Polynomial functions for configurational correlation functions in Gibbs energies of solid solutions using cluster variation method

Abstract

The cluster expansion – cluster variation methods (CE – CVM) offer a reliable framework to obtain short range order information for the chosen configurational state of a system accurate up to the basic cluster chosen in terms of the microscopic state variables called correlation functions (CFs). The calculation of the CFs involves solving a set of nonlinear equilibrium equations using compute intensive numerical methods. In this paper a method is presented to approximate the equilibrium values of CFs as polynomial functions of composition which eliminate the necessity of solving equilibrium equations. The coefficients of these polynomials are expressed as rational functions of temperature and system specific energy parameters. This method is comparable to standard CALPHAD methods in its ease of application without sacrificing information about short range order in the system.This procedure is applied to an A2–B32 system using tetrahedron approximation for the case of exclusive second neighbour pair interactions. These polynomials yield CFs comparable to those obtained from numerical solutions in the usual ranges of energy parameters and temperatures.