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Structure and other physical properties of magnesium vanadate glasses
Journal of Non-Crystalline Solids 258 (1999) 29±33
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Structure and other physical properties of magnesium vanadate glasses S. Sen, A. Ghosh * Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India Received 1 March 1999; received in revised form 22 July 1999
Abstract Structure and other physical properties of (100ÿx)MgO±xV2 O5 glasses of dierent compositions are reported in this paper. Dierent studies like X-ray diractograms and oxygen molar volume show that homogeneous glasses are obtained in the composition domain x 60±90 mol%. It has been observed that the network structure for all glass compositions is built up of VO4 polyhedra. The glass transition temperatures are observed to decrease with an increase in V2 O5 content in the compositions. An increase in the concentration of the reduced V4 ions with an increase in V2 O5 content is observed from the magnetic susceptibility studies. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Vanadate glasses [1±5] are of continuous interest due to their applicability in memory switching, electrical threshold and optical switching devices, etc. [6±8]. These glasses are semiconductors and their semiconducting nature arises from the presence of two valence states, V4 and V5 , of the vanadium ions [1±5,9,10]. Their electrical conduction processes occur due to the hopping of an unpaired 3d1 electron from a V4 site to a V5 site [9,10]. The unpaired electron induces a polarization of the vanadium ion and forms a polaron. Many studies have been reported on the electrical properties of vanadate glasses [1±5,9,10]. However, the structure of these glasses has not been studied as extensively [11,12]. A study of the infrared spectra of some vanadate glasses shows that
* Corresponding author. Tel.: +91-33 473 4971; fax: +91-33 473 2805; e-mail: [email protected]
the structure of these glasses depends on the nature of the network formers as well as the network modi®ers [11,12]. In this paper, we have studied the glass formation domain and the composition dependence of the structure and other physical properties of the MgO±V2 O5 glasses. Interestingly, we have observed that a glassy network structure can be obtained in a large composition domain in this system in which the V2 O5 acts as a unique glass network former and MgO as a modi®er. 2. Experiment Glass samples were prepared from the reagent grade chemical V2 O5 and MgO. These chemicals, in appropriate proportions (Table 1), were mixed uniformly. The mixtures were melted in the temperature range from 750°C to 1100°C depending on the composition. It was observed that the melting temperature decreased with an increase in the V2 O5 content. The melts were rapidly
0022-3093/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 5 6 2 - 1
ÿ6.399 ÿ6.321 ÿ6.242 ÿ6.208 331 276 250 240 3.90 3.86 3.79 3.75
395 380 320 275
Tg (°C) 5
0.033 0.037 0.043 0.045 20.74 20.81 20.90 20.93 22.22 22.24 22.26 22.28
Fig. 1 shows XRD patterns for all glass samples. Each pattern exhibits a broad diuse scattering at low angles, instead of crystalline peaks, con®rming a long range structural disorder
8.56 9.68 10.51 11.52 2.930 2.886 2.932 2.925 40 30 20 10 60 70 80 90
Density (g cmÿ3 ) 0.001 V2 O5 mol %
quenched between two brass plates to obtain glass samples of thickness 1 mm. Glass samples with MgO content 6 40 mol% were obtained by this method. X-ray diraction (XRD) patterns of the samples were recorded to ensure glass formation. Dierential thermal analysis (DTA) curves of the samples were recorded in a thermal analyzer with a heating rate of 20 C/min in air atmosphere. The density of the samples was measured at room temperature by the displacement method using acetone as an immersion liquid. The magnetic susceptibility of the samples at room temperature (Table 1) was determined using a vibrating sample magnetometer. Fourier-transform infrared (FTIR) spectra of the glass samples in KBr matrices were taken at room temperature in the range 400± 4000 cmÿ1 . 3. Results
MgO mol %
V0 (cm3 g atomÿ1 ) 0.17
log10 N (cmÿ3 ) 0.01
log10 ([V4 ] (cmÿ3 )) 0.01
C V4 =N 0.002
R (Ao ) 0.01
Tc (°C) 5
log10 vg (emu/g) 0.023
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33 Table 1 Compositions, density, oxygen molar volume, concentrations of total vanadium and V4 ions, their ratio, average vanadium site separation, glass transition temperature, crystallization temperature and magnetic susceptibility of magnesium vanadium glasses
30
Fig. 1. X-ray diractograms of some as-prepared samples: (a) 90V2 O5 ±10MgO; (b) 80V2 O5 ±20MgO; (c) 70V2 O5 ±30MgO; (d) 60V2 O5 ±40MgO.
