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, pp. 900-902
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As noted by Kitajgorodskij, in many crystal structures molecules with inherent symmetry may occupy Wyckoff special positions, so that molecular and crystallographic symmetry elements coincide, and this may affect the relative frequencies of occurrence of structures with particular space groups. Tables of the frequency of occurrence of space groups have been published by many authors, from Nowacki (1942) onwards. Some typical recent papers are Brock & Dunitz (1994), Donohue (1985), Mighell, Himes & Rodgers (1983), Padmaya, Ramakumar & Viswamitra (1990), Wilson (1988, 1990, 1993b,c), but many of them hardly go beyond recognizing the fact that structures frequently made use of molecular symmetry – Wilson (1988) explicitly chose to ignore it. The early work of Belsky, Zorky and their colleagues did not attract much attention outside Russian-speaking areas. Recently, however, there has been a spate of interest (Wilson, 1991, 1993b,c,d; Brock & Dunitz, 1994; Belsky, Zorkaya & Zorky, 1995). Earlier lack of results is partly due to the fact that the Cambridge Structural Database (Section 9.7.3) did not provide a search program that would distinguish between occupation of a general position and multiple occupation of special positions of the required symmetry (Wilson, 1993d, Section 3). Belsky, Zorkaya & Zorky (1995) were able to make this distinction, and their paper is the source of many of the statistics quoted without special citation here.
It would be interesting to know which space groups possess positions with the symmetry of each of the 32 point groups 1, , 2, m, 2/m, , . Volume A of International Tables for Crystallography (Hahn, 2005) enumerates the symmetry of all the special positions of a given space group, but does not readily answer the reverse question: which space groups contain special positions of given point group ? Some general points may be noted.
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References
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