Thermodynamics and Transport of Ionic and Electronic Defects in Crystalline Oxides

Abstract

The first part of this article concerns the thermodynamics of point defects. In the traditional analysis of reactions in which point defects are involved, point defects are assumed to be ideally diluted, which leads to familiar mass‐action‐type equations. In this article, situations in which deviations from ideal mass‐action‐type behavior occur are investigated by evaluating the influence of defect interactions on the chemical potentials of point defects. Expressions for chemical potentials are derived for the case of weak interactions between neighboring defects. Strong repelling interactions between neighboring defects are discussed using the concept of excluded configurations, and strong attractive interactions are analyzed by introducing clusters. The chemical potential of electrons occupying energy states in an electron band also is analyzed as a function of bandwidth and electron occupation number. An expression for the chemical potential of electrons in partially filled bands is derived, which incorporates the average density of states at the Fermi level. Also discussed is the relationship between formation energies and entropies of defects in oxides and the measurable energy and entropy part of the oxygen chemical potential. The second part of this article concerns the transport of ionic and electronic defects in oxides. Within the framework of irreversible thermodynamics, a formalism is presented that allows the description of the general case in which ambipolar diffusion of ions and electrons in oxides is governed by contributions of several ionic and electronic point defects. The formalism allows the handling of defect association, defect interactions, and coupling of the overall ionic and electronic fluxes. The origin of the coupling and its influence on the net oxygen transport and electric current density is investigated.