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.
Surface roughness
Each of the roughness parameters are calculated using a formula for describing the surface. Standard references that describe each in detail are Surfaces and their Measurement.
There are many different roughness parameters in use, but formula_1 is by far the most common, though this is often for historical reasons and not for particular merit, as the early roughness meters could only measure formula_1. Other common parameters include formula_3, formula_4, and formula_5. Some parameters are used only in certain industries or within certain countries. For example, the formula_6 family of parameters is used mainly for cylinder bore linings, and the "Motif parameters" are used primarily in the French automotive industry. The MOTIF method provides a graphical evaluation of a surface profile without filtering waviness from roughness. A "motif" consists of the portion of a profile between two peaks and the final combinations of these motifs eliminate ″insignificant″ peaks and retains ″significant″ ones. Please note that formula_1 is a dimensional unit that can be micrometer or microinch.