{ "id": "ep71mgjdk4", "slug": "small-angle-scattering", "title": "Small-angle scattering", "updated": "2026-10-25", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.physics", "label": "Physics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics" }, { "id": "physical.physics.matter-and-radiation", "label": "Matter and radiation physics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics.matter-and-radiation" }, { "id": "physical.physics.matter-and-radiation.condensed-matter", "label": "Condensed matter physics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics.matter-and-radiation.condensed-matter" }, { "id": "physical.physics.matter-and-radiation.condensed-matter.cm-structures", "label": "Crystal and structural condensed matter", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics.matter-and-radiation.condensed-matter.cm-structures" } ], "geo": [ { "id": "geo.nongeo.t1800.physical.physics.matter-and-radiation", "label": "Non-geographic · 1800 to 1945: Matter and radiation physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.physics.matter-and-radiation", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1800", "label": "Non-geographic · 1800 to 1945", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800" }, { "id": "geo.nongeo.t1800.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical" }, { "id": "geo.nongeo.t1800.physical.physics", "label": "Physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.physics" }, { "id": "geo.nongeo.t1800.physical.physics.matter-and-radiation", "label": "Matter and radiation physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.physics.matter-and-radiation" } ] }, { "id": "geo.nongeo.t1946.physical.physics.matter-and-radiation.condensed-matter.cm-structures", "label": "Non-geographic · 1946 to 2000: Crystal and structural condensed matter", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.matter-and-radiation.condensed-matter.cm-structures", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.physics", "label": "Physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics" }, { "id": "geo.nongeo.t1946.physical.physics.matter-and-radiation", "label": "Matter and radiation physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.matter-and-radiation" }, { "id": "geo.nongeo.t1946.physical.physics.matter-and-radiation.condensed-matter", "label": "Condensed matter physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.matter-and-radiation.condensed-matter" }, { "id": "geo.nongeo.t1946.physical.physics.matter-and-radiation.condensed-matter.cm-structures", "label": "Crystal and structural condensed matter", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.matter-and-radiation.condensed-matter.cm-structures" } ] } ], "excerpt": "Small-angle scattering is a family of experimental techniques that uses X-rays or neutrons to determine the size, shape, and molecular weight of structures on the nanometer scale.", "snippet": "Small-angle scattering is a family of experimental techniques that uses X-rays or neutrons to determine the size, shape, and molecular weight of structures on the nanometer scale.", "node": "physical.physics.matter-and-radiation.condensed-matter.cm-structures", "markdown": "# Small-angle scattering\n\nSmall-angle scattering (SAS) is a family of experimental techniques in which X-rays or neutrons elastically deflected by less than a few degrees are recorded far from the sample to determine the size, shape, molecular weight, and aggregation state of structures on the nanometer scale. The two main variants are small-angle [X-ray scattering](https://www.edgepedia.org/x-ray-scattering) (SAXS) and small-angle neutron scattering (SANS). Because the measurement works on particles in solution or in bulk, it does not require crystallization, fixation, or vitrification, and samples can be studied under near-native conditions at controlled temperatures, pressures, flows, and stresses, including time-resolved measurements.[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC8662971/) • [2](https://experiments.springernature.com/nature/primers/10.1038/s43586-021-00064-9) SAXS characterizes structure on the nanometer scale,[3](https://www.sciencedirect.com/science/article/pii/S2665928X20300180) and SAS more generally probes a mesoscopic scale of roughly 1–200 nm.