Coherent multiple scattering in small-angle scattering experiments: modeling approximations based on the Born expansion.

Frielinghaus, Henrich; Gommes, Cédric

doi:10.1107/S1600576725006685

Article (Scientific journals)

Coherent multiple scattering in small-angle scattering experiments: modeling approximations based on the Born expansion.

Frielinghaus, Henrich; Gommes, Cédric

2025 • In Journal of Applied Crystallography, 58 (Pt 5), p. 1553 - 1570

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/339264

DOI
10.1107/S1600576725006685

PubMed
41064418

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Keywords :

Mie scattering; USANS; USAXS; coherent multiple scattering; ultra-small-angle X-ray scattering; ultra-small-angle neutron scattering; Experiment modeling; Model approximations; Multiple-scattering; Small angle scattering; Small-angle scattering; Ultra small angle x ray scattering; Biochemistry, Genetics and Molecular Biology (all)

Abstract :

[en] We start from an analytical formulation for the coherent multiple scattering treatment - similar to Mie scattering - for spherical particles. Then, we revisit the Born approximation with an approximation for all higher-order terms. Finally, we draw conclusions from those calculations and formulate an approximative model to describe ultra-small-angle neutron scattering and ultra-small-angle X-ray scattering data. In all calculations, we can specify the conditions for coherent multiple scattering. Several examples are provided to show the quality of the simple approximation in comparison with exact calculations and experiments.

Disciplines :

Physics

Author, co-author :

Frielinghaus, Henrich ; Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science JCNS at MLZ, 85748 Garching, Germany

Gommes, Cédric ; Université de Liège - ULiège > Department of Chemical Engineering

Language :

English

Title :

Coherent multiple scattering in small-angle scattering experiments: modeling approximations based on the Born expansion.

Publication date :

01 October 2025

Journal title :

Journal of Applied Crystallography

ISSN :

0021-8898

eISSN :

1600-5767

Publisher :

International Union of Crystallography, United States

Volume :

Issue :

Pt 5

Pages :

1553 - 1570

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://journals.iucr.org/j/issues/2025/05/00/ge5173/ge5173.pdf

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Funding text :

We thank Liliana de Campo and Jitendra Mata from the instrument Kookaburra at ANSTO for providing scattering data. We thank Hitoshi Endo (JAEA, Japan) and Michael Monkenbusch (JCNS, Germany) for providing the original scattering data of microemulsions under film contrast. We thank Vitaliy Pipich from the instrument KWS-3 at FRM II, Garching, for providing measurements on BSA protein aggregates that were formulated by Frank Schreiber and Fajun Zhang at University T\u00FCbingen. No external funding has been raised for this research. Open access funding enabled and organized by Projekt DEAL. CJG is grateful to Fonds De La Recherche Scientifique \u2013 FNRS, Belgium, for a research associate position.

