Glass transitions and first order liquid-metal-to-semiconductor transitions in 4-5-6 covalent systems

&.-Klp

ELSEVIER

,OURNAL

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NON-CR Journal of Non-Crystalline Solids 205-207 (1996) 463-471

Section 5. Liquid-glass

transition, melting, amorphization and crystallization

Glass transitions and first order liquid-metal-to-semiconductor transitions in 4-5-6 covalent systems CA. Angel1 a!* ) S. Borick a, M. Grabow b a Departtnerlt

of Chemistry, Arizona State Uniuersiry, Tempe, AZ 85287-1604, b AT&T Bell Laboratories, Murray Hill, NJ, USA

USA

Abstract

In this paper the glass transition phenomenology for the 4-5-6 covalent system Ge-As-Se is reviewed and th argued that Ge- and Si-containing liquids should exhibit much of the phenomenology of the H,O-based and SiO systems which dominate the natural world. In both systems, aqueous solutions and silica-based glassformers, th glass-forming ranges are preceded by H,O-rich and SiO,-rich composition ranges in which there is a liquid-liquid separation. For both the aqueous systems and the 4-6 (and 4-5-6) systems, it is argued that the liquid-liquid transiti driven by a structural incompatibility of low temperature open network and high temperature, denser-packed structu latter being metallic in the cases of Ge and Si) which lead to first order phase transitions in the supercooling liqui argument is supported by showing that the phenomenologies of supercooled water and supercooled liquid silicon a similar. For the latter phenomenology, we turn to molecular dynamics computer simulations of liquid silicon us Stillinger-Weber potential which reproduces the melting point and many qualitative features of the real material. supercooled liquid state, S-W silicon shows, remarkably, all the anomalies in thermodynamic and diffusive pro known for supercooled water. These culminate in a directly observable, weak first order transition to the tetrahedral amorphous phase, (as suggested, but not established,for water) which then nucleatesthe crystallinepolymorphin with the experimental finding that liquid Ge can be supercooled to, but not below, the temperature estimated liquid-amorphous transition in liquid Ge.

1. Introduction Chalcogenide systems have been recognized as remarkable for their strongly glass-forming characteristics in certain composition domains for a long time [l]. Interest in these systems ran very high in

* Corresponding author. Tel.: -I- l-602 965 7217; fax: + I-602 965 2747; e-mail: [email protected].

the 1960s becauseof their potential as IR tra ting media and reversible switching materia The interest content of chalcogenide syste raised to a new level by the work of Phillip and Thorpe [5,6] who saw that their covalen ing character made them model systemsfor of constraint theory predictions [4-61. Tho particular predicted that a rapid increaseof m cal rigidity would set in when the bond passed a critical value [6]. The bond densit

0022-3093/96/$15.00 Copyright 6 1996 Elsevier Science B.V. All rights reserved. PII SOO22-3039(96)00261-X

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Fig. 1. The model covalent glass system Ge-As-Se, showing the domain of easy glass formation and the condition for rigidity percolation, (r> = 2.3. within this domain. The ternary composition lines on which interest is focused in this paper are AB, and CD.

called the average coordination number (meaning coordination of covalently bonded, as opposed to merely spacefilling, neighbors), was defined as

where n is the number of covalent bonds made by species i according to the (8 - n) valence electron rule and X is its mole fraction in the multicomponent solution. The argument [4-6] counts off the total degreesof freedom for a mole of atoms against the total of bond length and bond angle constraints imposed by the intact covalent bonds and predicts that rigidity should .percolate through the structure for any value of (r) greater than 2.4. An ideal system for testing these ideas is the ternary system Ge-As-Se in which all components are of similar mass(neighbors on the periodic table). Becauseof the different valences, 4, 3, and 2 respectively, the condition (r) = 2.4 can be satisfied for a range of different ternary mixtures [7] as shown by the line marked (r) = 2.4 in Fig. 1. Fig. 1 also shows the glass-forming region for moderate rate cooling of the liquid alloys. Although the prediction of breaks in the mechanical properties at ( r) = 2.4 has met with only moderate success[7] becauseof neglect of non-bonding interactions and other factors, it was found by Tatsumisago et al. [81 that properties characteristic of the viscous liquid and the glass transition showed special behavior near this ( r > value. We will give the first part of this paper to a review of the latter findings for thesesystems,which suggest that they may provide an excellent testing

