Four models for estimating the effect of short-range ordering (or clustering) on the equilibrium concentration of vacancies in binary alloys are developed in terms of statistical thermodynamics. The Smeared-Displacement, Simple-Displacement and Modified Vacancy Energy Models assume that the energy to produce a vacancy can be estimated from the change in bond energy when an atom is displaced from the bulk of the crystal to the surface. Each model differs, however, relative to the details of the environments about vacancies that are taken into consideration. All such models suggest that the vacancy concentration decreases as a result of ordering. The Vacancy-Energy Model is physically more realistic and more detailed but somewhat less tractable than the other models. It assumes that the energy to produce a vacancy depends primarily on the immediate environment of the vacancy .
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