Estimation of CE-CVM energy parameters from miscibility gap data

Abstract

The powerful framework of cluster expansion- cluster variation methods (CE- CVM) expresses alloy free energy in terms of energy (model) parameters, macroscopic variables (composition and temperature) and microscopic variables (correlation functions). A simultaneous optimization of thermodynamic and phase equilibria data using CE- CVM is critically dependent on giving good initial values of energy parameters, macroscopic and microscopic variables, respectively. No standard method for obtaining the initial values of the energy parameters is available in literature. As a starting point, a method has been devised to estimate the values of energy parameters from consolute point (miscibility gap maximum) data. Empirical relations among energy parameters, temperature (T c), composition (x c) andd 2 T/dx2 at the consolute point, have been developed using CE- CVM free energy functions for bcc and fcc structures in the tetrahedron and tetrahedronoctahedron approximations, respectively. Thus from the observed data ofT c,x c andd 2 T/dx2 in the above relations, good initial values of energy parameters can be obtained. Further, a necessary modification to the classical NR method for solving simultaneous nonlinear/transcendental equations with a double root in one variable and a simple root in the other has been presented.