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The influence of smooth (not step-like) variation of the dielectric function near a surface on reflectivity and scattering of X-rays is investigated theoretically. It is shown than the presence of the transition layer can essentially change the shape of differential scattering intensity diagram, especially when the incidence angle of X- ray beam is more than critical angle of the total external reflection. The application of model involved allows one to describe the Yoneda effect quantitatively (whereas it is impossible in the frames of a step- like model of the dielectric function).
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Igor A. Artioukov, Igor V. Kozhevnikov, "Effects of near-surface transition layer on x-ray reflection and scattering," Proc. SPIE 2453, X-Ray Optics and Surface Science, (23 January 1995); https://doi.org/10.1117/12.200272