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The semiconductor—Metal transition of liquid arsenic—Selenium mixtures at high temperatures and high pressures
NONtRY STAMNE SOLIDS ELSEWIER
Journal of Non-Crystalline Solids 205-207 (1996) 43-47
The semiconductor-metal transition of liquid arsenic-selenium mixtures at high temperatures and high pressures Hideoki Hoshino a3* , Takafumi Miyanaga b, Hiroyuki Hirohisa Endo e
Ikemoto ‘, Shinya Hosokawa d,
’ Facalt;of
Education, Hirosaki UniuersiO; BroAylo-cho I, 036 Hirosaki-ski, Japan Fatuity of Science, Hirosaki Uniuersir): 036 Hirosaki-shi. Japatl ’ Faculty ofScience. Toyama University, 930 Toyama, Japarl ’ Faculty of Sciewe, Hiroshima Uniuersify, 739 HiSashi-Hiroshilna, Japml ’ Faculty of Engineeriq, Fukui Instirute of Techology, 910 Fukui. Japan
Abstract The electrical conductivity g and thermoelectric power S of liquid As-Se mixtures (up to 10 at.‘% As) have been measured at high temperatures (up to 1500°C) and high pressures (up to 1200 bar). For these mixtures, broad maxima appear versus T curves. The maximum temperature r,,,, at which these in both the (a In c/W), versus T and the (-a In S/W), maxima occur decreases monotonically up to 30 at.% As. Around T,, the semiconductor-metal transition occurs. which is enhanced by applying pressure. It was found that r,, increases as the As concentration changes from 30 to 40 at.‘% As. The results of EXAFS suggest a substantial change in the local atomic configurationaroundAs atomsfor 30 at.% As.
1. Introduction The electrical and structural properties of amorphous and liquid As,Se, (1-As,Se,, 40 at.% As) have been the subject of numerous studies, which have shown that As,Se, has a network structure with threefold coordinated As and twofold coordinated Se atoms. Hosokawa et al. [I] have found for I-As2Se, that the semiconductor-to-metal transition (SMT), accompanied by volume contraction [2,3] occurs around 1000°C. Similar phenomena are observed for liquid Te-Se mixtures [4]. It has been reported that the SMT accompanied by the volume
contraction in liquid Te-Se mixtures arisesfrom the interchain interaction between shortened chains and is enhancedby application of pressure.In this paper, we report new results on the SMT of liquid As-Se mixtures that we obtained by measuring electrical conductivity and thermoelectric power at high temperatures and pressures.EXAFS experiments were carried out to determine the local structure around As atoms in connection with WT.
2. Experimental The mixtures were prepared by weighing 99.999% As, Se and Te and vacuum sealing them in silica glass ampoules.The constituents were reacted at 800°C for 10 h and then air-cooled to room pure
’ Corresponding author. Tel.: + 81-172 393 363; fax: + 51-172 393 363; e-mail: [email protected]. 0022-3093/96/S15.00 PII SOO22-3093(96)00212-S
Copyright 0 1996 Elsevier Science B.V. All rights resewed.
44
H. Hosltino
et ~1. / Jotmal
of Xon-Clystallimz
Solids 205-207
(1996)
43-47
i3
20
temperature. The electrical conductivity u of the liquid As-Se mixtures up to 40 at.% As was measured at pressures up to 1200 bar by using an internally heated autoclave up to 1500°C. The thermoelectric power S was measured simultaneously with u except for the mixture with 40 at.% As. The EXAFS experiments were made on the As and Te K-edges of the 1-AsTe, and I-As,Te, at 400°C using the spectrometer installed at the BL-1OB station of the Photon Factory at the National Laboratory for High Energy Physics (KEK). A typical photon flux was 10” photons/s with a positron beam energy of 3.0 GeV and a stored ring current of 180 mA. Further experimental details are described elsewhere [3,5.6].
