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OWL-4 25 7
C o n t r a c t N o . U-7405-eng-26
REACTOR CHEMISTRY DIVISION AN EMF STUDY OF LiF-BeF2
SOLUTIONS
B. F. Hitch and C. F. B a e s , Jr.
*.? 1
c
JULY 1968
OAK RIDGE NATIONAL LABORATORY Oak Ridge, T e n n e s s e e operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION
,
r
iii CONTENTS
............................................... Introduction ........................................... Experimental ........................................... Chemicals ......................................... Gases ........................................... Melt Components ................................. Reagents ........................................ Apparatus ......................................... Cell Design ..................................... HF-Hz Electrode ................................. Beryllium Electrode ............................. Flow Control of Gases ........................... Hydrogen Fluoride ............................. Hydrogen ..................................... Helium ........................................ Titration Assembly .............................. Electronic Equipment ............................ Procedure ........................................ Measurements .................................... Cell Potential ................................ H2 and HF Partial Pressures .................... Melt Temperature .............................. Calculations .................................. Systematic Errors ............................... Hydrogen D i f f u s i o n ............................ Thermal Diffusion ............................. Gas Cooling Effect on Electrodes .............. Melt Composition .............................. Melt Impurities ............................... Oxide Contamination of Melt .................... Summary ....................................... Random Errors .................................... Precision of Potential Measurements ........... Melt Temperature .............................. Melt Composition .............................. Titer Precision .............................. Temperature of Bubble-0-Meter ................. Flow Rate Determination ....................... Endpoint Precision ............................ H2 and HF Flow Rates .......................... Abstract
Page 1 2 6
7 7 10 11 11 11 11 11 13 13 13 13
14 14 15 15 18 18
19 19 19 20 21 22 22 22 22 22 23 23 23 23 23
iv i
ci ......................... Results ................................................. Tabulation ......................................... Experiments ...................................... S t a t i s t i c a l Error Analysis
.......................... Discussion .............................................. Thermodynamics of LiF-BeF2 ......................... Reference Electrodes ............................... Beryllium Electrode .............................. HF-H2 Electrode .................................. References .............................................. Corrected C e l l Potentials
i
23
25 m �
25 25
26 29
29 39 39 41
42
1
AN EMF STUDY OF LiF-BeF2 SOLUTIONS B. F. Hitch and C. F. Baes, Jr.
ABSTRACT The p o t e n t i a l of t h e c e l l Be
0
I BeF2,
LiF I HF ,H2 ,Pt
with t h e assumed c e l l r e a c t i o n
+
Be(s)
2HF(g)
t' BeF2(d) +
H2(g)
w a s measured over a composition range of 0.30 t o 0.90 mole f r a c t i o n BeF2 and a temperature range of 500 t o 900째C. Since t h i s c e l l p o t e n t i a l i s r e l a t e d t o t h e a c t i v i t y of BeF2 i n t h e s o l u t i o n s by D
P ?
c
a c t i v i t y c o e f f i c i e n t s could b e derived f o r BeF2 (and by a Gibbs-Duhem i n t e g r a t i o n f o r LiF). Usefully a c c u r a t e measurements could not b e made w i t h pure BeF2 i n t h e c e l l , hence values of EO w e r e c a l c u l a t e d using v a l u e s f o r aBeF2 derived from the phase diagram and previously reported h e a t of f u s i o n (1.13 kcal/mole) g i v i n g
Eo
=
2.4430
-
0.0007952T
This comparison of t h e emf d a t a w i t h t h e LiF-BeF2 phase diagram a l s o i n d i c a t e d t h a t t h e h e a t of f u s i o n f o r BeF2 i s < 2.0 kcal/mole. A power series i n xLiF w a s assumed f o r l o g YBeF2 and t h e c o e f f i c i e n t s determined by a least squares f i t t o t h e data. This gave log'BeF2
+
= (3.8780
(94.3997
-
2353*5)x2 T LiF
+
(-40.7375
+
84870*9)x4 T LiF
+
(-67.4178
+
36292.8
3 )xLiF
52923.5
5 lXLiF
Formation f r e e e n e r g i e s and h e a t s f o r BeF2 and Be0 were a l s o c a l c u l a t e d by combining t h e r e s u l t s of t h e g r e s e n t study w i t h a v a i l a b l e thermochemical data. The Be2+1 Be and HF,H2 Fe l e c t r o d e s performed acceptably f o r u s e as r e f e r e n c e e l e c t r o d e s , both being s t a b l e and reproducible.
I
/-
&> i
2
Molten fluoride interest
at this
ds
INTRODUCTION
I. mixtures
Laboratory
of LiF and BeF2 are of considerable since
they are the principal
*
constituents
r-
i
-4
in the molten-salt
reactor
(MSRE) fuel
and coolant
the molten LiF-BeF2 system has received a limited
number of emf investigations
considerable
electrode
general would facilitate
the determination
contained
fluoride
constituents
'
half-cells
Although
attention,
have been attempted.
development of reference
various
salts.
only The
for molten fluorides of electrode
and the detection
in
potentials
of certain
for
impurities
in these mixtures.
The purpose of this Be'(s)
investigation
was to study the cell
+ 2HF(g) 2 BeF2(d) + H2(g)
reaction
(1)
in the molten LiF-BeF2 system using Be2+ IBe0 and HF,H 2 IF- electrodes. Emf data obtained in this study would hopefully extend and improve the thermodynamics
of this
molten
fluoride
measurements should demonstrate reference salt
electrodes
solvent
in future
At the same time emf
electrodes
emf studies
in this
which may serve as important
molten
system.
Thus far activity from mass ,spectroscopic gram,
useful
system.
data for the LiF-BeF2 systems has been obtained of the vapor, 2,3 from the phase dia-
studies
495I from emf measurements,6
and from transpiration
data where
gaseous HF-H20 mixtures were equilibrated with the molten fluoride mixture. 7 The values'derived from the phase data, besides being non-isothermal,
have been limited
been difficult
to determine.
in accuracy because the BeF2 liquidus In addition,
the reported
has
values 4,5,7,8,9
3 f o r the h e a t of f u s i o n f o r BeF2 are not i n agreement. I
Mass s p e c t r o -
s c o p i c and emf values of t h e a c t i v i t y were determined f o r only a l i m i t ed number of compositions and temperatures.
Probably the b e s t a c t i v i -
t y values are t h o s e determined by Mathews and Baes
7
using a t r a n s p i r a -
t i o n method t o e q u i l i b r a t e gaseous HF-H20 mixtures w i t h molten LiF-BeF mixtures.
2
However, a c t i v i t i e s derived from t h e s e heterogeneous equi-
l i b r i a are somewhat l i m i t e d i n accuracy
(56 % )
and the e q u i l i b r i u m
q u o t i e n t s w e r e measured i n t h e presence of Be0 as a s a t u r a t i n g s o l i d which might have i n f l u e n c e d t h e a c t i v i t y values.
Direct determination of t h e a c t i v i t y of BeF2 by emf measurements should y i e l d more a c c u r a t e values over a g r e a t e r composition range than any of t h e methods p r e v i o u s l y mentioned.
D i r i a n , Romberger and Baes
10
measured t h e p o t e n t i a l of t h e following c e l l as a f u n c t i o n of temperature. BeO10.33 BeP2
- 0.67
LiFIJDl%,Pd
The c e l l r e a c t i o n i s t h a t shown i n eq. (1). Be2+IBeo and HF,H21F-
- were
The two e l e c t r o d e s
-
judged by Dirian e t a l , t o b e r e v e r s i b l e
from p o l a r i z a t i o n measurements. I n t h e p r e s e n t i n v e s t i g a t i o n these two e l e c t r o d e s w e r e used t o determine t h e c e l l p o t e n t i a l over a composition range of 0.30 t o 0.90 mole f r a c t i o n BeF2 and a temperature range of 500 t o 900째C (Fig. 1 ) . An attempt w a s made t o o b t a i n measurements i n pure BeF
2'
but results
of u s e f u l accuracy could n o t be o b t a i n e d presumably because of i t s high f
v i s c o s i t y and/or h i g h e l e c t r i c a l r e s i s t i v i t y .
is very viscous (about 180 p o i s e
11
1. The
Even a t 900째C, pure BeF
2
r e a c t i o n vessel w a s n o t heat-
ed above 900째C because of t h e tendency of n i c k e l t o s o f t e n a t such
4 The melting p o i n t s of mixtures below 0.33 BeF 2
e l e v a t e d temperatures.
W
i n c r e a s e r a p i d l y as t h e c o n c e n t r a t i o n approaches pure LiF as shown i n t h e LiF-BeF
2
12 phase diagram i n Fig. 1.
