*Article* **Synthesis of C/SiC Mixtures for Composite Anodes of Lithium-Ion Power Sources**

**Anastasia M. Leonova 1,\* , Oleg A. Bashirov 1, Natalia M. Leonova <sup>1</sup> , Alexey S. Lebedev <sup>2</sup> , Alexey A. Trofimov 1,3 and Andrey V. Suzdaltsev 1,3,\***


**\*** Correspondence: a.m.leonova@urfu.ru (A.M.L.); a.v.suzdaltsev@urfu.ru (A.V.S.)

**Abstract:** Nowadays, research aimed at the development of materials with increased energy density for lithium-ion batteries are carried out all over the world. Composite anode materials based on Si and C ultrafine particles are considered promising due to their high capacity. In this work, a new approach for carbothermal synthesis of C/SiC composite mixtures with SiC particles of fibrous morphology with a fiber diameter of 0.1–2.0 μm is proposed. The synthesis was carried out on natural raw materials (quartz and graphite) without the use of complex equipment and an argon atmosphere. Using the proposed method, C/SiC mixture as well as pure SiC were synthesized and used to manufacture anode half-cells of lithium-ion batteries. The potential use of the resulting mixtures as anode material for lithium-ion battery was shown. Energy characteristics of the mixtures were determined. After 100 cycles, pure SiC reached a discharge capacity of 180 and 138 mAh g−<sup>1</sup> at a current of C/20 and C, respectively, and for the mixtures of (wt%) 29.5C–70.5 SiC and 50Si–14.5C–35.5SiC discharge capacity of 328 and 400 mAh g−<sup>1</sup> at a current of C/2 were achieved. The Coulombic efficiency of the samples during cycling was over 99%.

**Keywords:** lithium-ion battery; silicon carbide; electrodeposited silicon; composite material; anode material; Coulombic efficiency

#### **1. Introduction**

Graphite is traditionally used as an anode material of lithium-ion batteries (LIBS) due to its relatively low cost, low volume expansion (up to 10%), high electrical conductivity, charge rate. On the other hand, this material capacity (up to 372 mAh g<sup>−</sup>1) [1–3] no longer meets the requirements of modern devices and machines for an increased energy density.

Promising anode materials with a higher specific capacity for LIBS are transition metal oxides [4–9], silicon [10–14], germanium [15–17], SiC [18,19], as well as various composite mixtures of the above materials with carbon [20–27]. Transition metal oxides seem to be cheap, easy to synthesize. They provide a relatively high capacity (theoretical up to 718 mAh g−<sup>1</sup> [4]; experimental up to 1150 mAh g−<sup>1</sup> [4]) and charge rate, but suffer from high volume expansion (about 96% [8]). Silicon also seems to be a suitable material that provides maximum capacity (theoretical up to 4200 mAh g−<sup>1</sup> [9–12], experimentally achieved—3900 mAh g−<sup>1</sup> [13]) and a sufficiently high charge rate, but drastic volume expansion (up to 300% [10–12]) still presents the biggest challenge to the realization of Si anodes. Germanium is a less accessible material with a lower capacity (theoretical, up to 1624 mAh g<sup>−</sup>1; experimental, up to 1248 mAh g−<sup>1</sup> [16]) compared to silicon, but it provides advantages such as higher electronic conductivity. Moreover, the diffusion coefficient of lithium ions in germanium is 400 times higher than in silicon [17].

**Citation:** Leonova, A.M.; Bashirov, O.A.; Leonova, N.M.; Lebedev, A.S.; Trofimov, A.A.; Suzdaltsev, A.V. Synthesis of C/SiC Mixtures for Composite Anodes of Lithium-Ion Power Sources. *Appl. Sci.* **2023**, *13*, 901. https://doi.org/10.3390/ app13020901

Academic Editor: Gaind P. Pandey

Received: 15 December 2022 Revised: 2 January 2023 Accepted: 6 January 2023 Published: 9 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

<sup>3</sup> Scientific-Research Department of Electrolysis, Institute of High-Temperature Electrochemistry UB RAS, Academicheskaya St. 20, 620137 Yekaterinburg, Russia

