Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

Atomic structure of pressure-induced amorphous semiconductors

O.I. Barkalov*, Institute of Solid State Physics, Russian Academy Sciences,142432 Chernogolovka Moscow district, Russia, barkalov@issp.ac.ru

and A.I. Kolesnikov, Argonne National Laboratory, Intense Pulsed Neutron Source, 9700 South

Cass Avenue, Argonne, Illinois 60439, USA

Summary

The paper will briefly review and discuss results of our investigations on the atomic correlations in amorphous Zn-Sb, GaSb, GaSb-Ge and Al-Ge alloys. These semiconductor alloys were prepared by solid state reactions in the course of heating the quenched high-pressure phases. Structure of the final products was studied by neutron diffraction for the Al-Ge, GaSb and GaSb-Ge alloys and by transmission electron microscopy for the Al-Ge and Zn-Sb ones. The experimental data obtained were used for reverse Monte Carlo atomic structure modelling of these alloys. The samples thus obtained were proved to be homogeneous bulk amorphous materials containing no crystalline inclusions.

Introduction

A process employing spontaneous amorphization of a quenched high-pressure phase in the course of heating from liquid nitrogen to ambient temperature at atmospheric pressure has recently been developed (Ponyatovsky E.G., 1991). Formation of the bulk amorphous alloys was demonstrated in the set of previous studies (Ponyatovsky E. G., 1992) for some binary systems of B-elements, including Zn-Sb, Al-Ge, GaSb and GaSb-Ge ones.

For Zn-Sb system composition of the amorphous alloy is Zn41Sb59 (here and below in atomic percents, at.%) which is close to that for the equilibrium equiatomic ZnSb. In the case of the Ga-Sb system, amorphous alloys can be obtained in the composition range 47.4-52.5 at.% of Sb, thus including the composition of the equiatomic low-pressure phase, GaSb-I. The closeness in composition of crystalline low-pressure phases and the amorphous alloys formed gives rise to a similarity in the short range order observed for these phases.

At normal pressure, the Al-Ge system is a binary system with the eutectic point at 424 oC and about 30 at. % of Ge (Hansen M., 1958). The equilibrium phase diagram by applying high pressure. The Ge solubility in Al increases up to 18 at.% at 7 GPa, and two intermediate phases are observed at higher pressures for Ge compositions of 68 and 45 to 50 at.% (Barkalov O.I., 1989). The recovered high-pressure γ -phase with 68 at.% Ge has a simple hexagonal structure and it transforms to the amorphous state on heating at normal pressure (Barkalov O.I., 1987; 1996). It was of considerable interest to investigate what changes were induced by a significantly large amount of trivalent Al in the tetrahedral network of amorphous tetravalent Ge.

By X-ray examination of the quenched high pressure phases it was shown (Antonov V.E., 1997) that a metallic phase with a β -Sn-type crystal structure was formed in GaSb-Ge alloys subjected to 7.0 GPa and 250 °C at Ge concentrations up to 30 at.% Ge. Thus, in order to have an initial single phase for high-pressure crystalline state and a 100% amorphized sample after the solid state amorphization, an alloy containing 24 at.% Ge was selected for further investigation.

The real structure and thermal stability of amorphous Zn41Sb59 and Al32Ge68 were studied by transmission electron microscopy. Measured neutron diffraction spectra of the bulk amorphous Al32Ge68, GaSb and Ga38Sb38Ge24 alloys were used for numerical characterization of their atomic correlations. The results were analyzed using Reverse Monte Carlo (RMC) simulations. The influence of Ge admixture on the structure of the Ga38Sb38Ge24 sample will be discussed.

