The Weber or Miller-Bravais indices makes use of four indices (hkil) where the equivalent reflections are permutations of the first 3 indices h, k, i.

A zone axis diffraction pattern is made by all the reflections that belong to the Zero Order Laue Zone and High Order Laue Zones.

Zone law: h u + k v + l w = n

specify that a (h,k,l) reflection is perpendicular to the [u,v,w] zone axis direction when n = 0.

• Zero Order Laue Zone : n = 0.
• First Order Laue Zone : n = 1.
• Second Order Laue Zone : n = 2.
• etc

Only reflections close enough to the Ewald sphere participate to the diffraction. They are organized in concentric circles (Fig. 1).

The 6 red reflections are {2, 0,-2} are Zeroth order Laue Order (ZOLZ), the green ones are First Oorder Laue Zone (FOLZ) and the blue ones are Second Order Laue Zone (SOLZ) reflections.

The circles (Laue Circles) the trace of the intersection of the Ewald sphere with the FOLZ and SOLZ. Note that, while the symmetry of the FOLZ 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.

Using 4 indices (hkil) or [uvtw] in hexagonal or trigonal crystals helps figure out equivalent (hkl) reflections or [u,v,w] directions. The transformation from 3 indices to 4 indices or their inverse are given in Figures 2a, 2b for the reflections and Figures 3a, 3b for the directions.

The simple change (h, k, l) to (h, k, (-h-k)=i, l) does not apply for [u,v,w] zone axis in hexagonal or trigonal crystals. For example [1,0,0] transforms in [2,-1,-1, 0] and [1,0,-1,0] into [2,1,0]. Alternatively the [uvw] to [uvtw] transform is given below (Fig. 3a):