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Electrical conductivity of amorphous V2O5–Sb2O3 thin films
March 1998
Materials Letters 34 Ž1998. 341–344
Electrical conductivity of amorphous V2 O5 –Sb 2 O 3 thin films S. Chakraborty, K. Suzuki, H. Sakata
)
Department of Applied Chemistry, Tokai UniÕersity, 1117 Kitakaname, Hiratsuka, Kanagawa 259-12, Japan Received 6 June 1997; revised 21 July 1997; accepted 21 July 1997
Abstract Amorphous thin films of V2 O5 –Sb 2 O 3 , in the molar ratio of V2 O5:Sb 2 O 3 as 100:0, 98:2, 94:6, 92:8 respectively, were obtained by the vacuum–evaporation technique. The dc conductivities of the films were measured in the temperature range of 303–423 K. The experimental data have been analyzed in light of the small polaronic hopping model of Mott and the percolation approach of Triberis and Friedman. The estimated model parameters are found to be consistent with the formation of localized states in these films. q 1998 Elsevier Science B.V. Keywords: Electrical conductivity; Amorphous thin films; V2 O5 -Sb 2 O 3
1. Introduction Since the pioneering work of Denton et al. w1x amorphous transition metal oxides have been extensively studied. Their semiconducting properties arise from the hopping of the unpaired electron between transition metal ions in different valence states. Though a lot of work has been done to investigate the electronic conduction process through V2 O5 based binary or ternary glasses, very little work has been reported on similar study on vanadate based thin films w2–6x. The aim of the present investigation is to study the dc electrical conductivities of amorphous V2 O5 –Sb 2 O 3 thin films obtained by vacuum evaporation technique. Contrary to our expectations of an increase in conductivity of these binary films Žcompared to the single component V2 O5 film. in
)
Corresponding author.
view of the reducing action of Sb 2 O 3 , as observed by Sakata et al. w7x for Sb 2 O 3 –SrO–V2 O5 glasses, the Sb ions in the film seem to hinder the electron transfer process and lower the conductivity. The experimental results have been analyzed with the small polaron hopping model of Mott w8,9x and the percolation theory of Triberis and Friedman w10x.
2. Experimental The amorphous films of V2 O5 –Sb 2 O 3 were obtained in the molar ratio of V2 O5 :Sb 2 O 3 as 100:0, 98:2, 94:6 and 92:8 as starting evaporant material, respectively, by the resistance heating evaporation technique. Appropriate proportions of the V2 O5 and Sb 2 O 3 Ž99.99% each purity. were mixed in air in an agate mortar for 20 min and then the batch was evaporated from an electrically heated platinum crucible kept at 690 to a Pyrex glass plate Ža7059. kept at a temper-
00167-577Xr98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 7 - 5 7 7 X Ž 9 7 . 0 0 1 9 5 - X
342
S. Chakraborty et al.r Materials Letters 34 (1998) 341–344
ature of 100, under a vacuum of 10y4 Pa. The deposition rate of the film was about 1 nm sy1 . The thickness of the film was 300 nm as measured by the surface profile tester ŽKosaka, Surfcorder SE-30A.. X-ray diffractometry ŽPhilips, X’Pert PW1830. was used to characterize the crystallinity or the structure of the samples. The dc electrical conductivity Ž s . measurements were taken on the films of dimension 5 = 1 mm, carefully protected from ambient moisture. Two parallel gold electrodes were evaporated on the films. The ohmic behaviour of the film was ascertained from the linearity of the current voltage curves. The temperature and current were measured with a digital thermometer ŽAdvantest, TR2114. and a picoampere meter ŽHewlett-Packard, 4140B. respectively. The current intensity in these films, after the application of a fixed voltage, remains constant with time implying that the electrical conduction in these films is electronic in nature.
3. Results and discussion The X-ray diffraction pattern of the as-deposited films indicated their amorphous nature. Fig. 1 shows the plot of the dc conductivities of the V2 O5 –Sb 2 O 3 films of various compositions as a function of inverse temperature. In the temperature
Fig. 1. Temperature dependence of dc conductivity for Žv . V2 O5, Ž'. 98V2 O5 –2Sb 2 O 3 , Ž`. 94V2 O5 –6Sb 2 O 3 , ŽI. 92V2 O5 – 8Sb 2 O 3 films. The solid lines are obtained by the least squares fitting method.
