Radial structure functions

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. 

Z neighbors. Phase correction of the Fourier transform by the backscattering phase shift of one of the absorber—neighbor pairs is also extensively used. This has the effect of correcting the distances observed in the radial structure function as well as emphasizing the contributions from the chosen ab-... 

Laperche Traina (1998) studied Pb uptake on hydroxyapatite at low initial solution concentration of Pb (103 mg/L). For this, EXAFS was used to characterize the local coordination environment of Pb on the apatite. The baseline corrected, Fourier-transformed EXAFS spectra revealed fc-values at >3 A, suggesting that Pb was not randomly sorbed. Radial structure functions (RSF) showed three intense peaks, characteristic of pyromorphite. 

ROBL RSF Rossendorf beamline Radial structure function... 

EXAFS data are processed to obtain radial structure functions (RSFs). First, the non-EXAFS components are subtracted from the data. Pre-edge absorption is removed using the Victoreen correction (International Tables for Crystallography, 1969) of the form AX + BX . The monotonic decrease of absorbance beyond the edge, called the photoelectric decay, is subtracted out after approximating it either by a second degree polynomial or a spline-function (Eccles, 1978). The normalized x(k) is then expressed as... 

The k3-weighted chi spectra and corresponding radial structure functions for the surface, subsurface, and sediment samples are presented in Figure 8.6. The top spectrum in both the left and right panels show representative fits for LCF and multishell fitting, respectively (dashed lines = fits and solid lines = raw data). For the topsoil sample, multishell fitting revealed that Zn was tetrahedrally coordinated to both O and S in the first coordination shell (N=4). The second-shell contribution could be fit with either a Zn or Fe atom at a distance of 3.49 A. Coordination numbers and distances of the O shell and the Zn shell are in line with those of franklinite. 

FIGURE 8.7 BulkZn-EXAFS k3-weighted chi (left panel) and corresponding radial structure functions (right panel) resulting from Fourier analysis of chi data for surface soil sample after each step in the sequential extraction. (Reprinted with permission from Scheinost, A.C. et al., Environ. Sci. Technol, 36, 5021, copyright 2002. American Chemical Society.)... 

Top right Fit of EXAFS region with cnbic spline and snbtraction yields EXAFS oscillations shown is the EXAFS weighted by k. Bottom left XANES spectral region expanded. Bottom right PCF or pair correlation function (also called Radial Structure Function to distinguish it from the X-ray analog RDF) shown is the Fourier transform of the spectram at the top left. 

Figure 27. Analysis of polarized EXAFS data, (a) EXAFS radial structure functions for irom oxide precipitates on quartz single crystal surfaces, r and m refer to the (1011 )and (1120) surface planes of quartz. The parallel and perpendicular refer to the polarization direction of the X-ray beam and thus the probe direction of the EXAFS scattering process, (b) Raw polarized EXAFS and fits for the same samples in (a), (c) Polarized stracture function simulations. Top radial stracture function for a single Fe atom within a 50-atom hematite crystal with [0001] orientation. Middle Same for 20-atom crystal. Bottom Weighted average of all Fe stracture func-tions in the 20-atom crystal. The analysis suggests highly textrrred hematite-like nanocrystals on the quartz surface but no epitaxial relationship. From Waychunas et al. (1999).

Figure 4. EXAFS data for the Np carboxy-telechelic polyisoprene, (a) k vs. k, (b) radial structure function. (Reprinted from ref. 11. Copyright 1988 American Chemical Society.)...

XAFS data, showing the formation of Ni-Al LDH phases on soil components, are shown in Figure 3.5 and Table 3.1. Radial structure functions (RSFs), collected from XAFS analyses, for Ni sorption on pyrophyllite, kaolinite, gibbsite, and montmorillonite were compared to the spectra of crystalline Ni(OH)2 and takovite. All spectra showed a peak at R 0.18 nm, which represents the first... 

Figure 3.7. Radial structure functions (achieved from XAFS analyses) for Ni sorption on pyrophyllite for reaction times up to 24 hours, demonstrating the appearance and growth of the second shell (peak at 2.8 A) contributions due to surface precipitation and growth of a mixed Ni-Al phase. (From Scheidegger et ah, 1998.)...

Fig -8. Co XAS results for sorption to a-Al203 (A) background subtracted k3 Co(II) EXAFS spectra as a function of surface coverage, 7, (B) fast Fourier transformed radial structure functions of Co(II) EXAFS, uncorrected for phase shift. Uncorrected peaks at approximately 2600 and 5500 pm in the sorption samples are primarily due to Co-Co second shell and Co-Co fourth-shell interactions, respectively (after Hayes Katz, 1996). 

In-situ EXAFS data obtained with the help of M. Subramanian and J. McBreen (BNL) are shown in Figure 2. The radial structure functions of Pt foil and Pt/Ru catalysts are compared. The spectrum for the Pt/Ru catalyst is dominated by Ru. The analysis shows that the smaller peak can be fitted by the one Pt atom coordinated to four Ru atoms. The Pt-Ru bond length is 2.69A, as in the Pt-Ru alloys. The Pt-Pt coordination is being analyzed. First results indicate that the Pt islands on Ru are very small, which is consistent with the HRTEM data. 

Fig. 3 shows Fourier transforms of P-weighted EXAFS spectra (RSFs Radial Structural Functions) of Pt foil and coat-Pt catalysts with the different Pt loading. A strong peak was observed at 2.7 A in the RSF of Pt foil. This peak could be... 

Figure 11. X-ray diffraction patterns and EXAFS radial structure functions of two poorly-ciystallized compounds. Both ferrihydrite and silicate glass look amorphous through XRD, but the former is as well short-range ordered as feroxyhite, whereas the latter is disordered even at the local scale. Ge02 is used as the EXAFS example instead of Si02 to better match the second-neighbor scattering factors for the Fe oxides.

Figure 48. Radial structure functions of Cl in different organochlorine compounds (used with permission from Elsevier Science from Huggins and Huffman 1995).

Figure 10. Radial structure functions (RSFs) of pyrophyllite samples reacted with Ni (reaction conditions are those given in Fig. 7) for a) 3 mo, b) 24 h, c) 12 h, d) 3 h, e) 75 min, and f) 15 min. The spectra are uncorrected for phase shift. Note the appearance of a peak at a R of about 2.8A with increasing reaction time. From Scheidegger et al. (7 7), with permission.

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