Silicon carbide is a perspective easily available anode material with high mechanical, chemical and thermal stability [18,19]. However, for lithiation, pure SiC must have a certain structure and size. Therefore, it is considered more as a matrix or substrate that allows to compensate the volume expansion of silicon. Nevertheless, several works have reported on the LIBs with SiC anode. In [28,29], a decrease in the thickness of SiC films or particles leads to an increase in their capacity from 300 to 1370 mAh g−<sup>1</sup> with a Coulombic efficiency of about 90%. This also explains the significant scatter of the SiC anode capacity in the available papers. Finally, recently a significant number of articles have been devoted to the development of LIBs with composite anode materials represented by silicon, graphite, SiC, SiO*x*, etc., including various sizes and structures: core–shell wires, tubes, needles, fibers, multilayer films of graphene and silicene [30–34]. Calculations showed improved electrochemical parameters of such structures during lithiation/delithiation [35]. Despite the advantages of such composite anodes, their relatively complex production should be noted. Often, single samples are presented in the existing works and nothing is reported about the large-scale production of the materials. At present, the carbothermal method is mainly used for the large-scale production of silicon carbide [36,37]. At the same time, many works are devoted to the metallothermic preparation of SiC [38,39], although these methods require further purification of carbide from intermediate synthesis products.

Previously, we showed the possibility of synthesizing ultrafine SiC fibers from cheap materials using carbothermal synthesis [40,41]. The feature of our method is the use of natural samples of pure quartz and graphite with a certain morphology and particle size. In this work, in addition to the obtaining of SiC, this approach was also used for obtaining of C/SiC mixtures suitable for use as composite anodes of lithium-ion power sources.

#### **2. Materials and Methods**

Scheme of the synthesis: The synthesis of SiC powder was carried out in a graphite crucible, which was placed in a protective alumina crucible. Mixture of SiO2 and graphite powder with molar ratio of 1–3 was prepared by hand mixing in agate mortar and placed in a crucible. Graphite crucible was covered with graphite cap and buried under extra graphite layer. Synthesis was conducted at a temperature of 1600 ◦C for 5 h under CO atmosphere. In such reactor and conditions, the atmosphere maintained stable due to the oxidation of graphite powder [40,41]. The scheme for the synthesis of SiC-based mixtures with different compositions is shown in Figure 1. It was shown experimentally that mixtures with 40–95 wt% SiC and unreacted graphite are formed during synthesis depending on the given SiO2:C ratio, temperature and synthesis duration; the products may also contain traces of silicon and its nonstoichiometric oxides, which are removed by additional treatment in the HF solution. Therefore, the primary synthesis products are the C/SiC mixtures. The ratio of components in such mixtures can be controlled in order to obtain required mixture.

**Figure 1.** Process flow diagram for obtaining C/SiC mixtures for the manufacture of LIBs anodes.

In this work we synthesized a C/SiC mixture and pure SiC that were studied in the anode half-cell of LIBs. Along with these materials, a composite anode based on the resulting C/SiC mixture with the addition of electrtodeposited silicon fibers from the KCl–K2SiF6 melt was also tested [42].

Analysis of the morphology and composition: The chemical and phase composition of the reagents and products was determined by inductively coupled plasma atomic emission

spectroscopy (AES-ICP) using iCAP 6300 Duo Spectrometer (Thermo Scientific, Waltham, MA, USA), X-ray phase analysis (XRD) using Rigaku D/MAX-2200VL/PC diffractometer (Rigaku, Tokyo, Japan) and Raman spectroscopy using U1000 Raman spectrometer (Renishaw, New Mills, UK). The morphology and elemental composition of the obtained samples were studied using a Tescan Vega 4 (Tescan, Brno–Kohoutovice, Czech Republic) scanning electron microscope with Xplore 30 EDS detector (Oxford, UK).

Electrochemical performance: Electrochemical performance of SiC, C/SiC and Si/C/SiC anodes were investigated in a 3-electrode half-cell. The obtained compositions were mixed with 10 wt% polyvinylidene fluoride dissolved in N-methyl-2-pyrollidone without any other additives. LIBs anode half-cell fabrication was performed in an argonfilled glove box (O2, H2O < 0.1 ppm). Stainless steel mesh with the applied composite anode material was used as the working electrode and two separate lithium strips as the counter and reference electrodes. All electrodes were divided by 2 layers of polypropylene separator and tightly placed in the cell. The cell was filled with 1 mL of electrolyte—1 M LiPF6 in a mixture of ethylene carbonate/dimethyl carbonate/diethyl carbonate (1:1:1 by volume). Electrochemical measurements and cycling experiments were performed using a Zive-SP2 potentiostat (WonATech, Seoul, Republic of Korea).

