International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 9.7, p. 897
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In his book2 Organicheskaya Kristallokhimiya, Kitajgorodskij (1955) treated the triclinic, monoclinic and orthorhombic space groups in considerable detail, analysing the possibility of (a) forming close-packed layers (six-point contact), and (b) close stacking of the layers. On this basis, he divided the layers and the space groups into four categories each. For the layers they are:
The categories of space groups are:
Kitajgorodskij expected the frequency of space groups to decrease in the order (1) > (2
) > (3
> (4
). In particular, `permissible space groups should be found but rarely, as exceptions'. The categorization is summarized in Table 9.7.1.1
, based on Table 8 of Kitajgorodskij (1955
).
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Kitajgorodskij's categorization proved very successful in broad outline, but Wilson's (1993b,c
) detailed statistics revealed about a dozen anomalous space-group types. The anomalies were of two kinds. The first was the frequent occurrence of molecules in general positions in space groups in which Kitajgorodskij expected molecules to use inherent symmetry in special positions. Wilson (1993a
) pointed out that in such cases structural dimers3 can be formed, with two molecules in general positions related by the required symmetry elements – both enantiomers would be required if the element were
or m. Such space groups could therefore be added to Kitajgorodskij's table, in the column for `molecular symmetry 1'. The second kind of anomaly was the fairly frequent occurrence of structures with the `impossible' space groups Pc and P2/c. These could be transferred from `impossible' to `permissible', subgroup (a), by the same packing argument that Kitajgorodskij had used for P1. These and a few other reclassifications are indicated in Table 9.7.1.1
, the new entries being enclosed in square brackets for distinction. Where the change is a transfer to a higher category, the original position of the space group is indicated in round brackets.
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