Difference between revisions of "Zone axis"

From Online Dictionary of Crystallography

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<Font color="blue">Axe de zone</Font> (''Fr'').  <Font color="red">Zonenachse</Font> (''Ge''). <Font color="green">Eje de zona</Font> (''Sp''). <Font color="brown">Ось зоны</Font> (''Ru''). <Font color="black"> Asse di zona </Font>(''It''). <Font color="purple">晶帯軸</Font> (''Ja'').
<font color="blue">Axe de zone</font> (''Fr'').  <font color="red">Zonenachse</font> (''Ge''). <font color="black">Asse di zona</font> (''It''). <font color="purple">晶帯軸</font> (''Ja''). <font color="brown">Ось зоны</font> (''Ru''). <font color="green">Eje de zona</font> (''Sp'').

Latest revision as of 14:58, 20 November 2017

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


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]


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

See also