Zone axis

From Online Dictionary of Crystallography

(Difference between revisions)
Jump to: navigation, search
m (color)
Line 9: Line 9:
''uh'' + ''vk'' + ''wl'' = 0
''uh'' + ''vk'' + ''wl'' = 0
</center>
</center>
 +
 +
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:
Line 25: Line 27:
</math>
</math>
</center>
</center>
 +
 +
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:
Line 36: Line 40:
</center>
</center>
 +
== History ==
 +
 +
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 (h1,k1,l1), (h2,k2,l2) 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. It is the zone law, or Zonenverbandgesetz.

Three lattice planes have a common zone axis (are in zone) if their Miller indices (h1,k1,l1), (h2,k2,l2), (h3,k3,l3) 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.

See also

Miller indices
reciprocal lattice