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ground for general theories of ergodicity breaking and the overall problem of the glass transition, The second part will be devoted to the broader aim of establishing a phenomenological relationship between silicon- (or germanium-) based covalent bonded alloy solutions and two other major classes of solutions which together control much of what happens in the liquid state of the natural world. These are the aqueoussolutions, typified by the well studied system H,O + LiCl [91, and the siliceous solutionstypified by the even more thoroughly studied system 50, + Na,O [lo]. We will reaffirm the idea that much that is interesting and unusual about the latter two systems is due to the intrinsic structural incompatibility, at low temperatures, of the tetrahedral network structure of the parent components and the structures of homogeneoussolutions which form at higher second component contents when the network has been sufficiently disrupted. Since binary solution data in the Si- (or corresponding Ge-) based systems at high Si contents are sparse,most of this part of the paper will be devoted to arguing, from experimental and computer simulation studies, that liquid silicon and germanium have the same special characteristics possessedby H,O and SiO, which dominate their binary solution behavior, hence their binary solutions should be phenomenological analogs.

2. Phenomenology of Ge-As-Se glass-forming solutions Studies of the heat capacity per mole of atoms through the glass transition in a series of glasses falling on the line AB in Fig. 1 show that the glass transition becomes weak and smeared out as the composition passesthrough the ( r) = 2.4 value. Fig. 2 showshow both the activation energy for viscosity and the change of heat capacity at Tg go through minimum values close to (r) = 2.4. A recent paper by Senapati and Varshneya [l 11 shows similar behavior for the related system Ge-Sb-Se and shows that a minimum also occurs in the change in expansion coefficient. The correlation seenin Fig. 2 is predictable from the CP minimum via the Adam-Gibbs equation for relaxation processes [12]. For instance, the shear

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relaxation time, TV, whose temperature dependence dominates that of the viscosity, is written according to Adam and Gibbs as rs = q/G,

= r. exp( C/T&)

(2) shear modulus at ACP controls the Eq. (I), it also from the Arrheof the Arrhenius

where v is the viscosity, G, is the high frequencies, wr z=- 1. Because temperature dependence of S, in controls the magnitude of deviations nius equation, hence also the slope plot of q measured at Tg. The reason for ACP having a minimum at ( u) = 2.4 is less obvious but must have to do with the bond distribution being optimal at this composition hence the drive to thermal disruption via increased degeneracy, a minimum. In terms of potential energy hypersurfaces [13], (r) = 2.4 must correspond to a hypersurface with a relatively small number of minima, presumably because of a more or less unique bond distribution. This would correspond to a small entropy and a small increase in entropy per unit increase in energy. It has been shown elsewhere [S] how the viscosity behavior at { Y) = 2.4 is that of a ‘strong’ liquid-even stronger than B,O, and certainly stronger than the tetrahedral network compound GeSe,. The system Se-(Ge:As) thus exhibits the full range of strong to

