- Email: [email protected]
The electronic properties and structure of liquid Tl-Se and Ga-Se alloys
s -Klg
iDV.QNA‘OF
ELSEVIER
Journal
of Non-Crystalline
Solids 205-207
(1996)
89-93
The electronic properties and structure of liquid Tl-Se and Ga-Se alloys. S.B. Lague a, AC. Barnes a,* , A.D. Archer a, W.S. Howells b a H.H. Wills Physics Laboratov, Royal b Ruthe$ord Appleton Laboratory,
Fort, Tyndall Auenue, Bristol, BS8 ITL, Chilton, Didcot, Oxon, OX1 I OQX, UK
UK
Abstract Liquid alloys of the group (III) elements (Ga, In and Tl) and the group (VI) elements (S, Se and Te) show a diverse range of behaviour. It is presumed that these properties arise due to the two possible valence states of the group (III) element and the tendency for the chalcogenide element to form pairs in the liquid state. In this paper results are presented showing that liquid Ga,Se,-, remains semiconducting with c < - 20 a-’ cm-’ for all compositions between 0.4 < x < 0.5 but becomes progressively more metallic for x > 0.5. In contrast liquid Tl,Se, --x remains a good semiconductor for all compositions up to x = 0.67 and then becomes more metallic. Using recent neutron diffraction data, it is demonstrated that the low conductivity of Tl-Se alloys is fully explained in terms of an ionic type semiconductor where the conductivity remains low due to the formation of charged Se, pairs in the liquid for x < 0.67. On the other hand, the semiconducting alloys of liquid Ga-Se are shown to be characterised as a low density tetrahedrally coordinated covalent type structure reminiscent of the solid state structures in which Ga-Ga bonding is known to occur. These results give strong clues in understanding the particularly unusual properties of liquid In-Se alloys.
1. Introduction The alloys of the group JII elements (Ga, In and Tl) with the chalcogenide elements (group VI: S, Se
and Te) form a large range of semiconducting crystals in the solid state. A characteristic of the group is that the preferred valence of the group III element changes from three to one on moving down the group. The electronic properties of liquid Tl-Se have been extensively studied in the past [l] and it shows a characteristic semiconducting behaviour at the stoichiometric
* Corresponding 925 5624.
composition
author.
Tel.: +44-l
0022-3093/96/$15.00 Copyright PII SOO22-3093(96)00217-7
T1,Se
which
contin-
17 928 8701; fax: + 44-117
0 1996 Elsevier
Science
uestowards seleniumrich compositionsuntil approximately 75 at% Se where the liquid phase separates. Recently Okada and Ohno [2] reported detailed measurementsfor liquid In-Se and reported no indication of compound
formation
at In,Se
indicating
that
monovalent (In’) ions do not occur in the liquid. However the liquid was found to be a good liquid semiconductor for all compositions between InSe and In,Se,. It was also noted that the conductivity showed a small peak as a function of composition at In,Se3. This behaviour has only been observed in two other materials, namely Ag-S and Ag-Se which are still not well understood. It is not clear if the unusual behaviour of liquid In-Se is linked to that of the Ag systemsor whether it is better understood as an effect of the possible mixed valence states or
B.V. All rights reserved.
