Statistical mechanical theory of fast interstitial diffusion in metals

Abstract

A statistical mechanical theory is developed with the assumption that radioactive tracers migrate through interstitial channels represented by a periodic potential energy with barrier height ϵ. If ϵ is much greater than both the thermal energy k B T and the maximum phonon energy k B Θ D( Θ D: Debye temperature), the diffusion coefficient D for a cubic crystal is given by D = 1 3 vlq ∗ exp(− ϵ k BT ) , where v and l are, respectively, the mean migration speed and mean straight path; q ∗ exp(− ϵ k BT ) represents the ratio of the number of migrating tracers to the total number of tracers. The results are used to discuss several outstanding features of fast diffusion in metals. These include the reason for why interstitial migration can lead to fast diffusion, strong dependence of fast diffusion on the tracer valence and the crystal structure, anomalous isotope effect for heavy diffusants in Pb and Sn, the correlation between activation energy and pre-exponential factor. The present model is quite different from the currently predominant hopping model. But both models are needed to describe a wide spectrum of atomic diffusion in solids.