Structure and dynamics of amorphous ZrBe alloys

Journal of Non-Crystalline Sol,ds 156-158 (1993)72-75 North-Holland

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Structure and dynamics of amorphous Zr-Be alloys A.M. Bratkovsky, S.L. Isakov, S.N. Ishmaev, I.P. Sadikov, A.V. Smirnov, G.F. Syrykh, M.N. Hlopkin and N.A. Chernoplekov Kurchatov Instttute, 123182 Moscow, Russta

The extensive study of the short-range order structure, atomic v~brat~on spectrum and electromc properties of amorphous alloys Zr l_cBec (c = 0 3-0.5) is performed using neutron scattering and specific heat measurements. An increase in the Be concentration m the amorphous alloy reduced the &stances between nearest s~mllar atoms, shifted and broadened the high-energy part of the vlbraUonal spectrum, increased the Debye temperature and decreased the density of the electron states as well as the superconducting transition temperature. An analysis of the partial radial &stribut~ons, obtained by Monte Carlo modeling, ln&cated that the atomic structure of the amorphous Z r - B e alloys was dominated by geometrical factors, such as the atom sizes and system composition. The density of the vibrational states calculated by the recursion method for the structural model with a large number of atoms reproduced well all the mare features of the experimental spectra.

1. Introduction The short-range order and dynamics of atoms, as well as the relationship between phonon and electron spectra of metallic glasses, are attracting major interest because of the unusual properties of these metastable systems. In studies of correlations at the level of partial atomic distributions, the most detailed information can be obtained by high-resolution neutron diffraction and inelastic scattering methods with the isotopic contrast of samples (see, for example, refs. [1-3]). The amorphous Z r - B e system is interesting because of the large difference in atom sizes and masses; alloys can become amorphous in a wide range of compositions. So, it is possible to identify the structural and dynamics characteristics of the individual components. In this case, we cannot effectively apply the isotope substitution method and in order to provide reliable interpretation of the partial distributions, it is necessary to use computer simulation methods.

Correspondence to: Dr S.N Ishmaev, Kurchatov Institute, 123182 Moscow, Russm. Tel.: +7-095 196 5973. Telefax: +7095 196 5973 Telex: shuya 411594.

2. Experimental Samples of Zrl_cBe c amorphous alloys with the concentrations c = 0.3, 0.4 and 0.5 were prepared by rapid quenching of the melt on a rotating copper disk in a helium atmosphere. Their atomic densities, n, were measured by the Archimedes method. The structure factor, S(Q), was measured by a time-of-flight neutron diffractometer at the Linac Fakel pulsed source [2] up to momentum transfer o 1 of Qmax= 41.5 A - . As a result, the reduced radial distribution function, G(r), was determined by Fourier transformation with high spatial resolution: Ar = 0.13 A. The same samples were used in a study of the generalized phonon spectrum, g(E), by the inelastic neutron scattering method employing a multi-detector time-of-flight spectrometer with a cold neutron source in the IR-8 reactor [4]. The incident neutron energy resolution, A E, was ~ 0.5 meV. The specific heat of samples was determined in the temperature range 1.6-40 K in magnetic fields 0 and 4 T by an adiabatic method [5] and the error was of the order of + 2%.

0022-3093/93/$06 00 © 1993 - Elsevier Science Publishers B V. All rights reserved

A.M. Bratkovsky et al. / a-Zr-Be alloys

73

3. Details of the calculations

4. Results

We have used the Monte Carlo method to construct the atomic model of the amorphous Z r - B e system with a simple potential of the Morse type [6], capable of reproducing the structural short-range order [7]. The constants entering the expression for the potential were chosen to be EBeBe//eZrZr ----0.55, EZrBoe = (EBeBeEZrZr)1/2, (rB~B~ = 2.28 ~, O'zrZr= 3.18 A, O'ZrB~= (trzrzr + O'B~ae)/2 and a = 4.53. We have simulated 500 particles placed inside a cube with periodic boundary conditions and experimental atomic density (table 1). The vibrational spectra of the Z r - B e amorphous alloys were calculated by the recursion method [8]. In this method, the density of the vibrational states was found by statistical averaging, over the amorphous system, of the imaginary part of the local Green's function, G,,(E 2) = E2 - D) Ii) (D is a dynamic matrix) associated with vibrations of an atom, i, which can be calculated using a continued fraction. We have used 15 pairs of the continued fraction coefficients calculated from our 500-atom model which was 'blown-up' and added with its 26 periodic images. The vibrational density of states was averaged over 75 atoms chosen near the centre of the cluster with the use of the quadrature terminator after Nex [9].

