## 3 Results and Discussion
### Formation of Nano-Titanium Dioxide as a Precursor
The average spectrum of the oxide inclusion is presented in Figure 4. It is obvious that this spectrum was a standard spectrum of \(\alpha\)-Al\({}_{2}\)O\({}_{3}\) with the characteristic bonds at 378 cm\({}^{-1}\), 417 cm\({}^{-1}\), 430 cm\({}^{-1}\), 448 cm\({}^{-1}\), 576 cm\({}^{-1}\), 644 cm\({}^{-1}\), and 749.5 cm\({}^{-1}\)[38]. It confirmed the XRD data about the synthesis of \(\alpha\)-Al\({}_{2}\)O\({}_{3}\) inside the aluminum matrix [36]. Figure 4: Raman spectrum of the oxide inclusion inside the Al matrix. Figure 3: Optic photo of the ingot (**a**) and cross-section (**b**) of Al-Al\({}_{2}\)O\({}_{3}\). Micro- and nanosized inclusions of aluminum oxide were also clearly visible in the micrographs in the optic microscope (Figure 5a) and in backscattered electrons in a scanning electron microscope (Figure 5b,c). The EDS spectrum of inclusion showed the content of aluminum and oxygen in the stoichiometric ratio of Al\({}_{2}\)O\({}_{3}\); inclusions of aluminum oxide had sizes close to 100 nm. A very uniform distribution of oxide inclusions inside aluminum grains of the cross-section of Al-Al\({}_{2}\)O\({}_{3}\) composite is presented in Figure 6.  
Inclusions in the form of long rods were crystals of iron aluminide Al\({}_{3}\)Fe (Figure 6), which were present in the starting aluminum as an admixture. According to the phase measurements of the cross-section of this sample, the Al area is 97.5%, Al\({}_{3}\)Fe-1.4%, and Al\({}_{2}\)O\({}_{3}\)-1.2%. The 3D image of the cross-section of AMMC (Figure 5d) also shows a uniform distribution of alumina nanoparticles inside the grain of the aluminum matrix. To prove the possibility of finding nanoparticles mainly inside the grain rather than at the grain boundary, as would be expected from classical considerations, we calculated the value of the critical nucleus (\(r_{c}\)) during the crystallization of aluminum using well-known Formula (7) [39]:  
\[r_{\rm C}=\frac{2\sigma T_{12}M}{Q_{12}\Delta T\rho}, \tag{7}\]  
where \(\sigma\) is the surface tension of the metal melt; \(T_{12}\) is the melting point of the metal; \(M\) is the molecular weight; \(Q_{12}\) is the heat of crystallization (heat of fusion); \(\Delta T\) is the supercooling of the melt, at which the nucleation of the crystallization center occurred; \(\rho\) is the density of the metal. As a result, the value of the radius of the critical nucleus of Al\({}_{2}\)O\({}_{3}\) was \(r_{c}\) = 108.33 nm. Thus, the size of the critical nucleus was three times larger than the initial size of the nanoparticles (30 nm), and the calculated value of synthesized \(\alpha\)- alumina in the aluminum matrix was very close to the experimental one, which varied from 100 to 150 nm. Thus, it can be assumed that nano-\(\alpha\) aluminum oxide formed as a result of the chemical interaction between fused aluminum and nanopowder of titanium dioxide and was not grouped along the grain boundaries but was uniformly distributed in the volume of the aluminum grain (Figures 5 and 6), which is a favorable factor in assessing the mechanical properties of the composite. The composite samples were dissolved in hydrochloric acid HCl solution to determine the quantitative content of aluminum oxide in the produced AMMCs using the volumetric method. The concentration of Al\({}_{2}\)O\({}_{3}\) in the composite was determined by the difference in hydrogen evolution. Figure 6: Elemental distribution map of the Al-1.2% Al\({}_{2}\)O\({}_{3}\) composite cross-section. The data in Table 2 elucidates that an increase in the exposure time and concentration of titanium dioxide in the melt leads to an increase in the mass fraction of aluminum oxide in the composite. However, when the titanium dioxide concentration increased significantly above 1% and exposure time was up to 9 h, it was not possible to obtain samples with a reinforcing phase concentration of more than 19%.