Vacancy-induced mechanical stabilization of cubic tungsten nitride

First-principles methods are employed to determine the structural, mechanical, and thermodynamic reasons for the experimentally reported cubic WN phase. The defect-free rocksalt phase is both mechanically and thermodynamically unstable, with a negative single crystal shear modulus C-44 = -86 GPa and a positive enthalpy of formation per formula unit H-f = 0.623 eV with respect to molecular nitrogen and metallic W. In contrast, WN in the NbO phase is stable, with C-44 = 175 GPa and H-f = -0.839 eV. A charge distribution analysis reveals that the application of shear strain along [ 100] in rocksalt WN results in an increased overlap of the t(2g) orbitals which causes electron migration from the expanded to the shortened W-W < 110 > bond axes, yielding a negative shear modulus due to an energy reduction associated with new bonding states 8.1-8.7 eV below the Fermi level. A corresponding shear strain in WN in the NbO phase results in an energy increase and a positive shear modulus. The mechanical stability transition from the NaCl to the NbO phase is explored using supercell calculations of the NaCl structure containing C-v = 0% - 25% cation and anion vacancies, while keeping the N-to-W ratio constant at unity. The structure is mechanically unstable for C-v < 5%. At this critical vacancy concentration, the isotropic elastic modulus E of cubic WN is zero, but increases steeply to E = 445 GPa for C-v = 10%, and then less steeply to E = 561 GPa for C-v = 25%. Correspondingly, the hardness estimated using Tian's model increases from 0 to 15 to 26 GPa as C-v increases from 5% to 10% to 25%, indicating that a relatively small vacancy concentration stabilizes the cubic WN phase and that the large variations in reported mechanical properties of WN can be attributed to relatively small changes in C-v.