Crystal family
The crystal family is a classification scheme for crystals based on their space group or point group . All point groups that can be described with the same conventional cell form a crystal family. Any centering is not taken into account. There are six crystal families.
The six crystal families
The crystal families correspond to the crystal systems with the one difference that the trigonal and the hexagonal crystal system together form the hexagonal crystal family. The reason for this lies in the fact that the rhombohedral grid system does not have a conventional cell, since in this grid system the 3-fold axis runs in the direction of the spatial diagonal and not in the direction of a grid axis. There are therefore the following six crystal families: triclinic, monoclinic, orthorhombic, tetragonal, hexagonal and cubic.
Remarks
The basis of the classification of a crystal is its space group , i.e. the set of its symmetry elements , and not the metric of its unit cell . Therefore, a crystal of space group P2 belongs to the monoclinic crystal family, even if its lattice happens to have a cubic metric. This classification makes sense because the space group also determines the macroscopic properties of the crystal and this crystal therefore behaves like a monoclinic and not like a cubic crystal.
When dividing the crystals into crystal families, there is a clear connection between family and lattice system, which there is no when dividing into crystal systems. By omitting the rhombohedral grid, one solves the complications that arise from the fact that not all space groups that belong to the 3 m holohedral can also be described with the rhombohedral grid. These problems are common.
The term crystal family is defined in the International Tables. In contrast to this, especially in the American and Russian literature, the term crystal system is understood to mean this division into crystal families.
The relationship between crystal family, crystal system and lattice system
| Crystal family | Crystal system | Bravais grid | Grid system |
|---|---|---|---|
| Triclinic | Triclinic | aP | a |
| Monoclinic | Monoclinic | mP, mS | m |
| Orthorhombic | Orthorhombic | oP, oS, oF, oI | O |
| Hexagonal | Trigonal | Mr | r |
| hP | H | ||
| Hexagonal | hP | H | |
| Tetragonal | Tetragonal | tP, tI | t |
| Cubic | Cubic | cP, cF, cI | c |
S means side-centered and summarizes the centerings A, B and C; a stands for English anorthic (= triklin, aP and a) and thus triclin is differentiated from tetragonal (tP and t). The Bravais lattice hP in the trigonal crystal system is identical to the hexagonal one, as is the lattice system h.
literature
- International Tables for Crystallography . Vol. A: Theo Hahn (Ed.): Space-group symmetry. Kluwer Academic Publishing Company, Dordrecht et al. 1983, ISBN 90-277-1445-2 .
- D. Schwarzenbach Kristallographie Springer Verlag, Berlin 2001, ISBN 3-540-67114-5