Elastic parameters of $\mathrm{IV}B$ transition-metal mononitrides, TiN, ZrN, and HfN in the cubic NaCl crystal structure have been calculated by means of density-functional theory with the generalized gradient approximation. The elastic constants $c_{11}$, $c_{12}$, and $c_{44}$ were shown to be sufficiently converged with the density of the $\mathbf{k}$-point mesh in the deformed Brillouin zone to discuss the elastic anisotropy of the systems. It was found that the anisotropy coefficient $\kappa \equiv (c_{11}-c_{12})∕2c_{44}$ increases with the atomic number of the metal element, i.e., HfN exhibits as strong anisotropy as $\kappa =2.02$. The Young’s modulus of HfN along ⟨100⟩ is approximately two times higher than that along ⟨111⟩. Moreover, analysis of the deformation energy by the applied strain modes shows that this elastic anisotropy originates from the strong covalent bonding between metal and nitrogen atoms along ⟨100⟩.

• Received 10 February 2006

DOI:https://doi.org/10.1103/PhysRevB.73.144113