Theory and Simulation of Transient Phonon Heat Conduction in Crystals

Abstract

First-principles calculations based on phonon Boltzmann transport theory have demonstrated that the phonon gas model is generally applicable for crystalline solids. However, this model is known to break down in some specific cases, such as in solids near their melting temperature or in highly conductive solids at low temperatures.

The first part of this dissertation focuses on assessing the validity of the phonon gas model at very high temperatures, particularly near the melting point. To achieve this, we implemented a computational algorithm to interpret experimental neutron or x-ray single-phonon scattering spectra using molecular dynamics-simulated single-phonon Green’s functions as input. In the case of silicon crystals, we find that the single-phonon approximation remains valid up to the melting temperature of 1600 K. However, perturbative calculations based on lower-order anharmonicity significantly underestimate the renormalized phonon frequency and phonon lifetime, underscoring the importance of non-perturbative models for renormalized phonon spectra at very high temperatures.

In the second part of this dissertation, we examine non-Fourier heat conduction phenomena under hydrodynamic conditions using a new theoretical framework for transient heat conduction. Through statistical analysis of a unified formula for transient heat flux in phonon gases, we propose a time-dependent Zwanzig theory for transient heat conduction, applicable in both the phonon second sound limit and the Fourier diffusion limit. A key finding of this work is the necessity of incorporating phonon heat dissipation dynamics into heat conduction theory via heat current Green’s functions. Our theory unveils the coexistence of both wave and diffusion dynamics across different temperatures and material types, with their interplay depending on time and length scales. We have calculated the phonon heat current Green's functions for silicon over the temperature range of 30 K to 300 K and compared our model with experimental data from transient thermal techniques, such as transient thermal grating experiments.