Functional EXAFS

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... 

EXAFS data are multiplied by ( = 1, 2, or 3) to compensate for amplitude attenuation as a function of k, and are normalized to the magnitude of the edge jump. Normalized, background-subtracted EXAFS data, versus k (such as... 

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

Figure 4.1-11 The EXAFS data and pseudo-radial distribution functions of Co(ll) in (a) basic and (b) acidic chloroaluminate ionic liquid. Reproduced from reference 46 with permission.

Figure 4.1-13 Comparison of the experimental without (—) and with (—) triphenylphosphine at (solid line) and fitted (dashed line) (a) EXAFS 80 °C and in the presence of triphenylphosphine and (b) pseudo-radial distribution functions and reagents at 50 °C for 20 min (—). Repro-...

Allen GC, Warren KD (1974) The Electronic Spectra of the Hexafluoro Complexes of the Second and Third Transition Series. 19 105-165 Alonso JA, Baibas LC (1993) Hardness of Metallic Clusters. 80 229-258 Alonso JA, Baibas LC (1987) Simple Density Functional Theory of the Electronegativity and Other Related Properties of Atoms and Ions. 66 41-78 Andersson LA, Dawson JH (1991) EXAFS Spectroscopy of Heme-Containing Oxygenases and Peroxidases. 74 1-40 Antanaitis BC, see Doi K (1988) 70 1-26... 

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 ... 

The essence of analyzing an EXAFS spectrum is to recognize all sine contributions in x(k)- The obvious mathematical tool with which to achieve this is Fourier analysis. The argument of each sine contribution in Eq. (8) depends on k (which is known), on r (to be determined), and on the phase shift

characteristic property of the scattering atom in a certain environment, and is best derived from the EXAFS spectrum of a reference compound for which all distances are known. The EXAFS information becomes accessible, if we convert it into a radial distribution function, 0 (r), by means of Fourier transformation ... 

Figure 4.11. Left Simulated EXAFS spectrum of a dimer such as Cu2, showing that the EXAFS signal is the product of a sine function and a backscattering amplitude F(k) divided by k, as expressed by Eq. (6). Note that F k)/k remains visible as the envelope around the EXAFS signal xW- Right The Cu EXAFS spectrum of a cluster such as CU2O is the sum of a Cu-Cu and a Cu-O contribution. Fourier analysis is the mathematical tool used to...

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 ... 

The copper EXAFS of the ruthenium-copper clusters might be expected to differ substantially from the copper EXAFS of a copper on silica catalyst, since the copper atoms have very different environments. This expectation is indeed borne out by experiment, as shown in Figure 2 by the plots of the function K x(K) vs. K at 100 K for the extended fine structure beyond the copper K edge for the ruthenium-copper catalyst and a copper on silica reference catalyst ( ). The difference is also evident from the Fourier transforms and first coordination shell inverse transforms in the middle and right-hand sections of Figure 2. The inverse transforms were taken over the range of distances 1.7 to 3.1A to isolate the contribution to EXAFS arising from the first coordination shell of metal atoms about a copper absorber atom. This shell consists of copper atoms alone in the copper catalyst and of both copper and ruthenium atoms in the ruthenium-copper catalyst. 

Figure 3. Comparison of EXAFS envelope functions derived from the inverse transforms in Figure 2 for silica supported copper and ruthenium-copper catalysts. Reproduced with permission from Ref. 8. Copyright 1980, American Institute of Physics.

The extended fine structure (EXAFS) was used to determine bond distances, coordination number and disorder. The near edge (XANES) was used as an Indication of electronic state. Significant results Include, 1) a reversible change of shape of clean supported metal clusters as a function of temperature, 2) supported Pt clusters have more disorder or strain compared to the bulk metal, and 3) a clear determination of the bonds between the catalytic metal atoms and the oxygen atoms of the support. 

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...

Calculations on the basis of density functional theory have been used to check the structure of Rh clusters supported on zeolite X the results indicate a slightly twisted prism, nearly matching the octahedron inferred on the basis of the EXAFS data [28,29]. (These clusters were inferred not to be bare but to have hydride ligands, as described later). 

Fig. 3 Ir4 cluster supported at the six-ring of zeolite NaX as represented by density functional theory samples were characterized by Extended X-ray absorption fine structure (EXAFS) spectroscopy and other techniques [32]...

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