An idealized model for a vacancy in a crystal lattice which permits vacancy migration is presented. It consists of a linear chain of atoms together with a substrate potential, with piecewise linear force laws between nearest-neighbor atoms and between atoms and substrate. The predictions of the Vineyard equilibrium rate theory are calculated explicitly for this model. A computer simultation procedure is described which reproduces some, although not all, of the statistical characteristics of thermal equilibrium. The jump rates observed in the simulation agree reasonably well with those predicted by the Vineyard theory.
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Weiner et al. (1966) studied this question.
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