- Email: [email protected]
Structural homogeneity of liquid selenium tellurium alloys
COMPUTATIONAL MATERIALS SCIENCE
ELSEVIER
Computational Materials Science 8 (1997) 208-212
Structural homogeneity
of liquid selenium tellurium alloys
Christophe Bichara
*
Abstract Tight binding Monte Carlo simulations of the structure of liquid selenium tellurium alloys have shown a clustering tendency between species with different coordination numbers. These results are in agreement with the conclusions that can be drawn from a simple statistical mechanical model previously developed for this system.
1. Introduction
As in a regular solution model, the total is a sum of first neighbor concentration-independent pair interactions. The binary Se-Te system is treated as a ternary one (Se, Te” and Tel”)., The connectivity of each atom is explicitly taken into account when deriving the Gibbs energy of mixing. This simple model is correct as far as a thermodynamic modeling is concerned, but the real system is in fact more complex, as shown in the case of pure tellurium by period tight binding Monte Carlo simulations [2]. In the three-fold coordinated metallic state. the three bonds around each tellurium atom are not equivalent (see Fig. 5 in Ref. [2]). Two of them are shorter, with a bond length (2.85 A> that corresponds to the intrachain distances in the solid. In this sense, the chain structure of tellurium is preserved in the liquid state. The length of the third bond is widely distributed, with a maximum around 3.15 A. This third distance is significantly shorter than the interchain distance in the solid state (3.47 A). In this sense, liquid tellurium can be viewed as ‘three-fold coordinated’. In the simple model mentioned above, the addition of selenium to pure tellurium stabilizes two-fold coordinated tellurium, the species with the -
energy
Liquid exhibit
binary
alloys
a particularly
of selenium interesting
and
behavior,
tellurium mainly
due to the structural changes in liquid tellurium. Liquid tellurium undergoes a semiconductor-to-metal transition around the melting temperature. This transition is driven by the gradual increase of the number of first neighbors when the temperature is raised. The consequences of this structural change are clearly reflected in the thermodynamic properties of mixing in the liquid state: the enthalpy of mixing is weakly negative (about - 2.4 kJ/mol) at temperatures just above the melting point of tellurium (450°C) and becomes positive in the tellurium-rich side at higher temperatures. This complex structural and thermodynamic behavior can be understood in a simple way. if one assumes that tellurium changes from a two-fold coordinated semiconducting state (Te”) at low temperature to a three-fold coordinated metallic state (Te”‘) at higher temperatures. A simple statistical thermodynamics model can be derived [l] with the following basic assumptions:
f Corresponding
0927.0256/97/$17.00 PI/
author. E-mail:
Copyright
SO927-0256(97)00034-7
[email protected].
0
1997 Elsevier
Science B.V.
All rights reserved
C. Bichara / Computational
Muterids
same coordination number (Tel’ and Se> exhibit a weak ordering tendency (in agreement with the fact that the solid state phase diagram displays a continuous solid solution) and species with different coordination numbers (Te”’ and Se) and (Te” and Ten’) have a tendency to segregate. As the entropy of mixing is strong enough, the alloy remains macroscopically homogenous in the experimentally accessible temperature range, but the question of the existence of microdomains (which size?, which composition?) is still open. Small angle neutron scattering experiments have been attempted without significant results [3], probably because either no microdomains of significant size exist or, if such microdomains exist, the contrast between them is too weak. It is interesting to notice that sulfur tellurium alloys, for which a similar behavior can be expected because selenium and sulfur are neighboring elements along column VI of the periodic table, do exhibit a closed miscibility gap in the liquid state. The aim of this note is to present a first approach to the study of the structure of this complex liquid alloy and to analyze the relative weight of the two competing effects that, according to the simple statistical thermodynamic model mentioned above, seem to govern the behavior of this system, namely: a weak chemical ordering tendency between selenium and tellurium and a clustering tendency due to the topological changes in the liquid structure. In this sense, the problems addressed here are related to the competing chemical and size effects that have been extensively discussed in the case of Au-Ni solid alloys [4].
