**Thermal Conductivity Calculation with the Molecular Dynamics Direct
Method I: More Robust Simulations of Solid Materials**

PC Howell, JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, 8, 2129-2143 (2011).

DOI: 10.1166/jctn.2011.1935

A widespread technique to calculate thermal conductivity kappa is the non-equilibrium direct method based on classical molecular dynamics, but despite its popularity there are still open questions regarding the data analysis. Here we use extensive simulations of bulk crystalline silicon with the Stillinger-Weber and Tersoff potentials as a test case to thoroughly examine the sensitivity to simulation parameters and fitting procedures in the solid state. We demonstrate that the transient behavior is well described by the solution to the continuum heat diffusion equation, so that no initial data has to be discarded. We show how best to fit temperature profiles while minimizing artifacts due to the non-linear regions which are usually present. The bulk thermal conductivity, kappa(infinity), can be obtained by extrapolating to infinitely large systems, and we demonstrate that both periodic and non- periodic boundary conditions give the same value for kappa(infinity). when analyzed correctly using high-quality data. However, in some circumstances simulations with non-periodic boundary conditions do not appear to reach steady-state even after 20 ns. For bulk Si modeled with the Stillinger-Weber potential we obtain kappa = 200 +/- 4 W/m-K at 500 K.

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