Correlation-function approach to multicomponent systems: Ternary alloys at intermediate temperatures

Abstract

In this last of three papers dealing with the correlation-function approach (CFA) to multicomponent alloys we look at the first-order approximation beyond the mean-field approximation (MFA) for ternary alloys. We first discuss the properties of binary phase diagrams (using clustering systems by way of example) in order to understand what information can be obtained from the CFA. We then briefly discuss previous theoretical attempts to go beyond the MFA for binary alloys using CFA-like formalism. Having examined binary alloys we then formulate the problem for ternary alloys, and present the results for the correlation functions for this system. The resulting equation for the transition temperature is a quartic in ${T}_{c}$, where ${T}_{c}$ is a stability temperature at which the alloy decomposes into separate phases, or assumes an ordered ground state. We look explicitly at the case of a symmetric ternary alloy, ${m}_{A}={m}_{B}=\frac{1}{2}(1\ensuremath{-}{m}_{C})$ with positive interactions of equal magnitude. We find that the resulting phase diagram can be appreciably changed from the MFA. We then discuss implications of the technique.