Mineralogy
"Hardness" is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 (talc) to 10 (diamond). A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends significantly on direction. Hardness can also be measured on an absolute scale using a sclerometer; compared to the absolute scale, the Mohs scale is nonlinear.
Superhard material
The incompressibility of a material is quantified by the bulk modulus B, which measures the resistance of a solid to volume compression under hydrostatic stress as B = −Vdp/dV. Here V is the volume, p is pressure, and dp/dV is the partial derivative of pressure with respect to the volume. The bulk modulus test uses an indenter tool to form a permanent deformation in a material. The size of the deformation depends on the material’s resistance to the volume compression made by the tool. Elements with small molar volumes and strong interatomic forces usually have high bulk moduli. Bulk moduli was the first major test of hardness and originally shown to be correlated with the molar volume (V) and cohesive energy (E) as B ~ E/V Bulk modulus was believed to be a direct measure of a material’s hardness but this no longer remains the dominant school of thought. For example, some alkali and noble metals (Pd, Ag) have anomalously high ratio of the bulk modulus to the Vickers of Brinell hardness. In the early 2000s, a direct relationship between bulk modulus and valence electron density was found as the more electrons were present the greater the repulsions within the structure were. Bulk modulus is still used as a preliminary measure of a material as superhard but it is now known that other properties must be taken into account.