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PHYSICAL REVIEW B

VOLUME 62, NUMBER 5

1 AUGUST 2000-I

Reversible phase transition between amorphous phases in a bulk Zn-Sb alloy under high pressures
V. E. Antonov, O. I. Barkalov,* V. K. Fedotov, A. I. Harkunov, A. I. Kolyubakin, and E. G. Ponyatovsky
Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow District, Russia

M. Winzenick
¨ Fachbereich Physik, Universitat GH Paderborn, D-33095 Paderborn, Germany Received 22 February 1999 A line of metastable equilibrium between two amorphous semiconductor phases was determined resistometrically in the T -P diagram of the Zn41Sb59 alloy in the temperature range from 17 to 75 ° C. The amorphous nature of both phases was examined by x-ray diffraction at high pressures using a diamond-anvil cell and synchrotron radiation. The starting bulk amorphous sample was prepared by solid-state transformation of the quenched crystalline high-pressure -Zn41Sb59 phase during its heating at ambient pressure.

I. INTRODUCTION

Among the methods of solid-state amorphization, spontaneous amorphization of quenched high-pressure phases during their heating at ambient pressure is one of the most advantageous for producing bulk homogeneous samples.1­3 Amorphous Zn41Sb594 and GaSb-Ge5 produced by this method were studied previously at high pressures and it was shown that below the temperature of crystallization to the thermodynamic equilibrium state, the amorphous states can undergo reversible first-order phase transitions to other phases. The reversibility of the phase transitions evidences that these amorphous states are phases, i.e., they correspond to minima of the Gibbs potential. The amorphous phases are metastable and the minima therefore are not the deepest of all possible ones, but their presence gives an opportunity to describe transitions of these phases in the framework of equilibrium thermodynamics. In the GaSb-Ge system, a reversible transition occurs between the amorphous semiconductor phase and the crystalline metallic high-pressure phase which was used before to produce this amorphous phase.5 The behavior of the amorphous semiconductor Zn41Sb59 phase is quite different. With increase in pressure at room temperature, it undergoes two first-order phase transitions:4 i a transition to another semiconductor phase near 2 GPa and ii a transition to a semimetallic phase around 5 GPa. The phase formed at pressures above 5 GPa was shown6 to be a crystalline phase, called , with a simple hexagonal structure, different from the structure of the high-pressure phase used to prepare the initial amorphous phase. The 2-GPa transition was reversible and was accompanied by a 0.8% decrease in volume.4 The structure of the semiconductor phase formed above 2 GPa was not studied immediately under pressure. Nevertheless, from the x-ray examination of the quenched Zn41Sb59 samples it was inferred that this phase is amorphous. A reversible first-order phase transition between amorphous phases was earlier distinctly observed only in water, for two amorphous dielectric modifications of ice;7 the corresponding metastable equilibrium phase diagram was calcu0163-1829/2000/62 5 /3130 6 /$15.00 PRB 62

lated in Ref. 8. No transitions between amorphous semiconductor phases have been observed so far. In the present work, the previous assumption4 that the 2 GPa transition of the initially amorphous Zn41Sb59 is a transition between two amorphous phases, am 1 and am 2 , was confirmed by in situ x-ray-diffraction experiments. The T -P region of thermal stability of the two amorphous phases with the transition lines for the forward am 1 am 2 and backward am 2 am 1 transition were determined by electrical resistance measurement. The am 1 am 2 metastable equilibrium was analyzed with the two-level model which was earlier applied successfully to construct the diagram of metastable equilibrium between the two modifications of amorphous ice and to describe the anomalous thermodynamic properties of these ices and liquid water.8
II. SAMPLE PREPARATION AND EXPERIMENTAL DETAILS

A 20-g ingot of a two-phase Zn41Sb59 alloy consisting of a mixture of semiconducting ZnSb and metallic antimony9 was prepared from 99.99 wt % pure Zn and Sb by melting in an evacuated quartz tube and quenching into a cold water bath. The central part of the ingot was powdered in an agate mortar to obtain a more homogeneous ZnSb Sb mixture and the powder was pressed into a pellet 8 mm in diameter and 5 mm thick. The pellet was put in a Teflon container, exposed to 7.5 GPa and 325 ° C for 24 h in a Toroid-type high-pressure chamber and cooled to 100 K together with the chamber before the pressure was released. The x-ray examination at 100 K and ambient pressure DRON-2.0 diffractometer, CuK radiation showed in agreement with earlier results10 that this procedure results in a complete transformation of the pellet to the high-pressure phase, which is stable at P 6.5 GPa over a narrow concentration interval around the Zn41Sb59 composition. This pellet was then brought to the amorphous state by heating to room temperature and used to prepare the samples. Energy dispersive x-ray diffraction EDXD on these samples under pressure was performed with synchrotron radiation and diamond-anvil cells DAC in HASYLAB at
3130 ©2000 The American Physical Society


