The authors review the development of extended x-ray absorption fine structure (EXAFS) within the last decade. Advances in experimental techniques have been largely stimulated by the availability of synchrotron radiation. The theory of EXAFS has also matured to the point where quantitative comparison with experiments can be made. The authors review in some detail the analysis of EXAFS data, starting from the treatment of raw data to the extraction of distances and amplitude information, and they also discuss selected examples of applications of EXAFS chosen to illustrate both the strength and limitations of EXAFS as a structural tool.

Extended x-ray absorption fine structure—its strengths and limitations as a structural tool

A procedure is described for determining interatomic distances $r$, coordination numbers $N$, and mean relative displacements $\ensuremath{\sigma}$ from extended x-ray absorption fine structure (EXAFS) data on disordered metallic systems. This procedure includes the case when the spectrometer has finite energy resolution. It is shown how the absolute value of the EXAFS can be determined. A way has been developed to determine the inelastic loss factors of the photoelectrons from model compounds of known structure. The procedure has been checked on four metallic systems (Cu, $\ensuremath{\alpha}\ensuremath{-}\mathrm{Al}\mathrm{Cu}$-AlCu, ${\ensuremath{\theta}}^{\ensuremath{'}}$ and $\ensuremath{\theta}$ AlCu). The accuracy of the analysis is 1% for the interatomic distances, 15% for the coordination numbers, and 20% for $\ensuremath{\sigma}$. The reliability of the data analysis, which depends strongly on the number of different atoms in a shell, on the magnitude of their mean relative displacement and on the difference in their backscattering power will be discussed at length.

Extended x-ray absorption fine structure analysis of interatomic distances, coordination numbers, and mean relative displacements in disordered alloys

Publisher Summary This chapter describes extended x-ray absorption fine structure spectroscopy (EXAFS) spectroscopy with a breadth sufficient to communicate to the non-expert potential of this technique. It discusses the theoretical underpinnings and experimental state of the art with depth sufficient to delineate clearly to a practitioner the capabilities and limitations of this spectroscopy. A especially useful expression is derived for the EXAFS from basic considerations, delineating explicitly the approximations required at each step. The more significant of these approximations are examined in the context of both theory and experiment. The calculation of EXAFS spectra is also discussed. The structural information content of the EXAFS is set forth explicitly and compared with the information available from a diffraction measurement. Finally, a survey is presented of the wide and growing variety of the applications of this technique, with particular emphasis on those in condensed matter physics.

Extended X-Ray Absorption Fine Structure Spectroscopy

The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born--von Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRDs of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths.

https://arxiv.org/pdf/cond-mat/0209603.pdf

Lattice dynamics and correlated atomic motion from the atomic pair distribution function

Extended x-ray-absorption fine-structure (EXAFS) of copper has been measured from 4 to 500 K and analyzed by the cumulant method, to check the effectiveness of EXAFS as a probe of local dynamics and thermal expansion. The comparison between parallel mean square relative displacements (MSRD) of the first four coordination shells has allowed detecting a significant deviation from a pure Debye behavior. The first-shell EXAFS thermal expansion is larger than the crystallographic one: the difference has allowed evaluating the perpendicular MSRD, whose Debye temperature is slightly larger than the one of the parallel MSRD, due to anisotropy effects. High-order first-shell cumulants are in good agreement with quantum perturbative models. The anharmonic contribution to the first-shell parallel MSRD amounts to less than 1.5 percent. The third cumulant cannot be neglected in the analysis, if accurate values of the first cumulant are sought; it cannot however be used to directly estimate the thermal expansion. The shape of the effective pair potential is independent of temperature; a rigid shift, partially due to the relative motion perpendicular to the bond direction, is however observed.

Extended x-ray-absorption fine-structure measurements of copper: Local dynamics, anharmonicity, and thermal expansion

An investigation of the dependence on temperature of the extended X-ray absorption fine structure (EXAFS) above the K-edges of Cu and Co in the metals and above the K-edges of Rb and Sr in the compounds RbCl, SrS, SrF2 and SrCl2 has been performed. For Cu, Co, RbCl and SrS, the values of the correlated mean square relative displacements of nearest-neighbour atoms derived from EXAFS spectra show a good agreement with those calculated from a Debye model. The experimental data obtained are also compared with available data for mean square displacements of the individual atoms calculated from more-refined lattice vibrational models and with Debye-Waller factors used in X-ray diffraction experiments.

https://iopscience.iop.org/article/10.1088/0022-3719/12/13/011/pdf

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Temperature dependence of the mean square relative displacements of nearest-neighbour atoms derived from EXAFS spectra