# Difference between revisions of "Zone axis"

### From Online Dictionary of Crystallography

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== See also == | == See also == | ||

− | + | *[[Miller indices]] | |

− | [[Miller indices]] | + | *[[polar lattice]] |

− | [[polar lattice]] | + | *[[reciprocal lattice]] |

− | [[reciprocal lattice]] | + | *[[zone]] |

− | [[zone]] | ||

[[Category:Morphological crystallography]] | [[Category:Morphological crystallography]] |

## Revision as of 17:04, 11 April 2017

Axe de zone (*Fr*); Zonenachse (*Ge*); Eje de zona (*Sp*); Ось зоны (*Ru*); Asse di zona (*It*); 晶帯軸 (*Ja*).

## Definition

A zone axis is a lattice row parallel to the intersection of two (or more) families of lattices planes. It is denoted by [*u* *v* *w*]. A zone axis [*u* *v* *w*] is parallel to a family of lattice planes of Miller indices (*hkl*) if:

*uh* + *vk* + *wl* = 0

This is the so-called Weiss law.

The indices of the zone axis defined by two lattice planes ([math] h_1, k_1, l_1 [/math]), ([math] h_2, k_2, l_2[/math]) are given by:

[math] {u\over { \begin{vmatrix} k_1 & l_1\\ k_2 & l_2\\ \end{vmatrix}}} = {v\over { \begin{vmatrix} l_1 & h_1\\ l_2 & h_2\\ \end{vmatrix}}} = {w\over { \begin{vmatrix} h_1 & k_1\\ h_2 & k_2\\ \end{vmatrix}} } [/math]

Conversely, any crystal face can be determined if one knows two zone axes parallel to it. It is the zone law, or *Zonenverbandgesetz*.

Three lattice planes have a common zone axis (*are in zone*) if their Miller indices ([math] h_1, k_1, l_1 [/math]), ([math] h_2, k_2, l_2[/math]), ([math] h_3, k_3, l_3[/math]) satisfy the relation:

[math] \begin{vmatrix} h_1 & k_1 & l_1\\ h_2 & k_2 & l_2\\ h_3 & k_3 & l_3\\ \end{vmatrix} = 0[/math]

## History

The notion of zone axis and the zone law were introduced by the German crystallographer Christian Samuel Weiss in 1804.