EXAFS Debye-Waller factor

Table 4.1 Calculated EXAFS Debye-Waller factors. ...

Photoionization and therefore EXAFS takes place on a time scale that is much shorter than that of atomic motions so the experiment samples an average configuration of the neighbors around the absorber. Therefore, we need to consider the effects of thermal vibration and static disorder, both of which will have the effect of reducing the EXAFS amplitude. These effects are considered in the so-called Debye-Waller factor which is included as... 

Melroy and co-workers88 recently reported on the EXAFS spectrum of Pb underpotentially deposited on silver (111). In this case, no Pb/Ag scattering was observed and this was ascribed to the large Debye-Waller factor for the lead as well as to the presence of an incommensurate layer. However, data analysis as well as comparison of the edge region of spectra for the underpotentially deposited lead, lead foil, lead acetate, and lead oxide indicated the presence of oxygen from either water or acetate (from electrolyte) as a backscatterer. 

FIGURE 7.12 Fourier tranform magnitude of kl (k) versus k theoretical EXAFS spectra generated from FEFFIT software by setting coordination numbers to their nominal values, and other EXAFS parameters as described in the experimental section. (Light solid line) Debye-Waller factor of 0.000 and (heavy solid line) Debye-Waller factor of 0.010. Grange of 2.5 to 10 A-1. 

The reason for multiplying with a k weighting factor is to compensate for the decrease of the EXAFS amplitudes at high k values due to the Debye-Waller factor, the backscattering amplitude, and the k 1 dependence of the EXAFS (see, e.g., Ref. (21)). 

Table 6.6 EXAFS analysis bond distances (dbond), coordination numbers (N), Debye-Waller factors (of and the parameter Eo-(Reproduced from Reference [30].)...

Table 1. Structural parameters deduced from EXAFS for a number of metallothioneins . R denotes the distance of scattering atoms from the absorbing atom is a Debye-Waller factor and...

Refined EXAFS parameter (coordination number N, distance r[A] and Debye-Waller factor... 

The accuracy of structural parameters extracted from EXAFS depends on many factors such as the disorder, the extension of the experimental spectra and quality of these data. Typical accuracies for the determination of parameters are 1% for interatomic distances, 15% for the coordination numbers and 20% for Debye-Waller factors [6], But, in a situation more complex where several shells must be fitted simultaneously, one must be satisfied with much less accurate results. 

Notation N, coordination number R, distance between absorber and backscatterer atom A a2, Debye-Waller factor AEo, inner potential correction. Commonly accepted error bounds on structural parameters obtained by EXAFS spectroscopy are N, 10-15% R, 0.02 A ... 

From equation 5, it is apparent that each shell of scatterers will contribute a different frequency of oscillation to the overall EXAFS spectrum. A common method used to visualize these contributions is to calculate the Fourier transform (FT) of the EXAFS spectrum. The FT is a pseudoradial-distribution function of electron density around the absorber. Because of the phase shift [< ( )], all of the peaks in the FT are shifted, typically by ca. —0.4 A, from their true distances. The back-scattering amplitude, Debye-Waller factor, and mean free-path terms make it impossible to correlate the FT amplitude directly with coordination number. Finally, the limited k range of the data gives rise to so-called truncation ripples, which are spurious peaks appearing on the wings of the true peaks. For these reasons, FTs are never used for quantitative analysis of EXAFS spectra. They are useful, however, for visualizing the major components of an EXAFS spectrum. 

The major source of uncertainty in parameter determination by EXAFS analysis arises from the correlation that exists between the coordination number (Nj) and the Debye-Waller factor (crj) for each shell. This correlation occurs through the amplitude of the backscattered wave [Eq. (4)] and results in the uncertainty in Nj being 25%. The primary manifestation of is in the relative phases of the outgoing and backscattered waves and, although Rj is strongly correlated to... 

Based on these analyses of EXAFS data, we propose that the structure of CdS-DMF nanocrystallites changes as shown in Scheme 1. When 0.2 equivalent of excess Cd + was added into the system, the adsorption of Cd + solvated by DMF occurred to the CdS-DMF surface and resulted in the formation of the sulfur surface vacancy on the surface of CdS-DMF. The change in the coordination number and the square of the Debye-Waller factor of the Cd-S and Cd-O shell support such changes in the surface structure on CdS-DMF nanocrystallites. 

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