C24h P6/mmm D16h I4/mcm D184h Pbca D152h Cmcm D172h I41/amd D194h P6m2 D13h P63/mmc D46h Fm3m F43m Pa3

O5h T2d T6h

Pearson symbola 5 cF4 cI2 hP2 cF8 tI4 tI2 hR2 hP3 hR1 oC8 cI58 cP20 cP8 oC4 cF8 cP2 cF8 hP4 hP4 hP6 hP6 tP4 tP4 hR6 oP8 tP4 hP12 oP4 cP8 oP8 oP8 cF16 tP16 hP6 tI16 oP16 oC8 tI4 hP2 hP8

Standard ASTM E157-82a symbolb 6 F B H F U U R H R Q B C C Q F C F H H H H T T R O T H O C O O F T H U O Q U H H

cF12 cF12 cP12

F F C

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Symmetry of Crystals

12-8 TABLE 5. Classification of Crystals Strukturbericht symbol 1 C3 C4 C6 C7 C11a C11b C12 C14 C15 C15b C16 C18 C19 C22 C23 C32 C33 C34 C36 C38 C40 C42 C44 C46 C49 C54 Cc Ce DO2 DO3 DO9 DO11 DO18 DO19 DO20 DO21 DO22 DO23 DO24 DOc DOe D13 D1a D1b D1c D1e D1f D21 D23 D2b D2c D2d D2f D2h D51 D52 D53

Section 12.indb 8

Structure name 2 Cu2O O2Ti CdI2 MoS2 C2Ca MoSi2 CaSi2 MgZn2 Cu2Mg AuBe5 Al2Cu FeS2 CdCl2 Fe2P Cl2Pb AlB2 Bi2STe2 AuTe2 MgNi2 Cu2Sb CrSi2 SiS2 GeS2 AuTe2 Si2Zr Si2Ti Si2Th CoGe2 As3Co BiF3 O3Re CFe3 AsNa3 Ni3Sn Al3Ni Cu3P Cu3P Al3Zr Ni3Ti SiU3 Ni3P Al4Ba MoNi4 Al4U PtSn4 B4Th BMn4 B6Ca NaZn13 Mn12Th MnU6 CaCu5 B12U Al6Mn α-Al2O3 La2O3 Mn2O3

Symmetry group International Schoenflies 3 4 Pn3m O4h P42/mnm D144h P3m1 D33d P63/mmc D46h I4/mmm D174h I4/mmm D174h R3m D53d P63/mmc D46h Fd3m O7h F43m or F23 T2d or T2 I4/mcm D184h Pnnm D122h R3m D53d P26m D13h Pnma D162h P6/mmm D16h R3m D53d C2/m (P2/m) C32h (C12h) P63/mmc D46h P4/nmm D74h P6222 D46 Ibam D262h Fdd2 C192v Pma2 C42v Cmcm D172h Fddd D242h I41/amd D194h Aba2 C172v Im3 T5h Fm3m O5h Pm3m O1h Pnma D162h P63/mmc D46h P63/mmc D46h Pnma D162h P3c1 D43d I4/mmm D174h I4/mmm D174h P63/mmc D46h I4/mcm D184h I4 S24 I4/mmm D174h I4/m C54h Imma D282h Aba2 C172v P4/mbm D54h Fddd D242h Pm3m O1h Fm3m O5h I4/mmm D174h I4/mcm D184h P6/mmm D16h Fm3m O5h Cmcm D172h R3c D63d P3m1 D33d Ia3 T7h

Pearson symbola 5 cP6 tP6 hP3 hP6 tI6 tI6 hR6 hP12 cF24 cF24 tI12 oP6 hR3 hP9 oP12 hP3 hR5 mC6 hP24 tP6 hP9 oI12 oF72 oP24 oC12 oF24 tI12 oC23 cI32 cF16 cP4 oP16 hP8 hP8 oP16 hP24 tI8 tI16 hP16 tI16 tI32 tI10 tI10 oI20 oC20 tP20 oF40 cP7 cF112 tI26 tI28 hP6 cF52 oC28 hR10 hP5 cI80

Standard ASTM E157-82a symbolb 6 C T H H U U R H F F U O R H O H R N H T H P S O Q S U Q B F C O H H O H U U H U U U U P Q T S C F U U H F Q R H B

4/28/05 1:54:24 PM

Symmetry of Crystals

12-9 TABLE 5. Classification of Crystals

Strukturbericht symbol 1 D58 D59 D510 D513 D5a D5c D71 D73 D7b D81 D82 D83 D84 D85 D86 D88 D89 D810 D811 D8a D8b D8e D8f D8h D8i D8l D8m D101 D102 E01 E11 E21 E24 E3 E93 E9a E9b F01 F51 F56 H11 H24 H25 L10 L12 L21 L22 L′2b L′3 L60

Section 12.indb 9

Structure name 2 S3Sb2 P2Zn3 C2C3 Al3Ni2 Si2U3 C3Pu2 Al4C3 P4Th3 B4Ta3 Fe3Zn10 Cu5Zn8 Al4Cu9 C6Cr23 Fe7W6 Cu15Si4 Mn5Si3 Co9S8 Al8Cr5 Al5Co2 Mn23Th6 σ-phase of Cr-Fe (Al,Zn)49Mg32 Ge7Ir3 B5W2 B5Mo2 B3Cr5 Si3W5 C3Cr7 Fe3Th7 ClFPb CuFeS2 CaO3Ti S3Sn2 Al2CdS4 SiFe3W3 Al7Cu2Fe AlLi3N2 NiSSb CrNaS2 CuS2Sb Al2MgO4 Cu3S4V AsCu3S4 AuCu AlCu3 AlCu2Mn Sb2Tl7 H2Th Fe2N CuTi3

Symmetry group International Schoenflies 3 4 Pnma D162h P42/mmc D94h Pnma D162h P3m1 D33d P4/mbm D54h I43d T6d R3m D53d I43d T6d Immm D252h Im3m O9h I43m T3d P43m T1d Fm3m O5h R3m D53d I43m T3d P63/mcm D36h Fm3m O5h R3m C53v P63/mcm D36h Fm3m O5h p42/mnm D144h Im3 Im3m P63/mmc R3m I4/mcm I4/mcm P31c P63mc P4/nmm I42d Pm3m Pnma I4 Fd3m P4/mnc Ia3 P213 R3m or R32 Pnma Fd3m P43m Pmn21 P4/mmm Pm3m Fm3m Im3m I4/mmm P63/mmc P4/mmm

T5h O9h D46h D53d D184h D184h C43v C46v D74h D122d O1h D162h S24 O7h D64h T7h T4 D53d or D73 D162h O7h T1d C72v D14h O1h O5h O9h D174h D46h D14h

Pearson symbola 5 oP20 tP40 oP20 hP5 tP10 cI40 hR7 cI28 oI14 cI52 cI52 cP52 cF116 hR13 cI76 hP16 cF68 hR26 hP28 cF116 tP30

Standard ASTM E157-82a symbolb 6 O T O H T B R B P B B C F R B H F R H F T

cI162 cI40 hP14 hR7 tI32 tI32 hP80 hP20 tP6 tI16 cP5 oP20 tI14 cF112 tP40 cI96 cP12 hR4 oP16 cF56 cP8 oP16 tP4 cP4 cF16 cI54 tI6 hP3 tP4

B B H R U U H H T U C O U F T B C R O F C O T C F B U H T

The first letter denotes the crystal system: triclinic (a), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal (h) and cubic (c). Trigonal (rhombohedral) system is denoted by combination hR. The second letter of Pearson’s symbol denotes lattice type: primitive (P), edge-(base-) centered (C), body-centered (I) or face-centered (F). The following number denotes number of atoms in the crystal unit cell.

Standard ASTM E157-82a has the Bravais lattices designations as following: C – primitive cubic; B – body-centered cubic; F – face-centered cubic; T – primitive tetragonal; U – body-centered tetragonal; R – rhombohedral; H – hexagonal; O – primitive orthorhombic; P – body-centered orthorhombic; Q – base-centered orthorhombic; S – face-centered orthorhombic; M – primitive monoclinic; N – centered monoclinic; A – triclinic.

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Symmetry of Crystals

12-10

References 1. A. Schoenflies, Kristallsysteme und Kristallstructur, Leipzig, 1891. 2. E. S. Fedorow, Zusammenstellung der kristallographischen Resultate, Zs. Krist., 20, 1892. 3. P. Groth, Elemente der physikalischen und chemischen Krystallographie, R. Oldenbourg, München/Berlin, 1921. 4. N. V. Belov, Class Method of Deriving Space Groups of Symmetry, Trudy Instituta Kristallodraffi imeni Fedorova (Transactions of the Fedorov Inst. of Crystallography), 5, 25, 1951, in Russian. 5. W. B. Pearson, Handbook of Lattice Spacings and Structures of Metals and Alloys, Vol. 1, Pergamon Press, 1958; Vol. 2, 1967. 6. Ch. Kittel, Introduction to Solid State Physics, John Wiley & Sons, 1956. 7. G. S. Zhdanov, Fizika Tverdogo Tela (Solid State Physics), Moscow University Press, 1962, in Russian. 8. M. J. Buerger, Elementary Crystallography, John Wiley & Sons, 1963. 9. F. D. Bloss, Crystallography & Crystal Chemistry, Holt, Rinehart & Winston, 1971. 10. T. Janssen, Crystallographic Groups, North-Holland/American Elsevier, 1973. 11. M. P. Shaskolskaya, Kristallografiya (Crystallography), Vysshaya Shkola, Moscow, 1976, in Russian. 12. T. Hahn, Ed., Internat. Tables for Crystallography, Vol. A, D. Reidel Publishing, Boston, 1983. 13. Crystal Data. Determinative Tables, Volumes 1–6, 1966–1983, JCPDSIntern Centre for Diffraction Data and U.S. Dept. of Commerce. 14. R. W. G. Wyckoff, Crystal Structures, 2nd ed., Volumes 1–6, Interscience, New York, 1963. 15. C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids, Clarendon Press, Oxford, 1972.

Section 12.indb 10

16. International Tables for Crystallography. Volume A, Space–Group Symmetry, T. Hahn, Ed., 1989; Volume B, Reciprocal Space, U. Schmueli, Ed.; Volume C, Mathematical, Physical and Chemical Tables, A. J. C. Wilson, Ed., Kluwer Academic Publishers, Dordrecht, 1989. 17. G. R. Desiraju, Crystal Engineering: The Design of Organic Solids, Elsevier, Amsterdam, 1989. 18. M. Senechal, Crystalline Symmetries: An Informal Mathematical Introduction, Adam Hilger Publ., Bristol, 1990. 19. C. Hammond, Introduction to Crystallography, Oxford University Press, 1990. 20. N.W. Alcock, Bonding and Structure: Structural Principles in Inorganic and Organic Chemistry, Ellis Norwood Publ., 1990. 21. T. C. W. Mak and G. D. Zhou. Crystallography in Modern Chemistry: A Resource Book of Crystal Structures, Wiley–Interscience, New York, 1992. 22. S. C. Abrahams, K. Mirsky, and R. M. Nielson, Acta Cryst, B52, 806 (1996); B52, 1057 (1996). 23. C. Marcos, A. Panalague, D. B. Morciras, S. Garcia-Granda and M. R. Dias. Acta Cryst, B52, 899 (1996). Crystallographic Computing 24. A. C. Larson, Crystallographic Computing, Manksgaard, Copenhagen, 1970. 25. G. M. Sheldrick, SHELXS86. Crystallographic Computing 3, Clarendon Press, Oxford, 1986; SHELXL93. Program for the Refinement of Crystal Structures, University of Göttingen Press, 1993. 26. Inorganic Crystal Structure Database, CD–ROM. Sci. Inf. Service. E-mail: SISI@Delphi.com.

4/28/05 1:54:27 PM

IONIC RADII IN CRYSTALS Ionic radii are a useful tool for predicting and visualizing crystal structures. This table lists a set of ionic radii Ri in Å units for the most common coordination numbers CN of positive and negative ions. The values are based on experimental crystal structure determinations, supplemented by empirical relationships, and theoretical calculations. The notation sq after the coordination number indicates a square configuration, while py indicates pyramidal. Ion

Anions F-1 Cl-1 Br-l I-l OH-1 O

-2

S Se-2 Te-2 Cations Ac+3 Ag+1 -2

Ag+2 Al+3

Am+3 Am+4 As+3 As+5 Au+1 Au+3 Ba+2

Be+2 Bi+3

Bi+5 Bk+3 Bk+4 Br+5 Br+7 C+4 Ca+2

Ri/Å

6 6 6 6 4 6 2 6 8 6 6 6

1.33 1.81 1.96 2.20 1.35 1.37 1.21 1.40 1.42 1.84 1.98 2.21

6 4 6 8 4sq 6 4 5 6 6 8 6 8 6 4 6 6 4sq 6 6 8 12 4 6 5 6 8 6 6 6 8 3py 4 6 4 6 6

1.12 1.00 1.15 1.28 0.79 0.94 0.39 0.48 0.54 0.98 1.09 0.85 0.95 0.58 0.34 0.46 1.37 0.64 0.85 1.35 1.42 1.61 0.27 0.45 0.96 1.03 1.17 0.76 0.96 0.83 0.93 0.31 0.25 0.39 0.15 0.16 1.00

Ion

Cd+2

Ce+4

Cf+3 Cf+4 Cl+5 Cl+7 Cm+3 Cm+4 Co+2

Co+3 Cr+2 Cr+3 Cr+4 Cr+6 Cs+1

Cu+1

Cu+2 Dy+2 Dy+3 Er

Eu+2

The advice of Howard T. Evans and Marvin J. Weber in preparing this table is appreciated.

References

1. Shannon, R. D., Acta Crystallogr. A32, 751, 1976. 2. Jia, Y. Q., J. Solid State Chem. 95, 184, 1991.

CN 8 10 12 4 6 8 12 6 8 10 12 6 8 10 12 6 6 8 3py 4 6 6 8 4 6 8 6 6 6 4 6 4 6 6 8 10 12 2 4 6 4sq 6 6 8 6 8 6 8 6 8 10

Ri/Å 1.12 1.23 1.34 0.78 0.95 1.10 1.31 1.01 1.14 1.25 1.34 0.87 0.97 1.07 1.14 0.95 0.82 0.92 0.12 0.08 0.97 0.85 0.95 0.56 0.65 0.90 0.55 0.73 0.62 0.41 0.55 0.26 0.44 1.67 1.74 1.81 1.88 0.46 0.60 0.77 0.57 0.73 1.07 1.19 0.91 1.03 0.89 1.00 1.17 1.25 1.35

Ion Eu+3 F+7 Fe+2

Fe+3

Fr+1 Ga+3 Gd+3 Ge+2 Ge+4 Hf+4

Hg+1 Hg+2

I+5 I+7 In+3 Ir+3 Ir+4 Ir+5 K+1

La+3

Li+1

Lu+3 Mg+2

Mn+2

CN 6 8 6 4 6 8 4 6 8 6 4 6 6 8 6 4 6 4 6 8 6 2 4 6 8 3py 6 4 6 4 6 6 6 6 4 6 8 12 6 8 10 12 4 6 8 6 8 4 6 8 4

Ri/Å 0.95 1.07 0.08 0.63 0.61 0.92 0.49 0.55 0.78 1.80 0.47 0.62 0.94 1.05 0.73 0.39 0.53 0.58 0.71 0.83 1.19 0.69 0.96 1.02 1.14 0.44 0.95 0.42 0.53 0.62 0.80 0.68 0.63 0.57 1.37 1.38 1.51 1.64 1.03 1.16 1.27 1.36 0.59 0.76 0.92 0.86 0.97 0.57 0.72 0.89 0.66

12-11

Section 12.indb 11

4/28/05 1:54:30 PM

Ionic Radii in Crystals

12-12 Ion

Mn+3 Mn+4 Mn+5 Mn+6 Mn+7 Mo+3 Mo+4 Mo+5 Mo+6

N+3 N+5 Na+1

Nb+3 Nb+4 Nb+5

Nd+3

Ni+2 Ni+3 Np+3 Np+4 Np+5 Np+6 Os+4 Os+5 Os+6 Os+8 P+5 Pa+3 Pa+4 Pa+5 Pb+2

Pb+4

Pd+2 Pd Pd+4 Pm+3 +3

Po+4

Section 12.indb 12

CN 6 8 6 4 6 4 4 4 6 6 4 6 4 6 7 6 6 4 6 8 9 12 6 8 6 4 6 8 6 8 9 12 4sq 6 6 6 6 6 6 6 6 6 4 4 6 6 6 6 6 8 10 12 4 6 8 4sq 6 6 6 6 8 6

Ri/Å 0.83 0.96 0.58 0.39 0.53 0.33 0.26 0.25 0.69 0.65 0.46 0.61 0.41 0.59 0.73 0.16 0.13 0.99 1.02 1.18 1.24 1.39 0.72 0.79 0.68 0.48 0.64 0.74 0.98 1.12 1.16 1.27 0.49 0.69 0.56 1.01 0.87 0.75 0.72 0.63 0.58 0.55 0.39 0.17 0.38 1.04 0.90 0.78 1.19 1.29 1.40 1.49 0.65 0.78 0.94 0.64 0.86 0.76 0.62 0.97 1.09 0.97

Ion Pr+3 Pr+4 Pt+2 Pt+4 Pu+3 Pu+4 Pu+5 Pu+6 Ra+2 Rb+1

Re+4 Re+5 Re+6 Re+7 Rh+3 Rh+4 Rh+5 Ru+3 Ru+4 Ru+5 Ru+7 Ru+8 S+4 S+6 Sb+3 Sb+5 Sc+3 Se+4 Se+6 Si+4 Sm+2 Sm+3

Sn+4

Sr+2

Ta+3 Ta+4 Ta+5 Tb+3 Tb+4

CN 6 8 6 8 4sq 6 6 6 6 6 6 8 12 6 8 10 12 6 6 6 4 6 6 6 6 6 6 6 4 4 6 4 6 4py 6 6 6 8 6 4 6 4 6 6 8 6 8 12 4 6 8 6 8 10 12 6 6 6 6 8 6 8

Ri/Å 0.99 1.13 0.85 0.96 0.60 0.80 0.63 1.00 0.86 0.74 0.71 1.48 1.70 1.52 1.61 1.66 1.72 0.63 0.58 0.55 0.38 0.53 0.67 0.60 0.55 0.68 0.62 0.57 0.38 0.36 0.37 0.12 0.29 0.76 0.76 0.60 0.75 0.87 0.50 0.28 0.42 0.26 0.40 1.19 1.27 0.96 1.08 1.24 0.55 0.69 0.81 1.18 1.26 1.36 1.44 0.72 0.68 0.64 0.92 1.04 0.76 0.88

Ion Tc+4 Te+4 Te+6 Th+4

Ti+2 Ti+3 Ti+4

Tl+1

Tl+3

Tm+2 Tm+3 U+3 U+4

U+5 U+6

V+2 V+3 V+4

V+5

W+4 W+5 W+6

Y+3

Yb+2 Yb+3 Zn+2

Zr+4

CN 6 4 6 4 6 6 8 10 12 6 6 4 6 8 6 8 12 4 6 8 6 7 6 8 6 6 8 12 6 2 4 6 8 6 6 5 6 8 4 5 6 6 6 4 5 6 6 8 9 6 8 8 9 4 6 8 4 6 8 9

Ri/Å 0.65 0.66 0.97 0.43 0.56 0.94 1.05 1.13 1.21 0.86 0.67 0.42 0.61 0.74 1.50 1.59 1.70 0.75 0.89 0.98 1.01 1.09 0.88 0.99 1.03 0.89 1.00 1.17 0.76 0.45 0.52 0.73 0.86 0.79 0.64 0.53 0.58 0.72 0.36 0.46 0.54 0.66 0.62 0.42 0.51 0.60 0.90 1.02 1.08 1.02 1.14 0.99 1.04 0.60 0.74 0.90 0.59 0.72 0.84 0.89

4/28/05 1:54:33 PM

POLARIZABILITIES OF ATOMS AND IONS IN SOLIDS H. P. R. Frederikse The polarization of a solid dielectric medium, P, is defined as the dipole moment per unit volume averaged over the volume of a crystal cell. A component of P can be expanded as a function of the electric field E: Pi = ∑ a j E j + ∑ bjk E j Ek j

For relatively small electric fields in isotropic substances P = χeE, where χe is the electric susceptibility. If the medium is made up of N atoms (or ions) per unit volume, the polarization is P = N pm where pm is the average dipole moment per atom. The polarizability α can be defined as pm = αE0 , where E0 is the local field at the position of the atom. Using the Lorentz method to calculate the local field one finds: P = N α ( E + 4 πP ) = χ e E

Together with the definition of the dielectric constant (relative permittivity), ε = 1+ 4πχe, this leads to: α=

3  ε − 1    4 πN  ε + 2 

2. Ionic polarization occurs in ionic materials because the electric field displaces cations and anions in opposite directions: Pi = NαiE0, where αi is the ionic polarizability. 3. Orientational polarization can occur in substances composed of molecules that have permanent electric dipoles. The alignment of these dipoles depends on temperature and leads to an orientational polarizability per molecule: αor = p2/3kT, where p is the permanent dipole moment per molecule, k is the Boltzmann constant, and T is the temperature. Because of the different nature of these three polarization processes the response of a dielectric solid to an applied electric field will strongly depend on the frequency of the field. The resonance of the electronic excitation in insulators (dielectrics) takes place in the ultraviolet part of the spectrum; the characteristic frequency of the lattice vibrations is located in the infrared, while the orientation of dipoles requires fields of much lower frequencies (below 1010 Hz). This response to electric fields of different frequencies is shown in Figure 1. Values of the electronic polarizabilities for selected atoms and ions are given in Table 1.

References

This expression is known as the Clausius-Mossotti equation. The total polarization associated with atoms, ions, or molecules is due to three different sources: 1. Electronic polarization arises because the center of the local electronic charge cloud around the nucleus is displaced under the action of the field: Pe = NαeE0 where αe is the electronic polarizability.

1. Kittel, C., Introduction to Solid State Physics, Fourth Edition, John Wiley & Sons, New York, 1971. 2. Lerner, R.G., and Trigg, G.L., Eds., Encyclopedia of Physics, Second Edition, VCH Publishers, New York, 1990. 3. Ralls, K.M., Courtney, T.H., and Wulff, J., An Introduction to Materials Science and Engineering, John Wiley & Sons, New York, 1976.

Real part of polarizability

Orientation

Ionic

Electronic

Frequency 1MHz

1GHz

1THz

1PHz

FIGURE 1. Schematic graph of the frequency dependence of the different contributions to polarizability.

12-13

Section 12.indb 13

4/28/05 1:54:38 PM

Polarizabilities of Atoms and Ions in Solids

12-14

TABLE 1. Electronic Polarizabilities in Units of 10–24 cm3 He 0.201 Li+ 0.029

Be2+ 0.008

B3+ 0.003

C4+ 0.0013

O2– 3.88

F– 1.04

Ne 0.39

Na+ 0.179

Mg2+ 0.094

Al3+ 0.052

Si4+ 0.0165

S2– 10.2

Cl– 3.66

Ar 1.62

K+ 0.83

Ca2+ 0.47

Sc3+ 0.286

Ti4+ 0.185

Se2– 10.5

Br– 4.77

Kr 2.46

Rb+ 1.40

Sr2+ 0.86

Y3+ 0.55

Zr4+ 0.37

Te2– 14.0

I– 7.1

Xe 3.99

Cs+ 2.42

Ba2+ 1.55

La3+ 1.04

Ce4+ 0.73

Data from Pauling, L., Proc. R. Soc. London, A114, 181, 1927. See also Jaswal, S.S. and Sharma, T.P., J. Phys. Chem. Solids, 34, 509, 1973. Values are appropriate for cgs units. To convert to SI, use the relation α(SI)/C m2V–1 = 1.11265.10–16 α(cgs)/cm3

Section 12.indb 14

4/28/05 1:54:39 PM

CRYSTAL STRUCTURES AND LATTICE PARAMETERS OF ALLOTROPES OF THE ELEMENTS H. W. King The crystal structures of the allotropic forms of the elements are presented in terms of the Pearson symbol, the Strukturbericht designation, and the prototype of the structure. The temperatures of the phase transformations are listed in degrees Celsius and the pressures are in the Gpa. A consistent nomenclature is used, whereby all allotropes are labeled by Greek letters. The lattice parameters of the units cells are given in nanometers (nm) and are considered to be accurate to ±2 in the last reported digit. This compilation is restricted to changes in crystal structures that occur as a result of a change in temperature or pressure. Low-

Element Ac Ag αAl βAl α´Am αAm βAm γAm αAr (βAr) αAs єAs Au βΒ αΒa βΒa γΒa αΒe βΒe γΒe αΒi βΒi γΒi σΒi єΒi ζΒi αΒk βΒk Βr C (graphite) C (diamond) C (hd) αCa βCa γCa Cd αCe βCe γCe δ-Ce α´Ce

temperature structures are included for the diatomic and rare gases, which show many similarities with respect to the metallic elements. The elements identified with an asterisk (*) have polymorphic structures based on different molecular configurations. The crystal data given for these elements refer to the most stable structure at room temperature. Reprinted with the permission of ASM International from T.Β. Massalski, Ed., Βinary Alloy Phase Diagrams, ASM International, Metals Park, Ohio, 1986; certain data on rare earth elements were provided by K.A. Gschneidner.

Temperature, °C 25 25 25 25 25 >769 >1074 25 <-189.35 <-189.40 25 >448 25 25 25 25 25 25 >1270 25 25 25 25 25 25 25 25 >977 <7.25 25

Pressure, GPa atm atm atm >20.5 atm atm atm >15 atm atm atm atm atm atm atm >5.33 >23 atm atm >9.3 atm >2.6 >3.0 >4.3 >6.5 >9.0 atm atm atm atm

Pearson symbol cF4 cF4 cF4 hP2 hP4 cF4 cI2 oC4 cF4 hP2 hR2 oC8 cF4 hR105 cI2 hP2 ? hP2 cI2 ? hR2 mC4 mP3 ? ? cI2 hP4 cF4 oC8 hP4

Space group Fm3m Fm3m Fm3m P63 /mmc P63/mmc Fm3m Im3m Cmcm Fm3m P63 /mmc R3m Cmca Fm3m R3m Im3m P63 /mmc ? P63 /mmc Im3m … r3m C2/m ? ? ? Im3m P63 /mmc Fm3m Cmca P63 /mmc

Strukturbericht designation Al A1 A1 A3 A3´ A1 A2 A20 A1 A3 A7 … A1 … A2 A3 … A3 A2 … A7 … … … … A2 A3´ A1 … A9

Prototype Cu Cu Cu Mg αLa Cu W αU Cu Mg αAs P(black) Cu βΒ W Mg … Mg W … αAs βBi … … … W αLa Cu Cl C (graphite)

0.5311 0.40857 0.40496 0.2693 0.34681 0.4894 ? 0.3063 0.5316 0.3760 0.41319 0.362 0.40782 1.017 0.50227 0.3901 … 0.22859 0.25515 … 0.47460 0.6674 0.605 … … 0.3800 0.3416 0.4997 0.668 0.24612

>60

cF8

Fd3m

C (diamond)

0.35669

25 25 >443 25 25 <-177 25 25 >726 25

HP atm atm >1.5 atm atm atm atm atm >5.4

hP4 cF4 cI2 ? hP2 cF4 hP4 cF4 cI2 oC4

P63 /mmc Fm3m Im3m … P63 /mmc Fm3m P63 /mmc Fm3m Im3m Cmcm

… A1 A2 … A3 A1 A3´ A1 A2 A20

C (hd) Cu W … Mg Cu αLa Cu W αU

0.2522 0.55884 0.4480 … 0.29793 0.485 0.36810 0.51610 0.412 0.3049

Lattice parameters, nm a

b … … … … … … … 0.5968 … … … 1.085 … … … … … … … … … 0.6117 0.42 … … … … … 0.449 … … … … … … … … … … … 0.5998

c … … … 0.4398 1.1241 … … 0.5169 … 0.6141 …… 0.448 … … … 0.6154 … 0.35845 … … … 0.3304 0.465 … … … 1.1069 … 0.874 0.6709 … 0.4119 … … … 0.56196 … 1.1857 … … 0.5215

Comment, c/a or α or β … … … 1.6331 2*1.621 … … … … 1.633 α = 54.12o … … α = 65.12o … 1.5775 … 1.5681 … … α = 57.23o β = 110.33o β = 85.33o … … … 2*1.620 … … 2.7258 … 1.633 … … … 1.8862 … 2*1.611 … … …

12-15

Section 12.indb 15

4/28/05 1:54:41 PM

Crystal Structures and Lattice Parameters of Allotropes of the Elements

12-16

Element αCf βCf Cl αCm βCm єCo αCo αCr α´Cr aCs βCs β´Cs γCs Cu α´Dy αDy βDy γDy Er αEs βEs Eu αF βF αFe γFe σFe єFe αGa βGa γGa αGd βGd γGd αGe βGe γGe σGe αH βH αHe βHe γHe αHf βHf αHg βHg γHg αHo βHo I In Ir K Kr αLa βLa γLa β´La αLi

Section 12.indb 16

Temperature, °C 25 >590 <-102 25 >1277 25 >422 25 25 25 25 25 25 25 <-187 25 >1381 25 25 25 ? 25 <-227.6 <-219.67 25 >912 >1394 25 25 25 -53 25 >1235 25 25 25 25 LT <-271.9 <-259.34 <-268.94 >-258 <-271.47 25 >1995 <-38.84 <-194 <-194 25 25 25 25 25 25 <-157.39 25 >310 >865 25 <-193

Pressure, GPa atm atm atm atm atm atm atm atm HP atm >2.37 >4.22 >4.27 atm atm atm atm >7.5 atm atm atm atm atm atm atm atm atm >13 atm >1.2 >3.0 atm atm >3.0 atm >12 >12→atm >12 atm atm atm 0.125 0.03 atm atm atm HP c.w. atm >7.5 atm atm atm atm atm atm atm atm >2.0 atm

Pearson symbol hP4 cF4 oC8 hP4 cF4 hP2 cF4 cI2 tI2 cI2 cF4 cF4 ? cF4 oC4 hP2 cI2 hR3 hP2 hP4 cF4 cI2 mC8 cP16 cI2 cF4 cI2 hP2 oC8 tI2 oC40 hP2 cI2 hR3 cF8 tI4 tP12 cI16 cF4 hP2 hP2 cF4 cI2 hP2 cl2 hR1 tI2 hR1 hP2 hR3 oC8 tI2 cF4 cI2 cF4 hP4 cF4 cI2 cF4 hP2

Space group P63 /mmc Fm3m Cmca P63 /mmc Fm3m P63 /mmc Fm3m Im3m I4/mmm Im3m Fm3m Fm3m … Fm3m Cmcm P63 /mmc Im3m R3m P63 /mmc P63 /mmc Fm3m Im3m C2/c Pm3n Im3m Fm3m Im3m P63 /mmc Cmca I4/mmm Cmcm P63 /mmc Im3m R3m Fd3m I41/amd P41212 Im3m Fm3m P63 /mmc P63 /mmc Fm3m Im3m P63 /mmc Im3m R3m I4/mmm ? P63 /mmc R3m Cmca I4/mmm Fm3m Im3m Fm3m P63 /mmc Fm3m Im3m Fm3m P63 /mmc

Strukturbericht designation A3´ A1 … A3´ A1 A3 A1 A2 … A2 A1 A1 … A1 … A3 A2 … A3 A3´ A1 A2 … … A2 A1 A2 A3 A11 A6 … A3 A2 … A4 A5 … … A1 A3 A3 A1 A2 A3 A2 A10 … … A3 … … A6 A1 A2 A1 A3´ A1 A2 A1 A3

Lattice parameters, nm Prototype αLa Cu Cl αLa Cu Mg Cu W α´Cr W Cu Cu … Cu α´Dy Mg W αSm Mg αLa Cu W αF γO W Cu W Mg αGa In γGa Mg W αSm C (diamond) βSn σGe γSi Cu Mg Mg Cu W Mg W αHg βHg … Mg αSm Cl In Cu W Cu αLa Cu W Cu Mg

a 0.339 ? 0.624 0.3496 0.4382 0.25071 0.35447 0.28848 0.2882 0.6141 0.6465 0.5800 … 0.36146 0.3595 0.35915 0.403 0.3436 0.35592 ? ? 0.45827 0.550 0.667 0.28665 0.36467 0.29315 0.2468 0.45186 0.2808 1.0593 0.36336 0.406 0.361 0.56574 0.4884 0.593 0.692 0.5338 0.3776 0.3555 0.4240 0.4110 0.31946 0.3610 0.3005 0.3995 … 0.35778 0.334 0.72697 0.3253 0.38392 0.5321 0.5810 0.37740 0.5303 0.426 0.517 0.3111

b … … 0.448 … … … … … … … … … … … 0.6184 … … … … … … … 0.338 … … … … … 0.76570 … 1.3523 … … … … … … … … … … … … … … … … … … … 0.47903 … … … … … … … … …

c 1.1015 … 0.826 1.1331 … 0.40686 … … 0.2887 … … … … … 0.5678 0.56501 … 2.483 0.55850 … … … 0.728 … … … … 0.396 0.45258 0.4458 0.5203 0.57810 … 2.603 … 0.2692 0.698 … … 0.6162 0.5798 … … 0.50510 … … 0.2825 … 0.56178 2.45 0.97942 0.49470 … … … 1.2171 … … … 0.5093

Comment, c/a or α or β 2*1.625 … … 2*1.621 … 1.6228 … … 1.002 … … … … … … 1.5732 … 4.5*1.606 1.5692 … … … β = 102.17o … … … … 1.603 … 1.588 … 0.5910 … 4*1.60 … 0.551 1.18 … … 1.632 1.631 … … 1.5811 … α = 70.53o 0.707 … 1.5702 4.5*1.63 … 1.5210 … … … 2*1.6125 … … … 1.637

4/28/05 1:54:45 PM

Crystal Structures and Lattice Parameters of Allotropes of the Elements

Element βLi γLi Lu Mg αMn βMn γMn σMn Mo αN βN γN αNa βNa Nb αNd βNd γNd Ne Ni αNp βNp γNp αO βO γO Os P (black) αPa βPa αPb βPb Pd αPm βPm αPo βPo αPr βPr γPr Pt αPu βPu γPu σPu σ´Pu єPu Ra αRb βRb γRb Re Rh Ru αS αSb βSb γSb σSb αSc

Section 12.indb 17

Temperature, °C 25 <-201 25 25 25 >710 >1079 >1143 25 <-237.6 <-210.00 <-253 <-233 25 25 25 >863 25 <-243.59 25 25 >280 >576 <-243.3 <-229.6 <-218.79 25 25 25 >1170 25 25 25 25 >890 25 >54 25 >795 25 25 25 >125 >215 >320 >463 >483 25 25 25 25 25 25 25 25 25 25 25 25 25

Pressure, GPa atm c.w. atm atm atm atm atm atm atm atm atm >3.3 atm atm atm atm atm >5.0 atm atm atm atm atm atm atm atm atm atm atm atm atm >10.3 atm atm atm atm atm atm atm >4.0 atm atm atm atm atm atm atm atm atm >1.08 >2.05 atm atm atm atm atm >5.0 >7.5 >14.0 atm

Pearson symbol cI2 cF4 hP2 hP2 cl58 cP20 cF4 cI2 cI2 cP8 hP4 tP4 hP2 cI2 cI2 hP4 cI2 cF4 cF4 cF4 oP8 tP4 cI2 mC4 hR2 cP16 hP2 oC8 tI2 cI2 cF4 hP2 cF4 hP4 cI2 cP1 hR1 hP4 cI2 cF4 cF4 mP16 mI34 oF8 cF4 tI2 cI2 cI2 cI2 ? ? hP2 cF4 hP2 oF128 hR2 cP1 hP2 mP3 hP2

Space group Im3m Fm3m P63 /mmc P63 /mmc I43m P4132 Fm3m Im3m Im3m Pa3 P63 /mmc P42 /mnm P63 /mmc Im3m Im3m P63 /mmc Im3m Fm3m Fm3m Fm3m Pnma P4212 Im3m C2m R3m Pm3n P63 /mmc Cmca I4/mmm Im3m Fm3m P63 /mmc Fm3m P63 /mmc Im3m Pm3m R3m P63 /mmc Im3m Fm3m Fm3m P21/m I2/m Fddd Fm3m I4/mmm Im3m Im3m lm3m … … P63 /mmc Fm3m P63/mmc Fddd R3m Pm3m P63 /mmc ? P63 /mm

Strukturbericht designation A2 A1 A3 A3 A12 A13 A1 A2 A2 … … … A3 A2 A2 A3´ A2 A1 A1 A1 Ac Ad A2 … … … A3 … Aa A2 A1 A3 A1 A3´ A2 Ah … A3´ A2 A1 A1 … … … A1 A6 A2 A2 A2 … … A3 A1 A3 A16 A7 Ah A3 … A3

12-17 Lattice parameters, nm

Prototype W Cu Mg Mg αMn βMn Cu W W αN βN γN Mg W W αLa W Cu Cu Cu αNp βNp W αO βO γO Mg P (black) αPa W Cu Mg Cu αLa W αPo βPo αLa W Cu Cu αPu βPu γPu Cu In W W W … … Mg Cu Mg αS αAs αPo Mg … Mg

a 0.35093 0.4388 0.35052 0.32094 0.89126 0.63152 0.3860 0.3080 0.31470 0.5661 0.4050 0.3957 0.3767 0.42906 0.33004 0.36582 0.413 0.480 0.4462 0.35240 0.6663 0.4883 0.352 0.5403 0.4210 0.683 0.27341 0.33136 0.3921 0.381 0.49502 0.3265 0.38903 0.365 (0.410) 0.3366 0.3373 0.36721 0.413 0.488 0.39236 0.6183 0.9284 0.31587 0.46371 0.33261 0.36343 0.5148 0.5705 … … 0.27609 0.38032 0.27058 1.0464 0.45067 0.2992 0.3376 0.556 0.33088

b … … … … … … … … … … … … … … … … … … … … 0.4723 … … 0.3429 … … … 1.0478 … … … … … … … … … … … … … 0.4822 1.0463 0.57682 … … … … … … … … … … 1.28660 … … … 0.404 …

c … … 0.55494 0.52107 … … … … … … 0.6604 0.5109 0.6154 … … 1.17966 … … … … 0.4887 0.3389 … 0.5086 … … 0.43918 0.43763 0.3235 … … 0.5387 … 1.165 … … … 1.18326 … … … 1.0963 0.7859 1.0162 … 0.44630 … … … … … 0.4458 … 0.42816 2.44860 … … 0.5341 0.422 0.52680

Comment, c/a or α or β … … 1.5832 1.6236 … … … … … … 1.631 1.291 1.634 … … 2*1.6124 … … … … … 0.694 … β = 132.53o α = 46.27o … 1.6063 … 0.825 … … 1.650 … 2*1.60 … … α = 98.08o 2*1.6111 … … … β = 101.97o β = 92.13o … … 1.3418 … … … … … 1.6145 … 1.5824 … α = 57.11o … 1.582 β = 86.0o 1.5921

4/28/05 1:54:47 PM

Crystal Structures and Lattice Parameters of Allotropes of the Elements

12-18

Element βSc γSe αSi βSi γSi σSi αSm βSm γ´Sm σSm αSn βSn γSn αSr βSr β´Sr Ta α´Tb aTb βTb γTb Tc αTe βTe γTe αTh βTh αTi βTi ωTi αTl βTl γTl Tm αU βU γU V W Xe αY βY αYb βYb γYb Zn αZr βZr ωZr

Section 12.indb 18

Temperature, °C >1337 25 25 25 25 25 25 >734 >922 25 <13 25 25 25 >547 25 25 <-53 25 >1289 25 25 25 25 25 25 >1360 25 >882 25 25 >230 25 25 25 >668 >776 25 25 <-111.76 25 >1478 <-3 25 >795 25 25 >863 25

Pressure, GPa atm atm atm >9.5 >16.0 >16→atm atm atm atm >4.0 atm atm >9.0 atm atm >3.5 atm atm atm atm >6.0 atm atm >2.0 >7.0 atm atm atm atm HP→atm atm atm HP atm atm atm atm atm atm atm atm atm atm atm atm atm atm atm HP→atm

Pearson symbol cI2 hP3 cF8 tI4 cI16 hP4 hR3 hP2 cI2 hP4 cF8 tI4 tI2 cF4 cI2 cI2 cI2 oC4 hP2 cI2 hR3 hP2 hP3 hR2 hR1 cF4 cl2 hP2 cl2 hP3 hP2 cI2 cF4 hP2 oC4 tP30 cI2 cI2 cI2 cF4 hP2 cI2 hP2 cF4 cI2 hP2 hP2 cI2 hP2

Space group Im3m P3121 Fd3m I41/amd Im3m P63 /mmc R3m P63 /mmc Im3m P63 /mmc Fd3m I41/amd ? Fm3m Im3m Im3m Im3m Cmcm P63 /mmc Im3m R3m P63 /mmc P3121 R3m R3m Fm3m Im3m P63 /mmc Im3m P6/mmm P63 /mmc Im3m Fm3m P63 /mmc Cmcm P42 /mnm Im3m Im3m Im3m Fm3m P63/mmc Im3m P63 /mmc Fm3m Im3m P63 /mmc P63 /mmc Im3m P6/mmm

Strukturbericht designation A2 A8 A4 A5 … A3´ … A3 A2 A3´ A4 A5 … A1 A2 A2 A2 … A3 A2 … A3 A8 A7 … A1 A2 A3 A2 … A3 A2 A1 A3 A20 Ab A2 A2 A2 A1 A3 A2 A3 A1 A2 A3 A3 A2 …

Lattice parameters, nm Prototype W γSe C (diamond) βSn γSi αLa αSm Mg W αLa C (diamond) βSn γSn Cu W W W α´Dy Mg W αSm Mg γSe αAs βPo Cu W Mg W ωTi Mg W Cu Mg αU βU W W W Cu Mg W Mg Cu W Mg Mg W ωTi

a (0.373) 0.43659 0.54306 0.4686 0.6636 0.380 0.36290 0.36630 (0.410) 0.3618 0.64892 0.58318 0.370 0.6084 0.487 0.4437 0.33030 0.3605 0.36055 (0.407) 0.341 0.2738 0.44566 0.469 0.3002 0.50842 0.411 0.29506 0.33065 0.4625 0.34566 0.3879 ? 0.35375 0.28537 1.0759 0.3524 0.30240 0.31652 0.6350 0.36482 (0.410) 0.38799 0.54848 0.444 0.26650 0.32316 0.36090 0.5036

b … … … … … … … … … … … … … … … … … 0.6244 … … … … … … … … … … … … … … … … 0.58695 … … … … … … … … … … … … … …

c … 0.49537 … 0.2585 … 0.628 2.6207 0.58448 … 1.166 … 0.31818 0.337 … … … … 0.5706 0.56966 … 2.45 0.4393 0.59264 … … … … 0.46835 … 0.2813 0.55248 … … 0.55540 0.49548 0.5656 … … … … 0.57318 … 0.63859 … … 0.49470 0.51475 … 0.3109

Comment, c/a or α or β … 1.1346 … 0.552 … 1.653 4*1.6048 1.5956 … 2*1.611 … 0.5456 0.91 … … … … … 1.5800 … 4*1.60 1.604 1.3298 α = 53.30o α = 103.3o … … 1.59873 … 0.6082 1.5983 … … 1.5700 … 0.526 … … … … 1.5711 … 1.6459 … … 1.8563 1.5929 … 0.617

4/28/05 1:54:49 PM

LATTICE ENERGIES H. D. B. Jenkins and H. K. Roobottom THERMOCHEMICAL CYCLE AND CALCULATED VALUES

METHOD OF ESTIMATION OF VALUES NOT TABULATED

Table 1 contains calculated values of the lattice energies (total lattice potential energies), UPOT , of crystalline salts, MaXb. UPOT is expressed in units of kilojoules per mole, kJ mol–1. M and X can be either simple or complex ions. Substances are arranged by chemical class. Also listed in the table is the lattice energy, UPOTBFHC, obtained from the application of the Born - Fajans - Haber cycle (BHFC) described below, using the “Standard Thermochemical Properties of Chemical Substances” table in Section 5 of this Handbook, References 1 through 4, and certain other data which are given in Table 3 below. The lattice enthalpy, ∆HL, is given by the cycle:

In cases where the lattice energy is not tabulated and we want to furnish an estimate, then the Kapustinskii equation5 can be used to obtain a value (in kJ mol–1): U POT =

121.4 z a z b v  0.0345  1 −  (ra + rb )  (ra + rb )

where za and zb are the moduli of the charges on the v ions in the lattice and ra and rb (in nm) are the thermochemical radii given in Table 2. The ra for metal ions is taken to be the Goldschmidt6 radius. To cite an example, if we wish to estimate the lattice energy of the salt [NH+4][HF–2] using the above procedure, we see that Table 2 gives the thermochemical radius (ra ) for NH+4 to be 0.136 nm and that for HF–2 (rb ) to be 0.172 nm. The lattice potential energy is then estimated to be 700 kJ mol–1 compared with the calculated value of 705 kJ mol–1 and the Born - Fajans - Haber cycle value of 658 kJ mol–1.

References

where (ss) is the standard state of the element concerned. The lattice enthalpy, ∆HL, is obtained using the equation: ∆H L = a∆f H o (M b+ , g ) + b∆f H o (X a− , g ) − ∆f H o (M a X b , c)

and is futher related to the total lattice potential energy, UPOT, by the relationship:  n n   ∆H L = U POT +  a  M − 2 + b  X − 2 RT   2 2  

where nM and nX equal 3 for monatomic ions, 5 for linear polyatomic ions and 6 for polyatomic non-linear ions.

1. Wagman, D. D., Evans, W. H., Parker, V. B., Schumm, R. H., Halow, I., Bailey, S. M., Churney, K. L., and Nuttall, R. L., The NBS Tables of Chemical Thermodynamic Properties, J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 2, 1982. 2. Chase, M. W., Davies, C. A., Downey, J. R., Frurip, D. J., McDonald, R. A., and Syverud, A. N., JANAF Thermochemical Tables, Third Edition, J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, 1985. 3. Lias, S. G., Bartmess, J. E., Liebman, J. F., Holmes, J. L., Levin, R. D., and Mallard, W. G., Gas-Phase Ion and Neutral Thermochemistry, J. Phys. Chem. Ref. Data, Vol. 17, Suppl. 1, 1988. 4. Jenkins, H. D. B., and Pratt, K. F., Adv. Inorg. Chem. Radiochem., 22, 1, 1978. 5. Kapustinskii, A. F., Quart. Rev., 10, 283-294, 1956. 6. Goldschmidt, V. M., Skrifter Norske Videnskaps-Akad. Oslo, I, Mat.Naturn. Kl, 1926. See also Dasent, W. E., Inorganic Energetics, 2nd ed., Cambridge University Press, 1982. 7. Jenkins, H. D. B., Roobottom, H. K., Passmore, J., and Glasser, L., J. Chem. Education, in press.

12-19

Section 12.indb 19

4/28/05 1:54:53 PM

Lattice Energies

12-20 Table 1. Lattice Energies (kJ mol –1) Substance Acetates Li(CH3COO) Na(CH3COO) K(CH3COO) Rb(CH3COO) Cs(CH3COO)

Calc. UPOT

UPOTBHFC

– 828 749 715 682

843 807 726 – –

Acetylides CaC2 SrC2 BaC2

2911 2788 2647

2902 2782 2652

Azides LiN3 NaN3 KN3 RbN3 CsN3 AgN3 TlN3 Ca(N3)2 Sr(N3)2 Ba(N3)2 Mn(N3)2 Cu(N3)2 Zn(N3)2 Cd(N3)2 Pb(N3)2

861 770 697 674 665 854 689 2186 2056 2021 2408 2730 2840 2446 –

875 784 – 691 674 910 742 2316 2187 – 2348 2738 2970 2576 2300

Bihalide Salts LiHF2 NaHF2 KHF2 RbHF2 CsHF2 NH4HF2 CsHCl2 Me4NHCl2 Et4NHCl2 Bu4NHCl2

821 755 657 627 607 705 601 427 346 290

847 748 660 631 – 658 – – – –

Bicarbonates NaHCO3 KHCO3 RbHCO3 CsHCO3 NH4HCO3

820 741 707 678 –

656 573 522 520 577

5146 5104 5021 7447 7406 10083 7447 7447 7406 7447 5104 7489 7489 7489

– – – – – – – – – – – – – –

Borides CaB6 SrB6 BaB6 YB6 LaB6 CeB6 PrB6 NdB6 PmB6 SmB6 EuB6 GdB6 TbB6 DyB6

Section 12.indb 20

Substance HoB6 ErB6 TmB6 YbB6 LuB6 ThB6

Calc. UPOT 7489 7489 7489 5146 7489 10167

UPOTBHFC – – – – – –

Borohydrides LiBH4 NaBH4 KBH4 RbBH4 CsBH4

778 703 655 648 628

– 694 638 – –

Borohalides LiBF4 NaBF4 KBF4 RbBF4 CsBF4 NH4BF4 KBCl4 RbBCl4 CsBCl4

699 657 611 577 556 582 506 489 473

749 674 616 590 565 – 497 486 –

Carbonates Li2CO3 Na2CO3 K2CO3 Rb2CO3 Cs2CO3 MgCO3 CaCO3 SrCO3 BaCO3 MnCO3 FeCO3 CoCO3 CuCO3 ZnCO3 CdCO3 SnCO3 PbCO3

2523 2301 2084 2000 1920 3138 2804 2720 2615 3046 3121 3443 3494 3121 2929 2904 2728

2254 2016 1846 1783 1722 3122 2811 2688 2554 3092 3169 3235 – 3273 3052 – 2750

Cyanates LiNCO NaNCO KNCO RbNCO CsNCO NH4NCO

849 807 726 692 661 724

– 816 734 – – –

Cyanides LiCN NaCN KCN RbCN CsCN Ca(CN)2 Sr(CN)2 Ba(CN)2 NH4CN AgCN

874 766 692 638 601 2268 2138 2001 617 (741)

759 686 – – 2240 – 2009 691 935

4/28/05 1:54:56 PM

Lattice Energies Substance Zn(CN)2 Cd(CN)2 Formates Li(HCO2) Na(HCO2) K(HCO2) Rb(HCO2) Cs(HCO2) NH4(HCO2)

12-21 Calc. UPOT 2809 2583

UPOTBHFC 2817 2591

865 791 713 685 651 715

– 804 722 – – –

7991 7301 6987 6653

– 7306 – 6643

Halates LiBrO3 NaBrO3 KBrO3 RbBrO3 CsBrO3 NaClO3 KClO3 RbClO3 CsClO3 LiIO3 NaIO3 KIO3 RbIO3 CsIO3

883 803 740 720 694 770 711 690 – 975 883 820 791 761

880 791 722 705 681 785 721 703 679 974 876 780 – –

Halides LiF LiCl LiBr LiI NaF NaCl NaBr NaI KF KCl KBr KI RbF RbCl RbBr RbI CsF CsCl CsBr CsI FrF FrCl FrBr FrI CuCl CuBr CuI AgF AgCl AgBr

1030 834 788 730 910 769 732 682 808 701 671 632 774 680 651 617 744 657 632 600 715 632 611 582 992 969 948 953 910 897

1049 864 820 764 930 790 754 705 829 720 691 650 795 695 668 632 759 670 647 613 – – – – 996 978 966 974 918 905

Germanates Mg2GeO4 Ca2GeO4 Sr2GeO4 Ba2GeO4

Section 12.indb 21

Substance AgI AuCl AuBr AuI InCl InBr InI TlF TlCl TlBr TlI Me4NCl Me4NBr Me4NI PH4Br PH4I BeF2 BeCl2 BeBr2 BeI2 MgF2 MgCl2 MgBr2 MgI2 CaF2 CaCl2 CaBr2 CaI2 SrF2 SrCl2 SrI2 BaF2 BaCl2 BaBr2 BaI2 RaF2 RaCl2 RaBr2 RaI2 ScCl2 ScBr2 ScI2 TiF2 TiCl2 TiBr2 TiI2 VCl2 VBr2 VI2 CrF2 CrCl2 CrBr2 CrI2 MoCl2 MoBr2 MoI2 MnF2 MnCl2 MnBr2 MnI2 FeF2

Calc. UPOT 881 1013 1029 1027 – – – – 738 720 692 566 553 544 616 590 3464 3004 2950 2780 2926 2477 2406 2293 2640 2268 2132 1971 2476 2142 1984 2347 2046 1971 1862 2284 2004 1929 1803 2380 2291 2201 2724 2439 2360 2259 2607 – – 2778 2540 2377 2269 2737 2742 2630 2644 2510 2448 2212 2849

UPOTBHFC 892 1066 1059 1070 764 767 733 850 751 734 710 – – – – – 3526 3033 2914 2813 2978 2540 2451 2340 2651 2271 – 2087 2513 2170 1976 2373 2069 1995 1890 – – – – – – – – 2514 2430 2342 2593 2534 2470 2939 2601 2536 2440 2746 2753 – – 2551 2482 – 2967

4/28/05 1:54:58 PM

Lattice Energies

12-22 Substance FeCl2 FeBr2 FeI2 CoF2 CoCl2 CoBr2 CoI2 NiF2 NiCl2 NiBr2 NiI2 PdCl2 PdBr2 PdI2 CuF2 CuCl2 CuBr2 CuI2 AgF2 ZnF2 ZnCl2 ZnBr2 ZnI2 CdF2 CdCl2 CdBr2 CdI2 HgF2 HgCl2 HgBr2 HgI2 SnF2 SnCl2 SnBr2 SnI2 PbF2 PbCl2 PbBr2 PbI2 ScF3 ScCl3 ScBr3 ScI3 YF3 YCl3 YI3 TiF3 TiCl3 TiBr3 TiI3 ZrCl3 ZrBr3 ZrI3 VF3 VCl3 VBr3 VI3 NbCl3 NbBr3 NbI3 CrF3

Section 12.indb 22

Calc. UPOT 2569 2515 2439 3004 2707 2640 2569 3098 2753 2729 2607 2778 2741 2748 3046 2774 2715 2640 2942 3021 2703 2648 2581 2809 2552 2507 2441 2757 2657 2628 2628 2551 2297 2251 2193 2535 2270 2219 2163 5492 4874 4729 4640 4983 4506 4240 5644 5134 5012 4845 – – – 5895 5322 5214 5121 5062 4980 4860 6033

UPOTBHFC 2641 2577 2491 3042 2706 2643 2561 3089 2786 2721 2637 2818 2751 2760 3102 2824 2774 – 2967 3053 2748 2689 2619 2830 2565 2517 2455 – 2664 2639 2624 – 2310 2256 2206 2543 2282 2230 2177 5540 4901 4761 – – 4524 4258 – 5153 5023 – 4791 4758 4591 – 5329 5224 5136 – – – 6065

Substance CrCl3 CrBr3 CrI3 MoF3 MoCl3 MoBr3 MoI3 MnF3 MnCl3 MnBr3 MnI3 TcCl3 TcBr3 TcI3 FeF3 FeCl3 FeBr3 FeI3 RuCl3 RuBr3 RuI3 CoF3 RhCl3 IrF3 IrBr3 NiF3 AuF3 AuCl3 ZnCl3 ZnBr3 ZnI3 AlF3 AlCl3 AlBr3 AlI3 GaF3 GaCl3 GaBr3 GaI3 InCl3 InBr3 InI3 TlF3 TlCl3 TlBr3 TlI3 AsBr3 AsI3 SbF3 SbCl3 SbBr3 SbI3 BiCl3 BiI3 LaF3 LaCl3 LaBr3 LaI3 CeCl3 CeI3 PrCl3

Calc. UPOT 5518 5355 5275 6459 5246 5156 5073 6017 5544 5448 5330 5270 5215 5188 5870 5364 5333 5117 5245 5223 5222 5991 5641 (6112) (4794) (6111) (5777) (4605) 5832 5732 5636 5924 5376 5247 5070 5829 5217 4966 4611 4736 4535 4234 5493 5258 5171 5088 5497 4824 5295 5032 4954 4867 4689 3774 4682 4263 4209 3916 4394 – 4322

UPOTBHFC 5529 – 5294 – 5253 – – – – – – – – – – 5436 5347 – 5257 5232 5235 – 5665 – – – – – – – – 6252 5513 5360 5227 6238 5665 5569 5496 5183 5117 5001 – 5278 – – 5365 5295 5324 4857 4776 4692 4707 – – 4242 – 3986 4348 4061 4387

4/28/05 1:55:01 PM

Lattice Energies Substance PrI3 NdCl3 SmCl3 EuCl3 GdCl3 DyCl3 HoCl3 ErCl3 TmCl3 TmI3 YbCl3 AcCl3 UCl3 NpCl3 PuCl3 PuBr3 AmCl3 TiF4 TiCl4 TiBr4 TiI4 ZrF4 ZrCl4 ZrBr4 ZrI4 MoF4 MoCl4 MoBr4 MoI4 SnCl4 SnBr4 PbF4 CrF2Cl CrF2Br CrF2I CrCl2Br CrCl2I CrBr2I CuFCl CuFBr CuFI CuClBr CuClI CuBrI FeF2Cl FeF2Br FeF2I FeCl2Br FeCl2I FeBr2I LiIO2F2 NaIO2F2 KIO2F2 RbIO2F2 CsIO2F2 NH4IO2F2 AgIO2F2 Hydrides LiH NaH KH

Section 12.indb 23

12-23 Calc. UPOT – 4343 4376 4393 4406 4481 4501 4527 4548 – – 4096 4243 4268 4289 (3959) 4293 10012 9431 9288 9108 8853 8021 7661 7155 8795 8556 8510 8427 8355 7970 9519 5795 5753 5669 5448 5381 5330 2891 2853 2803 2753 2694 2669 5711 5653 5569 5339 5272 5209 845 766 699 674 636 678 736 916 807 711

UPOTBHFC 4101 4415 4450 4490 4495 4529 4572 4591 4608 4340 4651 – – – – – – 9908 – 9059 8918 8971 8144 7984 7801 – 9603 9500 – 8930 8852 – – – – – 5429 5370 – – – – – – – – – – – – – 756 689 – – – 685 918 807 713

Substance RbH CsH VH NbH PdH CuH TiH ZrH HfH LaH TaH CrH NiH PtH AgH AuH TlH GeH PbH BeH2 MgH2 CaH2 SrH2 BaH2 ScH2 YH2 LaH2 CeH2 PrH2 NdH2 PmH2 SmH2 GdH2 AcH2 ThH2 PuH2 AmH2 TiH2 ZrH2 CuH2 ZnH2 HgH2 AlH3 FeH3 ScH3 YH3 LaH3 FeH3 GaH3 InH3 TlH3

Calc. UPOT 686 648 1184 1163 979 828 996 916 904 828 1021 1050 929 937 941 1033 745 950 778 3205 2791 2410 2250 2121 2711 (2598) 2380 2414 2448 2464 2519 2510 2494 2372 2711 2519 2544 2866 2711 2941 2870 2707 5924 5724 5439 5063 4895 5724 5690 5092 5092

UPOTBHFC 684 653 (1344) (1633) 1368 1254 1407 1590 – – – – – – – 1108 – – – 3306 2718 2406 2265 2133 2744 2733 2522 2509 2405 2394 – 2389 2651 – 2738 – – 2864 2999 – – – 5969 – – 4910 4493 – – – –

Hydroselenides NaHSe KHSe RbHSe CsHse

703 644 623 598

732 712 689 669

Hydrosulphides LiHS NaHS RbHS

768 723 655

862 771 682

4/28/05 1:55:03 PM

Lattice Energies

12-24 Substance CsHS NH4HS Ca(HS)2 Sr(HS)2 Ba(HS)2

Calc. UPOT 628 661 2184 2063 1979

Hydroxides LiOH NaOH KOH RbOH CsOH Be(OH)2 Mg(OH)2 Ca(OH)2 Sr(OH)2 Ba(OH)2 Ti(OH)2 Mn(OH)2 Fe(OH)2 Co(OH)2 Ni(OH)2 Pd(OH)2 Cu(OH)2 CuOH AgOH AuOH TlOH Zn(OH)2 Cd(OH)2 Hg(OH)2 Sn(OH)2 Pb(OH)2 Sc(OH)3 Y(OH)3 La(OH)3 Cr(OH)3 Mn(OH)3 Al(OH)3 Ga(OH)3 In(OH)3 Tl(OH)3 Ti(OH)4 Zr(OH)4 Mn(OH)4 Sn(OH)4

1021 887 789 766 721 3477 2870 2506 2330 2142 – 2909 2653 2786 2832 – 2870 1006 918 1033 705 2795 2607 2669 2489 2376 5063 4707 4443 5556 6213 5627 5732 5280 5314 9456 8619 10933 9188

1028 892 796 765 732 3620 2998 2637 2474 2330 2953 3008 3044 3109 3186 3189 3229 – 845 – 874 3151 2909 – 2721 – 5602 – – 6299 – – 6368 – – – – – 9879

Imides CaNH SrNH BaNH

3293 3146 2975

– – –

Metavanadates Li3VO4 Na3VO4 K3VO4 Rb3VO4 Cs3VO4

3945 3766 3376 3243 3137

– – – – –

848 755 685 662

854 763 694 671

Nitrates LiNO3 NaNO3 KNO3 RbNO3

Section 12.indb 24

UPOTBHFC 657 718 (2171) – (1956)

Substance CsNO3 AgNO3 TlNO3 Mg(NO3)2 Ca(NO3)2 Sr(NO3)2 Ba(NO3)2 Mn(NO3)2 Fe(NO3)2 Co(NO3)2 Ni(NO3)2 Cu(NO3)2 Zn(NO3)2 Cd(NO3)2 Sn(NO3)2 Pb(NO3)2

Calc. UPOT 648 820 690 2481 2268 2176 2062 2318 – 2560 – – 2376 2238 2155 2067

UPOTBHFC 650 832 707 2521 2247 2151 2035 2478 (2580) 2647 2729 2739 2649 2462 2254 2208

Nitrides ScN LaN TiN ZrN VN NbN CrN

7547 6876 8130 7633 8283 7939 8269

7506 6793 8033 7723 8233 8022 8358

Nitrites NaNO2 KNO2 RbNO2 CsNO2

774 699 724 690

772 687 765 –

Oxides Li2O Na2O K2O Rb2O Cs2O Cu2O Ag2O Tl2O LiO2 NaO2 KO2 RbO2 CsO2 Li2O2 Na2O2 K2O2 Rb2O2 Cs2O2 MgO2 CaO2 SrO2 KO3 BeO MgO CaO SrO BaO TiO VO MnO

2799 2481 2238 2163 2131 3273 3002 2659 (878) 799 741 706 679 2592 2309 2114 2025 1948 3356 3144 3037 697 4514 3795 3414 3217 3029 3832 3932 3724

2814 2478 2232 2161 2063 3189 2910 2575 (872) 821 751 721 696 2557 22717 2064 1994 1512 3526 3132 2977 707 4443 3791 3401 3223 3054 3811 3863 3745

4/28/05 1:55:06 PM

Lattice Energies Substance FeO CoO NiO PdO CuO ZnO CdO HgO GeO SnO PbO Sc2O3 Y2O3 La2O3 Ce2O3 Pr2O3 Nd2O3 Pm2O3 Sm2O3 Eu2O3 Gd2O3 Tb2O3 Dy2O3 Ho2O3 Er2O3 Tm2O3 Yb2O3 Lu2O3 Ac2O3 Ti2O3 V2O3 Cr2O3 Mn2O3 Fe2O3 Al2O3 Ga2O3 In2O3 Pb2O3 CeO2 ThO2 PaO2 VO2(g) NpO2 PuO2 AmO2 CmO2 TiO2 ZrO2 MoO2 MnO2 SiO2 GeO2 SnO2 PbO2 Perchlorates LiClO4 NaClO4 KClO4 RbClO4 CsClO4 NH4ClO4

Section 12.indb 25

12-25 Calc. UPOT 3795 3837 3908 3736 4135 4142 3806 3907 3919 3652 3520 13557 12705 12452 12661 12703 12736 12811 12878 12945 12996 13071 13138 13180 13263 13322 13380 13665 12573 – 15096 15276 15146 14309 15916 15590 13928 (14841) 9627 10397 10573 10644 10707 10786 10799 10832 12150 11188 11648 12970 13125 12828 11807 11217

UPOTBHFC 3865 3910 4010 – 4050 3971 – – – – – 13708 – – – – – – – – – – – – – – – – – 14149 14520 14957 15035 14774 – 15220 – – – – – – – – – – – – – – – – – –

709 643 599 564 636 583

715 641 595 576 550 580

Substance Ca(ClO4)2 Sr(ClO4)2 Ba(ClO4)2 Permanganates NaMnO4 KMnO4 RbMnO4 CsMnO4 Ca(MnO4)2 Sr(MnO4)2 Ba(MnO4)2

Calc. UPOT 1958 1862 1795

UPOTBHFC 1971 1862 1769

661 607 586 565 1937 1845 1778

– – – – – – –

11632 10602 10125 9652 7397 7251 8201 7427 7381

11407 10479 10075 9654 – 7300 – 7507 –

Selenides Li2Se Na2Se K2Se Rb2Se Cs2Se Ag2Se Tl2Se BeSe MgSe CaSe SrSe BaSe MnSe

2364 2130 1933 1837 1745 2686 2209 3431 3071 2858 2736 2611 3176

– – – – – – – – – 2862 – – –

Selenites Li2SeO3 Na2SeO3 K2SeO3 Rb2SeO3 Cs2SeO3 Tl2SeO3 Ag2SeO3 BeSeO3 MgSeO3 CaSeO3 SrSeO3 BaSeO3

2171 1950 1774 1715 1640 1879 2113 3322 3012 2732 2586 2460

– 1916 1749 1675 – – 2148 – 2998 – 2588 2451

Selenates Li2SeO4 Na2SeO4 K2SeO4 Rb2SeO4 Cs2SeO4 Cu2SeO4 Ag2SeO4 Tl2SeO4 Hg2SeO4 BeSeO4

2054 1879 1732 1686 1615 2201 2033 1766 2163 3448

– – – – – – – – – –

Phosphates Mg3(PO4)2 Ca3(PO4)2 Sr3(PO4)2 Ba3(PO4)2 MnPO4 FePO4 BPO4 AlPO4 GaPO4

4/28/05 1:55:08 PM

Lattice Energies

12-26 Substance MgSeO4 CaSeO4 SrSeO4

Calc. UPOT 2895 2632 2489

UPOTBHFC – – –

Sulphides Li2S Na2S K2S Rb2S Cs2S (NH4)2S Cu2S Ag2S Au2S Tl2S

2464 2192 1979 1929 1892 2008 2786 2606 2908 2298

2472 2203 (2052) 1949 1850 (2026) 2865 2677 – 2258

Sulphates Li2SO4 Na2SO4 K2SO4 Rb2SO4 Cs2SO4 (NH4)2SO4 Cu2SO4 Ag2SO4 Tl2SO4 Hg2SO4 CaSO4 SrSO4 BaSO4 MnSO4

2229 1827 1700 1636 1596 1766 2276 2104 1828 – 2489 2577 2469 2920

2142 1938 1796 1748 1658 1777 2166 1989 1722 2127 2480 2484 2374 2825

Ternary Salts Cs2CuCl4 Rb2ZnCl4 Cs2ZnCl4 Rb2ZnBr4 Cs2ZnBr4 Cs2ZnI4 CsGaCl4 NaAlCl4 CsAlCl4 NaFeCl4 Rb2CoCl4 Cs2CoCl4 K2PtCl4 Cs2GeF6 (NH4)2GeF6 Cs2GeCl6 K2HfCl6 K2IrCl6 Na2MoCl6 K2MoCl6 Rb2MoCl6 Cs2MoCl6 K2NbCl6 Rb2NbCl6 Cs2NbCl6 K2OsCl6 Cs2OsCl6 K2OsBr6 K2PdCl6 Rb2PdCl6

1393 1529 1492 1498 1454 1386 494 556 486 492 1447 1391 1574 1573 1657 1404 1345 1442 1526 1418 1399 1347 1375 1371 1381 1447 1409 1396 1481 1449

– – – – – – – – – – – – 1550 – – 1419 1461 1440 1504 1412 1399 1347 1398 1385 1344 1447 – – 1493 –

Section 12.indb 26

Substance Cs2PdCl6 Rb2PbCl6 Cs2PbCl6 (NH4)2PbCl6 K2PtCl6 Rb2PtCl6 Cs2PtCl6 (NH4)2PtCl6 Tl2PtCl6 Ag2PtCl6 BaPtCl6 K2PtBr6 Ag2PtBr6 K2PtI6 K2ReCl6 Rb2ReCl6 Cs2ReCl6 K2ReBr6 K2SiF6 Rb2SiF6 Cs2SiF6 Tl2SiF6 K2SnCl6 Rb2SnCl6 Cs2SnCl6 Tl2SnCl6 (NH4)2SnCl6 Rb2SnBr6 Cs2SnBr6 Rb2SnI6 Cs2SnBr6 K2TeCl6 Rb2TeCl6 Cs2TeCl6 Tl2TeCl6 (NH4)2TeCl6 K2RuCl6 Rb2CoF6 Cs2CoF6 K2NiF6 Rb2NiF6 Rb2SbCl6 Rb2SeCl6 Cs2SeCl6 (NH4)2SeCl6 (NH4)2PoCl6 Cs2PoBr6 Cs2CrF6 Rb2MnF6 Cs2MnF6 K2MnCl6 Rb2MnCl6 (NH4)2MnCl6 Cs2TeBr6 Cs2TeI6 K2TiCl6 Rb2TiCl6 Cs2TiCl6 Tl2TiCl6 K2TiBr6 Rb2TiBr6

Calc. UPOT 1426 1343 1344 1355 1468 1464 1444 1468 1546 1773 2047 1423 1791 1421 1416 1414 1398 1375 1670 1639 1604 1675 1363 1361 1358 1437 1370 1309 1306 1226 1243 1318 1321 1323 1392 1318 1451 1688 1632 1721 1688 1357 1409 1397 1420 1338 1286 1603 1688 1620 1462 1451 1464 1306 1246 1412 1415 1402 1560 1379 1341

UPOTBHFC – 1343 – – 1471 – – – – 1881 2070 1392 2276 – 1442 – – 1375 1765 1673 1498 – 1390 1363 – – 1344 – – – – 1320 – – – – – – – – – – – – – – – – – – – – – – – 1447 1416 1384 1553 1379 1331

4/28/05 1:55:11 PM

Lattice Energies Substance Cs2TiBr6 Na2UBr6 K2UBr6 Rb2UBr6 Cs2UBr6 K2WCl6 Rb2WCl6 Cs2WCl6 K2WBr6 Rb2WBr6 Cs2WBr6 K2ZrCl6 Rb2ZrCl6 Cs2ZrCl6

12-27 Calc. UPOT 1339 1504 1484 1473 1459 1398 1397 1392 1408 1361 1362 1339 1341 1339

Tellurides Li2Te Na2Te K2Te Rb2Te Cs2Te Cu2Te Ag2Te Tl2Te BeTe MgTe CaTe

UPOTBHFC 1306 – – – – 1423 1434 1366 1408 1391 1332 1371 – 1307

2212 1997 1830 1837 1745 2706 2607 2084 3319 2878 2721

– 2095 – – – 2683 2600 2172 – 3081 –

Calc. UPOT

Substance Thiocyanates LiCNS NaCNS KCNS RbCNS CsCNS NH4CNS Ca(CNS)2 Sr(CNS)2 Ba(CNS)2 Mn(CNS)2 Zn(CNS)2 Cd(CNS)2 Hg(CNS)2 Sn(CNS)2 Pb(CNS)2 Vanadates LiVO3 NaVO3 KVO3 RbVO3 CsVO3

UPOTBHFC

764 682 623 623 623 605 2184 2063 1979 2280 2335 2201 2146 2117 2058

(765) 682 616 619 568 611 2118 1957 1852 2351 2560 2374 2492 2142 –

810 761 686 657 628

– – – – –

TABLE 2. Thermochemical Radii (nm) Ion Singly Charged Anions AgF4AlBr4AlCl4AlF4AlH4AlI4AsF6AsO2Au(CN)2AuCl4AuF4AuF6B(OH)4BF4BH4BrBrF4BrO3CF3SO3CH3CO2ClClO2ClO3ClO4ClS2O6CNCr3O8CuBr4FFeCl4-

Section 12.indb 27

Radius 0.231 0.321 0.317 0.214 0.226 0.374 0.243 0.211 0.266 0.288 0.240 0.235 0.229 0.205 0.205 0.190 0.231 0.214 0.230 0.194 0.168 0.195 0.208 0.225 0.260 0.187 0.276 0.315 0.126 0.317

± 0.019 ± 0.023 ± 0.019 ± 0.023 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.038 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.049 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.049 ± 0.023 ± 0.019 ± 0.019 ± 0.019 ± 0.019

GaCl4HH2AsO4H2PO4HCO2HCO3HF2HSO4II2BrI3I4IBr2ICl2ICl4IO2F2IO3IO4IrF6MnO4MoF6MoOF5N3NCONbCl6NbF6Nb2F11NbO3NH2NH2CH2COONO2-

Ion

0.328 0.148 0.227 0.213 0.200 0.207 0.172 0.221 0.211 0.261 0.272 0.300 0.251 0.235 0.307 0.233 0.218 0.231 0.242 0.220 0.241 0.241 0.180 0.193 0.338 0.254 0.311 0.194 0.168 0.252 0.187

4/28/05 1:55:13 PM

Lattice Energies

12-28 NO3O2O3OHOsF6PaF6PdF6PF6PO3PtF6PuF5ReF6ReO4RuF6S6SCNSbCl6SbF6Sb2F11Sb3F14SeCl5SeCNSeHSHSO3FS3N3S3N3O4TaCl6TaF6TaO3UF6VF6VO3WCl6WF6WOF5-

Ion

Doubly Charged Anions AmF62Bi2Br82Bi6Cl202CdCl42CeCl62CeF62CO32CoCl42CoF42CoF62Cr2O72CrF62CrO42CuCl42CuF42GeCl62GeF62HfF62HgI42IrCl62MnCl62MnF42MnF62MoBr62-

Section 12.indb 28

0.200 0.165 0.199 0.152 0.252 0.249 0.252 0.242 0.204 0.247 0.239 0.240 0.227 0.242 0.305 0.209 0.320 0.252 0.312 0.374 0.258 0.230 0.195 0.191 0.214 0.231 0.252 0.352 0.250 0.192 0.301 0.235 0.201 0.337 0.246 0.241

Radius ± 0.019 ± 0.019 ± 0.034 ± 0.019 ± 0.020 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.038 ± 0.038 ± 0.038 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.038 ± 0.038 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019

0.255 0.392 0.501 0.307 0.352 0.249 0.189 0.306 0.209 0.256 0.292 0.253 0.229 0.304 0.213 0.335 0.244 0.248 0.377 0.332 0.314 0.219 0.241 0.364

± 0.019 ± 0.055 ± 0.073 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.031 ± 0.019 ± 0.019 ± 0.019

MoCl62MoF62MoO42NbCl62NH2Ni(CN)42NiF42NiF62O2O22OsBr62OsCl62OsF62PbCl42PbCl62PbF62PdBr62PdCl42PdCl62PdF62PoBr62PoI62Pt(NO2)3Cl32Pt(NO2)4Cl22Pt(OH)22Pt(SCN)62PtBr42PtBr62PtCl42PtCl62PtF62PuCl62ReBr62ReCl62ReF62ReF82ReH92ReI62RhF62RuCl62RuF62S2S2O32S2O42S2O52S2O62S2O72S2O82S3O62S4O62S6O62ScF62Se2SeBr62SeCl62SeO42SiF62SiO32SmF42Sn(OH)62SnBr62-

Ion

0.338 0.274 0.231 0.343 0.128 0.322 0.211 0.249 0.141 0.167 0.365 0.336 0.276 0.279 0.347 0.268 0.354 0.313 0.333 0.252 0.380 0.428 0.364 0.383 0.333 0.451 0.324 0.363 0.307 0.333 0.245 0.349 0.371 0.337 0.256 0.276 0.257 0.421 0.240 0.336 0.248 0.189 0.251 0.262 0.270 0.283 0.275 0.291 0.302 0.325 0.382 0.276 0.181 0.363 0.336 0.229 0.248 0.195 0.218 0.279 0.374

Radius ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.026 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.020 ± 0.019

4/28/05 1:55:16 PM

Lattice Energies SnCl62SnF62SnI62SO32SO42TcBr62TcCl62TcF62TcH92TcI62Te2TeBr62TeCl62TeI62TeO42Th(NO3)62ThCl62ThF62TiBr62TiCl62TiF62UCl62UF62VO32WBr62WCl62WO42WOCl52ZnBr42ZnCl42ZnF42ZnI42ZrBr42ZrCl42ZrCl62ZrF62-

Ion

Multi-Charged Anions AlH63AsO43CdBr64CdCl64CeF63CeF73Co(CN)63Co(NO2)63CoCl53CoF63Cr(CN)63CrF63Cu(CN)43Fe(CN)63FeF63HfF73InF63Ir(CN)63Ir(NO2)63Mn(CN)63Mn(CN)65MnCl64N3Ni(NO2)63-

Section 12.indb 29

12-29 0.345 0.265 0.427 0.204 0.218 0.363 0.337 0.244 0.260 0.419 0.220 0.383 0.353 0.430 0.238 0.424 0.360 0.263 0.356 0.335 0.252 0.354 0.256 0.204 0.363 0.339 0.237 0.334 0.335 0.306 0.219 0.384 0.334 0.306 0.348 0.258

0.256 0.237 0.374 0.352 0.278 0.282 0.349 0.343 0.320 0.258 0.351 0.254 0.312 0.347 0.298 0.277 0.268 0.347 0.338 0.350 0.401 0.349 0.180 0.342

± 0.042 ± 0.042 ± 0.038 ± 0.038 ± 0.038 ± 0.038 ± 0.038 ± 0.038 ± 0.038 ± 0.042 ± 0.038 ± 0.042 ± 0.038 ± 0.038 ± 0.042 ± 0.042 ± 0.038 ± 0.038 ± 0.038 ± 0.038 ± 0.042 ± 0.038 ± 0.042 ± 0.038

Ni(NO2)64NiF63O3P3PaF83PO43PrF63Rh(NO2)63Rh(SCN)63TaF83TbF73Tc(CN)65ThF73TiBr63TlF63UF73YF63ZrF73-

Ion

Singly Charged Cations N(CH3)4+ N2H5+ N2H62+ NH(C2H5)3+ NH3C2H5+ NH3C3H7+ NH3CH3+ NH3OH+ NH4+ NH3C2H4OH+ As3S4+ As3Se4+ AsCl4+ Br2+ Br3+ Br3Br5+ BrClCNH2+ BrF2+ BrF4+ C10F8+ C6F6+ Cl(SNSCN)2+ Cl2C=NH2+ Cl2F+ Cl3+ ClF2+ ClO2+ GaBr4I2+ I3+ I5+ IBr2+ ICl2+ IF6+ N(S3N2)2+ N(SCl)2+ N(SeCl)2+ N(SF2)2+ N2F+ NO+ NO2+

0.383 0.250 0.288 0.224 0.299 0.230 0.281 0.345 0.428 0.284 0.290 0.410 0.282 0.315 0.271 0.285 0.275 0.273

Radius ± 0.038 ± 0.042 ± 0.038 ± 0.042 ± 0.042 ± 0.042 ± 0.038 ± 0.038 ± 0.042 ± 0.042 ± 0.038 ± 0.042 ± 0.042 ± 0.038 ± 0.038 ± 0.042 ± 0.038 ± 0.038

0.234 0.158 0.158 0.274 0.193 0.225 0.177 0.147 0.136 0.203 0.244 0.253 0.221 0.155 0.204 0.238 0.229 0.175 0.183 0.172 0.265 0.228 0.347 0.173 0.165 0.182 0.147 0.118 0.317 0.185 0.225 0.263 0.196 0.175 0.209 0.258 0.186 0.246 0.214 0.156 0.145 0.153

± 0.019 ± 0.019 ± 0.029 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.019 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.038 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.036 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027

4/28/05 1:55:18 PM

Lattice Energies

12-30 Ion O2+ O2(SCCF3Cl)2+ ONCH3CF3+ OsOF5P(CH3)3Cl+ P(CH3)3D+ PCl4+ ReOF5S(CH3)2Cl+ S(N(C2H5)3)3+ S2(CH3)2Cl+ S2(CH3)2CN+ S2(CH3)3+ S2Br5+ S2N+ S2N2C2H3+ S2NC2(PhCH3)2+ S2NC3H4+ S2NC4H8+ S3(CH3)3+ S3Br3+ S3C3H7+ S3C4F6+ S3CF3CN+ S3Cl3+ S3N2+ S3N2Cl+ S4N3+ S4N3(Ph)2+ S4N4H+ S5N5+ S7I+ Sb(NPPh3)4+ SBr3+ SCH3O2+ SCH3P(CH3)3+ SCH3PCH3Cl2+ SCl(C2H5)2+ SCl2CF3+ SCl2CH3+ SCl3+ Se3Br3+ Se3Cl3+ Se3N2+ Se3NCl2+ Se6I+ SeBr3+ SeCl3+ SeF3+ SeI3+ SeN2Cl+ SeNCl2+ (SeNMe3)3+ SeS2N2+ SF(C6F5)2+ SF2CF3+ SF2N(CH3)2+ SF3+ SFS(C(CF3)2)2+ SH2C3H7+ SN+ SNCl5(CH3CN)-

0.140 0.275 0.200 0.246 0.197 0.196 0.235 0.245 0.207 0.439 0.265 0.223 0.233 0.267 0.159 0.211 0.310 0.218 0.225 0.239 0.245 0.199 0.261 0.263 0.233 0.201 0.232 0.231 0.316 0.178 0.257 0.262 0.518 0.220 0.183 0.248 0.205 0.207 0.207 0.204 0.185 0.253 0.245 0.288 0.163 0.260 0.182 0.192 0.179 0.238 0.196 0.157 0.406 0.282 0.294 0.198 0.210 0.172 0.275 0.210 0.158 0.290

Radius ± 0.027 ± 0.027 ± 0.027 ± 0.038 ± 0.027 ± 0.027 ± 0.027 ± 0.038 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.034 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.042 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.042 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.038

Ion (SNPMe3)3+ SNSC(CH3)N+ SNSC(CN)CH+ SNSC(Ph)N+ SNSC(Ph)NS3N2+ SNSC(PhCH3)N+ (Te(N(SiMe3)2)2+ Te(N3)3+ Te4Nb3OTe2I6+ TeBr3+ TeCl3+ TeCl3(15-crown-5)+ TeI3+ Xe2F11+ Xe2F3+ XeF+ XeF3+ XeF5+ XeOF3+

0.308 0.225 0.209 0.251 0.327 0.264 0.371 0.226 0.407 0.235 0.216 0.282 0.243 0.266 0.221 0.174 0.183 0.186 0.186

Radius ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027 ± 0.027

Doubly Charged Cations Co2S2(CO)62+ FeW(Se)2(CO)2+ I42+ Mo(Te3)(CO)42+ S192+ S2(S(CH3)2)22+ S2I42+ S3N22+ S3NCCNS32+ S3Se2+ S4N42+ S6N42+ S82+ Se102+ Se172+ Se192+ Se2I42+ Se3N22+ Se42+ Se4S2N42+ Se82+ SeN2S22+ (SNP(C2H5)3)22+ TaBr6Te(trtu)42+ Te(tu)42+ Te2(esu)4Br22+ Te2(esu)4Cl22+ Te2(esu)4I22+ Te2Se22+ Te2Se42+ Te2Se82+ Te3S32+ Te3Se2+ Te42+ Te82+ W(CO)4(h3-Te)2+ W2(CO)10Se42+

0.263 0.260 0.207 0.234 0.292 0.230 0.231 0.184 0.220 0.326 0.186 0.232 0.182 0.253 0.236 0.296 0.218 0.182 0.152 0.224 0.186 0.182 0.312 0.351 0.328 0.296 0.356 0.361 0.342 0.192 0.222 0.252 0.217 0.193 0.169 0.187 0.234 0.290

± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.049 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035 ± 0.035

Multi-Charged Cations I153+ Te2(su)64+

0.442 0.453

± 0.051 ± 0.034

Ligand abbreviations: su = selenourea; esu = ethyleneselenourea; tu = thiourea; ph = phenyl.

Section 12.indb 30

4/28/05 1:55:20 PM

Lattice Energies

12-31 TABLE 3. Ancillary Thermochemical Data (kJ mol–1) Species AsO43– BrO3– ClO4– CNCO32– Fe(NO3)2 HF2– HfCl62– IO2F2– IO3– IrCl62– LiCH3O2 NbCl62– NH2CH2CO2– O22– PdCl62– PO43– PtCl62– ReBr62– ReCl62– Ti(OH)2

Section 12.indb 31

State g g g g g c g g g g g c g g g g g g g g c

∆fHo (289) –145 –344 66 –321 (–448) –774 –1640 –693 –208 –785 (–745) –1224 –564 553 –749 291 –774 –689 –919 –778

4/28/05 1:55:20 PM

THE MADELUNG CONSTANT AND CRYSTAL LATTICE ENERGY If U is the crystal lattice energy and M is the Madelung constant, thena U=

Substance

NMzi z j e2 r

(1 − 1/n)

Ion type

Crystal formb

Sodium chloride, NaCl

–

M ,X

FCC

1.74756

Cesium chloride, CsCl

M+, X–

BCC

1.76267

Calcium chloride, CaCl2

M++, 2X–

Cubic

2.365

Calcium fluoride (fluorite), CaF2

M++, 2X–

Cubic

2.51939

Cadmium chloride, CdCl2

–

M , 2X

Hexagonal

2.244c

Cadmium iodide (α), CdI2

M++, 2X–

Hexagonal

2.355c

Magnesium fluoride, MgF2

M , 2X

Tetragonal

2.381c

Cuprous oxide (cuprite), Cu2O

2M+, X– –

Cubic

2.22124

Zinc oxide, ZnO

M ,X

Hexagonal

1.4985c

Sphalerite (zinc blende), ZnS

M++, X– –

FCC

1.63806

Wurtzite, ZnS

M ,X

Hexagonal

1.64132c

Titanium dioxide (anatase), TiO2

M4+, 2X– –

Tetragonal

2.400c

Titanium dioxide (rutile), TiO2

M , 2X

Tetragonal

2.408c

β-Quartz, SiO2

M , 2X

Hexagonal

2.2197c

Corundum, Al2O3

2M3+, 3X– –

Rhombohedral

4.1719

a b c

4+ 4+

–

––

–– ––

N is Avogadro’s number, zi and zj are the integral charges on the ions (in units of e), and e is the charge on the electron in electrostatic units (e = 4.803 × 10–10 esu). r is the shortest distance between cation-anion pairs in centimeters. Then U is in ergs (1 erg = 10–7 J). FCC = face centered cubic; BCC = body centered cubic. For tetragonal and hexagonal crystals the value of M depends on the details of the lattice parameters.

The Born Exponent, n is: Ion type

n 5

He, Li

Ne, Na+, F–

Ar, K , Cu , Cl +

–

Kr, Rb+, Ag+, Br–

Xe, Cs+, Au+, I–

For a crystal with a mixed-ion type, an average of the values of n in this table is to be used (6 for LiF, for example).

12-32

S12_07.indd 32

5/2/05 12:54:08 PM

ELASTIC CONSTANTS OF SINGLE CRYSTALS H. P. R. Frederikse This table gives selected values of elastic constants for single crystals. The values believed most reliable were selected from the original literature. The substances are arranged by crystal system and, within each system, alphabetically by name. A reference to the original literature is given for each value; a useful compilation of published values from many sources may be found in Reference 1 below. Data are given for the single-crystal density and for the elastic constants cij, in units of 1011 N/m2, which is equivalent to 1012 dyn/cm2.

General References 1. Simmons, G., and Wang, H., Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, Second Edition, The MIT Press, Cambridge, MA, 1971. 2. Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw-Hill, New York, 1972.

CUBIC CRYSTALS Name

Formula

Ď /g cmâ&#x20AC;&#x201C;3

T/K

Ref.

Aluminum Aluminum antimonide Ammonium bromide Ammonium chloride Argon Barium fluoride Barium nitrate Calcium fluoride Calcium telluride Cesium Cesium bromide Cesium chloride Cesium iodide Chromite Chromium Cobalt oxide Cobalt zinc ferrite Copper Gallium antimonide Gallium arsenide Gallium phosphide Garnet (yttrium-iron) Germanium Gold Indium antimonide Indium arsenide Indium phosphide Iridium Iron Lead Lead fluoride Lead nitrate Lead telluride Lithium Lithium bromide Lithium chloride Lithium fluoride Lithium iodide Magnesium oxide Magnetite Manganese oxide Mercury telluride Molybdenum Nickel

Al AlSb NH4Br NH4Cl Ar BaF2 Ba(NO3)2 CaF2 CaTe Cs CsBr CsCl CsI FeCr2O4 Cr CoO CoZnFeO2 Cu GaSb GaAs GaP Y3Fe2(FeO4)3 Ge Au InSb InAs InP Ir Fe Pb PbF2 Pb(NO3)2 PbTe Li LiBr LiCl LiF LiI MgO Fe3O4 MnO HgTe Mo Ni

2.6970 4.3600 2.4314 1.5279 1.7710 4.8860 3.2560 3.810 5.8544 1.9800 4.4560 3.9880 4.5250 4.4500 7.20 6.44 5.43 8.932 5.6137 5.3169 4.1297 5.17 5.313 19.283 5.7890 5.6720 4.78 22.52 7.8672 11.34 7.79 4.547 8.2379 0.5326 3.47 2.068 2.638 4.061 3.579 5.18 5.39 8.079 10.2284 8.91

298 300 300 290 4.2 298 293 298 298 78 298 298 298 RT 298 298 303 298 298 298 300 298 298 296.5 298 293 RT 300 298 296 300 293 303.2 298 RT 295 RT RT 298 RT 298 290 273 298

1 2 3 4 5 6 7 8 9 10 11 11 11 12 13 14 12 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 32 20 32 35 36 37 15

C11

1.0675 0.8939 0.3414 0.3814 0.0529 0.9199 0.2925 1.6420 0.5351 0.0247 0.3063 0.3644 0.2446 3.2250 3.398 2.6123 2.660 1.683 0.8839 1.1877 1.4120 2.680 1.2835 1.9244 0.6720 0.8329 1.0220 5.80 2.26 0.4966 0.8880 0.3729 1.0795 0.1350 0.3940 0.4927 1.1397 0.2850 2.9708 2.730 2.23 0.548 4.637 2.481

C12

0.6041 0.4427 0.0782 0.0866 0.0135 0.4157 0.2065 0.4398 0.3681 0.0206 0.0807 0.0882 0.0661 1.4370 0.586 1.4699 1.530 1.221 0.4033 0.5372 0.6253 1.106 0.4823 1.6298 0.3670 0.4526 0.5760 2.42 1.40 0.4231 0.4720 0.2765 0.0764 0.1144 0.1880 0.2310 0.4767 0.1400 0.9536 1.060 1.20 0.381 1.578 1.549

C44

0.2834 0.4155 0.0722 0.0903 0.0159 0.2568 0.1277 0.8406 0.1994 0.0148 0.0750 0.0804 0.0629 1.1670 0.990 0.8300 0.780 0.757 0.4316 0.5944 0.7047 0.766 0.6666 0.4200 0.3020 0.3959 0.4600 2.56 1.16 0.1498 0.2454 0.1347 0.1343 0.0878 0.1910 0.2495 0.6364 0.1350 1.5613 0.971 0.79 0.204 1.092 1.242

12-33

Section 12.indb 33

4/28/05 1:55:28 PM

Elastic Constants of Single Crystals

12-34 CUBIC CRYSTALS Name

Formula

ρ/g cm

T/K

Ref.

Niobium Palladium Platinum Potassium Potassium bromide Potassium chloride Potassium cyanide Potassium fluoride Potassium iodide Pyrite Rubidium Rubidium bromide Rubidium chloride Rubidium iodide Silicon Silver Silver bromide Sodium Sodium bromate Sodium bromide Sodium chlorate Sodium chloride Sodium fluoride Sodium iodide Spinel Strontium fluoride Strontium nitrate Strontium oxide Strontium titanate Tantalum Tantalum carbide Thallium bromide Thorium Thorium oxide Tin telluride Titanium carbide Tungsten Uranium carbide Uranium dioxide Vanadium Zinc selenide Zinc sulfide Zinc telluride Zirconium carbide

Nb Pd Pt K KBr KCl KCN KF KI FeS2 Rb RbBr RbCl RbI Si Ag AgBr Na NaBrO3 NaBr NaClO3 NaCl NaF NaI MgAl2O4 SrF2 Sr(NO3)2 SrO SrTiO3 Ta TaC TlBr Th ThO2 SnTe TiC W UC UO2 V ZnSe ZnS ZnTe ZrC

8.578 12.038 21.50 0.851 2.740 1.984 1.553 2.480 3.128 5.016 1.58 3.350 2.797 3.551 2.331 10.50 5.585 0.971 3.339 3.202 2.485 2.163 2.804 3.6689 3.6193 4.277 2.989 4.99 5.123 16.626 14.65 7.4529 11.694 9.991 6.445 4.940 19.257 13.63 10.97 6.022 5.262 4.088 5.636 6.606

300 300 300 295 298 298 RT 295 300 RT 170 300 300 300 298 300 300 299 RT 300 RT 298 300 300 298 300 293 300 RT 298 RT 298 300 298 300 RT 297 300 298 300 298 298 298 298

38 39 40 41 11 11 32 33 42 43 44 45 45 45 46 47 48 49 32 33 50 11 51 52 53 54 29 55 56 57 58 59 60 61 62 107 64 65 66 67 68 68 68 63

Section 12.indb 34

–3

C11

2.4650 2.2710 3.4670 0.0370 0.3468 0.4069 0.1940 0.6490 0.2710 3.818 0.0296 0.3152 0.3624 0.2556 1.6578 1.2399 0.5920 0.0739 0.5450 0.3970 0.4920 0.4947 0.9700 0.3007 2.9857 1.2350 0.4255 1.601 3.4817 2.6023 5.05 0.3760 0.7530 3.670 1.1250 5.00 5.2239 3.200 3.960 2.287 0.8096 1.0462 0.7134 4.720

C12

1.3450 1.7604 2.5070 0.0314 0.0580 0.0711 0.1180 0.1520 0.0450 0.310 0.0250 0.0500 0.0612 0.0382 0.6394 0.9367 0.3640 0.0622 0.1910 0.1001 0.1420 0.1288 0.2380 0.0912 1.5372 0.4305 0.2921 0.435 1.0064 1.5446 0.73 0.1458 0.4890 1.060 0.0750 1.13 2.0437 0.850 1.210 1.190 0.4881 0.6534 0.4078 0.987

C44

0.2873 0.7173 0.7650 0.0188 0.0507 0.0631 0.0150 0.1232 0.0364 1.094 0.0171 0.0380 0.0468 0.0278 0.7962 0.4612 0.0616 0.0419 0.1500 0.0998 0.1160 0.1287 0.2822 0.0733 1.5758 0.3128 0.1590 0.590 4.5455 0.8255 0.79 0.0757 0.4780 0.797 0.1172 1.75 1.6083 0.647 0.641 0.432 0.4405 0.4613 0.3115 1.593

4/28/05 1:55:30 PM

Elastic Constants of Single Crystals

12-35 TETRAGONAL CRYSTALS

Name

Formula

ρ/g cm

T/K

Ref.

Ammonium dihydrogen arsenate (ADA) Ammonium dihydrogen phosphate (ADP) Barium titanate Calcium molybdate Indium Magnesium fluoride Nickel sulfate hexahydrate Potassium dihydrogen arsenate (KDA) Potassium dihydrogen phosphate (KDP) Rubidium dihydrogen phosphate (RDP) Rutile Tellurium oxide Tin (white) Zircon

NH4H2AsO4

2.3110

298

0.6747

–0.106

0.1652

NH4H2PO4

1.8030

293

0.6200

–0.050

0.1400

BaTiO3 CaMoO4 In MgF2 NiSO4·6H2O KH2AsO4

5.9988 4.255 7.300 3.177 2.070 2.867

298 298 RT RT RT RT

70 79 71 72 73 12

2.7512 1.447 0.4450 1.237 0.3209 0.530

1.7897 0.664 0.3950 0.732 0.2315 –0.060

1.5156 0.466 0.4050 0.536 0.0209 –0.020

KH2PO4

2.388

0.7140

–0.049

RbH2PO4

2.800

298

0.5562

TiO2 TeO2 Sn ZrSiO4

4.260 5.99 7.29 4.70

298 RT 288 RT

75 76 77 78

2.7143 0.5320 0.7529 2.585

–3

C11

C12

C13

C16

C33

C44

C66

0.3022

0.0685

0.0639

0.3000

0.0910

0.0610

1.6486 1.265 0.4440 1.770 0.2931 0.370

0.5435 0.369 0.0655 0.552 0.1156 0.120

1.1312 0.451 0.1220 0.978 0.1779 0.070

0.1290

0.5620

0.1270

0.0628

–0.064

0.0279

0.4398

0.1142

0.0350

1.7796 0.4860 0.6156 1.791

1.4957 0.2120 0.4400 1.542

4.8395 1.0850 0.9552 3.805

1.2443 0.2440 0.2193 0.733

1.9477 0.5520 0.2336 1.113

0.134

ORTHORHOMBIC CRYSTALS Name

Formula

ρ/g cm

T/K

Ref.

Acenaphthene Ammonium sulfate Aragonite Barite Benzene Benzophenone Bronzite Calcium sulfate Celestite Cesium sulfate Fosterite Iodic acid Lithium ammonium tartrate Magnesium sulfate heptahydrate Natrolite Nickel sulfate heptahydrate Olivine Potassium pentaborate Potassium sulfate Rochelle salt Rubidium sulfate Sodium ammonium tartrate Sodium tartrate Strontium formate dihydrate Sulfur Thallium sulfate Topaz Uranium (alpha) Zinc sulfate heptahydrate

C12H10 (NH4)2SO4 CaCO3 BaSO4 C6H6 (C6H5)2CO (MgFe)SiO3 CaSO4 SrSO3 Cs2SO4 Mg2SiO4 HIO3 LiNH4C4H4O6·4H2O MgSO4·7H2O

1.220 1.774 2.93 4.40 1.061 1.219 3.38 2.962 3.96 4.243 3.224 4.630 1.71 1.68

293 293 RT RT 250 RT RT RT RT 293 298 RT RT RT

80 81 82 82 83 32 78 84 12 81 85 73 12 86

0.1380 0.3607 1.5958 0.8941 0.0614 0.1070 1.876 0.9382 1.044 0.4490 3.2848 0.3030 0.3864 0.325

0.0210 0.1651 0.3663 0.4614 0.0352 0.0550 0.686 0.1650 0.773 0.1958 0.6390 0.1194 0.1655 0.174

0.0410 0.1580 0.0197 0.2691 0.0401 0.0169 0.605 0.1520 0.605 0.1815 0.6880 0.1169 0.0875 0.182

0.1262 0.2981 0.8697 0.7842 0.0656 0.1000 1.578 1.845 1.061 0.4283 1.9980 0.5448 0.5393 0.288

0.0460 0.1456 0.1597 0.2676 0.0390 0.0321 0.561 0.3173 0.619 0.1800 0.7380 0.0548 0.2007 0.182

0.1117 0.3534 0.8503 1.0548 0.0583 0.0710 2.085 1.1180 1.286 0.3785 2.3530 0.4359 0.3624 0.315

0.0265 0.1025 0.4132 0.1190 0.0197 0.0203 0.700 0.3247 0.135 0.1326 0.6515 0.1835 0.1190 0.078

0.0290 0.0717 0.2564 0.2874 0.0378 0.0155 0.592 0.2653 0.279 0.1319 0.8120 0.2193 0.0667 0.156

0.0185 0.0974 0.4274 0.2778 0.0153 0.0353 0.544 0.0926 0.266 0.1323 0.8088 0.1736 0.2326 0.090

(Na,Al)SiO3 NiSO4·7H2O (MgFe)SiO4 KB5O8·4H2O K2SO4 NaK(C4H4O6)·4H2O Rb2SO4 NaNH4C4H4O6·4H2O Na2C4H4O6·2H2O Sr(CHO2)2·2H2O S TlSO4 Al2SiO3(OH,F)2 U ZnSO4·7H2O

2.25 1.948 3.324 1.74 2.665 1.79 3.621 1.587 1.794 2.25 2.07 6.776 3.52 19.0453 1.970

RT RT RT RT 293 RT 293 RT RT RT RT 293 RT 293 RT

78 86 87 71 81 71 81 12 12 12 12 81 82 88 86

0.716 0.353 3.240 0.582 0.5357 0.255 0.5029 0.3685 0.461 0.4391 0.240 0.4106 2.8136 2.1486 0.3320

0.261 0.198 0.590 0.229 0.1999 0.141 0.1965 0.2725 0.286 0.1037 0.133 0.2573 1.2582 0.4622 0.1720

0.297 0.201 0.790 0.174 0.2095 0.116 0.1999 0.3083 0.320 –0.149 0.171 0.2288 0.8464 0.2176 0.2000

0.632 0.311 1.980 0.359 0.5653 0.381 0.5098 0.5092 0.547 0.3484 0.205 0.3885 3.8495 1.9983 0.2930

0.297 0.201 0.780 0.231 0.1990 0.146 0.1925 0.3472 0.352 –0.014 0.159 0.2174 0.8815 1.0764 0.1980

1.378 0.335 2.490 0.255 0.5523 0.371 0.4761 0.5541 0.665 0.3746 0.483 0.4268 2.9452 2.6763 0.3200

0.196 0.091 0.667 0.164 0.195 0.134 0.1626 0.1058 0.124 0.1538 0.043 0.1125 1.0811 1.2479 0.0780

0.248 0.172 0.810 0.046 0.1879 0.032 0.1589 0.0303 0.031 0.1075 0.087 0.1068 1.3298 0.7379 0.1530

0.423 0.099 0.793 0.057 0.1424 0.098 0.1407 0.0870 0.098 0.1724 0.076 0.0751 1.3089 0.7454 0.0830

Section 12.indb 35

–3

C11

C12

C13

C22

C23

C33

C44

C55

C66

4/28/05 1:55:31 PM

Elastic Constants of Single Crystals

12-36 MONOCLINIC CRYSTALS Name

Formula

ρ/g cm

T/K

Ref.

Aegirine Anthracene Cobalt sulfate heptahydrate Diopside Dipotassium tartrate Feldspar (microceine) Ferrous sulfate heptahydrate Lithium sulfate monohydrate Naphthalene Potassium tartrate Sodium thiosulfate Stilbene Triglycine sulfate (TGS)

(NaFe)Si2O6 C14H10

3.50 1.258

RT RT

89 90

1.858 0.0852

0.685 0.0672

0.707 0.0590

0.098 –0.0192

1.813 0.1170

CoSO4·7H2O (CaMg)Si2O6 KHC4H4O6 KAlSi3O8

1.948 3.31 1.97 2.56

RT RT RT RT

86 91 12 92

0.335 2.040 0.4294 0.664

0.205 0.884 0.1399 0.438

0.158 0.0883 0.3129 0.259

0.016 –0.193 –0.0105 –0.033

0.378 1.750 0.3460 1.710

FeSO4·7H2O

1.898

0.349

0.208

0.174

–0.020

0.376

Li2SO4·H2O C10H8 K2C4H4O6 Na2S2O3 (C6H5CH)2 (NH2CH2COOH)3· H2SO4

2.221 1.127 1.987 1.7499 1.60 1.68

RT RT RT RT RT RT

32 93 32 12 94 32

0.5250 0.0780 0.3110 0.3323 0.0930 0.4550

0.1715 0.0445 0.1720 0.1814 0.0570 0.1720

0.1730 0.0340 0.1690 0.1875 0.0670 0.1980

–0.0196 –0.006 0.0287 0.0225 –0.003 –0.030

0.5060 0.0990 0.3900 0.2953 0.0920 0.3210

Name Aegirine Anthracene Cobalt sulfate heptahydrate Diopside Dipotassium tartrate Feldspar (microceine) Ferrous sulfate heptahydrate Lithium sulfate monohydrate Naphthalene Potassium tartrate Sodium thiosulfate Stilbene Triglycine sulfate (TGS)

Section 12.indb 36

–3

C11

C12

C13

C15

C22

C23 0.626 0.0375 0.158

C25 0.094 –0.0170 –0.018

C33 2.344 0.1522 0.371

C35 0.214 –0.0187 –0.047

C44 0.692 0.0272 0.060

C46 0.077 0.0138 0.016

C55 0.510 0.0242 0.058

C66 0.474 0.0399 0.101

0.482 0.1173

–0.196 0.0176

2.380 0.6816

–0.336 0.0294

0.675 0.0961

–0.113 –0.0044

0.588 0.1270

0.705 0.0841

0.192 0.172

–0.148 –0.019

1.215 0.360

–0.131 –0.014

0.143 0.064

–0.015 0.001

0.238 0.056

0.361 0.096

0.0368

0.0571

0.5400

–0.0254

0.1400

–0.0054

0.1565

0.2770

0.0230 0.1330 0.1713 0.0485 0.2080

–0.0270 0.0182 0.0983 –0.005 –0.0036

0.1190 0.5540 0.4590 0.0790 0.2630

0.0290 0.0710 –0.0678 –0.005 –0.0500

0.0330 0.0870 0.0569 0.0325 0.0950

–0.0050 0.0072 –0.0268 0.0050 –0.0026

0.0210 0.1040 0.1070 0.0640 0.1110

0.0415 0.0826 0.0598 0.0245 0.0620

4/28/05 1:55:33 PM

Elastic Constants of Single Crystals

12-37 HEXAGONAL CRYSTALS T/K

Ref.

C11

C12

C13

C33

C55

Name

Formula

ρ/g cm

Apatite Beryl Beryllium Beryllium oxide Cadmium Cadmium selenide Cadmium sulfide Cobalt Dysprosium Erbium Gadolinium Hafnium Ice Indium Magnesium Rhenium Ruthenium Thallium Titanium Titanium diboride Yttrium Zinc Zinc oxide Zinc sulfide Zirconium

Ca5(PO4)3(OH,F,Cl) Be3Al2Si6O18 Be BeO Cd CdSe

3.218 2.68 1.8477 3.01 8.652 5.655

RT RT 300 RT 300 298

12 12 95 96 97 68

1.667 2.800 2.923 4.70 1.1450 0.7046

0.131 0.990 0.267 1.68 0.3950 0.4516

0.655 0.670 0.140 1.19 0.3990 0.3930

1.396 2.480 3.364 4.94 0.5085 0.8355

0.663 0.658 1.625 1.53 0.1985 0.1317

CdS Co Dy Er Gd Hf H2O(solid) In Mg Re Ru Tl Ti TiB2

4.824 8.836 8.560 9.064 7.888 12.727 0.920 7.2788 1.7364 21.024 12.3615 11.560 4.5063 4.95

298 298 298 298 298 298 250 300 298 298 298 300 298 RT

98 99 100 100 101 102 103 104 105 100 100 106 102 107

0.8431 3.071 0.7466 0.8634 0.6667 1.881 0.1410 0.4535 0.5950 6.1820 5.6260 0.4080 1.6240 6.90

0.5208 1.650 0.2616 0.3050 0.2499 0.772 0.0660 0.4006 0.2612 2.7530 1.8780 0.3540 0.9200 4.10

0.4567 1.027 0.2233 0.2270 0.2132 0.661 0.0624 0.4151 0.2180 2.0780 1.6820 0.2900 0.6900 3.20

0.9183 3.581 0.7871 0.8554 0.7191 1.969 0.1515 0.4515 0.6155 6.8350 6.2420 0.5280 1.8070 4.40

0.1458 0.755 0.2427 0.2809 0.2089 0.557 0.0288 0.0651 0.1635 1.6060 1.8060 0.0726 0.4670 2.50

Y Zn ZnO ZnS Zr

4.472 7.134 5.6760 4.089 6.505

300 295 298 298 298

108 109 110 96 102

0.7790 1.6368 2.0970 1.2420 1.434

0.2850 0.3640 1.2110 0.6015 0.728

0.2100 0.5300 1.0510 0.4554 0.653

0.7690 0.6347 2.1090 1.4000 1.648

0.2431 0.3879 0.4247 0.2864 0.320

Name

Formula

ρ/g cm

T/K

Ref.

Aluminum oxide Aluminum phosphate Antimony Bismuth Calcite Hematite Lithium niobate Lithium tantalate Quartz Selenium Sodium nitrate Tourmaline

Al2O3 AlPO4

3.986 2.556

300 RT

111 73

4.9735 1.0503

1.6397 0.2934

1.1220 0.6927

–0.2358 –0.1271

4.9911 1.3353

1.4739 0.2314

Sb Bi CaCO3 Fe2O3 LiNbO3 LiTaO3 SiO2 Se NaNO3

6.70 9.80 2.712 5.240 4.70 7.45 2.6485 4.838 2.27 3.05

295 295 300 RT RT RT 298 300 RT RT

112 112 113 82 114 114 115 116 12 82

1.0130 0.6370 1.4806 2.4243 2.030 2.330 0.8680 0.1870 0.8670 2.7066

0.3450 0.2490 0.5578 0.5464 0.530 0.470 0.0704 0.0710 0.1630 0.6927

0.2920 0.2470 0.5464 0.1542 0.750 0.800 0.1191 0.2620 0.1600 0.0872

0.2090 0.0717 –0.2058 –0.1247 0.090 –0.110 –0.1804 0.0620 0.0820 –0.0774

0.4500 0.3820 0.8557 2.2734 2.450 2.750 1.0575 0.7410 0.3740 1.6070

0.3930 0.1123 0.3269 0.8569 0.600 0.940 0.5820 0.1490 0.2130 0.6682

–3

TRIGONAL CRYSTALS

Section 12.indb 37

–3

C11

C12

C13

C14

C33

C44

4/28/05 1:55:34 PM

Elastic Constants of Single Crystals

12-38

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

Section 12.indb 38

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4/28/05 1:55:35 PM

ELECTRICAL RESISTIVITY OF PURE METALS The first part of this table gives the electrical resistivity, in units of 10–8 Ω m, for 28 common metallic elements as a function of temperature. The data refer to polycrystalline samples. The number of significant figures indicates the accuracy of the values. However, at low temperatures (especially below 50 K) the electrical resistivity is extremely sensitive to sample purity. Thus the low-temperature values refer to samples of specified purity and treatment. The references should be consulted for further information on this point, as well as for values at additional temperatures. The second part of the table gives resistivity values in the neighborhood of room temperature for other metallic elements that have not been studied over an extended temperature range.

T/K

1 10 20 40 60 80 100 150 200 273 293 298 300 400 500 600 700 800 900

T/K

1 10 20 40 60 80 100 150 200 273 293 298 300 400 500 600 700 800 900

Aluminum 0.000100 0.000193 0.000755 0.0181 0.0959 0.245 0.442 1.006 1.587 2.417 2.650 2.709 2.733 3.87 4.99 6.13 7.35 8.70 10.18 Gold 0.0220 0.0226 0.035 0.141 0.308 0.481 0.650 1.061 1.462 2.051 2.214 2.255 2.271 3.107 3.97 4.87 5.82 6.81 7.86

References 1. C. Y. Ho, et al., J. Phys. Chem. Ref. Data, 12, 183–322, 1983; 13, 1069– 1096, 1984; 13, 1097–1130, 1984, 13, 1131–1172, 1984. 2. R. A. Matula, J. Phys Chem. Ref. Data, 8, 1147–1298, 1979. 3. T. C. Chi, J. Phys. Chem. Ref. Data, 8, 339–438, 1979; 8, 439–498, 1979. 4. K. H. Hellwege, Ed., Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, Group III, Vol. 15, Subvolume a, Springer-Verlag, Heidelberg, 1982. 5. L. A. Hall, Survey of Electrical Resistivity Measurements on 16 Pure Metals in the Temperature Range 0 to 273 K, NBS Technical Note 365, U.S. Superintendent of Documents, 1968.

Electrical Resistivity in 10–8 Ω m

Barium 0.081 0.189 0.94 2.91 4.86 6.83 8.85 14.3 20.2 30.2 33.2 34.0 34.3 51.4 72.4 98.2 130 168 216

Hafnium 1.00 1.00 1.11 2.52 4.53 6.75 9.12 15.0 21.0 30.4 33.1 33.7 34.0 48.1 63.1 78.5

Beryllium 0.0332 0.0332 0.0336 0.0367 0.067 0.075 0.133 0.510 1.29 3.02 3.56 3.70 3.76 6.76 9.9 13.2 16.5 20.0 23.7

Iron 0.0225 0.0238 0.0287 0.0758 0.271 0.693 1.28 3.15 5.20 8.57 9.61 9.87 9.98 16.1 23.7 32.9 44.0 57.1

Calcium 0.045 0.047 0.060 0.175 0.40 0.65 0.91 1.56 2.19 3.11 3.36 3.42 3.45 4.7 6.0 7.3 8.7 10.0 11.4 Lead

4.9 6.4 9.9 13.6 19.2 20.8 21.1 21.3 29.6 38.3

Cesium 0.0026 0.243 0.86 1.99 3.07 4.16 5.28 8.43 12.2 18.7 20.5 20.8 21.0

Lithium 0.007 0.008 0.012 0.074 0.345 1.00 1.73 3.72 5.71 8.53 9.28 9.47 9.55 13.4

Chromium

1.6 4.5 7.7 11.8 12.5 12.6 12.7 15.8 20.1 24.7 29.5 34.6 39.9 Magnesium 0.0062 0.0069 0.0123 0.074 0.261 0.557 0.91 1.84 2.75 4.05 4.39 4.48 4.51 6.19 7.86 9.52 11.2 12.8 14.4

Copper 0.00200 0.00202 0.00280 0.0239 0.0971 0.215 0.348 0.699 1.046 1.543 1.678 1.712 1.725 2.402 3.090 3.792 4.514 5.262 6.041 Manganese 7.02 18.9 54 116 131 132 132 136 139 143 144 144 144 147 149 151 152

12-39

Section 12.indb 39

4/28/05 1:55:38 PM

Electrical Resistivity of Pure Metals

12-40 T/K

Molybdenum 0.00070 0.00089 0.00261 0.0457 0.206 0.482 0.858 1.99 3.13 4.85 5.34 5.47 5.52 8.02 10.6 13.1 15.8 18.4 21.2

T/K

Sodium 0.0009 0.0015 0.016 0.172 0.447 0.80 1.16 2.03 2.89 4.33 4.77 4.88 4.93

1 10 20 40 60 80 100 150 200 273 293 298 300 400 500 600 700 800 900 1 10 20 40 60 80 100 150 200 273 293 298 300 400 500 600 700 800 900

Element Antimony Bismuth Cadmium Cerium (β, hex) Cerium (γ, cub) Cobalt Dysprosium Erbium Europium Gadolinium Gallium Holmium Indium Iridium Lanthanum Lutetium Mercury Neodymium Niobium

Section 12.indb 40

T/K

273 273 273 290–300 298 273 290–300 290–300 290–300 290–300 273 290–300 273 273 290–300 290–300 298 290–300 273

Nickel 0.0032 0.0057 0.0140 0.068 0.242 0.545 0.96 2.21 3.67 6.16 6.93 7.12 7.20 11.8 17.7 25.5 32.1 35.5 38.6

Palladium 0.0200 0.0242 0.0563 0.334 0.938 1.75 2.62 4.80 6.88 9.78 10.54 10.73 10.80 14.48 17.94 21.2 24.2 27.1 29.4

Platinum 0.002 0.0154 0.0484 0.409 1.107 1.922 2.755 4.76 6.77 9.6 10.5 10.7 10.8 14.6 18.3 21.9 25.4 28.7 32.0

Potassium 0.0008 0.0160 0.117 0.480 0.90 1.34 1.79 2.99 4.26 6.49 7.20 7.39 7.47

Rubidium 0.0131 0.109 0.444 1.21 1.94 2.65 3.36 5.27 7.49 11.5 12.8 13.1 13.3

Strontium 0.80 0.80 0.92 1.70 2.68 3.64 4.58 6.84 9.04 12.3 13.2 13.4 13.5 17.8 22.2 26.7 31.2 35.6

Tantalum 0.10 0.102 0.146 0.751 1.65 2.62 3.64 6.19 8.66 12.2 13.1 13.4 13.5 18.2 22.9 27.4 31.8 35.9 40.1

Tungsten 0.000016 0.000137 0.00196 0.0544 0.266 0.606 1.02 2.09 3.18 4.82 5.28 5.39 5.44 7.83 10.3 13.0 15.7 18.6 21.5

Vanadium

Zinc 0.0100 0.0112 0.0387 0.306 0.715 1.15 1.60 2.71 3.83 5.46 5.90 6.01 6.06 8.37 10.82 13.49

Electrical resistivity 10–8 Ω m 39 107 6.8 82.8 74.4 5.6 92.6 86.0 90.0 131 13.6 81.4 8.0 4.7 61.5 58.2 96.1 64.3 15.2

0.0145 0.039 0.304 1.11 2.41 4.01 8.2 12.4 18.1 19.7 20.1 20.2 28.0 34.8 41.1 47.2 53.1 58.7

Element Osmium Polonium Praseodymium Promethium Protactinium Rhenium Rhodium Ruthenium Samarium Scandium Terbium Thallium Thorium Thulium Tin Titanium Uranium Ytterbium Yttrium

T/K

273 273 290–300 290–300 273 273 273 273 290–300 290–300 290–300 273 273 290–300 273 273 273 290–300 290–300

Silver 0.00100 0.00115 0.0042 0.0539 0.162 0.289 0.418 0.726 1.029 1.467 1.587 1.617 1.629 2.241 2.87 3.53 4.21 4.91 5.64 Zirconium 0.250 0.253 0.357 1.44 3.75 6.64 9.79 17.8 26.3 38.8 42.1 42.9 43.3 60.3 76.5 91.5 104.2 114.9 123.1

Electrical resistivity 10–8 Ω m 8.1 40 70.0 75 est. 17.7 17.2 4.3 7.1 94.0 56.2 115 15 14.7 67.6 11.5 39 28 25.0 59.6

4/28/05 1:55:40 PM

ELECTRICAL RESISTIVITY OF SELECTED ALLOYS These values were obtained by fitting all available measurements to a theoretical formulation describing the temperature and composition dependence of the electrical resistivity of metals. Some of the values listed here fall in regions of temperature and composition where no actual measurements exist. Details of the procedure may be found in the reference.

Wt % Al 99a 95a 90b 85b 80b 70b 60b 50b 40c 30c 25f 15h 10g 5c 1b

Wt % Al 99c 95c 90c 10b 5b 1a

Wt % Cu 99c 95c 90c 85c 80c 70c 60c 50c 40c 30c 25c 15c 10c 5c 1c

Values of the resistivity are given in units of 10–8 Ω m. General comments in the preceding table for pure metals also apply here

Reference C. Y. Ho, et al., J. Phys. Chem. Ref. Data, 12, 183–322, 1983.

Aluminum-Copper 293 K 300 K

100 K

273 K

0.531 0.895 1.38 1.88 2.34 3.02 3.49 4.00

2.51 2.88 3.36 3.87 4.33 5.03 5.56 6.22 7.57 11.2 16.3

8.71 7.92 3.22

10.8 9.43 4.46

100 K

273 K

0.958 3.01 5.42 14.0 9.93 2.78

2.96 5.05 7.52 17.1 13.1 5.92

3.18 5.28 7.76 17.4 13.4 6.25

100 K

273 K

Copper-Gold 293 K

0.520 1.21 2.11 3.01 3.95 5.91 8.04 9.88 11.44 12.43 12.59 11.38 9.33 5.91 2.00

1.73 2.41 3.29 4.20 5.15 7.12 9.18 11.07 12.70 13.77 13.93 12.75 10.70 7.25 3.40

1.86 2.54 4.42 4.33 5.28 7.25 9.13 11.20 12.85 13.93 14.09 12.91 10.86 7.41 3.57

2.74 3.10 3.59 4.10 4.58 5.31 5.88 6.55 7.96 11.8 17.2 12.3 11.0 9.61 4.60

350 K

400 K

2.82 3.18 3.67 4.19 4.67 5.41 5.99 6.67 8.10 12.0 17.6

3.38 3.75 4.25 4.79 5.31 6.16 6.77 7.55 9.12 13.5 19.8

3.95 4.33 4.86 5.42 5.99 6.94 7.63 8.52 10.2 15.2 22.2

11.1 9.68 4.65

11.7 10.2 5.00

12.3 10.7 5.37

Aluminum-Magnesium 293 K 300 K 3.26 5.36 7.85 17.6 13.5 6.37 300 K 1.91 2.59 3.46 4.38 5.32 7.30 9.36 11.25 12.90 13.99 14.14 12.96 10.91 7.46 3.62

350 K 3.82 5.93 8.43 18.4 14.3 7.20 350 K 2.24 2.92 3.79 4.71 5.65 7.64 9.70 11.60 13.27 14.38 14.54 13.36 11.31 7.87 4.03

400 K 4.39 6.51 9.02 19.2 15.2 8.03 400 K 2.58 3.26 4.12 5.05 5.99 7.99 10.05 11.94 13.65 14.78 14.94 13.77 11.72 8.28 4.45

12-41

Section 12.indb 41

4/28/05 1:55:42 PM

Electrical Resistivity of Selected Alloys

12-42

Wt % Cu 99c 95c 90c 85c 80c 70i 60i 50i 40c 30i 25c 15c 10c 5c 1c

Wt % Cu 99c 95c 90c 85c 80c 70c 60c 50c 40c 30c 25c 15c 10c 5c 1c

Wt % Cu 99b 95b 90b 85b 80b 70b

Wt % Au 99c 95c 90i 85b 80b 70c 60b 50a 40a 30b 25b 15a 10a 5a 1a

Section 12.indb 42

100 K 1.45 6.19 12.08 18.01 23.89 35.73 45.76 50.22 36.77 26.73 22.22 13.49 9.28 5.20 1.81 100 K 0.91 2.99 5.69 8.30 10.74 15.67 20.45 26.07 33.53 45.03 44.12 31.79 23.00 13.09 8.97

273 K 2.71 7.60 13.69 19.63 25.46 36.67 45.43 50.19 47.42 40.19 33.46 22.00 16.65 11.49 7.23 273 K

Copper-Nickel 293 K 2.85 7.71 13.89 19.83 25.66 36.72 45.38 50.05 47.73 41.79 35.11 23.35 17.82 12.50 8.08

2.23 4.35 7.03 9.61 12.12 17.01 21.87 27.79 35.51 46.66 46.45 36.99 29.51 20.75 12.67

100 K

273 K

Copper-Zinc 293 K

0.671 1.54 2.33 2.93 3.44 4.08

1.84 2.78 3.66 4.37 5.01 5.87

100 K

273 K 2.69 5.21 8.01 10.50 12.75 18.23 26.70 27.23 24.65 20.82 18.86 15.08 13.25 11.49 10.07

2.91 7.82 13.96 19.90 25.72 36.76 43.35 50.01 47.82 42.34 35.69 23.85 18.26 12.90 8.37

Copper-Palladium 293 K 300 K

2.10 4.21 6.89 9.48 11.99 16.87 21.73 27.62 35.31 46.50 46.25 36.52 28.90 20.00 11.90

1.31 3.88 6.70 9.14 11.23 16.44 24.64 23.09 19.40 14.94 12.72 8.54 6.54 4.58 3.01

300 K

1.97 2.92 3.81 4.54 5.19 6.08 Gold-Palladium 293 K 2.86 5.35 8.17 10.66 12.93 18.46 26.94 27.63 25.23 21.49 19.53 15.77 13.95 12.21 10.85

2.27 4.40 7.08 9.66 12.16 17.06 21.92 27.86 35.57 46.71 46.52 37.16 29.73 21.02 12.93 300 K 2.02 2.97 3.86 4.60 5.26 6.15 300 K 2.91 5.41 8.22 10.72 12.99 18.54 27.02 27.76 25.42 21.72 19.77 16.01 14.20 12.46 11.12

350 K 3.27 8.22 14.40 20.32 26.12 36.85 45.20 49.73 48.28 44.51 39.67 27.60 21.51 15.69 10.63 350 K 2.59 4.74 7.41 10.01 12.51 17.41 22.30 28.25 36.03 47.11 46.99 38.28 31.19 22.84 14.82 350 K 2.36 3.33 4.25 5.02 5.71 6.67 350 K 3.32 5.79 8.56 11.10 13.45 19.10 27.63 28.64 26.74 23.35 21.51 17.80 16.00 14.26 12.99

400 K 3.62 8.62 14.81 20.70 26.44 36.89 45.01 49.50 48.49 45.40 42.81 31.38 25.19 18.78 13.18 400 K 2.92 5.08 7.74 10.36 12.87 17.78 22.69 28.64 36.47 47.47 47.43 39.35 32.56 24.54 16.68 400 K 2.71 3.69 4.63 5.44 6.17 7.19 400 K 3.73 6.17 8.93 11.48 13.93 19.67 28.23 29.42 27.95 24.92 23.19 19.61 17.81 16.07 14.80

4/28/05 1:55:44 PM

Electrical Resistivity of Selected Alloys

Wt % Au 99b 95a 90j 85j 80j 70j 60j 50j 40j 30a 25a 15a 10a 5i 1b

Wt % Fe 99a 95c 90c 85c 80c 70b 60c 50d 40d 30c 25b 15c 10c 5c 1b

Wt % Ag 99b 95b 90b 85k 80k 70k 60i 50k 40m 30b 25k 15i 10i 5b 1a

b c d e f g h i j k m

Section 12.indb 43

12-43

100 K

273 K

Gold-Silver 293 K

1.20 3.16 5.16 6.75 7.96 9.36 9.61 8.96 7.69 6.15 5.29 3.42 2.44 1.44 0.627

2.58 4.58 6.57 8.14 9.34 10.70 10.92 10.23 8.92 7.34 6.46 4.55 3.54 2.52 1.69

2.75 4.74 6.73 8.30 9.50 10.86 11.07 10.37 9.06 7.47 6.59 4.67 3.66 2.64 1.80

100 K

273 K

Iron-Nickel 293 K

10.9 18.7 24.2 27.8 30.1 32.3 53.8 28.4 19.6 15.3 14.3 12.6 11.4 9.66 7.17

12.0 19.9 25.5 29.2 31.6 33.9 57.1 30.6 21.6 17.1 15.9 13.8 12.5 10.6 7.94

3.32 10.0 14.5 17.5 19.3 20.9 28.6 12.3 7.73 5.97 5.62 4.97 4.20 3.34 1.66 100 K 0.839 2.528 4.72 6.82 8.91 13.43 19.4 29.3 40.8 37.1 32.4 21.0 14.95 8.91 3.97

273 K 1.891 3.58 5.82 7.92 10.01 14.53 20.9 31.2 42.2 40.4 36.67 27.08 21.69 15.98 11.06

300 K 2.80 4.79 6.78 8.36 9.55 10.91 11.12 10.42 9.11 7.52 6.63 4.72 3.71 2.68 1.84 300 K 12.4 20.2 25.9 29.7 32.2 34.4 58.2 31.4 22.5 17.7 16.4 14.2 12.9 10.9 8.12

Silver-Palladium 293 K 300 K 2.007 3.70 5.94 8.04 10.13 14.65 21.1 31.4 42.2 40.6 37.06 26.68 22.39 16.72 11.82

Uncertainty in resistivity is ± 2%. Uncertainty in resistivity is ± 3%. Uncertainty in resistivity is ± 5%. Uncertainty in resistivity is ± 7% below 300 K and ± 5% at 300 and 400 K. Uncertainty in resistivity is ± 7%. Uncertainty in resistivity is ± 8%. Uncertainty in resistivity is ± 10%. Uncertainty in resistivity is ± 12%. Uncertainty in resistivity is ± 4%. Uncertainty in resistivity is ± 1%. Uncertainty in resistivity is ± 3% up to 300 K and ± 4% above 300 K. Uncertainty in resistivity is ± 2% up to 300 K and ± 4% above 300 K.

2.049 3.74 5.98 8.08 10.17 14.69 21.2 31.5 42.2 40.7 37.19 27.89 22.63 16.98 12.08

350 K 3.22 5.19 7.19 8.75 9.94 11.29 11.50 10.78 9.46 7.85 6.96 5.03 4.00 2.96 2.12

400 K 3.63 5.59 7.58 9.15 10.33 11.68 11.87 11.14 9.81 8.19 7.30 5.34 4.31 3.25 2.42

400 K 18.7 26.8 33.2 37.3 40.0 42.4 73.9 43.7 34.0 27.4 25.1 21.1 18.9 16.1 12.8 350 K 2.35 4.04 6.28 8.38 10.47 14.99 21.6 32.0 42.3 41.3 38.1 29.3 24.3 18.8 13.92

400 K 2.66 4.34 6.59 8.68 10.78 15.30 22.0 32.4 42.3 41.7 38.8 30.6 25.9 20.5 15.70

4/28/05 1:55:46 PM

PERMITTIVITY (DIELECTRIC CONSTANT) OF INORGANIC SOLIDS H. P. R. Frederikse frequency of the measurement is given in the last column (i.r. indicates a measurement in the infrared). Substances are listed in alphabetical order by chemical formula.

This table lists the permittivity ε, frequently called the dielectric constant, of a number of inorganic solids. When the material is not isotropic, the individual components of the permittivity are given. A superscript S indicates a measurement made under constant strain (“clamped” dielectric constant). If the constraint is removed, the measurement yields εT, the “unclamped” or free dielectric constant. The temperature of the measurement is given when available; the symbol r.t. indicates a value at nominal room temperature. The Formula Ag3AsS3

Name Silver thioarsenate (Proustite)

Reference

Young, K. F. and Frederikse, H. P. R., J. Phys. Chem. Ref. Data, 2, 313, 1973.

T/K

εijk T 11

S 11

T 33

S 11

ε = 16.5, ε = 14.5 ε = 20.0 , ε = 18.0

AgBr AgCN AgCl AgNO3 AgNa(NO2)2 Ag2O (AlF)2SiO4

Silver bromide Silver cyanide Silver chloride Silver nitrate Silver sodium nitrite Silver oxide Aluminum fluosilicate (topaz)

Al2O3

Aluminum oxide (alumina)

AlPO4 AlSb AsF3 BN BaCO3 Ba(COOH)2

Aluminum phosphate Aluminum antimonide Arsenic trifluoride Boron nitride Barium carbonate Barium formate

BaCl2 BaCl2 ⋅ 2H2O BaF2 Ba(NO3)2

Barium chloride Barium chloride dihydrate Barium fluoride Barium nitrate

Ba2NaNb5O15

Barium sodium niobate (“Bananas”)

12.50 5.6 11.15 9.0 4.5 ± 0.5 8.8 ε 11 = 6.62 ε 22 = 6.58 ε 33 = 6.95 ε 11 = ε 22 = 9.34 ε33 = 11.54 T ε11 = 6.05

11.21 5.7 7.1 8.53 ε 11 = 7.9 ε22 = 5.9 ε33 = 7.5 9.81 9.00 7.32 4.95 S T ε11 = 222, ε11 = 235 S 22

T 22

ε = 227, ε = 247 S 33

T 33

ε = 32, ε = 51 BaO BaO2 BaS BaSO4 BaSnO3 BaTiO3

Barium oxide (baria) Barium peroxide Barium sulfide Barium sulfate Barium stannate Barium titanate

34 ± 1 10.7 19.23 11.4 18 T ε11 = 3600

Barium tungstate

r.t. r.t. r.t. r.t. 293 r.t. r.t. 297 297 297 298 298

2 × 107

r.t. 300 r.t. r.t. 291 r.t. r.t. r.t. r.t. r.t. 292 292

103 i.r.

296

104

106 5 × 105 9.4 ×109 7 × 103 7 × 103 7 × 103 102 – 8 × 109 102 – 8 × 109

i.r. 2 × 105 103 103 103 103 5 × 102 – 1011 2 × 105

296 296 248, 333 r.t. r.t. 288 298

60 × 107 2 × 106 7.25 × 106 108 25 × 105 105

298

2.5 × 108

T 33

298

105

S 33

298

2.5 × 108

298 298 297.5 297.5

1.6 × 103 1.6 × 103

ε = 80

BaWO4

2 × 107

298

ε = 150

Barium titanium niobate

r.t.

S 11

ε = 2300

Ba6Ti2Nb8O30

ν/Hz

ε11 = ε22 ≈ 190 ε33 ≈ 220 ε 11 = ε22 = 35.5 ± 0.2 ε33 = 37.2 ± 0.2

12-44

Section 12.indb 44

4/28/05 1:55:53 PM

Permittivity (Dielectric Constant) of Inorganic Solids Formula BaZrO3 Be3Al2Si6O18

Name Barium zirconate Beryllium aluminum silicate (Beryl)

BeCO3 BeO BiFeO3

Beryllium carbonate Beryllium oxide (beryllia) Bismuth iron oxide

Bi12GeO20 Bi(GeO4)3 Bi2O3 Bi4Ti3O12 C

C4H4O6

Bismuth germanite Bismuth germanate Bismuth sesquioxide Bismuth titanate Diamond Type I Type IIa Tartaric acid

C6H14N2O6

Ethylene diamine tartrate (EDT)

12-45 εijk 43 ε33 = 5.95 ε11 = ε22 = 6.86 9.7 7.35 ± 0.2 40 ± 3 S ε11 = 38

r.t. 293 r.t. r.t.

16 18.2 112 5.87 ± 0.19 5.66 ± 0.04 ε11 = ε22 = 4.3 ε33 = 4.5 ε13 = 0.55 T ε11 = 5.0

300 300 298 298 298

ε T22 = 8.3

293 293

T 13

ε = 0.7

293

T ε11 = 4.0

r.t.

C6H12O6NaBr

Dextrose sodium bromide

(CH3NH3)Al(SO4)2 ⋅ 2H2O Ca2B6O11 ⋅ 5H2O

Methyl ammonium alum (MASD)

Colemanite

CaCO3

Calcium carbonate

CaCeO3 CaF2 CaMoO4

Calcium cerate Calcium fluoride Calcium molybdate

Ca(NO3)2 CaNb2O6 Ca2Nb2O7 CaO CaS CaSO4 ⋅ 2H2O

Calcium nitrate Calcium niobate Calcium pyroniobate Calcium oxide Calcium sulfide Calcium sulfate dihydrate

CaTiO3 CaWO4

Calcium titanate Calcium tungstate

Cd3As2 CdBr2 CdF2 CdS

Cadmium arsenide Cadmium bromide Cadmium fluoride Cadmium sulfide

ε11 = 20 ε33 = 25 ε11 = 8.67 ε22 = 8.69 ε33 = 8.31 21 6.81 ε11 = ε22 = 24.0 ± 0.2 ε33 = 20.0 ± 0.2 6.54 ε11 = 22.8 ± 1.9 ~45 11.8 ± 0.3 6.699 ε11 = 5.10 ε22 = 5.24 ε33 = 10.30 165 ε11 = ε22 = 11.7 ± 0.1 ε33 = 9.5 ± 0.2 ε33 = 18.5 8.6 8.33 ± 0.08 ε11 = ε22 = 8.7 ε33 = 9.25 ε11 = ε22 = 8.37 ε33 = 9.00 εT11 = 8.48

2 × 106 103 103 103

103

293 293 r.t. r.t. r.t. r.t. 300 297.5 297.5 292 r.t. r.t. 283 r.t. r.t. r.t. r.t. r.t. 297.5 297.5 4 293 300 300 300 8 8

103 103 9.4 × 1010 9.4 × 1010 9.4 × 1010 5 × 102–1011 <10 <10 2 × 105 (5–500) × 103 5 × 107 2 × 106 7.25 × 106

1.59 × 103 1.59 × 103 5 × 105 105–107 i.r. i.r. i.r. i.r.

104

S 11

T 11

298

104

S 33

T 33

298

104

S 11

T 11

298

104

ε = 9.02, ε = 9.35 ε = 9.53, ε = 10.33

Section 12.indb 45

7 × 103 7 × 103 2 × 105 2 × 106 9.4 × 109

197

ε T33 = 9.48

Cadmium selenide

ν/Hz

293

T 33

ε = 6.0

CdSe

T/K r.t. 297 297 291 293 300

ε = 9.53, ε = 9.70

4/28/05 1:56:00 PM

Permittivity (Dielectric Constant) of Inorganic Solids

12-46 Formula

Name

CdTe

Cadmium telluride

Cd2Nb2O7 CeO2 CoNb2O6

Cadmium pyroniobate Cerium oxide Cobalt niobate

CoO Cr2O3

Cobalt oxide Chromic sesquioxide

CsAl(SO4)2 ⋅ 12H2O CsBr Cs2CO3 CsCl CsH2AsO4 CsH2PO4 CsH3(SeO3)2

Cesium alum Cesium bromide Cesium carbonate Cesium chloride Cesium dihydrogen arsenate (CDA) Cesium dihydrogen phosphate (CDP) Cesium trihydrogen selenite

CsI CsNO3

Cesium iodide Cesium nitrate

CsPbCl3 CuBr CuCl CuO Cu2O CuSO4 ⋅ 5H2O EuF2 Eu2(MoO4)3 EuS FeO Fe2O3 Fe2O3-α Fe3O4 GaAs

Cesium lead chloride Cuprous bromide Cuprous chloride Cupric oxide Cuprous oxide (Cuprite) Cupric sulfate pentahydrate Europium fluoride Europium molybdate Europium sulfide Ferrous oxide Ferric sesquioxide Ferric sesquioxide (hematite) Ferrosoferric oxide (magnetite) Gallium arsenide

GaP

Gallium phosphide

GaSb

Gallium antimonide

Gd2(MoO4)3

Gadolinium molybdate

Germanium

GeO2 HIO3

Germanium dioxide Iodic acid

HNH4(ClCH2COO)2 H2O

Hydrogen ammonium dichloroacetate Ice I (P = 0 kbar) Ice III (P = 3 kbar) Ice V (P = 5 kbar) Ice VI (P = 8 kbar) Mercurous chloride (Calumel) Mercuric chloride Mercurous sulfide (Cinnabar)

HgCl HgCl2 HgS

Section 12.indb 46

εijk ε S33 = 10.2, ε T33 = 10.65

T/K

ν/Hz

298

104

ε11 = ε22 = 10.60 ± 0.15 ε33 = 7.05 ± 0.05 500–580 7.0 ε11 = 18.4 ± 1.1 ε22 = 21.4 ± 1.1 ε33 = 33.0 ± 0.7 12.9 ε11 = ε22 = 13.3 ε33 = 11.9 8 5.0 6.38 6.53 7.2 4.8 6.15 ε11 = 80 ε22 = 63 ε33 = 12 6.31 ε11 = ε22 = 9.4 ε33 = 8.3 14.37 8.0 9.8 ± 0.5 18.1 7.60 ± 0.06 6.60 7.7 ± 0.2 9.5 13.10 ± 0.04 14.2 4.5 12 20 13.13 12.90 11.1 10.75 ± 0.1 15.69 15.7 εT = 10 ε S = 9.5 16.0 ± 0.3 15.8 ± 0.2 ε11 = ε22 = 7.44 ε11 = 7.5 ε22 = 12.4 ε33 = 8.1 ε[102] = 5.9 99 117 114 193 ε11 = ε22 = 14.0 6.5 ε11 = ε22 = 18.0 ε33 = 32.5

297 297 293 r.t. r.t. r.t. r.t. 298 298.5 298.5 315 (TN) r.t. 298 291 298 273 285 273 273 273 298 r.t. r.t. 300 293 r.t. r.t. r.t. r.t. 298 298 80 r.t. r.t. r.t. 300 4 r.t. 1.6 r.t. 4 298 298 4 r.t. r.t. r.t. r.t. r.t. r.t. 243 243 243 243 r.t. r.t. r.t. r.t.

i.r. i.r. 103 2 × 106 (5–500) × 103 (5–500) × 103 (5–500) × 103 102– 1010 103 103 6 × 1010 20–20 × 103 1.6 × 103 2 × 105 9.5 ×109 9.5 × 109 105 105 105 1.6 × 103 5 × 105 5 × 105 105–106 5 × 105 103 2 × 106 105 (1–300) × 103 5 × 102–105 2 × 106 105–107 6 × 1010 105–107 i.r. i.r. i.r. 103 9.2 × 109 500–3 × 1010 i.r. 103 103 103 105

1012 1012 i.r. i.r.

4/28/05 1:56:04 PM

Permittivity (Dielectric Constant) of Inorganic Solids Formula HgSe I2

Name Mercurous selenide Iodine

InAs

Indium arsenide

InP InSb KAl(SO4)2 ⋅ 12H2O KBr

Indium phosphide Indium antimonide Potassium alum Potassium bromide

KBrO3 KCN K2CO3 K2C4H4O6 ⋅ 1/2 H2O

Potassium bromate Potassium cyanide Potassium carbonate Dipotassium tartrate (DKT)

KCl

Potassium chloride

KClO3 KClO4 K2CrO4 KCr(SO4)2 ⋅ 12H2O KD2AsO4

Potassium chlorate Potassium perchlorate Potassium chromate Potassium chrome alum Potassium dideuterium arsenate (KDDA)

KD2PO4 KF KH2AsO4

Potassium dideuterium phosphate (KDDP) Potassium fluoride Potassium dihydrogen arsenate (KDA)

KH2PO4

Potassium dihydrogen phosphate (KDP)

K2HPO4 KI KIO3

Dipotassium monohydrogen orthophosphate Potassium iodide Potassium iodate

(K,H)Al3(SiO4)3 (K,H)Mg3Al(SiO4)3

Mica (muscovite) Mica (Canadian)

KNO2 KNO3 KNbO3 K3PO4 KSCN K2SO4 K2S3O6 K2S4O6 K2S5O6 ⋅ H2O K2S6O6 K2SeO4

Potassium nitrite Potassium nitrate Potassium niobate Potassium orthophosphate Potassium thiocyanate Potassium sulfate Potassium trithionate Potassium tetrathionate Potassium pentathionate Potassium hexathionate Potassium selenate

KSr2Nb5O15

Potassium strontium niobate

KTaNbO3

Potassium tantalate niobate (KTN)

KTaO3 LaScO3

Potassium tantalate Lanthanum scandate

Section 12.indb 47

12-47 εijk 25.6 ε11 = 6 ε22 = 3 ε33 = 40 14.55 ± 0.3 15.15 12.61 17.88 6.5 4.88 4.53 7.3 6.15 4.96 ε11 = 6.44 ε22 = 5.80 ε33 = 6.49 ε13 = 0.005 4.86 ± 0.02 4.50 5.1 5.9 7.3 6.5 ε11 = 70 ε33 = 31 50 ± 2 6.05 ε11 = 60 ε33 = 24 46 ε11 = 42 ε33 = 21 9.05 5.00 170 10 ε[101] ≈ 40,70 16.85 5.4 ε11 = ε22 = 6.9 ε33 = 7.3 25 4.37 700 7.75 7.9 6.4 5.7 5.5 7.8 7.8 ε11 = 5.9 ε22 = 7.7 ε11 = ε11 ≈ 1200 ε33 ≈ 800 34,000 6,000 242 30

T/K r.t. r.t. r.t. r.t. r.t. 4 r.t. 4 r.t. 300 4.2 r.t. r.t. 291 r.t. r.t. r.t. r.t. r.t. 4.2 r.t. r.t. r.t. 100–240 298 298 297 298 298 298 r.t. r.t. r.t. r.t. 255 293 r.t. r.t. 299 298 298 305 293 r.t. r.t. r.t. r.t. 293 293 293 293 r.t. r.t. 298 298 273 293 298 r.t.

ν/Hz 104–106 5 × 104–107 5 × 104–107 5 × 104–107 i.r. i.r. i.r. i.r. 20–20 × 103

2 × 106 2 × 106 2 × 105

5 × 103 2 × 106 2 × 106 6 × 107 175 × 103

103 2 × 106

103

2 × 106 9.4 × 1010 105 105 105 2 × 106 102–3 × 109 102–104 104 2 × 105 2 × 106 2 × 106 2 × 106 1.8 × 106 1.8 × 106 1.8 × 106 1.8 × 106 103 103

104 104 2 × 105

4/28/05 1:56:06 PM

Permittivity (Dielectric Constant) of Inorganic Solids

12-48 Formula LiBr Li2CO3 LiCl LiD LiF

Name Lithium bromide Lithium carbonate Lithium chloride Lithium deuteride Lithium fluoride

LiGaO2

Lithium metagallate

εijk 12.1 4.9 11.05 14.0 ± 0.5 9.00 9.11 T T ε11 = 7.0, ε 22 = 6.0 ε T33 = 9.5 S 11

Lithium-6 hydride Lithium-7 hydride Lithium trihydrogen selenite

LiI LiIO3

Lithium iodide Lithium iodate

LiNH4C4O6 ⋅ H2O

Lithium ammonium tartrate (LAT)

LiNa3CrO4 ⋅ 6H2O LiNa3MoO4 ⋅ 6H2O

Lithium trisodium chromate Lithium trisodium molybdate

LiNbO3

Lithium niobate

Li2SO4 ⋅ H2O

Lithium sulfate monohydrate

LiTaO3

Lithium tantalate

13.2 ± 0.5 12.9 ± 0.5 29 ε11 = 13.0 ε22 = 12.9 ε33 = 46 11.03 ε11 = ε22 = 65 ε33 = 554 T ε11 = 7.2

MgCO3 MgNb2O6

Lithium thallium tartrate (LTT) Magnesium borate monochloride (boracite) Magnesium carbonate Magnesium niobate

MgO (MgO)xAl2O3 MgSO4 MgSO4 ⋅ 7H2O MgTiO3 MgWO4

Magnesium oxide (Periclase) Spinel Magnesium sulfate Magnesium sulfate septahydrate Magnesium titanate Magnesium tungstate

MnNb2O6

Manganese niobate

MnO MnO2 Mn2O3 MnWO4

Manganese oxide (Pyrolusite) Manganese dioxide Manganese sesquioxide Manganese tungstate

Section 12.indb 48

r.t. r.t. r.t. r.t. 298 r.t. r.t. r.t. r.t. 294.5 298

104

2 × 106 103

298

ε T22 = 8.0

298

ε T33 = 6.9

298

8.0 ε11 = 6.7 ε33 = 5.3 ε11 = ε22 = 82 ε33= 30 ε11 = 5.6 ε22 = 10.3 ε33 = 6.5 ε13 = 0.07 ε11 = ε22 = 53 ε33 = 46 S S ε11 = ε 22 = 41

r.t. r.t. r.t. 298 298 298 298 298 298 r.t. r.t.

S 33

LiTIC4O6 ⋅ H2O Mg3B7O13Cl

ν/Hz 2 × 106 2 × 105 2 × 106 i.r. 102–107 102–107

r.t. S 22

ε = 6.8, ε = 5.8 Li6H Li7H LiH3(SeO3)2

T/K r.t. 291 r.t. r.t. 298 353

103 103 103 105 105

105 105

r.t.

ε = 43

r.t.

T T ε11 = ε 22 = 51

r.t.

ε T33 = 45

r.t.

ε11 ≈ 20 ε11 = 14.1

80 r.t.

8.1 ε11 = 16.4 ± 0.5 ε22 = 20.9 ± 0.5 ε33 = 32.4 ± 0.5 9.65 8.6 8.2 5.46 13.5 ε11 = 18.0 ± 1 ε22 = 18.0 ± 1 ε11 = 17.4 ± 2 ε22 = 16.1 ± 0.5 ε33 = 30.7 ± 1 12.8 ~104 8 ε11 = 19.3 ± 1.3

291 r.t. r.t. r.t. 298 r.t. r.t. r.t. r.t. r.t. r.t. r.t. r.t. r.t. r.t. 298 r.t. r.t.

5 × 105 2 × 105 (5–500) × 103 (5–500) × 103 (5–500) × 103 102–108

(5–500) × 103 (5–500) × 103 (5–500) × 103 (5–500) × 103 (5–500) × 103 6 × 1010 104 6 × 1010 (5–500) × 103

4/28/05 1:56:13 PM

Permittivity (Dielectric Constant) of Inorganic Solids Formula

Name

N(CH3)4HgBr3

N4(CH2)6 (ND4)2BeF4

Tetramethylammonium tribromomercurate (TTM) Tetramethylammonium triiodo mercurate (TTM) Hexamethylene tetramine (HMTA) Deuteroammonium fluoberyllate

(ND4)2SO4

Deuteroammonium sulfate

(NH2 ⋅ CH2COOH)3 ⋅ H2SO4

N(CH3)4HgI3

12-49 εijk ε22 = 14.3 ± 0.5 ε33 = 16.5 ± 1.1 ~10

T/K r.t. r.t. 233–373

~10

233–373

2.6 ± 0.2 ε11 = 10 ε22 = 9 ε33 = 9 ε11 = 9 ε22 = 10 ε33 = 9

r.t. r.t. r.t. r.t. r.t. r.t. r.t.

109–1010

Triglycine sulfate (TGS)

ε11 = 9 ε22 = 30 ε33 = 6.5

273 273 273

104 104 104

293

1.6 × 103

(NH2 ⋅ CH2COOH)3 ⋅ H2SeO4 (NH2 ⋅ CH2COOH)3 ⋅ H2BeF4 NH4Al(SO4)2 ⋅ 12H2O (NH4)2BeF4

Triglycine selenate (TGSe)

200

Triglycine fluorberyllate (TGFB) Ammonium alum Ammonium fluorberyllate

NH4Br NH4I (NH4)2C2H6O6

Ammonium bromide Ammonium iodide Ammonium tartrate

(NH4)2Cd2(SO4)3 NH4Cl NH4(ClCH2COO) NH4Cr(SO4)2 ⋅ 12H2O NH4HSO4 NH4H2AsO4

Ammonium cadmium sulfate Ammonium chloride Ammonium monochloroacetate Ammonium chrome alum Ammonium bisulfate Ammonium dihydrogen arsenate (ADA)

NH4H2PO4

Ammonium dihydrogen phosphate (ADP)

ND4D2PO4

Ammonium dideuterium phosphate (ADDP) Ammonium nitrate Ammonium sulfate

ε22 = 12 6 ε11 = ε22 = 7.8 ε33 = 7.1 ε11 = ε22 = 8.8 ε33 = 9.2 7.1 9.8 ε11 = 6.45 ε22 = 6.8 ε33 = 6.0 10.0 6.9 5 6.5 165 5.1 ε11 = ε22 = 85 ε33 = 22 ε11 = ε22 = 57.1 ± 0.6 ε33 = 14.0 ± 0.3 ε11 = ε22 = 74, ε33 = 24

NH4NO3 (NH4)2SO4

(NH4)2UO2(C2O4)2 (NH4)2UO2(C2O4)2 ⋅ 3H2O NaBr

Ammonium uranyl oxalate Ammonium uranyl oxalate trihydrate

NaBrO3

Sodium bromate

NaCN NaCO3 NaCO3 ⋅ 10H2O NaCl

Sodium cyanide Sodium carbonate Sodium carbonate decahydrate Sodium chloride

NaClO3

Sodium chlorate

Section 12.indb 49

ν/Hz (5–500) × 103 (5–500) × 103

Sodium bromide

273 r.t. 123 123 293 293 r.t. r.t. r.t. r.t. r.t. r.t. r.t. r.t. r.t. 273 265 298 298 294.5 294 300

104 1012 105 105 105 105 7 × 105 103 103 103 104 7 × 105 2 × 106 175 × 103 5 × 104 9.5 × 109 103 105–35 × 109 105–36 × 109 (5–50) × 103 105 105 105 105 104–3.3 × 109 104–3.3 × 109

10.7 ε11 = ε22 = 8.0 ε33 = 6.3 ε11 = ε22 = 10.0 ε33 = 9.3 8.03 6.06

322 123 123 293 293 r.t. r.t.

6.44 T ε11 = 5.70

298

1.6 × 103

298

103

7.55 8.75 5.3 5.9 5.45 T ε11 = 5.76

293 291 r.t. 298 4.2 301

105 2 × 105 6 × 107 102–107

5.28

r.t.

103

4/28/05 1:56:16 PM

Permittivity (Dielectric Constant) of Inorganic Solids

12-50 Formula NaClO4 NaF NaH3(SeO3)2 NaD3(SeO3)2 NaI NaK(C4H2D2O6) ⋅ 4D2O NaK(C4H4O6) ⋅ 4H2O NaNH4(C4H4O6) ⋅ 4H2O

Name Sodium perchlorate Sodium fluoride Sodium trihydrogen selenite Sodium trideuterium selenite Sodium iodide Sodium potassium tartrate tetradeutrate (double deuterated Rochelle salt) Sodium potassium tartrate tetrahydrate (Rochelle salt) Sodium ammonium tartrate (Ammonium Rochelle salt)

NaNbO3

Sodium niobate

NaNO2

Sodium nitrite

NaNO3 NaSO4 NaSO4 ⋅ 10H2O Na2SO4 ⋅ 5H2O Na2UO2(C2O4)2 NdAlO3 NdScO3 Ni3B7O13I NiNb2O6

Sodium nitrate Sodium sulfate Sodium sulfate decahydrate Sodium sulfate pentahydrate Sodium uranyl oxalate Neodymium aluminate Neodymium scandate Nickel iodine boracite Nickel niobate

NiO NiSO4 ⋅ 6H2O

Nickel oxide Nickel sulfate hexahydrate

NiWO4

Nickel tungstate

PbBr2 PbCO3 Pb(C2H3O2)2 PbCl2 Pb2CoWO6 PbF2 PbHfO3

Phosphorous (red) Phosphorous (yellow) Tetramethylphosphonium tribromomercurate (TTM) Lead bromide Lead carbonate Lead acetate Lead chloride Lead cobalt tungstate Lead fluoride Lead hafnate

PbI2 Pb3MgNb2O9 PbMoO4

Lead iodide Lead magnesium niobate Lead molybdate

Pb(NO3)2

Lead nitrate

PbNb2O6

Lead niobate

PbO PbS

Lead oxide Lead sulfide (Galena)

PbSO4 PbSe PbTa2O6

Lead sulfate Lead selenide Lead metatantalate

PbTe

Lead telluride

[P(CH3)4]HgBr3

Section 12.indb 50

εijk 5.76 5.08 ± 0.02 ε11 ≈ 75 ε11 ≈ 220 7.28 ± 0.03 ε11 = 70 ε22 = 8.9 ε11 = 170 ε22 = 9.1 ε11 = 8.4 ε22 = 9.2 ε33 = 9.5 ε33 = 670 ±13 ε11 = ε22 = 76 ± 2 ε11 = 7.4 ε22 = 5.5 ε33 = 5.0 6.85 7.90 5.0 7 5.18 17.5 27 ε11 = 14 ε11 = 16.0 ± 0.5 ε22 = 23.8 ± 1.8 ε33 = 31.3 ± 2.5 11.9 ε11 = 6.2 ε33 = 6.8 ε11 = 17.4 ± 2.4 ε22 = 13.6 ± 1.0 ε33 = 19.7 ± 0.6 4.1 3.6 ~10

T/K r.t. r.t. 273 273 r.t. 273 273 273 273 298 298 298 r.t. r.t. r.t. r.t. r.t. 292 r.t. r.t. 250–290 r.t. r.t. r.t. 260 r.t. r.t. r.t. 298 r.t. r.t. r.t. r.t. r.t. r.t. r.t. 233–373

>30 18.6 2.6 33.5 ~250 26.3 390 185 20.8 10,000 ε11 = 34.0 ± 0.4 ε33 = 40.6 ± 0.2 16.8 ε T33 = 180

293 288 290–295 273 r.t. r.t. 300 400 293 297 297.5 297.5 r.t.

25.9 190 200 ± 35 14.3 280 ε11 = ε22 ≈ 300 ε33 = 150 450

r.t. 77 r.t. 290— 295 r.t. r.t. r.t. r.t.

ν/Hz 103 5 × 103 2 × 105 2 × 105 103 103 103 103

5 × 105 5 × 105 5 × 105 2 × 105

300–104

(5–500) ×103 (5–500) × 103 (5–500) × 103 105

(5–500) × 103 (5–500) × 103 (5–500) × 103 108 108 (0.5–3) × 106 10.8 106 (0.5–3) × 106

105 (0.5–3) × 106 1.6 ± 103 1.6 ± 103 (0.5–3) × 106

298 2 × 106 i.r. i.r. 106 i.r. 104 104 i.r.

