Lattice Instabilities of Perovskite Oxides from First Principles

摘要

The theoretical and experimental investigation of the crystal structures and properties of complex oxides presents significant challenges, with corresponding potential rewards both for fundamental science and technology. First-principles density-functional-theory methods have emerged as a valuable tool for obtaining microscopic information about structural energetics and polarization in these systems, with continuing improvements in algorithms and computer hardware leading to a point where important questions can be addressed. This increased access to information can drive the development of a more comprehensive and powerful conceptual framework; such a framework is also very much needed to guide and interpret highly demanding experimental and computational investigations. The perovskites are a large, diverse, and well studied family of oxide materials of fundamental scientific interest and technological value, with virtually the full range of properties exhibited by complex oxides. The crystal structures of the perovskites can be described as distortions of a high-symmetry parent cubic perovskite structure, shown in Fig. 29.1. This structure is highly prone to instabilities, and only a few perovskite oxides have a cubic ground state structure (e.g. BaZrO_3). The structures of many others can be described by atomic displacement patterns corresponding to the "freezing in" of a single unstable normal mode, lowering the symmetry. This idea can be extended to more complicated structures involving the freezing in of several coupled modes (e.g. PbZrO_3). A description in terms of normal modes also provides a direct relationship to physical properties of the perovskites derived from structure and polarization. The lowest frequency modes contribute the most to the response to external perturbations and to the vibrational free energy (which, though anharmonicity, depends on structure), thus dominating the temperature dependence of structure and properties.