Zone axis

Axe de zone (Fr). Zonenachse (Ge). Eje de zona (Sp). Ось зоны (Ru). Asse di zona (It)

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 ($h_1, k_1, l_1$), ($h_2, k_2, l_2$) are given by:

${u\over { \begin{vmatrix} k_1 & l_1\\ k_2 & l_2\\ \end{vmatrix}}} = {v\over { \begin{vmatrix} l_1 & h_1\\ l_2 & h_2\\ \end{vmatrix}}} = {w\over { \begin{vmatrix} h_1 & k_1\\ h_2 & k_2\\ \end{vmatrix}} }$

Three lattice planes have a common zone axis (are in zone) if their Miller indices ($h_1, k_1, l_1$), ($h_2, k_2, l_2$), ($h_3, k_3, l_3$) satisfy the relation:

$\begin{vmatrix} h_1 & k_1 & l_1\\ h_2 & k_2 & l_2\\ h_3 & k_3 & l_3\\ \end{vmatrix} = 0$

See also

Miller indices
reciprocal lattice

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