Structural properties and electronic structure of low-compressibility materials: β-${\mathrm{Si}}_3$${\mathrm{N}}_4$ and hypothetical β-${\mathrm{C}}_3$${\mathrm{N}}_4$

We present a first-principles pseudopotential study of the structural and electronic properties of β-${\mathrm{Si}}_3$ ${\mathrm{N}}_4$ and the hypothetical compound β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$. β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$, which is ${\mathrm{C}}_3$ ${\mathrm{N}}_4$ in the β-${\mathrm{Si}}_3$ ${\mathrm{N}}_4$ structure, with C substituted for Si, is used as a prototype for investigating the properties of possible covalent C-N solids. The calculated lattice constant, bulk modulus, and electronic band structure of β-${\mathrm{Si}}_3$ ${\mathrm{N}}_4$ are in good agreement with experimental results. This gives support for the predicted properties of β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$. The bulk modulus of β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$ is found to be comparable to diamond, and its moderately large cohesive energy suggests that the prototype structure may be metastable. Although the crystal structure and the valencies of the constituent atoms are similar in β-${\mathrm{Si}}_3$ ${\mathrm{N}}_4$ and β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$, the electronic bonding properties in these two solids are found to differ. The large core size and repulsive p pseudopotential of the second-row element, Si, results in a more ionic Si-N bond compared with a covalent C-N bond.