3. Results When the pressure and the temperature are raised, c in the liquid As-Se mixtures increases. The sign of S for the mixtures is positive and S decreases nith increasing pressure and temperature. Fig. 1 shows the concentration variations of (T for the liquid As-Se mixtures at 600 bar and at different temperatures. At high temperature, a rapid increase in c is observed for a slight addition of As to liquid Se. The rate of the increase in u decreases as the As concentration increases, and a maximum appears around 35 at.% As at 600°C. ‘The pressure coefficients of (T: (a In c/W>,, and of S, (- a In S/aP), were deduced from experimental data on a(P, T) and S(P, T) for the various As concentrations. Fig. 2 shows a typical result for the variation of (a In a/aP), and ( - 8 In S/aP), with temperature for the mixture with 30 at.% As at 600 bar. Both (a In a/aP>, and (-a In S/W), have a maximum around 850°C. Similar behaviours in the pressure coefficients of w and S are observed for the As-Se mixtures with various As concentrations. Fig. 3 shows the variation of the temperature, T,.,,, with concentration. where (3 In c/aP>, or versus T curve has a maximum in ( -a 111 S/W), the liquid As-Se mixtures, together with those in the liquid Te-Se mixtures [4] for comparison. The temperature q,,, in the liquid Te-Se mixtures decreases monotonically with increasing Te concentration [5]. However. T,,, in the liquid As-Se mixtures abruptly
Se
30 aL%As
LO
50
Fig. 1. Variation of c with As concentration for liquid mixtures at different temperatures and at 600 bar.
As-Se
3CIal.%As 603 bar, 0
' 560
UT)
loo0
Fig. 2. Variation with temperature of the pressure coefficients of U, (a In (T /aP), and of S, (-a In S/aP),, for the liquid As-Se mixture with 30 at.% As at 600 bar. Lines are drawn as guides for the eye. The random uncertainty in each data point does not esceed the size of the symbol.
H. Hoshino
et al. / Journal
of Non-Crystalline
OS-LAS
at.%TeorAs
Fig. 3. Variation with concentrationof the temperaturecorresponding to the maximum in the (aln ,/aP), versus T plot, T max, for liquid As-Se mixtures (0) together with those for liquid Te-Se mixtures (A). Lines are drawn as guides for the eye.
increases as the As concentration changes from 30 to 40 at.% As, which suggests a substantial change in the local atomic configuration around As atoms. It is instructive to get information on the local structure of the liquid As-Se mixtures in this concentration range by means of EXAFS. Since the K-edge of As atoms is very close to that of Se atoms, the EXAFS oscillations due to both atoms overlap each other and the ambiguities of analyzing the EXAFS data are expected to be large. Therefore, the EXAFS experiments have been carried out on the liquid As-Te mixtures instead of the liquid As-Se mixtures, because the K-edge of As atoms is far away from that of Te atoms. It may be a reasonable assumption that the nature of the local bonding between liquid As-Se and liquid As-Te is quite similar at high temperature and pressure, since it is known [7] that the local structure of liquid Se becomes quite similar to that of liquid Te at high temperature and pressure. Here, it is noted that the disorder of the atomic arrangements due to the thermal agitation and large fluctuations in bond strength makes it difficult to analyze the local structure in the liquid state [8]. The amplitude of the EXAFS oscillation spectra
Solids 205-207
(1996)
43-47
45
x(k) of 1-AsTe, and 1-As,Te, around the As K-edge at 400°C is large in the low-k region; this feature is due to the backward scattering from Te atoms. In the EXAFS spectra x(k) around the As and Te K-eclges, distinct EXAFS oscillations remain up to 12 A-‘. Fig. 4 shows the magnitudes of the Fourier transform of kx(k), IF(u obtained around the central Te and As atoms for 1-AsTe, and l-As,Te, at 400°C. To derive the structural parameters, we carried out a curve fitting analysis [9] and calculated the back Fourier transform x(k) of IF(v)1 in the foJlowing regions around each peak: about 1.4 to 3.6 A at the As K-edge and about 1.5 to 4.0 A at the Te K-edge. The two-shell model was successful for the curve fitting. The main peaks of IF(r)1 for the As K-edges correspond to the As-Te covalent bond [lo] and those for the Te K-edges consist of Te-As and Te-Te bonds. For both mi$ures the As-Te distance is estimated t,” be 2.63 A; As-As, 2.48 A; and Te-Teb 2.75 A. Th,e distances involving As atoms (2.63 A and 2.48 A) agree well with the previous results [lo].
1
2
ii 5
Fig. 4. Magnitudes of the Fourier transform of k~(k), IF(r obtained around As and Te K-edges for I-AsTe, and I-As,Te, at 400°C.