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33
characteristic of amorphous network. In this way we observed glass formation for the compositions with V2 O5 content in the range 60±90 mol%. We show in Fig. 2 the room temperature FT-IR spectra in the range 400±4000 cmÿ1 for the glass compositions and also for the crystalline V2 O5 and MgO for comparison. All the spectra show a water band at 3400 cmÿ1 . A weak band at 2910±2920 cmÿ1 is also observed for some glasses. This band is attributed to ÿOH stretching peak. Another band at 1640±1620 cmÿ1 is observed which might be due to the ÿOH bending mode and obsorbed water [13]. All the peaks described above are due to the hygroscopic nature of the powdered samples [13,14]. We observe for V2 O5 a strong band at 1020 cmÿ1 which has been assigned to the vibration of the isolated V¸O vanadyl groups in VO5 trigonal bi-pyramids [15]. With the introduction of
Fig. 2. Room temperature FT-IR spectra of the V2 O5 ±MgO glasses and crystalline V2 O5 : (a) crystalline V2 O5 ; (b) 90V2 O5 ± 10MgO; (c) 80V2 O5 ±20MgO; (d) 70V2 O5 ±30MgO; (e) 60V2 O5 ± 40MgO; (f) crystalline MgO.
31
MgO, changes of this group are observed in the spectra. In the case of glasses containing 90, 80, 70 and 60 mol% V2 O5 this band vanished, instead a new band is observed at 985, 978, 967 and 960 cmÿ1 , respectively with reduced intensity in the spectra. Dimitriev and co-workers [11] reported that in glasses containing V2 O5 and MgO the band at 1020 cmÿ1 exists along with the formation of new bands in the range 980±910 cmÿ1 . The absorption bands in the range 980±910 cmÿ1 have been assigned to symmetric stretching vibrations of the isolated VO2 groups in VO4 polyhedra [16]. The oxygen molar volume V0 , occupied by 1 g atom of oxygen has been calculated from the density and composition using the formula reported earlier by Drake et al. [17] and its composition dependence is shown in Fig. 3. It is observed that V0 increases monotonically with an increase of the V2 O5 content in the composition which indicates that the topology of the network does not signi®cantly change with compositions. From the magnetic measurements and the glass compositions vanadium ions were found to exist in two oxidation states, e.g., V5 and V4 . The estimated concentration of V4 ([V4 ]) and the total vanadium ions (N) and their ratio (C) are shown in
Fig. 3. Composition dependence of the oxygen molar volume for the V2 O5 ±MgO glasses.
32
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33
Fig. 4. Dierential thermal analysis curves for the V2 O5 ±MgO glasses: (a) 90V2 O5 ±10MgO; (b) 80V2 O5 ±20MgO; (c) 70V2 O5 ± 30MgO; (d) 60V2 O5 ±40MgO.
Table 1. It is noticed that the total vanadium ion concentration N increases with the increase of the V2 O5 content in the compositions. The concentration of the V4 and C ions also increases with an increase of the V2 O5 content in the compositions. The average site separation (R) of the vanadium ions was calculated from the total vanadium ion concentrations assuming a uniform distribution of the ions in the glassy matrices. The values of R, shown in Table 1, increase with a decrease in V2 O5 content in the glass compositions. The dierent thermal analysis curves of all the samples are displayed in Fig. 4 which shows an endothermic dip due to glass transition and an exothermic peak due to crystallization. The glass transition temperature (Tg ) and the crystallization temperature (Tc ) were determined from the curves and are listed in Table 1. The composition dependence of the glass transition temperature is shown in Fig. 5. 4. Discussion We observe from the FT-IR studies (Fig. 2) that there is a pronounced eect of the introduction of
Fig. 5. Composition dependence of the glass transition temperature of the V2 O5 ±MgO glasses.
