Ab initio lattice dynamics and phase transformations of ZrO ₂

Zirconia, ZrO ₂, is one of the most important ceramic materials in modern technology. Its versatility is closely related to phase transformations. Although the transformations have been repeatedly investigated by experiments, fundamental aspects of the transformations are still under debate. In the present paper, we have made first principles calculations to study the lattice dynamics of ZrO ₂ polymorphs and phase transformation at finite temperatures. Cubic phase shows a soft mode at the X point in the Brillouin zone, which should spontaneously induce cubic-to-tetragonal transformation. In tetragonal and monoclinic ZrO ₂, all vibrational modes have real frequency. Calculations of Helmholtz free energies show that the tetragonal phase becomes more stable than the monoclinic phase above 1350 K, which is in quantitative agreement with experimental results. This confirms that vibrational entropy contributes to destabilize monoclinic ZrO ₂ at elevated temperatures.