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Bibliography

Authier, A. (2001). Dynamical theory of X-ray diffraction, pp. 534–551. Dordrecht: Springer Netherlands.
Ban, M., Woo, D., Hwang, J., Kim, S. & Lee, J. (2023). Acc. Chem. Res. 56, 3428–3440.
Barker, J. G., Glinka, C. J., Moyer, J. J., Kim, M. H., Drews, A. R. & Agamalian, M. (2005). J. Appl. Cryst. 38, 1004–1011.
Beaucage, G. (1996). J. Appl. Cryst. 29, 134–146.
Beck, C., Grimaldo, M., Braun, M. K., Bühl, L., Matsarskaia, O., Jalarvo, N. H., Zhang, F., Roosen-Runge, F., Schreiber, F. & Seydel, T. (2021). Soft Matter 17, 8506–8516.
Berk, N. & Hardman-rhyne, K. (1986). Phys. B+C 136, 218–222. Cahn, J. W. (1965). J. Chem. Phys. 42, 93–99.
Chong, Y. D. (2024). Quantum mechanics III. LibreTexts. https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_ III_(Chong).
Cohen-Tannoudji, C., Diu, B. & Laloë, F. (1986). Quantum mechanics, Vol. 2. Wiley VCH.
Copley, J. R. D. (1988). J. Appl. Cryst. 21, 639–644.
Dahl, M., Gommes, C. J., Haverkamp, R., Wood, K., Prévost, S., Schröer, P., Omasta, T., Stank, T. J., Hellweg, T. & Wellert, S. (2024). RSC Adv. 14, 28272–28284.
Daicic, J., Olsson, U., Wennerström, H., Jerke, G. & Schurtenberger, P. (1995). Phys. Rev. E 52, 3266–3269.
Debye, P., Anderson, H. R. & Brumberger, H. (1957). J. Appl. Phys. 28, 679–683.
Endo, H., Mihailescu, M., Monkenbusch, M., Allgaier, J., Gompper, G., Richter, D., Jakobs, B., Sottmann, T., Strey, R. & Grillo, I. (2001). J. Chem. Phys. 115, 580–600.
Faran, J. J. Jr (1951). J. Acoust. Soc. Am. 23, 405–418.
Gibaud, A. (1999). Specular reflectivity from smooth and rough surfaces, pp. 87–120. Berlin: Springer.
Glatter, O. & Kratky, O. (1982). Small-angle X-ray scattering. Academic Press.
Gommes, C. J., Zorn, R., Jaksch, S., Frielinghaus, H. & Holderer, O. (2021). J. Chem. Phys. 155, 024121.
Hamley, I. W. (2021). Small-angle scattering: theory, instrumentation, data, and applications. John Wiley & Sons.
Hansen, S. (2000). J. Appl. Cryst. 33, 1415–1421.
Hentschel, M. P., Hosemann, R., Lange, A., Uther, B. & Brückner, R. (1987). Acta Cryst. A43, 506–513.
Holderer, O., Landman, J., Kohlbrecher, J., Wu, B., Zolnierczuk, P., Müller, M., Frielinghaus, H., Förster, S., Schwärzer, K., Sagis, L., Shen, P., Yang, J. & Heiden-Hecht, T. (2025). Adv. Mater. Interfaces e00368.
Jaksch, S., Pipich, V. & Frielinghaus, H. (2021). J. Appl. Cryst. 54, 1580–1593.
Jensen, G. V. & Barker, J. G. (2018). J. Appl. Cryst. 51, 1455–1466.
Ji, Y., Radlinski, A. P., Blach, T., de Campo, L., Vu, P., Roshan, H. & Regenauer-Lieb, K. (2022). Fuel 325, 124957.
Kjems, J., Freltoft, T., Richter, D. & Sinha, S. (1986). Phys. B+C 136, 285–290.
Koberstein, J. T. & Stein, R. S. (1980). J. Polym. Sci. Polym. Phys. Ed. 18, 199–205.
Koutsioubas, A., Jaksch, S. & Pérez, J. (2016). J. Appl. Cryst. 49, 690–695.
Koutsioubas, A. & Pérez, J. (2013). J. Appl. Cryst. 46, 1884–1888.
Magerl, A., Lemmel, H., Appel, M., Weisser, M., Kretzer, U. & Zobel, M. (2024). J. Appl. Cryst. 57, 1282–1287.
Martin, J. E. (1986). J. Appl. Cryst. 19, 25–27.
Mazumder, S. & Sequeira, A. (1992). Pramana J. Phys. 38, 95–159.
Mie, G. (1908). Ann. Phys. 330, 377–445.
Monkenbusch, M. & Richter, D. (2007). C. R. Phys. 8, 845–864.
Munoz, P., Ilavsky, J., Newville, M., Wetter, N. U., Lourenço, R. A., Barbosa de Andrade, M., Martins, T. S., Dipold, J., Freitas, A. Z., Cides da Silva, L. C. & Oliveira, C. L. P. (2023). J. Appl. Cryst. 56, 1692–1706.
Nallet, F., Roux, D. & Milner, S. (1990). J. Phys. Fr. 51, 2333–2346.
Olaofe, G. O. (1970). Radio Sci. 5, 1351–1360.
Pedersen, J. S. (1997). Adv. Colloid Interface Sci. 70, 171–210.
Pospelov, G., Van Herck, W., Burle, J., Carmona Loaiza, J. M., Durniak, C., Fisher, J. M., Ganeva, M., Yurov, D. & Wuttke, J. (2020). J. Appl. Cryst. 53, 262–276.
Roe, R.-J. (2000). Methods of X-ray and neutron scattering in polymer science. Oxford University Press.
Roux, D., Cates, M. E., Olsson, U., Ball, R. C., Nallet, F. & Bellocq, A. M. (1990). Europhys. Lett. 11, 229–234.
Roux, D., Coulon, C. & Cates, M. E. (1992). J. Phys. Chem. 96, 4174–4187.
Schelten, J. & Schmatz, W. (1980). J. Appl. Cryst. 13, 385–390.
Schmitt, J., Kjellman, T., Kwas´niewski, P., Meneau, F., Pedersen, J. S., Edler, K. J., Rennie, A. R., Alfredsson, V. & Impéror-Clerc, M. (2016). Langmuir 32, 5162–5172.
Shen, J. & Maradudin, A. A. (1980). Phys. Rev. B 22, 4234–4240.
Siddique, T., Balu, R., Mata, J., Dutta, N. K. & Roy Choudhury, N. (2022). Polymers 14, 1980.
Skripov, V. P. & Skripov, A. V. (1979). Sov. Phys. Usp. 22, 389–410.
Soraruf, D., Roosen-Runge, F., Grimaldo, M., Zanini, F., Schweins, R., Seydel, T., Zhang, F., Roth, R., Oettel, M. & Schreiber, F. (2014). Soft Matter 10, 894–902.
Squires, G. L. (1996). Introduction to the theory of thermal neutron scattering. Courier Corporation.
Stephenson, J. (1966). J. Math. Phys. 7, 1123–1132.
Teubner, M. & Strey, R. (1987). J. Chem. Phys. 87, 3195–3200.
Tong, D. (2017). Lectures on topics in quantum mechanics. Lecture notes at University of Cambridge. https://www.damtp.cam.ac.uk/user/tong/topicsinqm.html.
Weiss, R. J. (1951). Phys. Rev. 83, 379–389.
Ye, X., Zhang, Q., Feng, C., Ge, H. & Jiao, Z. (1996). Phys. Rev. B 54, 14754–14757.
Zhang, F. & Ilavsky, J. (2010). Polym. Rev. 50, 59–90.