A Stabilization Mechanism of Zirconia Based on Oxygen Vacancies Only
  The microscopic mechanism leading to stabilization of cubic and tetragonal forms of zirconia (ZrO$_2$) is analyzed by means of a self-consistent tight-binding model. Using this model, energies and structures of zirconia containing different vacancy concentrations are calculated, equivalent in concentration to the charge compensating vacancies associated with dissolved yttria (Y$_2$O$_3$) in the tetragonal and cubic phase fields (3.2 and 14.4% mol respectively). The model is shown to predict the large relaxations around an oxygen vacancy, and the clustering of vacancies along the $<111 >$ directions, in good agreement with experiments and first principles calculations. The vacancies alone are shown to explain the stabilization of cubic zirconia, and the mechanism is analyzed. 
Stefano Fabris, Anthony T. Paxton and Michael W. Finnis