MgO on the V¸O bonds that are present in the VO5 polyhedra in crystalline V2 O5 . According to the structural model reported earlier [11], Mg ions may either occupy positions in the vanadate chain itself or may be located between vanadate chains and layers. In the ®rst case, Mg ions will break up some of the V±O±V bonds and form new V±O±Mg bridges. The in¯uence of Mg ions on the V¸O bonds in the glasses is restricted and it may have an indirect manifestation. On the other hand, in the second case Mg ions interact directly with the V¸O bonds, as a result of which these bonds will be longer and the frequencies of the vibration should be shifted towards lower wave-numbers. The shift of the bands for the glasses towards the lower wave-numbers implies that Mg ions in these compositions are located between vanadate chains and layers and the glass structure consists of VO4 polyhedra. It is observed in Fig. 5 that Tg gradually increases with the decreasing content of the V2 O5 in the composition. The previous studies of the differential thermal analysis of several glasses [18,19] have shown that Tg is strictly related to the density of cross-linking, the tightness of the packing in the network, the coordination of the network formers, etc. It has also been suggested [18] that the density
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33
of cross-linking and the molar oxygen volume have greater eects on Tg than the bond strength. The increase of Tg with the decrease of V2 O5 in the compositions is thus due to higher cross-linking density in the compositions than in the vitreous V2 O5 . As the content of V2 O5 is decreased in the composition, there is a continuous change of the glass matrix from 2D layer structure of crystalline V2 O5 to a more complicated 3D structure. The increase of oxygen molar volume (cf. Section 3) with a decrease of V2 O5 content in the compositions supports this conclusion. Table 1 indicates that the dierence between Tg and Tc is high and increases roughly with a decrease in V2 O5 content, suggesting greater stability for the glass compositions with lower V2 O5 content. The presence of unpaired 3d1 electrons in the 4 V state of vanadium gives rise to paramagnetic properties of these vanadate glasses. The magnetic susceptibility (Table 1) of the glasses shows an increase with an increase in the V2 O5 content. The concentration of V4 ions was calculated from the susceptibility data for the dierent glass compositions and has been discussed earlier in the text. 5. Conclusions Various investigations such as X-ray, molar volume, etc. carried out on the MgO±V2 O5 system show that homogeneous glasses can be obtained for 60±90 mol% V2 O5 . The presence of V4 and V5 ions is observed in all the glass compositions. The cross-linking density increases with the decreases of V2 O5 content in the compositions. Introduction of MgO into the V2 O5 matrix changes
33
the 2D layer structure of the crystalline V2 O5 into a more complicated 3D structure. The infrared studies of the glasses suggest that the glass network is built up of mainly VO4 polyhedra. Acknowledgements The authors acknowledge the ®nancial support by the CSIR, India (via grant No. 3(772)/95-EMRII) for this work. References [1] M. Sayer, A. Mansingh, Phys. Rev. B 6 (1972) 4629. [2] G.N. Greaves, J. Non-Cryst. Solids 11 (1973) 427. [3] C.H. Cheng, J.D. Meckenzie, L. Murawkski, Rev. Chem. Miner. 16 (1979) 308. [4] C.H. Cheng, J.D. Meckenzie, J. Non-Cryst. Solids 42 (1980) 151. [5] A. Ghosh, Phys. Rev. B 42 (1990) 5665. [6] A. Ghosh, J. Appl. Phys. 64 (1988) 2652. [7] J. Livage, J.P. Jollivet, E. Tronc, J. Non-Cryst. Solids 121 (1990) 35. [8] Y. Sakuri, J. Yamaki, J. Electrochem. Soc. 132 (1985) 512. [9] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1. [10] G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [11] V. Dimitrov, Y. Dimitiev, M. Arnaudov, D. Topalov, J. Non-Cryst. Solids 57 (1983) 147. [12] S. Mandal, A. Ghosh, Phys. Rev. B 48 (1993) 9388. [13] J.T. Quan, C.F. Adams, J. Phys. Chem. 70 (1966) 331. [14] N.F. Borelli, B.D. McSwain, S. Su, Phys. Chem. Glasses 4 (1963) 11. [15] E. Dachille, R. Roy, J. Am. Ceram. Soc. 42 (1965) 78. [16] I.L. Botto, E.J. Baran, P.J. Aymonino, Mh. Chem. 107 (1976) 1127. [17] C.F. Drake, J.A. Stephens, B. Yates, J. Non-Cryst. Solids 28 (1978) 61. [18] N.H. Roy, J. Non-Cryst. Solids 15 (1974) 423. [19] J.E. Shelby, J. Appl. Phys. 46 (1975) 193.