The lower BeF2 c o n c e n t r a t i o n s
(below 0.30 BeF ) were not i n v e s t i g a t e d t h e r e f o r e s i n c e t h e a c c e s s i b l e 2 temperature range was so l i m i t e d . According t o the assumed c e l l r e a c t i o n (eq. l ) , t h e c e l l p o t e n t i a l should be dependent on t h e a c t i v i t y of BeF2, t h e a c t i v i t y of b e r y l l i u m
metal, and t h e p a r t i a l p r e s s u r e s of HF and H2. E=Eo--
RT En 2F
~
Previous measurements"
i
pH2
aBeF2
H 'F
a Beo
w i t h the HF-H2 e l e c t r o d e , as w e l l as the pre-
s e n t ones, i n d i c a t e t h e gases t o be s u f f i c i e n t l y i d e a l a t t h e e l e v a t e d temperatures and low p r e s s u r e l e v e l s involved t o allow t h e use of p a r t i a l p r e s s u r e s i n p l a c e of f u g a c i t i e s i n t h i s Nernst expression. I n t h i s study mixtures of HF-H
2
were bubbled through molten
c
LiF-BeF2 and t h e p a r t i a l p r e s s u r e s of t h e gases determined by a l k a l i m e t r i c t i t r a t i o n and gas volume measurements.
The measured c e l l po-
t e n t i a l (E) w a s then c o r r e c t e d f o r the e f f e c t of t h e gas p r e s s u r e quotient.
D
RT Ec=E+-Iln 2F
The c o r r e c t e d p o t e n t i a l E
j i
1 I I I
Ec = Eo
sH2 2
(3)
D
HF C
is r e l a t e d t o t h e a c t i v i t y of BeF by 2
-RT En a 2F BeF2
(4)
assuming t h e a c t i v i t y of Beo t o b e u n i t y . Not a t i o n
The following n o t a t i o n w i l l b e used:
L4
d
*
It
P
ORNL-DWG 66-7632R3
900
I
I
I
848
n
800
700
V
0
w
60C 555
[L
3
!az 2w 500 w
I
458
I-
I
I
BeF2 (HIGH QUARTZ TYPE) +LIQUID
4 00 360 Li F+ Li2BeF4
300
Li28eFq+ BeF2 (HIGH QUARTZ TYPE 1
I
I %CI
280I
1
Li2BeF4
+
1
Lm o,
LiBeF3
20c I
I
J
I
I
I
LiBeF3 + BeF, ( HIGH QUARTZ TYPE) LiBeF3+!BeF2 (LOWIQUARTZ TYPE), 220
I
1 1
c
6
14
The number preceding "BeF2" denotes mole f ra c t i o n .
0.00 BeF2
L
Total pressure(atm), p a r t i a l pressures(atm), volume(R) p e r u n i t t i m e , and temperature(OK) i n t h e r e g i o n where gas e n t e r s t h e m e l t . Corresponding measurements a t t h e Bubble-OMeter.
Po Po ,Vo,To T' H2
Barometric p r e s s u r e and vapor p r e s s u r e of H 0 2 a t To.
B "i20
The approximate p a r t i a l p r e s s u r e of HF a t t h e titrator. ( s e e C a l c u l a t i o n s s e c t i o n below.)
piF
P r e s s u r e drop r e q u i r e d t o maintain gas flow
AP
. through t h e m e l t . C e l l p o t e n t i a l measured experimentally f o r a fixed BeF2 concentration and temperature.
E
The observed c e l l p o t e n t i a l c o r r e c t e d t o a gas p r e s s u r e q u o t i e n t of u n i t y (eq. 3).
EC
The s t a n d a r d c e l l p o t e n t i a l w i t h pure BeF2 as t h e s t a n d a r d state.
EO
11.
EXPERIMENTAL Chemicals
Gases
Commercial H
2
w a s p u r i f i e d by passage through a deoxo u n i t , a mag-
nesium p e r c h l o r a t e drying tube and, f i n a l l y , a l i q u i d N2 t r a p . hydrous HF (99.9%) w a s used without f u r t h e r p u r i f i c a t i o n .
An-
Commercial
H e w a s p u r i f i e d by passage through an ascarite t r a p , a magnesium per-
c h l o r a t e t r a p and, f i n a l l y , a l i q u i d N2 t r a p .
M e 1t Components
*;-
. I
Lithium f l u o r i d e (99.5%) w a s obtained from American Potash and
Chemical Corporation.
Beryllium f l u o r i d e w a s from t h r e e s o u r c e s :
*
. ,
LJ
7
Brush Beryllium Corporation, K and K L a b o r a t o r i e s , I n c . , and comm e r c i a l BeF2 d i s t i l l e d by t h e Reactor Chemistry Division a t Oak Ridge National Laboratory.
Most of t h e commercial BeF2 contained i m p u r i t i e s
which "poisoned" t h e e l e c t r o d e s ( s e e p. 20).
With t h e exception of one
composition, t h e d i s t i l l e d BeF2 w a s used throughout t h i s i n v e s t i g a t i o n s i n c e t h e p u r i t y w a s such t h a t no e l e c t r o d e "poisoning" w a s encountered. Reapen t s Reagent grade 1 N NaOH from F i s h e r Chemical Company w a s standardi z e d w i t h potassium a c i d p h t h a l a t e . Apparatus Experiments were c a r r i e d out i n t h e apparatus shown i n Fig. 2. C e l l Design
A s k e t c h of t h e n i c k e l r e a c t i o n v e s s e l used t o c o n t a i n t h e LiF-BeF
mixtures is shown i n Fig. 3.
2
This v e s s e l w a s constructed of 2-1/2-in.
schedule 40 n i c k e l p i p e and w a s s e p a r a t e d i n t o two compartments by a 1/16-in.
n i c k e l s h e e t which extended t o w i t h i n 1/2-in.
bottom.
The nickel s h e e t w a s welded so t h a t t h e only contact between
of t h e v e s s e l
t h e two compartments w a s through t h e 1/2-in. opening a t t h e bottom. v e s s e l w a s 10-in. j
The
long.
Each compartment w a s equipped w i t h t h e following: a 3/4-in.
Swagelok f i t t i n g through which m e l t components could b e added o r an e l e c t r o d e i n s e r t e d , a 1/4-in.
-. -5 ' /
4
gas e x i t tube, and a thermocouple w e l l .
The Swageloks were equipped with Teflon seals when t h e e l e c t r o d e s were inserted.
vis provided an e l e c t r i c a l i n s u l a t o r as w e l l as a leak-
t i g h t f i t t i n g f o r the 1/8-in.
n i c k e l tubing.
Cooling c o i l s were wrap-
ped around each Swagelok t o provide cooling when t h e r e a c t i o n v e s s e l
8
ORNL-DWG 67-13719
ANHYD
I He
a-
-
AMPLl FIER -RECORDER
I 1
COMPART-
I
NaOH SOLN
COMPARTMENTED REACTION VESSEL
NaOH SOLN
METER
Fig. 2. Schematic Diagram of Apparatus Used to Measure Cell Potentials in Molten LiF-BeF2 Mixtures.
9
ORNL-DWG 67-13720
3
Fig. 3. Compartmented Cell Used to Contain Molten LiF-BeF2 Mixtures.
10 I
w a s a t e l e v a t e d temperatures. The r e a c t i o n v e s s e l w a s l o c a t e d i n s i d e an u p r i g h t tube furnace, t h e temperature w a s c o n t r o l l e d by an L & N Series 60 D.A.T.
B
Control c
The temperature of t h e r e a c t i o n v e s s e l w a s checked w i t h a c a l i -
Unit.
b r a t e d Chromel-Alumel thermocouple and an L & N K-3 potentiometer. A 4-in.
diameter vessel, f i t t e d w i t h 1/2-in.
diameter e l e c t r o d e
compartments, w a s used f o r preliminary measurements.
Electrodes used
i n t h e c y l i n d r i c a l compartments were i n s u l a t e d from t h e compartment
w a l l s w i t h boron n i t r i d e s p a c e r s , b u t even then a c c i d e n t a l electrical s h o r t s were a problem.
The l a r g e compartments of t h e r e a c t i o n vessel
used i n t h e p r e s e n t i n v e s t i g a t i o n e l i m i n a t e d ' t h e need f o r i n s u l a t i n g s p a c e r s except t h e Teflon s e a l a t t h e top of t h e compartment, and no problems from e l e c t r i c a l s h o r t i n g w e r e encountered. HF-H2
Electrode An H ,HF,Pd e l e c t r o d e of t h e t y p e used by D i r i a n and Romberger
10
2
w a s used i n some of t h e preliminary measurements. produced s t a b l e p o t e n t i a l s b u t w a s q u i t e n o i s y
This e l e c t r o d e
(2 1 mv).
Platinum
gauze w a s s u b s t i t u t e d f o r t h e palladium and w a s found t o be j u s t as responsive and capable of very low n o i s e l e v e l s (0.1 mv)
.
The p l a t i n -
um gauze t y p e (Fig. 4) w a s used f o r a l l measurements i n t h i s i n v e s t i gation.
E l e c t r o d e s were prepared by forming an egg-shaped bag w i t h th-
gauze and s l i p p i n g t h e open end over 1/8-in. i t s e c u r e l y w i t h s m a l l diameter n i c k e l w i r e .
w a s crimped t o g e t h e r s o t h a t t h e HF-H
2
n i c k e l tubing and t y i n g The o t h e r end of t h e bag
mixture, p a s s i n g down through
t h e n i c k e l tubing had t o pass through t h e gauze.
The 1/8-in.
nickel
tubing t r a n s m i t t e d t h e HF-H2 mixture and provided e l e c t r i c a l c o n t a c t .