H. Hoshino
46
Teas
0.8 -
0.7 z
Te K-edge 400°C I
3-
_
Te-Te I
I
I
_ I
/titota' *d-C
2
of Non-Crystalline
et al. /Journal
-
_---
ti As-Te
(b) 0.6 0.3 0
Te
As K-edge 4OPC I 10
I 20
I 30
I
40
I 50
at % As Fig. 5. Variation with concentration of the coordination numbers N around the central Te (a) and As atoms (b), determined by curve fitting of the EXAFS data for the liquid As-Te mixtures at 400°C. The values for pure Te are from Ref. [5]. Lines are drawn as guides for the eye.
Fig. 5 shows the concentration variations of the coordination numbers, N, around the central Te and As atoms. The total N around the central Te atoms changes from 1.6 for I-AsTe, to 1.5 for l-As,Te, with increasing As concentration. The total N around the central As atoms varies from 2.8 for l-AsTe, to 3.0 for 1-As,Te, as the As concentration increases. It should be emphasized that N for As around the central As atoms changes from 0.4 for LAsTe, to 0.6 for 1-As,Te,, which suggests that the shortened Te chains replaced by As atoms begin to form a network by making bonds via trivalent As atoms. 4. Discussion The correlation between the neighbouring chains in the liquid Se is substantially reduced at high temperatures and the Se chains may behave like isolated or single chains, Upon adding As to liquid Se, the Se atoms in isolated chains are randomly replaced by As and the chain length becomes short at high temperatures. The shortened chain ends may be
Solids 205-207
(1996) 43-47
somewhat negatively charged, and the middle of the chains may be positively charged [ll]. The frequent transfer of the holes or electrons in the lone-pair orbitals between the mixed chains occurs at high temperatures, which results in the rapid increase of (+ and the volume contraction as shown in Fig. 1. Such isolated short Se chains are stacked and the metallic character becomes enhanced with pressure. This causes the broadening of the lone-pair band of Se atoms and the SMT around T,,,. The concentration variations of N in Fig. S(b) suggest that the number of As-As bond interconnected through the neighbouring chains begins to increase when the As concentration increases over 30 at.% As, which results in the extension of the network structure. The appearance of the As-As bond may lock the local structure in the liquid mixture [12]. This causes the abrupt increase of T,,, around 30 to 40 at.% As.
5. Conclusions It is concluded that T,,, observed in the (8 In a/W>, or (- a In S/W’), versus T curve indicates the SMT which is originated from the broadening of the lone-pair band due to the interchain interaction and the liquid As-Se mixture transforms from the isolated short chains to the network structure.
Acknowledgements The authors are grateful to Dr H. Sakane for helpful discussion on EXAFS experiments.
References [I] S. Hosokawa, Y. Sakaguchi, H. Hiasa and K. Tamura, J. Phys.: Condens. Matter 3 (1991) 6673. [2] S. Hosokawa, Y. Sakaguchi and K. Tamura, J. Non-Cry% Solids 150 (1992) 35. 131 K. Tamura, S. Hosokawa, M. Inui, M. Yao, H. Endo and H. Hoshino, J. Non-Cryst. Solids 150 (1992) 351. [4] M. Yao, K. Suzuki, H. Hoshino and H. Endo, J. Phys. (Paris) 41 (1980)
a-28.
H. Hoshino
et al./ Journal
of Non-Crystnlline
[5] T. Tsuzuki, M. Yao and H. Endo, J. Phys. Sot. Jpn. 64 (1995) 485. I63 S. Hosokawa, M. Yao, T. Yoshimura and H. Endo, J. Phys. Sot. Jpn. 54 (1985) 4717. [7] K. Tamura and S. Hosokawa, Ber. Bunsenges. Phys. Chem. 96 (1992) 68. [S] A. Di Cicco and A. Filipponi, J. Non-Cryst. Solids 156-158 (1993) 102.
Solids 20.5-207
(1996)
43-47
47
[9] A.G. McKale, B.W. Veal, A.P. Paulikans, S.-K. Chan and G.S. Knapp, J. Am. Chem. Sot. 110 (1988) 3763. [lo] S. Hosokawa, K. Tamura, M. Inui and H. Endo, J. Non-Cryst. Solids 156-158 (1993) 712. [ll] M. Cutler, S.S. Kao and L.A. Silvia, Phys. Rev. B41 (1990) 3339. 1121 J. Comet and D. Rossier, J. Non-Cryst. Solids 12 (1973) 85.
