# Thermal conductivity calculation in anisotropic crystals by molecular dynamics : application to alpha-Fe2O3

## TL;DR

This paper develops a molecular dynamics methodology to accurately calculate the thermal conductivity of anisotropic hematite crystals, emphasizing size effects, directional dependence, and temperature behavior in simulations.

## Contribution

It introduces an adapted potential and a comprehensive approach for calculating anisotropic thermal conductivity in hematite using non-equilibrium molecular dynamics.

## Key findings

- Both longitudinal and transverse sizes affect thermal conductivity results.
- Thermal conductivity varies with crystallographic direction, indicating anisotropy.
- Non-linear temperature dependence of thermal conductivity is observed in simulations.

## Abstract

In this work, we aim to study the thermal properties of materials using classical molecular dynamics simulations and specialized numerical methods. We focus primarily on the thermal conductivity \kappa using non-equilibrium molecular dynamics to study the response of a crystalline solid, namely hematite (alpha-Fe2O3), to an imposed heat flux as is the case in real life applications. We present a methodology for the calculation of \kappa as well as an adapted potential for hematite. Taking into account the size of the simulation box, we show that not only the longitudinal size (in the direction of the heat flux) but also the transverse size plays a role in the determination of \kappa and should be converged properly in order to have reliable results. Moreover we propose a comparison of thermal conductivity calculations in two different crystallographic directions to highlight the spatial anisotropy and we investigate the non-linear temperature behavior typically observed in NEMD methods.