As an approximate computation method, cluster expansion is a power series expansion of
the partition function, which was proposed by Mayer in 1941. In computational materials …

Structural models needed in calculations of properties of substitutionally random A 1− x B x
alloys are usually constructed by randomly occupying each of the N sites of a periodic cell …

Publisher Summary This chapter presents the formalism and applications of cluster
expansions to the problem of ab initio calculations of thermodynamic properties of crystalline …

Phase equilibria in alloys to a great extent are governed by the ordering behavior of alloy
species. One of the important goals of alloy theory is therefore to be able to simulate these …

Abstract The three-dimensional spin-1/2 Ising model with multiple-site interactions provides
a natural framework for describing the temperature-composition phase diagram of …

While as elemental solids, Al, Ni, Cu, Rh, Pd, Pt, and Au crystallize in the face-centered-
cubic (fcc) structure, at low temperatures, their 50%-50% compounds exhibit a range of …

Long-range ordered intermetallic compounds are good model systems for the basic study of
atomic migration in superstructures. The most promising are compounds exhibiting atomic …

States of (partial) order in binary-alloy systems are described by means of expansions in a
complete set of orthogonal cluster functions. The expectation value of the energy of such …

A theoretical study of thermodynamic properties and of the phase diagram for crystalline hcp-
based Cd-Mg alloys is presented. Many first-principles studies of phase diagrams for …

Ternary alloy energetics are examined for substitutional systems by a formal cluster
expansion. In contrast to the binary-alloy problem, several distinct basis sets are possible for …