Twinning by Pseudo-Merohedry

Twinning by Pseudo-Merohedry in SHELXL

Note: This tutorial uses older programs: shelxs, shelxl97, and shelxtl XP.
There are several different kinds of twinning in crystallography. This tutorial covers an example of a fairly common type: pseudo-merohedric twinning. This type of twinning is possible in crystals where the cell dimensions (by chance) mimic those of a higher-symmetry crystal system. The example here is chlorotetrakis-(imidazole)copper(II) chloride, C₁₂H₁₆Cl₂CuN₈, which forms monoclinic crystals with a β angle of almost exactly 90°. It has a cell that is metrically orthorhombic, even though the underlying symmetry is monoclinic. The structure is a copper complex with four imidazole ligands, one bound chlorine atom and a free chloride anion for charge balance. The finished structure looks like this:

Data collection and processing for this crystal were unremarkable, so this tutorial begins after data scaling and merging. Since the reciprocal lattices of pseudo-merohedric twin components overlap so well, there may be little if any splitting of reflections. There were no obvious signs in the diffraction images to suggest that the crystal was not actually orthorhombic. We therefore begin with just two files: the dataset k00070.hkl and an nreport file k00070.html. These files are available for download (click on boldface links) so that you can follow along with real data.

The tutorial is divided into four parts. The first uses XPREP to find the space group and to set up the '.ins' file to solve the structure. The second covers initial structure solution by direct methods with SHELXS. Here it becomes clear that although we can build a recognizable model, it fails to refine properly. The third part derives the twin law using purely geometric arguments. The last section describes application of a twin matrix, and subsequent SHELXL refinement with TWIN and BASF instructions. In the end, refinement is shown to be quite straightforward, in spite of the twinning.