### X-ray Spectroscopic Methods for Diagnosing Atomic and Electronic Structure
#### 3.1.1 Xps  
XPS is a widely used X-ray spectroscopic method for studying the characteristics of the filled inner (core) electron shells of atoms in solid, adsorbed, and gas-phase polyatomic systems [117; 118; 119]. Core-level photoemission spectra are used to measure the binding energy (\(E_{bin}\)) of the core electrons of atoms and their energy differences (chemical shifts) in various compounds. This method is based on measuring the kinetic energy of photoelectrons ejected from the inner electron shells of atoms when X-ray photons are absorbed and is schematically shown in Figure 7a. In this case, the photoelectron emission process is described by the following [PERSON]'s equation:  
\[h\
u=E_{bin}+E_{k}+\varphi, \tag{1}\]  
where \(h\
u\) is the energy of the incident photon, \(E_{bin}\) is the binding energy of the core-level electron, \(E_{k}\) is the kinetic energy of the photoelectron emitted as a result of the photoelectric effect, and \(\varphi\) is the work function of the spectrometer material [117]. Since the values of \(h\
u\) and \(\varphi\) are known, and \(E_{k}\) is determined experimentally, Equation (1) makes it easy to calculate \(E_{bin}\). Due to the fact that each chemical element has its own set of \(E_{bin}\) values for the inner electron shells, the photoelectron spectrum reflects the elemental composition of the substance and chemical states of its atoms. Thus, XPS can be used to obtain information about the concentration of elements by determining the relative total intensities of the corresponding photoelectron lines. An important role when considering XPS spectra is also played by the analysis of changes (chemical shifts) in the binding energies of the inner electron shells of an atom in its various compounds. In this case, very valuable information can be obtained about the chemical state of the atom absorbing the X-ray photon and its change when moving to another compound. Figure 7: Schematic representation of the photoionization process (core or valence electron) (**a**) and energy dependence of inelastic mean free path \(\lambda\) of photoelectrons calculated for the 41 elements from the often-used formula TPP-2 M (adapted from Ref. [120] with permission) (**b**). It should be noted that the radiation sources in laboratory XPS spectrometers are the characteristic Mg K\(\alpha\), Al K\(\alpha\), Ti L\(\alpha\), Cu L\(\alpha\), Ag L\(\alpha\), and other X-ray lines generated by an X-ray tube with a corresponding anode [117]. Of these, the Mg K\(\alpha\) and Al K\(\alpha\) lines are the most commonly used photon sources due to their narrow full width at half maximum (FWHM) (0.7-0.85 eV). They are also suitable for a wide range of operating binding energies (from the Fermi level to 1240 and 1470 eV, respectively). The inner electron shells of atoms can be ionized by X-ray photons at a sufficiently large depth relative to the surface of the material. However, not all of the generated photoelectrons leave the sample, and most of them are lost on the way to the surface due to various processes of their scattering. Ultimately, only photoelectrons from a thin near-surface layer can be detected, determined by the mean free path (\(\lambda\)) of the photoelectron in the material under study. As can be seen from Figure 7b, in the range of kinetic energies characteristic of XPS (<1500 eV), the electron mean free path is limited to several nanometers (about 1-5 nm), and in the energy range 50-200 eV, less than 1 nm. It should be noted that approximately 65% of the signal intensity is formed due to photoelectrons emitted from the surface layer with a thickness of less than \(\lambda\), 85% with a thickness of less than 2\(\lambda\), and 95% with a thickness of less than 3\(\lambda\). Thus, this method is surface-sensitive. A more advanced source of X-ray radiation is synchrotron radiation from modern electron storage rings.