Molecular Dynamics Simulation of Vacancy Cluster Formation in β- and α-$Si_3N_4$
Molecular dynamics simulation is used to study vacancy cluster formation in $β$- and $α$-$Si_3N_4$ 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 $β$ and $α$ can tolerate vacancies up to 12.8 at% and form clusters, confirming previous experimental data indicating 8 at% vacancy in $α$-$Si_3N_4$. However, 25.6 at% vacancy in $β$ results in complete amorphization, while the same amount in $α$ results in a transformation of a semi-amorphous $α$ phase to a defective $β$ phase, leading to the removal of the clusters in newly formed $β$. This clearly explains why cluster vacancies are not experimentally observed in $β$, considering that $β$-$Si_3N_4$ ceramics are produced from $α$. Furthermore, the lattice parameters of both modifications increase with increasing vacancy content, revealing the cause of different lattice constants that were previously reported for $α$-$Si_3N_4$.