2. Tight binding
model and computer
simulation
Science 8 (1997) 208-212
209
work on the pure elements. The total energy is the sum of an attractive electronic term, calculated in a tight binding approximation, and an empirical repulsive term. The attractive energy (E,> is due to the broadening of the electronic Ievels into a band of partially filled states. Its expression is: E, =
?En( / -3c
E)dE
(1)
where n(E) is the electronic density of states and Ef the Fermi level. The electronic density of states is approximated at the fourth moment level. The p-electron hopping plays the major role in the stabilization of the structure. Contrary to our previous work on selenium [7], the s electrons are also included and, consequently, a new set of parameters has been used for selenium. In this model, the only interactions between the chains are hopping electronic interactions leading to a covalent bond. Other contributions to the total energy, for example long range dispersion forces, are not included. The tight-binding hopping integrals between two atoms (i and j> are assumed to vary with the distance following:
(2) where the symbol h denotes the sscr, spa, ppa and ppr interactions and rO = 2.32 A is a distance unit. For all interactions, qA = 2. The damping term F is expressed by:
(3) An empirical repulsive term (E,) is added to prevent the atoms from collapsing. It is given by:
2.1. The model Elemental selenium has been studied by various approaches including ab-initio molecular dynamics [5,6] and the tight binding Monte Carlo simulation [7]. To our knowledge, no ab initio molecular dynamics study of liquid tellurium has been reported. This can be related to the difficulties encountered within the LDA approximation to stabilize the crystal structure of selenium or tellurium [8,9]. In order to study binary Se-Te melts we rely on our previous
This empirical repulsive term plays a key role for the stability of the structure. Therefore it seems pointless, in order to study a liquid structure, to develop the electronic density of states beyond the fourth moment level as long as the basic trends (directional bonding and ability to stabilize, at least qualitatively, the various high pressure phases) of the chemical bonding are well reproduced. The values of the main parameters used are given in Table 1. The
210 Table
C. Bichuru
/ Computcrtional
Materids
1
Se-Se
Se-Te
2.73
2.36
2.00
P&w
4.98
4.18
3.39
P ‘J
6.29
6.50
6.75
Vi’ (CL’)
9.98
9. I4
II.54
8 (1997)
208-212
very low (rejection rate of the order of 99% at T = 46O”C), but, as the MC runs are very long (at least 10,000 attempted displacement steps/atom and 200 attempted exchange steps/atom), the equilibrium of the system is reached.
Te-Te
4.4
Science
3. Results hopping integrals and repulsive pling are calculated by:
PSeTe
=
( P&Se +
PT~T~)/*
term for Se-Te
cou-
(5)
The prefactor V, SeTe is adjusted so as to obtain a correct order of magnitude for the enthalpy of mixing. 2.2. Computer
simulation
These preliminary calculations have been performed with a canonical algorithm (fixed number of atoms, volume and temperature) on a relatively small box containing 144 atoms with an average density (d = 0.0265 atoms/A’). The changes of density when varying the atomic concentrations are not taken into account. The Monte Carlo algorithm consists in two kinds of moves: atomic displacement moves and attempts to exchange the positions of two atoms of different kinds, which are accepted or rejected according to the classical Metropolis algorithm. If one considers the covalent bond 1enEths in pure crystalline Se (2.32 A> or Te (2.86 A) as indicative of their atomic sizes, it is clear that no exchange will be accepted for physically reasonable temperatures, even with the relatively soft repulsive potentials used ( pij are in the range 6-7). The reason why the crystals can accommodate such large atomic size differences is that the crystalline structures, which are made by stacking helical chains, are open and not very dense. In order to lower the rejection rate of the atomic exchanges during the Monte Carlo run, different tricks have been tried. First, taking advantage of the chain structure of the liquid, the two atoms to be exchanged are chosen as neighbors along a chain. Second, their positions are chosen so as to avoid the overlap with neighboring atoms, by treating the atoms as hard spheres. The efficiency of the process is still
