The ability to engineer materials on the nanoscale has given rise to the possibility of tailoring material properties such as the thermal conductivity. The alteration of the thermal properties is due to the interaction between the phonons and the geometry of these nano-structures. Phonons (i.e., lattice vibrations) are the primary energy carriers in insulating crystals, such as argon, silicon, and germanium. A fundamental understanding of the physics of phonon transport in such nano-structured materials and a means of computing their thermal conductivity are required to efficiently design these materials. Current techniques used to examine the lattice thermal conductivity of crystals use major approximations or are computationally intensive.;In this work, the anharmonic lattice dynamics method is presented and the challenges associated with implementing the method are addressed. The methodology is used to predict the thermal conductivity of crystalline argon in bulk. These predictions are validated with results from molecular dynamics simulations. The phonon properties predicted by the lattice dynamics method are used to show that some common assumptions and approximations about phonon transport are not true for all materials.;The lattice dynamics calculations are then used to study thermal transport in nano-structures. The boundaries and interfaces in thin films and superlattices present a modeling challenge. For thin films, a mode-dependent boundary scattering relation is derived and used to predict the in-plane thermal conductivity of argon and silicon thin films. For short period, ideal superlattices it is shown that the interfaces do not act as scattering sites but do affect the phonon population. The unique phonon properties in graphene and carbon nanotubes are predicted with lattice dynamics and compared to molecular dynamics predictions.;Finally, the unique abilities of the lattice dynamics techniques are used to assess the validity of quantum correcting classically-predicted thermal conductivities, such as those determined by molecular dynamics simulation. A direct assessment of the commonly used quantum corrects is made by self-consistently predicting the thermal conductivity for a quantum system and for the same system in the classical limit. These quantum corrections are shown to be inaccurate and the phonon properties are used to show that only methods that include the proper quantum phonon distribution in the prediction of the relaxation times can be used to predict a quantum thermal conductivity.;One technique that can be used to perform an accurate analysis of lattice thermal conductivity is the anharmonic lattice dynamics method. Anharmonic lattice dynamics is the natural extension of harmonic lattice dynamics, which can be used to calculate phonon frequencies. Anharmonic lattice dynamics provides detailed information about the phonon modes, such as frequencies, group velocities, and scattering rates, that is not typically found through other methods. Thus, it is an ideal method to use when predicting the thermal conductivity as the properties of the phonon modes provide additional insight into the physics of thermal transport.
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