Predicting phonon dispersion relations and lifetimes from the spectral energy density

Abstract

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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