{ "id": "epgv8hvgad", "slug": "extended-x-ray-absorption-fine-structure-spectroscopy", "title": "Extended X-ray absorption fine structure spectroscopy", "updated": "2026-10-15", "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.practice", "label": "Physics methods, practice, and community", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics.practice" }, { "id": "physical.physics.practice.x-ray-diffraction-and-spectroscopy", "label": "X-ray diffraction and spectroscopy", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics.practice.x-ray-diffraction-and-spectroscopy" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.physics.practice", "label": "Non-geographic · 1946 to 2000: Physics methods, practice, and community", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.practice", "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.practice", "label": "Physics methods, practice, and community", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.practice" } ] } ], "excerpt": "Extended X-ray absorption fine structure (EXAFS) spectroscopy is an element-specific X-ray technique that determines which neighbors surround an element, at what distances and numbers, probing local structure within about 5 Å without requiring long-range crystalline order.", "snippet": "Extended X-ray absorption fine structure (EXAFS) spectroscopy is an element-specific X-ray technique that determines which neighbors surround an element, at what distances and numbers, probing local structure within about 5 Å without requiring long-range crystalline order.", "node": "physical.physics.practice.x-ray-diffraction-and-spectroscopy", "markdown": "# Extended X-ray absorption fine structure spectroscopy\n\nExtended X-ray absorption fine structure (EXAFS) spectroscopy is an element-specific technique that measures the oscillations in X-ray absorption a few thousand eV above an element's absorption edge and converts them into local atomic structure: which neighbors surround the absorbing element, at what distances, in what numbers, and with what disorder. It probes the short-range environment up to approximately 5 Å and does not require long-range crystalline order, which makes it applicable to crystals, glasses, liquids, solutions, and heterogeneous mixtures.[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c) • [2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf) • [3](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf) EXAFS is the extended-region part of X-ray absorption spectroscopy (XAS); the near-edge region, XANES, is treated separately below.\n\n| Key fact | Detail |\n|---|---|\n| What it measures | Neighbor identity, interatomic distance, coordination number, and structural disorder around a chosen element[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c) |\n| Probed range | Local environment within about 5 Å of the absorbing atom[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c) |\n| Bond-length accuracy | 0.01–0.02 Å for interatomic distance R[4](https://arxiv.org/pdf/1312.5295) |\n| Coordination-number accuracy | About 10% (±0.3 for a well-separated first shell)[4](https://arxiv.org/pdf/1312.5295) • [5](https://www.hyomen.org/wp-content/uploads/papers/vol5_no4/asakura/asakura_86.pdf) |\n| Sensitivity | Elements detectable down to a few ppm[3](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf) |\n| Modern theory | Point-scattering theory with Fourier inversion, Sayers, Stern, and Lytle, 1971[6](https://doi.org/10.1103/physrevlett.27.1204) |\n| Where it is done | Predominantly synchrotron facilities; laboratory instruments increasingly available[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf) |\n\n## How it works\n\nWhen an X-ray photon is absorbed by an atom at or above a core-level binding energy (the absorption edge), a photoelectron is emitted. The oscillatory fine structure in the absorption coefficient arises from quantum interference between the emitted photoelectron wave and elastically scattered photoelectron waves from neighboring charge density.[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf) Constructive and destructive interference at the absorbing atom modulates the absorption probability as a function of photon energy, and the oscillation frequencies encode the distances to neighboring atoms.\n\nThe normalized fine structure is defined as \\( \\chi(E) = [\\mu(E) - \\mu_{0}(E)]/\\Delta\\mu_{0} \\), where \\( \\mu_{0} \\) is the smooth background absorption and \\( \\Delta\\mu_{0} \\) the edge jump.