Atomic structure of ferroelectric domain walls, free surfaces and steps

The goal of this thesis is to develop a general framework for lattice statics analysis of defects in ferroelectric Perovskites. The techniques presented here are general and can be easily applied to other systems as well. We present all the calculations and numerical examples for two technologically important ferroelectric materials, namely, PbTiO3 and BaTiO3. We use shell potentials, that are derived using quantum mechanics calculations, and analyze three types of defects: (i) 180° and 90° domain walls; (ii) free surfaces and (iii) steps in 180° domain walls. Our formulation assumes that, an interatomic potential is given. In other words, there is no need to have the force constants or restrict, the number of nearest neighbor interactions a priori. Depending on the defect and symmetry; the discrete governing equations are reduced to those for representatives of some equivalence classes. The idea of symmetry reduction in lattice statics calculations is one of the contributions of this thesis. We call our formulation of lattice statics 'inhomogeneous lattice statics' as we consider the fact that close to defects force constants (stiffness matrices) change. For defects with one-dimensional symmetry reduction we solve the discrete governing equations directly using a novel method in the setting of the theory of difference equations. This will be compared with the solutions obtained using discrete Fourier transform. For defects with two-dimensional symmetry reduction we solve the discrete governing equations using discrete Fourier transform. We calculate the fully nonlinear solutions using modified Newton-Raphson iterations and call the method 'inhomogeneous anharmonic lattice statics'. This work is aimed to fill the gap between quantum mechanics ab initio calculations and continuum models (based on Landau-Ginzberg-Devonshire theory) of ferroelectric domain walls.