90
S.B. L.ugue et al. / Jownal
of Non-Crystalline
homoatomic bonding of In in these materials. As the solid gallium and indium selenides have similar crystal structures it is instructive to compare the properties of liquid Ga-Se with those of Tl-Se and In-Se. We have therefore studied both the electronic properties and structure of liquid Ga-Se alloys. There are two well known crystalline semiconductors of Ga-Se which correspond to the compositions GaSe and Ga,Se, [4]. The latter is relatively straightforward to understand as a tetrahedral network of Ga and Se with a large number of vacancies arranged in a manner such that the divalent and trivalent requirements of the Ga and Se are satisfied according to the 8 -N rule. The structure of solid GaSe is more complex and is characterised by planes of Ga atoms which are tetrahedrally coordinated to three Se atoms and one Ga atom, and Se atoms which are coordinated to three Ga atoms. These planes are bound together by weak Van der Waals interactions. The existence of the Ga-Ga bonds explains the apparent divalency of Ga implied from the stoichiometry. InSe has a similar structure and its low conductivity is presumably explained by a similar local structure remaining in the liquid phase. In contrast, the low conductivity of liquid TlSe is believed to be due to the formation of Se, dimers and not Tl-Tl bonding. Interpreting the similarities and differences in the electronic properties of liquid Tl-Se, In-Se and Ga-Se is therefore a challenge in determining the relevance of valence and bonding in understanding the properties of this group of liquid semiconductors.
Solids 205-207
(1996)
89-93
The sample cell was calibrated using high purity mercury at room temperature. To prevent evaporation of selenium from the sample, oxidation of the sample, and bubble formation, the experiments were carried out in an argon atmosphere. The samples were also periodically agitated with a tungsten rod to remove any bubbles. The thermopower measurements were made using a high accuracy digital voltmeter (10 nV>. The temperature of the upper and lower electrodes were controlled independently using a twin zone furnace. The neutron diffraction experiments were carried out on samples of Ga,rSe, --x and Tl,Se, --x using the LAD time of flight spectrometer at the ISIS facility at the Rutherford Appleton Laboratory, UK. The samples were contained in silica ampoules and heated using the standard RAL vanadium furnace. The data was regrouped and corrected for attenuation and multiple scattering using the ATLAS data analysis package I.51at RAL.
3. Results The electrical conductivity fl and thermopower S of liquid Ga,Se,-, are shown in Fig. I and Fig. 2. Also plotted are the data for liquid Tl,Se, --x [I]. At the composition Ga,Se, o has a value of N 1000 1100
,
-E-TI4e -Ml3a.se
2. Experimental The electrical conductivity and thermopower of liquid Ga,Se, --x alloys were measured simultaneously in quartz cells using a four probe method described previously [3]. Contact to the samples was made using small graphite electrodes inserted through the quartz tube. These were secured in place using molybdenum bands to which molybdenum wires were attached. The temperature of each electrode was measured using a chrome1 alumel thermocouple fastened by a molybdenum band immediately over the graphite electrode. The thermopower of the samples was ‘measured with reference to both the molybdenum electrode and the chrome1 of the thermocouple.
40
50
60
70
at.% Se
Fig. 1. The electrical conductivity and Tl,Se,-, (at 700°C [I]).
of liquid
Ga,$el-,
(at 103O’C)
S.B. Lague
of Non-Crystalline
et al/Journal
Solids
20.5207
(1996)
89-93
91
G&e,
TI,Se,
30
40
50
60
-2.0
70
at.% Se Fig. 2. The thermopower Tl ,Se, --x (at 700°C [l]).
of liquid
Ga,Sel-,
(at 1030°C)
and
4. I 0
-I 2
4
6
8
10
r/A
Fig. 4. Neutron total G(r)‘s for liquid Ga,Se,-, (at 1030°C) and Tl,Se,-, (at 7OO’C). The typical Fourier transform termination errors are shown on the Ga,Se, curve.
&,S%
G&e
-0.5
Ga,Se
-1.0
0-l cm-’ which reduces to (+= 20 fiiz-’ cm-’ for GaSe and U= 3 R-’ cm-’ for Ga,Se,. The thermopowers of GaSe and Ga,Se, were found to be -50 PV K-’ and +90 WV K-’ respectively. dc/dT was positive for all the Ga-Se compositions studied. The neutron total structure factors (F(Q)) for liquid Tl,Se, --x and Ga,Se, --x for n = 0.67, 0.5 and 0.4 are shown in Fig. 3. The Fourier transforms of these functions to G(r) are shown in Fig. 4.