#### **3. Results**

#### *3.1. Samples Characterization*

C/SiC mixtures: Figure 2 shows a SEM-image of a C/SiC mixture and maps of elemental distribution after carbothermal synthesis and treatment in HF solution. The resulting mixture is represented by particles with a size of about 20–40 microns (graphite) and smaller fibers (SiC). According to X-ray microanalysis, the content of the elements was (wt%) silicon 47.5–51.3; carbon 47.7–51.7; oxygen—up to 1.6. The presence of oxygen could be due to both the insufficient treatment time of the mixture in the HF solution and the subsequent oxidation of the silicon or SiC presented in the mixture. According to ICP analysis, the resulting mixture contained 48.8–49.4 wt% silicon (the rest was carbon) and no more than 0.4 ppm of such impurities as Fe, Al, Ti and Ca. If we do not take into account the presence of oxygen, the ratio of components corresponds to a mixture of (wt%): 70.5SiC-29.5C.

**Figure 2.** SEM-images and elements distribution in a C/SiC mixture after carbothermal synthesis and treatment in HF solution.

SiC: Figure 3 shows a SEM-image of a typical SiC agglomerate obtained after annealing of residual carbon from a C/SiC mixture. Its total size is about 50–60 μm. It consists of fibers with a diameter of 0.1 to 2 μm. The obtained morphology is similar to the previously obtained samples of ultrafine SiC [40] since the reagents and the synthesis procedure were reproduced almost completely. The distribution of elements in the resulting SiC are also shown. Uniform distribution of silicon, carbon and oxygen is observed for this sample. According to X-ray microanalysis, the average content of elements at different points of the sample was (wt%): 68–69 silicon, 29–30 carbon, up to 1.6 oxygen. This ratio is close to the SiC stoichiometric composition.

**Figure 3.** SEM-images and elements distribution in a SiC sample after carbothermal synthesis, oxidation of unreacted graphite, and treatment in HF solution.

Figure 4 shows the X-ray diffraction patterns and Raman spectra for C/SiC and SiC samples. For the C/SiC sample there are peaks of residual SiO2 (21–22◦), carbon (26–27◦), as well as peaks indicating presence of two carbide modifications (α-SiC, β-SiC) in sample (35–36◦, 41.5◦, 44.5◦, 55◦ and 60◦). For the SiC sample, there are no peaks of C and SiO2; only additional signals of the β-SiC phase appear at 64.5◦. A similar picture is also observed in Raman spectra, in which responses of α-SiC and β-SiC carbide modifications at 770–793 cm–1 were fixed. In this case, for the SiC sample, there is also a response at 502 cm–1 that can correspond to both residual silicon and the β-SiC modification [43]. Moreover, there are lines near 1370, 1510 and 1585 cm−<sup>1</sup> on both spectra, which indicate the C–C bonds. In this work, the structure of the used graphite powder was not studied in detail. However, based on the absence of pronounced peaks and intensity ratio of carbon lines, one can only note the presence of different carbon structures [44–47]. For the SiC sample, the intensities of these lines are less pronounced.

**Figure 4.** X-ray diffraction patterns (**a**) and Raman spectra (**b**) for the obtained C/SiC and SiC samples.

Electrodeposited Si: Figure 5 shows a SEM-image of silicon deposits obtained by electrolysis of the (wt%) 98KCl–2K2SiF6 melt at a temperature of 780 ◦C and a cathode current density of 25 mA cm–2. A detailed procedure and parameters for silicon synthesis were provided earlier [42]. The resulting silicon deposits are arbitrarily shaped fibers with a diameter in the range of 0.45–0.55 μm and a length of up to 20–25 μm. According to X-ray microanalysis data, the oxygen content in the obtained silicon was from 1.2 to 1.5 wt% and other impurities did not exceed 0.18 ppm (mainly iron and nickel). Figure 6 shows the X-ray diffraction pattern and the Raman spectra of silicon deposit. As can be seen, the sample is represented by polycrystalline silicon with SiO2 impurities. This is also indicated by the Raman spectra of the sample in which only the Si–Si bond at 510 cm−<sup>1</sup> was found [43].

