EXAFS as a tool for catalyst characterization: a review of the ... - INT

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Figure 3: Fourier transform corresponding to EXAFS spectrum of metallic cobalt. When the contribution of two shells is not resolved in the Fourier spectrum, Fourier filtering can be used. By means of a filter function, specific peaks in the Fourier spectrum are separated from the rest of the spectrum. The product of the spectrum with this filter function is Fourier backtransformed into k space. This procedure separates the contribution of adjacent coordination shells so that the effect of only the coordination shell of interest is maintained. In fact, the Fourier backtransform is calculated by (13) where W(κ) is the window of the Fourier transform and W’(κ) is the window of the Fourier backtransform which separate the specific peak.
Thus, the resulting curves are fitted with the EXAFS formula to determine R, N and σ . In order to extract information about the local environment of the absorber, the backscattering amplitude and phase shift functions must be known. These functions can be obtained experimentally from EXAFS spectra of model compounds or calculated theoretically (Teo and Lee, 1979; McKale et al., 1988; Rehr, 1989). Experimental functions are extracted from reference compounds with known structures. However, it is not always possible to obtain experimental functions since the reference compounds do not exist or it is not possible to extract them (Vlaic et al., 1998). Furthermore, experimental phase and amplitude functions must be extracted by using the same integration limits and the same windows to the unknown sample in order to introduce the same truncation errors. In general, the accuracy of the analysis is about 0.01-0.02Å for the interatomic distances, 5 to 15% for the coordination numbers and 20% for σ (Lengeler and Eisenberger, 1980). The minimization procedure is carried over into the following function (Michalowicz, 1990): (14) where p i are the fitting parameters and W(k) is a weighting function. A residual factor is also defined by the following expression: (15) The number of parameters that can be determined from the EXAFS signal is related to the number of independent points, N ind , by N par = N ind – 1 (16) There is some uncertainty in the literature on how to calculate N ind . According to Stern (1993), the correct expression is given by (17) The fit quality is given by the chi-square function. Particularly in EXAFS this function is defined as follows: (18)
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Page 3 and 4: Figure 1: Regions of the X-ray abso
Page 5 and 6: The normalized EXAFS spectrum assoc
Page 7: (11) I 0 - modified BESSEL function
Page 11 and 12: Figure 4: Amplitude of the Radial D
Page 13 and 14: Therefore, the EXAFS analysis demon
Page 15 and 16: Bart, J.C.J. and Vlaic, G., Adv.Cat

EXAFS as a tool for catalyst characterization: a review of the ... - INT

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