Vacancy Hardening and Ordering in Rhenium Tungsten Carbides

Vacancies generally reduce the number of chemical bonds and hence cause structural softening. It is puzzling, however, that substoichiometric Re0.5W0.5C0.4with 60% carbon vacancies was identified as a superhard material. Here, we report the underlying mechanism responsible for such anomalous vacancy-induced hardening in the Re0.5W0.5C1–xsystem via first-principles calculations. The shear stiffness and hardness increase consistently with rising carbon vacancy concentration in Re0.5W0.5C1–xand reach the maximum at about x= 40%. Such an unexpected hardening phenomenon originates from a gradual relief of the shear-unstable dd bonding and unfavorable pd antibonding interactions owing to the formation of C-vacancies. We further predict that the simultaneous ordered vacancies of W and C atoms can produce a cubic crystalline Re2/3W1/3C that is isomorphic with the NbO type. The calculations on vibrational, mechanical, and electronic properties reveal that this phase has considerable structural stability and is a hard metallic material. This work not only elucidates the intriguing mechanism responsible for the vacancy hardening in this class of systems but also provides a new principle for the structural stability of other transition-metal compounds.