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

Experimental methods

To prepare the samples a crystalline powder of the initial alloys was first subjected to high pressure in quasihydrostatic cell of “Toroid“ type to attain single-phase high pressure state. The exact parameters of the synthesis for systems under investigation are presented in Table 1. This was subsequently followed by cooling under pressure to liquid nitrogen temperature and releasing pressure to atmospheric. The final amorphous pellets in the form of discs, 7 mm in diameter and about 2 mm thick, were produced by slow heating at about 20 °C /min to ~50-150 °C (see Table 1) in Perkin Elmer DSC 7 scanning calorimeter. After production, each tablet was checked for crystalline inclusions by X-ray diffraction and subsequently stored in a Dewar containing liquid nitrogen.

The samples for transmission electron microscopy in form of discs with 0.3 mm thickness were cut from the amorphous tablets by a wire saw. Electron microscopy foils were prepared by electrochemical thinning (hydrofluoric acid + acetic acid) of the slices mentioned above.

Table 1. High pressure synthesis parameters and obtaining of the amorphous state.

Synthesis parameters of HPP Obtaining of the amorphous phase Composition of the high

pressure phase, at. %

Pressure, GPa

Temperature, °С

Time, hours

Heated to the temperature (°С) with the heating rate (°С /min)

Zn41Sb59 7.0 350 24 to 50°С; 20°С /min GaSb 7.0 250 24 to 50°С; 20°С /min

Ga38Sb38Ge24 7.5 250 24 to 150°С; 20°С /min Al32Ge68 9.0 320 24 to 150°С; 20°С /min

An electron microscope (JEOL-100CX) with a low-temperature holder (GATAN) was used to study real structure of the samples by transmission electron microscopy (TEM). The investigations of Zn41Sb59 were carried out at -50 oC in order to avoid irradiation-induced crystallization. The samples were brittle, so they were placed between two copper grids before being inserted into the electron microscope holder. The Al32Ge68 samples were studied at room temperature and then heated in the microscope to 200 oC to crystallize them.

The neutron diffraction (ND) experiments were carried out on the LAD diffractometer at the ISIS pulsed neutron source at the Rutherford Appleton Laboratory, UK (Boland B., 1992). The pellets of the amorphous samples for neutron diffraction experiment were packed into a cylindrical vanadium container of 8.0 mm inner diameter. The measurements were carried out using a standard "orange" cryostat kept at a temperature of 100 K. The experiment consisted of four measurements: with the sample in the container, with the empty container, without the sample and container (the background measurement) and with a vanadium rod. The vanadium neutron cross section is almost entirely incoherent, and the latter measurement was used for normalisation of the sample data. The measured time-of-flight spectra were transformed to structure factors S(Q) by using the ATLAS correction program package (Soper A.K., 1989) The total radial distribution function, G(r), was calculated by the Fourier transformation of the S(Q) spectra (with Qmax=35 Å-1) using the standard transformation techniques.

To elucidate the partial atom-atom correlations in the amorphous alloy studied a reverse Monte Carlo (RMC) method was applied. The details of the RMC technique could be found in (McGreevy R.L., 1992).

Results

A bright-field image of the sample structure and corresponding electron diffraction pattern are shown in Figs. 1(a) and (c). There is no sign of crystal phase in the micrograph. The electron diffraction pattern contains only the diffuse halo typical of an amorphous phase. Both the micrograph and the diffraction pattern are similar to those seen for melt-quenched

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

Fig. 2. Total experimental structure factor for amorphous Al32Ge68 alloy at 100 K

Fig. 3. The total radial distribution function, G(r), for amorphous Al32Ge68 obtained by Fourier transformation of S(Q).

Fig. 1. Micrographs of amorphous Zn41Sb59 alloy (a) and the same region of the sample after crystallization (b); corresponding electron diffraction patterns (c) and (d).

metallic glasses. Heating the samples by an electron beam during the investigation led to crystallization of the irradiated part of the sample (Fig. 1(b)). The formation of ZnSb crystalline grains is demonstrated by the electron diffraction pattern (Fig. 1(d)). Crystallization of the samples proceeded very quickly and movement of the crystallization front could hardly be seen by eye. Figs. 1(b) and (d) show the structure and diffraction pattern of the same region of the sample shown in Fig. 1(a) after 1 min of observation (Aronin A.S., 1995).

