Understanding the Role of Atomic Vacancies in the Stability and Hardening of Cubic Tungsten and Molybdenum Nitrides

The experimentally reported cubic WN and MoN materials are of great technological and fundamental importance, but their structural stabilities and chemical compositions have generated increasing controversy, which has impeded an in-depth understanding of their structure-property relationships. Here, we show by first-principles calculations that the stoichiometric WN and MoN phases with the cF8 structure are thermodynamically, dynamically, and mechanically unstable, but the presence of disordered atomic vacancies not only restores the lattice stability but also causes an anomalous hardening phenomenon. Most remarkable is that the simultaneous 25% ordered metal and nonmetal vacancies in the cF8 structure lead to the formation of the highly stable and hard cP6 type. We demonstrate that such unusual behaviors originate from the presence of two kinds of bands near the Fermi level that respond oppositely to the stability and hardness of the cF8 structure. The present study reconciles the seemingly inconsistent theoretical and experimental results and provides an effective design mechanism for functional carbides and nitrides by tuning deficiency populations.