www.elsevier.com/locate/jnoncrysol
Structure and other physical properties of magnesium vanadate glasses S. Sen, A. Ghosh * Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India Received 1 March 1999; received in revised form 22 July 1999
Abstract Structure and other physical properties of (100ÿx)MgO±xV2 O5 glasses of dierent compositions are reported in this paper. Dierent studies like X-ray diractograms and oxygen molar volume show that homogeneous glasses are obtained in the composition domain x 60±90 mol%. It has been observed that the network structure for all glass compositions is built up of VO4 polyhedra. The glass transition temperatures are observed to decrease with an increase in V2 O5 content in the compositions. An increase in the concentration of the reduced V4 ions with an increase in V2 O5 content is observed from the magnetic susceptibility studies. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Vanadate glasses [1±5] are of continuous interest due to their applicability in memory switching, electrical threshold and optical switching devices, etc. [6±8]. These glasses are semiconductors and their semiconducting nature arises from the presence of two valence states, V4 and V5 , of the vanadium ions [1±5,9,10]. Their electrical conduction processes occur due to the hopping of an unpaired 3d1 electron from a V4 site to a V5 site [9,10]. The unpaired electron induces a polarization of the vanadium ion and forms a polaron. Many studies have been reported on the electrical properties of vanadate glasses [1±5,9,10]. However, the structure of these glasses has not been studied as extensively [11,12]. A study of the infrared spectra of some vanadate glasses shows that
* Corresponding author. Tel.: +91-33 473 4971; fax: +91-33 473 2805; e-mail: [email protected]
the structure of these glasses depends on the nature of the network formers as well as the network modi®ers [11,12]. In this paper, we have studied the glass formation domain and the composition dependence of the structure and other physical properties of the MgO±V2 O5 glasses. Interestingly, we have observed that a glassy network structure can be obtained in a large composition domain in this system in which the V2 O5 acts as a unique glass network former and MgO as a modi®er. 2. Experiment Glass samples were prepared from the reagent grade chemical V2 O5 and MgO. These chemicals, in appropriate proportions (Table 1), were mixed uniformly. The mixtures were melted in the temperature range from 750°C to 1100°C depending on the composition. It was observed that the melting temperature decreased with an increase in the V2 O5 content. The melts were rapidly
0022-3093/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 5 6 2 - 1
ÿ6.399 ÿ6.321 ÿ6.242 ÿ6.208 331 276 250 240 3.90 3.86 3.79 3.75
395 380 320 275
Tg (°C) 5
0.033 0.037 0.043 0.045 20.74 20.81 20.90 20.93 22.22 22.24 22.26 22.28
Fig. 1 shows XRD patterns for all glass samples. Each pattern exhibits a broad diuse scattering at low angles, instead of crystalline peaks, con®rming a long range structural disorder
8.56 9.68 10.51 11.52 2.930 2.886 2.932 2.925 40 30 20 10 60 70 80 90
Density (g cmÿ3 ) 0.001 V2 O5 mol %
quenched between two brass plates to obtain glass samples of thickness 1 mm. Glass samples with MgO content 6 40 mol% were obtained by this method. X-ray diraction (XRD) patterns of the samples were recorded to ensure glass formation. Dierential thermal analysis (DTA) curves of the samples were recorded in a thermal analyzer with a heating rate of 20 C/min in air atmosphere. The density of the samples was measured at room temperature by the displacement method using acetone as an immersion liquid. The magnetic susceptibility of the samples at room temperature (Table 1) was determined using a vibrating sample magnetometer. Fourier-transform infrared (FTIR) spectra of the glass samples in KBr matrices were taken at room temperature in the range 400± 4000 cmÿ1 . 3. Results
MgO mol %
V0 (cm3 g atomÿ1 ) 0.17
log10 N (cmÿ3 ) 0.01
log10 ([V4 ] (cmÿ3 )) 0.01
C V4 =N 0.002
R (Ao ) 0.01
Tc (°C) 5
log10 vg (emu/g) 0.023
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33 Table 1 Compositions, density, oxygen molar volume, concentrations of total vanadium and V4 ions, their ratio, average vanadium site separation, glass transition temperature, crystallization temperature and magnetic susceptibility of magnesium vanadium glasses
30
Fig. 1. X-ray diractograms of some as-prepared samples: (a) 90V2 O5 ±10MgO; (b) 80V2 O5 ±20MgO; (c) 70V2 O5 ±30MgO; (d) 60V2 O5 ±40MgO.
