First-principles study of structural, elastic, and electronic properties of chromium carbides

Based on the idea that the hardness of covalent crystal is intrinsic and equivalent to the sum of the resistance to the indenter of each bond per unit area, a semiempirical method for the evaluation of hardness of multicomponent crystals is presented. Applied to beta-BC2N crystal, the predicted value of hardness is in good agreement with the experimental value. It is found that bond density or electronic density, bond length, and degree of covalent bonding are three determinative factors for the hardness of a polar covalent crystal. Our method offers the advantage of applicability to a broad class of materials and initializes a link between macroscopic property and electronic structure from first principles calculation.