Table 1 Conductivity Ž s . and activation energy for conduction ŽW . in amorphous V2 O5 –Sb 2 O 3 thin films Sb 2 O 3 Žmol%.
s 300 K ŽS cmy1 .
W Ž303–423 K. a ŽeV.
0 2 6 8
8.12=10y5 2.05=10y5 5.19=10y6 2.47=10y6
0.364 0.390 0.418 0.433
a
Obtained by the best fit of the conductivity data.
range of measurement Ž303–423 K., the relationship between logŽ s T . and Ty1 is found to be linear and confirms the equation
s s s 0 exp Ž yWrkT . rT ,
Ž 1.
where W is the activation energy for electrical conduction, k the Boltzmann constant and T the absolute temperature. In Fig. 1 no change in slope of the Arrhenius plot was seen, hence W was considered to be single-valued for the measured range of temperature ŽTable 1.. Therefore we can conclude that conduction is due to the hopping of polarons from the lower valence state ŽV 4q . to the higher valence ŽV 5q . of the vanadium ions and occurs uniquely through the vanadium ions along V–O–V chains, similar to the case of vanadate glasses w11–15x. The room-temperature conductivity of amorphous V2 O5 film is about 8.12 = 10y5 S cmy1 , which is one order of magnitude higher than those found in the previous studies for V2 O5 thin films w16–18x. The value of s at any fixed temperature Žsay, 303 K. decreased with increasing Sb 2 O 3 content in the films ŽTable 1.. The evaporated Sb atom or ion occupies O 2y vacancy andror breaks the V–O–V chains without changing valence state of vanadium ions, thereby decreasing the density of the percolative conducting paths and hence the Sb ions in the films hinder the electron transfer process and as a result the conductivity decreases with the increase in the concentration of the Sb ions. The activation energies of different compositions of the films, as estimated from the slopes of the curves in Fig. 1, are found to increase with an increase in the Sb 2 O 3 content in the film. Next we discuss the applicability of the Austin– Mott theory w8,9x of small polaron hopping to the present system of films. The well-known expression
S. Chakraborty et al.r Materials Letters 34 (1998) 341–344
343
for the electrical conductivity for hopping of polaron is w8x
s s nph e 2 R 2 Nb C Ž 1 y C . exp Ž y2 a R . =exp Ž yWrkT . ,
Ž 2.
where nph is the optical phonon frequency, N is the number of transition metal ion sites per unit volume, R is the average site spacing, C is the fraction of reduced transition metal ion, a is the wave function decay constant, so that expŽy2 a R . represents electron overlap between sites, W is the activation energy for conduction and b s 1rkT, where k is the Boltzmann constant and T, the absolute temperature. Thus in Eq. Ž1 ., s 0 s nph Ne 2 R 2 C Ž1 y C .expŽy2 a R .rk. Assuming strong electron–phonon interaction, Austin and Mott w14x showed that W s WH q WD r2
Ž for T ) u Dr2.
Ž 3a .
and W s WD
Ž for T - u Dr4 . ,
Ž 3b .
where WH is the polaron hopping energy, WD is the disorder energy arising from energy differences of the neighbouring sites and u D is the Debye temperature. The importance of the tunneling term, viz. expŽy2 a R . in Eq. Ž2., can be realized by plotting log s against W at a chosen temperature for all compositions of the film. The temperature estimated from the slope of such a plot would be close to the experimental temperature when the hopping is considered in the adiabatic regime and different from the experimental temperature when the hopping is con-
Fig. 3. The plot of ln s vs. Ty1 r4 for Žv . V2 O5 , Ž'. 98V2 O5 – 2Sb 2 O 3 , Ž`. 94V2 O5 –6Sb 2 O 3 , ŽI. 92V2 O5 –8Sb 2 O 3 films. The solid lines are obtained by the least squares fitting method.
sidered in the nonadiabatic regime w11x. Fig. 2 shows such a plot at a chosen temperature, T s 423 K. The temperature Te , as estimated from the slope of the curve in Fig. 2 is 314 K, thereby suggesting that conduction is by nonadiabatic hopping process in the present system of amorphous films. Triberis and Friedman w10,19x applied the percolation treatment for both the low and high temperature regime of the small polaronic hopping. Considering the effect of correlation between successive impedances Z, due to the energy of the common site, the expression for critical impedance Zc , is as follows: Zc s Z0 exp Ž T0 T .
