Angle-dependent X-ray absorption correction in small- and wide-angle X-ray scattering : accounting for constrained scattering volume, beam profiles and capillary wall attenuation

Kovač, Jure (author), Jamnik, Andrej (author), Szilágyi, István (author), Tomšič, Matija (author)

A GPU-accelerated numerical method has been developed to calculate angle-dependent transmission factors A(2θ) for small- and wide-angle X-ray scattering (SWAXS) data collected with a Kratky-type camera using a line-collimated beam and a horizontal cylindrical capillary with a vertically oriented detector. The procedure extends path-length-based absorption correction to the Kratky-type geometry by averaging Beer–Lambert attenuation over the constrained illuminated scattering volume and by including experimentally measured primary beam profiles and capillary-wall absorption. Sensitivity analysis shows that the vertical illumination geometry dominates the calculated angle-dependent transmission factor, whereas the horizontal beam-width effect is negligible. Using measured beam profiles makes the correction instrument specific and avoids introducing an effective uniform beam height as an approximation. For strongly absorbing nona­fluoro-tert-butanol, the conventional scalar primary beam transmission correction fails after subtraction of empty-capillary scattering, while the numerical correction enables physically meaningful absolute-scale data reduction. Comparisons between independently calculated theoretical SWAXS intensities and the two reduced experimental datasets obtained sequentially using two different detectors in the same experiment on the same Kratky-type SWAXS camera provide a direct experimental cross check for the data-reduction workflow based on calculated transmission factors. They indicate that the observed limitation is associated with transmission measurement of a spectrally modified primary beam, rather than with the Kratky-type geometry itself. Importantly, the results show that the limitations of conventional scalar transmission corrections are not confined to extreme cases but may also affect routine water-based absolute-scale SWAXS calibration. A simple Beer–Lambert-type numerical scalar correction can still provide a useful qualitative approximation, whereas reliable quantitative analysis requires the full angle-dependent A(2θ) correction.

• Language: English
• Keywords: transmission correction coefficients, X-ray absorption correction, fluorinated liquids, Kratky cameras, absolute scaling, wide-angle X-ray scattering, WAXS, small-angle X-ray scattering, SAXS, SWAXS, perfluorinated alkyl substances, PFAS
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FKKT - Faculty of Chemistry and Chemical Technology
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 10 str.
• Numbering: Vol. 59, no. 5
• PID: 20.500.12556/RUL-188118
• UDC: 544.27
• ISSN on article: 1600-5767
• DOI: 10.1107/S1600576726006837
• COBISS.SI-ID: 288280579
• Publication date in RUL: 18.09.2026

Record is a part of a journal

• Title: Journal of applied crystallography
• Shortened title: J. appl. crystallogr.
• Publisher: Blackwell
• ISSN: 1600-5767
• COBISS.SI-ID: 22700071

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: koeficienti transmisijske korekcije, korekcija absorpcije rentgenskih žarkov, fluorirane tekočine, Kratkyjeve kamere, absolutno skaliranje, širokokotno sipanje rentgenskih žarkov, WAXS, malokotno sipanje rentgenskih žarkov, SAXS, SWAXS, perfluorirane alkilne snovi, PFAS