Fig. 1 shows the energy of mixing at T= 46O”C, compared to the experimental enthalpies of mixing quoted in Ref. [l]. As the prefactor of the repulsive heteroatomic term V,fCT’ has been adjusted for this purpose, the order of magnitude of the enthalpies of mixing is correct. The fluctuations of the energies are rather large (standard deviation = lo-*) due to the small size of the box, and the energy differences between the alloy and the pure elements are small (e.g. at 50% Te, ( USeT2) = - 2.174 eV/atom, (Us,) = - 2.1 19 eV/atom, ( CJTi,, > = - 2.196 eV/atom, so that AH,,,,, = - 0.0 16 eV/atom). Thus the error bars on the enthalpies of mixing are large. The interesting point to notice is that the minimum is clearly shifted to the tellurium-rich side. Such an effect is also clearly visible on the structure factors (S(q)) calculated from the pair correlation functions (g( r>> that are directly measured during the course of the run. They are plotted on Fig. 2 and can be compared with the experimental structure factors obtained by Bellissent [lo], plotted on Fig. 3. The continuous changes of the structure factors when the concentration is varied are rather well reproduced as far as the peak positions and heights are concerned. The same effect as that observed on the enthalpies of mixing is observed: the transition to a ‘tellurium-like’ structure takes place at too high tellurium concentrations. This is due to the choice of the Se-Te unlike-pair parameters defined by Eq. (5). We did not try to improve the choice of these parameters, as it requires performing a full set of calculations. and has little effect on the point we are interested in. A complete study of the ordering or clustering effects in the liquid has to be done in terms of the partial structure factors. This analysis, as well as a complete study of the semiconductormetal transition that takes place when varying the tellurium content in the melt, will be published elsewhere. It seems more appropriate to simply look
C. Bichura
0.00
0.10
/ Computational
0.20
0.30
Materials
0.40
Science
0.50
0.60
Fig. I. Energy of mixing at T = 460°C (full squares, with error bars), compared [l]. The thin solid line is a guide to the eye.
at typical configurations generated by the Monte Carlo process. Three-fold coordinated atoms (generally tellurium) are colored in black and two-fold coordinated atoms are in gray (see Fig. 4). The
8 (1997)
208-212
0.70
211
0.80
to the experimental
0.90
1 .oo
enthalpies
of mixing ( +
) quoted in Ref.
cut-off distances determining the coordination numbers are taken at the first minimum of the partial pair correlation functions (3.20, 2.85 and 2.55 A for Te-Te, Se-Te and Se-Se distances, respectively). A
4.00
3.50
3.00
2.50
g
2.50
a z
2.00
_i 1.50
I
2.00
1.50
1.00
1.00
0.50
0.00, 3
1
2
3
4
5
6
7
8
9
10
q (A-‘)
Fig. 2. Structure factors calculated at various tellurium concentrations (indicated), at T = 460°C. The different curves have been shifted to preserve legibility.
O.OOo
1
2
3
4I,!
5
6I,I,l,/,7
8
9
10
9 (A-‘)
Fig. 3. Experimental structure factors at various tellurium concentrations (indicated) obtained by Bellissent [lo]. The different curves have been shifted to preserve legibility.
212
C. Bicharu / Computcrtionul
Materials
Science 8 (1997) 208-212
neighboring atoms also build shorter interchain bonds is higher. These questions will be addressed in more detail elsewhere.