Figure 1 shows the total reduced radial distributions, G(r), of the amorphous Zr l_cBec system obtained from the measured structure factors as a weighted sum of the partial distributions of atoms, Gab(r):

(i1(

G(r) = fQm~M(Q)Q[S(Q)

- 1] sin(Qr) dQ

= EWabGab(r),

(1)

where M ( Q ) = s i n y / y (y = ~ Q / Q m ~ ) is a modification function in order to avoid artificial ripples owing to finite truncation; Wab = CaCbbab b~ (bE), Ca, Cb and b a, b b are the concentrations and the coherent neutron scattering lengths of the a and b (Be and Zr) atoms; (bE) = cab2a + cbb2b . The coefficients, Wab, for Zr and Be are comparable and we find that the G ( r ) function represents the contributions of all the partial distributions: BeBe, ZrBe and ZrZr. Using an expansion in three Gaussians, in the first coordination shell we determined the shortest interatomic distances, rab, listed in table 1. The distances rneBe and rzr # in the amorphous Z r - B e system are less than the 'diameters' of the corresponding atoms in pure metals (2RBe = 2.28 .A and 2Rzr = 3.23 A, 1 whereas rzm ~ > ~(ra~B~ + rz,zr)).

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Table 1 Dens~Ues, interatom~c d~stances, coordination numbers, characteristlcs of the superconducting transition, and of the electron and phonon spectra for the amorphous Zq_cBec alloys Zro7Be03

Zro6Be04 ZrosBe05

n (at nm-3)"

49 6

52 3

55 2

rBeBe (,A)

2.25

2.22

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rnezr (,~). rzrzr (,~) ZacB~: ZBezr ZZrBe ZZrZr Tc (K): A C / T c (mJK2mol-1): y (mJK 2 mol-l): 0 (K):

2.71 3 12 2.2 73 32 10.9 3.05 7.2 3.71 228

2.71 3.10 2.7 6.8 45 10.0 2.35 5.5 3.11 254

2 71 3.06 3.9 6.2 6.2 8.9 2.38 293

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r, A Fig. 1. The total reduced radial atomic distnbutlon function, G(r), of amorphous Zrl_cBe c alloys. The points are the experimental values and the curves are calculated.

74

A M. Bratkovsky et al / a-Zr-Be alloys

vibrational spectra, g~(E), of the Zr and Be atoms

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g(E) = ~ to~ e x p ( - 2 W ~ ) g , , ( E ) , /

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r, .~ Fig. 2. Partial radial dxstributions, Gab(r), obtained using the structure model of amorphous Zrl_cBe c alloys with c = 0.3 (o), 0 4 (zx), and 0.5 ( * )

The structure model calculations provided a satisfactory description experimental G(r) functions in a wide range of compositions with the same parameters for the interatomic potentials (see fig. 1). The positions of all the main peaks of G(r) were reproduced well. A shortcoming of this model was an overestimate of the maximum G(r) for the first BeBe coordination shell. The calculated partial distributions G a b ( r ) a r e plotted in fig. 2. The main structural changes associated with Be concentration in the alloy were due to deformation of the wide second maximum of G a b ( r ) and a slight increase of the splitting. The partial functions were used to calculate the coordination numbers, Zab, listed in table 1. In an analysis of the chemical short-range order, it is useful to employ a generalized parameters aw/amwax [10] and T~ab/T~arrbax [12] defined in terms of the Zab. A calculation gives the following low values: a w / a w max -__ -0.075, -0.021 and -0.017, "qab/~/~ax---- --0.039, 0.065 and 0.024 for c = 0.3, 0.4 and 0.5, respectively, indicating the absence of a significant chemical ordering in this amorphous system. The generalized density of the vibrational states, g(E), represents the sum of the partial

(2)

where to, = (c~%/rn~)/Y~(c~tr~/m~). ca, ~ and rn~ are the concentrations, neutron scattering cross-sections and the masses of the atoms; exp(- 2W~) is the Debye-Waller factor. The values of weighting factors to Be are 0.823, 0.882, and 0.923 for c = 0.3, 0.4 and 0.5, respectively. Therefore, the main contribution to g(E) comes from the vibrations of the Be atoms. Figure 3 shows the experimental and calculated g(E) spectra. The density of the vibrations splits into two clearly separate regions: 0-28 and 28-80 meV. An increase in the concentration of the light Be atoms reduces the density of states in the low energy part of the g(E) spectrum. The changes at the high energies are a shift of the spectrum maximum from 52 to 54 meV and an increase in the half-width of the distribution from 26 to 32 meV. On the whole, the calculations reproduce well the main singularities of g(E) and their variations with the composition of the alloy, but there are differences in details, particularly in the case of ¢ = 0.5 (eZrZr is selected to be 0.52 eV).

