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X-ray specular scattering from statistically rough surfaces: A novel theoretical approach based on the Green function formalism

Acta Crystallographica Section A: Foundations of Crystallography, ISSN: 0108-7673, Vol: 66, Issue: 6, Page: 640-648
2010
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The Green function formalism is applied to the problem of grazing-incidence small-angle X-ray scattering from statistically rough surfaces. Kirchhoffs integral equation is used to describe the X-ray wavefield propagation through a single rough surface separating vacuum and medium. Taking into account multiple diffuse X-ray scattering effects, the reflection R (θ) and transmission T (θ) coefficients of the specular wave are obtained using the Gaussian statistical model of rough surfaces in terms of the two-point height-height correlation function. In the limiting cases when the correlation length ξ is equal to zero or infinity, analytical formulae for the reflection R (θ) and transmission T (θ) coefficients of the specular wave are obtained. It is important that in the case ξ → they coincide with the corresponding reflection R (θ) and transmission T (θ) coefficients related to the conventional Debye-Waller approximation for describing the grazing X-ray scattering from a rough surface. In the case of finite values of correlation length ξ the reflection |R (θ)| and transmission |T (θ) | scans are numerically calculated. © 2010 International Union of Crystallography Printed in Singapore - all rights reserved.

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