4/28/05 1:56:19 PM

Permittivity (Dielectric Constant) of Inorganic Solids Formula

Name

PbTiO3 PbWO4

Lead titanate Lead tungstate

Pb(Zn1/3Nb2/3)O3 PbZrO3 RbAl(SO4)2 ⋅ 12H2O RbBr Rb2CO3 RbCl RbCr(SO4)2 ⋅ 12H2O RbF RbHSO4

Lead zinc niobate Lead zirconate Rubidium alum Rubidium bromide Rubidium carbonate Rubidium chloride Rubidium chrome alum Rubidium fluoride Rubidium bisulfate

RbH2AsO4 RbH2PO4 RbI RbInSO4 RbNO3

Rubidium dihydrogen arsenate (RDA) Rubidium dihydrogen phosphate (RDP) Rubidium iodide Rubidium indium sulfate Rubidium nitrate

Sulfur

SC(NH2)2

sublimed Thiourea

Sb2O3 Sb2S3

Antimonous sesquioxide Antimonous sulfide (stibnite)

Sb2Se3 SbSI

Antimonous selenide Antimonous sulfide iodide

Selenium (monocrystal)

Si SiC

(amorphous) Silicon Silicon carbide cubic 6H

Si3N4 SiO SiO2

Silicon nitride Silicon monoxide Silicon dioxide

Sm2(MoO4)3 SnO2

Samarium molybdate Stannic dioxide

SnSb SnTe Sr(COOH)2 ⋅ 2H2O SrCO3 SrCl2 SrCl2 ⋅ 6H2O SrF2 SrMoO4

Tin antimonide Tin telluride Strontium formate dihydrate Strontium carbonate Strontium chloride Strontium chloride hexahydrate Strontium fluoride Strontium molybdate

Section 12.indb 51

12-51 εijk 40 430 ~200 ε11 = ε22 = 23.6 ± 0.3 ε33 = 31.0 ± 0.4 7 200 5.1 4.83 4.87 ± 0.02 4.91 ± 0.02 5.0 5.91 ε11 = 7 ε22 = 8 ε33 = 10 3.90 6.15 4.94 ± 0.02 6.85 20—380 30 ε11 = 3.75 ε22 = 3.95 ε33 = 4.44 3.69 ε11 = ε22 ≈ 3 ε22 = 35 12.8 ε11 = ε33 = 15 ε33 = 180 ~110 2000 ε11 = ε22 ≈ 25 ε33 ≈ 5 × 104 ε11 = ε22 = 11 ε33 = 21 6.0 12.1

T/K 77 4.2 r.t. 297.5 297.5 300 400 r.t. 300 r.t. r.t. r.t. r.t. r.t. r.t. r.t. 273 285 r.t. r.t. 433–488 488–538 298 298 298 298 77–300 300 r.t. r.t. r.t. r.t. 273 r.t. 295 300 300 298 4.2

9.72 ε11 = ε22 = 9.66 ε33 = 10.03 9.7 ± 0.1 4.2 (film) 5.8 ε11 = 4.42 ε22 = 4.41 ε33 = 4.60 12 ε11 = ε22 = 14 ± 2 ε33 = 9.0 ± 0.5 147 1770 ± 300 6.1 8.85 9.19 8.52 6.50 ε11 = ε22 = 31.7 ± 0.2

r.t. r.t. r.t. 1.8 r.t. r.t. r.t. r.t. r.t. 298 r.t. r.t. r.t. r.t. r.t. 298 r.t. r.t. 300 297.5

ν/Hz 104–15 × 104 104–15 × 104 103 1.59 × 103 1.59 × 103 103, 300 × 103 1012 5 × 103 5 × 103 1012 2 × 106 105 105 105 9.5 × 109 9.5 × 109 5 × 103 106 106 102–103 102–103 102–103 102–103 103 103 (1.5–2) × 103 103 103 (10–16.5) × 109 105 103–105 103–105 24 × 109 24 × 109 102—1010 107—109 i.r. i.r. i.r. i.r. 103 103 9.4 × 1010 9.4 × 1010 9.4 × 1010 104–1010 104–1010 104–106 i.r. 103 2 × 105

5 × 102–1011 1.59 × 103

4/28/05 1:56:21 PM

Permittivity (Dielectric Constant) of Inorganic Solids

12-52 Formula

Name

Sr(NO3)2 Sr2Nb2O7

Strontium nitrate Strontium niobate

SrO SrS SrSO4 SrTiO3

Strontium oxide Strontium sulfide Strontium sulfate Strontium titanate

SrWO4

Strontium tungstate

Ta2O5

Tantalum pentoxide (tantala) α phase

Tb(MoO4)3

β phase Terbium molybdate

Tellurium

ThO2 TiO2

polycrystalline monocrystalline Thorium dioxide Titanium dioxide (rutile)

Ti2O3 TlBr TlCl TlI

Titanium sesquioxide Thallium bromide Thallous chloride Thallous iodide (orthorhombic)

TlNO3 TlSO4 UO2 WO3 YMnO3 Y2O3 YbMnO3 Yb2O3

Thallous nitrate Thallous sulfate Uranium dioxide Tungsten trioxide Yttrium manganate Yttrium sesquioxide Ytterbium manganate Ytterbium sesquioxide

ZnO

Zinc monoxide

εijk ε33 = 41.7 ± 0.2 5.33 ε11 = 75 ε22 = 46 ε33 = 43 13.3 ± 0.3 11.3 11.5 332 2080 ε11 = ε22 = 25.7 ± 0.2 ε33 = 34.1 ± 0.2 ε11 = ε22 = 30 ε33 = 65 24 11 ε11 = ε22 = 33 ε33 = 53 ε11 = ε22 = 33 ε33 = 54 27.5 28.0 18.9 ± 0.4 ε11 = ε22 = 86 ε33 = 170 30 30 32.2 ± 0.2 20.7 ± 0.2 37.3 16.5 25.5 24 300 20 10 20 5.0 (film) S ε11 = 8.33 S 33

ZnS

Zinc sulfide

Zinc selenide

77 77 292 298 100–200 100–200 r.t. r.t. r.t. r.t. r.t. 300 300 77 293 293 293 193 293 293 r.t. r.t. r.t. r.t. r.t.

103 103 1.6 × 103 1.6 × 103 103 103 103 9.4 × 109 9.4 × 109

i.r. i.r. 3 × 105 104–106 104–106 6 × 1010 103–107 103–105 104 107 5 × 105 5 × 105 3 × 105 2 × 107 106 2 × 107 103

r.t. r.t.

T ε11 = 9.26

r.t.

ε T33 = 11.0

r.t.

ε11 = 9.26 ε33 = 8.2 8.15 S ε11 = 8.08 ± 2%

r.t. r.t. r.t.

i.r.

104

S 11

298

104

T 11

ε = 8.14 ± 2%

104

T ε11 = 8.37 ± 2%

298

104

298

104

T 11

ε = ε11 = 9.12 ± 2%

ZnTe

Zinc telluride

ε = ε11 = 10.10 ± 2%

r.t.

ZnWO4 ZrO2

Zinc tungstate Zirconium dioxide (zirconia)

ε22 = 16.1 ± 0.5 12.5

r.t. r.t.

Section 12.indb 52

ν/Hz 1.59 × 103 2 × 105 103 103 103 2 × 106 7.25 × 106

ε = 8.84

ε = 8.32 ± 2%

ZnSe

T/K 297.5 292 r.t. r.t. r.t. 273 r.t. r.t. 298 78 297.5 297.5

(5–500) × 103 2 × 106

4/28/05 1:56:28 PM

CURIE TEMPERATURE OF SELECTED FERROELECTRIC CRYSTALS H. P. R. Frederikse The following table lists the major ferroelectric crystals and their Curie temperatures, TC.

Reference Young, K. F. and Frederikse, H. P. R., J. Phys. Chem. Ref. Data, 2, 313, 1973.

Formula

TC/K

Potassium dihydrogen phosphate group KDP KDA KDDP KDDA RDP RDA RDDP RDDA CDP CDA CDDA

KH2PO4 KH2AsO4 KD2 PO4 KD2AsO4 RbH2PO4 RbH2AsO4 RbD2PO4 RbD2AsO4 CsH2PO4 CsH2AsO4 CsD2AsO4

123 97 213 162 146 111 218 178 159 143 212

Rochelle salt group Rochelle salt Deuterated Rochelle salt Ammonium Rochelle salt LAT

NaKC4H4O6·4H2O NaKC4H2D2O6·4H2O NaNH4C4H4O6·4H2O LiNH4C4H4O6·H2O

255–297 251–308 109 106

Triglycine sulfate group TGS TGSe TGFB AFB HADA

(NH2CH2COOH)3·H2SO4 (NH2CH2COOH)3·H2SeO4 (NH2CH2COOH)3·H2BeF4 (NH4)2BeF4 HNH4(ClCH2COO)2

322 295 346 176 128

Perovskites and related compounds Barium titanate Lead titanate Potassium niobate Potassium tantalate niobate Lithium niobate Lithium tantalate Barium titanium niobate Ba-Na niobate (“Bananas”) Potassium iodate Lithium iodate Potassium nitrate Sodium nitrate Rubidium nitrate

BaTiO3 PbTiO3 KNbO3 KTa2/3Nb1/3O3 LiNBO3 LiTaO3 Ba6Ti2Nb8O30 Ba2NaNb5O15 KIO3 LiIO3 KNO3 NaNO3 RbNO3

406, 278, 193 765 712 241, 220, 170 1483 891 521 833 485, 343, 257–263, 83 529 397 548 437–487

Miscellaneous compounds Cesium trihydrogen selenite Lithium trihydrogen selenite Potassium selenate Methyl ammonium alum (MASD) Ammonium cadmium sulfate Ammonium bisulfate Ammonium sulfate Ammonium nitrate Colemanite Cadmium pyroniobite Gadolinium molybdate

CsH3(SeO3)2 LiH3(SeO3)2 K2SeO4 CH3NH3Al(SO4)2∙12H2O (NH4)2Cd2(SO4)3 (NH4)HSO4 (NH4)2SO4 NH4NO3 CaB3O4(OH)3∙H2O Cd2Nb2O7 Gd2(MoO4)3

143 TC > Tmp 93 177 95 271 224 398, 357, 305, 255 266 185 432

Name or acronym

12-53

Section 12.indb 53

4/28/05 1:56:30 PM

PROPERTIES OF ANTIFERROELECTRIC CRYSTALS H. P. R. Frederikse Some important antiferroelectric crystals are listed here with their Curie Temperatures TC. The last column gives the constant T0 which appears in the Curie-Weiss law describing the dielectric constant of these materials above the Curie Temperature: ε=const./(T–T0) Name or acronym ADP ADA ADDP ADDA AdDDP AdDDA Sodium niobate Lead hafnate Lead zirconate Lead metaniobate Lead metatantalate Tungsten trioxide Potassium strontium niobate Sodium nitrite Sodium trihydrogen selenite Sodium trideuterium selenite Ammonium trihydrogen periodate

Formula NH4H2PO4 NH4H2AsO4 NH4D2PO4 NH4D2AsO4 ND4D2PO4 ND4D2AsO4 NaNbO3 PbHfO3 PbZrO3 PbNb2O6 PbTa2O6 WO3 KSr2Nb5O15 NaNO2 NaH3(SeO3)2 NaD3(SeO3)2 (NH4)2H3IO6

TC/K 148 216 242, 245 299 243 304 911, 793 476 503 843 543 1010 427 437 193 271 245

T0/K

378 475 530 533 413 437 192 245

12-54

S12_13.indd 54

5/4/05 11:07:23 AM

Dielectric Constants of Glasses

Type Corning 0010 Corning 0080 Corning 0120 Pyrex 1710 Pyrex 3320 Pyrex 7040 Pyrex 7050 Pyrex 7052 Pyrex 7060 Pyrex 7070 Vycor 7230 Pyrex 7720 Pyrex 7740 Pyrex 7750 Pyrex 7760 Vycor 7900 Vycor 7910 Vycor 7911 Corning 8870 G. E. Clear (silica glass) Quartz (fused) a

487_S12.indb 55

Dielectric constant at 100 MHz (20°C) 6.32 6.75 6.65 6.00 4.71 4.65 4.77 5.07 4.70 4.00 3.83 4.50 5.00 4.28 4.50 3.9 3.8 3.8 9.5 3.81 3.75 (4.1 at 1 MHz)

Volume resistivity (In MΩ cm at 350°C ) 10 0.13 100 2,500 – 80 16 25 13 1,300 – 16 4 50 50 130 1,600 4,000 5,000 4,000–30,000 –

Loss factora 0.015 0.058 0.012 0.025 0.019 0.013 0.017 0.019 0.018 0.0048 0.0061 0.014 0.040 0.011 0.0081 0.0023 0.00091 0.00072 0.0085 0.00038 0.0002 (1 MHz)

Power factor × dielectric constant equals loss factor.

12-55

3/24/06 10:11:48 AM

PROPERTIES OF SUPERCONDUCTORS L. I. Berger and B. W. Roberts The following tables include superconductive properties of selected elements, compounds, and alloys. Individual tables are given for thin films, elements at high pressures, superconductors with high critical magnetic fields, and high critical temperature superconductors. The historically first observed and most distinctive property of a superconductive body is the near total loss of resistance at a critical temperature (Tc) that is characteristic of each material. Figure 1(a) below illustrates schematically two types of possible transitions The sharp vertical discontinuity in resistance is indicaHo ρ

tive of that found for a single crystal of a very pure element or one of a few well annealed alloy compositions. The broad transition, illustrated by broken lines, suggests the transition shape seen for materials that are not homogeneous and contain unusual strain distributions. Careful testing of the resistivity limit for superconductors shows that it is less than 4 × 10–23 ohm cm, while the lowest resistivity observed in metals is of the order of 10–13 ohm cm. If one compares the resistivity of a superconductive body to that of copper at room temperature, the superconductive body is at least 1017 times less resistive. –4πM

Normal

Hc Superconducting

0 (a)

(b)

Hcl Hc Mixed state (c)

Hc2

Hc3

FIGURE 1. Physical properties of superconductors. (a) Resistivity vs. temperature for a pure and perfect lattice (solid line); impure and/or imperfect lattice (broken line). (b) Magnetic-field temperature dependence for Type-I or “soft” superconductors. (c) Schematic magnetization curve for “hard” or Type-II superconductors.

The temperature interval ∆Tc, over which the transition between the normal and superconductive states takes place, may be of the order of as little as 2 × 10–5 K or several K in width, depending on the material state. The narrow transition width was attained in 99.9999% pure gallium single crystals. A Type-I superconductor below Tc, as exemplified by a pure metal, exhibits perfect diamagnetism and excludes a magnetic field up to some critical field Hc, whereupon it reverts to the normal state as shown in the H-T diagram of Figure 1(b). The magnetization of a typical high-field superconductor is shown in Figure 1(c). The discovery of the large current-carrying capability of Nb3Sn and other similar alloys has led to an extensive study of the physical properties of these alloys. In brief, a highfield superconductor, or Type-II superconductor, passes from the perfect diamagnetic state at low magnetic fields to a mixed state and finally to a sheathed state before attaining the normal resistive state of the metal. The magnetic field values separating the four stages are given as Hc1, Hc2, and Hc3. The superconductive state below Hc1 is perfectly diamagnetic, identical to the state of most pure metals of the “soft” or Type-I superconductor. Between Hc1 and Hc2 a “mixed superconductive state” is found in which fluxons (a minimal unit of magnetic flux) create lines of normal flux in a superconductive matrix. The volume of the normal state is proportional to –4πM in the “mixed state” region. Thus at Hc2 the fluxon density has become so great as to drive the interior volume of the superconductive body completely normal. Between Hc2 and Hc3 the superconductor has a sheath of current-carrying superconductive material at the body surface, and above Hc3 the normal state exists. With several types of careful measurement, it is possible to determine Hc1, Hc2, and Hc3. Table 6 contains some of the available data on high-field superconductive materials.

High-field superconductive phenomena are also related to specimen dimension and configuration. For example, the Type-I superconductor, Hg, has entirely different magnetization behavior in high magnetic fields when contained in the very fine sets of filamentary tunnels found in an unprocessed Vycor glass. The great majority of superconductive materials are Type-II. The elements in very pure form and a very few precisely stoichiometric and well annealed compounds are Type I with the possible exceptions of vanadium and niobium. Metallurgical Aspects. The sensitivity of superconductive properties to the material state is most pronounced and has been used in a reverse sense to study and specify the detailed state of alloys. The mechanical state, the homogeneity, and the presence of impurity atoms and other electron-scattering centers are all capable of controlling the critical temperature and the current-carrying capabilities in high-magnetic fields. Well annealed specimens tend to show sharper transitions than those that are strained or inhomogeneous. This sensitivity to mechanical state underlines a general problem in the tabulation of properties for superconductive materials. The occasional divergent values of the critical temperature and of the critical fields quoted for a Type-II superconductor may lie in the variation in sample preparation. Critical temperatures of materials studied early in the history of superconductivity must be evaluated in light of the probable metallurgical state of the material, as well as the availability of less pure starting elements. It has been noted that recent work has given extended consideration to the metallurgical aspects of sample preparation. Symbols in tables: Tc: Critical temperature; Ho: Critical magnetic field in the T = 0 limit; θD: Debye temperature; and γ: Electronic specific heat.

12-56

Section 12.indb 56

4/28/05 1:56:35 PM

Properties of Superconductors

Element Al Am* (α,?) Am* (β,?) Be Cd Ga Ga (β) Ga (γ) Ga (∆) Hf Hg (α) Hg (β) In Ir La (α) La (β) Lu Mo Nb Os Pa Pb Re Ru Sn Ta Tc Th Ti Tl U V W Zn Zr Zr (ω)

12-57

TABLE 1. Selective Properties of Superconductive Elements Tc(K) Ho(oersted) θD(K) 1.175 ± 0.002 104.9 ± 0.3 420 0.6 1.0 0.026 0.517 ± 0.002 28 ± 1 209 1.083 ± 0.001 58.3 ± 0.2 325 5.9, 6.2 560 7 950, HFa 7.85 815, HF 0.128 12.7 4.154 ± 0.001 411 ± 2 87, 71.9 3.949 339 93 3.408 ± 0.001 281.5 ± 2 109 0.1125 ± 0.001 16 ± 0.05 425 4.88 ± 0.02 800 ± 10 151 6.00 ± 0.1 1096, 1600 139 0.1 ± 0.03 350 ± 50 0.915 ± 0.005 96 ± 3 460 276 9.25 ± 0.02 2060 ± 50, HF 0.66 ± 0.03 70 500 1.4 7.196 ± 0.006 803 ± 1 96 1.697 ± 0.006 200 ± 5 4.5 0.49 ± 0.015 69 ± 2 580 3.722 ± 0.001 305 ± 2 195 4.47 ± 0.04 829 ± 6 258 411 7.8 ± 0.1 1410, HF 1.38 ± 0.02 1.60 ± 3 165 0.40 ± 0.04 56 415 2.38 ± 0.02 178 ± 2 78.5 0.2 5.40 ± 0.05 1408 383 0.0154 ± 0.0005 1.15 ± 0.03 383 0.85 ± 0.01 54 ± 0.3 310 0.61 ± 0.15 47 290 0.65, 0.95

γ(mJ mol–1K–1) 1.35

0.21 0.69 0.60

2.21 1.81 1.37 1.672 3.19 9.8 11.3 1.83 7.80 2.35 3.1 2.35 2.8 1.78 6.15 6.28 4.32 3.3 1.47 9.82 0.90 0.66 2.77

TABLE 2. Range of Critical Temperatures Observed for Superconductive Elements in Thin Films Condensed Element Al Be Bi Cd (Disordered) (Ordered) Ga Hg In La Mo a

Section 12.indb 57

Tc Range (K) 1.15–5.7 5–9.75 6.17–6.6 0.79–0.91 0.53–0.59 2.5–8.5 3.87–4.5 2.2–5.6 3.55–6.74 3.3–8.0

Usually at Low Temperatures

Comments HFa HF

HF HF

HF denotes high magnetic field superconductive properties.

Element Nb Pb Re Sn Ta Tc Ti Tl V W Zn

Tc Range (K) 2.0–10.1 1.8–7.5 1.7–7 3.5–6 <1.7–4.51 4.6–7.7 1.3 Max 2.33–2.96 1.8–6.02 <1.0–4.1 0.77–1.9

Comments

HFa

4/28/05 1:56:36 PM

Properties of Superconductors

12-58

Element Al As Ba II III IV Bi II III IV V VI VII(?) Ce (α) Ce (α′) Cs V Ga II II′ Ge Lu P

TABLE 3. Elements Exhibiting Superconductivity Under or After Application of High Pressure Tc Range (K) Pressure (kbar) Element Tc Range (K) Pressure (kbar) 3.55 160 1.98–0.075 0–62 Pb II 2.3 Max. “Plastic” 0.31–0.5 220–140 Re II 0.2–0.25 140–100 compression 2.6–2.7 1–1.8 55–85 Sb (prepared 120 1.8–5 85–144 kbar, held below 4.5–5.4 144–190 77K) 3.55–3.40 85–150 3.9 25–27 Sb II 6.75, 6.95 130 6.55–7.25 28–38 Se II 7.0, 8.7–6.0 43, 43–62 Si 6.7–7.1 120–130 5.2–4.85 125–160 6.7, 8.3 48–80 Sn II 5.30 113 8.55 90, 92–101 III 2.4–5.1 38–55 8.2 30 Te II 0.020–0.045 20–35 4.1–4.2 53–62 4.72–4 63–80 1.9–1.3 45–125 IV 1.5 >125 () 3.3–2.8 100–260 1.45 35 6.38 ≥35 Tl (cubic form) (hexagonal form) 1.95 35 7.5 ≥35 then P removed U 2.4–0.4 10–85 5.35 115 Y 1.7–2.5 110–160 60–130 0.022–1.0 45–190 Zr (omega form, metastable) 1–1.7 5.8 170

TABLE 4. Superconductive Compounds and Alloys

All compositions are denoted on an atomic basis, i.e., AB, AB2, or AB3 for compounds, unless noted. Solid solutions or odd compositions may be denoted as AzB1–z or AzB. A series of three or more alloys is indicated as AxB1–x or by actual indication of the atomic fraction range, such as A0–0.6B1–0.4. The critical temperature of such a series of alloys is denoted by a range of values or possibly the maximum value. The selection of the critical temperature from a transition in the effective permeability, or the change in resistance, or possibly the incremental changes in frequency observed by certain techniques is not often obvious from the literature. Most authors choose the

mid-point of such curves as the probable critical temperature of the idealized material, while others will choose the highest temperature at which a deviation from the normal state property is observed. In view of the previous discussion concerning the variability of the superconductive properties as a function of purity and other metallurgical aspects, it is recommended that appropriate literature be checked to determine the most probable critical temperature or critical field of a given alloy. A very limited amount of data on critical fields, Ho, is available for these compounds and alloys; these values are given at the end of the table.

A. Superconductors with Tc< 10 K Substance Ag3.3Al AgxAlyZn1-x-y AgBi2 Ag7F0.25N0.75O10.25 Ag2F Ag7FO8 Ag0.8–0.3Ga0.2–0.7 Ag4Ge Ag0.438Hg0.562 AgIn2 Ag0.1In0.9Te (n = 1.4 × 1022)* Ag0.2In0.8Te (n = 1.07 × 1022) AgLa AgLa (9.5 kbar) AgLu AgMo4S5 Ag1.2Mo6Se8

Section 12.indb 58

Tc, K

0.34 0.15 2.87–3.0 0.85–0.90 0.0.066 0.3 6.5–8 0.85 0.64 ~2.4 1.2–1.89 0.77–1.00 0.94 1.2 0.33 9.1 5.9

Crystal structure type

Substance

A12-cI58 (Mn) Cubic

Ag7NO11 AgxPb1-x Ag4Sn AgxSn1-x AgxSn1–x (film) AgTe3 AgTh AgTh2 Ag0.03Tl0.97 Ag0.94Tl0.06 AgY AgxZn1-x AlAu4 Al2Au Al2CMo3 Al2CaSi Al0.131Cr0.088V0.781 AlGe2

Cubic Hex., c.p. D82 C16 B1 B1 B2-cP2 (CsCl) B2 B2-cP2 hR15 (Mo6PbS8) Same

Tc, K

1.04 7.2 max. 0.1 1.5–3.7 2.0–3.8 2.6 2.2 2.26 2.67 2.32 0.33 0.5–0.845 0.4–0.7 0.1 9.8–10.2 5.8 1.46 1.75

Crystal structure type Cubic h**

Cubic C16-tI12 (Al2Cu) C16

B2-cP2 (CsCl) Like A13 C1-cF12 (CaF2) A13+trace 2nd. phase Cubic

4/28/05 1:56:38 PM

Properties of Superconductors Substance Al2Ge2U AlLa3 Al2La Al2Lu Al3Mg2 AlMo3 AlMo6Pd AlN Al2NNb3 Al3Nb AlOs Al3Os AlPb (film) Al2Pt Al5Re24 AlSb Al2Sc Al2Si2U AlTh2 Al3Th AlxTiyV1-x-y Al0.108V0.892 Al2Y Al3Yb AlxZn1-x AlZr3 AsBiPb AsBiPbSb AsHfOs AsHfRu As0.33InTe0.67 (n = 1.24 ×1022) As0.5InTe0.5 (n = 0.97 × 1022) As4La3 AsNb3 As0.50Ni0.06Pd0.44 AsNi0.25Pd0.75 AsOsZr AsPb AsPd2 (low-temp. phase) AsPd2 (high-temp. phase) AsPd5 As3Pd5 AsRh AsRh1.4–1.6 AsSn AsSn (n = 2.14 × 1022) As~2Sn~3 As3Sn4 (n = 0.56 × 1022) AsV3 Au5Ba AuBe Au2Bi Au5Ca AuGa2 AuGa Au0.40–0.92Ge0.60–0.08 AuIn2 AuIn AuLu AuNb3

Section 12.indb 59

Tc, K

1.6 5.57 3.23 1.02 0.84 0.58 2.1 1.55 1.3 0.64 0.39 5.90 1.2–7 0.48–0.55 3.35 2.8 1.02 1.34 0.1 0.75 2.05–3.62 1.82 0.35 0.94 0.5–0.845 0.73 9.0 9.0 3.2 4.9 0.85–1.15 0.44–0.62 0.6 0.3 1.39 1.6 8.0 8.4 0.60 1.70 0.46 1.9 0.58 < 0.03–0.56 4.10 3.41–3.65 3.5–3.6; 1.21–1.17 1.16–1.19 0.20 0.4–0.7 2.64 1.80 0.34–0.38 1.6 1.2 <0.32–1.63 0.2 0.4–0.6 <0.35 1.2

12-59 Crystal structure type

Substance

LI2-cP4 (Cu3Au) DO19 C15 C15-cF24 (Cu2Mg) F.C.C. A15

AuPb2 AuPb2 (film) AuPb3 AuPb3 (film) Au2Pb AuSb2 AuSn AuxSn1-x (film) Au5Sn AuTa4.3 Au3Te5 AuTh2 AuTl AuV3 AuxZn1-x AuZn3 AuxZr y AuZr3 B2Ba0.67Pt3 BCMo2 BCMo2 B2Ca0.67Pt3 B4ErIr4 B4ErRh4 B4ErRh4 BHf B4HoIr4 B4HoRh4 B2Ir3La B2Ir3Th B4Ir4Tm B6La B2LaRh3 B12Lu B2LuOs B2LuOs3 B4LuRh4 B2LuRu B4LuRu4 BMo

B4 A13 tI8 (Al3Ti) B2

C1 A12 B4-tI4 (Sn) C15-cF24 (Cu2Mg) LI2-cP4 (Cu3Au) C16-tI12 (Al2Cu) DO19 Cubic Cubic C15-cF24 (Cu2Mg) LI2-cP4 (Cu3Au) LI2 C22-hP9 (Fe2P) same B1 B1 cI28 (Th3P4) L12-tP32 C2 B81-hP4 (NiAs) C22-hP9 (Fe2P) Hexagonal C22 Complex B31 Hexagonal B1

Rhombohedral A15-cP8 (Cr3Si) D2d B20 C15 C15b C1-cF12 (CaF2) B31 Complex C1-cF12 Complex B2 A2

BMo2 BNb B4NdRh4 B2OsSc B2OsY B2Pt3Sr0.67 BRe2 B4Rh3.4Ru0.6 B4Rh4Sm B4Rh4Th B4Rh4Tm B4Rh4Tm B0.3Ru0.7 B4Ru4Sc B2Ru3Th B2Ru3Y B2Ru Y B4Ru4Y B12Sc BTa

Tc, K

3.15 4.3 4.40 4.25 1.18; 6–7 0.58 1.25 2.0–3.8 0.7–1.1 0.55 1.62 3.08 1.92 0.74 0.50–0.845 1.21 1.7–2.8 0.92 5.60 5.4 5.3–7.0 1.57 2.1 4.3 8.7 3.1 2.0 1.4 1.65 2.09 1.6 5.7 2.82 0.48 2.66 4.62 6.2 9.86 2.0 0.5 (extrapol.) 4.74 8.25 5.3 1.34 2.22 2.78 2.80; 4.6 8.38 2.7 4.3 9.8 5.4 2.58 7.2 1.79 2.85 7.80 1.4 0.39 4.0

Crystal structure type

C15 C2 B81 A3 A15-cP8 (Cr3Si) Cubic C16 A15 Cubic A3 A15 hP12 (B2BaPt3) Orthorhombic Same hP12 tP18 (B4CeCo4) oC108 (B4LuRh4) tP18 (B4CeCo4) Cubic tP18 oC108 hP6 (CaCu5) Same tP18 hP6 oP16 (B2LuRu) hP6 oC108 oP16 tI72 (B4LuRu4) C16 Bf tP18 oP16 oP16 hP12 (B2BaPt3) tI72 tP18 Same Same oC108 D102 tI72 hP6 Same oP16 tI72 Bf

4/28/05 1:56:40 PM

Properties of Superconductors

12-60 Substance BTa2 B6Th BW2 B 6Y B12Y BZr B12Zr BaBi3 Ba2Mo15Se19 BaxO3Sr1-xTi (n = 4.2 ×1019) Ba0.13O3W Ba0.14O3W BaRh2 Be22Mo Be8Nb5Zr2 Be0.98–0.92Re0.02–0.08 (quenched) Be0.957Re0.043 BeTc Be22W Be13W Bi3Ca Bi0.5Cd0.13Pb0.25Sn0.12 (weight fractions) BiCo Bi2Cs BixCu1-x (electrodeposited) BiCu Bi3Fe Bi0.019In0.981 Bi0.05In0.95 Bi0.10In0.90 Bi0.15–0.30In0.85–0.70 Bi0.34–0.48In0.66–0.52 Bi3In5 BiIn2 Bi2Ir Bi2Ir (quenched) BiK Bi2K BiLi Bi4–9Mg Bi3Mo BiNa BiNb3 BiNb3 (high pressure and temperature) BiNi Bi3Ni BiNi0.5Rh0.5 Bi0.5NiSb0.5 Bi1-0Pb0-1 Bi1-0Pb0-1 (film) Bi0.05–0.40Pb0.95–0.60 Bi2Pb BiPbSb Bi0.5Pb0.31Sn0.19 (weight fractions) Bi0.5Pb0.25Sn0.25 BiPd2 Bi0.4Pd0.6 BiPd

Section 12.indb 60

Tc, K

3.12 0.74 3.1 6.5–7.1 4.7 3.4 5.82 5.69 2.75 <0.1–0.55 1.9 <1.25–2.2 6.0 2.51 5.2 9.5–9.75 9.62 5.21 4.12 4.1 2.0 8.2 0.42–0.49 4.75 2.2 1.33–1.40 1.0 3.86 4.65 5.05 5.3–5.4 4.0–4.1 4.1 5.65 1.7–2.3 3.0–3.96 3.6 3.58 2.47 0.7–~1.0 3–3.7 2.25 4.5 3.05 4.25 4.06 3.0 2.0 7.26–9.14 7.25–8.67 7.35–8.4 4.25 8.9 8.5 8.5 4.0 3.7–4 3.7

Crystal structure type

Substance

C16-tI12 (Al2Cu)

Bi2Pd Bi2Pd BiPd0.45Pt0.55 BiPdSe BiPdTe BiPt Bi0.1PtSb0.9 BiPtSe BiPtTe Bi2Pt Bi2Rb BiRe2 BiRh Bi3Rh Bi4Rh BiRu Bi3Sn BiSn BixSny Bi3Sr Bi3Te Bi5Tl3 Bi0.26Tl0.74 Bi0.26Tl0.74 Bi2Y3 Bi3Zn Bi0.3Zr0.7 BiZr3 BrMo6Se7 Br3Mo6Se5 CCsx CFe3 CGaMo2 CHf0.5Mo0.5 CHf0.3Mo0.7 CHf0.25Mo0.75 CHf0.7Nb0.3 CHf0.6Nb0.4 CHf0.5Nb0.5 CHf0.4Nb0.6 CHf0.25Nb0.75 CHf0.2Nb0.8 CHf0.9–0.1Ta0.1–0.9 CK (excess K) C8K C2La C2Lu C0.40–0.44Mo0.60–0.56 C3MoRe C0.6Mo4.8Si3 CMo0.2Ta0.8 CMo0.5Ta0.5 CMo0.75Ta0.25 CMo0.8Ta0.2 CMo0.85Ta0.15 CMoxV1-x CMoxZr1-x C0.984Nb CNb2 CNbxTi1-x CNb0.1–0.9Zr0.9–0.1

C16

Cubic Tetragonal hP15 (Mo6PbS8) Tetragonal Hexagonal C15 Cubic (Be22Re) Cubic Cubic (Be22Re) Cubic Cubic (Be22Re) Tetragonal

C15

m** α-phase Same α- and β-phases

β-phase

C15 L1o, α-phase L1o A15-cP8 (Cr3Si) A15 B81 Orthorhombic B81-hP4 (AsNi) Same

H.C.P. to ε-phase t**

Hexagonal, ordered Orthorhombic

Tc, K

1.70 4.25 3.7 1.0 1.2 1.21 2.05; 1.5 1.45 1.15 0.155 4.25 1.9–2.2 2.06 3.2 2.7 5.7 3.6–3.8 3.8 3.85–4.18 5.62 0.75–1.0 6.4 4.4 4.15 2.25 0.8–0.9 1.51 2.4–2.8 7.1 7.1 0.020–0.135 1.30 3.7–4.1 3.4 5.5 6.6 6.1 4.5 4.8 5.6 7.0 7.8 5.0–9.0 0.55 0.39 1.66 3.33 9–13 3.8 7.6 7.5 7.7 8.5 8.7 8.9 2.9–9.3 9.8 9.8 9.1 <4.2–8.8 4.2–8.4

Crystal structure type Monoclinic, α-phase Tetragonal, β-phase B81-hP4 (NiAs) C2 C2 B81 B81-hP4 (NiAs) C2 C2 Hexagonal C15 B81 Orthorhombic (NiB3) Hexagonal m**

L12 Cubic, disordered L12, ordered (?)

hP15 (Mo6PbS8) Same Hexagonal DO11-oP16 (Fe3C) Hexagonal B1 B1 B1 B1 B1 B1 B1 B1 B1 B1 Hexagonal Hexagonal tI6 (CaC2) Same B1-cF8 D88 B1 B1 B1 B1 B1 B1 B1 B1 B1 B1

4/28/05 1:56:42 PM

Properties of Superconductors Substance CRbx (Au) CRe0.06W CRu C0.987Ta C0.848–0.987 CTa (film) CTa2 CTa0.4Ti0.6 Cta1–0.4W0–0.6 CTa0.2–0.9Zr0.8–0.1 CTc (excess C) CTi0.5–0.7W0.5–0.3 CW CW2 CW2 C2Y Ca3Co4Sn13 Ca3Ge13Rh4 CaHg CaHg3 CaIr2 Ca3Ir4Sn13 CaxO3Sr1-xTi (n = 3.7–11 × 1019) Ca0.1O3W CaPb CaRh2 CaRh1.2Sn4.5 CaTl3 Cd0.3–0.5Hg0.7–0.5 CdHg Cd0.0075–0.05In0.9925–0.95 Cd0.97Pb0.03 CdSn Cd0.17Tl0.83 Cd0.18Tl0.82 CeCo2 CeCo1.67Ni0.33 CeCo1.67Rh0.33 CexGd1-xRu2 CeIr3 CeIr5 Ce0.005La0.995 CexLa1-x CexPr1-xRu2 CexPt1-x CeRu2 Ce3Mo6Se5 Ce2Mo6Te6 CoxFe1-xSi2 CoHf2 CoLa3 Co4La3Sn13 CoLu3 CoxLuSny Co0–0.01Mo0.8Re0.2 Co0.02–0.10Nb3Rh0.98–0.90 CoxNi1-xSi2 Co0.5Rh0.5Si2 CoxRh1-xSi2 Co~0.3So~0.7

Section 12.indb 61

Tc, K

0.023–0.151 5.0 2.00 9.7 2.04–9.7 5.09 3.26 4.8 8.5–10.5 4.6–8.3 3.85 6.7–2.1 1.0 2.74 5.2 3.88 5.9 2.1 1.6 1.6 6.15 7.1 < 0.1–0.55 1.4–3.4 7.0 6.40 8.7 2.0 1.70–1.92 1.77; 2.15 3.24–3.36 4.2 3.65 2.3 2.54 0.84 0.46 0.47 3.2–5.2 3.34 1.82 4.6 1.3–6.3 1.4–5.3 0.7–1.55 6.0 5.7 1.7 1.4 (max.) 0.56 4.28 2.8 ~0.35 1.5 2–10 2.28–1.90 1.4 (max.) 2.5 3.65 (max.) ~0.35

12-61 Crystal structure type

Substance

Hexagonal

Co4Sc5Si10 CoSi2 CoxSnyYb Co3Th7 CoxTi1-x CoxTi1-x CoTi2 CoTi CoU CoU6 Co0.28Y0.72 CoY3 CoZr2 Co0.1Zr0.9 Cr0.6Ir0.4 Cr0.65Ir0.35 Cr0.7Ir0.3 Cr0.72Ir0.28 Cr3Ir Cr0–0.1Nb1–0.9 Cr0.80Os0.20 Cr3Os CrxRe1-x Cr0.4Re0.6 Cr0.8–0.6Rh0.2–0.4 Cr3Rh Cr3Ru (annealed) Cr2Ru Cr3Ru2 Cr0.1–0.5Ru0.9–0.5 CrxTi1-x CrxTi1-x Cr0.1Ti0.3V0.6 Cr0.0175U0.9825 Cs0.32O3W Cu0.15In0.85 (film) Cu0.04–0.08In0.94–0.92 CuLa Cu2Mo6O2S6 Cu2Mo6Se8 CuxPb1-x CuS CuS2 CuSSe CuSe2 CuSeTe CuxSn1-x CuxSn1-x (film, made at 10K) CuxSn1-x (film, made at 300K) CuTe2 CuTh2 Cu0–0.027V CuY CuxZn1-x DyMo6S8 ErxLa1-x ErMo6S8 ErMo6Se8 Fe3Lu2Si5 Fe0–0.04Mo0.8Re0.2 Fe0.05Ni0.05Zr0.90

hP2 (CW)

B1 L΄3 B1 B1 B1 Cubic B1 L΄3 F.C.C. tI6 (CaC2) cP40 (Pr3Rh2Sn13) Same B2-cP2 (CsCl) hP8 (Ni3Sn) C15 cP40

Hexagonal C15 cP40 B2-cP2 Tetragonal Tetragonal

C15 C15 C15 C15

C15 C15 hR15 (Mo6PbS8) Same C1 E93 cP40 cP40 A15 C1

Tc, K

5.0 1.40; 1.22 2.5 1.83 2.8 (max.) 3.8 (max.) 3.44 0.71 1.7 2.29 0.34 <0.34 6.3 3.9 0.4 0.59 0.76 0.83 0.45 4.6–9.2 2.5 4.68 1.2–5.2 2.15 0.5–1.10 0.3 3.3 2.02 2.10 0.34–1.65 3.6 (max.) 4.2 (max.) 5.6 0.75 1.12 3.75 4.4 5.85 9 5.9 5.7–7.7 1.62 1.48–1.53 1.5–2.0 2.3–2.43 1.6–2.0 3.2–3.7 3.6–7 2.8–3.7 <1.25–1.3 3.49 3.9–5.3 0.33 0.5–0.845 2.1 1.4–6.3 2.2 6.2 6.1 1–10 ~3.9

Crystal structure type tP38 (Co4Sc5Si10) C1 cP40 D102 Co in α-Ti Co in β-Ti E93 A2 B2, distorted D2c C16 A3 H.C.P. H.C.P. H.C.P. A15 A2 Cubic A15-cP8 (Cr3Si) D8b A3 A15-cP8 A15 D8b D8b-tP30 (CrFe) A3 Cr in α-Ti Cr in β-Ti β-phase Hexagonal

hR15 (Mo6PbS8) Same B18 C18 C18 C18 C18

C18 C16 A2 B2-cP2 (CsCl) hR15 hR15 hR15 tP40 (Fe3Sc2Si5)

4/28/05 1:56:44 PM

Properties of Superconductors

12-62 Substance

Tc, K

Fe3Re2 Fe3Sc2Si5 Fe3Si5Tm Fe3Si5Y2 Fe3Th7 FexTi1-x FexTi1-x FexTi0.6V1-x FeU6 Fe0.1Zr0.9 Ga0.5Ge0.5Nb3 Ga2Ge2U GaHf2 GaLa3 Ga3Lu Ga2Mo GaMo3 GaN (black) Ga0.7Pt0.3 GaPt GaSb (120kbar, 77K, annealed) GaSb (unannealed) Ga0–1Sn1–0 (quenched) Ga0–1Sn1–0 (annealed) GaTe Ga5V2 GaV4.5 Ga3Zr Ga3Zr5 GdxLa1-x GdMo6S8 GdMo6Se8 GdxOs2Y1-x GdxRu2Th1-x Ge10As4Y5 GeIr GeIrLa Ge10Ir4Lu5 Ge10Ir4Y5 Ge2La

~5.9 3.47–4.18 2.6–3.85 0.17 3.55 9.15 1.38 3.8 < 1.0–5.5 3.5 5.6 1.4–4.7 3.6 (max.) 9.06 4.7 1.64 2.60 2.62 1.49; 2.2

GeLaPt Ge13Lu3Os4 Ge10Lu5Rh4 Ge13Lu3Ru4 GeMo3 GeNb2 Ge0.29Nb0.71 GePt Ge3Rh5

3.53 3.6 2.79 2.3 1.43 1.9 6 0.40 2.12

GeRh Ge13Rh4Sc3 Ge10Rh4Y5 Ge13Ru4Y3 Ge2So GeTa3 Ge3Te4 (n = 1.06 × 1022) GexTe1-x (n = 8.5–64 × 1020)

0.96 1.9 1.35 1.7 1.3 8.0 1.55–1.80 0.07–0.41

Section 12.indb 62

6.55 4.52 1.3 2.4 1.86 3.2 (max.) 3.7 (max.) 6.8 (max.) 3.86 1.0 7.3 0.87 0.21 5.84 2.3 9.5 0.76 5.85 2.9 1.74 4.24

Crystal structure type

Substance

D8b-tP30 (FeCr) tP40 Same Same D10 Fe in α-Ti Fe in β-Ti

GeV3 Ge2Y Ge1.62Y Ge2Zr GeZr3 H0.33Nb0.67 H0.1Nb0.9 H0.05Nb0.95 H0.12Ta0.88 H0.08Ta0.92 H0.04Ta0.96 HfIrSi HfMo2 HfN0.989 Hf0–0.5Nb1–0.5 Hf0.75Nb0.25 HfOs2 HfOsP HfPRu HfRe2 Hf0.14Re0.86 Hf0.99–0.96Rh0.01–0.04 Hf0–0.55Ta1–0.45 HfV2 HgxIn1-x HgIn Hg2K Hg3K Hg4K Hg8K Hg3Li HgMg3 Hg2Mg Hg3Mg5 Hg2Na Hg4Na HgxPb1-x HgSn HgxTl1-x Hg5Tl2 HoxLa1-x Ho1.2Mo6Se8 In1–0.86Mg0–0.14 In2Mo6Te6 InNb3 (high pressure and temp.) In0.5Nb3Zr0.5 In0.11O3W In0.95–0.85Pb0.05–0.15 In0.98–0.91Pb0.02–0.09 InPb InPd InSb (quenched from 170 kbar into liquid N2) InSb (InSb)0.95–0.10Sn0.05–0.90 (various heat treatments) (InSb)0–0.07Sn1–0.93 In3Sn InxSn1-x

D2c A3 A15 B2-cP2 C16-tI12 (Al2Cu) B2-cP2 A15 B4 C1 B20 A5

mC24 (GaTe) Tetragonal (Mn2Hg5) D8b-hP16 (Mn5Si3) hR15 hR15 C15 tP38 (C04Sc5Si10) B31 tI12 (LaPtSi) tP38 tP38 Orthorhombic, distorted (Mn2Hg5) tI12 cP40 (Pr3Rh2Sn13) tP38 cP40 A15 A15 B31 Orthorhombic, related to InNi2 B31-oP8 (MnP) c P40 tP38 cP40 A15-cP8 (Cr3Si) Rhombohedral R1

Tc, K

6.01 3.80 2.4 0.30 0.4 7.28 7.38 7.83 2.81 3.26 3.62 3.50 0.05 6.6 8.3–9.5 > 4.2 2.69 6.1 9.9 4.80 5.86 0.85–1.51 4.4–6.5 8.9–9.6 3.14–4.55 3.81 1.20 3.18 3.27 3.42 1.7 0.17 4.0 0.48 1.62 3.05 4.14–7.26 4.2 2.30–4.19 3.86 1.3–6.3 6.1 3.395–3.363 2.6 4–8; 9.2 6.4 < 1.25–2.8 3.6–5.05 3.45–4.2 6.65 0.7 4.8 2.1 3.8–5.1

Crystal structure type A15 Cc oC12 (ZrSi2) L12-tP32 (Ti3P) B.C.C. Same Same B.C.C. Same Same C37-cP12 (Co2Si) hP24 (Ni2Mn) B1 A2 C14 C22-hP9 (Fe2P) Same C14 A12 A2 C15

Orthorhombic

Hexagonal hP8 (Na3As) tI6 (MoSi2) D8b-hP16 (Mn5Si3) Hexagonal

D102-hR12 (Be3Nb) hR15 (Mo6PbS8) A15 Hexagonal

B2 Like A5 B4

3.67–3.74 ~5.5 3.4–7.3

4/28/05 1:56:46 PM

Properties of Superconductors Substance In0.82–1Te (n = 0.83–1.71 × 1022) In1.000Te1.002 In3Te4 (n = 4.7 × 1021) InxTl1-x In0.8Tl0.2 In0.62Tl0.38 In0.78–0.69Tl0.22–0.31 In0.69–0.62Tl0.31–0.38 Ir2La Ir3La Ir3La7 Ir5La IrLaSi2 IrLaSi3 Ir2Lu Ir3Lu Ir4Lu5Si10 IrMo IrMo3 IrMo3 IrNb3 Ir0.4Nb0.6 Ir0.37Nb0.63 IrNb Ir1.15Nb0.85 Ir0.02Nb3Rh0.98 Ir0.05Nb3Rh0.95 Ir0.287O0.14Ti0.573 Ir0.265O0.035Ti0.65 IrxOs1-x Ir1.5Os0.5 IrOsY IrSiY IrSiZr Ir2Sc Ir2.5Sc Ir4Sc5Si10 Ir2Si2Th IrSi3Th IrSiTh Ir2Si2Y Ir4Si10Y5 Ir3Si5Y2 IrSn2 Ir2Sr Ir7Ta13 Ir0.5Te0.5 IrTe3 IrTh Ir2Th Ir3Th Ir3Th7 Ir5Th IrTi3 IrV2 IrW3 Ir0.28W0.72 Ir2Y Ir0.69Y0.31 Ir0.70Y0.30

Section 12.indb 63

12-63 Crystal structure type

Substance

1.02–3.45

3.5–3.7 1.15–1.25 2.7–3.374 3.223 2.760 3.18–3.32 2.98–3.3 0.48 2.32 2.24 2.13 2.03 2.7 2.47 2.89 3.9 < 1.0 9.6 6.8 1.9 9.8 2.32 7.9 4.6 2.43 2.38 5.5 2.30 0.3–0.98 2.4 2.6 2.70 2.04 2.07 2.46 8.46 2.14 1.75 6.50 2.60 3.10 2.83 0.65–0.78 5.70 1.2 ~3 1.18 < 0.37 6.50 4.71 1.52 3.93 5.40 1.39 3.82 4.49 2.18; 1.38 1.98; 1.44 2.16

B1 Rhombohedral

Ir2Y3 Ir3Y IrxY1-x Ir2Zr Ir0.1Zr0.9 K2Mo15S19 K0.27–0.31O3W K0.40–0.57O3W La0.55Lu0.45 La0.8Lu0.2 LaMg2 LaMo6S8 LaN LaOs2 LaPt2 La0.28Pt0.72 LaPtSi LaRh3 LaRh5 La7Rh3 LaRhSi2 La2Rh3Si5 LaRhSi3 LaRh2Si2 LaRu2 La3S4 La3Se4 LaSi2 LaxY1-x LaZn Li2Mo6S8 LiPb LuOs2 Lu0.275Rh0.725 LuRh5 Lu5Rh4Si10 LuRu2 Mg1.14Mo6.6S8 Mg2Nb Mg~0.47Tl~0.53 MgZn MnxTi1-x MnxTi1-x MnU6 Mo2N Mo6Na2S8 MoxNb1-x Mo5.25Nb0.75Se8 Mo6NdSa8 Mo3Os Mo0.62Cs0.38 Mo3P Mo6Pb1.2Se8 Mo0.5Pd0.5 Mo6PrSe8 MoRe MoRe3 MoxRe1-x Mo0.42Re0.58 MoRh MoxRh1-x

Tc, K

Tetragonal F.C.C. C15 D102 D102 oC16 (CeNiSi2) tI10 (BaNiSn3) C15 C15 tP38 (Co4Sc5Si10) A3 A15 D8b A15 D8b D8b D8b oP12 (IrTa) A15 A15 E93 E93 C14 C15 C37-oP12 (Co2Si) Same C15 C15 tP38 tI10 tI10 tI12 (LaPtSi) tI10 (Al4Ba) tP38 oI40 C1 C15 D8b-tP30 (FeCr) C2 Bf C15 D102 D2d A15 A15

C15 C15 C15

Tc, K

1.61 3.50 0.3–3.7 4.10 5.5 3.32 0.50 1.5 2.2 3.4 1.05 7.1 1.35 6.5 0.46 0.54 3.48 2.60 1.62 2.58 3.42 4.45 2.7 3.90 1.63 6.5 8.6 2.3 1.7–5.4 1.04 4.2 7.2 3.49 1.27 0.49 3.95 0.86 3.5 5.6 2.75 0.9 2.3 (max.) 1.1–3.0 2.32 5.0 8.6 0.016–9.2 6.2 8.2 7.2 5.65 5.31 6.75 3.52 9.2 7.8 9.25; 9.89 1.2–12.2 6.35 1.97 1.5–8.2

Crystal structure type D102-hR13 (Be3Nb) C15 A3 hR15 Hexagonal Tetragonal Hexagonal, La type Same C15 hR15 C15 C15 C15 tI12

D102 oC16 (CeNiSi2) oI40 (Co3Si5U2) tl10 (BaNiSn3) tl10 (Al4Ba) C15 D73 D73 Cc B2 hR15 C14 C15 tP38 (Co4So5Si10) C14 hR15 B2 A3-oP4 (AuCd) Mn in -Ti Mn in -Ti D2c F.C.C. hR15 hR15 hR15 A15 D8b DOe hR15 A3 hR15 D8b-tP30 A12 D8b A3 B.C.C.

4/28/05 1:56:48 PM

Properties of Superconductors

12-64 Substance MoRu Mo0.61Ru0.39 Mo0.2Ru0.8 Mo3Ru2 Mo4Ru2Te8 Mo6S8 Mo6S8Sc Mo6S8Sm1.2 Mo6S8Tb Mo6S8Tl Mo6S8Tm1.2 Mo6S8Y1.2 Mo6S8Yb Mo6.6S8Zn11 Mo3Sb4 Mo6Se8 Mo6Se8Sm1.2 Mo6Se8Sn1.2 Mo6Se8Tb Mo3Se3Tl Mo6Se8Tm1.2 Mo6Se8Yb Mo3Si MoSi0.7 MoxSiV3-x Mo5.25Ta0.75Te8 Mo6Te8 Mo0.16Ti0.84 Mo0.913Ti0.087 Mo0.04Ti0.96 Mo0.025Ti0.975 MoxU1-x MoxV1-x Mo2Zr NNb (film) NxOyTiz NxOyVz N0.34Re NTa (film) N0.6–0.987Ti N0.82–0.99V NZr N0.906–0.984Zr Na0.28–0.35O3W Na0.28Pb0.72 NbO NbOs2 Nb3Os Nb0.6Os0.4 Nb3Os0.02–0.10Rh0.98–0.90 Nb3P NbPRh Nb0.6Pd0.4 Nb3Pd0.02–0.10Rh0.92–0.90 Nb0.62Pt0.38 Nb5Pt3 Nb3Pt0.02–0.98Rh0.98–0.02 NbRe3 Nb0.38–0.18Re0.62–0.82 NbRe NbReSi

Section 12.indb 64

Tc, K

9.5–10.5 7.18 1.66 7.0 1.7 1.85 3.6 2.9 2.0 8.7 2.1 3.0 9.2 3.6 2.1 6.3 6.8 6.8 5.7 4.0 6.3 6.2 1.30 1.34 4.54–16.0 1.7 1.7 4.18; 4.25 2.95 2.0 1.8 0.7–2.1 0–~5.3 4.25–4.75 6–9 2.9–5.6 5.8–8.2 4–5 4.84 < 1.17–5.8 2.9–7.9 9.8 3.0–9.5 0.56 7.2 1.25 2.52 1.05 1.89; 1.78 2.42–2.30 1.8 4.08 1.60 2.49–2.55 4.21 3.73 2.52–9.6 5.27 2.43–9.70 3.8 5.1

Crystal structure type

Substance

A3 D8b A3 D8b-tP30 hR15 hR15 hR15 hR15 hR15 hR15 hR15 hR15 hR15 hR15

Nb3Rh Nb0.6Rh0.40 Nb0.9Rh1.1 Nb3Rh0.98–0.90Ru0.02–0.10 NbxRu1-x NbRuSi NbS2 NbS2

2.64 4.21 3.07 2.42–2.44 1.2–4.8 2.65 6.1–6.3 5.0–5.5

Nb3Sb Nb3Sb0–0.7Sn1–0.3 NbSe2 Nb1–1.05Se2 Nb3Se4 Nb3Si Nb3SiSnV3 NbSn2 Nb6Sn5 NbSnTaV NbSnV2 Nb2SnV NbxTa1-x Nb3Te4 NbxTi1-x Nb0.6Ti0.4 NbxU1-x Nb0.88V0.12 Nb0.5V1.5Zr Ni0.3Th0.7 NiZr2 Ni0.1Zr0.9 O3Rb0.27–0.29W OSn O3SrTi (n = 1.7–12.0 × 1019) O3SrTi (n = 1018–1021) O3SrTi (n = 1020) O3Sr0.08W OTi O3Tl0.30W OV3Zr3 OW3 (film) OsPti OsPZr OsReY Os2Sc OsTa Os3Th7 OsxW1-x OsW3 Os2Y Os2Zr OsxZr1-x PPb OsW2 PPd3.0–3.2 P3Pd7 (high temperature) P3Pd7 (low temperature) PRh PRh2 P4Rh5 PRhTa

0.2 6.8–18 5.15–5.62 2.2–7.0 2.0 1.5 4.0 2.60 2.8 6.2 5.5 9.8 4.4–9.2 1.8 0.6–9.8 9.8 1.95 (max.) 5.7 4.3 1.98 1.52 1.5 1.98 3.81 0.12–0.37 0.05–0.47 0.47 2–4 0.58 2.0–2.14 7.5 3.35; 1.1 1.2 7.4 2.0 4.6 1.95 1.51 0.9–4.1 ~3 4.7 3.0 1.5–5.6 7.8 3.81 <0.35–0.7 1.0 0.70 1.22 1.3 1.22 4.41

hR15 hR15 hR15 hR15 hP14 hR15 hR15 A15 A15 hR15 hR15

Cubic

C15 B1 Cubic Cubic F.C.C. B1 B1 B1 B1 B1 Tetragonal

A12 A15 D8b A15 L12tP32 (Ti3P) C37-oP12 (Co2Si) D8f plus cubic A15 D8b D8b A15 D8b-tP30 (FeCr) A15 D8b-tP30 oI36 (FeTiSi)

Tc, K

Crystal structure type A15 D8b plus other A3-oP4 (AuCd) A15 oI36 Hexagonal, NbSe2 type Hexagonal, three-layer type L12-tP32 (Ti3P) A15 Hexagonal Same hP14 L12 Orthorhombic oI44 (Sn5Ti6) A15 A15 A15 A2 hP14

A2 C15-hP12 (MgZn2) D102 A3 Hexagonal tP4 (PbO)

Hexagonal Hexagonal E93 A15 C22-hP9 (Fe2P) Same C14 C14 A12 D102 C14 C14

D8b-tP30 (FeCr) DO11 Rhombohedral Complex C1 oP28 (CaFe2O4) C37-oP12 (Co2Si)

4/28/05 1:56:49 PM

Properties of Superconductors Substance PRhZr PRuTi PRuZr PW3 Pb2Pd Pb4Pt Pb2Rh PbSb PbTe (plus 0.1 w/o Pb) PbTe (plus 0.1 w/o Te) PbTl0.27 PbTl0.17 PbTl0.12 PbTl0.075 PbTl0.04 Pb1–0.26Tl0–0.74 PbTl2 Pb3Zr5 PbZr3 Pd0.9Pt0.1Te2 Pd0.05Ru0.05Zr0.9 Pd2.2S (quenched) PdSb2 PdSb PdSbSe PdSbTe Pd4Se Pd6–7Se Pd2.8Se PdxSe1-x PdSi PdSn PdSn2 Pd2Sn Pd3Sn Pd2SnTm Pd2SnY Pd2SnYb PdTe PdTe1.02–1.08 PdTe2 PdTe2.1 PdTe2.3 Pd1.1Te Pd3Te PdTh2 Pd0.1Zr0.9 PtSb PtSi PtSn PtSn4 Pt3Ta7 PtTa3 PtTe PtTh Pt3Th7 Pt5Th PtTi3 Pt0.02U0.98 PtV2.5 PtV3

Section 12.indb 65

Tc, K

1.55 1.3 3.46 2.26 2.95 2.80 2.66 6.6 5.19 5.24–5.27 6.43 6.73 6.88 6.98 7.06 7.20–3.68 3.75–4.1 4.60 0.76 1.65 ~9 1.63 1.25 1.5 1.0 1.2 0.42 0.66 2.3 2.5 (max.) 0.93 0.41 3.34 0.41 0.47–0.64 1.77 4.92 1.79 2.3; 3.85 2.56–1.88 1.69 1.89 1.85 4.07 0.76 0.85 7.5 2.1 0.88 0.37 2.38 1.5 0.4 0.59 0.44 0.98 3.13 0.58 0.87 1.36 2.87–3.20

12-65 Crystal structure type

Substance

Same C22-hP9 (Fe2P) C37-oP12 DOe C16 Related to C16 C16

PtV3.5 Pt0.5W0.5 PtxW1-x Pt2Y3 Pt2Y Pt3Y7 PtZr Re2Sc Re24Sc5 ReSiTa Re3Si5Y2 Re3Ta2 Re0.64Ta0.36 Re3Ta Re24Ti5 RexTi1-x Re0.76V0.24 Re3V Re0.92V0.08 Re0.6W0.4 Re0.5W0.5 Re13W12 Re3W Re2Y Re2Zr Re3Zr Re6Zr Rh17S15 Rh~0.24Sc~0.76 Rh4Sc5Si10 Rh4Sc3Sn13 RhxSe1-x RhSi3Th Rh0.86Sc1.04Th Rh2Si2Y Rh3Si5Y2 Rh4Sn13Sr3 RhxSnyTh RhxSnyTm Rh4Sn13Y3 Rh2Sr Rh0.4Ta0.6 RhTe2 Rh0.67Te0.33 RhxTe1-x RhTh Rh3Th7 Rh5Th RhxTi1-x Rh0.02U0.98 RhV3 RhW RhY3 Rh2Y3 Rh3Y Rh5Y Rh3Y7 Rh0.005Zr (annealed) Rh0–0.45Zr1–0.55 Rh0.1Zr0.9 Ru2Sc RuSiTa

D88 A15 C6 Cubic C2 B81 C2 C2 Tetragonal Like Pd4Te B31 B31 C37 B82 DO3-cF16 (BiF3) Same Same B81 B81 C6 C6 C6 B81 cI2 (W) C16 A3 B81 B31 B81 C16-oC20 (PdSn4) D8b-tP30 A15-cP8 (Cr3Si) Orthorhombic Bf D102 A15 β-phase A15 A15

Tc, K

1.26 1.45 0.4–2.7 0.90 1.57; 1.70 0.82 3.0 4.2 2.2 4.4 1.76 1.4 1.46 6.78 6.60 6.6 (max.) 4.52 6.26 6.8 6.0 5.12 5.2 9.0 1.83 5.9 7.40 7.40 5.8 0.88; 0.92 8.54 4.5 6.0 (max.) 1.76 6.45 3.11 2.70 4.3 1.9 2.3 3.2 6.2 2.35 1.51 0.49 1.51 (max.) 0.36 2.15 1.07 2.25–3.95 0.96 0.38 ~3.4 0.65 1.48 1.07 0.56 0.32 5.8 2.1–10.8 9.0 1.67 3.15

Crystal structure type A15 A1

C15 D102 A3 C15-hP12 (MgZn2) A12-cI58 (Mg) oI36 (FeTiSi) tP40 (Fe3Sc2Si5) D8b-tP30 (FeCr) A12 A12-cI58 (Mn) A12 D8b D8b-tP30 A3 D8b D8b-tP30 A12-cI58 C14 C14 A12-cI58 Same Cubic tP38 cP40 tI10 tI12 tI10 oI40 cP40 cI2 (W) cP40 cP40 C15 D8b C2

Bf D102

A15 A3

C15 hP20 (Fe3Th7) H.C.P. C14 oI36

4/28/05 1:56:51 PM

Properties of Superconductors

12-66 Substance Ru3Si2Th Ru3Si2Y Ru1.1Sn3.1Y Ru2Th RuTi Ru0.05Ti0.95 Ru0.1Ti0.9 RuxTi0.6Vy Ru3U Ru0.45V0.55 RuW Ru2Y Ru2Zr Ru0.1Zr0.9 STh SbSn SbTa3 SbTi3 Sb2Ti7 Sb0.01–0.03V0.99–0.97 SbV3 SeTh SiMo3 Si2Th Si2Th SiV2.7Ru0.3 Si2W3 SiZr3 Sn0.174–0.104Ta0.826–0.896 SnTa3 SnTa3 SnTaV2 SnTa2V SnxTe1-x (n = 10.5–20 × 1020) Sn3Th SnTi3 SnxTl1-x SnV3 Sn0.02–0.057V0.98–0.943 SnZr3 Ta0.025Ti0.975 Ta0.05Ti0.95 Ta0.05–0.75V0.95–0.25 Ta0.8–1W0.2–0 Tc0.1–0.4W0.9–0.6 Tc0.50W0.50 Tc0.60W0.40 Tc6Zr TeY ThTl3 Th0–0.55Y1–0.45 Ti0.70V0.30 TixV1-x Ti0.5Zr0.5 (annealed) Ti0.5Zr0.5 (quenched) Tl3Y V2Zr V0.26Zr0.74 W2Zr YZn

Tc, K

3.98 3.51 1.3 3.56 1.07 2.5 3.5 6.6 (max.) 0.15 4.0 7.5 1.52 1.84 5.7 0.5 1.30–1.42 0.72 5.8 5.2 3.76–2.63 0.80 1.7 1.4 3.2 2.4 2.9 2.8; 2.84 0.5 6.5–< 4.2 8.35 6.2 2.8 3.7 0.07–0.22 3.33 5.80 2.37–5.2 3.8 2.87–~1.6 0.92 1.3 2.9 4.30–2.65 1.2–4.4 1.25–7.18 7.52 7.88 9.7 1.02 0.87 1.2–1.8 6.14 0.2–7.5 1.23 2.0 1.52 8.80 5.9 2.16 0.33

* n denotes current carriers concentration in cm–3.

Section 12.indb 66

Crystal structure type hP12 hP12 cP40 C15 B2

L12-cP4 B2 A3 C14 C14 A3 B1-cF8 (NaCl) B1 or distorted A15-cP8 (Cr3Si) Same A2 A15 B1-cF8 A15-cP8 Cc, α-phase C32, β-phase A15 L12-tP32 (Ti3P) A15 A15, highly ordered A15, partially ordered A15 A15 B1 L12-cP4 A15-cP8 A15 A2 A15-cP8 Hexagonal Hexagonal A2 A2 Cubic α plus plus α A12 B1-cF8 L12-cP4 Cubic

L12-cP4 C15 C15 B2-cP2 (CsCl)

B. Superconductors with Tc > 10Κ Substance Al2CMo3 Al0.5Ge0.5Nb Al~0.8Ge~0.2Nb3 AlNb3 AlNb3 A1xNb1–x A1xNb1–x A10.27Nb0.73–0.48V0–0.25 A1 NbxV1–x A10.1Si0.9V3 A1V3 AuNb3 Au0–0.3Nb1–0.7 Au0.02–0.98Nb3Rh0.98–0.02 AuNb3(1–x)V3x B0.03C0.51Mo0.47 B4LuRh4 B2LuRu B4Rh4Y B0.1Si0.9V3 BaBi0.2O3Pb0.8 Ba2CaCu2O8T12 Ba2Cu3LaO6 Ba2Cu3O7Tm Ba2Cu3O7Y (Ba,La)2CuO4 Bi2CaCu2O8Sr2 Br2Mo6S6 C3La CMo CMo2 C0.5MoxNb1–x CMoxTi1–x CMo0.83Ti0.17 C0–0.38N1–0.62Ta CNb (whiskers) CNb C0.7–1.0Nb0.3–0 CNbxTa1–x CNb0.6–0.9W0.4–0.1 C0.1Si0.9V3 CTa CTa1–0.4W0–0.6 C0.66Th0.13Y0.21 C3Y2 CW (Ca,La)2CuO4 Cu(La,Sr)2O4 Cu1.8Mo6S8 Cr0.3SiV2.7 GaNb3 GaxNb3Sn1–x GaV3 GaV2.1–3.5 GeNb3 GeNb3 (quenched) GexNb3Sn1–x Ge0.5Nb3Sn0.5 Ge0.1Si0.9V3 GeV3 InLa3

Tc,K

10.0 12.6 20.7 18.0 12.0 <4.2–13.5 12–17.5 14.5–17.5 4.4–13.5 14.05 11.8 11.5 1.1–11.0 2.53–10.9 1.5–11.0 12.5 11.7 10 11.3 15.8 13.2 120 80 101 90 36 110 13.8 11.0 14.3 12.2 10.8–12.5 10.2(max) 10.2 10.0–11.3 7.5–10.5 11.5 6–11 8.2–13.9 12.5–11.6 16.4 10.3 8.5–10.5 17 11.5 10 18 39 10.8 11.3 14.5 14–18.37 16.8 6.3–14.45 23.2 6–17 17.6–18.0 11.3 14.0 11 9.83; 10.4

Crystal structure type A13 A15 A15 A15 D8b A15 A15

A15 A15

(Cr3Si) (FeCr)

(Cr3Si)

A15 A15 (B4CeCo4) A15

A15

B1 B1 B1 B1

(B4CeCo4)

(K2NiF4) (Mo6PbS8) (C3Pu2) (NaC1) o**

B1 B1 B1 A15 B1 B1

A15 A15 A15 A15 A15 A15 A15 A15 A15 A15 LI2

(C3Pu2) (C3Pu2) (K2NiF4) (Mo6PbS8) (Cr3Si)

(AuCu3)

4/28/05 1:56:53 PM

Properties of Superconductors Substance In0–0.3Nb3Sn1–0.7 InV3 Ir0.4Nb0.6 LaMo6Se8 LiO4Ti2 MgB2 MoN Mo3Os Mo6Pb0.9S7.5 Mo3Re MoxRe1–x Mo0.52Re0.48 Mo0.57Re0.43 Mo~0.60Re0.395 MoRu Mo3Ru Mo6Se8T1 Mo0.3SiV2.7 Mn3Si Mo3Tc Mo0.3Tc0.7 MoxTc1–x MoTc3 NNb (whiskers) NNb (diffusion wires) N0.988Nb N0.824–0.988Nb N0.7–0.795Nb NNbxOy NNbxOy

Substance Ag2F Ag7NO11 Al2CMo3 BaBi3 Bi2Pt Bi3Sr Bi5Tl3 CdSn CoSi2 Cr0.1Ti0.3V0.6 In1-0.86Mg0-0.14

Section 12.indb 67

Tc,K

18.0–18.19 13.9 10 11.4 13.7 39.0±0.5 12; 14.8 12.7 15.2 10.0; 15 1.2–12.2 11.1 14.0 10.6 9.5–10.5 10.6 12.2 11.7 12.5 15 12.0 10.8–15.8 15.8 10–14.5 16.10 14.9; 17.3 14.4–15.3 11.3–12.9 13.5–17.0 6.0–11

12-67 Substance

Crystal structure type A15 A15

C32 A15 A15

A3 A15 A15 A15 A15 A15

B1 B1 B1

(FeCr) (Mo6PbS8) (A12MgO4) h* (Mo6PbS8)

(Mo6PbS8)

N100–42w/oNb0–58w/oTi N100–75w/oNb0–25w/oZr NNbxZr1–x N0.93Nb0.85Zr0.15 NTa NZr Nb3Pt Nb0.18Re0.82 Nb3Si Nb0.3SiV2.7 Nb3Sn Nb0.8Sn0.2 NbxSn1–x (film) Nb3Sn2 NbSnTa2 Nb2SnTa Nb2.5SnTa0.5 Nb2.75SnTa0.25 Nb3xSnTa3(1–x) Nb2SnTa0.5V0.5 NbTc3 Nb0.75Zr0.25 Nb0.66Zr0.33 PbTa3 RhTa3 RhZr2 Rh0–0.45Zr1–0.55 SiTi0.3V2.7 SiV3 SiV2.7Zr0.3

TABLE 5. Critical Field Data Ho (oersteds) 2.5 57 1700 740 10 530 >400 >266 105 1360 272.4–259.2

Substance InSb InxTl1-x In0.8Tl0.2 Mg0.47Tl0.53 Mo0.16Ti0.84 NbSn2 PbTl0.27 PbTl0.17 PbTl0.12 PbTl0.075 PbTl0.04

Tc,K

15–16.8 12.5–16.35 9.8–13.8 13.8 12–14 10.7 10.9 10 19 12.8 18.05 18.18; 18.5 2.6–18.5 16.6 10.8 16.4 17.6 17.8 6.0–18.0 12.2 10.5 10.8 10.8 17 10 10.8; 11.3 2.1–10.8 10.9 17.1 13.2

Crystal structure type

B1 B1 B1 B1 A15 A15 A15 A15 A15

A15 A15 A15 A15

(Mn)

o* t*

A15 A12

A15 A15 C16

(A12Cu)

A15 A15 A15

Ho (oersteds) 1100 252–284 252 220 <985 620 756 796 849 880 864

4/28/05 1:56:55 PM

Properties of Superconductors

12-68

TABLE 6. High Critical Magnetic-Field Superconductive Compounds and Alloys Substance

Hc1, kOe

9.8–10.2

C8K

0.39

C0.44Mo0.56 CNb CNb0.4Ta0.6 CTa CaxO3Sr1-xTi Cd0.1Hg0.9 (by weight) Cd0.05Hg0.95 Cr0.10Ti0.30V0.60 GaN GaxNb1-x GaSb (annealed) GaV1.95 GaV2.1-3.5 GaV3

12.5–13.5 8–10 10–13.6 9–11.4 <0.1–0.55

GaV4.5 HfxNby HfxTay Hg0.05Pb0.95 Hg0.101Pb0.899 Hg0.15Pb0.85 In0.98Pb0.02 In0.96Pb0.04 In0.94Pb0.06 In0.913Pb0.087 In0.316Pb0.684 In0.17Pb0.83 In1.000Te1.002 In0.95Tl0.05 In0.90Tl0.10 In0.83Tl0.17 In0.75Tl0.25 LaN La3S4 La3Se4 Mo0.52Re0.48

9.15

1.35 6.5 8.6 11.1

Mo0.6Re0.395

10.6

Mo0.5Ti0.5 Mo0.16Ti0.84

4.18

0.028

2.95 1.85–2.06

0.060

Mo0.913Ti0.087 Mo0.1-0.3U0.9-0.7 Mo0.17Zr0.83

Section 12.indb 68

Tc , K

Al2CMo3 AlNb3 BaxO3Sr1-xTi Bi0.5Cd0.1Pb0.27Sn0.13 BixPb1-x Bi0.56Pb0.44 Bi7.5w/oPb92.5w/ob Bi0.099Pb0.901 Bi0.02Pb0.98 Bi0.53Pb0.32Sn0.16 Bi1-0.93Sn0-0.07 Bi5Tl3 C8K (excess K)

<0.1–0.55 7.35–8.4 8.8

0.091 0.375 0.0039 max. 0.122 max. 0.29 0.46

6.4 0.55

5.6 5.85 4.24 5.3 6.3–14.45

6.75 3.45 3.68 3.90 4.2 3.5–3.7

0.087 0.12 0.19 0.22 0.002–0.004 0.23 0.28 0.071 0.725

0.4

0.235 0.23 0.1 0.1 0.095 ~10.17 0.155 0.263 0.257 0.242 0.216 0.45 ≈0.15 ≈0.2

156

Hc2, kOe

Hc3, kOe

1.2

>24 30 max. 15 2.32 2.8 0.73 >25 0–0.032 >5.6 0.160 (H⊥c) 0.730 (H|c) 0.025 (H⊥c) 0.250 (H|c) 98.5 16.9 14.1 4.6

3.06 4.2 4.2

0.34

2.04

0.31 84.4

2.16 0 4.2 4.2 3.5

>28 2.64 73e 230–300d 350e 500d 121c >52–>102 >28–>86 2.3 4.3 >13 0.12 0.18 0.55 3.7 2.8 1.2c 0.263 0.257 0.39 0.50 >25 >25 14–21 18–28 14–20 19–26 75c 98.7c 36–38 15 >25 30

Tobs, Ka

3.06 3.7 3.35 0.32 0.32 0.32 0.32 1.2 4.2 1.2 1.2

0 0 0 1.2 1.2

0.12 0.25 0.35 2.65 5.5

22–33 37–43 20–37 26–37

4.2 2.93 2.76 2.94 3.12 4.2 4.2 0 3.3 3.25 3.21 3.16 0.76 1.3 1.25 4.2 1.3 4.2 1.3 0 0 3.0 4.2

4/28/05 1:56:56 PM

Properties of Superconductors Substance

Tc , K

N(12.8 w/o)Nb NNb (wires)

15.2 16.1

NNbxO1-x NNbxZr1-x N0.93Nb0.85Zr0.15 Na0.086Pb0.914 Na0.016Pb0.984 Nb

13.5–17.0 9.8–13.8 13.8 9.15

Hc1, kOe

0.19 0.28

Nb Nb (unstrained) Nb (strained) Nb (cold-drawn wire) Nb (film) NbSc Nb3Sn

0.4–1.1 1.1–1.8 1.25–1.92 2.48

Nb0.1Ta0.9 Nb0.2Ta0.8 Nb0.65-0.73Ta0.02-0.10Zr0.25 NbxTi1-x

0.084

Nb0.222U0.778 NbxZr1-x

1.98

O3SrTi O3SrTi PbSb1 w/o(quenched) PbSb1 w/o(annealed) PbSb2.8 w/o(quenched) PbSb2.8 w/o(annealed) Pb0.871Sn0.129 Pb0.965Sn0.035 Pb1-0.26Tl0-0.74 PbTl0.17 Re0.26W0.74 Sb0.93Sn0.07 SiV3 SnxTe1–x Ta (99.95%)

Ta0.5Nb0.5 Ta0.65-0Ti0.35-1 Ta0.5Ti0.5 Te TcxW1-x Ti Ti0.75V0.25 Ti0.775V0.225 Ti0.615V0.385 Ti0.516V0.484 Ti0.415V0.585 Ti0.12V0.88 Ti0.09V0.91 Ti0.06V0.94

Section 12.indb 69

12-69

0.170

0.43 0.33

7.20–3.68 6.73 17.0

0.0049c 0.00195c

0.45 0.53

0.55 0.00043–0.00236 0.425 0.325 0.275 0.090

4.4–7.8 3.3 5.75–7.88

0.25c

5.3 4.7 7.07 7.20 7.49

0.029c 0.024c 0.050 0.062 0.078

Hc2, kOe

>9.5 153c 132 95 53 38 4- >130 >130 6.0 2.05 2.020 1.710 3–5.5 3.40 3.44 4.10 >25 >30 221 70 54 34 17 0.154 10 >70–>90 148 max. 120 max. 23 127 max. 94 max. 0.504c 0.420c >1.5 >0.7 >2.3 >0.7 1.1 0.56 2–6.9c 4.5c >30 0.12 156e 0.005–0.0775 1.850 1.425 1.175 0.375 3.55 >14–138 138 8–44 199c 172c 34 28 25 17.3 14.3 8.2

Hc3, kOe

13.2 0 4.2 8 12

Tobs, Ka

4.2 4.2

6–9.1 6.0–8.7 ≈10

1.4 4.2 4.2 4.2 4.2 4.2 4.2 4.2 14.15 15 16 17 4.195 4.2 4.2 1.2 4.2 1.2 1.2 4.2 0 0 4.2 4.2 4.2 4.2 0 0 3.7

2.7

28.1 16.4 12.7

0.012–0.079 1.3 2.27 2.66 3.72 4.2 1.2 1.2 0 4.2 4.2 0 0 4.2 4.2 4.2 4.2 4.2 4.2

4/28/05 1:56:58 PM

Properties of Superconductors

12-70 Substance

Tc , K

Ti0.03V0.97 TixV1-x V

5.31

V0.26Zr0.74

≈5.9

W (film)

1.7–4.1

a b c d e

Hc1, kOe

0.8 0.75 0.45 0.30 0.238 0.227 0.185 0.165

>34

6.8

Hc3, kOe

4.2 1.2 1.79 2 3 4 1.05 1.78 3.04 3.5 1

Tobs, Ka

Temperature of critical field measurement. w/o denotes weight percent. Extrapolated. Linear extrapolation. Parabolic extrapolation

References 1. B. W. Roberts, in Superconductive Materials and Some of Their Properties. Progress in Cryogenics, Vol. IV, 1964, pp. 160–231. 2. B. W. Roberts, Superconductive Materials and Some of Their Properties, NBS Technical Notes 408 and 482, U.S. Government Printing Office, 1966 and 1969; B. W. Roberts, J. Phys. Chem. Ref. Data, 5, 581, 1976. 3. B. W. Roberts, Properties of Selected Superconductive Materials, 1978 Supplement, NBS Technical Note 983, 1978. 4. T. Claeson, Phys. Rev., 147, 340, 1966. 5. C. J. Raub, W. H. Zachariasen, T. H. Geballe, and B. T. Matthias, J. Phys. Chem. Solids, 24, 1093, 1963. 6. T. H. Geballe, B. T. Matthias, V. B. Compton, E. Corenzwit, G. W. Hull, Jr., and L. D. Longinotti, Phys. Rev., 1A, 119, 1965. 7. C. J. Raub, V. B. Compton, T. H. Geballe, B. T. Matthias, J. P. Maita, and G. W. Hull, Jr., J. Phys. Chem. Solids, 26, 2051, 1965. 8. R. D. Blaugher, J. K. Hulm, and P. N. Yocom, J. Phys. Chem. Solids, 26, 2037, 1965. 9. T. Claeson and H. L. Luo, J. Phys. Chem. Solids, 27, 1081, 1966. 10. S. C. Ng and B. N. Brockhouse, Solid State Comm., 5, 79, 1967. 11. O. I. Shulishova and I. A. Shcherbak, Izv. AN SSSR, Neorg. Materials, 3, 1495, 1967. 12. T. F. Smith and H. L. Luo, J. Phys. Chem. Solids, 28, 569, 1967. 13. A. C. Lawson, J. Less-Common Metals, 23, 103, 1971. 14. R. Chevrel, M. Sergent, and J. Prigent, J. Solid State Chem., 3, 515, 1971. 15. M. Marezio, P. D. Dernier, J. P. Remeika, and B. T. Matthias, Mat. Res. Bull., 8, 657, 1973. 16. J. K. Hulm and R. D. Blaugher in Superconductivity in d- and f-Band Metals, D. H. Douglass, Ed., American Institute of Physics, 4, 1, 1972. 17. R. N. Shelton, A. C. Lawson, and D. C. Johnston, Mat. Res. Bull., 10, 297, 1975. 18. H. D. Wiesinger, Phys. Status Sol., 41A, 465, 1977. 19. O. Fisher, Applied Phys., 16, 1, 1978. 20. D. C. Johnston, Solid State Comm., 24, 699, 1977. 21. H. C. Ku and R. H. Shelton, Mat. Res. Bull., 15, 1441, 1980. 22. H. Barz, Mat. Res. Bull., 15, 1489, 1980. 23. G. P. Espinosa, A. S. Cooper, H. Barz, and J. P. Remeika, Mat. Res. Bull., 15, 1635, 1980. 24. E. M. Savitskii, V. V. Baron, Yu. V. Efimov, M. I. Bychkova, and L. F. Myzenkova, in Superconducting Materials, Plenum Press, 1981, p. 107. 25. R. Fluckiger and R. Baillif, in Topics in Current Physics, O. Fischer and M. B. Maple, Eds., Springer Verlag, 34, 113, 1982. 26. R. N. Shelton, in Superconductivity in d- and f-Band Metals, W. Buckel and W. Weber, Eds., Kernforschungszentrum, Karlsruhe, 1982, p. 123. 27. D. C. Johnston and H. F. Braun, Topics in Current Phys., 32, 11, 1982.

Section 12.indb 70

Hc2, kOe

3.8 108 max. 3.4 3.15 2.2 1.2

28. R. Chevrel and M. Sergent, Topics in Current Phys., 32, 25, 1982. 29. G. P. Espinosa, A. S. Cooper, and H. Barz, Mat. Res. Bull., 17, 963, 1982. 30. R. Muller, R. N. Shelton, J. W. Richardson, Jr., and R. A. Jacobson, J. Less-Comm. Met., 92, 177, 1983. 31. You-Xian Zhao and Shou-An He, in High Pressure in Science and Technology, North Holland, 22, 51, 1983. 32. You-Xian Zhao and Shou-An He, Solid State Comm., 24, 699, 1983. 33. G. P. Meisner and H. C. Ku, Appl. Phys., A31, 201, 1983. 34. R. J. Cava, D. W. Murphy, and S. M. Zahurak, J. Electrochem. Soc., 130, 2345, 1983. 35. R. N. Shelton, J. Less-Comm. Met., 94, 69, 1983. 36. B. Chevalier, P. Lejay, B. Lloret, Wang Xian–Zhong, J. Etourneau, and P. Hagenmuller, Annales de Chemie, 9, 191, 1984. 37. G. Venturini, M. Meot-Meyer, E. McRae, J. F. Mareche, and B. Rogues, Mat. Res. Bull., 19, 1647, 1984. 38. J. M. Tarascon, F. G. DiSalvo, D. W. Murphy, G. Hull, and J. V. Waszczak, Phys. Rev., 29B, 172, 1984. 39. G. V. Subba and G. Balakrishnan, Bull. Mat. Sci., 6, 283, 1984. 40. B. Batlog, Physica, 126B, 275, 1984. 41. M. J. Johnson, Ames Lab (USA) Report IS-T-1140, 1984. 42. I. M. Chapnik, J. Mat. Sci. Lett., 4, 370, 1985. 43. W. Rong-Yao, L. Q-Guang, and Z. Xiao, Phys. Status Sol., 90A, 763, 1985. 44. W. Xian-Zhong, B. Chevalier, J. Etourneau, and P. Hagenmuller, Mat. Res. Bull., 20, 517, 1985. 45. H. R. Ott, F. Hulliger, H. Rudigier, and Z. Fisk, Phys. Rev., 31B, 1329, 1985. 46. P. Villars and L. D. Calver, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, Vol. 1–3, ASM, 1985. 47. G. V. Subba Rao, K. Wagner, G. Balakhrishnan, J. Jakani, W. Paulus, and R. Scollhorn, Bull. Mat. Sci., 7, 215, 1985. 48. J. G. Bednorz and K. A. Muller, Zs. Physik, B64, 189, 1986. 49. W. Rong-Yao, Phys. Status Sol., 94A, 445, 1986. 50. H. D. Yang, R. N. Shelton, and H. F. Braun, Phys. Rev., 33B, 5062, 1986. 51. G. Venturini, M. Kanta, E. McRae, J. F. Mareche, B. Malaman, and B. Roques, Mat. Res. Bull., 21, 1203, 1986. 52. W. Rong-Yao, J. Mat. Sci. Lett., 5, 87, 1986. 53. M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang, and C. W. Chu, Phys. Rev. Lett., 58, 908, 1987. 54. R. J. Cava, R. B. Van Dover, B. Batlog, and E. A. Rietman, Phys. Rev. Lett., 58, 408, 1987. 55. L. C. Porter, T. J. Thorn, U. Geiser, A. Umezawa, H. H. Wang, W. K. Kwok, H-C. I. Kao, M. R. Monaghan, G. W. Crabtree, K. D. Carlson, and J. M. Williams, Inorg. Chem., 26, 1645, 1987. 56. A. M. Kini, U. Geiser, H-C. I. Kao, K. D. Carlson, H. H. Wang, M. R. Monaghan, and K. M. Williams, Inorg. Chem., 26, 1834, 1987.

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Properties of Superconductors 57. T. Penney, S. von Molnar, D. Kaiser, F. Holtzberg, and A. W. Kleinsasser, Phys. Rev., B38, 2918, 1988. 58. Y. K. Tao, J. S. Swinnea, A. Manthiram, J. S. Kim, J. B. Goodenoug, and H. Steinfink, J. Mat. Res., 3, 248, 1988. 59. G. G. Peterson, B. R. Weinberger, L. Lynds, and H. A. Krasinski, J. Mat. Res., 3, 605, 1988. 60. J. B. Torrance, Y. Tokura, A. Nazzai, and S. S. P. Parkin, Phys. Rev. Lett., 60, 542, 1988. 61. K. Kourtakis, M. Robbins, P. K. Gallagher, and T. Teifel, J. Mat. Res., 4, 1289, 1989. 62. J. C. Phillips, Physics of High-Tc Superconductors, Academic Press, 1989, p. 336. 63. Shui Wai Lin and L. I. Berger, Rev. Sci. Instrum., 60, 507, 1989. 64. M. Tinkham, Introduction to Superconductivity, McGraw–Hill, New York, 1975. 65. O. Fischer and M.B. Maple, Eds., Topics in Current Physics, Volume 32: Superconductivity in Ternary Compounds I; Volume 34: Superconductivity in Ternary Compounds II, Springer–Verlag, Berlin, 1982. 66. K. J. Dunn and F. P. Bundy, Phys. Rev., B25, 194, 1982. 67. A. Barone and G. Paterno, Physics and Applications of the Josephson Effect, Wiley, New York, 1982.

Section 12.indb 71

12-71 68. D. H. Douglass, Ed., Superconductivity in d- and f-Band Metals, Plenum Press, New York, 1976. 69. D. M. Ginsberg, Ed., Physical Properties of High Temperature Superconductors, (Volume II, 1990; Volume III, 1992; Volume V, 1996), World Scientific, Singapore. 70. T. Ishiguro and K. Yamji, Organic Superconductors, Springer-Verlag, Berlin, 1990. 71. Sh. Okada, K. Shimizu, T. C. Kobayashi, K. Amaya, and Sh. Endo., J. Phys. Soc. Jpn., 65, 1924, 1996. 72. A. Bourdillon and N. X. Tan Bourdillon, High Temperature Superconductors: Processing and Science, Academic Press, 1994. 73. J. M. Williams, J. R. Ferraro, R. J. Thorn, K. Carlson, U. Geiser, H. H. Wang, A. M. Kini, and M.-H. Whangbo, Organic Superconductors (Including Fullerenes): Synthesis, Structure, Properties, and Theory, Prentice–Hall, 1992. 74. J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Nature (London), 410, 63, 2001. 75. Y. Boguslavsky, G. K. Perkins, X. Qi, L. F. Cohen, and A. D. Caplin, Nature (London), 410, 563, 2001. 76. B. Q. Fu, Y. Feng, G. Yan, Y. Zhao, A. K. Pradhan, C. H. Cheng, P. Ji, X. H. Liu, C. F. Liu, L. Zhou, and K. F. Yau, J. Appl. Phys., 92, 7341, 2002.

4/28/05 1:57:00 PM

HIGH TEMPERATURE SUPERCONDUCTORS C. N. R. Rao and A. K. Raychaudhuri The following tables give properties of a number of high temperature superconductors. Table 1 lists the crystal structure (space group and lattice constants) and the critical transition temperature Tc for the more important high temperature superconductors so far studied. Table 2 gives energy gap, critical current density, and penetration depth in the superconducting state. Table 3 gives electrical and thermal properties of some of these materials in the normal state. The tables were prepared in November 1992 and updated in November 1994.

References

2. Rao, C. N .R., Ed., Chemistry of High-Temperature Superconductors, World Scientific, Singapore, 1991. 3. Shackelford, J. F., The CRC Materials Science and Engineering Handbook, CRC Press, Boca Raton, 1992, 98–99 and 122–123. 4. Kaldis, E., Ed., Materials and Crystallographic Aspects of HTcSuperconductivity, Kluwer Academic Publ., Dordrecht, The Netherlands, 1992. 5. Malik, S. K. and Shah, S. S., Ed., Physical and Material Properties of High Temperature Superconductors, Nova Science Publ., Commack, N.Y., 1994. 6. Chmaissem, O. et. al., Physica, C230, 231–238, 1994. 7. Antipov, E. V. et. al., Physica, C215, 1–10, 1993.

1. Ginsburg, D. M., Ed., Physical Properties of High-Temperature Superconductors, Vols. I–III, World Scientific, Singapore, 1989–1992.

TABLE 1. Structural Parameters and Approximate Tc Values of High-Temperature Superconductors Material

La2CuO4+δ La2-xSrx(Bax)CuO4 La2Ca1-xSrxCu2O6 YBa2Cu3O7 YBa2Cu4O8 Y2Ba4Cu7O15 Bi2Sr2CuO6 Bi2CaSr2Cu2O8 Bi2Ca2Sr2Cu3O10 Bi2Sr2(Ln1-xCex)2Cu2O10 Tl2Ba2CuO6 Tl2CaBa2Cu2O8 Tl2Ca2Ba2Cu3O10 Tl(BaLa)CuO5 Tl(SrLa)CuO5 (Tl0.5Pb0.5)Sr2CuO5 TlCaBa2Cu2O7 (Tl0.5Pb0.5)CaSr2Cu2O7 TlSr2Y0.5Ca0.5Cu2O7 TlCa2Ba2Cu3O8 (Tl0.5Pb0.5)Sr2Ca2Cu3O9 TlBa2(La1-xCex)2Cu2O9 Pb2Sr2La0.5Ca0.5Cu3O8 Pb2(Sr,La)2Cu2O6 (Pb,Cu)Sr2(La,Ca)Cu2O7 (Pb,Cu)(Sr,Eu)(Eu,Ce)Cu2Ox Nd2-xCexCuO4 Ca1-xSrxCuO2 Sr1-xNdxCuO2 Ba0.6K0.4BiO3 Rb2CsC60 NdBa2Cu3O7 SmBaSrCu3O7 EuBaSrCu3O7 GdBaSrCu3O7 DyBaSrCu3O7 HoBaSrCu3O7 ErBaSrCu3O7 (multiphase) TmBaSrCu3O7 (multiphase) YBaSrCu3O7 HgBa2CuO4 HgBa2CaCu2O6 (annealed in O2) HgBa2Ca2Cu3O8 HgBa2Ca3Cu4O10

Structure

Bmab; a = 5.355, b = 5.401, c = 13.15 Å I4/mmm; a = 3.779, c = 13.23 Å I4/mmm; a = 3.825, c = 19.42 Å Pmmm; a = 3.821, b = 3.885, c = 11.676 Å Ammm; a = 3.84, b = 3.87, c = 27.24 Å Ammm; a = 3.851, b = 3.869, c = 50.29 Å Amaa; a = 5.362, b = 5.374, c = 24.622 Å A2aa; a = 5.409, b = 5.420, c = 30.93 Å A2aa; a = 5.39, b = 5.40, c = 37 Å P4/mmm; a = 3.888, c = 17.28 Å A2aa; a = 5.468, b = 5.472, c = 23.238 Å; I4/mmm; a = 3.866, c = 23.239 Å I4/mmm; a = 3.855, c = 29.318 Å I4/mmm; a = 3.85, c = 35.9 Å P4/mmm; a = 3.83, c = 9.55 Å P4/mmm; a = 3.7, c = 9 Å P4/mmm; a = 3.738, c = 9.01 Å P4/mmm; a = 3.856, c = 12.754 Å P4/mmm; a = 3.80, c = 12.05 Å P4/mmm; a = 3.80, c = 12.10 Å P4/mmm; a = 3.853, c = 15.913 Å P4/mmm; a = 3.81, c = 15.23 Å I4/mmm; a = 3.8, c = 29.5 Å Cmmm; a = 5.435, b = 5.463, c = 15.817 Å P2212; a = 5.333, b = 5.421, c = 12.609 Å P4/mmm; a = 3.820, c = 11.826 Å I4/mmm; a = 3.837, c = 29.01 Å I4/mmm; a = 3.95, c = 12.07 Å P4/mmm; a = 3.902, c = 3.35 Å P4/mmm; a = 3.942, c = 3.393 Å Pm3m; a = 4.287 Å a = 14.493 Å Pmmm; a = 3.878, b = 3.913, c = 11.753 I4/mmm; a = 3.854, c = 11.62 I4/mmm; a = 3.845, c = 11.59 I4/mmm; a = 3.849, c = 11.53 Pmmm; a = 3.802, b = 3.850, c = 11.56 Pmmm; a = 3.794, b = 3.849, c = 11.55 Pmmm; a = 3.787, b = 3.846, c = 11.54 Pmmm; a = 3.784, b = 3.849, c = 11.55 Pmmm; a = 3.803, b = 3.842, c = 11.54 I4/mmm; a = 3.878, c = 9.507 I4/mmm; a = 3.862, c = 12.705 Pmmm; a = 3.85, c = 15.85 Pmmm; a = 3.854, c = 19.008

Tc/K (maximum value) 39 35 60 93 80 93 10 92 110 25 92 119 128 40 40 40 103 90 90 110 120 40 70 32 50 25 30 110 40 31 31 58 84 88 86 90 87 82 88 84 94 127 133 126

12-72

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High Temperature Superconductors

12-73 TABLE 2. Superconducting Properties

Jc (0): Critical current density extrapolated to 0 K λab: Penetration depth in a-b plane kB: Boltzmann constant Material Y Ba2Cu3O7 Bi2Sr2CaCu2O8 Tl2Ba3CaCu2O8 La2-xSrxCuO4, x = 0.15 Nd2-xCexCuO4

Form Single Crystal Single Crystal Ceramic Ceramic Ceramic

Energy gap (∆) 2∆ƒit/kBTc† 2∆pp/kBTc* 5–6 4–5 8–9 5.5–6.5 6–7 4–6 7–9 4–6 8 4–5

10–6 × Jc (0)/A cm–2 30 (film) 2 10 (film, 80 K)

λab/Å 1400 2700 2000

0.2 (film)

* Obtained from peak to peak value. † Obtained from fit to BCS-type relation.

ρab: ρc: +ve: –ve: nH: k: in plane: out of plane: Material YBa2Cu3O7 YBa2Cu4O8 Bi2Sr2CuO6 Bi2Sr2CaCu2O8 Tl2Ba2CuO6 Tl2Ba2Ca2Cu3O10 La2-xSrxCuO4, x = 0.12 La2-xSrxCuO4, x = 0.20 Nd2–xCexCuO4, x = 0.17 x = 0.15

TABLE 3. Normal State Properties

Resistivity in the a-b plane Resistivity along the c axis ρc has positive temperature coefficient of resistivity ρc has negative temperature coefficient of resistivity Hall density Thermal conductivity Along a-b plane Perpendicular to a-b plane ρab/µΩ cm ρc/mΩ cm Form 300 K 100 K 300 K Single crystal 110 35 5 Film 200–300 60–100 Single crystal 75 20 10 Film 100–200 20–50 Single crystal 300 150 5000 Single crystal 150 50 >1000 Single crystal 300–400 50–75 200–300 Ceramic ∗∗∗ ∗∗ Single crystal 900 350 200 Single crystal 400 200 80 Film 400 160 Single crystal 500 275 140–180 35 Film

dρc/dT

10–21 × nH/cm–3 300 K 100 K

+ve

11–16 5–9

4–6 2–3

–ve

14 22

–ve

+ve

3.1

2.5 ≈ 2*

+ve for T >225 K +ve for T >150 K

k/(mW/cm K) at 300 K in plane out of plane 120

50 (for x = 0.04)

2.5 10 8.4

6.3

53 32

17 11

250 (for x = 0.15)

* At 200 K ** ρ ~0.4 mΩ cm at 120 K *** ρ ~1.5 mΩ cm at 300 K

Section 12.indb 73

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ORGANIC SUPERCONDUCTORS H.P.R. Frederikse Although the vast majority of organic compounds are insulators, a small number of organic solids show considerable electrical conductivity. Some of these materials appear to be superconductors. The superconducting organics fall primarily into two groups: those containing fulvalenes (pentagonal rings containing sulfur or selenium) and those based on fullerenes, involving the nearly spherical cluster C60. The transition temperatures Tc of the fulvalene derivatives are shown in Table 1. The abbreviations of the various molecular groups are listed in Table 2 and their chemical structures are depicted in Figure 1. Most of the Tc’s are between 1 and 12 K. Several of the compounds only show superconductivity under pressure. The fullerenes are A3C60 compounds, where A represents a single or a combination of alkali atoms. The C60 cluster is shown in

Figure 2a, while Figure 2b illustrates how the alkali atoms fit into the A3C60 molecule to form the A15 crystallographic structure. Their superconducting transition temperatures range from 8 to 31.3 K (see Table 3).

References 1. Ishigura, T. and Yamaji, K., Organic Superconductors, Springer-Verlag, Berlin, 1990. 2. Williams, Jack M. et al., Organic Superconductors (Including Fullerenes), Prentice Hall, Englewood Cliffs, N.J., 1992. 3. The Fullerenes, Ed.: Krato, H. W., Fisher, J. E., and Cox, D. E., Pergammon Press, Oxford, 1993. 4. Schluter, M. et al., in The Fullerenes (Ref. 3), p. 303.

TABLE 1. Critical Pressure and Maximum Critical Temperature of Organic Superconductors Material (TMTSF)2PF6 (TMTSF)2AsF6 (TMTSF)2SbF6 (TMTSF)2TaF6 (TMTSF)2ClO4 (TMTSF)2ReO4 (TMTSF)2FSO3 (ET)4(ReO4)2 βL-(ET)2I3 βH-(ET)2I3 γ-(ET)3I2.5 ε-(ET)2I3(I8)0.5 α-(ET)2I3I2-doped αt-(ET)2I3 ε→β-(ET)2I3a θ-(ET)2I3 κ-(ET)2I3

Pc/kbar

6.5 9 11 12 0 9.5 5 4.5 0 0 0 0 0 0 0 0 0

Tc/K

1.2 1.3 0.4 1.4 1.4 1.3 3 2 1.4 8.1 2.5 2.5 3.3 8 6 3.6 3.6

Material β-(ET)2IBr2 β-(ET)2AuI2 (ET)4Hg2.89Cl8 (ET)4Hg2.89Br8 (ET)3Cl2(H2O)2 κ-(ET)2Cu(NCS)2 κ-(d-ET)2Cu(NCS)2 (DMET)2Au(CN)2 (DMET)2AuI2 (DMET)2AuBr2 (DMET)2AuCl2 (DMET)2I3 (DMET)2lBr2 (MDT-TTF)2AuI2 TTF[Ni(dmit)2]2 TTF[Pd(dmit)2]2 (CH3)4N[Ni(dmit)2]2

Pc/kbar

0 0 0 12 16 0 0 1.5 5 0 0 0 0 0 2 20 7

Tc/K

2.8 4.8 4.2 1.8 2 10.4 11.4 0.9 0.6 1.9 0.9 0.6 0.7 3.5 1.6b 6.5 5

Converted form ε-type to β-type by thermal treatment. For 7 kbar. From Ishigura, T. and Yamaji, K., Organic Superconductors, Springer-Verlag, Berlin, 1990. With permission. a

TABLE 2. List of Symbols and Abbreviations

TTF TMTSF BEDT-TTF or “ET” MDT-TTF DMET dmit Tc Pc

tetrathiafulvalene tetramethyltetraselenafulvalene bis(ethylenedithio)tetrathiafulvalene methylenedithiotetrathiafulvalene [dimethyl(ethylenedithio)diselenadithiafulvalene] 4,5-dimercapto-1,3-dithiole-2-thione transition temperature to superconducting state minimum pressure required for superconducting transition

12-74

Section 12.indb 74

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Organic Superconductors

12-75

H3C

CH3

H3C

CH3

TMTSF

TTF

Tetramethyltetraselenafulvalene H H H H

Tetrathiafulvalene

H H H H

BEDT − TTF or ET

DMET

Bis(ethylenedithio)tetrathiafulvalene Dimethyl(ethylenedithio)diselenadithiafulvalene

S S

S C S

S M

n–

S C S

C S

MDT − TTF

M=Ni, Pd, Pt M(dmit)22–

Methylenedithiotetrathiafulvalene

Ligand is 4,5-dimercapto-1.3-dithiole-2-thione

FIGURE 1. Structures of various donor molecules and acceptor species.

(001)

(010)

(100)

a b FIGURE 2. (a) C60 cluster placed in a fcc lattice. Each crystal axis crosses a double bond shared by two hexagons. (b) A hypothetical A3C60 with the A15 structure. The structure can be seen to be an ordered defect structure of A6C60.

Section 12.indb 75

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Organic Superconductors

12-76 TABLE 3. Unit Cell and Tc for FCC-A3 C60 Na2Rb0.5Cs0.5C60 Na2CsC60 No. 1a Na2CsC60 No. 2a K3C60 K2RbC60 Rb2KC60 No. 1a Rb2KC60 No. 2a Rb3C60 Rb2CsC60

Lattice parameter(s) (Ã&#x2026;) 14.148(3) 14.132(2) 14.176(9) 14.253(3) 14.299(2) 14.336(1) 14.364(5) 14.436(2) 14.493(2)

Tc/K 8.0 10.5 14.0 19.3 21.8 24.4 26.4 29.4 31.3

Samples labeled No. 1 and No. 2 have the same nominal composition. From Schluter, M et. al., The Fullerenes, Ed.: Krato, H.W., Fisher, J.E., and Cox, D.E., Pergamon Press, Oxford, 1993. With permission.

Section 12.indb 76

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PROPERTIES OF SEMICONDUCTORS L.I. Berger The term semiconductor is applied to a material in which electric current is carried by electrons or holes and whose electrical conductivity, when extremely pure, rises exponentially with temperature and may be increased from its low “intrinsic” value by many orders of magnitude by “doping” with electrically active impurities. Semiconductors are characterized by an energy gap in the allowed energies of electrons in the material which separates the normally filled energy levels of the valence band (where “missing” electrons behave like positively charged current carriers “holes”) and the conduction band (where electrons behave rather like a gas of free negatively charged carriers with an effective mass dependent on the material and the direction of the electrons’ motion). This energy gap depends on the nature of the material and varies with direction in anisotropic crystals. It is slightly dependent on temperature and pressure, and this depen-

dence is usually almost linear at normal temperatures and pressures. Data are presented in five tables. Table 1 lists the main crystallographic and semiconducting properties of a large number of semiconducting materials in three main categories: “Tetrahedral Semiconductors” in which every atom is tetrahedrally coordinated to four nearest neighbor atoms (or atomic sites) as for example in the diamond structure; “Octahedral Semiconductors” in which every atom is octahedrally coordinated to six nearest neighbor atoms—as for example the halite structure; and “Other Semiconductors.” Table 2 gives electrical, magnetic, and optical properties, while Tables 3 and 4 give more details on the semiconducting properties and band structures of the most common semiconductors. Table 5 lists semiconducting minerals with typical resistivity ranges.

TABLE 1. Physico-Chemical Properties of Semiconductors (Listed by Crystal Structure)

Substance

Average Lattice Molecular atomic parameters Density weight weight (Å, room temp.) (g/cm3)

Melting point (K)

Microhardness, N/mm2 (M-Mohs Scale)

Specific heat, J/kg·K (300 K)

Coefficient of Thermal Debye thermal linear conductivity temp. expansion [mW/cm·K (K) [10–6 K–1 (300K)] (300K)]

1.1. Tetrahedral (Adamantine) Semiconductors 1.1.1. Diamond Structure Elements (Strukturbericht symbol A4, Space Group Fd3m-O 7h ) C (Diamond)

12.01

3.56683

3.513

≈4713 (12.4 GPa) Transition to graphite > 980

10 (M)

471.5

28.09

5.43072

2.329

1687

11270 7644

Ge α-Sn

72.64

5.65754

5.323

1211.35

118.71

6.4912

5.769

505.1 (Tr. 286.4)

2340

1.18

9900(I) 23200(IIA) 13600(IIB)

702

645

2.6

1240

321.9

374

5.8

640

213

230

5.4 (220 K)

–

1.1.2. Sphalerite (Zinc Blende) Structure Compounds (Strukturbericht symbol B3 Space Group F 4 3m-Td2 ) I-VII Compounds CuF

82.54

41.27

4.255

CuCl

98.99

49.49

5.4057

3.53

695

2.3 (M)

490

240

12.1

8.4

CuBr

143.45

71.73

5.6905

4.98

770

2.5 (M)

381

207

15.4

12.5

6.60427

5.63

878

181

19.2

16.8

4.2

Cul

190.45

95.23

AgBr

187.77

93.89

AgI

234.77

117.39

6.502

1181

192

276

6.473 >1570 (Tr. 410)

2.5 (M)

270

5.67

2.5 (M)

232

134

–2.5

831 II-VI Compounds

BeS

41.08

20.54

4.865

2.36

BeSe

87.97

43.99

5.139

4.315

BeTe

136.61

68.31

5.626

5.090

BePo

(2318)

5.838

7.3

ZnO

81.39

40.69

4.63

5.675 2248

5.0 (M)

494

416

2.9

234

ZnS

97.46

48.72

5.4093

4.079 2100 (Tr. 1295)

1780

472

530

6.36

251

(109)

dec.

12-77

12-78

Substance

Properties of Semiconductors

Average Lattice Molecular atomic parameters Density weight weight (Å, room temp.) (g/cm3)

Melting point (K)

Microhardness, N/mm2 (M-Mohs Scale)

Specific heat, J/kg·K (300 K)

Coefficient of Thermal Debye thermal linear conductivity temp. expansion [mW/cm·K (K) [10–6 K–1 (300K)] (300K)]

ZnSe

144.34

72.17

5.6676

5.42

1790

1350

339

400

7.2

140

ZnTe

192.99

96.5

6.101

6.34

1568

900

264

223

8.19

108

ZnPo

(274)

(137)

6.309

CdS

144.48

72.24

5.832

4.826

1750

1250

330

219

4.7

200

CdSe

191.37

95.68

6.05

5.674

1512

1300

255

181

3.8

CdTe

240.01

120.00

6.477

5.86

1365

600

205

200

4.9

58.5

CdPo

(321)

(161)

6.665

HgS

232.66

116.33

5.8517

7.73

1820

3 (M)

210

HgSe

279.55

139.78

6.084

8.25

1070

2.5 (M)

178

151

5.46

HgTe

328.19

164.10

6.4623

8.17

943

300

164

242

4.6

793

≈1900

III-V Compounds BN

24.82

12.41

3.615

3.49

3239

10 (M)

BP(L.T.)

41.78

20.87

4.538

2.9

1398 (dec)

37000

200

BAs

85.73

42.87

4.777

≈2300

19000

≈625

AlP

57.95

28.98

5.451

2.42

≈2100

5.5 (M)

588

AlAs

101.90

50.95

5.6622

3.81

2013

5000

417

3.5

840

AlSb

148.74

74.37

6.1355

4.218

1330

4000

292

4.2

600

GaP

100.70

50.35

5.4905

4.13

1750

9450

446

5.3

752

GaAs

144.64

72.32

5.65315

5.316

1510

7500

344

5.4

560

GaSb

191.48

95.74

6.0954

5.619

980

4480

265

6.1

270

InP

145.79

72.90

5.86875

4.787

1330

4100

321

4.6

800

InAs

189.74

94.87

6.05838

5.66

1215

3300

268

249

4.7

290

InSb

236.58

118.29

6.47877

5.775

798

2200

144

202

4.7

160

≈980

320

920

Other sphalerite structure compounds MnS

87.00

MnSe

133.90

66.95

5.82

40.10

20.1

4.348

3.21

3070

Ga2Se3

376.32

75.26

5.429

4.92

1020

3160

Ga2Te3

522.24

104.45

5.899

5.75

1063

2370

In2Te3(H.T.)

608.44

121.7

6.173

5.8

940

1660

MgGeP2

158.84

β-SiC (3-C SiC)

43.5

39.71

5.011 2.9

4.9

8.9

5.652

ZnSnP2

246.00

61.5

5.65

ZnSnAs2(H.T.)

333.90

82.38

5.851

5.53

1050

1200

ZnSnSb2

427.56

106.89

6.281

5.67

870

76 2500

1.1.3. Wurtzite (Zincite) Structure Compounds (Strukturbericht symbol B4, Space Group P 63mc-C46v) I-VII Compounds CuCl

99.0

49.5

3.91

6.42

703

CuBr

143.45

71.73

4.06

6.66

770

Cul

190.45

95.23

4.31

7.09

Agl

234.77

117.40

4.580

7.494

BeO

25.01

12.51

2.698

4.380 7.39

II-VI Compounds MgTe

151.9

2800

76.0

4.54

3.85

≈2800

ZnO

81.37

40.69

3.24950 5.2069

5.66

2250

600

ZnS

97.43

48.72

3.8140 6.2576

4.1

2100

460

Properties of Semiconductors

Substance

12-79

Average Lattice Molecular atomic parameters Density weight weight (Å, room temp.) (g/cm3) 6.99

Melting point (K)

Microhardness, N/mm2 (M-Mohs Scale)

Specific heat, J/kg·K (300 K)

Coefficient of Thermal Debye thermal linear conductivity temp. expansion [mW/cm·K (K) [10–6 K–1 (300K)] (300K)]

ZnTe

192.99

46.50

4.27

CdS

144.48

72.23

4.1348 6.7490

4.82

1748

1568 401

CdSe

191.37

95.68

4.299

7.010

5.66

1512

316

CdTe

240.01

120.00

4.57

7.47

BP(H.T.)

41.79

20.90

3.562

5.900

AlN

40.99

20.50

3.111

4.978

3.26

≈2500

823

GaN

83.73

41.87

3.190

5.189

6.10

1500

656

InN

128.83

64.42

3.533

5.693

6.88

1200

556

III-V Compounds

Other wurtzite structure compounds MnS

87.00

43.5

3.985

6.45

MnSe

133.90

66.95

4.12

6.72

40.10

20.1

3.076

5.048

MnTe

182.54

91.27

4.078

6.701

Al2S3

150.14

30.03

3.579

5.829

2.55

1400

Al2Se3

290.84

58.17

3.890

6.30

3.91

1250

SiC

3.248

–

1.1.4. Chalcopyrite Structure Compounds (Strukturbericht symbol E11 , Space Group I 4 2d-D12 24 ) I-III-VI2 Compounds CuAlS2

154.65

38.66

5.323

10.44

3.47

2500

CuAlSe2

248.45

62.11

5.617

10.92

4.70

2260

CuAlTe2

345.73

86.43

5.976

11.80

5.50

2550

CuGaS2

197.39

49.53

5.360

10.49

4.35

2300

CuGaSe2

291.19

72.80

5.618

11.01

5.56

1970

4200

CuGaTe2

388.47

97.12

6.013

11.93

5.99

2400

3500

CuInS2

242.49

60.62

5.528

11.08

4.75

1400

2550

CuInSe2

336.29

84.07

5.785

11.56

5.77

1600

2050

CuInTe2

433.57

108.39

6.179

12.365

6.10

1660

400

CuTlS2

322.05

83.01

5.580

11.17

6.32

CuTlSe2(L.T.)

425.85

106.46

5.844

11.65

7.11

900

CuFeS2

183.51

45.88

5.29

10.32

4.088

1135

CuFeSe2

277.31

69.33

CuLaS2

266.58

66.65

5.65

10.86

AgAlS2

198.97

49.74

5.707

10.28

3.94

AgAlSe2

292.77

73.19

5.968

10.77

5.07

1220

AgAlTe2

390.05

97.51

6.309

11.85

6.18

1000

AgGaS2

241.71

60.43

5.755

10.28

4.72

AgGaSe2

335.51

83.88

5.985

10.90

5.84

1120

AgGaTe2

432.79

6.301

11.96

6.05

990

AgInS2(L.T.)

286.87

71.70

5.828

11.19

5.00

AgInSe2

380.61

95.15

6.102

11.69

5.81

1053 965

108.2

275

195

5.4

6.9

6.6

7.1

850

4400 1800

212

2250 1850

AgInTe2

477.89

119.47

6.42

12.59

6.12

AgFeS2

227.83

56.96

5.66

10.30

4.53

ZnSiP2

155.40

38.85

5.400

10.441

3.39

1640

1100

ZnGeP2

199.90

49.98

5.465

10.771

4.17

1295

8100

ZnSnP2

246.00

61.5

CdSiP2

202.43

50.61

30 9.49, 0.69

II-IV-V2 Compounds 180

6500 5.678

10.431

4.00

≈1470

10500

282

12-80

Substance

Properties of Semiconductors

Average Lattice Molecular atomic parameters Density weight weight (Å, room temp.) (g/cm3)

CdGeP2

246.94

61.74

5.741

10.775

CdSnP2

243.03

73.26

5.900

11.518

ZnSiAs2

242.20

60.55

5.61

10.88

ZnGeAs2

287.80

71.95

5.672

ZnSnAs2

333.90

83.48

CdSiAs2

290.34

72.58

5.884

CdGeAs2

334.83

83.71

5.9427 11.217 2

CdSnAs2

380.93

95.23

6.0944 11.918 2

Melting point (K)

4.48

Microhardness, N/mm2 (M-Mohs Scale)

Specific heat, J/kg·K (300 K)

Coefficient of Thermal Debye thermal linear conductivity temp. expansion [mW/cm·K (K) [10–6 K–1 (300K)] (300K)]

1049

5650

840

5000

4.70

1311

9200

11.153

5.32

1150

5.8515 11.704

5.53

1048 >1120

6850

5.60

938

4700

5.72

880

3450

10.882

110 195

140

6800

263

110

4550

271

150

1.1.5. Other Ternary Semiconductors with Tetrahedral Coordination I2-IV-VI3 Compounds Cu2SiS3(H.T.)

251.36

41.89

Cu2SiS3(L.T.)

3.684

6.004

3.81

5.290

10.156

3.63

1200

Cu2SiTe3

537.98

89.66

5.93

5.47

Cu2GeS3(H.T.)

295.88

49.31

5.317

4.45

5.327

5.215

4.46

Cu2GeSe3

436.56

72.76

5.589

5.485

5.57

Cu2GeTe3

582.51

97.09

5.958

5.935

5.92

Cu2SnS3

341.98

57.00

5.436

5.02

1110

2770

440

214

7.8

CuSnSe3

482.66

80.44

5.687

5.94

960

2510

310

148

8.9

Cu2SnTe3

628.61

104.77

6.048

6.51

680

1970

Ag2GeSe3

525.21

87.54

Ag2SnSe3

571.31

95.22

Ag2GeTe3

671.13

111.86

Ag2SnTe3

717.23

119.54

Cu3PS4

349.85

40.73

7.44

Cu3AsS4

393.79

49.22

6.43

6.14

4.37

931

Cu3AsSe4

581.37

72.67

5.570

10.957

5.61

733

Cu3SbS4

440.64

55.08

5.38

16.76

4.90

830

Cu3SbSe4

628.22

78.53

5.654

11.256

6.0

700

CuSi2P3

212.64

35.44

5.25

CuGe2P3

301.65

50.28

5.375

AgGe2P3

345.97

57.66

Cu2GeS3(L.T.)

1210

4550

510

254

7.2

1030

3840

340

168

8.4

2890

12 24 130 28 35 144

810 600 I3-V -VI4-Compounds 6.19 3.2

30.2

169

9.5

131

12.4

I-IV2-V3 Compounds 4.318

1113

8500

1015

6150

429

–

1.1.6. “Defect Chalcopyrite” Structure Compounds (Strukturbericht symbol E3, Space Group I 4 -S24 ) ZnAl2Se4

435.18

62.17

5.503

10.90

4.37

ZnAl2Te4(?)

629.74

84.96

5.904

12.05

4.95

ZnGa2S4(?)

333.06

47.58

5.274

10.44

3.80

ZnGa2Se4(?)

520.66

74.38

5.496

10.99

5.21

ZnGa2Te4(?)

715.22

102.17

5.937

11.87

5.67

ZnIn2Se4

610.86

87.27

5.711

11.42

5.44

1250

ZnIn2Te4

805.42

115.06

6.122

12.24

5.83

1075

CdAl2S4

294.61

42.09

5.564

10.32

3.06

CdAl2Se4

482.21

68.89

5.747

10.68

4.54

CdAl2Te4(?)

676.77

97.68

6.011

12.21

5.10

8.21

37.6

14.6

Properties of Semiconductors

Substance

12-81

Average Lattice Molecular atomic parameters Density weight weight (Å, room temp.) (g/cm3)

CdGa2S4

380.09

54.30

5.577

10.08

4.03

CdGa2Se4

567.69

81.10

5.743

10.73

5.32

CdGa2Te4

762.25

108.89

6.093

11.81

5.77

CdIn2Te4

852.45

121.78

6.205

12.41

5.9

HgAl2S4

382.79

54.68

5.488

10.26

4.11

Melting point (K)

Microhardness, N/mm2 (M-Mohs Scale)

Specific heat, J/kg·K (300 K)

Coefficient of Thermal Debye thermal linear conductivity temp. expansion [mW/cm·K (K) [10–6 K–1 (300K)] (300K)]

1060

HgAl2Se4

570.39

82.48

5.708

10.74

5.05

HgAl2Te4(?)

764.48

109.28

6.004

12.11

5.81

HgGa2S4

468.27

66.90

5.507

10.23

5.00

HgGa2Se4

655.87

93.70

5.715

10.78

6.18

HgIn2Se4

746.07

106.58

5.764

11.80

6.3

1100

HgIn2Te4(?)

940.63

134.38

6.186

12.37

6.3

980

3.21

3070

1.1.7. Other Adamantine Compounds α−SiC

40.10

20.10

Hg5Ga2Te8

2163.19

144.21

Hg5In2Te8

2253.39

150.23

Cdln2Se4

657.89

93.98

3.0817 15.12 6.235 6.328 a = c = 5.823

1.2. Octahedral Semiconductors 1.2.1. Halite Structure Semiconductors (Strukturbericht symbol B1, Space Group Fm3m-O5h) GeTe

200.21

100.10

5.98

SnSe

197.67

98.83

6.020

6.14

SnTe

246.31

123.15

6.313

6.45

1080 (max)

PbS

239.3

119.63

5.9362

7.61

1390

PbSe

286.2

143.08

6.1243

8.15

1340

PbTe

334.8

167.4

6.454

8.16

1180

7.98

880

1133

1.2.2. Selected Other Binary Halites BiSe

287.94

143.97

5.99

BiTe

336.58

168.29

6.47

EuSe

230.92

115.46

6.191

2300

GdSe

236.21

118.11

5.771

2400

NiO

74.69

37.35

4.1684

CdO

128.41

64.21

4.6953

SrS

119.69

59.84

6.0199

6.6

2.4

2260 1700

3.643

3000

1.3. Other Semiconductors 1.3.1. Antifluorite Structure Compounds (Fm3m–O5h ) Mg2Si

76.70

25.57

6.338

1.88

1375

11.5

Mg2Ge

121.22

40.4

6.380

3.08

1388

15.0

Mg2Sn

167.32

55.77

6.765

3.53

1051

9.9

Mg2Pb

225.81

85.27

6.836

5.1

823

10.0

1.3.2. Tetradymite Structure Compounds (R3m–D53d) Sb2Te3

626.3

125.26

4.25

30.3

6.44

Bi2Se3

654.84

130.97

4.14

28.7

7.51

895 979

167

Bi2Te3

800.76

160.15

4.38

30.45

7.73

858

155

24 16

12-82

Properties of Semiconductors

Substance

Average Lattice Molecular atomic parameters Density weight weight (Å, room temp.) (g/cm3)

Melting point (K)

Microhardness, N/mm2 (M-Mohs Scale)

Specific heat, J/kg·K (300 K)

Coefficient of Thermal Debye thermal linear conductivity temp. expansion [mW/cm·K (K) [10–6 K–1 (300K)] (300K)]

1.3.3. Skutterudite Structure Compounds (Im3–T5h) CoP3

151.85

37.96

7.7073

CoAs3

286.70

71.65

8.2060

>1270

CoSb3

424.18

106.05

9.0385

NiAs3

283.45

70.86

8.330

RhP3

195.83

48.96

7.9951

>1470

RhAs3

327.67

81.92

8.4427

>1270

RhSb3

468.16

117.04

9.2322

1170

IrP3

285.14

71.29

8.0151

7.36

>1470

IrAs3

416.98

104.25

8.4673

9.12

>1470

IrSb3

557.47

139.37

9.2533

9.35

1170

5.786

6.60

910

10.5

6.078

7.12

830

6.73

1230 1123

307

6.43 100

90 303

1.3.4. Selected Multinary Compounds AgSbSe2

387.54

96.88

AgSbTe2 (or Ag19Sb29Te52)

484.82

AgBiS2(H.T.)

380.97

95.24

5.648 5.82

121.2

AgBiSe2(H.T.)

474.77

118.69

AgBiTe2(H.T.)

572.05

143.01

6.155

Cu2CdSnS4

486.43

60.80

5.586

10.83

1.3.5. Some Elemental Semiconductors B

10.81

4.91

Se(gray)

78.96

4.36

12.6 4.95

2.34

2348

4.81

493

9.5 (M) 350

1277

1370

292.6

8.3

600

(||C) 17.89

(||C) 45.2

(⊥C) 74.09 Te

127.60

4.45

5.91

6.23

723

196.5

(⊥C) 13.1

16.8

(||C) 33.8 (⊥C) 19.7

TABLE 2. Basic Thermodynamic, Electrical, and Magnetic Properties of Semiconductors (Listed by Crystal Structure)

Substance

Miniumum Heat of Atomic room formation Volume Static magnetic temperature [kJ/mol compressibility dielectric susceptibility Index of energy gap (300K)] (10–10m2/N) constant (10–6 cgs) refraction (eV)

Mobility (room temp.) (cm2/V·s)

Breakdown voltage kV/mm

Electrons

Holes

Optical transition

5.4

1800

1400

500

1.12

1900

500

0.67

3800

1820

0.0; 0.8

2500

2400

Remarks

2.1. Adamantine Semiconductors 2.1.1. Diamond Structure Elements (Strukturbericht symbol A4, Space Group Fd 3m–O7h) C

714.4

324

291

α-Sn

267.5

5.7

–5.88

0.306

11.9

–3.9

0.768

–0.12

2.419 (589 nm) 3.49 (589 nm) 3.99 (589 nm) 2.75 (589 nm)

2.1.2. Sphalerite (Zinc Blende) Structure Compounds (Strukturbericht symbol B3 Space Group F 4 3m–T 2d) I-VII Compounds CuF CuCl 481 0.26 7.9 1.93 3.17

Nantokite

Properties of Semiconductors

Substance

12-83

CuBr Cul AgBr AgI BeS BeSe BeTe BePo ZnO ZnS ZnSe ZnTe ZnP CdS CdSe CdTe CdPo HgS HgSe HgTe

481 439 486 389

0.26 0.27 0.41

7.9 6.5 12.4 10

477

8.9

422 376

9.2 10.4

2.12 2.91 2.346 2.95 2.253 2.50 2.22 2.22 II-VI Compounds 4.17 3.61 1.45

–9.9

Mobility (room temp.) (cm2/V·s) Electrons

Holes

Optical transition

4000 30

d d i d

i i d

5(400˚C) d

2.356

3.54

180

2.89 3.56

2.58 2.26

540 340

28 100

Breakdown voltage kV/mm

Remarks

Marshite Bromirite Miersite

See 2.1.3. See also 2.1.3.

d d See 2.1.3. See 2.1.3.

339

7.2

2.50

1.44

1200

2.85 247 242

BN 815 BP(L.T.) BAs AlP AlAs 627 AlSb 585 0.571 GaP 635 0.110 GaAs 535 0.771 GaSb 493 0.457 InP 560 0.735 InAs 477 0.549 InSb 447 0.442 * i = indirect, d = direct, s = semimetal.

10.9 11 11.1 13.2 15.7 12.4 14.6 17.7

–13.8 –16.2 –14.2 –22.8 –27.7 –32.9

250

2.10 (α) –0.06 III-V Compounds 4.6 ≈2.1 ≈1.5 2.45 2.16 3.2 1.60 3.2 2.24 3.30 1.35 3.8 0.67 3.1 1.27 3.5 0.36 3.96 0.163

20000 25000

d ≈1.5 350

500 80 1200 200–400 300 8800 4000 4600 33000 78000

s s

Borazone Ignites 470K

420 550 150 400 1400 150 460 750

Metacinnabarite Tiemannite Coloradoite

i i i i d d d d d

Other sphalerite structure compounds MnS

See also 2.1.3. See also 2.1.3.

MnSe β-SiC Ga2Te3 271 In2Te3(H.T.) 198 MgGeP2 ZnSnP2 ZnSnAs2(H. T.) ZnSnSb2

2.697 –13.5 –13.6

2.3 1.35 1.04

4000 50 50

2.1 ≈0.7 0.4

2.1.3. Wurtzite (Zincite) Structure Compounds (Strukturbericht symbol B4, Space Group P 63 mc-C 46v) I-VII Compounds CuCl CuBr CuI AgI 2.63 II-VI Compounds BeO MgTe ZnO –350 3.2 180 ZnS –206 3.67 ZnTe –163

El–Td12 Same Same Same

Iodargirite

12-84

Substance

Properties of Semiconductors

CdS CdSe CdTe

8.45; 9.12

BP(H.T.) AlN GaN InN MnS MnSe SiC MnTe Al2S3 Al2Se3

Mobility (room temp.) (cm2/V·s) Electrons

Holes

350 900 650

40 50

2.32

2.42 1.74 1.50 III-V Compounds

Optical transition

d d

Breakdown voltage kV/mm

Remarks

Greenockide Cadmoselite

6.02 3.34 2.0 Other wurtzite structure compounds

2.654 ≈1.0 4.1 3.1

426 367

2.1.4 Chalcopyrite Structure Compounds (Strukturbericht symbol E11, Space Group I 4 2d-D 12 2d ) I-III-VI2 Compounds CuAlS2 0.106 2.5 CuAlSe2 2.67 CuAlTe2 0.88 CuCaS2 0.106 2.38 CuGaSe2 0.141 0.96, 1.63 CuGaTe2 0.227 0.82, 1.0 CuInS2 0.141 1.2 CuInSe2 0.187 0.86, 0.92 CuInTe2 0.278 0.95 CuTlS2 CuTlSe2 1.07 (L.T.) CuFeS2 0.53 CuFeSe2 0.16 CuLaS2 AgAlS2 AgAlSe2 0.7 AgAlTe2 0.56 AgGaS2 0.150 1.66 AgGaSe2 0.182 1.1 0.280 1.9 AgGaTe2 AglnS2 0.185 1.18 (L.T.) AgInSe2 0.238 0.96, 0.52 AgInTe2 0.338 AgFeS2 II-IV-V2 Compounds ZnSiP2 312 2.3 1000 ZnGeP2 293 2.2 ZnSnP2 275 1.45 CdSiP2 0.103 2.2 1000 CdGeP2 289 1.8 CdSnP2 270 1.5 ZnSiAs2 290 1.7 ZnGeAs2 271 –14.4 0.85 ZnSnAs2 252 –18.4 0.65 CdSiAs2 CdGeAs2

266

0.143

CdSnAs2

247

13.7

Chalcopyrite

50 300

Disorders at 910 K Disorders at 903 K

–23.4

1.6 0.53

–21.5

0.26

22000

250

Properties of Semiconductors

Substance

12-85

2.1.5. Other Ternary Semiconductors with Tetrahedral Coordination II2-IV-VI3 Compounds Cu2SiS3 (H.T.) Cu2SiS3 (L.T.) Cu2SiTe3 Cu2GeS3 –18.7 (H.T.) Cu2GeS3 (L.T.) Cu2GeSe3 211.5 –21.3 0.94 Cu2GeTe3 190.2 –23.4 Cu2SnS3 –18.2 0.91 CuSnSe3 –21.0 0.66 Cu2SnTe3 –28.4 –29.6 0.91 (77K) Ag2GeSe3 Ag2SnSe3 –29.5 0.81 Ag2GeTe3 –31.4 0.25 Ag2SnTe3 –31.0 0.08 II3-V-VI4 Compounds Cu3PS4 Cu3AsS4 269.6 –15.8 1.24 Cu3AsSe4 161.3 –13.1 0.88 Cu3SbS4 –8.3 0.74 Cu3SbSe4 127.1 –20.5 0.31 II-IV2-V3 Compounds CuSi2P3 CuGe2P3 0.12 0.90 AgGe2P3

Mobility (room temp.) (cm2/V·s) Electrons

Holes

Optical transition

Breakdown voltage kV/mm

Remarks

Wurtzite Tetragonal Cubic Cubic 360

Tetragonal

238

Same Same Cubic Cubic Cubic

405 870

Enargite Famatinite Famatinite

El El

2.1.6. “Defect Chalcopyrite” Structure Compounds (Strukturbericht symbol E3, Space Group I 4-S24) ZnAl2Se4 ZnAl2Te4(?) ZnGa2S4 ≈3.4 (?) ZnGa2Se4(?) ≈2.2 ZnGa2Te4(?) 1.35 ZnIn2Se4 206 1.82 35 ZnIn2Te4 198 1.2 CdAl2S4 CdAl2Se4 CdAl2Te4(?) CdGa2S4 256 3.44 60 CdGa2Se4 216 2.43 33 CdGa2Te4 Cdln2Te4 195 (1.26 or 0.9) 4000 HgAl2S4 HgAl2Se4 HgAl2Te4(?) HgGa2S4 249 2.84 HgGa2Se4 204 1.95 400 HgIn2Se4 196 0.6 290 HgIn2Te4(?) 188 0.86 200 2.1.7. Other Adamantine Compounds α−SiC Hg5Ga2Te8

10.2

–6.4

2.67

2.86

400

Hg5ln2Te8

0.7

2000

Cdln2Se4

1.55

6H structure B3 with superlattice B3 with superlattice

12-86

Substance

Properties of Semiconductors Miniumum Heat of Atomic room formation Volume Static magnetic temperature [kJ/mol compressibility dielectric susceptibility Index of energy gap (300K)] (10–10m2/N) constant (10–6 cgs) refraction (eV)

Mobility (room temp.) (cm2/V·s) Electrons

Holes

Optical transition

Breakdown voltage kV/mm

Remarks

2.2. Octahedral Semiconductors 2.2.1. Halite Structure Semiconductors (Strukturbericht symbol B1, Space Group Fm3m-O 5h) GeTe SnSe SnTe PbS 435 0.5 600 PbSe 393 161 0.37 1000 PbTe 393 280 0.26 1600 360 0.25 2.2.2. Selected Other Binary Halites BiSe BiTe EuSe GdSe NiO CdO 531 SrS

600 900 600

Altaite

0.4 1.8 2.0 or 3.7 2.5 4.1

4 100

2.3.1. Antifluorite Structure Compounds (Fm3m-O 5h ) Mg2Si 79.08 Mg2Ge Mg2Sn 76.57 Mg2Pb 52.72

0.77 0.74 0.36 0.1

405 520 320

2.3.2. Tetradymite Structure Compounds (R3m-D53d ) Sb2Te3 Bi2Se3 Bi2Te3

0.3 0.35 0.21

600 1140

0.43 0.69 0.63

2.3. Other Semiconductors 70 110 260

360 680

R3m (166)

5 h

2.3.3. Skutterudite Structure Compounds (Im3-T ) CoP3 CoAs3 CoSb3 RhP3 RhAs3 RhSb3 IrSb3

0.85 0.80 1.18

2.3.4. Selected Multinary Compounds AgSbSe2 AgSbTe2 (orAg19Sb29 Te52) AgBiS2 (H.T.) AgBiSe2 (H.T.) AgBiTe2 (H.T.) Cu2CdSnS4 2.3.5. Some Elemental Semiconductors B 397.1 Se(gray) Te

~4000 ~3000 700 ~3000 ~7000 1500

0.58 0.7, 0.27

–6.7 6.6 –22.1 (0.1 GHz) –39.5

1.16

3.4 2.5

1.55 1.5

3.3

0.33

1700

5 1200

P3121(152) Same

Properties of Semiconductors

12-87 TABLE 3. Semiconducting Properties of Selected Materials

Minimum energy gap (eV) Substance

R.T.

dEg/dT × 104 eV/˚C

dEg/dP × 106 eV·cm2/ kg

Si Ge α−Sn Te

1.107 0.67 0.08 0.33

1.153 0.744 0.094

–2.3 –3.7 –0.5

–2.0 +7.3

AlAs AlSb GaP GaAs GaSb InP InAs InSb

2.2 1.6 2.24 1.35 0.67 1.27 0.36 0.165

2.3 1.7 2.40 1.53 0.78 1.41 0.43 0.23

–3.5 –5.4 –5.0 –3.5 –4.6 –2.8 –2.8

–1.6 –1.7 +9.4 +12 +4.6 +8 +15

ZnO ZnS ZnSe ZnTe CdO CdS CdSe GdTe HgSe HgTe

3.2 3.54 2.58 2.26 2.5 ± .1 2.4 1.74 1.44 0.30 0.15

2.80

–9.5 –5.3 –7.2

+0.6 +5.7 +6 +6

1.85 1.56

–6 –5 –4.6 –4.1

PbS PbSe PbTe

0.37 0.26 0.25

0.28 0.16 0.19

+4 +4 +4

ZnSb CdSb Bi2S3 Bi2Se3 Bi2Te3 Mg2Si Mg2Ge Mg2Sn Mg3Sb2 Zn3As2 Cd3As2 GaSe GaTe InSe TlSe CdSnAs2 Ga2Te2 α-In2Te2 β-In2Te2 Hg5In2Te8 SnO2

0.50 0.45 1.3 0.27 0.13

0.56 0.57

–5.4

0.21 0.93 0.55 2.05 1.66 1.8 0.57 0.23 1.1 1.1 1.0 0.5

+3.3 +8

–1

0.77 0.74 0.33 0.32

1.80

–0.95 –6.4 –9 –3.5

–3.8 –3.6 –3.9

1.55 1.2

–7

Density of states Electron mobility and temperature electron dependence effective mass μn (cm2/V·s) mda (mo) –x Elements 1.1 1900 2.6 0.55 3800 1.66 0.02 2500 1.65 0.08 1100 III-V Compounds 1200 0.09 200 1.5 0.35 300 1.5 0.068 9000 1.0 0.050 5000 2.0 0.067 5000 2.0 0.022 33,000 1.2 0.014 78,000 1.6 II-VI Compounds 0.38 180 1.5 180 540 340 0.1 120 0.165 400 0.13 650 1.0 0.14 1200 0.030 20,000 2.0 0.017 25,000 Halite Structure Compounds 0.16 800 0.3 1500 0.21 1600 Others 0.15 10 0.15 300 200 600 0.58 1200 1.68 0.46 400 2.5 280 2 0.37 320 20 10 1.1 0.046 100,000 0.88

Density of states hole effective Mass mdp (mn) 0.56 0.3 0.3 0.19

0.4 0.5 0.5 0.23 0.41 0.4

Hole mobility and temperature dependence μp (cm2/V·s) 500 1820 2400 560 420 500 150 500 1400 200 460 750

–x 2.3 2.33 2.0

1.8 1.5 2.1 0.9 2.4 2.3 2.1

5(400˚C) 28 100 0.8 0.6 0.35

0.5

350

0.1 0.34 0.14

1000 1500 750

1.07

2000 1100 675 510 70 110 260 82 10

2.2 2.2 2.2 1.5 1.5

1.95

0.3 0.05

14 900 30 25,000

0.6

1.5

50 5 11,000 78

1.1

1.7

–4.8 0.7

12-88

Properties of Semiconductors TABLE 4. Band Properties of Semiconductors

4.1. Data on Valence Bands of Semiconductors (Room Temperature) Band curvature effective mass (Expressed as fraction of free electron mass) Substance

Heavy holes

Light holes

“Split-off” band holes

Energy separation of “split-off” band (eV)

4.1.1. Semiconductors with Valence Band Maximum at the Center of the Brillouin Zone (“F”) Si 0.52 0.16 0.25 0.044 Ge 0.34 0.043 0.08 0.3 Sn 0.3 AlAs AlSb 0.4 0.7 GaP 0.13 GaAs 0.8 0.12 0.20 0.34 GaSb 0.23 0.06 0.7 InP 0.21 InAs 0.41 0.025 0.083 0.43 InSb 0.4 0.015 0.85 CdTe 0.35 HgTe 0.5 4.1.2. Semiconductors with Multiple Band Maxima Band curvature effective masses Number of equivalent Substance valleys and direction PbSe 4 “L” [111] PbTe 4 “L” [111] Bi2Te3 6

Longitudinal mL 0.095 0.27 0.207

Transverse mT 0.047 0.02 ~0.045

Measured (light) hole mobility (cm2/V·s) 500 1820 2400 550 100 400 1400 150 460 750 50 350

Anistrophy K = mL/mT 2.0 10 4.5

Measured (light) hole mobility (cm2/V·s) 1500 750 515

4.2. Data on Conduction Bands of Semiconductors (Room Temperature Data) 4.2.1. Single Valley Semiconductors Substance Energy gap (eV) Effective mass (mo) Mobility (cm2/V·s) Comments GaAs

1.35

0.067

8500

InP InAs InSb CdTe

1.27 0.36 0.165 1.44

0.067 0.022 0.014 0.11

5000 33,000 78,000 1000

3(or 6?) equivalent [100] valleys 0.36 eV above this maximum with a mobility of ~50. 3(or 6?) equivalent [100] valleys 0.4 eV above this minimum. Equivalent valleys ~1.0 eV above this minimum. 4(or 8?) equivalent [111] valleys 0.51 eV above this minimum.

4.2.2. Multivalley Semiconductors

Substance Si Ge GaSb PbSe PbTe Bi2Te3

Energy gap 1.107 0.67 0.67 0.26 0.25 0.13

Number of equivalent valleys and direction 6 in [100] “Δ” 4 in [111] at “L” as Ge (?) 4 in [111] at “L” 4 in [111] at “L” 6

Band curvature effective mass Longitudinal mL 0.00 1.588 ~1.0 0.085 0.21

Transverse mT 0.192 0.0815 ~0.2 0.05 0.029

Anisotropy K = mL/mT 4.7 19.5 ~5 1.7 5.5 ~0.05

TABLE 5. Resistivity of Semiconducting Minerals Mineral Diamond (C) Sulfides Argentite, Ag2S Bismuthinite, Bi2S3 Bornite, Fe2S3 · nCu2S Chalcocite, Cu2S Chalcopyrite, Fe2S3 · Cu2S Covellite, CuS Galena, PbS Haverite, MnS2 Marcasite, FeS2 Metacinnabarite, HgS Millerite, NiS Molybdenite, MoS2

ρ (ohm · m) 2.7 1.5 to 2.0 × 10–3 3 to 570 1.6 to 6000 × 10–6 80 to 100 × 10–6 150 to 9000 × 10–6 0.30 to 83 × 10–6 6.8 × 10–6 to 9.0 × 10–2 10 to 20 1 to 150 × 10–3 2 × 10–6 to 1 × 10–3 2 to 4 × 10–7 0.12 to 7.5

Mineral Pentlandite, (Fe, Ni)4S4 Pyrrhotite, Fe7S4 Pyrite, FeS2 Sphalerite, ZnS Antimony-sulfur compounds Berthierite, FeSb2S4 Boulangerite, Pb5Sb3S11 Cylindrite, Pb3Sn4Sb2S14 Franckeite, Pb5Sn3Sb2S14 Hauchecornite, Ni4(Bi, Sb)2S14 Jamesonite, Pb4FeSb6S14 Tetrahedrite, Cu3SbS3 Arsenic-sulfur compounds Arsenopyrite, FeAsS

ρ (ohm · m) 1 to 11 × 10–6 2 to 160 × 10–6 1.2 to 600 × 10–3 2.7 × 10–3 to 1.2 × 104 0.0083 to 2.0 2 × 103 to 4 × 104 2.5 to 60 1.2 to 4 1 to 83 × 10–6 0.020 to 0.15 0.30 to 30,000 20 to 300 × 10–6

Properties of Semiconductors Cobaltite, CoAsS Enargite, Cu3AsS4 Gersdorfite, NiAsS Glaucodote, (Co, Fe)AsS Antimonide Dyscrasite, Ag3Sb Arsenides Allemonite, SbAs3 Lollingite, FeAs2 Nicollite, NiAs Skutterudite, CoAs3 Smaltite, CoAs2 Tellurides Altaite, PbTe Calavarite, AuTe2 Coloradoite, HgTe

12-89 6.5 to 130 × 10–3 0.2 to 40 × 10–3 1 to 160 × 10–6 5 to 100 × 10–6 0.12 to 1.2 × 10–6 70 to 60,000 2 to 270 × 10–6 0.1 to 2 × 10–6 1 to 400 × 10–6 1 to 12 × 10–6 20 to 200 × 10−6 6 to 12 × 10−6 4 to 100 × 10–6

References 1. Beer, A. C., Galvanomagnetic Effects in Semiconductors, Academic Press, New York, 1963. 2. Goryunova, N. A., The Chemistry of Diamond-Like Semiconductors, The MIT Press, Cambridge, MA, 1965. 3. Abrikosov, N. Kh., Bankina, V. F., Poretskaya, L. E., Shelimova, L. E., and Skudnova, E.V., Semiconducting II-VI, IV-VI, and V-VI Compounds, Plenum Press, New York, 1969. 4. Berger, L. I. and Prochukhan, V. D., Ternary Diamond-Like Semiconductors, Cons. Bureau/Plenum Press, New York, 1969. 5. Shay, J. L. and Wernick, J. H., Ternary Chalcopyrite Semiconductors: Growth, Electronic Properties, and Applications, Pergammon Press, 1975. 6. Bergman, R., Thermal Conductivity in Solids, Clarendon, Oxford, 1976. 7. Handbook of Semiconductors, Vol. 1, Moss, T.S. and Paul, W., Eds., Band Theory and Transport Properties; Vol. 2, Moss, T.S. and Balkanski, M., Eds., Optical Properties of Solids; Vol. 3, Moss, T.S. and Keller, S.P., Eds., Materials Properties and Preparation, North Holland Publ. Co., Amsterdam, 1980. 8. Böer, K. W., Survey of Semiconductor Physics, Van Nostrand Reinhold, 1990. 9. Rowe, D. M., Ed., CRC Handbook of Thermoelectrics, CRC Press, Boca Raton, FL, 1995. 10. Berger, L. I., Semiconductor Materials, CRC Press, Boca Raton, FL, 1997. 11. Glazov, V. M., Chizhevskaya, S.N., and Glagoleva, N.N., Liquid Semiconductors, Plenum Press, New York, 1969. 12. Phillips, J. C., Bonds and Bands in Semiconductors, Academic Press, New York, 1973. 13. Harrison, W. A., Electronic Structure and the Properties of Solids, Freeman Publ. House, San Francisco, 1980. 14. Balkanski, M., Ed., Optical Properties of Solids, North-Holland, Amsterdam, 1980.

Hessite, Ag2Te Nagyagite, Pb6Au(S,Te)14 Sylvanite, AgAuTe4 Oxides Braunite, Mn2O3 Cassiterite, SnO2 Cuprite, Cu2O Hollandite, (Ba, Na, K) Mn8O16 Ilmenite, FeTiO3 Magnetite, Fe3O4 Manganite, MnO · OH Melaconite, CuO Psilomelane, BaMn9O18 · 2H2O Pyrolusite, MnO2 Rutile, TiO2 Uraninite, UO2

4 to 100 × 10–6 20 to 80 × 10–6 4 to 20 × 10–6 0.16 to 1.0 4.5 × 10–4 to 10,000 10 to 50 2 to 100 × 10–3 0.001 to 4 52 × 10–6 0.018 to 0.5 6000 0.04 to 6000 0.007 to 30 29 to 910 1.5 to 200

15. Landolt-Börnstein. Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, Hellwege, K.-H. and Madelung, O., Eds., Volumes 17 and 22, Springer Verlag, Berlin, 1984 (and further). 16. Shklovskii, B. L. and Efros, A.L., Electronic Processes in Doped Semiconductors, Springer Verlag, Berlin, 1984. 17. Cohen, M. L. and Chelikowsky, J. R., Electronic Structure and Optical Properties of Semiconductors, Springer Verlag, New York, 1988. 18. Glass, J.T., Messier, R.F., and Fujimori, N., Eds., Diamond, Silicon Carbide, and Related Wide Bandgap Semiconductors, MRS Symposia Proc. 1652, Mater. Res. Soc., Pittsburgh, 1990. 19. Palik, E., Ed., Handbook of Optical Constants of Solids II, Academic Press, New York, 1991. 20. Reed, M., Ed., Semiconductors and Semimetals, Volume 35, Academic Press, Boston, 1992. 21. Haug, H. and Koch, S. W., Quantum Theory of the Optical and Electronic Properties of Semiconductors, 2nd Edition, World Scientific, Singapore, 1993. 22. Lockwood, D. J., Ed., Proc. 22nd Intl. Conf. on the Physics of Semiconductors, Vancouver, 1994, World Scientific, Singapore, 1994. 23. Morelli, D. T., Caillat, T., Fleurial, J.-P., Borschchevsky, A., Vandersande, J., Chen, B., and Uher, C., Phys. Rev., B51, 9622, 1995. 24. Caillat, T., Borshchevsky, A., and Fleurial, J.-P., J. Appl. Phys., 80, 4442, 1996. 25. Fleurial, J.-P.,Caillat, T., and Borshchevsky, A., Proc. XVI Intl. Conf. Thermoelectrics, Dresden, Germany, August 26–29, 1997 (in print). 26. Borshchevsky, A. et al., U.S. Patents 5,610,366 (March 1977) and 5,831,286 (March 1998) 27. Jarrendahl, K. and Davis, R. F., Semiconductors and Semimetals, Vol. 52, Y.S. Park, Ed., 1998, pp. 1–20. 28. Bettini, M., Solid State Comm.,13, 599, 1973. 29. Chen, A. and Sher, A., Semiconductor Alloys, Physics and Material Engineering, Plenum Press, New York, 1995. 30. Holloway, P. H. and McGuire, G. E., Eds., Handbook of Compound Semiconductors, Noyes Publ., Park Ridge, NJ, 1995.

DIFFUSION DATA FOR SEMICONDUCTORS B. L. Sharma The diffusion coefficient D in many semiconductors may be expressed by an Arrhenius-type relation

Abbreviations used in the table are

D = Do exp(–Q/kT) where Do is a frequency factor, Q is the activation energy for diffusion, k is the Boltzmann constant, and T is the absolute temperature. This table lists Do and Q for various diffusants in common semiconductors.

AES – Auger Electron Spectroscopy DLTS – Deep Level Transient Spectroscopy SEM – Scanning Electron Microscopy SIMS – Secondary Ion Mass Spectrometry D(c) – Concentration Dependent Diffusion Coefficient Dmax – Maximum Diffusion Coefficient (f ) – Fast Diffusion Component (i) – Interstitial Diffusion Component (s) – Slow Diffusion Component () – Parallel to c Direction (⊥) – Perpendicular to c Direction

Semiconductor Si

Frequency factor, Do (cm2/s)

Activation energy, Q(eV)

Temperature range (°C)

Method of measurement

6 × 10–1

1.03

120–1207

Electrical and SIMS

Li Na

2.5 × 10–3 1.65 × 10–3

0.65 0.72

25–1350 530–800

2 3

1.1 × 10–3

0.76

740–800

4 × 10–2 4.7 × 10–3 2 × 10–3 2.4 × 10–4 2.75 × 10–3 (D ~ 10–7) (D ~ 6 × 10–14) 1 × 10–1 2.46 2.4 × 101 1.38 1.8 3.74 × 10–1 6 × 101 7.85 × 10–1 1.94 × 101 1.37 1.65 × 101 8 × 10–2 (D ~ 3.9 × 10–13) 2.5 × 10–7 7.5 × 10–9 4.2 × 10–12 2 × 10–3 8 × 10–3 2.8 × 10–5 1.45 × 10–2 3.3 × 10–1 1.54 × 102 1.6 × 103 3.5 × 10–1 2.5 × 103 7.55 × 103 3.2 × 101 2.7 × 10–3

1.0 0.43 (i) 1.6 0.39 (i) 2.05 (s) – – 1.4 3.59 3.87 3.41 3.2 3.39 3.89 3.63 3.86 3.7 3.9 3.2 – 1.74 1.2 (s) 0.13 (f ) 2.9 3.0 0.95 1.79 2.92 4.65 4.77 3.92 4.97 5.08 4.25 2.8

800–1100 300–700 1100–1350 700–1300

Electrical Electrical and flame photometry Electrical and flame photometry Radioactive Radioactive Radioactive Radioactive

1050 1100 980–1270 1100–1250 840–1250 1119–1390 1025–1175 1143–1393 900–1050 1180–1389 1150–1242 1244–1338 1105–1360 1100–1250 1050 1100–1280 730–1270

Electrical Electrical and SIMS Electrical Electrical Electrical Electrical Electrical Electrical Radioactive Electrical Radioactive Electrical Electrical Radioactive SIMS Electrical Radioactive

8 1 9 10 11 12 13 12 14 12 15 12 16 1 1 1 1

1100–1250 1100–1280 947–1097 950–1200 1070–1400 855–1175 1200–1400 855–1000 1030–1302 1100–1300 1050–1294 800–1200

Radioactive Radioactive Neutron activation DLTS Radioactive SIMS Radioactive Radioactive Radioactive SIMS Neutron activation Out Diffusion; SIMS

1 1 1 17 18 19 20 21 21 22 23 1

Diffusant

Ag Au Be Ca Zn B Al Ga In Tl Sc Ce Pr Pm Er Tm Yb Ti C Si (self ) Ge

Sn N

Ref.

3 4 5 6 7

12-92

Section 12.indb 92

4/28/05 1:57:17 PM

Diffusion Data for Semiconductors Semiconductor

Diffusant P

Sb Bi Cr Mo W O S Se Te Mn Fe Co Ni Ru

Rh Pd Pt Os Ir Li Na Cu

Ag Au Be Mg Zn Cd B Al Ga In Tl Si Ge (self ) Sn P As Sb

Section 12.indb 93

Frequency factor, Do (cm2/s)

12-93 Activation energy, Q(eV)

Temperature range (°C)

2.02 × 101 1.1 7.4 × 10–2 6.0 × 101 6.55 × 10–2 2.29 × 101 1.29 × 101 2.14 × 10–1 1.03 × 103 1.08 1 × 10–2 (D ~ 2 × 10–10) (D ~ 10–12) 7 × 10–2 1.4 × 10–1 5.95 × 10–3 9.5 × 10–1 5 × 10–1 6.9 × 10–4 1.3 × 10–3 2 × 10–3 2 × 10–3 (D ~ 5 × 10–7 – 5 × 10–6) (D ~ 10–6–10–4) 2.95 × 10–4 1.5 × 102 (D ~ 2 × 10–6) 4.2 × 10–2 1.3 × 10–3 9.1 × 10–3 3.95 × 10–1 1.9 × 10–4 4 × 10–2 4 × 10–3 4.4 × 10–2 4 × 10–2 2.25 × 102 5 × 10–1 (D ~ 8 × 10–9) 5

3.87 3.4 3.3 4.2 3.44 4.1 3.98 3.65 4.64 3.85 1 – – 2.44 2.53 1.83 2.6 3.34 0.63 0.68 0.69 0.47 –

1100–1250 900–1200 1130–1405 950–1350 1167–1394 900–1250 1190–1398 1190–1405 1220–1380 1190–1394 1100–1250 1000 1100 700–1250 700–1160 975–1200 1050–1250 900–1250 900–1200 30–1250 700–1300 800–1300 1000–1280

Electrical Radioactive Electrical Radioactive Electrical Electrical Radioactive Electrical Electrical Electrical Radioactive DLTS DLTS SIMS SIMS Radioactive Electrical SIMS Radioactive Radioactive Radioactive Radioactive Electrical

10 24 25 26 27 28 29 27 16 27 30 1 1 31 32 33 34 1 35 36 37 38 1

– 0.22 (i) 2.22 – 1.3 0.46 0.57 2.03 0.18 (i) 0.99 (s) 0.33 (i) 1.0 (i) 2.23 (s) 2.5 2.5 – 2.7

1000–1200 702–1320 800–1000 1280 950–1250 350–800 800–500 700–850 750–900 600–700 350–750 700–900 800–900 600–900 720–900 900 600–900

Electrical Nuclear Activation Electrical Electrical Electrical Electrical Electrical Radioactive Radioactive

39 1 1 40 41 42 43 44 45 5 46, 47 48 49 50 1

1.75 × 109 1.8 × 109 1.0 × 103 ~1.6 × 102 1.4 × 102 3.4 × 101 1.8 × 104 3.3 × 101 1.7 × 103 2.4 × 10–1 2.48 × 101 7.8 1.7 × 10–2 3.3 2.1 3.2 1.0 × 101

4.4 4.55 3.45 ~3.24 3.35 3.1 3.67 3.02 3.4 2.9 3.14 2.95 1.9 2.5 2.39 2.41 2.5

760–915 600–900 554–905 750–850 554–916 600–900 554–919 700–855 800–930 650–900 549–891 766–928 – 600–900 700–900 700–855 600–900

Radioactive Radioactive Radioactive Radioactive Electrical Electrical Radioactive and electrical Radioactive Electrical SIMS Electrical SIMS Electrical SIMS Radioactive Radioactive (γ) resonance Radioactive Radioactive Radioactive Electrical Electrical Radioactive Radioactive and electrical

Method of measurement

Ref.

51 52 51 53 54 55 51 56 57 58 59 60 61 45 51 62 57 51

4/28/05 1:57:18 PM

Diffusion Data for Semiconductors

12-94 Semiconductor

GaAs

Diffusant

Temperature range (°C)

3.3 4 × 10–1 (D ~ 10–9) (D ~ 10–10) 5.6 1.3 × 10–1 1.6 × 10–1 8 × 10–1 5.3 × 10–1

2.57 2.08 – – 2.43 1.08 1.12 0.9 1.0

650–850 – 920 920 750–900 750–900 750–850 670–900 250–500

3 × 10–2 6 × 10–2 1.5 × 10–3 4 × 10–4 1 × 10–3 7.3 × 10–6 4 × 10–5 1.5 × 101 2.5 × 10–1 1.3 × 10–3 5 × 10–2 (D ~ 5 × 10–14) (D ~ 4 × 10–18–10–14) 4 × 10–5 1 × 107 (D ~ 7 × 10–11) (D ~ 1.04 × 10–16) 1.1 × 10–1 1.6 × 10–5 6 × 10–4 1 × 10–5 (D ~ 10–12–10–10)

0.53 0.98 0.6 0.8 1.0 1.2 1.22 2.49 3.0 2.2 2.43 – 4.3 2.6 5.6 – – 2.5 2.06 2.5 2 2.9

100–500 450–750 800–1000 500–1150 740–1025 800–990 800–1200 600–980 750–1000 800–1100 868–1149 1100 850–1100 1025–1100 1125–1230 1000 825 850–1050 650–850 1060–1200 800–1000 800–1150

7 × 10–1 2.04 × 10–6 7.9 × 10–3 2 × 10–3 1.85 × 10–2 1.1 × 101 3 × 103 1.5 × 10–1 6.5 × 10–1 4.2 × 10–2 2.2 × 10–3 5 × 102 1.2 × 10–1 2.3 × 10–16 2.3 × 10–4

3.2 0.83 (f ) 1.7 (s) 2.2 1.1 2.6 2.95 4.16 3.5 2.49 1.8 2.32 2.5 2.64 1.0 1.9 (s)

– 750–1000 700–900 800–1100 700–900 1000–1300 750–900 1025–1200 1000–1150 850–1100 850–1150 750–1050 800–1000 750–1050 800–1000 527–657

1.2 × 10–1 4.7 × 10–3 (D ~ 2 × 10–13 – 1 × 10–11) 1.5 × 10–6 3.2 × 103 1.2 × 10–7 2.4 × 10–5 1.3 × 10–5 3.4 × 104 (D ~ 2.4 × 10–13 – 1.37 × 10–11)

0.7 (f ) 0.9 2 0.72 3.15 0.53 0.8 1.1 3.45 –

277–657 470–650 510–600 640–800 658–700 320–650 320–650 500–650 658–700 400–500

Cd Hg Al Ga (self ) In C Si Ge Sn P As (self ) Cr

O S Se Te Mn Fe Co Tm Li

Cu Zn Cd Ga (self ) In Sn Sb (self ) Se

Section 12.indb 94

Activation energy, Q(eV)

Bi O S Se Te Fe Co Ni Li

Ag Au Be Mg Zn

GaSb

Frequency factor, Do (cm2/s)

Method of measurement

Ref.