[4](https://indico.ess.eu/event/3378/contributions/19042/attachments/15046/28294/IntroToSAS_FASEM_March2024.pdf)\n\n| Key fact | Detail |\n|---|---|\n| What is measured | Scattered intensity \\( I(q) \\) at angles below a few degrees; detectors sit meters from the sample, so instruments are large[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC8662971/) |\n| Accessible scale | About 1–100 nm for SAXS with ~0.1 nm X-rays;[5](https://www.ias.ac.in/article/fulltext/reso/010/06/0024-0034) ~1–200 nm for SAS overall[4](https://indico.ess.eu/event/3378/contributions/19042/attachments/15046/28294/IntroToSAS_FASEM_March2024.pdf) |\n| Core analysis | Guinier approximation gives \\( R_{g} \\) and \\( I(0) \\); \\( I(0) \\) gives molecular mass; indirect Fourier transform gives \\( p(r) \\) and \\( D_{\\mathrm{max}} \\)[6](https://www.nist.gov/system/files/documents/2024/08/16/SANS_Principles_2024.pdf) • [7](https://journals.iucr.org/m/issues/2017/05/00/tj5011/) |\n| SAXS sample needs | Roughly 20–30 µL at 1–10 mg/mL; seconds of exposure at a synchrotron[8](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624) |\n| SANS sample needs | About 200 µL or more at about 2 mg/mL; minutes-to-hours exposure; no radiation damage[8](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624) • [9](https://www.epj-conferences.org/articles/epjconf/pdf/2020/12/epjconf_jdn24_03002.pdf) |\n| Neutron match points | Lipids ~10–14%, proteins ~40–45%, carbohydrates ~47%, DNA/RNA ~65–72% \\( D_{2} \\)O[8](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624) |\n| Resolution limit | About 10 Å (1 nm) for solution SAXS of biomolecules[10](https://www.nature.com/articles/nprot.2014.116) |\n\n## How it works\n\nThe scattering vector has magnitude \\( q = (4\\pi/\\lambda)\\sin\\theta \\), where \\( 2\\theta \\) is the scattering angle and \\( \\lambda \\) the wavelength.[11](https://www.eng.uc.edu/~beaucag/Classes/Scattering/Guinier%20and%20Fournet%20SAXS%281955%29.pdf) • [6](https://www.nist.gov/system/files/documents/2024/08/16/SANS_Principles_2024.pdf) For X-rays or thermal neutrons with wavelength near 1 Å, an angle of 1° (about 0.017 rad) corresponds to a probed length scale of about 6 nm, which is why small angles probe nanometer structure.[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC8662971/) The measured intensity is \\( I(q) \\propto |F(q)|^{2} \\cdot S(q) \\), the product of a single-particle form factor and an interparticle structure factor; in dilute solution \\( S(q) = 1 \\).[6](https://www.nist.gov/system/files/documents/2024/08/16/SANS_Principles_2024.pdf)\n\nThe Guinier approximation states that at small \\( q \\) (\\( qR_{g} \\lesssim 1 \\)) the intensity follows \\( I(q) \\propto \\exp(-q^{2}R_{g}^{2}/3) \\), so the slope of a plot of \\( \\ln I \\) versus \\( q^{2} \\) yields the radius of gyration \\( R_{g} \\) and the intercept gives \\( I(0) \\).[6](https://www.nist.gov/system/files/documents/2024/08/16/SANS_Principles_2024.pdf) • [7](https://journals.iucr.org/m/issues/2017/05/00/tj5011/) This law provides a model-independent route to particle size,[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC8662971/) and for ideal monodisperse systems the Guinier plot is linear.[12](https://www.embl-hamburg.de/biosaxs/reprints/rop_2003.pdf) At high \\( q \\), structures with sharp interfaces follow Porod's law, \\( I(q) \\simeq q^{-4} \\), which is universal for clear-cut interfaces; exponents near 2 indicate flexible polymeric structures.[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC8662971/) Because \\( I(0) \\) is proportional to the square of the excess electrons (or contrast) in the particle, molecular mass follows when the concentration is known.[3](https://www.sciencedirect.com/science/article/pii/S2665928X20300180)\n\n## How it is done\n\nAn exactly matched solvent blank is required so background scattering can be subtracted to give the net macromolecule scattering,[13](https://www.nature.com/articles/nprot.2016.113) and samples must be pure and monodisperse because contaminants, aggregates, mismatched solvents, or radiation damage severely complicate analysis.[13](https://www.nature.com/articles/nprot.2016.113) [Experiments](https://www.edgepedia.org/experiments) run at low concentration, typically below 10 mg/mL, and a concentration series of three or more samples in the same buffer is measured to extrapolate to infinite dilution, since interparticle contributions extend into the useful q range.