4. Discussion
0
5
10
15
20
Q/A-’ Fig. 3. Neutron total 1030°C) and Tl,Se,-, the data points.
structure factors for liquid Ga,Se, --x (at (at 7OO’C) plotted as line segments through
At the composition Ga,Se the conductivity remains high (metallic) and the thermopower small, suggesting there is no tendency for strong compound formation at this composition. This contrasts sharply with the data for Tl-Se which shows a minimum at this composition. Hence there appears to be no ten-
92
S.B. Lugue et al. / Journal
of Non-Crystalline
dency of the Ga to form monovalent ions in this liquid. The minimum in CTat the composition Ga,Se, is completely consistent with the conclusion that Ga is essentially in its trivalent state at this composition. A change in the sign of the thermopower is also observed around this composition indicating a change from electron like conduction on the Ga rich side to hole like conduction on the Se rich side. Interestingly, at the composition GaSe the conductivity has a magnitude characteristic of a narrow definition liquid semiconductor [6] with a real gap in the density of states. Such a gap cannot be derived using any bonding scheme for GaSe which involves purely heteroatomic bonds. This data can be compared with the behaviour of liquid In,Se,-, [2] which shows similar trends except that CT suddenly rises at x = 0.42 to give a small maximum at the stoichiometric composition In, Se,. The neutron F(Q)s for the Ga,Se, and GaSe (Fig. 3) show strong oscillations out to high Q. This is consistent with strong local correlations in these liquids. The p
Solicls 205-207
(1996)
89-93
(7.288 fm and 7.97 fm respectively) the F(Q)s for Ga-Se approximate quite closely to S,, in the Bhatia-Thornton [9] representation of partial structure factors. This describesonly the atom-atom correlations and does not distinguish between atom types. Therefore from this data it is straightforward to determine the mean atomic coordination number ii in the liquid. In both of theseliquids there is a very clear first coordination sphere and ii determined by integrating to the first minimum in G(r) yields values of 2.7 in Ga,Se, and 3.0 in GaSe. This compares with values of 3.2 and 3.5 in the corresponding crystals. This suggeststhat the relatively open and low coordination number structures of the solidsare continued into the liquid phase.For Ga,Se there is a less well defined coordination shell and E determined by this procedure gives a value of 3.9 indicating a move to a higher coordination number at-_ this composition. The G(r)s for liquid Tl-Se show a much clearer behaviour. The composition Tl,Se has previously been studied to the partial structure factor level by Barnes and Guo [lo] who concluded the structure could be understood using a simple ionic picture of a liquid containing Tl+ and Se’- ions. From the data for TlSe and Tl,Se, it appearsthis structure doesnot change a great deal on adding selenbumapart from the observation of a peak at 2.34 A which correspondsto the Se-Se bond distance. Hence on adding Se to T1,Se it appearsthat the liquid remainsionic in characterexcept that the Se combinesto form charged Se, ions. It is the formation of these polyanions which is responsible for the low conductivity and high thermopower of this liquid over the composition range between T1,Se and Tl,Se,. In contrast, there is no evidence to suggestthat Ga forms Gaf ions in Ga,Se. This is consistent with the relatively high value observed for c in this alloy. The data obtained for GaSe and Ga,Se, showsclear evidence of strong tetrahedral (low coordination number) structuresreminiscent of the solids for theseliquids. This is particularly noticeable in Ga,Se,. Presumably the low conductivity of Ga-Se over the composition range GaSe to Ga,Se, is due to maintenance of a large essentially covalently bonded network in which both Ga-Se and Ga-Ga bonds occur. This is in direct contrast to the ionic like picture of T&Se. Recently an ab initio molecular dynamics study has
S.B. Lugue et al./JoumnE
of Non-Crystalline
Solids 205-207
(1996)
89-93
93
been carried out on liquid Ga-Se [ll]. These produced total structure factors in broad agreement with those shown here and a density of electronic states consistent with the observed conductivities. Close Ga-Ga distances were observed at all compositions in agreement with the suggestion above.
of the authors (S.B.L.) would like to thank the University of Bristol for the award of a PhD scholarship. They are also grateful to Professor J. Enderby, Professor M. Gillan, Dr J. Holender and F. Kirchkoff for useful discussions.
