CHARGE FLUCTUATIONS IN ALLOYS - A COARSE-GRAINED MODEL

A simple model is constructed to represent the electron density and th e electrostatics in a random alloy. The model is based on a jelliumlik e 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 app roach is justified for probing the effect caused by the Coulomb intera ction since its long-range nature averages over the details represente d by the shorter length scales. This model reproduces the q-V relation ship that was found in more realistic models, i.e., the charge on a si te 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 a round the results from the infinite sum. This correlation explains why two different views, one based on a long-range potential, the other o n a short-range screening, contain much of the same physics, and why, upon averaging the occupations of shells beyond the first two, the cha rge on a site is determined by the local environment.