X-ray diffraction analysis of modulated crystals: Review

The state of the art of X-ray diffraction analysis of modulated crystals is reviewed. The review begins with a brief historical overview followed by the consideration of the main concepts and notations used in this field. Then, methods of structural analysis of modulated crystals are considered with emphasis on recent achievements. The most interesting objects are listed, and the directions of investigation are outlined. Examples of analysis of both individual structures and families of modulated and incommensurate composite structures are given in terms of superspace symmetry.