Revisiting the theory of alloy thermal conductivity

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Seyf, Hamidreza
Henry, Asegun
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Current understanding of phonons is based on the phonon gas model (PGM). According to the PGM, the vibrational modes in a material are assumed to be plane-waves, hence they can be modeled as a gas of particles that exchange energy through scattering events. During the last 100 years, the PGM has provided great insights into thermal transport in pure homogeneous crystals. However, when one attempts to apply the PGM to understand behavior in non-idealized materials that contain some level of disorder, however, there is growing evidence to suggest that the PGM fails. The problem is that conceptually, when any level of disorder is introduced, whether compositional or structural, the character of vibrational modes in solids changes, yet the PGM continues to assume phonons are still waves. For example, the phonon contributions to alloy thermal conductivity rely on this assumption and are most often computed from the virtual crystal approximation (VCA). In this dissertation, we show that the conventional theory and understanding of phonons requires revision, because the critical assumption that all phonons/normal modes resemble plane waves with well-defined group velocities is no longer valid when disorder is introduced. Here, we first develop a new method for calculation of the degree of periodicity of individual vibrational modes in a generic solid, which is termed the eigenvector periodicity analysis (EPA). The EPA quantifies the extent to which a mode’s character corresponds to a propagating mode, e.g., exhibits plane wave modulation. Using this method, one can quantify what fraction of the modes in a given structure are propagating as a function of the degree of disorder. We apply this method to InxGa1-xAs and show that the character of phonons changes dramatically within the first few percent of impurity concentration, beyond which phonons more closely resemble the modes found in amorphous materials. We then devise two test cases to study and use a correlation-based theory, i.e., Green Kubo modal analysis (GKMA) to systematically examine the validity of the PGM/VCA in random alloys and investigate the fundamental reasons for failure of the PGM/VCA.
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