**Figure 5.** SEM-image and the elements distribution in a Si sample obtained by electrolysis of the (wt%) 98KCl-2K2SiF6 melt at a temperature of 780 ◦C and a cathode current density of 25 mA cm<sup>−</sup>2.

**Figure 6.** X-ray diffraction pattern (**a**) and the Raman spectra (**b**) of silicon deposit.

#### *3.2. Electrochemical Performance of the Comosite Anodes*

C/SiC composite anode: Figure 7 shows the change in the C/SiC composite anode potential during lithiation/delithiation, as well as changes in the discharge capacity and Coulombic efficiency of the sample during cycling. When the C/SiC composite anode sample was initially charged with a current of 0.1 C (first cycle) its charging capacity was 658 and discharge capacity was 322 mAh g−<sup>1</sup> (Coulombic efficiency is 49%). Such capacity loss is usually attributed to a solid–electrolyte interface (SEI) layer formation. All subsequent cycling was carried out at a current of 0.5 C. In the second cycle, the discharge capacity was 308 mAh g−<sup>1</sup> (Coulombic efficiency is 92%), and after the 100th cycle the discharge capacity was 328 mAh g−<sup>1</sup> (see Figure 7c). During cycling, the Coulombic efficiency of the C/SiC anode reached 99% and remained at this level even after capacity began to fade.

**Figure 7.** *Cont.*

**Figure 7.** Cycling of C/SiC electrode: (**a**) potential change during lithiation (dashed line) and delithiation (solid line); (**b**) discharge capacity and Coulombic efficiency; (**c**) CVs at different scan rates and log(*I*)–log(ν) dependencies; (**d**) EIS data with equivalent circuit diagram.

Figure 7c shows current–voltage dependences (CVs) characterizing the kinetics of charge and discharge of a C/SiC composite anode material. It can be noted that the beginning of the charge occurs at an electrode potential negatively than 0.22 V relative to the potential of the lithium electrode. This behavior may be due to the interaction of lithium ions with the electrode material, which is accompanied by the chemical formation of compounds. In this case the presence of several peaks in the cathode region of the CVs indicates the occurrence of several lithiation reactions. At a potential of about 0.05 V a lithium reduction wave is formed. During discharge in the anodic region of the CVs in the potential range from 0.05 to 0.5 V there are corresponding discharge (oxidation) peaks of lithium. Moreover, the shift in the peak potentials of the lithium reduction and oxidation indicates that the processes is not electrochemically reversible. Obviously, the irreversibility may be due to the interaction of lithium with the anode material. Since the LIBs capacity includes the contribution of both diffusion and capacitance reactions the expression [48] is valid for the usual lithiation/delithiation process:

$$
\log(I) = \log(a) + b \log(\mathbf{v}) \tag{1}
$$

where *I*—peak current, A; ν—potential sweep rate, V s<sup>−</sup>1; *a* and *b*—constants. In our case, the calculated *b* value was of 0.73 (see Figure 7c), which indicates the pseudocapacitive behavior of the C/SiC anode material [48]. This may be associated with a slow chemical reaction of silicon carbide with lithium. Figure 7d shows the electrochemical impedance spectra (frequency range from 100,000 to 1 Hz) of the sample after the forming cycle. The EIS contains two arcs corresponding to the processes of charge transfer through the electrolyte layer and between the electrode and electrolyte [49–51]. The obtained data can be described by a typical for LIBs equivalent circuit. It has two RC circuits connected in series and a resistance (Figure 7e). Parameters changes in this scheme during cycling have not yet been studied.

SiC anode: The cycling results of the SiC electrode are shown in Figure 8. When the SiC electrode sample was initially charged at a current of C/20 (first cycle) its charge capacity was only 78 and the discharge capacity was of 42 mAh g−<sup>1</sup> (Coulombic efficiency is 54%). During further cycling, the capacity gradually increased. After the 60 cycles at C/20, capacity increased up to 180 mAh g<sup>−</sup>1. This situation can be caused by gradual activation of the anode material accompanied by partial destruction of SiC and the formation of Li–C and Li–Si compounds [28,29] via the reactions:

$$\text{SiC} + \text{xLi}^+ + \text{x}^{\text{e}-} \rightarrow \text{Li}\_x\text{Si}\_y\text{C} + (1-y)\text{Si}\ (y<1) \tag{2}$$

$$\text{Si} + z\text{Li}^+ + ze^- \leftrightarrow \text{Li}\_2\text{Si} \tag{3}$$

**Figure 8.** Changes in the discharge capacity and Coulombic efficiency of the SiC sample during cycling at a current of C/20 and C.