Journal of Non-Crystalline Solids 205-207 (1996) 43-47
The semiconductor-metal transition of liquid arsenic-selenium mixtures at high temperatures and high pressures Hideoki Hoshino a3* , Takafumi Miyanaga b, Hiroyuki Hirohisa Endo e
Ikemoto ‘, Shinya Hosokawa d,
’ Facalt;of
Education, Hirosaki UniuersiO; BroAylo-cho I, 036 Hirosaki-ski, Japan Fatuity of Science, Hirosaki Uniuersir): 036 Hirosaki-shi. Japatl ’ Faculty ofScience. Toyama University, 930 Toyama, Japarl ’ Faculty of Sciewe, Hiroshima Uniuersify, 739 HiSashi-Hiroshilna, Japml ’ Faculty of Engineeriq, Fukui Instirute of Techology, 910 Fukui. Japan
Abstract The electrical conductivity g and thermoelectric power S of liquid As-Se mixtures (up to 10 at.‘% As) have been measured at high temperatures (up to 1500°C) and high pressures (up to 1200 bar). For these mixtures, broad maxima appear versus T curves. The maximum temperature r,,,, at which these in both the (a In c/W), versus T and the (-a In S/W), maxima occur decreases monotonically up to 30 at.% As. Around T,, the semiconductor-metal transition occurs. which is enhanced by applying pressure. It was found that r,, increases as the As concentration changes from 30 to 40 at.‘% As. The results of EXAFS suggest a substantial change in the local atomic configurationaroundAs atomsfor 30 at.% As.
1. Introduction The electrical and structural properties of amorphous and liquid As,Se, (1-As,Se,, 40 at.% As) have been the subject of numerous studies, which have shown that As,Se, has a network structure with threefold coordinated As and twofold coordinated Se atoms. Hosokawa et al. [I] have found for I-As2Se, that the semiconductor-to-metal transition (SMT), accompanied by volume contraction [2,3] occurs around 1000°C. Similar phenomena are observed for liquid Te-Se mixtures [4]. It has been reported that the SMT accompanied by the volume
contraction in liquid Te-Se mixtures arisesfrom the interchain interaction between shortened chains and is enhancedby application of pressure.In this paper, we report new results on the SMT of liquid As-Se mixtures that we obtained by measuring electrical conductivity and thermoelectric power at high temperatures and pressures.EXAFS experiments were carried out to determine the local structure around As atoms in connection with WT.
2. Experimental The mixtures were prepared by weighing 99.999% As, Se and Te and vacuum sealing them in silica glass ampoules.The constituents were reacted at 800°C for 10 h and then air-cooled to room pure
’ Corresponding author. Tel.: + 81-172 393 363; fax: + 51-172 393 363; e-mail: [email protected]. 0022-3093/96/S15.00 PII SOO22-3093(96)00212-S
Copyright 0 1996 Elsevier Science B.V. All rights resewed.
44
H. Hosltino
et ~1. / Jotmal
of Xon-Clystallimz
Solids 205-207
(1996)
43-47
i3
20
temperature. The electrical conductivity u of the liquid As-Se mixtures up to 40 at.% As was measured at pressures up to 1200 bar by using an internally heated autoclave up to 1500°C. The thermoelectric power S was measured simultaneously with u except for the mixture with 40 at.% As. The EXAFS experiments were made on the As and Te K-edges of the 1-AsTe, and I-As,Te, at 400°C using the spectrometer installed at the BL-1OB station of the Photon Factory at the National Laboratory for High Energy Physics (KEK). A typical photon flux was 10” photons/s with a positron beam energy of 3.0 GeV and a stored ring current of 180 mA. Further experimental details are described elsewhere [3,5.6].
