Hardness of covalent compounds: Roles of metallic component and d valence electrons

Based on the detailed analysis of chemical bonds, we present a Vickers hardness expression for the covalency-dominant crystals such as transition-metal carbides and nitrides. Hardness is dependent not only on bond length, bond density, and ionicity of bond [F. M. Gao et al., Phys. Rev. Lett. 91, 015502 (2003)] but also on the metallicity of bond and orbital form in the crystal structure of a compound, and all of these parameters can be determined by first-principles calculations. The calculated hardness using our expression has a good agreement with the experimental values for known monocarbides, mononitrides of transition metals, and cubic Zr3N4 with Th3P4 structure. In addition, we have predicted the Vickers hardness of the recently predicted tetragonal BC3 and tetragonal B2CN, and the recently synthesized pyrite PtN2 and marcasite OsN2. Our method offers one useful technique to search for superhard materials in transition-metal carbides and nitrides.