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DESY, Hamburg. A piece of amorphous Zn41Sb59 of nearly 150 m diameter and around 20 m thickness was loaded with white mineral oil and a few ruby grains into the central hole of the Inconel gasket in the DAC.11,12 The spectra were recorded by a Ge detector at an angle of 2 9.7174° over periods of 10 min in the course of the stepwise increase in pressure, which was measured by the ruby luminescence technique with a precision of 0.1 GPa with respect to the ruby scale.13 The electrical resistance was measured under pressure with samples in the form of bars 5 ­ 8 mm long and 1 1 mm2 across cut from the pellet of amorphous Zn41Sb59 with an abrasive wire saw. Crystallization of the samples was studied in a Toroid-type quasihydrostatic high-pressure chamber using hexagonal BN as pressure transmitting medium; the resistance was measured by a dc four-probe method with copper electrodes pressed against the sample. The transition between the amorphous phases was investigated under hydrostatic conditions in a piston-cylinder hydrostatic cell filled with silicon oil; the resistance was measured by a two-probe technique using copper electrodes soldered to the sample with indium at 165 ° C using ultrasonic soldering. Temperature and pressure were determined with accuracies of 0.3 GPa and 7 ° C, respectively, in the quasihydrostatic case and with 0.02 GPa and 1.5 ° C in the hydrostatic case. Before the high-pressure experiments, each Zn41Sb59 sample was investigated by x-rays at room temperature to ensure that no crystalline phases were present.
III. EXPERIMENTAL RESULTS A. High-pressure x-ray studies

FIG. 1. a Experimental EDXD spectrum of amorphous Zn41Sb59 in the diamond-anvil cell at ambient conditions. b The same spectrum after subtraction of the fluorescence lines. This spectrum is given here for comparison and is shown on a larger scale in Fig. 2 by the curve labelled ``0 GPa.'' The diffraction angle is 2 9.7174° . Positions of the fluorescence lines FL and of the escape lines EL are indicated with vertical bars.

Curve a in Fig. 1 shows the EDXD spectrum of the initial amorphous Zn41Sb59 sample in the DAC before application of pressure. In addition to the diffraction pattern from Zn41Sb59 , the spectrum contains two groups of strong fluorescence lines FL of Sb at 26.3 and 29.8 keV and a number of escape lines EL generated in the Ge detector. The diffraction angle 2 9.7174° was chosen for minimum overlap of the fluorescence lines with the diffraction halos of amorphous Zn41Sb59 . The profile of the pressure-independent fluorescence lines was derived from the EDXD spectra of crystalline -Zn41Sb59measured in a separate experiment, using a larger angle of 2 11.566° to avoid overlap of fluorescence and diffraction lines. This profile is subtracted from all the measured spectra for a more accurate evaluation of the shape and position of the diffraction halos of amorphous Zn41Sb59 . Curve b in Fig. 1 shows the resulting spectrum for ambient conditions and the whole set of the resulting spectra is presented in Fig. 2. The weak escape lines, which are also pressure independent, are not removed from the spectra in Fig. 2 and can serve as reference marks. The spectrum measured at 6.3 GPa contains one more detectable escape line positioned at 18 keV, which results from the 001 line of the phase. Additionally, most spectra exhibit weak and yet unidentified lines near 22.2 and 34.7 keV, which do not move with pressure and therefore do not belong to the diffraction pattern of the Zn41Sb59 sample.

