International
Tables for Crystallography Volume A Space-group symmetry Edited by Th. Hahn © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A. ch. 2.2, pp. 18-19
Section 2.2.4. International (Hermann–Mauguin) symbols for plane groups and space groups (cf. Chapter 12.2 )
a
Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany, and bLaboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands |
2.2.4. International (Hermann–Mauguin) symbols for plane groups and space groups (cf. Chapter 12.2 )
Both the short and the full Hermann–Mauguin symbols consist of two parts: (i) a letter indicating the centring type of the conventional cell, and (ii) a set of characters indicating symmetry elements of the space group (modified point-group symbol).
|
For the different crystal lattices, the Hermann–Mauguin space-group symbols have the following form:
Short and full Hermann–Mauguin symbols differ only for the plane groups of class m, for the monoclinic space groups, and for the space groups of crystal classes mmm, , , , and . In the full symbols, symmetry axes and symmetry planes for each symmetry direction are listed; in the short symbols, symmetry axes are suppressed as much as possible. Thus, for space group No. 62, the full symbol is and the short symbol is Pnma. For No. 194, the full symbol is and the short symbol is . For No. 230, the two symbols are and .
Many space groups contain more kinds of symmetry elements than are indicated in the full symbol (`additional symmetry elements', cf. Chapter 4.1 ). A complete listing of the symmetry elements is given in Tables 4.2.1.1 and 4.3.2.1 under the heading Extended full symbols. Note that a centre of symmetry is never explicitly indicated (except for space group ); its presence or absence, however, can be readily inferred from the space-group symbol.
2.2.4.2. Changes in Hermann–Mauguin space-group symbols as compared with the 1952 and 1935 editions of International Tables
Extensive changes in the space-group symbols were applied in IT (1952) as compared with the original Hermann–Mauguin symbols of IT (1935), especially in the tetragonal, trigonal and hexagonal crystal systems. Moreover, new symbols for the c-axis setting of monoclinic space groups were introduced. All these changes are recorded on pp. 51 and 543–544 of IT (1952). In the present edition, the symbols of the 1952 edition are retained, except for the following four cases (cf. Chapter 12.4 ).
|
References
Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). 1. Band, edited by C. Hermann. Berlin: Borntraeger. [Revised edition: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]Google ScholarInternational Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]Google Scholar
Heesch, H. (1929). Zur systematischen Strukturtheorie. II. Z. Kristallogr. 72, 177–201.Google Scholar