11 Beryllium E l e c t r o d e
These e l e c t r o d e s (Fig. 4) w e r e constructed by s l i p p i n g a b e r y l l i um metal c y l i n d e r (3/8-in.
over a 1/8-in.
1/8-in.
O.D.,
I.D.,
and 1/2-in.
length)
n i c k e l tube and crimping t h e n i c k e l tube s l i g h t l y on
each s i d e of t h e b e r y l l i u m c y l i n d e r t o hold i t s e c u r e l y .
w a s p o s i t i o n e d about 1/2-in.
The c y l i n d e r
from t h e t i p of the n i c k e l tube.
Lower-
i n g t h e b e r y l l i u m metal c l o s e r t o t h e t i p of t h e n i c k e l tube caused an increase i n the p o t e n t i a l noise.
This w a s probably due t o helium
bubbles temporarily i n s u l a t i n g t h e beryllium from t h e m e l t . i
The 1/8-
i n . n i c k e l tube w a s used t o bubble helium i n t o t h e compartment and t o provide e l e c t r i c a l c o n t a c t . Flow Control of Gases Hydrogen Fluoride.--
The HF manifold p r e s s u r e w a s c o n t r o l l e d by
* i
r e g u l a t i n g t h e temperature of t h e HF supply c y l i n d e r . c
w a s c o n t r o l l e d by a m a s s spectrometer l e a k valve.13
a monel tee where i t mixed w i t h H
2'
The flow of HF The gas flowed t o
The mixed gases were passed e i t h e r
d i r e c t l y t o t h e HF-H2 e l e c t r o d e o r a p o r t i o n w a s s p l i t o f f f o r i n fluent g a s analysis.
A p r e s s u r e r e l i e f v a l v e (Moore Products Company, d i f -
Hydrogen.--
f e r e n t i a l type flow c o n t r o l l e r , Model 63 BD, modified form) w a s used t o reduce t h e hydrogen manifold p r e s s u r e t o a c o n s t a n t v a l u e of 3.0 l b . gauge.
The flow w a s t h e n c o n t r o l l e d by a b r a s s needle v a l v e obtained
from Nuclear Products Company.
The H2 w a s then mixed w i t h the HF as
d e s c r i b e d above. Helium.--
Helium flow w a s c o n t r o l l e d w i t h t h e same t y p e n e e d l e
v a l v e used f o r t h e H2; no attempt w a s made t o c o n t r o l t h e manifold
I
12
ORNL-DWG
67
- 13 7 2 1 t
8
,
I
1
I
I
HF
- HZ
ELECTRODE
BERYLLIUM ELECTRODE
Fig. 4. HF-Hz and Beryllium Electrodes.
*
ib
13 p r e s s u r e s i n c e a constant flow through t h e beryllium e l e c t r o d e w a s unnecessary.
1
T i t r a t i o n Assembly
t
The NaOH t i t r a t i o n vessel w a s a 200-ml test tube.
A rubber stop-
p e r w a s i n s e r t e d i n t o the t e s t tube and w a s equipped w i t h t h e following: Teflon (1/4-in.
d i a . ) e n t r a n c e and e x i t tubes f o r g a s , a 5-ml Lab-
Crest microburet, and Beckman No. 39166 ( g l a s s , Ag-AgC1) e l e c t r o d e s .
A Beckman Zeromatic I1 pH meter w a s used t o determine t h e endpoint. The pH w a s maintained on t h e a l k a l i n e s i d e of t h e endpoint t o avoid
glass attack.
Duplicate t i t r a t i o n assemblies w e r e used t o measure in-
f l u e n t and e f f l u e n t HF c o n c e n t r a t i o n s . E l e c t r o n i c Equipment
. E
An L & N K-3 p o t e n t i o m e t e r , c a l i b r a t e d w i t h a s t a n d a r d c e l l from
Eppley Laboratory, I n c . , was used t o buck o u t most of the c e l l v o l t a g e . When the c e l l v o l t a g e exceeded t h e range of the p o t e n t i o m e t e r , a mercury b a t t e r y (Mallory Duracell No. RM 42R) w a s connected i n series t o extend t h e bucking v o l t a g e range.
The v o l t a g e of the b a t t e r y w a s
checked d a i l y w i t h the potentiometer, and i t proved t o be an extremely s t a b l e voltage source
0.02 mv/day).
The remainder of t h e c e l l v o l t -
age (< 100 mv) w a s coupled, through a P h i l b r i c k ModelMP s o l i d s t a t e o p e r a t i o n a l manifold equipped w i t h P65 AU a m p l i f i e r s , t o a Honeywell Brown E l e c t r o n i k r e c o r d e r . Procedure
Me as uremen ts s
W
The d a t a obtained f o r each c e l l measurement were c e l l p o t e n t i a l ,
c e l l temperature, and p a r t i a l p r e s s u r e s of HF and H2.
14 C e l l Potential.--
C e l l p o t e n t i a l measurements were always preced-
ed by s t a n d a r d i z a t i o n of the potentiometer a g a i n s t a s t a n d a r d c e l l and a check of t h e a m p l i f i e r zero on t h e recorder.
u I
During measurements of
t h e c e l l p o t e n t i a l , most of t h e v o l t a g e w a s bucked o u t by the potenrio-
W
meter ( o r potentiometer p l u s mercury b a t t e r y ) , and t h e remainder read o f f t h e recorder.
The n o i s e l e v e l - o f t h e p o t e n t i a l v a r i e d from 5 0.2
mv t o as high as 5 1.0 mv f o r t h e h i g h v i s c o s i t y m e l t s .
Although t h e
p o t e n t i a l f l u c t u a t e d as i n d i c a t e d , i t d i d n o t show any d r i f t toward a h i g h e r o r lower p o t e n t i a l . H2 and HF P a r t i a l Pressures.--
The d e t e r m i n a t i o n of p a r t i a l
p r e s s u r e s w a s made as follows: A measured volume of s t a n d a r d i z e d NaOH w a s added t o t h e
t i t r a t i o n vessel. The t i m e r e q u i r e d f o r t h e HF t o n e u t r a l i z e t h e b a s e w a s
determined. H
flow rates were determined by t h e use of a Bubble-0-
2 Meter.
I n f l u e n t p a r t i a l p r e s s u r e s were checked simultaneously i n experiments up t o .60 BeF2. P a r t i a l p r e s s u r e determinations were never begun u n t i l the
c e l l p o t e n t i a l had been s t e a d y f o r a t least 30 minutes.
Six t o t e n successive t i t r a t i o n s w e r e c a r r i e d out. The barometric p r e s s u r e , temperature of t h e t i t r a t i m assembly, and p r e s s u r e drop a c r o s s t h e system w e r e recorded. H e l i u m flowed through t h e beryllium e l e c t r o d e a t a rate of
30 t o 75 ml/min.
This flow rate provided adequate s p a r g i n g
f o r t h i s compartment and decreased t h e thermal g r a d i e n t s . H e l i u m a l s o p r o t e c t e d t h e e l e c t r o d e from any HF which might
bi
15
have e n t e r e d the compartment. M e l t Temperature.--
The temperature of the m e l t w a s determined by
a c a l i b r a t e d Chromel-Alumel thermocouple p o s i t i o n e d c a r e f u l l y t o the e x a c t depth of t h e e l e c t r o d e .
P o s i t i o n i n g w a s c a r r i e d o u t as accurate-
l y as p o s s i b l e t o reduce any e r r o r i n temperature readings caused by thermal g r a d i e n t s i n the m e l t . Calculations.-E
C
The r e q u i r e d c a l c u l a t i o n s t o e v a l u a t e P P and HF' H2
were c a r r i e d o u t as follows: (1)
The t i t r a t i o n t i m e s were averaged f o r a series of t i t r a t i o n s
of a f i x e d increment of s t a n d a r d base.
The gas volume passed w a s then
c a l c u l a t e d by (time of t i t r a t i o n ) / ( t i m e p e r 100 m l of gas) x 100 = m l of gas. (2)
The number of m i l l i m o l e s of HF removed from t h e H2 stream by
t h e t i t r a t i o n w a s c a l c u l a t e d by (ml NaOH)(conc. of NaOH) = millimoles HF.
(3)
It w a s found convenient f i r s t t o d e f i n e an approximate 0
p a r t i a l p r e s s u r e of HF (PHF) by i n t r o d u c i n g t h e s e measured q u a n t i t i e s i n t o t h e following s i m p l e gas l a w expression F ;'
-
-
.
( m o l e s HF) (0.08206) (abs t e m p . of Bubble-0-Meter) m l of H2 passed
The exact e x p r e s s i o n f o r t h e p a r t i a l p r e s s u r e of HF (PHF) a t the el e c t r o d e i n c l u d e s t h e e f f e c t of t h e p r e s s u r e drop (AP) caused by the p r e s s u r e r e q u i r e d t o maintain bubbling through t h e m e l t and subsequent t i t r a t o r , and the s a t u r a t i o n of t h e H2 stream w i t h w a t e r p r i o r t o measuring t h e flow rate.
