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Small-angle X-ray and neutron scattering

Abstract

Small-angle scattering (SAS) is a technique that is able to probe the structural organization of matter and quantify its response to changes in external conditions. X-ray and neutron scattering profiles measured from bulk materials or materials deposited at surfaces arise from nanostructural inhomogeneities of electron or nuclear density. The analysis of SAS data from coherent scattering events provides information about the length scale distributions of material components. Samples for SAS studies may be prepared in situ or under near-native conditions and the measurements performed at various temperatures, pressures, flows, shears or stresses, and in a time-resolved fashion. In this Primer, we provide an overview of SAS, summarizing the types of instrument used, approaches for data collection and calibration, available data analysis methods, structural information that can be obtained using the method, and data depositories, standards and formats. Recent applications of SAS in structural biology and the soft-matter and hard-matter sciences are also discussed.

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Fig. 1: Transmission and GISAS.
Fig. 2: Synchrotron SAXS instruments.
Fig. 3: SANS instruments.
Fig. 4: q-Axis calibration and I(q) absolute scaling.
Fig. 5: Basic scheme for data reduction.
Fig. 6: Example of beam geometry correction — slit smearing.
Fig. 7: Data merging.
Fig. 8: Representative results.
Fig. 9: Schematic display of scattering patterns from rod-like cylindrical particles in different concentration regimes and orientations.
Fig. 10: Example applications.

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Acknowledgements

The authors acknowledge the support of iNEXT-Discovery, project number 871037, funded by the Horizon 2020 programme of the European Commission and the Bundesministerium für Bildung und Forschung (BMBF) grant 16QK10A ‘SAS-BSOFT’ (to D.I.S.).

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Authors

Contributions

Introduction (C.M.J., D.I.S., J.S.P. and A.V.S.); Experimentation (C.M.J., D.I.S., J.I., A.Ma., S.H., A.Me., J.S.P. and A.V.S.); Results (C.M.J., D.I.S., J.I., J.S.P. and A.V.S.); Applications (C.M.J., D.I.S., J.I., S.H. and A.Me.); Reproducibility and data deposition (C.M.J., D.I.S. and J.I.); Limitations and optimizations (C.M.J., D.I.S., J.I., A.Ma., S.H., A.Me. and A.V.S.); Outlook (C.M.J., D.I.S., A.Ma. and A.V.S.); Overview of the Primer (D.I.S. and C.M.J.).

Corresponding authors

Correspondence to Cy M. Jeffries or Dmitri I. Svergun.

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The authors declare no competing interests.

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Nature Reviews Methods Primers thanks B. Abecassis, J. Lipfert, D. Zákutná and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Related links

Argonne National Laboratory SAXS and USAXS packages (Irena, Nika Indra): https://usaxs.xray.aps.anl.gov/software-description

As low as reasonably achievable (ALARA): https://www.cdc.gov/nceh/radiation/alara.html#::text=ALARA%20stands%20for%20%E2%80%9Cas%20low,time%2C%20distance%2C%20and%20shielding

BioXTAS RAW: https://bioxtas-raw.readthedocs.io/en/latest/

canSAS initiative: http://www.cansas.org

CCP-SAS web project: http://ccpsas.org/about.html

ESRF FIT2D home page: https://www.esrf.eu/computing/scientific/FIT2D/

ESRF SAXS program package: https://www.esrf.eu/home/UsersAndScience/Experiments/CBS/ID02/available_software/saxs-program-package.html

ESRF SAXS software tools: https://www.esrf.eu/home/UsersAndScience/Experiments/CBS/ID02/available_software.html

ESRF Scatter program for data analysis: https://www.esrf.eu/UsersAndScience/Experiments/CRG/BM26/SaxsWaxs/DataAnalysis/Scatter

European Molecular Biology Laboratory ATSAS data analysis software: https://www.embl-hamburg.de/biosaxs/software.html

European Molecular Biology Laboratory ATSAS online and web services: https://www.embl-hamburg.de/biosaxs/online.html

foXS: https://modbase.compbio.ucsf.edu/foxs/

GISAXS Community Website: http://gisaxs.com/index.php/Main_Page

GISAXS Community Website from the University of Hamburg: http://www.gisaxs.de/

GISAXS Community Website table of contents: http://gisaxs.com/index.php/Special:AllPages

GIXSGUI: https://www.aps.anl.gov/Science/Scientific-Software/GIXSGUI

HiPGISAXS: https://hipgisaxs.github.io/

ImageJ: https://imagej.nih.gov/ij/

Institut Laue-Langevin (ILL) - GRASP SANS analysis and data reduction: https://www.ill.eu/users/support-labs-infrastructure/software-scientific-tools/grasp

IsGISAXS: https://www.insp.upmc.fr/oxydes/IsGISAXS/isgisaxs.htm

Mantid: https://www.mantidproject.org/Main_Page

MULCh: ModULes for the analysis of Contrast variation data: https://smb-research.smb.usyd.edu.au/NCVWeb/

NIST Neutron activation and scattering calculator: https://www.ncnr.nist.gov/resources/activation/

NIST SANS and USANS data reduction and analysis software: https://www.nist.gov/ncnr/data-reduction-analysis/sans-software

