Correlation between hardness and elastic moduli of the covalent crystals

From a statistical manner, we collected and correlated experimental bulk (B), shear (G), Young’s modulus (E), and ductility (G/B) with Vickers hardness (Hv) for a number of covalent materials and fitted quantitative and simple Hv–G and Hv–E relationships. Using these experimental formulas and our first-principles calculations, we further predicted the microhardness of some novel potential hard/superhard covalent compounds (BC2N, AlMgB14, TiO2, ReC, and PtN2). It was found that none of them are superhard materials (Hv ⩾ 40 GPa) except BC2N. The present empirical formula builds up a bridge between Vickers hardness and first-principles calculations that is useful to evaluate and design promising hard/superhard materials.