Electrochemical methods for investigations in molten glass, illustrated at iron- and arsenic-doped soda-lime-silica glass melts

Journal of Non-Crystalline Solids 127 (1991) 197-206 North-Holland

197

Electrochemical methods for investigations in molten glass, illustrated at iron- and arsenic-doped soda-lime-silica glass melts Christian Rtissel a n d G e r o l d S p r a c h m a n n Universit~it Erlangen-Niirnberg, lnstitut fiir Werkstoffwissenschaften 111 (Glas und Keramik), Erlangen, Germany Received 18 May 1990 Revised manuscript received 18 September 1990

Electrochemical methods such as potentiometry, cyclic voltammetry, square-wave voltammetry, differential-pulse voltammetry and alternating-current voltammetry were applied to soda-lime-silica glass melts doped with Fe203 or A s 2 0 s. Square-wave voltammetry and alternating-current-voltammetry proved to possess the highest sensitivity and resolution although all standard potentials, corresponding to the reduction of As 5+ to As 3+ and to As °, or Fe 3+ to Fe 2÷, measured with the different voltammetric methods show good agreement. It is also shown in this paper that voltammetric methods are quite suitable for the determination of thermodynamic data such as A H ° and diffusion coefficients of polyvalent ions in molten glass.

I. Introduction Liquids of oxide glasses containing network modifiers are good ionic conductors at glass melting temperatures. Therefore, electrochemical methods developed for investigating aqueous solutions or organic electrolytes at room temperatures are applicable in glass liquids. For many years, it has been possible to measure the oxygen activity of a glass liquid [1-2] with the aid of sensors based on oxygen ion conducting solid electrolytes (mainly yttria stabilized zirconia) [3,4]. Over the past few years some potential-sweep voltammetric methods were applied to glass liquids. The first method used was cyclic voltammetry (CV) [5-8]. Square-wave voltammetry (SWV) [7-11], a fast pulse method, proved to have higher sensitivity and resolution than CV [7,8]. Besides these potentiodynamic methods, chronopotentiometry as a galvanostatic method was also used [12]. With the aid of voltammetric methods, it is possible, in principle, to investigate thermodynamic properties of polyvalent elements in molten glass and to determine their diffusion coefficients. It should be noted that the most non-electrochem-

ical methods, e.g. spectroscopic methods, are not appropriate at these temperatures. Voltammetric methods are also suitable for the quantitative in situ determination of polyvalent ions in molten glass [9]. In this paper, electrochemical methods such as potentiometry, cyclic voltammetry, square-wave voltammetry, differential-pulse voltammetry and alternating-current voltammetry are applied to soda-lime-silica glass melts doped with Fe203 or As205. This is the first reported use of the last two methods, being applied to glass liquids.

~. Experimental The electrochemical cell was the same for all methods and has already been described in detail [7-9]. Three electrodes are inserted into a glass melt. The working electrode is a platinum wire, the counter electrode is a platinum plate with a size of around 2 cm 2, and the reference electrode is a zirconia probe with air as reference gas (for a detailed description, see refs. [3,4]). All potentials

0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)

198

C. Riissel, G. Sprachmann /Electrochemicalmethodsfor investigations in molten glass

3. Theory I

//1"

I

I

i

"%

i

_ nf-II

\

[-]

\

\

\

Polyvalent ions in a molten glass are in equilibrium with physically dissolved oxygen: X

"-.

I

r" OJ 0 r~

time Fig. 1. Potential-time dependence of various electrochemical methods. (a) cyclic voltammetry; (b) square-wave voltammetry; (c) differential-pulse voltammetry; (d) ac voltammetry.

Me x+~ + n / 2 0 2- /~ Me x + n / 4 02,

(1)

where n is the number of electrons transferred, 02 is physically dissolved oxygen, and Me x+n, Me x indicate the polyvalent ion in its oxidized and in its reduced state. The equilibrium according to eq. (1) is shifted to the left when the temperature is decreased. The equilibration of a glass melt with a gas atmosphere is due to diffusion and therefore it is a relatively slow process. If the cooling of a melt is quick enough, its oxygen activity will decrease considerably, due to a decreasing equilibrium constant, K ([O 2-] can be assumed to be approximately constant, if the equilibrium is shifted or the temperature is changed):

