Molecular Dynamics Simulation of Vacancy Cluster Formation in \beta- and \alpha-$S{i}_3{N}_4$

Molecular dynamics simulation is used to study vacancy cluster formation in $\beta$- and $\alpha$-$S{i}_3{N}_4$ with varying vacancy contents (0 - 25.6 at%). Vacancies are randomly created in supercells, which were subsequently heat-treated for 114 nanoseconds. The results show that both $\beta$ and $\alpha$ can tolerate vacancies up to 12.8 at% and form clusters, confirming previous experimental data indicating 8 at% vacancy in $\alpha$-$S{i}_3{N}_4$. However, 25.6 at% vacancy in $\beta$ results in complete amorphization, while the same amount in $\alpha$ results in a transformation of a semi-amorphous $\alpha$ phase to a defective $\beta$ phase, leading to the removal of the clusters in newly formed $\beta$. This clearly explains why cluster vacancies are not experimentally observed in $\beta$, considering that $\beta$-$S{i}_3{N}_4$ ceramics are produced from $\alpha$. Furthermore, the lattice parameters of both modifications increase with increasing vacancy content, revealing the cause of different lattice constants that were previously reported for $\alpha$-$S{i}_3{N}_4$.