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fragile behavior previously only seen by reference to a variety of other liquids, hence this system is rich in the phenomenology of the liquid-to-glass transition. Being simply constituted (no internal degrees of freedom) it is therefore to be regarded as a model system. Addition of iodine, which would break up chain structures, might be expected to lead to even more fragile behavior, but this is not strongly supported by the available data [14]. Solutions with (r) > 2.4 are more than optimally constrained. The term ‘over-constrained’ has been used [6]. With an interest in the consequences of excessive overconstraint, we turn attention to the line CD in Fig. 1 which contains compositions on either side of {r) = 2.4 but avoids passing through any compound, e.g., GeSe, along the line Ge-S. By analogy with SiO,-based and H,O-based system behavior, we expect that, as the ultimately overconstrained composition, pure Ge, is approached, the alloy will become unstable with respect to two separate liquid or amorphous phases, one of which is the random network of a-Ge itself. While this remains to be documented experimentally, and will be difficult to establish except for a small range near the edge of the glass-forming edge (because of the strong tendency of a-Ge to crystallize at T > 800 K), we present reasons for expecting it, as follows. First, a-Ge has already been observed to form exothermically from a binary liquid system studied near its glass transition temperature: solutions of Ge in GeO, quite near the composition GeO, (hence at N 37 at.% Ge in the system Ge-0 (cf. Ge-Se)) were observed by de Neufville and Turnbull [15] to precipitate a-Ge from the glass, with release of heat, on reheating above the T, of 633 K. One of their suggested interpretations ii very close to our line of thought given above. Second, according to computer simulation studies [16] discussed below and reported in more detail elsewhere [17], Si shows all the anomalies exhibited by SiO, and H,O, both of whose binary solutions are known to exhibit the phenomenon of splitting out of a second liquid (or amorphous) phase at compositions rich in the pure ‘tetrahedral’ liquid. There is no reason to expect liquid Ge to behave differently. Hence we propose that Ge-Se and, more so, Ge-Te binary solutions will behave like SiO,-based and H,O-based solutions and split out an amorphous Ge

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Fig. 3. Coinparison of phase diagrams of systems in which tetrahedral structure of parent component bestows anomalous behavior, including density maxima and liquid-liquid phase separation, on the supercooled binary solutions. (a) H,O + LiCl; (b) SiO, + Na,O; (c) Ge -I- Se. The dashed line in the water-LiCl system lying below the liquidus line is the line of homogeneous nucleation temperatures obtained from emulsion studies, and now interpreted as a close reflection of the line of homogeneous solution-to-(solution + amorphous) transitions at which crystallization of ice Ic from the amorphous phase becomes extremely rapid. The dashed line in the SiO,-Na,O system is the known boundary of the homogeneous solurions before unmixing occurs. The dashed line below the liquidus in the Ge-Se system is our conjectured line of liquid solution-to-(solution + amorphous) transitions. The arrow on the water-LiCl diagram indicates the composition where evidence for liquid-liquid separation without ice formation has been reported [9].

phase from quenched binary glassesin restricted composition rangesas identified in the caption to the Fig. 3. Third, the metallic-liquid-to-covalentamorphous-network phase transition suggestedas a possibility by de Neufville and Turnbull [15] has actually been observed by Thompson et al. in laser melting and quenching experiments in the analogous case of silicon [18]. It even occurs at the same reduced temperature (TfB,/Tm = 0.88 where T, is the melting point) suggestedfor a first order liquidto-amorphous network (fragile-to-strong liquidliquid transition) in the caseof water [19]. ’ The relevant binary phasediagramsare shown in Fig. 3, and are annotatedin the captions to highlight the common oddities. Note that the two-liquid region at high temperaturesin the Ge-Se system [21] is a consequenceof the incompatibility of the metallic germanium liquid and the semiconducting binary

’ While computer simulations using different potentials, ST2, TIPLFP, SPC, deny this for normal pressure, they confirm it for somewhat ‘higher’ pressures. On the other hand, all the best equations of state require it for notial pressures, albeit in a region of considerable extrapolation, hence unreliability 1201.

