Extension of Darken's Equation to Binary Diffusion in Ceramics

Abstract

The idea of a “relaxation velocity” to compensate for the differing mobilities of the species has been useful in describing binary diffusion in gases, nonelectrolyte liquids, and metals. The application of the idea to binary ceramic systems, particularly those with a common anion, is considered. By making certain simplifying assumptions, (1) the volume of a ceramic is primarily determined by the volume of the anion and (2) the chemical potential of the anion does not depend on cation ratio as long as electrical neutrality is preserved, it is possible to arrive at the appropriate expression for the binary diffusion coefficients in terms of the self‐diffusion coefficients and valencies of all species and the activity of one of the compounds. This result is analyzed by considering the intrinsic flux densities of the species, the concentration distribution, and the relaxation velocity and marker movement for several cases and these are plotted schematically.