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Weathering and internal friction in glass
JOURNAL OF NON-CRYSTALLINESOLIDS3 (1970) 369--374 © North-Holland Publishing Co.
W E A T H E R I N G AND I N T E R N A L F R I C T I O N I N GLASS R. H. DOREMUS General Electric Research and Development Center, Schenectady, New York 12305, U.S.A.
Received 6 April 1970 Glass weathers by reaction of its alkali ions with water in air. An internal friction peak in glass at higher temperatures than the alkali ion peak is closelyrelated to weathering, since it appears in glasses that weather and is absent in those that do not. It is proposed that this peak results from the stress-induced motion of hydrogen ions that are introduced by reaction of sodium ions in the glass with atmospheric water and diffusion of the hydrogen ions so formed into the glass. Various experimental results are consistent with this mechanism; a previously proposed mechanism for this peak involving motion of nonbridging oxygen ions is unlikely. 1. Introduction
Weathering of glass results from a surface reaction with the atmosphere. The internal friction of glass is strongly affected by surface reactions 1), although short-range rearrangements of atoms in the bulk of the glass are usually thought to be responsible for the internal friction. A mechanism of internal friction involving long-range redistribution of atoms in a stress gradient agrees reasonably well with internal friction data2); with this mechanism there is sensitivity to surface reactions. In this paper an internal friction peak and weathering behavior in glass are correlated in terms of this mechanism. The internal friction of alkali silicate glasses shows a peak not far from room temperature at low frequencies. This peak results from the motion of the alkali ions, since it has the temperature dependence expected from their diffusion coefficients. A second peak at higher temperatures is observed in some glasses3-8); however, it is absent in othersg<2). This peak is usually attributed to the motion of nonbridging oxygen ionsZ-8). Nevertheless, there are serious doubts about this mechanism for the second peak, which are discussed in the next section. There is a close correlation between the rate of weathering of a silicate glass and the occurrence of this second peak; glasses weathering rapidly show the peak while those more stable do not. Weathering results from the exchange of hydrogen ions from water with alkali ions in the glass. This 369
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ion exchange can give rise to the second peak in the internal friction of the glass, as discussed in subsequent sections. 2. Nonbridging oxygen mechanism
The silicon-oxygen bond in fused silica has an energy of formation of over 50 kcal/molela), and in crystalline silicates the silicon-oxygen bond distance and bond angles are little affected by temperature or composition. Also the activation energy for viscous flow of silicates is high; for example, for soda-lime glasses it is about 100 kcal/mole at 500 to 600°C14). These results show the rigidity of the silicon-oxygen bond and make doubtful the proposals that the internal friction peak in alkali silicate glasses at temperatures of 100 to 200°C results from the motion of nonbridging oxygen ions. From the above figures one would expect an activation energy of at least 50 kcal/mole for transport of these ions, yet the activation energies for these peaks in a number of silicate glasses are substantially less than this value, being as low as 32 kcal/mole. The results of Kingery and Lecron 15) for the diffusion of lattice oxygen in a soda-lime glass when extrapolated to 200°C give a diffusion coefficient of 6 x 10 -28 cm2/sec. It is unlikely that an ion with such a low diffusion coefficient could contribute to a relaxation process at a frequency of one cps. The average distance that an ion with this diffusion coefficient could move in one second is less than 10-la cm. Several authors have claimed that the effect of glass composition on the second peak is consistent with the motion of nonbridging oxygen ions. However, several glasses containing many nonbridging oxygen associated with alkali ions show no intermediate peak8-tl), whereas at least one glass with no alkali ions did show this peak a). The mechanism proposed here gives a more consistent explanation of these composition effects. 3. Weathering of glass
When a binary sodium or potassium silicate glass is held in room air, it becomes covered with a white, powdery coating in a few hours or days, and if the humidity is high, the surface becomes sticky with moisture. These conditions result from the following chemical reaction between, for example, sodium ions in the glass and water in the air: 2 N a + + H 2 0 = N a 2 0 + 2 H +.
