Phonon heat conduction in layered anisotropic crystals

TL;DR

This paper extends an analytical Boltzmann equation solution to highly anisotropic crystals like graphite, revealing how phonon mean free paths and velocities influence directional thermal conductivity, and introduces a method to reconstruct anisotropic phonon spectra from heat conduction data.

Contribution

It provides a new analytical framework for understanding phonon heat conduction in anisotropic materials and a novel method to reconstruct phonon mean free paths without prior harmonic or anharmonic data.

Findings

Phonon mean free paths can be similar in cross-plane and in-plane directions.

Cross-plane thermal conductivity is mainly due to differences in group velocities and phonon frequencies.

A method to reconstruct anisotropic phonon spectra from quasiballistic heat conduction observations.

Abstract

The thermal properties of anisotropic crystals are of both fundamental and practical interest, but transport phenomena in anisotropic materials such as graphite remain poorly understood because solutions of the Boltzmann equation often assume isotropy. Here, we extend an analytical solution of the Boltzmann equation to highly anisotropic solids and examine its predictions for graphite. We show that the phonon mean free paths in the cross-plane direction can be comparable to those in the in-plane direction despite the low cross-plane thermal conductivity, which instead arises primarily from the differences in group velocities and phonon frequencies supported along each direction. Additionally, we demonstrate a method to reconstruct the anisotropic mean free path spectrum of crystals with arbitrary dispersion relations without any prior knowledge of their harmonic or anharmonic properties using observations of quasiballistic heat conduction.