Editing Extended X-ray absorption fine structure

{{short description|Measurement of X-ray absorption of a material as a function of energy}}
{{Technical |date=June 2019}}

[[File:XASFig.jpg|thumb|Three regions of XAS data|440x440px]] '''Extended X-ray absorption fine structure''' ('''EXAFS'''), along with X-ray absorption near edge structure ([[XANES]]), is a subset of X-ray absorption spectroscopy ([[X-ray absorption spectroscopy|XAS]]). Like other [[absorption spectroscopy|absorption spectroscopies]], XAS techniques follow [[Beer–Lambert law|Beer's law]]. The [[X-ray]] [[absorption coefficient]] of a material as a function of energy is obtained by directing X-rays of a narrow energy range at a sample, while recording the incident and transmitted x-ray intensity, as the incident x-ray energy is incremented.

When the incident x-ray energy matches the [[binding energy]] of an [[electron]] of an atom within the sample, the number of x-rays absorbed by the sample increases dramatically, causing a drop in the transmitted x-ray intensity. This results in an absorption edge. Every element has a set of unique absorption edges corresponding to different binding energies of its electrons, giving XAS element selectivity. XAS spectra are most often collected at [[synchrotron]]s because the high intensity of synchrotron X-ray sources allows the concentration of the absorbing element to reach as low as a few parts per million. Absorption would be undetectable if the source were too weak. Because X-rays are highly penetrating, XAS samples can be gases, solids or liquids.

==Background==

EXAFS [[Absorption spectrum|spectra]] are displayed as plots of the absorption coefficient of a given material versus [[energy]], typically in a 500 – 1000 [[Electron volt|eV]] range beginning before an [[absorption edge]] of an element in the sample. The x-ray absorption coefficient is usually normalized to unit step height. This is done by regressing a line to the region before and after the absorption edge, subtracting the pre-edge line from the entire data set and dividing by the absorption step height, which is determined by the difference between the pre-edge and post-edge lines at the value of E0 (on the absorption edge).

The normalized absorption spectra are often called [[XANES]] spectra. These spectra can be used to determine the average oxidation state of the element in the sample. The XANES spectra are also sensitive to the coordination environment of the absorbing atom in the sample.  Finger printing methods have been used to match the XANES spectra of an unknown sample to those of known "standards". Linear combination fitting of several different standard spectra can give an estimate to the amount of each of the known standard spectra within an unknown sample.

The dominant physical process in x-ray absorption is one where the absorbed photon ejects a core [[photoelectron]] from the absorbing atom, leaving behind a core hole.<ref>{{cite journal |last1=Glatzel |first1=Pieter |last2=Bergmann |first2=Uwe |title=High resolution 1s core hole X-ray spectroscopy in 3d transition metal complexes—electronic and structural information |journal=Coordination Chemistry Reviews |date=2005 |volume=249 |issue=1-2 |pages=65-95 |doi=10.1016/j.ccr.2004.04.011 |url=https://www.sciencedirect.com/science/article/pii/S0010854504001146|url-access=subscription }}</ref> The ejected photoelectron's energy will be equal to that of the absorbed photon minus the [[binding energy]] of the initial core state. The atom with the core hole is now excited and the ejected photoelectron interacts with electrons in the surrounding non-excited atoms.

<!-- Image with unknown copyright status removed: [[Image:EXAFS.png|thumb|300px|right|Schematics of the EXAFS process illustrating the origin of EXAFS oscillations due to the interference of outgoing and backscattered photoelectron wave.<ref>[http://www.p-ng.si/~arcon/xas/exafs/exafs.htm Extended X-Ray Absorption Fine Structure, Dr. Alojz Kodre ''et al.'']</ref>]] -->If the ejected photoelectron is taken to have a [[wave]]-like nature and the surrounding atoms are described as point scatterers, it is possible to imagine the [[backscatter]]ed electron waves interfering with the forward-propagating waves. The resulting interference pattern shows up as a [[modulation]] of the measured absorption coefficient, thereby causing the oscillation in the EXAFS spectra. A simplified plane-wave single-scattering theory has been used for interpretation of EXAFS spectra for many years, although modern methods (like FEFF, GNXAS) have shown that curved-wave corrections and multiple-scattering effects can not be neglected. The photelectron scattering amplitude in the low energy range (5-200 eV) of the photoelectron kinetic energy  become much larger so that multiple scattering events become dominant in the [[XANES]]  (or NEXAFS) spectra.

