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X-ray absorption fine structure (XAFS) is a specific structure observed in X-ray absorption spectroscopy (XAS). By analyzing the XAFS, information can be acquired on the local structure and on the unoccupied local electronic states.

Atomic spectra

The atomic X-ray absorption spectrum (XAS) of a core-level in an absorbing atom is separated into states in the discrete part of the spectrum called "bounds final states" or "Rydberg states" below the ionization potential (IP) and "states in the continuum" part of the spectrum above the ionization potential due to excitations of the photoelectron in the vacuum. Above the IP the absorption cross section attenuates gradually with the X-ray energy. Following early experimental and theoretical works in the thirties,^[1] in the sixties using synchrotron radiation at the National Bureau of Standards it was established that the broad asymmetric absorption peaks are due to Fano resonances above the atomic ionization potential where the final states are many body quasi-bound states (i.e., a doubly excited atom) degenerate with the continuum.^[2]

Spectra of molecules and condensed matter

The XAS spectra of condensed matter are usually divided in three energy regions:

Edge region

The edge region usually extends in a range of few eV around the absorption edge. The spectral features in the edge region i) in good metals are excitations to final delocalized states above the Fermi level; ii) in insulators are core excitons below the ionization potential; iii) in molecules are electronic transitions to the first unoccupied molecular levels above the chemical potential in the initial states which are shifted into the discrete part of the core absorption spectrum by the Coulomb interaction with the core hole. Multi-electron excitations and configuration interaction between many body final states dominate the edge region in strongly correlated metals and insulators. For many years the edge region was referred to as the “Kossel structure” but now it is known as "absorption edge region" since the Kossel structure refers only to unoccupied molecular final states which is a correct description only for few particular cases: molecules and strongly disordered systems.

X-ray Absorption Near Edge Structure

The XANES energy region^[3] extends between the edge region and the EXAFS region over a 50-100 eV energy range around the core level x-ray absorption threshold. Before 1980 the XANES region was wrongly assigned to different final states: a) unoccupied total density of states, or b) unoccupied molecular orbitals (kossel structure) or c) unoccupied atomic orbitals or d) low energy EXAFS oscillations. In the seventies, using synchrotron radiation in Frascati and Stanford synchrotron sources, it was experimentally shown that the features in this energy region are due to multiple scattering resonances of the photoelectron in a nanocluster of variable size. Antonio Bianconi in 1980 invented the acronym XANES to indicate the spectral region dominated by multiple scattering resonances of the photoelectron in the soft x-ray range^[4] and in the hard X-ray range.^[5] In the XANES energy range the kinetic energy of the photoelectron in the final state is between few eV and 50-100 eV. In this regime the photoelectron has a strong scattering amplitude by neighboring atoms in molecules and condensed matter, its wavelength is larger than interatomic distances, its mean free path could be smaller than one nanometer and finally the lifetime of the excited state is in the order of femtoseconds. The XANES spectral features are described by full multiple scattering theory proposed in the early seventies.^[6] Therefore, the key step for XANES interpretation is the determination of the size of the atomic cluster of neighbor atoms, where the final states are confined, which could range from 0.2 nm to 2 nm in different systems. This energy region has been called later (in 1982) also near-edge X-ray absorption fine structure (NEXAFS), which is synonymous with XANES. During more than 20 years the XANES interpretation has been object of discussion but recently there is agreement that the final states are "multiple scattering resonances" and many body final states play an important role.^[7]

Intermediate region

There is an intermediate region between the XANES and EXAFS regions where low n-body distribution functions play a key role.^[8]^[9]^[10]

Extended X-ray absorption fine structure

The oscillatory structure extending for hundreds of electron volts past the edges was called the “Kronig structure” after the scientist, Ralph Kronig, who assigned this structure in the high energy range ( i.e., for a kinetic energy range - larger than 100 eV - of the photoelectron in the weak scattering regime) to the single scattering of the excited photoelectron by neighbouring atoms in molecules and condensed matter.^[11]^[12]^[13]^[14]^[15] This regime was called EXAFS in 1971 by Sayers, Stern and Lytle. ^[16] ^[17] and it developed only after the use of intense synchrotron radiation sources.

Applications of x-ray absorption spectroscopy

X-ray absorption edge spectroscopy corresponds to the transition from a core-level to an unoccupied orbital or band and mainly reflects the electronic unoccupied states. EXAFS, resulting from the interference in the single scattering process of the photoelectron scattered by surrounding atoms, provides information on the local structure. Information on the geometry of the local structure is provided by the analysis of the multiple scattering peaks in the XANES spectra. The XAFS acronym has been later introduced to indicate the sum of the XANES and EXAFS spectra.