solution. This two-liquid region disappearsin the corresponding Ge-Te system in which the whole liquid range is metallic, so the Ge-Te phasediagram [21] looks more like the others, Fig. 3(a) and (b). Unfortunately the glass-forming composition range found between the compositions Ge-Se and GeSe, of the Ge-Se system also disappears.Thus we focus on the Ge-Se system and treat the two-liquid (metallic and semiconducting)range as a distraction to be ignored becauseour interest lies in the incompatibility of the sewziconductingbinary liquid with the semiconductkzg-tetrahedralphase which appears below a particular (metallic-liquid-to-semiconductor) transition temperature. The existence of the twoliquid region does, however, imply that the semiconducting solution - semiconductingtetrahedralphase unmixing line - will have a more complex shape than for the other systems(a) and (b) (seeSection 3). Unfortunately we do not yet have simulation data on Ge nor binary solution experiments on Ge-GeS quenchedsolutions.Thus in the remaining section of this paper we will support our casefor the solution analogies by emphasizing the phenomenological analogiesbetween water and liquid silicon (and germanium) both above and approaching the liquid-toamorphoustransition temperature. For this purpose,

C.A. Aqell

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Fig. 4. (a) Density of Si in atomic units (number of atoms/i3) in relation to temperature, for different states, showing maximum value in liquid at 1350°C. (b) Comparison of density temperature relations for H,O, SiO, and S-W silicon at zero pressure using reduced temperatures and densities, scaled by the densities and temperatures of maximum density. Values of pmrx (g/ml) for SiOz, Hz0 and S&S-W) are 2.23, 1.000, and 2.46, respectively. Corresponding values of Tp(,,,) (K) are 1823, 277, and 1375, respectively.

we will use both laboratory and computer simulation data.

3. First order transitions and the relation to water

in liquid

S-W

silicon

We commence with a comparison of the behavior of the densities in the liquid states as a function of pressure. Fig. 4(a) shows the effect of temperature on the density of silicon simulated using the Stillinger-Weber pair potential [22]. This potential, although intrinsically unable to reproduce the effect of Ihe electron delocalization which occurs at the crystal-liquid transition in real silicon (hence also at the liquid-amorphous transition), has been shown to

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give a good qualitative account of the major increase in coordination and density on fusion, and also reproduces the melting point of the diamond cubic crystal exactly. At very high pressures it also shows the crystallization of liquid into the K-8 phase of real silicon. Earlier studies of this potential by Liidke and Landman [23] showed many features which are reproduced, in greater detail, in the present study. Somewhat more accurate results are obtained by Jank and Hafner [24] using effective pair potentials with volume dependence derived from pseudopotential- and linear-response theories 12.51.The only way to cope fully with the metal-to-non-metal problem in simulation studies is to have the electrons treated explicitly, as is achieved in the Car-Parrinello approach [26] which has now been applied to Si [27] and Ge [28] for very small systems. In these, however, amorphous-amorphous phase transitions are obscured by the small system sizes. It is the large system sizes coupled with long runs of the present study which makes possible our success in observing the phenomena of interest to this paper, viz., the well defined density maxima seen in Fig. 4(a) and the liquid-amorphous phase change as well as the liquid tensile stability limit discussed below. The behavior of the density of S-W liquid silicon is compared with that of experimental water and experimental silicon dioxide in Fig. 4(b) using the same scaling scheme used in early comparisons of the latter two substances [29]. It appears that, relative to SiO,, the density maximum in silicon is quite sharply defined as in water. The effect of pressure (or tension) on the silicon density maximum is illustrated by the behavior of the isochoric cooling curves shown in Fig. 5(a). This behavior, which is highlighted by the dashed line drawn through the points of maximum density (isochoric pressure minima or tension maxima), may be compared with that known for laboratory water shown in Fig. 5(b) [29]. It appears that the density maximum in Si ‘washes out’ at high enough pressure though the possibility that this is due to equilibration problems probably cannot be excluded. Also included in Fig. 5(b) is the line of homogeneous nucleation temperatures, Th, obtained from emulsion measurements and the line of singular points, T,, obtained from data-fitting of divergent thermodynamic [29] and transport data (in particular

C.A. Angel1 et al. / Jolcmal of Non-Crystalline

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Fig. 5. (a) Pressure versus T for isochoric cooling of S-W silicon at different fractions of the crystal volume (in parentheses). Dashed line marks locus of density maxima, while thick solid lines mark loci of first order liquid-lo-amorphous transitions, and tensile limits at negative pressure. (b) Pressure dependence of the density maximum TMD and of the homogeneous nucleation temperature TH for water. The line T, is the line of supercooled liquid singularities obtained from analysis of diverging physical properties [29,30]. The line of liquid-to-amorphous transitions should lie between the latter two (from the reference).