[7](https://doi.org/10.1107/s1574870720007508) In the single-scattering picture, the oscillations are written as a sum over coordination shells:[8](https://docs.xrayabsorption.org/tutorials/XAFS_Fundamentals.pdf)\n\n\\[ \\chi(k) = \\sum_{j} \\frac{N_{j} S_{0}^{2} f_{j}(k)}{k R_{j}^{2}} e^{-2R_{j}/\\lambda(k)} e^{-2k^{2}\\sigma_{j}^{2}} \\sin\\left[2kR_{j} + \\delta_{j}(k)\\right] \\]\n\nHere \\( N_{j} \\) is the number of neighbors in shell \\( j \\), \\( R_{j} \\) the distance to them, \\( f_{j}(k) \\) and \\( \\delta_{j}(k) \\) the scattering amplitude and phase shift of the neighboring atoms, \\( \\sigma_{j}^{2} \\) the disorder in the neighbor distance, and \\( \\lambda(k) \\) the photoelectron mean free path.[8](https://docs.xrayabsorption.org/tutorials/XAFS_Fundamentals.pdf) Phase shifts are characteristic of particular atoms and largely independent of surroundings within a class of materials, so EXAFS can be calibrated on known structures and applied to unknown ones.[9](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.11.4836)\n\n## How it is done\n\nMost experiments are run at synchrotron beamlines, where a monochromator scans the photon energy across the chosen absorption edge while the absorption coefficient \\( \\mu(E) \\) is recorded. Transmission geometry is preferred for bulk homogeneous samples.[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c) [Fluorescence detection](https://www.edgepedia.org/fluorescence-detection) suits thick or dilute samples, for example 0.01 g/g Pd supported on CeO₂, though in some setups fluorescence can be count-rate-limited; with fast detectors and fluorescence-detected QEXAFS it can still support time-resolved measurements.[10](https://air.unimi.it/retrieve/e2bb3d13-7f61-4017-98dd-5048558e4fa4/Can%20J%20Chem%20Eng%20-%202021%20-%20Iglesias%E2%80%90Juez%20-%20Experimental%20methods%20in%20chemical%20engineering%20X%E2%80%90ray%20absorption%20spectroscopy%20XAS%20.pdf)\n\nData reduction follows a standard sequence: convert measured intensities to \\( \\mu(E) \\); subtract a smooth pre-edge background, usually a Victoreen or exponential function; identify the edge energy \\( E_{0} \\), often at the maximum of the first derivative of absorption; remove the post-edge background to isolate \\( \\chi = (\\mu - \\mu_{0})/\\Delta\\mu \\); convert energy to photoelectron wavenumber \\( k = \\sqrt{2m(E - E_{0})/\\hbar^{2}} \\); and [Fourier transform](https://www.edgepedia.org/fourier-transform) \\( \\chi(k) \\) into R-space.[3](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf) • [2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf) The resulting \\( \\tilde{\\chi}(R) \\) resembles a pair distribution function that is interpreted to yield quantitative local-structure information.[10](https://air.unimi.it/retrieve/e2bb3d13-7f61-4017-98dd-5048558e4fa4/Can%20J%20Chem%20Eng%20-%202021%20-%20Iglesias%E2%80%90Juez%20-%20Experimental%20methods%20in%20chemical%20engineering%20X%E2%80%90ray%20absorption%20spectroscopy%20XAS%20.pdf) • [11](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=915832)\n\nFitting is done by evaluating the EXAFS equation as a path expansion, with per-path parameters \\( N \\), \\( S_{0}^{2} \\), \\( F(k) \\), \\( R \\), \\( \\Phi(k) \\), \\( \\sigma^{2} \\), and \\( \\lambda(k) \\), as implemented in modern software such as Larch (xraylarch), the Python-based successor to Ifeffit.[12](https://docs.xrayabsorption.org/Workshops/APS2009/Ravel_advanced_topics.pdf)\n\nModern XAFS practice is dominated by synchrotron beamlines, where transmission or fluorescence detection is chosen to match the sample.[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf) Laboratory XAFS instruments are gaining popularity as cost-effective alternatives with unlimited availability compared with synchrotron beam time.[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf) Their trade-off is a relatively low signal-to-noise ratio that must be compensated by long acquisition times, which limits studies of very dilute samples.[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)\n\n## Origin\n\nTheories of the fine structure included a long-range-order theory for solids and a short-range-order theory for molecules; the effect was initially called the \"Kronig structure\".[13](https://journals.iucr.org/s/issues/2001/02/00/hi5548/hi5548.pdf) Despite this early theoretical basis, the technique found no applications until roughly the 1970s, because of a shortage of efficient X-ray sources and the lack of a suitable theory.