According to our preliminary ND experiments (Barkalov O.I., 1994) the effective coordination number for amorphous Zn41Sb59 alloy is 4.7, close to that for ZnSb crystalline compound, which is equal to 5. The correlation length of the atomic fluctuations, i.e., the scale of the atomic short-range order, is about 11 Å, been typical for amorphous materials. Positions of the main peaks of the radial distribution function could be explained if one supposes the short-range order of atomic arrangement in the amorphous alloy to be similar to that for crystalline ZnSb. Thus, the atomic local coordination in bulk amorphous Zn41Sb59 is basically tetrahedral, but the tetrahedral are deformed and interlinked.

For amorphous Al32Ge68 similar TEM results were observed, however, the alloy exhibited higher thermal stability and crystallized gradually at 200 oC (Barkalov O.I., 1996).

The aluminium and germanium nuclei are predominantly coherent scatterers of

neutrons. The corresponding scattering cross sections are coh

Alσ =1.495 barn and

coh

Geσ =8.42 barn. The relative weights of the oscillating part of Al-Al, Al-Ge and Ge-Ge partial

structure factors of the total S(Q) are 0.03, 0.16 and 0.81, respectively (ASHCROFT N.W., 1967).

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

Fig. 4 (a) Total experimental (points) and RMC fit (dashed line) reduced structure factors Q[S(Q)-1] for amorphous Al32Ge68. Partial radial distribution functions for amorphous Al32Ge68 obtained by RMC modeling: (b) GGeGe(r), (c) GAlGe(r), (d) GAlAl(r); (e) the partial Gij(r) plotted in a larger r scale for Al-Al, Al-Ge and Ge-Ge pairs by solid line with points, dashed line and solid line, respectively.

Figures 2 and 3 show the experimental structure factor S(Q) obtained and the corresponding total radial distribution function G(r) for the amorphous Al32Ge68 sample. The weight coefficients given above indicate that the curves in the figures are mainly represented by Ge-Ge and Al-Ge atomic correlations, while the Al-Al correlations are hardly discernible. The experimental data in Fig. 2 clearly show that the sample studied was a good quality amorphous material. No diffraction peaks, characteristic of crystalline inclusions, were observed in the diffraction pattern recorded at the largest diffraction angle (150o) which has the best resolution (0.5% ∆Q/Q). The maximum of the first and the second peaks in the S(Q) curve are at about 1.96 and 3.35 Å-1 and oscillations are clearly seen up to 30 Å-1.

The G(r) function for amorphous Al32Ge68, shown in Fig. 3, exhibits a distinct and narrow first peak at r1=2.478 Å. There is no sign of a prepeak indicating some kind of chemical ordering. The first peak is very well separated from the remainder of G(r) and this, in principle, makes it possible to accurately calculate the coordination number n, i.e. the average number of atoms in the nearest-neighbour shell. Performing the appropriate integration of the total radial distribution function up to 3 Å the value n=4.5 ± 0.1 is obtained. This is significantly larger than 4, which indicates that a well developed tetrahedral bonding network does not exist in amorphous Al32Ge68. It should though be noted that the ratio of

the positions of the second and the first peaks in G(r), 625.148.2/03.4/ 12 ≈≈rr is close to the tetrahedral value 1.633. However, in order to understand the structure of amorphous Al32Ge68 it is important to realize that the first peak exhibits a very distinct shoulder above 2.6 Å. The origin of this shoulder which, together with a tail, persists up to 3.1 Å can be explained as follows: from the composition of the alloy it can be evaluated that the probability for an Al atom to have another one or even two Al atoms as nearest neighbors is relatively high because the average number of Al atoms near Al atom is about 0.32x4.5=1.44. If it is assumed that Al and Ge atoms do not form any covalent bonds, it may, from a geometrical point of view, be easily anticipated that around an Al-Al dimer (or trimer) there will be a larger number of Ge atoms than would have been the case if only covalent bonds with tetrahedral coordination were possible. This would result in a coordination number for non-covalently bonded Al-Ge pairs greater than 4. Accordingly, the shoulder and the tail for the right-hand side of the first peak in the G(r) ranging up to 3.1 Å may correspond to Al-Ge and Al-Al nearest neighbour arrangements.

