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.