Laboratory Report Materials Chemistry Laboratory Diffusion of Ag in Glass Yufei Chang • Group H
Abstract The aim of this experiment was to understand the diffusion behavior of silver ions by analysing the concentrations profile of silver ions at different depths from the original surface at a certain temperature. A piece of glass was placed in a molten salt with silver ions to allow ion exchange. By plotting the log C versus x2 graph, the diffusion coefficient of silver ions was calculated, which was then compared with the self diffusion coefficient of sodium ions. It was found that the diffusion coefficient of silver ions was smaller than that of sodium ions, and the temperature, the ionic radius, the valency as well as the activation energy have effects on the value of diffusion coefficient.
Introduction In industry, the exchange diffusion of ions is commonly used to introduce ions with different sizes and perhaps different valency into the glass structure in order to produce chemically toughened glass. In this experiment, a glass sample is immersed into a molten salt to allow the exchange of sodium ions with the bigger silver ions. Thus, upon cooling, this replacement of ions causes the surface of the glass to be in a state of compression and the core in compensating tension. The surface compression of chemically strengthened glass may reach up to 690 MPa. The exchange diffusion process is affected by the diffusion coefficient, which in turn is determined by several factors – the ionic radius, the temperature, the viscosity, and the activation energy. The relationship is given by the Stoke – Einstein equation 1: D = kT/6πηa Where k = Boltzmann’s constant, T = temperature in Kelvin, the media, and a = the radius of the species.
= the viscosity of
In the experiment, the value of the inter-diffusion coefficient is obtained from the concentration profile of Ag. The concentration of which is the highest on the glass surface, and gradually reduces as moves to the centre. According to the relation:
Where C = concentration of Ag, Co = the concentration of Ag at the surface, x = the depth from the original surface, D = diffusion coefficient, and t = the time allowed for the diffusion process. A plot of lnC versus x2 should show a straight – line behaviour, and the diffusion coefficient could be calculated either from the gradient or the interception of the line with the y-axis.
Experimental Procedure • • • • • •
• •
Measured the dimensions and weighed four pieces of glass samples. One glass sample, together with a Pt wire cradle was placed into an AgNO3KNO3 molten salt at 370oC for 17 minutes. Washed the sample with water and acetone and weighed it in the Pt wire cradle. Diluted to produce the 5wt % HF etching solution, and measured 20ml of the solution into each of the nine beakers. The sample was etched for 9 times, in which the first time took 3 mins whereas each of the rest took 1 min. The sample was weighed and washed using the method described before after each etch, the water used to wash the sample was added into the etching solution. Diluted each etching solution to 50ml and analysed the solutions using the spectrometer. The concentration of Ag in each of the etching solutions was obtained by the computer.
Result Sample No
Dimensions (m)
Weight (g)
Density (kg.m⁻³)
1
L=0.0259 W=0.0253 T=0.00111
1.7696
2455
2
L=0.0243 W=0.0256 T=0.00088
1.3083
2389.89
3
L=0.0257 W=0.0256 T=0.00098
1.515
2354.31
4
L=0.0259 W=0.0256 T=0.00089
1.444
2447.46
Average density is 2411.67 The surface area of the first sample is 6.5527×10⁻³ m² The first sample was etched for 9 times in HF solutions. The sample length and width are significantly bigger than its thickness, so it is assumed that during each etch the surface area of sample stayed the same with only the depth reduced. From which the depth reduced (d), values of x are calculated below, where x4 = d1 + d2 + d3 + 0.5d4. The first etch was not taken into account of the calculation process, because this process took 3 minutes and aimed to wash off the remaining salt on the glass surface. Table 2
