Determination of Approximate Superstructures in the Urea-Hexadecane Inclusion Compound by Representation Analysis*

The inclusion compound of urea with hexadecane has a superstructure of an ideal hexagonal structure found in other members of the series of urea-n-paraffin adducts consisting essentially of honeycomb-like channels formed by the host into which the long chain molecules are embedded. In order to elucidate the nature of the superstructure, which manifests itself by addiditonal weaker reflexions ( h k l l 2) and (0 0 /) (all /= integer), it is expanded into basis functions trans­ forming as the irreducible representations (IR’s) of the average space group P6|22. Most of the IR’s can be ruled out by exploiting the symmetry of the diffraction pattern. For the remaining sets of basis functions a least squares fit to the measured intensities is performed separately for each IR. Those yielding reliable agreements are then taken as key IR’s describing the prevalent modulations. In this way it is possible to obtain valuable information about the main character­ istics of the superstructure, even if the true structure cannot be fully determined. In the present case a strong modulation belonging to the A3 IR was found to produce rotations of the urea molecules around axes parallel to the channels as well as slight lateral translations. An additional contribution from r 5 results in a superposition of individual orthorhombic domains with slightly different hydrogen bond angles. A phase transition below 147 K can be attributed to M2 and is connected with an ordering of the guest molecules and a simultaneous orthorhombic deformation of the channels.