the spin-lattice relaxation times of Lang and Liidemann [30]). The latter singularities are to be compared with the most spectacular feature of the liquid silicon simulations,a convincing example of which was first reported by Liidke and Landman [23]. These are the sudden occurrences, at temperatures which depend on the density of the silicon being simulated, of well-defined transitions from quite highly diffusive (Dsi = - low5 cm2 s - ‘> liquid states(whose coordination number changes with decreasing temperature), to essentially non-diffusive (‘amorphous’) phaseswith coordination number fixed at 4.1 inde-

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pendent of temperature. The transition to the amorphousphaseoccurs by nucleation at various points in the sample, and it is at the surface of these microdroplets that the crystallization of the system to the diamond cubic polymorph may be observed to initiate after a relatively short delay. At zero pressure,the transition was observed (see Fig. 4(a)) at 1060 K, well below the value 1480 K suggested by experiment [18] but close to the ‘amorphization temperature’ reported by Stich et al. [27] from ab initio simulations. Crystallization of Si was never observedat temperaturesabove this transition, despite the greater mobility of the ‘metallic’ liquid phase. This is entirely consistent with the recent observation by Filipponi and Dicicco [31] that levitated liquid Ge (metallic) can be supercooledto 680°C (- 260 K of supercooling). This temperature corresponds closely with the metallic-to-semiconducting liquid-liquid transition temperature calculated by Ponyatovsky and Barkalov [32] from their two-liquid model for silicon-like liquids. The temperature at which the transition occurs is depressedby increase of pressureas would be expected from the sign of the volume changeaccording to the Clapeyron equation. The observed transition temperaturesare plotted in Fig. 5(a). The pressure dependenceis comparable to, but smaller than, that of the melting transition. The occurrence during supercooling of a first order transition to a new amorphousphasewhich is of much higher viscosity, is exactly the interpretation that was recently given to the behavior of water during hyperquenching [lS], and is also exactly what is predicted by the Haar-Gallagher-Kell equation of state for water [33] which was developed to best representthe precisely determined behavior of laboratory water in its stable domain. On the other hand, the occurrenceof a first order transition in supercooling water at ambient temperature has been called into question by the results of computer simulations, using several different pair potentials, by Poole et al. [34] who find that such first-order transitions would only occur above a critical pressure.Whether or not the use of more realistic cooperative potentials will yield different results remains to be seen.According to the bond-modified van der Waals model for liquids with tetrahedral bonding [35] the two scenarios are closely related. It appearsfrom the present simu-

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lations that in S-W silicon, in contrast to the case of simulated water [34], the transition can be observed directly in simulations of reasonable length, and that it also can occur at ambient pressure. To summarize the phase behavior of liquid Si, heavy lines marking the loci of observed liquid-toamorphous transitions, liquid-to-cavitated-liquid transitions, and amorphous-to-cavitated-amorphous transitions have been added to Fig. 5(a). The latter lines fall at negative pressures and mark the tensile limits of the condensed phrases. * The tensile strength of the amorphous phase of Si seen in Fig. 5(a) is comparable to that of rigid ion SiO, [37]. In a binary system, the temperature of any liquid-amorphous transition will be depressed by addition of second components for the same reason that the melting point is depressed. Therefore, a subsidiary feature of any phase diagram for a system containing silicon, or water, plus some second component which is soluble in the nonnnE liquid phase, will be the separation of a viscous liquid or amorphous solid phase from the binary solution at some temperature below that of the pure component phase transition - as shown in two of the phase diagrams of Fig. 3. 3 In the Si- (or Ge-) based and the water-based systems, this amorphous phase separation will, however, be followed immediately by a crystallization of the amorphous phase unless the quenching is extremely rapid, or unless the solution composition is chosen so that the unmixing occurs very close to the T’, (i.e., higher Se contents). Finally in this demonstration of analogies we show in Fig. 6 the similar behavior of the transport coefficients in liquid S-W Si and laboratory water 139,401. Such similarity is in fact expected, in view of the negative expansivity regime common to each, from the Adam-Gibbs equation for the relaxation

