Studies in Molecular Dynamics. IX. Vacancies in Hard Sphere Crystals

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Abstract
The concentration of monovacancies as well as their entropy and volume of formation have been determined in a face‐centered hard sphere crystal at a series of densities. The results near the hard sphere melting density compare favorably with experiments on argon and metals. Although divacancies are shown to have an increasingly larger mobility relative to monovacancies with increasing pressure, they do not contribute significantly to diffusion because their equilibrium concentration is too low. It is shown also that two monovacancies interact significantly when separated by many lattice spacings. The free energy of association of higher vacancy clusters is found to be approximately proportional to the number of vacancy–vacancy contacts, so that compact clusters are stabilized relative to extended ones. This effect was found to be greatly enhanced for different shaped vacancy clusters in square‐well particle systems, by an additional amount corresponding to the potential difference in particle–vacancy contacts.