4. Conclusions
Fig. 4. A typical configuration with 70% tellurium atoms, clearly showing a clustering tendency between three-fold coordinated atoms (in black) and two-fold coordinated atoms (in gray).
clear clustering tendency appears between two-fold and three-fold coordinated species, in agreement with the thermodynamic arguments developed in Ref. [ 11. The size of the domains is typically of the order of 5 to 15 atoms. Of course, these numbers depend on the choice of the cut-off distances, and must be considered with caution. The physical reason for this clustering tendency is not clear. A possible explanation could be a ‘size’ effect: the bond length increases with the coordination number, so that three-fold coordinated atoms appear bigger than two-fold coordinated ones. It hardly seems possible that the small differences in the bond lengths (of the order of 0.05 A> could be responsible for the clear clustering tendency observed. Another possible explanation is simply the ‘stiffness’ of the chains: once a short interchain bond has been built, the probability that
The tight binding Monte Carlo simulations presented here yield a model liquid alloy in rather good agreement with the available structural and thermodynamic data, although the concentration dependence of the thermodynamic and structural properties is not fully satisfactory reproduced. This does not affect the conclusions of this first approach that support the existence of structural inhomogeneities in the melt: two-fold coordinated domains and three-fold coordinated domains tend to segregate, in agreement with the conclusions drawn from a previous thermodynamic analysis of this system [l].
References [II A. Amzil, M. Gilbert, C. Bichara, J.-C. Mathieu, J. Phys. 8 (1996) 5281-5293.
[21 C. Bichara, J.-Y. Raty, J.-P. Gaspard, Phys. Rev. B 53 (1) ( 1996) 206-2 I 1. 131 R. Bellisscnt, private communication. [41 C. Wolverton, Comput. Mater. Sci. 8 (1997) 107, and references therein. bl D. Hohl, R. Jones, Phys. Rev. B 42 (1991) 3856. [61 F. Kirchhoff, M. Gillan, J. Holender, J. Non-Cryst. Solids, to be published. (71 C. Bichara, A. Pellegatti, J.-P. Gaspard, Phys. Rev. B 49 (IO) (1994) 6581-6586. [81 G. Kresse, J. Furthmuller, J. Hafner. Phys. Rev. B 50 (1994) 13181. 191 F. Kirchhoff, N. Binggeli, G. Gaili, S. Massida, Phys. Rev. B 50 ( 1994) 9063. [lOI R. Bellissent, These de doctorat bs Sciences, Orsay, 1981, unpublished.
ELSEVIER
Computational Materials Science 8 (1997) 208-212
Structural homogeneity
of liquid selenium tellurium alloys
Christophe Bichara
*
Abstract Tight binding Monte Carlo simulations of the structure of liquid selenium tellurium alloys have shown a clustering tendency between species with different coordination numbers. These results are in agreement with the conclusions that can be drawn from a simple statistical mechanical model previously developed for this system.
1. Introduction
As in a regular solution model, the total is a sum of first neighbor concentration-independent pair interactions. The binary Se-Te system is treated as a ternary one (Se, Te” and Tel”)., The connectivity of each atom is explicitly taken into account when deriving the Gibbs energy of mixing. This simple model is correct as far as a thermodynamic modeling is concerned, but the real system is in fact more complex, as shown in the case of pure tellurium by period tight binding Monte Carlo simulations [2]. In the three-fold coordinated metallic state. the three bonds around each tellurium atom are not equivalent (see Fig. 5 in Ref. [2]). Two of them are shorter, with a bond length (2.85 A> that corresponds to the intrachain distances in the solid. In this sense, the chain structure of tellurium is preserved in the liquid state. The length of the third bond is widely distributed, with a maximum around 3.15 A. This third distance is significantly shorter than the interchain distance in the solid state (3.47 A). In this sense, liquid tellurium can be viewed as ‘three-fold coordinated’. In the simple model mentioned above, the addition of selenium to pure tellurium stabilizes two-fold coordinated tellurium, the species with the -
energy
Liquid exhibit
binary
alloys
a particularly
of selenium interesting
and
behavior,
tellurium mainly
due to the structural changes in liquid tellurium. Liquid tellurium undergoes a semiconductor-to-metal transition around the melting temperature. This transition is driven by the gradual increase of the number of first neighbors when the temperature is raised. The consequences of this structural change are clearly reflected in the thermodynamic properties of mixing in the liquid state: the enthalpy of mixing is weakly negative (about - 2.4 kJ/mol) at temperatures just above the melting point of tellurium (450°C) and becomes positive in the tellurium-rich side at higher temperatures. This complex structural and thermodynamic behavior can be understood in a simple way. if one assumes that tellurium changes from a two-fold coordinated semiconducting state (Te”) at low temperature to a three-fold coordinated metallic state (Te”‘) at higher temperatures. A simple statistical thermodynamics model can be derived [l] with the following basic assumptions:
f Corresponding
0927.0256/97/$17.00 PI/
author. E-mail:
Copyright
SO927-0256(97)00034-7
[email protected].