[13](https://www.nature.com/articles/nprot.2016.113) • [10](https://www.nature.com/articles/nprot.2014.116) In SEC-SAXS, chromatography separates the target from aggregates immediately before measurement; a combined sampler robot and HPLC system for biological SAXS was implemented at the SOLEIL SWING beamline by G. David and J. Pérez in 2009 in the [Journal of Applied Crystallography](https://www.edgepedia.org/journal-of-applied-crystallography).[3](https://www.sciencedirect.com/science/article/pii/S2665928X20300180) • [14](https://doi.org/10.1107/s0021889809029288)\n\nA measurement consists of data collection, a correction step (background, dark current, deadtime, polarization, self-absorption, and scaling to absolute units), and analysis.[15](https://iopscience.iop.org/article/10.1088/0953-8984/25/38/383201) The Kratky plot (\\( I(q) \\cdot q^{2} \\) versus \\( q \\)) shows a bell-shaped peak converging to the q-axis for folded globular proteins and fails to converge for flexible ones.[16](https://www-ssrl.slac.stanford.edu/smb-saxs/content/data-analysis-primer) Because data cover a limited, noisy q range, the pair distance distribution function \\( p(r) \\) is obtained by indirect Fourier transformation rather than direct [Fourier transform](https://www.edgepedia.org/fourier-transform); \\( D_{\\mathrm{max}} \\) is where \\( p(r) \\) falls to zero, and for homogeneous particles p(r) is the distribution of pair distances.[17](https://sastutorials.org/PairDistanceDistribution/PairDistanceDistribution.html) The indirect Fourier transform method for SAS data was published by O. Glatter in 1977 in the Journal of Applied Crystallography.[18](https://doi.org/10.1107/s0021889877013879) The useful data range for dilute monodisperse systems can be set a posteriori by Shannon-channel analysis (SHANUM), published by Petr V. Konarev and Dmitri I. Svergun in 2015 in IUCrJ.[19](https://doi.org/10.1107/s2052252515005163) Ab initio shape restoration by simulated annealing (DAMMIN) was published by D. I. Svergun in 1999 in the Biophysical Journal,[20](https://doi.org/10.1016/s0006-3495%2899%2977443-6) and the faster DAMMIF by Daniel Franke and Dmitri I. Svergun in 2009 in the Journal of Applied Crystallography.[21](https://doi.org/10.1107/s0021889809000338) Scattering from atomic coordinates can be computed with CRYSOL, published by D. Svergun, C. Barberato, and M. H. J. Koch in 1995 in the Journal of Applied Crystallography.[22](https://doi.org/10.1107/s0021889895007047) The unified Guinier/power-law approach of G. Beaucage, published in 1995 in the Journal of Applied Crystallography, spans multiple structural levels in one expression.[23](https://doi.org/10.1107/s0021889895005292)\n\n## Origin\n\nPublished observations of small-angle X-ray scattering appeared in the Indian Journal of Physics in a series of papers, culminating in a paper relating particle size and molecular weights to the extent of small-angle scattering; B. E. Warren made comparable observations on carbon blacks.[24](https://www.iucr.org/resources/commissions/small-angle-scattering/community) • [11](https://www.eng.uc.edu/~beaucag/Classes/Scattering/Guinier%20and%20Fournet%20SAXS%281955%29.pdf) André Guinier, working with a monochromator camera that reached angles down to about ten minutes of arc, observed diffuse spots near the direct beam in trials in 1937/38, independently of Warren.[25](https://www.iucr.org/__data/assets/pdf_file/0004/769/guinier.pdf) His 1939 paper in Annales de Physique, \"La diffraction des rayons X aux très petits angles\", presents the approximation now known as the Law of Guinier.[26](https://doi.org/10.1051/anphys/193911120161) • [25](https://www.iucr.org/__data/assets/pdf_file/0004/769/guinier.pdf) The observations on AlCu age-hardening gave the Guinier–Preston zones.[25](https://www.iucr.org/__data/assets/pdf_file/0004/769/guinier.pdf) The 1955 monograph by Guinier and Fournet covered the Debye approximation, the Kratky plot, and Porod's law; the field received particular attention only from the late 1930s.[11](https://www.eng.uc.edu/~beaucag/Classes/Scattering/Guinier%20and%20Fournet%20SAXS%281955%29.pdf) • [24](https://www.iucr.org/resources/commissions/small-angle-scattering/community) Neutron small-angle scattering of biological macromolecules in solution was published by H. B. Stuhrmann in 1974 in the Journal of Applied Crystallography.