Lattice dynamical studies of select MAX phases

Atomic vibrations weave into the fabric of the materials properties landscape in a diverse multitude of ways. They play a major role in specific heat and thermodynamic properties, they affect electronic transport as electron scatterers, they are central to thermal expansion and high-temperature thermal stability, and they alter the intensity of scattered data in probing the crystal structure of a material. While there are cases where the static lattice model gives a reasonable description of materials in the solid state, there are other situations where the assumption of immobile atoms locked into fixed sites fails dramatically. For this work, the role of atomic motion is investigated for a group of materials known as M_[n+1]AX_n ("MAX") phases. They are made up of M (a metal), A (an A-group element), and X (carbon or nitrogen) and exhibit a unique set of properties, combining some of the most desirable attributes of ceramics and metals. Because of their high thermal conductivity and high-temperature stability, their most promising applications are at elevated temperatures, including nuclear reactor cladding and heating elements. Atomic motion is central to understanding and predicting materials properties at high temperatures, especially high-temperature damping and thermal conductivity. The aim of this work is to investigate the lattice dynamics of select MAX phases through first-principles phonon calculations in order to provide a foundation for modeling their high-temperature properties. The phonon dispersions and density of states are computed. Based on the phonon properties, the theoretical temperature-dependent atomic displacement parameters and Raman-active modes are determined and compared to those determined experimentally from Raman spectroscopy and high-temperature neutron diffraction. The bond length behavior in one of the MAX phases, Ti₃GeC₂, suggests correlation between the thermal motion of the Ti and Ge atoms. A model is proposed for the effect of correlated motion on temperature-dependent bond lengths, which serves to explain the unusual bond expansion observed through Rietveld analysis of neutron time-of-flight data. Anharmonic effects are explore through first principles calculations of the mode-dependent Gruneisen parameters, which suggest localization and anharmonicity of the low-frequency phonon modes. Out of the 20 MAX phases studied in this thesis, the Al-containing phases show the best agreement between theory and experiment for their lattice dynamical properties. The Al-containing phases are also some of the most promising MAX phases for industrialization because of their high oxidation resistance and the low cost of their starting materials. This therefore suggests that the MAX phases that are most desirable commercially may also be the most reasonable to model at high temperatures. This work provides a basis for understanding important phenomena associated with phonons, interatomic bonding, and thermal vibrations in periodic systems, which is not only relevant to the fundamental properties of MAX phases but can be extended to other crystals in the solid state.