Hafnium nitride with thorium phosphide structure: Physical properties and an assessment of the Hf-N, Zr-N, and Ti-N phase diagrams at high pressures and temperatures

The physical properties of the new cubic phase of Hf3N4 as well as of isomorphic Zr3N4 and Ti3N4 are studied using first-principles calculations. Hf3N4, Zr3N4, and Ti3N4 are semiconductors with band gaps of 1.8, 1.1, and 0.6 eV, respectively. The band structure is characterized by the simultaneous presence of steep and extremely flat bands. The calculated shear modulus G indicates that the cubic Hf3N4 will be harder than the mononitride HfN. At ambient conditions, the cubic modifications of M3N4 (M = Hf, Zr, Ti) are metastable with respect to orthorhombic M3N4 phases, but the orthorhombic phases of Hf3N4 and Zr3N4 are stable with respect to the mononitrides and nitrogen.