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E, meV Fig 3. Comparison of the experimental (©) and calculated ( ) generalized vibrational spectra of atoms, g(E), m the amorphous Zr l_cBec alloys.

A.M. Bratkovsky et al. / a-Zr-Be alloys

02

greater than that predicted by the model ignoring the change in the interaction force between the atoms. One of the possible reasons for this stiffening of the system may be the screening influence of the electrons, which decreases as the density of the electron states at the Fermi level is reduced [11].

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E, rneV Fig. 4. Partial densities of states, gzr(E) and g~(E), for the amorphous Zr I _cBe c system. The curves are calculated using the structure model for c = 0.3 ( ), 0.4 ( - - - ) , and 0.5

(. . . . . . ).

Figure 4 gives the partial vibrational densities

gz~(E) and gBe(E). It shows that the low-energy part of g(E) is governed by the vibrations of the Zr atoms and the high-energy part is associated with Be atoms. The Zr-Be interaction hardly affects the density of the Zr states in spite of the large value of the coordination number Zzrae. The inaccuracies in the behavior of the calculated vibrational spectra may be due, in particular, to the electron contributions ignored in our simple model. Consequently, we investigated the dependence of the density of the electron states on the composition in these amorphous alloys by measuring the specific heat. In the absence of a magnetic field, the temperature dependence of the specific heat, C, of Zr0.7Be0.3 and Zr0.6Be04 samples exhibited an abrupt jump corresponding to the superconducting transition. A magnetic field of 4 T suppressed the superconductivity, which made it possible to determine the specific heat in the normal state right down to the lowest temperatures, T. Below 12 K, the temperature dependence of C was described by the usual law for metals: C = yT + [3T3, where 3' is proportional to the density of the electron states at the Fermi level and 13 = 12ar4R/503 is related to the phonon spectrum Debye 0 characteristic (R is the gas constant). The values of the parameters % 0, Tc and AC/T c are listed in table 1. We can see that both coefficient, 3', and the specific heat jump, AC/T~, are lower for samples with higher c, demonstrating that the density of the electron states decreases with Be concentration. The value of 0 increases with Be content and estimates show that it is

5. Conclusion

The structure and dynamics of the amorphous Zr-Be system were studied on the basis of the partial contributions. An increase in the Be concentration results in a tendency to shorten the distances between the like atoms without altering the distance rzrBe. The atomic vibration spectra were found to split into regions corresponding to the predominant vibrations of the light and heavy atoms. The spectrum deformations with the atomic composition are in accordance with the nature of changes in the short-range order and in the density of the electron states.

References [1] S.N. Ishmaev, S.L. Isakov, I.P. Sadlkov, E. Svab, L. Koszegt, A. Lovas and Gy. Meszaros, J. Non-Cryst Sohds 94 (1987) 11. [2] E. Svab and S.N. Ishmaev, in. Proc 5th Int. School on Neutron Physics, Alusta, 1986, ed. Joint Inst. Nucl. Research Dubna (1987) p. 287. [3] M.G. Zemlyanov, G F Syrykh, N.A. Chernoplekov and E. Svab, JETP 94 (1988) 365 (Sov Phys. JETP 67 (1988) 2381). [4] M.G. Zemlyanov, A.E. Golovin, S.P. Mironov, G.F. Syrykh, N.A. Chernoplekov and Y.L Shitikov, Prib. Tekh. Eksp. 5 (1973) 34 [5] M.N. Hlopkin, N.A. Chernoplekov and P.A. Cheremnykh, Preprlnt IAE-3549/10 (KIAE, Moscow, 1982). [6] D.O. Welch, G.I. Dienes and A. Paskin, J. Phys. Chem. 39 (1978) 589. [7] A.M. Bratkovsky and A.V. Smirnov, Phys. Lett. A146 (1990) 522. [8] R. Hydock, Solid State Phys. 35 (1980) 215 [9] C.M.M. Nex, Comp. Phys. Comm. 34 (1984) 101. [10] B.E. Warren, X-Ray Diffractmn (Addison-Wesley, Reading, MA, 1969). [11] G.F. Syrykh, M.G. Zemlyanov, N A. Chernoplekov and B I. Savel'ev, JETP 81 (1981) 308 (Soy Phys. JETP 54 (1981) 165). [12] G S Cargill III and F. Spaepen, J. Non-Cryst. Sohds 43 (1981) 91.