– Optical – – Radioactive Radioactive Radioactive Electrical Electrical and chemical Radioactive Ultrasonic Radioactive Radioactive Radioactive Electrical Electrical Radioactive Radioactive Radioactive Radioactive Radioactive AES Radioactive Radioactive Radioactive SIMS SIMS SIMS Radioactive Radioactive Reflectance measurements Radioactive SIMS

63 64 65 65 66 67 47 68

Chemical analysis Mass spectroscopy Radioactive Electrical Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Electrical and flame photometry

69 69 69 69 69 69 69 69 69 69 69 69

Radioactive Radioactive Electrical Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive

69 69 69 69 69 69 69 69 69

69 69 69 69 69 69 69 69 69 69 69 69 69 70 69 69 69 69 69 69 69 69 69 69 69

4/28/05 1:57:21 PM

Diffusion Data for Semiconductors Semiconductor

Activation energy, Q(eV)

Temperature range (°C)

3.8 × 10–4 5 × 10–2 5 × 102 – 8 20

1.20 1.9 (I) 2.3 (II) – 2.5 (I) 2.4 (II)

320–650 500–650 500–650 1000–1300 1050–1250 1100–1250

(Dmax ~ 2.4 × 10–9– 8.5 × 10–8)

–

900–1000

Mg Zn Ge Cr S Mn

5 × 10–5 1.0 – 6.2 × 10–4 3.2 × 103 2.1 × 109 1.1 × 10–6 1.6 × 10–1 2.8 × 10–3 3.8 × 10–3 3.6 × 10–4 1.32 × 10–5 1.37 × 10–4 1.6 × 10–8 (D ~ 2 × 10–9– 4 × 10–8) 1.8 1.1 × 10–7 (D ~ 7 × 10–13– 2 × 10–10) 1 × 105 (D ~ 3 × 10–8)

1.4 2.1 – 1.2 4.7 4.7 0.9 2.3 2.9 0.69 0.59 0.48 0.73 0.3 – 1.9 0.72 – 3.85 –

700–1050 700–1300 900–1000 900–1130 1120–1305 T < 950 950–1130 980–1180 850–1100 600–900 500–900 600–820 600–900 750–900 700–900 700–900 700–900 450-650 830–990 550

7 × 1010 – 3.6 × 10-4 (D ~ 2 × 10–8) – 3 6.8 × 105 9 × 10–1 3.6 × 10–3 2.2 × 10–2 7.3 × 10–4 5.8 × 10–3 1.98 × 10–6 4.2 × 10–3 3.11 × 10–3 7.4 × 10–4 1.45 × 10–5 6 × 105 3.74 × 10–6 1.49 × 10–6 3 × 107 6.78 12.6 3.43 × 10–5 7 × 10–4 9 × 10–4 3 × 10–5 1 × 10–7 7 × 10–4 5 × 10–1

5.65 – 1.94 – 2.9 2 3.4 1.8 0.52 0.54 0.26 0.65 1.17 0.96 1.17 1.15 1.32 4.0 1.17 1.17 4.45 2.2 2.2 1.28 0.28 1.08 0.37 0.25 0.32 1.35

900–1000 600–900 585–708 550 650–750 600–950 600–700 600–950 342–875 525–890 450–900 600–900 600–900 600–900 600–900 650–900 650–850 740–900 600–900 600–900 740–900 600–900 600–900 600–900 0–210 200–500 230–490 440–510 140–510 362–508

Diffusant Te Fe

GaP

InP

Ag Au

Fe Co Cu Ag Au Zn Cd

In (self ) Sn P (self ) Cr S Se Mn Fe

InAs

Co Cu Ag Au Mg Zn

InSb

Cd Hg In (self ) Ge Sn As (self ) S Se Te Li Cu Ag Au Zn

Section 12.indb 95

Frequency factor, Do (cm2/s)

12-95 Method of measurement

Ref.

Radioactive Radioactive

69 69

Radioactive Radioactive Diffusion (I) A face and (II) B face Atomic absorption analysis Electrical Radioactive Radioactive Radioactive; ESR Radioactive Radioactive; ESR

69 69

Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Electrical Radioactive Radioactive Electrical Electrical Radioactive Etching and cathodoluminescence Radioactive Radioactive Electrical Cathodoluminescence SIMS Radioactive SIMS Radioactive Radioactive Radioactive Radioactive Radioactive Electrical Radioactive Electrical Radioactive Radioactive Radioactive Electrical Electrical Radioactive Electrical Electrical Electrical Electrical Radioactive Radioactive Radioactive Radioactive Radioactive

69 69 69 69 69 69 69 69 69 69 69 69

69 69 69 69 69 69 69

69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69

4/28/05 1:57:22 PM

Diffusion Data for Semiconductors

12-96 Semiconductor

Diffusant Cd Hg In (self ) Sn Pb Sb (self )

AlAs AlSb

ZnS

S Se Te Fe Co Ga Zn Cu Zn Cd Al (self ) Sb (self ) Cu

Au Zn (self )

Cd Al In S (self )

ZnSe

Se Mn Li Cu Ag Zn (self ) Cd Al Ga In S Se (self )

ZnTe

Ni Li

Zn (self )

CdS

Section 12.indb 96

Al In Te (self ) Li Na

Frequency factor, Do (cm2/s)

Activation energy, Q(eV)

Temperature range (°C)

– 1 × 10–5 1.3 × 10–4 4 × 10–6 6 × 10–7 1.8 × 1013 5.5 × 10–8 (D ~ 2.7 × 10–15) 5.35 × 10–4 3.1 × 1013 9 × 10–2 1.6 1.7 × 10–7 1 × 10–7 2.7 × 10–11 (D ~ 2 × 10–18– 10–15) (D ~ 9 × 10–11) 3.5 × 10–3 3.3 × 10–1 D(c) ~ 4 × 10–12– 3 × 10–10 2 1 2.6 × 10–3 4.3 × 10–4 9.75 × 10–3 1.75 × 10–4 3 × 10–4 1.5 × 104 1 × 1016 (D ~ 10–10) 5.69 × 10–4 3 × 101 2.16 × 104 8 × 10–5 (D ~ 5 × 10–13) 2.3 × 103 2.66 × 10–6 1 × 10–4 1.7 × 10–5 2.2 × 10–2 9.8 6.39 × 10–4 2.3 × 10–2 1.81 × 102 – (D ~ 2 × 10–12) (D ~ 8 × 10–12) 1.3 × 101 2.3 × 10–1 (D ~ 1.5 × 10–8– 1.7 × 10–7) 2.9 × 10–2

1.5 1.1 1.2 1.17 1.45 4.3 0.75 – 1.91 4.3 1.4 1.87 0.57 0.25 0.39 3.6 – 0.36 1.93 – 1.88 1.7 0.79 0.64 1.04 1.16 1.5 3.26 6.5 – 1.28 2.2 3.15 2.2 – 2.46 0.49 0.66 0.56 1.18 3.0 1.87 1.8 3.0 1.3 – – 2.5 2.7 – 1.22 (s)

355–455 250–500 360–500 425–500 400–500 475–517 390–512 500 400–500 475–517 360–500 380–500 300–500 440–510 420–500 850–1100 557 150–500 660–860 900 570–620 570–620 470–750 250–1200 400–800 500–800 925<T<940 940<T<1030 1030<T<1075 1100 800–1000 750–1000 600–800 740–1100 1070 500–800 950–980 400–800 200–570 400–800 760–1150 700–950 800–1100 900–1100 700–850 940 1060 860–1020 1000–1050 740–910 400–700

SIMS Radioactive Electrical Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Electrical Electrical Radioactive Radioactive Radioactive AES SEM Radioactive Radioactive Radioactive X-ray X-ray Radioactive Electroluminescence Luminescence Radioactive Radioactive

69 69 69 69 69 69 69 71 69 69 69 69 69 69 69 70 69 69 69 69 69 69 69 69 69 69 69

72 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69

1.7 × 10–4 2.34 1.4 × 101 – 4 2 × 104 3 × 10–6 (D ~ 3 × 10–7)

0.78 (f ) 2.56 2.69 2.0 1.96 3.8 0.68 –

Luminescence Luminescence Radioactive Radioactive Radioactive X-ray microprobe Radioactive Electrical Luminescence Radioactive Luminescence Radioactive Photoluminescence Luminescence Luminescence Electron probe – X-ray microprobe Radioactive Radioactive Luminescence Nuclear and chemical analysis

760–860 667–1077 700–1000 1100–1300 727–977 610–960 800

Radioactive Radioactive Electrical and optical Radioactive Radioactive Microhardness Radioactive

69 69 69 69 69 69 69

Method of measurement

Ref.

4/28/05 1:57:24 PM

Diffusion Data for Semiconductors Semiconductor

Diffusant

Radioactive Radioactive

69 69

700–1100 667–967 650–930

69 69

2.03 (⊥) 1.6 2.05 2.4 – 10.4 – – 10.9 – 0.53 1.5 1.25 (I) 2.18 (II)

Radioactive Optical and microprobe Radioactive, optical and microprobe

800–1100 800–900 750–1050 900 700–1000 800 1000 570–900 960 22–400 700–1000 600–900 600–900

69 69 69 69 69 69 69 69 69 69 69 69

(D ~ 5.3 × 10–12– 6 × 10–11) 2.6 × 103

– 1.55

900–1000 700–1000

(D ~ 1.5 × 10–10) 3.7 × 10–4 8.2 × 10–8 –

– 0.67 0.64 –

300 97–300 290–350 700–800

Au Cd (self )

6.7 × 101 1.26 3.26 × 102 1.58 × 101

2.0 2.07 2.67 (I) 2.44 (II)

600–1000 700–1000 650–900

8 × 10–2 1.17 × 102 6.48 × 10–4

1.61 2.21 (I) 1.15 (II)

650–1000 500–850

Sn P As O

8.3 × 10–2 (D ~ 1.2 × 10–10) – 5.6 × 10–9 6.0 × 10–10 1.7 × 10–4 8.54 × 10–7

2.2 – – 1.22 0.29 1.35 1.42 (I)

700–925 900 850 200–650 650–900 700–1000 600–900

Radioactive Radioactive Radioactive Radioactive Radioactive Electrical Radioactive Luminescence Photoluminescence Ultrasonic Radioactive Radioactive; (I) saturated Cd and (II) saturated Se pressure Radioactive Radioactive; saturated Se pressure Ion microprobe Radioactive Ion backscattering Electrical and photoluminescence Radioactive Radioactive Radioactive; (I) saturated Cd and (II) saturated Te pressure Radioactive Radioactive; (I) saturated Cd and (II) saturated Te pressure Radioactive Radioactive – Mass spectrometry

1.66 × 10–4 7.1 × 10–2 (D ~ 4 × 10–8)

1.38 (II) 1.6 0.77

500–800 520–800 900

Radioactive Radioactive; (I) saturated Cd and (II) saturated Te pressure Radioactive Radioactive

69 69

P S (self ) Se Te Cl I Ni Yb Ag Cd (self )

P Se (self ) Li Cu Ag

Se Te (self )

Cl Fe

Section 12.indb 97

1 × 101 6.5 × 10–4 1.6 × 10–2 – (D ~ 1.2 × 10–9) 1.3 × 10–7 (D ~ 3 × 10–10) (D ~ 5 × 10–12) 6.75 × 10–3 (D ~ 1.3 × 10–9) 2 × 10–4 1.6 × 10–3 6.3 × 10–2 4.12 × 10–2

Ref.

500–800 720–1000

Cd (self ) Ga In

0.76 1.05 0.72 1.2 (s) 0.8 (f ) 1.8 0.86 (s) 0.66 (f ) 2.0 – 2.3 ()

Method of measurement 69 69 69 69

Au Zn

1.5 × 10–3 1.2 × 10–2 8 × 10–5 2.5 × 101 2.4 × 10–1 2 × 102 1.27 × 10–9 1.22 × 10–8 3.4 – 6 × 101

Temperature range (°C)

Radioactive Ultrasonic Electrical Radioactive

CdTe

Activation energy, Q(eV)

400–700 300–700 20–200 300–500

CdSe

Frequency factor, Do (cm2/s)

12-97

69 69 69 69 69 69 69 69 69

69 69 69 69 69

4/28/05 1:57:25 PM

Diffusion Data for Semiconductors

12-98 Semiconductor HgSe HgTe

Diffusant Sb Se (self ) Ag Zn Cd Hg (self ) In Sn

PbS

Te (self ) Mn Cu

PbSe

Pb (self ) S (self ) Ni Na

PbTe

Cu Ag Pb (self ) Sb Se (self ) Cl Ni Na Sn Pb (self ) Sb Te Cl Ni

Frequency factor, Do (cm2/s)

6.3 × 10–5 – 6 × 10–4 5 × 10–8 3.1 × 10–4 2 × 10–8 6 × 10–6 1.72 × 10–6 1.8 × 10–3 10–6 1.5 × 10–4 4.6 × 10–4 5 × 10–3 8.6 × 10–5 6.8 × 10–5 1.78 × 101 1.5 × 101 5.6 × 10–6 2 × 10–5 7.4 × 10–4 4.98 × 10–6 3.4 × 10–1 2.1 × 10–5 1.6 × 10–8 (D ~ 1 × 10–10) 1.7 × 10–1 3.1 × 10–2 2.9 × 10–5 4.9 × 10–2 2.7 × 10–6 (D > 2.3 × 10–10) (D > 1 × 10–6)

Activation energy, Q(eV)

Method of measurement

Ref.

540–630 200–400 250–350 250–350 250–350 200–350 200–300 200–300

Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive

69 69 69 69 69 69 69 69

200–400 250–350 150–450 100–400 500–800 500–750 200–500 400–850

Radioactive Radioactive Electrical Electrical Radioactive Radioactive Electrical Radioactive

69 69 69 69 69 69 69 69

93–520 400–850 400–800 650–850 650–850 400–850 700 600–850 500–800 250–500 500–800 500–800

Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive Radioactive

69 69 69 69 69 69 69 69 69 69 69 69

– –

700 700

Radioactive Radioactive

69 69

References 1. N. A. Stolwijk and H. Bracht, in Diffusion in Semiconductors and NonMetallic Solids, D. L. Beke, Ed., Springer-Verlag, Berlin, 1998, 2-1. 2. E. M. Pell, Phys. Rev., 119, 1960; 119, 1014, 1960. 3. L. Svob, Solid State Electron, 10, 991, 1967. 4. B. I. Boltaks and I. I. Sosinov, Zh. Tekh. Fiz., 28, 3, 1958. 5. R. N. Hall and J. N. Racette, J. Appl. Phys., 35, 379, 1964. 6. B. I. Boltaks and Hsueh Shih-Yin, Sov. Phys. Solid State, 2, 2383, 1961. 7. W. R. Wilcox and T. J. LaChapelle, J. Appl. Phys., 35, 240, 1964. 8. E. A. Taft and R. O. Carlson, J. Electrochem. Soc., 117, 711, 1970. 9. R. Sh. Malkovich and N. A. Alimbarashvili, Sov. Phys. Solid State, 4, 1725, 1963. 10. R. N. Ghoshtagore, Solid State Electron, 15, 1113, 1972. 11. C. Hill, Semiconductor Silicon 1981, H. R. Huff, R. J. Kreiger, and Y. Takeishi, Eds., p. 988, Electrochem. Soc., 1981. 12. R. N. Ghoshtagore, Phys. Rev. B, 3, 2507, 1971. 13. W. Rosnowski, J. Electrochem. Soc., 125, 957, 1978. 14. J. S. Makris and B. J. Masters, J. Appl. Phys., 42, 3750, 1971. 15. M. F. Millea, J. Phys. Chem. Solids, 27, 315, 1965 (refer Reference 2). 16. C. S. Fuller and J. A. Ditzenberger, J. Appl. Phys., 27, 544, 1956. 17. S. Hocine and D. Mathiot, Appl. Phys. Lett., 53, 1269, 1988. 18. R. C. Newman and J. Wakefield, J. Phys. Chem. Solids, 19, 230, 1961. 19. L. Kalinowski and R. Seguin, Appl. Phys. Lett., 35, 211, 1979; Appl. Phys. Lett., 36, 171, 1980. 20. R. F. Peart, Phys. Stat. Sol., 15, K 119, 1966. 21. G. Hettich, H. Mehrer and K. Maler, Inst. Phys. Conf. Ser., 46, 500, 1979.

Section 12.indb 98

Temperature range (°C)

0.85 – 0.8 0.6 0.66 0.6 0.9 0.66 (s) 0.80 (f ) 1.4 1.3 0.36 0.31 1.52 1.38 0.95 1.74 (s) 0.4 (f ) 0.31 0.35 0.83 2.0 1.2 0.45 – 1.91 1.56 0.6 1.54 0.75

22. M. Ogina, Y. Oana and M. Watanabe, Phys. Stat. Sol. (a), 72, 535, 1982. 23. T. H. Yeh, S. M. Hu, and R. H. Kastl, Appl. Phys., 39, 4266, 1968. 24. I. Franz and W. Langheinrich, Solid State Electron, 14, 835, 1971. 25. R. N. Ghoshtagore, Hys. Rev. B, 3, 389, 1971. 26. B. J. Masters and J. M. Fairfield, J. Appl. Phys., 40, 2390, 1969. 27. R. N. Goshtagore, Phys. Rev. B, 3, 397, 1971. 28. R. S. Fair and J. C. C. Tsai, J. Electrochem. Soc., 122, 1689, 1975. 29. J. J. Rohan, N. E. Pickering, and J. Kennedy, J. Electrochem. Soc., 106, 705, 1969. 30. W. Wuerker, K. Roy, and J. Hesse, Matsr. Res. Bull., 9, 971, 1974. 31. J. C. Mikkelsen, Jr., Appl. Phys. Lett., 40, 336, 1982. 32. S. Tang Lee and D. Nicols, Appl. Phys. Lett., 47, 1001, 1985. 33. P. L. Gruzin, S. V. Zemskii, A. D. Bullkin, and N. M. Makarov, Sov. Phys. Sem., 7, 1241, 1974. 34. N. S. Zhdanovich and Yu. I. Kozlov, Svoistva Legir, Poluprovodn., V. S. Zemskov, Ed., Nauka, Moscow, 1977, 115–120; Fiz Tekh. Poluprovod., 9, 1594, 1975. 35. D. Gilles, W. Bergholze, and W. Schroeter, J. Appl. Phys., 59, 3590, 1986. 36. E. R. Weber, Appl. Phys. A, 30, 1, 1983. 37. E. R. Weber, Properties of Silicon, EMIS Datareviews Ser. No. 4, INSPEC Publications, 1988, 409–451. 38. M. K. Bakhadyrkhanov, S. Zainabidinov, and A. Khamidov, Sov. Phys. Sem., 14, 243, 1980. 39. S. A. Azimov, M. S. Yunosov, F. K. Khatamkulov, and G. Nasyrov, Poluprovod., N. Kh. Abrikosov and V. S. Zemskov, Eds., Nauka, Moscow, 1975, 21–23.

4/28/05 1:57:26 PM

Diffusion Data for Semiconductors 40. S. A. Azimov, M. S. Yunosov, G. Nurkuziev, and F. R. Karimov, Sov. Phys. Sem., 12, 981, 1978. 41. S. A. Azimov, B. V. Umarov, and M. S. Yunusov, Sov. Phys. Sem., 10, 842, 1976. 42. C. S. Fuller and J. A. Ditzenberger, Phys. Rev., 91, 193, 1953. 43. B. Pratt and F. Friedman, J. Appl. Phys., 37, 1893, 1966. 44. M. Stojic, V. Spiric, and D. Kostoski, Inst. Phys. Conf. Ser., 31, 304, 1976. 45. B. I. Boltaks, Diffusion in Semiconductors, Inforsearch, London, 1963, 162. 46. A. A. Bugai, V. E. Kosenko, and E. G. Miselyuk, Zh. Tekh. Fiz., 27, 67, 1957. 47. L. Y. Wei, J. Phys. Chem. Solids, 18, 162, 1961. 48. V. E. Kosenko, Sov. Phys. Solid State, 4, 42, 1962. 49. W. C. Dunlap, Jr., Phys. Rev., 97, 614, 1955 50. Yu. I. Belyaev and V. A. Zhidkov, Sov. Phys. Solid State, 3, 133, 1961. 51. W. C. Dunlap, Jr. Phys. Rev., 94, 1531, 1954. 52. V. E. Kosenko, Sov. Phys. Solid State, 1, 1481, 1960. 53. P. Dorner, W. Gust, A. Lodding, H. Odelius, B. Predel, and U. Roll, Acta Metall., 30, 941, 1982. 54. W. Meer and D. Pommerrening, Z. Agnew. Phys., 23, 369, 1967. 55. U. Sodervall, H. Odelius, A. Lodding, U. Roll, B. Predel, W. Gust, and P. Dorner, Phil. Mag. A, 54, 539, 1986. 56. P. Dorner, W. Gust, A. Lodding, H. Odelius, B. Predel, and U. Roll, Z. Metalkd., 73, 325, 1982.

Section 12.indb 99

12-99 57. P. V. Pavlov, Sov. Phys. Solid State, 8, 2377, 1967. 58. V. I. Tagirov and A. A. Kuliev, Sov. Phys. Solid State, 4, 196, 1962. 59. J. Raisanen, J. Hirvonen, and A. Anttila, Solid State Electron., 24, 333, 1981. 60. C. Vogel, G. Hettich, and H. Mehrer, J. Phys. C., 16, 6197, 1983. 61. H. Letaw, Jr., W. M. Portnoy, and L. Slifkin, Phys. Rev., 102, 363, 1956. 62. W. Bosenberg, Z. Naturforsch., 10a, 285, 1955. 63. V. M. Glazov and V. S. Zemskov, Physicochemical Principles of Semiconductor Doping, Israel Program for Scientific Translation, Jerusalem, 1968. 64. J. W. Corbett, R. S. McDonald, and G. D. Watkins, J. Phys. Chem. Solids, 25, 873, 1964. 65. W. W. Tyler, J. Phys. Chem. Solids, 8, 59, 1959. 66. V. D. Ignatkov and V. E. Kosenko, Sov. Phys. Solid State, 4, 1193, 1962. 67. A. A. Bugal, V. E. Kosenko, and E. G. Miseluk, Zh. Tekh. Fiz., 27, 210, 1957. 68. F. van der Maesen and J. A. Brenkman, Phillips Res. Rep., 9, 255, 1954. 69. M. B. Dutt and B. L. Sharma, in Diffusion in Semiconductors and NonMetallic Solids, D. L. Beke, Ed., Springer-Verlag, Berlin, 1998, 3-1. 70. L. L. Chang and A. Koma, Appl. Physics Lett., 29, 138, 1976. 71. D. L. Kendall, Semiconductors and Semimetals, Vol. 4, R. K. Willardson and A. C. Beer, Eds., Academic, 1968, 255. 72. H. J. Biter and F. Williams, J. Luminescence, 3, 395, 1971.

4/28/05 1:57:27 PM

PROPERTIES OF MAGNETIC MATERIALS H. P. R. Frederikse

Glossary of Symbols Quantity

Symbol

Magnetic field Magnetic induction Magnetization Spontaneous magnetization Saturation magnetization Magnetic flux Magnetic moment Coercive field Remanence Saturation magnetic polarization Magnetic susceptibility Magnetic permeability Magnetic permeability of free space Saturation magnetostriction Curie temperature Néel temperature

H B M Ms M0 Φ m, µ Hc Br Js χ µ µ0 λ (∆l/l) TC TN

Units

A m-1 T (tesla) A m-1 A m-1 A m-1 Wb (weber) A m2 A m-1 T T

emu Oe (oersted) G (gauss) emu cm-3 emu cm-3 emu cm-3 maxwell erg/G Oe G G

H m–1 (henry/meter) H m–1 K K

K K

Magnetic moment µ = γħJ = g µB J where γ = gyromagnetic ratio; J = angular momentum; g = spectroscopic splitting factor (~2) µΒ = bohr magneton = 9.2741⋅10–24 J/T = 9.2741⋅10–21 erg/G Earth’s magnetic field H = 56 A m–1 = 0.7 Oe For iron: M0 = 1.7⋅106 A m–1; Br = 0.8⋅106 A m–1 1 Oe = (1000/4π) A m–1; 1 G = 10–4 T; 1 emu cm–3 = 103 A m–1 1 maxwell = 10–8 Wb µ0 = 4π 10–7 H m–1

Relation Between Magnetic Induction and Magnetic Field B (b) +Br (a) (c) +Hc

-Hc

(c)

-Br

FIGURE 1. Typical curve representing the dependence of magnetic induction B on magnetic field H for a ferromagnetic material. When H is first applied, B follows curve a as the favorably oriented magnetic domains grow. This curve flattens as saturation is approached. When H is then reduced, B follows curve b, but retains a finite value (the remanence Br) at H = 0. In order to demagnetize the material, a negative field –Hc (where Hc is called the coercive field or coercivity) must be applied. As H is further decreased and then increased to complete the cycle (curve c), a hysteresis loop is obtained. The area within this loop is a measure of the energy loss per cycle for a unit volume of the material.

(a) = Domain growth (b) = Field removal (c) = Hysteric curve on field

12-100

Section 12.indb 100

4/28/05 1:57:29 PM

Properties of Magnetic Materials

12-101 FIGURE 2. Schematic curve illustrating the B vs. H dependence for hard and soft magnetic materials. Hard materials have a larger remanence and coercive field, and a correspondingly large hysteresis loss.

Hard Soft H

Reference Ralls, K. M., Courtney, T. H., and Wulff, J., Introduction to Materials Science and Engineering, J. Wiley & Sons, New York, 1976, p. 577, 582. With permission.

Magnetic Susceptibility of the Elements

FIGURE 3. Molar susceptibility of the elements at room temperature (cgs units of 10–6 cm3/mol). Values are not available for Z = 9, 61, and 84–89; Fe, Co, and Ni (Z = 26–28) are ferromagnetic. Data taken from the table “Magnetic Susceptibility of the Elements and Inorganic Compounds” in Section 4.

Reference Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw Hill, New York, 1972, p. 5–224. With permission.

Section 12.indb 101

4/28/05 1:57:31 PM

Properties of Magnetic Materials

12-102 Ground State of Ions with Partly Filled d or f Shells Z

Element

Gr. state

1/2

3/2

V4+

1/2

3/2

V2+

3/2

Mn4+

3/2

Mn3+

1.73

1.55

1.8

1.73

1.55

1.8

2.83

1.63

2.8

F3/2

3.87

0.77

3.8

F3/2

3.87

0.77

3.7

F3/2

3.87

0.77

4.0

4.90

4.9

4.90

5.0

S5/2

5.92

5.9

S5/2

5.92

5.9

4.90

6.70

5.4

F9/2

3.87

6.54

4.8

2.83

5.59

3.2

D5/2

1.73

3.55

1.9

5/2

Fe3+

5/2

Co2+

3/2

9/2

Ni2+

1/2

5/2

pmeas

D3/2

pcalcb

D3/2

pcalca

pcalcc

a b c

Ce3+

1/2

5/2

Nd3+

3/2

9/2

Sm3+

5/2

Gd3+

7/2

Dy3+

5/2

15/2

Er3+

3/2

15/2

Yb3+

1/2

7/2

2.54

2.4

3.58

3.5

I9/2

3.62

3.5

2.68

H5/2

0.84

1.5

0.0

3.4

S7/2

7.94

8.0

9.72

9.5

H15/2

10.63

10.6

10.60

10.4

I15/2

9.59

9.5

7.57

7.3

F7/2

4.54

4.5

pcalc = 2[S(S + 1)]

1/2

pcalc = 2[J(J + 1)]1/2 pcalc = g[J(J + 1)]1/2

References 1. Jiles, D., Magnetism and Magnetic Materials, Chapman & Hall, London, 1991, p. 243.

Section 12.indb 102

F5/2

2. Kittel, C., Introduction to Solid State Physics, 6th Edition, J. Wiley & Sons, New York, 1986, pp. 405â&#x20AC;&#x201C;406. 3. Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Holt, Rinehart, and Winston, New York, 1976, p. 652.

4/28/05 1:57:33 PM

Properties of Magnetic Materials

12-103 Ferro- and Antiferromagnetic Elements

M0 is the saturation magnetization at T = 0 K nB is the number of Bohr magnetons per atom M0/gauss 22020 18170 6410

Fe Co Ni Cr Mn Ce Nd

nB 2.22 1.72 0.62

TC/K 1043 1388 627

Sm Eu Gd Tb

24880

7 9

293 220

TN/K

311 100 12.5 19.2 7.8 106 13.8 90.5

230.2 176 133 80 56

References 1. Ashcroft, N. W., and Mermin, N. D., Solid State Physics, Holt, Rinehart, and Winston, New York, 1976, p.652.

TC is the Curie temperature TN is the NĂŠel temperature Comments

c-Axis antiferromagnetic Basal plane modulation on hexagonal sites Cubic sites order (periodicity different from high-T phase) Ordering on hexagonal sites Cubic site order Spiral along cube axis Basal plane ferromagnet Basal plane spiral Basal plane ferromagnet Basal plane spiral Bunched cone structure Basal plane spiral c-Axis ferrimagnetic cone structure c-Axis modulated structure c-Axis ferrimagnetic cone structure c-Axis modulated structure 2. Gschneidner, K. A., and Eyring, L., Handbook on the Physics and Chemistry of Rare Earths, North Holland Publishing Co., Amsterdam, 1978.

Selected Ferromagnetic Compounds M0 is the saturation magnetization at T = 293 K Compound MnB MnAs MnBi MnSb Mn4N MnSi CrTe CrBr3 CrI3 CrO2 EuO EuS GdCl3 FeB Fe2B FeBe5 Fe3C FeP *

M0/gauss 152 670 620 710 183 247 270 515 1910* 1184* 550*

TC is the Curie temperature TC/K 578 318 630 587 743 34 339 37 68 386 77 16.5 2.2 598 1043 75 483 215

cub(FeSi) hex(NiAs) hex(BiI3) hex(BiI3) tetr(TiO2) cub cub orthorh orthorh tetr (CuAl2) cub(MgCu2) orthorh orthorh (MnP)

At T = 0 K

References 1. Kittel, C., Introduction to Solid State Physics, 6th Edition, J. Wiley & Sons, New York, 1986.

Section 12.indb 103

Crystal system orthorh(FeB) hex(FeB) hex(FeB) hex(FeB)

2. Ashcroft, N. W., and Mermin, N. D., Solid State Physics, Holt, Rinehart, and Winston, New York, 1976.

4/28/05 1:57:34 PM

Properties of Magnetic Materials

12-104

Magnetic Properties of High-Permeability Metals and Alloys (Soft) Js is the saturation polarization WH is the hysteresis loss per cycle TC is the Curie temperature

µi is the initial permeability µm is the maximum permeability Hc is the coercive force Material

Composition (mass %)

Iron Iron Silicon-iron Silicon-iron (110) [001] Silicon-iron {100} <100> Mild steel Hypernik Deltamax {100} <100> Isoperm {100} <100> 78 Permalloy Supermalloy Mumetal Hyperco Permendur 2V-Permendur Supermendur 25Perminvar 7Perminvar Perminvar (magnet. annealed) Alfenol (or Alperm) Alfer Aluminum-Iron Sendust

Commercial 99Fe Pure 99.9Fe 96Fe-4Si 97Fe-3Si 97Fe-3Si Fe-0.1C-0.1Si-0.4Mn 50Fe-50Ni 50Fe-50Ni 50Fe-50Ni 78Ni-22Fe 79Ni-16Fe-5Mo 77Ni-16Fe-5Cu-2Cr 64Fe-35Co-0.5Cr 50Fe-50Co 49Fe-49Co-2V 49Fe-49Co-2V 45Ni-30Fe-25Co 70Ni-23Fe-7Co 43Ni-34Fe-23Co 84Fe-16Al 87Fe-13Al 96.5Fe-3.5Al 85Fe-10Si-5Al

µi/µ0

200 25000 500 9000 800 4000 500 90 4000 100000 20000 650 500 800 400 850 3000 700 500 36000

References 1. McCurrie, R. A., Structure and Properties of Ferromagnetic Materials, Academic Press, London, 1994, p. 42.

Applications

µm/µ0

6000 350000 7000 40000 100000 1100 70000 200000 100 100000 1000000 100000 10000 6000 4000 60000 2000 4000 400000 55000 3700 19000 120000

Hc/A m–1 70 0.8 40 12 6 200 4 16 480 4 0.15 4 80 160 160 16 100 50 2.4 3.2 53 24 1.6

Js/T

2.16 2.16 1.95 2.01 2.01

1.60 1.55 1.60 1.05 0.79 0.75 2.42 2.46 2.45 2.40 1.55 1.25 1.50 0.8 1.20 1.90 0.89

WH/J m–3

TC/K

500 60 50–150 35–140

1043 1043 1008 1015 1015

753 773

50 2 20 300 1200 600 1150

651 673 673 1243 1253 1253 1253

723 673 753

2. Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw Hill, New York, 1972, p. 5–224.

Applications of High-Permeability Materials

Requirements

Power applications Distribution and power transformers

Low core losses, high permeability, high saturation magnetic polarization

High-quality motors and generators, stators and armatures, switchedmode power supplies Instrument transformers Audiofrequency transformers

Low core losses, high permeability, high magnetic polarization

Pulse transformers

High permeability Cores for inductor coils

Audiofrequency

Low hysteresis, high permeability

Carrier frequency

Very low hysteresis and eddy current loss

Radiofrequency

High permeability at low fields

Relays, switches Earth leakage circuit Magnetic shielding

Section 12.indb 104

}

Miscellaneous High permeability, low remanence, low coercivity Low core loss for AC applications

4/28/05 1:57:35 PM

Properties of Magnetic Materials

Applications

12-105 Applications of High-Permeability Materials

Requirements

Magnetic recording heads

High initial permeability, low or zero remanence

Magnetic amplifiers Saturable reactors Saturable transformers Transformer cores

Rectangular hysteresis loops, low hysteresis loss

}

Magnetic shunts for temperature compensation in magnetic circuits

Low Curie temperature, appropriate decrease in permeability with increase in temperature

Electromagnets in indicating instruments, fire detection, quartz watches, electromechanical devices

High permeability, high saturation magnetic polarization

Magnetic yokes in permanent magnet devices, such as lifting and holding magnets, loudspeakers

High permeability, high saturation magnetic polarization

Reference McCurrie, R. A., Structure and Properties of Ferromagnetic Materials, Academic Press, London, 1994. With permission.

Saturation Magnetostriction of Selected Materials

The tabulated parameter λs is related to the fractional change in length ∆l/l by ∆l/l = (3/2)λs(cos2θ – 1/3), where θ is the angle of rotation. Material

λs × 106 –7 +9 –33 –62 +27 0 +70 +30 +40 –110 –1560 +1753 +2000 +35 0

Iron Fe - 3.2% Si Nickel Cobalt 45 Permalloy, 45% Ni - 55% Fe Permalloy, 82% Ni - 18% Fe Permendur, 49% Co - 49% Fe - 2% V Alfer, 87% Fe - 13% Al Magnetite, Fe3O4 Cobalt ferrite, CoFe2O4 SmFe2 TbFe2 Tb0.3Dy0.7Fe1.93 (Terfenol D) Fe66Co18B15Si (amorphous) Co72Fe3B6Al3 (amorphous)

Reference McCurrie, R.A., Structure and Properties of Ferromagnetic Materials, Academic Press, London, 1994, p. 91; additional data provided by A.E. Clark, Adelphi, MD.

Properties of Various Permanent Magnetic Materials (Hard) Br is the remanence H is the flux coercivity B c H is the intrinsic coercivity i c

Composition Alnico1 20Ni;12Al;5Co Alnico2 17Ni;10Al;12.5Co;6Cu Alnico3 24-30Ni;12-14Al;0-3Cu Alnico4 21-28Ni;11-13Al;3-5Co;2-4Cu Alnico5 14Ni;8Al;24Co;3Cu Alnico6 16Ni;8Al;24Co;3Cu;2Ti Alnico8 15Ni;7Al;35Co;4Cu;5Ti Alnico9 15Ni;7Al;35Co;4Cu;5Ti Alnico12 13.5Ni;8Al;24.5Co;2Nb

S12_20.indd 105

(BH)max is the maximum energy product TC is the Curie temperature Tmax is the maximum operating temperature

Br/T

0.72 0.72 0.5–0.6 0.55–0.75 1.25 1.05 0.83 1.10 1.20

Hc/103 A m–1

53 1.6 1.45

Hc/103 A m–1

35 40–50 40–54 36–56 54 75 160 1.45 64

(BH)max/kJ m–3

25 13–14 10 11–12 40 52 45 75 76.8

TC/°C

Tmax/°C

850

520

850

520

5/2/05 1:05:18 PM

Properties of Magnetic Materials

12-106 Composition

Br/T

BaFe12O19 (Ferroxdur) SrFe12O19 LaCo5 CeCo5 PrCo5 NdCo5 SmCo5 Sm(Co0.76Fe0.10Cu0.14)6.8 Sm(Co0.65Fe0.28Cu0.05Zr0.02)7.7 Nd2Fe14B sintered Fe;52Co;14V (Vicalloy II) Fe;24Cr;15Co;3Mo (anisotropic) Fe;28Cr;10.5Co (Chromindur II) Fe;23Cr;15Co;3V;2Ti Cu;20Ni;20Fe (Cunife) Cu;21Ni;29Fe (Cunico) Pt;23Co Mn;29.5Al;0.5C (anisotropic)

References

Hc/103 A m–1

0.4 0.4 0.91 0.77 1.20 1.22 1.00 1.04 1.2 1.22 1.0 1.54 0.98 1.35 0.55 0.34 0.64 0.61

192 3.3

7.9 4.8 10 8.4 42 67 32 4 4 0.5 4 2.16

696 5 16 1120

1. McCurrie, R. A., Structure and Properties of Ferromagnetic Materials, Academic Press, London, 1994, p. 204.

Js is the saturation magnetic polarization TC is the Curie temperature ∆H is the line width Material

Js/T

Hc/103 A m–1

1.6 2.95

2.4

(BH)max/kJ m–3

29 30 164 117 286 295 196 212 264 280 28 76 16 44 12 8 76 56

TC/°C

400 400

480 300

350 120

Selected Ferrites

TC/°C

∆H/kA m–1

Applications

0.52 0.60 0.34 0.14 0.50 0.50 0.31 0.15 0.12 0.05 0.25 0.14 0.17 0.53 0.39

575 585 575 440 375 300 590 450 430 1860 290

Garnets Y3Fe5O12 Y3Fe5O12 (single crys.) (Y,Al)3Fe5O12 (Y,Gd)3Fe5O12 Sm3Fe5O12 Eu3Fe5O12 GdFe5O12

0.178 0.178 0.12 0.06 0.170 0.116 0.017

280 292 250 250 305 293 291

55 0.5 80 150

Microwave devices Microwave devices Microwave devices Microwave devices Microwave devices Microwave devices Microwave devices

0.45 0.34 0.28

430 470 130 390 500 450

1.5 12 25 16 8

Permanent magnets Microwave devices Microwave devices Microwave devices Microwave devices Permanent magnets

0.16 0.4

250 300 300 100 500 500 500 500 350

2. Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw Hill, New York, 1972, p. 5–165. 3. Jiles, D., Magnetism and Magnetic Materials, Chapman & Hall, London, 1991.

Spinels γ-Fe2O3 Fe3O4 NiFe2O4 MgFe2O4 NiZnFe2O4 MnFe2O4 NiCoFe2O4 NiCoAlFe2O4 NiAl0.35Fe1.65O4 NiAlFe2O4 Mg0.9Mn0.1Fe2O4 Ni0.5Zn0.5Al0.8Fe1.2O4 CuFe2O4 CoFe2O4 LiFe5O8

Hexagonal crystals BaFe12O19 Ba3Co2Fe24O41 Ba2Zn2Fe12O22 Ba3Co1.35Zn0.65Fe24O41 Ba2Ni2Fe12O22 SrFe12O19

Tmax/°C

450 450 567 380 620 637 700 800 800 300 700 630 630 630 410

455 520 670

Reference

350 70 120 50 140 330 67 32 56 17

Microwave devices Transformer cores Microwave devices Microwave devices Microwave devices Microwave devices Microwave devices Microwave devices Microwave devices Electromechanical transducers Microwave devices

McCurrie, R. A., Structure and Properties of Ferromagnetic Materials, Academic Press, London, 1994.

Section 12.indb 106

4/28/05 1:57:37 PM

Properties of Magnetic Materials

12-107 Spinel Structure (AB2O4)

FIGURE 4. Arrangement of metal ions in the two octants A and B, showing tetrahedrally (A) and octahedrally (B) coordinated sites. (Reprinted from McCurrie, R.A., Ferromagnetic Materials, Academic Press, London, 1994. With permission.)

A B O2-

Selected Antiferromagnetic Solids TN is the Néel temperature

Material

Structure

Binary oxides MnO FeO CoO NiO α-Mn2O3 CuO UO2 Er2O3 Gd2O3

cub(fcc) cub(fcc) cub(fcc) cub(fcc) cub monocl cub cub cub

122 198 291 525 90 230 30.8 3.4 1.6

orth orth orth orth orth orth cub cub orth cub* cub cub* cub cub cub* orth cub

282 100 750 224 760 118 110 5.3 141 673 125 88.3 115 275 60 149 82

Perovskites LaCrO3 LaMnO3 LaFeO3 NdCrO3 NdFeO3 YbCrO3 CaMnO3 EuTiO3 YCrO3 BiFeO3 KCoF3 KMnF3 KFeF3 KNiF3 NaMnF3 NaNiF3 RbMnF3 Spinels Co3O4 NiCr2O4

Section 12.indb 107

cub tetr

TN/K

40 65

Material

Structure

TN/K

ZnCr2O4 ZnFe2O4 GeFe2O4 MgV2O4 MnGa2O4

cub cub cub cub cub

NiAs and related structures CrAs CrSb CrSe MnTe NiS CrS

orth hex hex hex hex monocl

300 705–723 300 320–323 263 460

Rutile and related structures CoF2 CrF2 FeF2 MnF2 NiF2 CrCl2 MnO2 FeOF

tetr monocl tetr tetr tetr orth tetr tetr

38 53 79 67 83 20 84 315

Corundum and related structures Cr2O3 α-Fe2O3 FeTiO3 MnTiO3 CoTiO3

rhomb rhomb rhomb rhomb rhomb

318 948 68 41 38

VF3 and related structures CoF3 CrF3

rhomb rhomb

460 80

15 9 10 45 33

4/28/05 1:57:39 PM

Properties of Magnetic Materials

12-108 Material

Structure

FeF3 MnF3 MoF3

rhomb monocl rhomb

Miscellaneous K2NiF4 MnI2 CoUO4 CaMn2O4 CrN CeC2 FeSn Mn2P

tetr hex orth orth cub* tetr hex hex

TN/K

394 43 185 97 3.4 12 225 273 33 373 103

References 1. Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw Hill, New York, 1972, p. 5–168 to 5–183. 2. Kittel, C., Introduction to Solid State Physics, 6th Edition, J. Wiley & Sons, New York, 1986. 3. Ashcroft, N. W., and Mermin, N. D., Solid State Physics, Holt, Rinehart, and Winston, New York, 1976, p. 697.

* Distorted.

Section 12.indb 108

4/28/05 1:57:39 PM

ELECTRON WORK FUNCTION OF THE ELEMENTS The electron work function Φ is a measure of the minimum energy required to extract an electron from the surface of a solid. It is defined more precisely as the energy difference between the state in which an electron has been removed to a distance from the surface of a single crystal face that is large enough that the image force is negligible but small compared to the distance to any other face (typically about 10-4 cm) and the state in which the electron is in the bulk solid. In general, Φ differs for each face of a monocrystalline sample. Since Φ is dependent on the cleanliness of the surface, measurements reported in the literature often cover a considerable range. This table contains selected values for the electron work function of the elements which may be regarded as typical values for a reasonably clean surface. The method of measurement is indicated for each value. The following abbreviations appear: Element

Plane

Φ/eV

100 110 111 100 110 111 polycr 100 110 111 polycr polycr polycr polycr polycr polycr polycr polycr polycr polycr polycr 100 110 111 112 polycr 100 111 polycr polycr polycr polycr liquid polycr 100 110 111

4.64 4.52 4.74 4.20 4.06 4.26 (3.75) 5.47 5.37 5.31 (4.45) 2.52 4.98 4.34 (5.0) 2.87 4.08 2.9 5.0 4.5 1.95 5.10 4.48 4.94 4.53 2.5 4.67 4.81 4.32 2.90 5.0 3.9 4.475 4.09 5.67 5.42 5.76

As Au

B Ba Be Bi C Ca Cd Ce Co Cr Cs Cu

Eu Fe Ga Gd Ge Hf Hg In Ir

Method PE PE PE PE PE PE PE PE PE PE TH TH PE PE CPD PE CPD PE PE PE PE FE PE PE PE PE PE PE PE CPD CPD PE PE PE PE PE PE

Element K La Li Lu Mg Mn Mo

Na Nb

Nd Ni

Os Pb Pd Pt

Rb Re Rh

TE – Thermionic emission PE – Photoelectric effect FE – Field emission CPD – Contact potential difference polycr – Polycrystalline sample amorp – Amorphous sample Values in parentheses are only approximate.

References 1. Hölzl, J., and Schulte, F. K., Work Functions of Metals, in Solid Surface Physics, Höhler, G., Ed., Springer-Verlag, Berlin, 1979. 2. Riviere, J. C., Work Function: Measurements and Results, in Solid State Surface Science, Vol.1, Green, M., Ed., Decker, New York, 1969. 3. Michaelson, H. B., J. Appl. Phys., 48, 4729, 1977.

Plane

Φ/eV

210 polycr polycr polycr polycr polycr polycr 100 110 111 112 114 332 polycr 001 110 111 112 113 116 310 polycr 100 110 111 polycr polycr polycr 111 polycr 110 111 320 331 polycr polycr polycr

5.00 2.29 3.5 2.93 (3.3) 3.66 4.1 4.53 4.95 4.55 4.36 4.50 4.55 2.36 4.02 4.87 4.36 4.63 4.29 3.95 4.18 3.2 5.22 5.04 5.35 5.93 4.25 5.22 5.6 5.64 5.84 5.93 5.22 5.12 2.261 4.72 4.98

Method PE PE PE FE CPD PE PE PE PE PE PE PE PE PE TH TH TH TH TH TH TH PE PE PE PE PE PE PE PE PE FE FE FE FE PE TE PE

Element

Plane

Φ/eV

Method

Ru Sb

4.71 4.55 4.7 3.5 5.9 4.85 (4.91) 4.60 2.7 4.42 (2.59) 4.25 4.15 4.80 4.00 3.0 4.95 3.4 4.33 (3.84) 3.63 3.73 3.90 3.67 4.3 4.55 4.63 5.22 4.45 4.46 4.32 3.1 3.63

Y Zn

polycr amorp 100 polycr polycr n p 100 p 111 polycr polycr polycr polycr 100 110 111 polycr polycr polycr polycr polycr polycr 100 110 113 polycr polycr 100 110 111 113 116 polycr polycr

PE PE CPD CPD PE PE CPD TH TH TH TH TH PE PE TH PE CPD PE PE PE PE PE CPD FE FE FE FE TH PE PE

polycr polycr

(4.9) 4.05

CPD PE

Sc Se Si

Sm Sn Sr Ta

Tb Te Th Ti Tl U

V W

12-114

S12_21.indd 114

5/2/05 1:20:49 PM

SECONDARY ELECTRON EMISSION The secondary emission yield, or secondary emission ratio, δ, is the average number of secondary electrons emitted from a bombarded material for every incident primary electron. It is a function of the primary electron energy Ep. The maximum yield δmax corresponds to a primary electron energy Epmax (see figure). The two primary electron energies corresponding to a yield of unity are denoted the first and second crossovers (EI and EII). An insulat-

ing target, or a conducting target that is electrically floating, will charge positively or negatively depending on the primary electron energy. For EI < Ep < EII, δ > 1 and the surface charges positively provided there is a collector present that is positive with respect to the target. For Ep < EI or Ep > EII, δ < 1, and the surface charges negatively with respect to the potential of the source of primary electrons.

1.5 δmax δ 1.0 0.5

Ep EII EI max Primary Electron Energy (Ep) Element Ag Al Au B Ba Bi Be C (diamond) C (graphite) C (soot) Cd Co Cs Cu Fe Ga Ge Hg K Compound Alkali halides CsCl KBr (crystal) KCl (crystal) KCl (layer) KI (crystal) KI (layer) LiF (crystal) LiF (layer) NaBr (crystal) NaBr (layer) NaCl (crystal) NaCl (layer) NaF (crystal) NaF (layer) NaI (crystal) NaI (layer) RbCl (layer) Oxides Ag2O Al2O3 (layer) BaO (layer)

δmax 1.5 1.0 1.4 1.2 0.8 1.2 0.5 2.8 1.0 0.45 1.1 1.2 0.7 1.3 1.3 1.55 1.15 1.3 0.7

Epmax (eV) 800 300 800 150 400 550 200 750 300 500 450 600 400 600 400 500 500 600 200 δmax 6.5 14 12 7.5 10 5.6 8.5 5.6 24 6.3 14 6.8 14 5.7 19 5.5 5.8 1.0 2–9 2.3–4.8

EI (eV) 200 300 150 50 None None None None 300 None 300 200 None 200 120 75 150 350 None Epmax(eV) 1800 1600 1200 1600 700 1800 1200 600 1200 1300

400

EII (eV) >2000 300 >2000 600 None None None >5000 300 None 700 None None 1500 1400 None 900 >1200 None

Element Li Mg Mo Na Nb Ni Pb Pd Pt Rb Sb Si Sn Ta Th Ti Tl W Zr Compound BeO CaO Cu2O MgO (crystal) MgO (layer) MoO2 SiO2 (quartz) SnO2 Sulfides MoS2 PbS WS2 ZnS Others BaF2 (layer) CaF2 (layer) BiCs3 BiCs GeCs Rb3Sb SbCs3 Mica Glasses

δmax 0.5 0.95 1.25 0.82 1.2 1.3 1.1 >1.3 1.8 0.9 1.3 1.1 1.35 1.3 1.1 0.9 1.7 1.4 1.1

Epmax (eV) 85 300 375 300 375 550 500 >250 700 350 600 250 500 600 800 280 650 650 350 δmax 3.4 2.2 1.2 20–25 3–15 1.2 2.1–4 3.2 1.1 1.2 1.0 1.8 4.5 3.2 6 1.9 7 7.1 6 2.4 2–3

EI (eV) None None 150 None 150 150 250 120 350 None 250 125 None 250 None None 70 250 None

EII (eV) None None 1200 None 1050 >1500 1000 None 3000 None 2000 500 None >2000 None None >1500 >1500 None

Epmax(eV) 2000 500 400 1500 400–1500 400 640 500 350

1000 1000 700 450 700 350 300–450

12-115

Section 12.indb 115

4/28/05 1:58:02 PM

Optical Properties of Selected Elements J. H. Weaver and H. P. R. Frederikse These tables list the index of refraction n, the extinction coefficient k, and the normal incidence reflection R (φ = 0) as a function of photon energy E, which is expressed in electron volts (eV). To convert the energy in eV to the wavelength in µm, use λ = 1.2398/ E. To compute the dielectric function ˜ε = ε1 + iε2 from the complex ˜ = n + ik, use ε1 = n2 – k2 and ε2 = 2nk. index of refraction N The optical constants in these tables are abridged from three more extensive tabulations: •

• •

Optical Properties of Metals (OPM), Volumes I and II, Physics Data, Nr. 18-1 and 18-2, J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Fachinformationzentrum, Karlsruhe, Germany. Handbook of Optical Constants (HOC), Vol. I, 1985, and Vol. II, 1991. E. D. Palik, Ed., Academic Press, Inc., London. American Institute of Physics Handbook (AIPH), 3rd Edition, D. E. Gray, Ed., McGraw-Hill, New York, 1972.

tors are listed at the end of the tables. Generally, tabulated values for the optical properties are accurate to better than 10%. Data in parentheses are extrapolated or interpolated values. For most elements the spectral range covered is from the far infrared (0.010 or 0.10 eV) to the far ultraviolet (10, 30 or 300 eV). The intervals between successive energies in the tables are chosen in such a way that the major spectral features are preserved. Very small values of k are expressed in exponential notation, e.g., 1.23E-5 means 1.23 × 10-5. The following table is convenient for identifying the energy entries in these tables with the corresponding wavelengths: λ 1 mm 500 µm 100 µm 50 µm 10 µm 5 µm 1 µm

The first two of these major sources provide detailed comparisons of all optical data available in the literature at the time of the compilation. For critical applications the reader should refer to the original work. References for individual metals and semiconducEnergy (eV)

Aluminium1 0.040 98.595 0.050 74.997 0.060 62.852 0.070 53.790 0.080 45.784 0.090 39.651 0.100 34.464 0.125 24.965 0.150 18.572 0.175 14.274 0.200 11.733 0.250 8.586 0.300 6.759 0.350 5.438 0.400 4.454 0.500 3.072 0.600 2.273 0.700 1.770 0.800 1.444 0.900 1.264 1.000 1.212 1.100 1.201 1.200 1.260 1.300 1.468 1.400 2.237 1.500 2.745 1.600 2.625 1.700 2.143 1.800 1.741 1.900 1.488 2.000 1.304

12-120

k 203.701 172.199 150.799 135.500 123.734 114.102 105.600 89.250 76.960 66.930 59.370 48.235 40.960 35.599 31.485 25.581 21.403 18.328 15.955 14.021 12.464 11.181 10.010 8.949 8.212 8.309 8.597 8.573 8.205 7.821 7.479

R(φ = 0) 0.9923 0.9915 0.9906 0.9899 0.9895 0.9892 0.9889 0.9884 0.9882 0.9879 0.9873 0.9858 0.9844 0.9834 0.9826 0.9817 0.9806 0.9794 0.9778 0.9749 0.9697 0.9630 0.9521 0.9318 0.8852 0.8678 0.8794 0.8972 0.9069 0.9116 0.9148

Energy (eV) 2.200 2.400 2.600 2.800 3.000 3.200 3.400 3.600 3.800 4.000 4.200 4.400 4.600 4.800 5.000 6.000 6.500 7.000 7.500 8.000 8.500 9.000 9.500 10.000 10.500 11.000 11.500 12.000 12.500 13.000 13.500 14.000 14.200

n 1.018 0.826 0.695 0.598 0.523 0.460 0.407 0.363 0.326 0.294 0.267 0.244 0.223 0.205 0.190 0.130 0.110 0.095 0.082 0.072 0.063 0.056 0.049 0.044 0.040 0.036 0.033 0.033 0.034 0.038 0.041 0.048 0.053

k 6.846 6.283 5.800 5.385 5.024 4.708 4.426 4.174 3.946 3.740 3.552 3.380 3.222 3.076 2.942 2.391 2.173 1.983 1.814 1.663 1.527 1.402 1.286 1.178 1.076 0.979 0.883 0.791 0.700 0.609 0.517 0.417 0.373

R(φ = 0) 0.9200 0.9228 0.9238 0.9242 0.9241 0.9243 0.9245 0.9246 0.9247 0.9248 0.9248 0.9249 0.9249 0.9249 0.9244 0.9257 0.9260 0.9262 0.9265 0.9269 0.9272 0.9277 0.9282 0.9286 0.9293 0.9298 0.9283 0.9224 0.9118 0.8960 0.8789 0.8486 0.8312

E/eV 0.00124 0.00248 0.01240 0.02480 0.12398 0.24797 1.240

Energy (eV) 14.400 14.600 14.800 15.000 15.200 15.400 15.600 15.800 16.000 16.200 16.400 16.750 17.000 17.250 17.500 17.750 18.000 18.500 19.000 19.500 20.000 20.500 21.000 21.500 22.000 22.500 23.000 23.500 24.000 24.500 25.000 25.500 26.000

λ 6000 Å 5000 Å 4000 Å 3000 Å 2000 Å 1000 Å 400 Å

n 0.058 0.067 0.086 0.125 0.178 0.234 0.280 0.318 0.351 0.380 0.407 0.448 0.474 0.498 0.520 0.540 0.558 0.591 0.620 0.646 0.668 0.689 0.707 0.724 0.739 0.753 0.766 0.778 0.789 0.799 0.809 0.817 0.826

E/eV 2.066 2.480 3.100 4.133 6.199 12.398 30.996

k 0.327 0.273 0.211 0.153 0.108 0.184 0.073 0.065 0.060 0.055 0.050 0.045 0.042 0.040 0.038 0.036 0.035 0.032 0.030 0.028 0.027 0.025 0.024 0.023 0.022 0.021 0.021 0.020 0.019 0.018 0.018 0.017 0.016

R(φ = 0) 0.8102 0.7802 0.7202 0.6119 0.4903 0.3881 0.3182 0.2694 0.2326 0.2031 0.1789 0.1460 0.1278 0.1129 0.1005 0.0899 0.0809 0.0664 0.0554 0.0467 0.0398 0.0342 0.0296 0.0258 0.0226 0.0199 0.0177 0.0157 0.0140 0.0126 0.0113 0.0102 0.0092

Optical Properties of Selected Elements Energy (eV) 27.000 28.000 29.000 30.000 35.000 40.000 45.000 50.000 55.000 60.000 65.000 70.000 72.500 75.000 77.500 80.000 85.000 90.000 95.000 100.000 110.000 120.000 130.000 140.000 150.000 160.000 170.000 180.000 190.000 200.000 220.000 240.000 260.000 280.000 300.000

n 0.840 0.854 0.865 0.876 0.915 0.940 0.957 0.969 0.979 0.987 0.995 1.006 1.025 1.011 1.008 1.007 1.007 1.005 0.999 0.991 0.994 0.991 0.987 0.989 0.990 0.989 0.989 0.990 0.990 0.991 0.992 0.993 0.993 0.994 0.995

Carbon (diamond)2 0.06199 2.3741 0.06888 2.3741 0.07749 2.3745 0.08856 2.3750 0.1033 2.3757 0.1240 2.3765 0.1550 2.3772 0.1907 0.2066 2.3779 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 2.3787 0.32 0.33 0.34 0.35

k 0.015 0.014 0.014 0.013 0.010 0.008 0.007 0.006 0.005 0.004 0.004 0.004 0.004 0.024 0.025 0.024 0.028 0.031 0.036 0.030 0.025 0.024 0.021 0.016 0.015 0.014 0.011 0.010 0.009 0.007 0.006 0.005 0.004 0.003 0.002

3.1 E-05 5.7 E-05 1.21E-04 2.36E-04 3.82E-04 5.21E-04 2.96E-04 4.39E-04 2.75E-04 7.82E-05 1.32E-04 1.30E-04 1.11E-04 2.99E-05 1.89E-05 2.11E-05

R(φ = 0) 0.0076 0.0063 0.0053 0.0044 0.0020 0.0010 0.0005 0.0003 0.0001 0.0000 0.0000 0.0000 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0002 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.166 0.166 0.166 0.166 0.166 0.166 0.166 0.166

0.167

Energy (eV) 0.36 0.37 0.38 0.39 0.40 0.41 0.4133 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.4959 0.6199 0.8266 1.240 1.378 1.459 1.550 1.653 1.771 1.889 1.926 2.066 2.105 2.271 2.480 2.650 2.845 3.100 3.434 3.576 3.961 4.160 4.511 4.8187 5.00 5.30 5.35 5.40 5.50 5.55 5.60 5.80 6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00 7.10 7.15 7.20

12-121 n

2.3795

2.3801 2.3813 2.3837 2.3905 2.3934 2.3953 2.3975 2.4003 2.4036 2.4073 2.4084 2.4133 2.4147 2.4210 2.4299 2.4380 2.4627 2.4849 2.4955 2.5465 2.6205 2.6383

2.740 2.780 2.826 2.852 2.879 2.910 2.944 2.985 3.031 3.085 3.146 3.220 3.322 3.444 3.464 3.437

k 2.47E-05 2.80E-05 3.11E-05 3.67E-05 3.58E-05 3.25E-05 2.94E-05 2.87E-05 3.14E-05 3.62E-05 3.22E-05 1.57E-05 6.17E-06

3.82E-07

8.97E-07 1.29E-06 1.47E-06 2.98E-06 6.45E-06 1.04E-05 3.41E-05 5.48E-04 1.48E-03 5.02E-03 7.99E-03 8.62E-03 9.30E-03 9.74E-03 9.87E-03 1.10E-02 1.47E-02 2.20E-02 3.44E-02 5.24E-02 9.35E-02 0.210 0.307 0.388

R(φ = 0)

0.167

0.167 0.167 0.167 0.168 0.169 0.169 0.169 0.170 0.170 0.171 0.171 0.171 0.172 0.173 0.174 0.175 0.178 0.182 0.183 0.190 0.200 0.203

0.216 0.222 0.228 0.231 0.235 0.239 0.243 0.248 0.254 0.261 0.268 0.277 0.289 0.304 0.308 0.307

Energy (eV) 7.30 7.40 7.50 7.60 7.80 8.00 8.25 8.50 8.75 9.00 9.25 9.50 9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.20 12.40 12.60 12.80 13.00 13.50 14.00 14.50 15.00 15.50 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00

n 3.376 3.335 3.321 3.306 3.276 3.251 3.232 3.228 3.247 3.272 3.308 3.348 3.398 3.453 3.514 3.565 3.600 3.582 3.507 3.346 3.090 2.736 2.383 1.983 1.532 1.312 1.223 1.129 1.070 1.018 0.972 0.917 0.861 0.805 0.753 0.707 0.665 0.626 0.589 0.557 0.527 0.487 0.518 0.597 0.586 0.562 0.538 0.516 0.501 0.494 0.493

Cesium (evaporated)3 2.145 0.264 2.271 0.278 2.845 0.425 3.064 0.540 3.397 0.671 3.966 0.827 4.889 0.916

k 0.473 0.515 0.533 0.592 0.659 0.712 0.765 0.806 0.855 0.910 0.978 1.055 1.147 1.258 1.403 1.581 1.813 2.078 2.380 2.693 2.986 3.228 3.354 3.382 3.265 2.953 2.722 2.379 2.178 2.034 1.929 1.845 1.767 1.692 1.619 1.546 1.476 1.408 1.341 1.273 1.203 1.052 0.888 0.850 0.829 0.787 0.736 0.679 0.616 0.552 0.490

R(φ = 0) 0.303 0.300 0.299 0.300 0.300 0.300 0.301 0.303 0.308 0.314 0.322 0.331 0.342 0.355 0.371 0.389 0.411 0.434 0.460 0.488 0.518 0.551 0.580 0.610 0.641 0.627 0.604 0.557 0.526 0.504 0.489 0.482 0.477 0.474 0.471 0.467 0.463 0.459 0.455 0.449 0.442 0.413 0.330 0.270 0.268 0.265 0.260 0.252 0.239 0.221 0.201

1.123 0.950 0.438 0.320 0.233 0.174 0.143

0.631 0.561 0.235 0.127 0.057 0.018 0.007

Optical Properties of Selected Elements

12-122 Energy (eV)

Chromium4 0.06 21.19 0.10 11.81 0.14 15.31 0.18 8.73 0.22 5.30 0.26 3.91 0.30 3.15 0.42 3.47 0.54 3.92 0.66 3.96 0.78 4.13 0.90 4.43 1.00 4.47 1.12 4.53 1.24 4.50 1.36 4.42 1.46 4.31 1.77 3.84 2.00 3.48 2.20 3.18 2.40 2.75 2.60 2.22 2.80 1.80 3.00 1.54 3.20 1.44 3.40 1.39 3.60 1.26 3.80 1.12 4.00 1.02 4.20 0.94 4.40 0.90 4.50 0.89 4.60 0.88 4.70 0.86 4.80 0.86 4.90 0.86 5.00 0.85 5.10 0.86 5.20 0.87 5.40 0.93 5.60 0.95 5.80 0.97 6.00 0.94 6.20 0.89 6.40 0.85 6.60 0.80 6.80 0.75 7.00 0.74 7.20 0.71 7.40 0.69 7.60 0.66 7.80 0.67 8.00 0.68 8.20 0.71 8.50 0.74 9.0 0.83 9.50 0.92 10.00 0.98 10.50 1.01

42.00 29.76 26.36 25.37 20.62 17.12 14.28 8.97 7.06 5.95 5.03 4.60 4.43 4.31 4.28 4.30 4.32 4.37 4.36 4.41 4.46 4.36 4.06 3.71 3.40 3.24 3.12 2.95 2.76 2.58 2.42 2.35 2.28 2.21 2.13 2.07 2.01 1.94 1.87 1.80 1.74 1.74 1.73 1.69 1.66 1.59 1.51 1.45 1.39 1.33 1.23 1.15 1.07 1.00 0.92 0.81 0.74 0.73 0.72

R(φ = 0) 0.962 0.955 0.936 0.53 0.954 0.951 0.943 0.862 0.788 0.736 0.680 0.650 0.639 0.631 0.629 0.631 0.632 0.639 0.644 0.656 0.677 0.698 0.703 0.695 0.670 0.657 0.661 0.660 0.651 0.639 0.620 0.607 0.598 0.586 0.572 0.557 0.542 0.523 0.503 0.466 0.443 0.437 0.444 0.446 0.447 0.444 0.439 0.425 0.414 0.404 0.378 0.347 0.315 0.278 0.235 0.170 0.132 0.120 0.112

Energy (eV) 11.00 11.50 12.00 12.50 13.00 13.50 14.00 14.50 15.00 15.50 16.00 16.50 17.00 17.50 18.00 18.50 19.00 20.00 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 29.0 30.0

n 1.05 1.09 1.13 1.15 1.15 1.12 1.09 1.03 1.00 0.96 0.92 0.31 0.90 0.88 0.87 0.84 0.82 0.77 0.76 0.74 0.72 0.71 0.70 0.69 0.68 0.68 0.67 0.68 0.68 0.70 0.71 0.72 0.73 0.75 0.77 0.78

Cobalt, single crystal, 0.10 6.71 0.15 4.66 0.20 3.55 0.25 3.98 0.30 4.04 0.40 4.24 0.50 4.41 0.60 4.91 0.70 5.24 0.80 5.17 0.90 4.94 1.00 4.46 1.10 4.07 1.20 3.81 1.30 3.60 1.40 3.37 1.50 3.10 1.60 2.84 1.70 2.66 1.80 2.45 1.90 2.31 2.00 2.21 2.10 2.13

0.69 0.69 0.70 0.73 0.77 0.80 0.82 0.82 0.82 0.80 0.77 0.75 0.73 0.72 0.70 0.69 0.68 0.64 0.63 0.58 0.55 0.52 0.50 0.48 0.45 0.43 0.39 0.36 0.33 0.31 0.28 0.26 0.25 0.23 0.22 0.21

R(φ = 0) 0.103 0.100 0.101 0.108 0.119 0.128 0.135 0.142 0.143 0.141 0.139 0.134 0.132 0.130 0.129 0.130 0.131 0.130 0.129 0.121 0.116 0.112 0.109 0.105 0.101 0.096 0.089 0.080 0.072 0.063 0.055 0.048 0.043 0.037 0.032 0.030

→

∥ ĉ5 37.87 25.47 18.78 14.59 12.16 9.13 7.19 6.13 5.85 5.89 5.95 5.86 5.61 5.36 5.20 5.09 4.96 4.77 4.57 4.41 4.18 4.00 3.85

0.982 0.973 0.962 0.933 0.907 0.847 0.782 0.729 0.713 0.716 0.720 0.722 0.715 0.706 0.701 0.701 0.701 0.697 0.690 0.687 0.675 0.664 0.654

Energy (eV) 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.00 7.40 7.60 7.80 8.00

n 2.07 2.01 1.95 1.88 1.81 1.73 1.66 1.61 1.55 1.46 1.38 1.31 1.28 1.26 1.25 1.24 1.24 1.23 1.22 1.21 1.19 1.16 1.10 1.03 0.97 0.94 0.91 0.91 0.91 0.91 0.92 0.93 0.94 0.95

Cobalt, single crystal, 0.10 5.83 0.15 4.24 0.20 3.87 0.30 4.34 0.40 4.66 0.50 5.17 0.60 5.77 0.70 6.15 0.80 6.08 0.90 5.57 1.00 4.83 1.10 4.31 1.20 4.02 1.30 3.78 1.40 3.55 1.50 3.26 1.60 3.03 1.70 2.83 1.80 2.61 1.90 2.41 2.00 2.25 2.10 2.13 2.20 2.04 2.30 1.99 2.40 1.95

3.70 3.59 3.49 3.40 3.32 3.24 3.13 3.05 2.96 2.80 2.64 2.48 2.33 2.20 2.10 2.01 1.94 1.88 1.83 1.79 1.77 1.75 1.73 1.68 1.62 1.53 1.46 1.38 1.32 1.26 1.21 1.17 1.13 1.09

R(φ = 0) 0.642 0.634 0.627 0.622 0.618 0.615 0.607 0.600 0.594 0.579 0.563 0.544 0.519 0.495 0.471 0.452 0.435 0.423 0.411 0.403 0.399 0.400 0.406 0.407 0.401 0.386 0.368 0.345 0.326 0.305 0.286 0.269 0.253 0.239

→

⊥ ĉ5 32.36 21.37 15.53 10.01 7.39 5.75 5.17 5.20 5.61 5.93 5.94 5.60 5.34 5.16 5.05 4.93 4.74 4.60 4.45 4.27 4.09 3.89 3.72 3.56 3.44

0.979 0.965 0.042 0.865 0.785 0.709 0.682 0.685 0.702 0.715 0.721 0.711 0.701 0.694 0.692 0.692 0.687 0.684 0.683 0.677 0.670 0.659 0.646 0.632 0.620

Optical Properties of Selected Elements Energy (eV) 2.50 2.60 2.70 2.80 2.90 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80

n 1.90 1.86 1.79 1.72 1.66 1.60 1.50 1.42 1.36 1.33 1.31 1.28 1.27 1.26 1.25 1.24 1.22 1.21 1.17 1.11 1.04 0.98 0.94 0.92 0.91 0.91 0.91 0.92 0.93 0.94

3.34 3.26 3.19 3.11 3.03 2.94 2.78 2.62 2.47 2.33 2.21 2.12 2.03 1.95 1.90 1.84 1.80 1.78 1.76 1.74 1.69 1.62 1.54 1.46 1.38 1.32 1.26 1.21 1.17 1.13

Copper6 0.10 0.50 1.00 1.50 1.70 1.75 1.80 1.85 1.90 2.00 2.10 2.20 2.30 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40

29.69 1.71 0.44 0.26 0.22 0.21 0.21 0.22 0.21 0.27 0.47 0.83 1.04 1.12 1.15 1.17 1.18 1.23 1.27 1.31 1.34 1.34 1.42 1.49 1.52 1.53 1.47 1.38 1.28

71.57 17.63 8.48 5.26 4.43 4.25 4.04 3.85 3.67 3.24 2.81 2.60 2.59 2.60 2.50 2.36 2.21 2.07 1.95 1.87 1.81 1.72 1.64 1.64 1.67 1.71 1.78 1.80 1.78

R(φ = 0) 0.611 0.605 0.602 0.596 0.591 0.586 0.571 0.553 0.533 0.511 0.488 0.471 0.452 0.435 0.423 0.411 0.403 0.399 0.400 0.406 0.407 0.401 0.386 0.368 0.345 0.326 0.305 0.285 0.269 0.253 0.980 0.979 0.976 0.965 0.958 0.956 0.952 0.947 0.943 0.910 0.814 0.673 0.618 0.602 0.577 0.545 0.509 0.468 0.434 0.407 0.387 0.364 0.336 0.329 0.334 0.345 0.366 0.380 0.389

Energy (eV) 5.60 5.80 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 11.00 12.00 13.00 14.00 14.50 15.00 15.50 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00 41.00 42.00 43.00 44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00 56.00 57.00

12-123 n 1.18 1.10 1.04 0.96 0.97 1.00 1.03 1.03 1.03 1.03 1.04 1.07 1.09 1.08 1.06 1.03 1.01 0.98 0.95 0.91 0.89 0.88 0.88 0.90 0.92 0.94 0.96 0.96 0.92 0.88 0.86 0.85 0.86 0.88 0.89 0.90 0.91 0.92 0.92 0.92 0.93 0.93 0.93 0.94 0.94 0.94 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.96 0.96 0.96 0.96 0.96

1.74 1.67 1.59 1.37 1.20 1.09 1.03 0.98 0.92 0.87 0.82 0.75 0.73 0.72 0.72 0.72 0.71 0.69 0.67 0.62 0.56 0.51 0.45 0.41 0.38 0.37 0.37 0.40 0.40 0.38 0.35 0.30 0.26 0.24 0.22 0.21 0.20 0.20 0.19 0.19 0.18 0.17 0.17 0.16 0.16 0.15 0.15 0.15 0.15 0.14 0.14 0.14 0.13 0.13 0.13 0.12 0.12 0.12 0.11 0.11

R(φ = 0) 0.391 0.389 0.380 0.329 0.271 0.230 0.206 0.189 0.171 0.154 0.139 0.118 0.111 0.109 0.111 0.111 0.111 0.109 0.106 0.097 0.084 0.071 0.059 0.048 0.040 0.035 0.035 0.040 0.044 0.043 0.039 0.032 0.025 0.020 0.017 0.015 0.014 0.013 0.012 0.011 0.010 0.009 0.009 0.008 0.007 0.007 0.007 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004

Energy (eV) 58.00 59.00 60.00 61.00 62.00 63.00 64.00 65.00 66.00 67.00 68.00 69.00 70.00 75.00 80.00 85.00 90.00

n 0.96 0.97 0.97 0.97 0.97 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.98 0.98 0.97 0.96

0.11 0.11 0.11 0.11 0.11 0.10 0.10 0.10 0.10 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.08

Gallium (liquid)7 1.425 2.40 1.550 2.09 1.771 1.65 2.066 1.25 2.480 0.89 3.100 0.59

9.20 8.50 7.60 6.60 5.60 4.50

Germanium, single crystal8 0.01240 (4.0065) 3.00E-03 0.01364 4.0063 2.40E-03 0.01488 (4.0060) 1.70E-03 0.01612 (4.0060) 1.55E-03 0.01736 (4.0060) 1.50E-03 0.01860 1.50E-03 0.01984 1.60E-03 0.02108 1.60E-03 0.02232 1.55E-03 0.02356 1.53E-03 0.02480 1.50E-03 0.02604 1.25E-03 0.02728 8.50E-04 0.02852 6.50E-04 0.02976 7.00E-04 0.03100 3.9827 8.50E-04 0.03224 1.55E-03 0.03348 2.75E-03 0.03472 3.55E-03 0.03596 (3.9900) 3.05E-03 0.03720 2.75E-03 0.03844 2.70E-03 0.03968 (3.9930) 2.90E-03 0.04092 2.95E-03 0.04215 3.20E-03 0.04339 6.30E-03 0.04463 3.40E-03 0.04587 (3.9955) 2.50E-03 0.04711 2.10E-03 0.04835 2.00E-03 0.04959 8.00E-04 0.05083 1.40E-03 0.05207 1.35E-03 0.05331 1.10E-03 0.05455 8.00E-04

R(φ = 0) 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.900 0.898 0.898 0.897 0.898 0.896 0.361 0.361 0.361 0.361 0.361

0.358

0.359

0.360

Optical Properties of Selected Elements

12-124 Energy (eV) 0.05579 0.05703 0.05827 0.05951 0.06075 0.06199 0.06323 0.06447 0.06571 0.06695 0.06819 0.06943 0.07067 0.07191 0.07315 0.07439 0.07514 0.07749 0.07999 0.08266 0.08551 0.08920 0.09460 0.09840 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6

3.9992

(4.0000)

4.0009 4.0011 4.0013 4.0015

4.0063 4.0108 4.0246 4.0429 (4.074) (4.104) 4.180 4.275 4.285 4.325 4.385 4.420 4.495 4.560 4.635 4.763 4.897 5.067 5.380 5.588 5.748 5.283 5.062 4.610 4.340 4.180 4.082 4.035 4.037 4.082 4.141 4.157 4.128 4.070 4.020 3.985

k 6.00E-04 9.0 E-04 6.5 E-04 4.6 E-04 4.0 E-04 3.98E-04 4.0 E-04 4.3 E-04 4.4 E-04 4.3 E-04 3.1 E-04 3.3 E-04 3.8 E-04 3.3 E-04 2.5 E-04 1.9 E-04 1.58E-04 9.55E-05 1.71E-04 9.78E-05 5.77E-05 3.98E-05 4.59E-05 3.51E-05 3.70E-05

6.58E-07 1.27E-04 5.67E-03 7.45E-02 8.09E-02 0.103 0.123 0.167 0.190 0.298 0.345 0.401 0.500 0.540 0.933 1.634 2.049 2.318 2.455 2.384 2.309 2.240 2.181 2.140 2.145 2.215 2.340 2.469 2.579 2.667 2.759

R(φ = 0)

0.360

0.360 0.360 0.360 0.360

0.361 0.361 0.362 0.364 0.367 0.370 0.377 0.385 0.386 0.390 0.395 0.398 0.405 0.411 0.418 0.428 0.439 0.453 0.475 0.495 0.523 0.516 0.519 0.508 0.492 0.480 0.471 0.464 0.461 0.463 0.471 0.482 0.490 0.497 0.502 0.509

Energy (eV) 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0

n 3.958 3.936 3.920 3.905 3.869 3.745 3.338 2.516 1.953 1.720 1.586 1.498 1.435 1.394 1.370 1.364 1.371 1.383 1.380 1.360 1.293 1.209 1.108 1.30 1.10 1.00 0.92 0.92 0.92 0.93

k 2.863 2.986 3.137 3.336 3.614 4.009 4.507 4.669 4.297 3.960 3.709 3.509 3.342 3.197 3.073 2.973 2.897 2.854 2.842 2.846 2.163 2.873 2.813 2.34 2.05 1.80 1.60 1.40 1.20 1.14 1.00 0.86 0.237 0.179 0.144 0.110 0.0747 0.1020 0.0999 0.0856 0.0740 0.0651 0.0604

Gold, electropolished, Au (110)9 0.10 8.17 82.83 0.20 2.13 41.73 0.30 0.99 27.82 0.40 0.59 20.83 0.50 0.39 16.61 0.60 0.28 13.78 0.70 0.22 11.75 0.80 0.18 10.21 0.90 0.15 9.01 1.00 0.13 8.03 1.20 0.10 6.54 1.40 0.08 5.44 1.60 0.08 4.56 1.80 0.09 3.82 2.00 0.13 3.16 2.10 0.18 2.84

R(φ = 0) 0.517 0.527 0.539 0.556 0.579 0.612 0.659 0.705 0.713 0.702 0.690 0.677 0.664 0.650 0.636 0.622 0.609 0.600 0.598 0.602 0.479 0.632 0.641 0.517 0.489 0.448 0.348 0.282 0.262 0.167

0.995 0.995 0.995 0.995 0.994 0.994 0.994 0.993 0.993 0.992 0.991 0.989 0.986 0.979 0.953 0.925

Energy (eV) 2.20 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40

n 0.24 0.50 0.82 1.24 1.43 1.46 1.50 1.54 1.54 1.54 1.55 1.56 1.58 1.62 1.64 1.63 1.59 1.55 1.51 1.48 1.45 1.41 1.35 1.30 1.27 1.25 1.23 1.22 1.21 1.21 1.21 1.21 1.22 1.24 1.25 1.27 1.30 1.34 1.36 1.38 1.38 1.35 1.31 1.30 1.30 1.31 1.31 1.30 1.31 1.33 1.36 1.37 1.37 1.36 1.35 1.34 1.34 1.34 1.34 1.35

2.54 1.86 1.59 1.54 1.72 1.77 1.79 1.80 1.81 1.80 1.78 1.76 1.73 1.73 1.75 1.79 1.81 1.81 1.79 1.78 1.77 1.76 1.74 1.69 1.64 1.59 1.54 1.49 1.40 1.33 1.27 1.20 1.14 1.09 1.05 1.01 0.97 0.95 0.95 0.96 0.98 0.99 0.96 0.92 0.89 0.88 0.86 0.83 0.81 0.78 0.78 0.79 0.80 0.80 0.80 0.79 0.77 0.76 0.74 0.73

R(φ = 0) 0.880 0.647 0.438 0.331 0.356 0.368 0.368 0.369 0.371 0.368 0.362 0.356 0.349 0.346 0.351 0.360 0.366 0.369 0.368 0.367 0.368 0.370 0.370 0.364 0.354 0.344 0.332 0.319 0.295 0.275 0.256 0.236 0.218 0.203 0.190 0.177 0.167 0.162 0.161 0.164 0.169 0.171 0.165 0.155 0.147 0.144 0.140 0.133 0.126 0.122 0.121 0.124 0.126 0.127 0.125 0.123 0.120 0.116 0.113 0.111

Optical Properties of Selected Elements Energy (eV) 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.20 17.60 18.00 18.40 18.80 19.20 19.60 20.00 20.40 20.80 21.20 21.60 22.00 22.40 22.80 23.20 23.60 24.00 24.40 24.80 25.20 25.60 26.00 26.40 26.80 27.20 27.60 28.00 28.40 28.80 29.20 29.60 30.00

n 1.36 1.38 1.39 1.44 1.45 1.42 1.37 1.33 1.29 1.26 1.24 1.22 1.21 1.20 1.19 1.19 1.19 1.19 1.19 1.20 1.21 1.21 1.18 1.14 1.10 1.05 1.00 0.94 0.89 0.85 0.82 0.80 0.80 0.80 0.80 0.82 0.83 0.84 0.85 0.85 0.86 0.86 0.87 0.88 0.88 0.88 0.87 0.86

0.72 0.71 0.71 0.73 0.79 0.84 0.86 0.86 0.86 0.84 0.83 0.81 0.79 0.78 0.76 0.75 0.74 0.74 0.73 0.74 0.76 0.80 0.83 0.85 0.87 0.88 0.88 0.86 0.83 0.79 0.75 0.70 0.66 0.62 0.58 0.56 0.54 0.52 0.51 0.50 0.49 0.49 0.48 0.48 0.48 0.48 0.48 0.48

R(φ = 0) 0.109 0.108 0.109 0.115 0.127 0.137 0.140 0.140 0.139 0.135 0.132 0.127 0.123 0.119 0.116 0.114 0.111 0.109 0.109 0.110 0.116 0.125 0.133 0.141 0.149 0.156 0.162 0.164 0.163 0.157 0.149 0.138 0.125 0.113 0.101 0.090 0.084 0.079 0.074 0.071 0.068 0.065 0.063 0.062 0.062 0.062 0.064 0.064

→

Hafnium, single crystal, E ∥ ĉ10 0.52 1.48 4.11 0.56 1.84 3.29 0.60 2.34 2.62 0.66 3.21 2.13 0.70 3.70 2.03 0.76 4.31 2.10 0.80 4.61 2.31 0.86 4.71 2.70 0.90 4.64 2.85 0.95 4.54 2.96 1.00 4.45 3.00

0.747 0.615 0.486 0.428 0.441 0.476 0.504 0.533 0.541 0.545 0.545

Energy (eV) 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00

12-125 n 4.28 4.08 3.87 3.72 3.60 3.52 3.52 3.57 3.63 3.65 3.64 3.53 3.34 3.15 2.99 2.83 2.68 2.54 2.40 2.27 2.14 2.00 1.87 1.78 1.71 1.66 1.63 1.60 1.56 1.52 1.48 1.45 1.43 1.41 1.39 1.39 1.39 1.38 1.38 1.37 1.36 1.35 1.35 1.32 1.28 1.26 1.26 1.27 1.28 1.31 1.33 1.34 1.36 1.37 1.40 1.43 1.45 1.47 1.48 1.49

3.08 3.10 3.04 2.95 2.85 2.73 2.61 2.56 2.59 2.67 2.81 2.99 3.09 3.11 3.13 3.12 3.10 3.08 3.04 3.00 2.95 2.89 2.79 2.68 2.58 2.48 2.40 2.33 2.27 2.21 2.14 2.07 2.01 1.95 1.89 1.83 1.79 1.75 1.71 1.68 1.61 1.55 1.51 1.48 1.41 1.35 1.28 1.22 1.16 1.13 1.10 1.07 1.05 1.02 1.01 1.01 1.01 1.02 1.04 1.07

R(φ = 0) 0.547 0.544 0.536 0.525 0.514 0.500 0.488 0.485 0.489 0.498 0.511 0.526 0.534 0.537 0.540 0.542 0.542 0.543 0.544 0.544 0.544 0.544 0.538 0.528 0.517 0.503 0.491 0.481 0.473 0.466 0.455 0.442 0.431 0.420 0.407 0.394 0.382 0.373 0.364 0.356 0.341 0.324 0.314 0.308 0.295 0.278 0.258 0.240 0.224 0.212 0.204 0.197 0.191 0.183 0.179 0.178 0.180 0.183 0.186 0.193

Energy (eV) 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.20 17.60 18.00 18.40 18.80 19.00 19.60 20.00 20.60 21.00 21.60 22.00 22.60 23.00 23.60 24.00 24.60

n 1.50 1.48 1.46 1.41 1.36 1.32 1.28 1.24 1.20 1.16 1.13 1.10 1.07 1.04 1.02 0.96 0.92 0.88 0.84 0.83 0.83 0.81 0.79 0.79 0.83 0.81 0.79 0.79 0.80 0.81 0.84 0.87 0.89 0.93 0.94 0.97 0.99 1.01 1.03 1.06 1.07 1.09 1.09 1.10

1.10 1.14 1.18 1.21 1.22 1.22 1.22 1.21 1.20 1.19 1.17 1.16 1.14 1.12 1.10 1.06 1.01 0.96 0.90 0.83 0.80 0.76 0.70 0.64 0.60 0.60 0.55 0.50 0.46 0.42 0.38 0.34 0.33 0.32 0.31 0.30 0.29 0.28 0.28 0.28 0.28 0.29 0.30 0.31

R(φ = 0) 0.201 0.211 0.222 0.230 0.235 0.238 0.240 0.241 0.242 0.242 0.241 0.241 0.239 0.238 0.236 0.232 0.225 0.218 0.205 0.186 0.172 0.167 0.153 0.132 0.111 0.114 0.105 0.089 0.077 0.064 0.051 0.040 0.036 0.030 0.027 0.023 0.022 0.020 0.020 0.020 0.021 0.022 0.023 0.024

→

Hafnium, single crystal, E ⊥ ĉ10 0.52 2.25 4.65 0.56 2.34 3.66 0.60 2.84 2.89 0.66 3.71 2.35 0.70 4.26 2.21 0.76 4.97 2.33 0.80 5.41 2.62 0.86 5.46 3.36 0.90 5.22 3.62 0.95 4.95 3.72 1.00 4.76 3.76 1.10 4.43 3.80 1.20 4.07 3.74 1.30 3.79 3.55 1.40 3.61 3.36

0.723 0.623 0.512 0.469 0.482 0.521 0.554 0.593 0.601 0.602 0.602 0.601 0.594 0.578 0.561

Optical Properties of Selected Elements

12-126 Energy (eV) 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80

n 3.55 3.58 3.63 3.66 3.63 3.51 3.35 3.18 2.99 2.78 2.65 2.54 2.42 2.31 2.20 2.08 1.94 1.83 1.74 1.68 1.62 1.57 1.53 1.49 1.45 1.41 1.38 1.35 1.33 1.31 1.30 1.29 1.28 1.28 1.27 1.27 1.27 1.27 1.26 1.24 1.21 1.19 1.18 1.19 1.21 1.22 1.23 1.26 1.28 1.30 1.33 1.35 1.38 1.40 1.42 1.43 1.45 1.43 1.40 1.37

3.13 3.01 2.98 3.02 3.14 3.26 3.33 3.36 3.39 3.35 3.26 3.22 3.17 3.13 3.08 3.05 2.98 2.88 2.78 2.69 2.61 2.52 2.45 2.38 2.32 2.25 2.18 2.11 2.05 1.99 1.93 1.88 1.82 1.77 1.73 1.69 1.62 1.57 1.52 1.48 1.42 1.36 1.29 1.22 1.18 1.14 1.10 1.06 1.04 1.02 1.00 0.99 0.99 1.00 1.02 1.04 1.08 1.12 1.16 1.19

R(φ = 0) 0.540 0.529 0.526 0.530 0.541 0.551 0.558 0.563 0.568 0.569 0.562 0.560 0.559 0.558 0.558 0.561 0.560 0.555 0.547 0.538 0.529 0.519 0.510 0.501 0.493 0.484 0.474 0.462 0.451 0.438 0.427 0.415 0.402 0.389 0.379 0.367 0.349 0.335 0.322 0.313 0.302 0.285 0.265 0.244 0.230 0.217 0.206 0.194 0.187 0.180 0.174 0.173 0.173 0.174 0.178 0.184 0.193 0.204 0.214 0.223

Energy (eV) 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.20 17.60 18.00 18.40 18.80 19.00 19.60 20.00 20.60 21.00 21.60 22.00 22.60 23.00 23.60 24.00 24.60

n 1.32 1.27 1.23 1.19 1.15 1.12 1.08 1.05 1.03 1.00 0.97 0.92 0.88 0.83 0.80 0.79 0.80 0.77 0.76 0.76 0.81 0.78 0.77 0.77 0.79 0.80 0.82 0.86 0.88 0.91 0.93 0.96 0.97 1.00 1.01 1.03 1.05 1.06 1.07 1.09

1.21 1.21 1.20 1.20 1.19 1.17 1.16 1.14 1.12 1.10 1.08 1.04 0.99 0.94 0.88 0.81 0.77 0.73 0.68 0.61 0.58 0.57 0.53 0.48 0.44 0.39 0.36 0.33 0.32 0.31 0.30 0.29 0.29 0.28 0.28 0.27 0.28 0.28 0.29 0.30

Iridium11 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50

28.49 15.32 9.69 6.86 5.16 4.11 3.42 3.05 2.98 2.79 2.93 3.14 3.19 3.15 3.04 2.96 2.85 2.72 2.65

60.62 45.15 35.34 28.84 24.25 20.79 18.06 15.82 14.06 11.58 9.78 8.61 7.88 7.31 6.84 6.41 6.07 5.74 5.39

R(φ = 0) 0.230 0.234 0.235 0.237 0.237 0.237 0.237 0.236 0.235 0.233 0.231 0.226 0.219 0.211 0.196 0.177 0.160 0.154 0.140 0.119 0.099 0.102 0.092 0.077 0.065 0.053 0.041 0.032 0.030 0.025 0.023 0.021 0.020 0.019 0.019 0.018 0.019 0.020 0.021 0.022 0.975 0.973 0.972 0.969 0.967 0.964 0.960 0.954 0.944 0.925 0.895 0.862 0.840 0.822 0.808 0.791 0.779 0.767 0.750

Energy (eV) 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00

n 2.68 2.69 2.64 2.57 2.50 2.40 2.29 2.18 2.07 1.98 1.91 1.85 1.81 1.77 1.73 1.62 1.53 1.52 1.61 1.64 1.58 1.45 1.31 1.18 1.10 1.04 1.00 0.98 0.96 0.95 0.94 0.94 0.94 0.95 0.97 0.99 1.02 1.03 1.08 1.13 1.18 1.22 1.26 1.29 1.33 1.36 1.39 1.42 1.44 1.45 1.45 1.44 1.43 1.41 1.38 1.34 1.31 1.28 1.25 1.24

5.08 4.92 4.81 4.68 4.57 4.48 4.38 4.26 4.14 4.00 3.86 3.73 3.61 3.51 3.43 3.26 3.05 2.81 2.69 2.68 2.71 2.68 2.60 2.49 2.35 2.22 2.09 1.98 1.86 1.78 1.68 1.59 1.50 1.42 1.34 1.27 1.20 1.14 1.06 1.03 1.00 0.98 0.96 0.95 0.94 0.95 0.95 0.97 0.99 1.01 1.04 1.07 1.09 1.12 1.13 1.14 1.13 1.12 1.10 1.08

R(φ = 0) 0.728 0.716 0.710 0.704 0.699 0.697 0.695 0.692 0.689 0.682 0.673 0.665 0.655 0.646 0.640 0.629 0.610 0.573 0.541 0.535 0.549 0.561 0.567 0.570 0.559 0.543 0.522 0.499 0.474 0.454 0.427 0.401 0.375 0.345 0.318 0.290 0.262 0.241 0.208 0.191 0.179 0.171 0.164 0.160 0.157 0.159 0.161 0.163 0.169 0.175 0.182 0.187 0.193 0.200 0.206 0.208 0.208 0.206 0.203 0.199

Optical Properties of Selected Elements Energy (eV) 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.20 17.60 18.00 18.40 18.80 19.20 19.60 20.00 20.50 21.00 21.50 22.00 22.50 23.00 23.50 24.00 24.50 25.00 25.50 26.00 26.50 27.00 27.50 28.00 28.50 29.00 29.50 30.00 32.00 34.00 36.00 38.00 40.00

n 1.21 1.19 1.18 1.17 1.16 1.17 1.18 1.19 1.20 1.21 1.23 1.25 1.28 1.30 1.30 1.27 1.24 1.20 1.15 1.10 1.04 0.99 0.94 0.89 0.84 0.79 0.76 0.73 0.70 0.69 0.68 0.67 0.67 0.66 0.66 0.66 0.66 0.65 0.64 0.64 0.62 0.64 0.69 0.73 0.76

1.05 1.01 0.98 0.95 0.91 0.88 0.87 0.84 0.83 0.83 0.82 0.82 0.83 0.87 0.93 0.97 1.00 1.03 1.05 1.06 1.05 1.04 1.02 1.00 0.99 0.96 0.92 0.87 0.83 0.79 0.76 0.72 0.69 0.66 0.63 0.61 0.59 0.57 0.55 0.53 0.44 0.35 0.27 0.24 0.22

Iron5 0.10 0.15 0.20 0.26 0.30 0.36 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

6.41 6.26 3.68 4.98 4.87 4.68 4.42 4.14 3.93 3.78 3.65 3.52 3.43 3.33

33.07 22.82 18.23 13.68 12.05 10.44 9.75 8.02 6.95 6.17 5.60 5.16 4.79 4.52

R(φ = 0) 0.191 0.181 0.173 0.165 0.155 0.147 0.142 0.136 0.133 0.131 0.129 0.127 0.131 0.140 0.154 0.166 0.176 0.187 0.197 0.205 0.210 0.215 0.220 0.222 0.228 0.232 0.228 0.223 0.218 0.209 0.200 0.192 0.181 0.174 0.166 0.158 0.151 0.148 0.145 0.140 0.119 0.091 0.059 0.044 0.034 0.978 0.956 0.958 0.911 0.892 0.867 0.858 0.817 0.783 0.752 0.725 0.700 0.678 0.660

Energy (eV) 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.83 4.00 4.17 4.33 4.50 4.67 4.83 5.00 5.17 5.33 5.50 5.67 5.83 6.00 6.17 6.33 6.50 6.67 6.83 7.00 7.17 7.33 7.50 7.67 7.83 8.00 8.17 8.33 8.50 8.67 8.83 9.00 9.17 9.33

12-127 n 3.24 3.16 3.12 3.05 3.00 2.98 2.92 2.89 2.85 2.80 2.74 2.65 2.56 2.46 2.34 2.23 2.12 2.01 1.88 1.78 1.70 1.62 1.55 1.50 1.47 1.43 1.38 1.30 1.26 1.23 1.20 1.16 1.14 1.14 1.12 1.11 1.09 1.09 1.10 1.09 1.08 1.04 1.02 1.00 0.97 0.96 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.92 0.93 0.92 0.91

4.26 4.07 3.87 3.77 3.60 3.52 3.46 3.37 3.36 3.34 3.33 3.34 3.31 3.31 3.30 3.25 3.23 3.17 3.12 3.04 2.96 2.87 2.79 2.70 2.63 2.56 2.49 2.39 2.27 2.18 2.10 2.02 1.93 1.87 1.81 1.75 1.17 1.65 1.61 1.59 1.57 1.55 1.51 1.47 1.43 1.39 1.35 1.30 1.26 1.23 1.21 1.18 1.16 1.14 1.12 1.10 1.08 1.07 1.06 1.04

R(φ = 0) 0.641 0.626 0.609 0.601 0.585 0.577 0.573 0.563 0.563 0.562 0.563 0.567 0.567 0.570 0.576 0.575 0.580 0.580 0.583 0.580 0.576 0.572 0.565 0.556 0.548 0.542 0.534 0.527 0.510 0.494 0.482 0.470 0.451 0.435 0.425 0.408 0.401 0.383 0.373 0.366 0.365 0.365 0.358 0.351 0.346 0.333 0.327 0.311 0.298 0.288 0.279 0.272 0.265 0.258 0.251 0.246 0.240 0.236 0.233 0.231

Energy (eV) 9.50 9.67 9.83 10.00 10.17 10.33 10.50 10.67 10.83 11.00 11.17 11.33 11.50 11.67 11.83 12.00 12.17 12.33 12.50 12.67 12.83 13.00 13.17 13.33 13.50 13.67 13.83 14.00 14.17 14.33 14.50 14.67 14.83 15.00 15.17 15.33 15.50 15.67 15.83 16.00 16.17 16.33 16.50 16.67 16.83 17.00 17.17 17.33 17.50 17.67 17.83 18.00 18.17 18.33 18.50 18.67 18.83 19.00 19.17 19.33

n 0.90 0.90 0.89 0.88 0.87 0.87 0.87 0.88 0.89 0.91 0.92 0.93 0.93 0.93 0.92 0.91 0.90 0.89 0.98 0.87 0.86 0.85 0.84 0.84 0.83 0.82 0.81 0.81 0.80 0.80 0.79 0.79 0.78 0.78 0.78 0.78 0.77 0.77 0.77 0.77 0.78 0.78 0.78 0.77 0.78 0.78 0.78 0.78 0.77 0.77 0.78 0.78 0.78 0.78 0.77 0.77 0.77 0.77 0.76 0.76

1.02 1.00 0.99 0.97 0.94 0.91 0.89 0.87 0.85 0.83 0.83 0.84 0.84 0.84 0.84 0.84 0.84 0.83 0.83 0.82 0.81 0.80 0.79 0.78 0.77 0.76 0.75 0.73 0.72 0.71 0.79 0.69 0.67 0.66 0.65 0.64 0.63 0.62 0.61 0.60 0.58 0.58 0.57 0.56 0.55 0.55 0.54 0.54 0.53 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48

R(φ = 0) 0.226 0.221 0.218 0.213 0.203 0.196 0.189 0.179 0.170 0.162 0.159 0.159 0.160 0.162 0.163 0.163 0.165 0.164 0.165 0.166 0.166 0.162 0.161 0.160 0.159 0.157 0.154 0.151 0.149 0.146 0.144 0.141 0.138 0.135 0.131 0.238 0.126 0.123 0.119 0.116 0.112 0.110 0.107 0.106 0.103 0.102 0.100 0.098 0.097 0.095 0.092 0.091 0.090 0.089 0.089 0.088 0.087 0.087 0.088 0.087

Optical Properties of Selected Elements

12-128 Energy (eV) 19.50 19.67 19.83 20.00 20.17 20.33 20.50 20.67 20.83 21.00 21.17 21.33 21.50 21.67 21.83 22.00 22.17 22.33 22.50 22.67 22.83 23.00 23.17 23.33 23.50 23.67 23.83 24.00 24.17 24.33 24.50 24.67 24.83 25.00 26.00 27.00 28.00 29.00 30.00

n 0.75 0.75 0.75 0.74 0.74 0.74 0.74 0.73 0.73 0.73 0.72 0.72 0.72 0.72 0.72 0.72 0.71 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.73 0.73 0.74 0.74 0.74 0.74 0.74 0.75 0.75 0.75 0.76 0.78 0.79 0.81 0.82

0.47 0.47 0.46 0.45 0.44 0.44 0.42 0.43 0.42 0.41 0.40 0.39 0.38 0.38 0.37 0.36 0.35 0.34 0.34 0.33 0.32 0.31 0.30 0.29 0.28 0.28 0.27 0.27 0.26 0.26 0.25 0.25 0.24 0.24 0.21 0.18 0.16 0.14 0.13

Lithium12 0.14 0.54 0.75 1.05 1.35 1.65 1.95 2.25 2.55 2.85 3.15 3.45 3.75 4.05 4.35 4.65 4.95 5.25 5.55 5.85

0.659 0.661 0.561 0.448 0.338 0.265 0.221 0.206 0.217 0.247 0.304 0.334 0.345 0.346 0.333 0.317 0.302 0.299 0.310 0.342

38.0 12.6 7.68 5.58 4.36 3.55 2.94 2.48 2.11 1.82 1.60 1.45 1.32 1.21 1.11 1.01 0.906 0.795 0.688 0.594

R(φ = 0) 0.086 0.085 0.084 0.083 0.081 0.081 0.080 0.079 0.078 0.077 0.076 0.074 0.073 0.071 0.070 0.068 0.067 0.064 0.063 0.062 0.059 0.058 0.056 0.054 0.050 0.049 0.047 0.045 0.044 0.043 0.042 0.040 0.039 0.038 0.031 0.026 0.021 0.017 0.014 0.998 0.984 0.963 0.946 0.935 0.925 0.913 0.892 0.854 0.797 0.715 0.656 0.611 0.578 0.557 0.540 0.520 0.484 0.434 0.365

Energy (eV) 6.15 6.45 6.75 7.05 7.35 7.65 7.95 8.25 8.55 8.85 9.15 9.45 9.75 10.1 10.4 10.6

n 0.376 0.408 0.440 0.466 0.492 0.517 0.545 0.572 0.601 0.624 0.657 0.680 0.708 0.726 0.743 0.753

k 0.522 0.460 0.407 0.364 0.320 0.282 0.246 0.214 0.189 0.163 0.144 0.130 0.119 0.108 0.102 0.080

R(φ = 0) 0.306 0.256 0.214 0.183 0.155 0.131 0.109 0.091 0.075 0.063 0.050 0.042 0.034 0.029 0.025 0.022

Magnesium (evaporated)13 2.145 0.48 3.71 2.270 0.57 3.47 2.522 0.53 2.92 2.845 0.52 2.65 3.064 0.52 2.05 5.167 0.10 1.60 5.636 0.15 1.50 6.200 0.20 1.40 6.889 0.25 1.30 7.750 0.20 1.20 8.857 0.15 0.95 10.335 0.25 0.40

0.880 0.843 0.805 0.777 0.681 0.894 0.832 0.765 0.693 0.722 0.730 0.419

Manganese14 0.64 3.89 0.77 3.78 0.89 3.65 1.02 3.48 1.14 3.30 1.26 3.10 1.39 2.97 1.51 2.83 1.64 2.70 1.76 2.62 1.88 2.56 2.01 2.51 2.13 2.47 2.26 2.39 2.38 2.32 2.50 2.25 2.63 2.19 2.75 2.11 2.88 2.06 3.00 2.00 3.12 1.96 3.25 1.92 3.37 1.89 3.50 1.89 3.62 1.87 3.74 1.86 3.87 1.86 3.99 1.86 4.12 1.86

0.738 0.710 0.688 0.673 0.662 0.653 0.643 0.634 0.627 0.617 0.606 0.596 0.585 0.577 0.567 0.559 0.552 0.545 0.536 0.528 0.518 0.509 0.498 0.484 0.475 0.463 0.451 0.438 0.427

5.95 5.41 5.02 4.74 4.53 4.35 4.18 4.03 3.91 3.78 3.65 3.54 3.43 3.33 3.23 3.14 3.06 2.98 2.90 2.82 2.74 2.67 2.59 2.51 2.45 2.38 2.32 2.25 2.19

Energy (eV) 4.24 4.36 4.49 4.61 4.74 4.86 4.98 5.11 5.23 5.36 5.48 5.60 5.73 5.85 5.98 6.10 6.22 6.35 6.47 6.60

n 1.85 1.85 1.86 1.85 1.84 1.83 1.82 1.82 1.81 1.78 1.74 1.73 1.72 1.70 1.67 1.63 1.62 1.59 1.55 1.48

Mercury (liquid)15 0.2 13.99 0.3 11.37 0.4 9.741 0.5 8.528 0.6 7.574 0.8 6.086 1.0 4.962 1.2 4.050 1.4 3.324 1.6 2.746 1.8 2.284 2.0 1.910 2.2 1.620 2.4 1.384 2.6 1.186 2.8 1.027 3.0 0.898 3.2 0.798 3.4 0.713 3.6 0.644 3.8 0.589 4.0 0.542 4.2 0.507 4.4 0.477 4.6 0.452 4.8 0.431 5.0 0.414 5.2 0.401 5.4 0.394 5.6 0.386 5.7 0.386 5.8 0.386 5.9 0.385 6.0 0.386 6.1 0.388 6.2 0.390 6.3 0.399 6.4 0.412 6.5 0.428

2.14 2.08 2.03 1.99 1.94 1.91 1.86 1.82 1.79 1.76 1.73 1.70 1.67 1.64 1.61 1.58 1.55 1.52 1.50 1.47

14.27 11.95 10.65 9.805 9.195 8.312 7.643 7.082 6.558 6.054 5.582 5.150 4.751 4.407 4.090 3.802 3.538 3.294 3.074 2.860 2.665 2.502 2.341 2.195 2.058 1.929 1.806 1.687 1.569 1.454 1.396 1.341 1.287 1.232 1.176 1.118 1.058 1.002 0.949

R(φ = 0) 0.417 0.406 0.395 0.388 0.378 0.372 0.362 0.354 0.348 0.342 0.337 0.331 0.325 0.319 0.313 0.307 0.301 0.295 0.292 0.288 0.869 0.846 0.830 0.818 0.808 0.796 0.789 0.786 0.785 0.783 0.782 0.782 0.780 0.779 0.779 0.779 0.777 0.773 0.770 0.763 0.755 0.749 0.738 0.727 0.715 0.701 0.685 0.666 0.642 0.617 0.601 0.585 0.569 0.551 0.531 0.510 0.481 0.450 0.418

Optical Properties of Selected Elements Energy (eV) 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5

n 0.436 0.438 0.459 0.510 0.585 0.663 0.717 0.769 0.817 0.860 0.893 0.929 0.946 0.952 0.953 0.956 0.965 0.975 0.988 1.009 1.044 1.061 1.062 1.054 1.045 1.041 1.039 1.039 1.050 1.064 1.078 1.092 1.104 1.115 1.125 1.135 1.146 1.159 1.170 1.177 1.184 1.191 1.195 1.200 1.208

k 0.898 0.836 0.756 0.676 0.617 0.589 0.584 0.575 0.574 0.580 0.597 0.623 0.639 0.645 0.638 0.624 0.607 0.588 0.568 0.548 0.541 0.557 0.567 0.569 0.561 0.550 0.537 0.523 0.491 0.467 0.445 0.430 0.416 0.404 0.394 0.383 0.374 0.368 0.367 0.367 0.366 0.367 0.367 0.366 0.364

R(φ = 0) 0.392 0.367 0.320 0.255 0.191 0.148 0.128 0.111 0.100 0.094 0.093 0.096 0.098 0.099 0.097 0.093 0.087 0.082 0.076 0.069 0.066 0.069 0.071 0.072 0.070 0.068 0.065 0.062 0.055 0.050 0.045 0.042 0.040 0.038 0.037 0.035 0.034 0.034 0.034 0.034 0.034 0.035 0.035 0.035 0.035

Molybdenum16 0.10 18.53 0.15 8.78 0.20 5.10 0.25 3.36 0.30 2.44 0.34 2.00 0.38 1.70 0.42 1.57 0.46 1.46 0.50 1.37 0.54 1.35 0.58 1.34 0.62 1.38 0.66 1.43

68.51 47.54 35.99 28.75 23.80 20.84 18.44 16.50 14.91 13.55 12.36 11.34 10.44 9.67

0.985 0.985 0.985 0.984 0.983 0.982 0.980 0.978 0.975 0.971 0.966 0.960 0.952 0.942

Energy (eV) 0.70 0.74 0.78 0.82 0.86 9.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60

12-129 n 1.48 1.51 1.60 1.64 1.70 1.74 1.94 2.15 2.44 2.77 3.15 3.53 3.77 3.84 3.81 3.74 3.68 3.68 3.76 3.79 3.59 3.36 3.22 3.13 3.08 3.05 3.04 3.03 3.05 3.06 3.06 3.06 3.05 3.04 3.04 3.04 3.01 2.77 2.39 2.06 1.75 1.46 1.22 1.07 0.96 0.89 0.85 0.81 0.79 0.78 0.78 0.80 0.81 0.81 0.75 0.71 0.69 0.67 0.66 0.65

8.99 8.38 7.83 7.35 6.89 6.48 5.58 4.85 4.22 3.74 3.40 3.30 3.41 3.51 3.58 3.58 3.52 3.45 3.41 3.61 3.78 3.73 3.61 3.51 3.42 3.33 3.27 3.21 3.18 3.18 3.19 3.21 3.23 3.27 3.31 3.40 3.51 3.77 3.88 3.84 3.76 3.62 3.42 3.20 2.99 2.80 2.64 2.50 2.36 2.24 2.13 2.04 1.98 1.95 1.90 1.81 1.73 1.65 1.57 1.49

R(φ = 0) 0.932 0.921 0.906 0.892 0.876 0.859 0.805 0.743 0.671 0.608 0.562 0.550 0.562 0.570 0.576 0.576 0.571 0.565 0.562 0.578 0.594 0.591 0.582 0.573 0.565 0.566 0.550 0.544 0.540 0.540 0.541 0.543 0.546 0.550 0.554 0.564 0.576 0.610 0.640 0.658 0.678 0.695 0.706 0.706 0.700 0.688 0.674 0.660 0.641 0.619 0.592 0.568 0.548 0.542 0.552 0.542 0.530 0.512 0.495 0.475

Energy (eV) 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.00 15.60 16.00 16.60 17.00 17.60 18.00 18.60 19.00 19.60 20.00 20.60 21.00 21.60 22.00 22.60 23.00 23.60 24.00 24.60 25.00 25.60 26.00 26.50 27.00 27.50 28.00 28.50 29.00 29.50 30.00 31.00 32.00 33.00 34.00 35.00

n 0.65 0.65 0.67 0.69 0.71 0.74 0.77 0.81 0.86 0.91 0.98 1.05 1.12 1.18 1.23 1.25 1.26 1.25 1.23 1.20 1.17 1.15 1.13 1.13 1.14 1.15 1.14 1.10 1.04 0.94 0.87 0.77 0.71 0.66 0.64 0.62 0.61 0.61 0.60 0.59 0.58 0.58 0.58 0.60 0.62 0.66 0.68 0.71 0.73 0.76 0.79 0.81 0.83 0.86 0.88 0.92 0.92 0.90 0.91 0.87

1.41 1.33 1.25 1.19 1.12 1.05 0.99 0.93 0.88 0.83 0.79 0.77 0.78 0.80 0.85 0.89 0.92 0.98 1.00 1.02 1.02 1.01 1.00 0.99 0.99 1.01 1.04 1.10 1.12 1.14 1.12 1.08 1.02 0.94 0.89 0.81 0.77 0.71 0.69 0.63 0.60 0.53 0.49 0.43 0.39 0.35 0.33 0.31 0.29 0.28 0.27 0.26 0.26 0.26 0.26 0.29 0.32 0.33 0.34 0.37

R(φ = 0) 0.450 0.420 0.385 0.355 0.320 0.285 0.250 0.217 0.188 0.162 0.138 0.125 0.123 0.125 0.135 0.145 0.154 0.168 0.178 0.185 0.187 0.185 0.182 0.179 0.179 0.184 0.194 0.216 0.233 0.257 0.270 0.283 0.284 0.275 0.264 0.245 0.234 0.215 0.207 0.195 0.185 0.166 0.151 0.124 0.106 0.085 0.072 0.060 0.050 0.041 0.036 0.031 0.028 0.025 0.023 0.024 0.030 0.032 0.034 0.043

Optical Properties of Selected Elements

12-130 Energy (eV) 36.00 37.00 38.00 39.00 40.00

n 0.82 0.81 0.81 0.82 0.83

0.34 0.30 0.27 0.25 0.23

Nickel17 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.20 6.40

9.54 5.45 4.12 4.25 4.19 4.03 3.84 4.03 3.84 3.59 3.38 3.18 3.06 2.97 2.85 2.74 2.65 2.53 2.43 2.28 2.14 2.02 1.92 1.85 1.80 1.75 1.71 1.67 1.65 1.64 1.63 1.62 1.61 1.61 1.61 1.61 1.62 1.63 1.64 1.66 1.69 1.72 1.73 1.74 1.71 1.63 1.53 1.40 1.27 1.16 1.09 1.04 1.00 1.01

45.82 30.56 22.48 17.68 15.05 13.05 11.43 9.64 8.35 7.48 6.82 6.23 5.74 5.38 5.10 4.85 4.63 4.47 4.31 4.18 4.01 3.82 3.65 3.48 3.33 3.19 3.06 2.93 2.81 2.71 2.61 2.52 2.44 2.36 2.30 2.23 2.17 2.11 2.07 2.02 1.99 1.98 1.98 2.01 2.06 2.09 2.11 2.10 2.04 1.94 1.83 1.73 1.54 1.46

R(φ = 0) 0.043 0.038 0.033 0.029 0.025 0.983 0.978 0.969 0.950 0.934 0.918 0.900 0.864 0.835 0.813 0.794 0.774 0.753 0.734 0.721 0.708 0.695 0.688 0.679 0.677 0.670 0.659 0.649 0.634 0.620 0.605 0.590 0.575 0.557 0.542 0.525 0.509 0.495 0.480 0.467 0.454 0.441 0.428 0.416 0.405 0.397 0.393 0.392 0.396 0.409 0.421 0.435 0.449 0.454 0.449 0.435 0.417 0.371 0.345

Energy (eV) 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 20.50 21.00 21.50 22.00 22.50 23.00 23.50 24.00 24.50

n 1.01 1.02 1.03 1.03 1.03 1.02 1.01 1.01 1.00 0.99 0.98 0.97 0.97 0.96 0.95 0.95 0.95 0.95 0.95 0.95 0.97 0.99 1.01 1.04 1.05 1.07 1.07 1.07 1.08 1.08 1.08 1.08 1.07 1.07 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.96 0.94 0.92 0.91 0.90 0.90 0.89 0.89 0.90 0.91 0.91 0.91 0.92 0.91 0.90 0.90

1.40 1.35 1.30 1.27 1.24 1.22 1.18 1.15 1.13 1.11 1.08 1.05 1.01 0.99 0.96 0.93 0.89 0.87 0.83 0.80 0.76 0.75 0.73 0.72 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.70 0.70 0.71 0.70 0.70 0.70 0.70 0.69 0.69 0.68 0.67 0.66 0.64 0.63 0.61 0.58 0.56 0.54 0.51 0.49 0.47 0.46 0.45 0.44 0.44 0.44 0.43 0.43

R(φ = 0) 0.325 0.308 0.291 0.282 0.273 0.265 0.256 0.248 0.242 0.235 0.228 0.220 0.211 0.203 0.194 0.185 0.175 0.166 0.155 0.145 0.129 0.123 0.115 0.111 0.109 0.108 0.108 0.107 0.106 0.106 0.105 0.105 0.105 0.105 0.106 0.106 0.106 0.107 0.107 0.106 0.105 0.104 0.103 0.101 0.098 0.096 0.092 0.087 0.082 0.077 0.071 0.066 0.061 0.057 0.055 0.053 0.051 0.052 0.051 0.051

Energy (eV) 25.00 26.00 27.00 28.00 29.00 30.00 35.00 40.00 45.00 50.00 60.00 65.00 68.00 70.00 75.00 80.00 90.00

n 0.89 0.88 0.87 0.87 0.86 0.86 0.86 0.87 0.88 0.92 0.96 0.98 0.96 0.94 0.94 0.94 0.94

0.42 0.39 0.37 0.35 0.34 0.32 0.24 0.18 0.13 0.10 0.08 0.09 0.12 0.11 0.09 0.07 0.06

Niobium18 0.12 0.20 0.24 0.28 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25 2.35 2.45 2.55 2.65 2.75 2.85 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20

15.99 7.25 5.47 4.26 3.11 2.28 1.83 1.57 1.41 1.35 1.35 1.44 1.55 1.65 1.76 1.95 2.15 2.36 2.54 2.69 2.82 2.89 2.92 2.93 2.92 2.89 2.83 2.74 2.66 2.58 2.51 2.48 2.45 2.44 2.46 2.48 2.52 2.56 2.59 2.62 2.64 2.64

53.20 34.14 28.88 24.95 20.03 15.58 12.67 10.59 9.00 7.74 6.70 5.86 5.18 4.63 4.13 3.68 3.37 3.13 2.99 2.89 2.86 2.87 2.87 2.87 2.88 2.90 2.92 2.90 2.86 2.80 2.68 2.60 2.53 2.45 2.38 2.33 2.29 2.27 2.28 2.29 2.33 2.42

R(φ = 0) 0.050 0.046 0.042 0.040 0.037 0.034 0.022 0.014 0.008 0.004 0.002 0.002 0.004 0.004 0.003 0.002 0.002 0.979 0.976 0.975 0.974 0.970 0.964 0.956 0.947 0.935 0.918 0.893 0.857 0.814 0.768 0.715 0.650 0.595 0.552 0.527 0.510 0.505 0.505 0.505 0.505 0.506 0.509 0.512 0.511 0.507 0.500 0.485 0.475 0.465 0.453 0.442 0.435 0.428 0.426 0.427 0.429 0.434 0.447

Optical Properties of Selected Elements Energy (eV) 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.70 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.00 15.60 16.00 16.60 17.00 17.20 17.40 17.80 18.00 18.60 19.00 19.60 20.00

n 2.53 2.39 2.32 2.26 2.16 2.00 1.81 1.63 1.49 1.38 1.31 1.26 1.24 1.23 1.22 1.20 1.14 1.07 1.02 1.00 0.99 0.99 0.99 1.00 1.01 1.04 1.07 1.10 1.13 1.18 1.23 1.27 1.30 1.32 1.32 1.31 1.30 1.28 1.27 1.25 1.24 1.24 1.24 1.23 1.20 1.16 1.11 1.08 0.99 0.92 0.85 0.80 0.79 0.77 0.75 0.74 0.73 0.72 0.72 0.72

2.56 2.56 2.52 2.57 2.62 2.68 2.67 2.60 2.49 2.38 2.25 2.14 2.04 1.96 1.91 1.88 1.85 1.78 1.69 1.60 1.51 1.43 1.39 1.36 1.29 1.22 1.18 1.13 1.09 1.05 1.04 1.04 1.06 1.08 1.10 1.12 1.13 1.13 1.13 1.12 1.10 1.09 1.09 1.12 1.13 1.15 1.16 1.16 1.14 1.11 1.04 0.99 0.96 0.93 0.87 0.85 0.77 0.72 0.66 0.62

R(φ = 0) 0.467 0.470 0.465 0.475 0.487 0.505 0.518 0.522 0.520 0.512 0.496 0.480 0.460 0.441 0.430 0.427 0.430 0.428 0.412 0.390 0.365 0.340 0.328 0.315 0.290 0.265 0.245 0.227 0.209 0.194 0.187 0.185 0.190 0.195 0.200 0.204 0.207 0.209 0.210 0.209 0.204 0.200 0.201 0.208 0.216 0.225 0.234 0.238 0.247 0.250 0.245 0.240 0.236 0.230 0.217 0.209 0.185 0.170 0.150 0.137

Energy (eV) 20.60 21.00 21.60 22.00 22.60 23.00 23.60 24.00 24.60 25.00 25.60 26.00 26.60 27.00 27.60 28.00 28.60 29.00 29.60 30.00 31.00 32.00 33.00 34.00 35.20 36.00 37.50 39.50 40.50

12-131 n 0.71 0.72 0.75 0.78 0.82 0.85 0.88 0.91 0.94 0.96 0.99 1.00 1.03 1.04 1.06 1.08 1.11 1.13 1.16 1.18 1.18 1.20 1.21 1.20 1.17 1.15 1.07 0.95 0.92

0.55 0.50 0.43 0.40 0.35 0.33 0.30 0.29 0.28 0.27 0.26 0.26 0.25 0.25 0.25 0.24 0.24 0.25 0.26 0.28 0.31 0.34 0.38 0.42 0.47 0.50 0.53 0.50 0.47

Osmium (Polycrystalline)9 0.10 4.08 50.23 0.15 2.90 33.60 0.20 2.44 25.11 0.25 2.35 19.99 0.30 2.23 16.54 0.35 2.33 14.06 0.40 2.45 12.32 0.45 2.43 11.02 0.50 2.41 9.97 0.55 2.33 9.12 0.60 2.21 8.37 0.65 2.11 7.68 0.70 2.02 7.04 0.75 2.00 6.46 0.80 2.00 5.95 0.85 2.01 5.51 0.90 2.03 5.10 0.95 2.05 4.74 1.00 2.09 4.41 1.10 2.15 3.84 1.20 2.16 3.35 1.30 2.25 2.77 1.40 2.49 2.23 1.50 2.84 1.80 1.60 3.36 1.62 1.70 3.70 1.75 1.80 3.78 1.83 1.90 3.81 1.75 2.00 3.98 1.60 2.10 4.26 1.54

R(φ = 0) 0.119 0.100 0.075 0.063 0.045 0.038 0.029 0.025 0.022 0.020 0.018 0.017 0.016 0.015 0.015 0.015 0.016 0.017 0.020 0.023 0.026 0.031 0.038 0.044 0.051 0.056 0.064 0.063 0.059 0.994 0.990 0.985 0.977 0.969 0.955 0.940 0.927 0.913 0.901 0.890 0.877 0.862 0.842 0.820 0.796 0.769 0.742 0.712 0.651 0.592 0.506 0.419 0.369 0.379 0.411 0.423 0.418 0.418 0.432

Energy (eV) 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.30 10.40 10.50 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60

n 4.58 4.84 5.10 5.28 5.36 5.30 5.07 4.65 4.05 3.29 2.93 2.75 2.73 2.71 2.53 2.24 2.01 1.88 1.74 1.58 1.46 1.36 1.27 1.20 1.13 1.06 1.01 0.97 0.95 0.92 0.91 0.90 0.90 0.91 0.91 0.94 0.96 0.98 1.01 1.04 1.08 1.10 1.13 1.16 1.19 1.20 1.22 1.23 1.24 1.25 1.24 1.23 1.19 1.17 1.16 1.15 1.14 1.15 1.16 1.17

1.62 1.76 2.01 2.38 2.82 3.29 3.78 4.18 4.40 3.96 3.79 3.45 3.32 3.34 3.44 3.44 3.31 3.19 3.12 3.00 2.88 2.77 2.65 2.54 2.44 2.33 2.21 2.11 2.00 1.91 1.81 1.72 1.63 1.55 1.48 1.40 1.34 1.29 1.24 1.19 1.16 1.14 1.11 1.10 1.08 1.08 1.08 1.09 1.10 1.11 1.13 1.14 1.15 1.12 1.10 1.08 1.03 1.01 0.98 0.97

R(φ = 0) 0.457 0.479 0.506 0.532 0.557 0.580 0.603 0.624 0.639 0.614 0.607 0.577 0.562 0.565 0.584 0.599 0.598 0.592 0.596 0.597 0.593 0.589 0.582 0.575 0.571 0.562 0.548 0.532 0.514 0.497 0.476 0.451 0.426 0.400 0.375 0.344 0.319 0.296 0.274 0.255 0.238 0.229 0.217 0.209 0.203 0.201 0.200 0.201 0.203 0.206 0.213 0.217 0.223 0.216 0.211 0.205 0.191 0.183 0.174 0.170

Optical Properties of Selected Elements

12-132 Energy (eV) 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.20 17.60 18.00 18.40 18.80 19.20 19.60 20.00 20.40 20.80 21.20 21.60 22.00 22.40 22.80 23.20 23.60 24.00 24.40 24.80 25.20 25.60 26.00 26.40 26.80 27.20 28.00 28.40 28.80 29.20 29.60 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00

n 1.17 1.16 1.16 1.17 1.20 1.25 1.28 1.28 1.27 1.26 1.23 1.19 1.14 1.10 1.05 0.96 0.93 0.89 0.86 0.83 0.80 0.78 0.77 0.75 0.75 0.73 0.72 0.70 0.69 0.67 0.66 0.65 0.63 0.65 0.64 0.64 0.65 0.65 0.65 0.65 0.65 0.66 0.68 0.70 0.72 0.74 0.77 0.79 0.81 0.84

Palladium19 0.10 4.13 0.15 3.13 0.20 3.07 0.26 3.11 0.30 3.56 0.36 3.98 0.40 4.27 0.46 4.27 0.50 4.10

0.96 0.94 0.91 0.89 0.86 0.87 0.90 0.94 0.97 1.01 1.04 1.08 1.10 1.10 1.11 1.10 1.09 1.05 1.02 0.99 0.96 0.93 0.90 0.88 0.86 0.84 0.82 0.80 0.77 0.75 0.72 0.69 0.66 0.62 0.59 0.57 0.55 0.53 0.51 0.49 0.45 0.41 0.37 0.34 0.31 0.29 0.27 0.26 0.26 0.26

54.15 35.82 26.59 20.15 17.27 14.41 13.27 12.11 11.44

R(φ = 0) 0.169 0.165 0.156 0.148 0.140 0.140 0.147 0.157 0.167 0.178 0.189 0.200 0.210 0.219 0.227 0.239 0.240 0.240 0.237 0.235 0.230 0.226 0.220 0.217 0.211 0.209 0.207 0.205 0.202 0.199 0.195 0.189 0.183 0.165 0.156 0.148 0.140 0.134 0.128 0.121 0.111 0.095 0.079 0.068 0.057 0.048 0.040 0.035 0.031 0.026 0.994 0.990 0.983 0.971 0.955 0.932 0.916 0.902 0.896

Energy (eV) 0.56 0.60 0.72 0.80 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00

n 3.92 3.80 3.51 3.35 2.99 2.81 2.65 2.50 2.34 2.17 2.08 2.00 1.92 1.82 1.75 1.67 1.60 1.53 1.47 1.41 1.37 1.32 1.29 1.26 1.23 1.20 1.17 1.14 1.12 1.10 1.08 1.07 1.06 1.05 1.03 1.04 1.03 1.03 1.01 0.96 0.90 0.85 0.81 0.78 0.76 0.74 0.73 0.72 0.73 0.73 0.75 0.77 0.79 0.83 0.88 0.94 0.96 1.00 1.04 1.07

k 10.49 9.96 8.70 8.06 6.89 6.46 6.10 5.78 5.50 5.22 4.95 4.72 4.54 4.35 4.18 4.03 3.88 3.75 3.61 3.48 3.36 3.25 3.13 3.03 2.94 2.85 2.77 2.68 2.60 2.52 2.45 2.38 2.31 2.25 2.19 2.09 2.01 1.94 1.90 1.86 1.79 1.70 1.62 1.54 1.45 1.37 1.29 1.21 1.13 1.05 0.98 0.91 0.85 0.78 0.73 0.70 0.70 0.65 0.65 0.64

R(φ = 0) 0.883 0.876 0.854 0.840 0.811 0.800 0.790 0.781 0.774 0.767 0.755 0.745 0.737 0.729 0.721 0.714 0.707 0.700 0.693 0.685 0.676 0.668 0.658 0.648 0.639 0.630 0.622 0.613 0.602 0.591 0.581 0.570 0.558 0.547 0.537 0.510 0.493 0.476 0.470 0.472 0.474 0.463 0.449 0.437 0.418 0.397 0.375 0.350 0.316 0.287 0.255 0.223 0.195 0.163 0.133 0.117 0.114 0.097 0.094 0.090

Energy (eV) 9.50 10.00 10.50 11.00 11.50 12.00 12.50 13.00 13.50 14.00 14.50 15.00 15.50 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 20.50 21.00 21.50 22.00 22.50 23.00 23.50 24.00 25.00 26.40 27.80 29.20

n 1.12 1.14 1.16 1.18 1.19 1.20 1.19 1.18 1.18 1.17 1.15 1.13 1.10 1.08 1.06 1.07 1.06 1.07 1.07 1.08 1.08 1.07 1.03 0.99 0.95 0.91 0.88 0.86 0.85 0.84 0.81 0.80 0.81 0.82

0.65 0.65 0.65 0.64 0.65 0.66 0.67 0.67 0.67 0.67 0.68 0.69 0.68 0.66 0.63 0.61 0.61 0.59 0.59 0.59 0.61 0.65 0.67 0.67 0.66 0.64 0.62 0.59 0.56 0.54 0.51 0.43 0.38 0.35

Platinum20 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60

13.21 8.18 5.90 4.70 3.92 3.28 2.81 3.03 3.91 4.58 5.13 5.52 5.71 5.57 5.31 5.05 4.77 4.50 4.25 3.86 3.55 3.29 3.10 2.92 2.76

44.72 31.16 23.95 19.40 16.16 13.66 11.38 9.31 7.71 7.14 6.75 6.66 6.83 7.02 7.04 6.98 6.91 6.77 6.62 6.24 5.92 5.61 5.32 5.07 4.84

R(φ = 0) 0.089 0.088 0.087 0.086 0.087 0.089 0.091 0.091 0.092 0.093 0.095 0.098 0.096 0.092 0.086 0.081 0.080 0.077 0.077 0.077 0.080 0.090 0.098 0.103 0.103 0.103 0.101 0.097 0.091 0.086 0.084 0.066 0.052 0.046 0.976 0.969 0.962 0.954 0.945 0.936 0.922 0.882 0.813 0.777 0.753 0.746 0.751 0.759 0.762 0.763 0.765 0.763 0.762 0.753 0.746 0.736 0.725 0.716 0.706

Optical Properties of Selected Elements Energy (eV) 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40

n 2.63 2.51 2.38 2.30 2.23 2.17 2.10 2.03 1.96 1.91 1.87 1.83 1.79 1.75 1.68 1.63 1.58 1.53 1.49 1.45 1.43 1.39 1.38 1.36 1.36 1.36 1.36 1.36 1.38 1.39 1.42 1.45 1.48 1.50 1.50 1.49 1.48 1.48 1.47 1.47 1.47 1.47 1.47 1.48 1.49 1.49 1.49 1.48 1.46 1.43 1.40 1.37 1.35 1.33 1.31 1.30 1.29 1.29 1.29 1.29

4.64 4.43 4.26 4.07 3.92 3.77 3.67 3.54 3.42 3.30 3.20 3.10 3.01 2.92 2.76 2.62 2.48 2.37 2.25 2.14 2.04 1.95 1.85 1.76 1.67 1.61 1.54 1.47 1.40 1.35 1.29 1.26 1.24 1.24 1.25 1.23 1.22 1.20 1.18 1.17 1.15 1.14 1.13 1.12 1.11 1.12 1.13 1.15 1.15 1.16 1.15 1.14 1.12 1.10 1.08 1.06 1.04 1.01 1.00 0.97

R(φ = 0) 0.697 0.686 0.678 0.664 0.654 0.642 0.636 0.626 0.616 0.605 0.595 0.585 0.575 0.565 0.546 0.527 0.507 0.491 0.472 0.452 0.432 0.415 0.392 0.372 0.350 0.332 0.315 0.295 0.276 0.261 0.246 0.236 0.231 0.230 0.231 0.228 0.225 0.221 0.216 0.212 0.209 0.205 0.202 0.200 0.198 0.200 0.203 0.207 0.209 0.211 0.210 0.207 0.203 0.199 0.194 0.188 0.183 0.177 0.173 0.165

Energy (eV) 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 20.50 21.00 21.50 22.00 22.50 23.00 23.50 24.00 24.50 25.00 25.50 26.00 26.50 27.00 27.50 28.00 28.50 29.00 29.50 30.00

12-133 n 1.29 1.31 1.31 1.31 1.30 1.27 1.27 1.25 1.24 1.24 1.25 1.27 1.31 1.30 1.28 1.23 1.18 1.11 1.03 0.94 0.87 0.81 0.77 0.75 0.74 0.73 0.73 0.73 0.74 0.74 0.74 0.74 0.75 0.75 0.75 0.74 0.73

Potassium21 0.55 0.139 0.58 0.119 0.63 0.106 0.67 0.091 0.73 0.079 0.81 0.066 0.92 0.056 1.05 0.044 1.23 0.040 1.44 0.040 1.65 0.044 1.87 0.050 2.07 0.053 2.27 0.049 2.45 0.046 2.64 0.043 2.82 0.043 2.95 0.041 3.06 0.041 3.40 0.052 3.71 0.089 3.97 0.287

0.94 0.93 0.93 0.93 0.93 0.93 0.93 0.92 0.89 0.87 0.86 0.85 0.88 0.94 0.99 1.03 1.06 1.09 1.10 1.08 1.04 0.98 0.92 0.87 0.82 0.77 0.73 0.70 0.67 0.65 0.63 0.62 0.60 0.59 0.58 0.58 0.58

7.10 6.72 6.32 5.79 5.30 4.75 4.19 3.58 3.04 2.56 2.19 1.84 1.62 1.43 1.28 1.14 1.02 0.898 0.799 0.549 0.288 0.091

R(φ = 0) 0.158 0.155 0.155 0.155 0.156 0.157 0.155 0.151 0.146 0.142 0.138 0.135 0.142 0.157 0.171 0.184 0.197 0.212 0.226 0.238 0.240 0.235 0.226 0.213 0.201 0.187 0.174 0.162 0.150 0.142 0.136 0.130 0.125 0.121 0.118 0.120 0.124 0.989 0.990 0.990 0.990 0.989 0.989 0.988 0.987 0.985 0.979 0.970 0.955 0.943 0.938 0.933 0.928 0.919 0.913 0.905 0.852 0.719 0.310

Energy (eV) 4.00 4.065 4.133 4.203 4.275 4.350 4.428 4.509 4.592 4.679 4.769 4.862 4.959 5.061 5.166 5.276 5.391 5.510 5.637 5.767 6.048 6.199 6.358 6.526 6.702 6.888 7.085 7.293 7.514 7.749 7.999 8.260 8.551 8.856 9.184 9.537 9.919 10.33 11.0 12.0

n 0.34 0.38 0.41 0.45 0.48 0.52 0.55 0.58 0.61 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.79 0.81 0.83 0.85 0.87 0.88 0.90 0.91 0.92 0.92 0.93 0.93 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94

k 0.08 0.07 0.07 0.06 0.06 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.028

R(φ = 0) 0.245 0.204 0.177 0.145 0.125 0.101 0.085 0.072 0.060 0.049 0.043 0.037 0.032 0.027 0.023 0.019 0.016 0.015 0.012 0.009 0.007 0.006 0.005 0.004 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001

→

Rhenium, single crystal, E ∥ ĉ9 0.10 6.06 51.03 0.15 4.66 33.96 0.20 4.16 25.36 0.25 4.03 20.10 0.30 4.37 16.69 0.35 4.50 14.53 0.40 4.53 12.96 0.45 4.53 11.78 0.50 4.53 10.88 0.55 4.50 10.26 0.60 4.29 9.75 0.65 4.07 9.35 0.70 3.80 8.94 0.75 3.48 8.55 0.80 3.21 8.10 0.85 2.96 7.68 0.90 2.73 7.24 0.95 2.56 6.79 1.00 2.45 6.36

0.991 0.984 0.975 0.962 0.943 0.925 0.909 0.893 0.878 0.867 0.861 0.856 0.853 0.850 0.846 0.841 0.835 0.826 0.813

Optical Properties of Selected Elements

12-134 Energy (eV) 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20

n 2.38 2.35 2.39 2.44 2.50 2.59 2.70 2.82 2.90 2.97 3.03 3.06 3.07 3.06 3.02 2.96 2.89 2.89 2.99 3.11 2.90 2.83 2.93 2.86 2.81 2.86 2.81 2.56 2.41 2.39 2.34 2.20 2.02 1.83 1.65 1.54 1.45 1.32 1.26 1.20 1.16 1.12 1.08 1.05 1.05 1.05 1.06 1.09 1.11 1.13 1.16 1.18 1.20 1.23 1.25 1.28 1.29 1.30 1.30 1.29

5.61 5.02 4.54 4.13 3.79 3.49 3.27 3.10 3.00 2.91 2.86 2.84 2.82 2.81 2.80 2.77 2.68 2.57 2.47 2.57 2.68 2.50 2.48 2.56 2.51 2.55 2.74 2.83 2.71 2.68 2.75 2.81 2.84 2.80 2.71 2.59 2.50 2.31 2.23 2.15 2.06 1.99 1.89 1.80 1.71 1.62 1.55 1.48 1.43 1.39 1.34 1.32 1.29 1.26 1.25 1.25 1.25 1.26 1.27 1.28

R(φ = 0) 0.778 0.742 0.702 0.662 0.624 0.587 0.557 0.535 0.520 0.510 0.504 0.501 0.499 0.498 0.497 0.493 0.482 0.468 0.457 0.470 0.482 0.459 0.457 0.467 0.460 0.466 0.489 0.504 0.493 0.488 0.500 0.515 0.530 0.538 0.541 0.532 0.526 0.508 0.500 0.493 0.480 0.470 0.454 0.435 0.411 0.386 0.360 0.336 0.317 0.301 0.281 0.274 0.264 0.252 0.246 0.242 0.242 0.244 0.247 0.249

Energy (eV) 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.00 17.40 18.00 18.40 18.80 19.20 19.60 20.00 20.40 20.80 21.20 21.60 22.00 22.40 22.80 23.20 23.60 24.00 24.40 24.80 25.20 25.60 26.00 26.40 26.80 27.20 27.60 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00 42.00 44.00 46.00 48.00

n 1.28 1.26 1.24 1.23 1.22 1.21 1.22 1.22 1.24 1.27 1.29 1.29 1.26 1.23 1.19 1.14 1.12 1.07 0.99 0.93 0.87 0.81 0.77 0.73 0.70 0.67 0.64 0.61 0.58 0.55 0.53 0.51 0.50 0.48 0.48 0.47 0.47 0.47 0.47 0.48 0.48 0.49 0.50 0.51 0.54 0.57 0.62 0.66 0.68 0.72 0.76 0.79 0.82 0.85 0.89 0.88 0.88 0.89 0.85 0.82

1.28 1.28 1.26 1.24 1.21 1.18 1.16 1.13 1.12 1.11 1.15 1.19 1.22 1.25 1.27 1.29 1.30 1.30 1.30 1.29 1.28 1.25 1.21 1.18 1.14 1.11 1.08 1.04 1.01 0.97 0.93 0.89 0.85 0.80 0.76 0.72 0.68 0.65 0.61 0.57 0.54 0.51 0.48 0.45 0.39 0.33 0.29 0.26 0.24 0.21 0.20 0.20 0.19 0.20 0.21 0.26 0.26 0.29 0.32 0.30

R(φ = 0) 0.252 0.252 0.249 0.244 0.237 0.230 0.222 0.215 0.209 0.204 0.213 0.225 0.236 0.248 0.259 0.269 0.275 0.286 0.300 0.311 0.321 0.330 0.332 0.333 0.332 0.332 0.334 0.335 0.340 0.341 0.338 0.334 0.329 0.319 0.207 0.296 0.282 0.270 0.255 0.240 0.225 0.208 0.193 0.176 0.145 0.114 0.086 0.065 0.054 0.041 0.031 0.025 0.021 0.018 0.016 0.022 0.022 0.026 0.035 0.036

Energy (eV) 50.00 52.00 54.00 56.00 58.00

n 0.80 0.78 0.72 0.66 0.65

0.30 0.30 0.30 0.24 0.16

R(φ = 0) 0.038 0.044 0.055 0.061 0.055

→

Rhenium, single crystal, E ⊥ ĉ9 0.10 4.25 42.83 0.15 3.28 28.08 0.20 3.28 20.66 0.25 3.47 16.27 0.30 3.73 13.44 0.35 3.93 11.54 0.40 3.99 10.15 0.45 4.17 9.03 0.50 4.34 8.26 0.55 4.45 7.73 0.60 4.53 7.40 0.65 4.44 7.26 0.70 4.13 7.09 0.75 3.77 6.75 0.80 3.55 6.32 0.85 3.39 5.95 0.90 3.26 5.61 0.95 3.17 5.27 1.00 3.09 4.96 1.10 3.05 4.39 1.20 3.08 3.89 1.30 3.20 3.56 1.40 3.23 3.38 1.50 3.23 3.12 1.60 3.29 2.88 1.70 3.38 2.72 1.80 3.47 2.59 1.90 3.54 2.50 2.00 3.63 2.43 2.10 3.74 2.40 2.20 3.83 2.38 2.30 3.93 2.44 2.40 4.00 2.55 2.50 4.01 2.70 2.60 3.90 2.84 2.70 3.74 2.92 2.80 3.57 2.88 2.90 3.49 2.75 3.00 3.53 2.71 3.20 3.55 2.84 3.40 3.34 2.88 3.60 3.25 2.83 3.80 3.24 2.84 4.00 3.19 2.94 4.20 3.05 3.06 4.40 2.88 3.15 4.60 2.67 3.18 4.80 2.44 3.17 5.00 2.25 3.12 5.20 2.10 3.04 5.40 1.96 2.96 5.60 1.84 2.88 5.80 1.73 2.81 6.00 1.61 2.74

0.991 0.984 0.971 0.951 0.926 0.900 0.875 0.846 0.821 0.801 0.788 0.784 0.784 0.779 0.766 0.752 0.737 0.719 0.701 0.658 0.613 0.578 0.559 0.532 0.507 0.491 0.480 0.473 0.469 0.470 0.472 0.481 0.492 0.505 0.514 0.517 0.511 0.497 0.493 0.506 0.508 0.501 0.502 0.513 0.526 0.539 0.548 0.554 0.556 0.555 0.553 0.551 0.549 0.549

Optical Properties of Selected Elements Energy (eV) 6.20 6.40 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.00 17.40 18.00 18.40 18.80 19.20 19.60 20.00 20.40 20.80 21.20 21.60 22.00 22.40 22.80 23.20 23.60 24.00 24.40

n 1.51 1.42 1.28 1.22 1.16 1.12 1.12 1.08 1.05 1.05 1.05 1.06 1.07 1.09 1.11 1.14 1.17 1.20 1.24 1.29 1.33 1.36 1.38 1.37 1.36 1.33 1.31 1.28 1.26 1.23 1.22 1.20 1.19 1.20 1.22 1.27 1.31 1.31 1.28 1.24 1.17 1.14 1.06 0.95 0.88 0.82 0.76 0.72 0.67 0.64 0.61 0.60 0.58 0.57 0.56 0.55 0.53 0.52 0.50 0.49

2.64 2.56 2.37 2.28 2.19 2.08 1.98 1.93 1.83 1.74 1.66 1.58 1.52 1.46 1.41 1.36 1.31 1.27 1.24 1.22 1.23 1.25 1.28 1.31 1.33 1.34 1.34 1.33 1.32 1.29 1.26 1.23 1.20 1.16 1.13 1.12 1.17 1.23 1.28 1.33 1.37 1.38 1.39 1.38 1.36 1.33 1.29 1.25 1.21 1.15 1.10 1.06 1.02 0.98 0.95 0.92 0.89 0.85 0.82 0.79

R(φ = 0) 0.545 0.541 0.526 0.517 0.508 0.493 0.468 0.463 0.443 0.418 0.397 0.372 0.351 0.327 0.309 0.290 0.273 0.258 0.244 0.234 0.233 0.238 0.245 0.253 0.259 0.264 0.266 0.266 0.264 0.257 0.251 0.245 0.236 0.225 0.214 0.207 0.218 0.234 0.251 0.270 0.288 0.297 0.314 0.334 0.346 0.355 0.360 0.363 0.369 0.364 0.357 0.349 0.342 0.336 0.328 0.325 0.322 0.317 0.314 0.309

12-135

Energy (eV) 24.80 25.20 25.60 26.00 26.40 26.80 27.20 27.60 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00

n 0.48 0.47 0.47 0.46 0.46 0.46 0.47 0.48 0.49 0.51 0.55 0.59 0.64 0.67 0.70 0.74 0.77 0.80 0.84 0.88 0.87 0.87 0.88 0.84 0.82 0.80 0.77 0.71 0.66 0.64

0.75 0.72 0.68 0.64 0.61 0.57 0.53 0.50 0.47 0.41 0.34 0.29 0.26 0.24 0.22 0.20 0.19 0.19 0.19 0.21 0.25 0.25 0.28 0.31 0.30 0.30 0.30 0.29 0.23 0.16

Rhodium11 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.90 3.00

18.48 8.66 5.85 4.74 4.20 3.87 3.67 3.63 3.62 3.71 3.67 3.51 3.26 3.01 2.78 2.60 2.42 2.30 2.20 2.12 2.05 2.00 1.94 1.90 1.88 1.85 1.80 1.63 1.53

69.43 37.46 25.94 19.80 16.07 13.51 11.72 10.34 9.36 8.67 8.26 7.94 7.63 7.31 6.97 6.64 6.33 6.02 5.76 5.51 5.30 5.11 4.94 4.78 4.65 4.55 4.49 4.36 4.29

R(φ = 0) 0.303 0.295 0.286 0.276 0.263 0.249 0.231 0.216 0.198 0.164 0.129 0.097 0.072 0.060 0.047 0.036 0.029 0.023 0.018 0.016 0.023 0.023 0.026 0.035 0.036 0.039 0.044 0.055 0.061 0.055 0.986 0.977 0.967 0.955 0.941 0.925 0.908 0.887 0.867 0.848 0.837 0.832 0.829 0.827 0.823 0.818 0.813 0.805 0.798 0.789 0.780 0.772 0.765 0.756 0.748 0.743 0.742 0.748 0.753

Energy (eV) 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.60 11.00 11.60 12.00 12.60 13.00 13.60 14.00 14.60 15.00 15.60 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00

n 1.41 1.30 1.20 1.11 1.04 0.99 0.95 0.91 0.88 0.86 0.83 0.80 0.78 0.79 0.79 0.79 0.80 0.80 0.79 0.76 0.73 0.70 0.68 0.67 0.66 0.66 0.66 0.67 0.68 0.69 0.71 0.74 0.78 0.83 0.88 0.95 1.01 1.07 1.12 1.17 1.26 1.29 1.32 1.32 1.32 1.32 1.32 1.32 1.30 1.28 1.25 1.24 1.23 1.22 1.22 1.23 1.25 1.24 1.18 1.10

4.20 4.09 3.97 3.84 3.71 3.58 3.45 3.34 3.23 3.12 2.94 2.76 2.60 2.46 2.34 2.23 2.14 2.06 2.00 1.93 1.85 1.77 1.69 1.60 1.52 1.43 1.35 1.27 1.20 1.12 1.04 0.97 0.89 0.83 0.77 0.73 0.71 0.69 0.69 0.69 0.73 0.76 0.80 0.82 0.82 0.83 0.85 0.86 0.89 0.90 0.90 0.89 0.88 0.88 0.87 0.88 0.92 0.98 1.05 1.09

R(φ = 0) 0.760 0.764 0.767 0.769 0.768 0.764 0.759 0.753 0.747 0.739 0.722 0.706 0.684 0.659 0.635 0.613 0.591 0.573 0.561 0.556 0.544 0.534 0.518 0.498 0.476 0.452 0.423 0.394 0.363 0.329 0.288 0.252 0.212 0.179 0.148 0.125 0.110 0.102 0.098 0.098 0.106 0.113 0.124 0.127 0.129 0.131 0.134 0.138 0.144 0.147 0.147 0.147 0.145 0.144 0.143 0.145 0.155 0.172 0.193 0.213

Optical Properties of Selected Elements

12-136 Energy (eV) 20.50 21.00 21.50 22.00 22.50 23.00 23.50 24.00 24.50 25.00 25.50 26.00 26.50 27.00 27.50 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00

n 1.00 0.91 0.86 0.83 0.81 0.79 0.75 0.73 0.70 0.69 0.67 0.66 0.65 0.65 0.65 0.65 0.65 0.66 0.64 0.61 0.60 0.65 0.69 0.73 0.74 0.74 0.75

1.09 1.05 1.00 0.95 0.92 0.90 0.87 0.84 0.81 0.77 0.74 0.70 0.66 0.64 0.61 0.59 0.54 0.51 0.49 0.44 0.37 0.30 0.28 0.27 0.28 0.27 0.25

R(φ = 0) 0.230 0.234 0.228 0.219 0.214 0.213 0.214 0.210 0.208 0.202 0.195 0.188 0.176 0.168 0.159 0.152 0.137 0.127 0.127 0.126 0.110 0.074 0.058 0.049 0.047 0.045 0.041

→

Ruthenium, single crystal, E ∥ ĉ9 0.10 11.50 51.38 0.20 5.93 27.14 0.30 4.33 18.50 0.40 3.60 13.97 0.50 3.18 11.04 0.60 3.28 8.89 0.70 3.62 7.73 0.80 3.42 7.02 0.90 3.25 6.12 1.00 3.39 5.33 1.10 3.66 4.83 1.20 3.84 4.57 1.30 3.94 4.38 1.40 4.02 4.19 1.50 4.16 4.07 1.60 4.33 4.08 1.70 4.42 4.21 1.80 4.40 4.38 1.90 4.29 4.61 2.00 4.04 4.81 2.10 3.69 4.90 2.20 3.35 4.82 2.30 3.09 4.70 2.40 2.89 4.55 2.50 2.74 4.40 2.60 2.64 4.25 2.70 2.58 4.14 2.80 2.54 4.05 2.90 2.48 4.03 3.00 2.38 4.03 3.10 2.26 4.00 3.20 2.13 3.96

0.984 0.970 0.953 0.933 0.909 0.865 0.822 0.801 0.766 0.715 0.675 0.654 0.638 0.624 0.614 0.615 0.624 0.636 0.651 0.667 0.679 0.683 0.681 0.677 0.671 0.663 0.656 0.650 0.650 0.656 0.661 0.666

Energy (eV) 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.00 15.60 16.00 16.50 17.00

n 2.00 1.87 1.76 1.66 1.57 1.49 1.42 1.37 1.29 1.22 1.16 1.11 1.06 1.01 0.95 0.92 0.90 0.88 0.87 0.84 0.82 0.79 0.76 0.75 0.73 0.73 0.73 0.72 0.72 0.73 0.74 0.74 0.75 0.77 0.79 0.82 0.85 0.88 0.92 0.96 1.01 1.05 1.09 1.12 1.15 1.18 1.21 1.23 1.26 1.27 1.28 1.28 1.28 1.27 1.27 1.27 1.28 1.30 1.32 1.34

3.91 3.83 3.74 3.65 3.55 3.45 3.35 3.24 3.08 2.93 2.79 2.67 2.56 2.46 2.35 2.23 2.14 2.05 1.98 1.91 1.84 1.77 1.69 1.61 1.54 1.46 1.39 1.33 1.26 1.20 1.14 1.08 1.02 0.97 0.91 0.86 0.81 0.76 0.72 0.69 0.67 0.66 0.65 0.65 0.65 0.65 0.66 0.67 0.69 0.72 0.74 0.75 0.76 0.76 0.76 0.76 0.77 0.78 0.80 0.85

R(φ = 0) 0.671 0.673 0.674 0.675 0.673 0.672 0.668 0.661 0.649 0.639 0.628 0.617 0.607 0.600 0.593 0.576 0.559 0.545 0.531 0.521 0.510 0.500 0.489 0.472 0.455 0.433 0.411 0.391 0.366 0.342 0.318 0.295 0.267 0.243 0.217 0.190 0.167 0.144 0.125 0.110 0.100 0.094 0.090 0.088 0.087 0.088 0.090 0.092 0.098 0.104 0.108 0.111 0.114 0.114 0.114 0.114 0.115 0.118 0.123 0.136

Energy (eV) 17.50 18.00 18.50 19.00 19.50 20.00 20.50 21.00 21.50 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00

n 1.32 1.26 1.18 1.11 1.05 0.99 0.92 0.86 0.83 0.81 0.77 0.74 0.71 0.68 0.67 0.66 0.67 0.67 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.80 0.82 0.83

0.93 0.99 1.02 1.02 1.02 1.02 0.99 0.94 0.90 0.86 0.79 0.74 0.69 0.63 0.57 0.51 0.46 0.43 0.37 0.33 0.30 0.27 0.25 0.24 0.23 0.22 0.22 0.22

R(φ = 0) 0.155 0.173 0.185 0.192 0.199 0.208 0.212 0.209 0.203 0.193 0.182 0.171 0.163 0.154 0.140 0.124 0.107 0.097 0.084 0.070 0.058 0.048 0.039 0.035 0.039 0.027 0.024 0.022

→

Ruthenium, single crystal, E ⊥ ĉ5 0.10 11.85 50.81 0.20 6.68 27.18 0.30 4.94 18.92 0.40 3.90 14.51 0.50 3.27 11.63 0.60 2.98 9.54 0.70 2.82 7.99 0.80 2.73 6.71 0.90 2.82 5.54 1.00 3.17 4.59 1.10 3.69 3.91 1.20 4.28 3.66 1.30 4.66 3.72 1.40 4.86 3.79 1.50 4.99 3.89 1.60 5.08 4.03 1.70 5.12 4.22 1.80 5.10 4.45 1.90 4.96 4.78 2.00 4.61 5.06 2.10 4.21 5.09 2.20 3.94 5.00 2.30 3.69 4.97 2.40 3.44 4.88 2.50 3.27 4.77 2.60 3.14 4.66 2.70 3.06 4.59 2.80 2.99 4.59 2.90 2.87 4.64 3.00 2.64 4.69 3.10 2.40 4.64

0.983 0.966 0.950 0.933 0.915 0.888 0.856 0.815 0.751 0.670 0.604 0.585 0.593 0.601 0.609 0.618 0.629 0.642 0.660 0.677 0.682 0.681 0.684 0.684 0.681 0.677 0.674 0.676 0.686 0.701 0.710

Optical Properties of Selected Elements Energy (eV) 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.00 15.60 16.00 16.50

n 2.18 2.00 1.84 1.71 1.60 1.50 1.41 1.35 1.29 1.21 1.16 1.13 1.09 1.03 0.97 0.91 0.88 0.86 0.84 0.82 0.81 0.78 0.76 0.73 0.70 0.68 0.67 0.66 0.66 0.65 0.66 0.66 0.68 0.69 0.70 0.73 0.77 0.82 0.86 0.90 0.94 0.99 1.04 1.08 1.11 1.14 1.17 1.20 1.22 1.25 1.26 1.27 1.27 1.26 1.25 1.25 1.25 1.25 1.27 1.28

4.55 4.43 4.30 4.16 4.03 3.90 3.77 3.64 3.53 3.31 3.13 2.97 2.86 2.75 2.64 2.52 2.40 2.29 2.20 2.11 2.04 1.97 1.89 1.82 1.75 1.67 1.59 1.51 1.44 1.36 1.29 1.22 1.15 1.09 1.02 0.95 0.89 0.84 0.81 0.77 0.74 0.72 0.71 0.70 0.70 0.70 0.71 0.72 0.73 0.76 0.78 0.81 0.83 0.84 0.84 0.84 0.84 0.85 0.85 0.89

R(φ = 0) 0.717 0.721 0.723 0.723 0.722 0.721 0.718 0.713 0.707 0.694 0.679 0.662 0.652 0.648 0.643 0.635 0.622 0.605 0.591 0.576 0.564 0.556 0.545 0.538 0.527 0.513 0.496 0.476 0.454 0.430 0.403 0.378 0.346 0.317 0.286 0.251 0.216 0.185 0.163 0.143 0.127 0.115 0.108 0.104 0.102 0.101 0.102 0.104 0.107 0.113 0.118 0.124 0.129 0.132 0.132 0.133 0.133 0.134 0.134 0.145

Energy (eV) 17.00 17.50 18.00 18.50 19.00 19.50 20.00 20.50 21.00 21.50 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00

12-137 n 1.28 1.25 1.19 1.12 1.07 1.02 0.97 0.91 0.85 0.80 0.77 0.71 0.67 0.64 0.61 0.60 0.60 0.61 0.62 0.61 0.63 0.65 0.67 0.70 0.72 0.73 0.75 0.77 0.79

0.94 1.00 1.04 1.05 1.05 1.04 1.04 1.03 1.01 0.97 0.94 0.87 0.79 0.73 0.66 0.59 0.53 0.48 0.45 0.40 0.34 0.31 0.28 0.26 0.25 0.23 0.22 0.22 0.22

R(φ = 0) 0.158 0.175 0.190 0.200 0.205 0.212 0.219 0.228 0.234 0.234 0.233 0.229 0.218 0.205 0.194 0.177 0.155 0.134 0.123 0.114 0.093 0.077 0.065 0.054 0.047 0.041 0.035 0.031 0.028

