Thermal conductivity calculation in anisotropic crystals by molecular dynamics: Application to α-Fe₂O₃

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 κ using non-equilibrium molecular dynamics (NEMD) to study the response of a crystalline solid, namely hematite (α-Fe₂O₃), to an imposed heat flux as is the case in real life applications. We present a methodology for the calculation of κ 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 κ 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.