# 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 ($h_1, k_1, l_1$), ($h_2, k_2, l_2$) are given by:

${u\over { \begin{vmatrix} k_1 & l_1\\ k_2 & l_2\\ \end{vmatrix}}} = {v\over { \begin{vmatrix} l_1 & h_1\\ l_2 & h_2\\ \end{vmatrix}}} = {w\over { \begin{vmatrix} h_1 & k_1\\ h_2 & k_2\\ \end{vmatrix}} } .$

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 ($h_1, k_1, l_1$), ($h_2, k_2, l_2$), ($h_3, k_3, l_3$) satisfy the relation:

$\begin{vmatrix} h_1 & k_1 & l_1\\ h_2 & k_2 & l_2\\ h_3 & k_3 & l_3\\ \end{vmatrix} = 0.$

## History

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