As seen from Fig. 2, at room temperature and pressures up to 5.4 GPa, the spectra of Zn41Sb59 consist of two halos characteristic of amorphous materials. At a pressure of 6.0 GPa, the sample partly crystallized to a mixture of ZnSb Sb, and a peak composed of the strongest 112 and 121 lines of ZnSb and of the strongest 102 line of Sb appeared in the region of the first halo. At 6.3 GPa, the intensity of this peak was approximately the same whereas the amorphous phase mostly transformed to the simple hexagonal phase with the lattice parameters a 3.028( 5 ) å and c 2.760( 5 ) å in good agreement with previous results.6 The structure factor S ( Q ) , where Q is the momentum transfer, for amorphous Zn41Sb59 prepared by the same method as in this work was accurately determined earlier at ambient pressure by neutron diffraction.14 Figure 3 depicts these data together with the structure factor for the initial ambient pressure Zn41Sb59 sample calculated from the present EDXD data without corrections for the energy dependence of the incident beam intensity. It is seen that the positions and the widths of the first two halos are very similar in both S ( Q ) spectra. This comparison leads to the conclusion that the position and the width of these halos for Zn41Sb59 under pressure also can be determined reasonably well from the EDXD spectra. As is seen from Fig. 2, the width of both diffraction halos does not change significantly with pressures up to 6 GPa. The half-width Q 1 of the first halo of S ( Q ) can be used to give an estimate for the correlation length x i of the atomic short-range order in Zn41Sb59 according to the Scherrer forxi mula x i 2 / Q 1 . The resulting value of


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FIG. 4. The effect of pressure on the positions d 2 / Q of the centres of gravity for the first and second diffraction peaks in the EDXD spectra of amorphous Zn41Sb59 shown in Fig. 2. The diameter of the circles around data points corresponds to the experimental error.

FIG. 2. The EDXD spectra of the initially amorphous Zn41Sb59 alloy measured at room temperature and different pressures in the course of a stepwise pressure increase in a diamond-anvil cell using a diffraction angle of 2 9.7174° . The fluorescence lines occurring in all spectra at around 26.3 and 29.8 keV have been subtracted, their positions FL and the positions of the escape lines EL are indicated with solid vertical bars. The dotted bars indicate the positions, 22.2 keV and 34.7 keV, of two weak unidentified lines present in most spectra. The letter labels the Miller indices of the hexagonal phase formed at 6.3 GPa.

11 ­ 12 å remains constant for Zn41Sb59 within the pressure interval 0 ­ 6 GPa and is typical for amorphous materials. Figure 4 shows the pressure dependences of the positions of both diffraction halos of amorphous Zn41Sb59 in units of interatomic distances d 2 / Q . Both dependences are approximately linear at P 1.5 GPa and at P 1.5 GPa. The breaks in the slopes of both dependences are observed at about the same pressure of 1.45 GPa which is indicative of

some qualitative change in the amorphous state of the sample occurring at room temperature in the vicinity of this pressure. Further investigations Sec. III B showed that this is the same am 1 am 2 transition observed previously,4 but shifted to a lower pressure due to the more hydrostatic conditions of the present experiments. Note that the larger slopes d / P of both d ( P ) dependences for the am 1 phase correlate with its larger compressibility of about 0.026 GPa 1 compared to about 0.016 GPa 1 for the am 2 phase.4 Nearly invariable width of amorphous halos in the diffraction patterns of Zn41Sb59 throughout the studied pressure interval suggests that the am 2 state is single phase and that the am 2 phase therefore has the same composition as the am 1 phase. In fact, if the am 2 state were a mixture of amorphous phases with different compositions and, correspondingly, different diffraction patterns, one could expect at least a noticeable broadening of the amorphous halos after the am 1 am 2 transition.
B. T -P diagram of amorphous Zn41Sb59

FIG. 3. The structure factor S ( Q ) for amorphous Zn41Sb59 at ambient pressure. The open circles represent the result Ref. 14 of the neutron-diffraction measurement at 100 K. The solid line illustrates the x-ray data of this work shown in Fig. 2 by the curve ``0 GPa,'' both fluorescence and escape lines are removed.

