This paper investigates anharmonic phonon dispersion relations measured directly from molecular dynamics simulations at finite temperatures and pressure. The measured dynamical matrix and resulting anharmonic dispersion relations do not require an a-priori analytical expression regarding the strength of anharmonic processes. Therefore, no assumptions concerning the degree of anharmonicity are made beyond specifying an interatomic potential. We calculate phonon properties pertinent to thermal transport in graphene. Specifically, we demonstrate the calculation of phonon dispersion relations and group velocities over the entire Brillouin Zone, as well as the branch-dependent contribution to specific heat capacity and ballistic thermal conductance. We highlight the capabilities of this technique to lend fundamental insight into the anharmonic characteristics of phonon-mediated transport. Finally, we discuss how anharmonic phonon dispersion relations may be used to evaluate the differences in phonon properties between various interatomic potentials commonly used in the simulation of phonon-mediated thermal transport.

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