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.