Hardness of Nonmetallic Solids on an Atomic Basis

Abstract

Hardness values of 65 nonmetallic crystalline solids of 16 different structures are compared with data of a newly introduced concept: "the volumetric lattice energy." When such solids are classified according to a new interpretation of lattice anharmonicity, a set of linear interrelations is obtained which covers the entire hardness range. Thus, on the basis of interatomic cohesive forces, the over-all hardness of these solids becomes unambiguously defined. Hardness receives the dimension (ergs/${\mathrm{cm}}^3$) or (kcal/${\mathrm{cm}}^3$), and an absolute scale. Such hardness data become independent of anisotropy, structure type, and valency of the atoms. Conversion from relative to absolute hardness, as well as estimation of lattice energy data through appropriate hardness testing, becomes possible. For example, the extremely high hardness value of the rare type-II diamond could be determined to be 1.7 times that of the type-I diamond, purely from atomic data. Analogous treatment of the hardness of metallic solids poses additional problems.