### X-ray Spectroscopic Methods for Diagnosing Atomic and Electronic Structure
#### 3.1.3. NEXAFS and EXAFS
Thus, NEXAFS spectroscopy is one of the most informative methods for studying polyatomic systems due to its sensitivity to the ordering, binding energy, atomic orbital composition, and angular symmetry of empty MOs; bond lengths and angles; nearest neighborhood coordination, etc. [55; 59]. Studies of EXAFS spectra with the energy region of EXAFS oscillations from 30 to \(\sim\)1500 eV above the absorption edge allows one to determine with sufficiently high accuracy distances and coordination numbers around a specific absorbing atom, thus providing probing of the local atomic structure of a polyatomic system near the absorbing atom (Figure 11a) [128]. At present, it can be considered clear that the main features of the EXAFS structure are caused by the processes of elastic scattering of a photoelectron wave by the potential relief of the nearest neighborhood of the absorbing atom in a polyatomic system [129; 130]. This primary wave is scattered by neighboring atoms through acts of single backscattering of electrons and generates scattered waves that can interfere (constructively or destructively) with the primary wave (see Figure 12), which leads to the appearance of EXAFS oscillations [129]. In this case, the amplitude of the scattered electron wave is equal to the sum of contributions from each of the surrounding atoms [131]. To describe this process, it is necessary to determine the normalized EXAFS function \(\chi(k)\), which contains all the information about the oscillations of the photoionization cross sections of atoms in the substance. This function can be found through Equation (2):  
\[\chi(k)=\sum_{j}\frac{N_{j}\cdot f_{j}(k)\cdot e^{-2k^{2}\cdot\sigma_{j}^{2}}}{ k\cdot R_{j}^{2}}\cdot\sin\ [2k\cdot R_{j}+\delta_{j}(k)] \tag{2}\]  
where \(k\) is the wave number of the photoelectron wave, \(f_{j}(k)\) is the amplitude of the backscattered electron wave by atoms of the coordination sphere, \(\delta_{j}(k)\) are phase shifts, \(N_{j}\) is the number of neighboring atoms to atom \(j\), \(R_{j}\) is the distance to atom \(j\), and \(\sigma_{j}^{2}\) is the Debye-Waller factor, characterizing the root mean square amplitude of the deviation of the distance to atoms of type \(j\) from the average value caused by structural and thermal disorder [130]. In order to separate the contributions of individual coordination spheres from the overall function \(\chi(k)\), spectral analysis methods are used by expansion of the function \(\chi(k)\) into a Fourier integral (see Figure 13). Finally, a Fourier transform is performed into R-space, giving information about the interatomic distances between the absorbing atom and nearby atoms (see Figure 13d). In view of the above, EXAFS spectroscopy is most often used to obtain primary structural information about new chemical compounds (chemical bond lengths, coordination numbers, and type of atoms surrounding the studied one) within the range of 4-5 A (the first few coordination spheres). In this case, EXAFS spectroscopy is usually implemented for the 1s and 2\(p\) shells of elements with a charge number \(Z>20\)[128; 130]. It is important to note that X-ray absorption (NEXAFS, EXAFS) spectra can be measured in various modes such as transmission and fluorescence as well as total electron and Auger electron yield modes. More detailed information about each of these methods is given in [126; 128; 132]. At the same time, to measure the ones being studied, most researchers use synchrotron radiation beamlines at electron storage rings. EXAFS data  
Figure 12: Schematic view of the formation mechanism of EXAFS oscillations [131]. Figure 13: Steps of EXAFS data processing: (**a**) an experimental X-ray absorption spectrum; (**b**) the amplified NEXAFS region; (**c**) the normalized EXAFS curve (the oscillating part of the X-ray absorption coefficient); and (**d**) the Fourier transform (FT) of the normalized EXAFS curve; the maxima of the Fourier transform correspond to the coordination spheres around the central atom [129].