K

=

e -AG°/RT

~

e AS°/R e -AH°/RT

[Me*l

= ( a 0 2 ) n / 4 [MeX+,] ,

mentioned in this paper are referred to this electrode. The main part of the electronic equipment is the potentiostat. In principle, it is an operational amplifier adjusting the voltage between working and counter electrode in such a manner that the potential between working and reference electrode is equal to any required value. The potential-time dependence applied to the electrodes is different for each method (see fig. 1). In the case of cyclic voltammetry and squarewave voltammetry, electronics were self constructed and the potentiostat was connected via an analog/digital and a digital/analog converter to a microcomputer giving the potential-time dependence and recording the current. In the case of alternating-current voltammetry and differentialpulse voltammetry, a commercially available polarograph (Brucker Inst. E 310) was used. All experiments were carried out in a model glass melt with the basic composition of 74 mol% SiO 2, 16 mol% N a 2 0 , 10 mol% CaO, which was modified by adding FezO 3 or As205.

(2)

where AG o is standard free enthalpy, A H ° is standard enthalpy and AS ° is standard entropy. If the concentration of the polyvalent ion is large (Me20 x > 0.25 mol%), the redox ratio [MeX]/[Me ~+"] will remain constant because the concentration of physically dissolved oxygen is very small [13]:

AS°(T2)-aS°(T,) 4""t"°2 /"o2 : =

R

RT,

+

RT2

(3) It should be stated that, by contrast with [O2-], A H ° and AS ° can not, a priori, be assumed to be independent on temperature. From voltammetric methods, standard potentials, E 0, of redox pairs can he obtained: eo Me x+" + n e - ~ Me ~.

(4)

C Riissel, G. Sprachmann / Electrochemical methods for investigations in molten glass

If their standard potentials are measured against a zirconia/oxygen probe, they can be simply related to AG O and K of eq. (1):

AG°(T) = -nFEo(r ) = -RT

In K.

C

l?!~'~~""/b

0.5

(5)

The electrochemical behavior of Fe203- and As2Os-doped glass melts is already known from literature [7,8]. Iron may occur in glass melts as Fe 2+ or Fe3+: Fe3++ e - ~

Fe 2+.

_-

0

-0.5

- -. -.

b

(6) i

As205 exists predominantly in the oxidation states: As 5+ and As 3+, but if the glass melt has been treated with strong reducing agents, the oxidation state As ° may also be present [7,8]: AS

5 + 2e

199

e As 3+ 3~As °

-I000

-800

i

-600

i

i

-400

-200

E/mV

Fig. 3. Theoretical cyclic voltammogram for (a) one-, (b) twoand (c) three-electron step (0 = 1100° C).

(7)

4. Results and discussion

4.1. Potentiometry The potential difference between a large platinum grid and a zirconia electrode was measured as a function of time. At the initial temperature of 1350 o C, the melts were nearly equilibrated with air. Then the temperature was varied as shown in fig. 2. The cooling rate was rather high ( 2 0 ° C / m i n ) to avoid equilibration effects with

the gas atmosphere. Figure 2 shows the potential-temperature dependence measured in a glass melt doped with 0.5 mol% Fe203 and a glass melt doped with 0.5 mol% As205. A good linear correlation can be observed. It should be noted that in previous investigations [13-15] the same linear correlation between E and T has been observed. The oxygen activity can be calculated from the potential using eq. (8):

RT

E = --ln 4F

ao2 --, Po2

(8)

where Po2 is oxygen partial pressure of the reference gas (air p% = 0.21 bar) and ao~ is oxygen activity of the glass melt.

4.2. Cyclic voltarnmetry

0

2~

-200

-t~0( ./

I

i

600

800

i 1000

i 1200

I/.00

a}/°E Fig. 2. Experimental potential-temperature dependence of soda-time-silica glass melts doped with 0.5 tool% We203

(

) and 0.5 mol%A S 2 0 5

(-- --

--).

In this method a triangular potential-time dependence is applied to the working electrode (see fig. 1, graph a). The potential is scanned linearly from an initial value of 0 V to a negative value and then back again. Cyclic voltammetry is a very good method for application at room temperature. At glass melting temperatures, the signals are quite broad. Figure 3 shows cyclic voltammograms theoretically calculated [16] for a one-, a two- and three-electron transfer reaction at 1100 ° C. For all curves, an anodic and a cathodic peak potential can be seen. The mean value of these peak potentials is equal to the standard potential E 0 of the

200

C. Riissel, G. Sprachmann / Electrochemicalmethods for investigations in molten glass

C .<

0

-1 -2

-2 I

-800

I

i

-~00

-600

-4,

I

-200

j

I

-800

I

-600

I

-400

-200

0

0 ElmV

-

-

E/mY

=-

Fig. 4. Cyclic voltammogram for a soda-lime-silica glass melt

doped with 1 mol% Fe203 (@ = 1100o C, v = 1 V/s).

redox reaction. The peak separation AEp decreases with increasing n u m b e r of electrons transferred [17]: AEp -- 2 . 2 R T / n F .