As a result, a gradual conversion of SiC to Si and C occurs [28,29]. In turn, reactions (1) and (2) also explain the reason for the onset of lithium discharge on anodes with SiC at a potential 0.22 V more positive than the lithium potential (see Figure 7b). With an increase in the charge current to C, the discharge capacity decreased, while its value was stable during 100 cycle and the Coulombic efficiency was more than 99.2%. Relatively low capacity can be explained by the presence of voids (see Figure 3) and a lack of the electrical contact between stiff SiC wires.

Si/C/SiC anode: Figure 9 shows the changes of the Si/SiC/C electrode potential during lithiation and delithiation as well as changes in its discharge capacity and Coulombic efficiency during cycling. A voltage plateau below 0.1 V (Figure 9a) indicates lithiation of graphite and silicon; delithiation occurs at 0.15–0.4 V. Similar results were obtained for lithiation of the silicon anode [52]. In the first cycle at a current of C/20, the discharge capacity was 225 mAh g−<sup>1</sup> and the initial Coulombic efficiency was 54%. Coulombic efficiency gradually increased during further cycling at a current of 0.5C and remained above 98% after 20 cycles (Figure 9b). The discharge capacity gradually increased up to 525 mAh g−<sup>1</sup> after 40 cycles. The higher capacity value can be explained by the silicon lithiation in the anode material and the additional increase during cycling can be explained by the gradual activation of the electrode, as in the case of the SiC anode (see Figure 8a). The subsequent decrease in the discharge capacity to 400 mAh g−<sup>1</sup> by the 100th cycle may be due to the contact loss of part of the anode material with the substrate due to the local expansion and cracking of silicon.

Figure 9c shows the CVs obtained at different scan rates for the Si/SiC/C electrode. There are clear redox peaks indicating the charge and discharge of the sample. In this case the calculated value of *b* was 0.63 (see Figure 9c). This indicates that the operation of the Si/C/SiC electrode mainly proceeds under lithium diffusion conditions. A distinctive feature of the obtained CVs is also the fact that the charge and discharge currents of the anode sample are observed in a wider potential range (0.8–0.1 and 0.1–1.4 V respectively), which is due to the higher bonding energy of lithium with silicon and a larger number of compounds in the Li–Si system [52–54].

Figure 9d shows the electrochemical impedance spectrum of the Si/C/SiC sample after the forming cycle. One can note the relatively high resistance R1 (7.7 Ω), which can result in a significant change in the parameters of two series-connected RC chains (R2, C2, R3 and W1) [49,50]. The decrease in R1 will be the subject of our further research.

**Figure 9.** Cycling of Si/C/SiC electrode: (**a**) potential change during first cycle lithiation (dashed line) and delithiation (solid line); (**b**) discharge capacity and Coulombic efficiency; (**c**) CVs at different scan rates and log(*I*)–log(ν) dependencies; (**d**) EIS data with equivalent circuit diagram.

The lithiation mechanism of of the Si/C/SiC anode as a whole can be represented by the parallel flow of reactions (2) and (3) as well as reactions (4)–(6):

$$\rm{Li} + \rm{xLi^{+}} + \rm{xe^{-}} \leftrightarrow \rm{Li\_{x}Si} \tag{4}$$

$$\text{Li}\_{\text{x}}\text{Si} + y\text{Li}^{+} + ye^{-} \leftrightarrow \text{Li}\_{\text{(x}+y)}\text{Si} \tag{5}$$

$$\text{C} + z\text{Li}^+ + z\text{e}^- \leftrightarrow \text{Li}\_2\text{C} \tag{6}$$

Accurate estimation of the lithiated products and intermediate products (or its absence) on the basis of peak potentials is difficult. In the literature, there is a very wide spread of the potentials of the occurring reactions and the available analysis methods (EDX, XRD) do not allow one to make a local assessment with the required accuracy when a thick SEI layer is formed.