[27](https://doi.org/10.1107/s0021889874009071) A breakthrough for both techniques came in the 1970s with synchrotron radiation and neutron sources, the latter enabling contrast variation by \\( H_{2} \\)O/\\( D_{2} \\)O solvent exchange.[12](https://www.embl-hamburg.de/biosaxs/reprints/rop_2003.pdf)\n\n## Variants\n\nSAXS and SANS are complementary. SAXS needs small volumes (about 20–30 µL, though facility practice spans 5–50 µL) and seconds of synchrotron exposure; SANS requires at least 200 µL of sample at about 2 mg/mL concentration of the non contrast-matched component(s), gives noisier data from incoherent hydrogen scattering, and takes hours; most SANS is performed at neutron user facilities, although compact accelerator-driven neutron sources can also support SANS with more limited capabilities.[8](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624) • [28](https://www.sciencedirect.com/science/article/abs/pii/S1047847710001905) Compared with SAXS, radiation damage to a sample in SANS is unlikely because of the low neutron flux, but long exposures require time-stable samples and beam-related effects should still be monitored.[9](https://www.epj-conferences.org/articles/epjconf/pdf/2020/12/epjconf_jdn24_03002.pdf)\n\nContrast differs fundamentally between the probes. X-ray contrast is electron density; aqueous solvent is about 0.335 e Å⁻³ against about 0.43 e Å⁻³ for protein, so the excess contrast is small and low-background instruments are needed.[29](https://pubs.rsc.org/en/content/articlehtml/2024/cp/d4cp02001d) [Neutron scattering](https://www.edgepedia.org/neutron-scattering) lengths vary irregularly across the periodic table and are isotope dependent: b(\\( ^{1}\\mathrm{H} \\)) = −3.741 fm and b(\\( ^{2}\\mathrm{H} \\)) = 6.671 fm, with calculated scattering length densities of −5.6 ×10⁻⁷ Å⁻² for \\( H_{2} \\)O and 6.37 ×10⁻⁶ Å⁻² for \\( D_{2} \\)O.[30](https://indico.linxs.lu.se/event/226/contributions/1154/attachments/133/225/Lecture_2_-_SANScontrast.pdf) • [31](https://www.embl-hamburg.de/biosaxs/courses/embo2019/slides/blanchet-saxs-sans-facilities.pdf) Varying the \\( D_{2} \\)O fraction matches out components at characteristic points (lipids ~10–14%, proteins ~40–45%, carbohydrates ~47%, DNA/RNA ~65–72% \\( D_{2} \\)O),[8](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624) and deuterating one component lets SANS focus on that component within a complex; the match point is found by plotting \\( I(0) \\) from Guinier fits against solvent composition.[4](https://indico.ess.eu/event/3378/contributions/19042/attachments/15046/28294/IntroToSAS_FASEM_March2024.pdf) The zero average contrast (ZAC) condition, in which protiated and deuterated scatterers are mixed so the interaction term cancels, allows the single-particle form factor to be calculated; it is treated theoretically and experimentally by Mustapha Benmouna and Boualem Hammouda in 1997 in Progress in Polymer Science.[30](https://indico.linxs.lu.se/event/226/contributions/1154/attachments/133/225/Lecture_2_-_SANScontrast.pdf) • [32](https://doi.org/10.1016/s0079-6700%2896%2900004-4) Contrast-variation data from biomolecular assemblies are analyzed with MULCh, published by Andrew E. Whitten, Shuzhi Cai, and Jill Trewhella in 2008 in the Journal of Applied Crystallography.[33](https://doi.org/10.1107/s0021889807055136)\n\nWAXS extends the measurement to wider angles.[34](https://asuserwiki.atlassian.net/wiki/spaces/SAXS/pages/291045667) In grazing incidence, GISAXS and GISANS probe nanostructured thin films and buried interfaces; GISAXS was published for thin-film growth studies by J. R. Levine and colleagues in 1989 in the Journal of Applied Crystallography,[35](https://doi.org/10.1107/s002188988900717x) and the distorted-wave [Born approximation](https://www.edgepedia.org/born-approximation) needed to model multiple scattering near the critical angle was applied to grazing-incidence surface diffraction by George H. Vineyard in 1982 in [Physical Review B](https://www.edgepedia.org/physical-review-b).[36](https://doi.org/10.1103/physrevb.26.4146) • [37](https://www.neutron-sciences.org/articles/sfn/olm/2007/02/sfn2007009/sfn20070s9.pdf) Grazing-incidence simulations and fitting are supported by the BornAgain software, published by Gennady Pospelov and colleagues in 2020 in the Journal of Applied Crystallography.