1r4
,
3
Ž 4. y1
where T0 s 12.5 a rNk, a is the spatial extent of the electronic wave function and N is the density of states, and Z0 s kTe 2g 0
g 0 s Ž J 2r" . Ž pr4WH kT .
Fig. 2. Relationship between ln s and W at 423 K for different compositions of the film.
Ž 5. 1r2
,
Ž 6.
where J is the electron transfer integral. Fig. 3 shows the plot of ln s vs. Ty1 r4 for the various compositions of the films. The solid lines are obtained by the least squares fitting method. The values of T0 and N as estimated from the slope of the curves in Fig. 3 are tabulated in Table 2. In evaluating the density of states Ž N . from Eq. Ž4., a ˚ y1 . This value of a was was assumed to be 1 A chosen in accordance with the case of the vapour
S. Chakraborty et al.r Materials Letters 34 (1998) 341–344
344
Table 2 Model parameters obtained by fitting of the data with Triberis– Friedman model w10,19x Sb 2 O 3 Žmol%. 0
2
6
8
T0 ŽK. 1.26=10 9 1.70=10 9 2.30=10 9 2.68=10 9 y1 y3 . Ž N eV cm 1.15=10 20 8.55=10 19 6.32=10 19 5.42=10 19
deposited V2 O5 and Li xV2 O5 films studied by Murawski et al. w20x. The value of the density of states Ž10 20 eVy1 cmy3 . are physically reasonable for the formation of localized states in these films. It may be mentioned that the variable-range hopping model of Mott w8x, when applied to the present system of films, yield unacceptably large values of N and a .
4. Conclusion The conduction mechanism in the V2 O5 –Sb 2 O 3 thin films could be explained by the Mott’s theory w8,9x of hopping of small polarons in the nonadiabatic regime. Again the Triberis and Friedman percolation approach w10x in small polaronic hopping conduction could satisfactorily explain our data.
Acknowledgements One of the authors ŽS.C.. is grateful to the Matsumae International Foundation ŽJapan. for providing her a research fellowship.
References w1x E.P. Denton, H. Rawson, J.E. Stanworth, Nature 173 Ž1954. 1030. w2x N. Chopra, A. Mansingh, G.K. Chadha, J. Non-Cryst. Solids 126 Ž1990. 194. w3x G.A. Khan, C.A. Hogarth, J. Mater. Sci. 25 Ž1990. 504. w4x H. Ohtsuka, J. Yamaki, Jpn. J. Appl. Phys. 28 Ž1989. 2264. w5x L. Murawski, C. Gledel, C. Sanchez, J. Livage, J. Non-Cryst. Solids 89 Ž1987. 98. w6x F.A.S. Al-Ramadhan, C.A. Hogarth, Phys. Status Solidi A 87 Ž1985. 351. w7x H. Sakata, M. Amano, T. Ishiguro, T. Hirayama, J. Ceram. Soc. Jpn. 100 Ž1992. 1398. w8x N.F. Mott, J. Non-Cryst. Solids 1 Ž1968. 1. w9x I.G. Austin, N.F. Mott, Adv. Phys. 18 Ž1969. 41. w10x G.P. Triberis, L.R. Friedman, J. Phys. C 18 Ž1985. 2281. w11x M. Sayer, A. Mansingh, Phys. Rev. B 6 Ž1972. 4629. w12x L. Murawski, C.H. Chung, J.D. Mackenzie, J. Non-Cryst. Solids 32 Ž1979. 91. w13x A. Ghosh, B.K. Chaudhuri, J. Non-Cryst. Solids 83 Ž1986. 151. w14x H. Hirashima, M. Mitsuhashi, T. Yoshida, Yogyo-Kyokai-Shi 90 Ž1982. 411. w15x H. Mori, T. Kitami, H. Sakata, J. Non-Cryst. Solids 168 Ž1994. 157. w16x F.P. Koffyberg, F.A. Benko, Philos. Mag. B 38 Ž1978. 357. w17x T. Allersma, R. Hakim, R.T.W. Kennedy, J.D. Mackenzie, J. Chem. Phys. 46 Ž1967. 154. w18x C. Sanchez, R. Morineau, J. Livage, Phys. Status Solidi A 76 Ž1983. 661. w19x G.P. Triberis, J. Non-Cryst. Solids 74 Ž1985. 1. w20x L. Murawski, C. Sanchez, J. Livage, J.P. Audiere, J. NonCryst. Solids 124 Ž1990. 71.
