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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'').
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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="purple">Ось зоны</Font> (''Ru''); <Font color="black"> Asse di zona </Font>(''It''); <Font color="purple">晶帯軸</Font> (''Ja'').
<Font color="green">Eje de zona</Font> (''Sp''). <Font color="purple">Ось зоны</Font> (''Ru'').<Font color="black"> Asse di zona </Font>(''It'')
 
  
  

Revision as of 11:20, 26 February 2007

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

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