Direct Methods for Incommensurate Intergrowth Compounds. III. Solving the Average Structure in Multidimensional Space

A multidimensional direct method is proposed for ab initio phasing of the main reflections of incommensurate intergrowth compounds. This method represents an objective procedure for solving the average structure of composite crystals in multidimensional space. The 'normalized structure factors ' are calculated separately for different subsets of main reflections. The derivation of phase information of the reflections and the refinement are performed in multidimensional space. The proposed procedure is tested with known structures of the inorganic misfit layer compounds (LaS)l.laNbS2 and (PbS)~.IaTiS 2. The results show that the phases of the reflections thus obtained are sufficiently accurate to reveal the average structures of these composite crystals. 1