First-principles study of the high-temperature behaviors of the willemite-II and post-phenacite phases of silicon nitride

The structural and elastic properties of the recently-discovered wII- and δ-Si3N4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials. The elastic constants show that wII- and δ-Si3N4 are mechanically stable in the pressure ranges of 0-50 GPa and 40-50 GPa, respectively. The α→wII phase transition can be observed at 18.6 GPa and 300 K. The β→δ phase transformation occurs at pressures of 29.6, 32.1, 35.9, 39.6, 41.8, and 44.1 GPa when the temperatures are 100, 200, 300, 400, 500, and 600 K, respectively. The results show that the interactions among the N-2s, Si-3s, 3p bands (lower valence band) and the Si-3p, N-2p bands (upper valence band) play an important role in the stabilities of the wII and δ phases. Moreover, several thermodynamic parameters (thermal expansion, free energy, bulk modulus and heat capacity) of δ-Si3N4 are also obtained. Some interesting features are found in these properties. δ-Si3N4 is predicted to be a negative thermal expansion material. The adiabatic bulk modulus decreases with applied pressure, but a majority of materials show the opposite trend. Further experimental investigations with higher precisions may be required to determine the fundamental properties of wII- and δ-Si3N4.