Effective Pair-Interactions in Binary Alloys

Abstract

A number of diffuse scattering studies either with x-rays or neutrons have been done in order to study the local or short-range order (SRO) in binary systems, and mostly in alloys. The SRO as an example of a generalized susceptibility can be related to the pair-interactions between the different atoms [1,2]. The configurational energy may be described by (the lattice gas model or) the Ising model: $$H = \frac{1}{4}\sum\limits_{{j,i}} {V({{{\vec{r}}}_{i}} - {{{\vec{r}}}_{j}}){{\sigma }_{i}}{{\sigma }_{j}}}$$ (1) where the site occupation is denoted by σ i ±1. The attractive idea of using such pair-interactions is that one expects that they are not only capable of describing the attendant measured SRO configuration but also, perhaps the whole coherent binary phase diagram. But the application of such pair-interactions for the calculation of phase diagrams is restricted, since in real alloys the interactions may not only be pairwise and may also depend on composition and temperature etc. A further problem that the pair-interactions could have been only determined within a mean-field approximation [1,2], has meanwhile been solved by the Inverse Monte Carlo (IMC) method [3]. In the particular case of the Ni . 89 Cr . 11 alloy a remarkable agreement between the numerically exact result of the IMC method and the mean-field solution has been found [4]. However in general, this agreement can not be expected.. But the observation that the range of interaction for a real alloy may extend further than only to nearest and next-nearest neighbor is really a new challenge for the standard tools of statistical mechanics, for the Monte Carlo (MC) and even more for the Cluster Variation method (CVM).