Direct methods for incommensurate intergrowth compounds. I. Determination of the modulation

A direct method is proposed for the determination of the modulation in incommensurate intergrowth compounds. The method is based on a new type of Sayre equation that relates the phase of a satellite reflection to the sum of structure-factor products of pairs of main reflections. Phases of satellite reflections are thus uniquely determined by the phases of main reflections. This reflects the fact that the modulation in intergrowth structures is the result of the interaction of all of the subsystems that form the basic structure. Test calculations were done with experimental data of two known composite structures of the inorganic misfit layer compounds (LaS)_1.14NbS₂ and (PbS)_1.18TiS₂. The results showed that the method is accurate and efficient and is fully independent of any preliminary assumption of the model of modulation.