Structure and energetics of antiferroelectricPbZrO3

Structural instabilities and electronic properties of ${\mathrm{PrZrO}}_3$ are investigated using local-density calculations. Substantial hybridization is found in the electronic band structure, both between O 2p and Zr 4d states and between O 2p and Pb s and p states. A very strong Γ point phonon instability is present for the cubic perovskite structure. Relaxation, allowing only zone-center distortions, yields a large energy lowering of 0.253 eV, with bond-length changes in excess of 0.5 Å. Two related R point instabilities are found, both of which involve changes in Pb-O distances. The more unstable of these involves a 12° rotation of the O octahedra, with an energy lowering of 0.20 eV per formula unit. Total-energy calculations were performed for 40 atom unit cells with orthorhombic Pba2 and Pbam space groups as reported experimentally. Energies close to but still above the related Γ structure were obtained with experimentally determined atomic positions. However, after relaxation of the oxygen coordinates, the antiferroelectric structure is favored by 0.02 eV per formula unit. This ordering and the small ferroelectric-antiferroelectric energy difference is in accord with the Pb(Zr,Ti)${\mathrm{O}}_3$ phase diagram.