Open AccessA non‐mathematical introduction to the superspace description of modulated structures
Author(s) -
Wagner Trixie,
Schönleber Andreas
Publication year - 2009
Publication title -
acta crystallographica section b
Language(s) - English
Resource type - Journals
eISSN - 1600-5740
pISSN - 0108-7681
DOI - 10.1107/s0108768109015614
Subject(s) - superspace , crystal structure , knot (papermaking) , crystallography , lattice (music) , mathematics , physics , pure mathematics , mathematical physics , chemistry , materials science , composite material , supersymmetry , acoustics
The X‐ray analysis of (6 R ,7a S )‐6‐( tert ‐butyl‐dimethylsilanyloxy)‐1‐hydroxy‐2‐phenyl‐5,6,7,7a‐tetrahydropyrrolizin‐3‐one, C 19 H 27 NO 3 Si, 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 P 2 1 (α0γ)0; the (incommensurate) q vector components at 100 K are α = 0.1422 (2) and γ = 0.3839 (8).