As can be seen from Fig. 4(a) the agreement between the calculated and experimental structure factors is excellent (reduced structure factors Q[S(Q)-1] are shown in the figure for better comparison at higher Q values).

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

All features of the experimental curve are well reproduced over the whole Q range. Figure 4(b-e) shows the partial radial distribution functions, which give new and complementary information on the atom-atom correlations. It is clear from the figure that the shoulder at the right-hand side of the first peak in the total G(r) in Fig. 3 is really due to Al-Ge and Al-Al correlations. The first peak in these two radial distribution functions is rather broad, with the tail at the right-hand side extending above 3 Å. Very small correlations are seen up to 5.5 Å for Al-Al pairs and up to 7 Å for Al-Ge pairs. As for the Ge-Ge pair correlation function, it exhibits a very sharp first peak, with a maximum at 2.48 Å, which is slightly larger than the covalent diameter for a Ge atom (2.44 Å), and the first peak is well isolated from the second one. The intensity of the curve between these two peaks is close to zero which means that the atoms in Ge-Ge pairs are connected by rather well defined covalent bonds.

The interesting feature of the atomic distribution obtained by RMC calculation should be mentioned. Thus, the smallest distance between the Al-Ge atoms appears to be the shortest interatomic distance in the system (Figs. 4 c, e). This means that the closest Al-Ge pairs surely cannot be described by a common hard-spheres model.

Using the three-dimensional atomic coordinates obtained, the probability functions for atoms of type i having atoms of type j as nearest neighbours were calculated. The average coordination numbers (number of atoms in the first coordination sphere of radius 3.1 Å) calculated are: 1.37 for Al-Al, 4.16 for Al-Ge, 1.96 for Ge-Al and 2.88 for Ge-Ge pairs. One can conclude that most Ge-Ge nearest neighbours do not form tetrahedral units. The more probable elementary unit around a Ge atom consists of 2.88 other (covalently bonded) Ge atoms and 1.96 Al atoms, which means a Ge atom has 4.84 nearest neighbors in average. This is not seen from the analysis of the total radial distribution function G(r) discussed above because it represents the sum of partial Gij(r) weighted by the coefficients, which are small for Al containing correlations due to the small coherent neutron scattering cross-section for Al atoms.

The total coordination number for Al atoms (due to Al-Al and Al-Ge correlations) is 5.53 and it was expected to be large due to supposed non-covalent bonding between them. For Al-Al pairs the average coordination number is 1.37. Aluminium atoms are consequently connected mainly in groups of two or three atoms and do not construct a continuous network through the sample - there is no percolation of aluminium atoms in the sample.

Figs. 5 and 6(a) show the experimentally obtained structure factor S(Q) and the total radial distribution function for the amorphous Ga38Sb38Ge24. The experimental data clearly show that the sample studied is a good quality amorphous material. No diffraction peaks, characteristic of crystalline inclusions, are observed in the ND patterns even at large scattering angles. The possible inhomogeneity was also checked by small angle neutron scattering and it can be concluded that the sample studied is not only amorphous but also homogeneous.

The values of the full width at half maximum of the first two peaks of S(Q) are related to the correlation lengths in the amorphous sample by the expressions 1/2 QCC ∆= πχ and

2/2 QNN ∆= πχ for the chemical and density fluctuations respectively. For the Ga38Sb38Ge24

alloy the correlation lengths are found to be similar to those for amorphous Ge, =CCχ 15 Å

and =NNχ 11 Å, compared with =CCχ 19 Å and =NNχ 10 Å for amorphous GaSb. This

indicates that the chemical order in Ga38Sb38Ge24 is slightly lower than in amorphous GaSb (due to admixture of Ge), but the density fluctuations are about the same.