The [[wavelength]] of the photoelectron is dependent on the energy and phase of the backscattered wave which exists at the central atom. The wavelength changes as a function of the energy of the incoming photon. The [[phase (waves)|phase]] and [[amplitude]] of the backscattered wave are dependent on the type of atom doing the backscattering and the distance of the backscattering atom from the central atom. The dependence of the scattering on atomic species makes it possible to obtain information pertaining to the chemical coordination environment of the original absorbing (centrally excited) atom by analyzing these EXAFS data.

=== EXAFS Equation ===

[[File:EXAFS scattering cartoon.png|thumb|350px|Cartoon of the photoelectron scattering process.]]

The effect of the backscattered photoelectron on the absorption spectra is described by the EXAFS equation, first demonstrated by Sayers, Stern, and Lytle.<ref>{{cite journal | last1=Sayers | first1=Dale E. | last2=Stern | first2=Edward A. | last3=Lytle | first3=Farrel W. | title=New Technique for Investigating Noncrystalline Structures: Fourier Analysis of the Extended X-Ray—Absorption Fine Structure | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=27 | issue=18 | date=1 October 1971 | issn=0031-9007 | doi=10.1103/physrevlett.27.1204 | pages=1204–1207| bibcode=1971PhRvL..27.1204S }}</ref> The oscillatory part of the dipole matrix element is given by <math>\chi(k)</math>, where the sum is over the <math>j</math> sets of neighbors of the absorbing atom, <math>N_j</math> is the number of atoms at distance <math>R_j</math>, <math>k</math> is the [[wavenumber]] and is proportional to energy, <math>\sigma</math> is the thermal vibration factor with <math>\sigma_{j}^2</math> being the mean square amplitude of the atom's relative displacements, <math>\lambda(k)</math> is the mean free path of the photoelectron with momentum <math>k</math> (this is related to coherence of the quantum state), and <math>f_{j}(k)</math> is an element dependent scattering factor.

<math display="block">\chi(k) = \sum_j\frac{N_j e^{-2k^2 \sigma^2_j} e^{-2R_j / \lambda_k} f_{j}(k)}{k R^2_j}\sin[2 k R_j + \delta_{j}(k)]</math>

The origin of the oscillations in the absorption cross section are due to the <math>\sin</math> term which imposes the [[Wave interference | interference]] condition, leading to peaks in absorption when the wavelength of the photoelectron is equal to an integer fraction of <math>2R_{j}</math> (the round trip distance from the absorbing atom to the scattering atom). This is analogous to eigenstates of the [[particle in a box]] toy model. The <math>\delta_{j}</math> factor inside the <math>\sin</math> is an element dependent phase shift.

==Experimental considerations==

Since EXAFS requires a tunable x-ray source, data are frequently collected at [[synchrotron]]s, often at [[beamline]]s which are especially optimized for the purpose. The utility of a particular synchrotron to study a particular solid depends on the [[Luminosity#In scattering theory and accelerator physics|brightness]] of the x-ray flux at the absorption edges of the relevant elements.

Recent developments in the design and quality of crystal optics have allowed for some EXAFS measurements to take place in a lab setting,<ref>{{cite journal |last1=Mortensen |first1=Devon |last2=Seidler |first2=Gerald |title=Robust optic alignment in a tilt-free implementation of the Rowland circle spectrometer |journal=Journal of Electron Spectroscopy and Related Phenomena |date=2017 |volume=215 |pages=8-15 |doi=10.1016/j.elspec.2016.11.006 |url=https://www.sciencedirect.com/science/article/pii/S0368204816301025}}</ref> where the tunable x-ray source is achieved via a Rowland circle geometry. While experiments requiring high x-ray flux or specialized sample environments can still only be performed at synchrotron facilities, absorption edges in the 5 - 30 keV range are feasible for lab based EXAFS studies.<ref>{{cite journal |last1=Jahrman |first1=Evan |last2=Holden |first2=William |last3=Ditter |first3=Alexander |last4=Mortensen |first4=Devon |last5=Seidler |first5=Gerald |last6=Fister |first6=Timothy |last7=Kozimor |first7=Stosh |last8=Piper |first8=Louis |last9=Rana |first9=Jatinkumar |last10=Hyatt |first10=Neil |last11=Stennett |first11=Martin |title=An improved laboratory-based x-ray absorption fine structure and x-ray emission spectrometer for analytical applications in materials chemistry research |journal=Review of Scientific Instruments |date=2019 |volume=90 |pages=024106 |doi=10.1063/1.5049383 |url=https://pubs.aip.org/aip/rsi/article-pdf/doi/10.1063/1.5049383/15648807/024106\_1\_online.pdf}}</ref>

