The length dependence of the thermal conductivity over more than two decades is systematically studied for a range of materials, interatomic potentials and temperatures, by the atomistic approach-to-equilibrium molecular dynamics method (AEMD). By comparing the values of conductivity obtained for a given supercell length and maximum phonon mean-free-path (MFP), we find that such values are strongly correlated, demonstrating that the AEMD calculation with a supercell of finite length, actually probes the thermal conductivity corresponding to a maximum phonon MFP. As a consequence, the less pronounced length dependence usually observed for poorer thermal conductors, such as amorphous silica, is physically justified by their shorter average phonon MFP. Finally, we compare different analytical extrapolations of the conductivity to infinite length, and demonstrate that the frequently used Matthiessen rule is not applicable in AEMD. An alternative extrapolation more suitable for transient-time, finite-supercell simulations is derived. This approximation scheme can also be used to classify the quality of different interatomic potential models with respect to their capability of predicting the experimental thermal conductivity. * evelyne.lampin@univ-lille1.fr
A transient thermal regime is achieved in glassy GeTe by first-principles molecular dynamics following the recently proposed "approach-to-equilibrium" methodology. The temporal and spatial evolution of the temperature do comply with the time-dependent solution of the heat equation. We demonstrate that the time scales required to create the hot and the cold parts of the system and observe the resulting approach to equilibrium are accessible to first-principles molecular dynamics. Such a strategy provides the thermal conductivity from the characteristic decay time. We rationalize in detail the impact on the thermal conductivity of the initial temperature difference, the equilibration duration, and the main simulation features.
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