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

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 ΔK that describes the isotope effect in diffusion. Numerical results for Cu, Ag, Au, Al, Ni, Co, Pb, Na, and α-Fe are presented. The effect of both relaxation near the vacancy and temperature on ΔK are also studied.