Size effects in molecular dynamics thermal conductivity predictions

We predict the bulk thermal conductivity of Lennard-Jones argon and Stillinger-Weber silicon using the Green-Kubo (GK) and direct methods in classical molecular dynamics simulations. While system-size-independent thermal conductivities can be obtained with less than 1000 atoms for both materials using the GK method, the linear extrapolation procedure [Schelling et al., Phys. Rev. B 65, 144306 (2002)] must be applied to direct method results for multiple system sizes. We find that applying the linear extrapolation procedure in a manner consistent with previous researchers can lead to an underprediction of the GK thermal conductivity (e.g., by a factor of 2.5 for Stillinger-Weber silicon at a temperature of 500 K). To understand this discrepancy, we perform lattice dynamics calculations to predict phonon properties and from these, length-dependent thermal conductivities. From these results, we find that the linear extrapolation procedure is only accurate when the minimum system size used in the direct method simulations is comparable to the largest mean-free paths of the phonons that dominate the thermal transport. This condition has not typically been satisfied in previous works. To aid in future studies, we present a simple metric for determining if the system sizes used in direct method simulations are sufficiently large so that the linear extrapolation procedure can accurately predict the bulk thermal conductivity.