Theory of Disordered Four-Component Systems

Abstract

A formulation of the statistical correlations in four-component systems, with arbitrary composition and pairwise interatomic potentials of arbitrary range, is given. Exact formal expressions for the relevant short range order (SRO) parameters are derived. A procedure for consistently calculating the high temperature series expansions for the SRO parameters is given and the linear approximation, valid at elevated temperature, is worked out in detail. The linear results for the inverse lattice Fourier transforms of the SRO parameters are represented in a form analogous to the results of self-consistent mean field theories. The usefulness of such a representation lies in its qualitative validity even in the vicinity of the order-disorder transition point. The transition temperature is estimated through the singularity of the temperature derivative of the correlation parameters. The relevance of the given expression for the SRO for inferring possible ground state orderings, i.e. the actual spatial configurations that might obtain when the ordering sets in, is indicated. In the limit that the atomic composition of the one of the four constituents approaches zero, our results smoothly reduce to the previously derived linear results for ternary systems.