Microscopic analysis of the compressibility in the spinel phase of Si₃N₄

Quantum-mechanical static simulations of the high-pressure spinel phase of Si 3 N 4 have been performed to determine the unit cell geometry and the equation of state from 0 to 50 GPa. The application of the Bader theory to the ab initio electron density leads to quantum consistent atomic charges and volumes, the crystalline bonding graph, and the prediction of a highly ionic bonding. The computed thermodynamic properties have been interpreted in terms of the local behaviour of the Si and N quantum subgroups and constitutive unit cell polyhedra. We show that: i) the bulk compressibility can be estimated from the average of the tetrahedral and octahedral compressibilities, and ii) the N response to pressure controls the macroscopic behaviour. Our conclusions can be useful in the search of very hard, N-based materials.