The partial replacement of SiC with electrodeposited Si leads to an increase in the discharge capacity of the anode, while the cycling stability of the Si/C/SiC composite electrode is lower. In this regard, further work will be aimed at studying the morphology and composition of samples after cycling in order to identify ways to optimize anode composition.

#### **4. Conclusions**

Nowadays, one of the most popular issues is connected with the search of anode materials for high energy density lithium-ion batteries. One of the promising materials that meet these requirements are composite materials based on Si/C/SiC mixtures. In such materials, silicon provides increased capacitance, graphite provides high electrical conductivity and SiC provides strength and thermal stability.

In this work, we proposed a new approach for the fabrication of composite anodes based on SiC as well as mixtures of C/SiC and Si/C/SiC. The proposed approach includes carbothermal synthesis and makes it possible to exclude complex equipment and expensive reagents for the anode materials synthesis. Using the proposed method, samples of C/SiC and SiC were synthesized and investigated. A sample of Si/C/SiC was fabricated with the addition of electrodeposited silicon fibers. It was shown that the synthesized SiC is represented by agglomerates of carbide fibers with diameter ranging from 0.1 to 2 μm; the C/SiC mixture is represented by evenly distributed fibers over the matrix of unreacted graphite; silicon is represented by arbitrary shape fibers with a diameter ranging from 0.45 to 0.55 μm.

Electrochemical behavior of the synthesized samples was studied as part of the anode half-cell of a lithium-ion battery. The possibility of using the obtained samples as part of the composite anode is shown. After 100 cycles pure SiC reached a discharge capacity of 180 and 138 mAh g−<sup>1</sup> at a current of C/20 and C, respectively. The mixtures of (wt%) 29.5C-70.5 SiC and 50Si-14.5C-35.5SiC reached a discharge capacity of 328 and 400 mAh g−<sup>1</sup> respectively at a C/2 current. The Coulombic efficiency of sample cycling was over 99%. The parameters of the equivalent circuits of the half-cells were estimated and ways to optimize their manufacturing process are noted.

**Author Contributions:** Conceptualization, A.V.S.; methodology; A.M.L., A.S.L. and N.M.L.; validation, A.S.L. and A.V.S.; formal analysis, A.M.L., O.A.B. and N.M.L.; investigation, A.M.L., O.A.B., A.S.L. and N.M.L.; writing—original draft preparation, A.M.L., A.A.T. and A.V.S.; writing—review and editing, A.V.S.; supervision, A.V.S.; project administration, A.V.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** This work is performed in the frame of the State Assignment number 075-03- 2022-011 dated 01/14/2022 (the theme number FEUZ-2020-0037). The elemental composition of the samples was analyzed using the equipment of the Central Research Laboratory "Composition of compounds" (IHTE UB RAS).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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### *Article* **Disks of Oxygen Vacancies on the Surface of TiO2 Nanoparticles**

**Vladimir B. Vykhodets 1,\*, Tatiana E. Kurennykh <sup>1</sup> and Evgenia V. Vykhodets <sup>2</sup>**


**Abstract:** Oxide nanopowders are widely used in engineering, and their properties are largely controlled by the defect structure of nanoparticles. Experimental data on the spatial distribution of defects in oxide nanoparticles are unavailable in the literature, and in the work presented, to gain such information, methods of nuclear reactions and deuterium probes were employed. The object of study was oxygen-deficient defects in TiO2 nanoparticles. Nanopowders were synthesized by the sol–gel method and laser evaporation of ceramic targets. To modify the defect structure in nanoparticles, nanopowders were subjected to vacuum annealings. It was established that in TiO2 nanoparticles there form two-dimensional defects consisting of six titanium atoms that occupy the nanoparticle surface and result in a remarkable deviation of the chemical composition from the stoichiometry. The presence of such defects was observed in two cases: in TiO2 nanoparticles alloyed with cobalt, which were synthesized by the sol–gel method, and in nonalloyed TiO2 nanoparticles synthesized by laser evaporation of ceramic target. The concentration of the defects under study can be varied in wide limits via vacuum annealings of nanopowders which can provide formation on the surface of oxide nanoparticles of a solid film of titanium atoms 1–2 monolayers in thickness.