’ It is noteworthy that, if the system is held near the tensile limit of the metallic phase where it is also at the limit of its stability with respect to the tetrahedral (or ‘amorphous’) phase, then it will crystallize into an icosahedral phase [36]. In the laboratory this same phase can be made by heating NaSi in vacuum. s The extrapolation of the immiscibility boundary in the SiO, NaZO system raises the question of whether for SiO, there could ‘glass-glass’) transition to a be a ‘liquid-amorphous’ (actually cristobalite-like glass phase at * 850°C on very long time scales.

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Fig. 6. (a) Dependence of the diffusivity of liquid silicon S-W on the pressure, showing maxima which shift to higher pressures with decreasing temperature. The pressure dependence becomes extreme near the liquid-amorphous transition which itself moves to higher pressures with decreasing temperature as a direct result of the expansion on coordination decrease. For dashed iine through circles, see caption (b). (b) Behavior of experimental water diffusivity with pressure (see footnote 3) [38], analogous to that of Si in part (a). The circles show the pressures at which the temperature of the isotherm is the temperature of the density maximum. Data details are in Refs. [39,40] (by permission of American Institute of Physics).

time, Eq. (2). A negative expansivity requires, by a Maxwell relation, a positive pressure dependence of the entropy and hence, according to Eq. (2), a relaxation time which decreases with increasing pressure [38]. The parallels in behavior seen in Fig. 6 are impressive. Comparable results are obtained also for the temperature dependence of the diffusivity at con-

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stant pressure, each system showing extremely nonArrhenius behavior [ 171. Of course, future large sample ab initio simulations of liquid Si are sure to show quantitative differences from the behavior displayed here. However, it seems likely to us that the qualitative trends we discuss will hold true and that the analogies drawn in Fig. 3 will therefore be validated, 4. Concluding

remarks

(1) Simulation studies of binary systems in which Ge-Ge interactions are perturbed by Se additions would be very helpful in establishing the validity of the analogies being suggested in this paper. (2) While we referred earlier to the two-liquid region at high temperatures in the Ge-Se system as a ‘distraction to be ignored’ in the context of the analogies we were drawing, we note here that its presence implies the possibility, under supercooled conditions, of an intriguing, though short-lived, three-liquid co-existence involving metallic solution, semiconductor solution, and semiconducting tetrahedral liquid (called ‘amorphous’ phase in this paper). The latter would quickly crystallize. (3) While it is peripheral to the thrust of this paper, we feel the observation recorded in footnote 3, which is stimulated by this work, might be very important insofar as a very large body of work on phase-separated silicate glasses has been accumulated without any recognition of the possible relevance of a hidden phase transition in silica itself a possibility which could explain why the product of subliquidus urn-nixing in silicate glasses is often rich in silica as is necessary for the Vycor process to succeed. Acknowledgements This research was supported by the NSF under Solid State Chemistry Grant No. DMR 9108028-002 and by AT&T, Bell Labs. The authors are grateful to Professor J.E. Enderby and Professor J. Hafner for helpful comments on this work, and to Professor P.F. McMillan for drawing our attention to Ref. [31] and the paper cited in Ref. [36].

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References [l] H. Rawson, Inorganic Glass-forming Systems (Academic Press, London, 1967) p, 216. 121 R. Zallen, The Physics of Amorphous Solids (Wiley, New York, 1983). [3] S.R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. 141 J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. IS] J.C. Phillips and M.F. Thorpe, Solid State Commun. 53 (1986) 847. [6] M.F. Thorpe, J. Non-Cryst. Solids 57 (1983) 355. [7] B.L. Halfpap and S.M. Lindsay, Phys. Rev. Lett. 57 (1986) 847.

