Predicting self-diffusion in metal oxides from first principles: The case of oxygen in tetragonal ZrO₂

Abstract

Theoretical prediction of self-diffusion in a metal oxide in a wide range of thermodynamic conditions has been a long-standing challenge. Here, we establish that combining the formation free energies and migration barriers of all charged oxygen defects as calculated by density functional theory, within the random-walk diffusion theory framework, is a viable approach to predicting oxygen self-diffusion in metal oxides. We demonstrate this approach on tetragonal ZrO2 by calculating oxygen self-diffusivity as a function of temperature and oxygen partial pressure or, alternatively, temperature and off-stoichiometry. Arrhenius analysis on the isobaric (or constant off-stoichiometry) self-diffusivities yields a spectrum of effective activation barriers and prefactors. This provides reconciliation for the wide scatter in the experimentally determined activation barriers and prefactors for many oxides.