Atomistic expression of hardness

Hardness of nonmetallic solids, defined as resistance against structure breakdown, has been re-examined for 88 solids of 22 different structures. The validity of the previously proposed volumetric cohesive energy, U/V, as a direct measure of hardness, has been more fully substantiated by additional data. The essential subdivision of solids into “hard core” and “soft core” could be more clearly defined. A formula is proposed which expresses hardness in terms of physical constants and measurable physical parameters only. The formula shows hardness to be directly proportional to the force constants, a structure factor and the effective valency but inversely proportional to the interatomic distance. This formulation has a direct bearing on problems, such as hardness anisotropy and solid-solution hardness.