  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.
