**2.2. X-ray absorption near edge spectroscopy (XANES)**

photoelectron mean free path (how far the electron travels before scattering inelastically).

the central atom. Those processes (multi-excitations) refer to the excitations of the remaining *Z* − 1 "passive" electrons of the excited atom. This is a scale factor, and it is usually in the 0.7–1

This is valid for the plane wave approximation, *K* threshold, single scattering, single electron approximation and "sudden" approximation. A similar equation valid for the other edges (LIII, etc.) must be considered. The structural and non-structural parameters appearing in the equation sum up to compose the EXAFS spectrum. To access these parameters in an experimental EXAFS spectrum, a data analysis has to be performed. This procedure is time consuming and it should be considered the slow step of the overall XAFS

EXAFS data analysis is normally done by using code programs, which permit to calculate the theoretical EXAFS spectrum based on *ab initio* calculations, followed by a further step which compares the experimental signals to the theoretical ones (fitting procedures). A rather complete list of the available software can be found at: http://www.esrf.eu/Instrumentation/ software/data-analysis/Links/xafs. Typical widely used computer programs are GNXAS [33], FEFF [34, 35] and EXCURV [36]. EXCURV is a program, which simulates EXAFS spectra using rapid curved-wave theory. GNXAS package is based on multiple-scattering (MS) calculations and a fitting procedure of the raw experimental data, also allowing multiple edge fittings and a non-Gaussian distribution models for the atoms pair distribution. FEFF allows MS calculations of both EXAFS and XANES spectra for atomic clusters. The code yields scattering amplitudes and phases used in many modern XAFS analysis codes. It is also linked to the IFEFFIT package [37, 38], a suite of interactive code for XAFS analysis, combining high-quality and well-tested XAFS analysis algorithms, tools for general data manipulation and graphical

Two more considerations should be made on EXAFS data analysis. The first is that XAS (and therefore the results obtained by an EXAFS analysis) is a bulk technique and thus all the atoms irradiated by the beam contribute to the overall XAS spectrum. The same is true in the case of a multicomponent system (for instance two phases in equilibrium of a polymorphic species). Each component or phase gives its contributions. An example to disclose the simple component of a species, such as in the case of gold nanoparticles and its precursors, appeared [39]. Alternatively, an efficient use of chemometry has been proposed for the analysis of XAS data in such cases [40]. This approach has interesting implication for the interpretation of spectra recorded during an *operando* acquisition and an example will be presented in the next

The second consideration concerns the EXAFS data analysis of nanoparticles and nanostructures [41, 42]. This issue has been addressed for metal nanoparticles first [43], evidencing that

accounts for the shake-up/shake-off processes of

] (8)

<sup>2</sup> sin[2*<sup>k</sup> Rj* <sup>+</sup> *<sup>δ</sup>*(*k*)

2

range. By taking in consideration with these effects, the EXAFS equation becomes:

*Nj Fj* \_ (*k*) *k rj* <sup>2</sup> *e* <sup>−</sup>2*k*<sup>2</sup> *σ*2 *e* <sup>−</sup>2*Rj*/*Λ*(*k*) *S*0

Finally, the amplitude reduction term *S*<sup>0</sup>

methodology.

display of data.

section.

*<sup>χ</sup>*(*k*) <sup>=</sup> <sup>∑</sup><sup>j</sup>

58 X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation

The XANES region is sensitive to the geometrical structure of the metal center but also probes its effective charge. It turns out that the position of the edge (which can be evaluated by the edge inflection point) is shifted to higher energies when the formal valence of the photoabsorber increases. Below the absorption edge, the presence of pre-edge structures can be observed [44]. The occurrence of this peak in a metal (first raw transition metal) K-edge is due to 1s-3d electronic transition [45] that is electric-dipole forbidden but quadrupole allowed. Its intensity can be used as a probe for geometry, as the geometrical distortion of the metal core from centrosymmetric coordination favors the transition, while the energy position is relative to the metal core formal oxidation state. This fact is frequently used for investigating the charge associated to positive- and negative-electrode materials during reduction and oxidation reactions in batteries.

If we now consider the form of the absorption edge, it can be seen that it reflects the empty density of states and it strongly depends on the coordination, while the forms of the absorption traces up to 60–80 eV are due to the multiple scattering resonances of the ejected photoelectron. Several computer codes can simulate the XANES spectrum, such as above-mentioned FEFF, MXAN [46], FDMNES [47] and CTM4XAS [48], which are useful for the analysis of metal L-edges.