5. Conclusions
References
Measurements of the electronic properties and structure of liquid Ga-Se and Tl-Se have been presented. The results show that although Ga and Tl are in the same group in the periodic table, their behaviour in these materials is very different. Tl,Se, --x alloys are characterised by the formation of Tl+ ions in the melt. The low conductivity observed for 0.5
Acknowledgements This work (GR/H95105)
has been supported by the EPSRC who we gratefully acknowledge. One
[I] M. Cutler, Liquid Semiconductors (Academic Press, New York, 1977). [2] T. Okada and S. Ohno, J. Non-Cryst. Solids 156-158 (1993) 748. [3] A.C. Barnes, PhD thesis, University of Bristol (1986). [4] A.F. Wells, Structural Inorganic Chemistry (Clarendon, Oxford, 1984). [5] A.K. Soper, W.S. Howells and AC. Hannon, ATLAS Analysis of Time-of-Flight Diffraction Data from Liquid and Amorphous Samples, Rutherford-Appleton Laboratory report RAL-89-046 (1989). [6] J.E. Enderby and A.C. Barnes, Rep. Prog. Phys. 53 (1990) [7]- ;“‘T. Penfold and P.S. Salmon, Phys. Rev. Lett. 67 (1991) 97. IS] S. &man, K.J. Volin, D.G. Montague and D.L. Price, J. Non-Cryst. Solids 152 (1990) 168. [9] A.B. Bhatia and D.E. Thornton, Phys. Rev. B2 (1970) 3004. [IO] A.C. Barnes and C. Guo, J. Phys.: Condens. Matter 6 (1994) A229. [l I] J.M. Holender and M.J. Gillan, these Proceedings, p. 866.
iDV.QNA‘OF
ELSEVIER
Journal
of Non-Crystalline
Solids 205-207
(1996)
89-93
The electronic properties and structure of liquid Tl-Se and Ga-Se alloys. S.B. Lague a, AC. Barnes a,* , A.D. Archer a, W.S. Howells b a H.H. Wills Physics Laboratov, Royal b Ruthe$ord Appleton Laboratory,
Fort, Tyndall Auenue, Bristol, BS8 ITL, Chilton, Didcot, Oxon, OX1 I OQX, UK
UK
Abstract Liquid alloys of the group (III) elements (Ga, In and Tl) and the group (VI) elements (S, Se and Te) show a diverse range of behaviour. It is presumed that these properties arise due to the two possible valence states of the group (III) element and the tendency for the chalcogenide element to form pairs in the liquid state. In this paper results are presented showing that liquid Ga,Se,-, remains semiconducting with c < - 20 a-’ cm-’ for all compositions between 0.4 < x < 0.5 but becomes progressively more metallic for x > 0.5. In contrast liquid Tl,Se, --x remains a good semiconductor for all compositions up to x = 0.67 and then becomes more metallic. Using recent neutron diffraction data, it is demonstrated that the low conductivity of Tl-Se alloys is fully explained in terms of an ionic type semiconductor where the conductivity remains low due to the formation of charged Se, pairs in the liquid for x < 0.67. On the other hand, the semiconducting alloys of liquid Ga-Se are shown to be characterised as a low density tetrahedrally coordinated covalent type structure reminiscent of the solid state structures in which Ga-Ga bonding is known to occur. These results give strong clues in understanding the particularly unusual properties of liquid In-Se alloys.
