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Incorporation of interfacial roughness into recursion matrix formalism of dynamical X‐ray diffraction in multilayers and superlattices
Author(s) -
Lobach Ihar,
Benediktovitch Andrei,
Ulyanenkov Alexander
Publication year - 2017
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576717004137
Subject(s) - diffraction , superlattice , recursion (computer science) , formalism (music) , surface finish , surface roughness , materials science , x ray crystallography , optics , mathematical analysis , physics , condensed matter physics , mathematics , composite material , algorithm , art , musical , visual arts
Diffraction in multilayers in the presence of interfacial roughness is studied theoretically, the roughness being considered as a transition layer. Exact (within the framework of the two‐beam dynamical diffraction theory) differential equations for field amplitudes in a crystalline structure with varying properties along its surface normal are obtained. An iterative scheme for approximate solution of the equations is developed. The presented approach to interfacial roughness is incorporated into the recursion matrix formalism in a way that obviates possible numerical problems. Fitting of the experimental rocking curve is performed in order to test the possibility of reconstructing the roughness value from a diffraction scan. The developed algorithm works substantially faster than the traditional approach to dealing with a transition layer (dividing it into a finite number of thin lamellae). Calculations by the proposed approach are only two to three times longer than calculations for corresponding structures with ideally sharp interfaces.