Local Inelastic Shearing of Atoms

Inelastic shearing of atoms relative to one another is the mechanism that determines hardness. The shearing is localized at dislocation lines and at kinks along these lines. The kinks are very sharp in covalent crystals where they encompass only individual chemical bonds. On the other hand, in metal crystals they are often very extended. In metallic glasses they are localized in configurations that have a variety of shapes. In ionic crystals the kinks are localized in order to minimize the electrostatic energy. 

An antecedent of the bond modulus is the chemical hardness of Pearson (1997) which measures the stabilities of molecules. Also, bond moduli are proportional to the physical hardnesses of Yang, Parr, and Uytterhoeven (1987) which they proposed for minerals. 

The bond modulus is a quite simple parameter. It is the ratio of an atomic (or molecular) energy, and an atomic (or molecular) volume. Essentially all of the volumes of interest are known from crystallography, and the energies are 

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