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33
characteristic of amorphous network. In this way we observed glass formation for the compositions with V2 O5 content in the range 60±90 mol%. We show in Fig. 2 the room temperature FT-IR spectra in the range 400±4000 cmÿ1 for the glass compositions and also for the crystalline V2 O5 and MgO for comparison. All the spectra show a water band at 3400 cmÿ1 . A weak band at 2910±2920 cmÿ1 is also observed for some glasses. This band is attributed to ÿOH stretching peak. Another band at 1640±1620 cmÿ1 is observed which might be due to the ÿOH bending mode and obsorbed water [13]. All the peaks described above are due to the hygroscopic nature of the powdered samples [13,14]. We observe for V2 O5 a strong band at 1020 cmÿ1 which has been assigned to the vibration of the isolated V¸O vanadyl groups in VO5 trigonal bi-pyramids [15]. With the introduction of
Fig. 2. Room temperature FT-IR spectra of the V2 O5 ±MgO glasses and crystalline V2 O5 : (a) crystalline V2 O5 ; (b) 90V2 O5 ± 10MgO; (c) 80V2 O5 ±20MgO; (d) 70V2 O5 ±30MgO; (e) 60V2 O5 ± 40MgO; (f) crystalline MgO.
31
MgO, changes of this group are observed in the spectra. In the case of glasses containing 90, 80, 70 and 60 mol% V2 O5 this band vanished, instead a new band is observed at 985, 978, 967 and 960 cmÿ1 , respectively with reduced intensity in the spectra. Dimitriev and co-workers [11] reported that in glasses containing V2 O5 and MgO the band at 1020 cmÿ1 exists along with the formation of new bands in the range 980±910 cmÿ1 . The absorption bands in the range 980±910 cmÿ1 have been assigned to symmetric stretching vibrations of the isolated VO2 groups in VO4 polyhedra [16]. The oxygen molar volume V0 , occupied by 1 g atom of oxygen has been calculated from the density and composition using the formula reported earlier by Drake et al. [17] and its composition dependence is shown in Fig. 3. It is observed that V0 increases monotonically with an increase of the V2 O5 content in the composition which indicates that the topology of the network does not signi®cantly change with compositions. From the magnetic measurements and the glass compositions vanadium ions were found to exist in two oxidation states, e.g., V5 and V4 . The estimated concentration of V4 ([V4 ]) and the total vanadium ions (N) and their ratio (C) are shown in
Fig. 3. Composition dependence of the oxygen molar volume for the V2 O5 ±MgO glasses.
32
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33
Fig. 4. Dierential thermal analysis curves for the V2 O5 ±MgO glasses: (a) 90V2 O5 ±10MgO; (b) 80V2 O5 ±20MgO; (c) 70V2 O5 ± 30MgO; (d) 60V2 O5 ±40MgO.
Table 1. It is noticed that the total vanadium ion concentration N increases with the increase of the V2 O5 content in the compositions. The concentration of the V4 and C ions also increases with an increase of the V2 O5 content in the compositions. The average site separation (R) of the vanadium ions was calculated from the total vanadium ion concentrations assuming a uniform distribution of the ions in the glassy matrices. The values of R, shown in Table 1, increase with a decrease in V2 O5 content in the glass compositions. The dierent thermal analysis curves of all the samples are displayed in Fig. 4 which shows an endothermic dip due to glass transition and an exothermic peak due to crystallization. The glass transition temperature (Tg ) and the crystallization temperature (Tc ) were determined from the curves and are listed in Table 1. The composition dependence of the glass transition temperature is shown in Fig. 5. 4. Discussion We observe from the FT-IR studies (Fig. 2) that there is a pronounced eect of the introduction of
Fig. 5. Composition dependence of the glass transition temperature of the V2 O5 ±MgO glasses.