[14](https://onlinelibrary.wiley.com/doi/10.1002/anie.199400451)\n\nThe modern form of the method came from the collaboration of Dale E. Sayers, Edward A. Stern, and Farrel W. Lytle. The decisive step was their 1971 [Physical Review Letters](https://www.edgepedia.org/physical-review-letters) paper, in which they applied [Fourier analysis](https://www.edgepedia.org/fourier-analysis) to their point-scattering theory to invert experimental data into a radial structure function with determinable parameters of distance, number of atoms, and shell widths.[6](https://doi.org/10.1103/physrevlett.27.1204) Applied to germanium, the technique located first and second neighbors in amorphous Ge at the crystalline distance within the 1% measurement accuracy.[6](https://doi.org/10.1103/physrevlett.27.1204)\n\n## Variants\n\n**XANES/NEXAFS.** The features before and immediately after the edge, called X-ray absorption near-edge structure (XANES) or near-edge XAFS (NEXAFS), are sensitive to the density of electronic states near the [Fermi level](https://www.edgepedia.org/fermi-level), chemical state, local symmetry, and bonding, while EXAFS extends a few thousand eV above the edge and probes the spatial arrangement of nearest neighbors.[15](https://pubs.acs.org/chreay/article/121/2/882/385251/In-Situ-Operando-Electrocatalyst-Characterization)\n\n**Time-resolved modes.** Quick-scanning EXAFS (QEXAFS), introduced by R. Frahm in 1989 in Physica B Condensed Matter, uses continuously scanning monochromators and rapid data acquisition; published accounts place its time resolution in the millisecond range[15](https://pubs.acs.org/chreay/article/121/2/882/385251/In-Situ-Operando-Electrocatalyst-Characterization) • [16](https://doi.org/10.1016/0921-4526%2889%2990306-2) and, for full transmission-mode EXAFS spectra, at sub-second level.[17](https://pmc.ncbi.nlm.nih.gov/articles/PMC7285694/) Fluorescence-detected QEXAFS extends quick-scanning to dilute samples where transmission is not feasible.[17](https://pmc.ncbi.nlm.nih.gov/articles/PMC7285694/)\n\n**HERFD-XAS.** [High-energy-resolution fluorescence detection](https://www.edgepedia.org/high-energy-resolution-fluorescence-detection) records spectra element specifically, which benefits mixed-metal systems in catalysis and enzyme chemistry. Because it is hard-X-ray based, there are few limitations on the sample environment, making high-pressure studies and studies of complexes in solution easily feasible.[18](https://pubs.rsc.org/en/content/articlepdf/2014/cp/c4cp00904e)\n\n## Applications\n\nEXAFS is used wherever the local environment of a specific element matters. In catalysis and electrocatalysis, in situ and operando XAS follows structural transformations of working catalysts and detects intermediate species.[15](https://pubs.acs.org/chreay/article/121/2/882/385251/In-Situ-Operando-Electrocatalyst-Characterization) Because it does not require long-range order, it is particularly suited to disordered systems with local short-range order, such as glasses, solutions, liquids, and non-crystalline solids.[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)\n\n## Limitations and alternatives\n\nFor simple systems with one element in well-separated shells, EXAFS determines bond lengths with a precision of 0.001 nm (0.01 Å) and first-shell coordination number with an accuracy of ±0.3; a general estimate gives interatomic distance to 0.01–0.02 Å and coordination number to about 10%.[5](https://www.hyomen.org/wp-content/uploads/papers/vol5_no4/asakura/asakura_86.pdf) • [4](https://arxiv.org/pdf/1312.5295)\n\nSeveral failure modes limit what fits can deliver. [Curve fitting](https://www.edgepedia.org/curve-fitting) in complex systems is complicated by the number of data points, goodness of fit, parameter correlations, dependence on initial parameters, error estimation, and asymmetric distributions.[5](https://www.hyomen.org/wp-content/uploads/papers/vol5_no4/asakura/asakura_86.pdf) Thermal and structural disorder damp the fine structure exponentially through the [Debye–Waller factor](https://www.edgepedia.org/debye-waller-factor) \\( \\exp(-2k^{2}\\sigma^{2}) \\), suppressing high-k oscillations, especially at high temperature where \\( \\sigma \\) increases.[19](https://pubs.acs.org/jpccck/article/130/37/12975/5422125/Recovering-High-Temperature-EXAFS-Despite-Debye) Neighboring atoms with similar atomic number cannot be distinguished: C, N, and O, or S and Cl, or Mn and Fe.[10](https://air.unimi.it/retrieve/e2bb3d13-7f61-4017-98dd-5048558e4fa4/Can%20J%20Chem%20Eng%20-%202021%20-%20Iglesias%E2%80%90Juez%20-%20Experimental%20methods%20in%20chemical%20engineering%20X%E2%80%90ray%20absorption%20spectroscopy%20XAS%20.pdf) The probed volume is large, roughly mm² in area with mm-scale depth sensitivity, so results are ensemble-averaged values rather than single-particle measurements.