EXAFS function

Figure 4 The EXAFS function X( )> weighted by 1, experimentei dete for % monoleyer...

However, mathematics is essential to explain how structural data are derived from EXAFS. The EXAFS function, x(k), is extracted from the X-ray absorption spectrum in Fig. 4.10 by removing the approximately parabolic background and the step, i.e. the spectrum of the free atom. As in any scattering experiment, it is customary to express the signal as a function of the wavenumber, k, rather than of energy. The relation between k and the kinetic energy of the photoelectron is ... 

In a mono-atomic solid, the EXAFS function x k) is the sum of the scattering contributions of all atoms in neighboring coordination shells ... 

In the analysis of EXAFS data on bimetallic clusters, we consider two EXAFS functions, one for each component of the clusters (8,12-15.17). If the treatment is limited to contributions of near-est neighbor backscattering atoms, each of the functions will consist of two terms. For a bimetallic cluster composed of elements a and b, the EXAFS associated with element a is given by the expression ... 

In these expressions, the subscript outside the braces identifies the absorber atom, while the superscript identifies the backscattering atom. The contribution xjfK) of one type of backscattering atom to the total EXAFS function is given by the equation ... 

Fig. 5 XANES region, -weighted Fourier transformed of the raw EXAFS functions and the corresponding first shell filtered, Fourier back transform (a, b and c, respectively) of TS-1 activated at 400 °C (full lines), after interaction with water (wet sample, dashed lines) and after interaction with NH3 (Pnh3 = 50 Torr, dotted lines). Adapted from [64] with permission. Copyright (2002) by the ACS...

Figure 6.11 Absorption of X-rays as a function of photon energy E=hv by a free atom and by atoms in a lattice. The fine structure represents the EXAFS function.

The EXAFS function becomes understandable if we look at the Fourier transform of x(k), which resembles a radial distribution function ... 

Extract the EXAFS function %(k) from measured data. 

Figure 1.3 Left. Detailed view of the Nb K-edge XANES data of a pyridine salt of niobium-exchanged molybdo(vanado)phosphoric acid (NbPMo fVJpry) as a function of temperature [31]. A change in niobium oxidation state, from Nb5+ to Nb4+, is identified between 350 and 420°C by a relative increase in absorption about 19.002 keV, and can be connected with the activation of the catalyst for light alkane oxidation. Right. Radial Fourier-transform EXAFS function for the NbPMo (V)pyr sample heated to 420°C [31 ]. The two peaks correspond to the Nb-O (1.5 A) and Nb-Mo (3 A) distances in the heteropolymolybdate fragments presumed to be the active phase for alkane oxidation. (Reproduced with permission from Elsevier.)...

CO and particle size, 39 159 CO on zeolite-encaged metal, 39 158 EXAFS functions, 39 155-157 Pd particle location and size, 39 155-158... 

Figure 15.8 Fourier transform of Pt 7 -weighted EXAFS functions x k) for (a) Pt nanowire/FSM-16 (b) Pt nanoparticle/FSM-16 (c) Ptfoil.

Figure 15.12 (a) Fourier transforms of Pt P-weighted EXAFS functions x(k) for a HjPtCle/HMM-l sample with MeOH/HjO under the UV-irradiation forO, 4, 8, 12, 24 and 48h at 300 K, and Pt foil (b) changes of coordination numbers for Pt-Pt (red line) and... 

The EXAFS function is obtained from the X-ray absorption spectrum by subtracting the absorption due to the free atom. A Fourier transform of the EXAFS data gives a radial distribution function which shows the distribution of the neighbouring atoms as a function of internuclear distance from the absorbing atom. Shells of neighbours, known as coordination shells, surround the absorbing atom. Finally, the radial distribution function is fitted to a series of trial structural models until a structure which best fits the... 

There are two primary tasks in data analysis first, to extract the EXAFS function, %(k), from the px vs E data, second to determine the structural... 

In a monoatomic solid, each shell gives rise to a characteristic interference. This is expressed as follows in the EXAFS function %(fc) ... 

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