1. Introduction The alloys of the group JII elements (Ga, In and Tl) with the chalcogenide elements (group VI: S, Se
and Te) form a large range of semiconducting crystals in the solid state. A characteristic of the group is that the preferred valence of the group III element changes from three to one on moving down the group. The electronic properties of liquid Tl-Se have been extensively studied in the past [l] and it shows a characteristic semiconducting behaviour at the stoichiometric
* Corresponding 925 5624.
composition
author.
Tel.: +44-l
0022-3093/96/$15.00 Copyright PII SOO22-3093(96)00217-7
T1,Se
which
contin-
17 928 8701; fax: + 44-117
0 1996 Elsevier
Science
uestowards seleniumrich compositionsuntil approximately 75 at% Se where the liquid phase separates. Recently Okada and Ohno [2] reported detailed measurementsfor liquid In-Se and reported no indication of compound
formation
at In,Se
indicating
that
monovalent (In’) ions do not occur in the liquid. However the liquid was found to be a good liquid semiconductor for all compositions between InSe and In,Se,. It was also noted that the conductivity showed a small peak as a function of composition at In,Se3. This behaviour has only been observed in two other materials, namely Ag-S and Ag-Se which are still not well understood. It is not clear if the unusual behaviour of liquid In-Se is linked to that of the Ag systemsor whether it is better understood as an effect of the possible mixed valence states or
B.V. All rights reserved.
90
S.B. L.ugue et al. / Jownal
of Non-Crystalline
homoatomic bonding of In in these materials. As the solid gallium and indium selenides have similar crystal structures it is instructive to compare the properties of liquid Ga-Se with those of Tl-Se and In-Se. We have therefore studied both the electronic properties and structure of liquid Ga-Se alloys. There are two well known crystalline semiconductors of Ga-Se which correspond to the compositions GaSe and Ga,Se, [4]. The latter is relatively straightforward to understand as a tetrahedral network of Ga and Se with a large number of vacancies arranged in a manner such that the divalent and trivalent requirements of the Ga and Se are satisfied according to the 8 -N rule. The structure of solid GaSe is more complex and is characterised by planes of Ga atoms which are tetrahedrally coordinated to three Se atoms and one Ga atom, and Se atoms which are coordinated to three Ga atoms. These planes are bound together by weak Van der Waals interactions. The existence of the Ga-Ga bonds explains the apparent divalency of Ga implied from the stoichiometry. InSe has a similar structure and its low conductivity is presumably explained by a similar local structure remaining in the liquid phase. In contrast, the low conductivity of liquid TlSe is believed to be due to the formation of Se, dimers and not Tl-Tl bonding. Interpreting the similarities and differences in the electronic properties of liquid Tl-Se, In-Se and Ga-Se is therefore a challenge in determining the relevance of valence and bonding in understanding the properties of this group of liquid semiconductors.
Solids 205-207
(1996)
89-93
The sample cell was calibrated using high purity mercury at room temperature. To prevent evaporation of selenium from the sample, oxidation of the sample, and bubble formation, the experiments were carried out in an argon atmosphere. The samples were also periodically agitated with a tungsten rod to remove any bubbles. The thermopower measurements were made using a high accuracy digital voltmeter (10 nV>. The temperature of the upper and lower electrodes were controlled independently using a twin zone furnace. The neutron diffraction experiments were carried out on samples of Ga,rSe, --x and Tl,Se, --x using the LAD time of flight spectrometer at the ISIS facility at the Rutherford Appleton Laboratory, UK. The samples were contained in silica ampoules and heated using the standard RAL vanadium furnace. The data was regrouped and corrected for attenuation and multiple scattering using the ATLAS data analysis package I.51at RAL.
