Quasi-one-dimensional solutions for domain walls and their constraints in improper ferroelastics

Based on a Landau-Ginzburg model for improper ferroelastic perovskites, we have analyzed quasi-one-dimensional (Q1D) solutions for twin boundaries (domain walls) and the associated constraints. Because of the coupling of the order parameter to the elastic strain, in general domain walls must be described by fully three-dimensional (3D) solutions. Q1D solutions exist only with the presence of one of the following: (i) body force, (ii) surface stress, and (iii) interface dislocations. The shape change induced by the domain wall is also discussed for each of the above three cases. These conclusions hold quite generally for all Landau-Ginzburg models of improper ferroelastics.