Activation Volume Tensor for Oxygen-Vacancy Migration in Strained ${\mathrm{CeO}}_2$ Electrolytes

We examine the effect of mechanical strain on the migration of oxygen vacancies in fluorite-structured ceria by means of density functional theory calculations. Different strain states (uniaxial, biaxial and isotropic) and strain magnitudes (up to $\pm 7\%$) are considered. From the calculations we extract the complete activation volume tensor for oxygen-vacancy migration in ${\mathrm{CeO}}_2$, that is, all diagonal $\Delta V_{\mathrm{mig},kk}$ and off-diagonal $\Delta V_{\mathrm{mig},kl}$ tensor elements. These individual tensor elements are found, crucially, to be independent of strain state; they do, however, depend on stress ($\Delta V_{\mathrm{mig},kk}$) or effective pressure ($\Delta V_{\mathrm{mig},kl}$). Armed with knowledge of all tensor elements we predict strain states for which oxygen-ion transport in ceria is maximized. In general, with our approach the effect of an arbitrary strain state on the migration barrier for mass transport in a solid can be calculated quantitatively.