A simple model is constructed to represent the electron density and the electrostatics in a random alloy. The model is based on a jelliumlike approach and thus on the (local-) density-functional method, albeit with a very coarse mesh size to represent the charge density. A Thomas-Fermi approximation is used to represent the kinetic energy. This approach is justified for probing the effect caused by the Coulomb interaction since its long-range nature averages over the details represented by the shorter length scales. This model reproduces the $q-V$ relationship that was found in more realistic models, i.e., the charge on a site $q$ was linearly related to $V,$ the intersite Coulomb interaction. The origin of the $q-V$ relationship is thus traced to the charge tracking the potential via an effective Fermi level, i.e., a Thomas-Fermi-like mechanism. In this paper, the slope obtained from the $q-V$ relationship is seen to be a function of the shape approximation used to represent the potentials. Finally, a relationship between the local environment and the long-ranged Coulomb potential is investigated. A high degree of statistical correlation is found between the Madelung potential and the terms coming from the first two neighbor shells in a bcc lattice. The contributions of the first two terms in the sum are distributed around the results from the infinite sum. This correlation explains why two different views, one based on a long-range potential, the other on a short-range screening, contain much of the same physics, and why, upon averaging the occupations of shells beyond the first two, the charge on a site is determined by the local environment.

• Received 1 May 1997

DOI:https://doi.org/10.1103/PhysRevB.57.15140