Adaptive ferroelectric state at morphotropic phase boundary: Coexisting tetragonal and rhombohedral phases

With a focus on local symmetry, the microstructural basis for high piezoelectric performance in PbMg1/3Nb2/3O3–xPbTiO3 (PMN–PT) ceramics at the morphotropic phase boundary (MPB) composition was investigated by means of convergent-beam electron diffraction analysis and twin diffraction pattern analysis. The local structure was found to consist of coexisting (1 0 1)-type tetragonal nanotwins and (0 0 1)-type rhombohedral nanotwins. A phenomenological theory based on crystallography is proposed to show that such nanoscale coexistence can give rise to an average monoclinic structure through strain accommodation. The average monoclinic structures (Ma and Mc) vary with temperature and composition due to the dependence on temperature and composition of the lattice parameters. Based on in situ X-ray diffraction data, we demonstrate how the polarization rotates across the MPB region in PMN–PT ceramics with varying temperatures and compositions