→

Selenium, single crystal, E || ĉ22 0.01364 2.914 0.248 0.01488 3.175 9.95E-02 0.01612 3.263 2.13E-03 0.01736 3.306 3.81E-02 0.01860 3.330 7.04E-03 0.01984 3.346 4.23E-02 0.02108 3.358 3.40E-03 0.02232 3.366 5.31E-02 0.02356 3.372 1.96E-03 0.02480 3.377 2.39E-02 0.02604 3.380 0.02728 1.16E-02 0.02976 7.96E-03 0.03224 8.57E-03 0.03472 2.70E-02 0.03720 3.397 1.72E-02 0.04463 1.13E-02 0.04959 3.403 2.79E-03 0.05703 1.56E-03 0.06199 3.405 1.35E-03 0.06819 5.79E-04 0.07439 3.407 4.44E-04 0.08059 4.41E-04 0.08679 3.408 4.32E-04 0.09299 2.44E-04 0.09919 3.409 3.23E-04 0.1116 3.409 2.87E-04 0.1240 3.410 2.71E-04 0.2480 3.417 2.67E-04 0.3720 3.427 1.90E-04

0.242 0.272 0.282 0.287 0.290 0.291 0.293 0.294 0.294 0.295 0.295

0.297 0.298 0.298 0.298 0.298 0.299 0.299 0.299 0.299 0.301

Energy (eV) 0.4959 0.6199 0.7439 0.8679 0.9919 1.116 1.240 1.50 1.60 1.70 1.80 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.5 5.0 6.0 7.0 8.0 9.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0

n 3.442 3.462 3.486 3.516 3.551 3.592 3.640

4.46 4.79 4.49 4.28 4.40 4.59 4.44 3.92 3.69 3.39 (3.00) (2.65) (2.30) 1.92 1.50 1.57 1.84 1.35 1.35 0.92 1.00 0.81 0.65 0.65 0.69 0.81 0.91 0.86 0.85 0.87

k 1.41E-04 1.12E-04 9.42E-05 8.07E-05 7.11E-05 6.37E-05 5.81E-05 1.33E-04 1.59E-04 6.27E-04 2.20E-02 0.76 1.19 1.21 1.32 1.70 2.29 2.59 2.76 3.01

R(φ = 0) 0.302 0.304 0.307 0.310 0.314 0.319 0.324

2.78 2.31 1.49 1.45 1.68 1.64 1.07 1.10 0.91 0.61 0.48 0.36 0.25 0.18 0.15 0.13 0.11

0.528 0.482 0.288 0.276 0.353 0.342 0.238 0.232 0.211 0.160 0.120 0.076 0.030 0.011 0.012 0.011 0.008

Selenium, single crystal, E ⊥ ĉ22 0.01364 2.854 0.0239 0.01488 2.932 0.0325 0.01612 3.140 0.1750 0.01736 2.959 1.3300 0.01860 2.111 0.2550 0.01984 2.356 0.0746 0.02108 2.462 0.0276 0.02232 2.502 0.0442 0.02356 2.543 0.0097 0.02480 2.550 0.0239 0.02604 2.582 0.02728 2.600 0.0101 0.02976 2.576 9.95E-03 0.03224 2.598 1.16E-02 0.03472 2.607 1.68E-02 0.03720 2.613 1.54E-02 0.04463 1.17E-02 0.04959 2.627 3.58E-03 0.05703 8.65E-04

0.402 0.438 0.431 0.417 0.430 0.462 0.490 0.493 0.502 0.521

→

0.231 0.241 0.269 0.321 0.133 0.164 0.178 0.184 0.190 0.191 0.195 0.198 0.194 0.197 0.199 0.199 0.201

Optical Properties of Selected Elements

12-138 Energy (eV) 0.06199 0.06819 0.07439 0.08059 0.08679 0.09299 0.09919 0.1116 0.1240 0.2480 0.3720 0.4959 0.6199 0.7439 0.8679 0.9919 1.116 1.240 1.50 1.60 1.70 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.50 5.00 6.00 7.00 8.00 9.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00

n 2.632 2.635 2.636 2.637 2.638 2.639 2.645 2.652 2.654 2.675 2.692 2.713 2.739 2.772 2.816

3.32 3.38 3.07 2.93 3.00 3.12 3.30 3.35 3.22 3.06 2.84 2.51 2.18 1.75 1.25 1.32 1.62 1.81 1.66 1.72 1.25 0.98 0.68 0.61 0.73 0.78 0.78 0.78 0.80 0.79

k 2.07E-03 2.89E-04 1.59E-04 1.35E-04 1.42E-04 1.04E-04 8.95E-05 8.84E-05 8.51E-05 5.97E-05 5.44E-05 4.58E-05 3.82E-05 3.32E-05 2.96E-05 2.69E-05 2.48E-05 2.31E-05 7.37E-05 8.63E-05 3.60E-04 0.11 0.65 0.73 0.61 0.53 0.58 0.70 1.01 1.24 1.47 1.66 1.81 1.83 1.94 1.50 0.73 0.61 0.69 1.02 0.95 1.02 0.92 0.96 0.65 0.48 0.39 0.32 0.26 0.19 0.14

Silicon, single crystal23 0.01240 3.4185 2.90E-04 0.01488 3.4190 2.30E-04 0.01736 3.4192 1.90E-04 0.01984 3.4195 1.70E-04 0.02480 3.4197 0.03100 3.4199 0.04092 3.4200 0.04463 1.08E-04

R(φ = 0) 0.202 0.202 0.202 0.203 0.203 0.203 0.204 0.205 0.205 0.208 0.210 0.213 0.216 0.221 0.226

0.289 0.310 0.282 0.259 0.263 0.279 0.305 0.328 0.334 0.344 0.351 0.356 0.352 0.382 0.316 0.107 0.105 0.135 0.182 0.171 0.181 0.178 0.274 0.191 0.094 0.060 0.046 0.036 0.023 0.020 0.300 0.300 0.300 0.300 0.300 0.300 0.300

Energy (eV) 0.04959 0.05703 0.06199 0.06943 0.07439 0.08059 0.08679 0.09299 0.09919 0.1054 0.1116 0.1178 0.1240 0.1364 0.1488 0.1612 0.1736 0.1798 0.1860 0.1922 0.1984 0.2046 0.2108 0.2170 0.2232 0.2294 0.2356 0.2418 0.2480 0.3100 0.3626 0.4568 0.6199 0.8093 1.033 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5

n 3.4201 3.4204

(3.4207)

3.4215

(3.4230)

(3.4244)

3.4261 3.4294 3.4327 3.4393 3.4490 3.4784 3.5193 (3.5341)

3.673 3.714 3.752 3.796 3.847 3.906 3.969 4.042 4.123 4.215 4.320 4.442 4.583 4.753 4.961 5.222 5.570 6.062 6.709 6.522 5.610

k 9.15E-05 1.56E-04 2.86E-04 3.84E-04 7.16E-04 1.52E-04 1.02E-04 2.59E-04 1.77E-04 1.53E-04 2.02E-04 1.22E-04 6.76E-05 5.49E-05 2.41E-05 2.49E-05 1.68E-05 2.45E-05 2.66E-06 1.74E-06 8.46E-07 5.64E-07 4.17E-07 4.05E-07 3.94E-07 3.26E-07 2.97E-07 2.82E-07 1.99E-07

2.50E-09

1.30E-05 1.80E-04 2.26E-03 7.75E-03 5.00E-03 8.00E-03 1.00E-02 0.013 0.016 0.022 0.030 0.032 0.048 0.060 0.073 0.090 0.130 0.163 0.203 0.269 0.387 0.630 1.321 2.705 3.014

R(φ = 0) 0.300 0.300

0.300

0.300 0.301 0.301 0.302 0.303 0.306 0.311 0.312

0.327 0.331 0.335 0.340 0.345 0.351 0.357 0.364 0.372 0.380 0.390 0.400 0.412 0.426 0.442 0.461 0.486 0.518 0.561 0.592 0.575

Energy (eV) 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 12.0 14.0 16.0 18.0 20.0 22.14 24.31 26.38 28.18 30.24 31.79 34.44 36.47 38.75 40.00

n 5.296 5.156 5.065 5.016 5.010 5.020 4.888 4.086 3.120 2.451 1.988 1.764 1.658 1.597 1.570 1.571 1.589 1.579 1.471 1.340 1.247 1.180 1.133 1.083 1.010 0.847 0.682 0.563 0.478 0.414 0.367 0.332 0.306 0.257 0.275 0.345 0.455 0.567 0.675 0.752 0.803 0.834 0.860 0.877 0.899 0.913 0.925 0.930

k 2.987 3.058 3.182 3.346 3.587 3.979 4.639 5.395 5.344 5.082 4.678 4.278 3.979 3.749 3.565 3.429 3.354 3.353 3.366 3.302 3.206 3.112 3.045 2.982 2.909 2.73 2.45 2.21 2.00 1.82 1.66 1.51 1.38 0.963 0.641 0.394 0.219 0.0835 0.0405 0.0243 0.0178 0.0152 0.0138 0.0132 0.0121 0.0113 0.0104 0.0100

R(φ = 0) 0.564 0.563 0.568 0.577 0.591 0.614 0.652 0.703 0.726 0.740 0.742 0.728 0.710 0.693 0.675 0.658 0.646 0.647 0.663 0.673 0.675 0.673 0.672 0.673 0.677 0.688 0.691 0.693 0.691 0.688 0.683 0.672 0.661 0.590 0.460 0.297 0.159 0.079 0.038 0.020 0.012 0.008 0.006 0.004 0.003 0.002 0.002 0.001

Silver6 0.10 0.20 0.30 0.40 0.50 1.00 1.50 2.00 2.50 3.00 3.25

9.91 2.84 1.41 0.91 0.67 0.28 0.27 0.27 0.24 0.23 0.23

90.27 45.70 30.51 22.89 18.32 9.03 5.79 4.18 3.09 2.27 1.86

0.995 0.995 0.994 0.993 0.992 0.987 0.969 0.944 0.914 0.864 0.816

Optical Properties of Selected Elements Energy (eV) 3.50 3.60 3.70 3.77 3.80 3.90 4.00 4.10 4.20 4.30 4.50 4.75 5.00 5.50 6.00 6.50 7.00 7.50 8.00 9.00 10.00 11.00 12.00 13.00 14.00 14.50 15.00 16.00 17.00 18.00 19.00 20.00 21.00 21.50 22.00 22.50 23.00 23.50 24.00 24.50 25.00 25.50 26.00 26.50 27.00 27.50 28.00 28.50 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 38.00 40.00 42.00 44.00

n 0.21 0.23 0.30 0.53 0.73 1.30 1.61 1.73 1.75 1.73 1.69 1.61 1.55 1.45 1.34 1.25 1.18 1.14 1.16 1.33 1.46 1.52 1.61 1.66 1.72 1.64 1.56 1.42 1.33 1.28 1.27 1.29 1.35 1.37 1.34 1.26 1.17 1.10 1.04 0.99 0.95 0.91 0.90 0.89 0.89 0.89 0.90 0.91 0.92 0.93 0.93 0.92 0.90 0.88 0.86 0.89 0.89 0.90 0.90 0.90

1.42 1.13 0.77 0.40 0.30 0.36 0.60 0.85 1.06 1.13 1.28 1.34 1.36 1.34 1.28 1.18 1.06 0.91 0.75 0.56 0.56 0.56 0.59 0.64 0.78 0.88 0.92 0.91 0.86 0.80 0.75 0.71 0.75 0.80 0.87 0.93 0.94 0.93 0.90 0.87 0.83 0.78 0.74 0.69 0.65 0.62 0.59 0.57 0.56 0.54 0.53 0.53 0.51 0.49 0.45 0.44 0.39 0.37 0.35 0.33

R(φ = 0) 0.756 0.671 0.475 0.154 0.053 0.040 0.103 0.153 0.194 0.208 0.238 0.252 0.257 0.257 0.246 0.225 0.196 0.157 0.114 0.074 0.082 0.088 0.100 0.112 0.141 0.152 0.156 0.151 0.139 0.124 0.111 0.103 0.112 0.124 0.141 0.157 0.163 0.165 0.165 0.160 0.154 0.144 0.133 0.121 0.109 0.099 0.090 0.084 0.079 0.074 0.072 0.072 0.071 0.067 0.061 0.055 0.043 0.039 0.036 0.033

12-139

Energy (eV) 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00 62.00 64.00 66.00 68.00 70.00 72.00 74.00 76.00 78.00 80.00 85.00 90.00 95.00 100.00

n 0.90 0.89 0.88 0.89 0.88 0.87 0.87 0.87 0.88 0.88 0.88 0.87 0.83 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.86 0.87

Sodium24 0.55 0.58 0.63 0.67 0.73 0.81 0.92 1.05 1.23 1.44 1.65 1.87 2.07 2.27 2.45 2.64 2.82 2.95 3.06 3.20 3.40 3.71 3.97 6.199 6.358 6.526 6.702 6.888 7.130 7.328 7.583 7.847 8.015 8.634 9.143 9.709 10.20

0.262 0.241 0.207 0.175 0.147 0.123 0.099 0.078 0.064 0.053 0.050 0.049 0.053 0.059 0.063 0.066 0.068 0.068 0.069 0.065 0.061 0.055 0.049 0.390 0.454 0.485 0.533 0.574 0.616 0.641 0.674 0.700 0.710 0.762 0.800 0.819 0.843

0.32 0.31 0.29 0.28 0.17 0.26 0.24 0.22 0.21 0.21 0.21 0.21 0.20 0.18 0.17 0.16 0.15 0.14 0.11 0.08 0.06 0.04 9.97 9.45 8.80 8.09 7.42 6.67 5.82 5.11 4.35 3.72 3.22 2.76 2.48 2.23 2.07 1.88 1.76 1.63 1.54 1.47 1.33 1.13 1.01

R(φ = 0) 0.031 0.030 0.027 0.024 0.024 0.024 0.021 0.018 0.016 0.016 0.016 0.017 0.021 0.016 0.014 0.013 0.013 0.012 0.011 0.009 0.007 0.005 0.990 0.989 0.990 0.990 0.990 0.989 0.989 0.989 0.987 0.986 0.983 0.978 0.971 0.961 0.953 0.943 0.936 0.928 0.921 0.921 0.916 0.908 0.908 0.193 0.141 0.120 0.093 0.073 0.056 0.048 0.038 0.031 0.029 0.018 0.012 0.010 0.007

Energy (eV) 11.08 11.83 12.73 13.05 13.42 13.73 14.07 14.83 15.05 15.46 16.21 18.10 21.12 25.51 26.95 27.68 28.37 29.52

n 0.870 0.887 0.907 0.913 0.914 0.917 0.922 0.934 0.936 0.942 0.948 0.964 0.979 0.993 1.00 1.01 1.01 1.02

Tantalum16 0.10 10.14 0.15 9.45 0.20 5.77 0.26 3.67 0.30 2.87 0.38 2.03 0.50 1.37 0.58 1.15 0.70 0.96 0.78 0.89 0.90 0.84 1.00 0.89 1.10 0.93 1.20 0.98 1.30 1.00 1.40 1.04 1.50 1.09 1.60 1.15 1.70 1.24 1.80 1.35 1.90 1.57 2.00 1.83 2.10 2.10 2.20 2.36 2.30 2.56 2.40 2.68 2.50 2.75 2.60 2.80 2.70 2.84 2.80 2.85 2.90 2.84 3.00 2.81 3.20 2.73 3.40 2.61 3.60 2.49 3.80 2.40 4.00 2.36 4.20 2.35 4.40 2.39 4.60 2.45 4.80 2.53

66.39 46.41 35.46 27.53 23.90 18.87 14.26 12.19 9.92 8.77 7.38 6.47 5.75 5.14 4.62 4.15 3.73 3.33 2.95 2.60 2.24 1.99 1.84 1.81 1.86 1.92 1.98 2.02 2.08 2.14 2.20 2.24 2.31 2.33 2.30 2.22 2.14 2.06 2.01 2.00 2.06

R(φ = 0) 0.005 0.004 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.984 0.9834 0.982 0.981 0.980 0.978 0.974 0.970 0.962 0.956 0.942 0.992 0.899 0.872 0.842 0.805 0.762 0.707 0.640 0.560 0.460 0.388 0.354 0.351 0.365 0.378 0.388 0.395 0.405 0.412 0.420 0.425 0.432 0.435 0.430 0.418 0.406 0.392 0.384 0.384 0.394

Optical Properties of Selected Elements

12-140 Energy (eV) 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.20 12.40 12.60 12.80 13.00 13.60 14.00 14.60 15.00 15.60 16.00 16.60 17.00 17.60 18.00 18.60 19.00 19.60 20.00 20.60 21.00 21.60 22.00 22.60

n 2.58 2.52 2.31 2.06 1.83 1.63 1.48 1.37 1.29 1.23 1.18 1.15 1.13 1.12 1.11 1.11 1.12 1.13 1.14 1.17 1.19 1.21 1.21 1.21 1.21 1.20 1.19 1.18 1.16 1.15 1.13 1.11 1.09 1.07 1.05 1.02 1.00 0.98 0.96 0.94 0.93 0.91 0.90 0.85 0.80 0.72 0.68 0.63 0.60 0.60 0.55 0.53 0.53 0.53 0.54 0.55 0.57 0.64 0.64 0.69

2.20 2.44 2.61 2.67 2.63 2.56 2.45 2.33 2.22 2.11 2.01 1.91 1.82 1.75 1.68 1.61 1.55 1.50 1.45 1.41 1.40 1.38 1.38 1.38 1.37 1.37 1.37 1.37 1.36 1.36 1.35 1.35 1.34 1.33 1.32 1.31 1.29 1.28 1.26 1.24 1.22 1.16 1.15 1.15 1.13 1.08 1.04 0.97 0.92 0.92 0.79 0.71 0.65 0.57 0.52 0.44 0.39 0.34 0.32 0.27

R(φ = 0) 0.416 0.450 0.480 0.501 0.510 0.515 0.512 0.504 0.492 0.478 0.462 0.445 0.425 0.406 0.390 0.370 0.350 0.332 0.317 0.301 0.294 0.289 0.287 0.285 0.285 0.286 0.286 0.287 0.288 0.289 0.290 0.292 0.293 0.294 0.295 0.296 0.295 0.294 0.292 0.289 0.286 0.272 0.272 0.285 0.293 0.301 0.304 0.301 0.296 0.296 0.274 0.254 0.236 0.207 0.185 0.153 0.127 0.089 0.081 0.058

Energy (eV) 23.00 23.60 24.00 24.60 25.00 25.60 26.00 26.60 27.00 27.60 28.00 28.60 29.00 29.60 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00 Tellurium, 0.01364 0.01488 0.01612 0.01736 0.01860 0.01984 0.02108 0.02232 0.02356 0.02480 0.02604 0.02728 0.02976 0.03224 0.03472 0.03720 0.03968 0.04339 0.04711 0.05083 0.05579 0.06199 0.07439 0.08679 0.09919 0.12400 0.15500 0.20660 0.24800 0.31 0.35 0.41 0.5 0.6

n 0.73 0.80 0.80 0.82 0.83 0.86 0.88 0.87 0.87 0.89 0.90 0.91 0.92 0.94 0.95 0.97 0.98 0.98 0.99 0.99 0.99 0.99 0.98 0.97 0.95

0.24 0.26 0.26 0.25 0.25 0.24 0.25 0.26 0.25 0.23 0.23 0.22 0.22 0.22 0.22 0.23 0.24 0.25 0.25 0.26 0.27 0.28 0.28 0.29 0.29

R(φ = 0) 0.043 0.033 0.034 0.029 0.026 0.022 0.022 0.023 0.022 0.019 0.017 0.015 0.014 0.014 0.014 0.014 0.015 0.015 0.016 0.017 0.018 0.019 0.021 0.022 0.023

→

∥ ĉ25 4.82 5.26 5.47 5.59

5.94 5.96

5.98

6.246 6.253 6.286 6.316 6.372

6.53 6.71

0.118 0.0505 0.0278 0.0174 0.0796 0.0696 0.0749 0.1900 0.2220 0.0716 0.0682 0.0832 0.0149 2.14E-03 1.71E-02 3.71E-03 2.44E-03 1.59E-03 7.85E-04 7.38E-04 3.89E-04 3.09E-04 2.52E-04 2.96E-04 3.68E-04 3.34E-04

7.48E-05 1.18E-05 4.93E-04 6.74E-03 2.30E-02 7.50E-02

0.431 0.463 0.477 0.485

0.507 0.508

0.509

0.524 0.525 0.526 0.528 0.531

0.539 0.549

Energy (eV) 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 11.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 Tellurium, 0.01364 0.01488 0.01612 0.01736 0.01860 0.01984 0.02108 0.02232 0.02356 0.02480 0.02604 0.02728 0.02976 0.03224 0.03472 0.03720 0.03968 0.04339 0.04711 0.05083

n 7.00 7.23 7.48 7.70 6.99 7.11 6.75 6.89 4.67 4.94 3.94 3.25 2.73 2.30 1.69 1.33 1.32 1.63 1.72 1.73 1.78 1.83 1.72 1.54 1.55 0.99 1.47 0.86 0.80 0.79 0.67 0.59 0.48 0.74 0.83 0.85 0.87 0.89 0.90

k 0.24 0.48 0.94 1.56 2.22 2.46 2.91 3.70 4.67 5.16 5.08 4.77 4.42 4.16 3.44 2.64 1.96 1.60 1.57 1.45 1.36 1.36 1.51 1.37 1.23 0.93 1.25 0.86 0.77 0.76 0.59 0.49 0.31 0.20 0.18 0.15 0.12 0.090 0.045

R(φ = 0) 0.563 0.574 0.589 0.606 0.593 0.604 0.606 0.637 0.654 0.681 0.686 0.681 0.674 0.674 0.646 0.571 0.428 0.312 0.302 0.276 0.257 0.257 0.289 0.260 0.226 0.179 0.233 0.181 0.165 0.164 0.146 0.147 0.160 0.035 0.018 0.013 0.009 0.006 0.003

0.2980 0.0894 0.0535 0.4990 0.1170 0.0343 0.0421 0.1060 0.0880 0.0458 0.0928 0.0886 0.0232 3.06E-03 1.25E-02 2.65E-03 1.89E-03 1.41E-03 8.38E-04 6.79E-04

0.204 0.325 0.370 0.420

→

⊥ ĉ25 2.61 3.65 4.10 4.63

(4.42)

4.71 4.74

0.398

0.422 0.425

Optical Properties of Selected Elements Energy (eV) 0.05579 0.06199 0.07439 0.08679 0.09919 0.1240 0.1550 0.2066 0.2480 0.31 0.35 0.41 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 11.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0

n 4.77

4.796 4.809 4.838 4.864 4.929

4.90 4.93 4.95 5.10 5.22 5.35 5.17 5.56 5.88 6.10 5.94 5.10 4.24 3.57 3.03 2.51 1.72 1.32 1.28 1.47 1.74 1.94 2.19 2.48 2.60 2.59 2.39 1.11 2.08 0.99 0.84 0.87 0.59 0.64 0.52 0.50 0.56 0.54 0.50 0.48 0.46

k 1.59E-04 1.16E-04 7.23E-05 5.34E-05 4.28E-05 3.18E-05

2.19E-05 3.18E-05 7.89E-02 0.149

R(φ = 0) 0.427

0.429 0.430 0.432 0.434 0.439

0.11 0.13 0.22 0.45 0.63 0.63 1.15 1.80 2.69 3.61 3.77 3.75 3.63 3.39 2.70 2.01 1.28 0.82 0.51 0.39 0.32 0.40 0.69 0.91 1.00 1.24 1.11 1.04 1.01 0.87 0.87 0.55 0.41 0.38 0.29 0.25 0.20 0.17 0.088

0.437 0.439 0.441 0.452 0.461 0.472 0.462 0.488 0.517 0.545 0.571 0.594 0.593 0.591 0.588 0.578 0.532 0.440 0.251 0.132 0.104 0.118 0.148 0.192 0.226 0.245 0.235 0.259 0.224 0.215 0.237 0.182 0.282 0.144 0.161 0.165 0.110 0.113 0.127 0.135 0.140

Titanium (Polycrystalline)14 0.10 5.03 23.38 0.15 3.00 15.72 0.20 2.12 11.34 0.25 2.05 8.10 0.30 6.39 9.94 0.35 2.74 6.21

0.965 0.954 0.939 0.890 0.833 0.792

Energy (eV) 0.40 0.45 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.85 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20

12-141 n 2.49 3.35 4.43 4.71 4.38 4.04 3.80 3.62 3.47 3.35 3.28 3.17 2.98 2.74 2.54 2.36 2.22 2.11 2.01 1.92 1.86 1.81 1.78 1.75 1.71 1.68 1.63 1.59 1.55 1.50 1.44 1.37 1.30 1.24 1.17 1.11 1.08 1.06 1.04 1.05 1.13 1.17 1.21 1.24 1.27 1.17 1.24 1.21 1.15 1.11 1.08 1.04 1.05 1.06 1.07 1.11 1.09 1.11 1.10 1.10

4.68 3.25 3.22 3.77 3.89 3.82 3.65 3.52 3.40 3.30 3.25 3.28 3.32 3.30 3.23 3.11 2.99 2.88 2.77 2.67 2.56 2.47 2.39 2.34 2.29 2.25 2.21 2.17 2.15 2.12 2.09 2.06 2.01 1.96 1.90 1.83 1.78 1.73 1.62 1.45 1.33 1.29 1.23 1.21 1.20 1.16 1.21 1.22 1.21 1.18 1.14 1.06 1.02 0.97 0.95 0.94 0.92 0.93 0.94 0.95

R(φ = 0) 0.708 0.545 0.555 0.597 0.603 0.596 0.582 0.570 0.560 0.550 0.546 0.549 0.557 0.559 0.557 0.550 0.540 0.530 0.520 0.509 0.495 0.483 0.471 0.462 0.456 0.451 0.447 0.444 0.442 0.442 0.442 0.443 0.443 0.441 0.436 0.430 0.423 0.413 0.389 0.333 0.284 0.265 0.244 0.236 0.228 0.228 0.234 0.241 0.244 0.240 0.232 0.212 0.198 0.182 0.175 0.167 0.165 0.165 0.169 0.171

Energy (eV) 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.20 17.60 18.00 18.40 18.80 19.20 19.60 20.00 20.40 20.60 21.20 21.60 22.00 22.40 22.80 23.20 23.60 24.00 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 30.0

n 1.08 1.04 1.02 1.00 0.97 0.95 0.94 0.91 0.89 0.86 0.85 0.81 0.80 0.79 0.81 0.81 0.79 0.78 0.77 0.76 0.76 0.76 0.77 0.77 0.79 0.79 0.79 0.83 0.84 0.87 0.90 0.93 0.94 0.94 0.95 0.96 0.97 0.98 0.98 1.00 0.99 0.99 0.98 0.98 0.97 0.96 0.95 0.92 0.91 0.91 0.89 0.89 0.88 0.86 0.85 0.84 0.82 0.83 0.84

0.95 0.96 0.95 0.94 0.93 0.91 0.90 0.88 0.88 0.85 0.83 0.79 0.76 0.72 0.69 0.69 0.68 0.67 0.65 0.55 0.52 0.48 0.45 0.42 0.38 0.36 0.32 0.31 0.28 0.27 0.25 0.25 0.24 0.23 0.24 0.25 0.25 0.27 0.27 0.29 0.31 0.31 0.32 0.33 0.33 0.34 0.35 0.35 0.34 0.33 0.33 0.33 0.32 0.31 0.30 0.29 0.26 0.25 0.22

R(φ = 0) 0.175 0.181 0.181 0.182 0.182 0.181 0.179 0.179 0.180 0.178 0.175 0.167 0.162 0.152 0.139 0.139 0.139 0.137 0.132 0.106 0.097 0.087 0.077 0.069 0.058 0.052 0.045 0.037 0.030 0.025 0.020 0.017 0.165 0.017 0.016 0.016 0.017 0.018 0.019 0.020 0.023 0.024 0.025 0.027 0.028 0.030 0.031 0.033 0.032 0.032 0.032 0.032 0.032 0.032 0.033 0.033 0.029 0.027 0.022

Optical Properties of Selected Elements

12-142 Energy (eV) Tungsten27 0.10 0.20 0.25 0.30 0.34 0.38 0.42 0.46 0.50 0.54 0.58 0.62 0.66 0.70 0.74 0.78 0.82 0.86 0.90 0.94 0.98 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20

14.06 3.87 2.56 1.83 1.71 1.86 1.92 1.69 1.40 1.23 1.17 1.28 1.45 1.59 1.83 2.12 2.36 2.92 3.11 3.15 3.15 3.14 3.05 3.00 3.12 3.29 3.48 3.67 3.84 3.82 3.70 3.60 3.54 3.49 3.49 3.45 3.38 3.34 3.31 3.31 3.32 3.35 3.39 3.43 3.45 3.39 3.24 3.13 3.05 2.99 2.96 2.95 3.02 3.13 3.24 3.33 3.40 3.27

54.71 28.30 22.44 18.32 15.71 13.88 12.63 11.59 10.52 9.45 8.44 7.52 6.78 6.13 5.52 5.00 4.61 4.37 4.44 4.43 4.36 4.32 4.04 3.64 3.24 2.96 2.79 2.68 2.79 2.91 2.94 2.89 2.84 2.76 2.72 2.72 2.68 2.62 2.55 2.49 2.45 2.42 2.41 2.45 2.55 2.66 2.70 2.67 2.62 2.56 2.50 2.43 2.33 2.32 2.41 2.57 2.85 3.27

R(φ = 0)

0.983 0.981 0.980 0.979 0.973 0.963 0.954 0.952 0.952 0.948 0.938 0.917 0.888 0.856 0.810 0.759 0.710 0.661 0.660 0.658 0.653 0.649 0.627 0.590 0.545 0.515 0.500 0.494 0.507 0.518 0.518 0.512 0.506 0.497 0.494 0.493 0.487 0.480 0.472 0.466 0.461 0.459 0.460 0.465 0.476 0.485 0.488 0.482 0.476 0.468 0.460 0.451 0.440 0.442 0.455 0.475 0.505 0.548

Energy (eV) 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80 17.20 17.60 18.00 18.40 18.80 19.20 19.60 20.00 20.40 20.80 21.20 21.60 22.00 22.40

n 2.92 2.43 2.00 1.70 1.47 1.32 1.21 1.12 1.06 1.01 0.98 0.95 0.93 0.94 0.94 0.96 0.99 1.01 1.01 1.02 1.03 1.05 1.09 1.13 1.19 1.24 1.27 1.29 1.28 1.27 1.25 1.22 1.20 1.16 1.10 1.04 0.98 0.94 0.91 0.90 0.90 0.93 0.97 0.98 0.97 0.94 0.90 0.85 0.80 0.74 0.69 0.64 0.60 0.56 0.54 0.52 0.50 0.50 0.49 0.49

3.58 3.70 3.61 3.42 3.24 3.04 2.87 2.70 2.56 2.43 2.30 2.18 2.06 1.95 1.86 1.76 1.70 1.65 1.60 1.55 1.50 1.44 1.38 1.34 1.33 1.34 1.36 1.39 1.42 1.44 1.46 1.48 1.48 1.48 1.47 1.44 1.40 1.35 1.28 1.23 1.17 1.13 1.12 1.14 1.17 1.19 1.21 1.21 1.20 1.18 1.15 1.11 1.07 1.02 0.97 0.92 0.87 0.82 0.77 0.73

R(φ = 0) 0.586 0.618 0.637 0.643 0.646 0.640 0.631 0.619 0.607 0.593 0.573 0.556 0.533 0.505 0.481 0.449 0.422 0.401 0.388 0.369 0.352 0.329 0.307 0.287 0.274 0.270 0.274 0.282 0.290 0.297 0.305 0.313 0.318 0.323 0.329 0.333 0.332 0.325 0.312 0.296 0.276 0.255 0.246 0.249 0.260 0.273 0.289 0.304 0.317 0.330 0.340 0.347 0.353 0.354 0.350 0.342 0.331 0.318 0.303 0.287

Energy (eV) 22.80 23.20 23.60 24.00 24.40 24.80 25.20 25.60 26.00 26.40 26.80 27.00 27.50 28.00 28.50 29.00 29.50 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00

n 0.49 0.49 0.48 0.49 0.50 0.51 0.53 0.55 0.57 0.59 0.61 0.62 0.64 0.67 0.69 0.71 0.73 0.75 0.78 0.79 0.82 0.84 0.85 0.85 0.84 0.83 0.81 0.80

Vanadium9 0.10 12.83 0.20 3.90 0.28 2.13 0.36 1.54 0.44 1.28 0.52 1.16 0.60 1.10 0.68 1.07 0.76 1.08 0.80 1.10 0.90 1.18 1.00 1.34 1.10 1.60 1.20 1.93 1.30 2.25 1.40 2.48 1.50 2.57 1.60 2.57 1.70 2.52 1.80 2.45 1.90 2.36 2.00 2.34 2.10 2.31 2.20 2.28 2.30 2.23 2.40 2.15 2.50 2.02 2.60 1.89 2.70 1.74 2.80 1.61 2.90 1.48

0.69 0.66 0.62 0.57 0.53 0.49 0.46 0.43 0.40 0.38 0.37 0.36 0.34 0.32 0.31 0.30 0.30 0.29 0.29 0.29 0.28 0.29 0.31 0.32 0.33 0.33 0.33 0.33

45.89 24.30 17.35 13.32 10.74 8.93 7.59 6.54 5.67 5.30 4.50 3.80 3.26 2.88 2.71 2.72 2.79 2.84 2.88 2.88 2.85 2.81 2.78 2.80 2.83 2.88 2.91 2.92 2.89 2.85 2.80

R(φ = 0) 0.272 0.263 0.252 0.234 0.213 0.191 0.171 0.150 0.132 0.117 0.105 0.099 0.085 0.073 0.065 0.057 0.052 0.047 0.042 0.040 0.033 0.032 0.033 0.036 0.039 0.040 0.042 0.045 0.978 0.975 0.973 0.966 0.957 0.945 0.929 0.909 0.882 0.864 0.811 0.730 0.632 0.543 0.498 0.491 0.499 0.507 0.512 0.515 0.514 0.509 0.506 0.510 0.516 0.528 0.540 0.552 0.561 0.569 0.577

Optical Properties of Selected Elements Energy (eV) 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.33 7.66 8.00 8.33 8.66 9.00 9.50 10.00 10.50 11.00 11.50 12.00 12.50 13.00 13.50 14.00 14.50 15.00 15.50 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 20.50 21.00 21.50 22.00 22.50 23.00 23.50 24.00 24.50 25.00 25.50 26.00 26.50

n 1.36 1.16 0.99 0.87 0.80 0.78 0.80 0.83 0.87 0.90 0.91 0.93 0.94 0.96 0.98 0.97 0.97 0.97 0.98 0.97 0.98 0.98 0.98 0.98 0.96 0.94 0.91 0.89 0.87 0.88 0.90 0.89 0.88 0.87 0.86 0.86 0.86 0.86 0.85 0.84 0.84 0.83 0.82 0.82 0.82 0.82 0.81 0.81 0.81 0.81 0.81 0.81 0.82 0.82 0.82 0.83 0.83 0.83 0.83 0.84

2.73 2.55 2.37 2.17 1.96 1.76 1.60 1.47 1.38 1.31 1.26 1.18 1.14 1.09 1.06 1.02 0.98 0.94 0.91 0.89 0.87 0.85 0.81 0.81 0.79 0.77 0.74 0.71 0.65 0.58 0.58 0.57 0.55 0.53 0.51 0.49 0.47 0.46 0.45 0.43 0.41 0.40 0.38 0.37 0.35 0.34 0.32 0.31 0.29 0.28 0.27 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17

R(φ = 0) 0.582 0.585 0.586 0.575 0.547 0.503 0.449 0.400 0.355 0.326 0.304 0.271 0.258 0.235 0.223 0.212 0.199 0.185 0.175 0.170 0.162 0.155 0.146 0.145 0.142 0.136 0.133 0.126 0.112 0.091 0.089 0.086 0.082 0.079 0.075 0.070 0.065 0.062 0.061 0.059 0.056 0.054 0.051 0.048 0.045 0.043 0.041 0.038 0.036 0.033 0.032 0.029 0.027 0.025 0.024 0.022 0.020 0.019 0.018 0.016

12-143

Energy (eV) 27.00 27.50 28.00 28.50 29.00 29.50 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00

n 0.84 0.85 0.85 0.86 0.86 0.86 0.87 0.88 0.90 0.90 0.91 0.92 0.94 0.94 0.95 0.95 0.95

0.16 0.16 0.15 0.14 0.14 0.13 0.13 0.12 0.11 0.10 0.10 0.09 0.10 0.10 0.11 0.12 0.13

R(φ = 0) 0.015 0.014 0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.005

→

Zinc, E ∥ ĉ28 0.7514 1.9241 0.827 1.7921 0.866 1.5571 0.952 1.4824 0.992 1.5762 1.033 1.5407 1.078 1.5853 1.127 1.7768 1.181 1.9808 1.240 2.8821 1.305 3.2039 1.377 2.9459 1.459 3.2523 1.550 3.8086 1.653 3.7577 1.722 3.5908 1.823 3.4234 1.937 3.0132 1.984 1.8562 2.066 1.4856 2.094 1.2525 2.119 1.0017 2.275 0.7737 2.445 0.6395 2.666 0.4430 2.917 0.3589 3.220 0.3069 3.594 0.2737 4.065 0.2510 4.678 0.2354

7.5619 6.9973 6.7753 6.2296 5.8843 5.3192 4.9013 4.5307 4.2004 3.4766 3.0042 3.5761 4.2447 4.6212 4.6239 4.4614 4.3232 3.9974 3.9706 4.0555 3.9961 3.8683 3.9129 3.4013 3.1379 2.8140 2.5088 2.1737 1.8528 1.6357

0.883 0.874 0.881 0.868 0.847 0.823 0.793 0.748 0.701 0.575 0.520 0.584 0.640 0.657 0.659 0.650 0.642 0.624 0.690 0.737 0.762 0.789 0.832 0.821 0.851 0.853 0.847 0.828 0.799 0.776

7.4158 6.9688 6.6886 6.2212 5.8910 5.4001 4.9025 4.4062 4.0176 3.2873

0.905 0.892 0.892 0.881 0.863 0.850 0.822 0.746 0.684 0.555

→

Zinc, E ⊥ ĉ28 0.751 1.4469 0.827 1.4744 0.866 1.3628 0.952 1.3165 0.992 1.3835 1.033 1.2889 1.078 1.3095 1.127 1.6897 1.181 1.9701 1.240 2.8717

Energy (eV) 1.305 1.377 1.459 1.550 1.653 1.722 1.823 1.937 1.984 2.066 2.094 2.119 2.275 2.455 2.666 2.917 3.220 3.594 4.065 4.678

n 3.3991 3.1807 3.5064 4.1241 4.0269 3.9369 3.7549 3.4512 3.2515 2.0802 1.7084 1.3329 0.9725 0.7568 0.5470 0.4774 0.3911 0.3147 0.3013 0.2806

k 2.7684 3.4709 4.1994 4.7768 4.8027 4.6356 4.3042 4.1942 4.2980 4.7231 4.7923 4.4751 4.2879 3.7627 3.4277 3.0476 2.7463 2.3041 2.0077 1.7997

Zirconium (Polycrystalline)28 0.10 6.18 1.76 0.15 3.37 1.30 0.20 2.34 1.08 0.26 2.24 1.06 0.30 2.59 1.14 0.36 3.17 1.26 0.40 3.09 1.24 0.46 3.36 1.30 0.50 4.13 1.44 0.56 5.01 1.58 0.60 5.18 1.61 0.70 4.54 1.51 0.80 4.03 1.42 0.90 3.74 1.37 0.96 3.69 1.36 1.00 3.66 1.35 1.10 3.65 1.35 1.20 3.53 1.33 1.30 3.25 1.27 1.40 3.10 1.25 1.50 3.02 1.23 1.60 2.88 1.20 1.70 2.68 1.16 1.80 2.49 1.12 2.00 2.14 1.03 2.10 1.99 1.00 2.20 1.87 0.97 2.30 1.78 0.94 2.40 1.71 0.92 2.50 1.62 0.90 2.60 1.54 0.88 2.70 1.46 0.86 2.80 1.40 0.84 2.90 1.34 0.82 3.00 1.30 0.81 3.10 1.26 0.80 3.30 1.19 0.77 3.40 1.16 0.76 3.50 1.13 0.75

R(φ = 0) 0.497 0.569 0.630 0.664 0.667 0.657 0.635 0.631 0.644 0.738 0.774 0.791 0.825 0.824 0.845 0.834 0.835 0.821 0.789 0.770 0.300 0.123 0.058 0.052 0.073 0.110 0.105 0.123 0.175 0.231 0.242 0.202 0.168 0.149 0.145 0.143 0.142 0.134 0.116 0.106 0.100 0.091 0.078 0.067 0.047 0.040 0.034 0.030 0.027 0.024 0.022 0.019 0.018 0.016 0.016 0.015 0.014 0.013 0.013

Optical Properties of Selected Elements

12-144 Energy (eV) 3.60 3.70 3.80 3.90 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80

n 1.10 1.07 1.04 1.01 0.98 0.94 0.89 0.85 0.81 0.78 0.77 0.77 0.80 0.87 1.00 1.11 1.23 1.33 1.42 1.49 1.54 1.58 1.61 1.63 1.66 1.67 1.68 1.68 1.66

0.74 0.73 0.72 0.71 0.70 0.68 0.67 0.65 0.64 0.63 0.62 0.62 0.63 0.66 0.71 0.75 0.78 0.81 0.84 0.86 0.88 0.89 0.90 0.90 0.91 0.91 0.92 0.92 0.91

R(φ = 0) 0.013 0.013 0.012 0.012 0.012 0.013 0.013 0.014 0.014 0.015 0.016 0.016 0.014 0.013 0.012 0.013 0.014 0.016 0.018 0.020 0.022 0.023 0.024 0.025 0.026 0.026 0.026 0.026 0.026

Energy (eV) 9.00 9.20 9.40 9.60 9.80 10.00 10.20 10.40 10.50 10.60 10.80 11.00 11.20 11.40 11.60 11.80 12.00 12.40 12.80 13.20 13.60 14.00 14.40 14.80 15.20 15.60 16.00 16.40 16.80

n 1.65 1.63 1.60 1.57 1.52 1.47 1.42 1.35 1.32 1.28 1.23 1.19 1.16 1.13 1.11 1.09 1.08 1.05 1.01 0.98 0.95 0.92 0.89 0.90 0.92 0.95 0.98 1.01 1.04

References 1. Shiles, E., Sasaki, T., Inokuti, M., and Smith, D. Y., Phys. Rev. Sect. B, 22, 1612, 1980. 2. Edwards, D. F., and Philipp, H. R., in HOC-I, p. 665. 3. Ives, H. E., and Briggs, N. B., J. Opt. Soc. Am., 27, 395, 1937. 4. Bos, L. W., and Lynch, D. W., Phys. Rev. Sect. B, 2, 4567, 1970. 5. Weaver, J. H., Colavita, E., Lynch, D. W., and Rosei, R., Phys. Rev. Sect. B, 19, 3850, 1979. 6. Hagemann, H. J., Gudat, W., and Kunz, C., J. Opt. Soc. Am., 65, 742, 1975. 7. Schulz, L. G., J. Opt. Soc. Am., 47, 64, 1957. 8. Potter, R. F., in HOC-I, p. 465. 9. Olson, C. G., Lynch, D. W., and Weaver, J. H., unpublished. 10. Lynch, D. W., Olson, C. G., and Weaver, J. H., unpublished. 11. Weaver, J. H., Olson, C. G., and Lynch, D. W., Phys. Rev. Sect. B, 15, 4115, 1977. 12. Lynch, D. W., and Hunter, W. R., in HOC-II, p. 345. 13. Priol, M. A., Daudé, A., and Robin, S., Compt. Rend., 264, 935, 1967. 14. Johnson, P. B., and Christy, R. W., Phys. Rev. Sect. B, 9, 5056, 1974.

0.91 0.90 0.89 0.89 0.87 0.86 0.84 0.82 0.81 0.80 0.78 0.77 0.76 0.75 0.74 0.74 0.73 0.72 0.71 0.70 0.69 0.68 0.67 0.67 0.68 0.69 0.70 0.71 0.72

R(φ = 0) 0.025 0.025 0.024 0.023 0.021 0.020 0.018 0.016 0.016 0.015 0.014 0.014 0.013 0.013 0.013 0.013 0.013 0.012 0.012 0.012 0.013 0.013 0.013 0.013 0.013 0.013 0.012 0.012 0.012

Energy (eV) 17.20 17.60 18.00 18.40 18.80 19.20 19.60 20.00 20.60 21.00 21.60 22.00 22.60 23.00 23.60 24.00 24.60 25.00 25.60 26.00 26.60 27.00 27.60 28.00 28.60 29.00 29.60 30.00

n 1.09 1.13 1.17 1.21 1.24 1.27 1.29 1.30 1.29 1.27 1.23 1.20 1.15 1.12 1.08 1.05 1.02 1.00 0.97 0.95 0.91 0.88 0.84 0.83 0.82 0.81 0.82 0.82

0.74 0.75 0.76 0.78 0.79 0.80 0.80 0.81 0.80 0.80 0.78 0.77 0.76 0.75 0.73 0.73 0.71 0.71 0.69 0.69 0.67 0.66 0.65 0.64 0.64 0.64 0.64 0.64

R(φ = 0) 0.013 0.013 0.014 0.014 0.014 0.015 0.015 0.015 0.015 0.015 0.014 0.014 0.013 0.013 0.013 0.013 0.012 0.012 0.012 0.013 0.013 0.013 0.014 0.014 0.014 0.014 0.014 0.014

15. Arakawn, E. T., and Inagaki, T., in HOC-II, p. 461. 16. Weaver, J. H., Lynch, D. W., and Olson, D. G., Phys. Rev. Sect. B, 10, 501, 1973. 17. Lynch, D. W., Rosei, R., and Weaver, J. H., Solid State Commun., 9, 2195, 1971. 18. Weaver, J. H., Lynch, D. W., and Olson, C. G., Phys. Rev. Sect. B, 7, 4311, 1973. 19. Weaver, J. H., and Benbow, R. L., Phys. Rev. Sect. B, 12, 3509, 1975. 20. Weaver, J. H., Phys. Rev., Sect. B, 11, 1416, 1975. 21. Lynch, D. W., and Hunter, W. R., in HOC-II, p. 364. 22. Palik, E. D., in HOC-II, p. 691. 23. Edwards, D. F., in HOC-I, p. 547. 24. Lynch, D. W., and Hunter, W. R., in HOC-II, p. 354. 25. Palik, E. D., in HOC-II, p. 709. 26. Lynch, D. W., Olson, C. G., and Weaver, J. H., Phys. Rev. Sect. B, 11, 3671, 1975. 27. Weaver, J. H., Lynch, D. W., and Olson, C. G., Phys. Rev. Sect. B, 12, 1293, 1975. 28. Lanham, A. P., and Terherne, D. M., Proc. Phys. Soc., 83, 1059, 1964.

Elasto-optic, Electro-optic, and Magneto-optic Constants When a crystal is subjected to a stress field, an electric field, or a magnetic field, the resulting optical effects are in general dependent on the orientation of these fields with respect to the crystal axes. It is useful, therefore, to express the optical properties in terms of the refractive index ellipsoid (or indicatrix): x2 y2 z 2 + + =1 nx2 n 2y nz2

∑B x y ij

= 1 (i, j = 1, 2, 3)

where 1 1 Bij =   =  2   ε  ij  n  ij

ε is the dielectric constant or permeability; the quantity Bij is called impermeability. A crystal exposed to a stress S will show a change of its impermeability. The photo-elastic (or elasto-optic) constants, Pijkl, are defined by 1 1 ∆   = ∆  2  = ∑ Pijkl Skl  n  ij  ε  ij kl

where n is the refractive index and Skl are the strain tensor elements; the Pijkl are the elements of a 4th rank tensor. When a crystal is subjected to an electric field E, two possible changes of the refractive index may occur depending on the symmetry of the crystal. 1. All materials, including isotropic solids and polar liquids, show an electro-optic birefringence (Kerr effect) which is proportional to the square of the electric field, E: 1 ∆  2  = ∑ K ijkl Ek El = ∑ g ijkl pk pl  n  ij k k ,l =1, 2 ,3

where Ek and El are the components of the electric field and Pk and Pl the electric polarizations. The coefficients, Kijkl, are the quadratic electro-optic coefficients, while the constants gijkl are known as the Kerr constants. 2. The other electro-optic effect only occurs in the 20 piezoelectric crystal classes (no center of symmetry). This effect is known as the Pockels effect. The optical impermeability changes linearly with the static field

12-164

1 ∆  2  = ∑ rij ,k Ek  n  ij k

The coefficients rij,k have the name (linear) electro-optic coefficients. The values of the electro-optic coefficients depend on the boundary conditions. If the superscripts T and S denote, respectively, the conditions of zero stress (free) and zero strain (clamped) one finds: rijT = rijS + qikE e jk = rijS + PikE d jk

where ejk = (∂Tk/∂Ej)S and djk = (∂Sk/∂Ej)T are the appropriate piezoelectric coefficients. The interaction between a magnetic field and a light wave propagating in a solid or in a liquid gives rise to a rotation of the plane of polarization. This effect is known as Faraday rotation. It results from a difference in propagation velocity for left and right circular polarized light. The Faraday rotation, θF , is linearly proportional to the magnetic field H: θ F =VlH

where l is the light path length and V is the Verdet constant (minutes/oersted·cm). For ferromagnetic, ferrimagnetic, and antiferromagnetic materials the magnetic field in the above expression is replaced by the magnetization M and the magneto-optic coefficient in this case is known as the Kund constant K: Specific Faraday rotation F =KM

In the tables below the Faraday rotation is listed at the saturation magnetization per unit length, together with the absorption coefficient α, the temperature T, the critical temperature TC (or TN), and the wavelength of the measurement. In the tables that follow, the properties are presented in groups:

• Elasto-optic coefficients (photoelastic constants) • Linear electro-optic coefficients (Pockels constants) • Quadratic electro-optic coefficients (Kerr constants) • Magneto-optic coefficients: • Verdet constants • Faraday rotation parameters

Within each group, materials are classified by crystal system or physical state. References are given at the end of each group of tables.

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

12-165

ELASTO-OPTIC COEFFICIENTS (PHOTOELASTIC CONSTANTS) Name Cubic (43m, 432, m3m) Sodium fluoride Sodium chloride Sodium bromide Sodium iodide Potassium fluoride Potassium chloride Potassium bromide Potassium iodide Rubidium chloride Rubidium bromide Rubidium iodide Lithium fluoride Lithium chloride Ammonium chloride Cadmium telluride Calcium fluoride Copper chloride Copper bromide Copper iodide Diamond Germanium Gallium arsenide Gallium phosphide Strontium fluoride Strontium titanate KRS-5 KRS-6 Zinc sulfide

Formula NaF NaCl NaBr NaI KF KCl KBr KI RbCl RbBr RbI LiF LiCl NH4Cl CdTe CaF2 CuCl CuBr CuI C Ge GaAs GaP SrF2 SrTiO3 Tl(Br,I) Tl(Br,Cl) ZnS

Rare Gases

λ/µm 0.633 0.589 0.589 0.589 0.546 0.633 0.589 0.590 0.589 0.589 0.589 0.589 0.589 0.589 1.06 0.55–0.65 0.633 0.633 0.633 0.540–0.589 3.39 1.15 0.633 0.633 0.633 0.633 0.633 0.633

Formula

Neon (T = 24.3 K) Argon (T = 82.3 K) Krypton (T = 115.6 K) Xenon (T = 160.5 K)

p12 0.20 0.159 0.184 – 0.20 0.16 0.165 0.171 0.172 0.185 0.167 0.13 – 0.245 –0.017 0.226 0.250 0.195 0.151 0.123 –0.128 –0.140 –0.082 0.269 0.095 0.149 –0.337 –0.01

p44 –0.03 –0.011 –0.0036 0.0048 –0.029 –0.025 –0.022 – –0.041 –0.034 –0.023 –0.045 –0.0177 0.042 –0.057 0.0254 –0.082 –0.083 –0.068 –0.161 –0.072 –0.072 –0.074 0.0185 0.072 –0.0725 –0.164 0.075

p11

p12

p44

p11-p12 –0.12 –0.042 –0.035 –0.0141 0.06 0.06 0.047 0.041 0.116 0.108 0.095 –0.11 –0.0407 –0.103 –0.135 –0.183 –0.130 –0.123 –0.119 –0.385 –0.023 –0.025 –0.069 –0.189 – –0.289 –0.114 0.101

Ref. 1 2 1 3 1 4 5 6 7,8 7,8 7,8 5 3 9 10 11 12 12 12 13 14 15 15 16 17 18,20 19,20 15

p11-p12

Ref.

0.488 0.488 0.488 0.488

0.157 0.256 0.34 0.284

0.168 0.302 0.34 0.370

0.004 0.015 0.037 0.029

Formula Gd3Ga5O12 Y3Fe5O12 Y3Ga5O12 Y3Al5O12

λ/µm 0.514 1.15 0.633 0.633

p11 –0.086 0.025 0.091 –0.029

p12 –0.027 0.073 0.019 0.0091

p44 –0.078 0.041 0.079 –0.0615

p11-p12 –0.059 – – –0.038

Ref. 23 15 17 15

Cubic (23, m3) Barium nitrate

Formula Ba(NO3)2

λ/µm 0.589

p11

p44 –0.0205

Pb(NO3)2 NaBrO3 NaClO3 Sr(NO3)2

p13 p11–p13 = 0.713 0.20 0.213 0.20 0.316

Ref. 13

Lead nitrate Sodium bromate Sodium chlorate Strontium nitrate

p12 p11–p22 = 0.992 0.24 0.218 0.24 0.362

GGG YIG YGG YAG

Ne Ar Kr Xe

λ/µm

p11 0.08 0.115 0.148 – 0.26 0.22 0.212 0.212 0.288 0.293 0.262 0.02 – 0.142 –0.152 0.038 0.120 0.072 0.032 –0.278 –0.151 –0.165 –0.151 0.080 0.15 –0.140 –0.451 0.091

Garnets

Hexagonal (mmc, 6mm) Beryl Cadmium sulfide Zinc oxide Zinc sulfide

Formula Be3Al2Si6O18 CdS ZnO ZnS

λ/µm 0.589 0.633 0.633 0.633

0.589 0.589 0.589 0.41

–

0.162 0.185 0.162 0.178

–0.0198 –0.0139 –0.0198 –0.014

p11

p12

p13

p31

p33

0.0099 –0.142 ±0.222 –0.115

0.175 –0.066 ±0.099 0.017

0.191 –0.057 –0.111 0.025

0.313 –0.041 ±0.088 0.0271

0.023 –0.20 –0.235 –0.13

–0.011 –0.046 0 –0.086

p44 –0.152 –0.099 0.0585 –0.0627

21 22 21 22

24,25 26 26 27 Ref. 28 15,2 30 31

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

12-166 Trigonal (3m, 32, 3m) Sapphire Calcite Lithium niobate Lithium tantalate Cinnabar Quartz Proustite Sodium nitrite Tellurium

Formula Al2O3 CaCO3 LiNbO3 LiTaO3 HgS SiO2 Ag3AsS3 NaNO2 Te

Tetragonal (4/mmm, 42m, 422) Ammonium dihydrogen phosphate Barium titanate Cesium dihydrogen arsenate Magnesium fluoride Calomel Potassium dihydrogen phosphate Rubidium dihydrogen arsenate Rubidium dihydrogen phosphate Strontium barium niobate Strontium barium niobate Tellurium oxide Rutile Tetragonal (4, ¯4, 4/m) Cadmium molybdate Lead molybdate Sodium bismuth molybdate

Orthorhombic (222, m22, mmm) Ammonium chlorate Ammonium sulfate Rochelle salt Iodic acid (α) Sulfur (α) Barite Topaz

λ/µm 0.644 0.514 0.633 0.633 0.633 0.589 0.633 0.633 10.6

p11 –0.23 0.062 ±0.034 –0.081

p12 –0.03 0.147 ±0.072 0.081

0.16 ±0.10

0.27 ±0.19 ±0.21 0.130

0.155

Formula ADP BaTiO3 CDA MgF2 Hg2Cl2 KDP RDA RDP Sr0.75Ba0.25Nb2O6 Sr0.5Ba0.5Nb2O6 TeO2 TiO2

p12 0.10 0.24 0.205

p13 0.13 0.255 0.25

p12 0.24

p13 0.18

p21 0.23

(NH4)2SO4

0.633

0.26

0.19

±0.260

±0.230 ±0.27

NaKC4H4O6 HIO3 S BaSO4 Al2SiO4(OH,F)2

0.589 0.633 0.633 0.589 –

0.35 0.302 0.324 0.21 –0.085

0.41 0.496 0.307 0.25 0.069

0.42 0.339 0.268 0.16 0.052

0.37 0.263 0.272 0.34 0.095

λ/µm 0.589

p11 = 0.313 p12 = 0.251 p13 = 0.270 p15 = –0.10 p21 = 0.281 p22 = 0.252 p23 = 0.272

–0.030

0.29 ±0.24 ±0.25 –

–

p13 0.169 – 0.200 – ±0.256 0.174 0.200 0.218 0.08 0.17 0.340 –0.139

p16 – 0.017 –

λ/µm p11 0.633 –

Formula C2H7NO3S

p31 –0.04 0.241 ±0.178 0.089

±0.027 –

Formula NH4ClO3

Monoclinic (2, m, 2/m) Taurine

p14 0.00 –0.011 ±0.066 –0.026

p12 0.277 – 0.225 – ±0.440 0.282 0.239 0.240 0.10 0.08 0.187 0.143

p11 0.319 0.425 0.267 – ±0.551 0.287 0.227 0.273 0.16 0.06 0.0074 0.017

λ/µm 0.589 0.633 0.633 0.546 0.633 0.589 0.633 0.633 0.633 0.633 0.633 0.633

Formula λ/µm p11 0.633 0.12 CdMoO4 0.633 0.24 PbMoO4 NaBi(MoO4)2 0.633 0.243

p13 0.02 0.186 ±0.139 0.093 ±0.445 0.27 ±0.22 ±0.215 –

p22

0.28 0.412 0.301 0.24 –0.120

p23 0.20

p31 0.11 0.175 0.21

p31 0.197 – 0.195 – ±0.137 0.241 0.205 0.210 0.11 0.09 0.090 –0.080

p33 0.18 0.300 0.29

p41 0.01 –0.036 ±0.154 –0.085 – –0.047 – 0.055 –

p33 0.167 – 0.227 – ±0.010 0.122 0.182 0.208 0.47 0.23 0.240 –0.057

p44 – 0.067 –

p44 –0.10 –0.058 ±0.300 0.028 – –0.079 – –0.06 –

p44 –0.058 – – ±0.0776 – –0.019 – – – – –0.17 –0.009

p45 – –0.01 –

p61 – 0.013 –

p66 –0.091 – – ±0.0488 ±0.047 –0.064 – – – – –0.046 –0.060

p66 – 0.05 –

Ref. 15,32 33 15,34 15,35 36 37 38 39 15

Ref. 40 41 42 43 44 45 41 41 46 46 47 48

Ref. 49 52 –

p32 0.18

p33 ±0.02

p44 p55 <±0.02 –

±0.254 0.20

±0.26

0.26

0.015

±0.0015 0.012

0.34 0.304 0.310 0.19 0.065

0.35 0.345 0.232 0.22 0.085

0.36 0.336 0.270 0.31 –0.083

–0.030 0.084 0.143 0.002 –0.095

0.0046 –0.030 0.019 –0.012 –0.031

53 54 54 55 28

p25 = –0.0025 p31 = 0.362 p32 = 0.275 p33 = 0.308 p35 = –0.003 p44 = 0.0025 p46 = –0.0056

p31 0.19

p33 –0.20 0.139 ±0.060 –0.044 ±0.115 0.10 ±0.20

0.36 0.251 0.203 0.28 0.095

p51 = –0.014 p52 = 0.006 p53 = 0.0048 p55 = 0.047 p64 = 0.0024 p66 = 0.0028

p66 ±0.04

–0.025 0.098 0.118 0.037 0.098

Ref. 51

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants Isotropic Fused silica Water Polystyrene Lucite Orpiment Tellurium oxide Laser glasses

Dense flint glasses (examples)

Formula SiO2 H2O As2S3-glass TeO2-glass LGS-247-2 LGS-250-3 LGS-1 KGSS-1621 LaSF SF4 U10502 TaFd7

λ/µm 0.633 0.633 0.633 0.633 1.15 0.633 0.488

0.633

p11 0.121 ±0.31 ±0.30 ±0.30 0.308 0.257 ±0.168 ±0.135 ±0.214 ±0.205 0.088 0.215 0.172 0.099

p12 0.270 ±0.31 ±0.31 0.28 0.299 0.241 ±0.230 ±0.198 ±0.250 ±0.239 0.147 0.243 0.179 0.138

References A. Narasimhamurty, T. S., Photoelastic and Electro-Optic Properties of Crystals, Plenum Press, New York, 1981, pp. 290–293. B. Weber, M. J., Ed., CRC Handbook of Laser Science and Technology, Volume IV, Part 2, CRC Press, Boca Raton, FL, 1986, pp. 324–331. 1. Petterson, H. E., J. Opt. Soc. Am., 63, 1243, 1973. 2. Burstein, E. and Smith, P. L., Phys. Rev., 74, 229, 1948. 3. Pakhnev, A. V., et al., Sov. Phys. J. (transl.), 18, 1662, 1975. 4. Feldman, A., Horovitz, D., and Waxler, R. M., Appl. Opt., 16, 2925, 1977. 5. Iyengar, K. S., Nature (London), 176, 1119, 1955. 6. Bansigir, K. G. and Iyengar, K. S., Acta Crystallogr., 14, 727, 1961. 7. Pakhev, A. V., et al., Sov. Phys. J. (transl.), 20, 648, 1975. 8. Bansigir, K. G., Acta Crystallogr., 23, 505, 1967. 9. Krishna Rao, K. V. and Krishna Murty, V. G., Ind. J. Phys., 41, 150, 1967. 10. Weil, R. and Sun, M. J., Proc. Int. Symp. CdTe (Detectors), Strasbourg Centre de Rech. Nucl., 1971, XIX-1 to 6, 1972. 11. Schmidt, E. D. D. and Vedam, K., J. Phys. Chem. Solids, 27, 1563, 1966. 12. Biegelsen, D. K., et al., Phys. Rev. B, 14, 3578, 1976. 13. Helwege, K. H., Landolt-Börnstein, New Series Group III, Vol. II, Springer-Verlag, Berlin, 1979. 14. Feldman, A., Waxler, R. M., and Horovitz, D., J. Appl. Phys., 49, 2589, 1978. 15. Dixon, R. W., J. Appl. Phys., 38, 5149, 1967. 16. Shabin, O. V., et al., Sov. Phys. Sol. State (transl.), 13, 3141, 1972. 17. Reintjes, J. and Schultz, M. B., J. Appl. Phys., 39, 5254, 1968. 18. Rivoallan, L. and Favre, F., Opt. Commun., 8, 404, 1973. 19. Rivoallan, L. and Favre, F., Opt. Commun., 11, 296, 1974. 20. Afanasev, I. I., et al., Sov. J. Opt. Technol., 46, 663, 1979. 21. Rand, S. C., et al., Phys. Rev. B, 19, 4205, 1979. 22. Sipe, J. E., Can J. Phys., 56, 199, 1978. 23. Christyi, I. L., et al., Sov. Phys. Sol. State (transl.), 17, 922, 1975. 24. Narasimhamurty, T. S., Curr. Sci. (India), 23, 149, 1954. 25. Smith, T. M. and Korpel, A., IEEE J. Quant. Electron., QE-1, 283, 1965.

12-167 p44 –0.075

0.0045 0.0079

–0.030 –0.014 –0.004 –0.020

Ref. 15 15 25 25 15 56 57

26. Narasimhamurty, T. S., Proc. Ind. Acad. Sci., A40, 164, 1954. 27. Rabman, A., Bhagarantam Commem. Vol., Bangalore Print. and Publ., 173, 1969. 28. Eppendahl, R., Ann. Phys. (IV), 61, 591, 1920. 29. Laurenti, J. P. and Rouzeyre, M., J. Appl. Phys., 52, 6484, 1981. 30. Sasaki, H., et al., J. Appl. Phys., 47, 2046, 1976. 31. Uchida, N. and Saito, S., J. Appl. Phys., 43, 971, 1972. 32. Waxler, R. M. and Farabaugh, E. M., J. Res. Natl. Bur. Stand., A74, 215, 1970. 33. Nelson, D. F., Lazay, P. D., and Lax, M., Phys. Rev., B6, 3109, 1972. 34. O’Brien, R. J., Rosasco, G. J., and Weber, A., J. Opt. Soc. Am., 60, 716, 1970. 35. Avakyants, L. P., et al., Sov. Phys., 18, 1242, 1976. 36. Sapriel, J., Appl. Phys. Lett., 19, 533, 1971. 37. Narasimhamurty, T. S., J. Opt. Soc. Am., 59, 682, 1969. 38. Zubrinov, I. I., et al., Sov. Phys. Sol. State (transl.), 15, 1921, 1974. 39. Kachalov, O. V. and Shpilko, I. O., Sov. Phys. JETP (transl.), 35, 957, 1972. 40. Narasimhamurty, T. S., et al., J. Mater. Sci., 8, 577, 1973. 41. Tada, K. and Kikuchi, K., Jpn. J. Appl. Phys., 19, 1311, 1980. 42. Aleksandrov, K. S., et al., Sov. Phys. Sol. State (transl.), 19, 1090, 1977. 43. Afanasev, I. I., et al., Sov. Phys. Sol. State (transl.), 17, 2006, 1975. 44. Silvestrova, I. M., et al., Sov. Phys. Cryst. (transl.), 20, 649, 1975. 45. Veerabhadra Rao, K. and Narasimhamurty, T. S., J. Mater. Sci., 10, 1019, 1975. 46. Venturini, E. L., et al., J. Appl. Phys., 40, 1622, 1969. 47. Vehida, N. and Ohmachi, Y., J. Appl. Phys., 40, 4692, 1969. 48. Grimsditch, M. H. and Ramdus, A. K., Phys. Rev. B, 22, 4094, 1980. 49. Schinke, D. P. and Viehman,W., unpublished data. 50. Coquin, G. A., et al., J. Appl. Phys., 42, 2162, 1971. 51. Vasquez, F., et al., J. Phys. Chem. Solids, 37, 451, 1976. 52. Luspin, Y. and Hauret, G., C.R.Ac. Sci. Paris, B274, 995, 1972. 53. Narasimhamurty, T. S., Phys. Rev., 186, 945, 1969. 54. Haussühl, S. and Weber, H. J., Z. Kristall., 132, 266, 1970. 55. Vedam, K., Proc. Ind. Ac. Sci., A34, 161, 1951. 56. Yano, T., Fukumoto, A., and Watanabe, A., J. Appl. Phys., 42, 3674, 1971. 57. Manenkov, A. A. and Ritus, A. I., Sov. J. Quant. Electr., 8, 78, 1978. 58. Eschler, H. and Weidinger, F., J. Appl. Phys., 46, 65, 1975.

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

12-168

LINEAR ELECTRO-OPTIC COEFFICIENTS Name Cubic (¯43m) Cuprous bromide Cuprous chloride Cuprous iodide Eulytite (BSO) Germanium eulytite (BGO) Gallium arsenide Gallium phosphide Hexamethylenetetramine Sphalerite Zinc selenide Zinc telluride Cadmium telluride

Cubic (23) Ammonium chloride (77 K) Ammonium cadmium langbeinite Ammonium manganese langbeinite Thallium cadmium langbeinite Potassium magnesium langbeinite Bismuth monogermanate Bismuth monosilicate Sodium chlorate Sodium uranyl acetate Trenhydrobromide Trenhydrochloride

Formula CuBr CuCl CuI Bi4Si3O12 Bi4Ge3O12 GaAs GaP C6H12N4 ZnS ZnSe ZnTe CdTe

Formula

Tetragonal (4mm) Barium titanate Potassium lithium niobate Lead titanate Strontium barium niobate (SBN75) Strontium barium niobate (SBN46)

Formula NH4H2PO4 NH4D2PO4 NH4H2AsO4 CsH2AsO4 CsD2AsO4 KH2PO4 KD2PO4 KH2AsO4 KD2AsO4 RbH2PO4 RbH2AsO4 RbD2AsO4

– 0.546 0.546 0.546 0.546 – – 0.589 0.546 – – Ttran K 148 242 – 143 212 123 222 97 162 147 110 178

r41 pm/V 24.5 – – – – 8.6 8.8 12.5 – – – –

r63 pm/V –8.5 11.9 9.2 18.6 36.6 –10.5 23.8 10.9 18.2 15.5 13.0 21.4

Ttran

r13

r33

r51

pm/V

Formula BaTiO3 K3Li2Nb5O15 PbTiO3 Sr0.75Ba0.25Nb2O6 Sr0.46Ba0.54Nb2O6

r41 pm/V 1.5 0.70 0.53 0.37 0.40 3.3 3.3 0.4 0.87 1.5 1.7

λ/µm

NH4Cl (NH4)2Cd2(SO4)3 (NH4)2Mn2(SO4)3 Tl2Cd2(SO4)3 K2Mg2(SO4)3 Bi12GeO20 Bi12SiO20 NaClO3 NaUO2(CH3COO)3 N(CH2CH2NH2)3 3HBr N(CH2CH2NH2)3 3HCl

Tetragonal (¯42m) Ammonium dihydrogen phosphate (ADP) Ammonium dideuterium phosphate (AD*P) Ammonium dihydrogen arsenate (ADA) Cesium dihydrogen arsenate (CsDA) Cesium dideuterium arsenate (CsD*A) Potassium dihydrogen phosphate (KDP) Potassium dideuterium phosphate (KD*P) Potassium dihydrogen arsenate (KDA) Potassium dideuterium arsenate (KD*A) Rubidium dihydrogen phosphate (RDP) Rubidium dihydrogen arsenate (RDA) Rubidium dideuterium arsenate (RD*A)

r41 pm/V 0.85 3.6 –5.0 0.54 1.0 1.6 –1.07 0.78 2.1 2.0 4.2 6.8

λ/µm 0.525 0.633 0.55 0.63 0.63 10.6 0.56 0.633 0.65 0.546 3.41 3.39

406 693 765 330 602

8 8.9 13.8 6.7 ~180

28 5.9 5.9 1340 35

– – – 42 –

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

Hexagonal (6mm) Greenockite Greenockite (const. strain) Wurzite Zincite

Formula CdS CdS ZnS ZnO

Hexagonal (6) Lithium iodate Lithium potassium sulfate

Trigonal (3m) Cesium nitrate Lithium niobate Lithium tantalate Lithium sodium sulfate Tourmaline

Formula LiIO3 LiKSO4

Formula CsNO3 LiNbO3 LiTaO3 LiNaSO4 –

Trigonal (32) Cesium tartrate Cinnabar Potassium dithionate Strontium dithionate Quartz Selenium

Orthorhombic (222) Ammonium oxalate Rochelle salt

Orthorhombic (mm2) Barium sodium niobate (BSN) Potassium niobate

r13 pm/V

4.1 r13–r33 = 1.6

Ttran K 425 1483 890 – –

2.9 2.4 1.8 +2.6

r33 pm/V 6.4 –

r42 pm/V 1.4 –

r33 pm/V – 30.8 30.5 – –

Ttran K – 659 – – 1140 398

r11 pm/V 1.0 3.1 0.26 0.1 –0.47 2.5

r41 pm/V – 1.5 – – 0.2

r41 pm/V 230 –2.0

r52 pm/V 330 –1.7

– 8.6 8.4 – –

Ttran K

r23 pm/V 13 1.3

r13 pm/V 15 28

Formula

Ca2Nb2O7 (NH2CH2COOH)3·H2SO4

Ttrans K

– 322

r42 pm/V – 28 – – –

r63 pm/V 250 +0.32

r33 pm/V 48 64

r22 pm/V 0.33 7.2

r51 pm/V 3.7 – – –

r51 pm/V 3.3 –

r22 pm/V 0.43 7.0 – <0.02 0.3

– Tu = 297 Tl = 255

Ttrans K 833 476

2.0 – – –

r42 pm/V

r13 pm/V

Formula Cs2C4H4O6 HgS K2S2O6 SrS2O6·4H2O SiO2 Se

Formula Ba2NaNbO15 KNbO3

r33 pm/V

3.1 1.1 0.9 –1.4

Formula (NH4)2C2O4·4H2O KNaC4H4O6·4H2O

Monoclinic (2) Calcium pyroniobate Triglycine sulfate (TGS)

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r42 pm/V 92 380

r32 pm/V 13.7 13.6

References 1. Narasimhamurty, T. S., Photoelastic and Electro-Optic Properties of Crystals, Plenum Press, New York, 1981, pp. 405–407. 2. Weber, M. J., Ed., CRC Handbook of Laser Science and Technology, Vol. IV, CRC Press, Boca Raton, FL, 1986, pp. 258–278.

r51 pm/V 90 105

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QUADRATIC ELECTRO-OPTIC COEFFICIENTS Kerr Constants of Ferroelectric Crystals1,2 Name Barium titanate Strontium titanate Potassium tantalate niobate Potassium tantalate Lithium niobate Lithium tantalate Barium sodium niobate (BSN)

Formula BaTiO3 SrTiO3 KTa0.65Nb0.35O3 KTaO3 LiNbO3 LiTaO3 Ba0.8Na0.4Nb2O6

Ttran K 406 – 330 13 1483 938 833

λ µm 0.633 0.633 0.633 0.633 – – –

g11 1010 esu 1.33 – 1.50 – 0.94 1.0 1.55

g12 1010 esu –0.11 – –0.42 – 0.25 0.17 0.44

g11–g12 1010 esu 1.44 1.56 1.92 1.77 0.7 0.8 1.11

g44 1010 esu – 1.63 1.33 0.6 0.7

Kerr Constants of Selected Liquids2 K is the Kerr constant at a wavelength of 589 nm and at room temperature; ε is the static dielectric constant; tm is the melting point; and tb is the normal boiling point Name Carbon disulfide Acetone Methyl ethyl ketone Pyridine Ethyl cyanoacetate o-Dichlorobenzene Benzenesulfonyl chloride Nitrobenzene Ethyl 3-aminocrotonate Paraldehyde

Molecular formula CS2 C3H6O C4H8O C5H5N C5H7NO2 C6H4Cl2 C6H5ClO2S C6H5NO2 C6H11NO2 C6H12O3

K 10–7 esu +3.23 +16.3 +13.6 +20.4 +38.8 +42.6 +89.9 +326 +31.0 –23.0

Benzaldehyde

C7H6O

+80.8

p-Chlorotoluene o-Nitrotoluene m-Nitrotoluene p-Nitrotoluene Benzyl alcohol

C7H7Cl C7H7NO2 C7H7NO2 C7H7NO2 C7H8O

+23.0 +174 +177 +222 –15.4

m-Cresol

C7H8O

+21.2

m-Chloroacetophenone Acetophenone

C8H7ClO C8H8O

+69.1 +66.6

Quinoline Ethyl salicylate Carvone Ethyl benzoylacetate Water

C9H7N C9H10O3 C10H14O C11H12O3 H2O

+15.0 +19.6 +23.6 +16.0 +4.0

Dielectric constant at radio frequencies (108–109 Hz).

2.63 21.0 18.56 13.26 31.6 10.12 28.90 35.6 – 14.7 12.0a 17.85 14.1a 6.25 26.26 24.95 22.2 11.92 10.8a 12.44 5.0a 17.44 15.8a 9.16 8.48 11.2 13.50 80.10

tm °C –111.5 –94.8 –86.67 –42 –22.5 –16.7 +14.5 +5.7 +33.9 +12.6

tb °C +46.3 +56.1 +79.6 +115.23 205 180 247 210.8 210 124

–26

179.05

+7.5 –10 +15.5 +51.6 –15.3

162.4 222.3 232 238.3 205.8

+11.8

202.27

+19.7

202.3

–14.78 +1.3 <0 <0 0.00

237.16 231.5 230 270 100.0

References 1. Narasimhamurty, T. S., Photoelastic and Electro-Optic Properties of Crystals, Plenum Press, New York, 1981, p. 408. 2. Gray, D. E., Ed., AIP Handbook of Physics, McGraw Hill, New York, 1972, p. 6–241.

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

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MAGNETO–OPTIC CONSTANTS Verdet Constants of Non-Magnetic Crystals1 V is the Verdet constant; n is the refractive index; and λ is the wavelength. Material Al2O3 BaTaO3

Bi4Ge3O12 C (diamond) CaCO3 CaF2 Cd0.55Mn0.45Te CuCl GaSe KAl(SO4)2·12H2O KBr KCl KI KTaO3

LaF3 (H∥c)

MgAl2O4 NH4AlSO4·12H2O NH4Br NH4Cl NaBr NaCl NaClO3 NiSO4·6H2O SiO2 SrTiO3

ZnS ZnSe

T K 300 300 403 403 403 403 300 300 300 300 300 300 300 300 298 300 300 300 300 300 300 296 296 296 296 296 300 300 300 300 300 300 300 300 300 300 300 300 300 300 297 297 300 300 298 298 298 298 300 300 300 300 300 300 300

λ nm 546.1 589.3 427 496 620 826 442 632.8 1064 589.3 589.3 589.3 632.8 546.1 632.8 589.3 546.1 589.3 589.3 546.1 589.3 352 413 496 620 826 325 442 632.8 1064 589.3 589.3 589.3 546.1 589.3 546.1 546.1 589.3 546.1 589.3 546.1 589.3 546.1 589.3 413 496 620 826 546.1 589.3 476 496 514 587 632.8

1.771 1.768

2.077 2.048 2.031 2.417 1.658 1.434 1.93 1.456 1.564 1.560 1.490 1.673 1.666

1.639 1.615 1.601 1.592 1.718 1.459 1.711 1.643

1.544 1.515 1.511 1.546 1.544 2.627

2.368 2.826 2.759 2.721 2.627 2.592

V min/Oe cm 0.0240 0.0210 0.95 0.38 0.18 0.072 0.289 0.099 0.026 0.0233 0.019 0.0088 6.87 0.20 0.80 0.0124 0.0500 0.0425 0.0275 0.083 0.070 0.44 0.19 0.096 0.051 0.022 0.054 0.028 0.012 0.006 0.021 0.0128 0.0504 0.0410 0.0362 0.0621 0.0410 0.0345 0.0105 0.0081 0.0256 0.0221 0.0195 0.0166 0.78 0.31 0.14 0.066 0.287 0.226 1.50 1.04 0.839 0.529 0.406

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

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Verdet Constants of Rare-Earth Aluminum Garnets at Various Wavelengths1 The absorption coefficient α for these materials ranges from 0.2 to 0.6 cm–1 at 300 K. Material Tb2Al5O12

Dy3Al5O12 Ho3Al5O12 Er3Al5O12 Tm3Al5O12 Yb3Al5O12

T/K 300 77 4.2 1.45 300 300 300 300 298 77

λ = 405 nm –2.266

–1.241 –0.709 –0.189 +0.151 0.287 0.718

450 nm –1.565 –102.16

480 nm –1.290 –83.45

–200.95 –0.942 –0.320 –0.240 +0.103 0.215 0.540

–172.52 –0.803 –0.260 –0.154 +0.093 0.186 0.481

Verdet Constants for KDP-Type Crystals1

Measurements refer to T = 298 K and λ = 632.8 nm, with k ∥ [001]. V Material min/Oe cm KH2PO4 (KDP) KH0.3D1.7PO4 (KD*P) NH4H2PO4 (ADP) KH2AsO4 (KDA) KH0.1D1.9AsO4 (KD*A) NH4H2AsO4 (ADH)

0.0124 0.145 0.138 0.238 0.245 0.244

V in min/Oe cm 520 nm 546 nm –1.039 –0.912 –3.425 –3.051 –64.80 –58.35 –139.28 –125.07 –0.667 –0.592 –0.335 –0.304 –0.162 –0.157 0.076 0.069 0.140 0.133 0.393 0.342

578 nm –0.787 –2.603 –53.77 –111.27 –0.518 –0.299 –0.145 +0.059 0.116 0.302

635 nm –0.620 –2.008 48.39 97.47 –0.411 –0.105 +0.048 0.094 0.239

Verdet Constants of Gases2

670 nm –0.542 –1.815 –45.15 –93.42 –0.359 –0.206 –0.089

Values refer to T = 0°C and P = 101.325 kPa (760 mmHg); nD is the refractive index at a wavelength of 589 nm. 106 × V 3 min/Oe cm Gas (nD – 1) × 10 He 0.036 +0.40 Ar 2.81 +9.36 +6.29 H2 0.297 +6.46 N2 0.272 +5.69 O2 Air 0.293 +6.27 0.773 +31.9 Cl2 HCl 0.447 +21.5 0.63 +41.5 H2S 0.376 +19.0 NH3 CO 0.34 +11.0 0.45 +9.39 CO2 NO 0.297 –58 CH4 0.444 +17.4 +44.0 n-C4H10

Verdet Constants of Liquids2

nD is the refractive index at a wavelength of 589 nm and a temperature of 20°C, unless otherwise indicated. V is the Verdet constant. 102 × V Liquid λ/nm t/°C min/Oe cm nD P 589 33 +13.3 S 589 114 +8.1 1.929 (110°C) 589 20 +1.309 1.3328 H2O 589 19.7 +1.257 1.3384 D2O 578 97.4 +1.35 H3PO4 589 20 +4.255 1.6255 CS2 578–589 25.1 +1.60 1.463 (15°C) CCl4 578 18 +7.45 1.601 (14°C) SbCl5 578 17 –1.65 1.61 TiCl4 578 46 –5.3 TiBr4 Methanol 589 18.7 +0.958 1.3289 Acetone 578–589 20.0 +1.116 1.3585 Toluene 578–589 15.0 +2.71 1.4950 Benzene 578–589 15.0 +3.00 1.5005 Chlorobenzene 589 15 +2.92 1.5246 Nitrobenzene 589 15 +2.17 1.5523 Bromoform 589 17.9 +3.13 1.5960

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

12-173

Verdet Constants of Rare Earth Paramagnetic Crystals1 n is the refractive index, and V is the Verdet constant at the wavelength and temperature indicated. Rare Earth Ce3+(30%)

CaF2

Ce3+

CeF3

Pr3+(5%)

CaF2

Nd3+(2.9%) Nd3+

CaF2 NdF3

Eu3+(3%)

CaF2

Eu2+

EuF2

Tb3+

KTb3F10

Tb3+

LiTbF4

Tb3+

Tb3Ga5O12

Host

T/K 300 300 300 300 300 300 77 300 300 300 300 300 300 4.2 300 290 77 300 4.2 4.2 300 300 300 300 300 300 300 300 300 77 300 300 300 300 300 300 300 300 300 300

λ/nm 325 442 633 1064 442 633 633 1064 266 325 442 633 1064 426 442 633 633 1064 430 440 450 500 550 600 650 1064 325 442 633 633 1064 325 442 633 1064 500 570 633 830 1060

n 1.516 1.502 1.494 1.489 1.613 1.598 1.589 1.471 1.461 1.451 1.445 1.441 1.60 1.59 1.58

1.531 1.518 1.510 1.505 1.493 1.481 1.473 1.469 1.989 1.981 1.976 1.967 1.954

V min/Oe cm –0.956 –0.297 –0.111 –0.035 –1.05 –0.406 –1.418 –0.113 –0.172 –0.0818 –0.0089 –0.0168 –0.0045 –0.19 –0.553 –0.209 –0.755 –0.097 29 22 –4.5 –2.6 –1.6 –1.1 –0.8 –0.19 –2.174 –0.933 –0.386 –1.94 –0.114 –1.9 –0.98 –0.44 –0.13 –0.749 –0.581 –0.461 –0.21 –0.12

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

12-174

Verdet Constants of Paramagnetic Glasses1

The Verdet constant V is given at room temperature for the wavelengths indicated. Rare earth phosphate glasses of composition R2O3·xP2O5, where x is given in the second column Verdet constant V in min/Oe cm λ = 405 λ = 436 λ = 480 λ = 500 λ = 520 λ= 546 λ= 578 R x nm nm nm nm nm nm nm La 0.037 0.030 0.024 0.022 0.020 0.018 0.015 Ce 2.67 –0.672 0.510 –0.366 –0.326 –0.287 –0.253 –0.217 Pr 3.09 –0.447 –0.332 –0.283 –0.261 –0.236 –0.208 –0.182 Nd 2.92 –0.250 –0.209 –0.167 –0.155 –0.136 –0.134 –0.094 Sm 2.87 0.026 0.024 0.020 0.020 0.017 0.015 0.014 Eu 2.93 –0.025 –0.017 –0.010 –0.006 –0.006 –0.005 –0.004 Gd 3.01 0.018 0.015 0.014 0.012 0.012 0.011 0.011 Tb 2.94 –0.560 –0.458 –0.357 –0.323 –0.295 –0.261 –0.226 Dy 2.51 –0.540 –0.453 –0.359 –0.331 –0.301 0.268 –0.237 Ho 2.94 –0.299 –0.313 –0.156 –0.153 –0.138 –0.138 –0.119 Er 3.01 –0.139 –0.121 –0.100 –0.111 –0.095 –0.062 –0.060 Tm 2.79 0.019 0.013 0.012 0.009 0.008 0.006 0.005 Yb 3.01 0.087 0.072 0.056 0.050 0.045 0.041 0.036

λ= 600 nm –0.014 –0.197 –0.170 –0.080 0.012 –0.003 0.010 –0.206 –0.217 –0.110 –0.057 0.004 0.032

λ= 635 nm 0.013 –0.173 –0.150 –0.080 0.011 –0.002 0.009 –0.190 –0.197 –0.098 –0.051 0.004 0.029

λ= 670 nm – –0.150 –0.132 –0.071 0.010 –0.002 0.009 –0.164 –0.173 –0.084 –0.044 0.007 0.024

0.018 –0.146 –0.059 0.016 –0.016 0.017 –0.186 –0.177 –0.096 –0.040 0.021 0.043 –0.348 –0.332 –0.317

0.016 –0.128 –0.056 0.014 0.014 0.015 –0.167 –0.159 – –0.035 0.018 0.037 –0.306 –0.290 –0.271

0.014 –0.110 –0.046 0.012 –0.012 0.013 –0.142 –0.138 –0.074 –0.034 0.016 0.033 –0.265 –0.252 –0.243

The following are rare earth borate glasses with composition: for La and Pr: R2O3·xP2O5; for Tb–Pr and Dy–Pr: R2O3·xB2O3; and for other elements: R2O3·0.85La3O3·xB2O3. La Pr-La Nd-La Sm-La Eu-La Gd-La Tb-La Dy-La Ho-La Er-La Tm-La Yb-La Tb-Pr Dy-Pr Pr

3.04 5.44 5.41 4.97 4.69 4.71 4.73 4.88 4.36 4.50 4.75 8.58 4.99 4.63 2.56

0.043 –0.380 –0.180 0.032 –0.081 0.032 –0.512 –0.436 –0.269 –0.093 0.060 0.115 –0.940 –0.850 –0.843

0.036 –0.307 –0.147 0.030 –0.060 0.026 –0.419 –0.361 –0.252 –0.078 0.046 0.094 –0.786 – –0.646

0.029 –0.230 –0.120 0.025 –0.038 0.024 –0.319 –0.299 –0.123 –0.068 0.039 0.073 –0.560 – –0.471

0.026 –0.220 –0.111 0.024 –0.033 0.022 –0.288 –0.273 –0.131 –0.082 0.034 0.066 –0.536 –0.497 –0.480

0.023 –0.201 –0.096 0.022 –0.029 0.021 –0.262 –0.246 –0.112 – 0.031 0.060 –0.489 –0.465 –0.432

0.022 –0.178 –0.094 0.019 –0.024 0.020 –0.234 –0.220 –0.128 –0.045 0.026 0.054 –0.436 –0.413 –0.390

0.019 –0.153 –0.100 0.017 0.019 0.018 –0.205 –0.193 –0.104 –0.042 0.023 0.046 –0.380 –0.358 –0.334

Verdet Constants of Diamagnetic Glasses1

The Verdet constant V is given at room temperature for the wavelengths indicated. Verdet constant V in min/Oe cm Glass type Composition (wt. %) λ = 325 nm λ = 442 nm λ = 633 nm 100% SiO2 0.013 SiO2 100% B2O3 0.010 B2O3 0.079 0.033 0.022 CdO 47.5% CdO, 52.5% P2O5 0.072 0.044 0.020 ZnO 36.4% ZnO, 63.6% P2O5 88.9% TeO2, 11.1% P2O5 0.196 0.076 TeO2 63.1% ZrF4, 14.9% BaF2, 0.011 ZrF4 7.2% LaF3, 1.9% AlF3, 9.1% PbF2, 3.8% LiF

λ = 1064 nm

0.022

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

Bi2O3 PbO

Tl2O SnO TeO3

Sb2O3

95% Bi2O3, 5% B2O3 95% PbO, 5% B2O3 82% PbO, 18% SiO2 50% PbO, 15% K2O, 35% SiO2 95% Tl2O, 5% B2O3 82% Tl2O, 18% SiO2 50% Tl2O, 15% K2O, 35% SiO2 76% SnO, 13% B2O3, 11% SiO2 75% TeO2, 25% Sb2O3 80% TeO2, 20% ZnCl2 84% TeO2, 16% BaO 70% TeO2, 30% WO3 20% TeO2, 80% PbO 25% Sb2O3, 75% TeO2 75% Sb2O3, 75% Cs2O, 5% Al2O3 75% Sb2O3, 10% Cs2O, 10% Rb2O, 5% Al2O3

12-175

λ = 700 nm 0.086 0.093 0.077 0.032 0.092 0.100 0.036 0.071 0.076 0.073 0.056 0.052 0.128 0.076 0.074 0.078

λ = 853 nm 0.051 0.061 0.045 0.020 0.061 0.067 0.022 0.046 0.052 0.046 0.041 0.035 0.075 0.050 0.044 0.052

λ = 1060 nm 0.033 0.031 0.027 0.011 0.032 0.043 0.012 0.026 0.032 0.025 0.029 0.022 0.048 0.032 0.025 0.030

Verdet Constants of Commercial Glasses1

This table gives the density, ρ, refractive index at 589 nm, nD, and Verdet constant, V, for the wavelengths indicated; the data refer to room temperature. V in min/Oe cm Glass ρ nD λ = 365.0 nm λ = 404.7 nm λ = 435.8 nm λ = 546.1 nm λ = 578.0 nm type g/cm3 BSC 2.49 1.5096 0.0499 0.0392 0.0333 0.02034 0.01798 HC 2.53 1.5189 0.0561 0.0440 0.0372 0.0225 0.01995 LBC 2.87 1.5406 0.0609 0.0477 0.0403 0.0245 0.0216 LF 3.23 1.5785 0.1143 0.0850 0.0693 0.0394 0.0344 BLF 3.48 1.6047 0.1112 0.0832 0.0685 0.0393 0.0344 DBC 3.56 1.6122 0.0662 0.0517 0.0435 0.0261 0.0231 DF 3.63 1.6203 0.1473 0.1076 0.0872 0.0485 0.0423 EDF 3.9 1.6533 0.1725 0.1248 0.1007 0.0556 0.0483 The composition of the glasses in weight percent is: Glass type BSC HC LBC LF BLF DBC DF EDF

SiO2 69.6 72.0 57.1 52.5 45.2 36.2 46.3 40.6

B2O3 6.7 – 1.8 – – 7.7 – –

K2O 20.5 10.1 13.7 9.5 7.8 0.2 1.1 7.5

CaO 2.9 11.4 0.3 0.3 – 0.2 0.3 0.2

Al2O3 0.3 0.3 0.2 0.2 – 3.5 0.2 0.2

As2O3 0.1 0.2 0.1 0.1 0.4 0.7 0.1 0.2

Na2O – 6.1 – – – – 5.0 0.1

BaO – – 26.9 – 16.0 44.6 – –

References 1. Weber, M. J., CRC Handbook of Laser Science and Technology, Vol. IV, Part 2, CRC Press, Boca Raton, FL, 1988, pp. 299–310. 2. Gray, D. E., Ed., American Institute of Physics Handbook, Third edition, McGraw Hill, New York, 1972, p. 6–230.

ZnO – – – – 8.3 6.7 – –

PbO – – – 37.6 22.2 – 47.0 51.5

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

12-176

Faraday Rotation

Ferro-, Ferri-, and Antiferromagnetic Solids Tc

4 π Ms

2 F/α

Material

gauss

deg/cm

deg

1043

21,800

1390

18,200

633

6,400

Permalloy (Ni/Fe = 82/18) Ni/Fe = 100/0 Ni/Fe = 80/20 Ni/Fe = 60/40 Ni/Fe = 40/60 Ni/Fe = 20/80 Ni/Fe = 0/100 MnBi

803

10,700

4.4 × 105 6.5 × 105 7 × 105 7 × 105 2.9 × 105 5.5 × 105 5.5 × 105 5.5 × 105 0.8 × 105 2.6 × 105 1.5 × 105 1 × 105 1.2 × 105

6.5 × 105 5.0 × 105 4.2 × 105 3.5 × 105 – 6.1 × 105 4.5 × 105 3.6 × 105 – 5.8 × 105 4.8 × 105 4.1 × 105 6 × 105

1.4 2.6 3.3 4.0 – 1.8 2.4 2.7 – 0.9 0.6 0.25 0.4

300 300 300 300 300 300 300 300 300 300 300 300 300

500 1000 1500 2000 500 1000 1500 2000 500 1000 1500 2000 500

MnAs

313

–

CrTe

334

1015

FeRh Y3Fe5O12 (YIG)

333 560

– 2500

1.2 × 105 2.2 × 105 2.9 × 105 2.2 × 105 3.3 × 105 3.5 × 105 4.2 × 105 7.5 × 105 0.44 × 105 0.62 × 105 0.5 × 105 0.4 × 105 0.9 × 105 2400 1250 750 175

7.05 × 105 7.10 × 105 7.54 × 105 8.17 × 105 8.10 × 105 8.13 × 105 6.1 × 105 4.2 × 105 5.0 × 105 4.4 × 105 2.0 × 105 1.2 × 105 3.3 × 105 1500 1400 450 <0.06

0.34 0.62 0.77 0.54 0.81 0.86 1.4 3.6 0.174 0.28 0.5 0.7 0.56 3.2 1.8 3.3 >3 × 103

300 300 300 300 300 300 300 300 300 300 300 300 348 300 300 300 300

Gd3Fe5O12 (GdIG)

Tn = 564 T = 286

7300

NiFe2O4

858

3350

CoFe2O4

793

4930

MgFe2O4

593-713e

1450e

Li0.5Fe2.5O4

863–953e

3240e to 3900

BaFe12O19

723

–

Ba2Zn2Fe12O19

–

–2000 –1050 –300 –80 2.0 × 104 –1.0 × 104 –120 +75 +110 2.75 × 104 3.6 × 104 –2.5 × 104 –60 0 +35 –440 +10 +110 +135 –50 +75 +150 +165 90

6000 900 100 70 5.9 × 104 10 × 104 38 15 32 12 × 104 17 × 104 6 × 104 100 12 6 150 85 44 80 –38 20 20 22 120

0.6 2.3 6.0 2.3 0.7 0.2 6 10 7 0.5 0.4 0.8 1 0 11 6 0.2 5 3 3 7.5 15 15 1.5

300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300

632.8 632.8 632.8 632.8 632.8 632.8 450 900 500 900 550 900 700 555 625 770 5000 to 1500 500 600 800 1000 286 500 1500 3000 5000 286 400 660 2500 4000 6000 1500 3000 5000 7000 2000 3000 5000 7000 5000

639

6,000 10,800 14,900 14,400 19,400 21,600 7,700

–1

Elasto-Optic, Electro-Optic, and Magneto-Optic Constants

12-177

4 π Ms

2 F/α

Material

gauss

deg/cm

cm–1

deg

RbNiF3

220

1250

RbNi0.75Co0.25F3 RbFeF3

109 102

– –

FeF3

365

CrCl3

16.8

40 at 300 K 3880

CrBr3

32.5

3390

CrI3

2690

FeBO3

348

EuO

115 at 300 K 23700

EuS

16.3

–

EuSe

7.0

13,200

75 360 70 310 75 180 3400 1600 620 300 670 180 2000 –500 –1000 3 × 105 1.6 × 105 1.1 × 105 0.8 × 105 3200 450 –1.0 × 105 5 × 105 0.5 × 105 3 × 104 660 –1.6 × 105 –9.6 × 105 +5.5 × 105 1.45 × 105 0.95 × 105

65 35 10 70 25 9 7 3 1.5 2.5 14 4.4 200 300 70 3 × 103 1.4 × 104 6.3 × 103 3 × 103 140 38 0.5 × 104 9.7 × 104 7.8 × 104 >0.5 >1.0 0 3.3 × 104 1.2 × 105 80 60

2.0 20 14 9 6 40 900 1100 830 240 95 82 20 3 30 200 23 35 53 45 24 40 10 1.3 ~105 1300 – 58 9.2 3600 3170

300 77 77 77 77 77 82 82 82 82 300 300 1.5 1.5 1.5 1.5 1.5 1.5 1.5 300 300 5 5 5 20 20 6 6 6 4.2 4.2

7000 450a 600a 800a 1000a 600b 300c 400c 600c 800c 349d 522.5d 410 450 590 478 500 970 1000 500 700 1100 700 500 2500 10600 825 690 563 750 800

a b c d e

Measured along the C-axis (magnetic hard axis). Measured along the C-axis (magnetic easy axis). Measured along the C-axis ([100]-direction at room temperature). Strong natural birefringence interferes with the Faraday effect. Depends on heat treatment.

Reference 1. Weber, M. J., Ed., CRC Handbook of Laser Science and Technology, Vol. IV, Part 2, CRC Press, Boca Raton, FL, 1988, pp. 288–296.

NONLINEAR OPTICAL CONSTANTS H. P. R. Frederikse The relation between the polarization density P of a dielectric medium and the electric field E is linear when E is small, but becomes nonlinear as E acquires values comparable with interatomic electric fields (105 to 108 V/cm). Under these conditions the relation between P and E can be expanded in a Taylor’s series P = ε 0 χ (1 ) E + 2 χ ( 2 ) E 2 + 4 χ ( 3 ) E 3 + 

(1)

where εo is the permittivity of free space, while χ(1) is the linear and χ(2), χ(3) etc. the nonlinear optical susceptibilities. If we consider two optical fields, the first Ejω (along the j-direction at frequency ω1) and the second Ekω (along the k-direction at frequency ω2) one can write the second term of the Taylor’s series as follows 1

ω3 = ω1 ± ω2 ω1 ω2 Pi (ω1 ω2 ) = 2 χ ijk E j Ek

When ω1 ≠ ω2 the (parametric) mixing of the two fields gives rise to two new polarizations at the frequencies ω3 = ω1 + ω2 and ω3´ = ω1 – ω2. When the two frequencies are equal, ω1 = ω2 = ω, the result is Second Harmonic Generation (SHG): χijk(2ω, ω, ω), while equal and opposite frequencies, ω1 = ω and ω2 = –ω leads to Optical Rectification (OR): χijk(0, ω, –ω). In the SHG case the following convention is adopted: the second order nonlinear coefficient d is equal to one half of the second order nonlinear susceptibility dijk = 1/2 χ( 2 )

Because of the symmetry of the indices j and k one can replace these two by a single index (subscript) m. Consequently the notation for the SHG nonlinear coefficient in reduced form is dim where m takes the values 1 to 6. Only noncentrosymmetric crystals can possess a nonvanishing dijk tensor (third rank). The unit of the SHG coefficients is m/V (in the MKSQ/SI system). In centrosymmetric media the dominant nonlinearity is of the third order. This effect is represented by the third term in the Taylor’s series (Equation 1); it is the result of the interaction of a number of optical fields (one to three) producing a new frequency ω4 = ω1 + ω2 + ω3. The third order polarization is given by Pj (ω1 ω2 ω3 ) = g 4 χ jklm Ekω1 E1ω2 Emω3

This coefficient is a fourth rank tensor. In the THG case the matrices must be invariant under permutation of the indices k, l, and m; as a result the notation for the third order nonlinear coefficient can be simplified to Cjn. The unit of Cjn is m2·V–2 (in the MKSQ/SI system). Applications of second order nonlinear optical materials include the generation of higher (up to sixth) optical harmonics, the mixing of monochromatic waves to generate sum or difference frequencies (frequency conversion), the use of two monochromatic waves to amplify a third wave (parametric amplification) and the addition of feedback to such an amplifier to create an oscillation (parametric oscillation). Third order nonlinear optical materials are used for THG, selffocusing, four wave mixing, optical amplification, and optical conjugation. Many of these effects – as well as the variation and modulation of optical propagation caused by mechanical, electric, and magnetic fields (see the preceeding table on “Elasto-Optic, Electro-Optic, and Magneto-Optic Constants”) are used in the areas of optical communication, optical computing, and optical imaging.

References 1. Handbook of Laser Science and Technology, Vol. 111, Part 1; Weber, M. J. Ed., CRC Press, Boca Raton, FL, 1986. 2. Dmitriev, V.G., Gurzadyan, G.G., and Nikogosyan, D., Handbook of Nonlinear Optical Crystals, Springer-Verlag, Berlin, 1991. 3. Shen, Y.R., The Principles of Nonlinear Optics, John Wiley, New York, 1984. 4. Yariv, A., Quantum Electronics, 3rd edition, John Wiley, New York, 1988. 5. Bloembergen, N., Nonlinear Optics, W.A. Benjamin, New York, 1965. 6. Zernike F. and Midwinter, J.E., Applied Nonlinear Optics, John Wiley, New York, 1973. 7. Hopf, F.A. and Stegeman, G.I., Applied Classical Electrodynamics, Volume 2: Nonlinear Optics, John Wiley, New York, 1986. 8. Nonlinear Optical Properties of Organic Molecules and Crystals, Chemla, D. S., and Zyss, J., Eds., Academic Press, Orlando, FL, 1987. 9. Optical Phase Conjugation, Fisher, R. A., Ed., Academic Press, New York, 1983. 10. Zyss, J., Molecular Nonlinear Optics: Materials, Devices and Physics, Academic Press, Boston, 1994. 11. Nonlinear Optics, 5 articles in Physics Today, (Am. Inst. of Phys.), Vol. 47, No. 5, May, 1994.

Third Harmonic Generation (THG) is achieved when ω1 = ω2 = ω3 = ω. In this case the constant g4 = 1/4. The third order nonlinear coefficient C is related to the third order susceptibility as follows: C jklm = 1/4 χ jklm

12-174

Section 12.indb 174

4/28/05 1:59:45 PM

Nonlinear Optical Constants

12-175 Selected SHG Coefficients of NLO Crystals*

Symmetry Material

dim × 1012

class

GaAs GaP InAs

43 m 43 m 43 m

ZnSe

43 m

β-ZnS

43 m

ZnTe

43 m

CdTe Bi4GeO12 N4(CH2)6 (hexamine) LiIO3

43 m 43 m 43 m

ZnO

6 mm

α-ZnS

6 mm

CdS

6 mm

CdSe

6 mm

BaTiO3

4 mm

PbTiO3

4 mm

K3Li2Nb5O15

4 mm

K0.8Na0.2Ba2Nb5O15 SrBaNb5O15

4 mm 4 mm

NH4H2PO4 (ADP)

42 m

KH2PO4 (KDP)

42 m

KD2PO4 (KD*P)

42 m

KH2AsO4 (KDA)

42 m

CdGeAs2 AgGaS2

42 m 42 m

m/V d14 = 134.1 ± 42 d14 = 71.8 ± 12.3 d14 = 364 ± 47 d14 = 210 d14 = 78.4 ± 29.3 d36 = 26.6 ± 1.7 d14 = 30.6 ± 8.4 d36 = 20.7 ± 1.3 d14 = 92.2 ± 33.5 d14 = 83.2 ± 8.4 d36 = 89.6 ± 5.7 d14 = 167.6 ± 63 d14 = 1.28 d14 = 4.1 d33 = –7.02 d31 = –5.53 ± 0.3 d33 = –5.86 ± 0.16 d31= 1.76 ± 0.16 d15 = 1.93 ± 0.16 d33 = 11.37 ± 0.07 d33 = 37.3 ± 12.6 d31 = –18.9 ± 6.3 d15 = 21.37 ± 8.4 d33 = 25.8 ± 1.6 d31 = –13.1 ± 0.8 d15 = 14.4 ± 0.8 d33 = 54.5 ± 12.6 d31 = –26.8 ± 2.7 d33 = 6.8 ± 1.0 d31 = 15.7 ± 1.8 d15 = 17.0 ± 1.8 d33 = 7.5 ± 1.2 d31 = 37.6 ± 5.6 d15 = 33.3 ± 5 d33 = 11.2 ± 1.6 d31 = 6.18 ± 1.28 d15 = 5.45 ± 0.54 d31 = 13.6 ± 1.6 d33 = 11.3 ± 3.3 d31 = 4.31 ± 1.32 d15 = 5.98 ± 2 d36 = 0.53 d36 = 0.85 d36 = 0.44 d36 = 0.47 ± 0.07 d36 = 0.38 ± 0.016 d36 = 0.34 ± 0.06 d14 = 0.37 d36 = 0.43 ± 0.025 d36 = 0.39 ± 0.4 d36 = 351 ± 105 d36 = 18 ± 2.7

λ µm

Symmetry Material

class

42 m 42 m

10.6 1.058 1.058 10.6 10.6 1.058 10.6 1.058 10.6 1.058 1.058 10.6 1.064 1.06 1.06 1.064 1.058

AgGaSe2 (NH2)2CO (urea) AlPO4 Se Te SiO2 (quartz) HgS (C6H5CO)2 [benzil] β-BaB2O4 [BBO]

32 32 32 32 32 32 3m

LiNbO3

LiTaO3

Ag3AsS3 [proustite]

1.058 1.058 1.058 10.6 10.6 10.6 1.058 1.058 1.058 10.6 10.6 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 0.694 1.064 0.694 1.058 0.694 1.058 1.06 0.694 10.6 10.6

Ag3SbS3 [pyrargerite]

α-HIO3 NO2 · CH3NOC5H4 · (POM) Ba2NaNb5O15 [Banana]

222 222 mm 2

C6H4(NO2)2 [MDB]

mm 2

Gd2(MoO4)3

mm 2

KNbO3

mm 2

KTiOPO4 [KTP]

mm 2

NO2C6H4 · NH2 [mNA]

mm 2

C10H12N3O6 [MAP]

(NH2CH2COOH)3H2SO4 [TGS]

dim × 1012 m/V

λ µm

d36 = 37.4 ± 6.0 d36 = 1.3 d11 = 0.35 ± 0.03 d11 = 97 ± 25 d11 = 650 ± 30 d11 = 0.335 d11 = 50.3 ± 17 d11 = 3.6 ± 0.5 d22 = 2.22 ± 0.09 d31 = 0.16 ± 0.08 d33 = 34.4 d31 = –5.95 d22 = 2.76 d33 = –16.4 ± 2 d31 = –1.07 ± 0.2 d22 = +1.76 ± 0.2 d31 = 11.3 ± 2.5 d22 = 18.0 ± 2.5 d31 = 12.6 ± 4 d22 = 13.4 ± 4 d36 = 5.15 ± 0.16 d36 = 6.4 ± 1.0

10.6 1.06 1.058 10.6 10.6 1.064 10.6 1.064 1.06 1.06 1.06 1.06 1.06 1.058 1.058 1.058 10.6 10.6 10.6 10.6 1.064 1.064

d33 = –17.6 ± 1.28 d31 = –12.8 ± 1.28 d33 = 0.74 d32 = 2.7 d31 = 1.78 d33 = –0.044 ± 0.008 d32 = +2.42 ± 0.36 d31 = –2.49 ± 0.37 d33 = –19.58 ± 1.03 d32 = +11.34 ± 1.03 d31 = –12.88 ± 1.03 d33 = 13.7 d32 = ± 5.0 d31 = ± 6.5 d33 = 13.12 ± 1.28 d32 = 1.02 ± 0.22 d31 = 12.48 ± 1.28 d23 = 10.67 ± 1.3 d22 = 11.7 ± 1.3 d21 = 2.35 ± 0.5 d25 = –0.35 ± 0.3 d23 = 0.32

1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.064 1.06 1.06 1.06 1.064 1.064 1.064 1.064 1.064 1.064 1.064 0.694

* These data are taken from References 1 and 2.

Section 12.indb 175

4/28/05 1:59:47 PM

Nonlinear Optical Constants

12-176

Material NH4H2PO4 [ADP] C6H6 [benzene] CdGeAs2 p-type: 5 × 1016 cm–3 C40H56 [β-carotene] GaAs high-resistivity Ge LiIO3 KBr KCl KH2PO4 [KDP] Si p-type: 1014 cm–3 NaCl NaF

Selected THG Coefficients of Some NLO Materials* Cjn × 1020 NLO process m2/V–2 (–3ω,ω,ω,ω) C11 = 0.0104 C18 = 0.0098 (–3ω,ω,ω,ω) C11 = 0.0184 ± 0.0042 (–3ω,ω,ω,ω) C11 = 182 ± 84 C16 = 175 C18 = –35 (–3ω,ω,ω,ω) C11 0.263 ± 0.08 (–3ω,ω,ω,–ω) C11 = 62 ± 31 (–3ω,ω,ω,–ω) C11 = 23.5 ± 12 (–3ω,ω,ω,–ω) C12 = 0.2285 C35 = 6.66 ± 1 (–3ω,ω,ω,–ω) C11 = 0.0392 C18/C11 = 0.3667 (–3ω,ω,ω,–ω) C11 = 0.0168 C18/C11 = 0.28 (–3ω,ω,ω,–ω) C11–3C18 = 0.04 (–3ω,ω,ω,–ω) C11 = 82.8 ± 25 (–3,ω,ω,ω,–ω) C11 = 0.0168 C18/C11 = 0.4133 (–3ω,ω,ω,–ω) C11 = 0.0035

λ µm 1.06 1.06 1.89 10.6 10.6 10.6 1.89 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06

* These data are taken from Reference 1.

Section 12.indb 176

4/28/05 1:59:48 PM

Phase Diagrams H. P. R. Frederikse A phase is a structurally homogeneous portion of matter. Regardless of the number of chemical constituents of a gas, there is only one vapor phase. This is true also for the liquid form of a pure substance, although a mixture of several liquid substances may exist as one or several phases, depending on the interactions among the substances. On the other hand a pure solid may exist in several phases at different temperatures and pressures because of differences in crystal structure (Reference 1). At the phase transition temperature, Ttr, the chemical composition of the solid remains the same, but a change in the physical properties often will take place. Such changes are found in ferroelectric crystals (example BaTiO3) which develop a spontaneous polarization below Ttr, in superconductors (example Pb) which lose all electrical resistance below the transition point, and in many other classes of solids. In quite a few cases it is difficult to bring about the phase transition, and the high- (or low-) temperature phase persists in its metastable form. Many liquids remain in the liquid state for shorter or longer periods of time when cooled below the melting point (supercooling). However, often the slightest disturbance will cause solidification. Persistence of the high temperature phase in solid– solid transitions is usually of much longer duration. An example of this behavior is found in white tin; although gray tin is the thermodynamically stable form below Ttr (286.4 K), the metal remains in its undercooled, white tin state all the way to T = 0 K, and crystals of gray tin are very difficult to produce. A phase diagram is a map that indicates the areas of stability of the various phases as a function of external conditions (temperature and pressure). Pure materials, such as mercury, helium, water, and methyl alcohol are considered one-component systems and they have unary phase diagrams. The equilibrium phases in two-component systems are presented in binary phase diagrams. Because many important materials consist of three, four, and more components, many attempts have been made to deduce their multicomponent phase diagrams. However, the vast majority of systems with three or more components are very complex, and no overall maps of the phase relationships have been worked out. It has been shown during the last 20 to 25 years that very useful partial phase diagrams of complex systems can be obtained by means of thermodynamic modeling (References 2, 3). Especially for complicated, multicomponent alloy systems the CALPHAD method has proved to be a successful approach for producing valuable portions of very intricate phase diagrams (Reference 4). With this method thermodynamic descriptions of the free energy functions of various phases are obtained that are consistent with existing (binary) phase diagram information and other thermodynamic data. Extrapolation methods are then used to extend the thermodynamic functions into a ternary system. Comparison of the results of this procedure with available experimental data is then used to fine-tune the phase diagram and add ternary interaction functions if necessary. In principle this approximation strategy can be extended to four, five, and more component systems. The nearly two dozen phase diagrams shown below present the reader with examples of some important types of single and multicomponent systems, especially for ceramics and metal alloys. This makes it possible to draw attention to certain features like the kinetic aspects of phase transitions (see Figure 22, which presents a time-temperature-transformation, or TTT, diagram for the precipitation of α-phase particles from the β-phase in a Ti-Mo alloy; Reference 1, pp. 358–360). The general references listed below and the references to individual figures contain phase diagrams for many additional systems.

General References 1. Ralls, K. M., Courtney, T. H., and Wulff, J., Introduction to Materials Science and Engineering, Chapters 16 and 17, John Wiley & Sons, New York, 1976. 2. Kaufman, L., and Bernstein, H., Computer Calculation of Phase Diagrams, Academic Press, New York, 1970. 3. Kattner, U. R., Boettinger, W. J. B., and Coriell, S. R., Z. Metallkd., 87, 9, 1996. 4. Dinsdale, A. T., Ed., CALPHAD, Vol. 1–20, Pergamon Press, Oxford, 1977–1996 and continuing. 5. Baker, H., Ed., ASM Handbook, Volume 3: Alloy Phase Diagrams, ASM International, Materials Park, OH, 1992. 6. Massalski, T. B., Ed., Binary Alloy Phase Diagrams, Second Edition, ASM International, Materials Park, OH, 1990. 7. Roth. R. S., Ed., Phase Diagrams for Ceramists, Vol. I (1964) to Volume XI (1995), American Ceramic Society, Waterville, OH.

References to Individual Phase Diagrams Figure 1.

Carbon: Reference 7, Vol. X (1994), Figure 8930. Reprinted with permission. Figure 2. Si-Ge : Ref. 5, p. 2.231. Reprinted with permission. Figure 3. H2O (ice): See figure. Figure 4. SiO2: Reference 7, Vol. XI (1995), Figure 9174. Reprinted with permission. Figure 5. Fe-O: Darken, L.S., and Gurry, R.W., J. Am. Chem. Soc., 68, 798, 1946. Reprinted with permission. Figure 6. Ti-O: Reference 5, p. 2.324. Reprinted with permission. Figure 7. BaO-TiO2: Reference 7, Vol. III (1975), Figure 4302. Reprinted with permission. Figure 8. MgO-Al2O3: Reference 7, Vol. XI (1995), Figure 9239. Reprinted with permission. Figure 9. Y2O3-ZrO2: Reference 7, Vol. XI (1995), Figure 9348. Reprinted with permission. Figure 10. Si-N-Al-O (Sialon): Reference 7, Vol. X (1994), Figure 8759. Reprinted with permission. Figure 11. PbO-ZrO2-TiO2 (PZT): Reference 7, Vol. III (1975), Figure 4587. Reprinted with permission. Figure 12. Al-Si-Ca-O: Reference 7 (1964), Vol. I, Figure 630. Reprinted with permission. Figure 13. Y-Ba-Cu-O: Whitler, J.D., and Roth, R.S., Phase Diagrams for High Tc Superconductors, Figure S-082, American Ceramic Society, Waterville, OH, 1990. Reprinted with permission. Figure 14. Al-Cu: Reference 5, p. 2.44. Reprinted with permission. Figure 15. Fe-C: Ralls, K.M., Courtney, T.H., and Wulff, J., Introduction to Materials Science and Engineering, Figure 16.13, John Wiley & Sons, New York, 1976. Reprinted with permission. Figure 16. Fe-Cr: Reference 5, p. 2.152. Reprinted with permission. Figure 17. Cu-Sn: Reference 5, p. 2.178. Reprinted with permission. Figure 18. Cu-Ni: Reference 5, p. 2.173. Reprinted with permission. Figure 19. Pb-Sn (solder): Reference 5, p. 2.335. Reprinted with permission. Figure 20. Cu-Zn (brass): Subramanian, P.R., Chakrabarti, D.J., and Laughlin, D.E., Eds., Phase Diagrams of Binary Copper Alloys, p. 487, ASM International, Materials Park, OH, 1994. Reprinted with permission. Figure 21. Co-Sm: Reference 5, p. 2.148. Reprinted with permission. Figure 22. Ti-Mo: Reference 5, p. 2.296; Reference 1, p. 359. Reprinted with permission. Figure 23. Fe-Cr-Ni: Reference 5, Figure 48. Reprinted with permission.

12-181

Phase Diagrams

12-182 200

P/GPa

150

Diamond 100

50 Liquid A B 0

Graphite

2000

4000 T/K

6000

Figure 1. Phase diagram of carbon. (A) Martensitic transition: hex graphite → hex diamond. (B) Fast graphite-to-diamond transition. (C) Fast diamond-to-graphite transition.

Figure 2.

Si-Ge system.

Phase

(Ge,Si) High-pressure phases GeII SiII

Composition, mass % Si 0 to 100

Pearson symbol cF8

Space group – Fd3 m

– –

tI4 tI4

I41/amd I41/amd

Phase Diagrams

12-183 200

Liquid

150

VII

100

t/°C

0 V

III

VIII

I -50 II -100

-150 0

500

1000

1500

2000

2500

3000

3500

P/MPa

Figure 3. Diagram of the principal phases of ice. Solid lines are measured boundaries between stable phases; dotted lines are extrapolated. Ice IV is a metastable phase that exists in the region of ice V. Ice IX exists in the region below –100°C and pressures in the range 200–400 MPa. Ice X exists at pressures above 44 GPa. See Table 1 for the coordinates of the triple points, where liquid water is in equilibrium with two adjacent solid phases.

Table 1. Crystal Structure, Density, and Transition Temperatures for the Phases of Ice Phase

Crystal system

Ih Ic II III IV V

Hexagonal Cubic Rhombohedral Tetragonal Rhombohedral Monoclinic

VI VII VIII IX X

Tetragonal Cubic Tetragonal Tetragonal Cubic

Cell parameters a = 4.513; c = 7352 a = 6.35 a = 7.78; α = 113.1° a = 6.73; c = 6.83 a = 7.60; α = 70.1° a = 9.22; b = 7.54, c = 10.35; β = 109.2° a = 6.27; c = 5.79 a = 3.41 a = 4.80; c = 6.99 a = 6.73; c = 6.83 a = 2.83

References 1. Wagner, W., Saul, A., and Pruss, A., J. Phys. Chem. Ref. Data, 23, 515, 1994. 2. Lerner, R.G. and Trigg, G.L., Eds., Encyclopedia of Physics, VCH Publishers, New York, 1990.

Triple points

ρ/g cm-3

4 8 12 12 16 28

4 4 4 4 4 4

0.93 0.94 1.18 1.15 1.27 1.24

I-III: –21.99°C, 209.9 MPa

10 2 8 12 2

4 8 8 4 8

1.31 1.56 1.56 1.16 2.51

VI-VII: 82°C, 2216 MPa

III-V: –16.99°C, 350.1 MPa V-VI: 0.16°C, 632.4 MPa

3. Donnay, J.D.H. and Ondik, H.M, Crystal Data Determinative Tables, Third Edition, Volume 2, Inorganic Compounds, Joint Committee on Powder Diffraction Standards, Swarthmore, PA, 1973. 4. Hobbs, P.V., Ice Physics, Oxford University Press, Oxford, 1974. 5. Glasser, L., J. Chem. Edu., 81, 414, 2004.

Phase Diagrams

12-184 2000

Liq. Crist βQuartz

t/°C

1300° 34 kbars

1190° 1.43 kbars

Cal cula ted

1500

Trid

1000

Coesite

500

αQuartz Stishovite

60 80 P/kbar

100

120

SiO2 system. Crist = cristobalite; Trid = tridymite.

Atom % Oxygen

Liq. iron

A B

Liq. iron + Liq. oxide

Liquid oxide

R´ Liquid oxide + magnetite

δ-Iron + liq. oxide

I H

60 Liquid oxide + oxygen

Liq. iron

1600

1400

Magnetite

Figure 4.

3000

Magnetite + oxygen

Z 2600

γ-Iron + liq. oxide

N J .. Wustite γ-Iron .. + wustite

Hematite + oxygen

t/°C

1200

1000

.. Wustite + magnetite

2200

°F 1800

Magnetite + hematite

800 α-Iron .. + wustite

1400

600

1000 α-Iron + magnetite

FeO 400

Figure 5.

Fe-O system.

0 .2 .4 22

26 Mass % Oxygen

Fe3O4 28

Fe3O3 Z´ 30

Phase Diagrams Point

t/°C

A B C G H I J L N

12-185

1539 1528 1528 1400a 1424 1424 1371 911a 1371

pCO /pCO

0.16 22.60 22.84 25.60 25.31 23.16 23.10 22.91

0.209 0.209 0.263 16.2 16.2 0.282 0.447 0.282

Point

t/°C

Q R R´ S V Y Z Z´

560 1583 1583 1424 1597 1457 1457

pCO /pCO 2

23.26 28.30 28.07 27.64 27.64 28.36 30.04 30.6

1.05

16.2

Values for pure iron.

2200

Mass Percent Oxygen 10 20

40 TinO2n-1

2000 ~1885°C

1842°C 1870°C

1800

t/°C

~1250°C 1200

βTiO

(αTi)

1000

940°C

Ti3O

600

βTi1-xO

αTiO

882°C

Ti3O2

800

TiO (rutile)

1400

2 higher Magneli phases

γTiO

(βTi)

βTi2O3

1720°C 1670°C

1600

αTi1-xO

Ti2O 400 0

Figure 6.

30 40 Atomic Percent Oxygen

Ti-O system. Phase

(βTi) (αTi) Ti3O Ti2O γTiO Ti3O2 βTiO αTiO βTi1–xO αTi1–xO βTi2O3 αTi2O3 βTi3O5 αTi3O5 α´Ti3O5 γTi4O7 βTi4O7 αTi4O7 γTi5O9 βTi6O11 Ti7O13 Ti8O15 Ti9O17 Rutile TiO2 Metastable phases Anatase Brookite High-pressure phases TiO2-II TiO2-III

Composition, mass % O

Pearson symbol

Space group

0 to 3 0 to 13.5 ~8 to ~13 ~10 to 14.4 15.2 to 29.4 ~18 ~24 to ~29.4 ~25.0 ~29.5 ~29.5 33.2 to 33.6 33.2 to 33.6 35.8 35.8 35.8 36.9 36.9 36.9 37.6 38.0 38.3 38.5 38.7 40.1

cI2 hP2 hP~16 hP3 cF8 hP~5 c** mC16 oI12 tI18 hR30 hR30 m** mC32 mC32 aP44 aP44 aP44 aP28 aC68 aP40 aC92 aP52 tP6

Im¯3m P63/mmc P¯3c P¯3m1 Fm¯3m P6/mmm – A2/m or B*/* I222 I4/m R¯3c R¯3c – C2/m Cc P¯1 P¯1 P¯1 P¯1 A¯1 P¯1 A¯1 P¯1 P42/mnm

– –

tI12 oP24

I41/amd Pbca

– –

oP12 hP~48

Pbcn –

pO /atm 2 1 1 0.0575 1 1

Phase Diagrams

12-186 1600

TiO2 + Liq.

1500

Liquid

t /°C

1428° 1400 BaTiO3 + Liq.

~1357°

TiO2 + BaTi4O9

~1330°

~1320°

~1300°

1200

Figure 7.

60 BaO

Ba2Ti9O20

BaTi4O9

BaTiO3 + Ba6Ti17O40

Ba4Ti13O30

Ba6Ti17O40

1300

TiO2 + Ba2Ti9O20

100 TiO2

Mol %

BaO-TiO2 system.

2800

2600

2400 Spinel ss + Liquid

Periclase ss + Liquid

t/°C

2200 2105° Periclase 2000 ss

1995° Spinel ss

1800 Periclase ss + Spinel ss 1600 ~1500° Periclase + Spinel 1400 0 MgO Figure 8.

MgO-Al2O3 system.

40 Mol %

70 Al2O3

Phase Diagrams

12-187

Liquid

2800 Hss

Css + Liq. 2400 Yss + Hss 2000

Css

Css + Yss Yss

1700°C

t/°C

1650°± 50°

1600

(28%)

Css + 6:1

1375°

1325°± 25°

Tetss + Css

(55%)

1200

6:1ss

Css + 4:3 (95.5%) 490°

Zr3Y4O12

800

Tetss

4:3 + 1:6ss

400

Monss Monss + Css

0 Y2O3

60 Mol %

100 ZrO2

Figure 9. Y2O3-ZrO2 system. Css = cubic ZrO2 ss (fluorite-type ss); Yss = cubic Y2O3 ss; Tetss = tetragonal ZrO2 ss; Monss = monoclinic ZrO2 ss; Hss = hexagonal Y2O3 ss; 3:4 = Zr3Y4O12; 1:6 = ZrY6O11 ss.

Phase Diagrams

12-188 3(SiO2) 100

2(Al2O3)

Al6Si4O13 ss

Liquid ALON ss

1700°C

Mol %

40 β´

O´

Si2ON2

0 0 Si3N4

100 4(AIN)

Mol %

Figure 10. 3(SiO2)-Si3N4-4(AlN)-2(Al2O3) system. “Behavior” diagram at 1700°C. The labels 8H, 15R, 12H, 21R, 27R, 2Hδ indicate defect AlN polytypes. β´ = 3-sialon (Si6–xAlxOxN8–x); O´ = sialon of Si2ON2 type; X = SiAlO2N (“nitrogen mullite”). ALON ss = aluminum oxynitride ss extending from approximately Al7O9N to Al3O3N.

PbO

1100°C

Liq. + (PT-PZ)ss (PT-PZ)ss(rhom) (PZ-PT)ss(orth)

(PT-PZ)ss(tet) PbTiO3

PbZrO3

Zss + (PT-PZ)ss

-PZ PT Zss + ZT + (PT-PZ)ss

Tss

+ (P

T-P Z

)ss

+( Tss + ZT + (PT-PZ)ss

TiO2 (8%) Figure 11.

TiZrO4 Mol %

80 (86%)

PbO-ZrO2-TiO2 (PZT) system, subsolidus at 1100°C. P = PbO; T = TiO2; Z = ZrO2.

ZrO2

Phase Diagrams

Figure 12.

12-189

CaO-Al2O3-SiO2 system (temperatures in °C).

Crystalline Phases Notation Oxide formula SiO2 Cristobalite Tridymite Pseudowollastonite CaO·SiO2 Rankinite 3CaO·2SiO2 Lime CaO Corundum Al2O3 Mullite 3Al2O3·2SiO2 Anorthite CaO·Al2O3·2SiO2 Gehlenite 2CaO·Al2O3·SiO2

}

Temperatures up to approximately 1550°C are on the Geophysical Laboratory Scale; those above 1550°C are on the 1948 International Scale.

Phase Diagrams

12-190 BaO(BaCO3)

c1 P ss

Ba4Y2O7

Ba2CuO3

~4:1:2

~5:1:3

Ba2Y2O5

BaCuO2 b2

Ba3Y4O9

2:1:3

BaY2O4 1:2:1 a1

Y2Cu2O3 0 1/2(Y2O3)

b1 Mol %

c2 100 CuO

Figure 13. BaO-Y2O3-CuO system. 2:1:3 = Ba2YCu3O7–x; 1:2:1 = BaY2CuO5; 4:1:2 = Ba4YCu2O7.5+x; and 5:1:3 = Ba5YCu3O9.5 + x. The superconducting 2:1:3 phase was prepared using barium peroxide.

1100

Atomic Percent Copper 20 30 40

90 100 1084.87°

β0

1000 γ0

L 900

ε1

t/°C

800

700

γ1 660.452°C ε2

600

η1

548.2°C

500

ζ1

η2

400

(Al)

(Cu) ζ2

300 0 Al Figure 14.

567°C

Al-Cu system.

40 50 60 Mass Percent Copper

α2

100 Cu

Phase Diagrams

12-191 Phase (Al) θ η1 η2 ζ1 ζ2 ε1 ε2 δ γ0 γ1 β0 β α2 (Cu) Metastable phases θ´ β´ Al3Cu2

Composition, wt % Cu 0 to 5.65 52.5 to 53.7 70.0 to 72.2 70.0 to 72.1 74.4 to 77.8 74.4 to 75.2 77.5 to 79.4 72.2 to 78.7 77.4 to 78.3 77.8 to 84 79.7 to 84 83.1 to 84.7 85.0 to 91.5 88.5 to 89 90.6 to 100

Pearson symbol cF4 tI12 oP16 or oC16 mC20 hP42 (a) (b) hP4 (c) (d) cP52 (d) cI2 (e) cF4

Space group Fm¯3m I4/mcm Pban or Cmmm C2/m P6/mmm – – P63/mmc R¯3m – P¯43m – Im¯3m – Fm¯3m

– – 61 to 70

tP6 cF16 hp5

– Fm¯3m P¯3m1

(a) Monoclinic? (b) Cubic? (c) Rhombohedral. (d) Unknown. (e) D022-type long-period superlattice.

Atomic Percent Carbon 30 20

10 L

2000

(δFe)

L + C(graphite)

1500 1394°C

t/°C

(γFe), austenite

1153°C 2.1

4.2

1000 912°C

740°C 0.65 500 (αFe), ferrite

Figure 15.

6 8 Mass Percent Carbon

Fe-C system.

Phase (δFe) (γFe) (αFe) (C) Metastable/high-pressure phases (εFe) Martensite Fe4C Fe3C (θ) Fe5C2 (χ) Fe7C3 Fe7C3 Fe2C (η) Fe2C (ε) Fe2C (C)

Composition, mass % C 0 to 0.09 0 to 2.1 0 to 0.021 100

Pearson symbol cI2 cF4 cI2 hP4

Space group Im¯3m Fm¯3m Im¯3m P63/mmc

0 < 2.1 5.1 6.7 7.9 8.4 8.4 9.7 9.7 9.7 100

hP2 tI4 cP5 oP16 mC28 hP20 oP40 oP6 hP* hP* cF8

P63/mmc I4/mmm P¯43m Pnma C2/c P63mc Pnma Pnnm P6322 P¯3m1 Fd¯3m

Phase Diagrams

12-192 Atomic Percent Chromium 10

1900

100 1863°C

L 1700 1538°C 1500

1513°C 19.8

1394°C

t/°C

1300 (γFe) 1100 11.2 846°C

912°C 900

13.4 (αFe,δFe)

830°C 45

6.5 T C

770°C

700

(Cr)

500 47.2 300

F Figure 16.

100

Mass Percent Chromium

Fe-Cr system. Composition,

Pearson

Space

Phase

mass % Cr

symbol

group

(aFe, Cr)

0 to 100

cI2

(γFe)

0 to 11.2

cF4

Fm¯3m

42.7 to 48.2

tP30

P42/mnm

1200 0

1100

Im¯3m

Atomic Percent Tin 30 40 50

80 90 100

1084.87°C

1000 900 800

t/°C

755°C 13.5

796°C 22

700

25.6 30.6 676°C

γ ζ 586°C 24.6 520°C 15.8 27.0

(Cu)

600 500

ε δ

640°C

58.6

582°C 59

400

415°C

300

32.55

η 60.9

200 100

Cu-Sn system.

189°C

1.3

0 Cu

Figure 17.

92.4

~350°C

227°C 186°C

60.3

η´

40 50 60 Mass Percent Tin

99.3

231.9681°C

(Sn) 90 100 Sn

Phase Diagrams

12-193 Phase α β γ δ ζ ε η η´ (βSn) (αSn)

Composition, mass % Sn 0 to 15.8 22.0 to 27.0 25.5 to 41.5 32 to 33 32.2 to 35.2 27.7 to 39.5 59.0 to 60.9 44.8 to 60.9 ~100 100

Pearson symbol cF4 cI2 cF16 cF416 hP26 oC80 hP4 (a) tI4 cF8

Space group Fm¯3m Im¯3m Fm¯3m F¯43m P63 Cmcm P63/mmc – I41/amd Fd¯3m

(a) Hexagonal; superlattice based on NiAs-type structure.

Figure 18.

Cu-Ni system.

Phase (Cu, Ni) (above 354.5°C)

Composition, mass % Ni

Pearson symbol

0 to 100

cF4

Space group – Fm3 m

Phase Diagrams

12-194 Atomic Percent Tin 350

100

327.502°C

300

250 231.9681°C (Pb)

200

t/°C

183°C 18.3

97.8

61.9

150

100

(βSn)

Pb Figure 19.

Mass Percent Tin

Pb-Sn system. Phase (Pb) (βSn) (αSn) High-pressure phases ε(a) ε´(b)

100

Composition, mass % Sn 0 to 18.3 97.8 to 100 100

Pearson symbol cF4 tI4 cF8

Space group Fm¯3m I41/amd Fd¯3m

52 to 74 52

hP1 hP2

P6/mmm P63/mmc

(a) From phase diagram calculated at 2500 MPa. (b) This phase was claimed for alloys at 350°C and 5500 MPa.

Phase Diagrams

12-195

1100

Mass Percent Zinc 40 50 60

100

1064.62°C A

1000 D 36.8

900

31.9 902 B

L H 834°C

36.1 C

55.8 G

800

59.1

β 69.2 L

t/°C

700 600

α or (Cu)

500

454°C X 468 57 38.27 48.2 Y 44.8 E F

400

N 700°C 79.8 M 72.45

Q δ 76 P 87.9 O 598°C S 78 70 T 78 98.25 R 73.5 560°C 88

ε U

β´

425°C 97.17 W 419.58°C V

η or (Zn)

300 200 100

0 Cu

Figure 20.

40 50 60 Atomic Percent Zinc

Cu-Zn system. Phase

Composition, mass % Zn

Pearson symbol

α or (Cu)

0 to 38.95

cF4

36.8 to 56.5

cI2

Space group

Fm¯3m Im¯3m

Pm¯3m

β´

45.5 to 50.7

cP2

57.7 to 70.6

cI52

73.02 to 76.5

hP3

P¯6

78.5 to 88.3

hP2

P63/mmc

η or (Zn)

97.25 to 100

hP2

P63/mmc

I¯43m

100 Zn

Phase Diagrams

12-196 Atomic Percent Samarium 20 30 40 50

1495°C 1325°C

1260°C

βCo7Sm2

1200°C 1074°C

1074°C (γSm) 922°C

Co3Sm

(βSm) Co3Sm

αCo7Sm2

β → α

600

Co5-xSm

800 αCo17Sm2

t/°C

1000

1100°C Co19Sm5

(αCo)

βCo17Sm2

1240°C

1200

575°C

0 Co

Figure 21.

734°C 595°C

Co4Sm9

(εCo)

695°C 605

~93

~82

400 200

70 80 90100

CoSm3

1400

Co5+xSm

1600

(αSm)

Mass Percent Samarium

Co-Sm system. Phase

Composition, mass % Sm

Pearson symbol

(αCo)

0 to ~3.7

cF4

Fm¯3m

(εCo)

hP2

P63/mmc

βCo17Sm2

~23.0

hP38

P63/mmc

αCo17Sm2

~23.0

hR19

Co5 + xSm

~33 to 34

Space group

R¯3m

hP8

P6/mmm

–

Co5 - xSm

~34 to 35

–

Co19Sm5

~40.1

hR24

αCo7Sm2

~42.1

hR18

R¯3m

βCo7Sm2

~42.1

hP36

P63/mmc

Co3Sm

hR12

Co2Sm

56.0

hR4

hP48

–

R¯3m P63/mmc

R¯3m R¯3m

cF24

Fd¯3m

Co4Sm9

~85.1

o**

–

CoSm3

oP16

Pnma

(γSm)

~100

cI2

Im¯3m

(βSm)

~100

hP2

P63/mmc

(αSm)

~100

hR3

R¯3m

Other reported phases Co5Sm

~33.8

hP6

P6/mmm

Co2Sm5

~86.4

mC28

C2/c

100 Sm

Phase Diagrams

12-197 Atomic Percent Molybdenum 10

90 100 2623°

2600

2400 2200 2000 1800

t/°C

1600 1670°C 1400

(βTi,Mo)

1200 1000

882°C

~650°C

800

~695°C

600 400

~21

(αTi) 0

Ti Figure 22.

100

Mass Percent Molybdenum

Ti-Mo system.

Phase

Composition, mass % Mo

Pearson symbol

(βTi, Mo)

0 to 100

cI2

Space group – Im3 m

(αTi)

0 to 0.8

hP2

P63/mmc

α´

(a)

hP2

P63/mmc

α˝

(a)

oC4

Cmcm

(a)

hP3

P6/mmm

(a) Metastable.

to 800 Sta

700

sh Fini

t/°C

β + α´ (β + α)eqm

600

500

400

β + α´ 0.1

1.0

10 Time in Minutes

100

1000

Experimental time–temperature–transformation (TTT) diagram for Ti-Mo. The start and finish times of the isothermal precipitation reaction vary with temperature as a result of the temperature dependence of the nucleation and growth processes. Precipitation is complete, at any temperature, when the equilibrium fraction of α is established in accordance with the lever rule. The solid horizontal line represents the athermal (or nonthermally activated) martensitic transformation that occurs when the β phase is quenched.

Phase Diagrams

12-198 Cr

(Cr) + σ (Cr) + (γFe,Ni)

σ + (γFe,Ni)

um mi

Ma ss P

hro tC

erc en

(Cr)

en erc

t Ir

70 P ss Ma

) Ni

γF +(

18-8 Stainless steel

(γFe,Ni)

40 50 60 Mass Percent Nickel

Figure 23. The isothermal section at 900°C (1652°F) of the iron-chromium-nickel ternary phase diagram, showing the nominal composition of 18-8 stainless steel.

HEAT CAPACITY OF SELECTED SOLIDS This table gives the molar heat capacity at constant pressure of representative metals, semiconductors, and other crystalline solids as a function of temperature in the range 200 to 600 K.

References

2. Garvin, D., Parker, V. B., and White, H. J., CODATA Thermodynamic Tables, Hemisphere Press, New York, 1987. 3. DIPPR Database of Pure Compound Properties, Design Institute for Physical Properties Data, American Institute of Chemical Engineers, New York, 1987.

1. Chase, M. W., et al., JANAF Thermochemical Tables, 3rd ed., J. Phys. Chem. Ref. Data, 14, Suppl. 1, 1985. Cp in J/mol K Name Aluminum Aluminum oxide Anthracene Benzoic acid Beryllium Biphenyl Boron Calcium Calcium carbonate Calcium oxide Cesium chloride Chromium Cobalt Copper Copper oxide Copper sulfate Germanium Gold Graphite Hexachlorobenzene Iodine Iron Lead Lithium Lithium chloride Magnesium Magnesium oxide Manganese Naphthalene Potassium Potassium chloride Silicon Silicon dioxide Silver Sodium Sodium chloride Tantalum Titanium Tungsten Vanadium Zinc Zirconium

200 K

250 K

300 K

21.33 51.12 138.6 102.7 9.98 131.0 5.99 24.54 66.50 33.64 50.13 19.86 22.23 22.63 34.80 77.01

23.08 67.05 173.9 123.5 13.58 162.5 8.82 25.41 75.66 38.59 51.34 22.30 23.98 23.77

5.01 162.7 51.57 21.59 25.87 21.57 43.35 22.72

6.82 183.6 53.24 23.74 26.36 23.42 46.08 24.02

23.05 105.8 27.00 48.44 15.64 32.64

24.95 134.1 28.01 50.10 18.22 39.21

22.45 46.89 24.08 22.37 22.49 21.88 24.05 23.87

27.01 48.85 24.86 24.07 23.69 23.70 25.02 24.69

24.25 79.45 210.7 147.4 16.46 197.2 11.40 25.94 83.82 42.18 52.48 23.47 24.83 24.48 42.41 99.25 23.25 25.41 8.58 202.4 54.51 25.15 26.85 24.64 48.10 24.90 37.38 26.35 167.8 29.60 51.37 20.04 44.77 25.36 28.20 50.21 25.31 25.28 24.30 24.93 25.45 25.22

89.25

350 K

400 K

500 K

600 K

25.11 88.91 248.8 172.0 18.53

25.78 96.14 288.4

26.84 106.17

27.89 112.55

19.95

21.94

23.34

13.65 26.32 91.51 45.07 53.58 24.39 25.68 24.95 44.95 107.65 23.85 25.37 10.24

15.69 26.87 96.97 46.98 54.68 25.23 26.53 25.33 46.78 114.93 24.31 25.51 11.81

18.72 28.49 104.52 49.33 56.90 26.63 28.20 25.91 49.19 127.19 24.96 26.06 14.62

20.78 30.38 109.86 50.72 59.10 27.72 29.66 26.48 50.83 136.31 25.45 26.65 16.84

58.60 26.28 27.30 25.96 49.66 25.57 40.59 27.52 204.1

27.39 27.72 27.60 50.97 26.14 42.77 28.53

29.70 28.55 29.28 53.34 27.17 45.56 30.29

32.05 29.40 55.59 28.18 47.30 31.90

53.08 22.14 53.43 25.79

54.71 23.33 59.64 26.36

56.35 24.15 64.42 26.99

52.14 25.84 26.86 24.92 26.23 26.35 25.93

53.96 26.35 27.88 25.36 26.94 27.39 26.56

55.81 26.84 28.60 25.79 27.49 28.59 27.28

52.31 21.28 49.47 25.55 30.14 51.25 25.60 26.17 24.65 25.68 25.88 25.61

12-195

Section 12.indb 195

4/28/05 2:00:31 PM

Thermal and Physical Properties of Pure Metals This table gives the following properties for the metallic elements: tm: tb:

Melting point in °C Normal boiling point in °C, at a pressure of 101.325 kPa (760 Torr) ∆fusH: Enthalpy of fusion at the melting point in J/g ρ25: Density at 25°C in g/cm3 α: Coefficient of linear expansion at 25°C in K-1 (the quantity listed is 106 × α) cp: Specific heat capacity at constant pressure at 25°C in J/g K λ: Thermal conductivity at 27°C in W/cm K

References 1. Dinsdale, A. T., CALPHAD, 15, 317, 1991 (melting points, enthalpy of fusion). 2. Touloukian, Y. S., Thermophysical Properties of Matter, Vol. 12, Thermal Expansion, IFI/Plenum, New York, 1975 (coefficient of expansion, density). Metal (symbol) Actinium (Ac) Aluminum (Al) Antimony (Sb) Barium (Ba) Beryllium (Be) Bismuth (Bi) Cadmium (Cd) Calcium (Ca) Cerium (Ce) Cesium (Cs) Chromium (Cr) Cobalt (Co) Copper (Cu) Dysprosium (Dy) Erbium (Er) Europium (Eu) Gadolinium (Gd) Gallium (Ga) Gold (Au) Hafnium (Hf ) Holmium (Ho) Indium (In) Iridium (Ir) Iron (Fe) Lanthanum (La) Lead (Pb) Lithium (Li) Lutetium (Lu) Magnesium (Mg) Manganese (Mn) Mercury (Hg) Molybdenum (Mo) Neodymium (Nd) Neptunium (Np) Nickel (Ni)

Atomic weight 26.98 121.76 137.33 9.01 208.98 112.41 40.08 140.11 132.91 52.00 58.93 63.55 162.50 167.26 151.96 157.25 69.72 196.97 178.49 164.93 114.82 192.22 55.85 138.91 207.20 6.94 174.97 24.30 54.94 200.59 95.94 144.24 58.69

tb °C

tm °C 1050 660.32 630.628 727 1287 271.406 321.069 842 799 28.44 1907 1495 1084.62 1412 1529 822 1313 29.7666 1064.18 2233 1472 156.60 2446 1538 920 327.462 180.5 1663 650 1246 –38.8290 2623 1016 644 1455

3198 2519 1587 1897 2471 1564 767 1484 3443 671 2671 2927 2562 2567 2868 1529 3273 2204 2856 4603 2700 2072 4428 2861 3464 1749 1342 3402 1090 2061 356.62 4639 3074 2913

3. Ho, C. Y., Powell, R. W., and Liley, P. E., J. Phys. Chem. Ref. Data, 3, Suppl. 1, 1974 (thermal conductivity). 4. Cox, J. D., Wagman, D. D., and Medvedev, V. A., CODATA Key Values for Thermodynamics, Hemisphere Publishing Corp., New York, 1989 (heat capacity). 5. Glushko, V. P., Ed., Thermal Constants of Substances, VINITI, Moscow, (enthalpy of fusion, heat capacity). 6. Wagman, D. D., et. al., The NBS Tables of Chemical Thermodynamic Properties, J. Phys. Chem. Ref. Data, 11, Suppl. 2, 1982 (heat capacity). 7. Chase, M. W., et. al., JANAF Thermochemical Tables, 3rd ed., J. Phys. Chem. Ref. Data, 14, Suppl. 1, 1985 (heat capacity, enthalpy of fusion). 8. Gschneidner, K. A., Bull. Alloy Phase Diagrams, 11, 216–224, 1990 (various properties of the rare earth metals). 9. Hellwege, K. H., Ed., Landolt Börnstein, Numerical Values and Functions in Physics, Chemistry, Astronomy, Geophysics, and Technology, Vol. 2, Part 1, Mechanical-Thermal Properties of State, 1971 (density). 10. Physical Encyclopedic Dictionary, Vol. 1–5, Encyclopedy Publishing House, Moscow, 1960–66.

∆fus H J/g 399.9 162.5 51.8 876.0 53.3 55.2 213.1 39.0 15.7 404 272.5 203.5 68.1 119 60.6 63.6 80.0 64.6 152.4 103a 28.6 213.9 247.3 44.6 23.1 432 126a 348.9 235.0 11.4 390.7 49.5 13.5 290.3

ρ25 g/cm3 10 2.70 6.68 3.62 1.85 9.79 8.69 1.54 6.77 1.93 7.15 8.86 8.96 8.55 9.07 5.24 7.90 5.91 19.3 13.3 8.80 7.31 22.5 7.87 6.15 11.3 0.534 9.84 1.74 7.3 13.5336 10.2 7.01 20.2 8.90

α × 106 K-1

cp J/g K

23.1 11.0 20.6 11.3 13.4 30.8 22.3 6.3 97 4.9 13.0 16.5 9.9 12.2 35.0 9.4b 18 14.2 5.9 11.2 32.1 6.4 11.8 12.1 28.9 46 9.9 24.8 21.7 60.4 4.8 9.6

0.12 0.897 0.207 0.205 1.82 0.122 0.231 0.646 0.192 0.242 0.450 0.421 0.384 0.170 0.168 0.182 0.235 0.374 0.129 0.144 0.165 0.233 0.131 0.449 0.195 0.127 3.57 0.154 1.024 0.479 0.139 0.251 0.191

13.4

0.445

λ W/cm K 2.37 0.243 0.184 2.00 0.0787 0.968 2.00 0.113 0.359 0.937 1.00 4.01 0.107 0.145 0.139a 0.105 0.406 3.17 0.230 0.162 0.816 1.47 0.802 0.134 0.353 0.847 0.164 1.56 0.0782 0.0834 1.38 0.165 0.063 0.907

12-196

487_S12.indb 196

3/24/06 10:15:43 AM

Thermal and Physical Properties of Pure Metals Metal (symbol) Niobium (Nb) Osmium (Os) Palladium (Pd) Platinum (Pt) Plutonium (Pu) Polonium (Po) Potassium (K) Praseodymium (Pr) Promethium (Pm) Protactinium (Pa) Radium (Ra) Rhenium (Re) Rhodium (Rh) Rubidium (Rb) Ruthenium (Ru) Samarium (Sm) Scandium (Sc) Silver (Ag) Sodium (Na) Strontium (Sr) Tantalum (Ta) Technetium (Tc) Terbium (Tb) Thallium (Tl) Thorium (Th) Thulium (Tm) Tin (Sn) Titanium (Ti) Tungsten (W ) Uranium (U) Vanadium (V) Ytterbium (Yb) Yttrium (Y) Zinc (Zn) Zirconium (Zr) a

Estimated.

At 100°C.

487_S12.indb 197

Atomic weight 92.91 190.23 106.42 195.08

39.10 140.91 231.04 186.21 102.91 85.47 101.07 150.36 44.96 107.87 22.99 87.62 180.95 158.93 204.38 232.04 168.93 118.71 47.88 183.84 238.03 50.94 173.04 88.91 65.39 91.22

tm °C 2477 3033 1554.8 1768.2 640 254 63.38 931 1042 1572 696 3185 1964 39.30 2334 1072 1541 961.78 97.794 777 3017 2157 1359 304 1750 1545 231.93 1668 3422 1135 1910 824 1522 419.53 1854.7

tb °C

12-197 ∆fus H J/g

4744 5012 2963 3825 3228 962 759 3520 3000a

323 304.1 157.3 113.6 11.6

5596 3695 688 4150 1794 2836 2162 882.94 1382 5458 4265 3230 1473 4788 1950 2602 3287 5555 4131 3407 1196 3345 907 4409

324.5 258.4 25.6 381.8 57.3 314 104.6 113.1 84.8 202.1 339.7 67.9 20.3 59.5 99.7 60.4 295.6 284.5 38.4 422 44.3 128 108.1 230.2

59.6 48.9 53.4

ρ25 g/cm3 8.57 22.59 12.0 21.5 19.7 9.20 0.89 6.77 7.26 15.4 5 20.8 12.4 1.53 12.1 7.52 2.99 10.5 0.97 2.64 16.4 11 8.23 11.8 11.7 9.32 7.26 4.51 19.3 19.1 6.0 6.90 4.47 7.14 6.52

α × 106 K-1 7.3 5.1 11.8 8.8 46.7 23.5 83.3 6.7 11a

6.2 8.2

cp J/g K 0.265 0.130 0.244 0.133

0.757 0.193 0.19a

6.4 12.7 10.2 18.9 71 22.5 6.3

0.137 0.243 0.364 0.238 0.196 0.567 0.235 1.225 0.306 0.140

10.3 29.9 11.0 13.3 22.0 8.6 4.5 13.9 8.4 26.3 10.6 30.2 5.7

0.182 0.129 0.118 0.160 0.227 0.522 0.132 0.116 0.489 0.154 0.298 0.388 0.278

λ W/cm K 0.537 0.876 0.718 0.716 0.0674 0.20 1.024 0.125 0.15a

0.479 1.50 0.582 1.17 0.133 0.158 4.29 1.41 0.353 0.575 0.506 0.111 0.461 0.540 0.169 0.666 0.219 1.74 0.276 0.307 0.385 0.172 1.16 0.227

3/24/06 10:15:44 AM

THERMAL CONDUCTIVITY OF METALS AND SEMICONDUCTORS AS A FUNCTION OF TEMPERATURE This table gives the temperature dependence of the thermal conductivity of several metals and of carbon, germanium, and silicon. For graphite, separate entries are given for the thermal conductivity parallel (||) and perpendicular (â&#x160;Ľ) to the layer planes. The thermal conductivity of all these materials is very sensitive to impurities at low temperatures, especially below 100 K. Therefore, the values given here should be regarded as typical values for a highly purified specimen; the thermal conductivity of different specimens can vary by more than an order of magnitude in the low-temperature range. See Reference 2 for details.

T/K 1 2 3 4 5 6 7 8 9 10 15 20 30 40 50 60 70 80 90 100 150 200 250 300 350 400 500 600 800 1000 1200 1400 1600 1800 2000

Ag 39.4 78.3 115 147 172 187 193 190 181 168 96.0 51.0 19.3 10.5 7.0 5.5 4.97 4.71 4.60 4.50 4.32 4.30 4.29 4.29 4.27 4.25 4.19 4.12 3.96 3.79 3.61*

Al 41.1 81.8 121 157 188 213 229 237 239 235 176 117 49.5 24.0 13.5 8.5 5.85 4.32 3.42 3.02 2.48 2.37 2.35 2.37 2.40 2.40 2.36 2.31 2.18

Au 5.46 10.9 16.1 20.9 25.2 28.5 30.9 32.3 32.7 32.4 24.6 15.8 7.55 5.15 4.21 3.74 3.48 3.32 3.28 3.27 3.25 3.23 3.21 3.17 3.14 3.11 3.04 2.98 2.84 2.70 2.55

I 0.0138* 0.0461 0.108 0.206 0.344 0.523 0.762 1.05 1.40 3.96 7.87 18.8 29.4 35.3 37.4 36.9 35.1 32.7 30.0 19.5 14.1 11.0 8.95 7.55* 6.5*

References 1. Ho, C. Y., Powell, R. W., and Liley, P. E., J. Phys. Chem. Ref. Data, 1, 279, 1972. 2. White, G. K., and Minges, M. L., Thermophysical Properties of Some Key Solids, CODATA Bulletin No. 59, 1985.

Thermal Conductivity in W/cm K Carbon (C) Pyrolytic Diamond (type) graphite IIa IIb || â&#x160;Ľ 0.033* 0.111 0.261 0.494 0.820 1.24 1.77 2.41 3.17 8.65 16.8 38.9 65.9 92.1 112 119 117 109 100 60.2 40.3 29.7 23.0 18.5* 15.4*

0.0200* 0.0676 0.160 0.307 0.510 0.778 1.12 1.53 2.03 5.66 11.2 26.5 44.0 59.1 67.5 69.1 65.7 60.0 54.2 32.5 22.6 17.0 13.5 11.1* 9.32*

0.811

0.0116

4.20 9.86 16.4 23.1 29.8 36.6 42.8 47.5 49.7 45.1 32.3 24.4 19.5 16.2 13.9 10.8 8.92 6.67 5.34 4.48 3.84 3.33 2.93 2.62

0.0397 0.0786 0.120 0.152 0.173 0.181 0.181 0.176 0.168 0.125 0.0923 0.0711 0.0570 0.0477 0.0409 0.0322 0.0268 0.0201 0.0160 0.0134 0.0116 0.0100 0.00895 0.00807

Cr 0.402* 0.803 1.20 1.60 2.00 2.39 2.27 3.14 3.50 3.85 5.24 5.93 5.49 4.25 3.17 2.48 2.07 1.84 1.69 1.59 1.29 1.11 1.00 0.937 0.929 0.909 0.860 0.807 0.713 0.654 0.619 0.588 0.556 0.526* 0.494*

Cu 42.2 84.0 125 162 195 222 239 248 249 243 171 108 44.5 21.7 12.5 8.29 6.47 5.57 5.08 4.82 4.29 4.13 4.06 4.01 3.96 3.93 3.86 3.79 3.66 3.52 3.39

12-198

Section 12.indb 198

4/28/05 2:00:40 PM

Thermal Conductivity of Metals and Semiconductors as a Function of Temperature T/K 1 2 3 4 5 6 7 8 9 10 15 20 30 40 50 60 70 80 90 100 150 200 250 300 350 400 500 600 800 1000 1200 1400 1600 1800 2000 a

Fe 1.71 3.42 5.11 6.77 8.39 9.93 11.4 12.7 13.9 14.8 17.0 15.4 10.0 6.23 4.05 2.85 2.16 1.75 1.50 1.34 1.04 0.94 0.865 0.802 0.744 0.695 0.613 0.547 0.433 0.323 0.283 0.312 0.330 0.345*

Gea 0.274 2.06 5.35 8.77 11.6 13.9 15.5 16.6 17.3 17.7 17.3 14.9 10.8 7.98 6.15 4.87 3.93 3.25 2.70 2.32 1.32 0.968 0.749 0.599 0.495 0.432 0.338 0.273 0.198 0.174 0.174

Mg 9.86 19.6 29.0 37.6 45.0 50.8 54.7 56.7 57.0 55.8 41.1 27.2 12.9 7.19 4.65 3.27 2.49 2.02 1.78 1.69 1.61 1.59 1.57 1.56 1.55 1.53 1.51 1.49 1.46*

Ni 2.17 4.34 6.49 8.59 10.6 12.5 14.2 15.8 17.1 18.1 19.5 16.5 9.56 5.82 4.00 3.08 2.50 2.10 1.83 1.64 1.22 1.07 0.975 0.907 0.850 0.802 0.722 0.656 0.676 0.718 0.762 0.804

Pb 27.9 44.6 35.8 22.2 13.8 8.10 4.86 3.20 2.30 1.78 0.845 0.591 0.477 0.451 0.436 0.425 0.416 0.409 0.403 0.397 0.379 0.367 0.360 0.353 0.347 0.340 0.328 0.314

Sia

2.31 4.60 6.79 8.8 10.5 11.8 12.6 12.9 12.8 12.3 8.41 4.95 2.15 1.39 1.09 0.947 0.862 0.815 0.789 0.775 0.740 0.726 0.718 0.716 0.717 0.718 0.723 0.732 0.756 0.787 0.826 0.871 0.919 0.961 0.994*

0.0693* 0.454 1.38 2.97 5.27 8.23 11.7 15.5 19.5 23.3 41.6 49.8 48.1 35.3 26.8 21.1 16.8 13.4 10.8 8.84 4.09 2.64 1.91 1.48 1.19 0.989 0.762 0.619 0.422 0.312 0.257 0.235 0.221

12-199 Sn

183 323 297 181 117 76 52 36 26 19.3 6.3 3.2 1.79 1.33 1.15 1.04 0.96 0.915 0.880 0.853 0.779 0.733 0.696 0.666 0.642 0.622 0.596

Ti 0.0144* 0.0288* 0.0432 0.0575 0.0719 0.0863 0.101 0.115 0.129 0.143 0.212 0.275 0.365 0.390 0.374 0.355 0.340 0.326 0.315 0.305 0.270 0.245 0.229 0.219 0.210 0.204 0.197 0.194 0.197 0.207 0.220 0.236 0.253 0.270*

W 14.4 28.7 42.8 56.3 68.7 79.5 88.0 93.8 96.8 97.1 72.0 40.5 14.4 6.92 4.27 3.14 2.58 2.29 2.17 2.08 1.92 1.85 1.80 1.74 1.67 1.59 1.46 1.37 1.25 1.18 1.12 1.08 1.04 1.01 0.98

Values below 300 K are typical values.

