Zone (crystallography)
Under a zone is understood in the Crystallography a multitude of layers , which extend parallel cutting edges. The levels that belong to a zone are called tautozonal . The direction of the cutting edge is called the zone axis. The normal vectors of tautozonal planes lie in a plane on which the zone axis is perpendicular. Two intersecting planes clearly define a zone, since the line of intersection is the zone axis.
The zone axes are grid vectors of the real grid. They are therefore denoted by square brackets like points on the real grid: [uvw]. In contrast, the Miller indices of the levels are written in parentheses: (hkl). The zone in real space corresponds to one level in reciprocal space:
| designation | Real grid | Reciprocal grid | |
|---|---|---|---|
| Network level | (hkl) | level | Point |
| Zone | [and many more] | Point | level |
The zone equation
The zone equation describes the relationship between a plane (hkl) and a straight line [uvw] :
- .
This equation is fulfilled if the straight line [uvw] lies in the (hkl) plane, or if the plane (hkl) belongs to the zone [uvw].
example
The picture shows a schematic representation of the idiomorphic surfaces of bournonite . In surfaces a, e, l, m, f and b there is a common direction for all surfaces, which is perpendicular to the c-surface. Therefore, all of these areas belong to the [001] zone.
Applications
The stereographic projection of the planes of a zone form a great circle in the Wulff network . So one can determine preferred directions in the crystal with the help of the Wulff network. As a rule, these directions correspond to the axial directions of the crystal lattice.
The X-rays diffracted by the lattice planes of a zone lie on a cone whose axis is the zone axis. The opening angle is determined by the lattice constant of the zone axis. Therefore, all other rays can be blocked out with a circular aperture. This is used in the Weissenberg , Buerger and De Jong Bouman processes .
literature
- D. Schwarzenbach: Kristallographie Springer Verlag, Berlin 2001, ISBN 3-540-67114-5 .
- Will Kleber , Hans-Joachim Bautsch , Joachim Bohm , Detlef Klimm: Introduction to crystallography . 19th edition. Oldenbourg Wissenschaftsverlag, 2010, ISBN 978-3-486-59075-3 .
- Walter Borchard-Ott: Crystallography 7th edition, Springer Verlag, Berlin 2009, ISBN 978-3-540-78270-4 .
- Lothar Spieß, et al .: Modern X-ray diffraction 3rd edition, SpringerSpektrum, Wiesbaden 2019 ISBN 978-3-8348-1219-3 .