Universal phase diagram for high-piezoelectric perovskite systems

Strong piezoelectricity in perovskite-type ${\mathrm{PbZn}}_{\text{1−x}}{\mathrm{Ti}}_x{\mathrm{O}}_{\mathrm{3}}$ (PZT) and ${\mathrm{Pb(Zn}}_{\mathrm{1/3}}{\mathrm{Nb}}_{\mathrm{2/3}}{\mathrm{)O}}_{\mathrm{3}}{\mathrm{–PbTiO}}_{\mathrm{3}}$ (PZN–PT) systems is generally associated with the existence of a morphotropic phase boundary (MPB) separating regions with rhombohedral and tetragonal symmetry. An x-ray study of PZN–9% PT has revealed the presence of an orthorhombic phase at the MPB, and a near-vertical boundary between the rhombohedral and orthorhombic phases, similar to that found for PZT between the rhombohedral and monoclinic phases. We discuss the results in the light of a recent theoretical paper by Vanderbilt and Cohen [Phys. Rev. B 63, 94108 (2001)], which attributes these low-symmetry phases to the high anharmonicity in these oxide systems.