Defect ordering in aliovalently doped cubic zirconia from first principles

Defect ordering in aliovalently doped cubic-stabilized zirconia is studied using gradient corrected density-functional calculations. Intra- and intersublattice ordering interactions are investigated for both cation (Zr and dopant ions) and anion (oxygen ions and vacancies) species. For yttria-stabilized zirconia, the crystal structure of the experimentally identified, ordered compound $\ensuremath{\delta}\ensuremath{-}{\mathrm{Zr}}_{3}{\mathrm{Y}}_{4}{\mathrm{O}}_{12}$ is established, and we predict metastable zirconia-rich ordered phases. Anion vacancies repel each other at short separations, but show an energetic tendency to align as third-nearest neighbors along $〈111〉$ directions. Calculations with divalent (Be, Mg, Ca, Sr, Ba) and trivalent (Y, Sc, B, Al, Ga, In) oxides show that anion vacancies prefer to be close to the smaller of the cations (Zr or dopant ion). When the dopant cation is close in size to Zr, the vacancies show no particular preference, and are thus less prone to be bound preferentially to any particular cation type when the vacancies traverse such oxides. This ordering tendency offers insight into the observed high conductivity of ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}\ensuremath{-}$ and ${\mathrm{Sc}}_{2}{\mathrm{O}}_{3}$-stabilized zirconia, as well as recent results using, e.g., lanthanide oxides. The calculations point to ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ as a particularly promising stabilizer for high ionic conductivity. Thus we are able to directly link (thermodynamic) defect ordering to (kinetic) ionic conductivity in cubic-stabilized zirconia using first-principles atomistic calculations.