## 1 Introduction  
The physico-chemical and functional properties of oxide nanoparticles, which are widely employed in engineering, are largely dependent on the defect structure of nanoparticles, namely, the concentration of point defects, their type, and spatial distribution. In this field, works have mainly been devoted to defects that condition oxygen deficiency in nanoparticles compared to the stoichiometry [1, 2]. In addition, oxygen vacancies and clusters based on them strongly affect the electrical, magnetic, diffusion, catalytic, and other properties of oxide nanopowders [3, 4, 5]. For example, a concept of d\({}^{0}\)-magnetism was proposed [6], which helped to explain ferromagnetic properties observed on oxide nanopowders that did not contain any magnetic dopants by an oxygen deficiency in nanoparticles. Such results were obtained on the oxide powders of TiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), ZnO, In\({}_{2}\)O\({}_{3}\), HfO\({}_{2}\), CuO, and others [7, 8, 9, 10, 11]. The majority of results concerning the defect structure of oxide nanoparticles are obtained for the TiO\({}_{2}\) nanoparticles with the use of a large number of techniques [3, 5, 8, 12, 13, 14, 15]. They highlight a wide variety of types of point defects and the evolution of the defect structure under different treatments of nanopowders, say, oxygen annealing [3]. When investigating the defect structure, the most informative were the methods of positron annihilation [3, 5, 8, 12, 13, 14, 15], X-ray photoelectron spectroscopy [3, 5, 13], and photoluminescence [14]; as defects, there were specified oxygen and titanium vacancies [3, 8], interstitial titanium atoms [12], 3D vacancy clusters [8], complexes consisting of oxygen and titanium vacancies [3], Ti\({}^{3+}\) ions and oxygen vacancies [15], and others [12]. The diversity of defect types in the oxide nanoparticles is conditioned by a large number of atoms on the sample surface, the presence of defects - charge carriers, mixed cation valence, changing oxygen concentration upon different powder treatments, etc. With the bulk of important results accumulated on the types of defects in the oxide nanoparticles and their impact on the magnetic properties of nanoparticles [3; 16; 17; 18; 19; 20], the state-of-art in this field can hardly be considered sufficient. First, no measurements of the oxygen concentration were performed and, hence, it was not accounted for in the concentration balance. For this reason, it cannot be excluded that information on several defect types is lacking. The more probable it seems to take into account the selective sensitivity of many techniques to defects of different types. Second, there are no available experimental data on the spatial distribution of defects in nanoparticles gained by direct observations. Such experiments are necessary since the energy states of atoms near the surface and in the bulk are drastically different. In view of the above, this work is devoted to studying the defect structure of oxide nanoparticles via measurements of the oxygen concentration and using a technique that allows the determination of the defect concentration on the surface and in the bulk of nanoparticles. The choice of TiO\({}_{2}\) nanoparticles as the object for investigation is conditioned by a wide scope of practical applications of the dioxide titanium nanopowders [21; 22; 23; 24; 25]. The oxygen concentration was measured by the method of nuclear reactions (NRA); the error of measurements being about 0.5-1.0%, which makes it applicable only for nanopowders with rather a large oxygen deficiency compared to stoichiometry, at a level of several percent. Nanopowders of TiO\({}_{2}\) meet this condition [26]. The defect concentration was determined by the method of deuterium probes (DP) [2]. It is based on the dependence of the deuterium solubility in the oxide particles on the concentration of defects of a specified type.