The RDF(r) function for amorphous Ga38Sb38Ge24, shown in the Fig. 6(a), is very different from that obtained for bulk amorphous GaSb (Fig. 6(b)) in that it exhibits a very distinct split of the first peak. The positions of the two maxima are at 2.46 and 2.66 Å. The splitting of the first peak reflects the existence of two different nearest neighbor correlations. The covalent radii, rcov, for Ga, Sb and Ge, atoms are equal to 1.26, 1.38 and 1.22 Å, respectively. The first maximum in RDF(r) (r=2.46 Å) is close to 2rGe

cov and to rGecov+rGa

cov, and is thus obviously related to Ge-Ge and Ge-Ga correlations. The second maximum at r=2.66 Å corresponds to rGa

cov+rSbcov and rGe

cov+rSbcov and may thus be assigned to Ga-Sb and

Ge-Sb correlations. The shoulder observed on the right-hand side at 2.86 Å reveals the

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

Fig. 5. The structure factor S(Q) for amorphous Ga38Sb38Ge24 at 100 K.

Fig. 7. The experimental reduced structure factor Q[S(Q)-1] (points) and the RMC fit (solid line) for amorphous Ga38Sb38Ge24. Verticaly shifted short dashed line shows the reduced structure factor simulated at large Q values by using Eq. (1).

presence of Sb-Sb pairs. The Ga-Ga pair correlations, with 2rGacov=2.52 Å, if they exist, are

probably more spread over longer distances and may thus give contributions in between the above mentioned two maxima.

The total average coordination number for the nearest neighbors in amorphous Ga38Sb38Ge24 is 4.25, which indicates that the atomic arrangement in this alloy deviates from that of a regular tetrahedral network. However, the ratio between the position of the second peak (at ~4.19 Å) in RDF(r) and the average position for the first one (~2.59 Å) is close to the ideal tetrahedral value, 1.633.

The calculated S(Q) for both samples fit the experimental data very well as shown in Figs. 7 and 8 (top curve). The partial radial distribution functions Gij(r) obtained are plotted in Figs. 9

Fig. 6. The total radial distribution function, )(4)( 02 rGrrRDF ρπ= , for amorphous (a)

Ga38Sb38Ge24 and (b) GaSb alloys at 100 K. The insert shows the RDF(r) around the first peak for Ga38Sb38Ge24 in a larger r scale.

Fig. 8. The experimental reduced structure factor Q[S(Q)-1] (dashed line with points) and the RMC fit (solid line) for amorphous GaSb with: (a) no constraints on the chemical order in the alloy, and (b) with constraints, allowing only 10% of the nearest neighbors to be the atoms of the same type (see the text). The left and the right y-axis are for (a) and (b) curves, respectively.

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

Fig. 9. Partial radial distribution functions Gij(r) for amorphous Ga38Sb38Ge24 obtained by RMC modeling plotted in a whole simulated area (a), and in a larger r scale for the first peak only (b).

Fig. 10. The same as in the Fig. 9, for GaSb.

and 10. The RMC results for amorphous GaSb (Fig. 10) show the existence of a large amount of nearest neighbor pairs of the same kind of atoms, with a rather narrow distance distribution (the first peaks in Gij(r) functions for Ga-Ga and Sb-Sb). Their contributions to the second peak in G(r) are definitely the dominating ones. The intensity under the second peak for Ga-Sb correlations is small but not negligible (see Fig. 10) as should be the case for a tetrahedrally coordinated network with ideal chemical order. As for the results of RMC simulations for Ga38Sb38Ge24 (Fig. 9), the first peaks in the partial Gij(r)s exhibit a complicated behavior. The positions of the maxima correspond to the values for two maxima in the radial distribution function obtained by Fourier transformation of the experimental structure factor. The Ga-Sb, Ga-Ga and Sb-Sb correlations are similar to those obtained in RMC simulations for amorphous GaSb, but with broader distributions for pair correlations of atoms of the same type.

