On the optical theorem applicability using a self‐consistent wave approximation model for the grazing‐incidence small‐angle X‐ray scattering from rough surfaces

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Based on a self‐consistent wave approximation (SCWA) for describing the grazing‐incidence small‐angle X‐ray scattering (GISAXS) from a random rough surface, the optical theorem applicability is tested. Asymptotic solutions for the specular and diffuse GISAXS waves are used to evaluate the X‐ray energy flows through the planes far away from the surface interface, z→±∞. The conventional Fresnel expressions multiplied by the corresponding Debye–Waller factors are used for the specular waves, while the diffuse X‐ray energy flows are described in terms of the product of the statistical scattering factors ηR(, 0) and ηT(, 0) and the Fourier transform of the two‐point cumulant correlation function g 2(|x 1x 2|/l) ( is the grazing scattering angle with the surface, Φ is the azimuth scattering angle; 0 is the grazing‐incidence angle). It is shown that the optical theorem within the SCWA does hold in the case of infinite correlation lengths l→∞ (more precisely, kl0 2 >> 1, k is the X‐ray wavenumber in a vacuum). In a general case of the typical‐valued {0, σ, l} parameters the reflected and transmitted GISAXS wave flows are numerically integrated over the scattering reciprocal space to probe the optical theorem.

Document Type: Research Article

DOI: http://dx.doi.org/10.1107/S0108767312017448

Affiliations: Institute of Crystallography, Russian Academy of Sciences, Leninsky Prospect 59, 119333 Moscow, Russian Federation

Publication date: July 1, 2012

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