Figure 5 presents the T -P diagram for the phase transitions in the initially amorphous Zn41Sb59 . The diagram combines the data of electrical resistance measurements with the results of high-pressure EDXD experiments and the x-ray examination of quenched samples at ambient pressure and 100 K. The temperatures of crystallization of amorphous Zn41Sb59 at different pressures asterisks in Fig. 5 correspond to the midpoints of the step in the isobars of electrical resistance measured at increasing temperature. Three representative isobars are shown in Fig. 6. In the course of the measurement, the sample was held at each point until the slope of the log10 versus time decreased by a factor of 10, and the final value of log10 was plotted in the figure. This process took 1 ­ 5 h within the interval of crystallization, 10 ­ 20 min below and above this interval, and less than 5 min on further cooling of the crystallized sample. According to the DSC and dilatometric data,4 crystallizaSb on tion of amorphous Zn41Sb59 to a mixture of ZnSb heating at a rate of 5 ° C/ min at ambient pressure occurred in the temperature interval 180 ­ 230 ° C. As is seen in Fig. 5, in


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FIG. 5. T -P phase diagram for initially amorphous Zn41Sb59 . am 1 and am 2 are the low- and high-pressure amorphous semiconductor phases, is the high-pressure semimetal phase with a simple hexagonal lattice. The solid square stands for the am transition at increasing pressure. The asterisks show the positions of the irreversible transitions of am and phases to a mixture of ZnSb Sb at increasing temperature. The solid and open circles indicate the am 1 am 2 and am 2 am 1 transitions at increasing and decreasing pressure under hydrostatic conditions, the solid and open triangles show where these transitions occur under quasihydrostatic conditions.4 The star marks the tentative position of the critical point of the am 1 am 2 line. The two dashed lines starting from this point are the calculated spinodals.

the present experiments with much lower heating rate, this process is already mostly completed at 180 ° C. An increase in pressure leads to a significant decrease in the crystallization temperature down to about 80 ° C at 5 GPa. An increase in pressure in excess of 5 GPa at room temperature results in crystallization of amorphous Zn41Sb59 into the phase. The solid square in Fig. 5 represents the midpoint of the isothermal change for the electric resistance measured in the course of a stepwise increase in pressure with exposure times for every point depending on the log10 drift which continued for 1 ­ 3 h in the vicinity of the step and for 15 ­ 20 min otherwise. The shape of the log10 (P) dependence and the position of the step were close to those observed earlier.4 However, the step occurred in both cases at a pressure of about 5.4 GPa which is much lower than the pressure of about 6.3 GPa for the formation of the phase in the EDXD experiment, Fig. 2. Besides, at about 6 GPa the amorphous phase in the EDXD experiment was partly transformed to a mixture of ZnSb Sb. This mixture was never formed at room temperature in the electric resistance

FIG. 7. a The isotherms of the electric resistivity, , of the amorphous Zn41Sb59 sample measured under hydrostatic conditions in the course of a stepwise increase solid symbols and decrease open symbols in pressure. b The same isotherms modified to gain better visualization of the regions of phase transitions: the slope of each isotherm is reduced by subtracting a linear function adjusted to the initial portion of the curve measured at decreasing pressure.

FIG. 6. The isobars of the electric resistivity, , measured on stepwise heating solid symbols and cooling open symbols of the initially amorphous Zn41Sb59 samples.

measurements4 because the sample crystallized to the phase at a lower pressure. The lower formation pressure of the phase in the course of the electric resistance measurements resulted presumably from quasihydrostatic conditions of these experiments in contrast to nearly hydrostatic conditions of the EDXD experiments. The pressures for the transitions between the amorphous phases circles in Fig. 5 represent the positions of the steepest portions of the electrical resistance isotherms Fig. 7 measured under hydrostatic conditions. In comparison with the measurements under quasihydrostatic conditions4 triangles in Fig. 5 , one may notice a better accuracy of the transition pressure and temperature and, what is most important, an essential decrease in the hysteresis of the am 1 am 2 transformation thus providing a better localization of the am 1 am 2 equilibrium line given in Fig. 5 by the shortdashed line. The electrical resistance isotherms shown in Fig. 7 were measured with increasing and decreasing pressure in steps of 0.1 GPa. At 17 and 50 ° C, the sample was kept at each point until a tenfold decrease in the slope of the log10 versus time was obtained, which took from 1 h at the edges of the studied


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pressure interval to 15 h near the steepest portions of the log10 (P) dependences. At 75 ° C, partial crystallization of the sample to a mixture of ZnSb Sb contributed noticeably to the time dependence of log10 , and the 75 ° C isotherm was measured in an isochronic regime, by holding the sample at each given pressure for 3 h. Figure 7 shows the final ln values.
IV. DISCUSSION