3. Results The electrical conductivity fl and thermopower S of liquid Ga,Se,-, are shown in Fig. I and Fig. 2. Also plotted are the data for liquid Tl,Se, --x [I]. At the composition Ga,Se, o has a value of N 1000 1100
,
-E-TI4e -Ml3a.se
2. Experimental The electrical conductivity and thermopower of liquid Ga,Se, --x alloys were measured simultaneously in quartz cells using a four probe method described previously [3]. Contact to the samples was made using small graphite electrodes inserted through the quartz tube. These were secured in place using molybdenum bands to which molybdenum wires were attached. The temperature of each electrode was measured using a chrome1 alumel thermocouple fastened by a molybdenum band immediately over the graphite electrode. The thermopower of the samples was ‘measured with reference to both the molybdenum electrode and the chrome1 of the thermocouple.
40
50
60
70
at.% Se
Fig. 1. The electrical conductivity and Tl,Se,-, (at 700°C [I]).
of liquid
Ga,$el-,
(at 103O’C)
S.B. Lague
of Non-Crystalline
et al/Journal
Solids
20.5207
(1996)
89-93
91
G&e,
TI,Se,
30
40
50
60
-2.0
70
at.% Se Fig. 2. The thermopower Tl ,Se, --x (at 700°C [l]).
of liquid
Ga,Sel-,
(at 1030°C)
and
4. I 0
-I 2
4
6
8
10
r/A
Fig. 4. Neutron total G(r)‘s for liquid Ga,Se,-, (at 1030°C) and Tl,Se,-, (at 7OO’C). The typical Fourier transform termination errors are shown on the Ga,Se, curve.
&,S%
G&e
-0.5
Ga,Se
-1.0
0-l cm-’ which reduces to (+= 20 fiiz-’ cm-’ for GaSe and U= 3 R-’ cm-’ for Ga,Se,. The thermopowers of GaSe and Ga,Se, were found to be -50 PV K-’ and +90 WV K-’ respectively. dc/dT was positive for all the Ga-Se compositions studied. The neutron total structure factors (F(Q)) for liquid Tl,Se, --x and Ga,Se, --x for n = 0.67, 0.5 and 0.4 are shown in Fig. 3. The Fourier transforms of these functions to G(r) are shown in Fig. 4.
4. Discussion
0
5
10
15
20
Q/A-’ Fig. 3. Neutron total 1030°C) and Tl,Se,-, the data points.
structure factors for liquid Ga,Se, --x (at (at 7OO’C) plotted as line segments through
At the composition Ga,Se the conductivity remains high (metallic) and the thermopower small, suggesting there is no tendency for strong compound formation at this composition. This contrasts sharply with the data for Tl-Se which shows a minimum at this composition. Hence there appears to be no ten-
92
S.B. Lugue et al. / Journal
of Non-Crystalline
dency of the Ga to form monovalent ions in this liquid. The minimum in CTat the composition Ga,Se, is completely consistent with the conclusion that Ga is essentially in its trivalent state at this composition. A change in the sign of the thermopower is also observed around this composition indicating a change from electron like conduction on the Ga rich side to hole like conduction on the Se rich side. Interestingly, at the composition GaSe the conductivity has a magnitude characteristic of a narrow definition liquid semiconductor [6] with a real gap in the density of states. Such a gap cannot be derived using any bonding scheme for GaSe which involves purely heteroatomic bonds. This data can be compared with the behaviour of liquid In,Se,-, [2] which shows similar trends except that CT suddenly rises at x = 0.42 to give a small maximum at the stoichiometric composition In, Se,. The neutron F(Q)s for the Ga,Se, and GaSe (Fig. 3) show strong oscillations out to high Q. This is consistent with strong local correlations in these liquids. The p
Solicls 205-207
(1996)
89-93
