On the Isotope Effect in Interstitial Diffusion III. Quantum Corrections

Abstract

Abstract A one‐dimensional Prigogine‐Bak model of interstitial diffusion which has been discussed classically in two earlier papers, is treated quantum mechanically. By means of S‐matrix theory an energy transport equation is established for the diffusing particle. By solving this equation with the appropriate Prigogine‐Bak boundary condition, the quantum corrections for the frequency factor of the diffusion constant are obtained. It is found that the classical isotope effect is generally reduced by these corrections which are important for small interstitial masses and/or low temperatures.