Indexing of grazing-incidence X-ray diffraction patterns

Abstract

Grazing Incidence X-ray Diffraction (GIXD) has been established as a powerful tool for the structural characterization of thin films. However, indexing of the experimentally observed diffraction peaks without prior knowledge of the involved crystal lattices has turned out as a challenging task. During the last years a series of works were published which introduce indexing methods for different methods of GIXD experiments. Static GIXD measurements are performed at fixed sample positions for thin films with preferred orientation of the crystallites relative to the substrate surface but without any in-plane order. Rotated GIXD measurements use rotation of the thin film sample about the substrate normal and collect for each rotation angle a single detector image. This method is used for crystals with azimuthal alignments within the thin film. A comprehensive mathematical framework is developed which provides the assignment of Laue indices to the individual diffraction peaks. The algorithms are even reduced from the three-dimensional case to two-dimensional representation of the experimental results. Despite the fact that GIXD experiments provide only a limited number of diffraction peaks, indexing became possible even for thin film crystals with low symmetry, different preferred orientations and multiple azimuthal alignments.