(1)
The sodium oxide so formed reacts further with constituents of the air to form sodium hydroxide or sodium carbonate crystals (possibly hydrated) on
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the glass surface. If the humidity is high enough, these crystals absorb more water (deliquesce) until they are in liquid solution. The rate of the above weathering process is determined by the rate of interdiffusion of sodium and hydrogen ions in the glass. The mobility of the hydrogen ions is considerably lower than that of the sodium ions16); for example, Ehrmann et al. found that the mobility ratio was 1800 in a soda-lime silicate glass at 350°C17). If the glass surface is not saturated with hydrogen ions, the interdiffusion coefficient is close to the diffusion coefficient of the slower (hydrogen) ions; however, if the surface is saturated with hydrogen ions, the interdiffusion coefficient is higher, since an electric field is set up to keep the fluxes of sodium and hydrogen ions equal and preserve electrical neutrality 18). The weathering process is analogous to the first stage of dissolution of glass in water, which involves interdiffusion of alkali and hydrogen ions 19). The effects of changing glass composition on weathering and dissolution are, therefore, similar. These effects can be understood in terms of the interdiffusion model proposed above. The addition of alkaline earth ions to the glass reduces the diffusion coefficient of sodium ion, and doubtless hydrogen ion, in themZ0). Thus, lime in sodium silicate glasses improves their weathering properties by slowing interdiffusion of sodium and hydrogen ions. On the other hand the addition of aluminum to a sodium silicate glass increases the mobility of sodium, yet such glasses are more resistant to weathering than the simple sodium silicate glasses. This increased resistance results from an entirely different effect. The aluminosilicate groups in glass have less affinity for hydrogen ions compared to sodium ions than do simple SiO groups 21). Thus, in the sodium aluminosilicate glass the fraction of surface sodium groups that react with a given water concentration to form hydrogen ions is lower than for the simple sodium silicate glass; and, therefore, the amount of sodium coming out of the surface is cut down. 4. Internal friction in glass
The low temperature internal friction peak results from the diffusion of alkali ions. A proposed mechanism for this peak involves the buildup of ions at the sample surface under the influence of a stress gradient Z). It predicts the equality of activation energies for electrical conduction and internal friction found experimentally, and the measured positions of the peak agree reasonably well with those calculated. If there are two diffusing ions with different mobilities in the glass, the equations for this mechanism become much more complicated and depend upon the initial distribution of
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the ions. However, if the mobilities are quite different, one would expect a normal peak for the fast ion and a second peak resulting from interconnected motion of the two ions2~). The position and breadth of this second peak are very complicated functions of the ionic mobilities, the initial distribution of the two ions, and their relative response to the stress gradient, and have not been worked out in complete detail. However, qualitatively the slower ion should give rise to a broad peak at higher temperature at constant measuring frequency or at lower frequency at constant temperature. It is proposed that the second internal friction peak in glass results from the stress induced motion of hydrogen ions. These ions are introduced into the glass by reaction of sodium ions and water in the atmosphere at the glass surface and subsequent interdiffusion of the ions in the glass. The amount of hydrogen ions that can be introduced in this way can be roughly estimated from an extrapolated value of the diffusion coefficient of sodium in the glass. For a 25~ Na20-759/o SiO2 glass, the diffusion coefficient at 354°C is 1.9× 10 - 9 cm2/sec 23) and the activation energy for diffusion is estimated to be 16.7 kcal/mole from the temperature dependence of the electrical conductivity of the same glass 24) and the Einstein equation21). Thus the diffusion coefficient of sodium in this glass at 25°C is about 7 x 10 - 1 6 cm2/sec. The effective interdiffusion coefficient of sodium and hydrogen ions should be lower, as mentioned in the last section, perhaps about 1.5 x 10 - 1 7 cm2/sec. The mean distance x an ion with this diffusion coefficient D moves in time t is x=~/(2Dt). If t is three days, x is about 300A. Thus the concentration of hydrogen ions in these glasses should equal that of the sodium ions at the surface and then fall off to a low value over a distance of several hundred A from the glass surface. This