First-principles determination of the soft mode in cubic ZrO2

A direct approach to calculate the phonon dispersion using an ab initio force constant method is introduced. The phonon dispersion and structural instability of cubic ZrO2 are found using a supercell method in the local-density approximation. The force constants are determined from the Hellmann-Feynman forces induced by the displacement of an atom in the 2 x 2 x 2 fcc supercell. This size of the supercell gives ''exact'' phonon frequencies at Gamma,X,L,W Brillouin zone points. The phonon dispersion curves show a pronounced soft mode at the X point, in agreement with the experimentally observed cubic to tetragonal phase transition.