Molecular dynamics simulation of vacancy cluster formation in β- and α-Si₃N₄

Highlights

• MD simulation shows Si₃N₄ polymorphs can accommodate up to ~12% atomic vacancies.

• Due to energy and volume minimization atomic vacancies tend to form large clusters.

• High concentration of vacancies (25%) in α results in α to β transformation at 1900 K.

• Vacancy clustering results in significant fluctuation of lattice constants of β and α.

Abstract

Molecular dynamics simulation is used to study vacancy cluster formation in β- and α-Si₃N₄ with varying vacancy contents (0–25.6 at%). Vacancies are randomly created in supercells, which were subsequently heat-treated for 114 ns. 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-Si₃N₄. 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-Si₃N₄ 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-Si₃N₄.

Introduction

Silicon nitride (Si₃N₄) possesses excellent high-temperature stability, high thermal shock resistance, good creep behavior, and good corrosion and oxidation resistance [1], [2], [3]. It is very well known that lattice defects, particularly Schottky defects, play an important role in determining the overall properties of Si₃N₄ ceramics [4], [5]. The Schottky defects are either caused by the introduction of oxygen as an impurity or thermal annealing that results in the formation of simultaneous Si and N vacancies [6]. In the case of oxygen impurity, vacancies are created to maintain the overall charge neutrality of the lattice [7]. Although α-Si₃N₄¹ initially was assumed to be established by oxygen impurity, but later research showed that nearly pure α-Si₃N₄ can be synthesized [7]. For α-Si₃N₄, previous researches showed the presence of vacancy clusters (as large as 30 nm) or dislocation loops [8]. Such clusters or loops are not yet detected in β-Si₃N₄, seemingly due to the unstrained lattice of β-Si₃N₄ (while α-Si₃N₄ is strained) impeding Schottky defects formation. Moreover, it is assumed that Si and N mobilities are higher in β-Si₃N₄ than in α-Si₃N₄, so vacancies are assumed to get vanished in the later during high-temperature sintering [9]. This reasoning is based on the diffusion data of Kijima and co-workers [10], which are controversial, since, in spite of all similarities of β and α modifications, the activation energies of N diffusion in the former and latter are measured as 778 and 235 kJ/mol, respectively. Wang et al. [11] calculated the amount of Schottky defects in α-Si₃N₄ sintered at 1973 K to be 0.08 at%. This calculation is only based on a large cluster of vacancies (~25 nm in diameter), ignoring the smaller ones. Accordingly, using $D_N=4D_v\left[V_{{\mathit{Si}}_3{N}_4}\right]$, in which $D_N$, $D_v$, and $V_{{\mathit{Si}}_3{N}_4}$ are diffusion coefficient of N, diffusion coefficient of vacancy (estimated as 2 × 10⁻¹⁸ m²/s), and volumetric vacant fraction of Si₃N₄, respectively, Wang et al. [11] calculated the $D_N$ in α-Si₃N₄ as 6 × 10⁻²¹ m²/s. This is stated to be close to that obtained by extrapolation of Kajima’s data at 2000 K (10⁻¹⁹ m²/s) [10], although being two orders of magnitude different. Additionally, the extrapolation of Kajima’s data seems to be considerably (three orders of magnitude) miscalculated, since extrapolation of Kajima’s work yields diffusion coefficient of N as ~10⁻²² m²/s at 2000 K. The recent more accurate measurement by Schmidt [12] demonstrated that $D_N$ and $D_{\mathit{Si}}$ in both modifications are in the same orders of magnitude and $D_N$ in α-Si₃N₄ is ~6 × 10⁻¹⁹ m²/s at ~2000 K. Putting this in the formulae that Wang used, and considering $D_v$ as 2 × 10⁻¹⁸ m²/s, the $\left[V_{{\mathit{Si}}_3{N}_4}\right]$ is estimated as ~8 at%. Considering these discrepancies, in the present study, we have used molecular dynamics simulation (MD) to investigate the tolerance of both modification of silicon nitride to contain varying content of Si and N vacancies (0–25.6 at%) as well as their tendency to form cluster when heat-treated for long time (114 ns).