Ordering Energy and Effective Pairwise Interactions in a Binary Alloy of Simple Metals

Abstract

The pseudopotential theory of metals is applied to the case of a binary alloy with an arbitrary degree of order. A self-consistent screening potential which includes the effect of the total conduction-electron charge is derived to first order in a perturbation-theory expansion in the pseudopotential. Expressions are obtained for the conduction-electron contributions to the ordering energy and to the effective pairwise interactions among the ions in the alloy. If the conduction-electron energy may be expressed accurately to second order in the pseudopotential, this energy is shown to depend upon only two-particle correlations among the ion positions. Numerical values are obtained for the ordering energy and the pairwise interactions for stoichiometric LiMg. The ordering energy is not obviously inconsistent with experimental observations. If the ordering interaction is expressed approximately as a sum of two terms, one of which depends exponentially and the other sinusoidally on interionic separation, the former dominates throughout the region of the calculation.