| This thesis covers several topics concerning the study of complex materials systems by first-principles methods. It contains four chapters. A brief, introductory motivation of this work will be given in Chapter 1. In Chapter 2, I will give a short overview of the first-principles methods, including density-functional theory (DFT), planewave pseudopotential methods, and the Berry-phase theory of polarization in crystallines insulators. I then discuss in detail the locality and exponential decay properties of Wannier functions and of related quantities such as the density matrix, and their application in linear-scaling algorithms.; In Chapter 3, I investigate the interaction of oxygen vacancies and 180° domain walls in tetragonal PbTiO3 using first-principles methods. Our calculations indicate that the oxygen vacancies have a lower formation energy in the domain wall than in the bulk, thereby confirming the tendency of these defects to migrate to, and pin, the domain walls. The pinning energies are reported for each of the three possible orientations of the original Ti–O–Ti bonds, and attempts to model the results with simple continuum models are discussed.; CaCu3Ti4O12 (CCTO) has attracted a lot of attention recently because it was found to have an enormous dielectric response over a very wide temperature range. In Chapter 4, I study the electronic and lattice structure, and the lattice dynamical properties, of this system. Our first-principles calculations together with experimental results point towards an extrinsic mechanism as the origin of the unusual dielectric response. |