amount ot hydrogen ions would have a completely negligible effect on the internal friction if it resulted from local or short-range rearrangement of ions in the bulk of the glass. However, in the model involving long-range redistribution of ions throughout the glass in a stress gradient, the initial and boundary conditions at the surface become important. As mentioned above the exact theoretical position and shape of a peak resulting from two diffusing ions are not known, but qualitatively the broad peak found experimentally at higher temperatures than the alkali peak is in agreement with the proposal that it results from introduction of hydrogen ions. There are also several other experimental results that support this proposal, as described in the next paragraphs. The effects of glass composition on the second internal friction peak in glass agrees with the proposed mechanism. The peak is present in those glasses that show weathering and should, therefore, contain appreciable amounts of hydrogen ions from reaction with the atmosphere. This peak
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becomes less prominent as alkaline earth ions are added to the glassS); these ions reduce the diffusion coefficients of monovalent ions in the glass and, therefore, lead to lower hydrogen ion concentration. This peak is absent in several commercial glasses known for good weathering and chemical durability 9-11). The peak is also absent in alkali aluminosilicate glasses 12), in which the alumina reduces the amount of surface reaction with water, as mentioned in the last section. Vaugin et al. showed that when a fine glass fiber reacts with the atmosphere an internal friction peak slowly develops at higher temperatures than the alkali peak1). Their fibers were stored in a desicator and measured in a vacuum, under which conditions this peak did not develop. De Waa125) studied the internal friction of a sodium disilicate glass before and after exchange with hydrogen ions from a melt of NH4HSO4. He treated the glass for 2½ hr at 275 °C. At this temperature the effective interdiffusion coefficient of sodium and hydrogen ions is about 1.3 × 10-11 cm2/sec, so that the average distance of penetration of the hydrogen ions was about 5 pm. After this treatment De Waal found a substantial increase in the height of' the second internal friction peak at higher temperature, as would be expected if this peak resulted from hydrogen ions as proposed above. The amount of hydrogen ions introduced would be much too small to affect a peak resulting from local shifts of ions throughout the bulk of the glass. The above correlations between the proposed mechanism for the second internal friction peak in glass and experimental results on this peak, while not entirely conclusive, provide strong evidence that the peak results from hydrogen ions in the glass and is, therefore, closely linked with the weathering of the glass.
Acknowledgements This work was supported by Contract 68-C-0126 with the Office of Naval Research. John Nadeau reviewed the manuscript and provided helpful comments on it.
References 1) L. Vaugin, J. C. Breton, P. Gobin, Verres et Refractaires 23 (1969) 174. 2) R. H. Doremus, J. Appl. Phys, to be published. 3) For a review see J. L. Hopkins and C. K. Kurkjian, in: Physical Acoustics, Vol. IIB (Academic Press, New York, 1965) p. 114. 4) J. V. Fitzgerald, K. M. Laing and G. S. Bachman, J. Soc. Glass Technol. 36 (1952) 90. 5) K. E. Forry, J. Am. Cer. Soc. 40 (1957) 90. 6) H. R6tger, Glastech. Ber. 31 (1958) 54. 7) J. Mohyuddin and R. W. Douglas, Phys. Chem. Glasses 1 (1960) 71. 8) R.J. Ryder and G. E. Rindone, J. Am. Cer. Soc. 43 (1960) 662. 9) J. V. Fitzgerald, J. Am. Cer. Soc. 34 (1951) 388.
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10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)
R.H. DOREMUS
P. L. Kirby, J. Soc. Glass Technol. 39 (1955) 385. G.J. Copley and D. R. Oakley, Phys. Chem. Glasses 9 (1968) 141. D. E. Day and W. E. Steinkamp, J. Am. Cer. Soc. 52 (1969) 571. H.L. Schick, Chem. Rev. 54(1960) 331. G.W. Morey, The Properties of Glass (Reinhold, New York, 1954) p. 146. W. D. Kingery and J. A. Lecron, Phys. Chem. Glasses 1 (1960) 87. R. H. Doremus, in: Glass Electrodesfor Hydrogen and Other Cations, Ed. G. Eisenman (M. Dekker, New York, 1967) p. 129. P. Ehrmann, M. DeBilly and J. Zarzycki, Verres et Refractaires 15 (1964) 169. R. H. Doremus, J. Phys. Chem. 68 (1964) 2212. M.A. Rana and R. W. Douglas, Phys. Chem. Glasses 2 (1961) 179. G. Eisenman, Biophys. J. 2 (1962) 259. R. H. Doremus, in: Modern Aspects of the Vitreous State, Ed. J. D. Mackenzie, Vol. II, p. 51ft. R.J. Charles, J. Electrochem. Soc. 116 (1960) 1514. J. R. Johnson, R. H. Bristow and H. H. Blau, J. Am. Cer. Soc. 34 (1951) 165. E. Seddon, E. J. Tippett and W. E. L. Turner, J. Soc. Glass Technol. 16 (1932) 450. H. de Waal, J. Am. Cer. Soc. 52(1969) 165.
