Positions with symmetry

Wilson, A. J. C.; Karen, V. L.; Mighell, A.

doi:10.1107/97809553602060000623

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 9.7, pp. 902-903

Section 9.7.4.2. Positions with symmetry $[{\overline 1}]$

A. J. C. Wilson,^a ^‡ V. L. Karen^b and A. Mighell^b

^a St John's College, Cambridge CB2 1TP, England, and ^bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

9.7.4.2. Positions with symmetry $[{\overline 1}]$

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Many space groups are centrosymmetric (all those in the geometric classes $[\overline {1}]$ , 2/m, mmm, 4/m, 4/mmm, $[\overline {3}]$ , $[\overline {3}m]$ , 6/m, 6/mmm, $[m\overline {3}]$ , $[m{\overline {3}}m]$ ), but comparatively few of them possess special positions of symmetry $[\overline {1}]$ , as the centres of symmetry are often encumbered by other symmetry elements. All centres of symmetry in $[P\overline {1}]$ , P2₁/c and Pbca are free, as are some of those in $[P\overline {3}]$ and $[R\overline {3}]$ . When the encumbrance is an antitropic symmetry element, the special position can still be occupied by a molecule of symmetry $[\overline {1}]$ only, but when the encumbrance is syntropic or atropic the position cannot accommodate such a molecule. Table 9.7.2.1 indicates that there are 38 space groups with special positions of symmetry $[\overline {1}]$ , that 28 of them have examples of structures of some kind, and that ten have structures in which the centre of symmetry is actually used by a molecule.

The three space groups with no special positions except those of symmetry $[\overline {1}]$ are very popular, whether or not the centre of symmetry is actually used by the molecule. The single criterion `no special positions except possibly free centres of symmetry' thus selects the space groups favoured by structures in which inherent molecular symmetry is not used.

References

International Tables for Crystallography (2006). Vol. C. ch. 9.7, pp. 902-903