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.
Fracture toughness
In materials science, fracture toughness is a property which describes the ability of a material to resist fracture, and is one of the most important properties of any material for many design applications. The linear-elastic fracture toughness of a material is determined from the stress intensity factor (formula_1) at which a thin crack in the material begins to grow. It is denoted K and has the units of formula_2 or formula_3. Plastic-elastic fracture toughness is denoted by J, with the unit of J/cm or lbf-in/in, and is a measurement of the energy required to grow a thin crack.