# Zone axis

### From Online Dictionary of Crystallography

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

## 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. This 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.