Superspace group descriptions of the symmetries of incommensurate urea inclusion compounds

Urea inclusion compounds are a class of incommensurate composite crystals. The urea molecules form a three-dimensionally connected network, with approximate space group symmetry P6$_{1}$22. This network contains tunnels (channels), which accommodate guest molecules. The periodicities of the urea subsystem and the guest subsystem along the tunnel axis are mutually incommensurate. Depending on temperature, the guest subsystem exists with various degrees of disorder. This paper reports the application of the superspace formalism to describe the symmetries of incommensurate urea inclusion compounds. A list of superspace groups is given, compatible with the urea subsystem structure, and describing the possible guest subsystem structures. Particular attention is given to the relation between superspace symmetry, the various types of (dis)order in the guest subsystem, and the point-symmetry of the guest molecules. Incommensurate urea inclusion compounds containing n-alkane, diacyl peroxide and $\alpha $, $\omega $-dibromoalkane guest molecules are analysed in detail.