Zonal equation

(Crystallog.) the mathematical relation which belongs to all the planes of a zone, and expresses their common position with reference to the axes.

See also: Zonal

References in periodicals archive ?
To show that a face (hkl) lies in the zone [uvw], the zonal equation
First, a face shown by the zonal equation to be parallel to the [111] twin axis must, since this is a three-fold axis, have two more faces 120[degrees] apart from it in the zone.
This can be done for the various isometric forms by the following sequence of operations: (a) choose a Ft [l11] twinning axis on a crystal model or drawing; (b) identify faces which may make up a belly band on twinning; (c) show that the Miller Indicesa of a chosen face apparently parallel to the twin axis do indeed satisfy the zonal equation as before; and (d) show that an adjacent face with a similar orientation is 60[degrees] from the first face.
Actually, it can be shown algebraically that any form which satisfies the zonal equation will also satisfy the interfacial angle equals 60[degrees] requirement, thus making step (d) superfluous.
The cube {100}, octahedron {111}, all trisoctahedra {hhl}, and all tetrahexahedra {hk0} do not yield belly bands since they cannot satisfy the zonal equation.