Recent studies of short-range order in alloys: the Cowley theory revisited

We present comparisons of various statistical theories for effective pair interactions (EPI) in alloys. We then evaluate these EPIs using the Cowley theory, the Krivoglaz-Clapp-Moss (KCM) approximation, the γ-expansion method (GEM) of Tokar, Masanskii and co-workers, and the exact inverse Monte Carlo (IMC) method, introduced by Gerold and Kern. Via a series of model calculations on a hypothetical bcc alloy with a single nearest-neighbor interaction we show that the Cowley theory is successful in evaluating the EPIs in more dilute alloys but tends to overestimate the magnitude of the nearest-neighbor energy at higher concentrations, whereas the KCM expression becomes increasingly inaccurate at lower concentrations. In general, however, the approximate mean-field theories are most accurate at higher concentrations and higher temperatures. Recent studies of short-range order in single crystals are discussed in which these EPIs have been evaluated using the IMC, KCM, GEM and Cowley theories. Examples include the bcc alloy Fe0.53Cr0.47 and the fcc alloys Cu3Au, Cu0.69Zn0.31 and Ni0.89Cr0.11. In all cases the approximate expressions do quite well, especially the GEM.