3. Results When the pressure and the temperature are raised, c in the liquid As-Se mixtures increases. The sign of S for the mixtures is positive and S decreases nith increasing pressure and temperature. Fig. 1 shows the concentration variations of (T for the liquid As-Se mixtures at 600 bar and at different temperatures. At high temperature, a rapid increase in c is observed for a slight addition of As to liquid Se. The rate of the increase in u decreases as the As concentration increases, and a maximum appears around 35 at.% As at 600°C. ‘The pressure coefficients of (T: (a In c/W>,, and of S, (- a In S/aP), were deduced from experimental data on a(P, T) and S(P, T) for the various As concentrations. Fig. 2 shows a typical result for the variation of (a In a/aP), and ( - 8 In S/aP), with temperature for the mixture with 30 at.% As at 600 bar. Both (a In a/aP>, and (-a In S/W), have a maximum around 850°C. Similar behaviours in the pressure coefficients of w and S are observed for the As-Se mixtures with various As concentrations. Fig. 3 shows the variation of the temperature, T,.,,, with concentration. where (3 In c/aP>, or versus T curve has a maximum in ( -a 111 S/W), the liquid As-Se mixtures, together with those in the liquid Te-Se mixtures [4] for comparison. The temperature q,,, in the liquid Te-Se mixtures decreases monotonically with increasing Te concentration [5]. However. T,,, in the liquid As-Se mixtures abruptly
Se
30 aL%As
LO
50
Fig. 1. Variation of c with As concentration for liquid mixtures at different temperatures and at 600 bar.
As-Se
3CIal.%As 603 bar, 0
' 560
UT)
loo0
Fig. 2. Variation with temperature of the pressure coefficients of U, (a In (T /aP), and of S, (-a In S/aP),, for the liquid As-Se mixture with 30 at.% As at 600 bar. Lines are drawn as guides for the eye. The random uncertainty in each data point does not esceed the size of the symbol.
H. Hoshino
et al. / Journal
of Non-Crystalline
OS-LAS
at.%TeorAs
Fig. 3. Variation with concentrationof the temperaturecorresponding to the maximum in the (aln ,/aP), versus T plot, T max, for liquid As-Se mixtures (0) together with those for liquid Te-Se mixtures (A). Lines are drawn as guides for the eye.
increases as the As concentration changes from 30 to 40 at.% As, which suggests a substantial change in the local atomic configuration around As atoms. It is instructive to get information on the local structure of the liquid As-Se mixtures in this concentration range by means of EXAFS. Since the K-edge of As atoms is very close to that of Se atoms, the EXAFS oscillations due to both atoms overlap each other and the ambiguities of analyzing the EXAFS data are expected to be large. Therefore, the EXAFS experiments have been carried out on the liquid As-Te mixtures instead of the liquid As-Se mixtures, because the K-edge of As atoms is far away from that of Te atoms. It may be a reasonable assumption that the nature of the local bonding between liquid As-Se and liquid As-Te is quite similar at high temperature and pressure, since it is known [7] that the local structure of liquid Se becomes quite similar to that of liquid Te at high temperature and pressure. Here, it is noted that the disorder of the atomic arrangements due to the thermal agitation and large fluctuations in bond strength makes it difficult to analyze the local structure in the liquid state [8]. The amplitude of the EXAFS oscillation spectra
Solids 205-207
(1996)
43-47
45
x(k) of 1-AsTe, and 1-As,Te, around the As K-edge at 400°C is large in the low-k region; this feature is due to the backward scattering from Te atoms. In the EXAFS spectra x(k) around the As and Te K-eclges, distinct EXAFS oscillations remain up to 12 A-‘. Fig. 4 shows the magnitudes of the Fourier transform of kx(k), IF(u obtained around the central Te and As atoms for 1-AsTe, and l-As,Te, at 400°C. To derive the structural parameters, we carried out a curve fitting analysis [9] and calculated the back Fourier transform x(k) of IF(v)1 in the foJlowing regions around each peak: about 1.4 to 3.6 A at the As K-edge and about 1.5 to 4.0 A at the Te K-edge. The two-shell model was successful for the curve fitting. The main peaks of IF(r)1 for the As K-edges correspond to the As-Te covalent bond [lo] and those for the Te K-edges consist of Te-As and Te-Te bonds. For both mi$ures the As-Te distance is estimated t,” be 2.63 A; As-As, 2.48 A; and Te-Teb 2.75 A. Th,e distances involving As atoms (2.63 A and 2.48 A) agree well with the previous results [lo].
1
2
ii 5
Fig. 4. Magnitudes of the Fourier transform of k~(k), IF(r obtained around As and Te K-edges for I-AsTe, and I-As,Te, at 400°C.
