Molecular dynamics calculation of the ideal thermal conductivity of single-crystal α- andβ−Si3N4

The molecular dynamics method was used to simulate energy transport in α- and $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4$ single crystals. The simulation data, in conjunction with the Green-Kubo formulation, was used to calculate the thermal conductivity of the single crystals, as a function of temperature. Although a relatively small simulation supercell size was employed, the thermal conductivity could be estimated with a reasonable degree of accuracy. In addition, simulated elastic constants of the crystals were found to be in reasonable agreement with existing data obtained from the literature. At a temperature of 300 K, it was estimated that the thermal conductivity (in units of W ${\mathrm{m}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$) in α- and $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4,$ along the a and c directions, is approximately 105 and 225, and 170 and 450, respectively. The results were compared to existing experimental data and, in particular, to the well-known Slack’s equation. It was found that the current results are in reasonable agreement with existing results.