Effect of disorder on the dilute equilibrium vacancy concentrations of multicomponent crystalline solids

We develop statistical mechanical methods to predict the thermodynamic properties of dilute vacancies in multicomponent solids from first principles. The approach relies on a coarse-graining procedure to predict dilute vacancy concentrations with Monte Carlo simulations in alloys exhibiting varying degrees of short- and long-range order. We apply this approach to a study of vacancies in hcp based Ti-Al binary alloys and find a strong dependence of the equilibrium vacancy concentration on the Al concentration and the degree of long-range order, especially at low temperature.