Zone Axis

A zone axis diffraction pattern is made by all the reflections that belong to the zeroth order Laue Zone and higher order Laue zones. The zone Law:

specify that a (h,k,l) reflection is perpendicular to the [u,v,w] zone axis direction when n = 0.
Zeroth Order Laue Zone : n = 0.
First Order Laue Zone : n = 1.
Second Order Laue Zone : n = 2.
Only reflections close enough to the Ewald sphere participate to the diffraction pattern; they are organized into concentric circles.

Aluminium 100 kV (Laue condition) The black reflections are the 6 (2,0,-2), the dark gray ones are the 6 (2,2,-4) and light gray ones are the 6 (4,0,-4). They are all Zeroth Order Laue Zone reflections. The circle is the trace of the intersection of the Ewald sphere with the First order Laue zone. Note that, while the symmetry of the Zeroth Order Laue Zone is 6-fold, the symmetry of the First Order laue Zone is 3-fold. Thus the symmetry of the whole pattern is 3-fold as it has to be for a fcc crystal in a [1,1,1] direction.

Transformation of indices for hexagonal and trigonal crystals

Using 4 indices in hexagonal or trigonal crystals helps see equivalent [u,v,w] directions or (h,k,l) reflections.

3 to 4 indices	4 to 3 indices
		Reciprocal space.
		Direct space : Weber indices.