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Difference between revisions of "Zone axis"

From Online Dictionary of Crystallography

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''uh'' + ''vk'' + ''wl'' = 0
 
''uh'' + ''vk'' + ''wl'' = 0
 
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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:
 
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:
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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:
 
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:
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== History ==
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The notion of zone axis and the zone law were introduced by the German crystallographer Christian Samuel Weiss in 1804.
  
 
== See also ==
 
== See also ==

Revision as of 04:49, 2 July 2013

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.

See also

Miller indices
reciprocal lattice