(9)

Figure 4 shows an experimental cychc voltamm o g r a m recorded at 1100 ° C in a glass melt d o p e d with 1 mol% Fe203. Instead of a definite, well p r o n o u n c e d cathodic peak, only a plateau can be seen. On further decreasing the potential, the current decreases slightly again, due to cathodic decomposition of the silicate glass, forming elementary silicon or platinum-silicide at the electrode surface. During the anodic scan, the current increases again and reaches a m a x i m u m at - 3 9 0 mV. F r o m the estimated cathodic peak potential of - 7 0 0 mV, the standard potential of - 5 4 5 mV can be calculated. Figure 5 shows an experimental cyclic voltamm o g r a m recorded in a glass melt doped with 1 mol% A s 2 0 ~. For the cathodic scan, a m a x i m u m at - 4 4 0 mV can be seen, but the current also increases in the region from 0 to - 3 0 0 mV. For the anodic scan, a well p r o n o u n c e d peak at - 2 9 0 mV and a very b r o a d peak at about - 100 mV can be observed. The cathodic peak and the peak at - 2 9 0 mV correspond to the same reduction step, the reduction of As 3+ to metallic arsenic. F r o m the peak potentials, a standard potential of - 3 6 5 mV can be calculated. The shoulder of the cathodic scan and the b r o a d anodic peak at about - 1 0 0

Fig. 5. Cyclic voltammogram for a soda-lime-silica glass melt doped with 1 tool% As20s (,9 = 1100o C, v = 1 V/s). mV are both related to the first step, the reduction of As 5 + to As 3+. 4.3. Square-wave voltammetry

The p o t e n t i a l - t i m e dependence of square-wave voltammetry can be described as a staircase ramp, superimposed b y ' a rectangular wave form of comparably high frequency ( 5 - 5 0 0 s - t ) and amplitude ( 5 0 - 1 5 0 mY) (see fig. 1, graph b). The current is measured at the end of every half wave and then differentiated. Figure 6 shows a theoretical c u r r e n t - p o t e n t i a l curve calculated for a one-, two-

15

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10 E

b

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5

!/

~.I

i

J

-0.6

~1

k~,\

a

-0,4.

-0.2

0

E/V

Fig. 6. Theoretical square-wave voltammograms for (a) one-, (b) two- and (c) three-electron step (0 = 1100o C).

201

C. R~sel, G. Sprachmann / Electrochemicalmethodsfor inoestigations in molten glass

and three-electron step. Well pronounced peaks can be seen; the peak currents Ip increase if more than one electron is transferred [18]: Ip = A D t /2 A E r - 1 / 2 n 2 C const.,

(10)

where ~- is pulse time, AE is pulse potential, D is diffusion coefficient, A is electrode area, C is concentration of the polyvalent ion and const.--0 . 3 1 F Z / R T , if AE < 0 . 5 R T / 2 F . The half width of the peak (Ep/2) decreases with increasing n:

E

2

0

i

-800

(11)

Eel 2 = aT/n,

where a - 0.30 m V / K Figure 7 shows an experimental square-wave voltammogram recorded at 1100°C in a glass melt doped with 1 tool% Fe203. A well pronounced peak at - 5 6 0 mV can be observed; the increase of the current at potentials lower than - 8 0 0 mV is due to matrix effects as already mentioned in section 4.2. Figure 8 shows an experimental square-wave voltammogram, recorded at l l 0 0 ° C in a glass melt, doped with 1 mol% As205. Two peaks can be seen: the first at - 1 4 0 mV corresponds to the first step of eq. (7), the reduction of As 5+ to As 3+. The second peak at - 3 7 0 mV corresponds to the second step of eq. (7), the reduction of A s 3+ to metallic arsenic. The ratio of the peak currents of the first and second reduction steps is nearly equal to 4 : 9 , a ratio

< 1

.

