Thermal conductivity of crystals: A molecular-dynamics study of heat flow in a two-dimensional crystal

Abstract

We have studied steady-state heat flow in a two-dimensional crystal by the method of molecular dynamics. The model system contains 1000 particles on a triangular lattice interacting via the Lennard-Jones potential. The system is 50 unit cells long and 10 unit cells wide. We find that the thermal conductivity $\kappa$ of this system is consistent with $\frac{1}{T}$ behavior as expected when phonon-phonon scattering is the dominant mechanism for thermal resistance. We have also carried out similar calculations for three-dimensional Lennard-Jones systems in both fluid and crystalline configurations. The results for the fluid were in good agreement with earlier calculations but for the fcc solid system, 16 unit cells in length, $\kappa$ was independent of temperature. We determined that boundary scattering was the dominant resistive mechanism in this case. To escape the boundary-limited regime, the length of the three-dimensional crystal needs to be increased by at least a factor of 3. It is feasible to simulate a system of this size with the use of modern computers.