* Extrapolated.

Section 12.indb 199

4/28/05 2:00:43 PM

THERMAL CONDUCTIVITY OF ALLOYS AS A FUNCTION OF TEMPERATURE This table lists the thermal conductivity of selected alloys at various temperatures. The indicated compositions refer to weight percent. Since the thermal conductivity is sensitive to exact composition and processing history, especially at low temperatures, these values should be considered approximate.

References 1. Powell, R. L., and Childs, G. E., in American Institute of Physics Handbook, 3rd Edition, Gray, D. E., Ed., McGraw-Hill, New York, 1972. 2. Ho, C. Y., et al., J. Phys. Chem. Ref. Data, 7, 959, 1978.

Thermal conductivity in W/m K Alloy Aluminum:

Bismuth: Copper:

Ferrous:

Gold: Indium: Lead: Nickel:

Platinum: Silver: Tin: Titanium:

1100 2024 3003 5052 5083, 5086 Duralumin Rose metal Woodâ&#x20AC;&#x2122;s metal electrolytic tough pitch free cutting, leaded phosphorus, deoxidized brass, leaded bronze, 68% Cu; 32% Zn beryllium german silver silicon bronze A manganin constantan commercial pure iron plain carbon steel(AISI 1020) plain carbon steel(AISI 1095) 3% Ni; 0.7% Cr; 0.6% Mo 4% Si stainless steel 27% Ni; 15% Cr colbalt thermocouple 65% Au; 35% Ag 85.5% In; 14.5% Pb 60% Pb; 40% Sn (soft solder) 64.35% Pb; 35.65% In 80% Ni; 20% Cr contracid inconel monel 90% Pt; 10% Ir 90% Pt; 10% Rh silver solder normal Ag thermocouple 60% Sn; 40% Pb 5.5% Al; 2.5% Sn;0.2% Fe 4.7% Mn; 3.99% Al; 0.14% C

20 K

77 K

50 3.2 11 4.8 3 5.5

240 17 58 25 17 30 5.5 17 1300 800 42 12 16 17 7.5 3.4 3.2 8.6 72 20 8.5 6

270 56 140 77 55 91 8.3 23 550 460 120 39 48 36 17 11 14 17 106 58 31 22

220 95 150 120 95 140 14

220 130 160 140 120 160 16

400 380 190 70 92 70 20 23 17 19 82 65 41

8 55 20 24 24 44 9.1

0.8

2 1.7 8.6 12 7.8 28 3.26

390 380 220 120 110 90 23 30 22 22 76 65 45 33 20 14 11

0.2 0.5 0.9

2 4.2 7.1

7.3 12.5 15

9.5 13 20

12 230 55 1.8 1.7

34 310 51 4.3 4.5

4 330 200 7.5 2.3 2.3 2 0.75 0.48 0.9 15 13

0.3 1.2 1.9

48 16

194 K

6.4 6.5

273 K

20.2 12 13 15 21 31 30.1

7.8 8.5

373 K

573 K

973 K

180

380

370

350

113 25

172 30

35 24 16 12

36 28 19 16

30 26 25 21

16 24 31.4 30.5

19 30

26 43

8.4

10.8

12-200

Section 12.indb 200

4/28/05 2:00:48 PM

THERMAL CONDUCTIVITY OF CRYSTALLINE DIELECTRICS This table lists the thermal conductivity of a number of crystalline dielectrics, including some which find use as optical materials. Values are given at temperatures for which data are available.

Ther. cond. W/m K

Material

T/K

AgCl

223 273 323 373 398 540 723 315 315 358 417 315 358 377

1.3 1.2 1.1 1.1 2.9 3.2 3.5 6.4 17.7 15.6 13.3 35.8 35.4 35.6

4.2 20 35 77 373 523 773 4.2 20 77 194 273 373 973 8 10 20 77 283 323 373 1047 1475 1928 2111 225 260 305 370 5 30 40 100 250 300 4.2

110 3500 6000 1100 2.6 3.9 5.8 0.5 23 150 48 35 26 8 6.0 3.7 1.4 0.31 0.16 0.21 0.27 36.2 22.7 21.9 18.5 20 13.4 10.9 10.5 4.2 24.0 25.0 12.0 4.8 6.2 0.3

Al,B silicate (tourmaline) || to c axis Al,Be silicate (beryl) Al,F silicate (topaz) || to c axis Al,Fe silicate (garnet)

Al2O3 (sapphire): 36° to c axis

⊥ to c axis

Al2O3 (sintered)

As2S3 (glass) BN

BaF2

BaTiO3

BeO

Reference Powell, R. L., and Childs, G. E., in American Institute of Physics Handbook, 3rd Edition, Gray, D. E., Ed., McGraw-Hill, New York, 1972.

Material

Bi2Te3

C (diamond) type I

CaCO3 || to c axis ⊥ to c axis

CaF2

CaWO4 (scheelite) CdTe

CsBr

CsI

Cu2O (cuprite)

Fe3O4 (magnetite)

Glass: phoenix

plastic perspex

T/K 20 77 373 573 1273 80 204 303 370 4.2 20 77 194 273 83 273 83 194 273 373 83 223 273 323 373 422 160 297 422 223 273 323 373 223 273 323 373 102 163 299 360 4.5 20.5 126.5 304 4.2 20 77 4.2

Ther. cond. W/m K 16 270 210 120 29 6.4 2.8 3.6 4.6 13 800 3550 1450 1000 25 5.5 17 6.5 4.6 3.6 39 18 10 9.2 9 11.3 7.0 3.6 2.9 1.2 0.94 0.81 0.77 1.4 1.2 1 0.95 3.74 7.76 5.58 4.86 27.4 293.0 7.4 7.0 0.095 0.13 0.37 0.058

12-201

Section 12.indb 201

4/28/05 2:00:52 PM

Thermal Conductivity of Crystalline Dielectrics

12-202 Material pyrex

H2 (para + 0.5% ortho)

H2O (ice) He3 (high pressure)

He4 (high pressure)

I2 KBr

KCl

LaF3 LiF

MgO·Al2O3 (spinel) MnO

Section 12.indb 202

T/K

Ther. cond. W/m K

20 77 194 273 2.5 3 4 6 10 173 223 273 0.6 1 1.5 2 0.5 0.8 1 2 300 325 350 2 4.2 100 273 323 373 4.2 25 80 194 273 323 373 4.2 80 194 273 4.2 10 20 77 78 197 274 4.2 20 77 373 773 4.2 40 120 573

0.074 0.44 0.88 1 100 150 200 30 3 3.5 2.8 2.2 25 2 0.57 0.21 42 120 24 0.18 0.45 0.42 0.4 150 360 12 5 4.8 4.8 500 140 35 10 7.0 6.5 6.3 700 13 4.6 3.1 0.48 1.7 1.2 0.36 7.8 5.0 5.4 620 1800 150 13 8.5 0.25 55 8 3.5

Material

T/K

Ther. cond. W/m K

NaCl

4.2 20 77 273 323 373 5 50 100 2 3 4.2 10 20 77 194 230 273

440 300 30 6.4 5.6 5.4 1100 250 90 3.0 4.6 4.2 0.8 0.3 17 23 38 27

NaF

NH4Cl

NH4H2PO4 || to optic axis ⊥ to optic axis NiO

SiO2 (quartz) || to c axis

⊥ to c axis

SiO2 (fused silica)

SrTiO3

TlBr TlCl TiO2 (rutile) || to optic axis

⊥ to optic axis

315 339 313 342 4.2 40 194

0.71 0.71 1.26 1.34 5.9 400 82

20 194 273 20 194 273 4.2 20 77 194 273 373 673 5 30 40 100 250 300 316 311

720 20 12 370 10 6.8 0.25 0.7 0.8 1.2 1.4 1.6 1.8 2.4 21.0 19.2 18.5 12.5 11.2 0.59 0.75

4.2 20 273 4.2 20 273

200 1000 13 160 690 9

4/28/05 2:00:55 PM

THERMAL CONDUCTIVITY OF CERAMICS AND OTHER INSULATING MATERIALS Thermal conductivity values for ceramics, refractory oxides, and miscellaneous insulating materials are given here. The thermal conductivity refers to samples with density indicated in the second column. Since most of these materials are highly variable, the values should only be considered as a rough guide.

Material Alumina (Al2O3)

Dens. g/cm3

t °C

3.8

100 400 1300 1800 100 800 100 400 1000 –100 0 100 30 20 100 400 1000 1800 50 200 600 0

3.5 Al2O3 + MgO Asbestos

0.4

Asbestos + 85% MgO Asphalt Beryllia (BeO)

0.3 2.1 2.8

1.85

Brick, dry Brick, refractory: alosite aluminous diatomaceous

1.54

1.99 0.77 0.4

fireclay

silicon carbide

vermiculite

0.77

Calcium oxide

Cement mortar Charcoal Coal Concrete Cork

2 0.2 1.35 1.6 0.05 0.35

Cotton wool Diatomite

0.08 0.2

1000 400 1000 100 500 100 500 400 1000 200 600 200 600 100 400 1000 90 20 20 0 0 100 0 100 30 0

References 1. Powell, R. L., and Childs, G. E., in American Institute of Physics Handbook, 3rd Edition, Gray, D. E., Ed., McGraw-Hill, New York, 1972. 2. Perry, R. H., and Green, D., Perry’s Chemical Engineers’ Handbook, Sixth Edition, McGraw-Hill, New York, 1984.

Ther. cond. W/m K 30 13 6 7.4 17 7.6 15 10 5.6 0.07 0.09 0.10 0.08 0.06 210 90 20 15 64 40 23 0.04 1.3 1.2 1.3 0.2 0.24 0.08 0.1 1 1.2 2 2.4 0.26 0.31 16 9 7.5 0.55 0.055 0.26 0.8 0.03 0.04 0.06 0.08 0.04 0.05

Material

Dens. g/cm3 0.5

Ebonite Felt, flax Fuller’s earth Glass wool

Graphite 100 mesh 20-40 mesh Linoleum cork Magnesia (MgO)

1.2 0.2 0.3 0.53 0.2

0.48 0.7 0.54

MgO + SiO2 Mica: muscovite

phlogopite Canadian Micanite Mineral wool Perlite, expanded Plastics: bakelite celluloid polystyrene foam mylar foil nylon

0.15 0.1 1.3 1.4 0.05 0.05

polytetrafluoroethylene

urethane foam Porcelain Rock: basalt chalk

0.07

t °C 400 0 400 0 30 30 30 –200 to 20 50 100 300

Ther. cond. W/m K 0.09 0.09 0.16 0.16 0.05 0.04 0.1 0.005 0.04 0.05 0.08

40 40 20 100 400 1200 1700 100 400 1500

0.18 1.29 0.08 36 18 5.8 9.2 5.3 3.5 2.3

100 300 600 100 300

0.72 0.65 0.69 0.66 0.19

600 30 30 –200 to 20

0.2 0.3 0.04 0.002

20 30 –200 to 20 –200 to 20 –253 –193 25 –253 –193 25 230 20 90

1.4 0.02 0.033 0.0001 0.10 0.23 0.30 0.13 0.16 0.26 2.5 0.06 1

20 20

2 0.92

12-203

Section 12.indb 203

4/28/05 2:00:57 PM

Thermal Conductivity of Ceramics and Other Insulating Materials

12-204 Material granite limestone sandstone slate, ⊥ slate, || Rubber: sponge 92 percent Sand, dry Sawdust Shellac Silica aerogel Snow Steel wool Thoria (ThO2) Titanium dioxide

Section 12.indb 204

Dens. g/cm3

t °C

Ther. cond. W/m K

2.8 2 2.2

20 20 20 95 95

2.2 1 1.3 1.4 2.5

20 25 20 30 20 –200 to 20 0 55 100 400 1500 100 400 1200

0.05 0.16 0.33 0.06 0.23 0.003 0.16 0.09 10 5.8 2.4 6.5 3.8 3.3

0.2 1.5 0.2 0.1 0.25 0.1

Material

Dens. g/cm3

Uranium dioxide

Wood: balsa, ⊥ fir, ⊥ fir, || oak plywood pine, ⊥ pine, || walnut, ⊥ Wool Zinc oxide Zirconia (ZrO2) Zirconia + silica

0.11 0.54 0.54

0.45 0.45 0.65 0.09

t °C

Ther. cond. W/m K

100 400 1000

9.8 5.5 3.4

30 20 20 20 20 60 60 20 30 200 800 100 400 1500 200 600 1500

0.04 0.14 0.35 0.16 0.11 0.11 0.26 0.14 0.04 17 5.3 2 2 2.5 5.6 4.6 3.7

4/28/05 2:00:59 PM

THERMAL CONDUCTIVITY OF GLASSES This table gives the composition of various types of glasses and the thermal conductivity k as a function of temperature. Because

Vitreous silica

Type of glass

SiO2 (wt%) 100

of the variability of glasses, the data should be regarded as only approximate. Composition Other oxides (wt%)

t °C –150 –100 –50 0 50 100

k W/m K 0.85 1.05 1.20 1.30 1.40 1.50

B2O3

–100 0 100

1.00 1.25 1.40

Pyrex type chemicallyresistant borosilicate glasses

80–81

B2O3 Na2O Al

12–13 4 2

–100 0 100

0.90 1.10 1.25

Borosilicate crown glasses

60–65

B2O3

15–20

–100 0 100

0.65–0.75 0.90–0.95 1.00–1.05

65–70

B2O3

10–15

–100 0 100

0.75–0.80 0.95–1.00 1.05–1.15

70–75

B3O3

5–10

–100 0 100

0.80–0.85 1.05–1.10 1.15–1.20

55–65

ZnO Remainder: B2O3, Al2O3

5–15

–100 0 100

0.88–0.92 1.10–1.15 1.15–1.25

ZnO Remainder: Na2O, K2O

5–15

–100 0 100

0.60–0.70 0.70–0.90 0.85–0.95

ZnO Remainder: B2O3, Al2O3

15–25

–100 0 100

0.88–0.92 1.10–1.15 1.15–1.20

ZnO Remainder: Na2O, K2O

15–25

–100 0 100

0.65–0.80 0.85–0.95 0.90–1.05

ZnO Remainder: B2O3, Al2O3

5–15

–100 0 100

0.88–0.92 1.15–1.15 1.20–1.30

ZnO Remainder: Na2O, K2O

5–15

–100 0 100

0.70–0.85 0.90–1.05 1.00–1.15

ZnO

15–25

–100

0.90–0.95

Vycor glass

Zinc crown glasses (i)

Zinc crown glasses (ii)

65–75

12-205

Section 12.indb 205

4/28/05 2:01:01 PM

Thermal Conductivity of Glasses

12-206

Type of glass

SiO2 (wt%)

Composition Other oxides (wt%) Remainder: B2O3, Al2O3 ZnO Remainder: Na2O, K2O

k W/m K 1.15–1.15 1.20–1.25

15–25

–100 0 100

0.65–0.85 0.85–1.00 1.05–1.20

B2O3 Al2O3 BaO

12 8 48

–100 0 100

0.55 0.70 0.80

B2O3 Al2O3 ZnO BaO

6 2 8 43

–100 0 100

0.60 0.75 0.85

B2O3 Na2O K2O ZnO BaO

4 1 7 8 32

–100 0 100

0.65 0.75 0.90

B2O3 Na2O K2O ZnO BaO

2 5 15 2 10

–100 0 100

0.70 0.90 1.00

Borate glasses Borate flint glass

B2O3 Na2O K2O PbO Al2O3 ZnO

36 1 2 36 10 6

–100 0 100

0.55 0.65 0.80

Borate flint glass

B2O3 Al2O3 PbO

56 12 32

–100 0 100

0.50 0.65 0.85

Borate flint glass

B2O3 Al2O3 PbO

43 5 52

–100 0 100

0.40 0.55 0.70

Borate glass

B2O3 Al2O3 PbO K2O ZnO

55 14 11 4 12

–100 0 100

0.65 0.80 0.90

Borate crown glass

B2O3 Na2O K2O BaO PbO Al2O3

64 8 3 4 3 18

–100 0 100

0.50 0.65 0.85

Light borate crown glass

B2O3 Na2O

69 8

–100 0

0.55 0.70

Barium crown glasses

Section 12.indb 206

t °C 0 100

4/28/05 2:01:03 PM

Thermal Conductivity of Glasses

Type of glass

SiO2 (wt%)

Composition Other oxides (wt%) BaO 5 18 Al2O3

t °C 100

k W/m K 0.90

B2O3 ZnO

40 60

–100 0 100

0.65 0.75 0.85

Phosphate crown glasses Potash phosphate glass

P2O5 B2O3 K2O Al2O3 MgO

70 3 12 10 4

0 100

0.75 0.85

Baryta phosphate glass

P2O5 B2O3 Al2O3 BaO

60 3 8 28

0.75

Soda-lime glasses

Na2O CaO

17 8

–100 0 100

0.75 0.95 1.10

Na2O CaO

12 13

–100 0 100

0.90 1.10 1.15

Na2O CaO Al2O3

15 11 2

–100 0 100

0.80 1.00 1.15

Na2O CaO

25 10

–100 0 100

0.65 0.85 0.95

Na2O CaO

15 20

–100 0 100

0.85 1.00 1.10

Na2O CaO

20 20

–100 0 100

0.75 0.90 1.00

Na2O K2O CaO

9 11 5

–100 0 100

0.80 1.00 1.10

Na2O ZnO PbO

16 3 13

–100 0 100

0.65 0.85 1.00

PbO Others

25 10

–100 0 100

0.65–0.70 0.88–0.92 1.00–1.05

PbO

–100

0.60–0.65

Zinc borate glass

Other crown glasses Crown glass

High dispersion crown glass

Miscellaneous flint glasses (i) Silicate flint glasses Light flint glasses

Section 12.indb 207

12-207

4/28/05 2:01:04 PM

Thermal Conductivity of Glasses

12-208

Type of glass

SiO2 (wt%)

Composition Other oxides (wt%) Others 10

t °C 0 100

k W/m K 0.75–0.85 0.88–0.92

Ordinary flint glass

PbO Others

45 10

–100 0 100

0.50–0.60 0.65–0.75 0.80–0.85

Heavy flint glass

PbO Others

60 5

–100 0 100

0.45–0.50 0.60–0.65 0.70–0.75

Very heavy flint glasses

PbO Others

73 2

–100 0 100

0.40–0.45 0.55–0.60 0.63–0.67

PbO

–100 0 100

0.40 0.50 0.60

(ii) Borosilicate flint glass

B2O3 PbO Al2O3 K2O Na2O

31 25 7 3 1

–100 0 100

0.65 0.85 0.95

(iii) Barium flint glass

BaO PbO K2O Na2O ZnO Sb2O3

24 6 8 3 8 1

–100 0 100

0.60 0.70 0.85

K2O CaO

33 8

Fe2O3 Na2O MgO CaO Al2O3

10 17 4 3 2

–100 0 100

Fe2O3 Na2O3

15 18

0 100

0.88–0.92 1.00–1.05

Fe2O3 Na2O

20 18

0 100

0.85–0.90 0.95–1.00

Other glasses Potassium glass

Iron glasses

0.88–0.92

0.80 0.95 1.05

Rock glasses Obsidian Artificial diabase

Section 12.indb 208

1.35

100

1.25

4/28/05 2:01:06 PM

COMMERCIAL METALS AND ALLOYS This table gives typical values of mechanical, thermal, and electrical properties of several common commercial metals and alloys. Values refer to ambient temperature (0 to 25°C). All values should be regarded as typical, since these properties are dependent on the particular type of alloy, heat treatment, and other factors. Values for individual specimens can vary widely.

Common name Ingot iron Plain carbon steel AISI-SAE 1020 Stainless steel type 304 Cast gray iron Malleable iron Hastelloy C Inconel Aluminum alloy 3003, rolled Aluminum alloy 2014, annealed Aluminum alloy 360 Copper, electrolytic (ETP) Yellow brass (high brass) Aluminum bronze Beryllium copper 25 Cupronickel 30% Red brass, 85% Chemical lead Antimonial lead (hard lead) Solder 50-50 Magnesium alloy AZ31B Monel Nickel (commercial) Cupronickel 55-45 (constantan) Titanium (commercial) Zinc (commercial) Zirconium (commercial)

Thermal conductivity W/cm K

Density g/cm3

References 1. ASM Metals Reference Book, Second Edition, American Society for Metals, Metals Park, OH, 1983. 2. Lynch, C. T., CRC Practical Handbook of Materials Science, CRC Press, Boca Raton, FL, 1989. 3. Shackelford, J. F., and Alexander, W., CRC Materials Science and Engineering Handbook, CRC Press, Boca Raton, FL, 1991.

Coeff. of linear expansion 10–6/°C

Electrical resistivity µΩ cm

0.7 0.52

7.86 7.86

11.7 11.7

9.7 18

0.15 0.47

7.9 7.2 7.3 8.94 8.25 2.73 2.8 2.64 8.94 8.47 7.8 8.23 8.94 8.75 11.34 10.9 8.89 1.77 8.84 8.89 8.9 4.5 7.14 6.5

17.3 10.5 12 11.3 11.5 23.2 23.0 21.0 16.5 20.3 16.4 17.8 16.2 18.7 29.3 26.5 23.4 26 14.0 13.3 18.8 8.5 32.5 5.85

72 67 30 125 103 3.7 3.4 7.5 1.7 6.4 12 7

0.12 0.15 1.9 1.9 1.5 3.9 1.2 0.7 0.8 0.3 1.6 0.35 0.3 0.5 1.0 0.3 0.9 0.2 1.8 1.1 0.2

11 21 23 15 9 58 10 49 43 6 41

Modulus of elasticity GPa 205 205 195 90 170 200 200 70 70 70 120 100 120 130 150 90 13 20 – 45 180 200 160 110 – 95

Tensile strength MPa

Approx. melting point °C

–

1540 1515

550 180 345 780 800 110 185 325 300 300-800 400-600 500-1400 400-600 300-700 17 47 42 260 545 460 – 330-500 130 450

1425 1175 1230 1350 1370 650 650 565 1080 930 1050 925 1200 1000 327 290 215 620 1330 1440 1260 1670 419 1855

450

12-211

Section 12.indb 211

4/28/05 2:01:12 PM

HARDNESS OF MINERALS AND CERAMICS There are several hardness scales for describing the resistance of a material to indentation or scratching. This table lists a number of common materials in order of increasing hardness. Values are given, when available, on three different hardness scales: the original Mohs Scale (range 1 to 10); the modified Mohs Scale (range 1 Material Graphite Talc Alabaster Gypsum Halite (rock salt) Stibnite (antimonite) Galena Mica Calcite Barite Marble Aragonite Dolomite Fluorite Magnesia Apatite Opal Feldspar (orthoclase) Augite Hematite Magnetite Rutile Pyrite Agate Uranium dioxide Silica (fused) Quartz Flint Silicon Andalusite Zircon Zirconia Aluminum nitride Beryl Beryllia Topaz Garnet Emery Zirconium nitride Zirconium boride Titanium nitride Zirconia (fused) Tantalum carbide Tungsten carbide Corundum (alumina) Zirconium carbide Alumina (fused) Beryllium carbide Titanium carbide Carborundum (silicon carbide) Aluminum boride Tantalum boride Boron carbide Boron Titanium boride Diamond

Formula C 3MgO·4SiO2·H2O CaSO4·2H2O CaSO4·2H2O NaCl Sb2S3 PbS CaCO3 BaSO4 CaCO3 CaMg(CO3)2 CaF2 MgO CaF2·3Ca3(PO4)2 K2O·Al2O·6SiO2 Fe2O3 Fe3O4 TiO2 FeS2 SiO2 UO2 SiO2 SiO2 Si Al2OSiO4 ZrSiO4 ZrO2 AlN Be3Al2Si6O18 BeO Al2SiO4(OH,F)2 Al2O3·3FeO·3SiO2 Al2O3 (impure) ZrN ZrB2 TiN ZrO2 TaC WC Al2O3 ZrC Al2O3 Be2C TiC SiC AlB TaB2 B4C B TiB2 C

to 15), and the Knoop Hardness Scale. In the last case, a load of 100 g is assumed.

Reference

Shackelford, J. F. and Alexander, W., CRC Materials Science and Engineering Handbook, CRC Press, Boca Raton, FL, 1991. Mohs 0.5 1 1.7 2 2 2.0 2.5 2.8 3 3.3 3.5 3.5 3.5 4 5 5 5 6 6 6 6 6.2 6.3 6.5 6.7 7 7 7 7.5 7.5

Modified mohs 1 2

135

4 5

163 370 430

560 750

7 8

8 8+ 9

9 10

9 12 9.3

9.5 10

600 820

1200 1225

7.8 8

Knoop

1300 1340 1360 1510 1560 1770 1800 1880 2025 2150

2400 2470 2500 2500 2600 2800

2850 7000

12-212

Section 12.indb 212

4/28/05 2:01:14 PM

ORGANIC MAGNETS J.S. Miller Magnetic ordering, e.g., ferromagnetism, like superconductivity, is a property of a solid, not of an individual molecule or ion, and very rarely occurs for organic compounds. In contrast to superconductivity, where all electron spins pair to form a perfect diamagnetic material, magnetic ordering requires unpaired electron spins; hence, superconductivity and ferromagnetism are mutually exclusive. The vast majority of organic compounds are diamagnetic (i.e., all electron spins are paired), and a relative few possess unpaired electrons (designated by an arrow, â&#x2020;&#x2018;) and are paramagnetic (PM), i.e., they are oriented in random directions. A few organic solids, however, exhibit strong magnetic behavior and magnetically order as ferromagnets (FO) with all spins aligned in the same direc-

tion. In some cases the spins align in the opposite direction and compensate to form an antiferromagnet (AF). In some cases these spins are not opposed to each other and do not compensate and lead to a canted antiferromagnet or weak ferromagnet (WF). If the number of spins that align in one direction differs from the number of spins that align in the opposite direction, the spins cannot compensate and a ferrimagnet (FI) results. Metamagnets (MM) are antiferromagnets in which all the spins become aligned like a ferromagnet in an applied magnetic field. Above the ordering or critical temperature, Tc, all magnets are paramagnets (PM). Organic magnets all possess electron spins in p-orbitals, but these may be in conjunction with metal ion-based spins.

Paramagnet (PM) (random) arrangement of spins

Ferromagnetic (FO) ordering of spins

Antiferromagnetic (AF) ordering of spins

Ferrimagnetic (FI) ordering of spins

Canted antiferromagnet or weak ferromagnet (WF) ordering of spins

FIGURE 1.

Schematic illustration of the different types of magnetic behavior.

12-109

Section 12.indb 109

4/28/05 1:57:41 PM

Organic Magnets

12-110

Summary of the Critical Temperature, Tc, Saturation Magnetization, Ms, Coercive Field, Hcr, and Remanent Magnetization, Mr, for Selected Organic-Based Magnets Magnet α-1,3,5,7-Tetramethyl-2,6-diazaadamantane-N,N’-doxyl β-2-(4'-Nitrophenyl)-4,4,5,5-tetramethyl-4,5dihydro-1H-imidazol-1-oxyl-3-N-oxide {FeIII[C5(CH3)5]2}[TCNE] {MnIII[C5(CH3)5]2}[TCNE] {CrIII[C5(CH3)5]2}[TCNE] α-{FeIII[C5(CH3)5]2}[TCNQ] β-{FeIII[C5(CH3)5]2}[TCNQ] Tanol subarate NCC6F4CN2S2 MnII(hfac)2NITC2H5 MnII(hfac)2NIT(i-C3H8) [Mn(hfac)2]3[{ON[C6H3(t-C(CH3)3]2NO]2} [MnTPP][TCNE].2C6H5CH3 V[TCNE]x.yCH2Cl2 (x ~ 2; y ~ 0.5) Mn[TCNE]x.yCH2Cl2 (x ~ 2; y ~ 0.5) Fe[TCNE]x.yCH2Cl2 (x ~ 2; y ~ 0.5) Co[TCNE]x.yCH2Cl2 (x ~ 2; y ~ 0.5)

Type FO

Tc/K 1.48

FO FO FO FO MM FO MM WF FI FI FI FI FI FI FI FI

0.6 4.8 8.8 3.65 2.55 3.0 0.38 35.5 7.8 7.6 46 13 ~400 75 97 44

Ms/A m-1 48,300

Hcr/T <0.00001

Mr/A m-1 —

22,300 37,600 58,200 46,300 34,200 21,600 20,700 45 39,400 42,400 24,400 18,400 28,200 52,000 46,300 22,000

0.00008 0.10 0.12 — — — — 0.00009 0.03 <0.0005 — 2.4 0.0015 - 0.006 0.002 0.23 0.65

<200 2,300 3,700 — — — — — 27,600 <420 — 10,300 1,650 270 3 —

List of Symbols and Abbreviations Ms Hcr Tc Mr TCNE TCNQ

Saturation magnetization at 2 K Coercive Field Critical Temperature Remanent magnetization at 2 K Tetracyanoethylene 7,7,8,8-Tetracyano-p-quinodimethane

hfac NIT FO FI MM WF

2-(4’-Nitrophyenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1Himidazol-1-oxyl-3-N-oxide

1,3,5,7-Tetramethyl-2,6-diazaadamantane-N,N’-doxyl

M[C5(CH3)5]2(M = Cr, Mn, Fe)

Section 12.indb 110

Hexaﬂuoroacetonate Nitronyl nitroxide Ferromagnet Ferrimagnet Metamagnet Weak ferromagnet

TCNE

TCNQ

4/28/05 1:57:47 PM

Organic Magnets

12-111

Mn(hfac)2

Tanol subarate

NITR (R = C2H5, i-C3H8, n-C3H8)

MnTPP

References 1. Miller, J. S. and Epstein, A. J., Angew. Chem. Internat. Ed., 33, 385, 1994. 2. Chiarelli, R., Rassat, A., Dromzee, Y., Jeannin, Y., Novak, M. A., and Tholence, J. L., Phys. Scrip., T49, 706, 1993. 3. Kinoshita, M., Jap. J. Appl. Phys., 33, 5718, 1994. 4. Gatteschi, D., Adv. Mat., 6, 635, 1994.

Section 12.indb 111

{ON[C6H3(t-C(CH3)3]2NO]2}

NCC6F4CN2S2 5. Miller, J. S. and Epstein, A. J., J. Chem. Soc., Chem. Commun., 1319, 1998. 6. Broderick, W. E., Eichorn, D. M., Lu, X., Toscano, P. J., Owens, S. M. and Hoffman, B. M., J. Am. Chem. Soc., 117, 3641, 1995. 7. Banister, A. J., Bricklebank, N., Lavander, I., Rawson, J., Gregory, C. I., Tanner, B. K., Clegg, W. J., Elsegood, M. R., and Palacio, F., Angew. Chem. Internat. Ed., 35, 2533, 1996.

4/28/05 1:57:52 PM

OPTICAL PROPERTIES OF SELECTED INORGANIC AND ORGANIC SOLIDS L. I. Berger Optical properties of materials are closely related to their dielectric properties. The complex dielectric function (relative permittivity) of a material is equal to ε ( ω ) = ε′ ( ω ) – jε″ ( ω ),

where ε′(ω) and ε″(ω) are its real and imaginary parts, respectively, and ω is the angular frequency of the applied electric field. For a non-absorbing medium, the index of refraction is n = (εµ)1/2, where µ is the relative magnetic permeability of the medium (material); in the majority of dielectrics, µ ≅ 1. For many applications, the most important optical properties of materials are the index of refraction, the extinction coefficient, k , and the reflectivity, R. The common index of refraction of a material is equal to the ratio of the phase velocity of propagation of an electromagnetic wave of a given frequency in vacuum to that in the material. Hence, n 1. The optical properties of highly conductive materials like metals and semiconductors (at photon energy range above the energy gap) differ from those of optically transparent media. Free electrons absorb the incident electromagnetic wave in a thin surface layer (a few hundred nanometers thick) and then release the absorbed energy in the form of secondary waves reflected from the surface. Thus, the light reflection becomes very strong; for example, highly conductive sodium reflects 99.8% of the incident wave (at 589 nm). Introduction of the effective index of refraction, neff = (ε′)1/2 = n – jk , where ε′ = ε – jδ/ω εo, δ is the electrical conductivity of the material in S/m, and εo = 8.8542·10-12 F/m is the permittivity of vacuum, allows one to apply the expressions of the optics of transparent media to the conductive materials. It is clear that the effective index of refraction may be smaller than 1. For example, n = 0.05 for pure sodium and n = 0.18 for pure silver (at 589.3 nm). At very high photon energies, the quantum effects, such as the internal photoeffect, start playing a greater role, and the optical properties of these materials become similar to those of insulators (low reflectance, existence of Brewster’s angle, etc.). The extinction coefficient characterizes absorption of the electromagnetic wave energy in the process of propagation of a wave through a material. The wave intensity, I, after it passes a distance x in an isotropic medium is equal to I = I 0 exp ( – αx ),

where I0 is the intensity at x = 0 and α is called the absorption coefficient. For many applications, the extinction coefficient, k , which is equal to

12-141

λ k = α ------, 4π

where λ is the wavelength of the wave in the medium, is more commonly used for characterization of the electromagnetic losses in materials. Reflection of an electromagnetic wave from the interface between two media depends on the media indices of refraction and on the angle of incidence. It is characterized by the reflectivity, which is equal to the ratio of the intensity of the wave reflected back into the first medium to the intensity of the wave approaching the interface. For polarized light and two non-absorbing media, ( N1 – N2 ) -2 , R = ------------------------( N1 + N2 ) 2

where N1 = n1/cosθ1 and N2 = n2/cosθ2 for the wave polarized in the plane of incidence, and N1 = n1cosθ1 and N2 = n2cosθ2 for the wave polarized normal to the plane of incidence; θ1 and θ2 are the angles between the normal to the interface in the point of incidence and the directions of the beams in the first and second medium, respectively. The reflectivity at normal incidence in this case is R = [ ( n1 – n2 ) ⁄ ( n1 + n2 ) ]

For any two opaque (absorbing) media, the normal incidence reflectivity is ( n1 – n2 ) + k2 -. R = --------------------------------2 2 ( n1 + n2 ) + k2 2

In the majority of experiments, the first medium is air (n ≈ 1) , and hence, ( 1 – n ) + k. R = ----------------------------2 2 (1 + n) + k 2

The data on n and k in the following table are abridged from the sources listed in the references. The reflectivity at normal incidence, R, has been calculated from the last equation. For convenience, the energy E, wavenumber ν , and wavelength λ are given for the incidence radiation.

12-142

Optical Properties of Selected Inorganic and Organic Solids E/eV

2.194 2.168 2.141 2.123 2.098 2.094 2.091 2.073 2.060 2.049 2.036 2.023 2.013 2.009 2.000 1.987 1.977 1.974 1.962 1.953 1.949 1.937 1.925 1.922 1.905 1.893 1.881 1.859 1.848 1.845 1.842 1.831 1.826 1.821 1.818 1.815 1.807 1.802 0.06199 0.05904 0.05636 0.05391 0.04592 0.04428 0.04275 0.04133 0.03542 0.03100 0.03061 0.03024 0.02883 0.02850 0.02818 0.02755 0.02480 0.02254 0.02066 0.01907 0.01771

ν /cm–1

λ/µm

17700 17480 17270 17120 16920 16890 16860 16720 16610 16530 16420 16310 16230 16210 16130 16030 15940 15920 15820 15750 15720 15630 15530 15500 15360 15270 15170 14990 14900 14880 14860 14770 14730 14680 14660 14640 14580 14530 500.0 476.2 454.5 434.8 370.4 357.1 344.8 333.3 285.7 250.0 247.0 244.0 232.6 229.9 227.3 222.2 200.0 181.8 166.7 153.8 142.9

0.565 0.572 0.579 0.584 0.591 0.592 0.593 0.598 0.602 0.605 0.609 0.613 0.616 0.617 0.620 0.624 0.627 0.628 0.632 0.635 0.636 0.640 0.644 0.645 0.651 0.655 0.659 0.667 0.671 0.672 0.673 0.677 0.679 0.681 0.682 0.683 0.686 0.688 20.0 21.0 22.0 23.0 27.0 28.0 29.0 30.0 35.0 40.0 40.5 41.0 43.0 43.5 44.0 45.0 50.0 55.0 60.0 65.0 70.0

0.27 0.26 0.26

0.24 0.24 0.24

0.25 0.25 0.25 0.25 0.21 0.19 0.12 0.088 0.50 0.56 0.58 0.50 0.62 0.40 0.36 0.34 0.32

0.22 0.22 0.22 0.21 0.18 0.18 0.25 0.18 0.16 0.29 0.48 0.60 0.36 0.31 0.27 0.26 0.25

Crystalline Arsenic Selenide (As2Se3) [Ref. 1]* 0.30 0.25 0.20 0.17 0.13

0.10 0.079

0.26 0.26 0.23 0.20 0.17 0.15 0.12

0.050 0.097 0.082 0.063 0.031 0.051 0.038 0.030 0.020 0.022 0.017 0.012 8.6·10–3 6.4 5.2 3.1 1.7·10–3 2.0 1.3·10

–3

1.2·10–3 9.0·10–4 6.4 4.7

8.6·10–4 3.4

3.2 3.1 3.1 3.1 3.0 3.0 3.0 3.0 2.7 1.9 2.0 1.7 1.2 1.6 2.3 4.2 6.5 4.5 4.0 3.8 3.6

2.9 2.9 2.9 2.9 2.8 2.8 2.8 2.7 2.5 1.7 2.6 2.4 1.3 1.2 1.2 2.0 4.0 3.5 3.2 3.1 3.0

5.5 4.1 1.7·10–3 2.1·10–3 2.5·10–3 3.0·10–3 6.3·10–3 7.6·10–3 0.0092 0.011

3.3 2.5 3.6 0.17 0.089 0.097 0.19

1.8·10–3 2.2·10–3 2.6·10–3 3.1·10–3 6.4·10–3 7.7·10–3 0.0093 0.011 0.037 0.38 0.33 0.41 2.2 2.8 2.0 3.3 0.26 0.10 0.10 0.16 0.30

0.034 1.0 0.95 0.46 0.94 1.4

Optical Properties of Selected Inorganic and Organic Solids µm E/eV ν /cm–1 λ/µ n na nc k ka kc 0.01653 133.3 75.0 3.7 3.0 0.41 0.44 0.01550 125.0 80.0 3.8 3.1 0.29 0.40 0.01459 117.6 85.0 3.6 2.9 0.20 0.34 0.01378 111.1 90.0 3.2 2.6 0.43 0.49 0.01305 105.3 95.0 4.7 3.0 1.5 1.5 0.01240 100.0 100.0 4.4 2.7 0.22 0.81 0.01181 95.24 105.0 4.2 3.0 0.094 3.9 0.01127 90.91 110.0 4.1 5.3 0.059 0.70 0.01033 83.33 120.0 3.9 4.2 0.034 0.13 0.009537 76.92 130.0 3.9 4.0 0.024 0.069 0.008856 71.43 140.0 3.9 3.8 0.019 0.048 0.007749 63.50 160.0 3.8 3.7 0.014 0.032 0.006888 55.55 180.0 3.8 3.7 0.011 0.024 0.006199 50.0 200.0 3.8 3.6 0.0091 0.019 *Indices a and c relate to the radiation electric field parallel to the a and c axes of the crystal, respectively.

2.056 2.026 2.006 1.990 1.925 1.826 1.810 1.794 1.771 1.715 1.701 1.647 1.629 1.596 1.579 1.562 1.544 1.529 1.512 1.494 1.476 1.378 1.240 1.127 1.051 1.033 0.2555 0.2380 0.2344 0.1345 0.1339 0.1333 0.1308 0.1215 0.1203 0.1196 0.1178 0.1116 0.1004 0.09919 0.09795 0.09671 0.09299 0.08555

16580 16340 16180 16050 15530 14730 14600 14470 14290 13830 13720 13280 13140 12870 12740 12590 12450 12330 12200 12050 11910 11110 10000 9091 8475 8333 1980 1919 1890 1085 1080 1075 1055 980 970 965 950 900 810 800 790 780 750 690

0.603 0.612 0.618 0.623 0.644 0.679 0.685 0.691 0.700 0.723 0.729 0.753 0.761 0.777 0.785 0.794 0.803 0.811 0.820 0.830 0.840 0.90 1.00 1.10 1.18 1.20 5.05 5.21 5.29 9.22 9.26 9.30 9.48 10.20 10.31 10.36 10.53 11.11 12.35 12.50 12.66 12.82 13.33 14.49

Vitreous Arsenic Selenide (As2Se3) [Ref. 1] 0.12 0.11 0.099 9.0 5.6 1.4 0.012 0.0089 6.2 2.6 0.0022 0.00046 3.07 4.0 3.06 2.7 3.05 1.9 3.05 0.00013 3.04 0.000094 3.03 6.3 3.03 4.2 3.02 2.8 3.01 1.8 2.98 2.93 2.90 2.89 2.88 1.6·10–7 9.9·10–8 1.1·10–7 4.4 3.7 4.4 4.5 8.9 9.9·10–7 1.0·10–6 1.1 1.8 4.9 7.0·10–6 1.0·10–5 1.5 3.7 6.9

12-143 R

0.62 0.49 0.39 0.26 0.25 0.78 0.64 0.50 0.38

Ra 0.34 0.34 0.32 0.28 0.46 0.40 0.38 0.37 0.35 0.35 0.35 0.34 0.34 0.34

Rc 0.26 0.27 0.24 0.21 0.34 0.25 0.62 0.47 0.38 0.36 0.34 0.33 0.33 0.32

12-144

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.08431 0.08059 0.07811 0.07687 0.07563 0.07439 0.07315 0.07191 0.07067 0.06943 0.06633 0.06571 0.06509 0.06447 0.06075 0.06024 0.05331 0.05269 0.05207 0.05145 0.05083 0.05021 0.04959 0.04862 0.04679 0.04592 0.04509 0.04428 0.03875 0.03815 0.03757 0.02988 0.02952 0.02725 0.02362 0.01937 0.01922 0.01907 0.01734 0.01653 0.01642 0.01494 0.01246 0.007606 0.006199 0.004592 0.002799 0.001826 0.001273 0.0006491 0.0004376 0.0002903 0.0001716 0.00009047 0.00005621 0.00002774 0.00001439

ν /cm–1 680 650 630 620 610 600 590 580 570 560 535 530 525 520 490 485.9 430 425 420 415 410 405 400 392.2 377.4 370.4 363.6 357.1 312.5 307.7 303.0 241.0 238.1 219.8 190.5 156.2 155.0 153.8 139.9 133.3 132.5 120.5 100.5 61.35 50.00 37.04 22.57 14.73 10.27 5.236 3.530 2.341 1.384 0.7297 0.4534 0.2237 0.1161

λ/µ µm 14.71 15.38 15.87 16.13 16.39 16.67 16.95 17.24 17.54 17.86 18.69 18.87 19.05 19.23 20.41 20.58 23.26 23.53 23.81 24.10 24.39 24.69 25.0 25.5 26.5 27.0 27.5 28.0 32.0 32.5 33.0 41.5 42.0 45.5 52.5 64.0 64.5 65.0 71.5 75.0 75.5 83.0 99.5 163.0 200.0 270.0 443.0 679.0 974.0 1910.0 2833.0 4271.0 7224.0 13704 22056 44699 86153

2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.6 2.6 2.6 2.6 2.6 2.5 2.5 2.4 2.2 2.2 3.2 3.6 3.2 3.2 3.2 3.1 3.1 3.1 3.0 3.2 3.3 3.2 3.1 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

4.959 3.100

40000 25000

0.2500 0.40

Vitreous Arsenic Sulfide (As2S3) - [Ref. 2] 2.48 1.21 3.09 0.34

k 5.9 6.1 6.3 7.7 7.8 9.3·10–5 1.2·10–4 1.4 1.8 2.8 5.2 7.2·10–4 1.2·10–3 1.7 4.9 5.2 1.4 1.1·10–3 8.5·10–4 7.3 8.3 9.4·10–4 1.2·10–3 1.6 5.0 8.0·10–3 1.2·10–2 1.7 8.2 9.3·10–3 0.11 0.89 1.0 1.8 0.30 0.10 9.6·10–2 9.4 8.7 9.4 0.096 0.15 0.60 0.12

0.072 4.5 2.8 2.1 1.1·10–2 7.5·10–3 5.0 3.1 1.6·10–3 9.9·10–4 5.2 2.6

0.22 0.32 0.37 0.50 0.73 0.22 0.22 0.35 0.71 0.73 0.31 0.21 0.21 0.84 0.87 0.21 0.21 0.33 0.73 0.20 0.20 0.34 0.87 0.18 0.17 0.20 0.22 0.39 0.32 0.27 0.27 0.88 0.87 0.88 0.26 0.25 0.26 0.29 0.26 0.67 0.50 0.41 0.25 0.25 0.71 0.53 0.25 0.25 0.72 0.47

0.27 0.27

Optical Properties of Selected Inorganic and Organic Solids E/eV 2.48 1.879 1.240 0.6199 0.3100 0.2480 0.1736 0.1240 0.09299 0.07439 0.04959 0.03757 0.03100 0.02480 0.02066 0.01771 0.01550 0.01378 0.01240 0.008183 0.004029 0.002418 0.001984 0.001048 0.0001033 4.129·10–12

4.9 4.1 3.9 3.5 3.1 3.0 2.755 2.75 2.610 2.5 2.25 1.771 1.512 1.50 1.475 1.47 1.465 1.46 1.459 1.455 1.45 1.445 1.442 1.44 1.43 1.30 1.24 1.20 1.10 1.00 0.90 0.80 0.70

ν /cm–1 20000 15150 10000 5000 2500 2000 1400 1000 750 600 400.0 303.0 250.0 200.0 166.7 142.9 125.0 111.1 100 66 32.5 19.5 16 8.45 0.833 3.33·10–8

λ/µ µm 0.4999 0.66 1.0 2.0 4.0 5.0 7.143 10.00 13.33 16.67 25.0 33.0 40.0 50 60 70 80 90 100 152 308 513 625 1180 12000 3·1011

39520 33070 31460 28230 25000 24200 22220 22180 21050 20160 18150 14290 12200 12100 11900 11860 11820 11780 11760 11740 11690 11650 11630 11610 11530 10490 10000 9679 8872 8065 7259 6452 5646

0.2530 0.3024 0.3179 0.3542 0.4000 0.4133 0.45 0.4509 0.475 0.4959 0.5510 0.70 0.82 0.8266 0.840 0.8434 0.8463 0.8492 0.850 0.8521 0.8551 0.8580 0.860 0.8610 0.8670 0.9537 1.0 1.033 1.127 1.240 1.378 1.550 1.771

n 2.83 2.59 2.48 2.43 2.41 2.41 2.40 2.38 2.35 2.31 1.79 3.59 2.98 2.66 2.64 2.99 2.89 2.84 2.81 2.76 2.74 2.74 2.74 2.73 2.73 2.73

12-145 k 0.013 1.7·10–6 2.4·10–7

7.4·10–7 1.3·10–4 3.0·10–3 4.6·10–4 0.2 1.4 0.15 0.11 0.57 0.17 0.14 0.12 0.10 0.072 0.044 0.031 0.025 8.8·10–3 1.3·10–3

Cadmium Telluride (CdTe) - [Ref. 3] 2.48 2.04 2.33 1.59 2.57 1.90 2.89 1.52 3.43 1.02 3.37 0.861 3.080 0.485 3.23 0.636 3.045 3.14 0.525 3.05 0.411 2.861 0.210 2.880 0.040 2.98 0.319 2.905 0.00134 0.000671 3.37 1.89 2.948 1.08·10–4 2.9565 5.10·10–5 2.73 2.952 2.9479 1.37 2.9402 2.8720 2.840 2.8353 2.8050 2.7793 2.7537 2.7384 2.7223

R 0.23 0.20 0.18 0.17 0.17 0.17 0.17 0.17 0.16 0.16 0.085 0.38 0.25 0.21 0.22 0.25 0.24 0.23 0.23 0.22 0.22 0.22 0.22 0.22 0.22 0.22

0.39 0.32 0.37 0.34 0.34 0.32 0.27 0.29 0.28 0.26 0.23 0.23 0.25 0.24

0.24 0.24 0.24 0.32 0.24 0.23 0.23 0.23 0.23 0.22 0.22 0.22 0.21

12-146

E/eV 0.60 0.50 0.40 0.30 0.20 0.10 0.09 0.06819 0.0573 0.05 0.0469 0.04592 0.04133 0.04092 0.03720 0.03647 0.03596 0.03493 0.03472 0.03100 0.02917 0.02852 0.02728 0.02604 0.02480 0.02384 0.01798 0.01736 0.01550 0.01364 0.01240 0.009919 0.008679 0.007439 0.006199 0.004959 0.003720 0.023015 0.001550

155 145 130 110 90 70 40 23 7.0 6.0 5.00 4.00 3.00

Optical Properties of Selected Inorganic and Organic Solids

ν /cm–1 4839 4033 3226 2420 1613 806.5 725.9 550 462 403.3 378 370.3 333.3 330 300 294.1 290 281.7 280 250 235.3 230 220 210 200 192.3 145 140 125 110 100 80 70 60 50 40 30 18.563 12.50

48390 40330 32260 24200

λ/µ µm 2.066 2.480 3.100 4.133 6.199 12.40 13.78 18.18 21.6 24.80 26.5 27 30 30.30 33.33 34.00 34.48 35.5 35.71 40 42.5 43.48 45.45 47.62 50.00 52.0 68.97 71.43 80.0 90.91 100 125 142.9 166.7 200 250 333.3 800

0.007999 0.008551 0.009537 0.01127 0.01378 0.01771 0.03100 0.05391 0.1771 0.2066 0.2480 0.3100 0.4133

n 2.7086 2.6972 2.6878 2.6800 2.6722 2.6535 2.6482 2.623

R 0.21 0.21 0.21 0.21 0.21 0.20 0.20 0.20

3.8·10–6 2.5801

2.55916 2.531 2.494 2.478 2.459 2.378 2.289 2.224 2.137 2.013 1.8 6.778 4.598 3.868 3.649 3.415 3.348 3.299 3.263 3.236 3.217 538.71

0.19 8.0·10–5 9.88·10–5 2.86·10–4 3.34 4.97 8.93 5.77·10–3 7.91 6.76 1.18·10–2 6.93 1.87 2.47·10–2 3.4·10–2 4.97·10–2 6.21 5.2 4.50 0.294 9.47·10–2 5.68·10–2 0.0262 0.0189 1.39 1.03 7.52·10–3 3.2096 6.18

Gallium Arsenide (GaAs) - [Ref. 4] 0.0181 0.0203 0.0224 0.0278 0.0323 0.0376 0.0426 1.037 0.228 1.063 1.838 1.264 2.472 2.273 4.084 3.601 1.920 4.509 1.948

0.19 0.57 0.73 0.18 0.83 0.17 0.36 0.14 0.13 0.11 0.79 0.66 0.41 0.35 0.32 0.30 0.29 0.35 0.32 0.28 0.28 0.28

0.61 0.67 0.42 0.47

Optical Properties of Selected Inorganic and Organic Solids

E/eV 2.50 2.00 1.80 1.60 1.50 1.40 1.20 1.00 0.80 0.50 0.25 0.15 0.100 0.090 0.070 0.060 0.0495 0.03968 0.03496 0.02976 0.02066 0.01550 0.008266 0.002480 0.001240

154.0 110.0 100.0 80.0 50.0 27.0 25.0 20.0 15.0 5.5 4.68 3.50 3.00 2.78 2.621 2.480 2.18 2.000 1.6 1.240 0.6888 0.4769 0.1907 0.1550 0.1240 0.06199 0.03100

ν /cm–1 20160 16130 14520 12900 12100 11290 9679 8065 6452 4033 2016 1210 806.5 725.9 564.6 483.9 399.2 320 282 240 166.7 125 66.67 20 10

λ/µ µm 0.4959 0.6199 0.8888 0.7749 0.8266 0.8856 1.033 1.240 1.550 2.480 4.959 8.266 12.40 13.78 17.71 20.66 25.05 31.25 35.46 41.67 60 80 150 500 1000

n 4.333 3.878 3.785 3.700 3.666 3.6140 3.4920 3.4232 3.3737 3.3240 3.2978 3.2831 3.2597 3.2493 3.2081 3.1609 3.058 2.495 0.307 4.57 3.77 3.681 3.62 3.607 3.606

44360 37750 28230 24200 22420 21140 20000 17580 16130 12900 10000 5556 3846 1538 1250 1000 500 250

0.00805 0.0113 0.0124 0.0155 0.0248 0.0459 0.0496 0.0620 0.0826 0.2254 0.2649 0.3542 0.4133 0.4460 0.473 0.500 0.5687 0.62 0.7749 1.0 1.8 2.6 6.5 8.0 10 20 40

Gallium Phosphide (GaP) - [Ref. 5] 1.7·10–2 2.15·10–2 215·10–2 3.0·10–2 4.7·10–2 9.3·10–2 0.122 0.180 0.748 0.628 1.543 3.556 4.181 2.634 5.050 0.819 4.081 0.224 3.904 0.103 3.73 6.37·10–3 3.590 2.47·10–3 3.411 2.8·10–7 3.3254 3.209 3.1192 3.0439 3.0271 2.995 4.29·10–4 2.984 2.964 2.615 7.16·10–3 3.594 1.81·10–2

k 0.441 0.211 0.151 0.091 0.080 1.69·10–3

4.93·10–6 1.64·10–5 2.32·10–4 3.45·10–3 2.07·10–3 2.43·10–2 294·10–2 4.26·10–2 3.89·10–3 1.84·10–3 2.14·10–3 1.3·10–3

12-147

R 0.39 0.35 0.34 0.33 0.33 0.32 0.31 0.30 0.29 0.29 0.29 0.28 0.28 0.28 0.28 0.27 0.26 0.18 0.41 0.34 0.33 0.32 0.32 0.32

0.68 0.50 0.46 0.37 0.35 0.33 0.32 0.30 0.29 0.28 0.26 0.26 0.25 0.25 0.25 0.25 0.20 0.32

12-148

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.02480 0.01727 0.01168 0.006199 0.004133 0.001240

155 60 25 24 15 10 5.00 4.50 4.00 3.34 2.84 1.80 1.50 0.6 0.2480 0.1907 0.1653 0.06199 0.03100 0.02480 0.02244 0.02207 0.02033 0.01054 0.005579 0.001860 0.001240

25 20 15 10 6 5.0 4.0 3.5 3.0 2.5 2.44 1.86 1.8 1.7 1.6 1.5 1.2 1.0 0.6 0.35 0.32 0.20 0.1240 0.06199 0.04959

ν /cm–1 200 139.27 94.21 50.00 33.33 10.00

λ/µ µm 50 71.80 106.1 200 300 1000

40330 36290 32260 26940 22910 14520 12100 4839 2000 1538 1333 500 250 200 181 178 164 85 45 15 10

0.007999 0.02066 0.04959 0.05166 0.08266 0.1240 0.2480 0.2755 0.3100 0.3712 0.4366 0.6888 0.8266 2.066 5.0 6.5 7.5 20.00 40.00 50.00 55.25 56.18 60.98 117.6 222.2 666.7 1000

Indium Antimonide (InSb) - [Ref. 6] 4.77·10–3 7.30·10–2 1.15 .015 1.15 0.18 0.97 0.230 0.74 0.88 1.307 2.441 1.443 2.894 2.632 3.694 3.528 2.280 3.340 2.021 4.909 1.396 4.418 0.643 4.03 4.14 9.1·10–2 4.30 6.3·10–2 4.18 2.7·10–2 3.869 2.0·10–3 2.98 2.6·10–3 2.22 0.165 3.05 7.59 9.61 4.20 4.94 0.140 2.12 0.423 1.02 5.59 6.03 17.9 10.7 24.0

48390 40330 32260 28230 24200 20160 19680 15000 14520 13710 12900 12100 9679 8065 4839 2823 2581 1613 1000 500 400

0.04959 0.06199 0.08266 0.1240 0.2066 0.2480 0.3100 0.3542 0.4133 0.4959 0.5081 0.6666 0.6888 0.7293 0.7749 0.8266 1.033 1.240 2.066 3.542 3.875 6.199 10.00 20.00 25.00

Indium Arsenide (InAs) - [Ref. 7] 1.139 1.125 0.894 0.835 1.434 2.112 1.524 2.871 3.313 1.799 3.008 1.754 3.197 2.034 4.364 1.786 4.489 1.446 3.889 0.554 3.851 0.530 3.798 0.493 3.755 0.463 3.714 0.432 3.613 3.548 0.161 3.608 9.58·10–3 3.512 1.23·10–4 3.427 3.402 3.334 3.264

n 3.461 3.3922 3.3621 3.3447 3.3413 3.3319

k 5.77·10–3 4.34·10–3 4.26·10–3 1.3·10–4

R 0.30 0.30 0.29 0.29 0.29 0.29

0.53 0.60 0.61 0.45 0.45 0.47 0.41 0.36 0.37 0.39 0.38 0.35 0.25 0.14 0.84 0.70 0.44 0.14 0.88 0.93 0.94

0.168 0.225 0.336 1.071 0.45 0.58 0.39 0.37 0.41 0.45 0.44 0.36 0.35 0.35 0.34 0.34 0.32 0.31 0.32 0.31 0.30 0.30 0.29 0.28

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.04339 0.03720 0.03100 0.02765 0.02480 0.01984 0.01860 0.01736 0.01488 0.01240 0.009919 0.007439 0.004959 0.002480 0.001240

20 15 10 5.5 5.0 4.0 3.0 2.0 1.5 1.25 1.00 0.50 0.30 0.10 0.075 0.060 0.050 0.03992 0.03496 0.03100 0.02728 0.02480 0.02418 0.02232 0.01860 0.01240 0.009919 0.007439 0.004959 0.002480 0.001240

14.5 10 5 2.0 1.65 1.5 1.0 0.75 0.62 0.48 0.40 0.32

ν /cm–1 350 300 250 222 200 160 150 140 120 100 80 60 40 20 10

λ/µ µm 28.57 33.33 40.00 44.84 50.00 62.50 66.67 71.43 83.33 100.0 125.0 166.7 250.0 500 1000

n 3.182 2.988 1.970 5.90 6.91 5.27 5.27 3.99 3.91 3.85 3.817 3.793 3.778 3.769 3.766

44360 40330 32260 24200 16130 12100 10085 8068 4034 2420 806.8 605.1 484.1 403.4 322 282 250 220 200 195 180 150 100 80 60 40 20 10

0.06199 0.08266 0.1240 0.2254 0.2480 0.3100 0.4133 0.6199 0.8266 0.9915 1.239 2.479 4.131 12.39 16.53 20.66 24.79 31.06 35.46 40.00 45.45 50.0 51.28 55.56 66.67 100 125.0 166.7 250.0 500 1000.0

0.793 0.695 0.806 1.426 2.131 3.141 4.395 3.549 3.456 3.324 3.220 3.114 3.089 3.012 2.932 2.780 2.429 0.307 3.89 4.27 3.93 3.81 3.19 3.19 3.65 3.57 3.551 3.538 3.529 3.523 3.522

40330 16130 13310 12100 8065 6049 5001 3871 3226 2581

0.08551 0.1240 0.2480 0.6199 0.7514 0.8266 1.240 1.653 2.000 2.583 3.100 3.875

0.72 0.68 0.54 3.65 4.51 4.64 4.65 4.59 4.90 4.91 4.98

12-149

k 5.46·10–3 6.37·10–2 6.53 0.30 0.41 0.51 1.1·10–2 6.6·10–3 4.3·10–3

Indium Phosphide (InP) - [Ref. 8] 0.494 0.574 1.154 2.562 3.495 1.730 1.247 0.317 0.203

1.46·10–2 3.35·10–2 3.57 0.282 3.0·10–2 1.3·10–2 8.7·10–3

Lead Selenide (PbSe) - [Ref. 9] 0.20 0.50 1.2 2.9 1.73 2.64 1.1 0.269 0.770

0.173

R 0.27 0.25 0.11 0.74 0.56 0.47 0.47 0.36 0.35 0.35 0.34 0.34 0.34 0.37 0.34

0.79 0.61 0.38 0.43 0.32 0.31 0.29 0.28 0.26 0.26 0.25 0.24 0.22 0.17 0.35 0.39 0.35 0.34 0.27 0.27 0.32 0.32 0.31 0.31 0.31 0.31 0.31

0.51 0.46 0.52 0.44 0.42 0.44 0.44 0.44

12-150

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.20 0.1190 0.09919 0.07935 0.05951 0.04959 0.03968 0.02976 0.01984 0.009919 0.007935 0.004959 0.002480 0.001736 0.001240

150 125 100 80 60 25 18.0 14.0 10.0 4.95 4.0 3.00 2.90 2.75 2.55 2.00 1.60 1.24 1.03 0.650 0.496 0.400 0.3100 0.2480 0.1240 0.1033 0.08059 0.06819 0.04959 0.03720 0.02480 0.01378 0.01240 0.008856 0.006199 0.003100 0.001653 0.001240 0.0006199

150 125 100 75

ν /cm–1 1613 960 800 640 480 400 320 240 160 80 64 40 20 14 10

λ/µ µm 6.199 10.42 12.50 15.63 20.83 25.00 31.25 41.67 62.50 125.0 156.3 250.0 500.0 714.3 1000

39920 32260 24200 23390 22180 20570 16130 12910 10000 8333 5263 4000 3226 2500 2000 1000 833.3 650 550 400 300 200.0 111.1 100.0 71.43 50.0 25.00 13.33 10.00 5.000

0.008266 0.009919 0.01240 0.01550 0.02066 0.04959 0.06888 0.08856 0.1240 0.2505 0.3100 0.4133 0.4275 0.4509 0.4862 0.6199 0.7749 1.00 1.2 1.9 2.5 3.1 4.0 5 10 12 15.38 18.18 25.00 33.33 50 90 100 140 200 400 750 1000 2000

0.008266 0.009919 0.01240 0.01653

n 4.82 4.74 4.72 4.68 4.59 4.49 4.31 3.89 2.34 1.73 2.91 11.2 12.6 14.1 17.4

0.845 0.846 0.651 0.879 1.52 1.73 3.88 4.12 4.25 4.35 4.29 4.62 4.43 4.30 4.24 4.30 4.30 4.16 4.115 4.01 3.90 3.90 3.81 3.53 2.99 0.514 1.175 1.79 17.41 16.27 12.96 12.44 12.35 12.27

k 1.20·10–3 2.09·10–3 4.12·10–3 1.00·10–2 1.77·10–2 3.62·10–2 9.61·10–2 0.56 7.38 10.1 14.6 12.2 16.6 21.1

Lead Sulfide (PbS) - [Ref. 10] 3.86·10–3 5.59·10–3 1.54·10–2 2.88·10–2 6.17·10–2 0.171 0.294 0.665 1.050 2.10 2.83 3.00 2.70 2.33 2.00 1.48 0.94 0.597 0.458 0.318 0.235 2.27·10–2 6.38·10–4 9.25·10–4 6.32·10–3 1.14·10–2

1.59 8.48 10.51 17.94 2.20 0.495 0.228 0.167 0.0815 Lead Telluride (PbTe) - [Ref. 11] 2.37·10–3 9.71·10–3 4.39·10–2 6.43·10–2

R 0.43 0.42 0.42 0.42 0.41 0.40 0.39 0.24 0.18 0.88 0.90 0.88

0.43 0.55 0.53 0.51 0.48 0.47 0.43 0.43 0.41 0.39 0.39 0.39 0.39 0.38 0.37 0.36 0.35 0.35 0.34 0.31 0.25 0.94 0.94 0.89 0.79 0.73 0.72 0.72 0.72

Optical Properties of Selected Inorganic and Organic Solids E/eV 50 30 15 10 7.5 5.0 3.0 2.5 1.5 1.0 0.80 0.60 0.40 0.30 0.20 0.15 0.1017 0.08927 0.06943 0.04959 0.03968 0.02976 0.009919 0.007439 0.006199 0.004959 0.003720 0.002480 0.001240

2000 1496 1016 725 504 303 250 200 150 100 75 50 25 20 15.1 13 12.0 11.0 10.00 9 7 4.959 4.000 2.952 2.000 0.9919 0.7999 0.4959 0.4000 0.3100

ν /cm–1

40330 24200 20160 12100 8065 6452 4839 3226 2420 1613 1210 820 720 560 400 320 240 80 60 50 40 30 20 10

λ/µ µm 0.02480 0.04133 0.08266 0.1240 0.1653 0.2480 0.4133 0.4959 0.8266 1.240 1.550 2.066 3.100 4.133 6.199 8.266 12.20 13.89 17.86 25.00 31.25 41.67 125.0 166.7 200.0 250.0 333.3 500.0 1000

40000 32260 23810 16130 8000 6452 4000 3226 2500

6.199·10–4 8.287·10–4 1.220·10–3 1.710·10–3 2.460·10–3 4.092·10–3 4.959·10–3 6.199·10–3 8.265·10–3 1.240·10–2 1.653·10–2 2.480·10–2 4.959·10–2 6.199·10–2 8.211·10–2 9.537·10–2 0.1033 0.1127 0.12398 0.1375 0.1771 0.250 0.31 0.42 0.62 1.25 1.55 2.5 3.1 4.0

0.72 0.66 0.8 0.72 1.0 1.35 3.8 4.55 6.25 6.10 6.075 5.95 5.77 5.76 5.47 5.38 5.13 4.50 3.58 1.01 2.95 4.9 6.9 11.6 27.7 27.6 45.1

k 6.87·10–2 7.77·10–2 0.17 0.60 0.92 1.0 2.2 2.86 3.1 2.2 0.71 0.521 0.331 3.55·10–2

9.16·10–3 1.37·10–2 3.06·10–2 9.6·10–2 0.23 1.9 16.6 22.5 27.2 34.8 35.7 39.1 57.8

Lithium Fluoride (LiF) - [Ref. 12] 0.9999347 4.33·10–6 0.999883 1.28·10–5 0.999757 5.18·10–5 0.999643 1.62·10–4 0.999162 4.96·10–5 0.99752 3.12·10–4 0.99632 6.17·10–5 2.12·10–3 0.9899 3.54·10–3 0.9801 1.32·10–2 2.63·10–2 7.89·10–2 0.558 0.521 1.20 0.58 1.08 0.68 1.04 1.64 2.28 0.11 1.77 8.07·10–7 1.606 7.70·10–7 1.53 1.46 1.4189 1.4073 1.3978 1.3915 1.3851 1.3858 1.3731 1.3650 1.3493

12-151 ka

0.61 0.53 0.49 0.53 0.52 0.52 0.51 0.50 0.50 0.48 0.47 0.45 0.40 0.32 0.96 0.96 0.97 0.97 0.95 0.95 0.97

0.10 0.10 0.15 0.08 0.05 0.04 0.03 0.03 0.03 0.03 0.03 0.02

12-152

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.2480 0.2000 0.1698 0.1494 0.1240 0.1127 0.1033 0.09537 0.08679 0.07439 0.06199 0.05579 0.04959 0.03720 0.03100 0.02480 0.01240 0.06199 0.04959 0.02480 0.01378 4.798·10–4 1.464·10–4 4.053·10–5 1.861·10–7 3.718·10–8

2860.3 2855.3 2849.3 2835.8 2832.3 2829.8 2828.3 219 215 212.5 211 185.1 109.7 43 40 29.9 20.1 15.1 10.0 9.0 8.0 7.0 6.199 4.959 3.999 2.952 2.695 2.616 2.384 2.066 1.550 1.033 0.5166

ν /cm–1 2000 1613 1370 1205 1000 909.1 833.3 769.2 700 600 500 450 400 300 250 200 100.0 50.0 40.00 20.00 11.11 3.870 1.181 0.3269 1.501·10–3 2.999·10–4

λ/µ µm 5.0 6.2 7.3 8.3 10.0 11.0 12.0 13.0 14.29 16.67 20.00 22.22 25.00 33.33 40.00 50.00 100 200 250 500 900 2584 8469 30590 6.662·106 3.335·107

50000 40000 32260 23810 21740 21100 19230 16670 12500 8333 4167

4.3347·10–4 4.3423·10–4 4.3514·10–4 4.3721·10–4 4.3775·10–4 4.3814·10–4 4.3837·10–4 5.661·10–3 5.767·10–3 5.834·10–3 5.876·10–3 6.7·10–3 1.13·10–2 0.02883 0.03179 0.04147 0.06168 0.08211 0.1240 0.1378 0.1550 0.1771 0.20 0.25 0.31 0.42 0.46 0.474 0.52 0.60 0.80 1.2 2.4

n 1.3266 1.2912 1.2499 1.2036 1.1005 1.0208

0.508 0.124 0.306 0.191 0.208 8.76 4.64 3.69 3.067 3.067 3.067 3.067 3.023 3.023 3.023 3.018 3.018

k 1.8·10–6

2.6·10–3 8.0·10–3 1.9·10–2 3.7·10–2 7.74·10–2 0.804 1.47 1.88 2.71 3.91 0.287 0.102 0.106 4.0·10–2 2.2·10–2 6.3·10–3 3.1·10–3 1.19·10–3 6.20·10–4 2.63·10–4 1.6·10–5 1.6·10–5

Potassium Chloride (KCl) - [Ref. 13] 3.93·10–6 3.39·10–6 4.61·10–6 5.85·10–6 5.85·10–6 1.57·10–6 4.19·10–7 1.82·10–3 1.84·10–3 2.19·10–3 1.82·10–3 0.99874 0.99578 0.96 3.0·10–2 0.925 1.8·10–2 0.756 0.145 0.910 0.495 0.965 0.344 1.16 0.38 1.99 0.50 1.15 0.46 2.0 8.46·10–7 1.71739 1.58972 1.54005 1.50701 1.50115 7.6·10–11 1.49501 1.48969 1.48291 1.47813 1.47464

R 0.02

0.68 0.85 0.91 0.68 0.42 0.33 0.26 0.26 0.26

0.25 0.25 0.25

1.01·10–3 4.22·10–3

0.035 0.13 0.048 0.11 0.070

0.040

0.039 0.038 0.037 0.037

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.2480 0.2000 0.1512 0.09999 0.07560 0.04959 0.03999 0.02976 0.02728 0.02232 0.01860 0.01612 0.01240 0.008679 0.006199 0.001240 0.0006199 0.0004133

2000 1860 1609 1496 1204 1093 1016 798 597 396 303 201 151.2 99.99 49.59 40.00 31.00 25.00 20.00 15.00 13.00 11.00 10.00 9.00 7.00 6.00 4.9939 4.1034 3.0640 2.5504 2.4379 2.2705 2.1489 2.1411 2.1102 2.1041 1.9257 1.8892 1.8566 1.7549 1.4550

ν /cm–1 2000 1.613 1220 806.5 609.8 400.0 322.6 240 220 180 150 130 100 70 50 10.00 5.000 3.333

λ/µ µm 5.0 6.2 8.2 12.4 16.4 25.0 31.0 41.67 45.45 55.56 66.67 76.92 100.0 142.9 200.0 1000 2000 3000

48390 40278.4 33096.1 24712.3 20570.5 19662.5 18312.5 17332.3 17269.2 17019.5 16970.4 15531.6 15237.6 14974.2 14153.9 11735.6

6.199·10–4 6.665·10–4 7.705·10–4 8.287·10–4 1.030·10–3 1.134·10–3 1.220·10–3 1.554·10–3 2.077·10–3 3.131·10–3 4.092·10–3 6.168·10–3 8.2·10–3 1.24·10–2 2.50·10–2 3.10·10–2 4.00·10–2 0.04959 0.06199 0.08266 0.09537 0.1127 0.1240 0.1378 0.1771 0.2066 0.248272 0.302150 0.404656 0.486133 0.508582 0.546074 0.576959 0.579065 0.587561 0.589262 0.643847 0.656272 0.667815 0.706519 0.852111

n 1.47048 1.46796 1.46260 1.44611 1.42295 1.34059 1.2431 0.85 0.53 0.31 0.44 4.1 2.7 2.4 2.2

12-153 k

6.57·10–4 0.16 0.35 1.05 4.0 0.32 0.11 9.2·10–2

R 0.036 0.036 0.035 0.033 0.030 0.021 0.012

0.37 0.21 0.17 0.14

9.0·10–3 3.7·10–3 2.0·10–3 Silicon Dioxide (Glass) - [Ref. 14] 0.99993 1.503·10–5 0.99991 1.936·10–5 0.99989 9.941·10–6 0.99987 1.308·10–5 0.99980 2.916·10–5 0.99975 4.155·10–5 0.99971 5.423·10–5 0.99954 1.289·10–4 0.99917 3.560·10–4 0.99812 4.04·10–4 0.99678 9.91·10–4 0.99269 3.63·10–3 0.9871 7.3·10–3 0.9813 7.0·10–3 0.9164 6.5·10–2 0.907 9.2·10–2 0.851 0.156 0.733 0.325 0.859 0.585 1.168 0.711 1.368 0.747 1.739 0.569 2.330 0.323 1.904 1.89·10–2 1.600 1.543 1.50841 1.48719 1.46961 1.46313 1.46187 1.46008 1.45885 1.45877 1.45847 1.45841 1.45671 1.45637 1.45608 1.45515 1.45248

0.10 0.11 0.11 0.17 0.097 0.053 0.046 0.041 0.038 0.036 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.034 0.034 0.034

12-154

Optical Properties of Selected Inorganic and Organic Solids E/eV 1.0985 0.60243 0.35354 0.2976 0.2728 0.2480 0.2232 0.1984 0.1736 0.1674 0.1612 0.1500 0.1401 0.1302 0.1209 0.1091 0.09919 0.08989 0.06943 0.06199 0.04959 0.03720 0.01240 0.007439 0.002480

25 20 17.5 15 12.5 10 7.5 5 4 3 2.8 2.6 2.4 2.2 2 1.8 1.6 1.240 0.6199 0.3100 0.2480 0.2066 0.1771 0.1653 0.1459 0.1305 0.1240 0.1181 0.1153 0.1127 0.1078 0.1033 0.09537 0.08856

ν /cm–1 8860.06 4858.9 2851.4 2400 2200 2000 1800 1600 1400 1350 1300 1210 1130 1050 975 880 800 725 560 500 400 300 100 60 20

λ/µ µm 1.12866 2.0581 3.5070 4.176 4.545 5.000 5.556 6.250 7.143 7.407 7.692 8.265 8.850 9.524 10.26 11.36 12.50 13.79 17.86 20.00 25.0 33.33 100.0 166.7 500.0

n 1.44888 1.43722 1.40568 1.383 1.365 1.342 1.306 1.239 1.053 0.9488 0.7719 0.4530 0.3563 2.760 2.448 1.784 1.753 1.698 1.337 0.6616 2.739 2.210 1.967 1.959 1.955

40330 32260 24200 22580 20970 19360 17740 16130 14520 12900 10000 5000 2500 2000 1667 1492 1333 1176 1053 1000 952.4 930.2 909.1 869.6 833.3 769.2 714.3

0.04959 0.06199 0.07085 0.08266 0.09919 0.1240 0.1653 0.2480 0.3100 0.4133 0.4428 0.4769 0.5166 0.5636 0.6199 0.6888 0.7749 1.000 2.000 4.000 5.000 6.000 7.000 7.500 8.500 9.500 10.00 10.50 10.75 11.00 11.50 12.00 13.00 14.00

Silicon Monoxide (Noncrystalline) - [Ref. 15] 0.8690 0.2717 0.8853 0.4919 0.9825 0.5961 1.132 0.6651 1.283 0.6523 1.378 0.6843 1.593 0.7473 2.001 0.6052 2.141 0.4006 2.116 0.1211 2.085 0.08374 2.053 0.05544 2.021 0.03533 1.994 0.02153 1.969 0.01175 1.948 0.00523 1.929 0.00151 1.87 1.84 1.80 1.75 1.70 1.60 1.42 0.90 0.18 1.20 1.20 2.00 1.38 2.85 0.90 2.86 0.58 2.82 0.40 2.50 0.20 2.13 0.14 2.04 0.20 2.01 0.30

1.07·10–4 2.56·10–4 3.98·10–3 5.63·10–3 6.52·10–3 1.06·10–2 1.48·10–2 3.72·10–2 0.704 1.53 1.65 0.231 7.75·10–2 0.343 0.175 0.298 0.397 6.7·10–2 1.59·10–2 8.62·10–3 7.96·10–3

R 0.034 0.032 0.028 0.026 0.024 0.021

0.30 0.66 0.35 0.18 0.079 0.089 0.071 0.036 0.882 0.23 0.14 0.11 0.11 0.10

0.092 0.090 0.10 0.12 0.15 0.15 0.13 0.12 0.12 0.11 0.11 0.11 0.10 0.10 0.092 0.087 0.082 0.074 0.067 0.053

0.024 0.27 0.27 0.25 0.24 0.19 0.13 0.12 0.12

Optical Properties of Selected Inorganic and Organic Solids E/eV 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10.5 10 9.5 9 8 7 6 5 4.75 4.5 4 3.5 3 2.5 2 1.5 1

209.5 206 203 200 26.0 25.0 22.0 20.0 18.0 16.1 14.0 12.0 10.0 8.00 6.00 5.00 2.952 2.480 2.214 2.000 1.771 1.675 1.550 1.240 1.033 0.6888 0.4959

ν /cm–1

λ/µ µm

96790 88720 84690 80650 76620 72590 64520 56460 48390 40330 38310 36290 32260 28230 24200 20160 16130 12100 8065

0.05166 0.05391 0.05636 0.05904 0.06199 0.06526 0.06888 0.07293 0.07749 0.08266 0.08856 0.09537 0.1033 0.1127 0.1181 0.1240 0.1305 0.1378 0.1550 0.1771 0.2066 0.2480 0.2610 0.2755 0.3100 0.3542 0.4133 0.4959 0.6199 0.8266 1.240

48390 40330 23810 20000 17860 16130 14290 13510 12500 10000 8333 5556 4000

5.918·10–3 6.019·10–3 6.107·10–3 6.199·10–3 0.04769 0.04959 0.05636 0.06199 0.06888 0.07700 0.08856 0.1033 0.1240 0.1550 0.2066 0.2480 0.42 0.50 0.56 0.62 0.70 0.74 0.80 1.00 1.2 1.8 2.5

n na nc k ka Noncrystalline Silicon Nitride (Si3N4) - [Ref. 16] 0.655 0.420 0.625 0.481 0.611 0.560 0.617 0.647 0.635 0.743 0.676 0.841 0.735 0.936 0.810 1.03 0.902 1.11 1.001 1.18 1.111 1.26 1.247 1.35 1.417 1.43 1.657 1.52 1.827 1.53 2.000 1.49 2.162 1.44 2.326 1.32 2.651 0.962 2.752 0.493 2.541 0.102 2.278 4.9·10–3 2.234 1.2·10–3 2.198 2.2·10–4 2.141 2.099 2.066 2.041 2.022 2.008 1.998 Sodium Chloride (NaCl) - [Ref. 17] 2.54·10–3 2.62·10–3 2.08·10–3 1.92·10–3 0.83 0.15 0.83 0.18 0.83 0.31 0.88 0.34 0.89 0.33 0.74 0.45 0.98 0.89 1.22 0.79 1.55 0.71 1.38 1.10 1.75 1.65 1.56324 1.55157 1.54613 1.54228 1.53865 1.53728 1.53560 1.53200 1.53000 1.52712 1.52531

12-155 kc

R 0.28 0.22 0.16 0.19 0.21 0.23 0.26 0.25 0.26 0.26 0.26 0.27 0.28 0.29 0.29 0.29 0.28 0.27 0.26 0.23 0.19 0.15 0.15 0.14 0.13 0.13 0.12 0.12 0.11 0.11 0.11

0.015 0.018 0.057 0.036 0.033 0.084 0.17 0.12 0.12 0.20 0.074 0.060 0.048 0.047 0.046 0.045 0.045 0.045 0.045 0.044 0.044 0.043 0.043

12-156

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.4000 0.3263

ν /cm–1 3226 2632

λ/µ µm 3.1 3.8

n 1.52395 1.52226

0.2952 0.2755 0.2480 0.1240 0.1033 0.08856 0.07749 0.06888 0.06199 0.04959 0.04215 0.03720 0.03410 0.03286 0.03224 0.02480 0.02108 0.01984 0.01922 0.01860 0.01736 0.01612 0.01488 0.01240 0.009919 0.07439 0.04959 0.002480 0.001240 0.001033 0.0006888 0.0006199 0.0004959 0.0004797 0.0003875 0.0001464 0.00004053

2381 2222 2000 1000 833.3 714.3 625.0 555.5 500.0 400 340 300 275 265 260 200 170 160 155 150 140 130 120 100 80 60 40 20 10 8.333 5.556 5.000 4.000 3.869 3.125 1.181 0.3269

4.2 4.5 5.0 10.0 12.0 14.0 16.0 18.0 20.0 25.0 29.41 33.33 36.36 37.74 38.46 50.00 58.82 62.50 64.52 66.67 71.43 76.92 83.33 100.0 125.0 166.7 250.00 500.0 1000 1200 1800 2000 2500 2584 3200 8469 30590

1.52121 1.52036 1.51883 1.49473 1.48000 1.46188 1.4399 1.41364 1.3822 1.27 1.12 0.85 0.59 0.42 0.45 0.14 1.35 6.92 5.50 4.52 3.72 3.31 3.02 2.74 2.57 2.48 2.44 2.43 2.43

2000 1204 1016 901 798 707 597 377 201 100 61.99 41.33 31.00 24.80 17.71 13.78 12.40 9.919 8.266

6.199·10–4 1.030·10–3 1.220·10–3 1.376·10–3 1.554·10–3 1.754·10–3 2.077·10–3 9.50·10–3 6.168·10–3 1.240·10–2 2.000·10–2 3.000·10–2 4.000·10–2 5.000·10–2 7.000·10–2 9.000·10–2 0.1000 0.125 0.150

k (1.8±0.2) ·10–9

3.5·10–3 1.7·10–2 0.85 0.22 0.50 0.45 1.99 6.03 2.14 0.87 0.380 0.219 0.135 0.110 0.087 0.077 0.055 0.041 0.024 0.006 8.8·10–3 5.4·10–3

2.43 2.43 2.43 2.43

R 0.043 0.043 0.043 0.043 0.042 0.039 0.037 0.035 0.033 0.029 0.026 0.014 0.0032 0.18 0.084 0.26 0.22 0.89 0.87 0.59 0.49 0.41 0.33 0.29 0.25 0.22 0.19 0.18 0.18 0.17 0.17

0.17 4.4·10–3 2.1·10–3 3.3·10–3 5.8·10–4 2.5·10–4

Cubic Zinc Sulfide (ZnS) - [Ref. 18] 0.999904 1.76·10–5 0.999777 1.00·10–4 0.999838 3.61·10–5 0.999647 5.42·10–5 0.999520 8.28·10–5 0.999372 1.25·10–4 0.999160 2.19·10–4 0.99789 9.50·10–4 0.99553 4.82·10–3 0.99061 1.17·10–2 0.964 3.32·10–2 0.941 5.10·10–2 0.847 9.95·10–2 0.796 0.171 0.747 0.431 0.758 0.824 0.862 0.876 1.02 1.36 1.41 1.47

0.17 0.17

6.2·10–4

2.2·10–2 7.7·10–2 0.20 0.19 0.31 0.29

Optical Properties of Selected Inorganic and Organic Solids E/eV 6.199 6.00 4.00 3.00 2.50 2.30 2.00 1.75 1.55 1.40 1.240 1.00 0.80 0.6199 0.45 0.30 0.20 0.1550 0.1240 0.100 0.09 0.07999 0.07 0.06075 0.05 0.03546 0.03472 0.02480 0.01240 0.004955 0.004339 0.003720 0.003100 0.002480 0.001860

ν /cm–1 48390 32260 24200 20160 18550 16130 14110 12500 11290 10000 8065 6452 5000 3629 2420 1613 1250 1000 806.5 725.9 645.2 564.6 490 403.3 286 280 200 100 40 35 30 25 20 15

λ/µ µm 0.200 0.2066 0.3100 0.4133 0.4959 0.5391 0.6199 0.7085 0.7999 0.8856 1.000 1.240 1.550 2.000 2.755 4.133 6.199 8.0 10.00 12.4 13.78 15.5 17.71 20.41 24.80 34.97 35.71 50.00 100.0 250.0 285.7 333.3 400.0 500.0 666.7

4.960 4.769 4.593 4.426 4.276 4.133 4.000 3.875 3.758 3.647 3.543 3.444 3.351 2.255 2.067 1.378 1.305 1.078 1.033 0.9920 0.9538 0.9185 0.8857 0.8552

40000 38462 37037 35714 34483 33333 32258 31250 30303 29412 28571 27778 27027 18182 16667 11111 10526 8696 8333 8000 7692 7407 7143 6897

0.250 0.260 0.270 0.280 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.550 0.600 0.900 0.950 1.150 1.200 1.250 1.300 1.350 1.400 1.450

n 2.32 2.24 2.70 2.54 2.42 2.3950 2.3576 2.3319 2.3146 2.3033 2.2907 2.2795 2.2706 2.2631 2.2587 2.2529 2.2443 2.2213 2.1986 2.1969 2.1793 2.1518 2.1040 2.03 1.6866 3.29 9.54 3.48 3.06 2.903 2.899 2.896 2.894 2.892 2.890

12-157 k 1.62 1.65 0.44 4·10–2 3·10–2

3.50·10–6 3.02·10–6

6.2·10–6

4.5·10–6 8.8·10–6

3.82·10–3 8.0·10–3 8.3·10–2 5.2·10–2 3.1·10–2 5.8·10–3 6.2·10–3 7.0·10–3

R 0.32 0.59 0.22 0.19 0.17 0.17 0.16 0.16 0.16 0.16 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.14 0.14 0.14 0.14 0.14 0.13 0.12 0.065 0.28 0.66 0.31 0.26 0.24 0.24 0.24 0.24 0.24 0.24

Polytetrafluoroethylene (Teflon) - [Ref. 19] 0.970 0.972 0.975 0.978 0.980 0.983 0.986 0.988 0.990 0.991 0.992 0.992 0.993 0.993 0.992 0.992 0.991 0.991 0.990 0.990 0.989 0.988 0.988 0.989

12-158

Optical Properties of Selected Inorganic and Organic Solids E/eV 0.8267 0.8000 0.7750 0.7515 0.7294 0.7086 0.6889 0.6703 0.6526 0.6359 0.6200 0.6049 0.5905 0.5767 0.5636 0.5511 0.5487 0.5439 0.5415 0.5368 0.5345 0.5322 0.5299 0.5277 0.5232 0.5188 0.5167 0.5061 0.4960

ν /cm–1 6667 6452 6250 6061 5882 5714 5556 5405 5263 51282 5000 4878 4762 4651 4545 44444 44247 4386 4367 4329 4310 4292 4274 4255 4219 4184 4167 4082 4000

λ/µ µm 1.500 1.550 1.600 1.650 1.700 1.750 1.800 1.850 1.900 1.950 2.000 2.050 2.100 2.150 2.200 2.250 2.260 2.280 2.290 2.310 2.320 2.330 2.340 2.350 2.370 2.390 2.400 2.450 2.500

References 1. Arsenic Selenide D. J. Treacy in Handbook of Optical Constants of Solids, E. D. Palik, Editor, Academic Press, 1985, p. 623. (Hereafter abbreviated as HOCS.) R. Zallen, R. E. Drews, R. L. Emerald, and M. L. Slade, Phys. Rev. Lett. 26, 1564 (1971) R. Zallen, M. L. Slade, and A. T. Ward, Phys. Rev. B 3, 4257 (1971). U. Strom and P. C. Taylor, Phys. Rev. B 16, 5512 (1977). G. Lucovsky, Phys. Rev. B 6, 1480 (1972). C. T. Moynihan, P. B. Macedo, M. S. Maklad, R. K. Mohr, and R. E. Howard, J. Non-Cryst. Solids, 17, 369 (1975). Y. Ohmachi, J. Opt. Soc. Am. 63, 630 (1973). 2. Arsenic Sulfide D. J. Treacy in HOCS, 1985, p. 641. P. A. Young, J. Phys. C 4, 93 (1971). W. S. Rodny, I. H. Malitson, and T. A. King, J. Opt. Soc. Am. 48, 633 (1958). R. Zallen, R.E. Drew, R. L. Emerald, and M.L. Slade, Phys. Rev. Lett. 26, 1564 (1971). M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, Solid State Commun. 15, 855 (1974). P. B. Klein, P. C. Taylor, and D. J. Treacy, Phys. Rev. B16, 4511 (1977). G. Lucovsky, Phys. Rev. B 6, 1480 (1972). 3. Cadmium Telluride E. D. Palik in HOCS, 1985, p. 409. D. T. F. Marple and H. Ehrenreich, Phys. Lett. 8, 87 (1962). T. H. Myers, S. W. Edwards, and J. F. Schetzina, J. Appl. Phys. 52, 4231 (1981). D. T. F. Marple, Phys. Rev. 150, 728 (1966). A. N. Pikhtin and A. D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978). L. S. Ladd, Infrared Phys. 6, 145 (1966). J. E. Harvey and W. L. Wolfe, J. Opt. Soc. Am. 65, 1267 (1975).

R 0.989 0.988 0.988 0.987 0.986 0.986 0.985 0.980 0.978 0.978 0.970 0.959 0.951 0.946 0.966 0.965 0.964 0.963 0.961 0.959 0.957 0.956 0.954 0.951 0.950 0.949 0.947 0.946 0.945

A. Manabe, A. Mitsuishi, and H. Yoshinaga, Jpn. J. Appl. Phys. 6, 593 (1967). A. Manabe, A. Mitsuishi, H. Oshinaga, Y. Ueda, and H. Sei, Technol. Rep. Osaka Univ. Jpn. 17, 263 (1967). J. R. Birch and D. K. Murrey, Infrared Phys. 18, 283 (1978). 4. Gallium Arsenide E. D. Palik in HOCS, 1985, p. 429. M. Cardona, W. Gudat, B. Sonntag, and P. Y. Yu, in Proc. Intl. Conf. Phys. Semicond., 10th. Cambridge, 1970, p. 208. US Atom. Energy Commission, Oak Ridge, TN, 1970. H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963). J. B. Theeten, D. E. Aspnes, and R. P. H. Chang, J. Appl. Phys. 49, 6097 (1978). H. C. Casey, D. D. Sell, and K. W. Wecht, J. Appl. Phys. 46, 250 (1975). A. H. Kachare, W. G. Spitzer, F. K. Euler, and A. Kahan, J. Appl. Phys. 45, 2938 (1974). R. T. Holm, J. W. Gibson, and E. D. Palik, J. Appl. Phys. 48, 212 (1977). W. Cochran, S. J. Fray, F. A. Johnson, J. E. Quarrington, and N. Williams, J. Appl. Phys. Suppl. 32, 2102 (1961). C. P. Christensen, R. Joiner, S. K. T. Nieh, and W. H. Steier, J. Appl. Phys. 45, 4957 (1974). R. H. Stolen, Phys. Rev. B 11, 767 (1975); Appl. Phys. Lett. 15, 74 (1969). 5. Gallium Phosphide A. Borghesi and G. Guizzetti in HOCS, 1985, p. 445. M. Cardona, W. Gudat, B. Sonntag, and P. Y. Yu, Proc. Intl. Conf. Phys. Semicond. Cambridge, 1970, p. 208. US Atom. Energy Commission, Oak Ridge, TN, 1970. M. Cardona, W. Gudat, E. E. Koch, M. Skibowski, B. Sonntag, and P. Yu. Phys. Rev. Lett. 25, 659 (1970). S. E. Stokowski and D. D. Sell, Phys. Rev. B 5, 1636 (1972). S. A. Abagyan, G. A. Ivanov, Y. E. Shanurin, and V. I. Amosov, Sov. Phys. Semicond. 5, 889 (1971). P. G. Dean, G. Kaminsky, and R. B. Zetterstorm, J. Appl. Phys. 38, 3551 (1967).

Optical Properties of Selected Inorganic and Organic Solids D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983). 6. Indium Antimonide R. T. Holm in HOCS, 1985, p. 491. M. Cardona, W. Gudat, B. Sonntag, and P. Y. Yu, Proc. Int. Conf. Phys. Semicond., 10th. Cambridge, 1970, p. 208. US Atom. Comm., Oak Ridge, TN, 1970. H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963). D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983). T. S. Moss, S. D. Smith, and T. D. F. Hawkins, Proc. Phys. Soc. London 70B, 776 (1957). H. Yoshinaga and R. A. Oetjen, Phys. Rev. 101, 526 (1956). R. B. Sanderson, J. Phys. Chem. Solids 26, 803 (1965). 7. Indium Arsenide E. D. Palick and R. T. Holm in HOCS, 1985, p. 479. H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963). B. O. Seraphin and H. E. Bennett in Semiconductors and Semimetals (R. K. Willardson and A. C. Beer, Eds.), vol. 3, Academic, 1967, p. 499. D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983). J. R. Dixon and J. M. Ellis, Phys. Rev. 123, 1560 (1961). A. Memon, T. J. Parker, and J. R. Birch, Proc. SPIE, 289, 20 (1981). 8. Indium Phosphide O. J. Glembocki and H. Piller in HOCS, 1985, p. 503. M. Cardona, J. Appl. Phys. 32, 958 (1961); 36, 2181 (1965). D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983). G. D. Pettit and W. J. Turner, J. Appl. Phys. 36, 2081 (1965). R. Newman, Phys. Rev. 111, 1518 (1958). W. N. Reynolds, M. T. Lilburne, and R. M. Dell, Proc. Phys. Soc. London 71, 416 (1958). H. Jamshidi and T. J. Parker, Int. Meet. Infrared Mm. Waves, 7th., Marseilles, 1983. 9. Lead Selenide G. Bauer and H. Krenn in HOCS, 1985, p. 517. M. Cardona and D. L. Greenaway, Phys. Rev. A 133, 1685 (1964). T. S. Moss, Optical Properties of Semiconductors, Butterworth, 1959, p. 189. J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. A 140, 330 (1965). W. W. Scanlon, J. Phys. Chem. Solids, 8, 423 (1959). K. V. Vyatkin and A. P. Shotov, Sov. Phys. Semicond. 14, 785 (1980); Fiz. Tekh. Poluprovodn. 14, 1331 (1980). 10. Lead Sulfide G. Guizzetti and A. Borghesi in HOCS, 1985, p. 525. M. Cardona and R. Haensel, Phys. Rev. B 1, 2605 (1970). M. Cardona and D. L. Greenaway, Phys. Rev. A 133, 1685 (1964). M. Cardona, C. M. Penchina, E. E. Koch, and P. Y. Yu, Phys. Status Solidi B 53, 327 (1972). P. R. Wessel, Phys. Rev. 153, 836 (1967). C. E. Rossi and W. Paul, J. Appl. Phys. 38, 1803 (1967). J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. A 140, 330 (1965). 11. Lead Telluride G. Bauer and H. Krenn in HOCS, 1985, p. 535. M. Cardona and R. Haensel, Phys. Rev. B 1, 2605 (1970). M. Cardona and D. L. Greenaway, Phys. Rev. 133, A1685 (1964). D. M. Korn and R. Braunstein, Phys. Rev. B 5, 4837 (1972). W. W. Scanlon, J. Phys. Chem. Solids 8, 423 (1959). J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965). 12. Lithium Fluoride E. D. Palik and W. R. Hunter in HOCS, 1985, p. 675. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, and B. K. Fujikawa, Low Energy X-ray Diagnostics-1981 (D. T. Attwood and B. L. Henke, Eds.), AIP Conf. Proc. No. 75, 1981. A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Y. F. Shepelev, Opt. Spektrosk. 16, 168 (1964); 16, 310 (1964). F. C. Brown, C. Gahwiller, A. B. Kunz, and N. O. Lipari, Phys. Rev. Lett. 25, 927 (1970). A. Milgram and M. P. Givens, Phys. Rev. 125, 1506 (1962). T. Tomiki and T. Miyata, J. Phys. Soc. Jpn. 27, 658 (1969).

13.

14.

15.

16.

17.

18.

19.

12-159 A. Kachare, G. Andermann, and L. R. Brantley, J. Phys. Chem. Solids 33, 467 (1972). Potassium Chloride E. D. Palik in HOCS, 1985, p. 703. O. Aita, I. Nagakura, and T. Sagawa, J. Phys. Soc. Jpn. 30, 1414 (1971). A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Y. F. Shepelev, Opt. Spectrosc. 16, 168 (1964); Opt. Spektrosk. 16, 310 (1964). T. Tomika, J. Phys. Soc. Jpn. 22, 463 (1967). M. Antinori, A. Balzarotti, and M. Piacentini, Phys. Rev. B 7, 1541 (1973). H. H. Li, J. Phys. Chem. Ref. Data 5, 329 (1976). S. D. Allen and J. A. Harrington, Appl. Opt. 17, 1679 (1978). K. W. Johnson and E. E. Bell, Phys. Rev. 139A, 1295 (1965). Silicon Dioxide H. R. Philipp in HOCS, 1985, p. 749. J. Rife and J. Osantowski, J. Opt. Soc. Am. 70, 1513 (1980). B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, and B. K. Fujikawa, Low Energy X-ray Diagnostics-1981 (D. T. Attwood and B. L. Henke, Eds.), AIP Conf. Proc. No. 75, 1981. H. R. Philipp, Solid State Commun. 4, 73 (1966); J. Phys. Chem. Solids, 32, 1935 (1971). P. L. Lamy, Appl. Opt. 16, 2212 (1977). H. R. Philipp, J. Appl. Phys. 50 1053 (1979). D. G. Drummond, Proc. Roy. Soc. London, 153, 328 (1935). Silicon Monoxide H. R. Philipp in HOCS, 1985, p. 765. H. R. Philipp, J. Phys. Chem. Solids, 32, 1935 (1971). G. Hass and C. D. Salzberg, J. Opt. Soc. Am. 44, 181 (1954). E. Cremer, T. Kraus, and E. Ritter, Zs. Electrochem. 62, 939 (1958). A. P. Bradford, G. Hass, M. McFarland, and E. Ritter, Appl. Opt. 4, 971 (1965). Silicon Nitride H. R. Philipp in HOCS, 1985, p. 771. H. R. Philipp, J. Electrochem. Soc. 120, 295 (1973). J. B. Theeten, D. E. Aspnes, F. Simondet, M. Errman, and P. C. MÃ¼rau, J. Appl. Phys. 52, 6788 (1981). J. Bauer, Phys. Status Solidi, A 39, 411 (1977). Sodium Chloride J. E. Eldridge and E. D. Palik in HOCS, p. 775. J. A. Harrington, C. J. Duthler, F. W. Patten, and M. Hass, Solid State Commun. 18, 1043 (1976). T. Miyata and T. Tomiki, J. Phys. Soc. Jpn. 24, 1286 (1968); ibid., 22, 209 (1967). D. M. Roessler and W. C. Walker, J. Opt. Soc. Am. 58, 279 (1968). D. M. Roessler and W. C. Walker, Phys. Rev. 166, 599 (1968). S. Allen and J. A. Harrington, Appl. Opt. 17, 1679 (1978). O. Aita, I. Nagakura, and T. Sagawa, J. Phys. Soc. Jpn. 30, 1414 (1971). Zinc Sulfide E. D. Palik and A. Addamiano in HOCS, 1985, p. 597. B. L. Henke, P. L. Lee, T. J. Tanaka, R. L. Shimabukuro, and B. F. Fujikawa, Low Energy X-ray Diagnostics-1981 (D. T. Attwood and B. L. Henke, Eds.), AIP Conf. Proc. No. 75, 1981. M. Cardona and G. Harbeke, Phys. Rev. 137, A1467 (1965). Eastman Kodak, Publ. No. U-72, Rochester, New York (1981). C. A. Klein and R. N. Donadio, J. Appl. Phys. 51, 797 (1980). T. Deutsch, Proc. Int. Conf. Phys. Semicond., 6th Exeter 1962, p. 505. The Inst. of Physics and the Physical Soc., London, 1962. A. Manabe, A. Mitsuishi, and H. Yoshinaga, Jpn. J. Appl. Phys. 6, 593 (1967). W. W. Piper, D. T. F. Marple, and P. D. Johnson, Phys. Rev. 110, 323 (1958). Polytetrafluoroethylene J. W. L. Thomas (NIST), Private communication. NIST Certificate, STM 2044. P. Y. Barnes, E. A. Early, and A. C. Parr, NIST Special Publ. 250-48, NIST Measurement Services: Spectral Reflectance. Diffuse Reflectance Coatings and Materials Sections, Labsphere Catalog, 1996. A. Arecchi and C. Ryder (Labsphere, North Sutten, NJ), private communication.

FERMI ENERGY AND RELATED PROPERTIES OF METALS Lev. I. Berger In the classical Drude theory of metals, the Maxwell-Boltzmann velocity distribution of electrons is used. It states that the number of electrons per unit volume with velocities in the   range of d v about any magnitude v at temperature T is

EF =

where kF is the Fermi momentum or the Fermi wave vector

Ê m ˆ Ê mv 2 ˆ    f B (v )dv = nÁ ˜ expÁ ˜ dv Ë 2 pk B T ¯ Ë 2kB T ¯

kF = (3p2n)1/3

where n is the total number of conduction electrons in a unit volume of a metal, m is the free electron mass, and kB is the Boltzmann constant. In an attempt to explain a substantial discrepancy between the experimental data on the specific heat of metals and the values calculated on the basis of the Drude model, Sommerfeld suggested a model of the metal in which the Pauli exclusion principle is applied to free electrons. In this case, the Maxwell-Boltzmann distribution is replaced by the Fermi-Dirac distribution: 3   ˘ ¸Ô ˆ Ê m ˆ  ÔÏ ÈÊ mv 2 f (v )dv = 2 dv Ìexp ÍÁ - k B T0 ˜ k B T ˙ + 1˝ Ë h¯ ¯ ÔÓ ÎË 2 ˚ Ô˛

-1

e is the electron charge, and rB is the Bohr radius rB = 2/me2 = 0.529 ◊ 10–10 m

Another, more common expression for the Fermi energy is EF = 1 2 mv F2

where vF = kF/m is the Fermi velocity which can be expressed using the concept of the electron radius, rs. It is equal to radius of a sphere occupied by one free electron. If the total volume of a metal sample is V and the number of conduction electrons in this volume is N, then the volume per electron is equal to V 1 4 3 = = prS N n 3

Here h is the Planck constant and T0 is a characteristic temperature which is determined by the normalization condition n=



 2 k F2 Ê e 2 ˆ 2 =Á ˜ (k F rB ) 2m Ë 2kB ¯

and



Ú dv ◊ f ( v )

The magnitude of T0 is quite high; usually, T0 > 104 K. So, at common temperatures (T < 103 K), the free electron density of a metal is much smaller than in the case of the Maxwell-Boltzmann distribution. This allows us to explain why the experimental data on specific heat for metals are close to those for insulators. The maximum kinetic energy the electrons of a metal may possess at T = 0 K is called the Fermi energy, e.g.,

rS =

Ê 3 ˆ Ë 4 pn ¯

1/ 3

The following table contains information pertinent to the Sommerfeld model for some metals. The magnitudes of T0 are calculated using the expression T0 =

EF 58.2 ◊ 10 4 = K kB (rS / rB ) 2

Ground State Properties of the Electron Gas in Some Metals Metal Lia Nab Kb Rbb Csb Cu Ag Au Be Mg Ca Sr Ba Nb Fe Mnc Zn Cd

12-209

Valency 1 1 1 1 1 1 1 1 2 2 2 2 2 1 2 2 2 2

n/1028 m–3 4.70 2.65 1.40 1.15 0.91 8.47 5.86 5.90 24.7 8.61 4.61 3.55 3.15 5.56 17.0 16.5 13.2 9.27

rS/pm 172 208 257 275 298 141 160 159 99 141 173 189 196 163 112 113 122 137

rS/rB 3.25 3.93 4.86 5.20 5.62 2.67 3.02 3.01 1.87 2.66 3.27 3.57 3.71 3.07 2.12 2.14 2.30 2.59

EF/eV 4.74 3.24 2.12 1.85 1.59 7.00 5.49 5.53 14.3 7.08 4.69 3.93 3.64 5.32 11.1 10.9 9.47 7.47

T0/104 K 5.51 3.77 2.46 2.15 1.84 8.16 6.38 6.42 16.6 8.23 5.44 4.57 4.23 6.18 13.0 12.7 11.0 8.68

kF/1010 m–1 1.12 0.92 0.75 0.70 0.65 1.36 1.20 1.21 1.94 1.36 1.11 1.02 0.98 1.18 1.71 1.70 1.58 1.40

vF/106 m s-1 1.29 1.07 0.86 0.81 0.75 1.57 1.39 1.40 2.25 1.58 1.28 1.18 1.13 1.37 1.98 1.96 1.83 1.62

Fermi Energy and Related Properties of Metals

12-210

Ground State Properties of the Electron Gas in Some Metals Metal Hga Al Ga In Tl Sn Pb Bi Sb

Valency 2 3 3 3 3 4 4 5 5

n/1028 mâ&#x20AC;&#x201C;3 8.65 18.1 15.4 11.5 10.5 14.8 13.2 14.1 16.5

rS/pm 140 110 116 127 131 117 122 119 113

rS/rB 2.65 2.07 2.19 2.41 2.48 2.22 2.30 2.25 2.14

EF/eV 7.13 11.7 10.4 8.63 8.15 10.2 9.47 9.90 10.9

T0/104 K 8.29 13.6 12.1 10.0 9.46 11.8 11.0 11.5 12.7

kF/1010 mâ&#x20AC;&#x201C;1 1.37 1.75 1.66 1.51 1.46 1.64 1.58 1.61 1.70

vF/106 m s-1 1.58 2.03 1.92 1.74 1.69 1.90 1.83 1.87 1.96

At 78 K. At 5 K. a-phase. The data in the table are for atmospheric pressure and room temperature unless otherwise noted. b c

References 1. Drude, P., Ann. Physik, 1, 566, 1900; ibid., 3, 369, 1900. 2. Sommerfeld, A. and Bethe, H., Handbuch der Physik, Chapter 3, Springer, 1933.

3. Wyckoff, R. W. G., Crystal Structures, 2nd. ed., Interscience, 1963. 4. Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Holt, Rinehart and Winston, 1976.

ELECTRON INELASTIC MEAN FREE PATHS Cedric J. Powell The inelastic mean free path (IMFP) of electrons is defined as the average of distances, measured along the trajectories, that electrons with a given energy travel between inelastic collisions in the substance. It is an important parameter in analyzing results from surface-characterization techniques such as Auger electron spectroscopy, x-ray photoelectron spectroscopy, low-energy electron diffraction, and others. IMFPs can be measured by the elastic-peak electron spectroscopy technique and other methods, and they can be calculated from optical data. A detailed analysis of the experimental and theoretical considerations in obtaining reliable IMPF values can be found in reference 4. The table below gives recommended IMFP values for several elements, simple inorganic compounds, and organic materials. Values are given in Ångström units (1 Å = 10-10 m) for a range of

electron energies. Substances are given in alphabetical order by name, with elements and inorganic compounds listed before the organic materials.

References 1. Tanuma, S., Powell, C. J., and Penn, D. R., Surf. Interface Anal. 17, 911, 1991. 2. Tanuma, S., Powell, C. J., and Penn, D. R., Surf. Interface Anal. 17, 927, 1991. 3. Tanuma, S., Powell, C. J., and Penn, D. R., Surf. Interface Anal. 21, 165, 1994. 4. Powell, C. J., and Jablonski, A., J. Phys. Chem. Ref. Data 28, 19, 1999. 5. Tanuma, S., Powell, C. J., and Penn, D. R., Surf. Interface Anal., 37, 1, 2005.

Electron Inelastic Mean Free Path in Å Electron Energy in eV Substance Aluminum Bismuth Carbon Chromium Copper Gallium phosphide Gold Hafnium Indium phosphide Iridium Iron Lead(II) sulfide Lead(II) telluride Magnesium Molybdenum Nickel Niobium Osmium Palladium Platinum Potassium chloride Rhenium Rhodium Ruthenium Silicon Silicon carbide Silicon dioxide (vitreous) Silver Tantalum Titanium Tungsten Vanadium Yttrium Zinc sulfide Zirconium Adenine Bovine plasma albumin β-Carotene

Formula Al Bi C Cr Cu GaP Au Hf InP Ir Fe PbS PbTe Mg Mo Ni Nb Os Pd Pt KCl Re Rh Ru Si SiC SiO2 Ag Ta Ti W V Y ZnS Zr C5H5N5 C40H56

50 3.5 4.9 5.9 4.4 5.2 5.6 6.3 5.8 4.8 5.3 4.3 4.8 4.3 4.0 5.1 4.9 6.0 5.5 4.8 5.0 7.5 5.2 4.8 4.9 4.1 4.7 8.0 6.4 4.8 4.5 5.0 4.2 5.0 5.8 4.4 6.4 7.3 6.4

100 4.6 5.5 6.4 4.3 5.0 6.5 4.7 6.2 4.9 4.3 4.4 5.6 5.5 5.4 4.5 4.5 6.0 4.3 4.8 4.2 7.8 3.8 4.1 4.2 5.3 4.9 7.7 4.7 4.5 5.1 4.1 4.9 5.5 6.5 4.8 6.6 7.2 7.0

150 5.7 6.3 7.5 5.0 5.4 7.8 4.7 7.1 5.6 4.7 5.1 6.7 6.6 6.8 5.0 4.9 6.7 4.5 5.4 4.5 9.3 3.9 4.5 4.6 6.5 5.8 8.8 4.8 5.0 6.2 4.5 5.9 6.4 7.7 5.7 7.8 8.5 8.5

200 6.8 7.2 8.8 5.7 6.0 9.0 5.1 8.0 6.4 5.2 5.8 7.8 7.7 8.2 5.6 5.4 7.7 5.0 6.2 4.9 10.9 4.3 5.0 5.2 7.8 6.8 10.0 5.2 5.5 7.3 5.0 6.8 7.5 8.9 6.6 9.2 9.9 10.0

300 8.9 8.8 11.2 7.2 7.3 11.4 6.1 10.2 8.1 6.4 7.2 10.0 9.8 10.7 7.1 6.5 9.7 6.0 7.8 6.0 14.2 5.1 6.1 6.5 10.3 8.7 12.6 6.4 6.8 9.5 6.1 8.8 9.8 11.3 8.6 11.8 12.7 13.0

400 10.9 10.6 13.7 8.6 8.6 13.7 7.2 12.0 9.7 7.5 8.5 12.1 11.9 13.0 8.5 7.7 11.7 7.1 9.4 7.1 17.3 6.0 7.3 7.8 12.5 10.5 15.2 7.7 8.0 11.6 7.3 10.7 11.9 13.6 10.5 14.4 15.4 15.9

600 14.5 14.0 18.4 11.4 11.3 18.1 9.5 15.6 12.8 9.7 11.2 16.1 15.8 17.5 11.3 10.1 15.6 9.1 12.5 9.2 23.2 7.7 9.7 10.4 16.6 13.9 20.0 10.2 10.4 15.6 9.4 14.3 16.0 17.9 14.1 19.2 20.7 21.4

800 1000 1200 1400 1600 1800 2000 18.0 21.3 24.6 27.8 31.0 34.1 37.2 17.2 20.2 23.2 26.1 28.9 31.6 34.4 22.8 27.0 31.1 35.2 39.1 43.0 46.8 14.0 16.6 19.1 21.6 24.0 26.3 28.6 13.9 16.5 18.9 21.3 23.7 26.0 28.3 22.3 26.3 30.2 34.1 37.8 41.5 45.2 11.7 13.8 15.8 17.8 19.7 21.6 23.4 19.0 22.2 25.3 28.4 31.4 34.4 37.3 15.7 18.7 21.4 24.2 26.8 29.4 32.0 11.8 13.8 15.7 17.6 19.4 21.2 22.9 13.7 16.2 18.6 20.9 23.2 25.5 27.7 19.8 23.6 27.1 30.6 33.9 37.2 40.5 19.6 23.4 26.9 30.3 33.7 37.0 40.2 21.7 25.9 29.9 33.9 37.7 41.6 45.3 14.0 16.5 18.9 21.2 23.5 25.8 28.0 12.4 14.6 16.7 18.8 20.8 22.8 24.7 19.2 22.6 25.9 29.1 32.3 35.3 38.4 11.1 12.9 14.7 16.4 18.1 19.8 21.5 15.4 18.2 20.9 23.5 26.0 28.4 30.9 11.2 13.1 14.9 16.7 18.5 20.2 21.9 28.7 34.0 39.2 44.2 49.1 54.0 58.8 9.4 10.9 12.5 14.0 15.4 16.9 18.3 12.0 14.1 16.2 18.2 20.1 22.0 23.9 12.8 15.1 17.4 19.5 21.6 23.7 25.7 20.6 24.4 28.2 31.8 35.4 39.0 42.5 17.1 20.3 23.3 26.3 29.2 32.1 35.0 24.7 29.3 33.7 38.0 42.2 46.4 50.5 12.6 14.9 17.2 19.3 21.4 23.5 25.5 12.7 14.8 16.9 19.0 21.0 22.9 24.9 19.5 23.2 26.8 30.2 33.6 36.9 40.2 11.4 13.4 15.2 17.1 18.9 20.6 22.4 17.7 21.0 24.3 27.4 30.5 33.5 36.4 19.8 23.4 27.0 30.4 33.8 37.1 40.4 22.0 26.0 29.8 33.6 37.3 40.9 44.5 17.5 20.7 23.8 26.9 29.9 32.8 35.7 24.1 28.6 33.1 37.4 41.6 45.8 49.9 25.8 30.8 35.6 40.2 44.8 49.4 53.8 26.9 32.0 37.0 41.9 46.6 51.3 56.0

Ref. 5 1 1 1 4 2 4 1 2 1 1 2 2 1 1 4 1 1 1 1 2 1 1 1 1 2 2 4 1 1 1 1 1 2 1 3 3 3

12-112

Section 12.indb 112

4/28/05 1:57:55 PM

Electron Inelastic Mean Free Paths Substance Deoxyribonucleic acid (DNA) 1,6-Diphenyl-1,3,5hexatriene Guanine Hexacosane Kapton Polyacetylene Poly(butene-1-sulfone) Polyethylene Poly(methyl methacrylate) Polystyrene Poly(2-vinylpyridine)

Section 12.indb 113

Formula

C18H16 C5H5N5O C26H54

12-113 100

150

200

300

400

600

800

1000 1200 1400 1600 1800 2000

Ref.

7.3

8.5

9.8

12.6

15.4

20.7

25.9

30.8

35.6

40.3

44.9

49.4

53.8

6.4 6.2 7.0 7.0 5.3 7.1 6.9 7.8 6.9 6.9

7.0 6.2 7.6 6.8 5.7 7.2 7.2 7.9 7.3 7.3

8.4 7.2 9.2 7.9 6.8 8.5 8.6 9.3 8.7 8.7

9.9 8.4 10.9 9.2 7.9 9.9 10.1 10.8 10.2 10.3

12.9 10.8 14.1 11.7 10.2 12.7 13.0 13.9 13.2 13.3

15.8 13.1 17.2 14.2 12.5 15.4 15.9 16.9 16.1 16.2

21.3 17.5 23.2 19.0 16.9 20.7 21.4 22.7 21.6 21.8

26.7 21.8 29.2 23.7 21.1 25.8 26.8 28.3 27.1 27.3

31.8 25.9 34.7 28.2 25.1 30.6 31.8 33.7 32.2 32.5

36.8 29.9 40.1 32.5 29.0 35.3 36.8 38.8 37.2 37.5

41.7 33.8 45.4 36.7 32.8 39.9 41.6 43.9 42.1 42.4

46.4 37.6 50.6 40.9 36.5 44.4 46.3 48.9 46.9 47.3

51.1 41.4 55.7 44.9 40.2 48.8 51.0 53.8 51.6 52.0

55.7 45.1 60.7 49.0 43.8 53.2 55.6 58.6 56.2 56.7

3 3 3 3 3 3 3 3 3 3

4/28/05 1:57:57 PM

SELECTED PROPERTIES OF SEMICONDUCTOR SOLID SOLUTIONS L.I. Berger Alloy system

SixGe1-x

Limits of solubility

Energy gap in eV (300 K)

Adamantine Semiconductors IV-IV 0.8941+0.0421x+0.1691x2 0≤x≤1 0.7596+1.0860x+0.3306x2

Remarks, references Transition Γ - X [Ref.1] Trans. Γ - L [Ref. 1]

Adamantine Semiconductors III-V/III-V Common Anion AlxGa1-xN AlxGa1-xP AlxIn1-xP AlxGa1-xAs AlxIn1-xAs AlxGa1-xSb AlxIn1-xSb GaxIn1-xN GaxIn1-xP GaxIn1-xAs GaxIn1-xSb Common Cation GaNxAs1-x GaPxAs1-x GaPxAs1-x GaAsxSb1-x InPxAs1-x

0≤x≤1 0≤x≤0.5 0≤x≤0.44 0≤x≤0.5 0≤x≤1 0≤x<≤1 0≤x≤1 0≤x≤1 0≤x≤1 0≤x≤1 0<x<1 0≤x≤0.05 0<x<1 0≤x≤0.05 0≤x≤0.45, 0.6≤x≤1 0<x<1

2.28+0.16x at Γ: 134+2.23x; at X: 2.24+0.18x 1.42=0.75x [Ref.3]; 1.424+1.429x-0.14x2 [Ref.4] at Γ: 0.37+1.91x+0.74x2; at X: 1.8+0.4x 0.73+1.10x+0.47x2

Wurtzite Structure [Ref. 2 & 3] [Ref. 2] [Ref. 2]

0.360+0.629x+0.436x2 0.235+0.1653x+0.413x2

[Ref. 2 and 6] Trans. Γ8v- Γ6c [Ref. 2] [Ref. 6] Wurtzite [Ref. 8 and 10] [Ref. 2] [Ref. 5] [Ref. 2, see also Ref. 9]

1.42-9.9x 2.270-0.846x 1.515+1.172x+0.186x2 1.9715+0.144x+0.211x2 1.43-1.9x+1.2x2 0.356+0.675x+0.32x2

[Ref. 2] [Ref. 2] (at 2K, Γ−Γ) [Ref. 7] [Ref. 2] [Ref. 5] [Ref. 2]

1.950+1.487x-1.000x(1-x)

Adamantine Binary Semiconductors II-VI/II-VI [Ref. 3 and 6] Common Anion ZnxCd1-xS ZnxHg1-xS CdxHg1-xS ZnxCd1-xSe ZnxHg1-xSe CdxHg1-xSe ZnxCd1-xTe ZnxHg1-xTe CdxHg1-xTe

0≤x≤1 0≤x≤1 0≤x≤1 0.7≤x≤1 0≤x≤1 0≤x≤0.7 and 0.75≤x*≤1 0≤x≤1 0≤x≤1 0≤x≤1

Common Cation ZnSxSe1-x ZnSxTe1-x ZnSexTe1-x CdSxSe1-x CdSxTe1-x CdSexTe1-x HgSxSe1-x HgSxTe1-x HgSexTe1-x

0≤x≤1 0≤x≤0.1 and 0.9≤x*≤1 0≤x≤1 0≤x≤1 0≤x≤0.25 and 0.8≤x*≤1 0≤x≤0.4 and 0.6≤x*≤1 0≤x≤1 0≤x≤1 0≤x≤1

(ZnS)x(AlP)1-x (ZnSe)x(GaAs)1-x (CdTe)x(InAs)1-x (CdTe)x(AlSb)1-x (HgTe)x(InAs)1-x

Wurtzite Structure Wurtzite Structure at x<0.6

x*- Wurtzite Structure

x*- Wurtzite Structure Wurtzite Structure x*- Wurtzite Structure x*- Wurtzite Structure

Quaternary Adamantine Semiconductors II-VI/III-V [Ref. 6] 0.99≤x≤1 0≤x<1 0<x≤0.2 and 0.7≤x≤1 0≤x≤1 0≤x≤1

12-90

Section 12.indb 90

4/28/05 1:57:14 PM

Selected Properties of Semiconductor Solid Solutions Alloy system

Limits of solubility

12-91 Energy gap in eV (300 K)

Remarks, references

GaxIn1-xAsyP1-y

Quaternary Adamantine Semiconductors IIIx-III1-x-Vy - V1-y 0≤x≤1, 0≤x≤1 1.35+0.668x-1.068y+0.758x2+0.078y20.069xy-0.322x2y+0.03xy2

[Ref. 2 and 6]

AlxGayIn1-x-ySb

Quaternary Adamantine Semiconductors III1-x-y-IIIx-IIIy-V 0≤x≤1, 0≤y≤1 0.095+1.76x+0.28y+0.345(x2+y2)+0.085( 1-x-y)2 +xy (1-x-y)(23-28y)

[Ref. 2 and 6]

References 1. Krishnamurti, S., Sher, A., and Chen, A. Appl. Phys. Lett. 47, 160, 1985. 2. Madelung, O., Ed., Semiconductors Group IV Elements and III-V Compounds, Springer, 1991; Semiconductors Other than Group IV Elements and III-V Compounds, Springer, 1992. 3. Goryunova, N. A., Kesamanly, F.P., and Nasledov, D.N., Semiconductors and Semimetals, Vol. 4, 1968, p. 413. 4. El Allali, M., Sorensen, C. B., Veje, E., and Tideman-Peterson, P., Phys. Rev. B, 48, 4398, 1993.

Section 12.indb 91

5. Nahorny, R. E., Pollack, M. A., Johnson, W. D., and Barns, R. L. Appl. Phys. Lett. 33, 695, 1978. 6. Goryunova, N. A. Multicomponent Diamond-Like Semiconductors, Sov. Radio, Moscow, 1968 (in Russian). 7. Capizzi, M., Modesti, S., Martelli, F., and Frova, A., Solid State Comm. 39, 333, 1981. 8. Nakamura, S., Pearton, S., and Fasol, G., The Blue Laser Diode, 2nd ed., Springer, 2000. 9. Roth, A. P., Keeler, W. J., and Fortin, E. Canad. J. Phys. 58, 560, 1980. 10. Wu, J., Walukiewicz, Yu, K. M., Ager, J. W., Haller, E. E., Lu, H., and Schaff, W.J., Appl. Phys. Lett. 80, 4741, 2002.

4/28/05 1:57:14 PM

PROPERTIES OF ORGANIC SEMICONDUCTORS L. I. Berger

Substance Metal-Free Molecular Crystals 3-Acetylamino-N-methylphthalimide 3-Acetylamino-N-phenylphthalimide 4-Amino-N-cyclomethylphthalimide 4-Aminophthalimide Acridine Anthanthrene Anthanthrene Anthanthrone Anthracene Anthracene Anthracene 1,2-Benzanthracene Benzanthrone Benzene (liquid) Benzene (amorphous) Benzene (cryst.) Benzimidazole Benzophenone Benzo[f]quinoline Benzo[h]quinoline 3-Benzoylamino-N-methylphthalimide Benzpentacene Biphenyl Biphenyl o-Chloranil p-Chloranil Chlorpromazine Chrysene Chrysene Circumanthracene Coronene Coronene Cyananthrone 1,6-Diaminopyrene Dibenzpentacene Dinaphthopyrene 1,8-Diphenyl-1,3,5,7-octatetraene Diphenylpentacene 4,4′-Diphenylstilbene 4,4′-Diphenylstilbene Ferrocene Flavanthrone Fluorene Fluorene Fluoridine Hexacene Hexacene Hexamethylbenzene 3-Hydroxy-N-methylphthalimide Imidazole

12-92

Energy Gap, E, (in E/2 kT) eV 3.46 3.50 2.90 2.78 3.90 1.67 0.84 1.70 0.83 2.50 3.88 to 4.1 1.04 3.12 0.41 0.84 7 3.0 to 4.0 3.34 2.77 2.72 3.28 1.72 1.46 1.45 3.0 0.61 2.1 1.1 2.20 1.8 1.7 0.85 0.20 0.6 1.50 1.60 1.7 1.60 1.56 0.80 1.22 0.70 2.7 1.4 1.6 0.57 1.3 1.86 3.80 2.6

Room Temperature Electrical Resistivity, ohm · cm

Mobility, μ, cm2/V · s

Sign of Majority Carriers

Temperature Range, ºC 67 to 100 54 to 124 73 to 100 123 to 151

1.5 · 1019 1.5 · 1019 (15ºC) 7.7 · 1018 1.3 ∙ 1014 (15ºC) 1.5 ∙ 1011 >1015 1016 (30ºC) 1.6 · 1016 1015 5 · 1013

40 to 105 20 to 150 2.3 1.74(n), 2.07(p)

+ +&–

–

–14 to 5 –23 84 to 144 –23 to 14 30 to 50 84 to 112 0 to 150

1.7 · 1015 (50ºC)

20 to 70

1015 1012 (32ºC) 4 · 1019 (15ºC) 4 · 1019 6 · 1012 1.7 · 1017 1.7 · 1017 (15ºC) 1.2 · 107 108

20 to 130

+&–

32 to 80 25 to 90 60 to 80 30 to 125 0 to 150 25 to 90 72 to 191 0 to 150 160 to 280

1014 1.4 · 1011

6 · 1013 3.8 · 1010 (50ºC)

20 to 140

20 to 140 60 to 91 28 to 68

1011

Ref. 1 1 1 1 1 1 2 1 2 1 4 2 1 2 1 4 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 2 2 1 2 1 1 1 1

Properties of Organic Semiconductors

Substance Indanthrazine Indanthrone Indanthrone (black) Mesitylene (liquid) Mesonaphthodianthracene Mesonaphthodianthrene Mesonaphthodianthrone 3-Methoxy-N-methyl-phthalimide Naphthacene Naphthalene Naphthalene Naphthalene m-Naphthodianthrene m-Naphthodianthrone β-Naphthol β-Naphthoquinoline 1-Naphthylamine 1-Naphthylamine picrate 2-Naphthylphenyl sulphone 1-Nitronaphthalene Ovalene Pentacene Pentacene Perylene Perylene Phenanthrene Phenanthrene 1,10-Phenanthroline Phenazine Phenazine Phenothiazine Phenothiazine Phenylanthranilic acid 4-Phenylstilbene 4-Phenylstilbene Phosphonitrilic chloride trimer Phthalocyanine, PcH2 Phthalocyanine, PcH2 Pyranthrene Pyranthrene Pyranthrone Pyrene Pyrene 5,6-N-Pyridine-1,9-benzanthrone p-Quaterphenyl Quaterrylene p-Quinquiphenyl α-Resorcin β-Resorcin Salanil p-Sexiphenyl cis-Stilbene trans-Stilbene trans-Stilbene trans-Stilbene o-Terphenyl m-Terphenyl p-Terphenyl p-Terphenyl

12-93 Energy Gap, E, (in E/2 kT) eV 0.66 0.64 0.56 0.19 0.6 1.48 0.86 3.18 1.7 3.5 1.15 4.9 to 5.1 1.20 1.30 2.36 2.77 2.2 2.7 3.5 2.5 1.13 0.58 1.5 2.1 3.10 1.15 0.65 2.73 2.1 1.1 1.6 3.30 1.74 0.86 1.68 1.66 2 1.11 0.51 1.06 2.02 1.60 0.89 0.6 0.91 2.10 3.27 4.1 0.91 2.4 1.80 0.91 1.4

0.6 1.2

Room Temperature Electrical Resistivity, ohm · cm 1.4 · 1015 7.5 · 1014 2.5 · 108

Mobility, μ, cm2/V · s

Sign of Majority Carriers

4.0 · 1018 (15ºC)

1 · 1015 1014 2.8 · 1014 (50ºC) 4 · 1018 1.5 · 1018 2 · 105

2.3 · 1015 2.4 · 109 (50ºC) 6 · 1013 4.1 · 1013 1.3 · 1014

45 to 250 5 to 110 54 to 78 27 to 47 0.64(n), 1.50(p)

1015 1013 107 1 · 1015 4.5 · 1016 (15ºC) 3.9 · 1015 5 · 1017

5.53(n), 87.4(p)

1014 (25ºC)

+&–

– 2.45(n), 0.02(p)

+&–

0.1 to 0.4 1.2(n), 1.1(p)

+ +&–

0.50

1.0 · 1015 (50ºC) 105 2.0 · 1015 (50ºC) 2 · 1016 2 · 1018 104 7.0 · 1014 (50ºC)

3 · 10–5

+&–

40 to 150 40 to 150 60 to 110 25 to 42 28 to 98 67 to 102 25 to 44

7 · 1014 (100ºC) 1011

Temperature Range, ºC 30 to 125 30 to 125 30 to 125

– +

20 to 140 40 to 100 –213 12 to 72 50 to 90 98 to 143 50 to 150 87 to 119 140 to 220

26 to 350 100

40 to 150

– 30 to 94 30 to 94 20 to 40

2.4

+ +

10-5

+ + +

0.025

at 20 70 to 120

Ref. 1 1 1 2 2 1 1 1 1 1 2 4 1 1 1 1 1 1 1 1 1 2 1 1 4 1 2 1 1 4 1 4 1 1 2 1 1 4 1 2 1 1 4 2 2 1 2 1 1 1 2 1 1 2 4 1 1 2 1

Properties of Organic Semiconductors

12-94

Substance p-Terphenyl Tetracene Tetracene Tetracene 1,1,10,10-Tetracyanodecapentaene 1,1,6,6-Tetracyanohexatriene Tetracyanoethylene 7,7,8,8-Tetracyanoquinodimethane 1,1,8,8-Tetracyanooctatetraene Tetraphenylpentacene Tetrathiotetracene Triphenodioxazine Triphenyldiamine Violanthrene Isoviolanthrene Violanthrone Isoviolanthrone o-Xylene (liquid) m-Xylene (liquid) p-Xylene (liquid)

Energy Gap, E, (in E/2 kT) eV 0.66 1.7 3.4 2.24 1.54

3.2 · 1012 (50ºC)

1.42 1.62 0.46 1.65

1012

0.85 0.82 0.78 0.76 0.45 0.41 0.41

Long-Chain Compounds and Polymers Acrylic acid-amylproparylaniline copolymers Acrylic acid-methylproparylaniline copolymers Acrylic acid-octylproparylaniline copolymers Anthrone polymers [CH(AsF5)0.1]x [CH ∙ I0.22]x 1,6-Diacetylenes (cyclopolymerized) Ionene elastomers 1,3,4-Oxydiazole polymers Oxypyrrole polymer films Phenylformaldehyde polymeric pyrolysates a) Pyrolysis Temperature 600ºC b) 1200ºC Phenylthiocyanate polymers Polyacetylene (undoped) Polyacetylene (I2 doped) Polyacetylene (cis-rich, undoped) trans-Polyacetylene (I2 doped, 0.22 mole %) Polyacrylonitrile (heat treated 700ºC) Poly-5,5′-biisatyl thiophene-indophene Poly bis(amino)-phosphazenes Poly-5,5′-diisatylmetane-thiophene-indophenine Polyethylene Polyethylene (low density) Polyimide Polymalonitrile Poly(metalphthalocyanines) :Cu :Fe :Ni :Sb :Zn Poly-N-methylpyrrole Polyoxypyrrole (black) Polyphthalocyanines Polypyrrole

Room Temperature Electrical Resistivity, ohm · cm

1.9

0.81

0.5 to 0.8

air 0.84 vacuum 1.0 1.75 0.45 2.74 0.17 2.84 1.72 0.12 0.15 0.46 0.12 0.044 0.01 0.01

1013 1014

104 5 · 1014 2.1 · 1014 8.4 · 1013 2.3 · 1010 5.7 · 109

Mobility, μ, cm2/V · s 1.2(n), 0.80(p)

0.85

0.26(max) 0.65

– + – –

2 · 10–2

109–1010 109–1010 109–1010 0.28 ≥100 at 1.8 kbar ≥2 at 33 kbar 0.0005 trans 105, cis 109 1010–1014 2.7 ∙ 107 to 2.2 ∙ 108 3 ∙ 1012 0.125 27 0.0044 105–108 1010 0.04 107

air 2.6 ∙ 109 vacuum 3.1 ∙ 109 1.8 ∙ 1011 7.3 ∙ 104

Sign of Majority Carriers +&–

–

>68

0 to 150 20 to 140 at 20 40 to 105 40 to 150 40 to 150 40 to 150

Ref. 4 2 1 4 1 1 4 4 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3

–80 to 60 20 to 140

0.0014 7.84

– +

0.01

+ – +

4 ∙ 109

7 ∙ 106 1.1 ∙ 106 100 3.1 ∙ 106 5.3 ∙ 103 2 ∙ 106 1790 7 to 58

Temperature Range, ºC

–100 to 100 20 to 140 20 to 180 20 to 140 20 to 70 above Tg

–

–173 to 27 –193 to 250

3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Properties of Organic Semiconductors

Substance Polypyrroline II Polyselenomethylene Poly(2-vinylpyridine):I2 (1:2) PVC (commercial) PVC (commercial) PVC (pure) Salicylal-N-alkyliminate-Cu TTF-acetylacetonate polymers TTF-metal polymers

12-95 Energy Gap, E, Room Temperature (in E/2 kT) Electrical Resistivity, eV ohm · cm 1.74 0.7 to 2.62 >1013 0.12 1000 2.84–3.04 1.24–1.96 1.0±0.1 1.62 1.7 ∙ 1014 1.6 ∙ 104 1.6 ∙ 104

Mobility, μ, cm2/V · s

Sign of Majority Carriers

Temperature Range, ºC 20 to 120 –73 to 27 T<Tg T>Tg 0 to 30

References

1. F. Gutman and L. E. Lyons, Organic Semiconductors, John Wiley & Sons, New York, 1967. 2. Y. Okamoto and W. Brenner, Organic Semiconductors, Reinhold Publ. Corp., New York, 1964. 3. F. Gutman, H. Keyzer, L. E. Lyons, and R. B. Somoano, Organic Semiconductors, Part B, R. E. Krieger Publ. Co., Melbourne, FL, 1983. 4.. L. I. Berger, Semiconductor Materials, CRC Press, Boca Raton, FL, 1997.

Ref. 3 3 3 3 3 3 4 3 3

NOMENCLATURE FOR ORGANIC POLYMERS Robert B. Fox and Edward S. Wilks Organic polymers have traditionally been named on the basis of the monomer used, a hypothetical monomer, or a semi-systematic structure. Alternatively, they may be named in the same way as organic compounds, i.e., on the basis of a structure as drawn. The former method, often called “source-based nomenclature” or “monomer-based nomenclature”, sometimes results in ambiguity and multiple names for a single material. The latter method, termed “structure-based nomenclature”, generates a sometimes cumbersome unique name for a given polymer, independent of its source. Within their limitations, both types of names are acceptable and well-documented.1 The use of stereochemical descriptors with both types of polymer nomenclature has been published.2

Traditional Polymer Names Monomer-Based Names “Polystyrene” is the name of a homopolymer made from the single monomer styrene. When the name of a monomer comprises two or more words, the name should be enclosed in parentheses, as in “poly(methyl methacrylate)” or “poly(4bromostyrene)” to identify the monomer more clearly. This method can result in several names for a given polymer: thus, “poly(ethylene glycol)”, “poly(ethylene oxide)”, and “poly(oxirane)” describe the same polymer. Sometimes, the name of a hypothetical monomer is used, as in “poly(vinyl alcohol)”. Even though a name like “polyethylene” covers a multitude of materials, the system does provide understandable names when a single monomer is involved in the synthesis of a single polymer. When one monomer can yield more than one polymer, e.g. 1,3-butadiene or acrolein, some sort of structural notation must be used to identify the product, and one is not far from a formal structure-based name. Copolymers, Block Polymers, and Graft Polymers. When more than one monomer is involved, monomer-based names are more complex. Some common polymers have been given names based on an apparent structure, as with “poly(ethylene terephthalate)”. A better system has been approved by the IUPAC.1 With this method, the arrangement of the monomeric units is introduced through use of an italicized connective placed between the names of the monomers. For monomer names represented by A, B, and C, the various types of arrangements are shown in Table 1. Table 2 contains examples of common or semi-systematic names of copolymers. The systematic names of comonomers may also be used; thus, the polyacrylonitrile-block-polybutadieneblock-polystyrene polymer in Table 2 may also be named poly(prop-2-enenitrile)-block-polybuta-1,3-diene-blockpoly(ethenylbenzene). IUPAC does not require alphabetized names of comonomers within a polymer name; many names are thus possible for some copolymers. These connectives may be used in combination and with small, non-repeating (i.e. non-polymeric) junction units; see, for example, Table 2, line 8. A long dash may be used in place of the con-

13-1

nective -block-; thus, in Table 2, the polymers of lines 7 and 8 may also be written as shown on lines 9 and 10. IUPAC also recommends an alternative scheme for naming copolymers that comprises use of “copoly” as a prefix followed by the names of the comonomers, a solidus (an oblique stroke) to separate comonomer names, and addition before “copoly” of any applicable connectives listed in Table 2 except -co-. Table 3 gives the same examples shown in Table 2 but with the alternative format. Comonomer names need not be parenthesized. TABLE 1. IUPAC Source-Based Copolymer Classification No.

Copolymer type

Connective

Example

Unspecified or unknown

-co-

poly(A-co-B)

Random (obeys Bernoullian distribution)

-ran-

poly(A-ran-B)

Statistical (obeys known statistical laws)

-stat-

poly(A-stat-B)

Alternating (for two monomeric units)

-alt-

poly(A-alt-B)

Periodic (ordered sequence for 2 or more monomeric units)

-per-

poly(A-per-B-perC)

Block (linear block arrangement)

-block-

polyA-block-polyB

Graft (side chains connected to main chains)

-graft-

polyA-graft-polyB

TABLE 2. Examples of Source-Based Copolymer Nomenclature No. 1 2 3 4 5

Copolymer name poly(propene-co-methacrylonitrile) poly[(acrylic acid)-ran-(ethyl acrylate)] poly(butene-stat-ethylene-stat-styrene) poly[(sebacic acid)-alt-butanediol] poly[(ethylene oxide)-per-(ethylene oxide)-pertetrahydrofuran] polyisoprene-graft-poly(methacrylic acid) polyacrylonitrile-block-polybutadiene-block-polystyrene polystyrene-block-dimethylsilylene-block-polybutadiene polyacrylonitrile—polybutadiene—polystyrene polystyrene—dimethylsilylene—polybutadiene

6 7 8 9 10

TABLE 3. Examples of Source-Based Copolymer Nomenclature (Alternative Format) No. 1 2 3 4 5 6 7

Polymer name copoly(propene/methacrylonitrile) ran-copoly(acrylic acid/ethyl acrylate) stat-copoly(butene/ethylene/styrene) alt-copoly(sebacic acid/butanediol) block-copoly(acrylonitrile/butadiene/styrene) per-copoly(ethylene oxide/ethylene oxide/tetrahydrofuran) graft-copoly(isoprene/methacrylic acid)

13-2

Nomenclature for Organic Polymers

Source-based nomenclature for non-linear macromolecules and macromolecular assemblies is covered by a 1997 IUPAC document.11 The types of polymers in these classes, together with their connectives, are given in Table 4; the terms shown may be used as connectives, prefixes, or both to designate the features present.

poly(methacrylic acid)-blend-poly(ethyl acrylate) net-poly(4-methylstyrene-i-divinylbenzene)

TABLE 4. Connectives for Non-Linear Macromolecules and Macromolecular Assemblies

net-poly[styrene-alt-(maleic anhydride)]-i-(polyethylene glycol; polypropylene glycol)

No.

net-poly(ethyl methacrylate)-sipn-polyethylene

[net-poly(butadiene-stat-styrene)]-ipn-[net-poly(4methylstyrene-i-divinylbenzene)]

Type

Connective

Branched (type unspecified)

branch

Branched with branch point of functionality f

f-branch

Comb

comb

Cross-link

i (Greek iota)

Cyclic

cyclo

Interpenetrating polymer network

ipn

Long-chain branched

l-branch

Network

net

Polymer blend

blend

Polymer-polymer complex

compl

Semi-interpenetrating polymer network

sipn

Short-chain branched

sh-branch

Star

star

Star with f arms

f-star

TABLE 5. Non-Linear Macromolecules

6 7 8

Polymer name polyethylene-blend-polypropene

No. Polymer name 1 poly(methacrylic acid)comb-polyacrylonitrile

No. 1 3

Non-linear polymers are named by using the italicized connective as a prefix to the source-based name of the polymer component or components to which the prefix applies; some examples are listed in Table 5.

TABLE 6. Examples of Polymer Blends and Nets

Polymer structural features Comb polymer with a poly(methacrylic acid) backbone and polyacrylonitrile side chains comb-poly[ethylene-statComb polymer with unspecified (vinyl chloride)] backbone composition and statistical ethylene/vinyl chloride copolymer side chains polybutadiene-combComb polymer with butadiene (polyethylene; polypropene) backbone and side chains of polyethylene and polypropene star-(polyA; polyB; polyC; Star polymer with arms derived from polyD; polyE) monomers A, B, C, D, and E, respectively star-(polyA-block-polyBStar polymer with every arm block-polyC) comprising a tri-block segment derived from comonomers A, B, and C star-poly(propylene oxide) A star polymer prepared from propylene oxide 5-star-poly(propylene oxide) A 5-arm star polymer prepared from propylene oxide star-(polyacrylonitrile; A star polymer containing polypropylene) polyacrylonitrile arms of MW 10000 (Mr 10000: 25000) and polypropylene arms of MW 25000

Macromolecular assemblies held together by forces other than covalent bonds are named by inserting the appropriate italicized connective between names of individual components; Table 6 gives examples.

Structure-Based Polymer Nomenclature Regular Single-Strand Polymers Structure-based nomenclature has been approved by the IUPAC4 and is currently being updated; it is used by Chemical Abstracts.5 Monomer names are not used. To the extent that a polymer chain can be described by a repeating unit in the chain, it can be named “poly(repeating unit)”. For regular single-strand polymers, “repeating unit” is a bivalent group; for regular doublestrand (ladder and spiro) polymers, “repeating unit” is usually a tetravalent group.9 Since there are usually many possible repeating units in a given chain, it is necessary to select one, called the “constitutional repeating unit” (CRU) to provide a unique and unambiguous name, “poly(CRU)”, where “CRU” is a recitation of the names of successive units as one proceeds through the CRU from left to right. For this purpose, a portion of the main chain structure that includes at least two repeating sequences is written out. These sequences will typically be composed of bivalent subunits such as -CH2-, -O-, and groups from ring systems, each of which can be named by the usual nomenclature rules.6,7 Where a chain is simply one long sequence comprising repetition of a single subunit, that subunit is itself the CRU, as in “poly(methylene)” or “poly(1,4-phenylene)”. In chains having more than one kind of subunit, a seniority system is used to determine the beginning of the CRU and the direction in which to move along the main chain atoms (following the shortest path in rings) to complete the CRU. Determination of the first, most senior, subunit, is based on a descending order of seniority: (1) heterocyclic rings, (2) hetero atoms, (3) carbocyclic rings, and, lowest, (4) acyclic carbon chains. Within each of these classes, there is a further order of seniority that follows the usual rules of nomenclature. Heterocycles: A nitrogen-containing ring system is senior to a ring system not containing nitrogen.4,9 Further descending order of seniority is determined by: (i) the highest number of rings in the ring system (ii) the largest individual ring in the ring system (iii) the largest number of hetero atoms (iv) the greatest variety of hetero atoms Hetero atoms: The senior bivalent subunit is the one nearest the top, right-hand corner of the Periodic Table; the order of seniority is: O, S, Se, Te, N, P, As, Sb, Bi, Si, Ge, Sn, Pb, B, Hg. Carbocycles: Seniority4 is determined by: (i) the highest number of rings in the ring system (ii) the largest individual ring in the ring system (iii) degree of ring saturation; an unsaturated ring is senior to a saturated ring of the same size

Nomenclature for Organic Polymers

13-3

Carbon chains: Descending order of seniority is determined by: (i) chain length (longer is senior to shorter) (ii) highest degree of unsaturation (iii) number of substituents (higher number is senior to lower number) (iv) ascending order of locants (v) alphabetical order of names of substituent groups Among equivalent ring systems, preference is given to the one having lowest locants for the free valences in the subunit, and among otherwise identical ring systems, the one having least hydrogenation is senior. Lowest locants in unsaturated chains are also given preference. Lowest locants for substituents are the final determinant of seniority. Direction within the repeating unit depends upon the shortest path, which is determined by counting main chain atoms, both cyclic and acyclic, from the most senior subunit to another subunit of the same kind or to a subunit next lower in seniority. When identification and orientation of the CRU have been accomplished, the CRU is named by writing, in sequence, the names of the largest possible subunits within the CRU from left to right. For example, the main chain of the polymer traditionally named “poly(ethylene terephthalate)” has the structure shown in Figure 1. O ...

CH2 CH2

number of which are minimized. The constitutional units may include regular or irregular blocks as well as atoms or atomic groupings, and each is named by the method described above or by the rules of organic nomenclature. The solidus denotes an unspecified arrangement of the units within the main chain.10 For example, a statistical copolymer derived from styrene and vinyl chloride with the monomeric units joined head-to-tail is named “poly(l-chloroethylene/l-phenylethylene)”. A polymer obtained by 1,4-polymerization and both headto-head and head-to-tail 1,2- polymerization of 1,3-butadiene would be named “poly(but-1-ene-l,4-diyl/l-vinylethylene/2-vinylethylene)”.12 In graphic representations of these polymers, shown in Figure 2, the hyphens or dashes at each end of each CRU depiction are shown completely within the enclosing parentheses; this indicates that they are not necessarily the terminal bonds of the macromolecule.

Figure 2. Graphic representations of copolymers.

O C

C O

O CH2 CH2

C C

CH 2

O CH2

C O ... C O

Figure 1. Structure-based name: poly(oxyethyleneoxyterephthaloyl); traditional name: poly(ethylene terephthalate).

The CRU in Figure 1 is enclosed in brackets and read from left to right. It is selected because (1) either backbone oxygen atom qualifies as the “most senior subunit”, (2) the shortest path length from either -O- to the other -O- is via the ethylene subunit. Orientation of the CRU is thus defined by (1) beginning at the -Omarked with an asterisk, and (2) reading in the direction of the arrow. The structure-based name of this polymer is therefore “poly(oxyethyleneoxyterephthaloyl)”, not much longer than the traditional name and much more adaptable to the complexities of substitution. As organic nomenclature evolves, more systematic names may be used for subunits, e.g. “ethane-1,2-diyl” instead of “ethylene”. IUPAC still prefers “ethylene” for the -CH2-CH2- unit, however, but also accepts “ethane-1,2-diyl”. Structure-based nomenclature can also be used when the CRU backbone has no carbon atoms. An example is the polymer traditionally named “poly(dimethylsiloxane)”, which on the basis of structure would be named “poly(oxydimethylsilylene)” or “poly(oxydimethylsilanediyl)”. This nomenclature method has also been applied to inorganic and coordination polymers8 and to double-strand (ladder and spiro) organic polymers.9

Irregular Single-Strand Polymers Polymers that cannot be described by the repetition of a single CRU or comprise units not all connected identically in a directional sense can also be named on a structure basis.10 These include copolymers, block and graft polymers, and star polymers. They are given names of the type “poly(A/B/C...)”, where A, B, C, etc. are the names of the component constitutional units, the

A long hyphen is used to separate components in names of block polymers, as in “poly(A)—poly(B)—poly(C)”, or “poly(A) —X—poly(B)” in which X is a non-polymeric junction unit, e.g. dimethylsilylene. In graphic representations of these polymers, the blocks are shown connected when the bonding is known (Figure 3, for example); when the bonding between the blocks is unknown, the blocks are separated by solidi and are shown completely within the outer set of enclosing parentheses (Figure 4, for example).10,13

Figure 3. polystyrene—polyethylene—polystyrene.

Figure 4. poly[poly(methyl methacrylate)—polystyrene—poly(methyl acrylate)].

Graft polymers are named in the same way as a substituted polymer but without the ending “yl” for the grafted chain; the name of a regular polymer, comprising Z units in which some have grafts of “poly(A)”, is “poly[Z/poly(A)Z]”. Star polymers are treated as a central unit with substituent blocks, as in “tetrakis(polymethylene)silane”.10,13

Other Nomenclature Articles and Publications In addition to the Chemical Abstracts and IUPAC documents cited above and listed below, other articles on polymer nomenclature are available. A 1999 article lists significant documents on polymer nomenclature published during the last 50 years in books, encyclopedias, and journals by Chemical Abstracts,

13-4

Nomenclature for Organic Polymers

IUPAC, and individual authors.14 A comprehensive review of source-based and structure-based nomenclature for all of the major classes of polymers,15 and a short tutorial on the correct identification, orientation, and naming of most commonly encountered constitutional repeating units were both published in 2000.16

References and Notes 1. International Union of Pure and Applied Chemistry, Compendium of Macromolecular Nomenclature, Blackwell Scientific Publications, Oxford, 1991. 2. International Union of Pure and Applied Chemistry, Stereochemical Definitions and Notations Relating to Polymers (Recommendations 1980), Pure Appl. Chem., 53, 733-752 (1981). 3. International Union of Pure and Applied Chemistry, Source-Based Nomenclature for Copolymers (Recommendations 1985), Pure Appl. Chem., 57, 1427-1440 (1985). 4. International Union of Pure and Applied Chemistry, Nomenclature of Regular Single-Strand Organic Polymers (Recommendations 1975, Pure Appl. Chem., 48, 373-385 (1976). 5. Chemical Abstracts Service, Naming and Indexing of Chemical Substances for Chemical Abstracts, Appendix IV, Chemical Abstracts 1999 Index Guide. 6. International Union of Pure and Applied Chemistry, A Guide to IUPAC Nomenclature of Organic Compounds (1993), Blackwell Scientific Publications, Oxford, 1993. 7. International Union of Pure and Applied Chemistry, Nomenclature of Organic Chemistry, Sections A, B, C, D, E, F, and H, Pergamon Press, Oxford, 1979. 8. International Union of Pure and Applied Chemistry, Nomenclature of Regular Double-Strand and Quasi-Single-Strand Inorganic and

10.

11.

12.

13.

14.

15.

16.

Coordination Polymers (Recommendations 1984), Pure Appl. Chem., 57, 149-168 (1985). International Union of Pure and Applied Chemistry, Nomenclature of Regular Double-Strand (Ladder and Spiro) Organic Polymers (Recommendations 1993), Pure Appl. Chem., 65, 1561-1580 (1993). International Union of Pure and Applied Chemistry, Structure-Based Nomenclature for Irregular Single-Strand Organic Polymers (Recommendations 1994), Pure Appl. Chem., 66, 873-889 (1994). International Union of Pure and Applied Chemistry, “Source-Based Nomenclature for Non-Linear Macromolecules and Macromolecular Assemblies (Recommendations 1997).” Pure Appl. Chem., 69, 25112521 (1997). Poly(1,3-butadiene) obtained by polymerization of 1,3-butadiene in the so-called 1,4- mode is frequently drawn incorrectly in publications as -(CH2-CH=CH-CH2)n-; the double bond should be assigned the lowest locant possible, i.e. the structure should be drawn as –(CH=CH-CH2-CH2)n-. International Union of Pure and Applied Chemistry, “Graphic Representations (Chemical Formulae) of Macromolecules (Recommendations 1994).” Pure Appl. Chem., 66, 2469-2482 (1994). Wilks, E. S. Macromolecular Nomenclature Note No. 17: “Whither Nomenclature?” Polym. Prepr. 40(2), 6-11 (1999); also available at www.chem.umr.edu/~poly/nomenclature.html. Wilks, E. S. “Polymer Nomenclature: The Controversy Between Source-Based and Structure-Based Representations (A Personal Perspective).” Prog. Polym. Sci. 25, 9-100 (2000). Wilks, E. S. Macromolecular Nomenclature Note No. 18: “SRUs: Using the Rules.” Polym. Prepr. 41(1), 6a-11a (2000); also available at www.chem.umr.edu/~poly/nomenclature.html; a .pdf format version is also available.

SOLVENTS FOR COMMON POLYMERS Abbreviations: HC: hydrocarbons MEK: methyl ethyl ketone

Polyethylene (HDPE) Polypropylene (atactic) Polybutadiene Polystyrene Polyacrylates Polymethacrylates Polyacrylamide Poly(vinyl ethers) Poly(vinyl alcohol) Poly(vinyl acetate) Poly(vinyl chloride) Poly(vinylidene chloride) Poly(vinyl fluoride) Polyacrylonitrile Poly(oxyethylene) Poly(2,6-dimethylphenylene oxide) Poly(ethylene terephthalate) Polyurethanes (linear) Polyureas Polysiloxanes Poly[bis(2,2,2-trifluoroethoxy)-phosphazene]

THF: tetrahydrofuran DMF: dimethylformamide DMSO: dimethylsulfoxide

HC and halogenated HC HC and halogenated HC HC, THF, ketones ethylbenzene, CHCl3, CCl4, THF, MEK aromatic HC, chlorinated HC, THF, esters, ketones aromatic HC, chlorinated HC, THF, esters, MEK water halogenated HC, MEK, butanol glycols (hot), DMF aromatic HC, chlorinated HC, THF, esters, DMF THF, DMF, DMSO THF (hot), dioxane, DMF DMF, DMSO (hot) DMF, DMSO aromatic HC, CHCl3, alcohols, esters, DMF aromatic HC, halogenated HC phenol, DMSO (hot) aromatic HC, THF, DMF phenol, formic acid HC, THF, DMF THF, ketones, ethyl acetate

13-5

Section 13.indb 5

4/30/05 9:55:16 AM

GLASS TRANSITION TEMPERATURE FOR SELECTED POLYMERS Robert B. Fox Polymer names are based on the IUPAC structure-based nomenclature system described in the table “Naming Organic Polymers”. Within each category, names are listed in alphabetical order. Source-based and trivial names are also given (in italics) for the most common polymers. The table does not include polymers for which Tg is not clearly defined because of variability of structure or because of reactions taking place near the glass transition.

