On the Theory of X-Ray Diffraction and X-Ray Standing Waves in the Multilayered Crystal Systems

The theory for the Bragg dynamical X-ray diffraction and the yield of the secondary radiation scattered via incoherent channels under conditions of X-ray diffraction (X-ray standing wave technique) is developed for the crystal systems composed from many layers. The formulae are derived in a form suitable for a computer simulation of the experimental angular or energy spectra as well as for a determination of unknown parameters via fitting. The Bragg case (reflection) and the Laue case (transmission) are considered within the same approach. The universal computer program is created and its operation is demonstrated on two examples. It is shown that the model of the multilayered crystal system may be a useful tool for analyzing a lot of problems where the one-dimensional crystal-lattice distortions of different kinds influence the rocking curve and the curve of the secondary radiation yield. In the first example the In 0.5 Ga 0.5 P epitaxial film on the GaAs substrate is considered. The experimental angular spectra of the X-ray reflectivity and the yield of the In L α and P K α fluorescence in the Bragg case are described by fitting the parameters of the structure. In the second example the Laue case of X-ray diffraction in a sample having a monotonously increasing (decreasing) shift of the Bragg angle with increasing depth is analyzed. The phenomenon of the complete switching of the X-ray beam from the incident direction to the direction of reflection is calculated and discussed.