Editing Miller index (section)

==Crystallographic planes and directions==
{{More citations needed section|date=July 2019}}
[[Image:Cristal densite surface.svg|thumb|Dense crystallographic planes]]

Crystallographic directions are [[line (mathematics)|lines]] linking nodes ([[atom]]s, [[ion]]s or [[molecule]]s) of a crystal. Similarly, crystallographic [[plane (mathematics)|planes]] are ''planes'' linking nodes. Some directions and planes have a higher density of nodes; these dense planes have an influence on the behavior of the crystal:
*[[optics|optical properties]]: in condensed matter, [[light]] "jumps" from one atom to the other with the [[Rayleigh scattering]]; the [[velocity of light]] thus varies according to the directions, whether the atoms are close or far; this gives the [[birefringence]]
*[[adsorption]] and [[reactivity (chemistry)|reactivity]]: adsorption and chemical reactions can occur at atoms or molecules on crystal surfaces, these phenomena are thus sensitive to the density of nodes;
*[[surface tension]]: the condensation of a material means that the atoms, ions or molecules are more stable if they are surrounded by other similar species; the surface tension of an interface thus varies according to the density on the surface
** Pores and [[crystallite]]s tend to have straight grain boundaries following dense planes
**[[cleavage (crystal)|cleavage]]
*[[dislocation]]s ([[plastic deformation]])
**the dislocation core tends to spread on dense planes (the elastic perturbation is "diluted"); this reduces the [[friction]] ([[Peierls–Nabarro force]]), the sliding occurs more frequently on dense planes;
**the perturbation carried by the dislocation ([[Burgers vector]]) is along a dense direction: the shift of one node in a dense direction is a lesser distortion;
**the dislocation line tends to follow a dense direction, the dislocation line is often a straight line, a dislocation loop is often a [[polygon]].
For all these reasons, it is important to determine the planes and thus to have a notation system.