The existence of two nearest neighbor correlations for the sample studied results in an interesting behavior of the structure factor at large neutron momentum transfers. It is clearly seen in Fig. 7 that the reduced structure factor Q[S(Q)-1] oscillates around zero, but while the amplitude of the oscillations gradually decreases for the GaSb sample (see Fig. 8a), at first it decreases with Q (up to 15 Å-1), then increases with a maximum around 23-24 Å-1, and finally decreases again at higher Q for Ga38Sb38Ge24. This behavior can be understood by assuming that at high Q values the main contributions to S(Q) are determined by the short range orders. To interpret qualitatively this modulation the following approximation was used for the reduced structure factor at high momentum transfers (Etherington G., 1982)

) Q - ( rQ

) rQ ( n = ] 1 - )Q ( S[Q 2

i2

i

ii

i

σexpsin∑ (1)

Here ri represents the first and the second nearest atom-atom distances, and ni and iσ

are the coordination number and the spread of the corresponding atom-atom distribution, respectively.

The vertically shifted dashed line in Fig. 7 shows the fit to the experimental data by the above expression, where two first nearest neighbor distances, r11=2.46 Å and r12=2.66 Å, and the value of r2=4.19 Å were used, in accordance with the discussion on RDF(r) above, and ni and iσ being adjustable parameters. It is clear from Fig. 7, that the modulation observed in

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

the spectrum for Ga38Sb38Ge24 is due to the difference in the periods of the corresponding oscillations which, of course, in turn is due to the different r11 and r12 values.

It follows from RMC results obtained that Ge atoms do not construct a significant amount of amorphous clusters of tetrahedrally coordinated network because the average Ge-Ge coordination number, 0.75, is much smaller than 4, which is required for this situation. Actually, the value for GeGen is the smallest, which is easy to understand if one assumes a

random distribution of Ge atoms and takes the low Ge concentration in the sample into account. Thus, it can be concluded that in the amorphous alloy studied the Ge atoms randomly substitute the Ga and Sb atoms in the corresponding GaSb alloy, but in doing so the nearest neighbor distances between Ge and Ga/Sb atoms are modified in order to be closer to the value corresponding to the sum of their covalent radii. Note that the intensity of the second peak in the RMC simulated partial Gij(r) for Ge-Ge is higher compared to others (see Fig. 9), indicating some kind of ordering of Ge atoms on the apexes of tetrahedral units.

The partial Gij(r) curves for both GaSb and Ga38Sb38Ge24 show rather large chemical disorder. The nearest neighbors are expected to be the atoms predominantly of different kind, especially in the case of GaSb. Note, that the crystalline analogue of bulk amorphous GaSb, GaSb-I low-pressure phase with zinc-blende structure, has a completely chemically ordered structure, with the nearest neighbor pairs constructed exclusively from different atoms, Ga and Sb.

When using RMC, one can get several different atomic structures that fit the experimental S(Q) spectrum equally well, but generally one arrives at the most disordered one. In order to check for any other possible spatial arrangement of atoms in amorphous GaSb further RMC simulations were made. They were started from an ordered structure, corresponding to the crystal structure for GaSb-I, and included constraints restricting the existence of nearest neighbors of the same type of atoms at distances smaller than 3 Å (i.e. in the first coordination shell). It was impossible to fit the experimental data with these constraints. Changing the constraints to allow 10% of the atoms of the same kind to be nearest neighbors, did not improve the quality of the fit. The example of one of the ‘best’ fits with this kind of constraints is shown in Fig. 8(b). These calculations strongly support the RMC results obtained: that a large chemical disorder exists in both bulk amorphous Ga38Sb38Ge24 and GaSb alloys.

