Difference between revisions of "Zone axis"
From Online Dictionary of Crystallography
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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: | ||
| − | + | <center> | |
| + | <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> | ||
| + | </center> | ||
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: | ||
Revision as of 14:34, 6 February 2006
Axe de zone (Fr). Zonenachse (Ge). Eje de zona (Sp). Ось зоны (Ru).
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
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]
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]
See also
Miller indices
reciprocal lattice