Atomic structures and bondings of β- and spinel-${\mathrm{Si}}_{6-z}{\mathrm{Al}}_z{\mathrm{O}}_z{\mathrm{N}}_{8-z}$ by first-principles calculations

First-principles calculations of β- and spinel-sialons $\left({\mathrm{Si}}_{6-z}{\mathrm{Al}}_z{\mathrm{O}}_z{\mathrm{N}}_{8-z}\right)$ have been systematically made by a plane-wave pseudopotentials method, in order to find out atomic arrangements, bondings, and electronic structures of optimized structures. Al-O and Si-N bonds are found to be clearly preferred as compared with Si-O and Al-N bonds in two kinds of crystals. In the optimized structures, the band gap can be roughly approximated as the weighed average of those for end members, i.e., ${\mathrm{Si}}_3{\mathrm{N}}_4$ and ${\mathrm{Al}}_3{\mathrm{O}}_3\mathrm{N}.$ Few impuritylike states are formed near the band edges. Averaged bond-lengths of Al-X and Si-X (X=N and O) are almost constant and independent of z for a given site of each crystal. All of these results are consistent to experimental information thus far been available by nuclear magnetic resonance and extended x-ray absorption fine structures. Calculations of formation energies of β-sialons using supercells composed of 56 atoms suggest ordering of solute atoms to form a unique local structure is not likely to take place.