Grain-boundary diffusion of cations in fluorite-type oxides is faster but not always easier

Abstract

Cation diffusion in fluorite-type MO2 polycrystals has been observed in diverse experimental studies to occur much faster along grain boundaries than in the bulk phase. The activation enthalpy of grain-boundary diffusion (ΔH gb), relative to the value for bulk diffusion (ΔH b), is, in many cases, seemingly unphysical: specifically, the ratio r = ΔH gb/ΔH b approaches, or even exceeds, unity. In this study, we examined the behaviour of r, assuming that fast cation diffusion arises from the accumulation of cation vacancies in space-charge layers adjacent to grain boundaries. Taking an acceptor-doped MO2 oxide as our model system, we obtained, first, numerical solutions to a Poisson equation for equilibrium space-charge layers; and then, numerical solutions to the diffusion equation for cation diffusion occurring parallel to the interface. The resultant diffusion profiles displayed two features and were analysed according to the standard procedure to obtain the grain-boundary diffusion product. From a detailed analysis of our results, we conclude that, within our model, fast diffusion in space-charge layers can yield values of r that approach but do not exceed unity. In addition, we derive an empirical relationship that allows the grain-boundary diffusion product, the effective grain-boundary width and the grain-boundary diffusivity to be predicted with knowledge of space-charge parameters and the bulk diffusivity. Finally, we demonstrate that this relationship is also applicable to the fast grain-boundary diffusion of cations in acceptor-doped ABO3 perovskites.