W E A T H E R I N G AND I N T E R N A L F R I C T I O N I N GLASS R. H. DOREMUS General Electric Research and Development Center, Schenectady, New York 12305, U.S.A.
Received 6 April 1970 Glass weathers by reaction of its alkali ions with water in air. An internal friction peak in glass at higher temperatures than the alkali ion peak is closelyrelated to weathering, since it appears in glasses that weather and is absent in those that do not. It is proposed that this peak results from the stress-induced motion of hydrogen ions that are introduced by reaction of sodium ions in the glass with atmospheric water and diffusion of the hydrogen ions so formed into the glass. Various experimental results are consistent with this mechanism; a previously proposed mechanism for this peak involving motion of nonbridging oxygen ions is unlikely. 1. Introduction
Weathering of glass results from a surface reaction with the atmosphere. The internal friction of glass is strongly affected by surface reactions 1), although short-range rearrangements of atoms in the bulk of the glass are usually thought to be responsible for the internal friction. A mechanism of internal friction involving long-range redistribution of atoms in a stress gradient agrees reasonably well with internal friction data2); with this mechanism there is sensitivity to surface reactions. In this paper an internal friction peak and weathering behavior in glass are correlated in terms of this mechanism. The internal friction of alkali silicate glasses shows a peak not far from room temperature at low frequencies. This peak results from the motion of the alkali ions, since it has the temperature dependence expected from their diffusion coefficients. A second peak at higher temperatures is observed in some glasses3-8); however, it is absent in othersg<2). This peak is usually attributed to the motion of nonbridging oxygen ionsZ-8). Nevertheless, there are serious doubts about this mechanism for the second peak, which are discussed in the next section. There is a close correlation between the rate of weathering of a silicate glass and the occurrence of this second peak; glasses weathering rapidly show the peak while those more stable do not. Weathering results from the exchange of hydrogen ions from water with alkali ions in the glass. This 369
370
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ion exchange can give rise to the second peak in the internal friction of the glass, as discussed in subsequent sections. 2. Nonbridging oxygen mechanism
The silicon-oxygen bond in fused silica has an energy of formation of over 50 kcal/molela), and in crystalline silicates the silicon-oxygen bond distance and bond angles are little affected by temperature or composition. Also the activation energy for viscous flow of silicates is high; for example, for soda-lime glasses it is about 100 kcal/mole at 500 to 600°C14). These results show the rigidity of the silicon-oxygen bond and make doubtful the proposals that the internal friction peak in alkali silicate glasses at temperatures of 100 to 200°C results from the motion of nonbridging oxygen ions. From the above figures one would expect an activation energy of at least 50 kcal/mole for transport of these ions, yet the activation energies for these peaks in a number of silicate glasses are substantially less than this value, being as low as 32 kcal/mole. The results of Kingery and Lecron 15) for the diffusion of lattice oxygen in a soda-lime glass when extrapolated to 200°C give a diffusion coefficient of 6 x 10 -28 cm2/sec. It is unlikely that an ion with such a low diffusion coefficient could contribute to a relaxation process at a frequency of one cps. The average distance that an ion with this diffusion coefficient could move in one second is less than 10-la cm. Several authors have claimed that the effect of glass composition on the second peak is consistent with the motion of nonbridging oxygen ions. However, several glasses containing many nonbridging oxygen associated with alkali ions show no intermediate peak8-tl), whereas at least one glass with no alkali ions did show this peak a). The mechanism proposed here gives a more consistent explanation of these composition effects. 3. Weathering of glass
When a binary sodium or potassium silicate glass is held in room air, it becomes covered with a white, powdery coating in a few hours or days, and if the humidity is high, the surface becomes sticky with moisture. These conditions result from the following chemical reaction between, for example, sodium ions in the glass and water in the air: 2 N a + + H 2 0 = N a 2 0 + 2 H +.