0
1997 Elsevier
Science B.V.
All rights reserved
C. Bichara / Computational
Muterids
same coordination number (Tel’ and Se> exhibit a weak ordering tendency (in agreement with the fact that the solid state phase diagram displays a continuous solid solution) and species with different coordination numbers (Te”’ and Se) and (Te” and Ten’) have a tendency to segregate. As the entropy of mixing is strong enough, the alloy remains macroscopically homogenous in the experimentally accessible temperature range, but the question of the existence of microdomains (which size?, which composition?) is still open. Small angle neutron scattering experiments have been attempted without significant results [3], probably because either no microdomains of significant size exist or, if such microdomains exist, the contrast between them is too weak. It is interesting to notice that sulfur tellurium alloys, for which a similar behavior can be expected because selenium and sulfur are neighboring elements along column VI of the periodic table, do exhibit a closed miscibility gap in the liquid state. The aim of this note is to present a first approach to the study of the structure of this complex liquid alloy and to analyze the relative weight of the two competing effects that, according to the simple statistical thermodynamic model mentioned above, seem to govern the behavior of this system, namely: a weak chemical ordering tendency between selenium and tellurium and a clustering tendency due to the topological changes in the liquid structure. In this sense, the problems addressed here are related to the competing chemical and size effects that have been extensively discussed in the case of Au-Ni solid alloys [4].
2. Tight binding
model and computer
simulation
Science 8 (1997) 208-212
209
work on the pure elements. The total energy is the sum of an attractive electronic term, calculated in a tight binding approximation, and an empirical repulsive term. The attractive energy (E,> is due to the broadening of the electronic Ievels into a band of partially filled states. Its expression is: E, =
?En( / -3c
E)dE
(1)
where n(E) is the electronic density of states and Ef the Fermi level. The electronic density of states is approximated at the fourth moment level. The p-electron hopping plays the major role in the stabilization of the structure. Contrary to our previous work on selenium [7], the s electrons are also included and, consequently, a new set of parameters has been used for selenium. In this model, the only interactions between the chains are hopping electronic interactions leading to a covalent bond. Other contributions to the total energy, for example long range dispersion forces, are not included. The tight-binding hopping integrals between two atoms (i and j> are assumed to vary with the distance following:
(2) where the symbol h denotes the sscr, spa, ppa and ppr interactions and rO = 2.32 A is a distance unit. For all interactions, qA = 2. The damping term F is expressed by:
(3) An empirical repulsive term (E,) is added to prevent the atoms from collapsing. It is given by:
2.1. The model Elemental selenium has been studied by various approaches including ab-initio molecular dynamics [5,6] and the tight binding Monte Carlo simulation [7]. To our knowledge, no ab initio molecular dynamics study of liquid tellurium has been reported. This can be related to the difficulties encountered within the LDA approximation to stabilize the crystal structure of selenium or tellurium [8,9]. In order to study binary Se-Te melts we rely on our previous
This empirical repulsive term plays a key role for the stability of the structure. Therefore it seems pointless, in order to study a liquid structure, to develop the electronic density of states beyond the fourth moment level as long as the basic trends (directional bonding and ability to stabilize, at least qualitatively, the various high pressure phases) of the chemical bonding are well reproduced. The values of the main parameters used are given in Table 1. The
210 Table
C. Bichuru
/ Computcrtional
Materids
1
Se-Se
Se-Te
2.73
2.36
2.00
P&w
4.98
4.18
3.39
P ‘J
6.29
6.50
6.75
Vi’ (CL’)
9.98
9. I4
II.54
8 (1997)
208-212
very low (rejection rate of the order of 99% at T = 46O”C), but, as the MC runs are very long (at least 10,000 attempted displacement steps/atom and 200 attempted exchange steps/atom), the equilibrium of the system is reached.