NIST Scattering Length Density Calculator: https://www.ncnr.nist.gov/resources/sldcalc.html

NIST XCOM: Photon Cross Sections Database: https://www.nist.gov/pml/xcom-photon-cross-sections-database

NIST X-Ray Mass Attenuation Coefficients: https://www.nist.gov/pml/x-ray-mass-attenuation-coefficients

OneDep System: https://deposit-2.wwpdb.org/

Paul Scherrer Institute, PSI, SASfit package: https://www.psi.ch/en/sinq/sansi/sasfit

PDB-Dev databank: https://pdb-dev.wwpdb.org/

Pepsi-SAXS: https://team.inria.fr/nano-d/software/pepsi-saxs/

Protein Ensemble Database: https://proteinensemble.org

Resources from the National Institute of Standards and Technology: https://www.ncnr.nist.gov/resources/

SAS Portal: http://smallangle.org/

SASSIE-web: https://sassie-web.chem.utk.edu/sassie2/

SasView: https://www.sasview.org/

Saxier SAS forum: https://www.saxier.org/forum/

SAXSMoW (SAXS Molecular Weight): http://saxs.ifsc.usp.br/

ScÅtter, Lawrence Berkeley National Laboratory, Advanced Light Source: https://bl1231.als.lbl.gov/saxs_protocols/

SCATTER, ESRF: https://www.esrf.fr/UsersAndScience/Experiments/CRG/BM26/SaxsWaxs/DataAnalysis/Scatter

Small Angle Scattering Biological Data Bank (SASBDB): https://www.sasbdb.org/

UniProt nomenclature: www.uniprot.org

US-SOMO: https://somo.aucsolutions.com/

WAXSIS: http://waxsis.uni-goettingen.de/

Glossary

Summed convolution

The scattering intensities, I(q), may be conceptualized as the squared sum of the scattering wave amplitudes emanating from each scattering point. For coherent-elastic scattering events, if the distances between the scattering centres are spatially correlated, then the magnitude of the final scattered wave amplitudes (Fig. 1b) is dependent on the number and distribution of individual scattering centres and their respective scattering ‘power’ (the scattering length density).

Transmission geometry

A small-angle scattering (SAS) instrument configuration in which an incident X-ray or neutron beam travels through a sample that is placed in the beam path (typically perpendicular to the incident beam direction). The level at which the incident beam transmits through the sample is determined by numerous factors including the X-ray or neutron energy, the absorption and scattering properties of the sample and its thickness.

Grazing incidence

A small-angle scattering (SAS) instrument configuration in which an incident X-ray or neutron beam is directed at a very low incoming incident angle (the grazing incidence angle) towards a sample that is deposited on a surface (Fig. 2). The incident beam and the reflected beam generate scattering events that are dependent on numerous factors including the incident X-ray or neutron wavelength, the absorption and scattering properties of the sample, and the tilt angle of the sample surface relative to the incident beam.

Form factor

A term describing the squared magnitude of the q-dependent coherent scattering amplitudes arising from regions of excess scattering length density after background scattering contributions have been subtracted. The form factor represents scattering intensities from the distribution of distances between spatially correlated scattering centres within the particle and does not account for the distribution/interactions between the particles, which are described by the structure factor.

Radius of gyration

(Rg). The root mean squared distance calculated from the centre of contrast (typically the centre of mass).

Probable frequency of real-space distances p(r)

(Otherwise known as pair-distance distribution function). The inverse Fourier transform of the form factor that converts the reciprocal space scattering I(q) versus q into a frequency distribution, p, of real-space distances, r; that is, p(r) versus r.

Spallation

The process of applying proton bombardment to eject fragments from heavy metal target materials. Used to produce high-flux neutron beams without nuclear fission chain reaction.

Bragg reflections

Reflections that occur for periodic structures with a spacing d (such as crystal matrices) at a scattering angle θ that is described by the Bragg relation, 2dsinθ = , where n is a positive integer and λ the radiation wavelength. This can be observed in bulk or for ordered materials deposited on surfaces when a grazing incidence beam illuminates a 2D lattice with well-defined symmetry-related periodicity.

Core–shell and multiple-shell particles

Particles consisting of contiguous but spatially distinct layered regions of different average scattering length density. For example, a detergent micelle that in water forms an external layer of higher electron density (the hydrophilic heads) surrounded by a less electron-dense core (the hydrophobic tails).

Polydispersity

Systems containing a distribution of sizes, or displaying a level of non-uniformity of structural states. For example, a monomer–dimer particle equilibrium (a mixture of different molecular weights) or disordered polymers (that may have the same molecular weight but, when viewed as a population, sample different conformations in solution).

Centrosymmetrical potentials

Energy potentials that are distributed symmetrically with respect to a central point.

Mean-free path

The average distance travelled between successive collisions of an X-ray or neutron with the atoms of a material, which modifies the direction or energy of the X-rays or neutrons (for example, between multiple scattering events).

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Jeffries, C.M., Ilavsky, J., Martel, A. et al. Small-angle X-ray and neutron scattering. Nat Rev Methods Primers 1, 70 (2021). https://doi.org/10.1038/s43586-021-00064-9

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