Correlation Functions of Disordered Binary Alloys. I

An exact expression for the correlation functions (or Warren short-range order parameters) of an alloy of arbitrary composition and range of interaction is derived in terms of the Flinn operators. An approximate method of solution is found by replacing certain operators by their averages. One such choice leads to the equations formerly deduced by Cowley, and constitutes an alternative derivation of Cowley's theory. A second choice yields Zernike's equations and provides a method of comparing the approximations inherent in these two theories. Finally, a third solution is suggested which appears to have the same order of accuracy as the former two, but which has the advantage of being exactly soluble. It also provides an inversion formula which, in theory, can be used to infer the form of the two-particle interaction energy as a function of distance in the crystal. The theory is valid only above the ordering temperature of an alloy, but may be used with equal facility for a variety of alloys with differing compositions and ranges of interaction.