EXAFS oscillation

Self-absorption occurs when the path-length is too large [35] and the X-rays emitted have a significant probability of being absorbed by the remainder of the sample before being detected. This has the consequence of reducing the amplitude of the EXAFS oscillations and producing erroneous results. As the sample becomes more dilute this probability decreases. All the atoms in the sample determine the amount of self-absorption hence the need for thin samples. 

Background removal routines typically employ polynomial splines of some order (typically second or third order). These are defined over a series of intervals with the constraint that the function and a stipulated number of derivatives be continuous at the intersection between intervals. In addition, the observed EXAFS oscillations need to be normalized to a single-atom value and this is generally done by normalizing the data to the edge jump. 

Another noteworthy example is x-ray absorption fine structure (EXAFS). EXAFS data contain information on such parameters as coordination number, bond distances, and mean-square displacements for atoms that comprise the first few coordination spheres surrounding an absorbing element of interest. This information is extracted from the EXAFS oscillations, previously isolated from the background and atomic portion of the absorption, using nonlinear least-square fit procedures. It is important in such analyses to compare metrical parameters obtained from experiments on model or reference compounds to those for samples of unknown structure, in order to avoid ambiguity in the interpretation of results and to establish error limits. 

By Fourier transforming the EXAFS oscillations, a radial structure function is obtained (2U). The peaks in the Fourier transform correspond to the different coordination shells and the position of these peaks gives the absorber-scatterer distances, but shifted to lower values due to the effect of the phase shift. The height of the peaks is related to the coordination number and to thermal (Debye-Waller smearing), as well as static disorder, and for systems, which contain only one kind of atoms at a given distance, the Fourier transform method may give reliable information on the local environment. However, for more accurate determinations of the coordination number N and the bond distance R, a more sophisticated curve-fitting analysis is required. 

The extended X-ray absorption fine structure (EXAFS) portion of the spectrum extends above the edge in energy and arises from interferences between the photoelectron produced at the edge and photoelectrons backscattered by nearby atoms (e.g. ligand donor atoms) (Scott 1985). The frequency of EXAFS oscillations is directly... 

The Rh dimer after H2 adsorption exhibited similar EXAFS oscillation and Fourier transform to those for the fresh imprinted catalyst Detailed analysis of the EXAFS data confirmed retention of the local conformation of the Rh dimer with a Rh-Rh bond (CN = 1.3 0.4), two Rh-O bonds (CN = 1.7 0.5) and a Rh-P bond (CN = 1.2 0.2). No formation of Rh metallic particles was observed. However the Rh-Rh bond contracted from 0.268 0.001 to 0.265 0.001 nm with the hydride dimer, indicating stabilizahon of the dimer structure by electronic rearrangement due to monohydride coordination on both Rh atoms in the dimer. After reaction of the Rh-dimer hydride species with 3-methyl-2-pentene, the shrunken Rh-Rh bond of the monohydride species expanded again to recover the... 

The EXAFS oscillations arc suj rimposed on a smooth but much larger background absorption resulting from the electronic excitation of the metal atom. Thus, high quality EXAFS data cannot be obtained imless most stringent experimental conditions are met in terms of x-ray source, optics and detectors. In this section, some of these aspects are discussed. 

The adsorption site, i.e. the chemisorption position of the adatoms on (within, below) the substrate surface, thanks to the polarisation dependence of SEXAFS. Often a unique assignment can be derived from the analysis of both polarisation dependent bond lengths and relative coordination numbers. The relative, polarisation dependent, amplitudes of the EXAFS oscillations indicate without ambiguity the chemisorption position if such position is the same for all adsorbed atoms. More than one chemisorption site could be present at a time (surface defect sites or just several of the ideal surface sites). If the relative population of the chemisorption sites is of the same order of magnitude, then the analysis of the data becomes difficult, or just impossible. 

Fig. 1, Total electron yield (TEY) SEXAFS raw data on the K edge of Co overlayers on Si(lll) 7x7 surfaces, and of CoSij. The bottom curve is for 2 mono-layers of Co on Si(lll) as deposited at room temperature. The reaction of Co with the Si substrate is seen from the similarity of the EXAFS oscillations with those of the CoSij standard (top curve). The central spectrum was obtained from 30 ML Co/Si(lll) as deposited at room temperature, and it is dominated by the EXAFS of unreacted Co. (Rossi et al. unpublished results)...

The quasi-ideality of the (1 x l)Co/Cu(lll) and (1 x l)Co/Cu(110) monolayer interfaces allows a temperature dependent study of the polarisation dependent Debye Waller damping of the EXAFS oscillations i.e the analysis of the amplitude of the mean square relative displacements of the Co atoms parallel to the adsorbate layer, or perpendicular to it. The results are based on the analysis of data collected with the sample temperature T = 77 K and T = 300 K. The S—S and S—B (see above)... 

Fig. 6a-c. One monolayer of cobalt on copper (111), grazing incidence, T = 77 K and T = 300 K relevant steps of the EXAFS analysis, a Experimental absorption spectra b fourier transform of the EXAFS oscillations c inverse Fourier transform of the first neighbour peak as a function of photoelectron kinetic energy E... 

The best regression was determined using a minimization routine incorporated into the program which minimized the sum of squared residuals between the calculated and observed EXAFS oscillation, x and % The result was visually checked comparing the k and k weighted Fourier transforms of the regression and contributions of each regressed shell to the acquired data. 

Figure 2.6 Re Lm-edge EXAFS oscillations (a and b) and their Fouriertransforms (A and B) ofthe Re-CVD/ZSM-5. (a and A) After the treatment with NH3 at 553 Kfor2 h (4, see Figure 2.7) (band B) afterthe reaction with benzene and O2 at 553 K (5, see Figure 2.7). Solid and dotted lines in (A and B) represent observed and fitted spectra (both absolute and imaginary parts), respectively.

Finally it is noteworthy herein that the damping of EXAFS oscillations is not only due to the nanocrystalline size of ZnO particles but also to the fact that the solution is a mixture of different species, here ZnO and Zn precursors. The access by XAS to an average picture of the environment of the target atoms in various phases or in different crystallographic sites in a solid is sometimes a limitation of the technique. However, the identification and isolation of the different components of the mixture can allow access to its composition. This approach is for example illustrated in Ref. 29. Furthermore, with the advent of microbeams allowing spatial resolution information combined to spectrocopic ones, this drawback should be overcome in the next years for heterogeneous solid systems at the micron scale, as discussed in the last section. 

The spectral features of XANES have been interpreted as the result of multiple-scattering resonances of the low kinetic energy photoelectrons. Examples of the strong and sharp XANES peaks above the continuum threshold and below the beginning of the weak EXAFS oscillations in the absorption spectra of condensed molecular complexes, are shown in Fig. 4.6. 

FIGURE 39 Top Exponential decay of the sigma squared term as function of wave vector, k, in the backscattering function for two experimentally encountered values of a 0.01 (solid), and 0.003 (dashed). Bottom Effect of the larger a2-term (solid) on the EXAFS oscillations. Dashed line is with ct2 = 0.003. Assumed bond length = 2.3 A. 

Fig. 15. Pictorial view of the scattering processes of the excited internal photoelectron determining the EXAFS oscillations (single-scattering regime) and the resonances in the XANES (multiple-scattering regime). From Bianconi (30).

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