H. Hoshino
46
Teas
0.8 -
0.7 z
Te K-edge 400°C I
3-
_
Te-Te I
I
I
_ I
/titota' *d-C
2
of Non-Crystalline
et al. /Journal
-
_---
ti As-Te
(b) 0.6 0.3 0
Te
As K-edge 4OPC I 10
I 20
I 30
I
40
I 50
at % As Fig. 5. Variation with concentration of the coordination numbers N around the central Te (a) and As atoms (b), determined by curve fitting of the EXAFS data for the liquid As-Te mixtures at 400°C. The values for pure Te are from Ref. [5]. Lines are drawn as guides for the eye.
Fig. 5 shows the concentration variations of the coordination numbers, N, around the central Te and As atoms. The total N around the central Te atoms changes from 1.6 for I-AsTe, to 1.5 for l-As,Te, with increasing As concentration. The total N around the central As atoms varies from 2.8 for l-AsTe, to 3.0 for 1-As,Te, as the As concentration increases. It should be emphasized that N for As around the central As atoms changes from 0.4 for LAsTe, to 0.6 for 1-As,Te,, which suggests that the shortened Te chains replaced by As atoms begin to form a network by making bonds via trivalent As atoms. 4. Discussion The correlation between the neighbouring chains in the liquid Se is substantially reduced at high temperatures and the Se chains may behave like isolated or single chains, Upon adding As to liquid Se, the Se atoms in isolated chains are randomly replaced by As and the chain length becomes short at high temperatures. The shortened chain ends may be
Solids 205-207
(1996) 43-47
somewhat negatively charged, and the middle of the chains may be positively charged [ll]. The frequent transfer of the holes or electrons in the lone-pair orbitals between the mixed chains occurs at high temperatures, which results in the rapid increase of (+ and the volume contraction as shown in Fig. 1. Such isolated short Se chains are stacked and the metallic character becomes enhanced with pressure. This causes the broadening of the lone-pair band of Se atoms and the SMT around T,,,. The concentration variations of N in Fig. S(b) suggest that the number of As-As bond interconnected through the neighbouring chains begins to increase when the As concentration increases over 30 at.% As, which results in the extension of the network structure. The appearance of the As-As bond may lock the local structure in the liquid mixture [12]. This causes the abrupt increase of T,,, around 30 to 40 at.% As.
5. Conclusions It is concluded that T,,, observed in the (8 In a/W>, or (- a In S/W’), versus T curve indicates the SMT which is originated from the broadening of the lone-pair band due to the interchain interaction and the liquid As-Se mixture transforms from the isolated short chains to the network structure.
Acknowledgements The authors are grateful to Dr H. Sakane for helpful discussion on EXAFS experiments.
References [I] S. Hosokawa, Y. Sakaguchi, H. Hiasa and K. Tamura, J. Phys.: Condens. Matter 3 (1991) 6673. [2] S. Hosokawa, Y. Sakaguchi and K. Tamura, J. Non-Cry% Solids 150 (1992) 35. 131 K. Tamura, S. Hosokawa, M. Inui, M. Yao, H. Endo and H. Hoshino, J. Non-Cryst. Solids 150 (1992) 351. [4] M. Yao, K. Suzuki, H. Hoshino and H. Endo, J. Phys. (Paris) 41 (1980)
a-28.
H. Hoshino
et al./ Journal
of Non-Crystnlline
[5] T. Tsuzuki, M. Yao and H. Endo, J. Phys. Sot. Jpn. 64 (1995) 485. I63 S. Hosokawa, M. Yao, T. Yoshimura and H. Endo, J. Phys. Sot. Jpn. 54 (1985) 4717. [7] K. Tamura and S. Hosokawa, Ber. Bunsenges. Phys. Chem. 96 (1992) 68. [S] A. Di Cicco and A. Filipponi, J. Non-Cryst. Solids 156-158 (1993) 102.
Solids 20.5-207
(1996)
43-47
47
[9] A.G. McKale, B.W. Veal, A.P. Paulikans, S.-K. Chan and G.S. Knapp, J. Am. Chem. Sot. 110 (1988) 3763. [lo] S. Hosokawa, K. Tamura, M. Inui and H. Endo, J. Non-Cryst. Solids 156-158 (1993) 712. [ll] M. Cutler, S.S. Kao and L.A. Silvia, Phys. Rev. B41 (1990) 3339. 1121 J. Comet and D. Rossier, J. Non-Cryst. Solids 12 (1973) 85.