Many-Site Interactions and Correlations in Disordered Binary Alloys

An approximate method for obtaining the pair and higher-order correlation functions specifying the site-occupancy correlations in disordered substitutional binary alloys of arbitrary composition is described. The method is easily generalized from the usual pairwise interaction model to alloys with multi-site interactions. The value of $\frac{1}{z}$, where $z$ is the number of sites interacting with a given site, is used as a parameter of smallness to obtain a set of quasilinear equations which may be solved numerically for the correlation functions. The long range of the interatomic interactions found in many alloys would make $\frac{1}{z}$ seem a good expansion parameter. The validity of the solution is discussed. We use the method in a numerical analysis to investigate the effect of three-site interactions in a disordered face-centered-cubic binary alloy with a nearest-neighbor pair interaction and a "nearest-neighbor-triangle" triplet interaction. A simple analytic solution for a corresponding idealized meanfield situation is also carried out. An enlightening result is that the mean-field solution and the more realistic computer solution have similar general features. We also compare our solution with others for a choice of parameters in which comparison is possible.