## 3 Results and Discussion
### XPS Research of the Nanocomposites and Initial MWCNTs
A comparison of their integrated intensities makes it possible to determine the carbide stoichiometric formula as WC\({}_{0.88}\). The peaks O\({}_{1}\) and O\({}_{2}\) maxima correspond to W4f\({}_{7/2}\)- and W4f\({}_{5/2}\)- levels of oxide WO\({}_{3\text{-}\text{x}}\) tungsten atoms [85; 86; 92]. The O and O\({}_{1}\) bands in the oxygen and tungsten spectra are responsible for the W-O chemical bond formation. A comparison of their integrated intensities makes it possible to determine the oxide stoichiometric formula as WO\({}_{2.77}\). The peak O\({}_{3}\) maximum corresponds to W5p\({}_{3/2}\)- levels of W\({}^{6+}\) ion in oxide WO\({}_{3}\)[93]. According to TEM data, the MWCNTs coated with pyrolytic tungsten carbide (Figure 4b) have the average thickness of about 20-30 nm. Using this value of the WC\({}_{1\text{-}\text{x}}\) layer thickness and the mean free paths of the photoelectrons emitted with certain energies from the C1 level in the tungsten carbide and oxide it is possible to determine the thickness of the WO\({}_{3\text{-}\text{x}}\) layer from the analysis of the nanocomposite XPS W4f spectra. The \(I_{l}\) lines intensities in the XPS spectra describe the emission of electrons from the \(l\) level, and have a complex dependence:  
\[I_{l}\ =\ n_{l}\sigma_{l}l\lambda S\Big{(}1-e^{-\frac{d}{\lambda\cos 0}}\Big{)}, \tag{3}\]  
where \(n_{l}\) is the concentration of atoms, \(\sigma_{l}\) is the cross section for the photoelectron emission from the atom \(l\) subshell, which depends on the incident X-ray quantum energy \(h\
u\), \(J\) is the incident radiation intensity, \(\theta\) is the photoelectrons emission angle measured from the normal to the sample, \(\lambda\) is the electron mean free path in the studied sample, \(S\) is the detector sensitivity. It should be noted that \(\lambda\) is determined by the emitted photoelectron energy \(E_{kin}\). S depends on the incident quantum energy \(h\
u\), the specific of the analyzer operation, and shooting conditions. If the sample is semi-infinite, then the exponential term in formula (3) can be neglected. For a two-layer structure, when sample B is covered with a thin layer of another substance \(A\), the lines intensity in sample \(B\) XPS spectrum can be written as:  
\[I_{B}\ =\ n_{B}\sigma_{B}J_{B}\lambda_{B}S_{B}\Big{(}1-e^{-\frac{d_{B}}{\lambda_ {B}\cos 0}}\Big{)}e^{-\frac{d_{A}}{\lambda_{A}\cos 0}}. \tag{4}\]  
The second exponent in Formula (4) is related to the absorption of photoelectrons from sample B in the sample \(A\) covering layer. If we consider XPS spectra taken in the same geometry and for one type of atom, but in different compounds, then the quantities \(\sigma_{l}\), \(J\), \(S\) and \(\theta\) will be about the same. In the present work, the detector was oriented normally to the sample surface, i.e., the angle \(\theta=0\). Taking the WC\({}_{1\text{-}\text{x}}\) layer thickness \(d_{C}=20\) nm from Equations (3) and (4), it is possible to determine \(d_{O}\) (theeffective thickness of the WO\({}_{3\times}\) layer) from the ratios of the intensities of the peaks M and O in the XPS W4f spectra, which is equal to 3.3 nm. The photoelectrons mean free paths with an energy of 1445 eV in the oxide and in tungsten carbide were taken to be equal to the mean free paths for crystalline WO\({}_{3}\) (\(\lambda\) = 1.89 nm) and WC (\(\lambda\) = 2.35 nm) [94]. An analysis of the Equations (3) and (4) solution showed that at the available of these peaks intensities, a decrease in the carbide layer thickness up to \(d_{C}\) = 7 nm practically does not change the estimated tungsten oxide layer thickness \(d_{O}\), i.e., the semi-infinite layer approximation is fair for \(d_{C}\) > 7 nm. Then, with a tungsten carbide layer thickness of 20-30 nm and \(\lambda\) = 2.35 nm, the tungsten carbide coating layer can be considered semi-infinite. This allows us to estimate the upper bound on the relative sizes of the nanotube open surface in the nanocomposite.