Lattice vibrations in cubic, tetragonal, and monoclinic phases of ZrO₂

First principles calculations of the phonon dispersion relations and the phonon density of states for three zero-pressure zirconia phases are presented. The phonon dispersion relations of the tetragonal and monoclinic phases do not exhibit the imaginary frequencies, contrary to the cubic phase for which the imaginary soft mode is seen. For tetragonal and monoclinic phases the free energies versus temperature are calculated in harmonic approximation. They cross at 1560 K indicating the phase transition.