Physica B 192 (1993) 325-332 North-Holland zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA PHYSICA 1 zyxwvutsrq SDI: 0921-4526(93)E:O179-K Lattice dynamics of binary alloys C.M.I. Okoye* and Satya Pal Departmenf of Physics and Astronomy, University of Nigeria, Nsukka, Nigeria Received 3 August 1993 The lattice dynamics of the binary alloys Ni, ,,Pd, Js, Pd,, ,JPt,, ,h, Ni,, ,Fe,, , and Ni,, ,Co,, 5 has been studied within the framework of the transition metal model potential approach and the mean-crystal approximation. A short-range three-body interaction, incorporated in a phenomenological way in the study, leads to an improvement in the transverse branches of the phonon dispersion curves. The theoretically calculated phonon dispersion curves are found to be in good agreement with the experimental data zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1. Introduction The study of phonons in alloys has been subject of a considerable amount of theoretical and experimental investigations. The theoretical studies have mainly followed the use of the coherent potential approximation and its modi- fications [l-8]. Besides, some novel theoretical approaches [9-161 in terms of the Green func- tion technique and molecular dynamics have also been used in the past for the study of lattice dynamics of alloys. Of the various types of disordered systems, substitutional binary alloys of the type A,_,B, are among the simplest. Recently Upadhyaya et al. [17] have reported a model potential calculation, using the mean-crys- tal model, for the lattice dynamics of the Ni 0.55Pd0.45 alloy. They used the transition metal model potential (TMMP) of Animalu [18] to calculate the interatomic force constants (up to the 10th nearest neighbours) of the constituent metals nickel and palladium at the lattice con- stant of the alloy. The phonon dispersion curves of the alloy were then computed by using the force constants and mass of the alloy, obtained by the concentration averages of the force con- * Corresponding author. stants and masses of the component metals. Notwithstanding the agreement between their calculations and the experimental results, we feel that the basic assumption of their approach that the force constants in the alloy superimpose linearly is a poor approximation. Besides, the significance of these force constants for the alloy is, strictly speaking, no longer the same as in an ideal crystal because of the lack of periodicity in the presence of disorder in the lattice. These force constants, with the average mass, may be used for the computation of the elastic constants of the alloy which are related to small wave vectors and therefore to the long-wavelength limit, but their use in determining the phonon dispersion in an alloy can not be justified strictly. Moreover, in taking into account interactions with such a large number of neighbours the formulation becomes lengthy and the analysis in terms of 20 force constants somewhat tedious. The dispersion curves of the Ni-Pd alloy like the constituent metals Ni and Pd are dominated by the nearest-neighbour forces and their calcula- tions show that the contribution of the atoms beyond the 2nd nearest neighbours is quite insignificant - less than even 1% of the nearest- neighbour interaction. In the present paper, we report a simple and straightforward calculation of the lattice dynamics of binary alloys within the 0921-4526/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved