Acta Crystallographica Section B

Structural Science

Volume 65, Part 3 (June 2009)

feature articles

Acta Cryst. (2009). B65, 249-268 [ doi:10.1107/S0108768109015614 ]

A non-mathematical introduction to the superspace description of modulated structures

T. Wagner and A. Schönleber

Abstract: The X-ray analysis of (6R,7aS)-6-(tert-butyl-dimethylsilanyloxy)-1-hydroxy-2-phenyl-5,6,7,7a-tetrahydropyrrolizin-3-one, C₁₉H₂₇NO₃Si, revealed a diffraction pattern which is typical for modulated structures: strong Bragg peaks surrounded by weaker reflections which cannot be indexed with the same three reciprocal lattice vectors that are used to describe the strong peaks. For this class of crystal structures the concept of superspace has been developed which, however, for many crystallographers still constitutes a Gordian Knot. As a possible tool to cut this knot the crystal structure of the above-mentioned tetrahydropyrrolizinone derivative is presented as an illustrative example for handling and describing the modulated structure of a typical pharmaceutical (i.e. molecular) compound. Having established a working knowledge of the concepts and terminology of the superspace approach a concise and detailed description of the complete process of peak indexing, data processing, structure solution and structure interpretation is presented for the incommensurately modulated crystal structure of the above-mentioned compound. The superspace symmetry applied is P2₁( [alpha] 0 [gamma] )0; the (incommensurate) q vector components at 100 K are [alpha] = 0.1422 (2) and [gamma] = 0.3839 (8).

Keywords: molecular compound; incommensurately modulated structure; superspace; teaching.


	PDF file (202.8 kbytes) [ doi:10.1107/S0108768109015614/bk5084sup3.pdf ] Extra figures

	GIF image (680.5 kbytes) [ doi:10.1107/S0108768109015614/bk5084sup4.gif ] High-resolution animated version of Fig. 22

	GIF image (110.7 kbytes) [ doi:10.1107/S0108768109015614/bk5084sup5.gif ] Low-resolution animated version of Fig. 22

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