S

~

05

i

-890

i

-600

i

i

-400

-200

0

.EImV

Fig. 7. Square-wave voltammogram for a soda-lime-silica glass melt doped with 1 mol% Fe203 (@=ll00°C, AE =100 mV, r = 5 ms).

i

-600

i

i

-t.O0

-200

E/mV . . . . . . . Fig. 8. Square-wave voltammogram for a soda-lime-silica

glass melt doped with 1 tool% AS205 (0 =ll00°C, AE =100 mV, "r = 5 ms).

predicted from eq. (10), for a two- and three-electron step. 4.4. Differential pulse voltammetry

The potential-time dependence of differentialpulse voltammetry can be described as a potential ramp superimposed by potential pulses (see fig. 1, graph c). The duration of a pulse ~- is in the range of 10-100 ms, the time between two pulses is much longer, normally in the range of 0.5-2 s, and the pulse potential AE is 20-100 mV. The potential is scanned slowly at a rate of 5 to 20 m V / s . The current is measured immediately before and at the end of every pulse and then subtracted. This method was developed for electrochemical measurements at a mercury drop electrode. The theoretical current-potential curves are identical to those of fig. 6 and the standard potential is equal to the peak potential. Figure 9 shows an experimental differential-pulse voltammogram, recorded at 1100°C in a glass melt doped with 1 mol% F e 2 0 3 ('r = 5 ms, AE = 50 mV). The current begins to increase at a potential of - 1 0 0 mV and reaches a maximum at - 5 6 5 inV. A steep decrease of the current at - 6 8 0 mV is visible, which is not in accordance with theory and the theoretical current-potential curve. This steep decrease was observed for all differential-pulse voltammograms and could not be suppressed by the variation of experimental parameters such as scan rate,

202

C. Riissel, G. Sprachmann / Electrochemical methods for investigations in molten glass tial (Eat) and the current (Iac) at the peak potential, diffusion coefficients can be calculated: /p(aC) = n2F2A~ol/2DI/2CE, a c ) / R T , 0.6 E

\

0k,

0.2

I

-800

i

-600

i

i

-~-00

-200

ElmV

=-

9. Differential-pulsevoltammogramfor a soda-lime-silica glass melt doped with 1 mol% Fe203 (~=1100°C, AE ~ 50 mY). Fig.

A E and T. U p o n further decreasing the potential, the current increases again due to the decomposition of the glass matrix.

(12)

where ~0 = 2vf, and f is the frequency of the alternating potential. Figure 10 shows an experimental alternatingcurrent voltammogram, recorded at 1215°C in a glass melt doped with 1 tool% Fe203. The curves represent measurements at different frequencies in the range 11.6-1160 s -1. At higher frequencies, the shape of the curve changes. This effect is due to the increasing influence of the capacitance caused by the electrochemical double layer. At a frequency of 1160 Hz charge currents dominate Faradaic effects. At lower frequencies, the peak potentials are nearly identical to those measured by square-wave voltammetry. Figure 11 shows an experimental alternating-current voltammogram, recorded at 1120°C in a glass melt doped with 1 mol% As205. Two peaks are visible, corresponding to the reduction of As 5+ to As 3+ to As ° according to eq. (7). The frequency dependence of the currents for the first reduction step is shown in fig. 12. At comparably low frequencies, a good linear

4. 5. Alternating-current ooltammetry Figure 1, graph d shows the potential-time dependence of ac voltammetry. A potential ramp is superimposed by a sinusoidal alternating-potential with a frequency in the range of 10-2000 s -1 and an amplitude of 20-100 mV. Depending on the frequency and due to capacitive effects, the phase angle between the alternating potential and the alternating current deviates from zero. In principle, two kinds of measurements are possible: the current can be measured either at a phase angle of 0 o or 90 o. The current at 0 o is predominantly affected by Faradaic effects, while the current at 90 ° is mainly influenced by capacitive effects. The theoretical current-potential curves are identical to those shown in fig. 6, the peak potential is equal to the standard potential of the redox reaction. From the amplitudes of the poten-

h "~ 0.3 9 0.2 e

d 0.1

0

C

I

]

I

I

-800

-600

-400

-200 E/mY

=

Fig. 10. Alternating-current voltammogram for a soda-limesilica glass melt doped with 1 mol% Fe203 at 1215o C (Eac= 30 mV). (a) 11.6 s-l; (b) 17 s-i; (c) 35 s-l; (d) 77.5 s-l; (e) 116 s-l; (f) 170 s-l; (g) 350 s-l; (h) 775 s-l; (i) 1160 s -1.

