Investigation of tetragonal ReN2 and WN2 with high shear moduli from first-principles calculations

Two new transition metal dinitrides, ReN₂ and WN₂, with the P4/mmm structure are investigated by the first-principles calculations. The computed shear moduli of 327 GPa for ReN₂ and 334 GPa for WN₂ exceed those of all transition metal dinitrides previously reported. The estimated theoretical hardness are 46.3 GPa for ReN₂ and 47.9 GPa for WN₂, respectively. The calculated high shear moduli and hardness indicate that they are potential ultrahard materials. It is important to note that the computed hardness of the weakest bond are 34.7 GPa (W-N) for WN₂ and 33.1 GPa (Re-N) for ReN₂, much higher than that of 21.1 GPa (Re-B) for ReB₂, which suggests that tetragonal ReN₂ and WN₂ are probably harder than ReB₂. The total and partial electron density of states and the electron localization function for ReN₂ and WN₂ are analyzed. We attribute the high bulk modulus, shear modulus, and hardness to a three-dimensional covalently bonded framework in tetragonal ReN₂ and WN₂. Our calculations show that tetragonal ReN₂ is expected to be synthesized above 62.7 GPa and tetragonal WN₂ may be hard to be synthesized.