Discussion

It is interesting to compare the S(Q) and G(r) data for the amorphous Al32Ge68 alloy studied and for pure amorphous Ge produced by deposition technique (Etherington G., 1982) At first sight the spectra appear very similar, but the quantitative values are completely different. The amorphous Ge is less dense ( 0ρ =0.03975 at./Å3) compared to the Al32Ge68

alloy ( 0ρ =0.0458 at./Å3), but the peaks in the G(r) spectrum in the present study are slightly

shifted to larger distances (the position of the first peak in G(r) for amorphous Ge is at 2.463 Å (Etherington G., 1982). This results in the principal difference that the first coordination number for amorphous Al32Ge68 is 4.5 (with a contribution of only 2.88 due to Ge-Ge correlations) while it is 3.68 for amorphous Ge.

To understand large chemical disorder in the GaSb and GaSb-Ge amorphous alloys it is worth while to remember that both Ga38Sb38Ge24 and GaSb were produced by solid state amorphization in the course of slow heating of the quenched high pressure phases. The high pressure GaSb-II phase has been described as having a chemically disordered structure (Weir S.T., 1987; McMahon M. I., 1994). The amorphization process which takes place on heating from liquid nitrogen to 150 °C probably involves changes mainly in the local arrangements of atoms without any long distance displacement which is required to create chemical order in the sample.

Conclusions

For all alloys under investigation the sizes of the ordered regions fall into interval 10÷20 Å that is characteristic for classical thin amorphous ribbons and films prepared by

Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

rapid quenching and deposition techniques. Thus, these alloys correspond to b u l k a m o r p h o u s materials.

It is shown that for the amorphous Al32Ge68 alloy the effective coordination number (n=4.5) is appreciably higher than 4, which is characteristic for a tetrahedral coordination. The first peak of the total radial distribution function has a pronounced right-hand shoulder visible up to 3.1 Å.

The RMC calculations for amorphous Al32Ge68 have shown that the partial radial distribution function for Ge-Ge correlations exhibits a sharp peak at a distance close to the value for the Ge-Ge covalent bond, but Ge atoms do not form a tetrahedral arrangement (the corresponding first coordination number is n=2.88). It was found that the Al-Ge and Al-Al correlations (with total n=5.53) increase the effective coordination number to the observed value of 4.5 and result in the formation of the broad right-hand shoulder of the first peak in the total G(r) function. It is concluded also that aluminium atoms (n=1.37) do not construct a continuous network through the sample.

The Ga38Sb38Ge24 alloy produced by solid state amorphization of the quenched high pressure phase can be regarded as a homogenous bulk amorphous compound. The short range order in the amorphous Ga38Sb38Ge24 alloy is different from that for amorphous GaSb. The average nearest neighbor atomic coordination number obtained, 4.25, is greater than 4, indicating a distortion of an ideal tetrahedral arrangement in the alloy. Furthermore, there are two rather well defined nearest neighbor distances.

The results of the RMC simulations show a random distribution of Ge atoms in amorphous Ga38Sb38Ge24 alloy. The Ge atoms do not form any clusters with tetrahedrally coordinated arrangements, but randomly substitute the Ga and Sb atoms as compared to amorphous GaSb. Some degree of ordering of Ge atoms on the apexes of tetrahedral units in Ga38Sb38Ge24 can nevertheless be anticipated from the analyses of the RMC simulated partial G(r) functions. Large chemical disorder was found by RMC modeling to exist in amorphous Ga38Sb38Ge24 and GaSb alloys. About 30% of the nearest neighbors in the alloys are formed from atoms of the same kind (Ga-Ga and Sb-Sb pairs).

Acknowledgements

This work was supported by the Program “Physics and Mechanics of Extreme Conditions” of the Russian Academy of Sciences. One of the authors (O.I.B.) acknowledges the support to attend the conference from the Alexander von Humboldt Foundation and Russian Science Support Foundation.

References

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Joint 20th AIRAPT – 43th EHPRG, June 27 – July 1, Karlsruhe/Germany 2005

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