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Abstract

The molecular dynamics method was used to simulate energy transport in \ensuremath{\alpha}- and $\ensuremath{\beta}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ 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 ${\mathrm{m}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{K}}^{\mathrm{\ensuremath{-}}1}$) in \ensuremath{\alpha}- and $\ensuremath{\beta}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4},$ 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.