## 3 Results and Discussion
### Spatial Distribution of Defects Ti\({}_{6}\) in Nanoparticles  
In the investigation of spatial distribution and size of defects consisting of 6 titanium atoms, different versions are considered, namely, defects located in the bulk and on the surface of nanoparticles and two-dimensional or three-dimensional ones. To obtain information on these issues, the dependence \(C_{d}(S)\) was studied for the powders synthesized by the LE. As is seen in Figure 4, the experimental dependence \(C_{d}(S)\) matches Expression (2) at constant parameters \(N\), \(\Delta\), and \(y\), which indicates that the defects consisting of 12 oxygen vacancies are located on the surface and absent in the bulk of TiO\({}_{2}\) nanoparticles. Figure 3: Dependence of the oxygen concentration \(C_{O}\) in TiO\({}_{2}\) nanopowders on the defect concentration \(C_{d}\). Black points show results for powders synthesized by sol–gel method; red points, laser evaporation of ceramic target. The independence of the parameter \(N\) on \(S\) was experimentally shown in Section 3.1. As for the parameters \(\Delta\) and \(y\), it is conditioned by the application of technology of LE. In this case, the formation of the defect structure of the surface layer proceeds in two steps. In the first step, at high temperatures in a vacuum, there form nanoparticles of stoichiometric composition in the bulk with the surface atomic layer virtually depleted of oxygen. It was established that the thickness of the oxygen-depleted layer does not depend on \(S\) and is equal to 0.36 nm [26], which approximately matches up an oxide monolayer. In works fulfilled within the theory of density functional, the following theoretical explanation of this result was given, namely, the existence of an oxygen-free layer on the oxide surface is energetically more favorable than of stoichiometric composition TiO\({}_{2}\)[26; 30; 31]. In the second step, the powder is cooled to room temperature in air and oxygen enters into the surface layer of nanoparticles. Evidently, in this case, the thickness of the oxygen-deficient layer does not depend on \(S\). The amount of oxygen entering into nanoparticles depends on the regime of cooling the nanopowders. In this work, these regimes were the same for powders with different \(S\). We already mentioned above that the thickness of defects Ti\({}_{6}\) in nanoparticles synthesized by LE technology is within the atomic scale, whereas other linear dimensions are several times as high, i.e., the defects are two-dimensional. For nanoparticles synthesized by the SG method, no data on the spatial distributions of Ti\({}_{6}\) defects and inference on their two-dimensional or three-dimensional shape are presented in this work because of the lack of appropriate techniques. Yet, there are grounds to conclude that the Ti\({}_{6}\) defects in nanoparticles synthesized by the SG method also are two-dimensional and localized on the nanoparticle surface. In our opinion, these defects cannot occupy internal bulk regions of nanoparticles since the crystal structure of titanium dioxide with inner defects consisting of 12 oxygen vacancies will hardly be stable. At the same time, the presence of such defects on the surface of nanoparticles does not cause destruction of the crystal lattice of the oxide, which is evidenced by the results of works [26; 30; 31]. In the surface layer of TiO\({}_{2}\) particles, there are present two types of regions: (i) consisting of 6 titanium atoms and (ii) having composition close to stoichiometric TiO\({}_{2}\). It is worth estimating fractions of these regions. If to take up a constancy of distance between the titanium atoms upon the formation of the Ti\({}_{6}\) defect, the fraction of nanoparticle surface occupied by regions consisting of 6 titanium atoms is expressed as  
\[\propto=\frac{1-C_{O}/C_{O}^{0}}{\Delta\rho S(1-C_{O})}\leq 1. \tag{3}\]  
In Figure 5, the dependences \(\propto\left(C_{O}/C_{O}^{0}\right)\) calculated by Expression (3) for several values of \(S\) are shown.