Molecular dynamics simulation is used to study vacancy cluster formation in $beta$- and $alpha$-$Si_3N_4$ 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 $alpha$-$Si_3N_4$. 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 $beta$-$Si_3N_4$ 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 $alpha$-$Si_3N_4$.
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