0
The r e l a t i o n s h i p (eq. 11) between PHF and
16
Lid
PHF which i s r e q u i r e d w a s developed as follows: (3.1)
The system may b e v i s u a l i z e d as c o n s i s t i n g of t h r e e
-
t h e c e l l v e s s e l ( a t P , T I , t h e t i t r a t i o n assembly, and T t h e Bubble-0-Meter (at Pi, To). regions
(3.2)
Assuming t h a t t h e number of moles of HF p a s s i n g
through t h e c e l l assembly and i n t o t h e t i t r a t o r is t h e same f o r
a given t i m e i n t e r v a l , then
%F
-
PiF
vo
RTo
and
i II
'HF
I
I
E
%F=
/
RT
(Note t h a t t h e f i r s t expression i s merely a rearranged form of t h e previous equation which d e f i n e s P
0
HF
).
Combining t h e s e two e q u a t i o n s ,
'HF
- 0 - 'HF
(3.3)
-
Vo T TO
(5)
Moles of H2 passing through t h e c e l l and through t h e
Bubble-0-Meter
may be t r e a t e d i n a l i k e manner
-Vo= T -
V To
Po
HZ (3.4)
Combining equations (5) and (6)
(7)
i
17 The t o t a l p r e s s u r e a t t h e HF-H2 e l e c t r o d e i s
(3.5) ! j
z
PT = PB
+ AP
= 'HF
+
p ~ 2
1 !
'
3
..
H2
=pB+Ap-
'HF
and the t o t a l p r e s s u r e of the gas a t the Bubble-0-Meter
is
0
P; = PB = PO H2 + 'H20
.- .
P H2 O =
(3.6)
.
PB
0 - 'H20.
S u b s t i t u t i n g (8) and (9) i n t o equation (7)
.
and s o l v i n g e q u a t i o n (10) f o r P gives HF
c
I
8
PHF can b e e v a l u a t e d s i n c e a l l t h e o t h e r q u a n t i t i e s are known.
values f o r P
HF
The
then can be s u b s t i t u t e d i n t o equation (8) and t h e P H2
determined.
(4) Using t h e measured c e l l p o t e n t i a l (E) and t h e p a r t i a l pres) the corrected cell p o t e n t i a l was then
s u r e s of HF (PHF) and H2 (P
H2 c a l c u l a t e d by
D
H2
RT
EC
=E+-Rn2F
D2 A
The c e l l p o t e n t i a l
.
HF
E w a s recorded a f t e r gas e q u i l i b r a t i o n w i t h t h e
m e l t w a s accomplished, and t h e m e l t temperature w a s c o n s t a n t .
18
Gi
Systematic Errors The preceding method of c a l c u l a t i n g p a r t i a l p r e s s u r e s does n o t i n clude c o r r e c t i o n s f o r t h e d i f f u s i o n of H
2
t
through t h e w a l l s of t h e
n i c k e l r e a c t i o n v e s s e l , nor does i t consider t h e e f f e c t of thermal d i f fusion.
M e l t p u r i t y and composition should a l s o be considered as
sources of s y s t e m a t i c e r r o r s . Hydrogen Diffusion.--
According t o published d i f f u s i o n coef-
f i c i e n t s , 1 4 t h e d i f f u s i o n of H2 out of t h e n i c k e l r e a c t i o n vessel could b e a few m i l l i l i t e r s p e r minute a t e l e v a t e d temperatures.
The
r a t e of H d i f f u s i o n w a s measured experimentally by Mathews and Baes 2
i n a v e s s e l s i m i l a r t o t h e one used i n t h e p r e s e n t experiment. obtained t h e following rates: 6OO0C, 0.015 ml/sec.
Extxapolatioh of t h e s e measurements t o 8OOOC and
Typically emf experiments were conducted with a H
rate of 2.5 ml/sec.
They
7OO0C, 0.035 ml/sec; 65OoC, 0.025 ml/sec;
900째C y i e l d s d i f f u s i o n rates of 0.055 ml/sec and 0.075 m l / s e c , spectively.
7
re2 flow
This means t h a t t h e measured volume of H would 2
be i n e r r o r by 0.6% a t 6OO0C, 1.40% a t 7OO0C, 2.20% a t 800째C, and 3.00%
a t 900OC.
These e r r o r s i n p a r t i a l p r e s s u r e s would cause t h e c a l c u l a t e d
p o t e n t i a l t o be about 1.0 mV lower a t 7OO0C, 1.5 mV lower a t 800째C, and 2.0 mV a t 900째C.
As mentioned p r e v i o u s l y , t h e HF-H2 mixtures w e r e
analyzed b e f o r e and a f t e r e n t e r i n g t h e HF-H
2
e l e c t r o d e compartment, and
no discrepancy between t h e two could be detected.
These analyses were
performed p e r i o d i c a l l y on a l l compositions up t o .60 BeF and tempera2 t u r e s up t o 700OC.
?
Melts of h i g h e r BeF2 concentrations were n o t check-
ed i n t h i s manner because d i f f i c u l t y w a s encountered i n keeping t h e flow rate constant through t h e s e high v i s c o s i t y m e l t s when t h e s p l i t
1c
bi
19 flow technique w a s a t tempted. Since the H
2
d i f f u s i o n e f f e c t w a s not observed a t temperatures up
t o 7OO0C, the e r r o r s c a l c u l a t e d above seem t o b e somewhat high. Thermal Diffusion.--
Recognizing t h e p o s s i b i l i t y t h a t H2 and HF
might tend t o s e p a r a t e along t h e thermal g r a d i e n t i n t h e r e a c t i o n v e s s e l , w e c a r r i e d o u t an experiment t o see i f t h i s e f f e c t w a s s i g n i f i cant. The t o t a l flow of HF-H2 p a s s i n g through t h e HF-H
v a r i e d between 23 ml/min and 160 ml/min.
2
electrode was
The c e l l p o t e n t i a l i n c r e a s e d
by about one m i l l i v o l t over t h i s range; t h e i n c r e a s e i n c e l l p o t e n t i a l over t h e range of flow rates where p o t e n t i a l measurements were a c t u a l l y made (100-160 ml/min) w a s less than 0.3 m i l l i v o l t .
This i s thought t o
b e s u f f i c i e n t evidence t h a t t h e thermal d i f f u s i o n e f f e c t w a s not s i g *
=
n i f icant. I '
8 '
Gas Cooling E f f e c t on Electrodes.--
The experiment mentioned above
a l s o i n d i c a t e s t h a t cooling of t h e e l e c t r o d e s by gas flow could n o t have caused more t h a n a one m i l l i v o l t e r r o r i n t h e p o t e n t i a l measurements.
It w a s f e l t t h a t although t h e p o s s i b i l i t y of a s m a l l e r r o r in
p o t e n t i a l might r e s u l t from flow rates of 100-160 ml/min, vigorous agit a t i o n of t h e m e l t w a s necessary t o reduce the e f f e c t of thermal gradients i n the m e l t .
Melt Composition.--
A composition e r r o r which w a s discovered a t
t h e end of run No. 4 w a s a p p a r e n t l y caused by d i s t i l l a t i o n of BeF2 t o I
>
_
*
c o o l e r regions of t h e apparatus. 3
W ,
I n t h i s p a r t i c u l a r run, many a t t e m p t s
were made t o measure t h e c e l l p o t e n t i a l of pure BeF over a temperature 2 range of 800째C t o 900째C.
A t t h e s e e l e v a t e d temperatures t h e vapor
20
p r e s s u r e of BeF2 is a p p r e ~ i a b 1 e . l ~Evidently l o s s of BeF2 occurred during t h e p e r i o d s a t h i g h temperatures.
Subsequent a d d i t i o n s of LiF
w e r e made t o b r i n g t h e BeF composition down t o 0.90 BeF2, 0.80 BeF2, 2 0.70 BeF2, and f i n a l l y t o 0 . 3 3 BeF2.
The e r r o r w a s discovered a t 0 . 3 3
BeF s i n c e t h e p o t e n t i a l s d i d not correspond t o previous measurements. 2 A t t h i s p o i n t enough BeF. w a s added t o b r i n g t h e composition up t o a
2.
book value of 0.40 BeF temperature. LiF-BeF
2
2
p e r m i t t i n g thermal a n a l y s i s of t h e l i q u i d u s
Thermal -a n a l y s i s w a s c a r r i e d o u t and compared w i t h t h e
l i q u i d u s d a t a . l6 R e s u l t s i n d i c a t e d t h a t t h e t r u e composition
w a s 0 . 3 8 8 BeF2.
Assuming t h a t a l l or most of t h e BeF2 w a s l o s t b e f o r e
t h e L i F a d d i t i o n s w e r e begun, t h e compositions a t 0.90, 0.80,
and 0.70
BeF w e r e reduced t o 0.896, 0.791, and 0.686 BeF2, r e s p e c t i v e l y . 2 in E
C
i n t h e 0.60 BeF
2
Changes
t o 0.80 BeF2 regions are s m a l l ; t h u s , t h e compo-
s i t i o n e r r o r a t t h e s e concentrations should n o t b e s i g n i f i c a n t .
ever, t h e v a l u e s obtained f o r 0 . 3 3 BeF
2
How-
i n t h i s run w e r e more s e r i o u s l y
a f f e c t e d by t h e u n c e r t a i n t y i n composition and were n o t used. M e l t Impurities.--
Early i n t h e experimental work i t w a s found
t h a t commercial BeF2 which contained about 1000-2000 ppm s u l f u r and 1000 ppm t o t a l of Fe, C r , Cu, and N i caused "poisoning" of both electrodes.
