Weiss zone law

From Online Dictionary of Crystallography

Loi de la zone de Weiss (Fr). Weiss-Zonen Gesetz (Ge). Legge della zona di Weiss (It). ワイス晶帯則 (Ja). Ley de la zona de Weiss (Sp).

Weiss zone law, also known as Weiss zone rule, states that a lattice direction with indices [uvw] is contained in a lattice plane with Miller indices (hkl) if the following condition is satisfied:

hu + kv + lw = 0

A direction with indices [uvw] passes through lattice nodes with coordinates nu,nv,nw; for n = 0 the direction passes through the origin. A lattice plane of the family (hkl) passes through the origin if hx + ky + lz = 0, where x,y,z are the coordinates of any point on the plane. By replacing x,y,z with u,v,w we obtain Weiss zone law.