CLUSTER THEORIES FOR SUBSTITUTIONALLY DISORDERED ALLOYS

Abstract

This thesis is devoted to the study of substitutionally disordered alloys (mainly binary alloys) . The contents are divided into two parts. The first part deals with the theories developed for the elementary excitations in disordered systems. In particular, a single band tight, binding model Hamiltonian for electrons in disordered systems has been studied in detail. The single site coherent potential approxi-mation (SSCPA) , most commonly used in the study of elementary excitations in disordered systems, is not suitable for realistic systems where the constituents have different band widths and the .system possesses some short-range--order. it is also inadequate in situations where the mean free path of excitations is small. The SSCPA has, therefore, been generalized by many people in many ways so as to suit various situations. These cluster generalizations are usually very r tedious. We have studied a cluster generalization of SSCPA, which is computationally simple so that a numerical calculat-ion of the density of states is possible. We considered clusters made up of a central atom and its Z nearest neighbours. Then analogous to the SSCPA scattering from one such cluster embedded in an otherwise effective medium is considered. The effective medium is determined in different ways namely (1) in the self-consistent central site approximation, (ii) in the self-consistent, boundary site approximation and (iii) by imposing self-consistency conditions on the averaged T--matrix elements. The main assumption which reduces the computational -- iv.- effort to a manageable level without effecting the final results much, is that the various configurations for a fixed number of different kinds of atoms on the shell of nearest neighbours are taken to be indistinguishable. We have considered off-diagonal disorders of Shiba type where the hopping integral hAD is the geometric mean of hAA and as well as = the general case where hAA, hAB and hBB can take arbitrary values. In the former case the problem reduces to that of the diagonal disorder when one uses a renormalized propagator formulation. We have calculated the densities of states and the spectral densities of states for a wide range of parameters. Our results are in good agreement i.ith the exact results obtained from computer simulation or from the method of moments. A critical study of var-aus approximate cluster methods developed so far by various workers, has also been done.