== Applications ==

XAS is an interdisciplinary technique and its unique properties, as compared to x-ray diffraction, have been exploited for
understanding the details of local structure in:

* [[glass]], [[amorphous]] and [[liquid]] systems
* [[solid solution]]s
* [[Doping (semiconductor)|doping]] and [[Ion implantation|ionic implantation]] of materials for [[electronics]]
* local distortions of [[crystal lattice]]s
* [[organometallic chemistry|organometallic compounds]]
* [[metalloproteins]]
* [[Cluster chemistry|metal clusters]]
* vibrational dynamics{{Citation needed|date=February 2012}}
* [[ions]] in [[Solution (chemistry)|solution]]s
* chemical speciation analysis
XAS provides complementary to diffraction information on peculiarities of local structural and thermal disorder in crystalline and multi-component materials.

The use of atomistic simulations such as [[molecular dynamics]] or the [[reverse Monte Carlo]] method can help in extracting more reliable and richer structural information.

==Examples==
EXAFS is, like [[XANES]], a highly sensitive technique with elemental specificity.  As such, EXAFS is an extremely useful way to determine the chemical state of practically important species which occur in very low abundance or concentration. Frequent use of EXAFS occurs in [[environmental chemistry]], where scientists try to understand the propagation of [[pollutant]]s through an [[ecosystem]]. EXAFS can be used along with [[accelerator mass spectrometry]] in [[forensic]] examinations, particularly in [[Nuclear weapon|nuclear]] [[non-proliferation]] applications.

==History==

A very detailed, balanced and informative account about the history of EXAFS (originally called Kossel's structures) is given by [[R. Stumm von Bordwehr]].<ref>{{Cite journal|last=Bordwehr|first=R. Stumm von|date=1989|title=A History of X-ray absorption fine structure |journal=Annales de Physique |language=en|volume=14|issue=4|pages=377–465|doi=10.1051/anphys:01989001404037700|bibcode=1989AnPh...14..377S|issn=0003-4169}}</ref>
A more modern and accurate account of the history of XAFS (EXAFS and XANES) is given by the leader of the group that developed the modern version of EXAFS in an award lecture by Edward A. Stern.<ref>{{Cite journal|last=Stern|first=Edward A.|date=2001-03-01|title=Musings about the development of XAFS|journal=Journal of Synchrotron Radiation|volume=8|issue=2|pages=49–54|doi=10.1107/S0909049500014138|pmid=11512825|issn=0909-0495|doi-access=free}}</ref>

==See also==

* [[X-ray absorption spectroscopy]]
* [[X-ray absorption near edge structure]]
* [[Surface-extended X-ray absorption fine structure]]

==References==
{{Reflist}}

==Bibliography==
=== Books ===
* {{Cite book|title=XAFS for everyone|last=Calvin, Scott.|others=Furst, Kirin Emlet.|isbn=9781439878637|location=Boca Raton|oclc=711041662|date = 2013-05-20}}
* {{Cite book|title=Introduction to XAFS : a practical guide to X-ray absorption fine structure spectroscopy|last=Bunker, Grant, 1954-|date=2010|publisher=Cambridge University Press|isbn=9780511809194|location=Cambridge|oclc=646816275}}
* {{Cite book|title=EXAFS: Basic Principles and Data Analysis|last=Teo, Boon K.|date=1986|publisher=Springer Berlin Heidelberg|isbn=9783642500312|location=Berlin, Heidelberg|oclc=851822691}}
* {{Cite book|title=X-ray absorption : principles, applications, techniques of EXAFS, SEXAFS, and XANES|date=1988|publisher=Wiley|others=Koningsberger, D. C., Prins, Roelof.|isbn=0471875473|location=New York|oclc=14904784}}

