The factors behind the morphotropic phase boundary in piezoelectric perovskites

The best piezoelectric materials are solid solutions in the vicinity of the steep morphotropic phase boundary (MPB) separating rhombohedral and tetragonal phases in the composition-temperature plane. A classical example is the lead zirconate titanate [Pb(Zr(x)Ti(1-x))O(3), PZT] system, with x approximately 0.52, where the two phases are separated by a boundary extending from the lowest temperatures up to several hundred degrees. The origin of the boundary has been under keen studies for 40 years. Recent interest is largely due to the need to develop new, lead-free piezoelectrics, for which a natural starting point is to understand the properties of the present systems. Here, we demonstrate, through high-pressure (up to 8 GPa) neutron powder diffraction experiments and density functional theory computations on lead titanate (PbTiO(3), PT), that it is the competition between two factors which determines the MPB. The first is the oxygen octahedral tilting, giving advantage for the rhombohedral R3c phase, and the second is the entropy, which in the vicinity of the MPB favors the tetragonal phase above 130 K. If the two factors are in balance over a large temperature range, a steep phase boundary results in the pressure-temperature plane.