Theory of tetragonal twin structures in ferroelectric perovskites with a first-order phase transition

A three-dimensional Landau-Ginzburg model has been constructed to describe the tetragonal twin structures resulting from a first-order ${\mathit{O}}_{\mathit{h}\mathrm{-}}$ ${\mathit{C}}_{4\mathit{v}}$ proper ferroelectric phase transition in perovskites. The model takes into account the nonlinear and nonlocal characteristics of the polarization (order parameter) as well as the electromechanical coupling. Quasi-one-dimensional (Q1D) analytic solutions for the space profiles of the order parameter are obtained for a 180° twin and for a charge-neutral 90° twin with a special choice of parameters. Without the presence of interfacial defects, such as dislocations, the Q1D solutions require the support of inhomogeneous mechanical constraints. Elastic deformation and dimensional changes associated with the twin structures, and their implications on the piezoelectric effect in ferroelectric ceramics, are also addressed.