A crossover from high stiffness to high hardness. The case of osmium and its borides

Transition-metal light-element compounds are currently raising great expectations for hard and superhard materials. Using the widely attracting osmium (Os) and its borides (OsB, Os₂B₃ and OsB₂) as prototypes, we demonstrate by first-principles calculations that heavy transition metals, which possess high stiffness but low hardness, can be converted into highly hard materials by incorporating of light elements to form compounds. Such a crossover is a manifestation that the underlying sources of high stiffness and high hardness are fundamentally different. The stiffness is related to elastic deformation that is closely associated with valence electron density, whereas the hardness depends strongly on plastic deformation that is determined by bonding nature. Therefore, the incorporation of light atoms into transition metal should be a valid pathway of designing hard and superhard materials. This strategy is in principle also applicable to other transition-metal borides, carbides, and nitrides.