(7.288 fm and 7.97 fm respectively) the F(Q)s for Ga-Se approximate quite closely to S,, in the Bhatia-Thornton [9] representation of partial structure factors. This describesonly the atom-atom correlations and does not distinguish between atom types. Therefore from this data it is straightforward to determine the mean atomic coordination number ii in the liquid. In both of theseliquids there is a very clear first coordination sphere and ii determined by integrating to the first minimum in G(r) yields values of 2.7 in Ga,Se, and 3.0 in GaSe. This compares with values of 3.2 and 3.5 in the corresponding crystals. This suggeststhat the relatively open and low coordination number structures of the solidsare continued into the liquid phase.For Ga,Se there is a less well defined coordination shell and E determined by this procedure gives a value of 3.9 indicating a move to a higher coordination number at-_ this composition. The G(r)s for liquid Tl-Se show a much clearer behaviour. The composition Tl,Se has previously been studied to the partial structure factor level by Barnes and Guo [lo] who concluded the structure could be understood using a simple ionic picture of a liquid containing Tl+ and Se’- ions. From the data for TlSe and Tl,Se, it appearsthis structure doesnot change a great deal on adding selenbumapart from the observation of a peak at 2.34 A which correspondsto the Se-Se bond distance. Hence on adding Se to T1,Se it appearsthat the liquid remainsionic in characterexcept that the Se combinesto form charged Se, ions. It is the formation of these polyanions which is responsible for the low conductivity and high thermopower of this liquid over the composition range between T1,Se and Tl,Se,. In contrast, there is no evidence to suggestthat Ga forms Gaf ions in Ga,Se. This is consistent with the relatively high value observed for c in this alloy. The data obtained for GaSe and Ga,Se, showsclear evidence of strong tetrahedral (low coordination number) structuresreminiscent of the solids for theseliquids. This is particularly noticeable in Ga,Se,. Presumably the low conductivity of Ga-Se over the composition range GaSe to Ga,Se, is due to maintenance of a large essentially covalently bonded network in which both Ga-Se and Ga-Ga bonds occur. This is in direct contrast to the ionic like picture of T&Se. Recently an ab initio molecular dynamics study has
S.B. Lugue et al./JoumnE
of Non-Crystalline
Solids 205-207
(1996)
89-93
93
been carried out on liquid Ga-Se [ll]. These produced total structure factors in broad agreement with those shown here and a density of electronic states consistent with the observed conductivities. Close Ga-Ga distances were observed at all compositions in agreement with the suggestion above.
of the authors (S.B.L.) would like to thank the University of Bristol for the award of a PhD scholarship. They are also grateful to Professor J. Enderby, Professor M. Gillan, Dr J. Holender and F. Kirchkoff for useful discussions.
5. Conclusions
References
Measurements of the electronic properties and structure of liquid Ga-Se and Tl-Se have been presented. The results show that although Ga and Tl are in the same group in the periodic table, their behaviour in these materials is very different. Tl,Se, --x alloys are characterised by the formation of Tl+ ions in the melt. The low conductivity observed for 0.5
Acknowledgements This work (GR/H95105)
has been supported by the EPSRC who we gratefully acknowledge. One
[I] M. Cutler, Liquid Semiconductors (Academic Press, New York, 1977). [2] T. Okada and S. Ohno, J. Non-Cryst. Solids 156-158 (1993) 748. [3] A.C. Barnes, PhD thesis, University of Bristol (1986). [4] A.F. Wells, Structural Inorganic Chemistry (Clarendon, Oxford, 1984). [5] A.K. Soper, W.S. Howells and AC. Hannon, ATLAS Analysis of Time-of-Flight Diffraction Data from Liquid and Amorphous Samples, Rutherford-Appleton Laboratory report RAL-89-046 (1989). [6] J.E. Enderby and A.C. Barnes, Rep. Prog. Phys. 53 (1990) [7]- ;“‘T. Penfold and P.S. Salmon, Phys. Rev. Lett. 67 (1991) 97. IS] S. &man, K.J. Volin, D.G. Montague and D.L. Price, J. Non-Cryst. Solids 152 (1990) 168. [9] A.B. Bhatia and D.E. Thornton, Phys. Rev. B2 (1970) 3004. [IO] A.C. Barnes and C. Guo, J. Phys.: Condens. Matter 6 (1994) A229. [l I] J.M. Holender and M.J. Gillan, these Proceedings, p. 866.