Equilibrium and metastable phase transitions in silicon nitride at high pressure: A first-principles and experimental study

We have combined first-principles calculations and high-pressure experiments to study pressure-induced phase transitions in silicon nitride (Si${}_{3}$N${}_{4}$). Within the quasi-harmonic approximation, we predict that the $\ensuremath{\alpha}$ phase is always metastable relative to the $\ensuremath{\beta}$ phase over a wide pressure-temperature range. Our lattice vibration calculations indicate that there are two significant and competing phonon-softening mechanisms in the $\ensuremath{\beta}$-Si${}_{3}$N${}_{4}$, while phonon softening in the $\ensuremath{\alpha}$-Si${}_{3}$N${}_{4}$ is rather moderate. When the previously observed equilibrium high-pressure and high-temperature $\ensuremath{\beta}$ $\ensuremath{\rightarrow}$ $\ensuremath{\gamma}$ transition is bypassed at room temperature (RT) due to kinetic reasons, the $\ensuremath{\beta}$ phase is predicted to undergo a first-order structural transformation to a denser $P\overline{6}$ phase above 39 GPa. The estimated enthalpy barrier height is less than 70 meV$/$atom, which suggests that the transition is kinetically possible around RT. This predicted new high-pressure metastable phase should be classified as a ``postphenacite'' phase. Our high-pressure x-ray diffraction experiment confirms this predicted RT phase transition around 34 GPa. No similar RT phase transition is predicted for $\ensuremath{\alpha}$-Si${}_{3}$N${}_{4}$. Furthermore, we discuss the differences in the pressure dependencies of phonon modes among the $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ phases and the consequences on their thermal properties. We attribute the phonon modes with negative Gr\"uneisen ratios in the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases as the cause of the predicted negative thermal expansion coefficients (TECs) at low temperatures in these two phases, and predict no negative TECs in the $\ensuremath{\gamma}$ phase.