We predict the bulk thermal conductivity of Lennard-Jones argon and Stillinger-Weber silicon using the Green-Kubo ͑GK͒ and direct methods in classical molecular dynamics simulations. While system-sizeindependent 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 ͑2002͔͒ 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 K͒. 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.

Two methods for predicting phonon frequencies and relaxation times are presented. The first is based on quasiharmonic and anharmonic lattice dynamics calculations, and the second is based on a combination of quasiharmonic lattice dynamics calculations and molecular dynamics simulations. These phonon properties are then used with the Boltzmann transport equation under the relaxation-time approximation to predict the lattice thermal conductivity. The validity of the low-temperature assumptions made in the lattice dynamics framework are assessed by comparing to thermal conductivities predicted by the Green-Kubo and direct molecular dynamics methods for a test system of Lennard-Jones argon. The predictions of all four methods are in agreement at low temperature ͑20 K͒. At temperatures of 40 K ͑half the Debye temperature of Lennard-Jones argon͒ and below, the thermal-conductivity predictions from the two methods that use lattice dynamics calculations are within about 30% of those made using the more accurate Green-Kubo and direct molecular dynamics methods. The thermal-conductivity predictions using the lattice dynamics techniques become inaccurate at high temperature ͑above 40 K͒ due to the approximations inherent in the lattice dynamics framework. We apply the results to assess the validity of ͑i͒ the isotropic approximation in modeling thermal transport and ͑ii͒ the common assertion that low-frequency phonons dominate thermal transport. Lastly, we suggest approximations that can be made within the lattice dynamics framework that allow the thermal conductivity of Lennard-Jones argon to be estimated using two orders of magnitude less computing effort than the Green-Kubo or direct molecular dynamics methods.

We derive and validate a technique for predicting phonon dispersion relations and lifetimes from the atomic velocities in a crystal using the spectral energy density. This procedure, applied here to carbon nanotubes, incorporates the full anharmonicity of the atomic interactions into the lifetime and frequency predictions. It can also account for nonperiodic interactions between phonons and nonbonded molecules near the solid surface. We validate the technique using phonon properties obtained from anharmonic lattice dynamics calculations and thermal conductivities obtained from nonequilibrium molecular-dynamics simulation. DOI: 10.1103/PhysRevB.81.081411 PACS number͑s͒: 63.20.Ϫe, 63.22.Ϫm, 66.70.Ϫf Predicting and describing the behavior of semiconductors and dielectric materials requires knowledge of their phonon dispersion relations and lifetimes. At low temperatures, the phonon properties of a bulk crystal can be evaluated using harmonic and third-order anharmonic lattice dynamics calculations.1,2 In carbon nanotubes ͑CNTs͒, silicon nanowires, and other nanoscale materials in realistic environments, however, the phonons will scatter via interactions with nonbonded molecules at surfaces.3,4 Since these interactions are nonperiodic in time and space, their effects on the phonon properties cannot be directly incorporated into a lattice dynamics calculation. Challenges in predicting the phonon properties also arise with increasing temperature, as the magnitude of the atomic displacements grows and the influence of higher-order phonon scattering events becomes increasingly important.5 Since third-order anharmonic lattice dynamics calculations only account for three-phonon scattering events, the phonon lifetimes they predict at elevated temperatures are overestimated. 1 Herein, we derive and validate a straightforward technique for predicting phonon dispersion relations and lifetimes directly from the velocities of the atoms in a crystal using the phonon spectral energy density. This technique, which extends formulations developed by others, 6-9 naturally includes the full temperature-dependent anharmonicity of the atomic interactions and can be applied to both bulk crystals and crystals interacting with nonbonded molecules. We apply this technique to classical molecular-dynamics ͑MD͒ simulations of empty and water-filled ͑8,8͒ CNTs and use the predicted phonon properties to calculate the mode-by-mode contributions to the total thermal conductivity. Next, we compare the fully anharmonic phonon properties to those obtained from third-order anharmonic lattice dynamics calculations. Our findings indicate that, even at room temperature, neglecting higher-order scattering events in a CNT leads to an overestimation of the acoustic phonon lifetimes and the CNT length required to obtain fully diffusive phonon transport. We then use the spectral energy density to identify how interactions with confined water molecules shift the phonon frequencies, lower the phonon lifetimes, and reduce the CNT thermal conductivity.The emp...

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The in-plane phonon thermal conductivities of argon and silicon thin films are predicted from the Boltzmann transport equation under the relaxation time approximation. We model the thin films using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. The input required for the lattice dynamics calculations is obtained from interatomic potentials: Lennard-Jones for argon and Stillinger-Weber for silicon. The effect of the boundaries is included by considering only phonons with wavelengths that fit within the film and adjusting the relaxation times to account for mode-dependent, diffuse boundary scattering. Our model does not rely on the isotropic approximation or any fitting parameters. For argon films thicker than 4.3 nm and silicon films thicker than 17.4 nm, the use of bulk phonon properties is found to be appropriate and the predicted reduction in the in-plane thermal conductivity is in good agreement with results obtained from molecular dynamics simulation and experiment. We include the effects of boundary scattering without employing the Matthiessen rule. We find that the Matthiessen rule yields thermal conductivity predictions that are at most 12% lower than our more accurate results. Our results show that the average of the bulk phonon mean free path is an inadequate metric to use when modeling the thermal conductivity reduction in thin films.