# Extended X-ray absorption fine structure spectroscopy

Extended 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.<sup>[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c)</sup><sup> • </sup><sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup><sup> • </sup><sup>[3](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf)</sup> EXAFS is the extended-region part of X-ray absorption spectroscopy (XAS); the near-edge region, XANES, is treated separately below.

| Key fact | Detail |
|---|---|
| What it measures | Neighbor identity, interatomic distance, coordination number, and structural disorder around a chosen element<sup>[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c)</sup> |
| Probed range | Local environment within about 5 Å of the absorbing atom<sup>[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c)</sup> |
| Bond-length accuracy | 0.01–0.02 Å for interatomic distance R<sup>[4](https://arxiv.org/pdf/1312.5295)</sup> |
| Coordination-number accuracy | About 10% (±0.3 for a well-separated first shell)<sup>[4](https://arxiv.org/pdf/1312.5295)</sup><sup> • </sup><sup>[5](https://www.hyomen.org/wp-content/uploads/papers/vol5_no4/asakura/asakura_86.pdf)</sup> |
| Sensitivity | Elements detectable down to a few ppm<sup>[3](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf)</sup> |
| Modern theory | Point-scattering theory with Fourier inversion, Sayers, Stern, and Lytle, 1971<sup>[6](https://doi.org/10.1103/physrevlett.27.1204)</sup> |
| Where it is done | Predominantly synchrotron facilities; laboratory instruments increasingly available<sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup> |

## How it works

When 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.<sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup> 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.

The 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.<sup>[7](https://doi.org/10.1107/s1574870720007508)</sup> In the single-scattering picture, the oscillations are written as a sum over coordination shells:<sup>[8](https://docs.xrayabsorption.org/tutorials/XAFS_Fundamentals.pdf)</sup>

\[ \chi(k) = \sum_{j} \frac{N_{j} S_{0}^{2} f_{j}(k)}{k R_{j}^{2}} e^{-2R_{j}/\lambda(k)} e^{-2k^{2}\sigma_{j}^{2}} \sin\left[2kR_{j} + \delta_{j}(k)\right] \]

Here \( N_{j} \) 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.<sup>[8](https://docs.xrayabsorption.org/tutorials/XAFS_Fundamentals.pdf)</sup> 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.<sup>[9](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.11.4836)</sup>

## How it is done

Most 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.<sup>[1](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c)</sup> [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.<sup>[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)</sup>

Data 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.<sup>[3](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf)</sup><sup> • </sup><sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup> The resulting \( \tilde{\chi}(R) \) resembles a pair distribution function that is interpreted to yield quantitative local-structure information.<sup>[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)</sup><sup> • </sup><sup>[11](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=915832)</sup>

Fitting 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.<sup>[12](https://docs.xrayabsorption.org/Workshops/APS2009/Ravel_advanced_topics.pdf)</sup>

Modern XAFS practice is dominated by synchrotron beamlines, where transmission or fluorescence detection is chosen to match the sample.<sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup> Laboratory XAFS instruments are gaining popularity as cost-effective alternatives with unlimited availability compared with synchrotron beam time.<sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup> 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.<sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup>

## Origin

Theories 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".<sup>[13](https://journals.iucr.org/s/issues/2001/02/00/hi5548/hi5548.pdf)</sup> 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.<sup>[14](https://onlinelibrary.wiley.com/doi/10.1002/anie.199400451)</sup>

The 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.<sup>[6](https://doi.org/10.1103/physrevlett.27.1204)</sup> Applied to germanium, the technique located first and second neighbors in amorphous Ge at the crystalline distance within the 1% measurement accuracy.<sup>[6](https://doi.org/10.1103/physrevlett.27.1204)</sup>

## Variants

**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.<sup>[15](https://pubs.acs.org/chreay/article/121/2/882/385251/In-Situ-Operando-Electrocatalyst-Characterization)</sup>

