Analysis of the demixing of yttria-stabilized zirconia in an electric field for different diffusion mechanisms

Steady-state demixing of the cations in yttria-stabilized zirconia in an electric field is analyzed for diffusion via independent vacancies, by vacancy pairs and by vacancy triplets. We analyze two conditions, one (open system) where the vacancies are everywhere close to an internal surface, which allows the Schottky defect reaction to permit the equilibration of the concentration of the vacancies, the other (closed system) where such equilibration is only possible at the external surface. For diffusion via independent vacancies and vacancy pairs, critical values of the ratio of the yttrium to zirconium vacancy exchange frequencies causing yttrium enrichment at the cathode are determined. It is also shown that diffusion via the vacancy-triplet mechanism always leads to yttrium enrichment at the anode end. Using Monte Carlo simulation, we also verify the analysis of the situation where demixing occurs by independent cation vacancies in a closed system.