Te-Te
4.4
Science
3. Results hopping integrals and repulsive pling are calculated by:
PSeTe
=
( P&Se +
PT~T~)/*
term for Se-Te
cou-
(5)
The prefactor V, SeTe is adjusted so as to obtain a correct order of magnitude for the enthalpy of mixing. 2.2. Computer
simulation
These preliminary calculations have been performed with a canonical algorithm (fixed number of atoms, volume and temperature) on a relatively small box containing 144 atoms with an average density (d = 0.0265 atoms/A’). The changes of density when varying the atomic concentrations are not taken into account. The Monte Carlo algorithm consists in two kinds of moves: atomic displacement moves and attempts to exchange the positions of two atoms of different kinds, which are accepted or rejected according to the classical Metropolis algorithm. If one considers the covalent bond 1enEths in pure crystalline Se (2.32 A> or Te (2.86 A) as indicative of their atomic sizes, it is clear that no exchange will be accepted for physically reasonable temperatures, even with the relatively soft repulsive potentials used ( pij are in the range 6-7). The reason why the crystals can accommodate such large atomic size differences is that the crystalline structures, which are made by stacking helical chains, are open and not very dense. In order to lower the rejection rate of the atomic exchanges during the Monte Carlo run, different tricks have been tried. First, taking advantage of the chain structure of the liquid, the two atoms to be exchanged are chosen as neighbors along a chain. Second, their positions are chosen so as to avoid the overlap with neighboring atoms, by treating the atoms as hard spheres. The efficiency of the process is still
Fig. 1 shows the energy of mixing at T= 46O”C, compared to the experimental enthalpies of mixing quoted in Ref. [l]. As the prefactor of the repulsive heteroatomic term V,fCT’ has been adjusted for this purpose, the order of magnitude of the enthalpies of mixing is correct. The fluctuations of the energies are rather large (standard deviation = lo-*) due to the small size of the box, and the energy differences between the alloy and the pure elements are small (e.g. at 50% Te, ( USeT2) = - 2.174 eV/atom, (Us,) = - 2.1 19 eV/atom, ( CJTi,, > = - 2.196 eV/atom, so that AH,,,,, = - 0.0 16 eV/atom). Thus the error bars on the enthalpies of mixing are large. The interesting point to notice is that the minimum is clearly shifted to the tellurium-rich side. Such an effect is also clearly visible on the structure factors (S(q)) calculated from the pair correlation functions (g( r>> that are directly measured during the course of the run. They are plotted on Fig. 2 and can be compared with the experimental structure factors obtained by Bellissent [lo], plotted on Fig. 3. The continuous changes of the structure factors when the concentration is varied are rather well reproduced as far as the peak positions and heights are concerned. The same effect as that observed on the enthalpies of mixing is observed: the transition to a ‘tellurium-like’ structure takes place at too high tellurium concentrations. This is due to the choice of the Se-Te unlike-pair parameters defined by Eq. (5). We did not try to improve the choice of these parameters, as it requires performing a full set of calculations. and has little effect on the point we are interested in. A complete study of the ordering or clustering effects in the liquid has to be done in terms of the partial structure factors. This analysis, as well as a complete study of the semiconductormetal transition that takes place when varying the tellurium content in the melt, will be published elsewhere. It seems more appropriate to simply look
C. Bichura
0.00
0.10
/ Computational
0.20
0.30
Materials
0.40
Science
0.50
0.60
Fig. I. Energy of mixing at T = 460°C (full squares, with error bars), compared [l]. The thin solid line is a guide to the eye.
