SSimple Method for the Hardness Estimation of Inorganic Crystals by the Bond Valence Model

On the basis of the bond valence model, an empirical hardness estimation of inorganic crystals using a simple formula is presented. A new scale, the resistant force per unit area of chemical bond by bond valence, is proposed to be closely related to the hardness of crystals. For multibond crystal systems, the hardness can be equivalent to an average of the hardness of all binary systems in inorganic crystals.. Applied to gamma-A(3)N(4) (A = C, Si, Ge) nitride spinels and BC2N compounds, their calculated hardness agrees well with the available experimental results. Our empirical hardness method can offer a simple and reliable hardness prediction resulting from well-described chemical bonding by the bond valence model, which makes it powerful for exploring novel superhard materials.