EXAFS mean square displacement absorbing

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. 

Nj and Rj are the most important structural data that can be determined in an EXAFS analysis. Another parameter that characterizes the local structine aroimd the absorbing atom is the mean square displacement aj that siunmarizes the deviations of individual interatomic distances from the mean distance Rj of this neighboring shell. These deviations can be caused by vibrations or by structural disorder. The simple correction term exp [ 2k c ] is valid only in the case that the distribution of interatomic distances can be described by a Gaussian function, i.e., when a vibration or a pair distribution function is pmely harmonic. For the correct description of non-Gaussian pair distribution functions or of anhar-monic vibrations, different special models have been developed which lead to more complicated formulae [15-18]. This term, exp [-2k cj], is similar to the Debye-Waller factor correction used in X-ray diffraction however, the term as used here relates to deviations from a mean interatomic distance, whereas the Debye-Waller factor of X-ray diffraction describes deviations from a mean atomic position. 

Photoionization (and therefore EXAFS) takes place on a time scale that is very short relative to atomic motions, so the experiment samples an average configuration of the neighbors around the absorber. Thus, one needs 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 represents the mean-square relative displacement along the absorber-backscatterer direction and is given by... 

In Eq. (1), k is the photoelectron wave vector relative to Eq (k = 0) N is the the number of neighboring atoms of the same kind at a distance r., of is the mean-square relative displacement (MSRD) of the absorber-scatterer atom pair from their equilibrium inter-atomic distance or in molecular spectroscopy terminology, the mean-square amplitude of vibration other terms have their usual meaning Using standard Fourier transform and curve fitting procedures, we can derive the coordination number, bond length and local dynamics (MSRD) from EXAFS. 

The chemical implications of the EXAFS bond length and the mean-square relative displacement of the absorber-scatterer pair are best illustrated with a system of metal ions in aqueous solution and its correlation with the rate of water substitution reaction... 

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