The c e l l p o t e n t i a l would decay as much as 0.5 v o l t s .
Spectro-
graphic examination of t h e Be e l e c t r o d e showed t h a t Fe, C r , and N i had been reduced on t h e s u r f a c e of t h e e l e c t r o d e ; a l s o metallic i m p u r i t i e s o r i g i n a l l y i n t h e beryllium m e t a l w e r e much h i g h e r i n c o n c e n t r a t i o n on t
t h e e l e c t r o d e s u r f a c e a f t e r exposure t o t h e m e l t . Mn, and T i , t h e most abundant one being aluminum.
These included A l , 1
21 The platinum gauze on t h e HF-H2 e l e c t r o d e w a s darkened by exposure t o t h e s e contaminated m e l t s .
This e f f e c t w a s n o t pursued s i n c e i t w a s
a l r e a d y e v i d e n t t h a t BeF2 with t h e i m p u r i t i e s mentioned above w a s not 3
s u i t a b l e f o r use w i t h t h e beryllium e l e c t r o d e . D i s t i l l e d BeF2, containing only trace amounts of i m p u r i t i e s , w a s t e s t e d ; and none of t h e problems mentioned above were encountered.
This
material w a s used f o r a l l measurements i n t h i s i n v e s t i g a t i o n . Oxide Contamination of M e l t . - -
The oxide chemistry of LiF-BeF2
mixtures must b e considered s i n c e t h e r a w materials c o n t a i n s m a l l amounts of moisture, and s i n c e beryllium oxide is an impurity i n beryllium metal.
Moisture contamination of t h e m e l t w a s kept t o a minimum
by f r e e z i n g t h e mixtures p r i o r t o a d d i t i o n s of r a w materials.
Beryl-
l i u m f l u o r i d e w a s s t o r e d i n a dry box p r i o r t o use.
A s t a n d a r d p u r i f i c a t i o n procedure f o r removing oxides17 from f luo-
r i d e mixture is HF-H2 sparging.
This procedure w a s used throughout t h e
p r e s e n t i n v e s t i g a t i o n t o remove oxide i m p u r i t i e s from t h e m e l t s . tinuous use of HF-H
2
Con-
as one of t h e e l e c t r o d e materials undoubtedly k e p t
t h e oxide c o n c e n t r a t i o n s m a l l .
T y p i c a l l y , b e r y l l i u m m e t a l contains a-
bout 1000 t o 4000 ppm oxygen.’*
Using t h e l a r g e r v a l u e f o r oxide con-
tamination, ‘the m a x i m u m c o n c e n t r a t i o n of oxide c o n t r i b u t e d by t h e b e r y l I
lium e l e c t r o d e would have been 1 x
moles/kg, which is about one
o r d e r of magnitude below t h e s o l u b i l i t y of Be0.l’
Therefore, no s i g -
n i f i c a n t e r r o r i s expected due t o oxide contamination of t h e m e l t by a d d i t i o n of r a w materials o r from t h e m e t a l e l e c t r o d e .
22 Summary.-
The only known s y s t e m a t i c e r r o r s t h a t might b e s i g n i f i -
c a n t are t h o s e a t t r i b u t e d t o H
2
d i f f u s i o n and gas cooling of the
L4 *
These are o p p o s i t e i n e f f e c t , and both are expected t o b e
electrodes.
f.
w i t h i n t h e experimental scatter of t h e data. Random E r r o r s I n o r d e r t o o b t a i n a s a t i s f a c t o r y estimate of t h e expected prec i s i o n of t h e experimental measurements, t h e v a r i o u s random e r r o r s and t h e i r probable magnitude w e r e considered. P r e c i s i o n of P o t e n t i a l Measurements.-t e n t i a l f l u c t u a t i o n s were about
5
0.2 mV f o r mixtures up t o 0.60 BeF
These f l u c t u a t i o n s i n c r e a s e d t o about However, even a t t h e h i g h e r BeF
2
Typically s h o r t term po2'
2 1.0 mV f o r 0.90 BeF2 mixtures.
c o n c e n t r a t i o n s , t h e average v a l u e of
t h e p o t e n t i a l d i d n o t change more than
2
1.0 mV over a p e r i o d of one t o
two hours. Melt Temperature.--
+ 0.2OC.
The temperature of t h e m e l t w a s c o n t r o l l e d t o
The temperature g r a d i e n t i n t h e m e l t v a r i e d from about 2째C i n
m e l t s up t o 0.60 BeF2, t o a maximum of 9째C i n 0.90 BeF2.
However, care
w a s taken during each p o t e n t i a l measurement t o p o s i t i o n t h e thermocouple i n t h e m e l t so t h a t i t coincided w i t h i n rode depths. no more t h a n
If 1/8-in. of t h e elect-
This should have reduced t h e temperature u n c e r t a i n t y t o
2 0.5OC,
which corresponds t o an u n c e r t a i n t y of
5 0.4
mV
i n the potential. M e l t Composition.--
The LiF-BeF
2
mixtures w e r e prepared by adding
weighed amounts of t h e components t o t h e r e a c t i o n v e s s e l .
c i s i o n of weighing and t r a n s f e r r i n g materials t o t h e v e s s e l w a s about
+ 0.2%.
*
The preI
di
23
Commercial lN NaOH i n one q u a r t b o t t l e s w a s
T i t e r Precision.--
s t a n d a r d i z e d w i t h potassium a c i d p h t h a l a t e .
Agreement of t h e standard-
i z a t i o n values w a s about f.0.1% of t h e average value. i n b u r e t t e readings during HF t i t r a t i o n s w a s about Temperature of Bubble-0-Meter.--
The u n c e r t a i n t y
2 0.5%.
The Bubble-0-Meter
temperature,
which w a s t h e temperature of t h e gas as i t s volume w a s being measured, v a r i e d no more than & 0.1OC during a given experiment.
The same tem-
p e r a t u r e v a r i a t i o n a p p l i e s t o t h e t i t r a t i o n vessel where t h e H2 w a s s a t u r a t e d w i t h water.
~
Flow Rate Determination.--
rates w a s 0.1 s e c p e r 100 m l .
The p r e c i s i o n i n t h e timing of H2 flow For a t y p i c a l v a l u e of 50 seconds p e r
100 m l , t h i s would amount t o 0.2%. The p r e c i s i o n i n timing of t h e endpoints w a s
Endpoint Precision.--
about f. 0.3% of t h e measured value. H2 and HF Flow Rates.--
t h e measured value.
of HF.
2
flow r a t e w a s c o n s t a n t a t
2 0.1% of
Successive HF t i t r a t i o n s v a r i e d as much as & 1.0%
from t h e average value. I
The H
This was apparently due t o i r r e g u l a r flow rates
The v a r i a t i o n w a s random and no b i a s w a s noted.
The e r r o r in-
volved i n HF flow rate is much greater than any of t h e o t h e r e r r o r s ass o c i a t e d w i t h t h e c a l c u l a t i o n of PHF; t h e r e f o r e t h e o t h e r s w i l l be considered negligible. S t a t i s t i c a l E r r o r Analysis The probable e r r o r t o be expected i n t h e c a l c u l a t e d c e l l p o t e n t i a l , E f
C
w a s determined from t h e estimated magnitude of random e r r o r s i n
v a r i o u s q u a n t i t i e s which appear i n eq. 3.
I f t h e c o n t r i b u t i o n of each
observable i s r e l a t e d t o a c a l c u l a t e d f u n c t i o n Q and expressed as
24
CJ Q = f (a,b,c----),
t h e c o n t r i b u t i o n of such e r r o r s can b e c a l c u l a t e d .
l a w a normal d i s t r i b u t i o n , i t can be shown2'
I f the errors fol-
t
t h a t t h e following equaf
t i o n allows f o r p a r t i a l c a n c e l l a t i o n of e r r o r s of opposite s i g n :
x2
aQ2 = (aa) a a 2
+
x 2ab2 + (ac) 3 2 2 U c + ....
(ab)
Applying t h i s r e l a t i o n t o
P EC
RT =E+-!LnnF
H2 2 'HF
gives -
(13)
HF
D i f f e r e n t i a t i o n of t h e above q u a n t i t i e s may be c a r r i e d out t o o b t a i n D
-a = EC
aE
1
-a=E c
alr
-a +E
~R
R =n H2 y
,
aT 'HF
and
-
= PB + AP PHF. (It may b e r e c a l l e d t h a t P H2 AP may b e neglected, t h u s , P = PB PHF) H2
-
For t h e p r e s e n t a n a l y s i s
.
The expected u n c e r t a i n t y of Ec can now b e c a l c u l a t e d by
t
25 I
i
Evaluating t h e above equation numerically f o r t h e u n c e r t a i n t y i n t h e c a l c u l a t e d p o t e n t i a l , using t y p i c a l p a r t i a l p r e s s u r e s of HF and H2 a t a temperature of 1000째K and using t h e estimated u n c e r t a i n t i e s of
+ 0 . 5 O C , & 0.001 o2
=
2 0.5
mV,
a t m r e s p e c t i v e l y i n E, T , and PHF, one o b t a i n s
(5 x 10-4)2
+
-4 2 -1 2 (8.95 x 10 ) (5 x 10 )
+
-3 2 (2.103)2(1 x 10 )
EC
a2
= (2.50
+
+
(2.00
4.42
103
EC
a2
=
4.87 x
=
+ .0022
EC (J i
i
E
C
volts.
