Intrinsic hardness of covalent crystals: a unified multiparametric framework

Bond resistance, bond strength and electronegativity models have been widely utilized for predicting intrinsic hardness of novel covalent materials. Although these models are generally perceived to be distinct, this manuscript recognizes them to be drawing input parameters from the same basis set comprising of bond density, bond length, electronegativity, and coordination number, while primarily differing in the exponents assigned to them. A numerical bound on the feasible space of these exponents is derived, followed by a search operation of this space to determine optimal values. The resulting model yields hardness estimates in good conformance with experimental data for numerous binary and ternary ceramic compounds. The study also provides a plausible explanation for the diversity of parameter–exponent combinations in the existing intrinsic hardness models, that is derived from the variability exhibited by these exponents in capturing a given experimental dataset at a constant fitting error.