Anharmonic lattice statics analysis of 180 ° and 90° ferroelectric domain walls in PbTiO₃

This paper presents an anharmonic lattice statics analysis of 180 ° and 90 ° domain walls in tetragonal ferroelectric perovskites. We present all the calculations and numerical examples for the technologically important ferroelectric material PbTiO₃. We use shell potentials that are fitted to quantum mechanics calculations. Our formulation places no restrictions on the range of the interactions. This formulation of lattice statics is inhomogeneous and accounts for the variation of the force constants near defects. The discrete governing equations for perfect domain walls are reduced using symmetry conditions. We solve the linearized discrete governing equations directly using a novel method in the setting of the theory of difference equations. We calculate the fully nonlinear solutions using modified Newton–Raphson iterations.