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Polarization effects of X‐ray monochromators modeled using dynamical scattering theory
Author(s) -
Mendenhall Marcus H.,
Black David,
Windover Donald,
Cline James P.
Publication year - 2021
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273321003879
Subject(s) - monochromator , diffraction , optics , polarization (electrochemistry) , scattering , mosaicity , bragg's law , physics , x ray crystallography , perfect crystal , x ray , crystal (programming language) , beam (structure) , chemistry , condensed matter physics , wavelength , computer science , vacancy defect , programming language
The difference in the diffracted intensity of the σ‐ and π‐polarized components of an X‐ray beam in powder diffraction has generally been treated according to equations based on dipole scattering, also known as kinematic X‐ray scattering. Although this treatment is correct for powders and post‐sample analyzers known to be of high mosaicity, it does not apply to systems configured with nearly perfect crystal incident‐beam monochromators. Equations are presented for the polarization effect, based on dynamical diffraction theory applied to the monochromator crystal. The intensity of the π component relative to the σ component then becomes approximately proportional to |cos 2gθ m | rather than to cos 2 2gθ m , where gθ m is the Bragg diffraction angle of the monochromator crystal. This changes the predicted intensities of X‐ray powder diffraction patterns produced on instruments with incident‐beam monochromators, especially in the regions far from 2gθ = 90° in the powder pattern. Experimental data, based on well known standard reference materials, are presented, confirming that the dynamical polarization correction is required when a Ge 111 incident‐beam monochromator is used. The dynamical correction is absent as an option in the Rietveld analysis codes with which the authors are familiar.