We give a review of the theoretical approaches for predicting spectral phonon mean free path and thermal conductivity of solids. The methods can be summarized into two categories: anharmonic lattice dynamics calculation and molecular dynamics simulation. In the anharmonic lattice dynamics calculation, the anharmonic force constants are used first to calculate the phonon scattering rates, and then the Boltzmann transport equations are solved using either standard single mode relaxation time approximation or the Iterative Scheme method for the thermal conductivity. The MD method involves the time domain or frequency domain normal mode analysis. We present the theoretical frameworks of the methods for the prediction of phonon dispersion, spectral phonon relaxation time, and thermal conductivity of pure bulk materials, layer and tube structures, nanowires, defective materials, and superlattices. Several examples of their applications in thermal management and thermoelectric materials are given. The strength and limitations of these methods are compared in several different aspects. For more efficient and accurate predictions, the improvements of those methods are still needed.
Analysis of Transport Properties of the Randomly Moving Electrons in Metals