# Computational prediction of lattice thermal conductivity -- a comparison of molecular dynamics and Boltzmann transport approaches

## TL;DR

This paper compares molecular dynamics and Boltzmann transport approaches for predicting lattice thermal conductivity, highlighting their similarities, differences, and the effects of phonon statistics and scattering mechanisms.

## Contribution

It provides a detailed comparison of MD and BTE methods, including phonon scattering, renormalization, and quantum vs. classical statistics, revealing the origins of their agreement.

## Key findings

- MD and BTE results show apparent agreement due to error cancellations.
- Phonon statistics significantly affect scattering rates and thermal conductivity.
- Equipartition governs phonon statistics in MD simulations.

## Abstract

The predictive modeling of lattice thermal conductivity is of fundamental importance for the understanding and design of materials for a wide range of applications. Two major approaches, namely molecular dynamics (MD) simulations and calculations solving approximately the Boltzmann transport equation (BTE), have been developed to compute the lattice thermal conductivity. We present a detailed direct comparison of these two approaches, using as prototypical cases MgO and PbTe. The comparison, carried out using empirical potentials, takes into account the effects of fourth order phonon scattering, temperature-dependent phonon frequencies (phonon renormalization), and investigates the effects of quantum vs. classical statistics. We clarify that equipartition, as opposed to Maxwell Boltzmann, govern the statistics of phonons in MD simulations. We find that lattice thermal conductivity values from MD and BTE show an apparent, satisfactory agreement; however such an agreement is the result of error cancellations. We also show that the primary effect of statistics on thermal conductivity is via the scattering rate dependence on phonon populations.