(1)
The sodium oxide so formed reacts further with constituents of the air to form sodium hydroxide or sodium carbonate crystals (possibly hydrated) on
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the glass surface. If the humidity is high enough, these crystals absorb more water (deliquesce) until they are in liquid solution. The rate of the above weathering process is determined by the rate of interdiffusion of sodium and hydrogen ions in the glass. The mobility of the hydrogen ions is considerably lower than that of the sodium ions16); for example, Ehrmann et al. found that the mobility ratio was 1800 in a soda-lime silicate glass at 350°C17). If the glass surface is not saturated with hydrogen ions, the interdiffusion coefficient is close to the diffusion coefficient of the slower (hydrogen) ions; however, if the surface is saturated with hydrogen ions, the interdiffusion coefficient is higher, since an electric field is set up to keep the fluxes of sodium and hydrogen ions equal and preserve electrical neutrality 18). The weathering process is analogous to the first stage of dissolution of glass in water, which involves interdiffusion of alkali and hydrogen ions 19). The effects of changing glass composition on weathering and dissolution are, therefore, similar. These effects can be understood in terms of the interdiffusion model proposed above. The addition of alkaline earth ions to the glass reduces the diffusion coefficient of sodium ion, and doubtless hydrogen ion, in themZ0). Thus, lime in sodium silicate glasses improves their weathering properties by slowing interdiffusion of sodium and hydrogen ions. On the other hand the addition of aluminum to a sodium silicate glass increases the mobility of sodium, yet such glasses are more resistant to weathering than the simple sodium silicate glasses. This increased resistance results from an entirely different effect. The aluminosilicate groups in glass have less affinity for hydrogen ions compared to sodium ions than do simple SiO groups 21). Thus, in the sodium aluminosilicate glass the fraction of surface sodium groups that react with a given water concentration to form hydrogen ions is lower than for the simple sodium silicate glass; and, therefore, the amount of sodium coming out of the surface is cut down. 4. Internal friction in glass
The low temperature internal friction peak results from the diffusion of alkali ions. A proposed mechanism for this peak involves the buildup of ions at the sample surface under the influence of a stress gradient Z). It predicts the equality of activation energies for electrical conduction and internal friction found experimentally, and the measured positions of the peak agree reasonably well with those calculated. If there are two diffusing ions with different mobilities in the glass, the equations for this mechanism become much more complicated and depend upon the initial distribution of
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the ions. However, if the mobilities are quite different, one would expect a normal peak for the fast ion and a second peak resulting from interconnected motion of the two ions2~). The position and breadth of this second peak are very complicated functions of the ionic mobilities, the initial distribution of the two ions, and their relative response to the stress gradient, and have not been worked out in complete detail. However, qualitatively the slower ion should give rise to a broad peak at higher temperature at constant measuring frequency or at lower frequency at constant temperature. It is proposed that the second internal friction peak in glass results from the stress induced motion of hydrogen ions. These ions are introduced into the glass by reaction of sodium ions and water in the atmosphere at the glass surface and subsequent interdiffusion of the ions in the glass. The amount of hydrogen ions that can be introduced in this way can be roughly estimated from an extrapolated value of the diffusion coefficient of sodium in the glass. For a 25~ Na20-759/o SiO2 glass, the diffusion coefficient at 354°C is 1.9× 10 - 9 cm2/sec 23) and the activation energy for diffusion is estimated to be 16.7 kcal/mole from the temperature dependence of the electrical conductivity of the same glass 24) and the Einstein equation21). Thus the diffusion coefficient of sodium in this glass at 25°C is about 7 x 10 - 1 6 cm2/sec. The effective interdiffusion coefficient of sodium and hydrogen ions should be lower, as mentioned in the last section, perhaps about 1.5 x 10 - 1 7 cm2/sec. The mean distance x an ion with this diffusion coefficient D moves in time t is x=~/(2Dt). If t is three days, x is about 300A. Thus the concentration of hydrogen ions in these glasses should equal that of the sodium ions at the surface and then fall off to a low value over a distance of several hundred A from the glass surface. This