From a structural point of view, the only difference between amorphous phases with the same composition, like those in Zn41Sb59 , is their different short-range order. Therefore equilibria between such amorphous phases should be of the same type as those between different phases in onecomponent liquids which are considered as ``liquid-liquid'' or ``vapor-liquid'' equilibria depending on the density of the constituent phases. On the T -P diagrams, the lines of these equilibria terminate either in a point of intersection with another equilibrium line or in a critical point. The behavior of the electrical resistance of amorphous Zn41Sb59 suggests that the line of the am 1 am 2 equilibrium terminates in a critical point and that the critical temperature is of the order of 100 ° C as indicated by the star in Fig. 5. In fact, the am 1 am 2 and am 2 am 1 transitions are very sluggish and no acceleration is observed with increase in temperature from 17 to 75 ° C. At the same time, the rate of crystallization to a mixture of ZnSb Sb becomes noticeable at 75 ° C though this process requires diffusion of atoms over much longer distances than in the course of the isoconcentrational am 1 am 2 transformation. A significant decrease in the mobility of atoms is characteristic of systems approaching critical points. Therefore the critical temperature of the am 1 am 2 transformation should not be far above 75 ° C. With kinetics of isomorphic phase transitions as sluggish as in the case of amorphous Zn41Sb59 , one can expect that the am 1 am 2 transformation exhibits a clearly visible hysteresis until the volume effect of this transformation is zero, i.e., until the critical temperature is reached. As is seen from Fig. 5, linear extrapolations of the lines of the am 1 am 2 and am 2 am 1 transitions give zero hysteresis at a temperature of about 100 ° C. A fortunate feature of isomorphic transformations is the fact that the thermodynamic properties of both phases can be well described in many cases with one and a rather simple model Gibbs potential. In particular, these models allow a determination of spinodals which are useful for a better understanding of the hysteresis phenomena. Specifically, a simple two-level model which was first developed to describe the T -P diagram of cerium undergoing an isomorphic phase transition15 and then was successfully applied to the transition between amorphous phases of ice,8 will be applied here to the present case. The basic concept of this model assumes that both amorphous phases consist of clusters of two types, corresponding to the hypothetical short-range order in the first and in the second phase, respectively, at T 0 K. These clusters are considered as two components of the amorphous system and the Gibbs potential, G ( x ) , is written in the approximation of regular solutions. However, by contrast to the standard ap-

proximation of regular solutions, the concentration x is not an independent variable, but its value is determined by the minimum conditions: G / x 0 and 2 G / x 2 0. As a function of x, the Gibbs potential can have one or two minima depending on the T -P region. Two minimum values of G ( x ) are equal along a straight line which represents the first-order phase transformation between the two amorphous phases and terminates in a critical point at T cr where the two minima coincide and x 1 x 2 1/2. The points on the T -P plane, where one of the two minima of G ( x ) degenerates to an inflection point, form two lines starting from the critical point. These are spinodals, or the lines of complete loss of thermodynamic stability of one of the phases. The Gibbs potential thus constructed can be specified in a unique fashion by the values of four parameters:8,15 U, V , S , and E 0 , where U 2 RT cr is the mixing energy, V and S are the volume and entropy effects of the transition at any given temperature, E 0 is the difference between the internal energies of the components at 0 K. If, as discussed above, one adopts T cr 373 K and, correspondingly, U 6.2 kJ/mol, the other three constants can be derived from experiment. The volume effect of V / V 0.8% of the am 1 am 2 transition at room temperature has been measured before.4 The specific volume of V 16.4( 1 ) cm3 / mol of the am 1 phase at ambient conditions was determined by hydrostatic weighing in this work. Therefore V 0.13 cm3 / mol. With the line of the am 1 am 2 equilibrium drawn in the middle between the hysteresis branches Fig. 5 , a value of S 0.14 J/ ( K mol) can be obtained from the Clapeyron equation dT / dP V / S . The difference between the internal energies of the components at 0 K can be estimated as P 0 V 0 0.14 kJ/mol, where P 0 0.8 GPa results E0 from a linear extrapolation of the am 1 am 2 line to 0 K. V 0 0.17 cm3 / mol is the volume discontinuity at the am 1 am 2 transition at 0 K calculated from the roomtemperature value of V 0.13 cm3 / mol by using the temperature dependence of the ratio of V ( T )/ V ( 0 ) which is a unique function of the T / T cr ratio in the model used. The spinodals calculated with these values of the model parameters are plotted as dashed lines in Fig. 5. The am 1 state is no longer a phase above the spinodal on the right side of the critical point and the am 2 state cannot exist above the left spinodal. Actually, the spinodals outline the temperature dependence of the maximum possible hysteresis of the transformation. As is seen from Fig. 5, the hysteresis observed in the experiments is much smaller than the distance between the spinodals. At the same time, the large span of the spinodals shows that the thermodynamic stability of the am 1 and am 2 phases changes slowly over this large pressure interval, so the hysteresis of the am 1 am 2 transformation can be effectively influenced by other factors. This is illustrated in Fig. 5 by the fourfold decrease in the room-temperature hysteresis under hydrostatic conditions compared to the one observed in the presence of shear stresses in experiments with quasihydrostatic high pressures.4 The Gibbs potential, once constructed, allows a calculation of all thermodynamic properties of the system and, in particular, of the anomalies in the temperature dependences