All values of Tg cited in this table have been determined by differential scanning calorimetry (DSC) except those values indicated by:

Polymer name ACYCLIC CARBON CHAINS Polyalkadienes Poly(alkenylene) Polyalkadiene –[CH=CHCH2CH2]– Poly(cis-1-butenylene) cis-1,3-polybutadiene [PBD] Poly(trans-1-butenylene) trans-1,3-polybutadiene [PBD] Poly(1-chloro-cis-1-butenylene) cis-1,3-polychloroprene Poly(1-chloro-trans-1-butenylene) trans-1,3-polychloroprene Poly(1-methyl-cis-1-butenylene) cis-1,3-polyisoprene Poly(1-methyl-trans-1-butenylene) trans-1,3-polyisoprene Poly(1,4,4-trifluoro-1-butenylene)

(D) (Dil) (M)

dynamic method dilatometry mechanical method Glass transition temperature (Tg/K)

171 215 253 233 200 207 238

Polyalkenes Poly(alkylethylene) Poly(alkylethylene) -[RCHCH2]Poly(1-benzylethylene) Poly(1-butylethylene) Poly(1-cyclohexylethylene) (atactic) Poly(1-cyclohexylethylene) (isotactic) Poly(1,1-dimethylethylene) Polyisobutylene [PIB] Poly(ethylene) Poly(methylene) Poly(1-phenethylethylene) Poly(propylene) (isotactic) Poly(propylene) (syndiotactic) Poly[1-(2-pyridyl)ethylene] Poly[1-(4-pyridyl)ethylene] Poly(1-vinylethylene)

333 223 393 406 (D) 200 148 155 283 272 ca. 265 377 415 273

Polyacrylics Poly[1-(alkoxycarbonyl)ethylene) Poly(alkyl acrylate) –[(ROCO)CHCH2]– Poly[1-(benzyloxycarbonyl)ethylene] Poly[1-(butoxycarbonyl)ethylene] Poly(butyl acrylate) [PBA] Poly[1-(sec-butoxycarbonyl)ethylene] Poly[1-(butoxycarbonyl)-1-cyanoethylene] Poly[1-(butylcarbamoyl)ethylene] Poly(1-carbamoylethylene) Polyacrylamide [PAM] Poly(1-carboxyethylene)

279 219 (M) 251 358 319 (M) 438 379

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Section 13.indb 6

4/30/05 9:55:17 AM

Glass Transition Temperature for Selected Polymers Polymer name Poly(acrylic acid) [PAA] Poly[1-(2-chlorophenoxycarbonyl)ethylene] Poly[1-(4-chlorophenoxycarbonyl)ethylene] Poly[1-(4-cyanobenzyloxycarbonyl)ethylene] Poly[1-(2-cyanoethoxycarbonyl)ethylene] Poly[1-(cyanomethoxycarbonyl)ethylene)] Poly[1-(4-cyanophenoxycarbonyl)ethylene] Poly[1-(cyclohexyloxycarbonyl)ethylene] Poly[1-(2,4-dichlorophenoxycarbonyl)ethylene] Poly[1-(dimethylcarbamoyl)ethylene] Poly[1-(ethoxycarbonyl)ethylene] Poly(ethyl acrylate) [PEA] Poly[1-(ethoxycarbonyl)-1-fluoroethylene] Poly[1-(2-ethoxycarbonylphenoxycarbonyl)ethylene] Poly[1-(3-ethoxycarbonylphenoxycarbonyl)ethylene] Poly[1-(4-ethoxycarbonylphenoxycarbonyl)ethylene] Poly[1-(2-ethoxyethoxycarbonyl)ethylene] Poly[1-(3-ethoxypropoxycarbonyl)ethylene] Poly[1-(isopropoxycarbonyl)ethylene] Poly[1-(methoxycarbonyl)ethylene] Poly(methyl acrylate) [PMA] Poly[1-(2-methoxycarbonylphenoxycarbonyl)ethylene] Poly[1-(3-methoxycarbonylphenoxycarbonyl)ethylene] Poly[1-(4-methoxycarbonylphenoxycarbonyl)ethylene] Poly[1-(2-methoxyethoxycarbonyl)ethylene] Poly[1-(4-methoxyphenoxycarbonyl)ethylene] Poly[1-(3-methoxypropoxycarbonyl)ethylene] Poly[1-(2-naphthyloxycarbonyl)ethylene] Poly[1-(pentachlorophenoxycarbonyl)ethylene] Poly[1-(phenethoxycarbonyl)ethylene] Poly[1-(phenoxycarbonyl)ethylene] Poly[1-(m-tolyloxycarbonyl)ethylene] Poly[1-(o-tolyloxycarbonyl)ethylene] Poly[1-(p-tolyloxycarbonyl)ethylene] Poly[1-(2,2,2-trifluorethoxycarbonyl)ethylene]

13-7 Glass transition temperature (Tg/K) 326 331 317 277 433 Dil 363 292 333 362 249 316 303 297 310 223 218 267-270 283 319 311 340 223 324 198 358 420 270 330 298 325 316 263

Polymethacrylics Poly[1-(alkoxycarbonyl)-1-methylethylene] Poly(alkyl methacrylate) –[(ROCO)(Me)CCH2]– Poly[1-(benzyloxycarbonyl)-1-methylethylene] Poly[1-(2-bromoethoxycarbonyl)-1-methylethylene] Poly[(1-(butoxycarbonyl)-1-methylethylene] Poly(butyl methacrylate) [PBMA] Poly[1-(sec-butoxycarbonyl)-1-methylethylene] Poly[1-(tert-butoxycarbonyl)-1-methylethylene)] Poly[1-(2-chloroethoxycarbonyl)-1-methylethylene] Poly[1-(2-cyanoethoxycarbonyl)-1-methylethylene] Poly[1-(4-cyanophenoxycarbonyl)-1-methylethylene] Poly[1-(cyclohexyloxycarbonyl)-1-methylethylene] (atactic) Poly[1-(cyclohexyloxycarbonyl)-1-methylethylene)] (isotactic) Poly[1-(dimethylaminoethoxycarbonyl)-1-methylethylene] Poly[1-(ethoxycarbonyl)-1-ethylethylene] Poly[1-(ethoxycarbonyl)-1-methylethylene] (atactic) Poly(ethyl methacrylate) [PEMA] Poly[1-(ethoxycarbonyl)-1-methylethylene] (isotactic) Poly[1-(ethoxycarbonyl)-1-methylethylene)] (syndiotactic) Poly[1-(hexyloxycarbonyl)-1-methylethylene] Poly[1-(isobutoxycarbonyl)-1-methylethylene] Poly[1-(isopropoxycarbonyl)-1-methylethylene] Poly[1-(methoxycarbonyl)-1-methylethylene] (atactic) Poly(methyl methacrylate) [PMMA] Poly[1-(methoxycarbonyl)-1-methylethylene)] (isotactic) Poly[1-(methoxycarbonyl)-1-methylethylene)] (syndiotactic) Poly[1-(4-methoxycarbonylphenoxy)-1-methylethylene]

Section 13.indb 7

327 325 293 333 391 ca 315 364 428 356 324 292 300 338 285 339 268 326 354 378 311 378 379

4/30/05 9:55:17 AM

13-8 Polymer name Poly[1-(methoxycarbonyl)-1-phenylethylene)] (atactic) Poly[1-(methoxycarbonyl)-1-phenylethylene)] (isotactic) Poly[1-methyl-1-(phenethoxycarbonyl)ethylene] Poly[1-methyl-1-(phenoxycarbonyl)ethylene]

Glass Transition Temperature for Selected Polymers Glass transition temperature (Tg/K) 391 397 299 383

Polyvinyl ethers, alcohols, and ketones Poly(1-alkoxyethylene) Poly(alkyl vinyl ether) –[ROCHCH2]– Poly(1-hydroxyethylene) Poly(vinyl alcohol) –[HOCHCH2]– Poly(1-alkanoylethylene) Poly(alkyl vinyl ketone) –[RCOCHCH2]– Poly(1-butoxyethylene) Poly(1-sec-butoxyethylene) Poly(1-tert-butoxyethylene) Poly[1-(butylthio)ethylene] Poly(1-ethoxyethylene) Poly[1-(4-ethylbenzoyl)ethylene] Poly(1-hydroxyethylene) Poly(vinyl alcohol) [PVA] Poly(hydroxymethylene) Poly(1-isopropoxyethylene) Poly[1-(4-methoxybenzoyl)ethylene] Poly(1-methoxyethylene) Poly(methyl vinyl ether) [PMVE] Poly[1-(methylthio)ethylene] Poly(1-propoxyethylene) Poly[1-(trifluoromethoxy)trifluoroethylene]

218 253 361 253 230 325 358 (D) 407 270 319 (M) 242 272 224 268

Polyvinyl halides and nitriles Poly(1-haloethylene) Poly(vinyl halide) –[XCHCH2]– Poly(1-cyanoethylene) Poly(acrylonitrile) –[NCCHCH2]– Poly(1-chloroethylene) Poly(vinyl chloride) [PVC] Poly(chlorotrifluoroethylene) Poly(1-cyanoethylene) Polyacrylonitrile [PAN] Poly(1-cyano-1-methylethylene) Polymethacrylonitrile Poly(1,1-dichloroethylene) Poly(vinylidene chloride) Poly(1,1-difluoroethylene) Poly(vinylidene fluoride) Poly(1-fluoroethylene) Poly(vinyl fluoride) Poly(1-hexafluoropropylene) Poly[1-(2-iodoethyl)ethylene] Poly(tetrafluoroethylene) Poly[1-(trifluoromethyl)ethylene]

354 373 370 393 255 ca 233 314 (M) 425 343 (160) 300

Polyvinyl esters Poly[1-(alkanoyloxy)ethylene] Poly(vinyl alkanoate) –[RCOOCHCH2]– Poly(1-acetoxyethylene) Poly(vinyl acetate) [PVAc] Poly[1-(benzoyloxy)ethylene] Poly[1-(4-bromobenzoyloxy)ethylene] Poly[1-(2-chlorobenzoyloxy)ethylene] Poly[1-(3-chlorobenzoyloxy)ethylene] Poly[1-(4-chlorobenzoyloxy)ethylene] Poly[1-(cyclohexanoyloxy)ethylene] Poly[1-(4-ethoxybenzoyloxy)ethylene] Poly[1-(4-ethylbenzoyloxy)ethylene]

Section 13.indb 8

305 344 365 335 338 357 349 (M) 343 326

4/30/05 9:55:18 AM

Glass Transition Temperature for Selected Polymers Polymer name Poly[1-(4-isopropylbenzoyloxy)ethylene] Poly[1-(2-methoxybenzoyloxy)ethylene] Poly[1-(3-methoxybenzoyloxy)ethylene] Poly[1-(4-methoxybenzoyloxy)ethylene] Poly[1-(4-methylbenzoyloxy)ethylene] Poly[1-(4-nitrobenzoyloxy)ethylene] Poly[1-(propionoyloxy)ethylene] Polystyrenes Poly(1-phenylethylene) Polystyrene –[C6H5CHCH2]– Poly[1-(4-acetylphenyl)ethylene] Poly[1-(4-benzoylphenyl)ethylene] Poly[1-(4-bromophenyl)ethylene] Poly[1-(4-butoxyphenyl)ethylene] Poly[1-(4-butoxycarbonylphenyl)ethylene] Pol[(1-(4-butylphenyl)ethylene] Poly[1-(4-carboxyphenyl)ethylene] Poly[1-(2-chlorophenyl)ethylene] Poly[1-(3-chlorophenyl)ethylene] Poly[1-(4-chlorophenyl)ethylene] Poly[1-(2,4-dichlorophenyl)ethylene] Poly[1-(2,5-dichlorophenyl)ethylene] Poly[1-(2,6-dichlorophenyl)ethylene] Poly[1-(3,4-dichlorophenyl)ethylene] Poly[1-(2,4-dimethylphenyl)ethylene] Poly[1-(4-(dimethylamino)phenyl)ethylene] Poly[1-(4-ethoxyphenyl)ethylene] Poly[1-(4-ethoxycarbonylphenyl)ethylene] Poly[1-(4-fluorophenyl)ethylene] Poly[1-(4-iodophenyl)ethylene] Poly[1-(4-methoxyphenyl)ethylene] Poly[1-(4-methoxycarbonylphenyl)ethylene] Poly(1-methyl-1-phenylethylene) Poly(α-methylstyrene) Poly[1-(2-(methylamino)phenyl)ethylene] Poly(1-phenylethylene) Polystyrene [PS] Poly[1-(4-propoxyphenyl)ethylene] Poly[1-(4-propoxycarbonylphenyl)ethylene] Poly(1-o-tolylethylene)

13-9 Glass transition temperature (Tg/K) 342 338 ca 317 360 343 395 283 (M)

389 (M) 371 (M) 391 ca 320 (M) 349 (M) 279 386 (M) 392 363 383 406 379 440 401 385 398 (M) ca 359 (M) 367 (M) 368 429 386 386 (M) 373 462 (M) 373 343 (M) 365 (M) 409

CHAINS WITH CARBOCYCLIC UNITS Poly(arylenealkylene) –[–Ar–(CH2)n]– Poly[1-(2-bromo-1,4-phenylene)ethylene] Poly[1-(2-chloro-1,4-phenylene)ethylene] Poly[1-(2-cyano-1,4-phenylene)ethylene] Poly[1-(2,5-dimethyl-1,4-phenylene)ethylene] Poly[1-(2-ethyl-1,4-phenylene)ethylene] Poly[1-(1,4-naphthylene)ethylene] Poly[1-(1,4-phenylene)ethylene]

353 (M) 343 (M) 363 (M) 373 (M) 298 (M) 433 (M) ca 353 (M)

CHAINS WITH HETEROATOM UNITS Main chain oxide units Poly(oxyalkylene) Poly(alkylene oxide) –[O(CH2)n]– Poly[oxy(1,1-bis(chloromethyl)trimethylene)] Poly[oxy(1-(bromomethyl)ethylene)] Poly[oxy(1-(butoxymethyl)ethylene)] Poly[oxy(1-butylethylene)] Poly[oxy(1-tert-butylethylene)] Poly[oxy(1-(chloromethyl)ethylene)]

Section 13.indb 9

265 259 194 203 308 251

4/30/05 9:55:18 AM

13-10

Glass Transition Temperature for Selected Polymers

Polymer name Poly(epichlorohydrin) Poly[oxy(2,6-dimethoxy-1,4-phenylene)] Poly[oxy(1,1-dimethylethylene)] Poly[oxy(2,6-dimethyl-1,4-phenylene)] Poly[oxy(2,6-diphenyl-1,4-phenylene)] Poly[oxy(1-ethylethylene)] Poly(oxyethylidene) Polyacetaldehyde Poly[oxy(1-(methoxymethyl)ethylene)] Poly[oxy(2-methyl-6-phenyl-1,4-phenylene)] Poly[oxy(1-methyltrimethylene)] Poly[oxy(2-methyltrimethylene)] Poly(oxy-1,4-phenylene) Poly(phenylene oxide) [PPO] Poly[oxy(1-phenylethylene)] Poly(oxytetramethylene) Poly(tetrahydrofuran) [PTMO] Poly(oxytrimethylene)

Glass transition temperature (Tg/K) 440 264 482 493 203 243 211 428 223 (D) 218 358 313 189 195

Main-chain ester or anhydride units Poly(oxyalkyleneoxyalkanedioyl) Poly(alkylene alkanedioate)-–[O(CH2)mOCO(CH2)nCO]– Poly(oxyadipoyloxydecamethylene) Poly(oxyadipoyloxy-1,4-phenyleneisopropylidene-1,4-phenylene) Poly(oxycarbonyloxy-1,4-phenylene-isopropylidene-1,4-phenylene) Bisphenol A polycarbonate Poly(oxycarbonylpentamethylene) Poly(oxycarbonyl-1,4-phenylenemethylene-1,4-phenylene) Poly(oxycarbonyl-1,4-phenyleneisopropylidene-1,4-phenylene) Poly[oxy(2,6-dimethyl-1,4-phenyleneisopropylidene-3,5-dimethyl-1,4-phenylene)oxysebacoyl] Poly(oxyethylenecarbonyl-1,4-cyclohexylenecarbonyl) (trans) Poly(oxyethyleneoxycarbonyl-1,4-naphthylenecarbonyl) Poly(oxyethyleneoxycarbonyl-1,5-naphthylenecarbonyl) Poly(oxyethyleneoxycarbonyl-2,6-naphthylenecarbonyl) Poly(oxyethyleneoxycarbonyl-2,7-naphthylenecarbonyl) Poly(oxyethyleneoxyterephthaloyl) Poly(ethylene terephthalate) [PET] Poly(oxyisophthaloyl) Poly(oxy(1-oxo-2,2-dimethyltrimethylene)) Poly(pivalolactone) Poly(oxy-1,4-phenyleneisopropylidene-1,4-phenyleneoxysebacoyl) Poly(oxy-1,4-phenyleneoxy-1,4-phenyleneoxy-carbonyl-1,4-phenylene) [PEEK] Poly(oxypropyleneoxyterephthaloyl) Poly[oxyterephthaloyloxy(2,6-dimethyl-1,4-phenyleneisopropylidene-3,5-dimethyl-1,4-(D)phenylene)] Poly(oxyterephthaloyloxyoctamethylene) Poly(oxyterephthaloyloxy-1,4-phenyleneisopropylidene-1,4-phenylene) Poly(bisphenol A terephthalate) Poly(oxytetramethyleneoxyterephthaloyl) Poly(butylene terephthalate) [PBT]

217 341 422 213 395 333 318 291 337 344 386 392 342 403 (D) 263 280 416 341 498 318 (D) 478 323

Main-chain amide units Poly(iminoalkyleneiminoalkanedioyl) Poly(alkylene alkanediamide)–[NH(CH2)mNHCO(CH2)nCO]– Poly(iminoadipoyliminodecamethylene) Nylon 10,6 Poly(iminoadipoyliminohexamethylene) Nylon 6,6 Poly(iminoadipoyliminooctamethylene) Nylon 8,6 Poly[iminoadipoyliminotrimethylene(methylimino)trimethylene] Poly(iminocarbonyl-1,4-cyclohexylenemethylene) Poly[iminocarbonyl-1,4-phenylene(2-oxoethylene)iminohexamethylene] Poly(iminoethylene-1,4-phenyleneethyleneiminosebacoyl)

Section 13.indb 10

313 ca 323 318 278 466 377 378 (D)

4/30/05 9:55:19 AM

Glass Transition Temperature for Selected Polymers Polymer name Poly(iminohexamethyleneiminoazelaoyl) Nylon 6,9 Poly(iminohexamethyleneiminododecanedioyl) Nylon 6, 12 Poly(iminohexamethyleneiminopimeloyl) Nylon 6,7 Poly(iminohexamethyleneiminosebacoyl) Nylon 6,10 Poly(iminohexamethyleneiminosuberoyl) Nylon 6,8 Poly(iminoisophthaloylimino-4,4′-biphenylylene) Poly(iminoisophthaloyliminohexamethylene) Poly(iminoisophthaloyliminomethylene-1,4-cyclohexylenemethylene) Poly(iminoisophthaloyliminomethylene-1,3-phenylenemethylene) Poly[iminomethylene(2,5-dimethyl-1,4-phenylene)methyleneiminosuberoyl] Poly(imino-1,5-naphthyleneiminoisophthaloyl) Poly(imino-1,5-naphthyleneiminoterephthaloyl) Poly(iminooctamethyleneiminodecanedioyl) Nylon 8,10 Poly(iminooxalyliminohexamethylene) Nylon 6,2 Poly[imino(1-oxohexamethylene)] Nylon 6 Poly[imino(1-oxodecamethylene)] Nylon 10 Poly[imino(1-oxoheptamethylene)] Nylon 7 Poly[imino(1-oxo-3-methyltrimethylene] Poly[imino(1-oxononamethylene)] Nylon 9 Poly[imino(1-oxooctamethylene)] Nylon 8 Poly[imino(1-oxotrimethylene)] Nylon 3 Poly(iminopentamethyleneiminoadipoyl) Nylon 5,6 Poly[iminopentamethyleneiminocarbonyl-1,4-phenylene(2-oxoethylene)] Poly(imino-1,3-phenyleneiminoisophthaloyl) Poly(imino-1,4-phenyleneiminoterephthaloyl) Poly(iminopimeloyliminoheptamethylene) Nylon 7,7 Poly(iminoterephthaloylimino-4,4′-biphenylylene) Poly(iminotetramethyleneiminoadipoyl) Nylon 4,6 Poly[iminotetramethyleneiminocarbonyl-1,4-phenylene(2-oxoethylene)] Poly(iminotrimethyleneiminoadipoyliminotrimethylene) Poly[iminotrimethyleneiminocarbonyl-1,4-phenylene(2-oxoethylene)] Poly(oxy-1,4-phenyleneiminoterephthaloyl-imino-1,4-phenylene) Poly(sulfonylimino-1,4-phenyleneiminoadipoylimino-1,4-phenylene)

13-11 Glass transition temperature (Tg/K) 331 319 331 323 330 558 390 481 438 (M) 351 598 578 333 430 326 315 325 369 319 323 384 318 376 553 (M) 618 328 613 316 357 307 382 613 467

Main-chain urethane units Poly(oxyalkyleneoxycarbonyliminoalkyleneiminocarbonyl)–[O(CH2)mOCONH(CH2)nNHCO]– Poly(oxyethyleneoxycarbonyliminohexamethyleneiminocarbonyl) Poly[oxyethyleneoxycarbonylimino(6-methyl-1,3-phenylene)iminocarbonyl] Poly(oxyethyleneoxycarbonylimino-1,4-phenylenemethylene-1,4-phenyleneiminocarbonyl) Poly(oxyhexamethyleneoxycarbonyliminohexamethyleneiminocarbonyl) Poly[oxyhexamethyleneoxycarbonylimino(6-methyl-1,3-phenylene)iminocarbonyl] Poly(oxyhexamethyleneoxycarbonylimino-1,4-phenylenemethylene-1,4-phenyleneiminocarbonyl) Poly(oxyoctamethyleneoxycarbonyliminohexamethyleneiminocarbonyl) Poly[oxyoctamethyleneoxycarbonylimino(6-methyl-1,3-phenylene)iminocarbonyl] Poly(oxyoctamethyleneoxycarbonylimino-1,4-phenylenemethylene-1,4-phenyleneiminocarbonyl)

Section 13.indb 11

329 325 412 332 305 364 331 337 352

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13-12

Glass Transition Temperature for Selected Polymers

Polymer name Poly(oxytetramethyleneoxycarbonyliminohexamethyleneiminocarbonyl) Poly[oxytetramethyleneoxycarbonylimino(6-methyl-1,3-phenylene)iminocarbonyl] Poly(oxytetramethyleneoxycarbonylimino-1,4-phenylenemethylene-1,4-phenyleneiminocarbonyl)

Glass transition temperature (Tg/K) 332 315 382

Main-chain siloxanes Poly[oxy(dialkylsilylene)] Poly(dialkylsiloxane) –[O(R2Si)]– Poly[oxy(dimethylsilylene)] Poly(dimethylsiloxane) [PDMS] Poly[oxy(dimethylsilylene)oxy-1,4-phenylene] Poly[oxy(dimethylsilylene)oxy-1,4-phenyleneisopropylidene-1,4-phenylene] Poly[oxy(diphenylsilylene)] Poly(diphenylsiloxane) Poly[oxy(diphenylsilylene)-1,3-phenylene] Poly[oxy((methyl)phenylsilylene)] Poly[oxy((methyl)-3,3,3-trifluoropropylsilylene] Main-chain sulfur-containing units Poly(dithioethylene) Poly(dithiomethylene-1,4-phenylenemethylene) Poly(oxy-4,4′-biphenylylene-1,4-phenylenesulfonyl-1,4-phenylene) Poly(oxycarbonyloxy-1,4-phenylenethio-1,4-phenylene) Poly(oxyethylenedithioethylene) Poly[oxy(2-hydroxytrimethylene)oxy-1,4-phenylenesulfonyl-1,4-phenylene] Poly(oxymethyleneoxyethylenedithioethylene) Poly(oxy-1,4-phenylenesulfinyl-1,4-phenyleneoxy-1,4-phenylenecarbonyl-1,4-phenylene) Poly(oxy-1,4-phenylenesulfinyl-1,4-phenyleneoxy-1,4-phenyleneisopropylidene-1,4-phenylene) Poly(oxy-1,4-phenylenesulfonyl-1,4-phenylene) Poly(oxy-1,4-phenylenesulfonyl-4,4′-biphenylylenesulfonyl-1,4-phenylene) Poly[oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxy(2,6-dimethyl-1,4-phenylene)isopropylidene (3,5-dimethyl-1,4-phenylene)] Poly(oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxy-1,4-phenylenecarbonyl-1,4-phenylene) Poly[oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxy-1,4-phenylene(hexafluoroisopropylidene)1,4-phenylene] Poly(oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxy-1,4-phenyleneisopropylidene-1,4-phenylene) Poly(oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxy-1.4-phenylenemethylene-1,4-phenylene) Poly(oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxy-1.4-phenylenethio-1,4-phenylene) Poly(oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxyterephthaloyl) Poly(oxytetramethylenedithiotetramethylene) Poly(sulfonyl-1,2-cyclohexylene) Poly(sulfonyl-1,3-cyclohexylene) Poly(sulfonyl-1,4-phenylenemethylene-1,4-phenylene) Poly(thio-1,3-cyclohexylene) Poly[thio(difluoromethylene)] Poly(thioethylene) Poly[thio(1-ethylethylene] Poly[thio(1-methyl-3-oxotrimethylene)] Poly[thio(1-methyltrimethylene)] Pol[(thio(1-oxohexamethylene)] Poly(thio-1,4-phenylene) Poly(thiopropylene) Main-chain heterocyclic units Poly(1,3-dioxa-4,6-cyclohexylenemethylene) Poly(vinyl formal) Poly[(2,6-dioxopiperidine-1,4-diyl)trimethylene] Poly[(2-methyl-1,3-dioxa-4,6-cyclohexylene)methylene] Poly(vinyl acetal) Poly(1,4-piperazinediylcarbonyloxyethyleneoxycarbonyl) Poly(1,4-piperazinediylisophthaloyl) Poly[(2-propyl-1,3-dioxa-4,6-cyclohexylene)methylene] Poly(vinyl butyral) Poly(3,6-pyridazinediyloxy-1,4-phenyleneisopropylidene-1,4-phenyleneoxy) Poly(2,5-pyridinediylcarbonyliminohexamethyleneiminocarbonyl)

Section 13.indb 12

148 363 (M) 318 (M) 238 ca 331 187 <193 223 296 503 (M) ca 383 220 (M) 428 214 478 (M) 438 (M) 487 533 508 (M) 478 (M) 478 (M) 449 453 (M) 448 (M) 522 197 401 381 497 221 155 223 218 285 214 292 370 226 378 363 355 333 465 (M) 322 453 (M) 322

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DIELECTRIC CONSTANT OF SELECTED POLYMERS This table lists typical values of the dielectric constant (more properly called relative permittivity) of some important polymers. Values are given for frequencies of 1 kHz, 1 MHz, and 1 GHz; in most cases the dielectric constant at frequencies below 1 kHz does not differ significantly from the value at 1 kHz. Since the dielectric constant of a polymeric material can vary with density, degree of crystallinity, and other details of a particular sample, the values given here should be regarded only as typical or average values.

Name Polyacrylonitrile Polyamides (nylons) Polybutadiene Polycarbonate Polychloroprene (neoprene) Polychlorotrifluoroethylene Polyethylene Poly(ethylene terephthalate) (Mylar) Polyisoprene (natural rubber) Poly(methyl methacrylate) Polyoxymethylene (polyformaldehyde) Poly(phenylene oxide) Polypropylene Polystyrene Polysulfones Polytetrafluoroethylene (teflon) Poly(vinyl acetate) Poly(vinyl chloride) Poly(vinylidene chloride) Poly(vinylidene fluoride)

References 1. Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, p. 5-132, McGraw Hill, New York, 1972. 2. Anderson, H. L., Ed., A Physicistâ&#x20AC;&#x2122;s Desk Reference, American Institute of Physics, New York, 1989. 3. Brandrup, J., and Immergut, E. H., Polymer Handbook, Third Edition, John Wiley & Sons, New York, 1989.

t/Â°C 25 25 84 25 23 25 23 23 23 27 27 80 25 23 25 25 25 25 50 150 25 100 23 23

1 kHz 5.5 3.50 11 2.5 2.92 6.6 2.65 2.3 3.25 2.6 3.12 3.80 3.8 2.59 2.3 2.6 3.13 2.1

3.39 5.3 4.6 12.2

1 MHz 4.2 3.14 4.4

1 GHz 2.8 2.8

2.8 6.3 2.46

4.2 2.39

3.0 2.5 2.76 2.7

2.8 2.4 2.6 2.6

2.59 2.3 2.6 2.10 2.1 3.5 8.3 2.9 3.3 3.2 8.9

2.3 2.6 2.1

2.8 2.7 2.7 4.7

13-13

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PRESSURE-VOLUME-TEMPERATURE RELATIONSHIP FOR POLYMER MELTS Christian Wohlfarth Numerous theoretical equations of state for polymer liquids have been developed. These, at the minimum, have to provide accurate fitting functions to experimental data. However, for the purpose of this table, the empirical Tait equation along with a polynomial expression for the zero pressure isobar is used. This equation is able to represent the experimental data for the melt state within the limits of experimental errors, i.e., the maximum deviations between measured and calculated specific volumes are about 0.001-0.002 cm3/g. The general form of the Tait equation is: V(P,T) = V(0,T){1 – C ln[1 + P/B(T)]}

(1)

where the coefficient C is usually taken to be a universal constant equal to 0.0894. T is the absolute temperature in K and P the pressure in MPa. The volume V is the specific volume in cm3/g. The Tait parameter B(T) has the very simple meaning that it is inversely proportional to the compressibility κ at constant temperature and zero pressure: κ(0,T) = –[1/V(0,T)](dV/dP) = C/B(T)

(2)

The B(T) function is usually given by: B(T) = B0 exp[–B1(T-273.15)]

(3)

but, sometimes a polynomial expression is used: B(T) = b0 + b1(T-273.15) + b2(T-273.15)2

(4)

The zero-pressure isobar V(0,T) is usually given by: V(0,T) = A0 + A1(T-273.15) + A2(T-273.15)2

(5)

where A0, A1, A2 are specific constants for a given polymer (the expression T-273.15 is used because fitting to the zero-pressure isobar is usually done in terms of Celsius temperature). Other forms for V(0,T) are also found in the literature, such as V(0,T) = A3 exp[A4(T-273.15)]

(6)

V(0,T) = A5 exp(A6T1.5)

(7)

The Tait equation is particularly useful to calculate derivative quantities, such as the isothermal compressibility and the thermal expansivity coefficients. The isothermal compressibility κ(P,T) is derived from equation (1) as: κ(P,T) = –(1/V)(dV/dP) = 1/{[P + B(T)][1/C - ln(1 + P/B(T))]} (8) and the thermal expansivity α(P,T) as: α(P,T) = (1/V)(dV/dT) = α(0,T) – PB1κ(P,T)

(9)

where α(0,T) represents the thermal expansivity at zero (atmospheric) pressure and is calculated from any suitable fit for the zero-pressure volume, such as equations (5) through (7) above. Because polymer melt PVT-behavior depends only slightly on polymer molar mass above the oligomeric region, usually no information is given in the original literature for the average molar mass of the polymers. Table 1 summarizes the polymers or copolymers considered here and the experimental ranges of pressure and temperature over which data are available. In Table 2 the Tait-equation functions, with parameters obtained from the fit, are given for 90 polymer or copolymer melts.

References 1. Zoller, P., J. Appl. Polym. Sci., 23, 1051-1056, 1979. 2. Starkweather, H. W., Jones, G. A., and Zoller, P., J. Polym. Sci., Pt. B Polym. Phys., 26, 257-266,1988. 3. Fakhreddine, Y. A., and Zoller, P., J. Polym. Sci., Pt. B Polym. Phys., 29, 1141-1146, 1991. 4. Rodgers, P. A., J. Appl. Polym. Sci., 48, 1061-1080, 1993. 5. Rodgers, P. A., J. Appl. Polym. Sci., 48, 2075-2083, 1993. 6. Yi, Y. X., and Zoller, P., J. Polym. Sci., Pt. B Polym. Phys., 31, 779-788, 1993. 7. Callaghan, T. A., and Paul, D. R., Macromolecules, 26, 2439–2450, 1993. 8. Wang, Y. Z., Hsieh, K. H., Chen, L. W.,and Tseng, H. C., J. Appl. Polym. Sci., 53, 1191-1201, 1994. 9. Privalko, V. P., Arbuzova, A. P., Korskanov, V. V., and Zagdanskaya, N. E., Polym. Intern., 35, 161-169, 1994. 10. Sachdev, V. K., Yashi, U., and Jain, R. K., J. Polym. Sci., Pt. B Polym. Phys., 36, 841-850, 1998.

where A3 and A4 or A5 and A6 are again specific constants for a given polymer.

13-14

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Pressure-Volume-Temperature Relationship for Polymer Melts

13-15

TABLE 1. Names of the Polymers, Abbreviation Used, and Range of Experimental Data Applied in the Determination

of the Equation Constants

Polymer Ethylene/propylene copolymer (50 wt%) Ethylene/vinyl acetate copolymer 18 wt% vinyl acetate 25 wt% vinyl acetate 28 wt% vinyl acetate 40 wt% vinyl acetate Polyamide-6 Polyamide-11 Polyamide-66 cis-1,4-Polybutadiene Polybutadiene, 8% 1,2-content Polybutadiene, 24% 1,2-content Polybutadiene, 40% 1,2-content Polybutadiene, 50% 1,2-content Polybutadiene, 87% 1,2-content Poly(1-butene), isotactic Poly(butyl methacrylate) Poly(butylene terephthalate) Poly(ε-caprolactone) Polycarbonate-bisphenol-A Polycarbonate-bisphenol-chloral Polycarbonate-hexafluorobisphenol-A Polycarbonate-tetramethylbisphenol-A Poly(cyclohexyl methacrylate) Poly(2,5-dimethylphenylene oxide) Poly(dimethyl siloxane) Poly(dimethyl siloxane) Mn = 1000 Poly(dimethyl siloxane) Mn = 4000 Poly(dimethyl siloxane) Mn = 6000 Poly(epichlorohydrin) Poly(ether ether ketone) Poly(ethyl acrylate) Poly(ethyl methacrylate) Polyethylene, high density Polyethylene, linear Polyethylene, linear, high MW Polyethylene, branched Polyethylene, low density Polyethylene, low density, type A Polyethylene, low density, type B Polyethylene, low density, type C Poly(ethylene oxide) Poly(ethylene terephthalate) Poly(4-hexylstyrene) Polyisobutylene Polyisoprene, 8% 3,4-content Polyisoprene, 14% 3,4-content Polyisoprene, 41% 3,4-content Polyisoprene, 56% 3,4-content Poly(methyl acrylate) Poly(methyl methacrylate) Poly(4-methyl-1-pentene) Poly(α-methylstyrene) Poly(o-methylstyrene) Polyoxymethylene Phenoxya Polysulfoneb Polyarylatec Polypropylene, atactic

S13_05.indd 15

EP50

Symbol

EVA18 EVA25 EVA28 EVA40 PA6 PA11 PA66 cPBD PBD-8 PBD-24 PBD-40 PBD-50 PBD-87 iPB PnBMA PBT PCL PC BCPC HFPC TMPC PcHMA PPO PDMS PDMS-10 PDMS-40 PDMS-60 PECH PEEK PEA PEMA HDPE LPE HMLPE BPE LDPE LDPE-A LDPE-B LDPE-C PEO PET P4HS PIB PI-8 PI-14 PI-41 PI-56 PMA PMMA P4MP PαMS PoMS POM PH PSF PAr aPP

T/K 413-523

P/MPa 0.1-63

Ref. 4

385-491 367-506 367-508 348-508 509-569 478-542 519-571 277-328 298-473 298-473 298-473 298-473 298-473 406-519 307-473 508-576 373-421 424-613 428-557 432-553 491-563 396-471 473-593 298-343 304-420 298-418 291-423 333-413 619-671 310-490 386-434 413-476 415-473 410-473 398-471 394-448 385-498 385-498 385-498 361-497 547-615 303-403 326-383 298-473 298-473 298-473 298-473 310-493 387-432 514-592 473-533 412-471 463-493 341-573 475-644 450-583 353-393

0.1-177 0.1-177 0.1-177 0.1-177 0.1-196 0.1-200 0.1-196 0.1-284 0.1-200 0.1-200 0.1-200 0.1-200 0.1-200 0.1-196 0.1-200 0.1-200 0.1-200 0.1-177 0.1-200 0.1-200 0.1-160 0.1-200 0.1-177 0.1-100 0.1-250 0.1-250 0.1-250 0.1-200 0.1-200 0.1-196 0.1-196 0.1-196 0.1-200 0.1-200 0.1-200 0.1-196 0.1-196 0.1-196 0.1-196 0.1- 68 0.1-196 30-100 0.1-100 0.1-200 0.1-200 0.1-200 0.1-200 0.1-196 0.1-200 0.1-196 0.1-170 0.1-180 0.1-196 0.1-177 0.1-196 0.1-177 0.1-100

4 4 4 4 4 5 4 4 6 6 6 6 6 4 4 3 4 4 4 4 4 4 4 4 10 10 10 4 4 4 4 4 4 4 4 4 1 1 1 4 4 4 4 6 6 6 6 4 4 4 7 4 2 4 4 4 4

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13-16 Polymer Polypropylene, isotactic Polystyrene Poly(tetrafluoroethylene) Poly(tetrahydrofuran) Poly(vinyl acetate) Poly(vinyl chloride) Poly(vinyl methyl ether) Poly(vinylidene fluoride) Styrene/acrylonitrile copolymer 2.7 wt% acrylonitrile 5.7 wt% acrylonitrile 15.3 wt% acrylonitrile 18.0 wt% acrylonitrile 40 wt% acrylonitrile 70 wt% acrylonitrile Styrene/butadiene copolymer 10 wt% styrene 23.5 wt% styrene 60 wt% styrene 85 wt% styrene Styrene/methyl methacrylate copolymer 20 wt% methyl methacrylate 60 wt% methyl methacrylate N-Vinylcarbazole/4-ethylstyrene copolymer 50 mol% ethylstyrene N-Vinylcarbazole/4-hexylstyrene copolymer 80 mol% hexylstyrene 67 mol% hexylstyrene 60 mol% hexylstyrene 50 mol% hexylstyrene 40 mol% hexylstyrene 33 mol% hexylstyrene 20 mol% hexylstyrene N-Vinylcarbazole/4-octylstyrene copolymer 50 mol% octylstyrene N-Vinylcarbazole/4-pentylstyrene copolymer 50 mol% pentylstyrene a b c

S13_05.indd 16

Pressure-Volume-Temperature Relationship for Polymer Melts Symbol iPP PS PTFE PTHF PVAc PVC PVME PVdF

T/K 443-570 388-469 603-645 335-439 308-373 373-423 303-471 451-521

P/MPa 0.1-196 0.1-200 0.1- 39 0.1- 78 0.1- 80 0.1-200 0.1-200 0.1-200

Ref. 4 4 4 4 4 4 4 5

SAN3 SAN6 SAN15 SAN18 SAN40 SAN70

378-539 370-540 405-531 377-528 373-543 373-544

0.1-200 0.1-200 0.1-200 0.1-200 0.1-200 0.1-200

4 4 4 4 4 4

SBR10 SBR23 SBR60 SBR85

393-533 393-533 393-533 393-533

0.1-196 0.1-196 0.1-196 0.1-196

8 8 8 8

SMMA20 SMMA60

383-543 383-543

0.1-200 0.1-200

4 4

VCES50

393-443

30-100

VCHS80 VCHS67 VCHS60 VCHS50 VCHS40 VCHS33 VCHS20

313-423 333-423 383-453 373-443 423-493 463-523 473-523

30-100 30-100 30-100 30-100 30-100 30-100 30-100

9 9 9 9 9 9 9

VCOS50

403-453

30-100

VCPS50

383-443

30-100

Phenoxy = Poly(oxy-2-hydroxytrimethyleneoxy-1,4-phenyleneisopropylidene-1,4-phenylene) Polysulfone = Poly(oxy-1,4-phenylenesulfonyl-1,4-phenyleneoxy-1,4-phenyleneisopropylidene-1,4-phenylene) Polyarylate = Poly(oxyterephthaloyl/isophthaloyl T/I=50/50)oxy-1,4-phenyleneisopropylidene-1,4-phenylene

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Pressure-Volume-Temperature Relationship for Polymer Melts

13-17

TABLE 2. Tait Equation Parameter Functions for Polymer Melts

S13_05.indd 17

Polymer EP50 EVA18 EVA25 EVA28 EVA40 PA6 PA11 PA66 cPBD PBD-8 PBD-24 PBD-40 PBD-50 PBD-87 iPB PnBMA PBT PCL PC BCPC HFPC TMPC PcHMA PPO PDMS PDMS-10 PDMS-40 PDMS-60 PECH PEEK PEA PEMA HDPE LPE HMLPE BPE LDPE LDPE-A LDPE-B LDPE-C PEO PET P4HS PIB PI-8 PI-14 PI-41 PI-56 PMA PMMA P4MP

V(0,T)/cm3g–1 1.2291 + 5.799·10–5(T–273.15) + 1.964·10–6(T–273.15)2 1.02391 exp(2.173·10–5T1.5) 1.00416 exp(2.244·10–5T1.5) 1.00832 exp(2.241·10–5T1.5) 1.06332 exp(2.288·10–5T1.5) 0.7597 exp[4.701·10–4(T–273.15)] 0.9581 exp[6.664·10–4(T–273.15)] 0.7657 exp[6.600·10–4(T–273.15)] 1.0970 exp[6.600·10–4(T–273.15)] 1.1004 + 6.718·10–4(T–273.15) + 6.584·10–7(T–273.15)2 1.1049 + 6.489·10–4(T–273.15) + 7.099·10–7(T–273.15)2 1.1013 + 6.593·10–4(T–273.15) + 5.776·10–7(T–273.15)2 1.1037 + 5.955·10–4(T–273.15) + 7.789·10–7(T–273.15)2 1.1094 + 6.729·10–4(T–273.15) + 4.470·10–7(T–273.15)2 1.1417 exp[6.751·10–4(T–273.15)] 0.9341 + 5.5254·10–4(T–273.15) + 6.5803·10–6(T–273.15)2 + 1.5691·10–10(T–273.15)3 0.9640 – 1.017·10–3(T–273.15) + 3.065·10–6(T–273.15)2 0.9049 exp[6.392·10–4(T–273.15)] 0.73565 exp(1.859·10–5T1.5) 0.6737 + 3.634·10–4(T–273.15) + 2.370·10–7(T–273.15)2 0.6111 + 4.898·10–4(T–273.15) + 1.730·10–7(T–273.15)2 0.8497 + 5.073·10–4(T–273.15) + 3.832·10–7(T–273.15)2 0.8793 + 4.0504·10–4(T–273.15) + 7.774·10–7(T–273.15)2 – 7.7534·10–10(T–273.15)3 0.78075 exp(2.151·10–5T1.5) 1.0079 exp[9.121·10–4(T–273.15)] 0.8343 + 5.991·10–4(T–273.15) + 5.734·10–7(T–273.15)2 0.8018 + 7.072·10–4(T–273.15) + 3.635·10–7(T–273.15)2 0.8146 + 5.578·10–4(T–273.15) + 5.774·10–7(T–273.15)2 0.7216 exp[5.825·10–4(T–273.15)] 0.7158 exp[6.690·10–4(T–273.15)] 0.8756 exp[7.241·10–4(T–273.15)] 0.8614 exp[7.468·10–4(T–273.15)] 1.1595 + 8.0394·10–4(T–273.15) 0.9172 exp[7.806·10–4(T–273.15)] 0.8992 exp[8.502·10–4(T–273.15)] 0.9399 exp[7.341·10–4(T–273.15)] 1.1944 + 2.841·10–4(T–273.15) + 1.872·10–6(T–273.15)2 1.1484 exp[6.950·10–4(T–273.15)] 1.1524 exp[6.700·10–4(T–273.15)] 1.1516 exp[6.730·10–4(T–273.15)] 0.8766 exp[7.087·10–4(T–273.15)] 0.6883 + 5.90·10–4(T–273.15) 0.8251 + 6.77·10–4T 1.0750 exp[5.651·10–4(T–273.15)] 1.1030 + 6.488·10–4(T–273.15) + 5.125·10–7(T–273.15)2 1.0943 + 6.293·10–4(T–273.15) + 6.231·10–7(T–273.15)2 1.0951 + 6.188·10–4(T–273.15) + 6.629·10–7(T–273.15)2 1.0957 + 6.655·10–4(T–273.15) + 5.661·10–7(T–273.15)2 0.8365 exp[6.795·10–4(T–273.15)] 0.8254 + 2.8383·10–4(T–273.15) + 7.792·10–7(T–273.15)2 1.4075 – 9.095·10–4(T–273.15) + 3.497·10–6(T–273.15)2

PαMS PoMS POM PH PSF PAr aPP iPP

0.89365 + 3.4864·10–4(T–273.15) + 5.0184·10–7(T–273.15)2 0.9396 exp[5.306·10–4(T–273.15)] 0.7484 exp[6.770·10–4(T–273.15)] 0.76644 exp(1.921·10–5T1.5) 0.7644 + 3.419·10–4(T–273.15) + 3.126·10–7(T–273.15)2 0.73381 exp(1.626·10–5T1.5) 1.1841 – 1.091·10–4(T–273.15) + 5.286·10–6(T–273.15)2 1.1606 exp[6.700·10–4(T–273.15)]

B(T)/MPa 487.0 exp[–8.103·10–3(T–273.15)] 188.2 exp[–4.537·10–3(T–273.15)] 184.4 exp[–4.734·10–3(T–273.15)] 183.5 exp[–4.457·10–3(T–273.15)] 205.1 exp[–4.989·10–3(T–273.15)] 376.7 exp[–4.660·10–3(T–273.15)] 254.7 exp[–4.178·10–3(T–273.15)] 316.4 exp[–5.040·10–3(T–273.15)] 177.7 exp[–3.593·10–3(T–273.15)] 200.0 exp[–4.606·10–3(T–273.15)] 193.0 exp[–4.519·10–3(T–273.15)] 188.0 exp[–4.437·10–3(T–273.15)] 183.0 exp[–4.425·10–3(T–273.15)] 175.0 exp[–4.538·10–3(T–273.15)] 167.5 exp[–4.533·10–3(T–273.15)] 226.7 exp[–5.344·10–3(T–273.15)] 263.0 exp[–3.444·10–3(T–273.15)] 189.0 exp[–3.931·10–3(T–273.15)] 310.0 exp[–4.078·10–3(T–273.15)] 363.4 exp[–4.921·10–3(T–273.15)] 236.6 exp[–5.156·10–3(T–273.15)] 231.4 exp[–4.242·10–3(T–273.15)] 295.2 exp[–5.220·10–3(T–273.15)] 227.8 exp[–4.290·10–3(T–273.15)] 89.4 exp[–5.701·10–3(T–273.15)] 542.63 exp[–6.69·10–3(T–273.15)] 482.73 exp[–6.09·10–3(T–273.15)] 482.73 exp[–6.09·10–3(T–273.15)] 238.3 exp[–4.171·10–3(T–273.15)] 388.0 exp[–4.124·10–3(T–273.15)] 193.2 exp[–4.839·10–3(T–273.15)] 260.9 exp[–5.356·10–3(T–273.15)] 179.9 exp[–4.739·10–3(T–273.15)] 176.7 exp[–4.661·10–3(T–273.15)] 168.3 exp[–4.292·10–3(T–273.15)] 177.1 exp[–4.699·10–3(T–273.15)] 202.2 exp[–5.243·10–3(T–273.15)] 192.9 exp[–4.701·10–3(T–273.15)] 196.6 exp[–4.601·10–3(T–273.15)] 186.7 exp[–4.391·10–3(T–273.15)] 207.7 exp[–3.947·10–3(T–273.15)] 369.7 exp[–4.150·10–3(T–273.15)] 103.1 exp[–2.417·10–3(T–273.15)] 200.3 exp[–4.329·10–3(T–273.15)] 188.0 exp[–4.541·10–3(T–273.15)] 202.0 exp[–4.653·10–3(T–273.15)] 199.0 exp[–4.622·10–3(T–273.15)] 200.0 exp[–4.644·10–3(T–273.15)] 235.8 exp[–4.493·10–3(T–273.15)] 287.5 exp[–4.146·10–3(T–273.15)] 37.67 + 0.2134(T–273.15)] – 7.0445·10–4(T–273.15)2 297.7 exp[–4.074·10–3(T–273.15)] 261.9 exp[–4.114·10–3(T–273.15)] 305.6 exp[–4.326·10–3(T–273.15)] 359.9 exp[–4.378·10–3(T–273.15)] 365.9 exp[–3.757·10–3(T–273.15)] 296.9 exp[–3.375·10–3(T–273.15)] 162.1 exp[–6.604·10–3(T–273.15)] 149.1 exp[–4.177·10–3(T–273.15)]

5/2/05 1:36:57 PM

Pressure-Volume-Temperature Relationship for Polymer Melts

13-18 Polymer

PS PTFE PTHF PVAc PVC PVME PVdF SAN3 SAN6 SAN15 SAN18 SAN40 SAN70 SBR10 SBR23 SBR60 SBR85 SMMA20 SMMA60 VCES50 VCHS80 VCHS67 VCHS60 VCHS50 VCHS40 VCHS33 VCHS20 VCOS50 VCPS50

S13_05.indd 18

V(0,T)/cm3g–1

0.9287 exp[5.131·10 (T–273.15)] 0.3200 + 9.5862·10–4(T–273.15) 1.0043 exp[6.691·10–4(T–273.15)] 0.82496 + 5.820·10–4(T–273.15) + 2.940·10–7(T–273.15)2 0.7196 + 5.581·10–5(T–273.15) + 1.468·10–6(T–273.15)2 0.9585 exp[6.653·10–4(T–273.15)] 0.5790 exp[8.051·10–4(T–273.15)] 0.9233 + 3.936·10–4(T–273.15) + 5.685·10–7(T–273.15)2 0.9211 + 4.370·10–4(T–273.15) + 5.846·10–7(T–273.15)2 0.9044 + 4.207·10–4(T–273.15) + 4.077·10–7(T–273.15)2 0.9016 + 4.036·10–4(T–273.15) + 4.206·10–7(T–273.15)2 0.8871 + 3.406·10–4(T–273.15) + 4.938·10–7(T–273.15)2 0.8528 + 3.616·10–4(T–273.15) + 2.634·10–7(T–273.15)2 0.9053 exp(2.437·10–5T1.5) 0.8986 exp(2.317·10–5T1.5) 0.8812 exp(2.031·10–5T1.5) 0.8704 exp(1.846·10–5T1.5) 0.9063 + 3.570·10–4(T–273.15) + 6.532·10–7(T–273.15)2 0.8610 + 3.350·10–4(T–273.15) + 6.980·10–7(T–273.15)2 0.6676 + 6.63·10–4T 0.7753 + 6.17·10–4T 0.8028 + 6.50·10–4T 0.8213 + 6.23·10–4T 0.7827 + 5.05·10–4T 0.7805 + 4.92·10–4T 0.7710 + 4.86·10–4T 0.6416 + 5.42·10–4T 0.7081 + 7.40·10–4T 0.7814 + 4.36·10–4T –4

B(T)/MPa 216.9 exp[–3.319·10–3(T–273.15)] 425.2 exp[–9.380·10–3(T–273.15)] 178.6 exp[–4.223·10–3(T–273.15)] 204.9 exp[–4.346·10–3(T–273.15)] 294.2 exp[–5.321·10–3(T–273.15)] 215.8 exp[–4.588·10–3(T–273.15)] 244.0 exp[–5.210·10–3(T–273.15)] 239.8 exp[–4.376·10–3(T–273.15)] 226.9 exp[–4.286·10–3(T–273.15)] 238.4 exp[–3.943·10–3(T–273.15)] 240.4 exp[–3.858·10–3(T –273.15)] 289.3 exp[–4.431·10–3(T–273.15)] 335.4 exp[–3.923·10–3(T–273.15)] 530.3 exp[–3.99·10–3(T–273.15)] 551.6 exp[–4.17·10–3(T–273.15)] 486.0 exp[–4.34·10–3(T–273.15)] 356.7 exp[–4.24·10–3(T–273.15)] 232.0 exp[–4.143·10–3(T–273.15)] 261.0 exp[–4.611·10–3(T–273.15)] 5281.7 exp[–9.264·10–3(T–273.15)] 247.6 exp[–2.604·10–3(T–273.15)] 581.7 exp[–4.553·10–3(T–273.15)] 229.1 exp[–2.133·10–3(T–273.15)] 136.0 exp[–1.083·10–3(T–273.15)] 155.0 exp[–1.605·10–3(T–273.15)] 460.4 exp[–3.453·10–3(T–273.15)] 489.8 exp[–3.193·10–3(T–273.15)] 666.5 exp[–4.503·10–3(T–273.15)] 880.1 exp[–4.393·10–3(T–273.15)]

5/2/05 1:36:58 PM

UPPER CRITICAL (UCST) AND LOWER CRITICAL (LCST) SOLUTION TEMPERATURES OF BINAR Y POLYMER SOLUTIONS Christian Wohlfarth Liquid-liquid demixing in solutions of polymers in low molar mass solvents is not a rare phenomenon. Demixing depends on concentration, temperature, pressure, molar mass and molar mass distribution function of the polymer, chain branching and end groups of the polymer, the chemical nature of the solvent, isotope substitution in solvents or polymers, chemical composition of copolymers and its distributions, and other variables. Phase diagrams of polymer solutions can therefore show a quite complicated behavior when they have to be considered in detail (see Ref. 1a). Polymer solutions can undergo demixing when cooling a homogeneous solution as well as when heating such a solution. The corresponding cloud-point curves show a maximum (UCST behavior) or a minimum (LCST behavior). For common polymer solutions, the LCST region is at higher temperatures (in many cases near the critical temperature of the solvent) than the UCST region. The temperature range between both extrema provides the essential information where the one-phase region of a polymer solution can be found. In the case of monodisperse polymers the extrema are equal to the critical points. However, in the case of polydisperse polymers with distribution functions, these extrema are threshold temperatures whereas the critical point shifts to higher concentrations on the shoulder of the cloud-point curve. Usually, the critical concentration is much more strongly influenced than the critical temperature. Thus, the table below does not distinguish between threshold and critical temperatures. UCST and LCST values depend somewhat on pressure. LCST values in the table are usually given at the vapor pressure of the solvent at this temperature. UCST values are measured in most cases at normal pressure; data at higher pressures are neglected here. The interested reader can find such information, for example, in Refs. 76, 84, 104, 157, 165, 177, 185-187, or 192.

1 1È 1 ˆ˘ Ê 1 = Í1 + const.Á - ˜˙ Ë Tcrit q Î r 2r ¯ ˚

(1)

where r denotes the number of segments of a polymer (being proportional to the degree of polymerization or to the molar mass or molar volume of the polymer). Extrapolation to r Æ •, i.e., to infinite molar mass, leads to the value of the q-temperature. This qtemperature is the highest temperature for UCST behavior or the lowest temperature for LCST behavior and a given polymer/solvent pair. In the case of polydisperse polymers, the segment number in equation (1) is to be replaced by its weight average, rw (related to Mw). The constant in equation (1) reflects further thermodynamic properties of the given polymer/solvent pair, but should not depend on molar mass. A detailed discussion can be found in Ref. 1b. The printed table in the Handbook provides only one data line for a given polymer/solvent pair and does not show the molar mass dependence of UCST or LCST data. The entire table with all data at different molar masses for many of the systems is given in the electronic version, however. Nevertheless, the necessary molar mass information for a system is always provided in the table by the corresponding number average, Mn, mass average, Mw, or viscosity average, Mh, values of the polymer as given in the original sources. Mh/g mol-1

Solvent

(18% Acrylonitrile)

840000

Ethyl acetate

427

220

(26% Acrylonitrile)

1000000

Ethyl acetate

412

220

100000

Ethyl acetate

393

220

453

159

Polymer

Mn/g mol-1 Mw/g mol-1

However, UCST and LCST values of a given polymer/solvent pair depend strongly on the molar mass of the polymer. In the case of monodisperse polymers, this dependency can be described in good approximation by the so-called Shultz-Flory plot (see Refs. 6 and 8):

UCST/K LCST/K Ref

Acrylonitrile/butadiene copolymer

Butadiene/a-methylstyrene copolymer (10% a-Methylstyrene)

387

Carbon monoxide/ethylene copolymer (1:1, alternating) 1000000 Cellulose diacetate

1,1,1,3,3,3-Hexafluoro-2propanol 120000

59900

Benzyl alcohol

372

2-Butanone

279.7

471.5

111

2-Propanone

216.2

438.2

750000

N,N-Dimethylformamide

262

399

106

750000

Tetrahydrofuran

363

106

182

148

75500

59300

Cellulose diacetate/styrene graft copolymer (77.4 wt% grafted polystyrene)

Cellulose nitrate (13.3 wt% N) unknown

13-19

2-Propanone

328

13-20

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binar y Polymer Solutions

Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

Solvent

UCST/K LCST/K Ref

20000

Benzyl alcohol

322

2-Propanone

290.0

infinite

N,N-Dimethylformamide

413

infinite

3-Phenyl-1-propanol

321

310.69

Tetradecafluorohexane

332.59

195

Cellulose triacetate 100500

86 472.0

Cellulose tricaprylate

Decamethyltetrasiloxane N,N-Dimethylacrylamide/2-butoxyethyl acrylate copolymer (50 wt% 2-butoxyethyl acrylate) Water

<273.2

164

(15 wt% Butyl acrylate)

Water

346.2

164

(20 wt% Butyl acrylate)

Water

323.2

164

(30 wt% Butyl acrylate)

Water

294.2

164

(35 wt% Butyl acrylate)

Water

281.2

164

(50 wt% 2-Ethoxyethyl acrylate)

Water

319.2

164

(75 wt% 2-Ethoxyethyl acrylate)

Water

285.2

164

N,N-Dimethylacrylamide/butyl acrylate copolymer

N,N-Dimethylacrylamide/2-ethoxyethyl acrylate copolymer

N,N-Dimethylacrylamide/ethyl acrylate copolymer (25 wt% Ethyl acrylate)

Water

347.2

164

(30 wt% Ethyl acrylate)

Water

334.2

164

(50 wt% Ethyl acrylate)

Water

287.2

164

(55 wt% Ethyl acrylate)

Water

<273.2

164

(38 mol% 2-Methoxyethyl acrylate)

Water

353

184

(45 mol% 2-Methoxyethyl acrylate)

Water

333

184

(55 mol% 2-Methoxyethyl acrylate)

Water

315

184

(68 mol% 2-Methoxyethyl acrylate)

Water

305

184

(82 mol% 2-Methoxyethyl acrylate)

Water

288

184

(92 mol% 2-Methoxyethyl acrylate)

Water

283

184

(30 wt% Methyl acrylate)

Water

371.2

164

(40 wt% Methyl acrylate)

Water

338.2

164

(50 wt% Methyl acrylate)

Water

314.2

164

(55 wt% Methyl acrylate)

Water

294.2

164

(60 wt% Methyl acrylate)

Water

279.2

164

(70 wt% Methyl acrylate)

Water

<273.2

164

(20 wt% Propyl acrylate)

Water

353.2

164

(30 wt% Propyl acrylate)

Water

337.2

164

(40 wt% Propyl acrylate)

Water

294.2

164

(50 wt% Propyl acrylate)

Water

281.2

164

N,N-Dimethylacrylamide/2-methoxyethyl acrylate copolymer

N,N-Dimethylacrylamide/methyl acrylate copolymer

N,N-Dimethylacrylamide/propyl acrylate copolymer

Dimethylsiloxane/methylphenylsiloxane copolymer (15 wt% methylphenylsiloxane) 9100

41200

Anisole

291.45

198

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binar y Polymer Solutions Polymer

Mn/g mol-1 Mw/g mol-1 9100

Mh/g mol-1

41200

13-21

Solvent

UCST/K LCST/K Ref

2-Propanone

282.45

198

Ethylene/propylene copolymer (33 mol% ethylene) 145000

Cyclohexane

534

101

145000

Cyclopentane

490

101

145000

2,2-Dimethylbutane

428

101

145000

2,3-Dimethylbutane

452

101

145000

3,4-Dimethylhexane

541

101

145000

2,2-Dimethylpentane

472

101

145000

2,3-Dimethylpentane

500

101

145000

2,4-Dimethylpentane

464

101

145000

3-Ethylpentane

511

101

145000

Heptane

502

101

145000

Hexane

455

101

145000

2-Methylbutane

396

101

145000

Methylcyclohexane

558

101

145000

Methylcyclopentane

512

101

145000

2-Methylhexane

486

101

145000

Nonane

558

101

145000

Octane

528

101

145000

Pentane

409

101

145000

2,2,4,4-Tetramethylpentane

539

101

145000

2,2,3-Trimethylbutane

500

101

145000

2,2,4-Trimethylpentane

503

101

Ethylene/propylene copolymer (43 mol% ethylene) 70000

140000

Hexane

436

127

70000

140000

2-Methylpentane

474

127

70000

140000

Pentane

441

127

154000

2,2-Dimethylbutane

407

101

154000

2,3-Dimethylbutane

437

101

154000

2,2-Dimethylpentane

453

101

154000

2,3-Dimethylpentane

488

101

154000

2,4-Dimethylpentane

445

101

154000

3-Ethylpentane

500

101

154000

Heptane

493

101

154000

Hexane

443

101

154000

Pentane

395

101

154000

2,2,3-Trimethylbutane

488

101

154000

2,3,4-Trimethylhexane

565

101

154000

2,2,4-Trimethylpentane

484

101

236000

Cyclohexane

526

101

236000

Cyclopentane

481

101

236000

2,3-Dimethylbutane

429

101

236000

3,4-Dimethylhexane

530

101

236000

2,2-Dimethylpentane

444

101

236000

2,3-Dimethylpentane

482

101

236000

2,4-Dimethylpentane

434

101

Ethylene/propylene copolymer (53 mol% ethylene)

Ethylene/propylene copolymer (63 mol% ethylene)

13-22

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binar y Polymer Solutions

Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

Solvent

236000

3-Ethylpentane

492

101

236000

Heptane

485

101

236000

Hexane

436

101

236000

2-Methylbutane

348

101

236000

Methylcyclopentane

498

101

236000

Nonane

547

101

236000

Octane

512

101

236000

Pentane

387

101

236000

2,2,4,4-Tetramethylpentane

528

101

236000

2,2,3-Trimethylbutane

479

101

236000

2,2,4-Trimethylpentane

479

101

109000

2,2-Dimethylpentane

431

101

109000

2,4-Dimethylpentane

425

101

109000

Heptane

475

101

109000

Hexane

427

101

109000

Nonane

542

101

109000

Octane

509

101

109000

Pentane

378

101

109000

2,2,4,4-Tetramethylpentane

523

101

109000

2,2,4-Trimethylpentane

469

101

195000

Cyclohexane

522

101

195000

Cyclopentane

474

101

195000

2,2-Dimethylbutane

381

101

195000

2,3-Dimethylbutane

413

101

195000

2,4-Dimethylhexane

478

101

195000

2,5-Dimethylhexane

466

101

195000

3,4-Dimethylhexane

522

101

195000

2,2-Dimethylpentane

425

101

195000

2,3-Dimethylpentane

471

101

195000

2,4-Dimethylpentane

420

101

195000

3-Ethylpentane

478

101

195000

Heptane

468

101

195000

Hexane

425

101

195000

2-Methylbutane

327

101

195000

Methylcyclohexane

541

101

195000

Methylcyclopentane

493

101

195000

2-Methylhexane

453

101

195000

3-Methylhexane

459

101

195000

Nonane

540

101

195000

Octane

506

101

195000

Pentane

370

101

195000

2,2,4,4-Tetramethylpentane

519

101

195000

2,2,3-Trimethylbutane

461

101

195000

2,2,4-Trimethylpentane

460

101

UCST/K LCST/K Ref

Ethylene/propylene copolymer (75 mol% ethylene)

Ethylene/propylene copolymer (81 mol% ethylene)

Ethylene/vinyl acetate copolymer ( 2.3 wt% Vinyl acetate)

52000

465000

Diphenyl ether

404.2

143

( 4.0 wt% Vinyl acetate)

47000

280000

Diphenyl ether

392.5

143

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Mh/g mol-1

13-23

Polymer

Mn/g mol-1 Mw/g mol-1

Solvent

UCST/K LCST/K Ref

( 7.1 wt% Vinyl acetate)

34000

460000

Diphenyl ether

378.2

143

( 9.5 wt% Vinyl acetate)

53000

350000

Diphenyl ether

367.3

143

( 9.7 wt% Vinyl acetate)

55000

490000

Diphenyl ether

370.8

143

(12.1 wt% Vinyl acetate)

66000

300000

Diphenyl ether

360.4

143

(42.6 mol% Vinyl acetate)

14800

41500

Methyl acetate

307.0

130

Ethylene/vinyl alcohol copolymer (87.2 mol% Vinyl alcohol)

infinite

Water

463.55

285.65

(88.9 mol% Vinyl alcohol)

infinite

Water

449.15

290.75

(91.0 mol% Vinyl alcohol)

infinite

Water

428.45

302.95

(94.1 mol% Vinyl alcohol)

infinite

Water

389.25

324.45

Ethylene oxide/propylene oxide copolymer (20.0 mol% Ethylene oxide)

3400

Water

303

211

(27.0 mol% Ethylene oxide)

3000

Water

309

210

(30.0 mol% Ethylene oxide)

5400

Water

313

211

(38.5 mol% Ethylene oxide)

5000

Water

309

210

(50.0 mol% Ethylene oxide)

3900

Water

323

211

(58.8 mol% Ethylene oxide)

3000

Water

326.65

210 153

(72.4 mol% Ethylene oxide)

36000

Water

333

(79.5 mol% Ethylene oxide)

30800

Water

345

153

(86.6 mol% Ethylene oxide)

30100

Water

355.5

153

Gutta Percha 194000

Propyl acetate

318.95

Hydroxypropylcellulose 75000

Water

318.45

300000

Water

331.25

3100000

Water

315.15

172

N-Isopropylacrylamide/acrylamide copolymer (15 mol% Acrylamide) (30 mol% Acrylamide)

4500000

Water

326.15

172

(45 mol% Acrylamide)

3900000

Water

347.15

172

218

N-Isopropylacrylamide/1-deoxy-1methacrylamido-D-glucitol (12.9 mol% Glucitol)

78000

170000

Water

311.3

(13.7 mol% Glucitol)

51600

110000

Water

314.9

218

(14.0 mol% Glucitol)

145000

432000

Water

307.5

218

(10.56 mol% N-Isopropylmethacrylamide)

55300

177000

Water

307.15

212

N-Isopropylacrylamide/Nisopropylmethacrylamide copolymer (30.00 mol% N-Isopropylmethacrylamide)

28800

92000

Water

309.75

212

(39.99 mol% N-Isopropylmethacrylamide)

23100

74000

Water

311.05

212

(59.89 mol% N-Isopropylmethacrylamide)

23100

74000

Water

314.65

212

(79.81 mol% N-Isopropylmethacrylamide)

16600

53000

Water

317.35

212

(89.99 mol% N-Isopropylmethacrylamide)

14700

47000

Water

318.75

212

70000

Water

324.75

80000

Water

340.15

Pentane

403

Methylcellulose (about 30 mol% methyl subsitution) Methylcellulose/hydroxypropylcellulose copolymer (25 mol% methyl, 8 mol% hydroxypropyl subsitution) Natural rubber 300000 74500

2-Pentanone

274.45

13-24

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions

Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

Phenol-formaldehyde resin (acetylated) Poly(acrylic acid)

Solvent

UCST/K LCST/K Ref

2-Ethoxyethanol

378.2

200

120000

Tetrahydrofuran

268.3

189

1070000

1500000

Water

317.15

183

667000

1000000

Water

338.15

183

714000

1000000

Water

311.15

183

1420000

1700000

Water

322.65

183

857000

1200000

Water

334.65

183

Poly[bis(2,3-dimethoxypropanoxy) phosphazene] Poly[bis(2-(2’-methoxyethoxy)ethoxy) phosphazene] Poly[bis(2,3-bis(2-methoxyethoxy) propanoxy)phosphazene] Poly[bis(2,3-bis(2-(2’-methoxyethoxy) ethoxy)propanoxy)phosphazene] Poly[bis(2,3-bis(2-(2’-(2’’-dimethoxyethoxy) ethoxy)ethoxy)propanoxy)phosphazene] Poly(1-butene) (atactic) infinite

Anisole

359.4

infinite

Toluene

356.2

Anisole

362.3

Poly(1-butene) (isotactic) infinite

530000

Cyclopentane

498

102

530000

2,2-Dimethylbutane

444

102

530000

2,5-Dimethylhexane

519

102

530000

3,4-Dimethylhexane

559

102

530000

2,3-Dimethylpentane

517

102

530000

2,4-Dimethylpentane

480

102

530000

3-Ethylpentane

523

102

530000

Heptane

509

102

Hexane

464

102

2-Methylbutane

416

102

Nonane

564

102

Octane

540

102

Pentane

421

102

2,2,3-Trimethylbutane

507

102

infinite 530000 infinite 530000 infinite 530000 Poly(butyl methacrylate) 278000

470000

1-Butanol

287.15

132

278000

470000

Decane

357.25

132

278000

470000

Ethanol

315.25

132

278000

470000

Heptane

342.55

132

278000

470000

Octane

345.80

132

278000

470000

1-Pentanol

286.30

132

278000

470000

2-Propanol

294.90

132

278000

470000

2,2,4-Trimethylpentane

347.50

132

Poly(2-chlorostyrene) infinite

Benzene

298

infinite

Benzene

infinite

2-(Butoxyethoxy)ethanol

323.25

infinite

Butyl acetate

502.4

infinite

tert-Butyl acetate

338.55

Poly(4-chlorostyrene) 274.0

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

13-25

Solvent

UCST/K LCST/K Ref

infinite

Chlorobenzene

128.8

infinite

2-(Ethoxyethoxy)ethanol

300.95

infinite

Ethyl acetate

613.2

infinite

Ethylbenzene

283.2

infinite

Ethylbenzene

258.45

271.35

infinite

Ethyl chloroacetate

infinite

Isopropyl acetate

infinite

Isopropylbenzene

332.15

infinite

Isopropyl chloroacetate

264.95

337.75

348.65

infinite

Methyl chloroacetate

infinite

Propyl acetate

infinite

Tetrachloroethene

317.55

infinite

Tetrachloromethane

323.85

infinite

Toluene

236.8

908.7

Poly(decyl methacrylate) 390000

468000

1-Butanol

304.85

113

390000

468000

1-Pentanol

278.40

113

220000

252000

2-Propanol

346.85

132

Polydimethylsiloxane (cyclic) 9810

10300

2,2-Dimethylpropane

433

133

9810

10300

Tetramethylsilane

448

133, 171

Butane

392.95

Decane

603

2,2-Dimethylpropane

428

133 30

Polydimethylsiloxane 626000 infinite 14750

16370

infinite

Dodecane

643

626000

Ethane

259.65

100000

Ethoxybenzene

341.99

53 108

infinite

Heptane

528

infinite

Hexadecane

708

infinite

Hexane

493

infinite

Octane

553

infinite

Pentane

453

203000 14750

16370

Propane

340.15

Tetramethylsilane

443

133, 171

Poly(ethyl acrylate) 48000

1-Butanol

310.05

48000

Ethanol

301.15

380000

Methanol

287.25

48000

1-Propanol

305.15

Polyethylene (branched) 8400

32000

Diphenyl ether

384.7

95, 98

24000

123000

Diphenyl ether

396.7

95, 98

65000

425000

Diphenyl ether

415.3

95, 98

Polyethylene (linear) 20000

Anisole

368.15

20000

Benzyl acetate

459.65

20000

Benzyl phenyl ether

437.15

20000

Benzyl propionate

436.15

50900

Biphenyl

383.55

61100

Butyl acetate

448

25 497

13-26

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions

Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

Solvent

UCST/K LCST/K Ref

20000

4-tert-Butylphenol

466.15

134000

Cyclohexane

20000

Cyclohexanone

134000 36700

12000

49300

472

101

563.75

1-Decanol

400.15

Dibenzyl ether

448.65

134000

3,4-Dimethylhexane

515

101

134000

2,2-Dimethylpentane

399

101

134000

2,3-Dimethylpentane

463

101

134000

2,4-Dimethylpentane

395

101 95, 98

Diphenylmethane

400.25

1-Dodecanol

49300

7900

92000

20000

610.85 405.15

141 471

101

Heptane

464.70

414.65

1-Heptanol

440.15

1-Hexanol

458.15

154

20000

2-Methoxynaphthalene

427.65

20000

3-Methylbutyl acetate

407.15

134000

Methylcyclohexane

537

101

Methylcyclopentane

488

101

Nonane

531.90

82600

20000

1-Nonanol

431.15

20000

4-Nonylphenol

410.15

36700

49300

Octane

7900

92000

1-Octanol

426.65

20000

4-Octylphenol

424.65

134000

Pentane

20000

1-Pentanol

445.15

175000

Pentyl acetate

421

502.40

91 154 24

353

101 24

528

20000

4-tert-Pentylphenol

443.65

20000

Phenetole

366.65

134000

97700

3-Ethylpentane

Hexane

134000

60400

416.2

Dodecane

36700

Diphenyl ether

218000 134000

60400

Cyclopentane Decane

82600

49300

101 24

20000

150000

36700

518 389.65

20000

97200 60400

2,2,4,4-Tetramethylpentane

513

101

Tridecane

639.30

134000

2,2,3-Trimethylbutane

444

101

134000

2,3,4-Trimethylhexane

545

101

134000

2,2,4-Trimethylpentane

495

101

Undecane

583.95

82600

135900

Poly(ethylene glycol) 8000

tert-Butyl acetate

321.2

464.2

21200

tert-Butyl acetate

353.2

431.2

6100

6200

Water

404.79

185

10457

11615

Water

394.33

205

40800

151000

Water

378.25

205

22000

31500

Water

338

222

Poly(ethylene oxide)-bpoly[bis(methoxyethoxyethoxy)phosphazene] block copolymer (about 67 mol% Ethylene oxide)

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

Solvent

13-27

UCST/K LCST/K Ref

Poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer (about 30 mol% Ethylene oxide) 4400

Water

286.65

209

52000

Diphenyl ether

411.2

95, 98

2-Butanone

302.6

135

77400

1-Butanol

337.25

233600

2-Butanol

287

233600

2-Metyl-1-propanol

342

77400

1,2,3-Propanetriol

345

77400

1-Propanol

311

Anisole

377

Polyethylethylene 48000 Poly(p-hexylstyrene) infinite Poly(2-hydroxyethyl methacrylate)

Polyisobutylene infinite

72000

Benzene

703000

Butane

264.75

Cycloheptane

572

Cyclohexane

412

Cyclooctane

637

Cyclopentane

344

Decane

535

1500000

2,2-Dimethylbutane

376

1500000

2,3-Dimethylbutane

404

infinite

2,2-Dimethylhexane

454

infinite

2,4-Dimethylhexane

458

infinite

2,5-Dimethylhexane

446

infinite

3,4-Dimethylhexane

497

infinite

2,2-Dimethylpentane

404

infinite

2,3-Dimethylpentane

451

infinite

2,4-Dimethylpentane

403

infinite

3,3-Dimethylpentane

451

infinite

Diphenyl ether

infinite

Decane

infinite

Dodecane

infinite

Ethylbenzene

infinite

Ethylcyclopentane

infinite

Ethyl heptanoate

306

infinite

Ethyl hexanoate

330

infinite

3-Ethylpentane

458

infinite

Heptane

442

72000

Hexane

428.5

6030

infinite 1500000 infinite 1500000 infinite

540.5

306

3 585 582

249

30 34 3

524

34 3 3 34

2-Methylbutane

357.85

infinite

Methylcyclohexane

526

infinite

Methylcyclopentane

478

infinite

2-Methylheptane

466

infinite

3-Methylheptane

478

infinite

2-Methylhexane

426

infinite

3-Methylhexane

446

infinite

2-Methylpentane

376

13-28

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions

Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

infinite

Solvent

UCST/K LCST/K Ref

3-Methylpentane

405

470

2-Methylpropane

387

72000

Octane

506.0

6030

Pentane

403.55

72000

Pentane

373.5

470

Propane

358

infinite

Propylcyclopentane

547

infinite

Toluene

infinite

2,2,3-Trimethylbutane

445

infinite

2,2,4-Trimethylpentane

435

780000

2,5-Dimethylhexane

474.15

140

780000

3,4-Dimethylhexane

520.15

140

780000

2,2-Dimethylpentane

445.15

140

780000

2,3-Dimethylpentane

484.15

140

780000

2,4-Dimethylpentane

442.15

140

780000

3-Methylpentane

483.15

140

780000

Heptane

488.15

140

780000

Hexane

434.15

140

780000

Nonane

541.15

140

780000

Octane

509.15

140

780000

2,2,4,4-Tetramethylpentane

518.15

140

780000

2,3,4-Trimethylhexane

548.15

140

780000

2,2,4-Trimethylpentane

471.15

140

180000

2,5-Dimethylhexane

451.15

140

180000

3,4-Dimethylhexane

521.15

140

180000

2,2-Dimethylpentane

405.15

140

180000

2,3-Dimethylpentane

460.15

140

180000

2,4-Dimethylpentane

404.15

140

180000

3-Methylpentane

473.15

140

180000

Heptane

467.15

140

180000

Hexane

407.15

140

180000

Nonane

540.15

140

180000

Octane

503.15

140

180000

2,2,4,4-Tetramethylpentane

519.15

140

180000

2,3,4-Trimethylhexane

548.15

140

infinite

Phenetole

357

260

1,4-cis-Polyisoprene

1,4-trans-Polyisoprene

Poly(N-isopropylacrylamide) 5400

14000

Water

307.45

146

146000

530000

Water

305.85

146

5500

Water

306.2

223

6030

Water

306.2

223

Water

319.95

212

Poly(N-isopropylacrylamide)-poly[(Nacetylimino)ethylene] block copolymer (80 wt% N-Isopropylacrylamide) Poly(N-isopropylacrylamide)-poly[(Nacetylimino)ethylene] graft copolymer (75 wt% N-Isopropylacrylamide) Poly(N-isopropylmethacrylamide) 6250 Poly(methyl methacrylate)

20000

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Polymer

Mn/g mol-1 Mw/g mol-1

13-29

Mh/g mol-1

Solvent

UCST/K LCST/K Ref

127000

Acetonitrile

267.15

970000

Acetonitrile

303.15

50000

1-Butanol

353.25

infinite

2-Butanone

infinite

1-Chlorobutane

320

970000

2,2-Dimethyl-3-pentanone

301.55

127000

2,4-Dimethyl-3-pentanone

280.15

264000

2-Ethoxyethanol

312.15

77000

Ethyl acetate

290

2-Ethylbutanal

264.65

3-Heptanone

307.7

126

4-Heptanone

299.95

200000

127000 infinite 970000 infinite

3-Hexanone

infinite

Methyl acetate 50000 1400000

572400

595300

infinite infinite

196 533

190

16 522

451

80 2

2-Octanone

321.15

3-Octanone

329.88

166

1-Propanol

506 349.95

2-Propanone Tetra(ethylene glycol)

264000

463

400.15

3-Pentanone 50000

200000

1-Methyl-4isopropylbenzene

482

80 2

439 390.15

80 196

400000

Toluene

225.35

50000

Trichloromethane

231.15

Tri(ethylene glycol)

407.15

196

infinite

Acetonitrile

301

infinite

2-Butanone

infinite

1-Chlorobutane

infinite

4-Heptanone

infinite

3-Hexanone

infinite

Methyl acetate

200000

264000

Poly(methyl methacrylate) (isotactic) 461

464

309

454

319

522

279

511

441

infinite

3-Pentanone

497

infinite

2-Propanone

428

Butane

388

102

Poly(4-methyl-1-pentene) (isotactic) 152000 152000

Cyclopentane

505

102

152000

2,2-Dimethylbutane

462

102

152000

2,2-Dimethylpentane

499

102

152000

2,4-Dimethylpentane

499

102

infinite

Diphenyl

467.8

infinite

Diphenyl ether

483.2

Diphenylmethane

449.8

infinite

152000

3-Ethylpentane

532

102

152000

Heptane

522

102

152000

Hexane

487

102

152000

2-Methylbutane

431

102

152000

Nonane

579

102

152000

Octane

553

102

152000

Pentane

441

102

152000

2,2,3-Trimethylbutane

521

102

13-30

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions

Polymer

Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

Solvent

UCST/K LCST/K Ref

Poly(a-methylstyrene) 58500

61400

Butyl acetate

262.05

99100

113000

Cyclohexane

293.55

26000

31200

Cyclopentane

276.7

289000

transDecahydronaphthalene

273

69500

76500

Hexyl acetate

285.05

72000

75600

Methylcyclohexane

328.9

58500

61400

Pentyl acetate

287.1

457.15

181

435.95

181

152 181 508.15

181 203

484.6

181

Poly(2-methyl-5-vinylpyridine) 600000

Butyl acetate

287.95

263000

Ethyl butyrate

319.05

335000

Ethyl propionate

293.55

275000

3-Methylbutyl acetate

314.75

335000

4-Methyl-2-pentanone

299.95

170000

2-Methylpropyl acetate

312.35

165000

Pentyl acetate

316.95

284000

Propionitrile

262.35

152000

Propyl acetate

282.65

181000

Propyl propionate

312.15

233000

Tetrahydronaphthalene

316.95

Poly(1-pentene) (isotactic) 4500000

Cyclopentane

502

102

4500000

2,2-Dimethylbutane

457

102

4500000

3,4-Dimethylhexane

>569

102

4500000

2,2-Dimethylpentane

502

102

4500000

2,3-Dimethylpentane

529

102

4500000

2,4-Dimethylpentane

493

102

4500000

3-Ethylpentane

537

102

4500000

Heptane

522

102

4500000

Hexane

482

102

4500000

2-Methylbutane

422

102

4500000

Octane

556

102

4500000

Pentane

433

102

4500000

2,2,4-Trimethylpentane

527

102

Polypropylene (atactic) infinite

Diphenyl ether

infinite

Diethyl ether

383

Heptane

511

101

Hexane

441

242000 infinite

426.5

242000

2-Methylbutane

413

101

242000

Methylcyclohexane

564

101

Pentane

397

infinite Polypropylene (isotactic) 28000

Benzyl phenyl ether

429.2

28000

Benzyl propionate

405.2

28000

1-Butanol

395.2

28000

4-tert-Butylphenol

413.2

242000

Cyclohexane

540

101

242000

Cyclopentane

495

101

28000

Dibenzyl ether

433.2

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Polymer

Mn/g mol-1 Mw/g mol-1

13-31

Mh/g mol-1

Solvent

242000

2,2-Dimethylbutane

441

101

242000

2,3-Dimethylbutane

465

101

242000

3,4-Dimethylhexane

553

101

242000

2,2-Dimethylpentane

489

101

242000

2,3-Dimethylpentane

513

101

242000

2,4-Dimethylpentane

481

101

28000

Diphenyl

388.2

28000

Diphenyl ether

395.2

28000

Diphenylmethane

389.7

242000

3-Ethylpentane

28000

4-Ethylphenol

242000

Heptane

511

101

242000

Hexane

470

101

242000

2-Methylbutane

413

28000

3-Methylbutyl benzyl ether 384.2

UCST/K LCST/K Ref

520 457.2

101 31

242000

Methylcyclohexane

564

101

242000

Methylcyclopentane

518

101

28000

4-Methylphenol

479.2

28000

2-Methyl-1-propanol

395.2

242000

Nonane

571

101

242000

Octane

542

101

28000

4-Octylphenol

379.2

28000

4-Isooctylphenol

383.2

242000

Pentane

422

101

242000

2,2,4,4-Tetramethylpentane

548

101

242000

2,2,3-Trimethylbutane

511

101

242000

2,3,4-Trimethylhexane

585

101

242000

2,2,4-Trimethylpentane

510

101

31 31

Poly(propylene glycol) 1000

Hexane

575

Water

288.15 318.2

88 65

Benzene

538.7

Polystyrene 34900

37000 62600

3700

4000

Butanedioic acid dimethyl ester

335.15

1-Butanol

383.45

154

91700

97200

2-Butanone

448.8

545500

600000

Butyl acetate

489

181

104000

110000

tert-Butyl acetate

250.0

Butyl stearate

387.15

62600

417.9

74 2

18400

19200

1-Chlorododecane

274.65

154

18400

19200

1-Chlorohexadecane

337.05

154

18400

19200

1-Chlorooctadecane

365.55

154

18400

19200

1-Chlorotetradecane

309.35

154

46400

51000

Cyclodecane

278.9

128

46400

51000

Cycloheptane

276.2

128

34900

37000

Cyclohexane

285.6

Cyclohexanol

353.5

236000 46400

51000

Cyclooctane

275.2

91700

97200

Cyclopentane

275.2

510.9

60 8 128

445.5

13-32 Polymer

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Mn/g mol-1 Mw/g mol-1

Mh/g mol-1

Solvent

UCST/K LCST/K Ref

transDecahydronaphthalene

281.95

91500

97000 4800

Decane

360.95

154

3700

4000

1-Decanol

375.15

154 650

18700

19800

Diethyl ether

235.6

314.5

187000

200000

Diethyl malonate

285.8

589.6

47200

50000

Diethyl oxalate

280.05

151000

160000

Dimethoxymethane

240000

1,4-Dimethylcyclohexane

387

62600

Dimethyl malonate

409.15

62600

Dimethyl oxalate

453.15

570000

116000

Decyl acetate

131 401.2

482

116

123000

Dodecadeuterocyclohexane 298.10

224

25000

Dodecadeuteromethylcyclopentane

180

310.07

4800

Dodecane

368.65

154

4000

1-Dodecanol

379.75

154

Dodecyl acetate

285.2

104000

110000

Ethyl acetate

213.9

104000

110000

Ethyl butanoate

221000

239000

Ethylcyclohexane

330.52

9440

10000

Ethyl formate

272

900000

Bis(2-ethylhexyl) phthalate

283.05

4530

4800

Heptane

359

3700

4000

1-Dexadecanol

386.25

5500

5770

1,1,1,3,3,3-Hexadeutero-2propanone

270

436

157

1920

2030

Hexane

318

470

112

Hexanoic acid

448.15

1-Hexanol

372.15

154

62600

3-Hexanol

396.65

90000

Hexyl acetate

3700 infinite

62600 3700

4000

206 435.4

490.8

74 18

451

74 136

477

112 154

2 578

104000

110000

Methyl acetate

284.2

415.7

104000

110000

3-Methyl-1-butyl acetate

210.1

510.1

91700

97200

Methylcyclohexane

321.8

505.9

10750

11500

Methylcyclopentane

295

480

157

104000

110000

2-Methyl-1-propyl acetate

210.4

468.5

48000

Nitroethane

303.1

151

4800

Octadecane

403.55

154

3700

4000

1-Octadecanol

390.55

154

4530

4800

Octane

353

3700

4000

1-Octanol

372.35

62600 4800

527

112 154

1-Octene

355.15

Pentadecane

385.25

154

1100

Pentane

292

137

3700

4000

1-Pentanol

375.05

154

219800

233000

Pentyl acetate

100000

1-Phenyldecane

283.60

5500

5770

2-Propanone

251

12750

13500

Propionitrile

312

519

181 105

452

157 187

104000

110000

Propyl acetate

183.7

469.0

104000

110000

2-Propyl acetate

220.9

414.2

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Polymer

Mn/g mol-1 Mw/g mol-1 3700

4000

34900

37000

Mh/g mol-1

Solvent

UCST/K LCST/K Ref

1-Tetradecanol

383.25

Toluene 62600

13-33

154 567.2

Vinyl acetate

384.15

230000

Cyclohexane

297.1

155000

Cyclohexane

294.13

199

infinite

Cyclohexane

300

40000

Water

514

150000

Water

306.45

217

Polystyrene (three-arm star) 496.8

Polystyrene (four-arm star) Poly(trimethylene oxide) Poly(vinyl alcohol) Poly(N-vinyl caprolactam) Poly(vinyl chloride) 55000

Dibutyl phthalate

353

114

55000

Tricresyl phosphate

383

114

Dimethyl phthalate

355

219

85000 Poly(N-vinylisobutyramide) 66000

105600

Water

313.25

208

46500

98600

Deuterium oxide

307.2

173

83000

155000

Water

306.95

146

Water

313.5

176

Poly(vinyl methyl ether)

Poly(N-vinyl-N-propylacetamide) 30000 Styrene/acrylonitrile copolymer (21.1 wt% acrylonitrile)

infinite

Toluene

325.4

(23.2 wt% Acrylonitrile)

infinite

Toluene

355.1

(25.0 wt% Acrylonitrile)

90000

147000

Toluene

313.15

198

347000

Ethyl acetate

infinite

Cyclohexanol

334.65

114000

Butyl acetate

288.85

453.05

181

(51.0 wt% Acrylonitrile)

344.15

107

Styrene/methyl methacrylate copolymer (52.0 mol% Styrene) 38

Styrene/a-methylstyrene copolymer (20.0 mol% Styrene) 100000 100000

114000

Cyclohexane

285.85

484.85

181

100000

114000

Cyclopentane

290.95

421.05

181

100000

114000

transDecahydronaphthalene

264.15

181

100000

114000

Hexyl acetate

288.55

514.15

181

100000

114000

Pentyl acetate

303.15

480.65

181

1,1,2-Trichloro-1,2,2trifluoroethane

301.6

Trifluoronitrosomethane/ tetrafluoroethylene copolymer (1:1) alternating infinite

N-Vinylacetamide/vinyl acetate copolymer (58 mol% Vinyl acetate)

30000

57000

Water

340.15

(63 mol% Vinyl acetate)

27000

48600

Water

323.15

225 225

(78 mol% Vinyl acetate)

26000

46800

Water

282.15

225

298.25

121

Vinyl alcohol/vinyl butyrate copolymer (7.5 mol% Butyralized PVA)

infinite

Water

408.0

13-34

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions Mn/g mol-1 Mw/g mol-1

Polymer

Mh/g mol-1

Solvent

160000

Water

UCST/K LCST/K Ref

N-Vinylcaprolactam/N-vinylamine copolymer (3.8 mol% Vinyl amine) 308.8

176 225

N-Vinylformamide/vinyl acetate copolymer (60 mol% Vinyl acetate)

24000

45600

Water

310.15

(66 mol% Vinyl acetate)

25000

47500

Water

291.15

225

(73 mol% Vinyl acetate)

23000

50600

Water

277.15

225

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Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions 77. 78. 79. 80.

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13-35

123. Varennes, S., Charlet, G., and Delmas, G., Polym. Eng. Sci., 24, 98, 1984. 124. Hamano, K., Kuwahara, N., Koyama, T., and Harada, S., Phys. Rev. A, 32, 3168, 1985. 125. Kraemer, H. and Wolf, B.A., Makromol. Chem., Rapid Commun., 6, 21, 1985. 126. Herold, F.K. and Wolf, B.A., Mater. Chem. Phys., 14, 311, 1986. 127. Irani, C.A. and Cozewith, C., J. Appl. Polym. Sci., 31, 1879, 1986. 128. Cowie, J.M.G. and McEwen, I.J., Brit. Polym. J., 18, 387, 1986. 129. Krüger, B., Dissertation, TH Leuna-Merseburg, 1986. 130. Rätzsch, M.T., et al., J. Macromol. Sci.-Chem. A, 23, 1349, 1986. 131. Saeki, S., et al., Macromolecules, 19, 2353, 1986. 132. Sander, U. and Wolf, B.A., Angew. Makromol. Chem., 139, 149, 1986. 133. Barbarin-Castillo, J.-M., et al., Polym.Commun., 28, 212, 1987. 134. Gruner, K. and Greer, S.C., Macromolecules, 20, 2238, 1987. 135. Magarik, S.Ya., Filippov, A.P., and D’yakonova, N.V., Vysokomol. Soedin., Ser. A, 29, 698, 1987. 136. Rangel-Nafaile, C. and Munoz-Lara, J.J., Chem. Eng. Commun., 53, 177, 1987. 137. Kiepen, F. and Borchard, W., Macromolecules, 21, 1784, 1988. 138. Schuster, R., Diploma Paper, TH Leuna-Merseburg, 1988. 139. Tveekrem, J.L., Greer, S.C., and Jacobs, D.T., Macromolecules, 21, 147, 1988. 140. Bohossian, T., Charlet, G., and Delmas, G., Polymer, 30, 1695, 1989. 141. Chiu, G. and Mandelkern, L., Macromolecules, 23, 5356, 1990. 142. Goedel, W.A., et al., Ber. Bunsenges. Phys. Chem., 94, 17, 1990. 143. Van der Haegen, R. and Van Opstal, L., Makromol. Chem., 191, 1871, 1990. 144. Iwai, Y., et al., Sekiyu Gakkaishi, 33, 117, 1990. 145. Raetzsch, M.T., Krueger, B., and Kehlen, H., J. Macromol. Sci.-Chem. A, 27, 683, 1990. 146. Schild, H.G. and Tirrell, D.A., J. Phys. Chem., 94, 4352, 1990. 147. Stafford, S.G., Ploplis, A.C., and Jacobs, D.T., Macromolecules, 23, 470, 1990. 148. Akhmadeev, I.R., et al., Vysokomol. Soedin., Ser. B, 33, 543, 1991. 149. Bae, Y.C., Lambert, S.M., Soane, D.S., and Prausnitz, J.M., Macromolecules, 24, 4403, 1991. 150. Chu, B., Linliu, K., Xie, P., Ying, Q., Wang, Z., and Shook, J.W., Rev. Sci. Instr., 62, 2252, 1991. 151. Kawate, K., Imagawa, I., and Nakata, M., Polym. J., 23, 233, 1991. 152. Lee, K.D. and Lee, D.C., Pollimo, 15, 274, 1991. 153. Louai, A., Sarazin, D., Pollet, G., Francois, J., and Moreaux, F., Polymer, 32, 703, 1991. 154. Van Opstal, L., Koningsveld, R., and Kleintjens, L.A., Macromolecules, 24, 161, 1991. 155. Schubert, K.-V., Strey, R., and Kahlweit, M., J. Colloid Interface Sci., 141, 21, 1991. 156. Shen, W., Smith, G.R., Knobler, C.M., and Scott, R.L., J. Phys. Chem., 95, 3376, 1991. 157. Szydlowski, J. and Van Hook, W.A., Macromolecules, 24, 4883, 1991. 158. Tager, A.A., et al., Vysokomol. Soedin., Ser. B, 33, 572, 1991. 159. Wakker, A., Polymer, 32, 279, 1991. 160. Yokoyama, H., Takano, A., Okada, M., and Nose, T., Polymer, 32, 3218, 1991. 161. Heinrich, M. and Wolf, B.A., Polymer, 33, 1926, 1992. 162. Heinrich, M. and Wolf, B.A., Macromolecules, 25, 3817, 1992. 163. Lecointe, J.P., Pascault, J.P., Suspene, L., and Yang, Y.S., Polymer, 33, 3226, 1992. 164. Mueller, K.F., Polymer, 33, 3470, 1992. 165. Szydlowski, J., Rebelo, L., and Van HooK, W.A., Rev. Sci. Instrum., 63, 1717, 1992. 166. Xia, K.-Q., Franck, C., and Widom, B., J. Chem. Phys., 97, 1446, 1992. 167. Arnauts, J., Berghmans, H., and Koningsveld, R., Makromol. Chem., 194, 77, 1993. 168. Iwai, Y., Shigematsu, Y., Furuya, T., Fukuda, H., Arai, Y., Polym. Eng. Sci., 33, 480, 1993. 169. Wakker, A., Van Dijk, F., and Van Dijk, M.A., Macromolecules, 26, 5088, 1993.

13-36

Upper Critical (UCST) and Lower Critical (LCST) Solution Temperatures of Binary Polymer Solutions

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198. Schneider, A., Dissertation, Johannes Gutenberg Universität Mainz. 1998. 199. Terao, K., et al., Macromolecules, 31, 6885, 1998. 200. Yamagishi, T.-A., et al., Macromol. Chem. Phys., 199, 423, 1998. 201. Lau, A.C.W. and Wu, C., Macromolecules, 32, 581, 1999. 202. Nakata, M., Dobashi, T., Inakuma, Y.-I., and Yamamura, K., J. Chem. Phys., 111, 6617, 1999. 203. Pruessner, M.D., Retzer, M.E., and Greer, S.C., J. Chem. Eng. Data, 44, 1419, 1999. 204. Shimofure, S., Kubota, K., Kita, R., and Dobashi, T., J.Chem.Phys., 111, 4199, 1999. 205. Fischer, V. and Borchard, W., J. Phys. Chem. B, 104, 4463, 2000. 206. Imre, A., and Van Hook, W.A., Macromolecules, 33, 5308, 2000. 207. Koizumi, J., et al., J. Phys. Soc. Japan, 69, 2543, 2000. 208. Kunugi, S., Tada, T., Yamazaki, Y., Yamamoto, K., and Akashi, M., Langmuir, 16, 2042, 2000. 209. La Mesa, C., J. Therm. Anal. Calorim., 61, 493, 2000. 210. Persson, J., et al., Bioseparation, 9, 105, 2000. 211. Persson, J., Kaul, A., and Tjerneld, F., J. Chromatogr. B, 743, 115, 2000. 212. Djokpe, E. and Vogt, W., Macromol. Chem. Phys., 202, 750, 2001. 213. Kujawa, P. and Winnik, F.M., Macromolecules, 34, 4130, 2001. 214. Pendyala, K.S., Greer, S.C., and Jacobs, D.T., J. Chem. Phys., 115, 9995, 2001. 215. Berlinova, I. V., Nedelcheva, A. N., Samchikov, V., and Ivanov, Ya., Polymer, 43, 7243, 2002. 216. Freitag, R. and Garret-Flaudy, F., Langmuir, 18, 3434, 2002. 217. Maeda, Y., Nakamura, T., and Ikeda, I., Macromolecules, 35, 217, 2002. 218. Rebelo, L.P.N., et al., J., Macromolecules, 35, 1887, 2002. 219. Safronov, A.P. and Somova, T.V., Vysokomol. Soedin., Ser. A, 44, 2014, 2002. 220. Vshvikov, S.A., Rusinova, E.V., and Gur’ev, A.A., Vysokomol. Soedin., Ser. B, 44, 504, 2002. 221. Zhou, C.-S., An, X.-Q., Xia, K.-Q., Yin, X.-L., and Shen, W.-G., J. Chem. Phys., 117, 4557, 2002. 222. Chang, Y., Powell, E.S., Allcock, H.R., Park, S.M., and Kim, C., Macromolecules, 36, 2568, 2003. 223. David, G., et al., Eur. Polym. J., 39, 1209, 2003. 224. Siporska, A., Szydlowski, J., and Rebelo, L.P.N., Phys. Chem. Chem. Phys., 5, 2996, 2003. 225. Yamamoto, K., Serizawa, T., and Akashi, M., Macromol. Chem. Phys., 204, 1027, 2003.

Vapor Pressures (Solvent Activities) for Binary Polymer Solutions Christian Wohlfarth

stated, even though the temperature dependence of aA is relatively small for the temperature ranges where most of the experimental data exist.

The vapor pressure of a binary polymer solution is given by the activity of the solvent A, aA. Solvent activities in polymer solutions are measured either by the isopiestic method applying a reference system whose solvent activity is precisely known or by determining the solvent partial pressure, PA, and calculating the activity of the solvent by equation (1):

(

)

 B –V L P – P s   AA A ( A )  aA =( PA /P ) exp    RT   s A

References 1. Wohlfarth, C., Methods for the measurement of solvent activity of polymer solutions, in Handbook of Solvents, Wypych, G., Ed., ChemTec Publishing, Toronto, 2000, 146. 2. Wen, H., Elbro, H. S., and Alessi, P., Polymer Solution Data Collection. I. Vapor-liquid equilibrium; II. Solvent activity coefficients at infinite dilution; III. Liquid-liquid equilibrium, Chemistry Data Series, Vol. 15, DECHEMA, Frankfurt am Main, 1992. 3. Danner, R. P. and High, M. S., Handbook of Polymer Solution Thermodynamics, American Institute of Chemical Engineers, New York, 1993. 4. Wohlfarth, C., Vapour-Liquid Equilibrium Data of Binary Polymer Solutions: Physical Science Data, 44, Elsevier, Amsterdam, 1994. 5. Wohlfarth, C., CRC Handbook of Thermodynamic Data of Copolymer Solutions, CRC Press, Boca Raton, FL, 2001. 6. Wohlfarth, C., CRC Handbook of Thermodynamic Data of Aqueous Polymer Solutions, CRC Press, Boca Raton, FL, 2003. 7. Wang, K., Hu, Y., and Wu, D. T., J. Chem. Eng. Data, 39, 916, 1994. 8. Choi, J. S., Tochigi, K., and Kojima, K., Fluid Phase Equil., 111, 143, 1995. 9. Tochigi, K., Kurita, S., Ohashi, M., and Kojima, K., Kagaku Kogaku Ronbunshu, 23, 720, 1997. 10. Wong, H. C., Campbell, S. W., and Bhethanabotla, V. R., Fluid Phase Equil., 139, 371, 1997. 11. Kim, J., Joung, K. C., Hwang, S., Huh, W., Lee, C. S., and Yoo, K.-P., Korean J. Chem. Eng., 15, 199, 1998. 12. Kim, N. H., Kim, S.J., Won, Y. S., and Choi, J. S., Korean J. Chem. Eng., 15, 141, 1998. 13. Feng, W., Wang, W., and Feng, Z., J. Chem. Ind. Eng. (China), 49, 271, 1998. 14. French, R. N. and Koplos, G. J., Fluid Phase Equil., 160, 879, 1999. 15. Striolo, A. and Praunsitz, J. M., Polymer, 41, 1109, 2000. 16. Fornasiero, F., Halim, M., and Prausnitz, J. M., Macromolecules, 33, 8435, 2000. 17. Wong, H. C., Campbell, S. W., and Bhethanabotla, V. R., Fluid Phase Equil., 179, 181, 2001. 18. Wibawa, G., Takahashi, M., Sato, Y., Takishima, S., and Masuoka, H., J. Chem. Eng. Data, 47, 518, 2002. 19. Wibawa, G., Hatano, R., Sato, Y., Takishima, S., and Masuoka, H., J. Chem. Eng. Data, 47, 1022, 2002. 20. Pfohl, O., Riebesell, C., and Dohrn, R., Fluid Phase Equil., 202, 289, 2002. 21. Jung, J. K., Joung, S. N., Shin, H.Y., Kim, S. Y., Yoo, K.-P., Huh, W., Lee, C. S., Korean J. Chem. Eng., 19, 296, 2002. 22. Kang, S., Huang, Y., Fu, J., Liu, H., and Hu, Y., J. Chem. Eng. Data, 47, 788, 2002.

(1)

where BAA is the second virial coefficient, P is the saturation vapor pressure, and VAL is the molar volume of the pure solvent A at the measuring temperature T. The exponential term is neglected in quite a lot of original papers, however, and only the reduced vapor pressures are given (such data are indicated by an asterisk in the table below). Vapor pressures of polymer solutions have been measured since the 1940s, but the amount of experimental data for polymer solutions is still relatively small in comparison to lowmolecular mixtures and solutions. The data scatter with respect to temperature, concentration, molar mass, and other polymer characterization variables. Furthermore, the concentration range for measuring vapor pressures in good thermodynamic quality is often limited to the polymer mass fraction range between 0.4 and 0.85. A recent review on methods for the measurement of vapor pressures/solvent activities of polymer solutions and on related problems is given in Ref. [1]. Experimental data have been collected in several books [2-6]. The table in this Handbook provides data for a number of polymer solutions as smoothed values over the complete range of solvent activities between 0 (polymer mass fraction = 1) and 1 (polymer mass fraction = 0). For this purpose, the data were selected from data books [4–6] as well as from a number of original sources [7–22] which are not included in these books. The appropriate data were smoothed. The final table provides then the polymer mass fractions at given fixed solvent activities between 0.1 and 0.9. Of course, the user must keep in mind that the activity vs. concentration range of the experimental data is sometimes smaller than the below given complete range, thus the smoothed data should be used with sufficient care. Generally, vapor pressures or solvent activities of binary polymer solutions depend on molar mass. However, for high molecular weight polymers (well above the oligomer region), this molar-mass dependence can be neglected in many cases. Therefore, the table below presents only data for polymer solutions where the number average molar mass, Mn, is in the order of 105 g/mol or even higher, therefore, the molar mass is not specified. The temperature is s A

Solvent Activity aA as Function of Temperature and Mass Fraction Polymer/ solvents

aA: T/K

0.1

Acrylonitrile/Styrene Copolymer (28 wt% Acrylonitrile) Benzene*) 1,2-Dimethylbenzene*) 1,3-Dimethylbenzene*) 1,4-Dimethylbenzene*) Propylbenzene*) Toluene*)

S13_07.indd 37

343.15 398.15 398.15 398.15 398.15 343.15

0.982 0.983 0.983 0.983 0.987 0.982

0.2

0.3

0.962 0.964 0.965 0.964 0.972 0.962

0.940 0.942 0.944 0.942 0.955 0.940

0.4 0.5 0.6 Mass Fraction of the Polymer 0.915 0.918 0.921 0.918 0.935 0.915

0.886 0.890 0.893 0.890 0.913 0.886

0.851 0.857 0.861 0.857 0.885 0.851

0.7

0.8

0.9

0.809 0.817 0.821 0.817 0.851 0.809

0.753 0.764 0.769 0.763 0.804 0.753

0.670 0.685 0.690 0.684 0.732 0.669

13-37

4/13/06 8:10:34 AM

Vapor Pressures (Solvent Activities) for Binary Polymer Solutions

13-38

S13_07.indd 38

Polymer/ aA: 0.1 solvents T/K Butadiene/Styrene Copolymer (41 wt% Styrene) 343.15 0.968 Benzene*) 343.15 0.978 Cyclohexane*) 398.15 0.974 Ethylbenzene*) 398.15 0.977 Mesitylene*) 343.15 0.970 Toluene*)

0.2

0.3

0.4 0.5 0.6 Mass Fraction of the Polymer

0.7

0.8

0.9

0.934 0.953 0.945 0.950 0.936

0.896 0.925 0.912 0.921 0.899

0.853 0.893 0.875 0.887 0.857

0.805 0.856 0.831 0.847 0.808

0.748 0.811 0.779 0.799 0.751

0.680 0.754 0.713 0.738 0.682

0.591 0.678 0.625 0.656 0.591

0.461 0.556 0.491 0.526 0.456

Cellulose Triacetate Dichloromethane Trichloromethane

298.15 298.15

0.979 0.978

0.956 0.953

0.930 0.924

0.899 0.892

0.863 0.853

0.819 0.806

0.762 0.747

0.683 0.665

0.554 0.533

Dextran Water

313.15

0.988

0.975

0.960

0.942

0.921

0.894

0.860

0.810

0.725

Hydroxyethylcellulose Water

368.15

0.988

0.974

0.958

0.939

0.915

0.884

0.841

0.775

0.650

Hydroxypropylstarch Water

293.15

0.989

0.977

0.963

0.947

0.927

0.903

0.872

0.827

0.749

Nitrocellulose Ethyl acetate Ethyl formate Ethyl propionate Methyl acetate 2-Propanone Propyl acetate

293.15 293.15 293.15 293.15 293.15 293.15

0.938 0.958 0.941 0.890 0.922 0.937

0.885 0.916 0.889 0.820 0.861 0.881

0.835 0.873 0.839 0.763 0.807 0.827

0.786 0.828 0.789 0.711 0.756 0.775

0.737 0.780 0.739 0.660 0.706 0.722

0.685 0.728 0.685 0.609 0.653 0.665

0.627 0.668 0.625 0.554 0.596 0.602

0.560 0.595 0.555 0.490 0.530 0.528

0.471 0.494 0.460 0.406 0.443 0.426

Polybutadiene (random cis-trans-vinyl) Benzene 298.15 Cyclohexane 298.15 Dichloromethane 298.15 Hexane 298.15 Tetrachloromethane 298.15 Toluene 298.15 Trichloromethane 298.15

0.964 0.974 0.951 0.984 0.932 0.969 0.925

0.925 0.945 0.902 0.965 0.865 0.935 0.855

0.884 0.913 0.852 0.943 0.799 0.898 0.788

0.839 0.876 0.800 0.916 0.731 0.856 0.720

0.788 0.833 0.745 0.881 0.660 0.809 0.650

0.731 0.782 0.684 0.837 0.585 0.754 0.578

0.663 0.719 0.616 0.775 0.503 0.688 0.498

0.578 0.635 0.532 0.683 0.409 0.603 0.406

0.455 0.507 0.415 0.534 0.288 0.476 0.289

1,4-cis-Polybutadiene Benzene Cyclohexane Dichloromethane Hexane Tetrachloromethane Toluene Trichloromethane

298.15 298.15 298.15 298.15 298.15 298.15 298.15

0.966 0.977 0.948 0.983 0.936 0.969 0.915

0.930 0.951 0.898 0.963 0.871 0.936 0.840

0.890 0.922 0.848 0.941 0.805 0.900 0.770

0.846 0.888 0.796 0.916 0.736 0.860 0.702

0.796 0.849 0.742 0.886 0.665 0.815 0.634

0.738 0.803 0.683 0.850 0.588 0.763 0.562

0.668 0.747 0.616 0.804 0.505 0.701 0.485

0.580 0.677 0.536 0.741 0.409 0.622 0.396

0.450 0.581 0.424 0.639 0.287 0.506 0.283

Poly(butyl acrylate) Benzene Dichloromethane Tetrachloromethane Toluene Trichloromethane

298.15 298.15 298.15 298.15 298.15

0.964 0.868 0.932 0.967 0.901

0.926 0.801 0.868 0.932 0.811

0.887 0.744 0.805 0.893 0.733

0.845 0.690 0.742 0.849 0.662

0.799 0.636 0.677 0.801 0.595

0.749 0.577 0.607 0.744 0.529

0.691 0.511 0.529 0.676 0.459

0.619 0.430 0.438 0.590 0.381

0.519 0.318 0.317 0.463 0.282

Poly(butyl methacrylate) Benzene 1-Butanol 2-Butanol 2-Butanone Butyl acetate*) Cyclohexane Cyclopentane Diethyl ether*) 1,4-Dimethylbenzene Ethylbenzene Methyl acetate

313.15 313.15 313.15 313.15 308.15 313.15 313.15 298.15 333.15 333.15 313.15

0.971 0.991 0.992 0.982 0.982 0.985 0.984 0.987 0.971 0.969 0.984

0.939 0.980 0.982 0.963 0.961 0.968 0.965 0.973 0.940 0.935 0.965

0.902 0.968 0.969 0.940 0.936 0.948 0.944 0.956 0.905 0.899 0.944

0.861 0.953 0.953 0.914 0.908 0.925 0.918 0.937 0.866 0.859 0.920

0.813 0.936 0.933 0.884 0.875 0.899 0.886 0.914 0.822 0.815 0.891

0.756 0.914 0.906 0.846 0.836 0.866 0.846 0.885 0.770 0.764 0.856

0.685 0.885 0.869 0.799 0.789 0.823 0.792 0.848 0.706 0.704 0.811

0.592 0.842 0.815 0.732 0.730 0.764 0.714 0.795 0.622 0.627 0.748

0.453 0.762 0.719 0.623 0.652 0.666 0.579 0.703 0.497 0.517 0.645

4/13/06 8:10:35 AM

Vapor Pressures (Solvent Activities) for Binary Polymer Solutions

S13_07.indd 39

Polymer/ solvents 2-Methyl-1-propanol Octane 1-Propanol 2-Propanol 2-Propanone Propyl acetate Toluene

aA: T/K 333.15 313.15 333.15 313.15 313.15 313.15 313.15

0.1

0.2

0.3

0.988 0.988 0.990 0.991 0.989 0.980 0.971

0.974 0.974 0.980 0.981 0.976 0.957 0.939

Poly(Îľ-caprolacton) Tetrachloromethane*)

338.15

0.956

Poly(dimethylsiloxane) Chlorodifluoromethane Cyclohexane Hexane Pentane Pentane

298.15 303.15 303.15 308.15 423.15

Poly(ethyl acrylate) Benzene Dichloromethane Tetrachloromethane Toluene Trichloromethane

13-39 0.7

0.8

0.9

0.958 0.959 0.967 0.970 0.961 0.932 0.903

0.4 0.5 0.6 Mass Fraction of the Polymer 0.940 0.919 0.893 0.942 0.921 0.896 0.952 0.934 0.911 0.956 0.939 0.918 0.944 0.921 0.892 0.903 0.870 0.830 0.863 0.818 0.764

0.860 0.865 0.881 0.889 0.850 0.780 0.698

0.815 0.823 0.834 0.845 0.783 0.714 0.613

0.744 0.758 0.746 0.755 0.647 0.612 0.485

0.910

0.864

0.815

0.762

0.704

0.637

0.554

0.438

0.976 0.979 0.982 0.982 0.984

0.950 0.955 0.962 0.962 0.966

0.921 0.928 0.939 0.940 0.946

0.888 0.898 0.912 0.913 0.922

0.850 0.863 0.880 0.881 0.893

0.805 0.822 0.842 0.842 0.858

0.750 0.770 0.793 0.791 0.813

0.677 0.702 0.724 0.720 0.749

0.565 0.596 0.611 0.600 0.641

298.15 298.15 298.15 298.15 298.15

0.970 0.900 0.950 0.972 0.866

0.939 0.830 0.900 0.942 0.776

0.904 0.768 0.848 0.910 0.701

0.866 0.709 0.794 0.874 0.632

0.823 0.648 0.736 0.833 0.566

0.774 0.584 0.672 0.786 0.499

0.716 0.512 0.598 0.730 0.428

0.641 0.427 0.509 0.659 0.349

0.533 0.313 0.385 0.555 0.248

Poly(ethylene oxide) Benzene 2-Butanone Cyclohexane Methanol 2-Propanone Water

323.15 353.15 353.15 303.15 353.15 293.15

0.972 0.981 0.989 0.964 0.979 0.977

0.942 0.959 0.976 0.927 0.947 0.951

0.908 0.934 0.960 0.887 0.896 0.923

0.869 0.902 0.943 0.844 0.815 0.890

0.824 0.863 0.921 0.797 0.719 0.852

0.771 0.813 0.893 0.744 0.625 0.806

0.706 0.746 0.855 0.682 0.532 0.748

0.620 0.651 0.798 0.604 0.434 0.671

0.490 0.503 0.688 0.494 0.315 0.550

Poly(ethylenimine) Water

353.15

0.975

0.947

0.917

0.883

0.845

0.801

0.748

0.680

0.581

Poly(ethyl methacrylate) Benzene Dichloromethane Tetrachloromethane Toluene Trichloromethane

298.15 298.15 298.15 298.15 298.15

0.970 0.912 0.935 0.974 0.859

0.938 0.838 0.873 0.945 0.760

0.903 0.769 0.812 0.913 0.678

0.864 0.703 0.750 0.877 0.604

0.821 0.636 0.686 0.836 0.533

0.771 0.567 0.616 0.787 0.464

0.712 0.491 0.540 0.727 0.392

0.637 0.404 0.449 0.647 0.313

0.529 0.292 0.328 0.527 0.217

Polyisobutylene Benzene Cyclohexane Cyclopentane 1,4-Dimethylbenzene 2,2-Dimethylbutane Ethylbenzene Heptane Hexane Octane Tetrachloromethane Toluene Trichloromethane 2,4,4-Trimethylpentane

313.15 313.15 313.15 313.15 298.15 313.15 298.15 298.15 298.15 298.15 313.15 298.15 298.15

0.984 0.976 0.977 0.979 0.983 0.979 0.983 0.980 0.983 0.962 0.984 0.969 0.981

0.965 0.950 0.952 0.955 0.964 0.955 0.964 0.959 0.963 0.921 0.966 0.935 0.961

0.945 0.921 0.924 0.929 0.942 0.927 0.942 0.934 0.940 0.877 0.944 0.899 0.937

0.921 0.888 0.892 0.899 0.917 0.895 0.917 0.906 0.914 0.829 0.918 0.858 0.911

0.892 0.850 0.855 0.863 0.887 0.857 0.887 0.873 0.883 0.776 0.884 0.813 0.879

0.858 0.805 0.812 0.821 0.852 0.810 0.851 0.834 0.845 0.715 0.840 0.761 0.842

0.813 0.749 0.758 0.767 0.806 0.750 0.804 0.784 0.797 0.643 0.779 0.698 0.794

0.751 0.676 0.687 0.694 0.743 0.668 0.741 0.715 0.729 0.552 0.688 0.619 0.730

0.645 0.563 0.579 0.579 0.640 0.535 0.637 0.606 0.617 0.423 0.537 0.503 0.628

1,4-cis-Polyisoprene Benzene 2-Butanone Cyclohexane Dichloromethane 1,4-Dimethylbenzene

313.15 353.15 313.15 298.15 313.15

0.982 0.986 0.978 0.969 0.977

0.962 0.970 0.954 0.935 0.951

0.937 0.953 0.928 0.898 0.923

0.908 0.933 0.899 0.857 0.892

0.873 0.910 0.865 0.811 0.857

0.827 0.883 0.825 0.757 0.816

0.766 0.850 0.778 0.693 0.767

0.679 0.808 0.716 0.610 0.704

0.537 0.746 0.625 0.488 0.613

4/13/06 8:10:37 AM

Vapor Pressures (Solvent Activities) for Binary Polymer Solutions

13-40

S13_07.indd 40

Polymer/ solvents Ethylbenzene Methyl acetate Octane Propyl acetate Tetrachloromethane Toluene Trichloromethane

aA: T/K 313.15 313.15 313.15 333.15 298.15 313.15 298.15

0.1

0.2

0.3

0.7

0.8

0.9

0.928 0.900 0.948 0.942 0.800 0.927 0.807

0.4 0.5 0.6 Mass Fraction of the Polymer 0.898 0.864 0.823 0.862 0.820 0.773 0.926 0.901 0.871 0.916 0.886 0.850 0.737 0.672 0.602 0.898 0.865 0.827 0.747 0.685 0.620

0.978 0.968 0.984 0.983 0.929 0.978 0.930

0.954 0.935 0.967 0.964 0.864 0.954 0.867

0.774 0.717 0.834 0.803 0.526 0.782 0.547

0.709 0.649 0.785 0.738 0.435 0.725 0.462

0.612 0.554 0.711 0.633 0.316 0.645 0.346

Poly(methyl acrylate) Benzene Dichloromethane Tetrachloromethane Toluene Trichloromethane

298.15 298.15 298.15 298.15 298.15

0.979 0.917 0.963 0.981 0.912

0.956 0.851 0.924 0.960 0.830

0.930 0.791 0.882 0.936 0.753

0.901 0.732 0.838 0.909 0.678

0.867 0.671 0.788 0.878 0.603

0.826 0.605 0.733 0.840 0.527

0.776 0.532 0.668 0.792 0.446

0.710 0.444 0.586 0.727 0.357

0.608 0.326 0.470 0.626 0.248

Poly(methyl methacrylate) Benzene 2-Butanone*) Cyclohexanone*) Dichloromethane Ethyl acetate*) Toluene Trichloromethane

298.15 308.15 323.15 298.15 308.15 298.15 298.15

0.982 0.989 0.978 0.939 0.986 0.981 0.924

0.961 0.976 0.954 0.882 0.969 0.959 0.848

0.938 0.961 0.928 0.825 0.950 0.935 0.771

0.912 0.945 0.899 0.766 0.928 0.908 0.694

0.881 0.925 0.866 0.704 0.902 0.877 0.616

0.843 0.900 0.827 0.637 0.869 0.841 0.536

0.795 0.869 0.781 0.560 0.826 0.795 0.451

0.729 0.825 0.723 0.468 0.763 0.736 0.358

0.622 0.751 0.640 0.343 0.649 0.646 0.246

Poly(Îą-methylstyrene) Cumene Îą-Methylstyrene

338.15 338.15

0.984 0.978

0.965 0.954

0.944 0.927

0.918 0.896

0.887 0.859

0.848 0.816

0.796 0.761

0.721 0.687

0.593 0.570

Poly(propylene oxide) Benzene Metvhanol

333.15 298.15

0.967 0.992

0.932 0.982

0.893 0.970

0.850 0.955

0.801 0.936

0.744 0.910

0.675 0.872

0.588 0.812

0.460 0.689

Polystyrene Benzene 2-Butanone*) Cyclohexane Cyclohexanone*) Dichloromethane 1,3-Dimethylbenzene*) 1,4-Dimethylbenzene Ethyl acetate*) Hexane 2-Propanone Propyl acetate Tetrachloromethane Toluene Trichloromethane

333.15 298.15 313.15 313.15 298.15 323.15 423.15 313.15 423.15 323.15 343.15 298.15 313.15 298.15

0.978 0.986 0.990 0.970 0.949 0.980 0.974 0.976 0.980 0.991 0.983 0.961 0.981 0.949

0.953 0.971 0.978 0.937 0.899 0.956 0.944 0.948 0.958 0.980 0.965 0.917 0.959 0.898

0.924 0.954 0.965 0.900 0.849 0.926 0.911 0.918 0.933 0.969 0.943 0.869 0.933 0.847

0.891 0.935 0.949 0.858 0.797 0.891 0.872 0.882 0.904 0.955 0.919 0.814 0.901 0.793

0.852 0.912 0.931 0.810 0.743 0.846 0.826 0.841 0.869 0.938 0.891 0.751 0.861 0.736

0.804 0.885 0.908 0.753 0.684 0.791 0.770 0.791 0.827 0.918 0.858 0.678 0.809 0.675

0.742 0.851 0.877 0.684 0.617 0.723 0.698 0.728 0.772 0.892 0.815 0.592 0.738 0.604

0.657 0.804 0.833 0.593 0.536 0.638 0.601 0.642 0.697 0.854 0.758 0.486 0.638 0.519

0.521 0.724 0.754 0.459 0.423 0.524 0.452 0.507 0.574 0.788 0.667 0.344 0.481 0.400

Poly(tetramethylene glycol) Methanol

303.15

0.981

0.961

0.938

0.913

0.883

0.849

0.806

0.751

0.671

Poly(vinyl acetate) Benzene 1-Butanol 2-Butanol 2-Butanone 1,2-Dichloroethane*) 1,4-Dimethylbenzene Ethylbenzene Methanol Methyl acetate 2-Methyl-1-propanol 1-Propanol 2-Propanol

313.15 313.15 313.15 313.15 300.15 313.15 313.15 333.15 313.15 353.15 353.15 353.15

0.985 0.992 0.987 0.980 0.955 0.990 0.990 0.990 0.976 0.984 0.987 0.988

0.967 0.982 0.972 0.958 0.906 0.978 0.979 0.978 0.949 0.966 0.972 0.974

0.945 0.971 0.956 0.934 0.851 0.964 0.966 0.965 0.919 0.946 0.955 0.958

0.919 0.958 0.937 0.906 0.790 0.948 0.950 0.949 0.886 0.924 0.936 0.940

0.886 0.942 0.915 0.873 0.722 0.928 0.932 0.931 0.849 0.899 0.914 0.919

0.844 0.923 0.889 0.835 0.644 0.903 0.910 0.908 0.805 0.868 0.888 0.894

0.784 0.896 0.856 0.787 0.556 0.868 0.880 0.877 0.752 0.832 0.856 0.863

0.696 0.856 0.813 0.724 0.450 0.814 0.836 0.834 0.684 0.784 0.815 0.820

0.548 0.779 0.747 0.626 0.315 0.705 0.759 0.757 0.583 0.715 0.753 0.754

4/13/06 8:10:38 AM

Vapor Pressures (Solvent Activities) for Binary Polymer Solutions Polymer/ solvents 2-Propanone Propyl acetate Tetrahydrofuran Toluene

aA: T/K 333.15 333.15 323.15 333.15

0.1

0.2

0.3

0.983 0.979 0.973 0.983

0.963 0.955 0.943 0.965

Poly(vinyl chloride) 2-Butanone*) Cyclohexanone*)

313.15 333.15

0.976 0.971

Poly(vinyl methyl ether) Benzene*) Chlorobenzene*) 1,2-Dimethylbenzene*) Ethylbenzene*) Propylbenzene*)

298.15 343.15 363.15 343.15 373.15

Poly(4-vinylpyridine) Methanol 2-Propanol

13-41 0.7

0.8

0.9

0.940 0.930 0.911 0.944

0.4 0.5 0.6 Mass Fraction of the Polymer 0.913 0.880 0.838 0.901 0.869 0.831 0.874 0.831 0.781 0.920 0.891 0.857

0.784 0.786 0.720 0.815

0.707 0.728 0.640 0.756

0.578 0.645 0.519 0.664

0.949 0.934

0.920 0.889

0.887 0.839

0.849 0.781

0.804 0.714

0.749 0.635

0.676 0.536

0.566 0.397

0.969 0.972 0.973 0.978 0.977

0.935 0.941 0.943 0.954 0.951

0.897 0.906 0.910 0.927 0.923

0.855 0.867 0.871 0.895 0.890

0.807 0.822 0.826 0.857 0.852

0.751 0.769 0.772 0.811 0.808

0.683 0.705 0.705 0.753 0.752

0.596 0.620 0.616 0.672 0.678

0.466 0.494 0.478 0.542 0.563

343.15 343.15

0.986 0.989

0.971 0.977

0.953 0.964

0.931 0.948

0.905 0.928

0.871 0.904

0.825 0.872

0.756 0.826

0.627 0.743

Poly(1-vinyl-2-pyrrolidinone) Water

368.15

0.984

0.966

0.946

0.924

0.899

0.870

0.835

0.790

0.727

Starch (amorphous) Water

383.15

0.991

0.981

0.970

0.956

0.939

0.918

0.889

0.845

0.754

Styrene/Methyl methacrylate Copolymer (41.45 wt% Styrene) 308.15 0.982 0.963 Benzene*)

0.940

0.913

0.881

0.841

0.789

0.716

0.590

Vinyl acetate/Vinyl chloride Copolymer (12 wt% Vinyl acetate) Benzene 398.15 0.976 0.949 Chlorobenzene 398.15 0.984 0.965 1,4-Dimethylbenzene 398.15 0.989 0.977 Ethylbenzene 398.15 0.989 0.976 Octane 398.15 0.992 0.982

0.918 0.944 0.963 0.961 0.971

0.883 0.920 0.946 0.944 0.958

0.841 0.891 0.926 0.924 0.942

0.791 0.856 0.899 0.899 0.922

0.728 0.810 0.863 0.866 0.893

0.643 0.746 0.807 0.818 0.847

0.509 0.638 0.692 0.735 0.739

*)Â aA = PA / PAS

S13_07.indd 41

4/13/06 8:10:38 AM

SPECIFIC ENTHALPIES OF SOLUTION OF POLYMERS AND COPOLYMERS Christian Wohlfarth

Enthalpies of solution or mixing, expressed as the enthalpy change per unit mass of polymer, are given in the table at infinite dilution, i.e., a very small amount of polymer and a large excess of solvent were mixed isothermally to form a homogeneous solution. By thermodynamics, ∆sol HB∞ or ∆M HB∞ are obtained from the following derivatives:

∆sol HB∞ = lim (∂∆ sol h / ∂mB )P ,T ,m

∆M HB∞ = lim (∂∆ M h / ∂mB ) P ,T ,m

mB →0

j ≠B

(1)

(2)

with a unit of J/g. Thus, they are the partial specific enthalpies of solution or mixing of the polymer B at infinite dilution where ∆solh or ∆Mh is the extensive enthalpy of the solution or mixing process. The state of the polymer before dissolution can significantly affect the enthalpy of solution. The dissolving of a semicrystalline polymer requires an additional amount of heat associated with the disordering of crystalline regions. Consequently, its enthalpy of Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

solution is usually positive and depends on the degree of crystallinity of the given polymer sample. An amorphous polymer below its glass transition temperature, Tg (see the Tg-table of this Section), often dissolves with the release of heat. The enthalpy of solution of a glassy polymer is additionally dependent to some extent on the thermal history of the glass-forming process. An amorphous polymer above Tg can show endothermic or exothermic dissolution behavior depending on the nature of the solvent and the interaction energies involved as is the case for any enthalpy of mixing. This enthalpy of mixing is then independent of any crystalline or glassy aspects of the polymer. It can be obtained without difficulties for liquid/molten polymers mixed with a solvent. Therefore, the enthalpies given in the table are either enthalpies of solution or enthalpies of mixing, depending on the state of the polymer. The enthalpies depend on temperature and molar mass. The necessary molar mass information for a system is provided in the table (if available) by the corresponding number average, Mn, mass average, Mw, or viscosity average, Mη, values of the polymer as given in the original sources. Outside the oligomer range, specific enthalpies of solution or mixing do not remarkably depend on molar mass, however. More enthalpy data of polymer-solvent systems can be found in Ref. 106. ∆HB∞/ J/g

Solvent

T/K

Benzene Benzene Benzene

298.15 298.15 298.15

N,N-Dimethylformamide

323.15

−32

(13 wt% Acrylonitrile)

N,N-Dimethylformamide

293.15

−38

(13 wt% Acrylonitrile)

N,N-Dimethylformamide

308.15

−22

(13 wt% Acrylonitrile)

N,N-Dimethylformamide

323.15

−18

(13 wt% Acrylonitrile)

N,N-Dimethylformamide

338.15

−15

(13 wt% Acrylonitrile)

N,N-Dimethylformamide

353.15

−12

(29 wt% Acrylonitrile)

N,N-Dimethylformamide

295.15

−42

(29 wt% Acrylonitrile)

N,N-Dimethylformamide

308.15

−27

(29 wt% Acrylonitrile)

N,N-Dimethylformamide

323.15

−21

(29 wt% Acrylonitrile)

N,N-Dimethylformamide

338.15

−19

(29 wt% Acrylonitrile)

N,N-Dimethylformamide

353.15

−16

(40 wt% Acrylonitrile)

N,N-Dimethylformamide

295.15

−47

(40 wt% Acrylonitrile)

N,N-Dimethylformamide

308.15

−30

(40 wt% Acrylonitrile)

N,N-Dimethylformamide

323.15

−28

(40 wt% Acrylonitrile)

N,N-Dimethylformamide

338.15

−18

(40 wt% Acrylonitrile)

N,N-Dimethylformamide

353.15

−17

Benzene

298.15

−11

Cyclohexanone

298.15

−15

Trichloromethane

298.15

−38

Acrylonitrile/butadiene copolymer (18 wt% Acrylonitrile) (26 wt% Acrylonitrile) (40 wt% Acrylonitrile)

0.0 −1.9 −2.9

Ref. 18 18 18

Acrylonitrile/isoprene copolymer (15 mol% Isoprene) Acrylonitrile/vinyl chloride copolymer

Benzylcellulose

13-42

487_S13.indb 42

3/27/06 2:37:08 PM

Specific Enthalpies of Solution of Polymers and Copolymers Solvent

T/K

∆HB∞/ J/g

Ref.

(50/50 Iso/terephtaloyl chloride)

N,N-Dimethylacetamide

298.15

−56

(50/50 Iso/terephtaloyl chloride)

1,1,2,2-Tetrachloroethane

298.15

+72

(10 wt% Styrene)

Benzene

293.65

4.9

(30 wt% Styrene)

Benzene

293.65

3.0

(30 wt% Styrene)

Benzene

298.15

3.0

(50 wt% Styrene)

Benzene

293.65

1.8

(60 wt% Styrene)

Benzene

293.65

0.0

(70 wt% Styrene)

Benzene

293.65

0.0

(75 wt% Styrene)

Benzene

298.15

1.5

(80 wt% Styrene)

Benzene

293.65

−0.6

(90 wt% Styrene)

Benzene

293.65

−4.9

Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

13-43

Bisphenol A-isophthaloyl chloride/terephthaloyl chloride

Butadiene/styrene copolymer

Butyl methacrylate/isobutyl methacrylate copolymer (50 wt%/50 wt%) Glass

150000

Cyclohexanone

303.15

5.9

Liquid

150000

Cyclohexanone

303.15

14.0

Butyl methacrylate/methyl methacrylate copolymer (45 wt%/55 wt%) Glass

107000

250000

Cyclohexanone

304.15

−5.4

Liquid

107000

250000

Cyclohexanone

304.15

+9.1

Cellulose acetate (52.2 wt% Acetate)

Formic acid

298.15

−30

(55.8 wt% Acetate)

Formic acid

298.15

−44

(52.5 wt% Acetate)

Methyl acetate

298.15

−80

(48 wt% Acetate)

2-Propanone

298.15

−35

(52.2 wt% Acetate)

2-Propanone

298.15

−30

(55.8 wt% Acetate)

2-Propanone

298.15

−26

(56 wt% Acetate)

2-Propanone

298.15

−45

(56 wt% Acetate)

2-Propanone

298.15

−30

Cellulose triacetate 2-Propanone

298.15

−29

Trichloromethane

298.15

−47

Dextran 8200

10400

Dimethylsulfoxide

298.15

−185

75900

101000

Dimethylsulfoxide

298.15

−187

75900

101000

1,2-Ethanediol

298.15

−98

75900

101000

Formamide

298.15

−228

8200

10400

Water

298.15

−140

75900

101000

Water

298.15

−150

Water

298.15

−123

(33 mol% Ethylene)

Cyclohexane

298.15

1.4

(63 mol% Ethylene)

Cyclohexane

298.15

8.1

(75 mol% Ethylene)

Cyclohexane

298.15

11.8

(33 mol% Ethylene)

Cyclooctane

298.15

1.2

(amorph) Ethylene/propylene copolymer

487_S13.indb 43

3/27/06 2:37:08 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-44 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

∆HB∞/ J/g

Solvent

T/K

(63 mol% Ethylene)

Cyclooctane

298.15

(75 mol% Ethylene)

Cyclooctane

(33 mol% Ethylene)

Cyclopentane

(63 mol% Ethylene)

Cyclopentane

298.15

1.1

(33 mol% Ethylene)

cis-Decahydronaphthalene

298.15

−2.4

(63 mol% Ethylene)

cis-Decahydronaphthalene

298.15

2.4

(75 mol% Ethylene)

cis-Decahydronaphthalene

298.15

3.9

(33 mol% Ethylene)

trans-Decahydronaphthalene

298.15

−4.8

(63 mol% Ethylene)

trans-Decahydronaphthalene

298.15

−1.3

(75 mol% Ethylene)

trans-Decahydronaphthalene

298.15

−0.3

(63 mol% Ethylene)

3,3-Diethylpentane

298.15

−1.4

(75 mol% Ethylene)

3,3-Diethylpentane

298.15

<0.1

(63 mol% Ethylene)

2,2-Dimethylpentane

298.15

5.3

(75 mol% Ethylene)

2,2-Dimethylpentane

298.15

2.3

(63 mol% Ethylene)

2,3-Dimethylpentane

298.15

0.7

(75 mol% Ethylene)

2,3-Dimethylpentane

298.15

0.4

(33 mol% Ethylene)

2,4-Dimethylpentane

298.15

−1.2

(63 mol% Ethylene)

2,4-Dimethylpentane

298.15

3.0

(75 mol% Ethylene)

2,4-Dimethylpentane

298.15

0.2

(33 mol% Ethylene)

3,3-Dimethylpentane

298.15

−2.7

(63 mol% Ethylene)

3,3-Dimethylpentane

298.15

0.3

(33 mol% Ethylene)

Dodecane

298.15

−0.1

(63 mol% Ethylene)

Dodecane

298.15

0.8

(75 mol% Ethylene)

Dodecane

298.15

−4.0

(63 mol% Ethylene)

3-Ethylpentane

298.15

2.6

(75 mol% Ethylene)

3-Ethylpentane

298.15

−0.6

(33 mol% Ethylene)

2,2,4,4,6,8,8Heptamethylnonane

298.15

−0.5

(63 mol% Ethylene)

2,2,4,4,6,8,8Heptamethylnonane

298.15

2.2

(75 mol% Ethylene)

2,2,4,4,6,8,8Heptamethylnonane

298.15

−0.9

(33 mol% Ethylene)

Hexadecane

298.15

0.7

(63 mol% Ethylene)

Hexadecane

298.15

−1.1

(75 mol% Ethylene)

Hexadecane

298.15

−4.6

(63 mol% Ethylene)

3-Methylhexane

298.15

0.7

(75 mol% Ethylene)

3-Methylhexane

298.15

1.7

(33 mol% Ethylene)

Octane

298.15

−1.6

(63 mol% Ethylene)

Octane

298.15

3.6

(75 mol% Ethylene)

Octane

298.15

0.3

(33 mol% Ethylene)

2,2,4,6,6-Pentamethylheptane 298.15

−0.3

(63 mol% Ethylene)

2,2,4,6,6-Pentamethylheptane 298.15

3.6

(75 mol% Ethylene)

2,2,4,6,6-Pentamethylheptane 298.15

0.0

(63 mol% Ethylene)

2,2,4,4-Tetramethylpentane

298.15

2.7

(75 mol% Ethylene)

2,2,4,4-Tetramethylpentane

298.15

3.1

(33 mol% Ethylene)

2,2,4-Trimethylpentane

298.15

−0.2

(63 mol% Ethylene)

2,2,4-Trimethylpentane

298.15

1.9

(75 mol% Ethylene)

2,2,4-Trimethylpentane

298.15

3.5

487_S13.indb 44

Ref.

6.9

298.15

8.6

298.15

−3.5

3/27/06 2:37:09 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

13-45 ∆HB∞/ J/g

Ref.

298.15

−0.5

104

304.65

−1.3

Solvent

T/K

Cyclopentanone Tetrahydrofuran

Water

293.15

−92

Water

323.15

−63

Trichloromethane

303.15

Ethylene/vinylacetate copolymer (85 wt% Vinyl acetate) (70 wt% Vinyl acetate)

220000

Gelatine

Guttapercha Isobutyl methacrylate/methyl methacrylate copolymer (51 wt%/49 wt%) Glass

150000

Cyclohexanone

303.15

−11

Liquid

150000

Cyclohexanone

303.15

Benzene

298.15

Benzene

298.15

Natural rubber

Nitrocellulose

487_S13.indb 45

16600

2-Butanone

298.15

−80

23000

2-Butanone

298.15

−81

40000

2-Butanone

298.15

−81

Butyl acetate

293.15

−75

Butyl acetate

298.15

−75

Butyl acetate

298.15

−73

Butyl acetate

303.15

−75

Butyl acetate

308.15

−71

Butyl acetate

313.15

−65

Butyl acetate

313.15

−67

Butyl acetate

318.15

−59

Butyl acetate

323.15

−54

Butyl acetate

328.15

−50

Butyl acetate

333.15

−59

Butyl acetate

343.15

−55

Butyl acetate

353.15

−47

Diethyl ether

295.15

−62

Dibutyl phthalate

273.15

−45

Dibutyl phthalate

298.15

−46

Dibutyl phthalate

313.15

−46

Dibutyl phthalate

333.15

−42

Ethanol

295.15

−46

Ethyl acetate

293.15

−76

Ethyl acetate

298.15

−75

Ethyl acetate

303.15

−69

Ethyl acetate

308.15

−61

Ethyl acetate

313.15

−54

Ethyl acetate

318.15

−50

Ethyl acetate

323.15

−50

Ethyl acetate

328.15

−50

Methanol

293.15

−69

3/27/06 2:37:10 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-46 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

Ref.

Methanol

298.15

−56

Methanol

303.15

−50

Methanol

308.15

−50

Methanol

313.15

−50

Methanol

318.15

−50

Methanol

323.15

−50

Methanol

328.15

−50

2,4-Pentanedione

298.15

−74

2-Pentanone

298.15

−64

2-Propanone

273.15

−75

2-Propanone

293.15

−75

2-Propanone

298.15

−83

2-Propanone

298.15

−68

2-Propanone

298.15

−71

2-Propanone

298.15

−74

2-Propanone

298.15

−79

2-Propanone

298.15

−75

2-Propanone

303.15

−60

2-Propanone

308.15

−51

2-Propanone

313.15

−50

2-Propanone

313.15

−65

2-Propanone

318.15

−50

2-Propanone

323.15

−50

2-Propanone

323.15

−50

2-Propanone

328.15

−50

Pyridine

298.15

−106

Tri(4-methylphenyl) phosphate

298.15

−16

Tri(4-methylphenyl) phosphate

313.15

−28

Tri(4-methylphenyl) phosphate

333.15

−41

Tri(4-methylphenyl) phosphate

343.15

−44

Tri(4-methylphenyl) phosphate

353.15

−47

Formic acid

295.15

−53

Tricresol

323.55

−66

Tricresol

345.55

−66

Nylon-6 (unoriented)

Poly(acrylonitrile)

487_S13.indb 46

0.0

Benzene

298.15

N,N-Dimethylformamide

295.15

−23

N,N-Dimethylformamide

298.15

−21

N,N-Dimethylformamide

298.15

−43

N,N-Dimethylformamide

308.15

−17

N,N-Dimethylformamide

323.15

−13

3/27/06 2:37:10 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

13-47 Solvent

T/K

∆HB∞/ J/g

Ref.

N,N-Dimethylformamide

323.15

−15

N,N-Dimethylformamide

338.15

−10

Dimethylsulfoxide

298.15

−70

160000

Dichloroacetic acid

303.15

−35

160000

1,2-Dichloroethane

303.15

−1.6

Poly(γ-benzyl-l-glutamate)

Polybutadiene Benzene

298.15

6.1

Benzene

298.15

7.1

Benzene

298.15

10.5

2,2,4-Trimethylpentane

298.15

1.1

1,4-cis-Polybutadiene low

Cyclohexane

298.15

5.4

low

Cyclooctane

298.15

5.8

low

Cyclopentane

298.15

<0.1

low

cis-Decahydronaphthalene

298.15

4.2

low

trans-Decahydronaphthalene

298.15

2.6

low

3,3-Diethylpentane

298.15

5.2

low

2,2-Dimethylpentane

298.15

4.1

low

2,3-Dimethylpentane

298.15

4.5

low

2,4-Dimethylpentane

298.15

3.2

low

3,3-Dimethylpentane

298.15

3.2

low

Dodecane

298.15

4.2

low

3-Ethylpentane

298.15

3.7

low

2,2,4,4,6,8,8Heptamethylnonane

298.15

4.8

low

Hexadecane

298.15

4.9

low

3-Methylhexane

298.15

3.6

low

Octane

298.15

4.3

low

2,2,4,6,6-Pentamethylheptane 298.15

5.0

low

2,2,4,4-Tetramethylpentane

298.15

5.8

low

2,3,3,4-Tetramethylpentane

298.15

5.1

20000

Cyclohexane

298.15

1.0

20000

Cyclooctane

298.15

1.8

20000

Cyclopentane

298.15

−2.9

Poly(1-butene)

487_S13.indb 47

20000

cis-Decahydronaphthalene

298.15

<0.1

20000

trans-Decahydronaphthalene

298.15

−2.0

20000

Decane

298.15

1.2

20000

3,3-Diethylpentane

298.15

−2.6

20000

2,2-Dimethylpentane

298.15

−4.0

20000

2,3-Dimethylpentane

298.15

−2.8

20000

2,4-Dimethylpentane

298.15

−2.3

20000

3,3-Dimethylpentane

298.15

−2.2

20000

Dodecane

298.15

2.1

3/27/06 2:37:11 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-48 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

20000

3-Ethylpentane

298.15

−2.8

20000

Heptane

298.15

0.0

20000

Hexadecane

298.15

3.0

20000

Hexane

298.15

−1.2

20000

3-Methylhexane

298.15

−2.1

20000

Nonane

298.15

0.9

20000

Octane

298.15

0.4

20000

2,2,4,6,6-Pentamethylheptane 298.15

20000

Pentane

298.15

20000

Tetradecane

20000

2,2,4,4-Tetramethylpentane

20000 20000

Ref.

0.6

−2.6

298.15

2.7

298.15

−1.4

2,3,3,4-Tetramethylpentane

298.15

−2.2

2,2,4-Trimethylpentane

298.15

−0.5

2-Propanone

298.15

0.8

Poly(butyl acrylate) Poly(butyl methacrylate) Glass

91300

210000

Cyclohexanone

304.15

7.7

Liquid

91300

210000

Cyclohexanone

304.15

8.2

2-Propanone

298.15

19.5

Benzene

298.15

0.5

1,2-Dichlorobenzene

303.05

Polychloroprene Poly(2,6-dimethyl phenylene oxide) 17000

46400

Poly(dimethylsiloxane) Benzene

298.15

11.2

20000

Benzene

298.15

13.5

100000

Benzene

298.15

14.2

170000

Bromocyclohexane

303.15

10.2

80000

2-Butanone

293.15

14.4

2-Butanone

303.15

14.2

170000

2-Butanone

303.15

14.7

80000

2-Butanone

308.15

14.3

80000

2-Butanone

323.15

14.3

80000

Butyl acetate

298.15

6.1

80000

Butyl propanoate

298.15

4.9

100000

Chlorobenzene

298.15

7.5

Cyclohexane

298.15

3.0

20000

Cyclohexane

298.15

5.2

100000

Cyclohexane

298.15

5.2

20000

Cyclooctane

298.15

6.8

20000

Cyclopentane

298.15

1.0

13000

30900

13000

487_S13.indb 48

20000

cis-Decahydronapthalene

298.15

7.1

20000

trans-Decahydronapthalene

298.15

4.3

20000

Decamethyltetrasiloxane

297.65

0.45

20000

Decane

298.15

3.8

20000

Decane

298.15

3.9

3/27/06 2:37:12 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

80000

Decane

298.15

3.8

80000

Decyl acetate

298.15

4.5

80000

Dibutyl ether

298.15

0.6

80000

Diethoxymethane

298.15

1.8

80000

Diethyl ether

298.15

−1.3

20000

3,3-Diethylpentane

298.15

1.9

80000

Dihexyl ether

298.15

3.0

80000

1,2-Dimethoxyethane

298.15

12.2

80000

Dimethoxymethane

298.15

7.4

13000

1,2-Dimethylbenzene

298.15

4.3

13000

1,3-Dimethylbenzene

298.15

3.0

∆HB∞/ J/g

Ref.

1,4-Dimethylbenzene

298.15

3.2

20000

1,4-Dimethylbenzene

298.15

4.2

80000

2,6-Dimethyl-4-heptanone

293.15

6.1

20000

2,2-Dimethylpentane

298.15

0.8

20000

2,3-Dimethylpentane

298.15

1.4

20000

2,4-Dimethylpentane

298.15

1.6

20000

3,3-Dimethylpentane

298.15

0.5

80000

Dipentyl ether

298.15

2.1

80000

Dipropyl ether

298.15

−1.2

20000

Dodecamethylpentasiloxane

297.65

−0.3

20000

Dodecane

297.65

4.5

20000

Dodecane

298.15

4.4

80000

Dodecane

298.15

4.5

80000

Ethyl acetate

298.15

12.7

170000

Ethyl acetate

303.15

13.7

13000

Ethylbenzene

298.15

6.4

20000

Ethylbenzene

298.15

6.2

80000

Ethyl butanoate

298.15

6.0

80000

Ethyl decanoate

298.15

3.8

80000

Ethyl dodecanoate

298.15

3.8

80000

Ethyl heptanoate

298.15

4.1

80000

Ethyl hexanoate

298.15

4.3

80000

Ethyl nonanoate

298.15

3.7

80000

Ethyl octanoate

298.15

3.8

20000

3-Ethylpentane

298.15

0.6

80000

Ethyl propanoate

298.15

8.0

20000

2,2,4,4,6,8,8Heptamethylnonane

298.15

3.5

13000

Heptane

298.15

1.8

20000

Heptane

298.15

1.9

20000

Heptane

297.65

2.0

20000

Heptane

298.15

2.0

80000

Heptane

298.15

2.0

100000

Heptane

298.15

2.1

170000

Heptane

303.15

1.9

80000

3-Heptanone

308.15

8.8

80000

3-Heptanone

323.15

8.8

13000

487_S13.indb 49

13-49

3/27/06 2:37:12 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-50 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

20000

Hexadecane

297.65

20000

Hexadecane

20000

Hexamethyldisiloxane

20000 170000

Ref.

5.5

298.15

5.5

298.15

−1.2

Hexamethyldisiloxane

298.15

−1.6

Hexamethyldisiloxane

303.15

−1.5

20000

Hexane

297.65

0.7

20000

Hexane

298.15

0.7

80000

Hexane

298.15

0.7

170000

Hexane

303.15

0.3

80000

Hexyl acetate

298.15

5.0

Isopropylbenzene

298.15

4.1

Methyl butanoate

298.15

8.6

Methylcyclohexane

298.15

2.9

100000

Methylcyclohexane

298.15

1.9

80000

Methyl decanoate

298.15

4.8

20000

3-Methylhexane

298.15

1.3

80000

Methyl hexanoate

298.15

5.3

80000

Methyl octanoate

298.15

5.0

80000

4-Methyl-2-pentanone

293.15

9.9

80000

4-Methyl-2-pentanone

308.15

9.0

80000

Methyl propanoate

298.15

12.1

20000

Nonane

297.65

3.4

20000

Nonane

298.15

3.3

80000

Nonane

298.15

3.4

80000

Octamethylcyclotetrasiloxane 293.15

−0.4

20000

Octamethyltrisiloxane

297.65

−0.6

20000

Octamethyltrisiloxane

298.15

−0.8

170000

Octamethyltrisiloxane

303.15

−1.0

20000

Octane

297.65

2.6

20000

Octane

298.15

2.4

20000

Octane

298.15

2.6

80000

Octane

298.15

2.6

20000

2,2,4,6,6-Pentamethylheptane 298.15

2.7

20000

Pentane

298.15

−0.9

20000

Pentane

298.15

−0.9

80000

Pentane

298.15

−1.0

80000

Pentyl acetate

298.15

5.8

80000

Pentyl propanoate

298.15

3.8

80000

Propyl acetate

298.15

8.6

170000

Propyl acetate

303.15

9.9

80000

Propyl propanoate

298.15

5.6

100000

Tetrachloromethane

298.15

2.4

20000

Tetradecane

297.65

5.1

20000

Tetradecane

298.15

5.1

80000

Tetradecane

298.15

5.1

20000

2,2,4,4-Tetramethylpentane

298.15

2.1

20000

2,2,4,4-Tetramethylpentane

298.15

2.3

13000 80000 13000

487_S13.indb 50

∆HB∞/ J/g

3/27/06 2:37:13 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

13-51

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

20000

2,3,3,4-Tetramethylpentane

298.15

1.9

Ref.

Toluene

298.15

5.5

20000

Toluene

298.15

6.7

20000

Tridecane

297.65

4.8

80000

Tridecane

298.15

4.8

13000

1,3,5-Trimethylbenzene

298.15

3.7

20000

2,2,4-Trimethylpentane

298.15

1.4

20000

Undecane

297.65

4.2

80000

Undecane

298.15

4.3

13000

Polyethylene Semicrystalline

65000

1-Chloronaphthalene

373.15

780

Semicrystalline

65000

1-Chloronaphthalene

383.15

980

Semicrystalline

65000

1-Chloronaphthalene

393.15

800

Liquid

65000

1-Chloronaphthalene

403.15

Semicrystalline

144000

1-Chloronaphthalene

383.15

920

Semicrystalline

144000

1-Chloronaphthalene

393.15

990

Semicrystalline

144000

1-Chloronaphthalene

403.15

690

Liquid

144000

1-Chloronaphthalene

413.15

Liquid

144000

1-Chloronaphthalene

423.15

Semicrystalline

670000

1-Chloronaphthalene

363.15

380

Semicrystalline

670000

1-Chloronaphthalene

373.15

430

Semicrystalline

670000

1-Chloronaphthalene

383.15

165

Liquid

670000

1-Chloronaphthalene

393.15

Liquid

670000

1-Chloronaphthalene

403.15

Semicrystalline

900000

1-Chloronaphthalene

391.80

245

105

Semicrystalline

900000

Cyclohexane

379.50

205

105

Semicrystalline

900000

Cyclopentane

380.00

190

105

Alkathene

Decahydronaphthalene

349.85

142

Rigidex-3

Decahydronaphthalene

366.65

180

Rigidex-50

Decahydronaphthalene

374.05

233

Decahydronaphthalene

384.00

260

105

Semicrystalline

1,2-Dichloroethane

333.15

Semicrystalline

1,2-Dichloroethane

338.15

Semicrystalline

1,2-Dichloroethane

343.15

Semicrystalline

1,2-Dichloroethane

348.15

Semicrystalline

900000

Semicrystalline

10000

1,4-Dimethylbenzene

354.15

139

Semicrystalline

11800

1,4-Dimethylbenzene

352.15

139

Semicrystalline

15600

1,4-Dimethylbenzene

353.65

154

Semicrystalline

15600

1,4-Dimethylbenzene

363.65

113

15600

1,4-Dimethylbenzene

368.65

104

Semicrystalline

900000

2,4-Dimethylpentane

393.00

230

105

Semicrystalline

900000

2,2,4,4,6,8,8Heptamethylnonane

399.50

170

105

Semicrystalline

900000

Hexadecane

399.50

262

105

Semicrystalline

900000

2-Methylbutane

394.20

165

105

1,2,3,4Tetrahydronaphthalene

373.15

940

Semicrystalline

487_S13.indb 51

65000

3/27/06 2:37:14 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-52

Solvent

T/K

∆HB∞/ J/g

Ref.

65000

1,2,3,4Tetrahydronaphthalene

383.15

990

65000

1,2,3,4Tetrahydronaphthalene

393.15

790

Liquid

65000

1,2,3,4Tetrahydronaphthalene

403.15

Semicrystalline

84000

1,2,3,4Tetrahydronaphthalene

373.15

835

Semicrystalline

130000

1,2,3,4Tetrahydronaphthalene

353.15

630

Semicrystalline

130000

1,2,3,4Tetrahydronaphthalene

373.15

520

Liquid

130000

1,2,3,4Tetrahydronaphthalene

393.15

144000

1,2,3,4Tetrahydronaphthalene

373.15

610

144000

1,2,3,4Tetrahydronaphthalene

383.15

1200

144000

1,2,3,4Tetrahydronaphthalene

393.15

1130

Semicrystalline

144000

1,2,3,4Tetrahydronaphthalene

403.15

800

Liquid

144000

1,2,3,4Tetrahydronaphthalene

413.15

136

Liquid

144000

1,2,3,4Tetrahydronaphthalene

423.15

Semicrystalline

310000

1,2,3,4Tetrahydronaphthalene

343.15

485

Semicrystalline

670000

1,2,3,4Tetrahydronaphthalene

353.15

560

670000

1,2,3,4Tetrahydronaphthalene

363.15

560

670000

1,2,3,4Tetrahydronaphthalene

373.15

460

670000

1,2,3,4Tetrahydronaphthalene

383.15

155

Liquid

670000

1,2,3,4Tetrahydronaphthalene

393.15

Liquid

670000

1,2,3,4Tetrahydronaphthalene

403.15

Polymer

Mn/ g/mol

Semicrystalline Semicrystalline

Semicrystalline Semicrystalline Semicrystalline

Mw/ g/mol

Mη/ g/mol

Semicrystalline

16000

Toluene

353.15

110

Semicrystalline

22000

Toluene

358.35

118

22000

Toluene

367.35

106

1,2,4-Trichlorobenzene

386.50

255

105

180

Benzene

303.15

110

385

Benzene

303.15

560

Benzene

303.15

1050

Benzene

303.15

1610

Benzene

303.15

140

1940

Benzene

303.15

215

3200

Benzene

303.15

195

4330

Benzene

303.15

195

Semicrystalline Semicrystalline

900000

Poly(ethylene glycol)

487_S13.indb 52

3/27/06 2:37:14 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

5850 9950 43400

13-53 Solvent

T/K

∆HB∞/ J/g

Ref.

Benzene

303.15

190

Benzene

303.15

195

Benzene

303.15

190

400

420

Trichloromethane

303.15

−79

590

615

Trichloromethane

303.15

−88

180

Water

303.15

−136

200

Water

321.35

−125

355

Water

303.15

−159

400

Water

321.35

−150

560

Water

303.15

−150

990

Water

321.35

−101

1050

Water

303.15

−106

1460

Water

321.35

−137

1610

Water

303.15

−6

1940

Water

303.15

3200

Water

303.15

4330

Water

303.15

5850

Water

303.15

Water

303.15

14000

Water

303.15

14000

Water

313.15

20300

Water

303.15

34500

Water

303.15

43300

Water

303.15

+40

250

Tetrachloromethane

303.15

250

Tetrachloromethane

318.15

9950

Poly(ethylene glycol) dimethyl ether −12 −7.6

95 95

Tetrachloromethane

303.15

−12

520

550

Tetrachloromethane

303.15

−12

520

550

Tetrachloromethane

303.15

−7.6

Trichloromethane

303.15

−184

Trichloromethane

303.15

−135

230

Dodecane

302.15

274

Dodecane

302.15

318

Dodecane

302.15

362

Dodecane

302.15

406

Dodecane

302.15

400

250 520

550

95 95

Poly(ethylene glycol) monododecyl ether

Poly(ethylene glycol) monomethyl ether 353

377

Trichloromethane

303.15

−125

550

580

Trichloromethane

303.15

−117

Poly(ethylene oxide) Semicrystalline

6000

Dichloromethane

303.15

+84

Liquid

6000

Dichloromethane

303.15

−160

487_S13.indb 53

3/27/06 2:37:15 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-54 Polymer

Mn/ g/mol

Mw/ g/mol

Semicrystalline

6000

Liquid

6000

Quenched

1520

1720

Annealed

1520

Quenched

1520

Annealed Quenched

Mη/ g/mol

∆HB∞/ J/g

Solvent

T/K

Trichloromethane

303.15

+52

Trichloromethane

303.15

−186

Water

293.15

−403

1720

Water

293.15

−392

1720

Water

298.15

−180

1520

1720

Water

298.15

−150

1520

1720

Water

303.15

+68

Annealed

1520

1720

Water

303.15

+109

Liquid

6000

Water

303.15

−50

Quenched

6840

7525

Water

293.15

−28

Annealed

6840

7525

Water

293.15

+209

Quenched

6840

7525

Water

298.15

+241

Annealed

6840

7525

Water

298.15

+540

Quenched

16600

19600

Water

293.15

−160

Annealed

16600

19600

Water

293.15

−143

Quenched

16600

19600

Water

298.15

+59

Annealed

16600

19600

Water

298.15

+155

Quenched

16600

19600

Water

303.15

+353

Annealed

16600

19600

Water

303.15

+490

20000

Water

298.15

+10

765

1023

Anisole

299.15

2.1

102

765

1023

Benzene

299.15

−0.04

102

765

1023

Benzonitrile

299.15

−4.4

102

765

1023

Bromobenzene

299.15

−3.9

102

765

1023

2-Butanone

299.15

1.9

102

765

1023

Chlorobenzene

299.15

−3.9

102

765

1023

1-Chlorobutane

299.15

−4.0

102

765

1023

1-Chloroheptane

299.15

1.5

102

765

1023

Cyclohexane

299.15

102

765

1023

N,N-dimethylaniline

299.15

−8.2

102

765

1023

Ethyl acetate

299.15

4.2

102

765

1023

Ethylbenzene

299.15

−1.4

102

765

1023

Ethyl benzoate

299.15

−0.7

102

765

1023

Nitrobenzene

299.15

4.6

102

765

1023

1-Nitropropane

299.15

8.4

102

765

1023

Pyridine

299.15

−6.7

102

765

1023

1,1,2,2-Tetrachloroethane

299.15

765

1023

Tetrachloromethane

299.15

765

1023

1,1,1-Trichloroethane

299.15

765

1023

Trichloromethane

299.15

−20

102

Semicrystalline

Ref.

Polyindene

−19

102

−2.5

102

−1.8

102

Polyisobutylene

487_S13.indb 54

360

700

Benzene

298.15

1000

2000

Benzene

298.15

1300

2500

Benzene

298.15

30000

Benzene

297.65

30000

Benzene

298.15

3/27/06 2:37:16 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

∆HB∞/ J/g

Solvent

T/K

Benzene

303.15

48000

Benzene

303.4

50000

Benzene

303.15

72000

Benzene

300.15

72000

Benzene

323.15

72000

Benzene

343.15

72000

Benzene

375.15

72000

Benzene

394.15

9.2

72000

Benzene

423.15

3.5

72000

Benzene

437.15

−0.5

72000

Benzene

453.15

−4.7

90000

Benzene

298.15

6.7

160000

Benzene

303.15

560000

Benzene

298.15

Benzene

298.15

6.8

Benzene

298.15

6.8

30000

Chlorobenzene

297.65

30000

Chlorobenzene

298.15

50000

Chlorobenzene

303.15

160000

Chlorobenzene

303.15

44700

487_S13.indb 55

13-55 Ref.