[38](https://doi.org/10.1107/s1600576719016789)\n\n## Applications\n\nIn structural biology, SAXS yields the mass, radius of gyration, and maximum diameter of monodisperse macromolecules, plus cross-sectional size and linear mass density for filaments,[8](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624) and provides shape information for proteins and assemblies not amenable to crystallography, NMR, or EM; complementary data such as NMR chemical-shift perturbations, crosslinking/MS, FRET, and H/DX-MS help discriminate among ambiguous models.[39](https://link.springer.com/article/10.1186/1472-6807-12-17) Neutron contrast variation revealed that DNA is wrapped around the outside of nucleosome core particles 22 years before the first high-resolution crystal structure of the nucleosome appeared,[40](https://onlinelibrary.wiley.com/doi/10.1002/pro.351) and SANS with perdeuteration resolved the conformation of the PAN unfoldase within a PAN–20S proteasome complex even in the presence of large aggregates.[9](https://www.epj-conferences.org/articles/epjconf/pdf/2020/12/epjconf_jdn24_03002.pdf) Time-resolved work reaches about 100 ps at modern synchrotrons and 10–100 fs with X-ray lasers.[8](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624)\n\n## Limitations and alternatives\n\nSeveral failure modes are diagnosed from the Guinier plot. Aggregation causes an upturn (\"smiling\") with increased \\( R_{g} \\) and \\( I(0) \\), while interparticle Coulombic repulsion causes a downturn (\"frowning\"); a linear Guinier plot is necessary but not sufficient for accurate interpretation.[40](https://onlinelibrary.wiley.com/doi/10.1002/pro.351) X-rays are much more damaging to macromolecules than neutrons because they induce free-radical chemistry; synchrotron SAXS delivers doses in the 1–10 kGy range, damage shows as aggregation, fragmentation, or unfolding tracked through \\( R_{g} \\), molecular weight, and integrated intensity versus dose, and the best countermeasures are flowing or oscillating the sample, adding radical scavengers such as glycerol or ascorbate, and cryocooling to 100 K.[13](https://www.nature.com/articles/nprot.2016.113) • [41](https://ecommons.cornell.edu/server/api/core/bitstreams/06bfe0fb-49d2-4034-9e73-2813b9a384b4/content)\n\nThe deeper limitation is information content. Only intensity is measured, so the phase problem prevents full retrieval of the original structure,[15](https://iopscience.iop.org/article/10.1088/0953-8984/25/38/383201) and unambiguous reconstruction of a high-resolution 3D structure from a 1D SAS profile is impossible in general because the inverse problem is poorly conditioned.[42](https://link.springer.com/article/10.1134/S1990747821040097) Rotational averaging of tumbling molecules, not detector resolution, limits the information content,[40](https://onlinelibrary.wiley.com/doi/10.1002/pro.351) so different models can share similar SAXS profiles;[39](https://link.springer.com/article/10.1186/1472-6807-12-17) ab initio models of the insulin receptor-related receptor ectodomain from DAMMIN and GASBOR fit equally well (\\( \\chi^{2} \\) = 1.1–1.3) yet differed greatly in conformation.[42](https://link.springer.com/article/10.1134/S1990747821040097) SAXS is limited to roughly 10 Å resolution,[10](https://www.nature.com/articles/nprot.2014.116) and the value \\( 2\\pi/s_{\\mathrm{max}} \\) is only a nominal resolution limit that can never be achieved.[7](https://journals.iucr.org/m/issues/2017/05/00/tj5011/) Against cryo-EM, NMR, and crystallography, SAXS offers near-native solution conditions, broad size coverage (1–10 kDa proteins to several-hundred-MDa particles, typically tens to hundreds of micrograms of protein per measurement), and seconds of synchrotron exposure, at the cost of much lower information content per measurement.[28](https://www.sciencedirect.com/science/article/abs/pii/S1047847710001905) • [39](https://link.springer.com/article/10.1186/1472-6807-12-17) The Porod–Debye law has been applied to characterize flexible and intrinsically unstructured biological macromolecules by Robert P. Rambo and [John A. Tainer](https://www.edgepedia.org/john-a-tainer) in 2011 in [Biopolymers](https://www.edgepedia.org/biopolymers),[43](https://doi.org/10.1002/bip.21638) and the Guinier–Porod model for generalized power-law regimes was published by Boualem Hammouda in 2010 in the Journal of Applied Crystallography.