Extended X-ray absorption fine structure

In the X-ray fluorescence spectrum of tin, as in those of other elements, transitions such as 3d l.s and 4 7 l.v, which are forbidden by the selection rules, may be observed very weakly due to perturbations by neighbouring atoms. 

A feature of L spectra of atoms with Z 40 is the absence of the (32 transition, which is intense in atoms, such as gold, with higher atomic numbers. 

In atoms in which electrons in M or N shells take part to some extent in molecular orbital formation some transitions in the L spectrum may be broadened. Similarly, in an M emission spectrum, in which the initial vacancy has been created in the M shell, there is a greater tendency towards broadening due to molecular orbital involvement. 

As early as the 1930s X-ray absorption experiments were being carried out using a continuum source of X-rays (the bremsstrahlung mentioned in Section 8.1.1.1), a dispersive 

This is similar to Equation (2.16) in which 70 and I are the intensities of the incident and transmitted radiation, respectively, and l is the pathlength of the absorbing sample. 

The EXAFS technique exploits the absorption edges observed when the energy of an 

X-ray beam incident upon a sample coincides with the energy required to eject 

X-ray absorption spectrum for the Fe(n) caperone protein yeast frataxin. The X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) regions are labeled. Reprinted from [71]. Copyright 2007 John Wiley Sons. 

The EXAFS experiment simply involves measuring the absorption spectrum in the vicinity of the absorption edge for the chosen element. This, of course, is easier said than done. A high-intensity, tunable X-ray source is required, and in practice almost aU experiments use synchrotron radiation, which gives useful spectra for solids, liquids or concentrated solutions in a few minutes. The K edges of elements down to about phosphorus or sulfur can be smdied by this method, and typically spectroscopy at the L edges is used for elements heavier than indium (Z = 49). For lighter elements, down to carbon, a laser-produced plasma can 

The EXAFS intensity oscillations are described by Eq. 10.19, which gives the relative modulation, X, of the absorption coefficient, fi, of the atom as a function of the variable k (the photoelectron wave vector). 

Note that the form of Eq. 10.19 is analogous to that used to describe diffraction of electrons by gases (Eq. 10.4), with the variable k in one equivalent to s in the other, and so the principles of analysis are much the 

X-ray absorption spectrum (Co K edge) of the dicobalt complex [CpCoPPh2]2. Redrawn with permission from [73]. Copyright 1978 American Chemical Society. 

In order to go further in describing the local structure around zirconium in the melt. X-ray absorption experiments were performed at the Zr K-edge to be compared with the NMR results. 

The authors thank the Program CNRS-PACEN and more precisely the PCR ANSF for financial support. L.M. acknowledges the Region Centre council for his doctoral grant. 

and Chung, K.M. (2001) AMBIDEXTER nuclear energy complex a practicahle approach for rekindhng nuclear energy apphcation. Nucl. Eng. Des, 207(1), 11-19. 

Kimura, I. (1995) Review of cooperative research on thorium fuel cycle as a promising energy source in the next century. Prog. Nucl. Energy, 29(Suppl), 445-452. 

Delpech, S., Merle-Lucotte, E., Heuer, D. et al. (2009) Reactor physic and reprocessing scheme for innovative molten salt reactor system. /. Eluorine Chem, 130(1), 11-17. 

Site selectivity in many applications of X-ray spectroscopy was stressed in section 11.2 the different absorption edges are often widely separated in energy by a broad band of continuum states containing rather little atomic structure. This allows one to study the immediate surroundings of specific atoms. 

For excitation from core states of atoms to a final continuum state in the solid, an important observation is the occurrence of quasiperiodic modulations in the intensity of the observed continuous spectrum. These modulations are readily explained as arising from interference between the wave of the escaping electron, and a backscattering off the nearest neighbour atoms. They are called extended X-ray absorption fine structure or EXAFS for short. They are very important, because they can be rather simply analysed to yield the distance between the atom on which the core excitation has taken place and its nearest neihbours. There is an extensive literature on this technique [643] which is a very powerful one, since it can be applied to all kinds of compounds each atom has its own particular, quasiatomic core states, and so the method is atom-specific. The only complication is when the same atom can occupy two different sites with different nearest neighbours. 

6 k) is the phase shift associated with a reflected wave from the nearest neighbour atoms  

The superposition of the outgoing and incoming waves alters the wave function of the photoelectron at the site of the given emitter. The final state wave function, /), becomes q + (psc) where (pe and (pscSXQ the emitted and scattered wave functions. The photoelectron absorption process involves the final state wave function and the quantum mechanical expression for the X-ray absorption coefficient is given by. 