Etch Number
Mass removed (kg)
Volume removed m³
Depth removed m
x/m
2
4.2×10⁻⁶
1.742×10⁻⁹
2.658×10⁻⁶
1.329×10⁻⁶
3
4.5×10⁻⁶
1.866×10⁻⁹
2.848×10⁻⁶
4.082×10⁻⁶
4
3.4×10⁻⁶
1.4098×10⁻⁹
2.151×10⁻⁶
6.582×10⁻⁶
5
3.6×10⁻⁶
1.493×10⁻⁹
2.278×10⁻⁶
8.796×10⁻⁶
6
3.2×10⁻⁶
1.327×10⁻⁹
2.025×10⁻⁶
10.9475×10⁻⁶
7
3.6×10⁻⁶
1.493×10⁻⁹
2.278×10⁻⁶
13.279×10⁻⁶
8
3.4×10⁻⁶
1.4098×10⁻⁹
2.151×10⁻⁶
15.314×10⁻⁶
9
3.4×10⁻⁶
1.4098×10⁻⁹
2.151×10⁻⁶
18.541×10⁻⁶
Table 3 Concentration 1/ppm
ln(concentration/ppm
0.3641
-1.0103267
0.3317
-1.1035243
0.2391
-1.430873405
x2/m2 1.77E-12
1.67E-11 4.33E-11
0.1042
-2.26144315
7.74E-11
0.0218
-3.825845309
1.20E-10
0.0054
-5.221356325
1.76E-10
0.0038
-5.572754212
2.35E-10
0.0024
-6.032286542
3.44E-10
Fig 1
According to Equation [1] ln C = ln [Cσ/(πDt)0.5] – ln [x2/(4Dt)] The gradient of the best fit line = – 2 x 1010 = – 1/(4Dt) t = 17 x 60 = 1020 s DAg = 6.13 x 10-15 m2s-1 at T = 370 oC Therefore, the diffusion coefficient D is worked out,which is 4.902*10-14m2s-1.
Discussion The reason why glass is doped with other ions is to improve its property. The manufacturing process and transportation might leave small surface defects on glass, which makes the glass surface under tension so that it is brittle and can not withstand large stress. When doping with bigger ions (such as in this case Na is substituted by Ag ions), thus, upon cooling the surface of glass is under compression, which toughen the glass.
According to Table 1, the densities of soda-lime glass samples vary by a big amount, because samples are not perfect squares, this is the reason why the average value is used in the calculation. In fact, the theoretical value for the inter -diffusion coefficient of Ag is much smaller than the value we got through the experiment. I think this is because some error involves during the experiment especially making mistakes in measuring the dimensions of the sample silica glass. If we compare the theoretical value for diffusion coefficient of Ag to the value with 2.4*10-14m2s-1 at 390℃for selfdiffusion coefficient of Na+ , DAg must be lower than DNa.. According to , a small increase in T will give a big rise in D. Our experiment was carried out at 370℃ and so experiment for self- diffusion coefficient of Na+ at 390℃ will give a higher value than DAg 's. Also, by theory, at a higher temperature, more ions have energy greater than the activation energy, as a result, there is a bigger driving force for ions to diffuse and hence a bigger diffusion coefficient is observed. The diffusion coefficient is inversely proportional to the ionic radius according to the Stokes-Einstein equation.D = kT/(6πηa) Na+ ion has one positive charge and its ionic radius is about 0.95Å. K+ has an ionic radius of 1.33Å which is much bigger than Na+ ion and this is the reason why Na+ ion can not exchange during the diffusion process. Ca2+ has a similar radius size compare to
Na+. However, Ca2+ ion has two positive charges but Na+ ion only have 1 and this makes it can not exchange Ca2+ during the diffusion process as well.
Conclusion After the experiment and some calculation, diffusion coefficient D is worked out to be 4.902*10-14m2s-1. In fact, the theoretical value of diffusion coefficient is quite a lot smaller than it. The main reason for this happen is due some error involve when measuring the dimensions of sample. Theoretically, however, Sodium ions have a higher diffusion coefficient when it is hold at 390℃ than silver ions when it is carried at 370℃. A small increase in T will give a big rise in D. Sodium ion can not exchange potassium ions this is because potassium ion is much larger than it. Because sodium ion only has one positive charge while calcium ions has tow so sodium ion can not exchange calcium ion as well.
Reference Labscript
1. “Atkins’ Physical Chemistry”, Peter Atkins, Julio De Paula, 8th Edition, p660. 2. “Atkins’ Physical Chemistry”, Peter Atkins, Julio De Paula, 8th Edition, p1017. The ionic radius of silver is obtained from http://www.absoluteastronomy.com/topics/Ionic_radius