A General Framework for Understanding Negative Thermal Expansion in Complex Oxides from First Principles

Many of the functional properties of ABO₃ perovskite oxides (for example, ferroelectricity) are strongly linked to particular phonon modes in the material. In addition, in many cases it is possible to formulate simple guidelines or ‘rules of thumb’ that link crystal structure and chemistry to specific lattice dynamical characteristics. The thermal transport properties of perovskites are thus potentially highly tunable and dynamically controllable with external fields. We use first-principles density functional theory to formulate a general framework for understanding negative thermal expansion (NTE) in complex oxides, which we demonstrate for the test case of PbTiO₃. Although the origin of NTE is often ascribed to negative Grüneisen parameters or rigid unit modes (RUMS), our results suggest that neither are necessary conditions for NTE. We find that hybridization between different electronic states has a significant effect on both the elastic properties and lattice dynamics of PbTiO₃ in general, and its NTE behavior in particular. Our work has implications for the understanding of, discovery and design of NTE in perovskites and other families of inorganic materials.