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of the volume and of heat capacity at ambient pressure related to the am 1 am 2 transformation. However, in amorphous Zn41Sb59 these anomalies cannot be observed because the am 1 phase transforms on heating above 50 ° C into one more amorphous modification, other than am 2 , and this transformation is accompanied by a volume increase of a few percent and by a rather large heat release.4 The transformation is irreversible at atmospheric pressure, but at high pressures and room temperature the am 1 phase is formed again long before the am 1 am 2 transition occurs.4 With respect to the occurrence of three different amorphous semiconductor phases in the Zn41Sb59 alloy, one should note the following: In the Zn-Sb system, there are three semiconductor compounds, ZnSb, Zn4 Sb3 and Zn3 Sb2 , and the latter two have even various polymorphic modifications.9 Therefore the characteristic feature of this system is, that many different crystal structures have close values of the Gibbs free energy. On the other hand, there is an empirical rule for glasses, saying that the local atomic structure of a glass is similar to that of one of the crystalline forms of the material.16 The am 1 phase has the same type of local atomic structure as crystalline ZnSb compound.14 One could expect that the two other amorphous phases also are analogs of certain crystalline phases in the Zn-Sb system and that these amorphous phases have values of the Gibbs free energy close to the one of the am 1 phase. If this is the case, the relative stability of amorphous phases in Zn41Sb59 should strongly depend on temperature and pressure, and phase transitions between different amorphous phases can occur even within the rather limited T -P region of their thermal stability.
V. SUMMARY

side by a line of crystallization resulting in a mixture of Sb. This line descends from about 180 ° C at ambiZnSb ent pressure to about 80 ° C at 5 GPa. At pressures exceeding 5 ­ 6 GPa, amorphous Zn41Sb59 crystallizes to the phase with a simple hexagonal structure. Inside the region bounded by the crystallization lines, a reversible first-order phase transition between two different amorphous phases, am 1 and am 2 , with the same Zn41Sb59 composition is found to occur at pressures around 1 GPa. The line of the am 1 am 2 metastable equilibrium is experimentally determined at temperatures from 17 to 75 ° C and evidences are given that this line terminates in a critical point at a temperature of about 100 ° C. Within the framework of a two-level model, the Gibbs potential of amorphous Zn41Sb59 is constructed and the lines of a complete loss of thermodynamic stability spinodals are calculated for both amorphous phases. The given T -P diagram is the first example of a diagram with a line of phase equilibrium between two different amorphous semiconductor phases.

ACKNOWLEDGMENTS

The T -P region of thermal stability of amorphous Zn41Sb59 is shown to be bounded on the high-temperature

This work was supported by Grant Nos. 99-02-17007 and 96-15-96806 from the Russian Foundation for Basic Research and by Grant No. 34-1997 for young scientists from the Russian Academy of Sciences. One of the authors O.I.B. thanks the Alexander von Humboldt Foundation for support and thanks HASYLAB for financial support and the hospitality during his stay at DESY, Hamburg. Financial support by the German Ministry of Research and Technology under Contract No. 05647PPA is gratefully acknowledged. The authors are grateful to Professor W. B. Holzapfel and G. Grosse for helpful discussions and would like to ¨ thank W. Brockling for technical assistance.

¨ *Present address: Fachbereich Physik, Universitat-GH-Paderborn,
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