References

^ Fano, Ugo (1935). "Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d'arco". Il Nuovo Cimento (in Italian). 12 (3). Springer Science and Business Media LLC: 154–161. doi:10.1007/bf02958288. ISSN 0029-6341. S2CID 119640917.
^ FANO, U.; COOPER, J. W. (1968-07-01). "Spectral Distribution of Atomic Oscillator Strengths". Reviews of Modern Physics. 40 (3). American Physical Society (APS): 441–507. doi:10.1103/revmodphys.40.441. ISSN 0034-6861.
^ D. C. Koningsberger, R. Prins (eds) A. Bianconi "X-ray absorption: Principles, applications, techniques of EXAFS, SEXAFS and XANES" (Chemical Analysis 92), Wiley, New York (1988) pp 573-662 ISBN 978-0-471875475
^ Bianconi, Antonio (1980). "Surface X-ray absorption spectroscopy: Surface EXAFS and surface XANES". Applications of Surface Science. 6 (3–4). Elsevier BV: 392–418. doi:10.1016/0378-5963(80)90024-0. ISSN 0378-5963.
^ Belli, M.; Scafati, A.; Bianconi, A.; Mobilio, S.; Palladino, L.; Reale, A.; Burattini, E. (1980). "X-ray absorption near edge structures (XANES) in simple and complex Mn compounds". Solid State Communications. 35 (4). Elsevier BV: 355–361. doi:10.1016/0038-1098(80)90515-3. ISSN 0038-1098.
^ Dehmer, J. L.; Dill, Dan (1975-07-28). "Shape Resonances in K-Shell Photoionization of Diatomic Molecules". Physical Review Letters. 35 (4). American Physical Society (APS): 213–215. doi:10.1103/physrevlett.35.213. ISSN 0031-9007.
^ Rehr, J.J.; Ankudinov, A.L. (2005). "Progress in the theory and interpretation of XANES". Coordination Chemistry Reviews. 249 (1–2). Elsevier BV: 131–140. doi:10.1016/j.ccr.2004.02.014. ISSN 0010-8545.
^ Benfatto, M.; Natoli, C. R.; Bianconi, A.; Garcia, J.; Marcelli, A.; et al. (1986-10-15). "Multiple-scattering regime and higher-order correlations in x-ray-absorption spectra of liquid solutions". Physical Review B. 34 (8). American Physical Society (APS): 5774–5781. doi:10.1103/physrevb.34.5774. ISSN 0163-1829. PMID 9940417.
^ Filipponi, Adriano; Di Cicco, Andrea; Natoli, Calogero Renzo (1995-12-01). "X-ray-absorption spectroscopy and n-body distribution functions in condensed matter. I. Theory". Physical Review B. 52 (21). American Physical Society (APS): 15122–15134. doi:10.1103/physrevb.52.15122. ISSN 0163-1829. PMID 9980866.
^ Filipponi, Adriano; Di Cicco, Andrea (1995-12-01). "X-ray-absorption spectroscopy andn-body distribution functions in condensed matter. II. Data analysis and applications". Physical Review B. 52 (21). American Physical Society (APS): 15135–15149. doi:10.1103/physrevb.52.15135. ISSN 0163-1829. PMID 9980867.
^ Rehr, J. J.; Albers, R. C. (2000-07-01). "Theoretical approaches to x-ray absorption fine structure". Reviews of Modern Physics. 72 (3). American Physical Society (APS): 621–654. doi:10.1103/revmodphys.72.621. ISSN 0034-6861.
^ de Groot, Frank (2001). "High-Resolution X-ray Emission and X-ray Absorption Spectroscopy". Chemical Reviews. 101 (6). American Chemical Society (ACS): 1779–1808. doi:10.1021/cr9900681. hdl:1874/386323. ISSN 0009-2665. PMID 11709999. S2CID 44020569.
^ X-ray Absorption: principles, applications and techniques of EXAFS, SEXAFS and XANES, edited by D.C. Koeningsberger, R. Prins, John Wiley & Sons 1988.
^ Principles and Applications of EXAFS, Chapter 10 in Handbook of Synchrotron Radiation, pp 995–1014. E. A. Stern and S. M. Heald, E. E. Koch, ed., North-Holland, 1983.
^ B.-K. Teo, EXAFS: basic principles and data analysis, Springer 1986
^ Sayers, Dale E.; Stern, Edward A.; Lytle, Farrel W. (1971-11-01). "New Technique for Investigating Noncrystalline Structures: Fourier Analysis of the Extended X-Ray—Absorption Fine Structure". Physical Review Letters. 27 (18). American Physical Society (APS): 1204–1207. doi:10.1103/physrevlett.27.1204. ISSN 0031-9007.
^ Lytle, Farrel W. (1999-05-01). "The EXAFS family tree: a personal history of the development of extended X-ray absorption fine structure". Journal of Synchrotron Radiation. 6 (3). International Union of Crystallography (IUCr): 123–134. doi:10.1107/s0909049599001260. ISSN 0909-0495. PMID 15263225.