[20](https://www.cell.com/matter/pdf/S2590-2385%2823%2900466-6.pdf)\n\nAgainst X-ray total scattering, EXAFS signals are sensitive to partial pair-distribution functions specific to the absorbing atom, an advantage for minority species that a single PDF cannot offer.[20](https://www.cell.com/matter/pdf/S2590-2385%2823%2900466-6.pdf)\n\n## References\n\n1. [X-ray absorption spectroscopy, a beginner's guide (IOPscience)](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c)\n2. [X-ray absorption spectroscopy (Primer, Chantler & Diaz-Moreno 2024)](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)\n3. [Fundamentals of XAFS (Newville, Reviews in Mineralogy and Geochemistry 78)](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf)\n4. [The historical development of X-ray Absorption Fine Spectroscopy and of its applications to Materials Science](https://arxiv.org/pdf/1312.5295)\n5. [Problems in EXAFS analysis and its future prospects (Asakura, Surface Science series)](https://www.hyomen.org/wp-content/uploads/papers/vol5_no4/asakura/asakura_86.pdf)\n6. [Dale E. Sayers, Edward A. Stern, Farrel W. Lytle (1971). New Technique for Investigating Noncrystalline Structures: Fourier Analysis of the Extended X-Ray, Absorption Fine Structure. Physical Review Letters.](https://doi.org/10.1103/physrevlett.27.1204)\n7. [EXAFS: theory and approaches](https://doi.org/10.1107/s1574870720007508)\n8. [Fundamentals of XAFS](https://docs.xrayabsorption.org/tutorials/XAFS_Fundamentals.pdf)\n9. [Extended x-ray-absorption fine-structure technique. III. Determination of physical parameters (Stern, Sayers & Lytle, 1975)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.11.4836)\n10. [Experimental methods in chemical engineering: X-ray absorption spectroscopy, XAS, XANES, EXAFS (Iglesias-Juez et al., Can J Chem Eng 2021)](https://air.unimi.it/retrieve/e2bb3d13-7f61-4017-98dd-5048558e4fa4/Can%20J%20Chem%20Eng%20-%202021%20-%20Iglesias%E2%80%90Juez%20-%20Experimental%20methods%20in%20chemical%20engineering%20X%E2%80%90ray%20absorption%20spectroscopy%20XAS%20.pdf)\n11. [Quantitative EXAFS Analysis (NIST)](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=915832)\n12. [Advanced Topics in EXAFS Analysis](https://docs.xrayabsorption.org/Workshops/APS2009/Ravel_advanced_topics.pdf)\n13. [Musings about the development of XAFS (E. A. Stern, personal recollection)](https://journals.iucr.org/s/issues/2001/02/00/hi5548/hi5548.pdf)\n14. [X-Ray Absorption Spectroscopy of Amorphous Solids, Liquids, and Catalytic and Biochemical Systems, Capabilities and Limitations](https://onlinelibrary.wiley.com/doi/10.1002/anie.199400451)\n15. [In Situ/Operando Electrocatalyst Characterization by X-ray Absorption Spectroscopy (Chemical Reviews)](https://pubs.acs.org/chreay/article/121/2/882/385251/In-Situ-Operando-Electrocatalyst-Characterization)\n16. [QEXAFS: X-ray absorption studies seconds (Physica B Condensed Matter, 1989)](https://doi.org/10.1016/0921-4526%2889%2990306-2)\n17. [Fluorescence-detected quick-scanning X-ray absorption spectroscopy](https://pmc.ncbi.nlm.nih.gov/articles/PMC7285694/)\n18. [HERFD-XAS and valence-to-core-XES: new tools to push the limits in research with hard X-rays?](https://pubs.rsc.org/en/content/articlepdf/2014/cp/c4cp00904e)\n19. [Recovering High-Temperature EXAFS Despite Debye–Waller Damping by Modulation-Excitation XAS (J. Phys. Chem. C)](https://pubs.acs.org/jpccck/article/130/37/12975/5422125/Recovering-High-Temperature-EXAFS-Despite-Debye)\n20. [S2590 2385(23)00466 6 (cell.com)](https://www.cell.com/matter/pdf/S2590-2385%2823%2900466-6.pdf)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Physics › Physics methods, practice, and community › X-ray diffraction and spectroscopy*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 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": [], "url": "https://www.edgepedia.org/extended-x-ray-absorption-fine-structure-spectroscopy", "markdown_url": "https://www.edgepedia.org/extended-x-ray-absorption-fine-structure-spectroscopy.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. 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Edgepedia Community License 1.0.", "speakable": "Extended X-ray absorption fine structure spectroscopy is an element-specific X-ray technique that determines which neighbors surround an element, at what distances and numbers, probing local structure within about 5 Å without requiring long-range crystalline order." }