First-principles study of high-pressure phase transitions in Si$_{3}$N$_{4}$*

We have performed a systematic theoretical study of phase transitions in Si$_{3}$N$_{4}$ at high-pressure. We calculated the Gibbs free energies of the ground state $\beta $ phase and the high-pressure $\gamma $ phase at various temperatures and pressures based on the first- principles density functional theory and the statistical quasi-harmonic theory. The thermal equations of state and the Clapeyron slope of the $\beta $-to- $\gamma $ transition at high-pressure are determined and compared with available experimental data. In addition to the recently discovered high- pressure $\gamma $-phase, we predict a new high-pressure phase of hexagonal symmetry. This new high-pressure phase is likely to exist metastably at the high pressure \textit{and room temperature}, and it is associated with a non \AA-point soft phonon distortion. The structural and elastic properties and the stability condition of this predicted metastable high-pressure phase will be discussed.