New insight on cubic–tetragonal–monoclinic phase transitions in ZrO₂: ab initio study and symmetry analysis

A group-theory analysis of temperature-induced phase transitions in ZrO 2 has been performed in the framework of the group–subgroup relationship tree (Bärnighausen tree) with the computer tools of the Bilbao Crystallographic Server. The transition paths including symmetry-allowed intermediate phases have been established. The active irreducible representations corresponding to soft phonon modes and spontaneous deformation strains responsible for the phase transitions have been determined. The phonon mode frequencies at the symmetry points of the Brillouin zones of cubic, tetragonal and monoclinic phases have been calculated using the ab initio density functional theory method. As a result, the soft modes and their symmetries have been revealed, which are in a complete agreement with the group-theoretical predictions.