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Anisotropic Elasticity Corrections for Reflection Efficiency and X‐ray Standing‐Wave Patterns using Bent Crystals
Author(s) -
Chukhovskii F. N.,
Hölzer G.,
Wehrhan O.,
Förster E.
Publication year - 1996
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/s0021889896002208
Subject(s) - bent molecular geometry , dimensionless quantity , optics , diffraction , anisotropy , elasticity (physics) , bragg's law , crystal (programming language) , physics , reflection (computer programming) , materials science , condensed matter physics , molecular physics , computer science , mechanics , composite material , thermodynamics , programming language
Anisotropic elasticity corrections are taken into account to evaluate the reflection efficiency I int and the X‐ray standing‐wave patterns (XSWP) P ( Δθ , Φ ) for bent crystals, where Δθ is the angular coordinate associated with the conventional rocking curve and the phase Φ = hr p is related to the position with respect to the crystalline lattice of the adsorbed atoms on the crystal surface, contributing to the XSWP. Analytical expressions are derived for the uniform strain‐gradient parameter B = ¼ ( ∂ 2 / ∂ s 0 ∂ Sh ) [ hu ( r )] governing the peculiarities of the Bragg diffraction within elastically bent crystals, where h is the reflecting vector, u ( r ) is the displacement vector and s 0 and s h are the dimensionless coordinates along the incident and diffracted waves, respectively. The cases of the so‐called free and forced bending in the Johann and von Hamos geometries are considered. The results of the anisotropic elasticity corrections depending on the crystal‐surface orientation are presented for bent silicon (111) and quartz (10.0) and (10.) orientations.