Using Molecular Dynamics to Calculate the Lattice Thermal Conductivity of Lower Mantle Minerals with Impurities

Thermal conductivity is a key parameter for Earth models involving heat flow across the core-mantle boundary. It is not currently possible to measure the thermal conductivity of minerals at lower mantle temperatures, meaning that lower temperature experimental values must be extrapolated, introducing considerable uncertainty. Furthermore, the effect of impurities, such as Fe and Al, is poorly constrained. In view of this, we use two complementary theoretical methods to determine the lattice thermal conductivity of (Fe,Mg)SiO3 bridgmanite, with varying concentration and distribution of Fe impurities. First, we utilise the direct method (non-equilibrium molecular dynamics), which allows thermal conductivity to be calculated, via Fourier's law, from the ratio of an imposed heat-flux and induced thermal gradient. Second, equilibrium molecular dynamics is employed to measure the time-dependence of instantaneous heat-flux variations, which are related to thermal conductivity via the Green-Kubo equation. We find that both methods have finite-size effects, which must be resolved before considering the important issue of impurity content. These effects are assessed using interatomic potentials, in order to reach the requisite large simulation sizes (up to approximately 60,000 atoms) on a reasonable timescale. Our work provides a systematic study of the effects to consider when calculating the thermal conductivity of minerals at lower mantle conditions.