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.
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Belak et al. (2015) studied this question.
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