The c a l c u l a t e d s t a n d a r d d e v i a t i o n of
2
2.2 mV i s s l i g h t l y l a r g e r t h a n
t h e s t a n d a r d d e v i a t i o n obtained from least squaring t h e a c t u a l data. The range of t h e s t a n d a r d d e v i a t i o n f o r t h e a c t u a l d a t a w a s about 1.0 mV t o 2.0 mV.
The major u n c e r t a i n t y i s i n t h e PHF term and is due t o t h e
l i m i t e d p r e c i s i o n of HF flow. 111.
RESULTS
Tabulation Table 1 contains t h e d a t a obtained from each experiment, arranged according t o m e l t compos i t ion. Experiments Four s e p a r a t e series of experiments were conducted during t h i s investigation.
The c e l l p o t e n t i a l of each m e l t composition w a s determined
26
f o r a range of temperatures.
I n the f i r s t series the r e a c t i o n vessel
w a s i n i t i a l l y loaded w i t h 0.33 BeF2.
Subsequent a d d i t i o n s of BeF w e r e 2
0.50 BeF2, and t o made t o b r i n g t h e c o n c e n t r a t i o n s up t o 0.40 BeF 2’ 0.60 BeF2. I n t h e second series t h e r e a c t i o n v e s s e l w a s i n i t i a l l y loaded with pure BeF
2’
enough LiF w a s then added t o g i v e 0.90 BeF2, 0.80 BeF2, 0.70
BeF2, 0.60 BeF2, 0.50 BeF2, 0.40 BeF2, and f i n a l l y 0.33 BeF2. o r two determinations w e r e made f o r 0.60 BeF
2
Only one
and lower BeF compo2
s i t i o n s s i n c e t h e s e were checks of previous measurements. Pure BeF w a s a l s o t h e i n i t i a l composition f o r t h e t h i r d series of 2 measurements.
S u b s e q u e n t a d d i t i o n s of L i F w e r e m a d e t o give 0 . 9 0 , 0 . 8 0 ,
0 . 7 0 , 0.60, and 0.33 BeF2. BeF
2
A s p r e v i o u s l y mentioned t h e d a t a f o r 0.33
w a s considered t o be i n e r r o r and w a s n o t used. I n t h e l a s t series of measurements t h e r e a c t i o n v e s s e l w a s loaded
i n i t i a l l y w i t h 0.33 BeF 2’
Enough L i F w a s added t o g i v e 0.30 BeF2; t h e n
BeF w a s added t o b r i n g t h e composition back t o 0.33 BeF2. 2 Corrected C e l l P o t e n t i a l s The c o r r e c t e d c e l l p o t e n t i a l s (E ) f o r v a r i o u s compositions are C
p l o t t e d as a f u n c t i o n of temperature and shown i n Fig. 5.
E
C
i s assumed
t o be a l i n e a r f u n c t i o n of temperature, Ec = A+BT, over the temperature
range i n v e s t i g a t e d .
The d a t a p o i n t s f o r each composition were least
squared, and t h e c a l c u l a t e d l i n e s are a l s o shown i n Fig. 5.
The para-
meters from t h e least squaring treatment are l i s t e d i n Table 2.
27
(YINL-DWG 67-137231
I
I
0.10 BeF, Q80. 0.90 &F2
600
650
700
600
650
Is0
650
100
100 ,150
800 TEMPERATURE CCI
750 800 850
800 850
900
850
900
950
Fig. 5. Correlation of Pressure Corrected Cell Potentials for Various Compositions as a Function of Temperature.
28
Table 1. Pressure Corrected C e l l P o t e n t i a l s (Ec) Obtained from Measurements i n Molten LiF-BeF, 'BeF
Temp. 2
("a
E (volts) C
0.30 0.30 0.30 0.30 0.30 0.30
585.1 646.0 696.2 732.0 609.2 681.0
1.8864 1.8447 1.8126 1.7882 1.8680 1.8213
0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
562.9 514.0 601.0 649.5 698.0 624.1 565 .O 720.8 529.0 617.2 617.2 550.0 624.5 671.0 812.0
1.8812 1.9152 1.8561 1.8230 1.7891 1.8397 1.8757 1.7653 1.9035 1.8436 1.8396 1.8857 1.8356 1.8016 1.7081
0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40
597.5 609.5 609.5 661.2 686.6 685.8 528.2 528.2 536.5 535.0 706.0 706.0
1.8069 1.8000 1.7991 1.7623 1.7430 1.7478 1.8578 1.8578 1.8540 1.8522 1.7337 1.7316
0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
632.8 561.5 728.0 707.0 658.0 617.3 568.3 546.6 503-3 511.8
1.7516 1.8022 1.6765 1.6972 1.7340 1.7629 1.7991 1.8127 1.8467 1.8387
Temp. ("C)
E (volts)
0.50 0.50 0.50 0.50
608.5 613.1 685.2 681.0
1.7671 1.7648 1.7116 1.7163
0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60
637.0 566.5 735.0 637.0 591.1 521.0 591.0 591.0 521.2 710.0 709.0 662.0
1.7263 1.7856 1.6555 1.7283 1.7656 1.8160 1.7672 1.7667 1.8170 1.6760 1.6771 1.7128
0.70 0.70 0.70 0.70 0.70 0.70
760.0 706.5 609.6 562.0 663.0 794.9
1.6310 1.6736 1.7477 1.7844 1.7085 1.6079
0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80
800.4 751.0 656.5 632.5 704.9 754.0 681.0 633.5 611.5 639.7 887.5 810.0 735.4 663.0 616.0 814.1
1.6027 1.6335 1.7132 1.7252 1.6725 1.6321 1.6907 1.7205 1.7484 1.7206 1.5304 1.5967 1.6482 1.7051 1.7387 i.5909
XBeF
2
C
h3
1
XBeF
2 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90
Temp.
Ec ( v o l t s )
804.1 866.0 754.8 706.2 778.0 876.5 802.5 702.0
1.5819 1.5307 1.6208 1.6613 1.5996 1.5277 1.5905 1.6620
("a
t
?
, 29
Table 2.
Parameters from Correlation of E as a Function of C
Temperature a t Specified Compositions (Ec = a+bT) 'BeF2
Intercept (a)
5u
5 u)x
(Slope
UEcx10 3 ( v o l t s )
(b 1
0.30
2.45212
0.0053
-
0.6607
0.0080
0.98
0.33
2.46021
0.0048
0.6944
0.0077
2.28
0.40
2.4258
0.0040
-
0.7091
0.0065
1.56
0.50
2.4179
0.0041
0.7369
0.0065
1.68
0.60
2.4162
0.0054
-
0.7537
0.0061
1.98
0.70
2.4226
0.0049
0.7643
0.0071
1.42
0.80
2.4149
0.0072
-
0.7595
0.0101
3.28
0.90
2.4296,
0.0162
-
0.7861
0.0205
3.54
~~
~
IV.
DISCUSSION
Thermodynamics of LiF-BeF2 The a c t i v i t y of BeF2 may be c a l c u l a t e d from eq. (4) using the emf d a t a (Ec) obtained i n t h i s study i f t h e a p p r o p r i a t e values f o r t h e s t a n d a r d c e l l p o t e n t i a l (Eo) are known. 0
a1 attempts w e r e m a d e t o determine E
As mentioned previously, sever-
experimentally, b u t values of use-
f u l accuracy could not b e obtained because of high m e l t v i s c o s i t y and p o s s i b l y because of high electrical r e s i s t i v i t y . The values of Ec obtained f o r v a r i o u s BeF2 compositions do not lend
themselves t o d i r e c t e x t r a p o l a t i o n t o E
0
.
However, t h e standard c e l l
p o t e n t i a l may b e c a l c u l a t e d by r e l a t i n g d a t a i n t h i s study w i t h the BeF2 l i q u i d u s d a t a i n t h e following manner. 0
I f t h e assumption i s made t h a t
t h e standard c e l l p o t e n t i a l (E ) v a r i e s l i n e a r l y w i t h temperature
30
(Eo = A+BT)*
E
LiJ
then eq. (4) may b e w r i t t e n
C
= (A+BT)
. . fin aBeF2
-E fin
0
aBeF2
2F[(A+BT) =
- Ec]
i
RT
It is t h e n p o s s i b l e t o equate eq. (15) t o
fin aBeF2 (BeF2 s a t ' n ) =
AHf 1 1 - -(R T - -1 Tf
(16)
(where AHf is t h e h e a t of f u s i o n of BeF2 and Tf i s the melting p o i n t of pure BeF ) t o o b t a i n a r e l a t i o n s h i p between A, B, AHf and E c a l c u l a t e d 2 C
a t t h e BeF l i q u i d u s temperatures and compositions. 2
Combining eqs. (15)
and (16).
2F[ (A+BT)
-
Ec] =
RT
-
AHf 1 -(R
T
1 - -Tf 1
which s i m p l i f i e s t o 2F Ec
--
T
-
(2FB
-
+
-)
(2FA
+ AHf)r1 .