Materials Letters 34 Ž1998. 341–344
Electrical conductivity of amorphous V2 O5 –Sb 2 O 3 thin films S. Chakraborty, K. Suzuki, H. Sakata
)
Department of Applied Chemistry, Tokai UniÕersity, 1117 Kitakaname, Hiratsuka, Kanagawa 259-12, Japan Received 6 June 1997; revised 21 July 1997; accepted 21 July 1997
Abstract Amorphous thin films of V2 O5 –Sb 2 O 3 , in the molar ratio of V2 O5:Sb 2 O 3 as 100:0, 98:2, 94:6, 92:8 respectively, were obtained by the vacuum–evaporation technique. The dc conductivities of the films were measured in the temperature range of 303–423 K. The experimental data have been analyzed in light of the small polaronic hopping model of Mott and the percolation approach of Triberis and Friedman. The estimated model parameters are found to be consistent with the formation of localized states in these films. q 1998 Elsevier Science B.V. Keywords: Electrical conductivity; Amorphous thin films; V2 O5 -Sb 2 O 3
1. Introduction Since the pioneering work of Denton et al. w1x amorphous transition metal oxides have been extensively studied. Their semiconducting properties arise from the hopping of the unpaired electron between transition metal ions in different valence states. Though a lot of work has been done to investigate the electronic conduction process through V2 O5 based binary or ternary glasses, very little work has been reported on similar study on vanadate based thin films w2–6x. The aim of the present investigation is to study the dc electrical conductivities of amorphous V2 O5 –Sb 2 O 3 thin films obtained by vacuum evaporation technique. Contrary to our expectations of an increase in conductivity of these binary films Žcompared to the single component V2 O5 film. in
)
Corresponding author.
view of the reducing action of Sb 2 O 3 , as observed by Sakata et al. w7x for Sb 2 O 3 –SrO–V2 O5 glasses, the Sb ions in the film seem to hinder the electron transfer process and lower the conductivity. The experimental results have been analyzed with the small polaron hopping model of Mott w8,9x and the percolation theory of Triberis and Friedman w10x.
2. Experimental The amorphous films of V2 O5 –Sb 2 O 3 were obtained in the molar ratio of V2 O5 :Sb 2 O 3 as 100:0, 98:2, 94:6 and 92:8 as starting evaporant material, respectively, by the resistance heating evaporation technique. Appropriate proportions of the V2 O5 and Sb 2 O 3 Ž99.99% each purity. were mixed in air in an agate mortar for 20 min and then the batch was evaporated from an electrically heated platinum crucible kept at 690 to a Pyrex glass plate Ža7059. kept at a temper-
00167-577Xr98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 7 - 5 7 7 X Ž 9 7 . 0 0 1 9 5 - X
342
S. Chakraborty et al.r Materials Letters 34 (1998) 341–344
ature of 100, under a vacuum of 10y4 Pa. The deposition rate of the film was about 1 nm sy1 . The thickness of the film was 300 nm as measured by the surface profile tester ŽKosaka, Surfcorder SE-30A.. X-ray diffractometry ŽPhilips, X’Pert PW1830. was used to characterize the crystallinity or the structure of the samples. The dc electrical conductivity Ž s . measurements were taken on the films of dimension 5 = 1 mm, carefully protected from ambient moisture. Two parallel gold electrodes were evaporated on the films. The ohmic behaviour of the film was ascertained from the linearity of the current voltage curves. The temperature and current were measured with a digital thermometer ŽAdvantest, TR2114. and a picoampere meter ŽHewlett-Packard, 4140B. respectively. The current intensity in these films, after the application of a fixed voltage, remains constant with time implying that the electrical conduction in these films is electronic in nature.
3. Results and discussion The X-ray diffraction pattern of the as-deposited films indicated their amorphous nature. Fig. 1 shows the plot of the dc conductivities of the V2 O5 –Sb 2 O 3 films of various compositions as a function of inverse temperature. In the temperature
Fig. 1. Temperature dependence of dc conductivity for Žv . V2 O5, Ž'. 98V2 O5 –2Sb 2 O 3 , Ž`. 94V2 O5 –6Sb 2 O 3 , ŽI. 92V2 O5 – 8Sb 2 O 3 films. The solid lines are obtained by the least squares fitting method.
