On the Dynamical Theory of Diffusion in Crystals. III. Some Model Calculations and Relation to Continuum Theory

Abstract

Some simple models are considered which permit exact evaluation of the various dynamical parameters of the theory of crystal diffusion previously proposed. The models considered suggest that: (a) The jump frequency is insensitive to the normal mode modifications produced by the adjacent vacancy. (b) There is considerable relaxation about a vacancy. (c) The volume of formation of a vacancy is related to the molar volume by ΔV*≈V/(γG—⅓), where γG is the Gruneisen constant. The restrictions of the models are briefly analyzed, and the mass dependence proposed by Bak and Prigogine is compared with the quasi-equilibrium model and the discrepancy discussed.