[S] M. Talsumisago, B.L. Halfpap, J.L. Green, S.M. Lindsay and C.A. Angell, Phys. Rev. Lett. 64 (1990) 1549. [9] C.A. Angel1 and E.J. Sare, J. Chem. Phys. 49 (1968) 4713; 52 (1970) 1058; H. Kanno, J. Phys. Chem. 91 (1987) 1967; D.R. MacFarlane, Cryoletters 6 (1985) 33; 23 (1986) 230. [IO] N.J. Kreidl, in: Glass: Science and Technology, Vol. 1, ed. D.R. Uhlmann and N.J. Kreidl (Academic Press, New York, 1983) p, 105. [ll] U. Senapati and A.K. Varshneya, J. Non-Cry& Solids 185 (1995) 289, 1121 G. Adam and J.H. Gibbs, J. Chem. Phys. 43 (1965) 139. 1131 CA. Angell, J. Non-Cryst. Solids 131-133 (1991) 13. El41 J. Lucas, H.L. Ma, X.H. Zhang, H. Senapati, R. BShmer and CA. Angell, J. Solid State Chem. 96 (1992) 181. i153 J.P. de Neufville and D. Turnbull, Faraday Sot. Discuss. 327 (1971) 180. [16] M.H. Grabow and G.H. Gilmer, Mater. Res. Sot. Symp. Proc. 141 (1989) 341. [17] M.H. Grabow, S.S. Borick and CA. Angell, to be published. [18] M.O. Thompson, G.J. Galvin and J.W. Mayer, Phys. Rev. Lett. 52 (1984) 2360. [I91 CA. Angell, J. Phys. Chem. 97 (1993) 6339. [20] S.B. Kisilev, J.M.H. Levelt-Sengers and Q, Zheng, Proc. Water and Steam Conf. (19951, in press. [21] Z.U. Borisova, Glassy Semiconductors (Plenum, New York, 1981); H. Ipser, M. Gambino and W. Schuster, Monatsschr. Chem. 113 (1982) 389. 1221 F.H. Stillinger and T. Weber, Phys. Rev. B31 (1985) 5262. [23] W.D. Liidke and U. Landman, Phys. Rev. B 37 (1988) 4656; 40 (1989)

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W. Jank and J. Hafner, Phys. Rev. B41 (1990) 1497; J. Phys.: Condens. Mater. 1 (1989) 4235. [25] J. Hafner, From Hamiltonians to Phase Diagrams (Springer, Berlin, 1987). [26j R. Car and M. Parrinello, Phys. Rev. Lett. 55 (1985) 2471. 1271 I. Stich, R. Car and M. Parrinello, Phys. Rev. Lett. 63 (1989) 2240; Phys. Rev. B44 (1991) 4262. I281 G. Kresse and J. Hafner, Phys. Rev B49 (1994) 14251. I291 C.A. Angel1 and H. Kanno, Science 193 (1976) 1121; J. Chem. Phys. 73 (1980) 1940. [30] E.W. Lang and H.-D. Lidemann, J. Chem. Phys. 67 (1977) 718; Angew. Chem, Int. Ed. Engl. 21 (1982) 315. 1311 A. Filipponi and A. Dicicco, Phys. Rev. B51 (1995) 12322. [24]

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1321 E.G. Ponyatovsky and 0.1. Barkalov, Mater. Sci. Rep. 8 (1992) 147. [33] L. Haar, J. Gallagher and G.S. Kell, National Bureau of Standards - National Research Council Steam Tables (MCGraw-Hill, New York, 1985). [34] P.H. Poole, F. Sciortino, U. Essmann and H.E. Stanley, Nature (London) 360 (1992) 324; Phys. Rev. E48 (1993) 3799, 4605. [35] P.H. Poole, F. Sciortino, T. Grande, H.E. Stanley and CA. Angell, Phys. Rev. Lett. 73 (1994) 1632.

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