Table 1 Conductivity Ž s . and activation energy for conduction ŽW . in amorphous V2 O5 –Sb 2 O 3 thin films Sb 2 O 3 Žmol%.
s 300 K ŽS cmy1 .
W Ž303–423 K. a ŽeV.
0 2 6 8
8.12=10y5 2.05=10y5 5.19=10y6 2.47=10y6
0.364 0.390 0.418 0.433
a
Obtained by the best fit of the conductivity data.
range of measurement Ž303–423 K., the relationship between logŽ s T . and Ty1 is found to be linear and confirms the equation
s s s 0 exp Ž yWrkT . rT ,
Ž 1.
where W is the activation energy for electrical conduction, k the Boltzmann constant and T the absolute temperature. In Fig. 1 no change in slope of the Arrhenius plot was seen, hence W was considered to be single-valued for the measured range of temperature ŽTable 1.. Therefore we can conclude that conduction is due to the hopping of polarons from the lower valence state ŽV 4q . to the higher valence ŽV 5q . of the vanadium ions and occurs uniquely through the vanadium ions along V–O–V chains, similar to the case of vanadate glasses w11–15x. The room-temperature conductivity of amorphous V2 O5 film is about 8.12 = 10y5 S cmy1 , which is one order of magnitude higher than those found in the previous studies for V2 O5 thin films w16–18x. The value of s at any fixed temperature Žsay, 303 K. decreased with increasing Sb 2 O 3 content in the films ŽTable 1.. The evaporated Sb atom or ion occupies O 2y vacancy andror breaks the V–O–V chains without changing valence state of vanadium ions, thereby decreasing the density of the percolative conducting paths and hence the Sb ions in the films hinder the electron transfer process and as a result the conductivity decreases with the increase in the concentration of the Sb ions. The activation energies of different compositions of the films, as estimated from the slopes of the curves in Fig. 1, are found to increase with an increase in the Sb 2 O 3 content in the film. Next we discuss the applicability of the Austin– Mott theory w8,9x of small polaron hopping to the present system of films. The well-known expression
S. Chakraborty et al.r Materials Letters 34 (1998) 341–344
343
for the electrical conductivity for hopping of polaron is w8x
s s nph e 2 R 2 Nb C Ž 1 y C . exp Ž y2 a R . =exp Ž yWrkT . ,
Ž 2.
where nph is the optical phonon frequency, N is the number of transition metal ion sites per unit volume, R is the average site spacing, C is the fraction of reduced transition metal ion, a is the wave function decay constant, so that expŽy2 a R . represents electron overlap between sites, W is the activation energy for conduction and b s 1rkT, where k is the Boltzmann constant and T, the absolute temperature. Thus in Eq. Ž1 ., s 0 s nph Ne 2 R 2 C Ž1 y C .expŽy2 a R .rk. Assuming strong electron–phonon interaction, Austin and Mott w14x showed that W s WH q WD r2
Ž for T ) u Dr2.
Ž 3a .
and W s WD
Ž for T - u Dr4 . ,
Ž 3b .
where WH is the polaron hopping energy, WD is the disorder energy arising from energy differences of the neighbouring sites and u D is the Debye temperature. The importance of the tunneling term, viz. expŽy2 a R . in Eq. Ž2., can be realized by plotting log s against W at a chosen temperature for all compositions of the film. The temperature estimated from the slope of such a plot would be close to the experimental temperature when the hopping is considered in the adiabatic regime and different from the experimental temperature when the hopping is con-
Fig. 3. The plot of ln s vs. Ty1 r4 for Žv . V2 O5 , Ž'. 98V2 O5 – 2Sb 2 O 3 , Ž`. 94V2 O5 –6Sb 2 O 3 , ŽI. 92V2 O5 –8Sb 2 O 3 films. The solid lines are obtained by the least squares fitting method.
sidered in the nonadiabatic regime w11x. Fig. 2 shows such a plot at a chosen temperature, T s 423 K. The temperature Te , as estimated from the slope of the curve in Fig. 2 is 314 K, thereby suggesting that conduction is by nonadiabatic hopping process in the present system of amorphous films. Triberis and Friedman w10,19x applied the percolation treatment for both the low and high temperature regime of the small polaronic hopping. Considering the effect of correlation between successive impedances Z, due to the energy of the common site, the expression for critical impedance Zc , is as follows: Zc s Z0 exp Ž T0 T .
