Thermodynamics of ionic diffusion and oxidation rate equations

Abstract

Diffusional flux equations for individual lattice species and defects are related to phenomenological mass-transport equations using the concept of relative building units. These units conserve sites and charge but represent local constitutional change within a crystal resulting either from equilibration with another phase or from diffusion within the crystal. Using the example of a metal deficit, solid solution oxide (A_1ξ B_ξ)_1−δ0, a simple thermodynamic method is arrived at for producing an exhaustive listing of units capable of participating in diffusion during an oxidation reaction. A combination of the flux contributions due to these different units then permits a calculation of the phenomenological transport coefficients in terms of microscopic kinetic and concentration variables. This description, together with a precise statement of the Gibbs-Duhem equation, permits an examination of the usual approximations in oxidation rate equations: the neglect of diffusional interactions and of nonstoichiometry.