Structure determination of modulated structures by powder X-ray diffraction and electron diffraction

Since the first discovery and description of materials, whose structures are not periodic, enormous efforts have been made in studying these aperiodic structures. With these efforts including the development of superspace group theory and structure solution algorithms, numerous incommensurately modulated structures which represent the vast majority of known aperiodic structures have been determined with single crystal X-ray diffraction data. However, the determination of modulated structures remains very difficult for polycrystalline materials. Powder X-ray diffraction and electron microscopy techniques yield remarkable information for polycrystalline materials. By combining these two methods, modulated structures of polycrystalline materials that impede solution by conventional methods can be determined. The power of these methods is illustrated with the examples of the determination of modulated structures of polycrystalline materials.