Electric-field induced polarization paths in Pb(Zr_1-xTi_x)O₃ alloys

Properties of Pb(Zr_1-xTi_x)O₃ (PZT) for compositions x near the morphotropic phase boundary and under an electric field are simulated using an ab initio based approach. Applying an electric field of [111] orientation to tetragonal PZT (e.g., x=0.50) leads to the expected sequence of tetragonal, A-type monoclinic, and rhombohedral structures. However, the application of a field of orientation [001] to rhombohedral PZT (e.g., x=0.47) does not simply reverse this sequence. Instead, the system follows a complicated path involving also triclinic and C-type monoclinic structures. These latter phases are found to exhibit huge shear piezoelectric coefficients.