Thermal and elastic properties of perovskite oxides from first principles

182 pagesThe ABO3 perovskite oxide system is known to exhibit many technologically relevant materials properties, including ferroelectricity, ferromagnetism and antiferromagnitism, ferroelasticity, colossal magnetoresistance, and ultra-low thermal conductivity. Additionally, the wide choice of candidates for A and B, and extensive development of successful strain-engineering methods through epitaxial growth, provides a large design space through which these properties can be enhanced, suppressed, or controlled. In this dissertation, I explore the thermal and elastic properties of perovskite oxides, primarily ferroelectric PbTiO3, using theory and first-principles computation. In Chapter 1, I outline many the basic theoretical definitions techniques used throughout the text, covering thermal expansion, the theory of phonons, and density functional theory. In Chapter 2, I use first-principles theory to show that the ingredients assumed to be essential to the occurrence of negative thermal expansion (NTE) – rigid unit phonon modes with negative Grüneisen parameters– are neither sufficient nor necessary for a material to undergo volumetric NTE. Instead, I find that NTE in PbTiO3 involves a delicate interplay between the phonon properties of a material (Grüneisen parameters) and its anisotropic elasticity. These unique insights open new avenues in our fundamental understanding of the thermal properties of materials, and in the search for NTE in new materials classes. In Chapter 3, I explore thermal expansion behavior further. While it has certainly been recognized that mismatch in the thermal expansion coefficients of the bulk and substrate material will contribute to the misfit strain, the significance of this contribution for ferroelectric perovskite thin-films has not been systematically explored. I use first-principles density functional theory and the example of ferroelectric PbTiO3 thin-films on various substrates to show that ignoring the thermal expansion of the substrate (that is, assuming that the in-plane lattice parameter of the film remains roughly constant as a function of temperature) results in ferroelectric transition temperatures and structural trends that are completely qualitatively different from calculations in which thermal expansion mismatch is properly taken into account. This work suggests that the concept of a misfit strain defined as a single number is particularly ill-defined for PbTiO3 and invites further study of the interplay between thermal expansion mismatch and structural and functional properties in other thin-filmmaterials. In Chapter 4, I build off this work by using the Grüneisen theory of thermal expansion in combination with density functional calculations and the quasiharmonic approximation to uncover mechanisms of thermal expansion in PbTiO3 thin-films in terms of elastic and vibrational contributions to the free energy. Surprisingly, I find that although the structural parameters of PbTiO3 thin-films evolve with temperature as if they are dominated by linear elasticity, PbTiO3 thin-films are strongly anharmonic, with large changes in the elastic constants and Grüneisen parameters with both misfit strain and temperature. I show that a fortuitous near-cancellation between different types of anharmonicity gives rise to the behavior. My results illustrate the importance of high-order phonon-strain anharmonicity in determining the temperature-dependent structural parameters of PbTiO3 thin-films, and highlight the complex manner in which thermal expansion, misfit strain and elastic and vibrational properties are intertwined. In Chapter 5, I attempt to explore the chemical origins of the materials properties that play a role in the previous chapters. While DFT can be used to calculate what values these properties take in a given material, it does not tell us the origins of those properties in terms of chemistry and bonding, the language we use to both explain the driving physics behind existing materials properties, as well as to synthesize new materials with desired properties. Even for “routine” calculations of, for example, elastic properties or vibrational phonon frequencies, translating the quantitative results of a simulation into physical insights or design rules for enhancing or adjusting those properties remains challenging. Here, I discuss a new computational technique I have developed to rigorously relate the elastic, vibrational, and phase behavior of materials to specific chemical bonds in the crystal. The goal of this project is to gain chemical intuition with respect to controlling macroscale material properties. For example, if each bond in a crystal could be rigorously and sensibly assigned a portion of the total bulk modulus, such that the total stiffness of the system could be expressed as a sum over bonds, then we can understand how each bond is contributing to the macroscale behavior under hydrostatic stress, as well as develop an under- standing as to why that compressibility would evolve given changes in structure, pressure, or through chemical substitution. I have implemented a proof- of-concept of this method in software, building off of the open-source Quantum Espresso and Wannier90 projects. Finally, in Chapter 6, I discuss current directions and future work based to further explore and build off of the the concepts I have established in this dissertation