Electronic structure of cubic and tetragonal zirconia

The electronic structure of tetragonal zirconia with ${\mathit{D}}_{4\mathit{h}}^{15}$ symmetry is investigated using density-functional theory. The Kohn-Sham equations are solved by applying the full-potential linearized augmented-plane-wave method. The total energy as a function of the lattice parameters shows that at zero temperature tetragonal zirconia is more stable than cubic zirconia. The calculated elastic constants are consistent with experimental data. High-temperature results are simulated by introducing a semiempirical volume expansion. The calculated displacement in the positions of the oxygen atoms follows the experimental results, but the tetragonal distortion as a function of temperature shows larger differences with experiment. At expanded volumes the tetragonal structure is always more stable than the cubic structure, but the energy differences are of the same order of magnitude as the thermal energies.