Experimental observation of grazing-incidence X-ray back-diffraction with large angular dispersion

We report the first experimental observation of grazing-incidence X-ray back-diffraction (GIXBD) exhibiting exceptionally large angular dispersion. An angular dispersion rate (ADR) of 44.4 ± 9.3 µrad meV −1 was measured from a Si (12 4 0) crystal with a surface miscut angle of 89.926°, representing the largest ADR reported for X-ray back-diffraction. The observed diffraction behaviour is quantitatively reproduced by the full dynamical theory of X-ray diffraction. A kinematic formulation based on Snell's law provides a simple geometrical interpretation of the grazing-incidence limit beyond the conventional DuMond analysis and predicts a large but finite ADR, thereby avoiding the apparent divergence of the conventional treatment. These results provide the first experimental validation of GIXBD, establish a physically consistent description of angular dispersion in the extreme grazing-incidence limit and provide a sound physical basis for future ultra-high-resolution crystal X-ray optics.