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 ${\mathrm{H}\mathrm{f}}_3{\mathrm{N}}_4$ as well as of isomorphic ${\mathrm{Z}\mathrm{r}}_3{\mathrm{N}}_4$ and ${\mathrm{T}\mathrm{i}}_3{\mathrm{N}}_4$ are studied using first-principles calculations. ${\mathrm{H}\mathrm{f}}_3{\mathrm{N}}_4$, ${\mathrm{Z}\mathrm{r}}_3{\mathrm{N}}_4$, and ${\mathrm{T}\mathrm{i}}_3{\mathrm{N}}_4$ 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 ${\mathrm{H}\mathrm{f}}_3{\mathrm{N}}_4$ will be harder than the mononitride HfN. At ambient conditions, the cubic modifications of $M_3{\mathrm{N}}_4$ ($M=\mathrm{H}\mathrm{f}$, Zr, Ti) are metastable with respect to orthorhombic $M_3{\mathrm{N}}_4$ phases, but the orthorhombic phases of ${\mathrm{H}\mathrm{f}}_3{\mathrm{N}}_4$ and ${\mathrm{Z}\mathrm{r}}_3{\mathrm{N}}_4$ are stable with respect to the mononitrides and nitrogen.