Theory of Phenomenological Coefficients in Solid‐State Diffusion. II. Cluster Expansion for Ionic Crystals

Publisher Website
Google Scholar
Abstract
Previously derived time correlation formulas for phenomenological coefficients of solid‐statediffusion are studied. The model is that the system evolves by the master equation of a Markoff process and is characterized by known defect‐configuration dependent jump probabilities. To study the effect of defect interactions on matter transport the cluster and diagram expansion methods of equilibrium theory are used to convert the expressions to series expansions in powers of defect concentrations, the migration mechanisms being vacancy and interstitial. The coefficients of the expansion are cluster summations dependent on concentration through equilibrium correlation functions. To obtain convergent summations for ionic crystals a further chain summation step like that of Mayer ionic solution theory, as well as an additional bond summation of a different kind, are necessary. Formal results are given for ionic conducting crystals whose defect composition is arbitrary except that there are no macroscopic amounts of vacancy‐migrating impurities (although the results suffice for substitutional tracerdiffusion in such crystals). A preliminary classification into cycle, two defect, three defect, ··· diagrams and future applications are briefly indicated.

This publication has 17 references indexed in Scilit: