Ferroelectric Domain Walls Approaching Morphotropic Phase Boundary

Domain walls play an important role in tailoring the properties of ferroic materials. We employ a Landau-Ginzburg thermodynamic model to investigate the ferroelectric domain walls around the morphotropic phase boundary (MPB) which contribute to the large piezoelectric response, including 90° domain wall for tetragonal (T) symmetry and 109° and 71° domain walls for rhombohedral (R) symmetry. The domain wall energy for each type of domain wall has been analytically calculated by quasi-one-dimensional solution of the spatial evolution for polarization. Our results suggest that the domain wall energies for both T-T and R-R domains decrease as the composition approaches MPB accompanied by the vanishing of polarization anisotropy, which can be viewed as the origin for the experimentally observed miniaturized domains. In addition, the reduced domain wall energy caused by the polarization anisotropy vanishing is responsible for the large piezoelectric response due to the displacement of domain walls.