**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<sup>[15](https://pubs.acs.org/chreay/article/121/2/882/385251/In-Situ-Operando-Electrocatalyst-Characterization)</sup><sup> • </sup><sup>[16](https://doi.org/10.1016/0921-4526%2889%2990306-2)</sup> and, for full transmission-mode EXAFS spectra, at sub-second level.<sup>[17](https://pmc.ncbi.nlm.nih.gov/articles/PMC7285694/)</sup> Fluorescence-detected QEXAFS extends quick-scanning to dilute samples where transmission is not feasible.<sup>[17](https://pmc.ncbi.nlm.nih.gov/articles/PMC7285694/)</sup>

**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.<sup>[18](https://pubs.rsc.org/en/content/articlepdf/2014/cp/c4cp00904e)</sup>

## Applications

EXAFS 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.<sup>[15](https://pubs.acs.org/chreay/article/121/2/882/385251/In-Situ-Operando-Electrocatalyst-Characterization)</sup> 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.<sup>[2](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)</sup>

## Limitations and alternatives

For 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%.<sup>[5](https://www.hyomen.org/wp-content/uploads/papers/vol5_no4/asakura/asakura_86.pdf)</sup><sup> • </sup><sup>[4](https://arxiv.org/pdf/1312.5295)</sup>

Several 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.<sup>[5](https://www.hyomen.org/wp-content/uploads/papers/vol5_no4/asakura/asakura_86.pdf)</sup> 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.<sup>[19](https://pubs.acs.org/jpccck/article/130/37/12975/5422125/Recovering-High-Temperature-EXAFS-Despite-Debye)</sup> Neighboring atoms with similar atomic number cannot be distinguished: C, N, and O, or S and Cl, or Mn and Fe.<sup>[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)</sup> 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.<sup>[20](https://www.cell.com/matter/pdf/S2590-2385%2823%2900466-6.pdf)</sup>

Against 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.<sup>[20](https://www.cell.com/matter/pdf/S2590-2385%2823%2900466-6.pdf)</sup>

## References

1. [X-ray absorption spectroscopy, a beginner's guide (IOPscience)](https://google.iopscience.iop.org/article/10.1088/2515-7655/ae6e6c)
2. [X-ray absorption spectroscopy (Primer, Chantler & Diaz-Moreno 2024)](https://www.ph.unimelb.edu.au/~chantler/opticshome/xrayopt/ChantlerDiaz-Moreno2024.pdf)
3. [Fundamentals of XAFS (Newville, Reviews in Mineralogy and Geochemistry 78)](https://millenia.cars.aps.anl.gov/xraylarch/downloads/2018Workshop/NewvilleEXAFS_RIMG78_ColorPreprint.pdf)
4. [The historical development of X-ray Absorption Fine Spectroscopy and of its applications to Materials Science](https://arxiv.org/pdf/1312.5295)
5. [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)
6. [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)
7. [EXAFS: theory and approaches](https://doi.org/10.1107/s1574870720007508)
8. [Fundamentals of XAFS](https://docs.xrayabsorption.org/tutorials/XAFS_Fundamentals.pdf)
9. [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)
10. [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)
11. [Quantitative EXAFS Analysis (NIST)](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=915832)
12. [Advanced Topics in EXAFS Analysis](https://docs.xrayabsorption.org/Workshops/APS2009/Ravel_advanced_topics.pdf)
13. [Musings about the development of XAFS (E. A. Stern, personal recollection)](https://journals.iucr.org/s/issues/2001/02/00/hi5548/hi5548.pdf)
14. [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)
15. [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)
16. [QEXAFS: X-ray absorption studies seconds (Physica B Condensed Matter, 1989)](https://doi.org/10.1016/0921-4526%2889%2990306-2)
17. [Fluorescence-detected quick-scanning X-ray absorption spectroscopy](https://pmc.ncbi.nlm.nih.gov/articles/PMC7285694/)
18. [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)
19. [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)
20. [S2590 2385(23)00466 6 (cell.com)](https://www.cell.com/matter/pdf/S2590-2385%2823%2900466-6.pdf)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Physics methods, practice, and community › X-ray diffraction and spectroscopy*

*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*

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