A calculation of cluster effects in disordered alloys

Abstract

A general method is presented of incorporating the effects of clusters of constituent atoms in the calculation of the excitation density of states in a disordered material. An unknown parameter is introduced into the logarithm of the secular determinant of the problem and subsequently determined self-consistently by minimizing approximately the interaction between clusters. The single-site version of this procedure reproduces the density of states of the coherent potential approximation whilst an expansion in terms of important clusters leads to results exhibiting the fine structure attributed to localized modes. The results for the phonon spectra of a one-dimensional random binary alloy are in good agreement with those of previous 'exact' methods.