560000

Chlorobenzene

298.15

360

700

Cyclohexane

298.15

3.8

1000

2000

Cyclohexane

298.15

1.2

1300

2500

Cyclohexane

298.15

1.1

4500

Cyclohexane

298.15

−0.6

30000

Cyclohexane

297.65

−0.7

30000

Cyclohexane

298.15

−0.6

50000

Cyclohexane

303.15

−0.7

160000

Cyclohexane

303.15

−0.6

1990000

Cyclohexane

298.15

−0.7

4500

Cyclooctane

298.15

+0.3

4500

Cyclopentane

298.15

−5.9

4500

cis-Decahydronaphthalene

298.15

0.2

4500

trans-Decahydronaphthalene

298.15

−0.8

30000

Decane

297.65

−0.5

50000

Decane

303.15

−0.5

30000

Dibutyl ether

297.65

1.2

30000

Diethyl ether

297.65

2.8

30000

Diethyl ether

297.65

2.8

4500

3,3-Diethylpentane

298.15

−1.4

30000

Dihexyl ether

297.65

0.9

4500

2,2-Dimethylpentane

298.15

−1.1

4500

2,3-Dimethylpentane

298.15

−1.9

4500

2,4-Dimethylpentane

298.15

−1.1

4500

3,3-Dimethylpentane

298.15

−1.7

30000

Dipentyl ether

297.65

1.0

30000

Dipropyl ether

297.65

1.8

3/27/06 2:37:16 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-56 Polymer

487_S13.indb 56

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

360

700

Dodecane

298.15

1.9

1000

2000

Dodecane

298.15

0.7

1300

2500

Dodecane

298.15

0.5

4500

Dodecane

298.15

0.2

30000

Dodecane

297.65

−0.1

30000

Dodecane

298.15

−0.1

48000

Ethylbenzene

291.15

9.5

48000

Ethylbenzene

343.15

3.6

30000

Ethyl decanoate

297.65

3.0

30000

Ethyl heptanoate

297.65

5.6

30000

Ethyl hexadecanoate

297.65

1.3

30000

Ethyl hexanoate

297.65

6.7

30000

Ethyl nonanoate

297.65

3.7

30000

Ethyl octanoate

297.65

4.6

4500

3-Ethylpentane

298.15

−2.0

30000

Ethyl tetradecanoate

297.65

1.8

4500

2,2,4,4,6,8,8Heptamethylnonane

298.15

−0.5

360

700

Heptane

298.15

−0.5

1000

2000

Heptane

298.15

−1.0

1300

2500

Heptane

298.15

−1.4

4500

Heptane

298.15

−1.7

30000

Heptane

297.65

−1.8

30000

Heptane

298.15

−2.0

50000

Heptane

303.15

−1.8

160000

Heptane

303.15

−1.6

Heptane

298.15

−1.4

Ref.

Heptane

298.15

−1.4

360

700

Hexadecane

298.15

4.5

1000

2000

Hexadecane

298.15

2.1

1300

2500

Hexadecane

298.15

1.0

4500

Hexadecane

298.15

0.9

30000

Hexadecane

297.65

0.04

30000

Hexane

297.65

−2.5

30000

Hexane

298.15

−2.6

50000

Hexane

303.15

−2.5

72000

Hexane

303.15

−1.8

72000

Hexane

324.15

−2.3

72000

Hexane

348.15

−2.9

72000

Hexane

373.15

−3.7

72000

Hexane

393.15

−5.3

72000

Hexane

408.15

−6.7

72000

Hexane

423.15

−9.0

72000

Hexane

433.15

−9.9

160000

Hexane

303.15

−2.5

30000

2-Methylbutane

297.65

−3.1

30000

Methylcyclohexane

297.65

−1.2

50000

Methylcyclohexane

303.15

−1.2

3/27/06 2:37:17 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

13-57

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

160000

Methylcyclohexane

303.15

−1.2

4500

3-Methylhexane

298.15

−1.0

30000

3-Methylpentane

297.65

−2.8

30000

Nonane

297.65

−0.8

4500

Nonane

298.15

−0.8

4500

Octane

298.15

−1.1

30000

Octane

297.65

−1.2

72000

Octane

303.15

−0.3

72000

Octane

324.15

−0.8

72000

Octane

348.15

−0.9

72000

Octane

373.15

−1.1

72000

Octane

393.15

−1.3

72000

Octane

423.15

−3.6

4500

2,2,4,6,6-Pentamethylheptane 298.15

−0.1

360

700

Pentane

298.15

−1.9

1000

2000

Pentane

298.15

−2.9

1300

2500

Pentane

298.15

−3.2

30000

Pentane

297.65

−3.6

72000

Pentane

303.15

−2.8

72000

Pentane

333.15

−3.4

72000

Pentane

352.15

−4.5

72000

Pentane

365.15

−5.5

360

700

Tetrachloromethane

298.15

5.9

1000

2000

Tetrachloromethane

298.15

5.8

1300

2500

Tetrachloromethane

298.15

5.0

1990000

Tetrachloromethane

298.15

4.1

30000

Tetradecane

297.65

0.0

4500

2,2,4,4-Tetramethylpentane

298.15

−0.6

4500

2,3,3,4-Tetramethylpentane

298.15

−2.3

50000

Toluene

303.15

7.4

160000

Toluene

303.15

7.4

1990000

Toluene

298.15

8.8

Toluene

298.15

1.8

Ref.

Toluene

298.15

1.8

30000

Tridecane

297.65

−0.04

4500

2,2,4-Trimethylpentane

298.15

−0.4

30000

2,2,4-Trimethylpentane

297.65

−0.6

1990000

2,2,4-Trimethylpentane

298.15

0.0

2,2,4-Trimethylpentane

298.15

0.0

30000

2,2,4-Trimethylpentane

298.15

0.0

Undecane

297.65

−0.4

Poly(isobutyl methacrylate) Glass

260000

Cyclohexanone

303.15

−5.2

Liquid

260000

Cyclohexanone

303.15

2-Propanone

298.15

Poly(methyl acrylate)

487_S13.indb 57

0.0

3/27/06 2:37:18 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-58 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

Ref.

Poly(methyl methacrylate) Glass

73900

170000

Cyclohexanone

304.15

−14

Liquid

73900

170000

Cyclohexanone

304.15

1930

1,2-Dichloroethane

298.15

−20

240000

1,2-Dichloroethane

298.15

−27

53000

Ethylbenzene

298.15

−31

180000

Ethylbenzene

298.15

−29

28900

35900

4-Methyl-2-pentanone

303.15

−21

93940

101000

4-Methyl-2-pentanone

303.15

−24

137000

215000

4-Methyl-2-pentanone

303.15

−28

2-Propanone

298.15

−30

93940

101000

Toluene

303.15

−22

689000

782000

Toluene

303.15

−24

12000

Trichloromethane

298.15

−65

54000

Trichloromethane

298.15

−80

80000

Trichloromethane

298.15

−81

100000

Trichloromethane

298.15

−84

320000

Trichloromethane

298.15

−83

93940

101000

Trichloromethane

303.15

−71

689000

782000

Trichloromethane

303.15

−72

2320000

Trichloromethane

303.15

−73

Cyclohexane

303.15

−7.1

Poly(4-methyl-1-pentene) Semicrystalline

350000

Poly(α-methylstyrene) 1030 1820

1180

Toluene

298.15

1430

Toluene

298.15

−30

2230

Toluene

298.15

−34

Toluene

298.15

−37

1920

Toluene

298.15

−39

3280

Toluene

298.15

−46

5260

Toluene

298.15

−46

8600

Toluene

298.15

−45

12200

Toluene

298.15

−46

10500

Toluene

310.15

53000

Toluene

310.15

−13

55000

Toluene

333.15

−16

87000

Toluene

298.15

−17

87000

Toluene

310.15

−16

87000

Toluene

333.15

−11

Acetic acid

298.15

100

Acetonitrile

298.15

100

1,2-Dichloroethane

298.15

100

2700

3300

−8.4

Poly(2-methyl-5-vinyltetrazole)

487_S13.indb 58

N,N-Diethylacetamide

298.15

100

N,N-Dimethylformamide

298.15

100

Dimethylsulfoxide

298.15

100

3/27/06 2:37:18 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

13-59 Solvent

T/K

∆HB∞/ J/g

Ref.

Formamide

298.15

100

Formic acid

298.15

110

100

Nitromethane

298.15

100

Pyridine

298.15

100

7000

Benzene

298.15

7000

Benzene

303.15

7000

Benzene

308.15

Poly(octamethylene oxide)

Polypentenamer 50000

Cyclohexane

298.15

4.6

50000

Cyclooctane

298.15

5.1

50000

Cyclopentane

298.15

−2.3

50000

cis-Decahydronaphthalene

298.15

2.6

50000

trans-Decahydronaphthalene

298.15

<0.1

50000

3,3-Diethylpentane

298.15

2.4

50000

2,2-Dimethylpentane

298.15

3.3

50000

2,3-Dimethylpentane

298.15

2.2

50000

2,4-Dimethylpentane

298.15

3.3

50000

3,3-Dimethylpentane

298.15

2.7

50000

Dodecane

298.15

2.9

50000

3-Ethylpentane

298.15

2.1

50000

2,2,4,4,6,8,8Heptamethylnonane

298.15

3.2

50000

Hexadecane

298.15

2.6

50000

3-Methylhexane

298.15

2.4

50000

Octane

298.15

2.2

50000

2,2,4,6,6-Pentamethylheptane 298.15

3.8

50000

2,2,4,4-Tetramethylpentane

298.15

4.5

50000

2,3,3,4-Tetramethylpentane

298.15

2.4

50000

2,2,4-Trimethylpentane

298.15

4.3

Poly(m-phenyleneisophthalamide) Glass

N,N-Dimethylacetamide

298.15

−171

Semicrystalline

N,N-Dimethylacetamide

298.15

−128

Glass

N,N-Dimethylformamide

298.15

−149

Semicrystalline

N,N-Dimethylformamide

298.15

−125

Glass

1-Methyl-2-pyrrolidone

298.15

−177

Semicrystalline

1-Methyl-2-pyrrolidone

298.15

−118

18000

Benzene

298.15

6000

Cyclohexane

298.15

2.3

18000

Cyclohexane

298.15

3.9

6000

Cyclooctane

298.15

3.0

6000

Cyclopentane

298.15

−2.3

6000

cis-Decahydronaphthalene

298.15

0.5

Polypropylene (atactic)

487_S13.indb 59

3/27/06 2:37:19 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-60 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

6000

trans-Decahydronaphthalene

298.15

∆HB∞/ J/g −2.4

Ref. 74

18000

Decane

298.15

3.1

6000

3,3-Diethylpentane

298.15

−3.9

18000

1,2-Dimethylbenzene

298.15

18000

1,3-Dimethylbenzene

298.15

18000

1,4-Dimethylbenzene

298.15

6000

2,2-Dimethylpentane

298.15

−2.2

6000

2,3-Dimethylpentane

298.15

−2.5

6000

2,4-Dimethylpentane

298.15

−1.8

6000

3,3-Dimethylpentane

298.15

−3.0

6000

Dodecane

298.15

1.7

18000

Ethylbenzene

298.15

6000

3-Ethylpentane

298.15

−2.5

6000

2,2,4,4,6,8,8Heptamethylnonane

298.15

−0.7

6000

Heptane

298.15

−1.6

18000

Heptane

298.15

0.5

6000

Hexadecane

298.15

2.3

18000

Hexane

298.15

−1.4

6000

3-Methylhexane

298.15

−1.8

6000

Nonane

298.15

0.8

18000

Nonane

298.15

2.4

6000

Octane

298.15

−1.2

18000

Octane

298.15

1.0

6000

2,2,4,6,6-Pentamethylheptane 298.15

−0.2

18000

Pentane

298.15

−4.7

18000

Tetrachloromethane

298.15

6.6

6000

2,2,4,4-Tetramethylpentane

298.15

−0.8

6000

2,3,3,4-Tetramethylpentane

298.15

−3.1

18000

Toluene

298.15

18000

Trichloromethane

298.15

6000

2,2,4-Trimethylpentane

298.15

−1.0

1-Chloronaphthalene

383.15

1-Chloronaphthalene

393.15

170

1-Chloronaphthalene

403.15

245

1-Chloronaphthalene

423.15

275

1,2,3,4Tetrahydronaphthalene

373.15

140

1,2,3,4Tetrahydronaphthalene

383.15

215

1,2,3,4Tetrahydronaphthalene

393.15

330

1,2,3,4Tetrahydronaphthalene

403.15

330

1,2,3,4Tetrahydronaphthalene

413.15

335

1,2,3,4Tetrahydronaphthalene

423.15

290

Polypropylene (isotactic)

S13_08.indd 60

4/10/06 11:53:13 AM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

13-61 Solvent

T/K

∆HB∞/ J/g

Ref.

Poly(propylene glycol) 150

Benzene

321.35

200

103

425

Benzene

321.35

103

2025

Benzene

321.35

103

150

Ethanol

321.35

103

425

Ethanol

321.35

103

2025

Ethanol

321.35

103

396

412

Tetrachloromethane

303.15

4.7

396

412

Tetrachloromethane

318.15

5.2

1900

Tetrachloromethane

303.15

−8.2

1900

Tetrachloromethane

318.15

Trichloromethane

303.15

−81

Water

298.15

−165

150

Water

321.35

−90

103

425

Water

321.35

−95

103

1900 400

Polystyrene 600

Benzene

298.15

−1.3

600

Benzene

313.15

−2.5

900

Benzene

291.15

900

Benzene

318.15

2000

Benzene

291.15

2000

Benzene

318.15

5000

Benzene

291.15

−23

5000

Benzene

318.15

−12

10300

Benzene

291.15

−26

10300

Benzene

318.15

−18

Benzene

298.15

Benzene

296.15

29000

Benzene

298.15

−5.0

30000

Benzene

298.15

−7.5

59000

Benzene

298.15

−13

91000

Benzene

298.15

−15

Benzene

318.15

−21

142000

Benzene

298.15

−17

190000

Benzene

303.15

−18

18000 20000

97200

−5.8 −16 −6.8

−4.1 −15

54 54 54 54

19 9

Benzene

300.15

−16

216000

Benzene

298.15

−18

272000

Benzene

298.15

−21

300000

Benzene

298.15

−21

Benzene

298.15

−27

Benzene

298.15

−10

20000

Butyl acetate

296.15

−13

20000

2-Butanone

296.15

−15

142000

2-Butanone

296.15

−17

190000

Butylbenzene

303.15

−14

Chlorobenzene

293.15

−32

Chlorobenzene

298.15

5.4

214000

150000 266000

487_S13.indb 61

−10

3/27/06 2:37:20 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-62 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

Ref.

Chlorobenzene

293.15

−39

1260

Cyclohexane

298.15

1910

Cyclohexane

298.15

5.4

3160

Cyclohexane

298.15

−5.4

3980

Cyclohexane

298.15

−6.9

5630

Cyclohexane

298.15

−9.3

9070

Cyclohexane

298.15

Cyclohexane

296.15

2.5

Cyclohexane

303.15

−2.1

Cyclohexane

293.15

−14

Cyclohexanone

298.15

−29

Cyclohexene

296.15

−9.4

Decahydronaphthalene

303.15

3.8

1,2-Dichlorobenzene

303.05

20000

1,2-Dimethylbenzene

296.15

−13

20000

1,3-Dimethylbenzene

296.15

−12

20000 190000 22400 20000 190000 110000

115000

190000

1,3-Dimethylbenzene

303.15

−15

190000

1,4-Dioxane

303.15

−12

Ethyl acetate

296.15

−11

142000

Ethyl acetate

296.15

−13

785

Ethylbenzene

298.15

0.0

18000

Ethylbenzene

298.15

−3.8

18000

Ethylbenzene

298.15

−3.9

30000

Ethylbenzene

298.15

−5.7

35000

Ethylbenzene

298.15

−6.5

45000

Ethylbenzene

298.15

−8.4

91000

Ethylbenzene

298.15

−11

142000

Ethylbenzene

298.15

−13

216000

Ethylbenzene

298.15

−17

20000

Ethylbenzene

303.15

−22

113000

122000

Ethylbenzene

306.65

−24

113000

122000

Ethylbenzene

317.15

−19

113000

122000

Ethylbenzene

337.15

−11

113000

122000

Ethylbenzene

347.15

−6.4

113000

122000

Ethylbenzene

350.65

−4.9

113000

122000

Ethylbenzene

366.65

−2.3

113000

122000

Ethylbenzene

367.15

−2.1

113000

122000

Ethylbenzene

368.65

−2.6

113000

122000

Ethylbenzene

372.15

−4.2

113000

122000

Ethylbenzene

378.15

−4.6

113000

122000

Ethylbenzene

385.15

−5.7

60000

Ethylbenzene

293.15

−34

190000

Ethylbenzene

303.15

−15

272000

Ethylbenzene

298.15

−18

272000

Ethylbenzene

298.15

−18

413000

Ethylbenzene

298.15

−24

Ethylbenzene

293.15

−34

150000

487_S13.indb 62

−11

3/27/06 2:37:21 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

∆HB∞/ J/g

Ref.

Ethylbenzene

298.15

−17

−30

Ethylbenzene

298.15

1260

2-Propanone

298.15

1910

2-Propanone

298.15

3160

2-Propanone

298.15

−16

3980

2-Propanone

298.15

−17

5630

2-Propanone

298.15

−19

9070

2-Propanone

298.15

−21

20000

2-Propanone

296.15

−11

Propylbenzene

303.15

−14

Styrene

296.15

−18

Styrene

296.15

−35

Tetrachloromethane

298.15

−22

600

Toluene

296.15

−2.1

600

Toluene

309.15

−1.8

600

Toluene

318.15

−1.5

1260

Toluene

296.15

1260

Toluene

303.15

−8.0

1260

Toluene

309.15

−5.9

1260

Toluene

318.15

−3.4

1260

Toluene

328.15

−2.3

1260

Toluene

338.15

−1.9

1260

Toluene

346.65

−1.3

1910

Toluene

298.15

1910

Toluene

318.15

−6.7

1910

Toluene

338.15

−3.4

1910

Toluene

348.15

−2.5

3160

Toluene

298.15

−23

3980

Toluene

298.15

−24

3980

Toluene

318.15

−17

3980

Toluene

338.15

−10

5630

Toluene

298.15

−26

9070

Toluene

298.15

−28

−33

190000 20000 413000

270000

20000

487_S13.indb 63

13-63

−0.6

−7.7

−11

−16

Toluene

298.15

600

Toluene

298.15

−1.4

600

Toluene

313.15

−3.2

900

Toluene

291.15

−7.3

900

Toluene

318.15

−6.6

2000

Toluene

291.15

2000

Toluene

318.15

5000

Toluene

291.15

−21

5000

Toluene

318.15

−11

10300

Toluene

291.15

−24

10300

Toluene

318.15

−15

97200

Toluene

318.15

−17

9000

Toluene

310.15

Toluene

296.15

−11 −7.2

−9.2 −17

54 54

54 92 9

3/27/06 2:37:22 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-64 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

∆HB∞/ J/g

Solvent

T/K

20400

Toluene

298.15

−8.2

Ref.

20400

Toluene

310.15

−8.4

20400

Toluene

333.15

−6.4

47000

Toluene

310.15

−5.0

50000

Toluene

333.15

−6.8

Toluene

303.15

−21

113000

122000

Toluene

304.15

−29

113000

122000

Toluene

306.15

−27

113000

122000

Toluene

306.65

−26

113000

122000

Toluene

316.15

−23

113000

122000

Toluene

333.15

−15

113000

122000

Toluene

337.15

−12

113000

122000

Toluene

346.15

−8.3

113000

122000

Toluene

347.15

−7.8

113000

122000

Toluene

348.15

−8.2

113000

122000

Toluene

350.65

−6.5

113000

122000

Toluene

359.15

−4.3

113000

122000

Toluene

362.15

−2.7

113000

122000

Toluene

369.15

−3.3

113000

122000

Toluene

372.15

−2.8

115000

Toluene

310.15

−5.0

150000

Toluene

293.15

−34

Toluene

303.15

−18

Toluene

300.15

−19

Toluene

303.15

−18

Toluene

293.15

−34

Toluene

298.65

−39

Toluene

308.15

−34

Toluene

318.15

−30

Toluene

333.15

−23

Toluene

343.15

−13

60000

190000 214000 250000

Toluene

353.15

−13

600

Trichloromethane

298.15

−13

600

Trichloromethane

313.15

900

Trichloromethane

291.15

−22

900

Trichloromethane

313.15

−15

2000

Trichloromethane

291.15

−28

2000

Trichloromethane

313.15

−16

5000

Trichloromethane

291.15

−30

5000

Trichloromethane

313.15

−18

10300

Trichloromethane

291.15

−33

10300

Trichloromethane

313.15

−23

Trichloromethane

298.15

−17

Trichloromethane

313.15

−25

1,3,5-Trimethylbenzene

296.15

−11

1,3,5-Trimethylbenzene

303.15

−13

22400 97200 20000 190000

−9.9

Poly(tetramethylene oxide)

487_S13.indb 64

3/27/06 2:37:22 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

13-65 ∆HB∞/ J/g

Solvent

T/K

650

Benzene

313.15

4.0

Ref.

1000

Benzene

313.15

2.0

2000

Benzene

313.15

1.1

650

1,2-Dichloroethane

313.35

3.1

2000

1,2-Dichloroethane

313.35

0.3

650

1,2-Dimethylbenzene

313.15

5.9

1000

1,2-Dimethylbenzene

313.15

1.8

2000

1,2-Dimethylbenzene

313.15

0.9

650

1,3-Dimethylbenzene

313.15

6.4

1000

1,3-Dimethylbenzene

313.15

0.6

2000

1,3-Dimethylbenzene

313.15

0.8

650

1,4-Dimethylbenzene

313.15

4.3

1000

1,4-Dimethylbenzene

313.15

1.8

2000

1,4-Dimethylbenzene

313.15

0.7

650

1,4-Dioxane

321.35

4.0

1000

1,4-Dioxane

321.35

2.3

2000

1,4-Dioxane

321.35

1.0

650

Ethylbenzene

313.15

6.9

1000

Ethylbenzene

313.15

3.4

2000

Ethylbenzene

313.15

−0.05

650

Propylbenzene

313.15

5.8

1000

Propylbenzene

313.15

1.3

2000

Propylbenzene

313.15

0.9

650

Tetrachloromethane

313.15

3.3

1000

Tetrachloromethane

313.15

1.4

2000

Tetrachloromethane

321.35

0.7

650

Toluene

313.15

4.3

1000

Toluene

313.15

2.0

2000

Toluene

313.15

0.9

650

1,3,5-Trimethylbenzene

313.15

6.1

1000

1,3,5-Trimethylbenzene

313.15

2.7

2000

1,3,5-Trimethylbenzene

313.15

0.6

Poly(vinyl acetate)

487_S13.indb 65

140000

Benzene

298.15

2.3

350000

2-Butanone

303.15

−1.7

350000

Butyl acetate

303.15

1.0

135000

Chlorobenzene

298.15

5.0

350000

Ethyl acetate

303.15

−6.7

Ethyl acetate

303.15

0.0

26000

3-Heptanone

303.15

7.0

350000

3-Heptanone

303.15

4.9

140000

Methanol

298.15

350000

Methyl acetate

303.15

350000

2-Pentanone

93000

2-Propanone

350000

−45

−9.7

303.15

0.0

303.15

−0.4

2-Propanone

303.15

−3.9

2-Propanone

303.15

−2.9

3/27/06 2:37:23 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-66 Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Solvent

T/K

350000

Propyl acetate

303.15

Tetrahydrofuran

304.65

Trichloromethane

298.15

Ethanol

298.15

150000 140000

∆HB∞/ J/g

Ref.

−2.7

4.5

Poly(vinyl alcohol) 3.8

9.6

Ethanol

298.15

7260

Water

303.15

−34

17000

Water

303.15

−18

61600

Water

303.15

−41

Water

303.15

−8.4

Poly(vinyl chloride) Chlorobenzene

298.15

−17

Glass

23200

Cyclohexanone

303.15

−27

Liquid

23200

Cyclohexanone

303.15

Glass

38700

Cyclohexanone

303.15

Liquid

38700

Cyclohexanone

303.15

Glass

53500

Cyclohexanone

303.15

Liquid

53500

Cyclohexanone

303.15

Glass

66700

Cyclohexanone

303.15

Liquid

66700

Cyclohexanone

303.15

Glass

136000

Cyclohexanone

303.15

Liquid

136000

Cyclohexanone

303.15

Glass

155400

Cyclohexanone

303.15

Liquid

155400

Cyclohexanone

303.15

48000

Cyclopentanone

298.15

−28

104

1,2-Dichloroethane

323.65

1,2-Dichloroethane

328.15

1,2-Dichloroethane

333.15

1,2-Dichloroethane

368.15

1,2-Dichloroethane

373.15

1,2-Dichloroethane

378.15

−7.5 −29 −6.6 −28 −6.3 −29 −6.1 −31 −5.8 −32 −5.8

59 59 59 59 59 59 59 59 59 59 59

N,N-Dimethylformamide

293.15

−28

N,N-Dimethylformamide

308.15

−19

N,N-Dimethylformamide

323.15

−14

N,N-Dimethylformamide

338.15

−7.5

2.4

N,N-Dimethylformamide

353.15

Glass

23200

Tetrahydrofuran

303.15

−34

Liquid

23200

Tetrahydrofuran

303.15

−14

Glass

38700

Tetrahydrofuran

303.15

−35

Liquid

38700

Tetrahydrofuran

303.15

−14

Glass

53500

Tetrahydrofuran

303.15

−39

Liquid

53500

Tetrahydrofuran

303.15

−14

Glass

66700

Tetrahydrofuran

303.15

−36

Liquid

66700

Tetrahydrofuran

303.15

−14

Glass

136000

Tetrahydrofuran

303.15

−39

Liquid

136000

Tetrahydrofuran

303.15

−14

Glass

155400

Tetrahydrofuran

303.15

−39

487_S13.indb 66

3/27/06 2:37:24 PM

Specific Enthalpies of Solution of Polymers and Copolymers Polymer

Mn/ g/mol

Liquid

155400

Mw/ g/mol

Mη/ g/mol

13-67 Solvent

T/K

∆HB∞/ J/g

Ref.

Tetrahydrofuran

303.15

−14

N,N-Dimethylformamide

298.15

−28

Water

298.15

−139

Poly(1-vinyl-3,5-dimethyl-1,2,4-triazole)

Poly(1-vinylimidazole) 20700

Acetic acid

298.15

−393

20700

Butanoic acid

298.15

−322

20700

N,N-Dimethylacetamide

298.15

−48

20700

N,N-Dimethylformamide

298.15

−48

20700

1-Methyl-2-pyrrolidinone

298.15

−54

20700

Pentanoic acid

298.15

−325

20700

Propanoic acid

298.15

−278

20700

Water

298.15

−119

18900

Acetic acid

298.15

−88

18900

Butanoic acid

298.15

−60

Poly(1-vinylpyrazole)

18900

N,N-Dimethylacetamide

298.15

−26

18900

N,N-Dimethylformamide

298.15

−28

18900

Pentanoic acid

298.15

−52

18900

Propanoic acid

298.15

−36

32000

Trichloromethane

298.15

−75

32000

Water

298.15

−150

Poly(1-vinyl-2-pyrrolidone)

Poly(1-vinyl-1,2,4-triazole) 69500

Acetic acid

298.15

−85

69500

Butanoic acid

298.15

−74

69500

N,N-Dimethylacetamide

298.15

−49

69500

N,N-Dimethylformamide

298.15

−47

69500

1-Methyl-2-pyrrolidinone

298.15

−55

69500

Pentanoic acid

298.15

−75

69500

Propanoic acid

298.15

−72

69500

Water

298.15

−68

(9 wt% Vinyl acetate)

2-Propanone

298.15

6.3

(44 wt% Vinyl acetate)

2-Propanone

298.15

4.6

(57 wt% Vinyl acetate)

2-Propanone

298.15

0.0

(67 wt% Vinyl acetate)

2-Propanone

298.15

−1.3

(4.2 mol% Vinyl acetate) 7560

Water

303.15

−41

(4.3 mol% Vinyl acetate) 64300

Water

303.15

−49

(9.0 mol% Vinyl acetate) 66900

Water

303.15

−55

(10.3 mol% Vinyl acetate) 7970

Water

303.15

−41

(15.3 mol% Vinyl acetate) 8300

Water

303.15

−60

Vinyl acetate/vinyl alcohol copolymer

487_S13.indb 67

3/27/06 2:37:24 PM

Specific Enthalpies of Solution of Polymers and Copolymers

13-68

Solvent

T/K

∆HB∞/ J/g

Ref.

(15.4 mol% Vinyl acetate) 70700

Water

303.15

−65

(19.5 mol% Vinyl acetate) 73100

Water

303.15

−66

(22.1 mol% Vinyl acetate) 8800

Water

303.15

−60

(26.2 mol% Vinyl acetate) 77000

Water

303.15

−64

(30.6 mol% Vinyl acetate) 9370

Water

303.15

−53

(34.0 mol% Vinyl acetate) 81600

Water

303.15

−60

(34.7 mol% Vinyl acetate) 9670

Water

303.15

−44

Polymer

Mn/ g/mol

Mw/ g/mol

Mη/ g/mol

Vinyl acetate/vinyl chloride copolymer (90 wt% Vinyl chloride) Glass

12400

26000

Cyclohexanone

304.15

−37

101

Liquid

12400

26000

Cyclohexanone

304.15

−16

101

Trichloromethane

297.15

−17

Vinyl chloride/vinylidene chloride copolymer

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

487_S13.indb 68

Liepatoff, S. and Preobagenskaja, S., Kolloid Z. Z. Polym., 68, 324, 1934. Kargin, V. and Papkov, S., Acta Physicochim. URSS, 3, 839, 1935. Papkov, S. and Kargin, V., Acta Physicochim. URSS, 7, 667, 1937. Tager, A. and Kargin, V., Acta Physicochim. URSS, 14, 713, 1941. Raine, H.C., Richards, R.B., and Ryder, H., Trans Faraday Soc., 41, 56, 1945. Roberts, D.E., Walton, W.W., and Jessup, R.S., J. Polym. Sci., 2, 420, 1947. Tager, A. and Sanatina, V., Kolloidn. Zhur., 12, 474, 1950. Glikman, S.A. and Root, L.A., Zh. Obshch. Khim., 21, 58, 1951. 35. Hellfritz, H., Makromol. Chem., 7, 191, 1951. 36. Tager, A. and Vershkain, R., Kolloidn. Zhur., 13, 123, 1951. Tager, A.A., and Kargin, V.A., Kolloidn. Zhur., 14, 367, 1952. 37. Tager, A.A. and Dombek, Zh.S., Kolloidn. Zhur., 15, 69, 1953. 38. Daoust, H. and Rinfret, M., Can. J. Chem., 32, 492, 1954. Gatovskaya, T.V., Kargin, V.A., and Tager, A.A., Zh. Fiz. Khim., 29, 883, 1955. 39. Oya, S., Chem. High Polym. Japan, 12, 122, 1955. Schulz, G.V., Guenner, K. von, and Gerrens, H., Z. Phys. Chem., N. F., 40. 4, 192, 1955. Tager, A.A., Kosova, L.K., Karlinskaya, D.Yu., and Yurina, I.A., Kolloid. 41. Zhur., 17, 315, 1955. 42. Tager, A.A. and Kosova, L.K., Kolloid. Zhur., 17, 391, 1955. Tager, A.A., Krivokorytova, R.V., and Khodorov, P.M., Dokl. Akad. 43. Nauk SSSR, 100, 741, 1955. Glikman, S.A. and Root, L.A., Kolloidn. Zhur., 18, 523, 1956. 44. Jenckel, E. and Gorke, K., Z. Elektrochem., 60, 579, 1956. Lipatov, Yu.S., Kargin, V.A., and Slonimskii, G.L., Zh. Fiz. Khim., 30, 45. 1202, 1956 46. Meerson, S.I. and Lipatov, S.M., Kolloidn.,Zh., 18, 447, 1956. 47. Mikhailov, N.V. and Fainberg, E.Z., Kolloidn. Zhur., 18, 44, 1956. Struminskii, G.V. and Slonimskii, G.L., Zh. Fiz. Khim., 30, 1941, 1956. 48. Gal’perin, D.I. and Moseev, L.I., Kolloidn. Zhur., 19, 167, 1957. 49. Akhmedov, K.S., Uzb. Khim. Zh. (1), 19, 1958. 50. Kargin, V.A. and Lipatov, Yu.S., Zh. Fiz. Khim., 32, 326, 1958. Meerson, S.I. and Lipatov, S.M., Kolloidn. Zhur., 20, 353, 1958. 51. Tager, A.A. and Galkina, L.A., Nauchn. Dokl. Vyssh. Shkol., Khim. Khim. Tekhnol., (2), 357, 1958. 52. Tager, A. A. and Kargin, V. A., Zh. Fiz. Khim., 32, 1362, 1958. 53. Tager, A. A. and Kargin, V. A., Zh. Fiz. Khim., 32, 2694, 1958. 54. Tager, A.A. and Iovleva, M., Zh. Fiz. Khim., 32, 1774, 1958. 55. Horth, A., Patterson, D., and Rinfret, M., J. Polym. Sci., 39. 189, 1959.

Zelikman, S.G. and Mikhailov, N.V., Vysokomol. Soedin., 1, 1077, 1959. Mueller, F.H. and Engelter, A., Kolloid Z., 171, 152, 1960. Delmas, G., Patterson, D., and Boehme, A., Trans. Faraday Soc., 58, 2116, 1962. Delmas, G., Patterson, D., and Somcynsky, T., J. Polym. Sci., 57, 79, 1962. Tager, A.A. and Podlesnyak, A.I., Vysokomol. Soedin., Ser. A, 5, 87, 1963. Delmas, G., Patterson, D., and Bhattacharyya, S.N., J. Phys. Chem., 68, 1468, 1964. Patterson, D., J. Polym. Sci.: Part A, 2, 5177, 1964. Zverev, M.P., Barash, A.N., and Zubov, P.I., Vysokomol. Soedin., Ser. A, 6, 1012, 1964. Cottam, B.J., Cowie, J.M.G., and Bywater, S., Makromol. Chem., 86, 116, 1965. Bianchi, U., Pedemonte, E., and Rossi, C., Makromol. Chem., 92, 114, 1966. Cuniberti, C. and Bianchi, U., Polymer, 7, 151, 1966. Giacommeti, G. and Turolla, A., Z. Phys. Chem., N.F., 51, 108, 1966. Schreiber, H.P. and Waldman, M.H., J. Polym. Sci.: Part A-2, 5, 555, 1967. Goldfarb, J. and Rodriguez, S., Makromol. Chem., 116, 96, 1968. Maron, S.H. and Daniels, C.A., J. Macromol. Sci.-Phys. B, 2, 769, 1968. Morimoto, S., J. Polym. Sci.: Part A-1, 6, 1547, 1968. Bianchi, U., Cuniberti, C., Pedemonte, E., and Rossi, C., J. Polym. Sci.: Part A-2, 7, 855, 1969. Gerth, Ch. and Mueller, F.H., Kolloid-Z. Z. Polym., 241, 1071, 1970. Liddell, A.H. and Swinton, F.L., Discuss. Faraday Soc., 49, 115, 1970. Morimoto, S., Nippon Kagaku Zasshi, 91, 31, 1970. Nakayama, H., Bull. Chem. Soc. Japan, 43, 1683, 1970.

3/27/06 2:37:25 PM

Specific Enthalpies of Solution of Polymers and Copolymers 56. Blackadder, D.A. and Roberts, T.L., Angew. Makromol. Chem., 27, 165, 1972. 57. Maron, S.H. and Filisko, F.E., J. Macromol. Sci.-Phys. B, 6, 57, 1972. 58. Maron, S.H. and Filisko, F.E., J. Macromol. Sci.-Phys. B, 6, 79, 1972. 59. Maron, S.H. and Filisko, F.E., J. Macromol. Sci.-Phys. B, 6, 413, 1972. 60. Sokolova, D.F., Sokolov, L.B., and Gerasimov, V.D., Vysokomol. Soedin., Ser. B, 14, 580, 1972. 61. Chahal, R.S., Kao, W.-P., and Patterson, D., J. Chem. Soc., Faraday Trans. I, 69, 1834, 1973. 62. Delmas, G. and Tancrede, P., Eur. Polym. J., 9, 199, 1973. 63. Filisko, F.E., Raghava, R.S., and Yeh, G.S.Y., J. Macromol. Sci.-Phys. B, 10, 371, 1974. 64. Ikeda, M., Suga, H., and Seki, S., Polymer, 16, 634, 1975. 65. Kiselev, V.P., Shakhova, E.M., Fainberg, E.Z., Virnik, A.D, and Rogovin, Z.A., Vysokomol. Soedin., Ser. B, 18, 847, 1976. 66. Petrosyan, V.A., Gabrielyan, G.A., and Rogovin, Z.A., Arm. Khim. Zhur., 29, 516, 1976. 67. Deshpande, D.D. and Prabhu, C.S., Macromolecules, 10, 433, 1977. 68. Miura, T. and Nakamura, M., Bull. Chem. Soc. Japan, 50, 2528, 1977. 69. Sokolova, D.F., Kudim, T.V., Sokolov, L.B., Zhegalova, N.I., and Zhuravlev, N.D., Vysokomol. Soedin., Ser. B, 20, 596, 1978. 70 Basedow, A.M. and Ebert, K.H., J. Polym. Sci.: Polym. Symp., 66, 101, 1979. 71 Koller, J., Dissertation, TU München, 1979. 72. Lee, J.-O., Ono, M., Hamada, F., and Nakajima, A., Polym. Bull., 1, 763, 1979. 73. Phuong-Nguyen, H. and Delmas, G., Macromolecules, 12, 740, 1979. 74. Phuong-Nguyen, H. and Delmas, G., Macromolecules, 12, 746, 1979. 75. Basedow, A.M., Ebert, K.H., and Feigenbutz, W., Makromol. Chem., 181, 1071, 1980. 76. Graun, K., Dissertation, TU München, 1980. 77. Shiomi, T., Izumi, Z., Hamada, F., and Nakajima, A., Macromolecules, 13, 1149, 1980. 78. Shiomi, T., Kohra, Y., Hamada, F., and Nakajima, A., Macromolecules, 13, 1154, 1980. 79. Aharoni, S.M., Charlet, G., and Delmas, G., Macromolecules, 14, 1390, 1981. 80. Ochiai, H., Ohashi, T., Tadokoro, Y., and Murakami, I., Polym. J., 14, 457, 1982. 81. Sharma, S.C., Mahajan, R., Sharma, V.K., and Lakhanpal, M.L., Indian J. Chem., 21A, 682, 1982. 82. Sharma, S.C., Mahajan, R., Sharma, V.K., and Lakhanpal, M.L., Indian J. Chem., 21A, 685, 1982. 83. Lakhanpal, M.L. and Parashar, R.N., Indian J. Chem., 22A, 48, 1983. 84. Daoust, H. and St-Cyr, D., Macromolecules, 17, 596, 1984. 85. Aeleni, N., Mater. Plast. (Bucharest), 22, 92, 1985. 86. Sharma, S.C. and Sharma, V.K., Indian J. Chem., 24A, 292, 1985.

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87. Sharma, S.C., Bhalla, S., and Sharma, V.K., Indian J. Chem., 25A, 131, 1986. 88. Sharma, S.C., Syngal, M., and Sharma, V.K., Indian J. Chem., 26A, 285, 1987. 89. Aukett, P.N. and Brown, C.S., J. Therm. Anal., 33, 1079, 1988. 90. Lanzavecchia, L. and Pedemonte, E., Thermochim. Acta, 137, 123, 1988. 91. Tager, A.A., Safronov, A.P., Voit, V.V., Lopyrev, V.A., Ermakova, T.G., Tatarova, L.A., and Shagelaeva, N.S., Vysokomol. Soedin., Ser. A, 30, 2360, 1988. 92. Pedemonte, E. and Lanzavecchia, L., Thermochim. Acta, 162, 223, 1990. 93. Shiomi, T., Ishimatsu, H., Eguchi, T., and Imai, K., Macromolecules, 23, 4970, 1990. 94. Tager, A.A. and Safronov, A.P., Vysokomol. Soedin., Ser. A, 33, 67, 1991. 95. Zellner, H., Dissertation, TU München, 1993. 96. Brunacci, A., Pedemonte, E., Cowie, J.M.G., and McEwen, I. J., Polymer, 35, 2893, 1994. 97. Carlsson, M., Hallen, D., and Linse, P., J. Chem. Soc. Faraday Trans., 91, 2081, 1995. 98. Sato, T., Tohyama, M., Suzuki, M., Shiomi, T.,and Imai, K., Macromolecules, 29, 8231, 1996. 99. Shiomi, T., Tohyama, M., Endo, M., Sato, T., and Imai, K., J. Polym. Sci.: Part B: Polym. Phys., 34, 2599, 1996. 100. Kizhnyaev, V.N., Gorkovenko, O.P., Bazhenov, D.N., and Smirnov, A.I., Vysokomol. Soedin., Ser. A, 39, 856, 1997. 101. Sato, T., Suzuki, M., Tohyama, M., Endo, M., Shiomi, T., and Imai, K., Polym. J., 29, 417, 1997. 102. Vanderryn, J. and Zettlemoyer, A.C., Ind. Eng. Chem., Chem. Eng. Data Ser., 2, 56, 1957. 103. Parashar, R. and Sharma, S.C., Indian J. Chem., 27A, 1092, 1988. 104. Righetti, M.C., Cardelli, C., Scalari, M., Tombari, E., and Conti, G., Polymer, 43, 5035, 2002. 105. Phuong-Nguyen, H. and Delmas, G., J. Solution Chem., 23, 249, 1994. 106. Wohlfarth, C., CRC Handbook of Enthalpy Data of Polymer-Solvent Systems, CRC Press, Boca Raton, 2006.

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Astronomical Constants Victor Abalakin The constants in this table are based primarilarly on the set of constants adopted by the International Astronomical Union (IAU) in 1976. Updates have been made when new data were available. All values are given in SI Units; thus masses are expressed in kilograms and distances in meters. The astronomical unit of time is a time interval of one day (1 d) equal to 86400 s. An interval of 36525 d is one Julian century (1 cy). Defining constants Gaussian gravitational constant Speed of light Primary constants Light-time for unit distance (1 ua) Equatorial radius of earth Equatorial radius of earth (IUGG value) Dynamical form-factor for earth Geocentric gravitational constant Constant of gravitation Ratio of mass of moon to that of earth General precession in longitude, per Julian century, at standard epoch J2000 Obliquity of the ecliptic at standard epoch J2000

References 1. Seidelmann, P. K., Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, CA, 1990. 2. Lang, K. R., Astrophysical Data: Planets and Stars, Springer-Verlag, New York, 1992. 3. The Astronomical Almanac for the Year 2005, U.S. Government Printing Office, Washington, and Her Majesty’s Stationary Office, London (2003).

k = 0.01720209895 m3 kg–1 s–2 c = 299792458 m s–1 τA = 499.004782 s ae = 6378140 m ae = 6378136 m J2 = 0.001082626 GE = 3.986005 × 1014 m3s–2 G = 6.6742 × 10–11 m3kg–1s–2 µ = 0.01230002 1/µ = 81.300587 ρ = 5029″.0966 ε = 23°26′21″.448

Derived constants Constant of nutation at standard epoch J2000 Unit distance (ua = cτA) Solar parallax (π0 = arcsin(ae/ua)) Constant of aberration for standard epoch J2000 Flattening factor for the earth Heliocentric gravitational constant (GS = A3k2/D2) Ratio of mass of sun to that of the earth (S/E) = (GS)/(GE)) Ratio of mass of sun to that of earth + moon Mass of the sun (S = (GS)/G)

N = 9″.2025 ua = 1.49597870660× 1011 m π0 = 8″.794148 κ = 20″.49552 f = 1/298.257 = 0.00335281 GS = 1.32712438 × 1020 m3 s–2 S/E = 332946.0 (S/E)/(1 + µ) = 328900.5 S = 1.98844 × 1030 kg

Ratios of mass of sun to masses of the planets Mercury Venus Earth + moon Mars Jupiter Saturn Uranus Neptune Pluto

6023600 408523.5 328900.5 3098710 1047.355 3498.5 22869 19314 3000000

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Properties of the Solar System The following tables give various properties of the planets and characteristics of their orbits in the solar system. Certain properties of the sun and of the earth’s moon are also included. Explanations of the column headings: • • • •

Den.: mean density in g/cm3 Radius: radius at the equator in km Flattening: degree of oblateness, defined as (re–rp )/re, where re and rp are the equatorial and polar radii, respectively Potential coefficients: coefficients in the spherical harmonic representation of the gravitational potential U by the equation U(r,φ) = (GM/r) [1 – Σ Jn(a/r)n Pn(sin φ)]

where G is the gravitational constant, r the distance from the center of the planet, a the radius of the planet, M the mass, φ the latitude, and Pn the Legendre polynomial of degree n.

• •

Gravity: acceleration due to gravity at the surface Escape velocity: velocity needed at the surface of the planet to escape the gravitational pull Dist. to sun: semi-major axis of the elliptical orbit (1 ua = 1.496 × 108 km) ε: eccentricity of the orbit Ecliptic angle: angle between the planetary orbit and the plane of the earth’s orbit around the sun Inclin.: angle between the equatorial plane and the plane of the planetary orbit Rot. period: period of rotation of the planet measured in earth days Albedo: ratio of the light reflected from the planet to the light incident on it Tsur: mean temperature at the surface Psur: pressure of the atmosphere at the surface

• • • • • • • •

Planet Mercury Venus Earth (Moon) Mars Jupiter Saturn Uranus Neptune Pluto

Mass 1024 kg 0.33022 4.8690 5.9742 0.073483 0.64191 1898.8 568.50 86.625 102.78 0.015

Den. g/cm3 5.43 5.24 5.515 3.34 3.94 1.33 0.70 1.30 1.76 1.1

Radius km 2439.7 6051.9 6378.140 1738 3397 71492 60268 25559 24764 1151

Flattening 0 0 0.00335364 0 0.00647630 0.0648744 0.0979624 0.0229273 0.0171 0

The following general information on the solar system is of interest: Mass of the earth = Me = 5.9742 × 1024 kg Total mass of planetary system = 2.669 × 1027 kg = 447 Me Total angular momentum of planetary system = 3.148 × 1043 kg m2/s Total kinetic energy of the planets = 1.99 × 1035 J Total rotational energy of planets = 0.7 × 1035 J Properties of the sun: Mass = 1.9891 × 1030 kg = 332946.0 Me Radius = 6.9599 × 108 m Surface area = 6.087 × 1018 m2 Volume = 1.412 × 1027 m3 Mean density = 1.409 g/cm3 Gravity at surface = 27398 cm/s2 Escape velocity at surface = 6.177 × 105 m/s Effective temperature = 5780 K Total radiant power emitted (luminosity) = 3.86 × 1026 W Surface flux of radiant energy = 6.340 × 107 W/m2 Flux of radiant energy at the earth (Solar Constant) = 1373 W/m2

References 1. Seidelmann, P. K., Ed., Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, CA, 1992. 2. Lang, K. R., Astrophysical Data: Planets and Stars, Springer-Verlag, New York, 1992. 3. Allen, C. W., Astrophysical Quantities, Third Edition, Athlone Press, London, 1977.

103 J2 0.027 1.08263 0.2027 1.964 14.75 16.45 12 4

Potential coeffients 106 J3 106 J4 –2.54 36 –580 –1000

–1.61

Gravity cm/s2 370 887 980 162 371 2312 896 777 1100 72

Escape vel. km/s 4.25 10.4 11.2 2.37 5.02 59.6 35.5 21.3 23.3 1.1

14-2

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Properties of the Solar System

Planet Mercury Venus Earth (Moon) Mars Jupiter Saturn Uranus Neptune Pluto

Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto

487_S14.indb 3

Dist. to sun ua

14-3 Ecliptic angle

0.38710 0.72333 1.00000

0.2056 0.0068 0.0167

7.00° 3.39°

1.52369 5.20283 9.53876 19.19139 30.06107 39.52940

0.0933 0.048 0.056 0.046 0.010 0.248

1.85° 1.31° 2.49° 0.77° 1.77° 17.15°

Tsur K 440 730 288 218 129 97 58 56 50

Psur bar

CO2

2 × 10–15 90 1 0.007

96.4% 0.03% 95.32%

1 × 10–5

Inclin. 0° 177.3° 23.45° 6.68° 25.19° 3.12° 26.73° 97.86° 29.56° 118°

3.4% 78.08% 2.7%

69 ppm 20.95% 0.13%

Rot. period d

Albedo

58.6462 –243.01 0.99726968 27.321661 1.02595675 0.41354 0.4375 –0.65 0.768 –6.3867

0.106 0.65 0.367 0.12 0.150 0.52 0.47 0.51 0.41 0.3

Atmospheric composition H2O H2 He 0.1% 0 to 3% 0.03%

86.1% 92.4% 89% 89%

98%

13.8% 7.4% 11% 11%

4 ppm 0.93% 1.6%

No. of satellites 0 0 1 2 16 18 15 8 1

18 ppm 3 ppm

20 ppm 1 ppm 0.07%

4/10/06 12:01:58 PM

where G is the gravitational constant, r the distance from the center of the planet, a the radius of the planet, M the mass, φ the latitude, and Pn the Legendre polynomial of degree n.

• •

• • • • • • • •

Planet Mercury Venus Earth (Moon) Mars Jupiter Saturn Uranus Neptune Pluto*

14-2

Mass 1024 kg 0.33022 4.8690 5.9723 0.073483 0.64191 1898.8 568.50 86.625 102.78 0.015

Den. g/cm3 5.43 5.24 5.515 3.34 3.94 1.33 0.70 1.30 1.76 1.1

Radius km 2439.7 6051.9 6378.140 1738 3397 71492 60268 25559 24764 1151

Flattening 0 0 0.00335364 0 0.00647630 0.0648744 0.0979624 0.0229273 0.0171 0

The following general information on the solar system is of interest: Mass of the earth = Me = 5.9723 × 1024 kg Total mass of planetary system = 2.669 × 1027 kg = 447 Me Total angular momentum of planetary system = 3.148 × 1043 kg m2/s Total kinetic energy of the planets = 1.99 × 1035 J Total rotational energy of planets = 0.7 × 1035 J Properties of the sun: Mass = 1.98844 × 1030 kg = 332946.0 Me Radius = 6.961 × 108 m Surface area = 6.087 × 1018 m2 Volume = 1.412 × 1027 m3 Mean density = 1.409 g/cm3 Gravity at surface = 27398 cm/s2 Escape velocity at surface = 6.177 × 105 m/s Effective temperature = 5780 K Total radiant power emitted (luminosity) = 3.846 × 1026 W Surface flux of radiant energy = 6.340 × 107 W/m2 Flux of radiant energy at the Earth (Solar Constant) = 1367.5 W/m2

103 J2 0.027 1.08263 0.2027 1.964 14.75 16.45 12 4

Potential coeffients 106 J3 106 J4 –2.54 36 –580 –1000

–1.61

Gravity cm/s2 370 887 980 162 371 2312 896 777 1100 72

Escape vel. km/s 4.25 10.4 11.2 2.37 5.02 59.6 35.5 21.3 23.3 1.1

Properties of the Solar System

Planet Mercury Venus Earth (Moon) Mars Jupiter Saturn Uranus Neptune Pluto*

Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto*

Dist. to sun ua 0.38710 0.72333 1.00000 1.52369 5.20283 9.53876 19.19139 30.06107 39.52940

Tsur K 440 730 288 218 129 97 58 56 50

Psur bar 2 × 10–15 90 1 0.007

1 × 10–5

14-3

ε 0.2056 0.0068 0.0167 0.0933 0.048 0.056 0.046 0.010 0.248

CO2 96.4% 0.03% 95.32%

Ecliptic angle 7.00° 3.39°

Inclin. 0° 177.3° 23.45° 6.68° 25.19° 3.12° 26.73° 97.86° 29.56° 118°

1.85° 1.31° 2.49° 0.77° 1.77° 17.15°

3.4% 78.08% 2.7%

69 ppm 20.95% 0.13%

Rot. period d 58.6462 –243.01 0.99726968 27.321661 1.02595675 0.41354 0.4375 –0.65 0.768 –6.3867

Atmospheric composition H2O H2 He 2% 98% 0.1% 0 to 3% 0.03% 86.1% 13.8% 92.4% 7.4% 89% 11% 89% 11%

No. of satellites 0 0 1

Albedo 0.106 0.65 0.367 0.12 0.150 0.52 0.47 0.51 0.41 0.3

Ar 4 ppm 0.93% 1.6%

2 16 18 15 8 1

18 ppm 3 ppm

20 ppm 1 ppm 0.07%

* The International Astronomical Union passed resolutions in August 2006 that defined Pluto as a “dwarf planet” and recognized it as the prototype of a new category of Trans-Neptunian Objects. See <http://www.iau.org/fileadmin/content/pdfs/Resolution_GA26-5-6.pdf>.

Satellites of the Planets This table gives characteristics of the known satellites of the planets. The parameters covered are: • • • • • • • •

Orbital period in units of earth days. An R following the value indicates a retrograde motion. Distance from the planet, as measured by the semi-major axis of the orbit. Eccentricity of the orbit. Inclination of the satellite orbit with respect to the equator of the planet. Mass of the satellite relative to the planet. Radius of the satellite in km. Mean density of the satellite. Geometric albedo, which is a measure of the fraction of incident sunlight reflected by the satellite.

Orb. Period Planet Earth Mars Jupiter

Saturn

Uranus

14-4

I II I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII I II III IV

Satellite Moon Phobos Deimos Io Europa Ganymede Callisto Amalthea Himalia Elara Pasiphae Sinope Lysithea Carme Ananke Leda Thebe Adrastea Metis Mimas Enceladus Tethys Dione Rhea Titan Hyperion Iapetus Phoebe Janus Epimetheus Helene Telesto Calypso Atlas Prometheus Pandora Pan Ariel Umbriel Titania Oberon

d 27.321661 0.31891023 1.2624407 1.769137786 3.551181041 7.15455296 16.6890184 0.49817905 250.5662 259.6528 735 R 758 R 259.22 692 R 631 R 238.72 0.6745 0.29826 0.294780 0.942421813 1.370217855 1.887802160 2.736914742 4.517500436 15.94542068 21.2766088 79.3301825 550.48 R 0.6945 0.6942 2.7369 1.8878 1.8878 0.6019 0.6130 0.6285 0.5750 2.52037935 4.1441772 8.7058717 13.4632389

References 1. Seidelmann, P. K., Ed., Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, CA, 1992. 2. Lang, K. R., Astrophysical Data: Planets and Stars, Springer-Verlag, New York, 1992. 3. Burns, J. A., and Matthews, M. S., Eds., Satellites, University of Arizona Press, Tucson, 1986.

Distance 103 km 384.400 9.378 23.459 422 671 1070 1883 181 11480 11737 23500 23700 11720 22600 21200 11094 222 129 128 185.52 238.02 294.66 377.40 527.04 1221.83 1481.1 3561.3 12952 151.472 151.422 377.40 294.66 294.66 137.670 139.353 141.700 133.583 191.02 266.30 435.91 583.52

Rel. Eccentricity 0.054900489 0.015 0.0005 0.004 0.009 0.002 0.007 0.003 0.15798 0.20719 0.378 0.275 0.107 0.20678 0.16870 0.14762 0.015

Inclination 18.28–28.58° 1.0° 0.9–2.7° 0.04° 0.47° 0.21° 0.51° 0.40° 27.63° 24.77° 145° 153° 29.02° 164° 147° 26.07° 0.8°

0.0202 0.00452 0.00000 0.002230 0.00100 0.029192 0.104 0.02828 0.16326 0.007 0.009 0.005

1.53° 1.86° 1.86° 0.02° 0.35° 0.33° 0.43° 14.72° 177° 0.14° 0.34° 0.0°

0.000 0.003 0.004

0.3° 0.0° 0.0°

0.0034 0.0050 0.0022 0.0008

0.3° 0.36° 0.14° 0.10°

mass 0.01230002 1.5 × 10–8 3 × 10–9 4.68 × 10–5 2.52 × 10–5 7.80 × 10–5 5.66 × 10–5 3.8 × 10–9 5.0 × 10–9 4 × 10–10 1 × 10–10 0.4 × 10–10 0.4 × 10–10 0.5 × 10–10 0.2 × 10–10 0.03 × 10–10 4 × 10–10 0.1 × 10–10 0.5 × 10–10 8.0 × 10–8 1.3 × 10–7 1.3 × 10–6 1.85 × 10–6 4.4 × 10–6 2.38 × 10–4 3 × 10–8 3.3 × 10–6 7 × 10–10

1.56 × 10–5 1.35 × 10–5 4.06 × 10–5 3.47 × 10–5

Radius km 1738 13.5 × 10.8 × 9.4 7.5 × 6.1 × 5.5 1815 1569 2631 2400 135 × 83 × 75 93 38 25 18 18 20 15 8 55 × 45 12.5 × 10 × 7.5 20 196 250 530 560 765 2575 205 × 130 × 110 730 110 110 × 100 × 80 70 × 60 × 50 18 × 16 × 15 17 × 14 × 13 17 × 11 × 11 20 × 10 70 × 50 × 40 55 × 45 × 35 10 579 586 790 762

Den. g/cm3 3.34 <2 <2 3.55 3.04 1.93 1.83

1.44 1.13 1.20 1.41 1.33 1.88 1.15

1.55 1.58 1.69 1.64

Albedo 0.12 0.06 0.07 0.61 0.64 0.42 0.20 0.05 0.03 0.03

0.05 0.05 0.05 0.5 1.0 0.9 0.7 0.7 0.21 0.3 0.2 0.06 0.8 0.8 0.7 0.5 0.6 0.9 0.6 0.9 0.5 0.34 0.18 0.27 0.24

Satellites of the Planets

14-5 Orb. Period

Planet

Neptune

Pluto*

V VI VII VIII IX X XI XII XIII XIV XV I II III IV V VI VII VIII I

Satellite Miranda Cordelia Ophelia Bianca Cressida Desdemona Juliet Portia Rosalind Belinda Puck Triton Nereid Naiad Thalassa Despina Galatea Larissa Proteus Charon

d 1.41347925 0.335033 0.376409 0.434577 0.463570 0.473651 0.493066 0.513196 0.558459 0.623525 0.761832 5.8768541 R 360.13619 0.294396 0.311485 0.334655 0.428745 0.554654 1.122315 6.38725

Distance 103 km 129.39 49.77 53.79 59.17 61.78 62.68 64.35 66.09 69.94 75.26 86.01 354.76 5513.4 117.6 73.6 52.6 62.0 50.0 48.2 19.6

Rel. Eccentricity 0.0027 <0.001 0.010 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 0.000016 0.7512 <0.001 <0.001 <0.001 <0.001 <0.0014 <0.001 <0.001

Inclination 4.2° 0.1° 0.1° 0.2° 0.0° 0.2° 0.1° 0.1° 0.3° 0.0° 0.31° 157.345° 27.6° 4.74° 0.21° 0.07° 0.05° 0.20° 0.55° 99°

mass 0.08 × 10–5

2.09 × 10–4 2 × 10–7

0.22

Radius km 240 13 15 21 31 27 42 54 27 33 77 1353 170 29 40 74 79 104 × 89 218 × 208 × 201 593

Den. g/cm3 1.25

2.05

Albedo 0.27 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.7 0.4 0.06 0.06 0.06 0.06 0.06 0.06 0.5

Mass, Dimensions, and Other Parameters of the Earth This table is a collection of data on various properties of the Earth. Most of the values are given in SI units. Note that 1 ua (astronomical unit) = 149,597,870 km.

Mass Major orbital semi-axis

Quantity

Distance from sun at perihelion Distance from sun at aphelion Moment of perihelion passage Moment of aphelion passage Siderial rotation period around sun Mean rotational velocity Mean equatorial radius Mean polar compression (flattening factor) Difference in equatorial and polar semi-axes Compression of meridian of major equatorial axis Compression of meridian of minor equatorial axis Equatorial compression Difference in equatorial semi-axes Difference in polar semi-axes Polar asymmetry Mean acceleration of gravity at equator Mean acceleration of gravity at poles Difference in acceleration of gravity at pole and at equator Mean acceleration of gravity for entire surface of terrestrial ellipsoid Mean radius Area of surface Volume Mean density Siderial rotational period Rotational angular velocity Mean equatorial rotational velocity Rotational angular momentum Rotational energy Ratio of centrifugal force to force of gravity at equator Moment of inertia Relative braking of earth’s rotation due to tidal friction Relative secular acceleration of earth’s rotation Not secular braking of earth’s rotation Probable value of total energy of tectonic deformation of earth Secular loss of heat of earth through radiation into space Portion of earth’s kinetic energy transformed into heat as a result of lunar and solar tides in the hydrosphere Differences in duration of days in March and August Corresponding relative annual variation in earth’s rotational velocity Presumed variation in earth’s radius between August and March Annual variation in level of world ocean Area of continents

487_S14.indb 9

Uorb ā α a–c αa αb ε a–b cN – cS η ge gp gp – ge

Value 5.9723·1027 1.000000 1.4959787·108 0.9833 1.0167 Jan. 2, 4 h 52 min July 4, 5 h 05 min 31.5581·106 365.25636 29.78 6378.140 1/298.257 21.385 1/295.2 1/298.0 1/30 000 213 ~70 ~1.10–5 9.78036 9.83208 5.172

g R S V ρ P ω v L E qc I ∆ωe/ω ∆ωi/ω ∆ω/ω Et ∆′Ek

9.7978 6371.0 5.10·108 1.0832·1012 5.515 86,164.09 7.292116·10–5 0.46512 5.861·1033 2.137·1029 0.0034677 = 1/288 8.070·1037 –4.2·10–8 +1.4·10–8 –2.8·10–8 ~1·1023 1·1023

m/s2 km km2 km3 g/cm3 s rad/s km/s Js J

1.3·1023 0.0025 (March-August)

J/century s

2.9·10–8 (Aug.-March) –9.2 (Aug.-March) ∼10 (Sept.-March) 1.49·108 29.2

cm cm km2 % of surface

rπ rα Tπ Tα Porb

∆″Ek ∆P ∆*ω/ω ∆*R ∆ho SC

g ua km ua ua

Unit

s d km/s km km

m m m/s2 m/s2 cm/s2

kg m2 century–1 century–1 century–1 J/century J/century

14-9

4/10/06 12:02:10 PM

Mass, Dimensions, and Other Parameters of the Earth

14-10 Quantity

Symbol So

Mean height of continents above sea level Mean depth of world ocean Mean thickness of lithosphere within the limits of the continents Mean thickness of lithosphere within the limits of the ocean Mean rate of thickening of continental lithosphere Mean rate of horizontal extension of continental lithosphere Mass of crust Mass of mantle Amount of water released from the mantle and core in the course of geological time Total reserve of water in the mantle Present content of free and bound water in the earth’s lithosphere Mass of hydrosphere Amount of oxygen bound in the earth’s crust Amount of free oxygen Mass of atmosphere Mass of biosphere Mass of living matter in the biosphere Density of living matter on dry land Density of living matter in ocean Age of the earth Age of oldest rocks Age of most ancient fossils

hC ho hc.l. ho.l. ∆h/∆t ∆l/∆t ml

Area of world ocean

487_S14.indb 10

mh ma mb

3.61·108 70.8 875 3794 35 4.7 10 – 40 0.75 – 20 2.36·1022 4.05·1024 3.40·1021 2·1023 2.4·1021 1.664·1021 1.300·1021 1.5·1018 5.136·1018 1.148·1016 3.6·1014 0.1 15·10–8 4.55·109 4.0·109 3.4·109

Value

Unit km2 % of surface m m km km m/106 y km/106 y kg kg kg kg kg kg kg kg kg kg kg g/cm2 g/cm3 y y y

4/10/06 12:02:11 PM

GEOLOGICAL TIME SCALE Period or epoch

Beginning and end, in 106 years

Key events

0–10,000 y ± 2,000 y 10,000–1,000,000 y ± 50,000 y

Homo Erectus breakout

1.8–5.3 5–25 25–37 37–55 55–67

Ape man fossils Origin of grass Rise of cats, dogs, pigs Debut of hoofed mammals Earliest primates

Mesozoic era Cretaceous Jurassic Triassic

67–138 138–208 208–245

Demise of dinosaurs First birds Appearance of dinosaurs

Paleozoic era Permian Carboniferous Devonian Silurian Ordovician Cambrian

245–290 290–360 360–410 410–435 435–520 520–570

Flowers, insect pollination First conifers First vertebrates ashore Spore-bearing plants First animals ashore Vertebrates appear

Pre-Cambrian Pre-Cambrian III (Proterozoic) Pre-Cambrian II (Archean) Pre-Cambrian I (Hadean)

570–2500 2500–3800 3800–4450

First plants, jellyfish Photosynthetic bacteria Earth formed 4600 million years ago

Cenozoic era Quaternian Contemporary Pleistocene Tertiary Pliocene Miocene Oligocene Eocene Paleocene

Reference: Calder, N., Timescale - An Atlas of the Fourth Dimension, Viking Press, New York, 1983.

14-11

Section 14.indb 11

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ACCELERATION DUE TO GRAVITY The acceleration due to gravity is tabulated here as a function of latitude and height above the earth’s surface. Values were calculated from the expression g/(m/s2) = 9.780356 (1 + 0.0052885 sin2 φ – 0.0000059 sin2 2 φ) – 0.003086 H

Reference Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, 4th ed., Air Force Geophysics Laboratory, 1985, p. 14–17.

where φ is the latitude and H is the height in kilometers.

φ 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

H=0 9.78036 9.78075 9.78191 9.78381 9.78638 9.78956 9.79324 9.79732 9.80167 9.80616 9.81065 9.81501 9.81911 9.82281 9.82601 9.82860 9.83051 9.83168 9.83208

H = 1 km 9.77727 9.77766 9.77882 9.78072 9.78330 9.78647 9.79016 9.79424 9.79858 9.80307 9.80757 9.81193 9.81602 9.81972 9.82292 9.82551 9.82743 9.82860 9.82899

H = 5 km 9.76493 9.76532 9.76648 9.76838 9.77095 9.77413 9.77781 9.78189 9.78624 9.79073 9.79522 9.79958 9.80368 9.80738 9.81058 9.81317 9.81508 9.81625 9.81665

H = 10 km 9.74950 9.74989 9.75105 9.75295 9.75552 9.75870 9.76238 9.76646 9.77081 9.77530 9.77979 9.78415 9.78825 9.79195 9.79515 9.79774 9.79965 9.80082 9.80122

14-12

Section 14.indb 12

4/27/05 5:03:28 PM

DENSITY, PRESSURE, AND GRAVITY AS A FUNCTION OF DEPTH WITHIN THE EARTH This table gives the density ρ, pressure p, and acceleration due to gravity g as a function of depth below the earth’s surface, as calculated from the model of the structure of the earth in Reference 1. The model assumes a radius of 6371 km for the earth. The boundary between the crust and mantle (the Mohorovicic discontinuity) is taken as 21 km, while in reality it varies considerable with location.

Crust

Depth km

ρ g/cm3

0 3

1.02 1.02

0 3

981 982

3 21

2.80 2.80

3 5

982 983

3.49 3.51 3.52 3.48 3.44 3.40 3.37 3.34 3.37 3.47 3.59 3.95 4.54 4.67 4.81

5 12 19 26 33 39 56 73 89 106 124 199 328 466 607

983 983 984 984 984 985 987 989 991 993 994 999 997 992 991

Mantle (solid) 21 41 61 81 101 121 171 221 271 321 371 571 871 1171 1471

p kbar

g cm/s2

References 1. Anderson, D. L., and Hart, R. S., J. Geophys. Res., 81, 1461, 1976. 2. Carmichael, R. S., CRC Practical Handbook of Physical Properties of Rocks and Minerals, p. 467, CRC Press, Boca Raton, FL, 1989.

Depth km 1771 2071 2371 2671 2886

ρ g/cm3 4.96 5.12 5.31 5.45 5.53

p kbar 752 903 1061 1227 1352

g cm/s2 994 1002 1017 1042 1069

Outer core (liquid) 2886 2971 3371 3671 4071 4471 4871 5156

9.96 10.09 10.63 11.00 11.36 11.69 11.99 12.12

1352 1442 1858 2154 2520 2844 3116 3281

1069 1050 953 874 760 641 517 427

Inner core (solid) 5156 5371 5771 6071 6371

12.30 12.48 12.52 12.53 12.58

3281 3385 3529 3592 3617

427 355 218 122 0

14-13

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OCEAN PRESSURE AS A FUNCTION OF DEPTH AND LATITUDE The following table is based upon an ocean model which takes into account the equation of state of standard seawater and the dependence on latitude of the acceleration of gravity. The tabulated pressure value is the excess pressure over the ambient atmospheric pressure at the surface.

Depth (meters) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000

References 1. International Oceanographic Tables, Volume 4, Unesco Technical Papers in Marine Science No. 40, Unesco, Paris, 1987. 2. Saunders, P. M., and Fofonoff, N. P., Deep-Sea Res. 23, 109–111, 1976.

Pressure in MPa at the Specified Latitude 0° 0.0000 5.0338 10.0796 15.1376 20.2076 25.2895 30.3831 35.4886 40.6056 45.7342 50.8742 56.0255 61.1882 66.3619 71.5467 76.7426 81.9493 87.1669 92.3950 97.6346 102.8800

15° 0.0000 5.0355 10.0832 15.1431 20.2148 25.2985 30.3940 35.5012 40.6201 45.7505 50.8924 56.0456 61.2100 66.3857 71.5724 76.7701 81.9788 87.1983 92.4284 97.6698 102.9170

30° 0.0000 5.0404 10.0930 15.1577 20.2344 25.3231 30.4236 35.5358 40.6598 45.7952 50.9421 56.1004 61.2700 66.4508 71.6427 76.8456 82.0594 87.2841 92.5194 97.7661 103.0185

45° 0.0000 5.0471 10.1064 15.1778 20.2613 25.3568 30.4641 35.5832 40.7140 45.8564 51.0102 56.1755 61.3521 66.5399 71.7388 76.9488 82.1697 87.4016 92.6440 97.8978 103.1572

60° 0.0000 5.0537 10.1198 15.1980 20.2882 25.3905 30.5047 35.6307 40.7683 45.9176 51.0785 56.2508 61.4344 66.6292 71.8352 77.0523 82.2804 87.5193 92.7689 98.0300 103.2961

75° 0.0000 5.0586 10.1296 15.2127 20.3080 25.4153 30.5345 35.6654 40.8082 45.9626 51.1285 56.3059 61.4947 66.6947 71.9059 77.1282 82.3614 87.6057 92.8606 98.1269 103.3981

90° 0.0000 5.0605 10.1333 15.2182 20.3153 25.4244 30.5453 35.6782 40.8229 45.9791 51.1469 56.3262 61.5168 66.7187 71.9318 77.1560 82.3911 87.6373 92.8941 98.1624 103.4355

14-14

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4/27/05 5:03:30 PM

PROPERTIES OF SEAWATER In addition to the dependence on temperature and pressure, the physical properties of seawater vary with the concentration of the dissolved constituents. A convenient parameter for describing the composition is the salinity, S, which is defined in terms of the electrical conductivity of the seawater sample. The defining equation for the practical salinity is: S = a0 + a1K1/2 + a2K + a3K3/2 + a4K2 + a5K5/2, where K is the ratio of the conductivity of the seawater sample at 15°C and atmospheric pressure to the conductivity of a potassium chloride solution in which the mass fraction of KCl is 0.0324356, at the same temperature and pressure. The values of the coefficients are: a0 = 0.0080 a3 = 14.0941 a1 = –0.1692 a4 = –7.0261 a2 = 25.3851 a5 = 2.7081 Σ ai = 35.0000 Thus when K = 1, S = 35 exactly (S is normally quoted in units of ‰, i.e., parts per thousand). The value of S can be roughly equated with the mass of dissolved material in grams per kilogram of seawater. Salinity values in the open oceans at mid latitudes typically fall between 34 and 36.

It is customary in oceanography to define the pressure at a given point as the pressure due to the column of water between that point and the surface. Thus by convention P = 0 at the sea surface. To a good approximation the pressure in decibars (dbar) can be equated to the depth in meters. Thus at 45° latitude the pressure is 5000 dbar at 4902 m, 10000 dbar at 9700 m. The first table below gives several properties of seawater as a function of temperature for a salinity of 35. The second and third give density and electrical conductivity as a function of salinity at several temperatures, and the fourth lists typical concentrations of the main constituents of seawater as a function of salinity. The final table gives the freezing point as a function of salinity and pressure.

References 1. The Practical Salinity Scale 1978 and the International Equation of State of Seawater 1980, Unesco Technical Papers in Marine Science No. 36, Unesco, Paris, 1981; sections No. 37, 38, 39, and 40 in this series give background papers and detailed tables. 2. Kennish, M. J., CRC Practical Handbook of Marine Science, CRC Press, Boca Raton, FL, 1989. 3. Poisson, A. IEEE J. Ocean. Eng. OE-5, 50, 1981. 4. Webster, F., in AIP Physics Desk Reference, E. R. Cohen, D. R. Lide and G. L. Trigg, Eds., Springer-Verlag, New York, 2003.

Properties of Seawater as a Function of Temperature at Salinity S = 35 and Normal Atmospheric Pressure ρ = density in g/cm3 β = (1/ρ) (dρ/dS) = fractional change in density per unit change in salinity α = –(1/ρ) (dρ/dt) = fractional change in density per unit change in temperature (°C–1) t/°C 0 5 10 15 20 25 30 35 40

ρ/g cm–3 1.028106 1.027675 1.026952 1.025973 1.024763 1.023343 1.021729 1.019934

107β 7854 7717 7606 7516 7444 7385 7338 7300 7270

107 α/°C–1 526 1136 1668 2141 2572 2970 3341 3687 4004

κ = electrical conductivity in S/cm η = viscosity in mPa s (equal to cP) cp = specific heat in J/kg °C v = speed of sound in m/s

κ/S cm–1 0.029048 0.033468 0.038103 0.042933 0.047934 0.053088 0.058373

η/mPa s 1.892 1.610 1.388 1.221 1.085 0.966 0.871

cp/J kg–1 °C–1 v/m s–1 3986.5 1449.1 3986.3

1489.8

3993.9

1521.5

4000.7

1545.6

4003.5

1563.2

Density of Surface Seawater in g/cm3 as a Function of Temperature and Salinity t/°C 0 5 10 15 20 25 30 35 40

S=0 0.999843 0.999967 0.999702 0.999102 0.998206 0.997048 0.995651 0.994036 0.992220

S=5 1.003913 1.003949 1.003612 1.002952 1.002008 1.000809 0.999380 0.997740 0.995906

S = 10 1.007955 1.007907 1.007501 1.006784 1.005793 1.004556 1.003095 1.001429 0.999575

S = 15 1.011986 1.011858 1.011385 1.010613 1.009576 1.008301 1.006809 1.005118 1.003244

S = 20 1.016014 1.015807 1.015269 1.014443 1.013362 1.012050 1.010527 1.008810 1.006915

S = 25 1.020041 1.019758 1.019157 1.018279 1.017154 1.015806 1.014252 1.012509 1.010593

S = 30 1.024072 1.023714 1.023051 1.022122 1.020954 1.019569 1.017985 1.016217 1.014278

S = 35 1.028106 1.027675 1.026952 1.025973 1.024763 1.023343 1.021729 1.019934 1.017973

S = 40 1.032147 1.031645 1.030862 1.029834 1.028583 1.027128 1.025483 1.023662 1.021679

14-15

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Properties of Seawater

14-16 Electrical Conductivity of Seawater in S/cm as a Function of Temperature and Salinity t/°C 0 5 10 15 20 25 30

S=5 0.004808 0.005570 0.006370 0.007204 0.008068 0.008960 0.009877

S = 10 0.009171 0.010616 0.012131 0.013709 0.015346 0.017035 0.018771

S = 15 0.013357 0.015441 0.017627 0.019905 0.022267 0.024703 0.027204

S = 20 0.017421 0.020118 0.022947 0.025894 0.028948 0.032097 0.035330

S = 25 0.021385 0.024674 0.028123 0.031716 0.035438 0.039276 0.043213

S = 30 0.025257 0.029120 0.033171 0.037391 0.041762 0.046267 0.050888

S = 35 0.029048 0.033468 0.038103 0.042933 0.047934 0.053088 0.058373

S = 40 0.032775 0.037734 0.042935 0.048355 0.053968 0.059751 0.065683

Composition of Seawater and Ionic Strength at Various Salinities (Ref. 2) Constituent

Cl– Br– F– SO42– HCO3– NaSO4– KSO4– Na+ K+ Mg2+ Ca2+ Sr2+ MgHCO3+ MgSO4 CaSO4 NaHCO3 H3BO3 Ionic strength

S = 30 0.482 0.00074 0.0104 0.00131 0.0085 0.00010 0.405 0.00892 0.0413 0.00131 0.00008 0.00028 0.00498 0.00102 0.00015 0.00032 0.5736

Expressed as molality S = 35 0.562 0.00087 0.00007 0.0114 0.00143 0.0108 0.00012 0.472 0.01039 0.0483 0.00143 0.00009 0.00036 0.00561 0.00115 0.00020 0.00037 0.6675

S = 40 0.650 0.00100

S = 30 16.58 0.057

0.0122 0.00100 0.0139 0.00015 0.544 0.01200 0.0561 0.00154 0.00011 0.00045 0.00614 0.00126 0.00024 0.00042 0.7701

0.97 0.078 0.98 0.013 9.03 0.338 0.974 0.051 0.007 0.023 0.582 0.135 0.012 0.019

As grams per kilogram of seawater S = 35 S = 40 19.33 22.36 0.067 0.078 0.001 1.06 1.14 0.085 0.059 1.25 1.60 0.016 0.020 10.53 12.13 0.394 0.455 1.139 1.323 0.056 0.060 0.008 0.009 0.030 0.037 0.655 0.717 0.152 0.166 0.016 0.020 0.022 0.025

Freezing Point of Seawater in °C as a Function of Salinity and Pressure P/dbar 0 50 100 500

S14_09.indd 16

S=0 0.000 –0.038 –0.075 –0.377

5 –0.274 –0.311 –0.349 –0.650

10 –0.542 –0.580 –0.618 –0.919

15 –0.812 –0.849 –0.887 –1.188

20 –1.083 –1.121 –1.159 –1.460

25 –1.358 –1.396 –1.434 –1.735

30 –1.638 –1.676 –1.713 –2.014

35 –1.922 –1.960 –1.998 –2.299

40 –2.212 –2.250 –2.287 –2.589

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ABUNDANCE OF ELEMENTS IN THE EARTH’S CRUST AND IN THE SEA This table gives the estimated abundance of the elements in the continental crust (in mg/kg, equivalent to parts per million by mass) and in seawater near the surface (in mg/L). Values represent the median of reported measurements. The concentrations of the less abundant elements may vary with location by several orders of magnitude.

Element Ac Ag Al Ar As Au B Ba Be Bi Br C Ca Cd Ce Cl Co Cr Cs Cu Dy Er Eu F Fe Ga Gd Ge H He Hf Hg Ho I In Ir K Kr La Li Lu Mg Mn Mo

Abundance Crust mg/kg 5.5 × 10–10 7.5 × 10–2 8.23 × 104 3.5 1.8 4 × 10–3 1.0 × 101 4.25 × 102 2.8 8.5 × 10–3 2.4 2.00 × 102 4.15 × 104 1.5 × 10–1 6.65 × 101 1.45 × 102 2.5 × 101 1.02 × 102 3 6.0 × 101 5.2 3.5 2.0 5.85 × 102 5.63 × 104 1.9 × 101 6.2 1.5 1.40 × 103 8 × 10–3 3.0 8.5 × 10–2 1.3 4.5 × 10–1 2.5 × 10–1 1 × 10–3 2.09 × 104 1 × 10–4 3.9 × 101 2.0 × 101 8 × 10–1 2.33 × 104 9.50 × 102 1.2

Sea mg/L 4 × 10–5 2 × 10–3 4.5 × 10–1 3.7 × 10–3 4 × 10–6 4.44 1.3 × 10–2 5.6 × 10–6 2 × 10–5 6.73 × 101 2.8 × 101 4.12 × 102 1.1 × 10–4 1.2 × 10–6 1.94 × 104 2 × 10–5 3 × 10–4 3 × 10–4 2.5 × 10–4 9.1 × 10–7 8.7 × 10–7 1.3 × 10–7 1.3 2 × 10–3 3 × 10–5 7 × 10–7 5 × 10–5 1.08 × 105 7 × 10–6 7 × 10–6 3 × 10–5 2.2 × 10–7 6 × 10–2 2 × 10–2 3.99 × 102 2.1 × 10–4 3.4 × 10–6 1.8 × 10–1 1.5 × 10–7 1.29 × 103 2 × 10–4 1 × 10–2

References 1. Carmichael, R. S., Ed., CRC Practical Handbook of Physical Properties of Rocks and Minerals, CRC Press, Boca Raton, FL, 1989. 2. Bodek, I., et al., Environmental Inorganic Chemistry, Pergamon Press, New York, 1988. 3. Ronov, A. B., and Yaroshevsky, A. A., “Earth’s Crust Geochemistry” , in Encyclopedia of Geochemistry and Environmental Sciences, Fairbridge, R. W., Ed., Van Nostrand, New York, 1969.

Element N Na Nb Nd Ne Ni O Os P Pa Pb Pd Po Pr Pt Ra Rb Re Rh Rn Ru S Sb Sc Se Si Sm Sn Sr Ta Tb Te Th Ti Tl Tm U V W Xe Y Yb Zn Zr

Abundance Crust mg/kg 1.9 × 101 2.36 × 104 2.0 × 101 4.15 × 101 5 × 10–3 8.4 × 101 4.61 × 105 1.5 × 10–3 1.05 × 103 1.4 × 10–6 1.4 × 101 1.5 × 10–2 2 × 10–10 9.2 5 × 10–3 9 × 10–7 9.0 × 101 7 × 10–4 1 × 10–3 4 × 10–13 1 × 10–3 3.50 × 102 2 × 10–1 2.2 × 101 5 × 10–2 2.82 × 105 7.05 2.3 3.70 × 102 2.0 1.2 1 × 10–3 9.6 5.65 × 103 8.5 × 10–1 5.2 × 10–1 2.7 1.20 × 102 1.25 3 × 10–5 3.3 × 101 3.2 7.0 × 101 1.65 × 102

Sea mg/L 5 × 10–1 1.08 × 104 1 × 10–5 2.8 × 10–6 1.2 × 10–4 5.6 × 10–4 8.57 × 105 6 × 10–2 5 × 10–11 3 × 10–5 1.5 × 10–14 6.4 × 10–7 8.9 × 10–11 1.2 × 10–1 4 × 10–6 6 × 10–16 7 × 10–7 9.05 × 102 2.4 × 10–4 6 × 10–7 2 × 10–4 2.2 4.5 × 10–7 4 × 10–6 7.9 2 × 10–6 1.4 × 10–7 1 × 10–6 1 × 10–3 1.9 × 10–5 1.7 × 10–7 3.2 × 10–3 2.5 × 10–3 1 × 10–4 5 × 10–5 1.3 × 10–5 8.2 × 10–7 4.9 × 10–3 3 × 10–5

14-17

Section 14.indb 17

4/27/05 5:03:35 PM

SOLAR SPECTRAL IRRADIANCE The solar luminosity (total radiant power emitted) is 3.86⋅1026 W, of which 1373 W/m2 reaches the top of the earth’s atmosphere. To a zeroth approximation the sun can be considered a black body with an effective temperature of 5780 K, which implies a peak in the radiation at around 0.520 µm (5200 Å). The actual solar spectral emission is more complex, especially at ultraviolet and shorter wavelengths. The graph below, which was taken from Reference 1, summarizes the solar irradiance at the top of the atmosphere in the range 0.3 to 10 µm.

References 1. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. 2. Pierce, A. K., and Allen, R. G., “The Solar Spectrum between 0.3 and 10 µm” , in The Solar Output and Its Variation, White, O. R., Ed., Colorado Associated University Press, Boulder, CO, 1977. 3. Lang, K. R., Astrophysical Data. Planets and Stars, Springer-Verlag, New York, 1992.

2000 1800

Irradiance in W m -2 µm-1

1600 1400 1200 1000 800 600 400 X10

200 0

0.3

0.4

0.5

0.7

1.0

Wavelength in µm

14-18

Section 14.indb 18

4/27/05 5:03:38 PM

U.S. STANDARD ATMOSPHERE (1976) A Standard Atmosphere is a hypothetical vertical distribution of atmospheric temperature, pressure, and density which is roughly representative of year-round, midlatitude conditions. Typical uses are to serve as a basis for pressure altimeter calibrations, aircraft performance calculations, aircraft and rocket design, ballistic tables, meteorological diagrams, and various types of atmospheric modeling. The air is assumed to be dry and to obey the perfect gas law and the hydrostatic equation which, taken together, relate temperature, pressure, and density with vertical position. The atmosphere is considered to rotate with the earth and to be an average over the diurnal cycle, the semiannual variation, and the range from active to quiet geomagnetic and sunspot conditions. The U.S. Standard Atmosphere, (1976) is an idealized, steadystate representation of mean annual conditions of the earth’s atmosphere from the surface to 1000 km at latitude 45°N, as it is assumed to exist during a period with moderate solar activity. The defining meteorological elements are sea-level temperature and pressure and a temperature-height profile to 1000 km. The 1976 Standard Atmosphere uses the following sea-level values which have been standard for many decades: Temperature — 288.15 K (15°C) Pressure — 101325 Pa (1013.25 mbar, 760 mm of Hg, or 29.92 in. of Hg)

Density — 1225 g/m3 (1.225 g/L) Mean molar mass — 28.964 g/mol The parameters included in this condensed version of the U.S. Standard Atmosphere are: Z — Height (geometric) above mean sea level in meters T — Temperature in kelvins P — Pressure in pascals (1 Pa = 0.01 millibars) ρ — Density in kilograms per cubic meter (1 kg/m3 = 1 g/L) n — Number density in molecules per cubic meter ν — Mean collision frequency in collisions per second l — Mean free path in meters η — Absolute viscosity in pascal seconds (1 Pa s = 1000 cP) k — Thermal conductivity in joules per meter second kilogram (W/m K) vs — Speed of sound in meters per second g — Acceleration of gravity in meters per second square The sea-level composition (percent by volume) is taken to be: N2 — 78.084% O2 — 20.9476 Ar — 0.934 CO2 — 0.0314 Ne — 0.001818

He — 0.000524 Kr — 0.000114 Xe — 0.0000087 CH4 — 0.0002 H2 — 0.00005

The T and P columns for the troposphere and lower stratosphere were generated from the following formulas: H ≤ 11000 m 11000 m < H ≤ 20000 m 20000 m < H ≤ 32000 m

T/K 288.15 – 0.0065 H 216.65 216.65 + 0.0010(H–20000)

where H = rZ/(r + Z) is the geopotential height in meters and r is the mean earth radius at 45° N latitude, taken as 6356766 m. For altitudes up to 32 km, ρ = 0.003483677(P/T) in the units used here. Formulas for the other quantities may be found in the references.

P/Pa 101325(288.15/T)–5.25577 22632 e–0.00015768832(H–11000) 5474.87(216.65/T)34.16319

References 1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976. 2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985.

14-19

Section 14.indb 19

4/27/05 5:03:39 PM

U.S. Standard Atmosphere (1976)

14-20 Z/m –5000 –4500 –4000 –3500 –3000 –2500 –2000 –1500 –1000 –500 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 10500 11000 11500 12000 12500 13000 13500 14000 14500 15000 16000 17000 18000 19000 20000 21000 22000 23000 24000 25000 26000 27000 28000 29000 30000 31000 32000 33000 34000 35000

Section 14.indb 20

T/K 320.68 317.42 314.17 310.91 307.66 304.41 301.15 297.90 294.65 291.40 288.15 284.90 281.65 278.40 275.15 271.91 268.66 265.41 262.17 258.92 255.68 252.43 249.19 245.94 242.70 239.46 236.22 232.97 229.73 226.49 223.25 220.01 216.77 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 217.58 218.57 219.57 220.56 221.55 222.54 223.54 224.53 225.52 226.51 227.50 228.49 230.97 233.74 236.51

P/Pa 1.778E+05 1.685E+05 1.596E+05 1.511E+05 1.430E+05 1.352E+05 1.278E+05 1.207E+05 1.139E+05 1.075E+05 1.013E+05 9.546E+04 8.988E+04 8.456E+04 7.950E+04 7.469E+04 7.012E+04 6.579E+04 6.166E+04 5.775E+04 5.405E+04 5.054E+04 4.722E+04 4.408E+04 4.111E+04 3.830E+04 3.565E+04 3.315E+04 3.080E+04 2.858E+04 2.650E+04 2.454E+04 2.270E+04 2.098E+04 1.940E+04 1.793E+04 1.658E+04 1.533E+04 1.417E+04 1.310E+04 1.211E+04 1.035E+04 8.850E+03 7.565E+03 6.467E+03 5.529E+03 4.729E+03 4.048E+03 3.467E+03 2.972E+03 2.549E+03 2.188E+03 1.880E+03 1.610E+03 1.390E+03 1.197E+03 1.031E+03 8.891E+02 7.673E+02 6.634E+02 5.746E+02

ρ/kg m–3 1.931 1.849 1.770 1.693 1.619 1.547 1.478 1.411 1.347 1.285 1.225 1.167 1.112 1.058 1.007 0.957 0.909 0.863 0.819 0.777 0.736 0.697 0.660 0.664 0.590 0.557 0.526 0.496 0.467 0.440 0.414 0.389 0.365 0.337 0.312 0.288 0.267 0.246 0.228 0.211 0.195 0.166 0.142 0.122 0.104 8.891E–02 7.572E–02 6.451E–02 5.501E–02 4.694E–02 4.008E–02 3.426E–02 2.930E–02 2.508E–02 2.148E–02 1.841E–02 1.579E–02 1.356E–02 1.157E–02 9.887E–03 8.463E–03

n/m–3 4.015E+25 3.845E+25 3.680E+25 3.520E+25 3.366E+25 3.217E+25 3.102E+25 2.935E+25 2.801E+25 2.672E+25 2.547E+25 2.427E+25 2.311E+25 2.200E+25 2.093E+25 1.990E+25 1.891E+25 1.795E+25 1.704E+25 1.616E+25 1.531E+25 1.450E+25 1.373E+25 1.299E+25 1.227E+25 1.159E+25 1.093E+25 1.031E+25 9.711E+24 9.141E+24 8.598E+24 8.079E+24 7.585E+24 7.016E+24 6.486E+24 5.996E+24 5.543E+24 5.124E+24 4.738E+24 4.380E+24 4.049E+24 3.461E+24 2.959E+24 2.529E+24 2.162E+24 1.849E+24 1.574E+24 1.341E+24 1.144E+24 9.759E+23 8.334E+23 7.123E+23 6.092E+23 5.214E+23 4.466E+23 3.828E+23 3.283E+23 2.813E+23 2.406E+23 2.056E+23 1.760E+23

ν/s–1 1.151E+10 1.096E+10 1.044E+10 9.933E+09 9.448E+09 8.982E+09 8.623E+09 8.106E+09 7.693E+09 7.298E+09 6.919E+09 6.556E+09 6.208E+09 5.874E+09 5.555E+09 5.250E+09 4.959E+09 4.680E+09 4.414E+09 4.160E+09 3.918E+09 3.687E+09 3.467E+09 3.258E+09 3.058E+09 2.869E+09 2.689E+09 2.518E+09 2.356E+09 2.202E+09 2.056E+09 1.918E+09 1.787E+09 1.653E+09 1.528E+09 1.412E+09 1.306E+09 1.207E+09 1.116E+09 1.032E+09 9.538E+08 8.153E+08 6.969E+08 5.958E+08 5.093E+08 4.354E+08 3.716E+08 3.173E+08 2.712E+08 2.319E+08 1.985E+08 1.700E+08 1.458E+08 1.250E+08 1.073E+08 9.219E+07 7.925E+07 6.818E+07 5.852E+07 5.030E+07 4.331E+07

l/m 4.208E–08 4.395E–08 4.592E–08 4.800E–08 5.019E–08 5.252E–08 5.447E–08 5.757E–08 6.032E–08 6.324E–08 6.633E–08 6.961E–08 7.310E–08 7.680E–08 8.073E–08 8.491E–08 8.937E–08 9.411E–08 9.917E–08 1.046E–07 1.103E–07 1.165E–07 1.231E–07 1.302E–07 1.377E–07 1.458E–07 1.545E–07 1.639E–07 1.740E–07 1.848E–07 1.965E–07 2.091E–07 2.227E–07 2.408E–07 2.605E–07 2.818E–07 3.048E–07 3.297E–07 3.566E–07 3.857E–07 4.172E–07 4.881E–07 5.710E–07 6.680E–07 7.814E–07 9.139E–07 1.073E–06 1.260E–06 1.477E–06 1.731E–06 2.027E–06 2.372E–06 2.773E–06 3.240E–06 3.783E–06 4.414E–06 5.146E–06 5.995E–06 7.021E–06 8.218E–06 9.601E–06

η/Pa s 1.942E–05 1.927E–05 1.912E–05 1.897E–05 1.882E–05 1.867E–05 1.852E–05 1.836E–05 1.821E–05 1.805E–05 1.789E–05 1.774E–05 1.758E–05 1.742E–05 1.726E–05 1.710E–05 1.694E–05 1.678E–05 1.661E–05 1.645E–05 1.628E–05 1.612E–05 1.595E–05 1.578E–05 1.561E–05 1.544E–05 1.527E–05 1.510E–05 1.493E–05 1.475E–05 1.458E–05 1.440E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.422E–05 1.427E–05 1.432E–05 1.438E–05 1.443E–05 1.448E–05 1.454E–05 1.459E–05 1.465E–05 1.470E–05 1.475E–05 1.481E–05 1.486E–05 1.499E–05 1.514E–05 1.529E–05

k/J m–1s–1K–1 0.02788 0.02763 0.02738 0.02713 0.02688 0.02663 0.02638 0.02613 0.02587 0.02562 0.02533 0.02511 0.02485 0.02459 0.02433 0.02407 0.02381 0.02355 0.02329 0.02303 0.02277 0.02250 0.02224 0.02197 0.02170 0.02144 0.02117 0.02090 0.02063 0.02036 0.02009 0.01982 0.01954 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01953 0.01961 0.01970 0.01978 0.01986 0.01995 0.02003 0.02011 0.02020 0.02028 0.02036 0.02044 0.02053 0.02073 0.02096 0.02119

vs/m s–1 359.0 357.2 355.3 353.5 351.6 349.8 347.9 346.0 344.1 342.2 340.3 338.4 336.4 334.5 332.5 330.6 328.6 326.6 324.6 322.6 320.6 318.5 316.5 314.4 312.3 310.2 308.1 306.0 303.9 301.7 299.5 297.4 295.2 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 296.4 297.1 297.7 298.4 299.1 299.7 300.4 301.1 301.7 302.4 303.0 304.7 306.5 308.3

g/m s–2 9.822 9.830 9.819 9.818 9.816 9.814 9.813 9.811 9.810 9.808 9.807 9.805 9.804 9.802 9.801 9.799 9.797 9.796 9.794 9.793 9.791 9.790 9.788 9.787 9.785 9.784 9.782 9.781 9.779 9.777 9.776 9.774 9.773 9.771 9.770 9.768 9.767 9.765 9.764 9.762 9.761 9.758 9.754 9.751 9.748 9.745 9.742 9.739 9.736 9.733 9.730 9.727 9.724 9.721 9.718 9.715 9.712 9.709 9.706 9.703 9.700

4/27/05 5:03:43 PM

U.S. Standard Atmosphere (1976) Z/m 36000 38000 40000 42000 44000 46000 48000 50000 52000 54000 56000 58000 60000 65000 70000 75000 80000 85000 90000 95000 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000 200000 220000 240000 260000 280000 300000 320000 340000 360000 380000 400000 450000 500000 550000 600000 650000 700000 750000 800000 850000 900000 950000 1000000

Section 14.indb 21

T/K 239.28 244.82 250.35 255.88 261.40 266.93 270.65 270.65 269.03 263.52 258.02 252.52 247.02 233.29 219.59 208.40 198.64 188.89 186.87 188.42 195.08 240.00 360.00 469.27 559.63 634.39 696.29 747.57 790.07 825.16 854.56 899.01 929.73 950.99 965.75 976.01 983.16 988.15 991.65 994.10 995.83 998.22 999.24 999.67 999.85 999.93 999.97 999.98 999.99 1000.00 1000.00 1000.00 1000.00

P/Pa 4.985E+02 3.771E+02 2.871E+02 2.200E+02 1.695E+02 1.313E+02 1.023E+02 7.978E+01 6.221E+01 4.834E+01 3.736E+01 2.872E+01 2.196E+01 1.093E+01 5.221 2.388 1.052 4.457E–01 1.836E–01 7.597E–02 3.201E–02 7.104E–03 2.538E–03 1.251E–03 7.203E–04 4.542E–04 3.040E–04 2.121E–04 1.527E–04 1.127E–04 8.474E–05 5.015E–05 3.106E–05 1.989E–05 1.308E–05 8.770E–06 5.980E–06 4.132E–06 2.888E–06 2.038E–06 1.452E–06 6.447E–07 3.024E–07 1.514E–07 8.213E–08 4.887E–08 3.191E–08 2.260E–08 1.704E–08 1.342E–08 1.087E–08 8.982E–09 7.514E–09

ρ/kg m–3 7.258E–03 5.367E–03 3.996E–03 2.995E–03 2.259E–03 1.714E–03 1.317E–03 1.027E–03 8.056E–04 6.390E–04 5.045E–04 3.963E–04 3.097E–04 1.632E–04 8.283E–05 3.992E–05 1.846E–05 8.220E–06 3.416E–06 1.393E–06 5.604E–07 9.708E–08 2.222E–08 8.152E–09 3.831E–09 2.076E–09 1.233E–09 7.815E–10 5.194E–10 3.581E–10 2.541E–10 1.367E–10 7.858E–11 4.742E–11 2.971E–11 1.916E–11 1.264E–11 8.503E–12 5.805E–12 4.013E–12 2.803E–12 1.184E–12 5.215E–13 2.384E–13 1.137E–13 5.712E–14 3.070E–14 1.788E–14 1.136E–14 7.824E–15 5.759E–15 4.453E–15 3.561E–15

14-21 n/m–3 1.509E+23 1.116E+23 8.308E+22 6.227E+22 4.697E+22 3.564E+22 2.738E+22 2.135E+22 1.675E+22 1.329E+22 1.049E+22 8.239E+21 6.439E+21 3.393E+21 1.722E+21 8.300E+20 3.838E+20 1.709E+20 7.116E+19 2.920E+19 1.189E+19 2.144E+18 5.107E+17 1.930E+17 9.322E+16 5.186E+16 3.162E+16 2.055E+16 1.400E+16 9.887E+15 7.182E+15 4.040E+15 2.420E+15 1.515E+15 9.807E+14 6.509E+14 4.405E+14 3.029E+14 2.109E+14 1.485E+14 1.056E+14 4.678E+13 2.192E+13 1.097E+13 5.950E+12 3.540E+12 2.311E+12 1.637E+12 1.234E+12 9.717E+11 7.876E+11 6.505E+11 5.442E+11

ν/s–1 3.736E+07 2.794E+07 2.104E+07 1.594E+07 1.215E+07 9.318E+06 7.208E+06 5.620E+06 4.397E+06 3.452E+06 2.696E+06 2.095E+06 1.620E+06 8.294E+05 4.084E+05 1.918E+05 8.656E+04 3.766E+04 1.560E+04 6.440E+03 2.680E+03 5.480E+02 1.630E+02 7.100E+01 3.800E+01 2.300E+01 1.500E+01 1.000E+01 7.200 5.200 3.900 2.300 1.400 9.300E–01 6.100E–01 4.200E–01 2.900E–01 2.000E–01 1.400E–01 1.000E–01 7.200E–02 3.300E–02 1.600E–02 8.400E–03 4.800E–03 3.100E–03 2.200E–03 1.700E–03 1.400E–03 1.200E–03 1.000E–03 8.700E–04 7.500E–04

l/m 1.120E–05 1.514E–05 2.034E–05 2.713E–05 3.597E–05 4.740E–05 6.171E–05 7.913E–05 1.009E–04 1.272E–04 1.611E–04 2.051E–04 2.624E–04 4.979E–04 9.810E–04 2.035E–03 4.402E–03 9.886E–03 2.370E–02 5.790E–02 1.420E–01 7.880E–01 3.310 8.800 1.800E+01 3.300E+01 5.300E+01 8.200E+01 1.200E+02 1.700E+02 2.400E+02 4.200E+02 7.000E+02 1.100E+03 1.700E+03 2.600E+03 3.800E+03 5.600E+03 8.000E+03 1.100E+04 1.600E+04 3.600E+04 7.700E+04 1.500E+05 2.800E+05 4.800E+05 7.300E+05 1.000E+06 1.400E+06 1.700E+06 2.100E+06 2.600E+06 3.100E+06

η/Pa s 1.543E–05 1.572E–05 1.601E–05 1.629E–05 1.657E–05 1.685E–05 1.704E–05 1.703E–05 1.696E–05 1.660E–05 1.640E–05 1.612E–05 1.584E–05 1.512E–05 1.438E–05 1.376E–05 1.321E–05 1.265E–05

k/J m–1s–1K–1 0.02142 0.02188 0.02233 0.02278 0.02323 0.02376 0.02397 0.02397 0.02384 0.02340 0.02296 0.02251 0.02206 0.02093 0.01978 0.01883 0.01800 0.01716

vs/m s–1 310.1 313.7 317.2 320.7 324.1 327.5 329.8 329.8 328.8 325.4 322.0 318.6 315.1 306.2 297.1 289.4 282.5 275.5

g/m s–2 9.697 9.690 9.684 9.678 9.672 9.666 9.660 9.654 9.648 9.642 9.636 9.632 9.624 9.609 9.594 9.579 9.564 9.550 9.535 9.520 9.505 9.476 9.447 9.418 9.389 9.360 9.331 9.302 9.274 9.246 9.218 9.162 9.106 9.051 8.997 8.943 8.889 8.836 8.784 8.732 8.680 8.553 8.429 8.307 8.188 8.072 7.958 7.846 7.737 7.630 7.525 7.422 7.322

4/27/05 5:03:45 PM

U.S. Standard Atmosphere (1976)

14-22

FIGURE 1. Temperature-height profile for U.S. Standard Atmosphere.

FIGURE 3. Mean molecular weight as a function of geometric altitude.

1000 900

GEOMETRIC ALTITUDE, km

800 700 600 500 400 300

O1 O2 N2 Ar H1 He TOTAL

200 100 0 8 10 1010 1012 1014 1016 1018 1020 1022 1024 1026 NUMBER DENSITY, m-3

FIGURE 2. Total pressure and mass density as a function of geometric altitude.

Section 14.indb 22

FIGURE 4. Number density of individual species and total number density as a function of geometric altitude.

4/27/05 5:03:49 PM

U.S. Standard Atmosphere (1976)

14-23

FIGURE 5. Collision frequency as a function of geometric altitude.

FIGURE 7. Mean air-particle speed as a function of geometric altitude.

FIGURE 6. Mean free path as a function of geometric altitude.

FIGURE 8. Dynamic viscosity as a function of geometric altitude.

Section 14.indb 23

4/27/05 5:03:52 PM

14-24

U.S. Standard Atmosphere (1976)

90 80

GEOMETRIC ALTITUDE, km

70 60 50 40 30 20 10 0 .017 .018 .019 .020 .021 .022 .023 .024 .025 .026 COEFFICIENT OF THERMAL CONDUCTIVITY, W/(m â&#x2039;&#x2026; K) FIGURE 9. Coefficient of thermal conductivity as a function of geometric altitude.

FIGURE 11. Molecular-diffusion and eddy-diffusion coefficients as a function of geometric altitude.

FIGURE 10. Speed of sound as a function of geometric altitude.

FIGURE 12. Acceleration of gravity as a function of geometric altitude.

Section 14.indb 24

4/27/05 5:03:55 PM

GEOGRAPHICAL AND SEASONAL VARIATION IN SOLAR RADIATION This table gives the amount of solar radiation reaching a unit area at the top of the earth’s atmosphere per day as a function of latitude and approximate date. It is based upon a solar constant (total energy per unit area at the earth’s average orbital distance) of 1373 W/m2. Absorption of radiation by the atmosphere is not taken into consideration.

Reference List, R. J., Smithsonian Meteorological Tables, Seventh Edition, Smithsonian Institution Press, Washington, D.C., 1962.

Daily Solar Radiation in MJ/m2 May 6 May 29 Jun. 2 32.8 42.4 45.7 32.3 41.8 45.0 31.8 39.9 43.0 34.4 39.7 41.6 36.8 40.7 42.0 38.6 41.3 42.1 39.4 41.1 41.4 39.2 39.7 39.7 37.9 37.4 37.1 35.5 34.1 33.5 32.3 30.0 29.2 28.0 25.2 24.1 23.1 19.7 18.5 17.5 14.0 12.6 11.7 8.2 7.0 5.9 2.9 2.0 1.0

Jul. 15 42.2 41.6 39.7 39.4 40.5 41.1 40.8 39.5 37.2 34.0 29.9 25.1 19.7 13.9 8.2 2.9

Aug. 8 32.5 32.0 31.5 34.0 36.5 38.3 39.1 38.9 37.6 35.2 32.0 27.8 22.8 17.4 11.6 5.9 1.0

Aug. 31 17.7 17.7 22.0 26.7 30.8 33.9 36.3 37.5 37.7 36.6 34.6 31.5 27.4 22.6 17.2 11.3 5.3 0.3

Jan. 13

Feb. 4

Feb. 26

3.1 8.7 14.9 21.0 26.7 31.9 36.3 39.7 42.2 43.5 43.8 43.2 42.1 42.4 44.4 45.1

1.0 6.2 12.3 18.4 24.1 29.3 33.8 37.3 39.7 41.1 41.3 40.5 38.6 36.0 33.3 33.8 34.4

0.3 5.6 11.7 17.8 23.5 28.4 32.7 35.9 38.0 39.1 39.0 37.7 35.2 31.9 27.7 22.9 18.4 18.4

Lat. 90° 80 70 60 50 40 30 20 10 0 –10 –20 –30 –40 –50 –60 –70 –80 –90

Mar. 21 6.6 13.0 19.0 24.4 29.1 32.9 35.7 37.4 38.0 37.4 35.7 32.9 29.1 24.4 19.0 13.0 6.6

Apr. 13 18.0 18.0 22.3 27.0 31.1 34.3 36.7 38.0 38.1 37.1 35.0 31.8 27.8 22.8 17.3 11.4 5.4 0.3

Lat. 90° 80 70 60 50 40 30 20 10 0 –10 –20 –30 –40 –50 –60 –70 –80 –90

Sep. 23

Oct. 16

Nov. 8

6.5 12.9 18.8 24.1 28.7 32.5 35.3 37.0 37.6 37.0 35.3 32.5 28.7 24.1 18.8 12.9 6.5

0.3 5.5 11.6 17.6 23.1 28.2 32.3 35.5 37.6 38.6 38.5 37.2 34.8 31.5 27.3 22.6 18.2 18.2

1.0 6.2 12.1 18.2 23.9 29.1 33.5 36.9 39.4 40.7 40.9 40.1 38.3 35.7 33.0 33.5 34.0

Nov. 30

3.1 8.7 14.8 20.9 26.6 31.8 36.1 39.5 42.0 43.3 43.6 43.1 41.9 42.2 44.2 44.8

Dec. 22

2.1 7.5 13.5 19.8 25.7 31.1 35.8 39.6 42.4 44.2 45.0 44.8 44.4 45.9 48.1 48.8

14-25

Section 14.indb 25

4/27/05 5:03:57 PM

INFRARED ABSORPTION BY THE EARTHâ&#x20AC;&#x2122;S ATMOSPHERE Several constituents of the earthâ&#x20AC;&#x2122;s atmosphere absorb infrared radiation. At ground level the strongest absorbers are H2O and CO2, but 30 to 40 other compounds can make significant contributions. The centers of the most important absorption bands are listed below: Molecule H2O H2O H2O CO2 CO2 O3 O3 O3 N2O N2O N2O CO CH4 CH4

Vibrational mode Bend Symmetric O-H stretch Antisymmetric O-H stretch Bend Antisymmetric C-O stretch Bend Antisymmetric O-O stretch Symmetric O-O stretch Bend N-O stretch N-N stretch C-O stretch Degenerate deformation Degenerate stretch

Band center in cm-1 1595 3657 3756 667 2349 701 1042 1103 589 1285 2224 2143 1306 3019

The HITRAN Molecular Spectroscopy Database (References 1 and 2) is a compilation of wavenumbers and intensities of more than 1.7 million spectral lines of atmospheric constituents. It is a valuable resource for calculating transmission of the atmosphere, radiative energy transfer, and other phenomena. The graph below, which was supplied by Walter J. Lafferty (Reference 3), gives the transmittance of the atmosphere for one set of conditions.

References 1. Rothman, L. S., et al., J. Quant. Spectros. Radiat. Transfer 82, 5, 2003; ibid., to be published, 2005. 2. HITRAN Molecular Spectroscopy Database, <http://cfa-www. Harvard.edu/HITRAN/hitrandata04/>. 3. Lafferty, W. J., Some Aspects of High Resolution Molecular Spectroscopy, in Lectures on Molecular Physics, Institute for the Structure of Matter, Centro de Fisica Miguel A. Catalan, Madrid, 1997.

Transmittance of U.S. Standard Atmosphere at Ground Level for a Path of 1 km at 296 K

Wavenumber in cm-1

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ATMOSPHERIC CONCENTRATION OF CARBON DIOXIDE, 1958â&#x20AC;&#x201C;2004 The data in this table were taken at the Mauna Loa Observatory in Hawaii and represent averages adjusted to the 15th of each month. The last column gives the average over the year. The concentration of CO2 is given in parts per million by volume. Data from other measurement sites may be found in Reference 1. The first graph illustrates the seasonal variation of CO2 concentration and the steady increase over the last 45 years. The second graph summarizes the growth in the emissions of CO2 into the atmosphere as a result of burning of fossil fuels (Reference 2).

References 1. Keeling, C.D., and Whorf, T.P., Atmospheric carbon dioxide record from Mauna Loa, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, TN, 2005; <cdiac.esd.ornl.gov/trends/co2/sio-mlo.htm>. 2. Marland, G., Boden, T. A., and Andres, R. J., Global, Regional, and National CO2 Emissions. In Trends: A Compendium of Data on Global Change, 2001. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, TN; <cdiac.esd.ornl.gov/trends/emis/tre_glob.htm>.

CO2 Concentration in ppm at Mauna Loa Year 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

487_S14.indb 27

Jan.

Feb. 316.47 316.97 317.70 318.56 319.08

March 315.71 316.65 317.58 318.54 319.69 319.86

April 317.45 317.72 319.03 319.48 320.58 321.39

315.58 316.43 316.89 317.94 318.74 319.57 319.44 320.62 322.33 322.57 324.00 325.06 326.17 326.77 328.54 329.35 330.40 331.74 332.92 334.97 336.23 338.01 339.23 340.75 341.37 343.70 344.97 346.29 348.02 350.43 352.76 353.66 354.72 355.98 356.70 358.36 359.96 362.05 363.18 365.32 368.15 369.14 370.28

320.44 321.59 322.50 323.15 324.42 325.98 326.68 327.63 329.56 330.71 331.41 332.56 333.41 335.39 336.76 338.36 340.47 341.61 342.52 344.50 346.00 346.96 348.47 351.72 353.07 354.70 355.75 356.72 357.16 358.91 361.00 363.25 364.00 366.15 368.87 369.46 371.50

320.89 322.39 323.04 323.89 325.64 326.93 327.18 327.75 330.30 331.48 332.04 333.50 334.70 336.64 337.96 340.08 341.38 342.70 343.10 345.29 347.43 347.86 349.42 352.22 353.68 355.39 357.16 357.81 358.38 359.97 361.64 364.03 364.57 367.31 369.59 370.52 372.12

322.13 323.70 324.42 325.03 326.66 328.14 327.78 329.72 331.50 332.65 333.31 334.58 336.07 337.76 338.89 340.77 342.51 343.57 344.94 347.08 348.35 349.55 350.99 353.59 355.42 356.20 358.60 359.15 359.46 361.27 363.45 364.72 366.35 368.61 371.14 371.66 372.87

May 317.50 318.29 320.03 320.58 321.01 322.24 322.24 322.16 324.07 325.00 325.57 327.38 328.07 328.92 330.07 332.48 333.08 333.96 334.87 336.74 338.01 339.47 341.46 342.91 344.13 345.75 347.43 348.93 350.21 351.84 354.22 355.67 357.16 359.33 359.66 360.28 361.68 363.79 365.41 366.80 369.29 371.00 371.82 374.02

June 318.16 319.59 319.77 320.61 321.47 321.89 321.87 323.75 324.09 325.36 326.70 327.66 328.57 329.09 332.07 332.25 333.59 334.34 336.27 337.89 339.29 341.17 342.25 343.35 345.32 346.79 348.25 349.54 351.25 353.79 355.13 356.22 358.24 359.25 359.59 360.94 363.26 364.97 365.62 368.87 370.35 371.70 373.30

July 315.85 316.55 318.18 318.58 319.61 319.74 320.44 321.21 322.41 322.55 324.14 325.89 326.35 327.37 328.05 330.87 331.18 331.91 333.05 334.93 336.54 337.73 339.56 340.49 342.06 343.99 345.40 346.56 347.94 349.52 352.39 353.90 354.82 356.18 357.03 357.58 359.55 361.90 363.65 364.47 367.64 369.27 370.12 371.62

Aug. 314.93 314.80 315.91 316.79 317.40 317.77 318.70 318.87 320.37 320.92 322.11 323.67 324.69 325.43 326.32 329.31 329.40 330.06 330.94 332.75 334.68 336.09 337.60 338.43 339.82 342.39 343.28 344.69 345.91 348.11 350.44 351.67 352.91 354.03 355.00 355.52 357.49 359.46 361.49 362.51 365.77 366.94 368.12 369.55

Sept. 313.19 313.84 314.16 314.99 316.26 316.21 316.70 317.81 318.64 319.26 320.33 322.38 323.10 323.36 324.84 327.51 327.44 328.56 329.30 331.58 332.76 333.91 335.88 336.69 337.97 339.86 341.07 343.09 344.86 346.44 348.72 349.80 350.96 352.16 353.01 353.70 355.84 358.06 359.46 360.19 363.90 364.63 366.62 367.96

Oct. 313.34 313.84 315.31 315.42 315.99 316.87 317.30 318.10 319.39 320.25 321.78 323.07 323.57 325.20 327.18 327.37 328.34 328.94 331.16 332.54 333.86 336.02 336.85 337.86 339.99 341.35 342.80 344.17 346.36 348.88 349.99 351.18 352.21 353.31 353.98 355.99 357.75 359.60 360.77 364.23 365.12 366.73 368.09

Nov. 313.34 314.82 315.00 316.10 316.69 317.06 317.68 318.87 319.79 320.72 321.33 322.85 324.01 324.80 326.50 328.16 328.46 329.49 330.31 332.40 333.92 335.29 337.10 338.36 339.26 341.16 342.98 344.24 345.66 347.81 350.07 351.30 352.83 353.75 354.16 355.33 357.58 359.56 360.76 362.43 365.46 366.67 368.29 369.68

Dec. 314.67 315.59 316.19 317.01 317.69 318.36 318.71 319.42 321.03 321.96 322.90 324.12 325.13 326.01 327.55 328.64 329.58 330.76 331.68 333.85 334.95 336.73 338.21 339.61 340.49 342.99 344.22 345.56 346.90 348.96 351.34 352.53 354.21 354.99 355.40 356.80 359.04 360.70 362.33 364.28 366.97 368.01 369.53 371.24

Annual 315.98 316.91 317.65 318.45 318.99 320.03 321.37 322.18 323.05 324.62 325.68 326.32 327.46 329.68 330.25 331.15 332.15 333.90 335.50 336.85 338.69 339.93 341.13 342.78 344.42 345.91 347.15 348.93 351.48 352.91 354.19 355.59 356.37 357.04 358.89 360.88 362.64 363.76 366.63 368.31 369.48 371.02

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Atmospheric Concentration of Carbon Dioxide, 1958â&#x20AC;&#x201C;2004

14-28 Year 2002 2003 2004

Jan. 372.43 374.68 376.79

Feb. 373.09 375.63 377.37

March 373.52 376.11 378.41

April 374.86 377.65 380.52

May 375.55 378.35 380.63

June 375.40 378.13 379.57

July 374.02 376.62 377.79

Aug. 371.49 374.50 375.86

Sept. 370.71 372.99 374.06

Oct. 370.24 373.00 374.24

Nov. 372.08 374.35 375.86

Dec. 373.78 375.70 377.48

Annual 373.10 375.64 377.38

CO2 Concentration at Mauna Loa

CO2 Emmissions from Burning of Fossil Fuels

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487_S14.indb 28

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4/10/06 12:02:49 PM

MEAN TEMPERATURES IN THE UNITED STATES, 1900–1992 Historical records of atmospheric temperatures have been analyzed to obtain mean temperatures in °C for 23 climatically distinct regions of the United States. The table below gives the average over these 23 regions, which cover completely the contiguous 48 states. Data for the individual regions and for other parts of the world may be found in the references. The data are presented as temperature anomalies, i.e., as deviations (in °C) from the average temperature at each individual recording station over a 1961–1990 reference period. The trend in the temperature anomaly thus gives an indication of the long-term variation in average temperatures.

Year 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941

CY Mean 0.46 –0.21 –0.14 –0.77 –0.72 –0.45 –0.04 –0.23 –0.11 –0.36 –0.14 0.02 –0.88 –0.23 –0.05 –0.11 –0.77 –1.34 –0.14 –0.16 –0.37 0.87 0.01 –0.10 –1.01 0.20 –0.01 0.20 –0.08 –0.68 –0.12 0.81 –0.14 0.35 0.86 0.12 –0.10 –0.13 0.71 0.38 0.06 0.79

Winter 0.07 –0.69 –0.84 –1.86 –1.86 0.23 1.09 0.73 0.82 –2.08 0.52 –1.50 –0.74 0.48 –0.37 –0.29 –1.93 –2.02 0.69 –0.83 1.56 –0.44 0.23 0.13 –0.44 0.97 1.11 –0.40 –1.94 0.07 1.16 1.75 –0.60 1.45 0.84 –2.23 –0.65 1.31 0.36 0.03 1.56

CY Mean: Calendar year mean (January-December) Winter: December-February Spring: March-May Summer: June-August Fall: September-November

References 1. Karl, T. R., Easterling, D. R., Knight, R. W., and Hughes, P. Y., in Trends ’93: A Compendium of Data on Global Change, p. 686, Boden, T. A., Kaiser, D. P., Sepanski, R. J., and Stoss, F. W., Eds., ORNL/CDIAC-65, Oak Ridge National Laboratory, Oak Ridge, TN, 1994. 2. Carbon Dioxide Information Analysis Center, WWW site <http:// cdiac.esd.ornl.gov/ftp/trends93>.

Spring 0.21 –0.46 0.48 0.10 –0.39 0.67 –0.69 –0.61 0.36 –1.06 0.95 0.20 –0.75 –0.65 0.04 –0.18 –0.36 –1.75 0.30 0.00 –0.96 0.83 0.15 –1.02 –1.27 0.57 –0.58 0.41 –0.28 0.30 0.09 –0.71 –0.58 –0.08 0.77 0.12 0.48 –0.24 0.98 0.34 –0.10 0.44

Summer 0.27 0.48 –0.58 –0.83 –0.92 –0.32 –0.42 –0.85 –0.64 0.06 –0.55 –0.19 –0.76 –0.07 0.14 –1.16 –0.30 –0.73 0.03 0.12 –0.67 0.52 0.16 –0.07 –0.64 0.05 –0.27 –0.83 –0.43 –0.39 –0.07 0.51 0.26 0.45 0.86 0.31 1.00 0.66 0.39 0.18 0.18 0.28

Fall 0.85 –0.28 0.12 –1.02 –0.21 –0.25 –0.10 –0.39 –0.59 0.01 0.13 –0.62 –0.51 0.22 0.32 0.31 –1.23 –1.04 –0.09 –0.13 0.02 0.32 0.41 –0.09 –0.53 –0.41 0.02 0.83 –0.08 –0.78 –0.25 1.41 –0.78 0.54 0.82 –0.47 –0.32 –0.03 0.08 0.15 0.12 0.85

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Mean Temperatures in the United States, 1900-1992

14-30 Year 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

S14_16.indd 30

CY Mean 0.01 –0.17 0.04 –0.02 0.53 0.10 –0.22 0.05 –0.37 –0.45 0.03 0.61 0.57 –0.25 –0.05 0.45 0.14 0.12 –0.27 –0.01 –0.04 –0.06 –0.27 –0.03 –0.34 –0.13 –0.28 –0.06 –0.12 –0.04 –0.13 0.48 0.16 –0.09 –0.62 0.32 –0.37 –0.53 0.18 0.64 –0.08 0.40 0.21 –0.26 0.93 0.67 –0.07 –0.30 0.72 0.77

Winter 0.35 0.20 0.61 0.30 –0.26 0.47 –0.67 –0.77 0.39 0.05 0.68 1.91 1.47 –0.33 –0.16 1.02 0.93 –0.60 0.43 –0.02 –0.52 –1.35 –1.30 –0.07 –0.31 0.23 –0.31 –0.36 –0.17 –0.08 0.20 –0.23 0.52 0.63 0.88 –1.95 –1.31 –2.92 0.72 0.90 –0.86 2.33 –0.78 –0.78 0.22 1.52 –0.26 –0.28 0.41 0.32 2.48

Spring 0.22 –0.46 –0.38 0.25 1.21 –0.42 –0.01 0.39 –1.02 –0.69 –0.40 0.03 –0.22 0.12 –0.42 0.44 0.06 0.16 –0.98 –0.17 –0.09 0.61 –0.24 –0.56 –0.25 –0.05 –0.16 –0.54 –0.44 –0.99 0.26 0.47 0.74 –0.79 –0.09 1.07 0.23 0.09 –0.25 0.80 0.03 –0.36 –0.30 1.24 1.22 0.97 –0.06 0.36 0.72 1.36 0.82

Summer 0.08 0.54 –0.20 –0.47 –0.21 0.03 0.02 0.33 –0.86 –0.30 0.49 0.31 0.36 0.19 0.01 0.25 0.11 0.50 0.01 0.18 –0.41 0.12 –0.08 –0.42 –0.07 –0.37 –0.12 0.12 0.32 0.01 –0.19 0.22 –0.32 0.03 –0.54 0.60 0.09 –0.21 0.43 0.57 –0.11 0.58 0.31 –0.23 0.45 0.33 0.57 0.12 0.41 0.56 –0.70

Fall 0.06 –0.79 0.43 0.08 0.18 0.85 –0.15 0.23 0.13 –0.70 –1.22 0.31 0.70 –0.60 –0.37 –0.13 0.45 –0.52 0.56 –0.29 0.65 1.38 –0.40 0.28 –0.13 –0.32 0.01 –0.16 –0.07 0.56 0.05 0.90 –0.39 –0.20 –1.72 0.68 0.21 –0.07 –0.04 0.36 0.06 0.94 0.07 0.05 0.49 –0.17 0.04 –0.27 0.66 –0.31

5/2/05 1:51:29 PM

GLOBAL TEMPERATURE TREND, 1856–2004 This table and graph summarize the trend in annual mean global surface temperature from 1856 to 2004. The values were calculated from mean temperature anomalies by assuming an absolute global mean of 14.00°C, which is the best estimate for the 1961–1990 period. The 95% confidence interval for the annual mean temperature values since 1951 is ± 0.12°C; prior to 1900 this interval is ± 0.18°C. Year 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886

t/°C 13.621 13.538 13.584 13.775 13.628 13.596 13.473 13.727 13.526 13.733 13.777 13.709 13.775 13.695 13.704 13.649 13.734 13.673 13.624 13.576 13.548 13.789 13.943 13.713 13.704 13.754 13.738 13.682 13.651 13.650 13.746

Year 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917

t/°C 13.657 13.689 13.800 13.587 13.647 13.593 13.551 13.586 13.638 13.801 13.814 13.661 13.750 13.808 13.744 13.651 13.555 13.557 13.629 13.708 13.495 13.523 13.553 13.558 13.535 13.594 13.607 13.752 13.841 13.627 13.505

Year 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948

Reference Jones, P. D., Parker, D. E., Osborn, T. J., and Briffa, K. R., Global and hemispheric temperature anomalies--land and marine instrumental records, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, TN; <cdiac.esd.ornl.gov/trends/temp/jonescru/jones.html>.

t/°C 13.590 13.708 13.707 13.783 13.677 13.701 13.653 13.754 13.884 13.782 13.773 13.639 13.848 13.901 13.863 13.761 13.861 13.828 13.879 13.976 14.076 13.962 13.917 14.028 13.980 14.001 14.158 14.039 13.880 13.895 13.907

Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979

t/°C 13.903 13.790 13.907 13.975 14.045 13.830 13.811 13.728 13.994 14.061 14.014 13.972 14.015 14.008 14.039 13.767 13.834 13.916 13.907 13.895 14.040 13.969 13.813 13.959 14.093 13.829 13.877 13.800 14.057 13.964 14.067

Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

t/°C 14.102 14.133 14.019 14.226 14.031 14.014 14.096 14.253 14.240 14.163 14.310 14.251 14.116 14.179 14.232 14.373 14.227 14.411 14.579 14.340 14.290 14.422 14.475 14.475 14.455

Annual Mean Global Temperature in °C

487_S14.indb 31

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ATMOSPHERIC ELECTRICITY Hans Dolezalek, Hannes Tammet, John Latham, and Martin A. Uman

I. SURVEY AND GLOBAL CIRCUIT Hans Dolezalek

The science of atmospheric electricity originated in 1752 by an experimental proof of a related earlier hypothesis (that lightning is an electrical event). In spite of a large effort, in part by such eminent physicists as Coulomb, Lord Kelvin, and many others, an overall, proven theory able to generate models with sufficient resolution is not yet available. Generally accepted and encompassing text books are now more than 20 years old. The voluminous proceedings of the, so far, nine international atmospheric electricity conferences (1954 to 1992) give much valuable detail and demonstrate impressive progress, as do a number of less comprehensive textbooks published in the last 20 years, but a general theory as indicated above is not yet created. Only now, certain related measuring techniques and mathematical possibilities are emerging. Applications to practical purposes do exist in the field of lightning research (including the electromagnetic radiation emanating from lightning) by the establishment of lightning-location networks and by the now developing possibility to detect electrified clouds which pose hazards to aircraft. Application of atmospheric electricity to other parts of meteorology seems to be promising but so far has seldom been instituted. Because some atmospheric electric signals propagate around the earth and because of the existence of a global circuit, applications for the monitoring of global change processes and conditions are now being proposed. Significant secular changes in the global circuit would indicate a change in the global climate; the availability of many old data (about a span of 100 years) could help detect a long-term trend. The concept of the “global circuit” is based on the theory of the global spherical capacitor: both, the solid (and liquid) earth as one electrode, and the high atmospheric layers (about the ionosphere) as the other, are by orders of magnitude more electrically conductive than the atmosphere between them. According to the “classical picture of atmospheric electricity”, this capacitor is continuously charged by the common action of all thunderstorms to a d.c. voltage difference of several hundred kilovolts, the earth being negative. The much smaller but still existing conductivity of the atmosphere allows a current flowing from the ionosphere to the ground, integrated for all sink areas of the whole earth, of the order of 1.5 kA. In this way, a global circuit is created with many generators and sinkareas both interspaced and distributed over the whole globe, all connected to two nodes: ionosphere and ground. Within the scope of the global circuit, for each location, the current density (order of several pA/m2) is determined by the voltage difference between ionosphere and ground (which is the same for all locations but varying in time) and the columnar resistance reaching from the ground up to the ionosphere (in the order of 1017 Ωm2). Natural processes, especially meteorological processes and some human activity, which produce or move electric charges (“space charges”) or affect the ion distribution, constitute local generators and thereby “local circuits”, horziontally and/or in parallel or antiparallel to the local part of the global circuit. In many cases, the local currents are much stronger than the global ones, making the measurement of the global current at a given location and/or during a period of time very difficult or, often, impossible. The strongest local circuits usually occur with certain weather conditions (precipitation, fog, high wind, blown-up dust or snow, heavy cloudiness) which make measurement of the global circuit impossible everywhere: but even in their absence local generators exist in varying magnitudes and of different characters. The separation

of the local and global shares in the measured values of current density is a central problem of the science of atmospheric electricity. Aerological measurements are of high value in this regard. The above description is within the “classical picture” of atmospheric electricity, a group of hypotheses to explain the electrification of the atmosphere. It is probably fundamentally correct but certainly not complete; it has not yet been confirmed by systems of measurements resulting in no inner contradictions. In particular, extraterrestrial influences must be permitted; their general significance is still under debate. Within this “classical picture” a kind of electric standard atmosphere may be constructed as shown in Table 1. Values with a star, *, are rough average values from measurement. A star in parentheses, (*), points to a typical value from one or a few measurements. All other values have been calculated from starred values, under the assumption that at 2 km 50% and at 12 km 90% of the columnar resistance is reached. Voltage drop along one of the partial columns can be calculated by subtracting the value for the lower column from that of the upper one. Columnar resistances, conductances, and capacitances are valid for that particular part of the column which is indicated at the left. Capacitances are calculated with the formula for plate capacitors, and this fact must be considered also for the time constants for columns. According to measurements, U, the potential difference between 0 m and 65 km may vary by a factor of approximately 2. The total columnar resistance, Rc, is estimated to vary up to a factor of 3, the variation being due to either reduction of conductivity in the exchange layer (about lowest 2 km of this table) or to the presence of high mountains; in both cases the variation is caused in the troposphere. Smaller variations in the stratosphere and mesosphere are being discussed because of aerosols there. The air-earth current density in fair weather varies by a factor of 3 to 6 accordingly. Conductivity near the ground varies by a factor of about 3 but only decreasing; increase of conductivity due to extraordinary radioactivity is a singular event. The field strength near the ground varies as a consequence of variations of air-earth current density and conductivity from about 1/3 to about 10 times of the value quoted in the table. Conductivity near the ground shows a diurnal and an annual variation which depends strongly on the locality: air-earth current density shows a diurnal and annual variation because the earth-ionosphere potential difference undergoes such variations, and also because the columnar resistance is supposed to have a diurnal and probably an annual variation. Conductivities and air-earth current densities on high mountains are greater than at sea level by factors of up to 10. Conductivity decreases when atmospheric humidity increases. Values for space charges are not quoted because measurements are too few to allow calculation of average values. Values of parameters over the oceans are still rather uncertain. Theoretically, in fair-weather conditions, Ohm’s law must be fulfilled for the electric field, the conduction current density, and the electrical conductivity of the atmosphere. Deviations point to shortcomings in the applied measuring techniques. Data which are representative for a large area (in the extreme, “globally representative data”, i.e. data on the global circuit), can on the ground be obtained only by stations on an open plane and only if local generators are either small or constant or are independently measured. Certain measurements with instrumented aircraft provide globally representative information valid for the period of the actual measurement.

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Atmospheric Electricity

14-33

TABLE 1. Electrical Parameters of the Clear (Fair-Weather) Atmosphere, Pertinent to the Classical Picture of Atm. Electricity (Electric Standard Atmosphere) Part of atmosphere for Potential which the values are Currents, I, in A; differences, U, in calculated (elements are and current V; field strength E in free, cloudless densities, in V/m; U = 0 at atmosphere) i, in A/m2 sea level Volume element at about i = 3 × 10-12* E0 = 1.2 × 102* sea level, 1 m3 Lower column of 1 m2 At upper end: i = 3 × 10-12 cross section from sea U1 = 1.8 × 105 level to 2 km height Volume element at about i = 3 × 10-12 E2 = 6.6 × 101 2 km height, 1 m3 Center column of 1 m2 At upper end: i = 3 × 10-12 cross section from 2 to Um = 3.15 × 105 12 km Volume element at about i = 3 × 10-12 E12 = 3.9 × 100 12 km height, 1 m3 Upper column of 1 m2 At upper end: i = 3 × 10-12 cross section from 12 to Uu = 3.5 × 105 65 km height Whole column of 1 m2 At upper end: i = 3 × 10-12 cross section from 0 to U = 3.5 × 105 65 km height Total spherical capacitor i = 1.5 × 103 U = 3.5 × 105* 14 2 area: 5 ×10 m

Resistances, R, in Ω; columnar resistances,Rc , in Ω m2 and resistivities, ρ, in Ω m ρ0 = 4 × 1013

Conductances, G, Capacitances, C, in in Ω-1; columnar F; columnar conductances Gc, capacitances,Cc , in Ω-1m2; total in F m-2 and Time constants τ, conductivities, capacitivities, in seconds γ, in Ω-1m-1 ε, in F m-1 γ0 = 2.5 × 10-14 ε0 = 8.9 × 10-12* τ0 = 3.6 × 102

Rc1 = 6 × 1016

Gc1 = 1.7 × 10-17

Ccl = 4.4 × 10-15

τc1 = 2.6 × 102

ρ2 = 2.2 × 1013(*)

γ2 = 4.5 × 10-14

ε2 = 8.9 × 10-12*

τ2 = 2 × 102

Rcm = 4.5 × 1016

Gcm = 5 × 10-17

Ccm = 8.8 × 10-16

τcm = 1.8 × 101

ρ12 = 1.3 × 1012(*)

γ12 = 7.7 × 10-13

ε12 = 8.9 × 10-12

τ12 = 1.2 × 101

Rcu = 1.5 × 1016

Gcu = 2.5 × 10-17

Ccu = 1.67 × 10-16

τcm = 6.7 × 100

Rc = 1.2 × 1017

Gc = 8.3 × 10-18

Cc = 1.36 × 10-16

τc = 1.64 × 101

R = 2.4 × 102

G = 4.2 × 10-3

C = 6.8 × 10-2

τ = 1.64 × 101

Note: All currents and fields listed are part of the global circuit, i.e., circuits of local generators are not included. Values are subject to variations due to latitude and altitude of the point of observation above sea level, locality with respect to sources of disturbances, meteorological and climatological factors, and man-made changes. For more explanations, see text.

II. AIR IONS

Hannes Tammet

The term “air ions” signifies all airborne particles which are the carriers of the electrical current in the air and have drift velocities determined by the electric field. The probability of electrical dissociation of molecules in the atmospheric air under thermodynamic equilibrium is near to zero. The average ionization at the ground level over the ocean is 2∙106 ion pairs m-3s-1. This ionization is produced mainly by cosmic rays. Over the continents the ionizing radiation from soil and from radioactive substances in the air each add about 4∙106 m-3s-1. The total average ionization rate of 107 m3s-1 is equivalent to 17 μR/h which is a customary expression of the background level of the ionizing radiations. The ionization rate over the ground varies in space due to the radioactivity of soil, and in time depending on the exchange of air between the atmosphere and radon-containing soil. Radioactive pollution increases the ionization rate. A temporary increase of about 10 times was registered in Sweden after the Chernobyl accident in 1986. The emission of Kr85 from nuclear power plants can noticeably increase the global ionization rate in the next century. The ionization rate decreases with altitude near the ground and increases at higher altitudes up to 15 km, where it has a maximum of about 5∙107 m-3s-1. Solar X-ray and extreme UV radiation cause a new increase at altitudes over 60 km. Local sources of air ions are point discharges in strong electric fields, fluidization of charged drops from waves, etc. The enhanced chemical activity of an ion results in a chain of ion-molecule reactions with the colliding neutrals, and, in the first microsecond of the life of an air ion, a charged molecular cluster called the cluster ion is formed. According to theoretical calcula-

Section 14.indb 33

tions in the air free from exotic trace gases the following cluster ions should be dominant: NO3− ∙(HNO3)·H2O, NO2−·(H2O)2, NO3− ∙H2O, O2−·(H2O)4, O2−·(H2O)5, H3O+·(H2O)6, NH4+·(H2O)2, NH4+·(H2O), H3O+·(H2O)5, NH4+·NH3 A measurable parameter of air ions is the electrical mobility k, characterizing the drift velocity in the unit electric field. The mobility is inversely proportional to the density of air, and the results of measurements are as a rule reduced to normal conditions. According to mobility the air ions are called: fast or small or light ions with mobility k > 5·10-5 m2V-1s1 , intermediate ions, and slow or large or heavy ions with mobility k > 10-6 m2V-1s1. The boundary between intermediate and slow ions is conventional. Cluster ions are fast ions. The masses of cluster ions may be measured with mass spectrometers, but the possible ion-molecule reactions during the passage of the air through nozzles to the vacuum chamber complicate the measurement. Mass and mobility of cluster ions are highly correlated. The experimental results5 can be expressed by the empirical formula

m≈

850 u −4

-1 −1

[ 0.3 + k / (10 m V s )] 2

where u is the unified atomic mass unit. The value of the transport cross-section of a cluster ion is needed to calculate its mobility according to the kinetic theory of Chapman and Enskog. The theoretical estimation of transport cross-sections is rough and cannot be used to identify the chemi-

4/27/05 5:04:17 PM

Atmospheric Electricity

14-34 cal structures of cluster ions. Mass spectrometry is the main technique of identification of cluster ions.2 Märk and Castleman4 presented an overview of over 1000 publications on the experimental studies of cluster ions. Most of them present information about ions of millisecond age range. The low concentration makes it difficult to get detailed information about masses and mobilities of the natural atmospheric ions at ground level. The results of a 1-year continuous measurement6 are as follows: Average mobility The corresponding mass The corresponding diameter The average concentration The corresponding conductivity

+ ions 1.36 190

– ions 1.56 130

unit 10-4m2V-1s1 u

0.69 400

0.61 360

nm 106m-3

8.7

9.0

The distribution of tropospheric cluster ions according to the mobility and estimated mass is depicted in Figure 1. The problems and results of direct mass spectrometry of natural cluster ions are analyzed by Eisele2 for ground level and by Meyerott, Reagan and Joiner5 for stratospheric measurements. Air ions in the high atmosphere are a subject of ionospheric physics. During its lifetime (about 1 min), a cluster ion at ground level collides with nearly 1012 molecules. Thus the cluster ions are able to concentrate trace gases of very low concentration if they have an extra high electron or proton affinity. For example, Eisele2 demond P0 p-1+p1 p-2+p2 Pq>2 k1

3 98 2 0 0 15000

10 90 10 0 0 1900

30 70 30 0 0 250

100 42 48 10 0 28

FIGURE 1. Average mobility and mass spectra of natural tropospheric cluster ions. Concentrations of the mobility fractions were measured in a rural site every 5 min over 1 year.6 Ion mass is estimated according to the above empirical formula.

Section 14.indb 34

strated that a considerable fraction of positive atmospheric cluster ions in the unpolluted atmosphere at ground level probably consist of a molecule derived from pyridine. The concentration of these constituents is estimated to be about 10-12. Therefore, air- ion mass and mobility spectrometry is considered as a promising technique for trace analysis in the air. Mass and mobility spectrometry of millisecond-age air ions has been developed as a technique of chemical analysis known as “plasma chromatography”.1 The sensitivity of the detection grows with the age of the cluster ions measured. The mechanisms of annihilation of cluster ions are ion-ion recombination (on the average 3%) and sedimentation on aerosol particles (on the average 97% of cluster ions at ground level). The result of the combination of a cluster ion and neutral particle is a charged particle called an aerosol ion. In conditions of detailed thermodynamic equilibrium the probability that a spherical particle of diameter d carries q elementary charges is calculated from the Boltzmann distribution: pq (d ) = (2πd /d0 )1/2 exp(−q 2 d0 /2d ) where d0 = 115 nm (at 18°C). The supposition about the detailed equilibrium is an approximation and the formula is not valid for particles less than d0. On the basis of numerical calculations by Hoppel and Frick3 the following charge probabilities can be derived:

300 24 41 23 12 5.1

1000 14 25 21 40 1.11

3000 8 15 14 63 0.33

nm % % % % 10-9 m2V-1s-1

FIGURE 2. Mobility and size spectra of tropospheric aerosol ions.6 The wide bars mark the fraction concentrations theoretically estimated on the basis of the standard size distribution of tropospheric aerosol. The pin bars with head + and – mark average values of positive and negative aerosol ion fraction concentrations measured in a rural site every 5 min during 4 months.

4/27/05 5:04:22 PM

Atmospheric Electricity The last line of the table presents the mobility of a particle carrying one elementary charge. The distribution of the atmospheric aerosol ions over mobility is demonstrated in Figure 2. Although the concentration of aerosol in continental air at ground level is an order of magnitude higher than the concentration of cluster ions, the mobilities of aerosol ions are so small that their percentage in air conductivity is less than 1%. A specific class of aerosol ions are condensed aerosol ions produced as a result of the condensation of gaseous matter on the cluster ions. In aerosol physics the process is called ion-induced nucleation; it is considered as one among the processes of gas-toparticle conversion. The condensed aerosol ions have an inherent charge. Their sizes and mobilities are between the sizes and mobilities of cluster ions and of ordinary aerosol ions. Water and standard constituents of atmospheric air are not able to condense on the cluster ions in the real atmosphere. Thus the concentration of condensed aerosol ions depends on the trace constituents in the air and is very low in unpolluted air. Knowledge about condensed aerosol ions is poor because of measurement difficulties.

References 1. Carr, T. W., Ed., Plasma Chromatography, Plenum Press, New York and London, XII + 259 pp., 1984. 2. Eisele, F. L., Identification of Tropospheric Ions, J. Geophys. Res., vol. 91, no. D7, pp. 7897–7906, 1986. 3. Hoppel, W. A., and Frick, G. M., The Nonequilibrium Character of the Aerosol Charge Distributions Produced by Neutralizers, Aerosol Sci. Technol., vol. 12, no. 3, pp. 471–496, 1990. 4. Mark, T. D., and Castleman, A. W., Experimental Studies on Cluster Ions, in Advances in Atomic and Molecular Physics, vol. 20, pp. 65– 172, Academic Press, 1985. 5. Meyerott, R. E., Reagan, J. B., and Joiner, R. G., The Mobility and Concentration of Ions and the Ionic Conductivity in the Lower Stratosphere, J. Geophys. Res., vol. 85, no. A3, pp. 1273–1278, 1980. 6. Salm, J., Tammet, H., Iher, H., and Hörrak, U., Atmospheric Electrical Measurements in Tahkuse, Estonia (in Russian), in Voprosy Atmosfernogo Elektrichestva, pp. 168–175, Gidrometeoizdat, Leningrad, 1990.

III. THUNDERSTORM ELECTRICITY John Latham The development of improved radar techniques and instruments for in-cloud electrical and physical measurements, coupled with a much clearer recognition by the research community that establishment of the mechanism or mechanisms responsible for electric field development in thunderclouds, culminating in lightning, is inextricably linked to the concomitant dynamical and microphysical evolution of the clouds, has led to significant progress over the past decade. Field studies indicate that in most thunderclouds the electrical development is associated with the process of glaciation, which can occur in a variety of incompletely understood ways. In the absence of ice, field growth is slow, individual hydrometeor charges are low, and lightning is produced only rarely. Precipitation — in the solid form, as graupel — also appears to be a necessary ingredient for significant electrification, as does significant convective activity and mixing between the clouds and their environments, via entrainment. Increasingly, the view is being accepted that charge transfer leading to field-growth is largely a consequence of rebounding collisions between graupel pellets and smaller vapor-grown ice crystals, followed by the separation under gravity of these two types

Section 14.indb 35

14-35 of hydrometeor. These collisions occur predominantly within the temperature range –15 to –30°C, and for significant charge transfer need to occur in the presence of supercooled cloud droplets. The field evidence is inconsistent with an inductive mechanism, and extensive laboratory studies indicate that the principal charging mechanism is non-inductive and associated — in ways yet to be identified — with differences in surface characteristics of the interacting hydrometeors. Laboratory studies indicate that the two most favored sites for corona emission leading to the lightning discharge are the tips of ephemeral liquid filaments, produced during the glancing collisions of supercooled raindrops, and protuberances on large ice crystals or graupel pellets. The relative importance of these alternatives will depend on the hydrometeor characteristics and the temperature in the regions of strongest fields; these features are themselves dependent on air-mass characteristics and climatological considerations. A recently identified but unresolved question is why, in continental Northern Hemisphere thunderclouds at least, the sign of the charge brought to ground by lightning is predominantly negative in summer but more evenly balanced in winter.

IV. LIGHTNING Martin A. Uman From both ground-based weather-station data and satellite measurements, it has been estimated that there are about 100 lightning discharges, both cloud and ground flashes, over the whole earth each second; representing an average global lightning flash density of about 6 km-2yr-1. Most of this lightning occurs over the earth’s land masses. For example, in central Florida, where thunderstorms occur about 90 days/yr, the flash density for discharges to earth is about 15 km-2yr-1. Some tropical areas of the earth have thunderstorms up to 300 days/yr. Lightning can be defined as a transient, high-current electric discharge whose path length is measured in kilometers and whose most common source is the electric charge separated in the ordinary thunderstorm or cumulonimbus cloud. Well over half of all lightning discharges occur totally within individual thunderstorm clouds and are referred to as intracloud discharges. Cloudto-ground lightning, however, has been studied more extensively than any other lightning form because of its visibility and its more practical interest. Cloud-to-cloud and cloud-to-air discharges are less common than intracloud or cloud-to-ground lightning. Lightning between the cloud and earth can be categorized in terms of the direction of motion, upward or downward, and the sign of the charge, positive or negative, of the developing discharge (called a leader) which initiates the overall event. Over 90% of the worldwide cloud-to-ground discharges is initiated in the thundercloud by downward-moving negatively charged leaders and subsequently results in the lowering of negative charge to earth. Cloudto-ground lightning can also be initiated by downward-moving positive leaders, less than 10% of the worldwide cloud-to-ground lightning being of this type although the exact percentage is a function of season and latitude. Lightning between cloud and ground can also be initiated by leaders which develop upward from the earth. These upward-initiated discharges are relatively rare, may be of either polarity, and generally occur from mountaintops and tall man-made structures. We discuss next the most common type of cloud-to-ground lightning. A negative cloud-to-ground discharge or flash has an overall duration of some tenths of a second and is made up of vari-

4/27/05 5:04:23 PM

14-36 ous components, among which are typically three or four highcurrent pulses called strokes. Each stroke lasts about a millisecond, the separation time between strokes being typically several tens of milliseconds. Such lightning often appears to “flicker” because the human eye can just resolve the individual light pulse associated with each stroke. A drawing of the components of a negative cloud-to-ground flash is found in Figure 3. Some values for salient parameters are found in Table 1. The negatively charged stepped leader initiates the first stroke in a flash by propagating from cloud to ground through virgin air in a series of discrete steps. Photographically observed leader steps in clear air are typically 1 μs in duration and tens of meters in length, with a pause time between steps of about 50 μs. A fully developed stepped leader lowers up to 10 or more coulombs of negative cloud charge toward ground in tens of milliseconds with an average downward speed of about 2 × 105 m/s. The average leader current is in the 100 to 1000 A range. The steps have pulse currents of at least 1 kA. Associated with these currents are electric- and magnetic-field pulses with widths of about 1 μs or less and risetimes of about 0.1 μs or less. The stepped leader, during its trip toward ground, branches in a downward direction, resulting in the characteristic downwardbranched geometrical structure commonly observed. The electric potential of the bottom of the negatively charged leader channel with respect to ground has a magnitude in excess of 107 V. As the leader tip nears ground, the electric field at sharp objects on the ground or at irregularities of the ground itself exceeds the breakdown value of air, and one or more upward-moving discharges (often called upward leaders) are initiated from those points, thus beginning the attachment process. An understanding of the physics of the attachment process is central to an understanding of the operation of lightning protection of ground-based objects and the effects of lightning on humans and animals, since it is the attachment process that determines where the lightning connects to objects on the ground and the value of the early currents which flow. When one of the upward-moving discharges from the ground (or from a lightning rod or an individual) contacts the tip of the downward-moving stepped leader, typically some tens of meters above the ground, the leader tip is effectively connected to ground potential. The negatively charged leader channel is then discharged to earth when a ground potential wave, referred to as the first return stroke, propagates continuously up the leader path. The upward speed of a return stroke near the ground is typically near one third the speed of light, and the speed decreases with height. The first return stroke produces a peak current near ground of typically 30 kA, with a time from zero to peak of a few microseconds. Currents measured at the ground fall to half of the peak value in about 50 μs, and currents of the order of hundreds of amperes may flow for times of a few milliseconds up to several hundred milliseconds. The longer-lasting currents are known as continuing currents. The rapid release of return stroke energy heats the leader channel to a temperature near 30,000 K and creates a high-pressure channel which expands and generates the shock waves that eventually become thunder, as further discussed later. The return stroke effectively lowers to ground the charge originally deposited onto the stepped-leader channel and additionally initiates the lowering of other charges which may be available to the top of its channel. First return-stroke electric fields exhibit a microsecond scale rise to peak with a typical peak value of 5 V/m, normalized to a distance of 100 km by an inverse distance relationship. Roughly half of the field rise to peak, the so-called “fast transition”, takes place in tenths of a microsecond, an observation that can only be made if the field propagation is over a highly conducting surface such as salt water.

Section 14.indb 36

Atmospheric Electricity After the first return-stroke current has ceased to flow, the flash, including charge motion in the cloud, may end. The lightning is then called a single-stroke flash. On the other hand, if additional charge is made available to the top of the channel, a continuous or dart leader may propagate down the residual first-stroke channel at a typical speed of about 1 × 107 m/s. The dart leader lowers a charge of the order of 1 C by virtue of a current of about 1 kA. The dart leader then initiates the second (or any subsequent) return stroke. Subsequent return-stroke currents generally have faster zero-to-peak rise times than do first-stroke currents, but similar maximum rates of change, about 100 kA/μs. Some leaders begin as dart leaders, but toward the end of their trip toward ground become stepped leaders. These leaders are known as dartstepped leaders and may have different ground termination points (and separate upward leaders) from the first stroke. Most often the dart-stepped leaders are associated with the second stroke of the flash. Nearly half of all flashes exhibit more than one termination point on ground with the distance between separate terminations being up to several kilometers. Subsequent return-stroke radiated electric and magnetic fields are similar to, but usually a factor of two or so smaller, than first return-stroke fields. About one third of all multiple-stroke flashes has at least one subsequent stroke which is larger than the first stroke. Cloud-to-ground flashes that lower positive charge, though not common, are of considerable practical interest because their peak currents and total charge transfer can be much larger than for the more common negative ground flash. The largest recorded peak currents, those in the 200- to 300-kA range, are due to the return strokes of positive lightning. Such positive flashes to ground are initiated by downward-moving leaders which do not exhibit the distinct steps of their negative counterparts. Rather, they show a luminosity which is more or less continuous but modulated in intensity. Positive flashes are generally composed of a single stroke followed by a period of continuing current. Positive flashes are probably initiated from the upper positive charge in the thundercloud charge dipole when that cloud charge is horizontally separated from the negative charge beneath it, the source of the usual negative cloud-to-ground lightning. Positive flashes are relatively common in winter thunderstorms (snow storms), which produce few flashes overall, and are relatively uncommon in summer thunderstorms. The fraction of positive lightning in summer thunderstorms apparently increases with increasing latitude and with increasing height of the ground above sea level. Distant lightning return stroke fields are often referred to as sferics (called “atmospherics” in the older literature). The peak in the sferics frequency spectrum is near 5 kHz due to the bipolar or ringing nature of the distant return-stroke electromagnetic signal and to the effects of propagation. Thunder, the acoustic radiation associated with lightning, is sometimes divided into the categories “audible”, sounds that one can hear, and “infrasonic”, below a few tens of hertz, a frequency range that is inaudible. This division is made because it is thought that the mechanisms that produce audible and infrasonic thunder are different. Audible thunder is thought to be due to the expansion of a rapidly heated return stroke channel, as noted earlier, whereas infrasonic thunder is thought to be associated with the conversion to sound of the energy stored in the electrostatic field of the thundercloud when lightning rapidly reduces that cloud field. The technology of artificially initiating lightning by firing upward small rocket trailing grounded wire of a few hundred meters length has been well-developed during the past decade. Such “triggered” flashes are similar to natural upward-initiated discharges from tall structure. They often contain subsequent strokes which,

4/27/05 5:04:23 PM

Atmospheric Electricity

14-37

FIGURE 3. Sequence of steps in cloud-to-ground lightning.

when they occur, are similar to the subsequent strokes in natural lightning. These triggered subsequent strokes have been the subject of considerable recent research. Also in the past 10 years or so sophisticated lightning locating equipment has been installed throughout the world. For example, all ground flashes in the U.S. are now centrally monitored for research, for better overall weather prediction, and for hazard warning for aviation, electric utilities and other lightning-sensitive facilities. Information on lightning physics can be found in M. A. Uman, The Lightning Discharge, Academic Press, San Diego, 1987; on lightning death and injury in Medical Aspects of Lightning Injury, C. Andrews, M. A. Cooper, M. Darveniza, and D. Mackerras, Eds.,

Section 14.indb 37

CRC Press, 1992. Ground flash location information for the U.S., in real time or archived, is available from Geomet Data Service of Tucson, AZ, which is also a source of the names of providers of those data in other countries. Table 2 has data for cloud-to-ground lightning discharges bringing negative charge to earth. The values listed are intended to convey a rough feeling for the various physical parameters of lightning. No great accuracy is claimed since the results of different investigators are often not in good agreement. These values may, in fact, depend on the particular environment in which the lightning discharge is generated. The choice of some of the entries in the table is arbitrary.

4/27/05 5:04:27 PM

Atmospheric Electricity

14-38 TABLE 2. Data for Cloud-to-Ground Lightning Discharges Stepped leader Length of step, m Time interval between steps, µs Average speed of propagation of stepped leader, m/sb Charged deposited on stepped-leader channel, coulombs Dart leader Speed of propagation, m/sb Charged deposited on dart-leader channel, coulombs Return strokec Speed of propagation, m/sb Maximum current rate of increase, kA/µs Time to peak current, µs Peak current, kA Time to half of peak current, µs Charge transferred excluding continuing current, coulombs Channel length, km Lightning flash Number of strokes per flash Time interval between strokes in absence of continuing current, ms Time duration of flash, s Charge transferred including continuing current, coulombs a b

Minimuma

Representative values

Maximuma

3 30 1.0 × 105 3

50 50 2.0 × 105 5

200 125 3.0 × 106 20

1.0 × 106 0.2

1.0 × 107 1

2.4 × 107 6

2.0 × 107 <1 <1 2 10 0.02 2

1.0 × 108 100 2 30 50 3 5

2.0 × 108 400 30 200 250 20 15

1 3 10-2 3

4 60 0.5 30

26 100 2 200

The words maximum and minimum are used in the sense that most measured values fall between these limits. Speeds of propagation are generally determined from photographic data and are “two-dimensional”. Since many lightning flashes are not vertical, values stated are probably slight underestimates of actual values. First return strokes have longer times to current peak and generally larger charge transfer than do subsequent return strokes.

Adapted from Uman, M.A., Lightning, Dover Paperbook, New York, 1986, and Uman, M.A., The Lightning Discharge, Academic Press, San Diego, 1987.

Section 14.indb 38

4/27/05 5:04:27 PM

SPEED OF SOUND IN VARIOUS MEDIA The speed of sound in various solids, liquids, and gases is given in these tables. While only a single parameter v is needed for liquids and gases, sound propagation in isotropic solids is characterized by three velocity parameters. For a solid of infinite extent (or of finite extent if all dimensions are much larger than a wavelength), there are two relevant quantities, vl: velocity of longitudinal waves vs: velocity of shear waves. For a cylindrical rod with diameter much smaller than a wavelength, vext : velocity of extensional waves along the rod. (Torsional waves in the rod are propagated at the same speed as sheer waves in an infinite solid.) Table 1 lists values for a variety of solid materials. Table 2 covers gases liquids and gases; values for cryogenic liquids are given at the normal boiling point. Table 3 gives the speed of sound in pure

water and in seawater of salinity S = 3.5% as a function of temperature. All values are in meters per second and are given for normal atmospheric pressure.

References 1. Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw Hill, New York, 1972. 2. Anderson, H.L., Ed., A Physicist’s Desk Reference, American Institute of Physics, New York, 1989. 3. Younglove, B. A., Thermophysical Proeprties of Fluids. Part I, J. Phys. Chem. Ref. Data, 11, Suppl. 1, 1982. 4. Younglove, B. A., and Ely, J. F., Thermophysical Properties of Fluids. Part II, J. Phys. Chem. Ref. Data, 16, 577, 1987. 5. Haar, L., Gallagher, J. S., and Kell, G. S., NBS/NRC Steam Tables, Hemisphere Publishing Corp., New York, 1984. 6. Mason, W. P., Physical Acoustics and the Properties of Solids, D. Van Nostrand Co., Princeton, N.J., 1958. 7. Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, II/5, Molecular Acoustics, Springer-Verlag, Heidelberg, 1967.