Theoretical expression for xih) was derived by Sayers et al. (1971) using single scattering formalism and back scattering of planar waves from shells of atoms surrounding a given emitter and it is given by. 

One of the serious limitations of EXAFS technique is with regard to phase parameters. These are quite generally obtained from analysis of EXAFS of crystalline compounds of known structure. In order that such phase information be transferable, the structure around the given atom should be very similar. This admittedly is a weakness because the structure of the glass is clearly unknown. Further use of these phase parameters in fitting the experimental EXAFS of a glass imposes a genetic influence on the structure in the sense that it tries to fit the EXAFS of unknown with as many subshells of atoms (as many sets of phase parameters) as there are in the model crystalline compound. 

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EXAFS Extended X-ray absorption fine structure spectroscopy. A spectroscopic technique which can determine interatomic distances very precisely. 

EXAFS Extended x-ray absorption fine structure [177, 178] Variation of x-ray absorption as a function of x-ray energy beyond an absorption edge the probability is affected by backscattering of the emitted electron from adjacent atoms Number and interatomic distance of surface atoms... 

Lee P A, Citrin P H, Eisenberger P and Kincaid B M 1981 Extended x-ray absorption fine structure—its strengths and limitations as a structural tool Rev. Mod. Rhys. 53 769-806... 

Stdhr J, Kollin E B, Fischer D A, Flastings J B, Zaera F and Sette F 1985 Surface extended x-ray-absorption fine structure of low-Z adsorbates studied with fluorescence detection Rhys. Rev. Lett. 55 1468-71... 

Ingalls R, Crozier E D, Whitmore J E, Seary A J and Tranquada J M 1980 Extended x-ray absorption fine structure of sodium bromide and germanium at high pressure J. Appl. Phys. 51 3158... 

Figure 8.34 Experimental method for extended X-ray absorption fine structure (EXAFS)...

Figure 8.38 Curve fitting of Mo extended X-ray absorption fine structure (EXAFS) for Mo(SC6H4NH)3, taking into account (a) sulphur and (b) sulphur and nitrogen atoms as near neighbours. (Reproduced, with permission, trom Winnick, H. and Doniach, S. (Eds), Synchrotron Radiation Research, p. 436, Plenum, New York, 1980)...

Surface Extended X-Ray Absorption Fine Structure and Near Edge X-Ray Absorption Fine Structure (SEXAFS/NEXAFS)... 

This chapter contains articles on six techniques that provide structural information on surfaces, interfeces, and thin films. They use X rays (X-ray diffraction, XRD, and Extended X-ray Absorption Fine-Structure, EXAFS), electrons (Low-Energy Electron Diffraction, LEED, and Reflection High-Energy Electron Diffraction, RHEED), or X rays in and electrons out (Surfece Extended X-ray Absorption Fine Structure, SEXAFS, and X-ray Photoelectron Diffraction, XPD). In their usual form, XRD and EXAFS are bulk methods, since X rays probe many microns deep, whereas the other techniques are surfece sensitive. There are, however, ways to make XRD and EXAFS much more surfece sensitive. For EXAFS this converts the technique into SEXAFS, which can have submonolayer sensitivity. 

Alternatives to XRD include transmission electron microscopy (TEM) and diffraction, Low-Energy and Reflection High-Energy Electron Diffraction (LEED and RHEED), extended X-ray Absorption Fine Structure (EXAFS), and neutron diffraction. LEED and RHEED are limited to surfaces and do not probe the bulk of thin films. The elemental sensitivity in neutron diffraction is quite different from XRD, but neutron sources are much weaker than X-ray sources. Neutrons are, however, sensitive to magnetic moments. If adequately large specimens are available, neutron diffraction is a good alternative for low-Z materials and for materials where the magnetic structure is of interest. 

The discovery of the phenomenon that is now known as extended X-ray absorption fine structure (EXAFS) was made in the 1920s, however, it wasn t until the 1970s that two developments set the foundation for the theory and practice of EXAFS measurements. The first was the demonstration of mathematical algorithms for the analysis of EXAFS data. The second was the advent of intense synchrotron radiation of X-ray wavelengths that immensely facilitated the acquisition of these data. During the past two decades, the use of EXAFS has become firmly established as a practical and powerfiil analytical capability for structure determination. ... 

SEXAFS Surface Extended X-Ray Absorption Fine Structure... 

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