Ferroelectric materials with a perovskite crystal structure are widely used in applications like actuators, sensors and sonar systems. The most widely spread commercial material is Pb(Zr[1−x]Ti[x])O3 due to its outstanding electromechanical properties and large temperature range. Based on the Landau-Ginzburg-Devonshire (LGD) thermodynamic theory, Haun at al. were able to describe lead-based composition material. However, many effects do still not fit the prediction of LGD and need further investigation. One such phenomenon happens near the so-called morphotropic boundary (MPB).
The MPB separates the tetragonal phase from a rhombohedral phase. In the vicinity of the MPB, the Pb(Zr[1−x]Ti[x])O3 -material passes through a minimum in the coercive field and a maximum in the obtainable electromechanical strain. The experimentally determined strain is much larger than theoretically predicted. The reason for this discrepancy is the complex interplay of the different strain mechanisms and field induced phase transitions dependent on grain orientation . For adjusting the theoretical prediction to the macroscopic observations, one possible approach  relies on measurements of the spontaneous strains for different phases using diffraction techniques. As a result, phase-dependent electrostrictive appliances QT and QR for tetragonal and rhombohedral phases are obtained.
The aim of this work is to combine the LGD theory with a phase-field approach incorporating continuum mechanics of the elastic field  and to enable simulations of polarization domains inside the grain structures of different simultaneously present crystalline phases. In this presentation, the theory and fundamental model equations are explained and simulation results are shown in comparison with experimental data.