Tf
This r e l a t i o n s h i p permits c o r r e l a t i o n of t h e d a t a (Ec) obtained i n t h e p r e s e n t i n v e s t i g a t i o n w i t h t h e phase diagram data.12
A p l o t of t h e a-
bove expression as 2FE /T vs 1 / T should b e l i n e a r s i n c e t h e i n t e r c e p t C
and s l o p e c o n t a i n only constants.
Using t h e least s q u a r e parameters f o r
each composition (Table 2 ) , v a l u e s f o r E
C
were c a l c u l a t e d f o r t h e
l i q u i d u s temperatures a t 0.515, 0.60, 0.70, 0.801and 0.90 BeF2 (see f o o t n o t e ) and t h e n p l o t t e d according t o eq. (17) (Fig. 6 ) .
The r e s u l t -
i n g p o i n t s follow t h e p r e d i c t e d l i n e a r r e l a t i o n s h i p w i t h i n t h e i r pre-
* Using
t h e h e a t c a p a c i t y d a t a i n t h e JANAF Tables (Ref. 21), t h e ACp e f f e c t over a temperature range of 450" 900째C w a s evaluated and found t o be n e g l i g i b l e .
-
z
31
dicted uncertainties. Intercept =
Parameters f o r t h
-
Slope = 113.84 The p o i n t a t 0.90 BeF
2
0.03805
least squared l i n e are:
5 0.0034,(Kcal/'K)
5 2.48 ,(Kcal)
= 2FA
= 2FB
+ AHf
-AH
(18)
Tf (19)
w a s n o t used because the u n c e r t a i n t y i n E
C
is
relatively large. Values f o r A and B were c a l c u l a t e d using v a r i o u s l i t e r a t u r e values f o r t h e h e a t of f u s i o n of BeF2 and a melting p o i n t of 555째C f o r pure BeF2.
A t a b u l a t i o n of t h e s e v a l u e s is shown i n Table 3.
The v a l u e s of
A and B which are c o n s i s t e n t w i t h v a l u e s obtained i n t h e p r e s e n t in-
v e s t i g a t i o n are those f o r which t h e h e a t of f u s i o n is assumed t o b e 2.0 kcal/mole o r less as shown i n Fig. 7.
A heat of f u s i o n f o r BeF2 >2.0
kcal/mole y i e l d s v a l u e s of Eo which are g r e a t e r than corresponding v a l u e s of Ec a t t h e h i g h e r BeF2 concentration.
This c r e a t e s an impossible
s i t u a t i o n where t h e a c t i v i t y of BeF i n t h e mixture is g r e a t e r t h a n t h e 2 a c t i v i t y of pure l i q u i d BeF2.
Thus measurements i n t h e p r e s e n t study
c l e a r l y support t h e lower v a l u e s f o r t h e h e a t of f u s i o n f o r BeF
8 99 2'
The e m f data (Ec) obtained i n t h e p r e s e n t study w e r e f i t t e d by
least s q u a r e s t o t h e expressions l i s t e d i n Table 4 , using t h e lowest l i t e r a t u r e v a l u e (1.13 kcal/mole) f o r t h e h e a t of f u s i o n of BeF2. p l o t of t h e smoothed l i n e s f o r E shown i n Fig. 8.
C
A
a t v a r i o u s BeF c o n c e n t r a t i o n s i s 2
The p r e s s u r e c o r r e c t e d c e l l p o t e n t i a l s (E ) d i f f e r e d C
by 1.4097 s t a n d a r d d e v i a t i o n s from t h e smoothed v a l u e s given by eq. 4-1 (Table 4 ) , and t h e average d e v i a t i o n of Ec from smoothed v a l u e s w a s approximately
2
2.5 mV.
The average d e v i a t i o n is c o n s i s t e n t w i t h the
v a l u e p r e d i c t e d by t h e e r r o r a n a l y s i s f o r E
C
.
32
ORNL- DWG 67-13722
I
a14t
a5t5 Be5
0.13t
/
7
0.t2c
elu"
h
v
LL (u
0.110
0.100
0.090
I
1.20
1.25
1.30
t .40
1.35
1.45
t.50
t.55
looo/TPK)
Fig. 6. Correlation of E C
with BeF2 Liquidus Data.
,-
33
ORNL-DWG 68-230
1.825
5
1.800
1.775
v)
4-
Y
1.750
lu" L3
2 1.725 0
lu
A fff =2.00kcaI/mole' A Hf =5.80 kcal/mole
'
1.700
1.675
1.650 550
575
600
TI
625
650
675
700
T ("C)
Fig. 7. Effect of the Heat of Fusion of BeF2 in Determining Eo The solid lines represent Ec for various mole fraction (dashed lines). of BeF2.
4
U
34
Table 3.
Calculated Parameters f o r the Standard C e l l P o t e n t i a l of
Pure BeF2 (Eo = A
+ BT)
Assuming Various Values f o r the
Heat of Fusion of BeF2 Heat of Fusion of BeF2
(kcal/mole)
,(a>
0.70
2.4525
1.00
2.4460
1.13
2.4432
1.60
2.4330
2.00
2.4241
2.50
2.4135
5.80
2.3420
(a)
From eq. (19).
(b)
From eq. (18).
(b) Bx 10
-
Ref,
No.
.8065 .7986 .7952
9
.7829
8
.7725 .7594 .6730
7
35
Expressions f o r C e l l P o t e n t i a l s and A c t i v i t y
Table 4.
C o e f f i c i e n t s i n the LiF-BeF2 System
Eq. No.
i
c
-
2.3RT a 2F l o g xBeF2 -- 2F
4- 1
EC
4-2
Eo = 2.4430
4- 3
log'BeF2
4-4
L
(a)
= Eo
-
0.000795211
= (3.8780
(-40.7375
+
(94.3997
+
(-67.4178
l o g yLiF = 0.9384
-
(a>
2353.5)x2 T LIF
-
+
log'BeF2
+
-
36292. 81x3 LiF
84870.9
+
4 IXLiF
52923.5
5 IXLiF
232.08 T
+
(-36.9734
+
+
(126.0947
-
+
(-158.4173
+
(67.4178
14652.7)x2 BeF2 74588.5
+
T
3 IXBeF2
113592.3
4 IXBeF2
- 52923.5)x5 T BeF2
C a l c u l a t e d u s i n g a heat of f u s i o n f o r BeF2 = 1.13 kcal/mole.
36
ORNL-DWG 67- I3718
2.0(
1.9c
1.80
-n
c
> 0
lu" 1.70
\ \
1.60
\ t.50
500
600
700
800
i2
900
T ("C)
Fig. 8. Correlation of Pressure Corrected Cell Potentials Ec as a Function of Temperature Using Smoothed Parameters.
37
A Gibbs-Duhem i n t e g r a t i o n of t h e expression f o r y i
BeF2
Table 4 ) w a s
1..
c a r r i e d o u t t o g i v e t h e corresponding e x p r e s s i o n f o r yLiF (eq. 4-4, Table 4 ) .
The i n t e g r a t i o n c o n s t a n t f o r eq. 4-4 w a s determined by com-
p a r i s o n with yLiF v a l u e s derived from t h e l i q u i d u s d a t a l 2 and a h e a t of f u s i o n of 6.47 kcal/mole f o r LiF.
A more a c c u r a t e e v a l u a t i o n of t h e
i n t e g r a t i o n c o n s t a n t should b e p o s s i b l e when t h e h e a t of mixing measurements of Holm and Kleppa22 become a v a i l a b l e f o r t h e LiF-BeF2 system. Smoothed v a l u e s of yBeF2 are shown as a f u n c t i o n of composition a t s e v e r a l temperatures i n Fig. 9.
These r e s u l t s are c o n s i s t e n t w i t h t h o s e
obtained by Mathews and Baes7 over a composition range 0.30 t o 0.60 BeF 2' However, a t x
BeF2
> 0.60 t h e r e s u l t s are not i n agreement.
The v a l u e s
o b t a i n e d i n t h e p r e s e n t s t u d y are thought t o be t h e more r e l i a b l e s i n c e they are c o n s i s t e n t w i t h b o t h t h e phase d a t a and w i t h a low h e a t of c
f u s i o n f o r BeF 2' I
The previous measurements a t compositions > 0.60 BeF2
might be i n e r r o r because of d i f f i c u l t i e s i n mixing LiF-BeF
2
at high
BeF2 c o n c e n t r a t i o n s and because of t h e e f f e c t s of Be0 s a t u r a t i o n .
In
t h e p r e s e n t s t u d y i t was found t h a t a t 0.90 BeF2, a well-mixed m e l t w a s n o t o b t a i n e d u n t i l t h e temperature w a s raised above 8 5 0 째 C .
This pro-
cedure w a s followed f o r a l l h i g h BeF2 c o n c e n t r a t i o n s t o ensure proper mixing of the LiF-BeF2.
Another p o s s i b l e e r r o r i n t h e previous measure-
ments could have been t h e presence of Be0 as a s a t u r a t i n g s o l i d .
