Progress in phase field simulations of piezoelectric materials

Piezoelectric materials can convert mechanical energy to electric energy and vice versa, and they are widely used in transducers and actuators. The best piezoelectricity normally appears at the so called morphotropic phase boundary(MPB) in the phase diagram of ferroelectric solid solutions. Thus understanding the mechanism of good piezoelectric properties at the MPB can guide designing new piezoelectric materials. This review summarized the progress in simulating the microstructure of piezoelectric materials at the MPB as well as the mechanism of good piezoelectric property there through phase field simulations. On the microstructure, we obtained hierarchical nanodomain structure as observed by experiments of phase field simulation and our work showed that these nanodomains are the newly discovered monoclinic phase and this new phase is stabilized by long range electrostatic energy and elastic energy. On the piezoelectric property, we showed that the good piezoelectric property appearing at the MPB mainly comes from the contributions from polarization rotation rather than domain wall movement by phase field simulation.