Application of Continuous Displacement Treatment of CVM to Binary Alloy Systems

Abstract

Statistical mechanics methods such as Cluster Variation Method (CVM) designed for working with lattice statics are based on the assumption that atoms sit on lattice points. We extend the conventional CVM [1] and present a method of taking into account continuous displacement of atoms from their reference lattice points. The basic idea is to treat an atom which is displaced by r from its reference lattice point as a species designated by r. Then the summation over the species in the conventional CVM changes into an integral over r. An example of the 1-D case was done successfully before [2]. The similar treatments have also been done for pure 2-D systems [3,4] as well as for lattice defects in 2-D crystals [5]. It is the purpose of the present paper to investigate the local lattice distortion on the alloy phase stability by using the continuous CVM.