Theory of oxidation/reduction-induced valence transformations of metal ion dopants in oxide crystals mediated by oxide-vacancy diffusion: II. Kinetic analysis

We consider theoretically valence transformations of doping metal ions in oxide crystals induced by oxidation and reduction obtained by changes in the ambient oxygen partial pressure. Three types of oxygen vacancies are assumed to mediate transformations: neutral, singly ionized, and doubly ionized. In the companion part I paper we provide thermodynamic analyses yielding concentration relations among the oxygen vacancy, metal ions, holes and electrons, as functions of the ambient oxygen pressure. In the present companion part II paper we provide time dependent concentration profiles of the various species and reaction rate profiles. The diffusion exhibits a complex behavior; under some conditions, it may be described by a constant diffusivity, and is symmetric with respect to oxidation and reduction. However, under a wide range of conditions, the ionic state changes are highly asymmetric with respect to oxidation and reduction. For example, in the case of a neutral vacancy, a very narrow reaction front may establish during reduction. In the inverse (oxidation) process, however, the different species' profiles are quite smooth.