C. Ri~sel, G. Sprachmann

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Electrochemical methods for investigations in molten glass 0.8 X~

-o

/O"

0.6~ i

~

0

E

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O ~

,,,'

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•

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1

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-400

-200

0

ElmV

--

:"//~ U 0 • ,,"11/

0.2

-600

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4 0

---

Fig. 11. Alternating-current voltammogram for a s o d a - l i m e silica glass melt doped with 1 mol% As205 at 1120 ° C (Eac = 30 mV). Frequencies as fig. (10).

correlation between Ip(ac) and ¢t- can be observed as predicted by eq. (12). At frequencies higher than 77.5 s - l , the shape of the curve changes and predominantly capacitive effects are observed. At still higher frequencies, the peak current approaches a nearly constant value (see fig. 12). The measured peak potentials for the AszO 5and the Fe203-doped glass melts have almost the same value as those measured by square-wave voltammetry (see table 1). However, the peak potentials depend slightly on the frequency as

I

I

10

20 _

_

I

30

f112/s1/2

=_

Fig. 12. Frequency dependence of the peak currents, related to the A s S + / A s 3+ reduction step at different temperatures. n, 1315°C; t~, 1225°C; o, 1130°C; ©, 1030°C.

shown in fig. 11, especially in the case of A s 2 0 5 d o p e d glass. The peak currents at a frequency of 77 s -t were corrected by vector addition to account for double layer effects and glass melt resistance [19]. Figure 13 shows diffusion coefficients, calculated from the corrected peak currents. The diffusion coefficients decrease remarkably with decreasing temperature. A good linear correlation of the plot log D against T -1 can be seen for the Fe 3+ and As 5+ diffusion coefficients.

Table 1 Standard potentials (vs. ZrO2/air), measured at 1 1 0 0 ° C with different electrochemical methods in soda-lime-silica glass melts, doped with Fe203 or As205 Method

E 0 (mV) (Fe 3 + / F e 2 + )

E 0 (mV) (As 5 + / A s 3 + )

E 0 (mV) (As 3 + / A s °)

Cyclic voltammetry Square-wave voltammetry Differential-pulse voltammetry Alternating-current voltammetry

- 545 - 555 - 567

~) -140 b)

- 363 - 367 b)

-- 570

-- 120 ( - 140)

-- 360 ( - 380)

") Not sufficiently defined to calculate E o. b) NOt measured.

204

C Riissel, G. Sprachmann / Electrochemicalmethodsfor investigations in molten glass

-6

0 ~ 0 ~

o~ C

o~

o~

E ~ -7 ~g "o

-8

I

i

l

i

6

6.5

7

7.5

11T]IO-~ K-1

=

Fig. 13. Diffusion coefficients as a function of temperature, o, iron; 0, arsenic.

0

/"

/

oJ °

-~00

,00 //.J ~o

oJ ° =

,

-6oo

o....- - ~ I

900

-s00 Zo

w

1000

1100

1200

1300

1400

O/°C Fig. 14. Standard potentials of the 0 F e 3 + / F e 2+ and the • A s S + / A s 3+ reduction step as a function of the temperature, measured by alternating-current voltamrnetry.

205

c. Riissel, G. Sprachmann / Electrochemicalmethodsfor investigations in molten glass 4.6. Discussion: comparison of the different methods

Table 1 shows the standard potentials E o referred to the ZrO2/air electrode, measured at 1100 ° C with different electrochemical methods in soda-lime-silica glass melts doped with Fe203 and As205. E 0 of the Fe3+/Fe2+-reduction step is slightly different for each method. The highest standard potential was measured by cyclic voltammetry ( - 545 mV) and differs by only 25 mV from the lowest standard potential measured by alternating-current voltammetry ( - 5 7 0 mV); the E 0values from the other methods are within these limits. The standard potential of the AsS+/As 3+ reduction step was measured by square-wave voltammetry ( - 1 4 0 mV) and by alternating-current voltammetry ( - 1 2 0 mV to - 1 4 0 mV). Although the latter value depends slightly on the applied frequency, the agreement of these two values is quite good. As already mentioned, E 0 of this reduction step could not be measured by cyclic voltammetry because the relevant peaks were not defined well enough. Similarly, good agreement could also be observed for the standard potentials of the As3+/As ° reduction step. All standard potentials decreased with decreasing temperature. Figure 14 shows a plot E 0 against the temperature. A good linear correlation can be observed. It should be noted that, in the temperature range investigated, there is no sign of any temperature dependence of A H °, which therefore can be considered as temperature-independent. A linear correlation between E 0 (or AG °) and T has already been observed in refs. [7,8]. Fairly equivalent results, linear correlations between In K and 1 / T , also have been obtained in refs. [20-27], although temperature-dependent standard data have also been reported [28]. Table 2 summarizes standard free enthalpies AH ° of the reactions according to eqs. (13) and (14) calculated from the results of different electrochemical methods: Fe3++ ½ 0 2 - ~ Fe2++ ¼02,