The
s o l u b i l i t y of Be0 might tend t o i n f l u e n c e t h e BeF2 a c t i v i t y more a t h i g h BeF
2
concentrations. The f r e e energy and h e a t of the c e l l r e a c t i o n (eq. 1 ) w e r e calcu-
3
ki
l a t e d assuming a h e a t of kusion f o r BeF2 = 1.13 kcal/mole.
These v a l u e s
combined w i t h t h e a v a i l a b l e thermochemical v a l u e s f o r HF21 w e r e used
38
ORNL-DWG 68- 231
h 1.0
0.8
t
hâ&#x20AC;&#x2122; 0.6
n
z
4
,p0.4 u
m
h
0.2
0.I 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
XBeF,
Fig. 9. Activity Coefficients in Molten LiF-BeF2 Mixtures.
1.O
39 t o d e r i v e t h e f r e e energy and h e a t of formation f o r l i q u i d BeF2 a t 900°K (Table 5).
Mathews and Baes7 measured t h e e q u i l i b r i u m q u o t i e n t f o r t h e
react i o n
I f eq. (20) i s combined with t h e r e a c t i o n i n eq. (1) t h e r e s u l t i n g rea c t i o n is
The f r e e energy and h e a t bf . t h i s l a s t r e a c t i o n thus could b e obtained by combining t h e two sets of measurements, and, s i n c e t h e thermochemical d a t a f o r H 0 are a c c u r a t e l y known, improved f r e e energy and h e a t s of 2 formation f o r Be0 could be c a l c u l a t e d .
These are shown i n Table 5.
The
preceding c a l c u l a t i o n s f o r BeF2 and Be0 w e r e made f o r a temperature of II
900°K.
Values f o r o t h e r temperatures were generated using t h e h e a t
c a p a c i t y d a t a i n t h e JANAF Tables.
21
Reference Electrodes Both e l e c t r o d e h a l f - c e l l s used i n t h e p r e s e n t i n v e s t i g a t i o n performed acceptably f o r use as reference e l e c t r o d e s , both being s t a b l e and
reproducible.
I
B e r y l l i u m Electrode
The BelBe”
e l e c t r o d e should work w e l l i n any m e l t containing beryl-
I
lium i o n s and no r e d u c i b l e c a t i o n s .
P o t e n t i a l f l u c t u a t i o n s due t o t h i s
e l e c t r o d e were masked i n t h e p r e s e n t study by t h e f l u c t u a t i o n s due t o t h e HF-H2 e l e c t r o d e , b u t should b e less t h a n
5 0 . 1 mV.
Beryllium e-
I B
W
l e c t r o d e s w e r e f a b r i c a t e d from t h r e e d i f f e r e n t batches of beryllium
metal and no d i s c r e p a n c i e s i n p o t e n t i a l s were noted when t h e e l e c t r o d e s
Formation Heats and F r e e Energies of BeF, and Be0
Table 5. Compound
Temp.
State
AHf (kcal/mole)
(OK)
AGf (kcal /mole) ~
BeF2
29 8
BeF2
800
. crys t .
BeF2
900
Liquid
BeF2
1000
Liquid
crys t
- 246.01
(-242.30
~~
2 2)22
- 244.75 -
243.12
(2 1.1)
242.54
- 234.39 - 215.50 - 211.90 - 208.47
(-230.98
2
2) 22
P
.
Be0
29 8
crys t
Be0
800
Cryst.
Be0
900
c r y st
Be0
1000
Cryst.
.
0
-
145.85
(-143.10
145.68 145.57 145.46
(2 1.5)
2 0.1)22
- 138.36 - 125.70 -
123.20 120.73
(-136.12
1.5)
2 0.1)
22
I
41
i
were interchanged.
Therefore, t h e e l e c t r o d e response does not appear t o
be a f u n c t i o n of a p a r t i c u l a r b a t c h of b e r y l l i u m metal. The b e r y l l i u m e l e c t r o d e does n o t appear t o be s u i t a b l e f o r s m a l l
c e l l compartments s i n c e m a s s t r a n s f e r causes t h e e l e c t r o d e t o become enl a r g e d due t o spongy d e p o s i t i o n of t h e B e metal, and e v e n t u a l l y e l e c t r i c a l s h o r t s develop between the e l e c t r o d e and t h e c e l l compartment w a l l .
HF-H
2
Electrode
The P t , HF,H2 IF- e l e c t r o d e should be a s u i t a b l e r e f e r e n c e e l e c t r o d e
i n any f l u o r i d e - c o n t a i n i n g m e l t where t h e r e i s no p o s s i b i l i t y of oxidat i o n by HF o r r e d u c t i o n by H2.
The s o l u b i l i t y of HF i n LiF-BeF2 i s
low23 (about 0.0003 mole f r a c t i o n f o r t h e p a r t i a l p r e s s u r e s of HF used i n t h i s s t u d y ) , and no s i g n i f i c a n t s o l u b i l i t y of H2 is expected i n t h i s system.
P o t e n t i a l f l u c t u a t i o n s due t o t h i s e l e c t r o d e appear t o be a
f u n c t i o n of t h e m e l t v i s c o s i t y .
F l u c t u a t i o n s a r e about
2
.1 mV i n m e l t s
w i t h a v i s c o s i t y of one p o i s e o r less. The p r e c i s i o n of t h i s e l e c t r o d e w a s l i m i t e d somewhat i n t h e p r e s e n t s t u d y by t h e method of HF d e l i v e r y , as previously mentioned.
In future
experiments t h e H -HF mixture w i l l b e obtained by p a s s i n g H through a 2 2 thermostated NaHF2 bed.
It is hoped t h a t t h i s w i l l be a more p r e c i s e
method of producing mixtures of HF and H2 of c o n s t a n t composition.
42
REFERENCES 1. W. R. G r i m e s , MSRP Semiann. Prog. R e p t . J u l v 31. 1964, ORNL-3708, p. 230.
12, -- 1073
2.
J. Berkowitz and W. A. Chupka, Ann. N. Y. Acad. Sci.,
3.
A. Buchler and J. L. S t a u f f e r , "Vaporization i n t h e Lithium FluorideBeryllium Fluoride System," SM-66/26 i n Thermodynamics, v o l . &, IAEA, Vienna, 1966.
4.
T. Fdrland, "Thermodynamics of Fused S a l t Systems," p. 156 i n Fused S a l t s , ed. by B. R. Sundheim, McGraw-Hill, New York, 1964.
5.
J. Lumsden, Thermodynamics of Molten S a l t Mixtures, p. 227, Academic P r e s s , London, 1966.
6.
A. Buchler, Study of High Temperature Thermodynamics of Light Metal Compounds, Army Research Office (Durham, N. C.) Progr. Rept. No.
9 (Contract DA-19-020-ORD-5584)
(1960)
Sept. 30, 1963.
-z,
7.
A. L. Mathews and C. F. Baes, Jr., J. Inor. Chem.,
8.
J. A. Blauer e t a l . , J. Phys. Chem.,
9.
A. R. Taylor and T. E. Gardner, Some Thermal P r o p e r t i e s of B e r y l l i u m Fluoride from 8" t o 1,200째K, U.S. Bureau of Mines, Rept. No. RI-6644 (1965).
$2, --
373 (1968).
1069 (1965).
10.
G. Dirian, K. A. Romberger, and C. F. Baes, Jr., Reactor Chem. Div. Ann. Progr. Rept. Jan. 31, 1965, Om-3789, pp. 76-79.
11.
C. T. Moynihan and S. Cantor, Reactor Chem. Div. Ann. Progr. Rept. D ~ c . 31, 1966, ORNL-4076, p. 25.
12.
R. E. Thoma e t a l . , submitted f o r p u b l i c a t i o n i n J. Nucl. Mat.
13.
Diaphragm Type Adjustable Leak Valve (Ref. No. C-I 244928) obtained from ORGDP, O a k Ridge, Tenn.
14.
S. Dushman, S c i e n t i f i c Foundations of Vacuum Technique, pp. 607-618, Wiley and Sons, N. Y., 1949.
15.
S.. Cantor e t a l . , Reactor Chem. D i v . Ann. Progr. R e p t . Dec. 31, 1965, ORNL-3913, p. 27.
16.
Temperature-Composition values used h e r e f o r t h e BeF l i q u i d u s were 2 supplied by S. Cantor of t h i s Laboratory.
bd
43
17.
J. H. S h a f f e r , MSRP Semiann. Prog. Rept. J u l y 31, 1964, ORNL-3708, p. 288.
18.
G. E. Darwin and J. H. Buddery, Beryllium, p. 85, Butterworths
S c i e n t i f i c P u b l i c a t i o n s , London, 1960.
I
c
19.
B. F. Hitch and C. F. Baes, Jr., Reactor Chem. Div. Ann. Propr. Rept. Dec. 31, 1966, ORNL-4076, p. 19.
20.
H. D. Young, S t a t i s t i c a l Treatment of Experimental Data, p. 96, M c G r a w - H i l l , New York, 1962.
21.
JANAF Thermochemical Tables, Clearing House f o r Federal S c i e n t i f i c and Technical Information, U.S. Dept. of Commerce, Aug., 1965.
22.
0. J. Kleppa, p r i v a t e communication.
23.
P. E. F i e l d and J. H. S h a f f e r , J. Phys. Chem.,
11, -- 3320
(1967).
45
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