Jump rate of the fcc vacancy in the short-memory–augmented-rate-theory approximation. II. Dynamical conversion coefficient and isotope-effect factor

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Abstract
The framework of short-memory–augmented-rate theory is employed to partition the vacancy jump rate into two factors related, respectively, to the Vineyard theory and to corrections for multiple barrier crossings inherent in the dynamics. This paper treats the second of the factors using molecular dynamics to locate critical trajectories that lie on invariant manifolds of the dynamical systems, starting from states of motion in the saddle plane. For models of Ar, Cu, and Ag the errors of the Vineyard treatment are negligible at low temperature and contribute a rate reduction of only ∼10% at the melting temperature. These factors are, however, strongly mass dependent and give dominant contributions to the isotope effect. Our calculations reproduce the experimentally observed κ≃0.87 near the melting temperature very well, and are similarly model insensitive; κ decreases nonlinearly from its harmonic value at T=0 as the temperature is increased. Detailed examination of trajectories shows that the isotope effect is largely determined by the deformation of the manifolds caused by core repulsive forces. In effect, the isotope dependence derives mainly from infrequent energetic collisions that take place in jump events.