MgO on the V¸O bonds that are present in the VO5 polyhedra in crystalline V2 O5 . According to the structural model reported earlier [11], Mg ions may either occupy positions in the vanadate chain itself or may be located between vanadate chains and layers. In the ®rst case, Mg ions will break up some of the V±O±V bonds and form new V±O±Mg bridges. The in¯uence of Mg ions on the V¸O bonds in the glasses is restricted and it may have an indirect manifestation. On the other hand, in the second case Mg ions interact directly with the V¸O bonds, as a result of which these bonds will be longer and the frequencies of the vibration should be shifted towards lower wave-numbers. The shift of the bands for the glasses towards the lower wave-numbers implies that Mg ions in these compositions are located between vanadate chains and layers and the glass structure consists of VO4 polyhedra. It is observed in Fig. 5 that Tg gradually increases with the decreasing content of the V2 O5 in the composition. The previous studies of the differential thermal analysis of several glasses [18,19] have shown that Tg is strictly related to the density of cross-linking, the tightness of the packing in the network, the coordination of the network formers, etc. It has also been suggested [18] that the density
S. Sen, A. Ghosh / Journal of Non-Crystalline Solids 258 (1999) 29±33
of cross-linking and the molar oxygen volume have greater eects on Tg than the bond strength. The increase of Tg with the decrease of V2 O5 in the compositions is thus due to higher cross-linking density in the compositions than in the vitreous V2 O5 . As the content of V2 O5 is decreased in the composition, there is a continuous change of the glass matrix from 2D layer structure of crystalline V2 O5 to a more complicated 3D structure. The increase of oxygen molar volume (cf. Section 3) with a decrease of V2 O5 content in the compositions supports this conclusion. Table 1 indicates that the dierence between Tg and Tc is high and increases roughly with a decrease in V2 O5 content, suggesting greater stability for the glass compositions with lower V2 O5 content. The presence of unpaired 3d1 electrons in the 4 V state of vanadium gives rise to paramagnetic properties of these vanadate glasses. The magnetic susceptibility (Table 1) of the glasses shows an increase with an increase in the V2 O5 content. The concentration of V4 ions was calculated from the susceptibility data for the dierent glass compositions and has been discussed earlier in the text. 5. Conclusions Various investigations such as X-ray, molar volume, etc. carried out on the MgO±V2 O5 system show that homogeneous glasses can be obtained for 60±90 mol% V2 O5 . The presence of V4 and V5 ions is observed in all the glass compositions. The cross-linking density increases with the decreases of V2 O5 content in the compositions. Introduction of MgO into the V2 O5 matrix changes
33
the 2D layer structure of the crystalline V2 O5 into a more complicated 3D structure. The infrared studies of the glasses suggest that the glass network is built up of mainly VO4 polyhedra. Acknowledgements The authors acknowledge the ®nancial support by the CSIR, India (via grant No. 3(772)/95-EMRII) for this work. References [1] M. Sayer, A. Mansingh, Phys. Rev. B 6 (1972) 4629. [2] G.N. Greaves, J. Non-Cryst. Solids 11 (1973) 427. [3] C.H. Cheng, J.D. Meckenzie, L. Murawkski, Rev. Chem. Miner. 16 (1979) 308. [4] C.H. Cheng, J.D. Meckenzie, J. Non-Cryst. Solids 42 (1980) 151. [5] A. Ghosh, Phys. Rev. B 42 (1990) 5665. [6] A. Ghosh, J. Appl. Phys. 64 (1988) 2652. [7] J. Livage, J.P. Jollivet, E. Tronc, J. Non-Cryst. Solids 121 (1990) 35. [8] Y. Sakuri, J. Yamaki, J. Electrochem. Soc. 132 (1985) 512. [9] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1. [10] G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [11] V. Dimitrov, Y. Dimitiev, M. Arnaudov, D. Topalov, J. Non-Cryst. Solids 57 (1983) 147. [12] S. Mandal, A. Ghosh, Phys. Rev. B 48 (1993) 9388. [13] J.T. Quan, C.F. Adams, J. Phys. Chem. 70 (1966) 331. [14] N.F. Borelli, B.D. McSwain, S. Su, Phys. Chem. Glasses 4 (1963) 11. [15] E. Dachille, R. Roy, J. Am. Ceram. Soc. 42 (1965) 78. [16] I.L. Botto, E.J. Baran, P.J. Aymonino, Mh. Chem. 107 (1976) 1127. [17] C.F. Drake, J.A. Stephens, B. Yates, J. Non-Cryst. Solids 28 (1978) 61. [18] N.H. Roy, J. Non-Cryst. Solids 15 (1974) 423. [19] J.E. Shelby, J. Appl. Phys. 46 (1975) 193.