Twinning - Programs For Indexing, Structure Refinement And Determining The Relationship Between The Twin Components. Robert A. Sparks (503) 842-8237

Programs have been written which analyze twinned crystals and produce structures which are almost as good as those produced routinely with single crystals. Twinned crystals can be classified as merohedral (all reflections of one twin exactly overlap all reflections of the other twin) or non-merohedral (some reflections do not exactly overlap). This talk is about non- merohedrally twinned crystals. A program has been written which finds several orientation matrices where each orientation matrix generates integer indices for a large fraction of the reflections. The user selects one of these solutions. Those reflections which fit with integer indices are then discarded. Orientation matrices for the remainder of the reflections are then found. The unit cell parameters must be the same for one of these solutions and for the original user selected solution. A program has been written to compare two complementary orientation matrices (one for the first twin component and the other for the second twin component). The program determines what the rotation function is between the two orientations matrices. Usually the function is a rotation about a normal to a crystal face (perpendicular twinning) or about a crystal edge (parallel twinning). The rotation angle is usually 180 degrees. These cases are usually samples that consist of alternating layers of crystallites. Every other layer has the same orientation. For those cases where the angle is a few degrees (for example, the angle is 1 to 5 degrees) the sample probably consists of two or more crystallites which have almost the same orientation. These samples are often described as split crystals. Data is collected on the Siemens SMART diffractometer and integrated twice with SAINT- once for each orientation matrix. A program then analyzes the resulting intensity data files and discards those reflections which partially overlap. A new combined intensity data file is used as input to SHELXTL for structure refinement. Many twinned structures have been analyzed, solved and refined with these programs. The algorithms will be described. Examples of twinned structures will be presented. The reason why these structures twin will be discussed.