Prediction of spinel structure and properties of single and double nitrides

Lattice constants, bulk moduli, band gaps, electronic bonding, and the stability of 20 new nitrides with spinel structure are studied by first-principles calculations. Double nitrides ${\mathrm{AB}}_{2}{\mathrm{N}}_{4}$ are found to be stable when the counterparts ${\mathrm{BA}}_{2}{\mathrm{N}}_{4}$ are metastable except for ${\mathrm{TiZr}}_{2}{\mathrm{N}}_{4}.$ The four single nitrides ${\mathrm{C}}_{3}{\mathrm{N}}_{4},$ ${\mathrm{Si}}_{3}{\mathrm{N}}_{4},$ ${\mathrm{Ge}}_{3}{\mathrm{N}}_{4},$ and ${\mathrm{Sn}}_{3}{\mathrm{N}}_{4}$ have direct band gaps at the \ensuremath{\Gamma} point ranging from 1.14 to 3.45 eV while ${\mathrm{Zr}}_{3}{\mathrm{N}}_{4}$ and ${\mathrm{Ti}}_{3}{\mathrm{N}}_{4}$ have small indirect gaps. For double nitrides, both metallic and insulating band structures are possible. The total bond orders of the stable double nitrides are larger than those of constituent single nitrides. Among them, ${\mathrm{CSi}}_{2}{\mathrm{N}}_{4}$ shows exceptionally strong covalent bonding and a large bulk modulus. A simple scaling law based on bond lengths can describe the bulk moduli of these spinel nitrides quite well.