at typical configurations generated by the Monte Carlo process. Three-fold coordinated atoms (generally tellurium) are colored in black and two-fold coordinated atoms are in gray (see Fig. 4). The
8 (1997)
208-212
0.70
211
0.80
to the experimental
0.90
1 .oo
enthalpies
of mixing ( +
) quoted in Ref.
cut-off distances determining the coordination numbers are taken at the first minimum of the partial pair correlation functions (3.20, 2.85 and 2.55 A for Te-Te, Se-Te and Se-Se distances, respectively). A
4.00
3.50
3.00
2.50
g
2.50
a z
2.00
_i 1.50
I
2.00
1.50
1.00
1.00
0.50
0.00, 3
1
2
3
4
5
6
7
8
9
10
q (A-‘)
Fig. 2. Structure factors calculated at various tellurium concentrations (indicated), at T = 460°C. The different curves have been shifted to preserve legibility.
O.OOo
1
2
3
4I,!
5
6I,I,l,/,7
8
9
10
9 (A-‘)
Fig. 3. Experimental structure factors at various tellurium concentrations (indicated) obtained by Bellissent [lo]. The different curves have been shifted to preserve legibility.
212
C. Bicharu / Computcrtionul
Materials
Science 8 (1997) 208-212
neighboring atoms also build shorter interchain bonds is higher. These questions will be addressed in more detail elsewhere.
4. Conclusions
Fig. 4. A typical configuration with 70% tellurium atoms, clearly showing a clustering tendency between three-fold coordinated atoms (in black) and two-fold coordinated atoms (in gray).
clear clustering tendency appears between two-fold and three-fold coordinated species, in agreement with the thermodynamic arguments developed in Ref. [ 11. The size of the domains is typically of the order of 5 to 15 atoms. Of course, these numbers depend on the choice of the cut-off distances, and must be considered with caution. The physical reason for this clustering tendency is not clear. A possible explanation could be a ‘size’ effect: the bond length increases with the coordination number, so that three-fold coordinated atoms appear bigger than two-fold coordinated ones. It hardly seems possible that the small differences in the bond lengths (of the order of 0.05 A> could be responsible for the clear clustering tendency observed. Another possible explanation is simply the ‘stiffness’ of the chains: once a short interchain bond has been built, the probability that
The tight binding Monte Carlo simulations presented here yield a model liquid alloy in rather good agreement with the available structural and thermodynamic data, although the concentration dependence of the thermodynamic and structural properties is not fully satisfactory reproduced. This does not affect the conclusions of this first approach that support the existence of structural inhomogeneities in the melt: two-fold coordinated domains and three-fold coordinated domains tend to segregate, in agreement with the conclusions drawn from a previous thermodynamic analysis of this system [l].
References [II A. Amzil, M. Gilbert, C. Bichara, J.-C. Mathieu, J. Phys. 8 (1996) 5281-5293.
[21 C. Bichara, J.-Y. Raty, J.-P. Gaspard, Phys. Rev. B 53 (1) ( 1996) 206-2 I 1. 131 R. Bellisscnt, private communication. [41 C. Wolverton, Comput. Mater. Sci. 8 (1997) 107, and references therein. bl D. Hohl, R. Jones, Phys. Rev. B 42 (1991) 3856. [61 F. Kirchhoff, M. Gillan, J. Holender, J. Non-Cryst. Solids, to be published. (71 C. Bichara, A. Pellegatti, J.-P. Gaspard, Phys. Rev. B 49 (IO) (1994) 6581-6586. [81 G. Kresse, J. Furthmuller, J. Hafner. Phys. Rev. B 50 (1994) 13181. 191 F. Kirchhoff, N. Binggeli, G. Gaili, S. Massida, Phys. Rev. B 50 ( 1994) 9063. [lOI R. Bellissent, These de doctorat bs Sciences, Orsay, 1981, unpublished.