Possible space groups

Pandey, D.; Krishna, P.

doi:10.1107/97809553602060000618

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. 9.2, pp. 755-756

Section 9.2.1.5. Possible space groups

D. Pandey^c and P. Krishna^b

9.2.1.5. Possible space groups

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It was shown by Belov (1947) that consistent combinations of the possible symmetry elements in close packing of equal spheres can give rise to eight possible space groups: P3m1, $[P\bar3m1]$ , $[P\bar6m2]$ , [P6_3mc] , [P6_3/mmc] , R3m, $[R\bar 3m]$ , and Fm3m. The last space group corresponds to the special case of cubic close packing $[/ABC/\ldots]$ . The tetrahedral arrangement of Si and C in SiC does not permit either a centre of symmetry $[(\bar1)]$ or a plane of symmetry (m) perpendicular to [00.1]. SiC structures can therefore have only four possible space groups P3m1, R3m1, [P6_3mc] , and $[F\bar43m]$ . CdI₂ structures can have a centre of symmetry on octahedral voids, but cannot have a symmetry plane perpendicular to [00.1]. CdI₂ can therefore have five possible space groups: P3m1, $[P\bar3m]$ , R3m, $[R\bar3m]$ , and . Cubic symmetry is not possible in CdI₂ on account of the presence of Cd atoms, the sequence $[/A\gamma BC\beta AB\alpha C/]$ representing a 6R structure.

References

Belov, N. V. (1947). The structure of ionic crystals and metal phases. Moscow: Izd. Akad. Nauk SSSR. [In Russian.]Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 9.2, pp. 755-756