A single-site theory for binary alloys with environmental and off-diagonal disorder

Abstract

A new approach is presented for a single-site theory of binary alloys with environmental disorder and arbitrary forms of off-diagonal disorder. The method involves rederiving the off-diagonal disorder theory of Blackman et al. (1971) using the cumulant diagram approach and extending it to include the fluctuations in the diagonal elements due solely to the atomic environments. The theory differs from that of Kaplan et al. (1980), but has correct limiting behaviour, including the independent band limit. Some numerical results are given. The technique also allows the inclusion of short-range order in the atomic distribution for arbitrary forms of off-diagonal disorder. As an example, the self-consistent quasi-crystalline approximation is applied to a phonon system.