(13)

ASS++ O2-~-- As3++ 1 0 2.

(14)

The potentiometric values were calculated from fig. 1 and a similar measurement in an As205-

Table 2 The standard free enthalpy, AH°, measured by different electrochemical methods in a soda-lime-silica glass melt doped with Fe203or As205 Method

AH° (kJ mol -l) (Fe3+/Fe 2+ )

AH° (kJ mol -z ) (As5+/As 3+ )

Potentiometry Square-wave voltammetry Alternating-current voltammetry Mean value

118

222

102

230

108 109 + 9

202 218 +_16

doped glass melt using eq. (3) assuming AH ° and AS ° to be independent of temperature. The voltammetric data were calculated from the temperature dependence of the standard potentials using eqs. (2) and (5). Comparing the data in table 2, the values obtained by different electrochemical methods show fairly good agreement. The values of AH ° for the reduction of Fe 3+ (see eq. (13)) are all in the range of 102-118 kJ mol - t with a mean value of 109 +_ 9 kJ mo1-2. For the reduction of As ~+ (see eq. (14)) all AH°-values are in the range of 202-230 kJ mo1-1, with a mean value of 218 +_ 16 kJ mo1-1.

5. Conclusions

In principle, all electrochemical methods investigated are suitable for measurements in molten glass. However, the square-wave voltammetry and the alternating-current voltammetry are preferable, because they have higher sensitivity and resolution than the more commonly used cyclic voltammetry. Thermodynamic data such as E 0 and AH ° show fairly good agreement for all methods investigated. Parts of this investigation were conducted with the kind support of the Arbeitsgemeinschaft Industrieller Forschungsvereinigungen (AIF), KiSln (Germany), by agency of the Hiittentechnische Vereinigung der Deutschen Glasindustrie, Frankfurt (Germany), through the resources of the Bundesministerium fiir Wirtschaft.

206

C. Riissel, G. Sprachmann / Electrochemical methods for investigations in molten glass

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[15] A. Paul, J. Non-Cryst. Solids 71 (1985) 269. [16] D. Britz, Digital Simulation in Electrochemistry (Springer, Berlin, 1981). [17] R.S. Nicholson and I. Shain, Anal. Chem. 36 (1964) 706. [18] J.G. Osteryoung and J.J. O'Dea, in: Electroanalytical Chemistry, ed. A.J. Bard, Vol. 14 (Dekker, New York, 1986) p. 209. [19] A.J. Bard and L.R. Fauckner, Electrochemical Methods Fundamentals and Application (Wiley, New York, 1980). [20] A. Paul and R.W. Douglas, Phys. Chem. Glasses 6 (1965) 212. [21] A. Paul and R.W. Douglas, Phys. Chem. Glasses 7 (1966) 1. [22] D. Lahiri, B. Mukherjee and R.N. Majumdar, Glastech. Ber. 47 (1974) 1. [23] R. Majumdar and D. Lahiri, J. Am. Ceram. Soc. 58 (1975) 99. [24] S. Singh, G. Prasad and P. Nath. J. Mater. Sci. 16 (1981) 2176. [25] W.D. Johnston, J. Am. Ceram. Soc. 47 (1964) 198. [26] R. Pyare and P. Nath, J. Am. Ceram. Soc. 65 (1982) 549. [27] R. Pyare and P. Nath, J. Non-Cryst. Solids 69 (1984) 59. [28] B. Stahlberg, B.D. Mosel, W. Miiller-Warmuth and F.G.K. Baucke, Glastech. Ber. 61 (1988) 335.