Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 79

The elements of point symmetry which may be observed in crystals are the rotation axes 1, 2, 3, 4 and 6, the inversion axes and , and the mirror plane, m (which is equivalent to ). These symmetry elements may occur either alone or in various possible combinations with each other to give a total of 32 possible crystallographic point groups. The method of drawing and labelling point groups used here is the same as that recommended in International Tables for X‐ray Crystallography, Vol 1. The symbols for the different point symmetry elements are given in Table 1.28. The thirty‐two point groups, classified according to their crystal system, are listed in Table 1.29 and shown diagrammatically in Appendix E.

Table 1.28 Point symmetry elements

Symmetry element	Written symbol	Graphical symbol
Rotation axes	1	None
2
3
4
6
Inversion axes		Nonea _____b
Mirror plane	m	____

^a The inversion axis, , equivalent to a centre of symmetry, is represented as a small open circle, o, in space groups, but does not have a formal graphical representation in point groups, even though it is present in many point groups.

^b The inversion axis, does not have a separate graphical symbol other than that of the mirror plane equivalent to it.

Table 1.29 The thirty‐two point groups

Crystal system	Point group
Triclinic	1,
Monoclinic	2, m, 2/m
Orthorhombic	222, mm2, mmm
Tetragonal	4, , 4/m, 422, 4mm, 2m, 4/mmm
Trigonal	3, , 32, 3m, m
Hexagonal	6, , 6/m, 622, 6mm, m2, 6/mmm
Cubic	23, m3, 432, m, m3m