Difference between revisions of "Asymmetric unit"
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| − | < | + | <font color="blue">Unité asymétrique</font> (''Fr''). <font color="red">Asymmetrische Einheit</font> (''Ge''). <font color="black">Unità asimmetrica</font> (''It''). <font color="Purple">非対称単位</font> (''Ja''). <font color="green">Unidad asimétrica</font> (''Sp''). |
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An asymmetric unit of a space group is a simply connected smallest closed part of space from which, by application of all symmetry operations of the space group, the whole space is filled. This implies that: | An asymmetric unit of a space group is a simply connected smallest closed part of space from which, by application of all symmetry operations of the space group, the whole space is filled. This implies that: | ||
| − | *mirror planes must form boundary planes of the | + | *mirror planes must form boundary planes of the asymmetric unit; |
| − | *rotation axes must form boundary edges of the | + | *rotation axes must form boundary edges of the asymmetric unit; |
| − | *inversion centres must either form vertices of the | + | *inversion centres must either form vertices of the asymmetric unit or be located at the midpoints of boundary planes or boundary edges. |
These restrictions do not hold for screw axes and glide planes. | These restrictions do not hold for screw axes and glide planes. | ||
| − | In mathematics | + | The term 'asymmetric unit' does not mean that this region has an asymmetric shape. In mathematics it is called ''fundamental region'' or ''fundamental domain''. |
==See also== | ==See also== | ||
*[[Unit cell]] | *[[Unit cell]] | ||
| − | * | + | *Illustrations of the asymmetric units of the 230 space groups can be obtained from [http://cci.lbl.gov/asu_gallery/ http://cci.lbl.gov/asu_gallery/] |
| + | *Chapter 2.1.3.8 of ''International Tables for Crystallography, Volume A'', 6th edition | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Latest revision as of 18:06, 8 November 2017
Unité asymétrique (Fr). Asymmetrische Einheit (Ge). Unità asimmetrica (It). 非対称単位 (Ja). Unidad asimétrica (Sp).
An asymmetric unit of a space group is a simply connected smallest closed part of space from which, by application of all symmetry operations of the space group, the whole space is filled. This implies that:
- mirror planes must form boundary planes of the asymmetric unit;
- rotation axes must form boundary edges of the asymmetric unit;
- inversion centres must either form vertices of the asymmetric unit or be located at the midpoints of boundary planes or boundary edges.
These restrictions do not hold for screw axes and glide planes.
The term 'asymmetric unit' does not mean that this region has an asymmetric shape. In mathematics it is called fundamental region or fundamental domain.
See also
- Unit cell
- Illustrations of the asymmetric units of the 230 space groups can be obtained from http://cci.lbl.gov/asu_gallery/
- Chapter 2.1.3.8 of International Tables for Crystallography, Volume A, 6th edition