Site preference of Y and Mn in nonstoichiometric BaTiO3 from first principles

$\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ is often doped with Y and/or Mn to realize a range of desired properties. Yet, existing canonical models of their defect chemistry cannot explain various observed phenomena outside of the high temperature electrical conductivity measurements to which they were fit. Existing models assume Y substitutes exclusively for Ba or Ti despite experiments showing Y is amphoteric, substituting predominantly for Ba or Ti depending on the cation nonstoichiometry. Existing models assume Mn forms isolated ${\mathrm{Mn}}_{\text{Ti}}$ exclusively, but experiments have shown complexes of ${\mathrm{Mn}}_{\mathrm{Ti}}$ with native oxygen vacancies (${\mathrm{Mn}}_{\mathrm{Ti}}\text{\ensuremath{-}}{\mathrm{v}}_{\text{O}}$) form in significant concentrations. Additionally, recent computational works in ${\mathrm{SrTiO}}_{3}$ suggest A-site substitutional defects may form in greater concentrations in a configuration with reduced symmetry relative to the on-site geometry. To address these inconsistencies, we developed a hybrid functional density functional theory informed grand canonical defect model with the ability to simulate specific nonstoichiometries without ad hoc assumptions about the bulk chemical potentials. Using this model, the site preference of Y and Mn in $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ as a function of the Ba/Ti ratio was evaluated in the context of a more complete set of defects including: native cation vacancies, on-site and reduced symmetry A-site defects, isolated B-site defects, and ${\mathrm{X}}_{\text{B}}\text{\ensuremath{-}}{\mathrm{v}}_{\text{O}}$ defects. The results reproduce experimental observations of yttrium's amphotericity and significant concentrations of ${\mathrm{Mn}}_{\mathrm{Ti}}\text{\ensuremath{-}}{\mathrm{v}}_{\text{O}}$. Both and Y and Mn are found to substitute predominantly for Ba at Ba/Ti = 0.99 and Ti at Ba/Ti = 1.01, but neither are found to substitute exclusively for Ba or Ti within the range of experimentally accessible Ba/Ti ratios at 1400 ${}^{\ensuremath{\circ}}\mathrm{C}$.