[44](https://doi.org/10.1107/s0021889810015773)\n\n## References\n\n1. [Small-angle scattering for beginners](https://pmc.ncbi.nlm.nih.gov/articles/PMC8662971/)\n2. [Small-angle X-ray and neutron scattering (Nature Reviews Methods Primers), reference list page](https://experiments.springernature.com/nature/primers/10.1038/s43586-021-00064-9)\n3. [Methods, development and applications of small-angle X-ray scattering to characterize biological macromolecules in solution (Curr. Res. Struct. Biol., 2020)](https://www.sciencedirect.com/science/article/pii/S2665928X20300180)\n4. [Introduction to small-angle scattering (ESS lecture, Judith Houston, March 2024)](https://indico.ess.eu/event/3378/contributions/19042/attachments/15046/28294/IntroToSAS_FASEM_March2024.pdf)\n5. [Small-angle X-ray scattering (Resonance, June 2005)](https://www.ias.ac.in/article/fulltext/reso/010/06/0024-0034)\n6. [SANS Principles & Practice (NIST/UMD summer school, July 2024)](https://www.nist.gov/system/files/documents/2024/08/16/SANS_Principles_2024.pdf)\n7. [Progress in small-angle scattering from biological solutions at high-brilliance synchrotrons (IUCrJ, 2017)](https://journals.iucr.org/m/issues/2017/05/00/tj5011/)\n8. [Emerging applications of small angle solution scattering in structural biology (Protein Science, 2014)](https://onlinelibrary.wiley.com/doi/10.1002/pro.2624)\n9. [The power of SANS, combined with deuteration and contrast variation, for structural studies of functional biomacromolecular systems](https://www.epj-conferences.org/articles/epjconf/pdf/2020/12/epjconf_jdn24_03002.pdf)\n10. [Synchrotron-based small-angle X-ray scattering of proteins in solution (Nature Protocols, 2014)](https://www.nature.com/articles/nprot.2014.116)\n11. [Guinier and Fournet SAXS(1955) (eng.uc.edu)](https://www.eng.uc.edu/~beaucag/Classes/Scattering/Guinier%20and%20Fournet%20SAXS%281955%29.pdf)\n12. [Svergun & Koch, Small-angle scattering studies of biological macromolecules in solution (Rep. Prog. Phys. 2003)](https://www.embl-hamburg.de/biosaxs/reprints/rop_2003.pdf)\n13. [Preparing monodisperse macromolecular samples for successful biological small-angle X-ray and neutron-scattering experiments (Nature Protocols, 2016)](https://www.nature.com/articles/nprot.2016.113)\n14. [G. David, J. Pérez (2009). Combined sampler robot and high-performance liquid chromatography: a fully automated system for biological small-angle X-ray scattering experiments at the Synchrotron SOLEIL SWING beamline. Journal of Applied Crystallography.](https://doi.org/10.1107/s0021889809029288)\n15. [Everything SAXS: small-angle scattering pattern collection and correction](https://iopscience.iop.org/article/10.1088/0953-8984/25/38/383201)\n16. [Data Analysis Primer (SSRL SMB SAXS)](https://www-ssrl.slac.stanford.edu/smb-saxs/content/data-analysis-primer)\n17. [Tutorial: Pair distance distribution, p(r)](https://sastutorials.org/PairDistanceDistribution/PairDistanceDistribution.html)\n18. [O. Glatter (1977). A new method for the evaluation of small-angle scattering data. Journal of Applied Crystallography.](https://doi.org/10.1107/s0021889877013879)\n19. [Petr V. Konarev, Dmitri I. Svergun (2015). 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Journal of Applied Crystallography.](https://doi.org/10.1107/s0021889810015773)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Physics › Matter and radiation physics › Condensed matter physics › Crystal and structural condensed matter*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026; Oct 25, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [ "https://www.eng.uc.edu/~beaucag/Classes/Scattering/Guinier%20and%20Fournet%20SAXS%281955%29.pdf" ], "url": "https://www.edgepedia.org/small-angle-scattering", "markdown_url": "https://www.edgepedia.org/small-angle-scattering.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Small-angle scattering\", Edgepedia (EdgeChat), https://www.edgepedia.org/small-angle-scattering. Edgepedia Community License 1.0.", "credit_md": "\"[Small-angle scattering](https://www.edgepedia.org/small-angle-scattering)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/small-angle-scattering](https://www.edgepedia.org/small-angle-scattering). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Small-angle scattering\", Edgepedia (EdgeChat), https://www.edgepedia.org/small-angle-scattering. Edgepedia Community License 1.0.", "speakable": "Small-angle scattering is a family of experimental techniques that uses X-rays or neutrons to determine the size, shape, and molecular weight of structures on the nanometer scale." }