Fullab initiogeometry optimization of all known crystalline phases ofSi3N4

The crystal structures of the four experimentally observed phases of ${\mathrm{Si}}_3{\mathrm{N}}_4$ with space groups ${P6\mathrm{}}_3/m,$ ${P6\mathrm{}}_3,$ ${P3\mathrm{}}_1/c,$ and ${\mathrm{Fd}}_3/m$ are fully optimized by means of first-principles total-energy calculations. The relaxation of all internal parameters is achieved by using a simple finite difference method. For $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4,$ the structure ${P6\mathrm{}}_3$ without the mirror symmetry has a lower energy than the ${P6\mathrm{}}_3/m$ with mirror symmetry by 0.238 eV per formula unit. The calculated ground-state properties are found to be in good agreement with experimental values.