amount ot hydrogen ions would have a completely negligible effect on the internal friction if it resulted from local or short-range rearrangement of ions in the bulk of the glass. However, in the model involving long-range redistribution of ions throughout the glass in a stress gradient, the initial and boundary conditions at the surface become important. As mentioned above the exact theoretical position and shape of a peak resulting from two diffusing ions are not known, but qualitatively the broad peak found experimentally at higher temperatures than the alkali peak is in agreement with the proposal that it results from introduction of hydrogen ions. There are also several other experimental results that support this proposal, as described in the next paragraphs. The effects of glass composition on the second internal friction peak in glass agrees with the proposed mechanism. The peak is present in those glasses that show weathering and should, therefore, contain appreciable amounts of hydrogen ions from reaction with the atmosphere. This peak
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becomes less prominent as alkaline earth ions are added to the glassS); these ions reduce the diffusion coefficients of monovalent ions in the glass and, therefore, lead to lower hydrogen ion concentration. This peak is absent in several commercial glasses known for good weathering and chemical durability 9-11). The peak is also absent in alkali aluminosilicate glasses 12), in which the alumina reduces the amount of surface reaction with water, as mentioned in the last section. Vaugin et al. showed that when a fine glass fiber reacts with the atmosphere an internal friction peak slowly develops at higher temperatures than the alkali peak1). Their fibers were stored in a desicator and measured in a vacuum, under which conditions this peak did not develop. De Waa125) studied the internal friction of a sodium disilicate glass before and after exchange with hydrogen ions from a melt of NH4HSO4. He treated the glass for 2½ hr at 275 °C. At this temperature the effective interdiffusion coefficient of sodium and hydrogen ions is about 1.3 × 10-11 cm2/sec, so that the average distance of penetration of the hydrogen ions was about 5 pm. After this treatment De Waal found a substantial increase in the height of' the second internal friction peak at higher temperature, as would be expected if this peak resulted from hydrogen ions as proposed above. The amount of hydrogen ions introduced would be much too small to affect a peak resulting from local shifts of ions throughout the bulk of the glass. The above correlations between the proposed mechanism for the second internal friction peak in glass and experimental results on this peak, while not entirely conclusive, provide strong evidence that the peak results from hydrogen ions in the glass and is, therefore, closely linked with the weathering of the glass.
Acknowledgements This work was supported by Contract 68-C-0126 with the Office of Naval Research. John Nadeau reviewed the manuscript and provided helpful comments on it.
References 1) L. Vaugin, J. C. Breton, P. Gobin, Verres et Refractaires 23 (1969) 174. 2) R. H. Doremus, J. Appl. Phys, to be published. 3) For a review see J. L. Hopkins and C. K. Kurkjian, in: Physical Acoustics, Vol. IIB (Academic Press, New York, 1965) p. 114. 4) J. V. Fitzgerald, K. M. Laing and G. S. Bachman, J. Soc. Glass Technol. 36 (1952) 90. 5) K. E. Forry, J. Am. Cer. Soc. 40 (1957) 90. 6) H. R6tger, Glastech. Ber. 31 (1958) 54. 7) J. Mohyuddin and R. W. Douglas, Phys. Chem. Glasses 1 (1960) 71. 8) R.J. Ryder and G. E. Rindone, J. Am. Cer. Soc. 43 (1960) 662. 9) J. V. Fitzgerald, J. Am. Cer. Soc. 34 (1951) 388.
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10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)
R.H. DOREMUS
P. L. Kirby, J. Soc. Glass Technol. 39 (1955) 385. G.J. Copley and D. R. Oakley, Phys. Chem. Glasses 9 (1968) 141. D. E. Day and W. E. Steinkamp, J. Am. Cer. Soc. 52 (1969) 571. H.L. Schick, Chem. Rev. 54(1960) 331. G.W. Morey, The Properties of Glass (Reinhold, New York, 1954) p. 146. W. D. Kingery and J. A. Lecron, Phys. Chem. Glasses 1 (1960) 87. R. H. Doremus, in: Glass Electrodesfor Hydrogen and Other Cations, Ed. G. Eisenman (M. Dekker, New York, 1967) p. 129. P. Ehrmann, M. DeBilly and J. Zarzycki, Verres et Refractaires 15 (1964) 169. R. H. Doremus, J. Phys. Chem. 68 (1964) 2212. M.A. Rana and R. W. Douglas, Phys. Chem. Glasses 2 (1961) 179. G. Eisenman, Biophys. J. 2 (1962) 259. R. H. Doremus, in: Modern Aspects of the Vitreous State, Ed. J. D. Mackenzie, Vol. II, p. 51ft. R.J. Charles, J. Electrochem. Soc. 116 (1960) 1514. J. R. Johnson, R. H. Bristow and H. H. Blau, J. Am. Cer. Soc. 34 (1951) 165. E. Seddon, E. J. Tippett and W. E. L. Turner, J. Soc. Glass Technol. 16 (1932) 450. H. de Waal, J. Am. Cer. Soc. 52(1969) 165.