Generalized bond-strength model of Vickers hardness: Application to Cr4B, CrB, CrB2, CrB4, Mo2B, MoB2, OsB2, ReB2,WB2, WB3 and Ti1.87B50

The bond-strength model of Vickers hardness is generalized that can be utilized for any structure with covalent or polar-covalent bonds. We have applied the method to Cr4B, CrB, CrB2, CrB4, Mo2B, MoB2, OsB2, ReB2, WB2, WB3 and Ti1.87B50, and found the hardness of these borides to be within the range of 9-33 GPa, in good agreement with experimental data. The generalization of the well-tried bond-strength model is inevitable for complex structures, opens up broader applications of its use and forms a practical tool for material scientists in the design of superhard materials.