From Online Dictionary of Crystallography
Axe de zone (Fr); Zonenachse (Ge); Eje de zona (Sp); Ось зоны (Ru); Asse di zona (It); 晶帯軸 (Ja).
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
This is the so-called Weiss law.
The indices of the zone axis defined by two lattice planes (h1,k1,l1), (h2,k2,l2) are given by:
Conversely, any crystal face can be determined if one knows two zone axes parallel to it. It is the zone law, or Zonenverbandgesetz.
Three lattice planes have a common zone axis (are in zone) if their Miller indices (h1,k1,l1), (h2,k2,l2), (h3,k3,l3) satisfy the relation:
The notion of zone axis and the zone law were introduced by the German crystallographer Christian Samuel Weiss in 1804.