SUMMARY

Current understanding of phonons is based on the phonon gas model (PGM). According to the PGM, the vibrational modes in the crystal are assumed to be plane-waves, hence they can be treated as a gas of particles which exchange energy through scattering events. During the last decades, 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, 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, I 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the critical assumption that all phonons/normal modes resemble plane waves with well-defined group velocities is no longer valid when disorder is introduced.