Enhanced Hardness in Transition-Metal Monocarbides via Optimal Occupancy of Bonding Orbitals

An efficient strategy that can guide the synthesis of materials with superior mechanical properties is important for advanced material/device design. Here, we report a feasible way to enhance hardness in transition-metal monocarbides (TMCs) by optimally filling the bonding orbitals of valence electrons. We demonstrate that the intrinsic hardness of the NaCl- and WC-type TMCs maximizes at valence electron concentrations of about 9 and 10.25 electrons per cell, respectively; any deviation from such optimal values will reduce the hardness. Using the spark plasma sintering technique, a number of W_1-ReC (x = 0-0.5) have been successfully synthesized, and powder X-ray diffractions show that they adopt the hexagonal WC-type structure. Subsequent nanoindentation and Vickers hardness measurements corroborate that the newly developed W_1-ReC samples (x = 0.1-0.3) are much harder than their parent phase (i.e., WC), marking them as the hardest TMCs for practical applications. Furthermore, the hardness enhancement can be well rationalized by the balanced occupancy of bonding and antibonding states. Our findings not only elucidate the unique hardening mechanism in a large class of TMCs but also offer a guide for the design of other hard and superhard compounds such as borides and nitrides.