DIMS - a direct-method program for incommensurate modulated structures

A direct-method program, DIMS (direct methods for incommensurate modulated structures), has been written to solve the phase problem of incommensurate structures with one-dimensional modulation. The program uses conventional structure factors instead of normalized structure factors in the phase derivation. It derives phases for satellite reflections by making use of the known phases of main reflections, which can be calculated from the known basic structure or high-resolution electron-microscope images of the sample, or derived by a conventional structure-analysis method involving only main reflections. Two types of phase relationship are used in the program. The first type consists of one main reflection and two satellites of the same order. This type of relationship is used to relate phases of satellites belonging to the same order with phases of main reflections. The second type of relationship consists of three satellites belonging to at least two different orders. This type of relationship is used to link satellites of different orders. X-ray as well as electron diffraction data from a dozen incommensurate modulated structures have been used to test the program. Two typical examples are described.