Atomistic Design for Thermal Transport From First Principals

This research investigation centered on a theory-based exploration of the thermal properties of complex oxides, in particular the microscopic mechanism of thermal expansion behavior of tetragonal PbTiO3. This ferroelectric perovskite oxide is stable from 0K to 760K, upon which it undergoes a structural phase transition and becomes cubic. In the tetragonal phase, PbTiO3 exhibits negative thermal expansion (NTE) from room temperature to the structural phase transition1,2, meaning that its volume decreases with increasing temperature. The microscopic mechanism driving this behavior is currently unknown, though NTE behavior in materials similar to perovskite oxides (ie, complex oxide systems with polyhedral groups displaying rotational phonon modes) has been explained using the concept of rigid unit modes (RUMs). However, even though perovskite oxides display many “RUM-like” phonon modes, no examples exist to date of RUM-driven NTE in a perovskite system3 .Therefore, the research undertaken here is directed towards answering this question – is NTE in PbTiO3 driven by RUMs, or something else? An understanding of the microscopic mechanism could be used to enhance this behavior in known NTE systems, or to design new ones entirely. Using Density Functional Theory (DFT), I modeled how the structure of this material changed over temperature using the quasiharmonic approximation. Upon reproducing experimental results, I was then able to examine the contributions of the anharmonicity of each phonon mode to the overall NTE behavior, an approach only available through computational means like DFT. I was able to quantify this anharmonicity through the use of the mode Grüneisen tensor defined in literature, as well as a mode Grüneisen parameter of my own design. I was also able to identify a relationship between the diagonal elements of the mode Grüneisen tensor and the coefficient of thermal expansion along each axis, showing that, contrary to current literature4, negative bulk Grüneisen parameters are not required for NTE in non-cubic systems. Though more work must be done to confirm these results, I don’t believe the RUM framework fully explains NTE in PbTiO3. This framework only considers vibrational energy governed by phonons, not static, ground-state energy governed by elasticity. The tendency for the c-axis of tetragonal PbTiO3 to shrink while the a-axis lengthens is a consequence of an elastic coupling term between strain in both axes – in other words, a Poisson’s ratio effect. I plan to submit a paper to a peer-reviewed journal regarding these results by the end of this semester.