IUCr journals

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

Acta Cryst. (2009). B65, 249–268 (doi.org/10.1107/S0108768109015614)

[Missing translational symmetry] Missing translational symmetry in the modulated crystal structure of C19H27NO3Si.
Diffraction patterns of modulated structures cannot be indexed with three integer numbers. The necessity to use four or more indices instead must be understood as a loss of translational symmetry in three dimensions. To restore this periodicity the concept of higher-dimensional space was developed during the second half of the last century. In this paper it is introduced in a strictly non-mathematical way, and the complete structure determination process within this so-called superspace approach is illustrated using the incommensurately modulated crystal structure of a typical organic compound, C19H27NO3Si.

T. Wagner and A. Schönleber