1r4
,
3
Ž 4. y1
where T0 s 12.5 a rNk, a is the spatial extent of the electronic wave function and N is the density of states, and Z0 s kTe 2g 0
g 0 s Ž J 2r" . Ž pr4WH kT .
Fig. 2. Relationship between ln s and W at 423 K for different compositions of the film.
Ž 5. 1r2
,
Ž 6.
where J is the electron transfer integral. Fig. 3 shows the plot of ln s vs. Ty1 r4 for the various compositions of the films. The solid lines are obtained by the least squares fitting method. The values of T0 and N as estimated from the slope of the curves in Fig. 3 are tabulated in Table 2. In evaluating the density of states Ž N . from Eq. Ž4., a ˚ y1 . This value of a was was assumed to be 1 A chosen in accordance with the case of the vapour
S. Chakraborty et al.r Materials Letters 34 (1998) 341–344
344
Table 2 Model parameters obtained by fitting of the data with Triberis– Friedman model w10,19x Sb 2 O 3 Žmol%. 0
2
6
8
T0 ŽK. 1.26=10 9 1.70=10 9 2.30=10 9 2.68=10 9 y1 y3 . Ž N eV cm 1.15=10 20 8.55=10 19 6.32=10 19 5.42=10 19
deposited V2 O5 and Li xV2 O5 films studied by Murawski et al. w20x. The value of the density of states Ž10 20 eVy1 cmy3 . are physically reasonable for the formation of localized states in these films. It may be mentioned that the variable-range hopping model of Mott w8x, when applied to the present system of films, yield unacceptably large values of N and a .
4. Conclusion The conduction mechanism in the V2 O5 –Sb 2 O 3 thin films could be explained by the Mott’s theory w8,9x of hopping of small polarons in the nonadiabatic regime. Again the Triberis and Friedman percolation approach w10x in small polaronic hopping conduction could satisfactorily explain our data.
Acknowledgements One of the authors ŽS.C.. is grateful to the Matsumae International Foundation ŽJapan. for providing her a research fellowship.
References w1x E.P. Denton, H. Rawson, J.E. Stanworth, Nature 173 Ž1954. 1030. w2x N. Chopra, A. Mansingh, G.K. Chadha, J. Non-Cryst. Solids 126 Ž1990. 194. w3x G.A. Khan, C.A. Hogarth, J. Mater. Sci. 25 Ž1990. 504. w4x H. Ohtsuka, J. Yamaki, Jpn. J. Appl. Phys. 28 Ž1989. 2264. w5x L. Murawski, C. Gledel, C. Sanchez, J. Livage, J. Non-Cryst. Solids 89 Ž1987. 98. w6x F.A.S. Al-Ramadhan, C.A. Hogarth, Phys. Status Solidi A 87 Ž1985. 351. w7x H. Sakata, M. Amano, T. Ishiguro, T. Hirayama, J. Ceram. Soc. Jpn. 100 Ž1992. 1398. w8x N.F. Mott, J. Non-Cryst. Solids 1 Ž1968. 1. w9x I.G. Austin, N.F. Mott, Adv. Phys. 18 Ž1969. 41. w10x G.P. Triberis, L.R. Friedman, J. Phys. C 18 Ž1985. 2281. w11x M. Sayer, A. Mansingh, Phys. Rev. B 6 Ž1972. 4629. w12x L. Murawski, C.H. Chung, J.D. Mackenzie, J. Non-Cryst. Solids 32 Ž1979. 91. w13x A. Ghosh, B.K. Chaudhuri, J. Non-Cryst. Solids 83 Ž1986. 151. w14x H. Hirashima, M. Mitsuhashi, T. Yoshida, Yogyo-Kyokai-Shi 90 Ž1982. 411. w15x H. Mori, T. Kitami, H. Sakata, J. Non-Cryst. Solids 168 Ž1994. 157. w16x F.P. Koffyberg, F.A. Benko, Philos. Mag. B 38 Ž1978. 357. w17x T. Allersma, R. Hakim, R.T.W. Kennedy, J.D. Mackenzie, J. Chem. Phys. 46 Ž1967. 154. w18x C. Sanchez, R. Morineau, J. Livage, Phys. Status Solidi A 76 Ž1983. 661. w19x G.P. Triberis, J. Non-Cryst. Solids 74 Ž1985. 1. w20x L. Murawski, C. Sanchez, J. Livage, J.P. Audiere, J. NonCryst. Solids 124 Ž1990. 71.