Trigonal crystal system
The trigonal crystal system is one of the seven crystal systems in crystallography. It includes all point groups with a threefold rotation or axis of rotary inversion. The trigonal crystal system is closely related to the hexagonal crystal system, and together with him the hexagonal crystal family.
The trigonal point groups
The trigonal crystal system comprises the point groups. These are all the point groups of the hexagonal crystal family in which there is a space group with rhombohedral centering - the space groups of the hexagonal crystal system can all be described by the primitive hexagonal axis system. The trigonal crystal system thus includes all subgroups of the point group, who have a 3- fold axis. In contrast to the hexagonal point groups this point groups all have a cubic upper group. The following table provides an overview of the space groups of the trigonal crystal system.
The axis systems of the trigonal crystal system
For a description of trigonal space groups, two different grid systems are used: the hexagonal and rhombohedral the. These are described in detail in the article hexagonal crystal system. The terms trigonal and rhombohedral are clearly defined in modern parlance:
- Trigonal is the name for a set of symmetry groups.
- Rhombohedral is the name of a grid system.
The trigonal crystal classes
To describe the trigonal crystal classes in Hermann- Mauguin symbolism symmetry operations are given with respect to a given direction in the grid system.
Axis in the hexagonal system: the first symbol in the direction of c- axis ( <001 > ). Second symbol in the direction of a- axis (<100 > ). Third symbol in a direction perpendicular to an a- and c-axis (<120 > ). The generally non-equivalent direction < 210 > is also often specified for the third direction. Even though this is especially used to indicate the position of the symmetry elements does not matter, this claim does not comply with the conventions.
In the rhombohedral axis system: 1 symbol in the direction of the body diagonal (< 111> ). Second symbol in the direction of a face diagonal (< 110> ).
Characteristic of all space groups of the trigonal crystal system is the 3 (or 3) at the 1st digit of the space group symbol.
For information on the physical properties means: - Due to the symmetry forbidden. Means: Due to the symmetry allowed. About the magnitude of the effect can be made due to the symmetry no statement, but one can assume that this effect is never exactly disappear.
More trigonal crystallized chemical substances, see Category: Trigonal crystal system
Crystal forms of the trigonal crystal system
Trigonal trapezohedron
Quartz crystal