TABLE 1. Speed of Sound in Solids at Room Temperature Name

vl/m s–1

vs/m s–1

vext/m s–1

Metals Aluminum, rolled Beryllium Brass (70 Cu, 30 Zn) Constantan Copper, annealed Copper, rolled Duralumin 17S Gold, hard-drawn Iron, cast Iron, electrolytic Iron, Armco Lead, annealed Lead, rolled Magnesium, annealed Molybdenum Monel metal Nickel Platinum Silver Steel (1% C) Steel, 347 Stainless

6420 12890 4700 5177 4760 5010 6320 3240 4994 5950 5960 2160 1960 5770 6250 5350 6040 3260 3650 5940 5790

3040 8880 2110 2625 2325 2270 3130 1200 2809 3240 3240 700 690 3050 3350 2720 3000 1730 1610 3220 3100

5000 12870 3480 4270 3810 3750 5150 2030 4480 5120 5200 1190 1210 4940 5400 4400 4900 2800 2680 5180 5000

Name Steel, K9 Tin, rolled Titanium Tungsten, annealed Tungsten, drawn Zinc, rolled Other materials Fused silica Glass, heavy silicate flint Glass, light borate crown Glass, pyrex Lucite Nylon 6-6 Polyethylene Polystyrene Rubber, butyl Rubber, gum Rubber, neoprene Tungsten carbide

vl/m s–1 5940 3320 6070 5220 5410 4210

vs/m s–1 3250 1670 3125 2890 2640 2440

vext/m s–1 5250 2730 5090 4620 4320 3850

5968

3764

5760

3980

2380

3720

5100 5640 2680 2620 1950 2350 1830 1550 1600 6655

2840 3280 1100 1070 540 1120

4540 5170 1840 1800 920 1840

3980

6220

14-39

Section 14.indb 39

4/27/05 5:04:28 PM

Speed of Sound in Various Media

14-40 TABLE 2. Speed of Sound in Liquids and Gases Name Liquids Acetone Argon Benzene Bromobenzene Butane 1-Butanol Carbon disulphide Chlorobenzene Cyclohexane 1-Decene Diethyl ether Ethane Ethanol Ethylene Ethylene glycol Fluorobenzene Glycerol Helium Heptane 1-Heptene Hexane Hydrogen Iodobenzene Mercury Methane Methanol Nitrobenzene Nitrogen 1-Nonene Octane 1-Octene Oxygen

t/°C

v/m s–1

20 –185.9 25 20 –0.5 20 25 20 19 20 25 –88.6 20 –103.8 25 20 25 –268.9 20 20 20 –252.9 20 25 –161.5 20 25 –195.8 20 20 20 –183.0

1203 813 1310 1169 1034 1258 1140 1311 1280 1250 976 1326 1162 1309 1658 1183 1904 180 1162 1128 1083 1101 1114 1450 1337 1121 1463 939 1218 1197 1184 906

t/°C

Name 1-Pentadecene Pentane Propane 1-Propanol Tetrachloromethane Trichloromethane 1-Undecene Water Water (sea, S = 3.5%)

20 20 –42.1 20 25 25 20 25 25

Gases at 1 atm Air, dry Ammonia Argon Carbon monoxide Carbon dioxide Chlorine Deuterium Ethane Ethylene Helium Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen iodide Hydrogen sulfide Methane Neon Nitric oxide Nitrogen Nitrous oxide Oxygen Sulfur dioxide Water (steam)

25 0 27 0 0 0 0 27 27 0 27 0 0 0 0 27 0 10 27 0 27 0 100

v/m s–1 1351 1008 1158 1223 930 987 1275 1497 1535 346 415 323 338 259 206 890 312 331 965 1310 200 296 157 289 450 435 325 353 263 330 213 473

TABLE 3. Speed of Sound in Water and Seawater (S = 3.5%) at Different Temperatures t/°C 0 10 20 25 30 40 50 60 70 80

Section 14.indb 40

Water 1401.0 1447.8 1483.2 1497.4 1509.5 1528.4 1541.4 1549.5 1553.2 1552.8

v/m s–1 Seawater 1449.4 1490.4 1522.2 1535.1 1546.2

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ATTENUATION AND SPEED OF SOUND IN AIR AS A FUNCTION OF HUMIDITY AND FREQUENCY This table gives the attenuation and speed of sound as a function of frequency at various values of relative humidity. All values refer to still air at 20°C.

Frequency (Hz)

Attenuation (dB/km)

Speed (m/s)

References 1. Tables of Absorption and Velocity of Sound in Still Air at 68°F (20°C), AD-738576, National Technical Information Service, Springfield, VA. 2. Evans, L. B., Bass, H. E., and Sutherland, L. C., J. Acoust. Soc. Am., 51, 1565, 1972. Frequency (Hz)

Attenuation (dB/km)

Speed (m/s)

Relative humidity 0% 20 0.51 40 1.07 50 1.26 63 1.43 100 1.67 200 1.84 400 1.96 630 2.11 800 2.27 1250 2.82 2000 4.14 4000 8.84 6300 14.89 10000 26.28 12500 35.81 16000 52.15 20000 75.37 40000 267.01 63000 644.66 80000 1032.14

343.477 343.514 343.525 343.536 343.550 343.559 343.561 343.562 343.562 343.562 343.562 343.564 343.565 343.566 343.566 343.567 343.567 343.567 343.567 343.567

Relative humidity 60% 20 0.02 40 0.06 50 0.09 63 0.15 100 0.34 200 0.99 400 1.94 630 2.57 800 2.94 1250 4.01 2000 6.55 4000 18.73 6300 42.51 10000 101.84 12500 155.67 16000 247.78 20000 373.78 40000 1195.37 63000 2220.64 80000 2951.71

344.182 344.183 344.183 344.184 344.185 344.190 344.197 344.200 344.201 344.202 344.203 344.204 344.204 344.206 344.208 344.211 344.215 344.238 344.262 344.274

Relative humidity 30% 20 0.03 40 0.11 50 0.17 63 0.25 100 0.50 200 1.01 400 1.59 630 2.24 800 2.85 1250 5.09 2000 10.93 4000 38.89 6300 90.61 10000 204.98 12500 294.08 16000 422.51 20000 563.66 40000 1110.97 63000 1639.47 80000 2083.08

343.807 343.808 343.810 343.810 343.814 343.821 343.826 343.827 343.828 343.828 343.829 343.831 343.836 343.846 343.854 343.865 343.877 343.911 343.924 343.929

Relative humidity 100% 20 0.01 40 0.04 50 0.06 63 0.09 100 0.22 200 0.77 400 2.02 630 3.05 800 3.57 1250 4.59 2000 6.29 4000 13.58 6300 27.72 10000 63.49 12500 96.63 16000 154.90 20000 237.93 40000 884.28 63000 1973.62 80000 2913.01

344.685 344.685 344.685 344.685 344.686 344.689 344.695 344.699 344.701 344.704 344.705 344.706 344.706 344.706 344.707 344.708 344.709 344.718 344.731 344.742

14-41

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SPEED OF SOUND IN DRY AIR The values in this table were calculated from the equation of state for dry air (average molecular weight 28.96) treated as a real gas. Values refer to standard atmospheric pressure. The speed of sound varies only slightly with pressure; at two atmospheres and –100°C the value decreases by 0.13%, while at two atmospheres and 80°C the speed increases by 0.04%. t/°C –100 –95 –90 –85 –80 –75 –70 –65 –60 –55 –50 –45 –40

vs/m s–1 263.5 267.3 271.1 274.8 278.5 282.1 285.7 289.2 292.7 296.1 299.5 302.9 306.2

t/°C –35 –30 –25 –20 –15 –10 –5 0 5 10 15 20 25

Reference Sytchev, V. V., Vasserman, A. A., Kozlov, A. D., Spiridonov, G. A., and Tsymarny, V. A., Thermodynamic Properties of Air, Hemisphere Publishing Corp., New York, 1987.

vs/m s–1 309.5 312.7 315.9 319.1 322.3 325.4 328.4 331.5 334.5 337.5 340.4 343.4 346.3

t/°C 30 35 40 45 50 55 60 65 70 75 80

vs/m s–1 349.1 352.0 354.8 357.6 360.4 363.2 365.9 368.6 371.3 374.0 376.7

14-42

Section 14.indb 42

4/27/05 5:04:32 PM

MUSICAL SCALES Equal Tempered Chromatic Scale A4 = 440 Hz

Note C0 C#0 D0 D#0 E0 F0 F#0 G0 G#0 A0 A#0 B0 C1 C#1 D1 D#1 E1 F1 F#1 G1 G#1 A1 A#1 B1

Note C0 D0 E0 F0 G0 A0 B0 C1 D1 E1 F1 G1 A1 B1

Frequency 16.35 17.32 18.35 19.45 20.60 21.83 23.12 24.50 25.96 27.50 29.14 30.87 32.70 34.65 36.71 38.89 41.20 43.65 46.25 49.00 51.91 55.00 58.27 61.74

Frequency 16 18 20 21.33 24 26.67 30 32 36 40 42.67 48 53.33 60

Note C2 C#2 D2 D#2 E2 F2 F#2 G2 G#2 A2 A#2 B2 C3 C#3 D3 D#3 E3 F3 F#3 G3 G#3 A3 A#3 B3

International Concert Pitch Frequency Note 65.41 C4 69.30 C#4 73.42 D4 77.78 D#4 82.41 E4 87.31 F4 92.50 F#4 98.00 G4 103.83 G#4 110.00 A4 116.54 A#4 123.47 B4 130.81 C5 138.59 C#5 146.83 D5 155.56 D#5 164.81 E5 174.61 F5 185.00 F#5 196.00 G5 207.65 G#5 220.00 A5 233.08 A#5 246.94 B5

Frequency 261.63 277.18 293.66 311.13 329.63 349.23 369.99 392.00 415.30 440.00 466.16 493.88 523.25 554.37 587.33 622.25 659.26 698.46 739.99 783.99 830.61 880.00 932.33 987.77

Note C6 C#6 D6 D#6 E6 F6 F#6 G6 G#6 A6 A#6 B6 C7 C#7 D7 D#7 E7 F7 F#7 G7 G#7 A7 A#7 B7 C8

Frequency 1046.50 1108.73 1174.66 1244.51 1318.51 1396.91 1479.98 1567.98 1661.22 1760.00 1864.66 1975.53 2093.00 2217.46 2349.32 2489.02 2637.02 2793.83 2959.96 3135.96 3322.44 3520.00 3729.31 3951.07 4186.01

Note C2 D2 E2 F2 G2 A2 B2 C3 D3 E3 F3 G3 A3 B3

Scientific or Just Scale C4 = 256 Hz Frequency Note 64 C4 72 D4 80 E4 85.33 F4 96 G4 106.67 A4 120 B4 128 C5 144 D5 160 E5 170.67 F5 192 G5 213.33 A5 240 B5

Frequency 256 288 320 341.33 384 426.67 480 512 576 640 682.67 768 853.33 960

Note C6 D6 E6 F6 G6 A6 B6 C7 D7 E7 F7 G7 A7 B7 C8

Frequency 1024 1152 1280 1365.33 1536 1706.67 1920 2048 2304 2560 2730.67 3072 3413.33 3840 4096

14-43

Section 14.indb 43

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CHARACTERISTICS OF HUMAN HEARING The human ear is sensitive to sound waves with frequencies in the range from a few hertz to almost 20 kHz. Auditory response is usually expressed in terms of the loudness level of a sound, which is a measure of the sound pressure. The reference level, which is given in the unit phon, is a pure tone of frequency 1000 Hz with sound pressure of 20 µPa (in cgs units, 2·10–4 dyn/cm2 ); loudness level is usually expressed in decibels (dB) relative to this reference level. If a normal observer perceives an arbitrary sound to

be equally loud as this reference sound, the sound is said to have the loudness level of the reference. The sensitivity of the typical human ear ranges from about 0 dB, the threshold loudness level, to about 140 dB, the level at which pain sets in. The minimum detectable level thus represents a sound wave of pressure 20 µPa and intensity (power density) 10–16 W/cm2. The following figure illustrates the frequency dependence of the threshold for an average young adult.

Frequency in Hz The relation between loudness level and frequency for a typical person is expressed by the following table: Sound pressure level in dB relative to 20 µPa 10 20 30 40 50 60 70 80 90 100

125

500

4 17 34 52 70 86 98 108

16 27 39 52 65 76 86 96 105

Thus, a 10,000 Hz tone at a pressure level of 50 dB seems equally loud as a 1000 Hz tone at a pressure of 35 dB. The term noise refers to any unwanted sound, either a pure tone or a mixture of frequencies. Since the sensitivity of the ear is fre-

Frequency in Hz 1000 4000 10 18 20 28 30 37 40 45 50 54 60 64 70 73 80 83 90 94 100 106

8000

10000

11 21 30 38 47 56 66 77 88

17 26 35 44 54 64 74 86

quency dependent, as illustrated by the above table, noise level is expressed in a frequency-weighted scale, known as A-weighting. Decibel readings on this scale are designated as dBa. Typical noise levels from various sources are illustrated in this table:

14-44

Section 14.indb 44

4/27/05 5:04:37 PM

Characteristics of Human Hearing

14-45

Source Rocket engine Jet aircraft engine Light aircraft, cruising Tractor, 150 hp Electric motor, 100 hp at 2600 rpm Pneumatic drill Subway train Vacuum cleaner Heavy automobile traffic Conversational speech Whispered speech Background noise, recording studio

Recommended noise thresholds in the workplace have been established by the American Conference of Government Industrial Duration of exposure 24 h 8h 4h 1h 30 min 15 min 2 min 28 s 0.11 s

Noise level in dBa 200 160 140 115 105 100 90 85 75 65 40 25-30

Hygenists. Some examples of the maximum safe levels for different daily exposure times are given below. Max. level in dBa 80 85 88 94 97 100 109 115 139

No exposure greater than 140 dBa is permitted. Further details may be found in Reference 3.

References 1. Anderson, H. L., Ed., A Physicistâ&#x20AC;&#x2122;s Desk Reference, American Institute of Physics, New York, 1989, chap. 2. 2. Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw Hill, New York, 1972, chap. 3.

Section 14.indb 45

3. Threshold Limit Values for Chemical Substances and Physical Agents; Biological Exposure Indices, 1999 Edition, American Conference of Governmental Industrial Hygienists, 1330 Kemper Meadow Drive, Cincinnati, OH 45240-1634.

4/27/05 5:04:38 PM

Interstellar Molecules Frank J. Lovas and Lewis E. Snyder A number of molecules have been detected in the interstellar medium, in circumstellar envelopes around evolved stars, and comae and tails of comets through observation of their microwave, infrared, or optical spectra. The following list gives the molecules and the particular isotopic species that have been reported thus far. Molecules are listed by molecular formula in the Hill order. All species not footnoted otherwise are observed in interstellar clouds, while some are also found in comets and circumstellar clouds. The list was last updated in November 2005 and lists 147 molecules (263 isotopic forms). Molecular formula AlCl

Name Aluminum monochloride

AlF CAlN CF+ CH CH+ CHN

Aluminum monofluoride Aluminum isocyanide Fluoromethylidynium ion Methylidyne Methyliumylidene Hydrogen cyanide

CHN

Hydrogen isocyanide

CHNO

Isocyanic acid

CHNS CHO CHO+

Isothiocyanic acid Oxomethyl Oxomethylium

CHO+ CHO2+ CHS+ CH2 CH2N+ CH2N CH2N2 CH2O

14-6

Hydroxymethylidyne Hydroxyoxomethylium Thiooxomethylium Methylene Iminomethylium Methylene amidogen Cyanamide Formaldehyde

CH2O2

Formic acid

CH2S

Thioformaldehyde

Isotopic species AlCla Al37Cla AlFa AlNCa CF+ CH CH+ HCN H13CN HC15N DCN HNC H15NC HN13C DNC D15NC HNCO DNCO HNCS HCO HCO+ H13CO+ HC17O+ HC18O+ DCO+ D13CO+ HOC+ HOCO+ HCS+ CH2 HCNH+ CH2N NH2CN H2CO H213CO H2C18O HDCO D2CO HCOOH H13COOH HCOOD DCOOH H2CS H213CS

References 1. Lovas, F. J., Recommended Rest Frequencies for Observed Interstellar Molecule Microwave Transitions - 1991 Revision, J. Phys. Chem. Ref. Data, 21, 181–272, 1992. 2. Snyder, L. E., Cometary Molecules, Internat. Astron. Union Symposium No. 150, Astrochemistry of Cosmic Phenomena, Ed. P.D. Singh, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 427–434 (1992).

Molecular formula

Name

CH3 CH3N

Methyl Methanimine

CH3NO

Formamide

CH3O+ CH4 CH4O

Hydroxy methylium ion Methane Methanol

CH4S CH5N CMgN CMgN

Methanethiol Methylamine Magnesium cyanide Magnesium isocyanide

Cyanide radical

CN+ CNNa CNSi CNSi CN2 CO

Cyanide radical ion Sodium cyanide Silicon cyanide Silicon isocyanide Cyanoimidogen Carbon monoxide

CO+ COS

Carbon monoxide ion Carbon oxysulfide

CO2 CO2+ CP

Carbon dioxide Carbon dioxide ion Carbon phosphide

Isotopic species H2C34S HDCS D2CS CH3 a CH2NH 13 CH2NH NH2CHO NH213CHO H2COH+ CH4 CH3OH 13 CH3OH CH318OH CH2DOH CH3OD CHD2OH CD3OH CH3SH CH3NH2 MgCNa 24 MgNCa 25 MgNCa 26 MgNCa CN 13 CN C15N CN+ b NaCNa SiNCa SiNCa NCNb CO 13 CO C17O C18O 13 18 C O CO+ OCS OC34S O13CS 18 OCS CO2 CO2+ b CPa

Interstellar Molecules Molecular formula CS

Name Carbon monosulfide

CSi C2 C2H

Silicon carbide Dicarbon Ethynyl

C2HN C2H2 C2H2N C2H2O C2H3N

Cyanomethylene Acetylene Cyanomethyl Ketene Acetonitrile

C2H3N C2H4 C2H4O C2H4O C2H4O C2H4O2 C2H4O2 C2H4O2 C2H6 C2H6O C2H6O C2H6O C2H6O2 C2O C2S

Isocyanomethane Ethylene Acetaldehyde Ethylene oxide Ethenol Methyl formate Acetic acid Glycolaldehyde Ethane trans-Ethanol gauche-Ethanol Dimethyl ether Ethylene glycol Oxoethenylidene Thioxoethenylidene

C2Si

Silicon dicarbide

C3 C3H C3H C3HN

Tricarbon Cyclopropenylidyne Propenylidyne Cyanoacetylene

C3HN C3HN

Isocyanoacetylene 1,2-Propadienylidene, 3imino Cyclopropenylidene

C3H2

C3H2 C3H2N+ C3H2O C3H2O

Propadienylidene Protonated cyanoacetylene 2-Propynal Cyclopropenone

14-7 Isotopic species CS C33S C34S C36S 13 CS 13 34 C S SiCa C2 C2H 13 CCH C13CH C2D HCCN HCCH CH2CN H2CCO CH3CN 13 CH3CN CH313CN CH3C15N CH2DCN CH3NC H2CCH2 CH3CHO c-C2H4Oc CH2CHOH CH3OCHO CH3COOH CH2OHCHO CH3CH3b t-CH3CH2OH g-CH3CH2OH CH3OCH3 HOCH2CH2OH CCO CCS CC34S c-SiC2 c-29SiC2 c-30SiC2 c-Si13CC C3 c-C3H l-C3H HCCCN H13CCCN HC13CCN HCC13CN HCCC15N DCCCN HCCNC HNCCC c-C3H2 c-H13CCCH c-HC13CCH c-C3HD l-H2CCC HCCCNH+ HCCCHO c-C3H2O

Molecular formula C3H3N C3H4

C3H4O C3H5N C3H6O C3H6O C3N C3O C3S C3Si C4H

C4HN C4H2 C4H2 C4H3N C4H3N C4Si C5 C5H C5HN

C5H4 C5N C6H C6H2 C6H2 C6H3N C6H6 C7H C7HN C8H C9HN C11HN ClH ClK ClNa FH FeO HLi

Isotopic Name species Acrylonitrile (vinyl cyanide) CH2CHCN Propyne CH3CCH CH3C13CH 13 CH3CCH CH2DCCH CH3CCD Propenal CH2CHCHO Propanenitrile (ethyl CH3CH2CN cyanide) Acetone (CH3)2CO Propanal CH3CH2CHO Cyanoethynyl CCCN 1,2-Propadienylidene, 3-oxo CCCO 1,2-Propadienylidene, 3CCCS thioxo Silicon tricarbon SiC3 1,3-Butadiynyl radical HCCCC H13CCCC HC13CCC HCC13CC HCCC13C DCCCC 3-Cyano-1,2HCCCCN propadienylidene Butatrienylidene H2CCCC 1,3-Butadiyne HCCCCHa 2-Butynenitrile CH3CCCN Cyanoallene CH2CCHCN Silicon tetracarbide SiC4a Pentacarbon C5a 2,4-Pentadiynylidyne HCCCCC 2,4-Pentadiynenitrile HCCCCCN H13CCCCCN HC13CCCCN HCC13CCCN HCCC13CCN HCCCC13CN DCCCCCN 1,3-Pentadiyne CH3C4H 1,3-Butadiynylium, 4-cyano C5N 1,3,5-Hexatriynyl HCCCCCC 1,3,5-Hexatriyne HCCCCCCHa 1,2,3,4,5H2CCCCCC Hexapentaenylidene Methylcyanodiacetylene CH3C4CN Benzene C6H6 2,4,6-Heptatriynylidyne HCCCCCCC 2,4,6-Heptatriynenitrile HC7N 1,3,5,7-Octatetraynyl HC8 2,4,6,8-Nonatetraynenitrile HC9N 2,4,6,8,10HC11N Undecapentaynenitrile Hydrogen chloride H35Cl H37Cl Potassium chloride K35Cla K37Cla Sodium chloride Na35Cla Na37Cla Hydrogen fluoride HF Iron monoxide FeO 7 LiH Lithium hydride

Interstellar Molecules

14-8 Molecular formula HN HNO HN2+

Name Imidogen Nitrosyl hydride Hydrodinitrogen(1+)

Hydroxyl

HO+ HS H2 H2N H2O

Oxoniumylidene Mercapto Hydrogen Amidogen Water

H2O+ H2S

Oxoniumyl Hydrogen sulfide

H3+

Trihydrogen ion

H3N

Ammonia

H3O+

Oxonium hydride

Isotopic species HN HNO N2H+ 15 NNH+ N15NH+ N2D+ OH 17 OH 18 OH HO+ b SH H2 NH2 H2O H218O HDO H2O+b H2S H234S HDS D2S H3+ H2D+ D2H+ NH3 15 NH3 NH2D NHD2 ND3 H3O+

Molecular formula H4Si NO NP NS

Name Silane Nitric oxide Phosphorus nitride Nitrogen sulfide

NSi N2 N2+ N2O OS

Silicon nitride Nitrogen Nitrogen ion Nitrous oxide Sulfur monoxide

OS+ OSi

Sulfur monoxide ion Silicon monoxide

O2S

Sulfur dioxide

SSi

Silicon monosulfide

Disulfur

l- before the isotopic species indicates a linear configuration, while c- indicates a cyclic molecule. a Reported only in circumstellar clouds. b Reported only in comets.

Isotopic species SiH4a NO NP NS N34S SiN N2 N2+ b N 2O SO 34 SO 33 SO S18O SO+ SiO Si18O 29 SiO 30 SiO SO2 33 SO2 34 SO2 OS18O SiS Si33S Si34S 29 SiS 30 SiS Si36S S2b

STANDARD ITS-90 THERMOCOUPLE TABLES The Instrument Society of America (ISA) has assigned standard letter designations to a number of thermocouple types having specified emf-temperature relations. These designations and the approximate metal compositions which meet the required relations, as well as the useful temperature ranges, are given below: Type B Type E Type J Type K Type N Type R Type S Type T

(Pt + 30% Rh) vs. (Pt + 6% Rh) (Ni + 10% Cr) vs. (Cu + 43% Ni) Fe vs. (Cu + 43% Ni) (Ni + 10% Cr) vs. (Ni + 2% Al + 2% Mn + 1% Si) (Ni + 14% Cr + 1.5% Si) vs. (Ni + 4.5% Si + 0.1% Mg) (Pt + 13% Rh) vs. Pt (Pt + 10% Rh) vs. Pt Cu vs. (Cu + 43% Ni)

0 to 1820°C –270 to 1000°C –210 to 1200°C –270 to 1372°C –270 to 1300°C –50 to 1768°C –50 to 1768°C –270 to 400°C

The compositions are given in weight percent, and the positive leg is listed first. It should be emphasized that the standard letter

designations do not imply a precise composition but rather that the specified emf-temperature relation is satisfied. The first set of tables below lists, for each thermocouple type, the emf as a function of temperature on the International Temperature Scale of 1990 (ITS-90). The coefficients in the equation used to generate the table are also given. The second set of tables gives the inverse relationships, i.e., the coefficients in the polynomial equation which expresses the temperature as a function of thermocouple emf. The accuracy of these equations is also stated. Further details and tables at closer intervals may be found in Reference 1.

References 1. Burns, G. W., Seroger, M. G., Strouse, G. F., Croarkin, M. C., and Guthrie, W. F., Temperature-Electromotive Force Reference Functions and Tables for the Letter-Designated Thermocouple Types Based on the ITS-90, Natl. Inst. Stand. Tech. (U.S.) Monogr. 175, 1993. 2. Schooley, J. F., Thermometry, CRC Press, Boca Raton, FL, 1986.

Type B Thermocouples: emf-Temperature (°C) Reference Table and Equations °C 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

emf in Millivolts 0 10 0.000 –0.002 0.033 0.043 0.178 0.199 0.431 0.462 0.787 0.828 1.242 1.293 1.792 1.852 2.431 2.499 3.154 3.230 3.957 4.041 4.834 4.926 5.780 5.878 6.786 6.890 7.848 7.957 8.956 9.069 10.099 11.263 12.433 13.591

10.215 11.380 12.549 13.706

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C 20 30 40 50 60 70 80 90 100 –0.003 –0.002 –0.000 0.002 0.006 0.011 0.017 0.025 0.033 0.053 0.065 0.078 0.092 0.107 0.123 0.141 0.159 0.178 0.220 0.243 0.267 0.291 0.317 0.344 0.372 0.401 0.431 0.494 0.527 0.561 0.596 0.632 0.669 0.707 0.746 0.787 0.870 0.913 0.957 1.002 1.048 1.095 1.143 1.192 1.242 1.344 1.397 1.451 1.505 1.561 1.617 1.675 1.733 1.792 1.913 1.975 2.037 2.101 2.165 2.230 2.296 2.363 2.431 2.569 2.639 2.710 2.782 2.854 2.928 3.002 3.078 3.154 3.308 3.386 3.466 3.546 3.626 3.708 3.790 3.873 3.957 4.127 4.213 4.299 4.387 4.475 4.564 4.653 4.743 4.834 5.018 5.111 5.205 5.299 5.394 5.489 5.585 5.682 5.780 5.976 6.075 6.175 6.276 6.377 6.478 6.580 6.683 6.786 6.995 7.100 7.205 7.311 7.417 7.524 7.632 7.740 7.848 8.066 8.176 8.286 8.397 8.508 8.620 8.731 8.844 8.956 9.182 9.296 9.410 9.524 9.639 9.753 9.868 9.984 10.099 10.331 11.497 12.666 13.820

10.447 11.614 12.782

10.563 11.731 12.898

Temperature ranges and coefficients of equations used to compute the above table: The equations are of the form: E = c0 + c1t + c2t2 + c3t3 + … cntn, where E is the emf in millivolts, t is the tem-

10.679 11.848 13.014

10.796 11.965 13.130

10.913 12.082 13.246

11.029 12.199 13.361

11.146 12.316 13.476

11.263 12.433 13.591

perature in degrees Celsius (ITS- 90), and c0, c1, c2, c3, etc. are the coefficients. These coefficients are extracted from Reference 1.

15-1

Section 15.indb 1

5/3/05 9:11:19 AM

Standard ITS-90 Thermocouple Tables

15-2 0 °C to 630.615 °C c0 c1 c2 c3 c4 c5 c6 c7 c8

= = = = = = = = =

630.615 °C to 1820 °C

0.000 000 000 0 − 2.465 081 834 6 × 10−4 5.904 042 117 1 × 10−6 − 1.325 793 163 6 × 10−9 1.566 829 190 1 × 10−12 − 1.694 452 924 0 × 10−15 6.299 034 709 4 × 10−19 ………… …………

−3.893 816 862 1 … 2.857 174 747 0 × 10-2 −8.488 510 478 5 × 10−5 1.578 528 016 4 × 10−7 −1.683 534 486 4 × 10−10 1.110 979 401 3 × 10−13 −4.451 543 103 3 × 10−17 9.897 564 082 1 × 10−21 −9.379 133 028 9 × 10−25

Type E Thermocouples: emf-Temperature (°C) Reference Table and Equations °C -200 -100 0 °C 0 100 200 300 400 500 600 700 800 900 1000

emf in Millivolts 0 -10 -8.825 -9.063 -5.237 -5.681 0.000 -0.582 0 10 0.000 0.591 6.319 6.998 13.421 14.164 21.036 21.817 28.946 29.747 37.005 37.815 45.093 45.900 53.112 53.908 61.017 61.801 68.787 69.554 76.373

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C -20 -30 -40 -50 -60 -70 -80 -90 -9.274 -9.455 -9.604 -9.718 -9.797 -9.835 -6.107 -6.516 -6.907 -7.279 -7.632 -7.963 -8.273 -8.561 -1.152 -1.709 -2.255 -2.787 -3.306 -3.811 -4.302 -4.777 20 30 40 50 60 70 80 90 1.192 1.801 2.420 3.048 3.685 4.330 4.985 5.648 7.685 8.379 9.081 9.789 10.503 11.224 11.951 12.684 14.912 15.664 16.420 17.181 17.945 18.713 19.484 20.259 22.600 23.386 24.174 24.964 25.757 26.552 27.348 28.146 30.550 31.354 32.159 32.965 33.772 34.579 35.387 36.196 38.624 39.434 40.243 41.053 41.862 42.671 43.479 44.286 46.705 47.509 48.313 49.116 49.917 50.718 51.517 52.315 54.703 55.497 56.289 57.080 57.870 58.659 59.446 60.232 62.583 63.364 64.144 64.922 65.698 66.473 67.246 68.017 70.319 71.082 71.844 72.603 73.360 74.115 74.869 75.621

-8.825 -5.237 100 6.319 13.421 21.036 28.946 37.005 45.093 53.112 61.017 68.787 76.373

perature in degrees Celsius (ITS- 90), and c0, c1, c2, c3, etc. are the coefficients. These coefficients are extracted from Reference 1.

–270 to 0°C c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13

-100

0°C to 1000°C

0.000 000 000 0 ... 5.866 550 870 8 × 10−2 4.541 097 712 4 × 10−5 –7.799 804 868 6 × 10–7 –2.580 016 084 3 × 10–8 –5.945 258 305 7 × 10–10 –9.321 405 866 7 × 10–12 –1.028 760 553 4 × 10–13 –8.037 012 362 1 × 10–16 –4.397 949 739 1 × 10–18 –1.641 477 635 5 × 10–20 –3.967 361 951 6 × 10–23 –5.582 732 872 1 × 10–26 –3.465 784 201 3 × 10–29

0.000 000 000 0 … 5.866 550 871 0 × 10–2 4.503 227 558 2 × 10–5 2.890 840 721 2 × 10–8 –3.305 689 665 2 × 10–10 6.502 440 327 0 × 10–13 –1.919 749 550 4 × 10–16 –1.253 660 049 7 × 10–18 2.148 921 756 9 × 10–21 –1.438 804 178 2 × 10–24 3.596 089 948 1 × 10–28 ………… ………… …………

Type J Thermocouples: emf-Temperature (°C) Reference Table and Equations Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90)

°C -200 -100 0

Section 15.indb 2

emf in Millivolts 0 -10 -7.890 -8.095 -4.633 -5.037 0.000 -0.501

-20

-30

-40

-50

-60

-5.426 -0.995

-5.801 -1.482

-6.159 -1.961

-6.500 -2.431

-6.821 -2.893

-70 -7.123 -3.344

Reference junctions at 0 °C -80 -90 -7.403 -3.786

-7.659 -4.215

-100 -7.890 -4.633

5/3/05 9:11:20 AM

Standard ITS-90 Thermocouple Tables

15-3

°C 0 100 200 300 400

emf in Millivolts 0 0.000 5.269 10.779 16.327 21.848

10 0.507 5.814 11.334 16.881 22.400

20 1.019 6.360 11.889 17.434 22.952

30 1.537 6.909 12.445 17.986 23.504

40 2.059 7.459 13.000 18.538 24.057

50 2.585 8.010 13.555 19.090 24.610

60 3.116 8.562 14.110 19.642 25.164

70 3.650 9.115 14.665 20.194 25.720

500 600 700 800 900

27.393 33.102 39.132 45.494 51.877

27.953 33.689 39.755 46.141 52.500

28.516 34.279 40.382 46.786 53.119

29.080 34.873 41.012 47.431 53.735

29.647 35.470 41.645 48.074 54.347

30.216 36.071 42.281 48.715 54.956

30.788 36.675 42.919 49.353 55.561

31.362 37.284 43.559 49.989 56.164

31.939 37.896 44.203 50.622 56.763

32.519 38.512 44.848 51.251 57.360

33.102 39.132 45.494 51.877 57.953

1000 1100 1200

57.953 63.792 69.553

58.545 64.370

59.134 64.948

59.721 65.525

60.307 66.102

60.890 66.679

61.473 67.255

62.054 67.831

62.634 68.406

63.214 68.980

63.792 69.553

Temperature ranges and coefficients of equations used to compute the above table: The equations are of the form: E = c0 + c1t + c2t2 + c3t3 + … cntn, where E is the emf in millivolts, t is the tem-

c1 c2 c3 c4 c5 c6 c7 c8

= = = = = = = = =

Reference junctions at 0 °C 80 90 4.187 4.726 9.669 10.224 15.219 15.773 20.745 21.297 26.276 26.834

100 5.269 10.779 16.327 21.848 27.393

perature in degrees Celsius (ITS-90), and c0, c1, c2, c3, etc. are the coefficients. These coefficients are extracted from Reference 1.

–260°C to 760°C

760°C to 1200°C

0.000 000 000 0 …

2.964 562 568 1 × 102

−1.497 612 778 6 … 3.178 710 392 4 × 10−3 −3.184 768 670 1 × 10−6 1.572 081 900 4 × 10−9 −3.069 136 905 6 × 10−13 ………… ………… …………

5.038 118 781 5 × 10−2 3.047 583 693 0 × 10−5 −8.568 106 572 0 × 10−8 1.322 819 529 5 × 10−10 −1.705 295 833 7 × 10−13 2.094 809 069 7 × 10−16 −1.253 839 533 6 × 10−19 1.563 172 569 7 × 10−23

Type K Thermocouples: emf-Temperature (°C) Reference Table and Equations °C -200 -100 0 °C 0 100 200 300 400

emf in Millivolts 0 -10 -5.891 -6.035 -3.554 -3.852 0.000 -0.392 0 10 0.000 0.397 4.096 4.509 8.138 8.539 12.209 12.624 16.397 16.820

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C -20 -30 -40 -50 -60 -70 -80 -90 -6.158 -6.262 -6.344 -6.404 -6.441 -6.458 -4.138 -4.411 -4.669 -4.913 -5.141 -5.354 -5.550 -5.730 -0.778 -1.156 -1.527 -1.889 -2.243 -2.587 -2.920 -3.243 20 30 40 50 60 70 80 90 0.798 1.203 1.612 2.023 2.436 2.851 3.267 3.682 4.920 5.328 5.735 6.138 6.540 6.941 7.340 7.739 8.940 9.343 9.747 10.153 10.561 10.971 11.382 11.795 13.040 13.457 13.874 14.293 14.713 15.133 15.554 15.975 17.243 17.667 18.091 18.516 18.941 19.366 19.792 20.218

-100 -5.891 -3.554 100 4.096 8.138 12.209 16.397 20.644

500 600 700 800 900

20.644 24.905 29.129 33.275 37.326

21.071 25.330 29.548 33.685 37.725

21.497 25.755 29.965 34.093 38.124

21.924 26.179 30.382 34.501 38.522

22.350 26.602 30.798 34.908 38.918

22.776 27.025 31.213 35.313 39.314

23.203 27.447 31.628 35.718 39.708

23.629 27.869 32.041 36.121 40.101

24.055 28.289 32.453 36.524 40.494

24.480 28.710 32.865 36.925 40.885

24.905 29.129 33.275 37.326 41.276

1000 1100 1200 1300

41.276 45.119 48.838 52.410

41.665 45.497 49.202 52.759

42.053 45.873 49.565 53.106

42.440 46.249 49.926 53.451

42.826 46.623 50.286 53.795

43.211 46.995 50.644 54.138

43.595 47.367 51.000 54.479

43.978 47.737 51.355 54.819

44.359 48.105 51.708

44.740 48.473 52.060

45.119 48.838 52.410

Temperature ranges and coefficients of equations used to compute the above table: The equations are of the form: E = c0 + c1t + c2t2 + c3t3 + … cntn, where E is the emf in millivolts, t is the temperature in degrees Celsius (ITS-90), and c0, c1, c2, c3, etc. are the coefficients. In the 0°C to 1372°C range there is also an exponen-

Section 15.indb 3

tial term that must be evaluated and added to the equation. The c1 ( t –126.9686 )2

exponential term is of the form: c0 e , where t is the temperature in °C, e is the natural logarithm base, and c0 and c1 are the coefficients. These coefficients are extracted from Reference 1.

5/3/05 9:11:22 AM

Standard ITS-90 Thermocouple Tables

15-4 c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10

= = = = = = = = = = =

-270°C to 0°C 0.000 000 000 0 3.945 012 802 5 × 10−2 2.362 237 359 8 × 10−5 −3.285 890 678 4 × 10−7 −4.990 482 877 7 × 10−9 −6.750 905 917 3 × 10−11 −5.741 032 742 8 × 10−13 −3.108 887 289 4 × 10−15 −1.045 160 936 5 × 10−17 −1.988 926 687 8 × 10−20 −1.632 269 748 6 × 10−23

0°C to 1372°C −1.760 041 368 6 × 10−2 3.892 120 497 5 × 10−2 1.855 877 003 2 × 10−5 −9.945 759 287 4 × 10−8 3.184 094 571 9 × 10−10 −5.607 284 488 9 × 10−13 5.607 505 905 9 × 10−16 −3.202 072 000 3 × 10−19 9.715 114 715 2 × 10−23 −1.210 472 127 5 × 10−26 ……

0°C to 1372°C (Exponential term) 1.185 976 × 10−1 −1.183 432 × 10−4 .…… .…… .…… .…… .…… .…… .…… .…… .……

Type N Thermocouples: emf-Temperature (°C) Reference Table and Equations °C -200 -100 0 °C 0 100 200 300 400

emf in Millivolts 0 -10 3.990 -4.083 -2.407 -2.612 0.000 -0.260 0 10 0.000 0.261 2.774 3.072 5.913 6.245 9.341 9.696 12.974 13.346

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C -20 -30 -40 -50 -60 -70 -80 -90 -4.162 -4.226 -4.277 -4.313 -4.336 -4.345 2.808 2.994 3.171 3.336 -3.491 3.634 -3.766 -3.884 -0.518 -0.772 -1.023 -1.269 -1.509 1.744 -1.972 -2.193 20 30 40 50 60 70 80 90 0.525 0.793 1.065 1.340 1.619 1.902 2.189 2.480 3.374 3.680 3.989 4.302 4.618 4.937 5.259 5.585 6.579 6.916 7.255 7.597 7.941 8.288 8.637 8.988 10.054 10.413 10.774 11.136 11.501 11.867 12.234 12.603 13.719 14.094 14.469 14.846 15.225 15.604 15.984 16.366

-100 -3.990 -2.407 100 2.774 5.913 9.341 12.974 16.748

500 600 700 800 900

16.748 20.613 24.527 28.455 32.371

17.131 21.003 24.919 28.847 32.761

17.515 21.393 25.312 29.239 33.151

17.900 21.784 25.705 29.632 33.541

18.286 22.175 26.098 30.024 33.930

18.672 22.566 26.491 30.416 34.319

19.059 22.958 26.883 30.807 34.707

19.447 23.350 27.276 31.199 35.095

19.835 23.742 27.669 31.590 35.482

20.224 24.134 28.062 31.981 35.869

20.613 24.527 28.455 32.371 36.256

1000 1100 1200 1300

36.256 40.087 43.846 47.513

36.641 40.466 44.218

37.027 40.845 44.588

37.411 41.223 44.958

37.795 41.600 45.326

38.179 41.976 45.694

38.562 42.352 46.060

38.944 42.727 46.425

39.326 43.101 46.789

39.706 43.474 47.152

40.087 43.846 47.513

Temperature ranges and coefficients of equations used to compute the above table: The equations are of the form: E = c0 + c1t + c2t2 + c3t3 + … cntn, where E is the emf in millivolts, t is the tem-

c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10

Section 15.indb 4

= = = = = = = = = = =

–270°C to 0°C 0.000 000 000 0 … 2.615 910 596 2 × 10−2 1.095 748 422 8 × 10−5 – 9.384 111 155 4 × 10−8 – 4.641 203 975 9 × 10−11 – 2.630 335 771 6 × 10−12 – 2.265 343 800 3 × 10−14 – 7.608 930 079 1 × 10−17 – 9.341 966 783 5 × 10−20 ………. ……….

perature in degrees Celsius (ITS-90), and c0, c1, c2, c3, etc. are the coefficients. These coefficients are extracted from Reference 1.

0°C to 1300°C 0.000 000 000 0… 2.592 939 460 1 × 10–2 1.571 014 188 0 × 10–5 4.382 562 723 7 × 10–8 –2.526 116 979 4 × 10–10 6.431 181 933 9 × 10–13 –1.006 347 151 9 × 10–15 9.974 533 899 2 × 10–19 –6.086 324 560 7 × 10–22 2.084 922 933 9 × 10–25 –3.068 219 615 1 × 10–29

5/3/05 9:11:23 AM

Standard ITS-90 Thermocouple Tables

15-5

Type R Thermocouples: emf-Temperature (°C) Reference Table and Equations °C 0 °C 0 100 200 300 400

emf in Millivolts 0 -10 0.000 -0.051 0 10 0.000 0.054 0.647 0.723 1.469 1.558 2.401 2.498 3.408 3.512

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C -20 -30 -40 -50 -60 -70 -80 -90 -0.100 -0.145 -0.188 -0.226 20 30 40 50 60 70 80 90 0.111 0.171 0.232 0.296 0.363 0.431 0.501 0.573 0.800 0.879 0.959 1.041 1.124 1.208 1.294 1.381 1.648 1.739 1.831 1.923 2.017 2.112 2.207 2.304 2.597 2.696 2.796 2.896 2.997 3.099 3.201 3.304 3.616 3.721 3.827 3.933 4.040 4.147 4.255 4.363

-100 100 0.647 1.469 2.401 3.408 4.471

500 600 700 800 900

4.471 5.583 6.743 7.950 9.205

4.580 5.697 6.861 8.073 9.333

4.690 5.812 6.980 8.197 9.461

4.800 5.926 7.100 8.321 9.590

4.910 6.041 7.220 8.446 9.720

5.021 6.157 7.340 8.571 9.850

5.133 6.273 7.461 8.697 9.980

5.245 6.390 7.583 8.823 10.111

5.357 6.507 7.705 8.950 10.242

5.470 6.625 7.827 9.077 10.374

5.583 6.743 7.950 9.205 10.506

1000 1100 1200 1300 1400

10.506 11.850 13.228 14.629 16.040

10.638 11.986 13.367 14.770 16.181

10.771 12.123 13.507 14.911 16.323

10.905 12.260 13.646 15.052 16.464

11.039 12.397 13.786 15.193 16.605

11.173 12.535 13.926 15.334 16.746

11.307 12.673 14.066 15.475 16.887

11.442 12.812 14.207 15.616 17.028

11.578 12.950 14.347 15.758 17.169

11.714 13.089 14.488 15.899 17.310

11.850 13.228 14.629 16.040 17.451

1500 1600 1700

17.451 18.849 20.222

17.591 18.988 20.356

17.732 19.126 20.488

17.872 19.264 20.620

18.012 19.402 20.749

18.152 19.540 20.877

18.292 19.677 21.003

18.431 19.814

18.571 19.951

18.710 20.087

18.849 20.222

Temperature ranges and coefficients of equations used to compute the above table: The equations are of the form: E = c0 + c1t + c2t2 + c3t3 + ... cntn, where E is the emf in millivolts, t is the temc0 c1 c2 c3 c4 c5 c6 c7 c8 c9

= = = = = = = = = =

–50°C to 1064.18°C 0.000 000 000 00 ... 5.289 617 297 65 × 10–3 1.391 665 897 82 × 10–5 –2.388 556 930 17 × 10–8 3.569 160 010 63 × 10–11 –4.623 476 662 98 × 10–14 5.007 774 410 34 × 10–17 –3.731 058 861 91 × 10–20 1.577 164 823 67 × 10–23 –2.810 386 252 51 × 10–27

perature in degrees Celsius (ITS-90), and c0, c1, c2, c3, etc. are the coefficients. These coefficients are extracted from Reference 1.

1064.18°C to 1664.5°C 2.951 579 253 16 … –2.520 612 513 32 × 10–3 1.595 645 018 65 × 10–5 –7.640 859 475 76 × 10–9 2.053 052 910 24 × 10–12 –2.933 596 681 73 × 10–16 …………. …………. …………. ………….

1664.5°C to 1768.1°C 1.522 321 182 09 × 102 –2.688 198 885 45 × 10–1 1.712 802 804 71 × 10–4 –3.458 957 064 53 × 10–8 –9.346 339 710 46 × 10–15 …………. …………. …………. …………. ………….

Type S Thermocouples: emf-Temperature (°C) Reference Table and Equations. °C 0 °C 0 100 200 300 400

emf in Millivolts 0 -10 0.000 -0.053 0 10 0.000 0.055 0.646 0.720 1.441 1.526 2.323 2.415 3.259 3.355

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C -20 -30 -40-50 -60 -70 -80 -90 -0.103 -0.150 -0.194 -0.236 20 30 40 50 60 70 80 90 0.113 0.173 0.235 0.299 0.365 0.433 0.502 0.573 0.795 0.872 0.950 1.029 1.110 1.191 1.273 1.357 1.612 1.698 1.786 1.874 1.962 2.052 2.141 2.232 2.507 2.599 2.692 2.786 2.880 2.974 3.069 3.164 3.451 3.548 3.645 3.742 3.840 3.938 4.036 4.134

-100 100 0.646 1.441 2.323 3.259 4.233

500 600 700 800 900

4.233 5.239 6.275 7.345 8.449

4.332 5.341 6.381 7.454 8.562

4.432 5.443 6.486 7.563 8.674

4.532 5.546 6.593 7.673 8.787

4.632 5.649 6.699 7.783 8.900

4.732 5.753 6.806 7.893 9.014

4.833 5.857 6.913 8.003 9.128

4.934 5.961 7.020 8.114 9.242

5.035 6.065 7.128 8.226 9.357

5.137 6.170 7.236 8.337 9.472

5.239 6.275 7.345 8.449 9.587

1000 1100 1200

9.587 10.757 11.951

9.703 10.875 12.071

9.819 10.994 12.191

9.935 11.113 12.312

10.051 11.232 12.433

10.168 11.351 12.554

10.285 11.471 12.675

10.403 11.590 12.796

10.520 11.710 12.917

10.638 11.830 13.038

10.757 11.951 13.159

Section 15.indb 5

5/3/05 9:11:25 AM

Standard ITS-90 Thermocouple Tables

15-6

Type S Thermocouples: emf-Temperature (°C) Reference Table and Equations. °C 1300 1400 1500 1600 1700

emf in Millivolts 0 -10 13.159 13.280 14.373 14.494 15.582 16.777 17.947

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C -20 -30 -40-50 -60 -70 -80 -90 -100 13.402 13.523 13.644 13.766 13.887 14.009 14.130 14.251 14.373 14.615 14.736 14.857 14.978 15.099 15.220 15.341 15.461 15.582

15.702 16.895 18.061

15.822 17.013 18.174

15.942 17.131 18.285

16.062 17.249 18.395

Temperature ranges and coefficients of equations used to compute the above table: The equations are of the form: E = c0 + c1t + c2t2 + c3t3 + … cntn, where E is the emf in millivolts, t is the tem-

c0 c1 c2 c3 c4 c5 c6 c7 c8

= = = = = = = = =

–50°C to 1064.18°C 0.000 000 000 00 ... 5.403 133 086 31 × 10–3 1.259 342 897 40 × 10–5 –2.324 779 686 89 × 10–8 3.220 288 230 36 × 10–11 –3.314 651 963 89 × 10–14 2.557 442 517 86 × 10–17 –1.250 688 713 93 × 10–20 2.714 431 761 45 × 10–24

16.182 17.366 18.503

16.301 17.483 18.609

16.420 17.600

16.539 17.717

16.658 17.832

16.777 17.947

perature in degrees Celsius (ITS-90), and c0, c1, c2, c3, etc. are the coefficients. These coefficients are extracted from Reference 1.

1064.18°C to 1664.5°C 1.329 004 440 85 … 3.345 093 113 44 × 10–3 6.548 051 928 18 × 10–6 –1.648 562 592 09 × 10–9 1.299 896 051 74 × 10–14 …………. …………. …………. ………….

1664.5°C to 1768.1°C 1.466 282 326 36 × 102 –2.584 305 167 52 × 10–1 1.636 935 746 41 × 10– 4 –3.304 390 469 87 × 10–8 –9.432 236 906 12 × 10–15 …………. …………. …………. ………….

Type T Thermocouples: emf-Temperature (°C) Reference Table and Equations. °C -200 -100 0 °C 0 100 200 300 400

emf in Millivolts 0 -10 -5.603 -5.753 -3.379 -3.657 0.000 -0.383 0 10 0.000 0.391 4.279 4.750 9.288 9.822 14.862 15.445 20.872

Thermocouple emf as a Function of Temperature in Degrees Celsius (ITS-90) Reference junctions at 0 °C -20 -30 -40 -50 -60 -70 -80 -90 -5.888 -6.007 -6.105 -6.180 -6.232 -6.258 -3.923 -4.177 -4.419 -4.648 -4.865 -5.070 -5.261 -5.439 -0.757 -1.121 -1.475 -1.819 -2.153 -2.476 -2.788 -3.089 20 30 40 50 60 70 80 90 0.790 1.196 1.612 2.036 2.468 2.909 3.358 3.814 5.228 5.714 6.206 6.704 7.209 7.720 8.237 8.759 10.362 10.907 11.458 12.013 12.574 13.139 13.709 14.283 16.032 16.624 17.219 17.819 18.422 19.030 19.641 20.255

Temperature ranges and coefficients of equations used to compute the above table: The equations are of the form: E = c0 + c1t + c2t2 + c3t3 + … cntn, where E is the emf in millivolts, t is the tem-

c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14

Section 15.indb 6

= = = = = = = = = = = = = = =

270 °C to 0 °C 0.000 000 000 0 ... 3.874 810 636 4 × 10−2 4.419 443 434 7 × 10−5 1.184 432 310 5 × 10−7 2.003 297 355 4 × 10−8 9.013 801 955 9 × 10−10 2.265 115 659 3 × 10−11 3.607 115 420 5 × 10−13 3.849 393 988 3 × 10−15 2.821 352 192 5 × 10−17 1.425 159 477 9 × 10−19 4.876 866 228 6 × 10−22 1.079 553 927 0 × 10−24 1.394 502 706 2 × 10−27 7.979 515 392 7 × 10−31

-100 -5.603 -3.379 100 4.279 9.288 14.862 20.872

perature in degrees Celsius (ITS-90), and c0, c1, c2, c3, etc. are the coefficients. These coefficients are extracted from Reference 1.

0 °C to 400 °C 0.000 000 000 0 ... 3.874 810 636 4 × 10−2 3.329 222 788 0 × 10−5 2.061 824 340 4 × 10−7 −2.188 225 684 6 × 10−9 1.099 688 092 8 × 10−11 −3.081 575 877 2 × 10−14 4.547 913 529 0 × 10−17 −2.751 290 167 3 × 10−20 ………… ………… ………… ………… ………… …………

5/3/05 9:11:26 AM

Standard ITS-90 Thermocouple Tables

15-7

Type B Thermocouples: Coefficients (ci) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges Temperature range: emf range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 = c8 =

250 °C to 700 °C 0.291 mV to 2.431 mV 9.842 332 1 × 101 6.997 150 0 × 102 −8.476 530 4 × 102 1.005 264 4 × 103 −8.334 595 2 × 102 4.550 854 2 × 102 −1.552 303 7 × 102 2.988 675 0 × 101 −2.474 286 0 …

700 °C to 1820 °C 2.431 mV to 13.820 mV 2.131 507 1 × 102 2.851 050 4 × 102 −5.274 288 7 × 101 9.916 080 4 ... −1.296 530 3 ... 1.119 587 0 × 10−1 −6.062 519 9 × 10−3 1.866 169 6 × 10−4 −2.487 858 5 × 10−6

NOTE— The above coefficients are extracted from Reference 1 and are for an expression of the form shown in Section 10.3.2. They yield approximate values of temperature that agree within ±0.03 °C with the values given in Table 10.2.

Type E Thermocouples: Coefficients (ci) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges Temperature range: emf range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 = c8 =

-200 °C TO 0 °C -8.825 mV to 0.0 mV 0.000 000 0 … 1.697 728 8 × 101 −4.351 497 0 × 10−1 −1.585 969 7 × 10−1 −9.250 287 1 × 10−2 −2.608 431 4 × 10−2 −4.136 019 9 × 10−3 −3.403 403 0 × 10−4 −1.156 489 0 × 10−5

c9 =

…….

0 °C to 1000 °C 0.0 mV to 76.373 mV 0.000 000 0 … 1.705 703 5 × 101 −2.330 175 9 × 10−1 6.543 558 5 × 10−3 −7.356 274 9 × 10−5 −1.789 600 × 10−6 8.403 616 5 × 10−8 −1.373 587 9 × 10−9 1.062 982 3 × 10−11 −3.244 708 7 × 10−14

Type J Thermocouples: Coefficients (ci) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges Temperature range: emf Range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 = c8 =

-210 °C to 0 °C -8.095 mVto 0.0 mV 0.000 000 0… 1.952 826 8 × 101 −1.228 618 5 … −1.075 217 8 … −5.908 693 3 × 10−1 −1.725 671 3 × 10−1 −2.813 151 3 × 10−2 −2.396 337 0 × 10−3 −8.382 332 1 × 10−5

0 °C to 760 °C 0.0 mV to 42.919 mV 0.000 000 … 1.978 425 × 101 −2.001 204 × 10−1 1.036 969 × 10−2 −2.549 687 × 10−4 3.585 153 × 10−6 −5.344 285 × 10−8 5.099 890 × 10−10 …….

760 °C to 1200 °C 42.919 mV to 69.553 mV −3.113 581 87 × 103 3.005 436 84 × 102 −9.947 732 30 … 1.702 766 30 × 10−1 1.430 334 68 × 10−3 4.438 860 84 × 10−6 ……. ……. …….

Section 15.indb 7

5/3/05 9:11:27 AM

Standard ITS-90 Thermocouple Tables

15-8

Type K Thermocouples: Coefficients (ci) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges Temperature range: emf Range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 = c8 = c9 =

– 200 °C to 0 °C − 5.891 mV to 0.0 mV 0.000 000 0 … 2.517 346 2 × 101 −1.166 287 8 … − 1.083 363 8 … −8.977 354 0 × 10−1 −3.734 237 7 × 10−1 −8.663 264 3 × 10−2 −1.045 059 8 × 10−2 −5.192 057 7 × 10−4 …….

0 °C to 500 °C 0.0 mV to 20.644 mV 0.000 000 … 2.508 355 × 101 7.860 106 × 10−2 −2.503 131 × 10−1 8.315 270 × 10−2 −1.228 034 × 10−2 9.804 036 × 10−4 −4.413 030 × 10−5 1.057 734 × 10−6 −1.052 755 × 10−8

500 °C to 1372 °C 20.644 mV to 54.886 mV −1.318 058 × 102 4.830 222 × 101 −1.646 031 … 5.464 731 × 10−2 −9.650 715 × 10−4 8.802 193 × 10−6 3.110 810 × 10−8 ……. ……. …….

NOTE—The above coefficients are extracted from Reference 1 and are for an expression of the form shown in Section 10.3.2. They yield approximate values of temperature that agree within ±0.05 °C with the values given in Table 10.8.

Type N Thermocouples: Coefficients (ci) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges

Temperature range: emf Range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 = c8 = c9 =

–200 °C to 0 °C −3.990 mV to 0.0 mV 0.000 000 0 … 3.843 684 7 × 101 1.101 048 5 … 5.222 931 2 … 7.206 052 5 … 5.848 858 6 … 2.775 491 6 … 7.707 516 6 × 10−1 1.158 266 5 × 10−1 7.313 886 8 × 10−3

0 °C to 600 °C 0.0 mV to 20.613 mV 0.000 00 … 3.868 96 × 101 −1.082 67 … 4.702 05 × 10−2 −2.121 69 × 10−6 −1.172 72 × 10−4 5.392 80 × 10−6 −7.981 56 × 10−8 ……… ………

600 °C to 1300 °C 20.613 mV to 47.513 mV 1.972 485 × 101 3.300 943 × 101 −3.915 159 × 10−1 9.855 391× 10−3 −1.274 371 × 10−4 7.767 022 × 10−7 ……… ……… ……… ………

NOTE—The above coefficients are extracted from Reference 1 and are for an expression of the form shown in Section 10.3.2. They yield approximate values of temperature that agree within ± 0.04 °C with the values given in Table 10.10.

Type R Thermocouples: Coefficients (ci) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges Temperature range: emf Range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 = c8 = c9 = c10 =

− 50 °C to 250 °C − 0.226 mV to 1.923 mV 0.000 000 0 … 1.889 138 0 × 102 −9.383 529 0 × 101 1.306 861 9 × 102 −2.270 358 0 × 102 3.514 565 9 × 102 −3.895 390 0 × 102 2.823 947 1 × 102 −1.260 728 1 × 102 3.135 361 1 × 101 −3.318 776 9 …

250 °C to 1200 °C 1.923 mV to 13.228 mV 1.334 584 505 × 101 1.472 644 573 × 102 −1.844 024 844 × 101 4.031 129 726 … −6.249 428 360 × 10− 1 6.468 412 046 × 10− 2 −4.458 750 426 × 10− 3 1.994 710 149 × 10− 4 −5.313 401 790 × 10−6 6.481 976 217 × 10− 8 ………

1064°C to 1664.5 °C 11.361 mV to 19.739 mV −8.199 599 416 × 101 1.553 962 042 × 102 −8.342 197 663 4.279 433 549 × 10-1 −1.191 577 910× 10-2 1.492 290 091× 10-4 ……… ……… ……… ……… ………

1664.5 °C to 1768.1 °C 19.739 mV to 21.103 mV 3.406 177 836 × 104 −7.023 729 171 × 103 5.582 903 813 × 102 −1.952 394 635 × 101 2.560 740 231 × 10−1 ……… ……… ……… ……… ……… ………

NOTE—The above coefficients are extracted from Reference 1 and are for an expression of the form shown in Section 10.3.2. They yield approximate values of temperature that agree within ±0.02 °C with the values given in Table 10.12.

Section 15.indb 8

5/3/05 9:11:27 AM

Standard ITS-90 Thermocouple Tables

15-9

Type S Thermocouples: Coefficients (ci) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges Temperature range: emf Range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 = c8 = c9 =

–50 °C to 250 °C –0.235 mV to 1.874 mV 0.000 000 00 . . . 1.849 494 60 × 102 -8.005 040 62 × 101 1.022 374 30 × 102 -1.522 485 92 × 102 1.888 213 43 × 102 -1.590 859 41 × 102 8.230 278 80 × 101 -2.341 819 44 × 101 2.797 862 60 . . .

250 °C to 1200 °C 1.874 mV to 11.950 mV

1.291 507 177 × 101 1.466 298 863 × 102 -1.534 713 402 ×101 3.145 945 973 . . . -4.163 257 839 × 10-1 3.187 963 771 × 10-2 -1.291 637 500 × 10-3 2.183 475 087 × 10-5 -1.447 379 511 × 10-7 8.211 272 125 × 10-9

1064 °C to 1664.5 °C 10.332 mV to 17.536 mV

-8.087 801 117 ×101 1.621 573 104 × 102 -8.536 869 453 . . . 4.719 686 976 × 10-1 -1.441 693 666 × 10-2 2.081 618 890 × 10-4 ………. ………. ………. ……….

1664.5 °C to 1768.1 °C 17.536 mV to 18.693 mV

5.333 875 126 × 104 -1.235 892 298 × 104 1.092 657 613 × 103 -4.265 693 686 × 101 6.247 205 420 × 10-1 ………. ………. ………. ………. ……….

NOTE—The above coefficients are extracted from Reference 1 and are for an expression of the form shown in Section 10.3.2. They yield approximate values of temperature that agree within ± 0.02 °C with the values given in Table 10.14.

Type T Thermocouples: Coefficients (ci) of Polynomials for the Computation of temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges

Temperature range: emf Range: c0 = c1 = c2 = c3 = c4 = c5 = c6 = c7 =

–200 °C to 0 °C –5.603 mV to 0.0 mV 0.000 000 0 . . . 2.594 919 2 × 101 -2.131 696 7 × 10-1 7.901 869 2 × 10-1 4.252 777 7 × 10-1 1.330 447 3 × 10-1 2.024 144 6 × 10-2 1.266 817 1 × 10-3

0 °C to 400 °C 0.0 mV to 20.872 mV 0.000 000 . . . 2.592 800 × 101 -7.602 961 × 10-1 4.637 791 × 10-2 -2.165 394 × 10-3 6.048 144 × 10-5 -7.293 422 × 10-7 ……….

NOTE—The above coefficients are extracted from Reference 1 and are for an expression of the form shown in Section 10.3.2. They yield approximate values of temperature that agree within ± 0.04 °C with the values given in Table 10.16.

Section 15.indb 9

5/3/05 9:11:28 AM

Laboratory Solvents and Other Liquid Reagents This table summarizes the properties of 575 liquids that are commonly used in the laboratory as solvents or chemical reagents. The properties tabulated are: Mr : tm: tb : ρ:

Molecular weight Melting point in °C Normal boiling point in °C Density in g/mL at the temperature in °C indicated by the superscript η: Viscosity in mPa s (1 mPa s = 1 centipoise) ε: Dielectric constant at ambient temperature (15 to 30°C) Dipole moment in D μ: cp: Specific heat capacity of the liquid at constant pressure at 25°C in J/g K vp: Vapor pressure at 25°C in kPa (1 kPa = 7.50 mmHg) FP: Flash point in °C Fl.Lim: Flammable (explosive) limit in air in percent by volume Autoignition temperature in °C IT TLV Threshold limit for allowable airborne concentration in parts per million by volume at 25°C and atmospheric pressure

Name

Mol. form.

t m/°C

t b/°C

Acetaldehyde

C2H4O

44.052

-123.37

20.1

Acetic acid Acetic anhydride Acetone Acetone cyanohydrin Acetonitrile Acetophenone Acetyl bromide Acetyl chloride Acrolein Acrylic acid Acrylonitrile Allyl alcohol Allylamine 2-Amino-2-methyl-1propanol 3-Amino-1-propanol Aniline Anisole Antimony(V) chloride Antimony(V) fluoride Arsenic(III) chloride Benzaldehyde Benzene Benzeneacetonitrile Benzeneethanamine Benzeneethanol Benzenemethanethiol Benzenesulfonyl chloride Benzenethiol Benzonitrile Benzoyl chloride Benzyl acetate Benzyl alcohol Benzylamine 2,2’-Bioxirane

C2H4O2 C4H6O3 C3H6O C4H7NO C2H3N C8H8O C2H3BrO C2H3ClO C3H4O C3H4O2 C3H3N C3H6O C3H7N C4H11NO

60.052 102.089 58.079 85.105 41.052 120.149 122.948 78.497 56.063 72.063 53.063 58.079 57.095 89.136

16.64 -74.1 -94.7 -19 -43.82 20.5 -96 -112.8 -87.7 12.5 -83.48 -129 -88.2 25.5

C3H9NO C6H7N C7H8O Cl5Sb F5Sb AsCl3 C7H6O C6H6 C8H7N C8H11N C8H10O C7H8S C6H5ClO2S C6H6S C7H5N C7H5ClO C9H10O2 C7H8O C7H9N C4H6O2

75.109 93.127 108.138 299.024 216.752 181.280 106.122 78.112 117.149 121.180 122.164 124.204 176.621 110.177 103.122 140.567 150.174 108.138 107.153 86.090

12.4 -6.02 -37.13 4 8.3 -16 -57.1 5.49 -23.8 <0 -27 -30 14.5 -14.93 -13.99 -0.4 -51.3 -15.4

487_S15.indb 13

2.0

Data on the temperature dependence of viscosity, dielectric constant, and vapor pressure can be found in the pertinent tables in this Handbook.

References 1. Lide, D. R., Handbook of Organic Solvents, CRC Press, Boca Raton, FL, 1994. 2. Lide, D. R., and Kehiaian, H. V., Handbook of Thermophysical and Thermochemical Data, CRC Press, Boca Raton, FL, 1994. 3. Riddick, J. A., Bunger, W. B., and Sakano, T. K., Organic Solvents, Fourth Edition, John Wiley & Sons, New York, 1986. 4. Fire Protection Guide to Hazardous Materials, 11th Edition, National Fire Protection Association, Quincy, MA, 1994. 5. Urben, P. G., Ed., Bretherick’s Handbook of Reactive Chemical Hazards, 5th Edition, Butterworth-Heinemann, Oxford, 1995. 6. 2004 TLV’s and BEI’s, American Conference of Governmental Industrial Hygienists, 1330 Kemper Meadow Drive, Cincinnati, OH 45240-1634, 2004.

ρ/g mL-1 η/mPa s ε

μ/D

cp/J g-1K-1 vp/kPa

FP/ °C Fl. lim.

IT/°C TLV/ppm

21.0

2.750

2.020

120

-39

4-60%

175

117.9 139.5 56.05 95 81.65 202 76 50.7 52.6 141 77.3 97.0 53.3 165.5

1.044625 1.08220 0.784525 0.93219 0.785720 1.028120 1.662516 1.105120 0.84020 1.051120 0.800725 0.854020 0.75820 0.93420

1.056 0.843 0.306

6.20 22.45 21.01

1.70 ≈ 2.8 2.88

2.053 1.648 2.175

2.07 0.680 30.8

0.369 1.681

36.64 17.44

3.92 3.02

2.229 1.703

4-20% 2.7-10.3% 3-13% 2.2-12% 3-16%

463 316 465 688 524 570

10 5 500 4.6 20 10

0.368

15.8

2.72 3.1

1.491

11.9 0.049 16.2 38.4 36.2 0.53 14.1 3.14 33.1

39 49 -20 74 6 77

390 220 438 481 378 374

0.1 2 2 0.5

187.5 184.17 153.7 140 dec 141 130 178.8 80.09 233.5 195 218.2 194.5 251 dec 169.1 191.1 197.2 213 205.31 185 144

0.982426 1.021720 0.994020 2.34 3.10 2.150 1.040125 0.876520 1.020515 0.964025 1.020220 1.05820 1.347015 1.077520 1.009315 1.212020 1.055020 1.041924 0.981320 1.11320

0.783418

1.218

3.85 1.056

2.8-31% 2.4-8% 3-17% 3-18% 2-22%

33.0 19.7

3.87 1.60 1.2

7.06 4.30 3.222

1.13 1.38

2.061 1.840

0.090 0.472

80 70 52

1.3-11%

1.59 3.0 0 3.5

1.621 1.741

5.38 0.169 12.7 0.012

63 -11 113

1-8%

2.068

0.01

0.604

17.85 2.2825 17.87

1.267

12.31 4.705 28.90 4.26 25.9 23.0 5.34 11.916 5.18

5.47 1.624

2.022 2.05 2.392

4 -26 50 0 21 -29 67

1.23 4.18

1.572 1.602

1.22 1.71

0.989 2.015

0.008 0.26 0.11 0.084 0.022 0.015 0.096

615 475

192 498

0.5

0.1 72 90 93

460 436

0.5 10

15-13

3/20/06 11:35:43 AM

Laboratory Solvents and Other Liquid Reagents

15-14 Name Bis(2-aminoethyl)amine N,N’-Bis(2-aminoethyl)-1,2ethanediamine Bis(2-chloroethyl) ether Bis(chloromethyl) ether Bis(2-ethylhexyl) phthalate Bis(2-hydroxyethyl) sulfide Boron tribromide Boron trichloride Bromine Bromobenzene 1-Bromobutane 2-Bromobutane, (±)Bromochloromethane Bromodichloromethane Bromoethane Bromoethene 2-Bromo-2-methylpropane 1-Bromopentane 1-Bromopropane 2-Bromopropane 3-Bromopropene 2-Bromotoluene Bromotrichloromethane Butanal 1,3-Butanediol 1,4-Butanediol 2,3-Butanediol 2,3-Butanedione Butanenitrile 1-Butanethiol 2-Butanethiol Butanoic acid Butanoic anhydride 1-Butanol 2-Butanol 2-Butanone trans-2-Butenal cis-2-Butenoic acid 2-Butoxyethanol Butyl acetate sec-Butyl acetate Butyl acrylate Butylamine sec-Butylamine tert-Butylamine Butylbenzene tert-Butylbenzene Butyl benzoate tert-Butyl ethyl ether tert-Butyl hydroperoxide 1-tert-Butyl-4-methylbenzene Butyl vinyl ether γ-Butyrolactone Carbon disulfide Chloroacetaldehyde Chloroacetone Chloroacetyl chloride 2-Chloroaniline 3-Chloroaniline Chlorobenzene 2-Chloro-1,3-butadiene 1-Chlorobutane 2-Chlorobutane Chlorocyclohexane Chlorodibromomethane Chloroethane

487_S15.indb 14

Mol. form.

t m/°C

t b/°C

C4H13N3 C6H18N4

103.166 146.234

-39 12

207 266.5

C4H8Cl2O C2H4Cl2O C24H38O4 C4H10O2S BBr3 BCl3 Br2 C6H5Br C4H9Br C4H9Br CH2BrCl CHBrCl2 C2H5Br C2H3Br C4H9Br C5H11Br C3H7Br C3H7Br C3H5Br C7H7Br CBrCl3 C4H8O C4H10O2 C4H10O2 C4H10O2 C4H6O2 C4H7N C4H10S C4H10S C4H8O2 C8H14O3 C4H10O C4H10O C4H8O C4H6O C4H6O2 C6H14O2 C6H12O2 C6H12O2 C7H12O2 C4H11N C4H11N C4H11N C10H14 C10H14 C11H14O2 C6H14O C4H10O2 C11H16 C6H12O C4H6O2 CS2 C2H3ClO C3H5ClO C2H2Cl2O C6H6ClN C6H6ClN C6H5Cl C4H5Cl C4H9Cl C4H9Cl C6H11Cl CHBr2Cl C2H5Cl

143.012 114.958 390.557 122.186 250.523 117.169 159.808 157.008 137.018 137.018 129.384 163.829 108.965 106.949 137.018 151.045 122.992 122.992 120.976 171.035 198.274 72.106 90.121 90.121 90.121 86.090 69.106 90.187 90.187 88.106 158.195 74.121 74.121 72.106 70.090 86.090 118.174 116.158 116.158 128.169 73.137 73.137 73.137 134.218 134.218 178.228 102.174 90.121 148.245 100.158 86.090 76.141 78.497 92.524 112.942 127.572 127.572 112.557 88.536 92.567 92.567 118.604 208.280 64.514

-51.9 -41.5 -55 -10.2 -45 -107 -7.2 -30.72 -112.6 -112.65 -87.9 -57 -118.6 -139.54 -16.2 -88.0 -110.3 -89.0 -119 -27.8 -5.65 -96.86 -77 20.4 7.6 -1.2 -111.9 -115.7 -165 -5.1 -75 -88.6 -88.5 -86.64 -76 15 -74.8 -78 -98.9 -64.6 -49.1 <-72 -66.94 -87.85 -57.8 -22.4 -94 6 -52 -92 -43.61 -112.1 -16.3 -44.5 -22 -1.9 -10.28 -45.31 -130 -123.1 -131.3 -43.81 -20 -138.4

178.5 106 384 282 91 12.65 58.8 156.06 101.6 91.3 68.0 90 38.5 15.8 73.3 129.8 71.1 59.5 70.1 181.7 105 74.8 207.5 235 182.5 88 117.6 98.5 85.0 163.75 200 117.73 99.51 79.59 102.2 169 168.4 126.1 112 145 77.00 62.73 44.04 183.31 169.1 250.3 72.6 89 dec 190 94 204 46 85.5 119 106 208.8 230.5 131.72 59.4 78.4 68.2 142 120 12.3

ρ/g mL-1 η/mPa s ε

μ/D

cp/J g-1K-1 vp/kPa

FP/ °C Fl. lim.

IT/°C TLV/ppm

0.956920

12.62 10.76

1.9

2.462

0.03

2-7%

358

1.2220 1.32315 0.98125 1.179325 2.6

21.20 3.51 5.3 28.61

2.6

1.545

0.143

3%-

369

2.84

1.804

0.00000005 218 0.08 160

5 0.001 0.3

3.1028 1.495020 1.275820 1.258520 1.934420 1.98020 1.460420 1.493320 1.427820 1.218220 1.353720 1.314020 1.39820 1.423220 2.01225 0.801620 1.005320 1.017120 1.003320 0.980818 0.793620 0.841620 0.829520 0.952825 0.966820 0.809520 0.806320 0.799925 0.851620 1.026720 0.901520 0.882520 0.874820 0.889820 0.741420 0.724620 0.695820 0.860120 0.866520 1.00020 0.73625 0.896020 0.861220 0.788820 1.129620 1.263220 1.19 1.1520 1.420220

0.944 1.074 0.606

0.374

0.489 0.458 0.471

0.553

1.426 2.54 3.10 0.405

0.685

0.574

0.950

9.01 5.63 10.98 6.31 8.09 9.46 7.0 4.641 2.405 13.45 28.8 31.9 4.04 24.83 5.204 5.645 2.98 12.8 17.84 17.26 18.56

9.30 5.07 5.135 5.25 4.71 58.5 2.359 2.359 5.52

0.41

2.03 1.42 2.17 2.20 2.18 2.21 ≈ 1.9

0.925 1.007 1.102 0.875 0.702 1.075

2.72

2.270 2.521 2.220 2.363

2.58

2.378 1.961 1.958 2.450

0.731 12.2

2.627 1.813 1.773

48.4 0.150 0.280 0.005 16.5

2.301 1.898

1.65

2.027 1.793 2.391 2.656 2.201 1.361

2.1 1.9 1.87 1.0 1.28 1.3 ≈0 ≈ 0.83

0.352

0.753 0.422

39.0 2.6320

13.40 13.3 5.6895 4.914 7.276 8.564 7.9505 9.45

≈0 1.25 4.27 0

2.316 1.642 1.003

2.23 1.77 1.69

156 28.2 0.556 5.26 9.32 19.5 62.5 141 17.7 1.68 18.6 28.9 18.6 0.17 5.35 15.7 0.008 0.002 0.02 7.45 2.55 6.07 10.8 0.221 0.07 0.86 2.32 12.6 4.92 0.06 0.15 1.66

3.9 1.53

1.66 1.8 2.78 3.67

298 1

0.911 0.474 0.983 0.798

2.13

3.32 1.216120 1.105820 0.95620 0.885720 0.873220 1.00020 2.45120 0.92390

3.1484 5.45 7.315 8.64

0 0 0 1.70 2.08 2.23 1.7

1.558 1.334

2.05 2.04 2.1

1.891

2.05

1.617

0.1 51 18 21

2.6-6.6%

565 265 200

7-8% 9-15%

511 530

5 0.5

32 490 -1 79

4.4-7.3%

295

-22 121 121

2-12.5%

218 395 402

27 24 2 -23 72 54 37 24 -9 13 69 22 31 29 -12 -9 -9 71 60 107

>1.6%

501 0.5

2-10% 0.9-5.8% 1-11% 2-10% 1-11% 2.1-15.5%

443 279 343 405 404 232

4-13% 2-8% 1.7-9.8% 1.7-9.9% 2-10%

238 425 292 312

2-9% 0.8-5.8% 0.7-5.7%

380 410 450

20 100 200 0.3 20 150 200 2 5

0.09 6.65 0.43 48.2

27 68 -9 98 -30

2 3.33 0.034 0.0156 1.6 29.5 13.7 21.0 1.0

28 -20 -12 -10 32

1-10% 4-20% 2-10%

160

-50

4-15%

1 255 1-50%

705 593

10 1 1 0.05

10 10

240

519

100

3/20/06 11:35:47 AM

Laboratory Solvents and Other Liquid Reagents Name 2-Chloroethanol 2-Chloroethyl vinyl ether (Chloromethyl)benzene Chloromethyl methyl ether 1-Chloro-2-methylpropane 2-Chloro-2-methylpropane 1-Chloronaphthalene 1-Chlorooctane 1-Chloropentane 2-Chlorophenol 1-Chloropropane 2-Chloropropane 3-Chloro-1,2-propanediol 3-Chloropropanenitrile 2-Chloropropene 3-Chloropropene Chlorosulfonic acid 2-Chlorotoluene 4-Chlorotoluene Chromyl chloride trans-Cinnamaldehyde o-Cresol m-Cresol p-Cresol Cyanogen chloride Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclohexylamine 1,3-Cyclopentadiene Cyclopentane Cyclopentanol Cyclopentanone cis-Decahydronaphthalene trans-Decahydronaphthalene Decamethylcyclopentasiloxane Decanal Decane Decanoic acid 1-Decanol 1-Decene Diacetone alcohol Dibenzyl ether Dibromodifluoromethane 1,2-Dibromoethane Dibromomethane 1,2-Dibromotetrafluoroethane Dibutylamine Dibutyl ether Di-tert-butyl peroxide Dibutyl phthalate Dibutyl sebacate Dibutyl sulfide Dichloroacetic acid o-Dichlorobenzene m-Dichlorobenzene trans-1,4-Dichloro-2-butene Dichlorodimethylsilane 1,1-Dichloroethane 1,2-Dichloroethane 1,1-Dichloroethene cis-1,2-Dichloroethene trans-1,2-Dichloroethene Dichloromethane

487_S15.indb 15

Mol. form.

t m/°C

t b/°C

C2H5ClO C4H7ClO C7H7Cl C2H5ClO C4H9Cl C4H9Cl C10H7Cl C8H17Cl C5H11Cl C6H5ClO C3H7Cl C3H7Cl C3H7ClO2 C3H4ClN C3H5Cl C3H5Cl ClHO3S C7H7Cl C7H7Cl Cl2CrO2 C9H8O C7H8O C7H8O C7H8O CClN C4H8 C6H12 C6H12O C6H10O C6H10 C6H13N C5H6 C5H10 C5H10O C5H8O C10H18 C10H18 C10H30O5Si5

80.513 106.551 126.584 80.513 92.567 92.567 162.616 148.674 106.594 128.556 78.541 78.541 110.540 89.524 76.525 76.525 116.525 126.584 126.584 154.900 132.159 108.138 108.138 108.138 61.471 56.107 84.159 100.158 98.142 82.143 99.174 66.102 70.133 86.132 84.117 138.250 138.250 370.770

-67.5 -70 -45 -103.5 -130.3 -25.60 -2.5 -57.8 -99.0 9.4 -122.9 -117.18 -51 -137.4 -134.5 -80 -35.8 7.5 -96.5 -7.5 31.03 12.24 34.77 -6.5 -90.7 6.59 25.93 -27.9 -103.5 -17.8 -85 -93.4 -17.5 -51.90 -42.9 -30.4 -38

128.6 108 179 59.5 68.5 50.9 259 183.5 108.4 174.9 46.5 35.7 213 dec 175.5 22.6 45.1 152 159.0 162.4 117 246 191.04 202.27 201.98 13 12.6 80.73 160.84 155.43 82.98 134 41 49.3 140.42 130.57 195.8 187.3 210

1.201920 1.049520 1.100420 1.06310 0.877320 0.842020 1.188025 0.873420 0.882020 1.263420 0.889920 0.861720 1.32518 1.157320 0.901720 0.937620 1.75 1.082520 1.069720 1.91 1.049720 1.032735 1.033920 1.018540 1.18620 0.70380 0.773925 0.962420 0.947820 0.811020 0.819120 0.802120 0.745720 0.948820 0.948720 0.896520 0.865925 0.959320

C10H20O C10H22 C10H20O2 C10H22O C10H20 C6H12O2 C14H14O CBr2F2 C2H4Br2 CH2Br2 C2Br2F4 C8H19N C8H18O C8H18O2 C16H22O4 C18H34O4 C8H18S C2H2Cl2O2 C6H4Cl2 C6H4Cl2 C4H6Cl2 C2H6Cl2Si C2H4Cl2 C2H4Cl2 C2H2Cl2 C2H2Cl2 C2H2Cl2 CH2Cl2

156.265 142.282 172.265 158.281 140.266 116.158 198.260 209.816 187.861 173.835 259.823 129.244 130.228 146.228 278.344 314.461 146.294 128.942 147.002 147.002 124.997 129.061 98.959 98.959 96.943 96.943 96.943 84.933

-4.0 -29.6 31.4 6.9 -66.3 -44 1.8 -110.1 9.84 -52.5 -110.32 -62 -95.2 -40 -35 -10 -79.7 10 -17.0 -24.8 1.0 -16 -96.9 -35.7 -122.56 -80.0 -49.8 -97.2

208.5 174.15 268.7 231.1 170.5 167.9 298 22.76 131.6 97 47.35 159.6 140.28 111 340 344.5 185 194 180 173 155.4 70.3 57.3 83.5 31.6 60.1 48.7 40

0.83015 0.726625 0.885840 0.829720 0.740820 0.938720 1.042820

15-15

ρ/g mL-1 η/mPa s ε

2.168325 2.496920 2.14925 0.767020 0.768420 0.70420 1.046520 0.940515 0.838620 1.563420 1.305920 1.288420 1.18325 1.06425 1.175720 1.245425 1.21320 1.283720 1.256520 1.326620

3.59 0.334 0.303

μ/D

cp/J g-1K-1 vp/kPa

25.80

1.78

6.854

1.8

1.44

7.027 9.663 5.04 5.05 6.654 7.40 8.588

2.00 2.13 1.57 2.00 2.16

1.713 1.867 1.307 1.335

2.05 2.17

1.2

1.468 1.683

0.164 24.9 19.9 42.7 0.003 0.11 4.36 0.308 45.8 68.9

FP/ °C Fl. lim.

IT/°C TLV/ppm

60 27 67

5-16%

425

1%-

585

-6 0 121 70 13 64 <-18 -32

2-8.7%

1.6-8.6%

260

2.6-11% 2.8-11%

520 593

76 -37 -32

4.5-16% 2.9-11%

485

>558

31.0

0.314

8.92 8.2

1.647 1.94

0.964 0.837

4.721 6.25

1.56 2.21

1.635 1.318

110 48.9 0.42 0.482 0.4

1 50 0.025

12.91

17.72 6.76 12.44 13.05

0.894 57.5 2.02 0.625 1.944

2.0243 16.40 16.1 2.2176 4.547

0.413

1.9687 18.5 13.58 2.219 2.184 2.50

3.04 1.948

1.45 1.48 1.48 2.8331 0 ≈0 2.87 0.33 1.3 0.419 ≈0 3.3 ≈0 ≈0

0.838

1.9853

≈0

10.91 0.756 2.80

7.93 2.136 18.2 3.821

≈0 3.2

1.595 0.980

4.9612 7.77 2.34 2.765 3.0830

0.918 0.637 16.63

1.324 1.044

6.58 4.54 4.29 8.33 10.12 5.02

0.66 1.2 1.43

2.160 2.080 2.044

1.841 2.079 1.856 1.805

1.837 2.119 1.84 1.678 1.653

2.210 2.761 2.341 2.144 1.905

0.005 0.041 0.019 0.017 157 13.0 0.10 0.53 11.8 1.20 58.5 42.3 0.294 1.55 0.10 0.164 0.02 0.02 0.170 0.009 0.210 0.224 110 1.55 6.12 43.4 0.34 0.898 3.43

1.0 1.17

0.724 0.61 0.69 2.266 2.136

2.82 2.48 1.61

1.789 1.968 1.943

2.50 1.72

1.105 1.163

0.09 0.03 0.18 0.252

1.276 1.298 1.148 1.201 1.205 1.192

18.9 30.5 10.6 80.0 26.8 44.2 58.2

81 86 86

>1.4% >1.1% >1.1%

599 558 558

5 5 5 0.3

<10 -20 68 44 -12 31

>1.8% 1-8% 1-9% 1-9% >1.2% 1-9%

245 300 420 310 293

-25 51 26

2%-

361

100 50 20 300 10 75 600

1-5%

255

0.8-5.4%

210

2-7%

288 235 643

82 <55 58 135

50 100

47 25 18 157 178 76

1-6% 1.5-7.6%

194

>0.5% >0.4%

402 365

0.4

66 72

2-9%

648

<21 -17 13 -28 6 2

3.4-9.5% 5-11% 6-16% 7-16% 3-15% 6-13% 13-23%

0.005 0.464 0.779 0.445 0.317 0.413

10.10 10.42 4.60 9.20 2.14 8.93

2.06 1.8 1.34 1.90 0 1.60

458 413 570 460 460 556

100 10 5 200 200 50

3/20/06 11:35:51 AM

Laboratory Solvents and Other Liquid Reagents

15-16 Name (Dichloromethyl)benzene 1,1-Dichloropropane 1,2-Dichloropropane, (±)1,3-Dichloropropane 2,3-Dichloropropene 2,4-Dichlorotoluene Dicyclohexylamine Diethanolamine 1,1-Diethoxyethane 1,2-Diethoxyethane Diethylamine N,N-Diethylaniline o-Diethylbenzene m-Diethylbenzene p-Diethylbenzene Diethyl carbonate Diethylene glycol Diethylene glycol diethyl ether Diethylene glycol dimethyl ether Diethylene glycol monobutyl ether Diethylene glycol monoethyl ether Diethylene glycol monoethyl ether acetate Diethylene glycol monomethyl ether Diethyl ether Diethyl maleate Diethyl malonate Diethyl oxalate Diethyl phthalate Diethyl succinate Diethyl sulfate Diethyl sulfide Diiodomethane Diiodosilane Diisobutylamine Diisopentyl ether Diisopropylamine Diisopropyl ether 1,2-Dimethoxyethane Dimethoxymethane Dimethylacetal N,N-Dimethylacetamide 2,3-Dimethylaniline 2,6-Dimethylaniline N,N-Dimethylaniline 2,2-Dimethylbutane 2,3-Dimethylbutane 3,3-Dimethyl-2-butanone Dimethylcarbamic chloride Dimethyl disulfide N,N-Dimethylethanolamine N,N-Dimethylformamide 2,6-Dimethyl-4-heptanone 1,1-Dimethylhydrazine Dimethyl phthalate 2,6-Dimethylpyridine Dimethyl sulfate Dimethyl sulfide Dimethyl sulfoxide 1,4-Dioxane 1,3-Dioxolane Dipentyl ether Dipropylamine

487_S15.indb 16

Mol. form.

t m/°C

t b/°C

C7H6Cl2 C3H6Cl2 C3H6Cl2 C3H6Cl2 C3H4Cl2 C7H6Cl2 C12H23N C4H11NO2 C6H14O2 C6H14O2 C4H11N C10H15N C10H14 C10H14 C10H14 C5H10O3 C4H10O3 C8H18O3

161.029 112.986 112.986 112.986 110.970 161.029 181.318 105.136 118.174 118.174 73.137 149.233 134.218 134.218 134.218 118.131 106.120 162.227

-17 -100.53 -99.5 10 -13.5 -0.1 28 -100 -74.0 -49.8 -38.8 -31.2 -83.9 -42.83 -43 -10.4 -45

205 88.1 96.4 120.9 94 201 256 dec 268.8 102.25 121.2 55.5 216.3 184 181.1 183.7 126 245.8 188

1.2625 1.132120 1.156020 1.178525 1.21120 1.247620 0.912320 1.096620 0.825420 0.835125 0.705620 0.930720 0.880020 0.860220 0.862020 0.969225 1.119715 0.906320

C6H14O3

134.173

-68

162

0.943420

C8H18O3

162.227

-68

231

0.955320

C6H14O3

134.173

196

0.988520

1.6

C8H16O4

176.211

218.5

1.009620

1.8

C5H12O3

120.147

193

1.03520

1.6

C4H10O C8H12O4 C7H12O4 C6H10O4 C12H14O4 C8H14O4 C4H10O4S C4H10S CH2I2 H2I2Si C8H19N C10H22O C6H15N C6H14O C4H10O2 C3H8O2 C4H10O2 C4H9NO C8H11N C8H11N C8H11N C6H14 C6H14 C6H12O C3H6ClNO C2H6S2 C4H11NO C3H7NO C9H18O C2H8N2 C10H10O4 C7H9N C2H6O4S C2H6S C2H6OS C4H8O2 C3H6O2 C10H22O C6H15N

74.121 172.179 160.168 146.141 222.237 174.195 154.185 90.187 267.836 283.911 129.244 158.281 101.190 102.174 90.121 76.095 90.121 87.120 121.180 121.180 121.180 86.175 86.175 100.158 107.539 94.199 89.136 73.094 142.238 60.098 194.184 107.153 126.132 62.134 78.133 88.106 74.079 158.281 101.190

34.5 223 200 185.7 295 217.7 208 92.1 182 150 139.6 172.5 83.9 68.4 84.5 42 64.5 165 221.5 215 194.15 49.73 57.93 106.1 167 109.74 134 153 169.4 63.9 283.7 144.01 188 dec 37.33 189 101.5 78 190 109.3

0.713820 1.066220 1.055120 1.078520 1.23214 1.040220 1.17225 0.836220 3.321120

-25

-116.2 -8.8 -50 -40.6 -40.5 -21 -24 -103.91 6.1 -1 -73.5 -61 -85.4 -69.20 -105.1 -113.2 -18.59 <-15 11.2 2.42 -98.8 -128.10 -52.5 -33 -84.67 -59 -60.48 -41.5 -57.20 5.5 -6.1 -31.7 -98.24 17.89 11.85 -97.22 -69 -63

ρ/g mL-1 η/mPa s ε

0.319

30.2

0.989

0.224

0.422

μ/D

6.9

2.1

8.37 10.27

1.8 2.08

5.68

1.70

25.75 3.80 3.90 3.680 5.15 2.594 2.369 2.259 2.820 31.82 5.70

2.8 1.4

1.10 2.3

7.23

2.0

4.2666 7.560 7.550 8.266 7.86 6.098 29.2 5.723 5.32

cp/J g-1K-1 vp/kPa

1.320

2.817 0.393 0.379 0.455

3.805 7.30 2.644

2.6-7.8%

0.5

0.7-6%

662 230 205 312 630 395 450 430

2-17%

224

0.315

2.188

0.0032

2.243

0.017

0.029

110

2.256

0.024

1-23%

240

1.15

2.369

180 350

400

1.779 1.784 1.647

-45 121 93 76 161 90 104

2-36%

2.54 2.49

71.7 0.015 0.048 0.030 0.002 0.15 0.05 7.78 0.172

>0.7%

457

0.6

0.972 0.210 10.7 19.9 9.93 53.1 22.9 0.075

1.54 1.08

1.900 0.500

1.23 1.15 1.13

2.394

2.016

1.63 1.68 ≈0 ≈0

1.971 1.771 2.227 2.201

0.45 0.107 42.5 31.3 4.27

9.6

1.8

1.551

0.794

38.25 9.91

3.82 2.7

14.36

1.7

0.284 1.987 1.177

8.66 7.33 55.0 6.70 47.24 2.2189

2.060 2.090 2.731 1.561 1.728

0.517

2.798 2.923

1.554 3.96 0 1.19 1.20 1.03

1.901 1.958 1.726 1.593 1.579 2.500

3.82 0.9 0.439 0.23 20.9 0.001 0.746 0.13 64.4 0.084 4.95 14.6 0.13 3.21

4.90 1.869 1.889 12.73

557

2.043

3.7

1.300 0.351 0.361

3-15%

1.80 2.307 2.104

0.92

0.7

38.85

>99 172 -21 27 -23 85 57 56 55 25 124 82

2.22 2.01 2.195 2.313

2.122 2.145 2.129

1.927

IT/°C TLV/ppm

0.055 0.003 <0.01 3.68 4.33 30.1 0.025 0.13 0.14 0.13 1.63 0.001 0.10

0.723 0.777720 0.715320 0.719225 0.863725 0.859320 0.850120 0.937225 0.993120 0.984220 0.955720 0.644425 0.661620 0.722925 1.16825 1.062520 0.886620 0.944525 0.806220 0.79122 1.190520 0.922620 1.332220 0.848320 1.101025 1.033720 1.06020 0.783320 0.740020

0.06 9.09 6.62 2.44

FP/ °C Fl. lim.

2-13% 2-10% 2-10%

425

436

-1 -28 -2 -32

1.1-7.1% 1-8%

316 443 202 237

5 250

70 97 96 63 -48 -29

2-12% >1%

490

1.2-7% 1.2-7%

371 405 405

5 500 500

2-15% 1-7% 2-95% >0.9%

445 396 249 490

10 25 0.01 0.6

2.2-20% 3-42% 2-22%

188 206 215 180

0.1 10

2-14%

1000

24 58 49 -15 146 83 -37 95 12 2 57 17

20 20

170 299

3/20/06 11:35:55 AM

Laboratory Solvents and Other Liquid Reagents Name Dipropylene glycol monomethyl ether Dipropyl ether Dodecane 1-Dodecanol 1-Dodecene Epichlorohydrin 1,2-Epoxybutane 1,2-Epoxy-4(epoxyethyl)cyclohexane 1,2-Ethanediamine 1,2-Ethanediol 1,2-Ethanediol, diacetate 1,2-Ethanediol, dinitrate 1,2-Ethanedithiol Ethanethiol Ethanol Ethanolamine 4-Ethoxyaniline Ethoxybenzene 2-Ethoxyethanol 2-Ethoxyethyl acetate Ethyl acetate Ethyl acetoacetate Ethyl acrylate Ethylamine N-Ethylaniline Ethylbenzene Ethyl benzoate Ethyl butanoate 2-Ethyl-1-butanol Ethyl chloroacetate Ethyl chloroformate Ethyl cyanoacetate Ethyleneimine Ethyl formate 2-Ethylhexanal 2-Ethyl-1,3-hexanediol 2-Ethyl-1-hexanol 2-Ethylhexyl acetate Ethyl lactate Ethyl 3-methylbutanoate Ethyl 2-methylpropanoate Ethyl nitrite Ethyl propanoate Ethyl silicate Eucalyptol Fluorobenzene Fluorosulfonic acid Formamide Formic acid Furan Furfural Furfuryl alcohol Germanium(IV) chloride Glycerol Glycerol triacetate Glycerol trioleate Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanone 3-Heptanone 4-Heptanone 1-Heptene Hexachloro-1,3-butadiene

487_S15.indb 17

Mol. form.

t m/°C

t b/°C

C7H16O3

148.200

-80

188.3

C6H14O C12H26 C12H26O C12H24 C3H5ClO C4H8O C8H12O2

102.174 170.334 186.333 168.319 92.524 72.106 140.180

-114.8 -9.57 23.9 -35.2 -26 -150 <-55

C2H8N2 C2H6O2 C6H10O4 C2H4N2O6 C2H6S2 C2H6S C2H6O C2H7NO C8H11NO C8H10O C4H10O2 C6H12O3 C4H8O2 C6H10O3 C5H8O2 C2H7N C8H11N C8H10 C9H10O2 C6H12O2 C6H14O C4H7ClO2 C3H5ClO2 C5H7NO2 C2H5N C3H6O2 C8H16O C8H18O2 C8H18O C10H20O2 C5H10O3 C7H14O2 C6H12O2 C2H5NO2 C5H10O2 C8H20O4Si C10H18O C6H5F FHO3S CH3NO CH2O2 C4H4O C5H4O2 C5H6O2 Cl4Ge C3H8O3 C9H14O6 C57H104O6 C7H14O C7H16 C7H14O2 C7H16O C7H14O C7H14O C7H14O C7H14 C4Cl6

60.098 62.068 146.141 152.062 94.199 62.134 46.068 61.083 137.179 122.164 90.121 132.157 88.106 130.141 100.117 45.084 121.180 106.165 150.174 116.158 102.174 122.551 108.524 113.116 43.068 74.079 128.212 146.228 130.228 172.265 118.131 130.185 116.158 75.067 102.132 208.329 154.249 96.102 100.070 45.041 46.026 68.074 96.085 98.101 214.42 92.094 218.203 885.432 114.185 100.202 130.185 116.201 114.185 114.185 114.185 98.186 260.761

11.14 -12.69 -31 -22.3 -41.2 -147.88 -114.14 10.5 4.6 -29.43 -70 -61.7 -83.8 -45 -71.2 -80.5 -63.5 -94.96 -34 -98 <-15 -21 -80.6 -22.5 -77.9 -79.6 <-100 -40 -70 -80 -26 -99.3 -88.2 -73.9 -82.5 0.8 -42.18 -89 2.49 8.3 -85.61 -38.1 -14.6 -51.50 18.1 -78 -4 -43.4 -90.55 -7.17 -33.2 -35 -39 -33 -118.9 -21

15-17

ρ/g mL-1 η/mPa s ε

μ/D

cp/J g-1K-1 vp/kPa

FP/ °C Fl. lim.

90.08 216.32 260 213.8 118 63.4 227

0.746620 0.749520 0.830924 0.758420 1.181220 0.829720 1.096620

1.21 ≈0

2.169 2.206 2.351 2.143 1.422 2.039

21 74 127 79 31 -22

117 197.3 190 198.5 146.1 35.0 78.29 171 254 169.81 135 156.4 77.11 180.8 99.4 16.5 203.0 136.19 212 121.3 147 144.3 95 205 56 54.4 163 244 184.6 199 154.5 135.0 110.1 18 99.1 168.8 176.4 84.73 163 220 101 31.5 161.7 171 86.55 290 259

0.897920 1.113520 1.104320 1.491820 1.23420 0.831525 0.789320 1.018020 1.065216 0.965120 0.925325 0.974020 0.900320 1.036810 0.923420 0.68915 0.962520 0.862625 1.041525 0.873525 0.832620 1.158520 1.135220 1.065420 0.83225 0.920820 0.854020 0.932522 0.831925 0.871820 1.032820 0.865620 0.86820 0.89915 0.884325 0.932020 0.926720 1.022520 1.726 1.133420 1.22020 0.951420 1.159420 1.129620 1.88 1.261320 1.158320 0.91515 0.813225 0.679525 0.912425 0.821920 0.811120 0.818320 0.817420 0.697020 1.55625

152.8 98.4 222.2 176.45 151.05 147 144 93.64 215

IT/°C TLV/ppm

0.95

0.396 1.383 1.20 1.073

3.38 2.0120 5.82 2.152 22.6

≈0 1.8 1.891

8.35 0.016 0.000016 0.019 2.2 31.7

1.3-7% >0.6%

188 203 275

4-21% 1.7-19%

411 439

0.5 0.1

16.06

0.287 1.074 21.1 1.197

0.423

2.05 0.631 0.639

13.82 41.4 7.7 28.26 7.26 6.667 25.3 31.94 7.43 4.216 13.38 7.567 6.0814 14.0 6.05 8.7 5.87 2.4463 6.20 5.18 6.19

0.380

9.736 31.62 18.3 8.57

6.27

18.73 7.58 15.4 4.71

1.99 2.28 2.34 2.03 1.60 1.69 2.3 1.45 2.1 2.2 1.78

2.872 2.394 2.121

1.898 2.438 3.201 1.870 2.339 2.845 1.937 1.906

1.96 1.22

2.884

0.59 2.00 1.74

1.726 1.638 1.963

2.17 1.90 1.9

1.947

1.74 1.8 2.4

2.438

2.015

1.62 0.01 0.030 0.009

40 111 88

70.3 7.87 0.05 0.0007 0.204 0.71 0.24 12.6 0.095 5.14 141 0.039 1.28 0.04 2.01 0.206 0.640

-17 13 86 116 63 43 56 -4 57 10 -16 85 21 88 24 57 64 16 110 -11 -20 44 127 73 71 46

0.003 28.9 32.3

0.019 0.09

2.150

5.76 2.50 4.57 5.465

1.74

1.60

1.523

3.34 1.607 0.361 1.587

111.0 51.1 2.94 42.1 16.85

2.389 2.151 1.686 1.698 2.079

934

46.53 7.11 3.109 9.07 1.9209 3.04 11.75 11.95 12.7 12.60 2.092 2.55

3.73 1.425 0.66 3.5 1.9 0 2.6

1.07 3.25 135 4.97 1.17 0.260 10.4 0.08 0.01 5.75 80.0 0.29 0.097

2.377 1.763

<0.01 <0.01

2.015 2.242 2.039 2.342 2.037

0.46 6.09 0.001 0.0044 0.49 0.5 0.164 7.52 0.13

0.501

0.550

0.387 3.84 5.81 0.714

0.340

≈0

2.6 2.78 ≈0

1.920 1.749

2.157

3-12% 3-22% 1.6-8.4%

385 398 482

10 40 0.05

13 -35 12 52 48 -15

2.8-18% 3-19% 3-24%

300 363 410

0.5 1000 3

3-18% 2-8% 2-12% 1-10% 1.4-14% 4-14%

235 379 426 295 372 385

5 5 400

1-7%

432 490 463

5 5 100

500 3.3-55% 3-16% 0.9-7.2% 0.8-9.7% 1-8% >1.5%

320 455 190 360 231 268 400

4-50% 1.9-11%

90 440

0.5 100

154 50 -36 60 75

18-57% 2-14% 2-19% 2-16%

434

10 5

316 491

2 10

199 138

3-19% 1%-

370 433

2.7

-4

1-7%

204 275

400

39 46 49 -1

1-8%

393

50 50 50

260 610

0.02

3/20/06 11:35:59 AM

Laboratory Solvents and Other Liquid Reagents

15-18 Name Hexachloro-1,3cyclopentadiene Hexafluorobenzene Hexamethyldisiloxane Hexamethylphosphoric triamide Hexanal Hexane Hexanedinitrile Hexanoic acid 1-Hexanol 2-Hexanone 1-Hexene Hexyl acetate Hydrazine Hydrazoic acid Hydrogen cyanide Hydrogen peroxide 3-Hydroxypropanenitrile Indan Indene Iodine bromide Iodine chloride Iodobenzene 1-Iodobutane Iodoethane Iodomethane 1-Iodopropane 2-Iodopropane Iron pentacarbonyl Isobutanal Isobutyl acetate Isobutyl acrylate Isobutylamine Isobutylbenzene Isobutyl formate Isobutyl isobutanoate Isopentane Isopentyl acetate Isophorone Isopropenyl acetate Isopropenylbenzene Isopropyl acetate Isopropylamine Isopropylbenzene Isopropylbenzene hydroperoxide 1-Isopropyl-2-methylbenzene 1-Isopropyl-3-methylbenzene 1-Isopropyl-4-methylbenzene Isoquinoline d-Limonene l-Limonene Mesityl oxide Methacrylic acid Methanol 2-Methoxyaniline 4-Methoxybenzaldehyde 2-Methoxyethanol 2-Methoxyethyl acetate Methyl acetate Methyl acrylate 2-Methylacrylonitrile 2-Methylaniline 3-Methylaniline N-Methylaniline Methyl benzoate

487_S15.indb 18

Mol. form.

t m/°C

t b/°C

C5Cl6

272.772

-9

239

C6F6 C6H18OSi2 C6H18N3OP

186.054 162.377 179.200

5.03 -66 7.2

C6H12O C6H14 C6H8N2 C6H12O2 C6H14O C6H12O C6H12 C8H16O2 H4N2 HN3 CHN H2O2 C3H5NO C9H10 C9H8 BrI ClI C6H5I C4H9I C2H5I CH3I C3H7I C3H7I C5FeO5 C4H8O C6H12O2 C7H12O2 C4H11N C10H14 C5H10O2 C8H16O2 C5H12 C7H14O2 C9H14O C5H8O2 C9H10 C5H10O2 C3H9N C9H12 C9H12O2

100.158 86.175 108.141 116.158 102.174 100.158 84.159 144.212 32.045 43.028 27.026 34.015 71.078 118.175 116.160 206.808 162.357 204.008 184.018 155.965 141.939 169.992 169.992 195.896 72.106 116.158 128.169 73.137 134.218 102.132 144.212 72.149 130.185 138.206 100.117 118.175 102.132 59.110 120.191 152.190

C10H14 C10H14 C10H14 C9H7N C10H16 C10H16 C6H10O C4H6O2 CH4O C7H9NO C8H8O2 C3H8O2 C5H10O3 C3H6O2 C4H6O2 C4H5N C7H9N C7H9N C7H9N C8H8O2

134.218 134.218 134.218 129.159 136.234 136.234 98.142 86.090 32.042 123.152 136.149 76.095 118.131 74.079 86.090 67.090 107.153 107.153 107.153 136.149

ρ/g mL-1 η/mPa s ε

μ/D

80.26 99 232.5

1.618420 0.763820 1.0320

-56 -95.35 1 -3 -47.4 -55.5 -139.76 -80.9 1.4 -80 -13.29 -0.43 -46 -51.38 -1.5 40 27.39 -31.3 -103 -111.1 -66.4 -101.3 -90 -20 -65.9 -98.8 -61 -86.7 -51.4 -95.8 -80.7 -159.77 -78.5 -8.1 -92.9 -23.2 -73.4 -95.13 -96.02

131 68.73 295 205.2 157.6 127.6 63.48 171.5 113.55 35.7 26 150.2 221 177.97 182 116 dec 100 dec 188.4 130.5 72.3 42.43 102.5 89.5 103 64.5 116.5 132 67.75 172.79 98.2 148.6 27.88 142.5 215.2 94 165.4 88.6 31.76 152.41 153

0.833520 0.660625 0.967620 0.921225 0.813620 0.811320 0.668525 0.877915 1.0036 0.687620 1.44 1.040425 0.963920 0.996025 4.3 3.24 1.830820 1.615420 1.935720 2.278920 1.748920 1.704220 1.520 0.789120 0.871220 0.889620 0.72425 0.853220 0.877620 0.854220 0.620120 0.87615 0.925520 0.909020 0.910620 0.871820 0.689120 0.864025 1.0320

-71.5 -63.7 -67.94 26.47 -74.0

178.1 175.1 177.1 243.22 178 178 130 162.5 64.6 224 248 124.1 143 56.87 80.7 90.3 200.3 203.3 196.2 199

0.876620 0.861020 0.857320 1.091030 0.841120 0.84320 0.865320 1.015320 0.791420 1.092320 1.11915 0.964720 1.007419 0.934220 0.953520 0.800120 0.998420 0.988920 0.989120 1.083725

-59 16 -97.53 6.2 0 -85.1 -70 -98.25 <-75 -35.8 -14.41 -31.3 -57 -12.4

cp/J g-1K-1 vp/kPa

FP/ °C Fl. lim.

IT/°C TLV/ppm

1.701925

2.79

0.300

4.58 0.583 0.252 0.876 0.183

0.01

2.029 2.179 31.3

5.5

1.8865

≈0

2.600 13.03 14.56 2.077 4.42 51.7

1.13

114.9 74.6

2.7 ≈0 1.75 1.70 2.985 1.573 3.2

1.357

1.554 0.556 0.469 0.703 0.653

4.59 6.27 7.82 6.97 7.07 8.19 2.602 5.068

0.571

4.43 2.318 6.41

0.214

1.845 4.72

0.726 1.24 1.70 1.93 1.976 1.62 2.04 1.95 2.75 1.9 1.3 ≈0 1.88 1.9 0.13 1.9

2.33 2.28

1.47 0.602 0.544

0.364

3.82 3.31 2.04 1.857

11.3 5.57

2.101 2.270 1.190 1.937 2.353 2.130 2.178 1.961 3.086

1.48 20.2 <0.01 0.005 0.11 1.54 24.8 0.185 1.91 68.2 98.8 0.26 0.010 0.2 0.220

2.612 2.619 1.609 1.609

0.676

0.325 0.737

1.191 1.918 1.791

5.6268 2.381

2.2322 11.0 2.3746 2.3738 15.6 33.0 5.230 22.0 17.2 8.25 7.07 7.03 6.138 5.816 5.96 6.642

1.19 0.79

≈0 2.73

0.778 0.738 0.888 0.746 0.535 1.228 2.013 2.505 1.793

2.284 1.909 1.834 1.711 1.952 2.771 1.753

1.761 1.519 1.828

2.8 1.65 1.70

2.165 1.871 2.531

2.36 2.1 1.72 1.77 3.69 1.6 1.45

2.249 2.624 1.916 1.845 1.883 1.96 2.118 1.933 1.625

1.9

3.59 0.133 1.85 18.2 53.9 5.75 9.36 4 23.0 2.39 19.0 0.257 5.34 0.552 91.7 0.728 0.06 6.02 0.40 7.88 78.0 0.61 0.004 0.2 0.22 0.19 0.007 0.277 0.254 1.47 0.12 16.9 0.013 0.004 1.31 0.67 28.8 11.0 8.26 0.043 0.036 0.05 0.052

32 -22 93 102 63 25 -26 45 38 -18

1-8% 2-5%

1-8% 1.2-6.9%

225 550 380 290 423 253

5-100% 6-40%

538

50 2

5 50 0.01 0.11 4.7 1

129 10

0.1 -18 18 30 -9 55 5 38 -51 25 84 26 54 2 -37 36

1.6-10.6% 196 1-11% 421 427 2-12% 378 0.8-6% 427 2-9% 320 1-8% 432 1.4-7.6% 420 1-8% 360 1-4% 460 432 1.9-6.1% 574 2-8% 460 402 1-7% 424

1-6%

436

0.7-6.1%

237

31 77 11 118

1-7% 1.6-8.8% 6-36%

344 68 464

15 20 200 0.1

39 49 -10 -3 1 85

2-14% 2-12% 3-16% 2.8-25% 2-6.8%

285 392 454 468

5 5 200 2 1 2 2 0.5

482

150

600 50 5 50 100 5 50

3/20/06 11:36:03 AM

Laboratory Solvents and Other Liquid Reagents Name 2-Methyl-1,3-butadiene Methyl butanoate 3-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-2-butanol 3-Methyl-2-butanol, (±)3-Methyl-2-butanone 2-Methyl-1-butene 2-Methyl-2-butene Methyl tert-butyl ether Methyl chloroacetate Methylcyclohexane Methylcyclopentane N-Methylformamide Methyl formate 5-Methyl-2-hexanone Methylhydrazine Methyl isocyanate Methyl lactate, (±)Methyl methacrylate 1-Methylnaphthalene Methyloxirane 2-Methylpentane 3-Methylpentane 2-Methyl-2,4-pentanediol 2-Methyl-1-pentanol 4-Methyl-2-pentanol 4-Methyl-2-pentanone 2-Methylpropanenitrile 2-Methyl-2-propanethiol Methyl propanoate 2-Methylpropanoic acid 2-Methyl-1-propanol 2-Methyl-2-propanol 2-Methylpyridine 3-Methylpyridine 4-Methylpyridine N-Methyl-2-pyrrolidone Methyl salicylate 4-Methylstyrene Morpholine β-Myrcene Nickel carbonyl L-Nicotine Nitric acid 2-Nitroanisole Nitrobenzene Nitroethane Nitromethane 1-Nitropropane 2-Nitropropane N-Nitrosodiethylamine N-Nitrosodimethylamine 2-Nitrotoluene 3-Nitrotoluene Nonane Nonanoic acid 1-Nonanol 1-Nonene 4-Nonylphenol cis,cis-9,12-Octadecadienoic acid cis-9-Octadecenoic acid Octane Octanoic acid 1-Octanol 2-Octanol

487_S15.indb 19

Mol. form.

t m/°C

t b/°C

C5H8 C5H10O2 C5H10O2 C5H12O C5H12O C5H12O C5H10O C5H10 C5H10 C5H12O C3H5ClO2 C7H14 C6H12 C2H5NO C2H4O2 C7H14O CH6N2 C2H3NO C4H8O3 C5H8O2 C11H10 C3H6O C6H14 C6H14 C6H14O2 C6H14O C6H14O C6H12O C4H7N C4H10S C4H8O2 C4H8O2 C4H10O C4H10O C6H7N C6H7N C6H7N C5H9NO C8H8O3 C9H10 C4H9NO C10H16 C4NiO4 C10H14N2 HNO3 C7H7NO3 C6H5NO2 C2H5NO2 CH3NO2 C3H7NO2 C3H7NO2 C4H10N2O C2H6N2O C7H7NO2 C7H7NO2 C9H20 C9H18O2 C9H20O C9H18 C15H24O C18H32O2

68.118 102.132 102.132 88.148 88.148 88.148 86.132 70.133 70.133 88.148 108.524 98.186 84.159 59.067 60.052 114.185 46.072 57.051 104.105 100.117 142.197 58.079 86.175 86.175 118.174 102.174 102.174 100.158 69.106 90.187 88.106 88.106 74.121 74.121 93.127 93.127 93.127 99.131 152.148 118.175 87.120 136.234 170.734 162.231 63.013 153.136 123.110 75.067 61.041 89.094 89.094 102.134 74.081 137.137 137.137 128.255 158.238 144.254 126.239 220.351 280.446

-145.9 -85.8 -29.3 -117.2 -9.1

-10.4 15.5 -53.46 12.4 -5 -81.3 42 -7

34.0 102.8 176.5 131.1 102.4 112.9 94.33 31.2 38.56 55.0 129.5 100.93 71.8 199.51 31.7 144 87.5 39.5 144.8 100.5 244.7 35 60.26 63.27 197.1 149 131.6 116.5 103.9 64.2 79.8 154.45 107.89 82.4 129.38 144.14 145.36 202 222.9 172.8 128 167 43 (exp 60) 247 83 272 210.8 114.0 101.19 131.1 120.2 176.9 152 222 232 150.82 254.5 213.37 146.9 ≈ 295

C18H34O2 C8H18 C8H16O2 C8H18O C8H18O

282.462 114.229 144.212 130.228 130.228

13.4 -56.82 16.5 -14.8 -31.6

-93.1 -137.53 -133.72 -108.6 -32.1 -126.6 -142.42 -3.8 -99 -52.36 -45 -47.55 -30.43 -111.9 -153.6 -162.90 -50 -90 -84 -71.5 -0.5 -87.5 -46 -101.9 25.69 -66.68 -18.14 3.67 -23.09 -8 -34.1 -4.8 -19.3 -79 -41.6 10.5 5.7 -89.5 -28.38 -108 -91.3

360 125.67 239 195.16 179.3

15-19

ρ/g mL-1 η/mPa s ε

0.67920 0.898420 0.93120 0.810420 0.809620 0.818020 0.805120 0.650420 0.662320 0.735325 1.23620 0.769420 0.748620 1.01119 0.971320 0.88820

0.541

2.098 5.48

μ/D

cp/J g-1K-1 vp/kPa

0.25

2.240 1.941 1.930 2.382 2.803

0.63 3.69 3.55

0.203

0.679 0.479 1.678 0.325

15.63 5.78 12.1 10.37 2.180 1.979

1.82

2.089 2.241 2.179 2.127

12.0 2.024 1.9853 189.0 9.20 13.53

≈0 ≈0 3.83 1.77

21.75

≈ 2.8

6.32 2.915

1.67 ≈0 2.01 ≈0 ≈0 2.9

1.882 1.886 2.096 1.983 2.928

0.923027 1.092820 0.937725 1.020220 0.8590 0.65025 0.659825 0.92315 0.826320 0.807520 0.796525 0.770420 0.794325 0.915020 0.968120 0.801820 0.788720 0.944320 0.956620 0.954820 1.023025 1.18125 0.917325 1.000520 0.801315 1.3125 1.009720 1.55 1.254020 1.203720 1.044825 1.137120 0.996125 0.982125 0.942220 1.004820 1.161119 1.158120 0.719220 0.905220 0.828020 0.725325 0.95020 0.902220 0.893520 0.698625 0.907325 0.826225 0.819320

0.286 0.306

4.07 0.545

0.431 1.226 3.33 4.31

2.02

1.886 1.886 23.4

13.11 24.42 5.475 6.200 2.58 17.93 12.47 10.18 11.10 12.2 32.55 8.80 7.42 2.3

1.910 1.578 2.073 2.248 2.213 2.843 2.427 2.672 2.130

4.29 1.66 1.08 1.64 1.7 1.85 2.40 2.70 4.1 2.47

1.943 1.964 2.449 2.949 1.703 1.704 1.707 3.105 1.637

1.55

1.892

73.4 4.30 0.067 0.315 2.19 1.20 6.99 81.4 62.1 33.6 1.0 6.18 18.3 0.03 78.1 0.691 6.61 57.7 0.62 5.10 0.009 71.7 28.2 25.3 <0.01 0.236 0.698 2.64 24.2 11.5 0.17 1.39 5.52 1.5 0.795 0.759 0.04 0.015 0.245 1.34 0.280

FP/ °C Fl. lim.

IT/°C TLV/ppm

-54 14

1.5-8.9%

395

43 19 38

1.2-9% 1.2-9%

416 350 437

200 -20 -20 50 57 -4 -29

7.5-18.5% 1-7% 250 1-8% 258

-19 36 -8 -7 49 10

5-23% 1-8% 2.5-92% 5.3-26% >2.2% 1.7-8.2%

449 191 194 534 385

57 96 96 53 37

1-10% 0.8-11% 1-11%

346 454 538 290

1.198

1.863 0.688 0.630 0.798

0.665 7.01 9.12 0.586

26.26 24.95 1.9722 2.475 8.83 2.180

2.17 5.0 4.22 3.23 3.46 3.66 3.73

1.509 1.790 1.746 1.97 1.911

8.34 0.002 0.03 2.79 4.79 1.36 2.3

≈0

1.474 1.474 2.217 2.290 2.470 2.142

0.73 0.0014 0.03 0.570 0.00005 0.00050 0.714

1.18 ≈0 1.15 1.8 1.71

2.043 2.229 2.066 2.344 2.535

≈0 0.79

1.744

400

100 50 0.01 0.02 50

529 -37 3.1-27.5% 449 <-29 1-7% 264 -7 1.2-7% 278 102 1-9% 306 54 1.1-9.65% 310 41 1-6% 18 1-8% 448 8 482 <-29 -2 2.5-13% 469 56 2-9.2% 481 28 2-11% 415 11 2-8% 478 39 538

2 500 500 25 25 50

50 100

50 20 0.05 0.1 2

8.937 45.75 35.6 29.11 37.27 24.70 26.74

100

88 28 35 36 24

106 106 31

2-9% 3-17% 7-22% 2%3-11%

0.8-2.9%

482 414 418 421 428

1 100 20 25 10

205

2 2 200

260 26

2.754

0.508 5.02 7.29 6.49

2.336 1.948 2.85 10.30 8.13

0.000001 1.86 0.0002 0.01

189 13 81 88

1-7%

363 206

300

270 265

3/20/06 11:36:06 AM

Laboratory Solvents and Other Liquid Reagents

15-20 Name 2-Octanone 1-Octene Oxetane 2-Oxetanone Oxirane Oxiranemethanol, (±)Paraldehyde Parathion Pentachloroethane cis-1,3-Pentadiene trans-1,3-Pentadiene Pentanal Pentane Pentanedial 1,5-Pentanediol 2,4-Pentanedione 1-Pentanethiol Pentanoic acid 1-Pentanol 2-Pentanol 3-Pentanol 2-Pentanone 3-Pentanone 1-Pentene cis-2-Pentene trans-2-Pentene Pentyl acetate Pentylamine Perchloric acid Peroxyacetic acid Phenol 2-Phenoxyethanol Phenylhydrazine 1-Phenyl-2-propylamine, (±)Phosphinic acid Phosphoric acid Phosphorothioc trichloride Phosphorus(III) bromide Phosphorus(III) chloride Phosphoryl chloride α-Pinene β-Pinene Piperidine Propanal 1,2-Propanediol 1,3-Propanediol Propanenitrile Propanoic acid Propanoic anhydride 1-Propanol 2-Propanol Propargyl alcohol Propyl acetate Propylamine Propylbenzene Propyl butanoate Propylene carbonate Propyl formate Propyl propanoate Pyridine Pyrrole Pyrrolidine 2-Pyrrolidone Quinoline Safrole Salicylaldehyde

487_S15.indb 20

Mol. form.

t m/°C

t b/°C

C8H16O C8H16 C3H6O C3H4O2 C2H4O C3H6O2 C6H12O3 C10H14NO5PS C2HCl5 C5H8 C5H8 C5H10O C5H12 C5H8O2 C5H12O2 C5H8O2 C5H12S C5H10O2 C5H12O C5H12O C5H12O C5H10O C5H10O C5H10 C5H10 C5H10 C7H14O2 C5H13N ClHO4 C2H4O3 C6H6O C8H10O2 C6H8N2 C9H13N

128.212 112.213 58.079 72.063 44.052 74.079 132.157 291.261 202.294 68.118 68.118 86.132 72.149 100.117 104.148 100.117 104.214 102.132 88.148 88.148 88.148 86.132 86.132 70.133 70.133 70.133 130.185 87.164 100.459 76.051 94.111 138.164 108.141 135.206

-16 -101.7 -97 -33.4 -112.5 -45 12.6 6.1 -28.78 -140.8 -87.4 -91.5 -129.67 -14 -18 -23 -75.65 -33.6 -77.6 -73 -69 -76.8 -39 -165.12 -151.36 -140.21 -70.8 -55 -112 -0.2 40.89 14 20.6

172.5 121.29 47.6 162 10.6 167 dec 124.3 375 162.0 44.1 42 103 36.06 188 dec 239 138 126.6 186.1 137.98 119.3 116.25 102.26 101.7 29.96 36.93 36.34 149.2 104.3 ≈ 90 dec 110 181.87 245 243.5 203

H3O2P H3O4P Cl3PS Br3P Cl3P Cl3OP C10H16 C10H16 C5H11N C3H6O C3H8O2 C3H8O2 C3H5N C3H6O2 C6H10O3 C3H8O C3H8O C3H4O C5H10O2 C3H9N C9H12 C7H14O2 C4H6O3 C4H8O2 C6H12O2 C5H5N C4H5N C4H9N C4H7NO C9H7N C10H10O2 C7H6O2

65.997 97.995 169.398 270.686 137.332 153.331 136.234 136.234 85.148 58.079 76.095 76.095 55.079 74.079 130.141 60.095 60.095 56.063 102.132 59.110 120.191 130.185 102.089 88.106 116.158 79.101 67.090 71.121 85.105 129.159 162.185 122.122

26.5 42.4 -36.2 -41.5 -93.6 1.18 -64 -61.5 -11.02 -80 -60 -27.7 -92.78 -20.5 -45 -124.39 -87.9 -51.8 -93 -84.75 -99.6 -95.2 -48.8 -92.9 -75.9 -41.70 -23.39 -57.79 25 -14.78 11.2 -7

130 407 125 173.2 76.1 105.5 156.2 166 106.22 48 187.6 214.4 97.14 141.15 170 97.2 82.3 113.6 101.54 47.22 159.24 143.0 242 80.9 122.5 115.23 129.79 86.56 251 237.16 234.5 197

ρ/g mL-1 η/mPa s ε 0.82020 0.714920 0.893025 1.146020 0.882110 1.114325 0.994320 1.268120 1.679620 0.691020 0.671025 0.809520 0.626220

0.991420 0.972125 0.85020 0.933925 0.814420 0.809420 0.820320 0.80920 0.809825 0.640520 0.655620 0.643125 0.875620 0.754420 1.77 1.22615 1.054545 1.10222 1.098620 0.930625

0.447

9.51 2.113

12.42 1.079

μ/D

cp/J g-1K-1 vp/kPa

FP/ °C Fl. lim.

IT/°C TLV/ppm

2.7 ≈0 1.94 4.18 1.89

2.132 2.148

0.12 2.30

52 21

230

1.694 1.998

0.3 175

74 -20

>2.9% 3-100%

429

1.6

>1.3%

238

1.43

0.5 1 2 0.01

2.25

3.716 2.319

0.224

10.00 1.8371

3.62 3.47 4.15 0.470 0.444 0.195

26.2 26.524 4.847 2.661 15.13 13.71 13.35 15.45 17.00 2.011

0.702

4.79 4.27

12.40 13.03

0.92 0.500 0.585

0.859

≈0

2.317

2.5 2.8

3.08 2.08

1.61 1.7 1.66 1.64 2.7 2.82 ≈ 0.5 ≈0 ≈0 1.75

2.059 2.361 2.716 2.719 2.137 2.216 2.196 2.163 2.239 2.005 2.501

1.224

2.123

7.15

2.007

0.478 50.6 54.7 4.58 68.3

12 -40

0.001 1.02 1.83 0.024 0.259 0.804 1.10 4.97 4.72 85.0 66.0 67.4 0.60 4.00

129 34 18 96 33 34 41 7 13 -18 <-20 <-20 16 -1

1.93 0.055 0.001 0.003 0.06

41 79 1.8-8.6% 121 88 <100

2-8%

222 260

50 600 0.05

335 340

1-10% 1.2-9% 1.2-9% 2-8% >1.6% 1.5-8.7%

1-8% 2.2-22%

400 300 343 435 452 450 275

200 200

360

715

5 0.1

1.49 1.480 1.635 2.8 1.574 1.645 0.853925 0.86025 0.860620 0.865725 1.036120 1.053820 0.781820 0.988225 1.011020 0.799725 0.780925 0.947820 0.887820 0.717320 0.859325 0.873020 1.204720 0.907320 0.880920 0.981920 0.969820 0.858620 1.12020 1.097715 1.100020 1.167420

0.25

4.94 0.529

1.573 0.321 40.4 0.294 1.030 1.945 2.04 0.544 0.376

0.485 0.879 1.225 0.704 3.34

3.498 14.1 2.1787 2.4970 4.33 18.5 27.5 35.1 29.7 3.44 18.30 20.8 20.18 20.8 5.62 5.08 2.370 4.3 66.14 6.92 5.249 13.260 8.00 8.30 28.18 9.16 18.35

0.56 2.54

1.2 2.72 2.2 2.5 4.05 1.75 1.55 1.56 1.13 1.8 1.17 ≈0

0.905

2.113 2.362 2.507 2.166 2.063 1.806 2.395 2.604 1.921 2.776 1.786

4.9 1.89

2.141 1.945

2.21 1.74 1.6 3.5 2.29

1.678 1.903 2.202 1.99 1.51

2.86

1.818

0.38 16.1 4.97 0.64 0.61 4.28 42.2 0.02 0.007 6.14 0.553 0.45 2.76 6.02 4.49 42.1 0.45 0.618 0.05 10.9 1.88 2.76 1.10 8.40 0.011 0.01 0.075

0.2 0.1 33 38 16 -30 99 2 52 63 23 12 36 13 -37 30 37 135 -3 79 20 39 3 129

255 275 1-10% 2.6-17% 3-13%

207 371 400 3-14% 512 2.9-12.1% 465 1.3-9.5% 285 2-14% 412 2-13% 399 2-8% 2-10% 1-6%

450 318 450

10 200 200 1 200

455 2-12%

482

480 100 78

3/20/06 11:36:10 AM

Laboratory Solvents and Other Liquid Reagents Name Selenium chloride Selenium oxychloride Selenium oxyfluoride Styrene Sulfolane Sulfur chloride Sulfur dichloride Sulfuric acid Sulfuryl chloride α-Terpinene 1,1,2,2-Tetrabromoethane Tetrabromosilane 1,1,2,2-Tetrachloro-1,2difluoroethane 1,1,1,2-Tetrachloroethane 1,1,2,2-Tetrachloroethane Tetrachloroethene Tetrachloromethane Tetrachlorosilane Tetradecane Tetraethylene glycol Tetrafluoroboric acid Tetrahydrofuran Tetrahydrofurfuryl alcohol 1,2,3,4Tetrahydronaphthalene Tetrahydropyran Tetrahydrothiophene Tetramethylsilane Tetramethylurea Tetranitromethane Thionyl bromide Thionyl chloride Thiophene Tin(IV) chloride Titanium(IV) chloride Toluene Toluene-2,4-diisocyanate Tribromomethane Tributylamine Tributyl borate Tributyrin Trichloroacetaldehyde 1,2,4-Trichlorobenzene 1,1,1-Trichloroethane 1,1,2-Trichloroethane Trichloroethene Trichloroethylsilane Trichlorofluoromethane Trichloromethane (Trichloromethyl)benzene Trichloromethylsilane Trichloronitromethane 1,2,3-Trichloropropane Trichlorosilane 1,1,2-Trichloro-1,2,2trifluoroethane Tri-o-cresyl phosphate Tridecane 1-Tridecene Triethanolamine Triethylamine Triethylene glycol Triethylene glycol dimethyl ether Triethyl phosphate Trifluoroacetic acid (Trifluoromethyl)benzene

487_S15.indb 21

15-21

Mol. form.

t m/°C

t b/°C

Cl2Se2 Cl2OSe F2OSe C8H8 C4H8O2S Cl2S2 Cl2S H2O4S Cl2O2S C10H16 C2H2Br4 Br4Si C2Cl4F2

228.83 165.86 132.96 104.150 120.171 135.037 102.971 98.080 134.970 136.234 345.653 347.702 203.830

-85 8.5 15 -30.65 27.6 -77 -122 10.31 -51

130 dec 177 125 145 287.3 137 59.6 337 69.4 174 243.5 154 92.8

2.774 2.44 2.8 0.901625 1.272318 1.69 1.62 1.8 1.680 0.837519 2.965520 2.8 1.595150

C2H2Cl4 C2H2Cl4 C2Cl4 CCl4 Cl4Si C14H30 C8H18O5 BF4H C4H8O C5H10O2 C10H12

167.849 167.849 165.833 153.823 169.897 198.388 194.226 87.813 72.106 102.132 132.202

-70.2 -42.4 -22.3 -22.62 -68.74 5.82 -6.2 -108.44 <-80 -35.7

130.2 145.2 121.3 76.8 57.65 253.58 328 130 dec 65 178 207.6

1.5406 1.595320 1.623020 1.594020 1.5 0.759620 1.128515 ~1.8 0.883325 1.052420 0.964525

C5H10O C4H8S C4H12Si C5H12N2O CN4O8 Br2OS Cl2OS C4H4S Cl4Sn Cl4Ti C7H8 C9H6N2O2 CHBr3 C12H27N C12H27BO3 C15H26O6 C2HCl3O C6H3Cl3 C2H3Cl3 C2H3Cl3 C2HCl3 C2H5Cl3Si CCl3F CHCl3 C7H5Cl3 CH3Cl3Si CCl3NO2 C3H5Cl3 Cl3HSi C2Cl3F3

86.132 88.172 88.224 116.161 196.033 207.873 118.970 84.140 260.521 189.678 92.139 174.156 252.731 185.349 230.151 302.363 147.387 181.447 133.404 133.404 131.388 163.506 137.368 119.378 195.474 149.480 164.376 147.431 135.452 187.375

-49.1 -96.2 -99.06 -0.6 13.8 -50 -101 -38.21 -34.07 -24.12 -94.95 20.5 8.69 -70 <-70 -75 -57.5 16.92 -30.01 -36.3 -84.7 -105.6 -110.44 -63.41 -4.42 -90 -64 -14.7 -128.2 -36.22

88 121.1 26.6 176.5 126.1 140 75.6 84.0 114.15 136.45 110.63 251 149.1 216.5 234 307.5 97.8 213.5 74.09 113.8 87.21 100.5 23.7 61.17 221 65.6 112 157 33 47.7

0.881420 0.998720 0.64819 0.968720 1.638020

C21H21O4P C13H28 C13H26 C6H15NO3 C6H15N C6H14O4 C8H18O4

368.363 184.361 182.345 149.188 101.190 150.173 178.227

11 -5.4 -13 20.5 -114.7 -7 -45

410 235.47 232.8 335.4 89 285 216

1.195520 0.756420 0.765820 1.124220 0.727520 1.127415 0.98620

C6H15O4P C2HF3O2 C7H5F3

182.154 114.023 146.110

-56.4 -15.2 -28.95

215.5 73 102.1

1.069520 1.535125 1.188420

0 5.39 24.8

ρ/g mL-1 η/mPa s ε

1.631 1.064920 2.234 1.73 0.866820 1.224420 2.878825 0.777020 0.856720 1.035020 1.51220 1.45925 1.339020 1.439720 1.464220 1.237320 1.487920 1.478825 1.372320 1.27320 1.655820 1.388920 1.331 1.563525

μ/D

cp/J g-1K-1 vp/kPa

46.2 0.695

2.4737 43.26 4.79 2.915 9.1 2.4526 6.72

0.123 4.8 0.36 1.81 1.38 0

2.52 1.437 0.844 0.908 99.4 2.13

0.456 2.14

8.50 2.268 2.2379 2.0343 20.44

0.793 0.545 0.421 0.537

1.724 1.50 609 0.347

0.808

0.479

0.003

0.852

7.51

0.92 0.967 0.865 0.850 0.855

47 62 45

5-12% 20-54%

112 182

>0.5%

200

2.208

1.6 0.622 2.42 15.2 31.3 0.002 0.000001

2-12% 1.5-9.7% 1-5%

321 282 385

335

1.74 1.90 0 3.5 0

1.82

-20

1.45 0.55 0

1.017 1.471 0.634 0.766 1.707 1.653 0.517

9.54 2.45 94.2 0.138 1.13 0.84 16.0 10.6

3.79 0.003 0.726 0.01

4 127 83 63 93 180

7.243 7.1937 3.390 3.00 4.8069 6.9

0.99 0.8 0.77

1.837 1.025 1.76 1.4 0.8 2.04 0.46 1.04 2.03 1.91

1.245

6.66 0.057 16.5 3.1 9.91 6.29 106 26.2 0.35 22.5 3.18 0.492

0.908

44.8

1.57 2.206 2.149 2.61 2.173 2.18

0.0000002 0.005 0.0047 <0.01 7.70 0.0002

1.289

15.1 5.14

1.082 1.131 0.947 0.885 0.957 1.091

0.86 2.41 6.7 2.0213 2.139 29.36 2.418 23.69 7.62

2.87 ≈0 ≈0 3.6 0.66

13.20 8.42 9.22

3.1 2.28 2.86

1 500

5.66

2.313

0.05

-14 75 71

7.319 7.5 0.326 0.656

18.7

21.6 0.100 0.05

0.37

490

1.416 0.993

1.720 1.774 1.645

2.379 8.433 4.404 2.340 2.23 5.72 6.8

1-7%

IT/°C TLV/ppm

1.75 2.1 ≈0

1.921 23.10 2.317 9.06 8.675 2.739

1.857

1.32 0 0 0 ≈0

31 177

7.52 13.48 2.771

0.973

0.560

1.747 1.498

0.02 0.56 0.81 <0.01 1.27 17.9

FP/ °C Fl. lim.

1 25 5

200

77 0.005 1 -1

105 -1 32 32 22

127 -9 71 -50

1-7% 0.9-9.5%

480

50 0.005 0.5

1-5% >0.5%

407

2.5-6.6% 8-13% 6-28% 8-11%

571 500 460 420

7.6->20%

211 >404

5 350 10 50 1000 10 0.1 0.1 10

3.2-12.6% 104

1000 225 79 79 179 -7 177 111 115

385

1-10% 1-8% 1-9%

249 371

0.01

0.8 1

454

3/20/06 11:36:14 AM

Laboratory Solvents and Other Liquid Reagents

15-22 Name

Mol. form.

t m/°C

t b/°C

1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene Trimethyl borate Trimethylchlorosilane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane Trimethyl phosphate 2,4,6-Trimethylpyridine Trinitroglycerol Undecane Vanadium(IV) chloride Vanadyl trichloride Vinyl acetate 4-Vinylcyclohexene Water o-Xylene m-Xylene p-Xylene 2,4-Xylenol

C9H12 C9H12 C9H12 C3H9BO3 C3H9ClSi C8H18 C8H18 C3H9O4P C8H11N C3H5N3O9 C11H24 Cl4V Cl3OV C4H6O2 C8H12 H2O C8H10 C8H10 C8H10 C8H10O

120.191 120.191 120.191 103.912 108.642 114.229 114.229 140.074 121.180 227.087 156.309 192.753 173.299 86.090 108.181 18.015 106.165 106.165 106.165 122.164

-25.4 -43.77 -44.72 -29.3 -40 -107.3 -100.9 -46 -46 13.5 -25.5 -25.7 -79 -93.2 -108.9 0.00 -25.2 -47.8 13.25 24.5

176.12 169.38 164.74 67.5 60 99.22 114.8 197.2 170.6 exp 218 195.9 148 127 72.8 128 100.0 144.5 139.12 138.37 210.98

487_S15.indb 22

ρ/g mL-1 η/mPa s ε 0.894420 0.875820 0.861525 0.91525 0.85625 0.687825 0.726220 1.214420 0.916622 1.593120 0.740220 1.816 1.829 0.925625 0.829920 0.9970 0.880210 0.859625 0.856625 0.965020

1.098

0.890 0.760 0.581 0.603

μ/D

cp/J g-1K-1 vp/kPa

2.656 2.377 2.279 2.2762

≈0 ≈0 0

1.800 1.789 1.741 1.828

1.943 1.9780 20.6 7.807 19.25 1.9972 3.05 3.4

≈0 ≈0 3.2 2.05

2.093 2.150

≈0

2.207

1.79

1.969

1.8546 0.64 ≈0 0 1.4

4.180 1.753 1.724 1.710

80.100 2.562 2.359 2.2735 5.060

FP/ °C Fl. lim. 0.8-6.6% 1-6% 1-5%

IT/°C TLV/ppm

0.20 0.30 0.33 17.2 30.7 6.50 3.60 0.11 4.1 0.00005 0.05

44 44 50 -8 -28 -12 <21 107

470 500 559

25 25 25

395 418 425

300 300

270

0.05

15.4 1.87 3.17 0.88 1.13 1.19 0.022

-8 16

2.6-13.4% 402 269

10 0.1

32 27 27

1-7% 1-7% 1-7%

100 100 100

463 527 528

3/20/06 11:36:16 AM

DEPENDENCE OF BOILING POINT ON PRESSURE The normal boiling point of a liquid is defined as the temperature at which the vapor pressure reaches standard atmospheric pressure, 101.325 kPa. The change in boiling point with pressure may be calculated from the representation of the vapor pressure by the Antoine Equation, ln p = A1 – A2/(T + A3) where p is the vapor pressure, T the absolute temperature, and A1, A2, and A3 are constants. This table, which has been calculated using the Antoine constants in Reference 1, gives values of ∆t/∆p for a number of liquids, in units of both °C/kPa and °C/mmHg. The correction to the boiling point is generally accurate to 0.1 to 0.2 °C as long as the pressure is within 10% of standard atmospheric pressure. A slightly less accurate estimate of ∆t/∆p may be obtained from the Clausius-Clapeyron equation, with the assumption that the tb Compound Acetaldehyde Acetic acid Acetone Acetonitrile Ammonia Aniline Anisole Benzaldehyde Benzene Bromine Butane 1-Butanol Carbon disulfide Chlorine Chlorobenzene 1-Chlorobutane Chloroethane Chloroethylene Cyclohexane Cyclohexanol Cyclohexanone Decane Dibutyl ether Dichloromethane Diethyl ether Dimethyl sulfoxide 1,4-Dioxane Dipropyl ether Ethanol Ethyl acetate Ethylene glycol Heptane Hexafluorobenzene Hexane

change in volume upon vaporization equals the ideal-gas volume of the vapor. This leads to the equation ∆t/∆p = RTb2 /p0 ∆vapH(Tb) where R is the molar gas constant, p0 is 101.325 kPa, Tb is the normal boiling point temperature (absolute), and ∆vapH(Tb) is the molar enthalpy of vaporization at the normal boiling point. Values of the last quantity may be obtained from the table “Enthalpy of Vaporization” in Section 6.

Reference 1. Lide, D. R., and Kehiaian, H. V., CRC Handbook of Thermophysical and Thermochemical Data, CRC Press, Boca Raton, FL, 1994, pp. 49-59.

∆t/∆p

°C

°C/kPa

20.1 117.9 56.0 81.6 -33.33 184.1 153.7 179.0 80.0 58.8 -0.5 117.7 46.2 -34.04 131.7 78.6 12.3 -13.3 80.7 160.8 155.4 174.1 140.2 39.6 34.5 189.0 101.5 90.0 78.2 77.1 197.3 98.5 80.2 68.7

0.261 0.324 0.289 0.316 0.198 0.378 0.367 0.392 0.321 0.300 0.267 0.278 0.304 0.224 0.365 0.321 0.262 0.241 0.328 0.344 0.382 0.388 0.363 0.276 0.278 0.379 0.321 0.326 0.249 0.300 0.331 0.336 0.305 0.314

°C/mmHg 0.0348 0.0432 0.0385 0.0421 0.0264 0.0504 0.0489 0.0523 0.0428 0.0400 0.0356 0.0371 0.0405 0.0299 0.0487 0.0428 0.0349 0.0321 0.0437 0.0459 0.0509 0.0517 0.0484 0.0368 0.0371 0.0505 0.0428 0.0435 0.0332 0.0400 0.0441 0.0448 0.0407 0.0419

Compound 1-Hexanol Hydrogen fluoride Iodomethane Isobutane Methanol Methyl acetate Methyl formate N-Methylaniline N-Methylformamide Nitrobenzene Nitromethane 1-Octanol Pentane 1-Pentanol Phenol Propane 1-Propanol 2-Propanol Pyridine Pyrrole Pyrrolidine Styrene Sulfur dioxide Tetrachloroethylene Tetrachloromethane Toluene Trichloroethylene Trichloromethane Trimethylamine Water o-Xylene m-Xylene p-Xylene

∆t/∆p

°C

°C/kPa

157.6 20.1 42.5 -11.7 64.6 56.8 31.7 196.2 199.5 210.8 101.1 195.1 36.0 137.9 181.8 -42.1 97.2 82.3 115.2 129.7 86.5 145.1 -10.05 121.3 76.8 110.6 87.2 61.1 2.8 100.0 144.5 139.1 138.3

0.318 0.276 0.291 0.254 0.251 0.282 0.582 0.396 0.371 0.418 0.320 0.360 0.289 0.296 0.349 0.224 0.261 0.247 0.340 0.330 0.309 0.369 0.221 0.354 0.325 0.353 0.330 0.302 0.248 0.276 0.373 0.368 0.369

°C/mmHg 0.0424 0.0368 0.0388 0.0339 0.0335 0.0376 0.0776 0.0528 0.0495 0.0557 0.0427 0.0480 0.0385 0.0395 0.0465 0.0299 0.0348 0.0329 0.0453 0.0440 0.0412 0.0492 0.0295 0.0472 0.0433 0.0471 0.0440 0.0403 0.0331 0.0368 0.0497 0.0491 0.0492

15-26

Section 15.indb 26

5/3/05 9:11:53 AM

EBULLIOSCOPIC CONSTANTS FOR CALCULATION OF BOILING POINT ELEVATION The boiling point Tb of a dilute solution of a non-volatile, nondissociating solute is elevated relative to that of the pure solvent. If the solution is ideal (i.e., follows Raoult’s Law), the amount of elevation depends only on the number of particles of solute present. Hence the change in boiling point ∆Tb can be expressed as ∆Tb = Eb m2 where m2 is the molality (moles of solute per kilogram of solvent) and Eb is the Ebullioscopic Constant, a characteristic property of Compound Acetic acid Acetone Acetonitrile Aniline Anisole Benzaldehyde Benzene 1-Butanol Carbon disulfide Chlorobenzene 1-Chlorobutane Cyclohexane Cyclohexanol Decane Dichloromethane Diethyl ether Dimethyl sulfoxide 1,4-Dioxane Ethanol Ethyl acetate Ethylene glycol Heptane

Eb/K kg mol–1 3.22 1.80 1.44 3.82 4.20 4.24 2.64 2.17 2.42 4.36 3.13 2.92 3.5 6.10 2.42 2.20 3.22 3.01 1.23 2.82 2.26 3.62

the solvent. The Ebullioscopic Constant may be calculated from the relation Eb = R Tb2 M/∆vapH where R is the molar gas constant, Tb is the normal boiling point temperature (absolute) of the solvent, M the molar mass of the solvent, and ∆vapH the molar enthalpy (heat) of vaporization of the solvent at its normal boiling point. This table lists Eb values for some common solvents, as calculated from data in the table “Enthalpy of Vaporization” in Section 6. Compound Hexane Iodomethane Methanol Methyl acetate N-Methylaniline N-Methylformamide Nitrobenzene Nitromethane 1-Octanol Phenol 1-Propanol 2-Propanol Pyridine Pyrrole Pyrrolidine Tetrachloroethylene Tetrachloromethane Toluene Trichloroethylene Trichloromethane Water o-Xylene

Eb/K kg mol–1 2.90 4.31 0.86 2.21 4.3 2.2 5.2 2.09 5.06 3.54 1.66 1.58 2.83 2.33 2.32 6.18 5.26 3.40 4.52 3.80 0.513 4.25

15-27

Section 15.indb 27

5/3/05 9:11:53 AM

CRYOSCOPIC CONSTANTS FOR CALCULATION OF FREEZING POINT DEPRESSION The freezing point Tf of a dilute solution of a non-volatile, nondissociating solute is depressed relative to that of the pure solvent. If the solution is ideal (i.e., follows Raoult’s Law), this lowering is a function only of the number of particles of solute present. Thus the absolute value of the lowering of freezing point ∆Tf can be expressed as ∆Tf = Ef m2 where m2 is the molality (moles of solute per kilogram of solvent) and Ef is the Cryoscopic Constant, a characteristic property of the Compound Acetamide Acetic acid Acetophenone Aniline Benzene Benzonitrile Benzophenone (+)-Camphor 1-Chloronaphthalene o-Cresol m-Cresol p-Cresol Cyclohexane Cyclohexanol cis-Decahydronaphthalene trans-Decahydronaphthalene Dibenzyl ether p-Dichlorobenzene Diethanolamine Dimethyl sulfoxide

Ef/K kg mol–1 3.92 3.63 5.16 5.23 5.07 5.35 8.58 37.8 7.68 5.92 7.76 7.20 20.8 42.2 6.42 4.70 6.17 7.57 3.16 3.85

solvent. The Cryoscopic Constant may be calculated from the relation Ef = R Tf2 M/∆fusH where R is the molar gas constant, Tb is the freezing point temperature (absolute) of the solvent, M the molar mass of the solvent, and ∆fusH the molar enthalpy (heat) of fusion of the solvent. This table lists cryscopic constants for selected substances, as calculated from data in the table “Enthalpy of Fusion” in Section 6. Compound 1,4-Dioxane Diphenylamine Ethylene glycol Formamide Formic acid Glycerol Methylcyclohexane Naphthalene Nitrobenzene Phenol Pyridine Quinoline Succinonitrile 1,1,2,2-Tetrabromoethane 1,1,2,2-Tetrachloro-1,2-difluoroethane Toluene p-Toluidine Tribromomethane Water p-Xylene

Ef/K kg mol–1 4.63 8.38 3.11 4.25 2.38 3.56 2.60 7.45 6.87 6.84 4.26 6.73 19.3 21.4 41.0 3.55 4.91 15.0 1.86 4.31

15-28

Section 15.indb 28

5/3/05 9:11:54 AM

FREEZING POINT LOWERING BY ELECTROLYTES IN AQUEOUS SOLUTION Reference Forsythe, W. E., Smithsonian Physical Tables, Ninth Edition, Smithsonian Institution, Washington, 1956. Compound CaCl2 CuSO4 HCl HNO3 H2SO4 KBr KCl KNO3 K2SO4 LiCl MgSO4 NH4Cl NaCl NaNO3

0.05 0.25 0.13 0.18 0.18 0.20 0.18 0.17 0.17 0.23 0.18 0.13 0.17 0.18 0.18

0.10 0.49 0.23 0.36 0.35 0.39 0.36 0.35 0.33 0.43 0.35 0.24 0.34 0.35 0.36

Lowering of freezing point of water (in Â°C) as function of molality (mol/kg) 0.25 0.50 0.75 1.00 1.50 2.00 2.50 1.27 2.66 4.28 6.35 10.78 15.27 20.42 0.47 0.96 0.90 1.86 2.90 4.02 6.63 9.94 0.88 1.80 2.78 3.80 5.98 8.34 10.95 0.96 1.95 3.04 4.28 7.35 11.35 16.32 0.92 1.78 0.86 1.68 2.49 3.29 4.88 6.50 8.14 0.78 1.47 2.11 2.66 1.01 1.87 0.88 1.80 2.78 0.55 1.01 1.50 2.08 3.41 0.85 1.70 2.55 0.85 1.68 2.60 0.80 1.62 2.63 3.10

3.00 28.08

13.92

9.77

15-29

Section 15.indb 29

5/3/05 9:11:54 AM

DETERMINATION OF RELATIVE HUMIDITY FROM DEW POINT The relative humidity of a water vapor-air mixture is defined as 100 times the partial pressure of water divided by the saturation vapor pressure of water at the same temperature. The relative humidity may be determined from the dew point tdew, which is the temperature at which liquid water first condenses when the

mixture is cooled from an initial temperature t. This table gives relative humidity as a function of the dew point depression t – tdew for several values of the dew point. Values are calculated from the vapor pressure table in Section 6.

tdew/°C t – tdew 0.0 0.2 0.4 0.6 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.9 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0

tdew/°C

–10

100 99 97 95 94 92 91 90 88 87 86 84 83 82 80 79 78 77 76 75 73 72 71 70 69 69 67 66 65 64 63 62 61 60 60 59 58 57 56 55 54

100 99 97 96 94 93 92 90 89 88 87 85 84 83 82 81 80 79 77 76 75 74 73 72 71 70 69 68 67 66 66 65 64 63 62 61 60 60 59 58 57

100 99 97 96 95 94 92 91 90 89 88 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 69 68 67 66 65 64 63 63 62 61 60 60

100 99 98 96 95 94 93 92 91 90 88 87 86 85 84 83 82 81 80 79 78 77 77 76 75 74 73 72 71 70 70 69 68 67 66 66 65 64 63 63 62

100 99 98 97 96 94 93 92 91 90 89 89 87 86 85 84 83 82 82 81 80 79 78 77 76 75 75 74 73 72 71 71 70 69 68 68 67 66 65 65 64

t – tdew 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0

–10

54 53 52 51 51 50 49 48 48 47 45 44 42 41 39 38 37 35 34 33 32 31 30 29 28 27 26 25 24 24 22 21 19 18 17 16 15 14 13 12

56 56 55 54 53 53 52 51 51 50 48 47 45 44 42 41 40 38 37 36 35 34 33 32 31 30 29 28 27 26 25 23 22 21 19 18 17 16 15 14

59 58 57 57 56 55 55 54 53 53 51 49 48 47 45 44 43 41 40 39 38 37 36 35 34 33 32 31 30 29 27 26 24 23 22 21 20 19 18 17

61 60 60 59 58 58 57 56 56 55 54 52 51 49 48 46 45 44 43 42 40 39 38 37 36 35 34 33 33 32 30 29 27 26 24 23 22 21 20 19

63 63 62 61 61 60 59 59 58 57 56 55 53 52 50 49 48 47 45 44

15-31

Section 15.indb 31

5/3/05 9:11:57 AM

DETERMINATION OF RELATIVE HUMIDITY FROM WET AND DRY BULB TEMPERATURES Relative humidity may be determined by comparing temperature readings of wet and dry bulb thermometers. The following table, extracted from more extensive U.S. National Weather Service tables, gives the relative humidity as a function of air temperature

td (dry bulb) and the difference td – tw between dry and wet bulb temperatures. The data assume a pressure near normal atmospheric pressure and an instrumental configuration with forced ventilation. (td – tw)/°C

td/°C –10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 35 40

0.5 83 86 88 89 90 91 91 92 93 93 94 94 95 95 95 96 96 96 96 96 96 97 97

1.0 67 71 74 77 79 81 84 85 86 87 88 89 90 90 91 91 92 92 92 93 93 94 94

1.5 51 57 61 66 69 72 76 78 79 81 82 83 85 85 86 87 87 88 88 89 89 90 91

2.0 35 43 49 55 60 64 68 71 73 75 77 78 79 81 82 83 83 84 85 85 86 87 88

2.5 19 29 37 44 50 55 60 63 66 69 71 73 75 76 77 78 80 80 81 82 83 84 85

3.0

3.5

4.0

4.5

5.0

5.5

6.0

15 25 33 40 46 52 57 60 63 66 68 70 71 73 74 76 77 78 78 79 81 82

8 23 31 38 44 49 54 57 60 63 65 67 69 70 72 73 74 75 76 78 80

12 22 29 37 43 48 51 55 58 60 63 65 66 68 69 71 72 73 75 77

12 21 29 36 41 46 50 53 56 58 61 63 64 66 67 69 70 72 74

13 22 29 35 40 44 48 51 54 57 59 61 62 64 65 67 69 72

5 14 22 29 35 39 43 47 50 53 55 57 59 61 62 64 67 69

7 16 24 29 34 39 42 46 49 51 54 56 58 59 61 64 67

(td – tw)/°C td/°C 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

6.5 9 17 24 29 34 38 42 45 48 50 53 54 56 58 60 61 62 63 64

7.0

7.5

8.0

8.5

9.0

10.0

11.0

12.0

13.0

14.0

15.0

11 19 24 29 34 38 41 44 47 49 51 53 55 57 58 59 61 62

5 14 20 25 30 34 38 41 44 46 49 51 52 54 56 57 58 59

8 15 21 26 30 34 37 40 43 46 48 50 51 53 54 56 57

10 16 22 26 30 34 37 40 43 45 47 49 51 52 54 54

6 12 18 23 27 31 34 37 40 42 44 46 48 50 51 53

5 10 15 20 24 28 31 34 37 39 41 43 45 47 48

8 14 18 22 26 29 32 35 37 39 41 43 44

7 12 17 20 24 27 30 32 35 37 39 40

6 11 15 19 22 25 28 30 33 35 36

6 10 14 18 21 24 26 29 31 33

5 10 13 17 20 23 25 27 29

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CONSTANT HUMIDITY SOLUTIONS Anthony Wexler An excess of a water soluble salt in contact with its saturated solution and contained within an enclosed space produces a constant relative humidity and water vapor pressure according to

where p0 is the vapor pressure of pure water at temperature T as given in the table in Section 6 titled “Vapor Pressure of Water from 0 to 370°C”.

RH = A exp(B/T)

References

where RH is the percent relative humidity (generally accurate to ±2 %), T is the temperature in kelvin, and the constants A and B and the range of valid temperatures are given in the table below. The vapor pressure, p, can be calculated from p = (RH/100) × p0

Compound NaOH · H2O LiBr · 2H2O ZnBr2 · 2H2O KOH · 2H2O LiCl · H2O CaBr2 · 6H2O LiI · 3H2O CaCl2· 6H2O MgCl2· 6H2O NaI · 2H2O Ca(NO3)2 · 4H2O Mg(NO3)2 · 6H2O NaBr · 2H2O NH4NO3 KI SrCl2 · 6H2O NaNO3 NaCl NH4Cl KBr (NH4)2SO4 KCl Sr(NO3)2 · 4H2O BaCl2 · 2H2O CsI KNO3 K2SO4

Temperature range (°C) 15—60 10—30 5—30 5—30 20—65 11—22 15—65 15—25 5—45 5—45 10—30 5—35 0—35 10—40 5—30 5—30 10—40 10—40 10—40 5—25 10—40 5—25 5—25 5—25 5—25 0—50 10—50

1. Wexler, A. S. and Seinfeld, J. H., Atmospheric Environment, 25A, 2731, 1991. 2. Greenspan, L., J. Res. National Bureau of Standards, 81A, 89, 1977. 3. Broul, et al., Solubility of Inorganic Two-Component Systems, Elsevier, New York, 1981. 4. Wagman, D. D. et al., J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 2, 1982.

RH (25°C) 6 6 8 9 11 16 18 29 33 38 51 53 58 62 69 71 74 75 79 81 81 84 85 90 91 92 97

A 5.48 0.23 1.69 0.014 14.53 0.17 0.15 0.11 29.26 3.62 1.89 25.28 20.49 3.54 29.35 31.58 26.94 69.20 35.67 40.98 62.06 49.38 28.34 69.99 70.77 43.22 86.75

B 27 996 455 1924 –75 1360 1424 1653 34 702 981 220 308 853 254 241 302 25 235 203 79 159 328 75 75 225 34

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