Lattice-Dynamical Theory of the Diffusion Process. I. Isotope Effect in Cubic Metals

Abstract

A lattice-dynamical theory of diffusion based on the fluctuations in a certain reaction co-ordinate first used by Flynn is presented. The theory of vibrations of isotopic impurities in a crystal is applied to evaluate the parameter $\Delta K$ that describes the isotope effect in diffusion. Numerical results for Cu, Ag, Au, Al, Ni, Co, Pb, Na, and $\alpha -\mathrm{F}\mathrm{e}$ are presented. The effect of both relaxation near the vacancy and temperature on $\Delta K$ are also studied.