Anisotropic elasticity of IVB transition-metal mononitrides determined by ab initio calculations

Elastic parameters of IVB 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 k-point mesh in the deformed Brillouin zone to discuss the elastic anisotropy of the systems. It was found that the anisotropy coefficient kappa equivalent to(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 >.