===Book chapters===
* {{cite book|last1=Kelly|first1=S. D.|title=Methods of Soil Analysis Part 5|chapter=Analysis of Soils and Minerals Using X-ray Absorption Spectroscopy|date=2008|url=https://dl.sciencesocieties.org/publications/books/abstracts/sssabookseries/methodsofsoilan5/387|work=SSSA Book Series|publisher=Soil Science Society of America|language=en|doi=10.2136/sssabookser5.5.c14|isbn=9780891188575|access-date=2019-07-16|last2=Hesterberg|first2=D.|last3=Ravel|first3=B.|last4=Ulery|first4=April L.|last5=Richard Drees|first5=L.|chapter-url=http://epsc511.wustl.edu/Kelly_XAFS_Chapter14.pdf|archive-date=2019-07-16|archive-url=https://web.archive.org/web/20190716213340/https://dl.sciencesocieties.org/publications/books/abstracts/sssabookseries/methodsofsoilan5/387|url-status=dead}}

=== Papers ===
* {{cite journal | last=Stern | first=Edward A. | title=Musings about the development of XAFS | journal=[[Journal of Synchrotron Radiation]] | publisher=International Union of Crystallography (IUCr) | volume=8 | issue=2 | date=1 February 2001 | issn=0909-0495 | doi=10.1107/s0909049500014138 | pmid=11512825 | pages=49–54| url=http://journals.iucr.org/s/issues/2001/02/00/hi5548/hi5548.pdf }}
* {{cite journal | last1=Rehr | first1=J. J. | last2=Albers | first2=R. C. | title=Theoretical approaches to x-ray absorption fine structure | journal=[[Reviews of Modern Physics]] | publisher=American Physical Society (APS) | volume=72 | issue=3 | date=1 June 2000 | issn=0034-6861 | doi=10.1103/revmodphys.72.621 | pages=621–654| bibcode=2000RvMP...72..621R }}
* {{cite journal | last1=Filipponi | first1=Adriano | last2=Di Cicco | first2=Andrea | last3=Natoli | first3=Calogero Renzo | title=X-ray-absorption spectroscopy and n-body distribution functions in condensed matter. I. Theory | journal=[[Physical Review B]] | publisher=American Physical Society (APS) | volume=52 | issue=21 | date=1 November 1995 | issn=0163-1829 | doi=10.1103/physrevb.52.15122 | pmid=9980866 | pages=15122–15134| bibcode=1995PhRvB..5215122F }}
* {{cite journal | last=de Groot | first=Frank | title=High-Resolution X-ray Emission and X-ray Absorption Spectroscopy | journal=[[Chemical Reviews]] | publisher=American Chemical Society (ACS) | volume=101 | issue=6 | year=2001 | issn=0009-2665 | doi=10.1021/cr9900681 | pmid=11709999 | pages=1779–1808| hdl=1874/386323 | s2cid=44020569 | hdl-access=free }}
* F.W. Lytle, [http://www.exafsco.com/techpapers/index.html "The EXAFS family tree: a personal history of the development of extended X-ray absorption fine structure"],
* {{cite journal | last1=Sayers | first1=Dale E. | last2=Stern | first2=Edward A. | last3=Lytle | first3=Farrel W. | title=New Technique for Investigating Noncrystalline Structures: Fourier Analysis of the Extended X-Ray—Absorption Fine Structure | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=27 | issue=18 | date=1 October 1971 | issn=0031-9007 | doi=10.1103/physrevlett.27.1204 | pages=1204–1207| bibcode=1971PhRvL..27.1204S }}
* A. Kodre, I. Arčon, Proceedings of 36th International Conference on Microelectronics, Devices and Materials, MIDEM, Postojna, Slovenia, October 28–20, (2000), p.&nbsp;191-196

==External links==
{{commons category}}
*[https://xrayabsorption.org International X-ray Absorption Society]
*[http://leonardo.phys.washington.edu/feff/ FEFF Project, University of Washington, Seattle] {{Webarchive|url=https://web.archive.org/web/20220121080247/http://leonardo.phys.washington.edu/feff/ |date=2022-01-21 }}
*[http://gnxas.unicam.it GNXAS project and XAS laboratory, Università di Camerino]
*[http://www.dragon.lv/exafs EXAFS Spectroscopy Laboratory (Riga, Latvia)]
*[https://xafs.xrayabsorption.org Community web site for XAFS]

{{Branches of Spectroscopy}}
{{Authority control}}

[[Category:X-ray absorption spectroscopy]]