**Keywords:** nanoparticles; TiO2; oxygen vacancies; nuclear reactions; deuterium probes

**Citation:** Vykhodets, V.B.; Kurennykh, T.E.; Vykhodets, E.V. Disks of Oxygen Vacancies on the Surface of TiO2 Nanoparticles. *Appl. Sci.* **2022**, *12*, 11963. https://doi.org/ 10.3390/app122311963

Academic Editor: Suzdaltsev Andrey

Received: 27 October 2022 Accepted: 18 November 2022 Published: 23 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **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 [3–5]. For example, a concept of d0-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 TiO2, Al2O3, ZnO, In2O3, HfO2, CuO, and others [7–11].

The majority of results concerning the defect structure of oxide nanoparticles are obtained for the TiO2 nanoparticles with the use of a large number of techniques [3,5,8,12–15]. 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 [3,5,8,12–15], 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], Ti3+ 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 [3,16–20], 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 TiO2 nanoparticles as the object for investigation is conditioned by a wide scope of practical applications of the dioxide titanium nanopowders [21–25]. 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 TiO2 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. The application of the DP method was reasonable since, first, it is sensitive to defects bringing about oxygen deficiency [2] and, second, owing to a drastic difference in its basic principles from those of the earlier applied techniques, it enables one to detect defects of unknown types. The NRA and DP techniques have already been used to measure the oxygen and defect concentrations in oxide nanoparticles [2,26–28], but in these works, the type of defects and their spatial distribution in nanoparticles were not the subject of research.

#### **2. Experimental**

#### *2.1. Synthesis of Oxide Nanopowders*

Nanopowders were produced by the technology of laser evaporation of ceramic target (LE) [26] and sol–gel method (SG) [16,29]. As an LE, pills of titanium dioxide 60 mm in diameter were produced by pressing at room temperature, with the specific surface area of micropowder being 2 m2/g. For vaporizing, a fiber-ytterbium laser was used with a wavelength of 1.07 μm and a maximal power output of 1 kW; the frequency of laser pulses was 5 kHz, duration was 50 μs. To produce nanopowders with a different specific area, the type of inert gas (argon or helium), gaseous pressure, and laser power were varied. For the synthesis of titanium oxide nanoparticles doped with cobalt ions by the SG method [29], acid hydrolysis of organometallic precursors was employed; in our case, titanium isopropyl oxide (Titanium (IV) isopropoxide) and cobalt (II) acetylacetonate as a source of metal ions. All reagents used were obtained from Sigma Aldrich. The preliminary required amounts of titanium isopropoxide (2 mL) and cobalt acetylacetonate complex were placed in a 5 mL test tube; then, 2 mL of acetone was poured into it. After vigorous shaking, a bluish-brown solution was formed. The solution was left overnight. Then, 1 mL of hydrochloric acid (0.1M) was poured into the solution. The hydrolysis reaction occurs almost instantly; however, for the process to run uniformly throughout the entire volume of the colloid, it was subjected to intensive ultrasonic action using an ultrasonic activator with a submerged titanium probe. Ultrasound exposure was 30 s. Then, the particles were separated by centrifugation (10,000 RPM) for 10 min and washed with acetone. The washing process was repeated three times. The resulting precipitate was dried at 70 ◦C. The precursor was further calcined in air at different temperatures (from 300 to 500 ◦C). Figure 1 shows micrographs of nanoparticles calcined at 400 and 500 ◦C, the image was obtained using transmission electron microscopy (TEM).

**Figure 1.** TEM micrographs of the TiO2 nanoparticles calcined at 400 ◦C (**A**) and 500 ◦C (**B**).

#### *2.2. Methods of Nuclear Reactions and Deuterium Probes*

All nanopowders predominantly contained such phases of titanium dioxide as anatase, rutile, brookite, and their mixtures. Data on the phase composition are given in more detail in Section 3.1. In the current approach, the defect structure is characterized by the oxygen concentration *CO* and defect concentration *Cd* and real defects contain a certain number of elementary point defects. Hence, a real defect can comprise vacancies and interstitial atoms of oxygen and titanium. Within the approach accepted, an oxygen vacancy cannot be distinguished from an interstitial titanium atom, the same as a titanium vacancy from an interstitial oxygen atom. When interpreting the results of studying the thus prepared samples, we considered solely oxygen vacancies as the most realistic elementary point defects. In the DP technique, after annealing in gaseous deuterium, nanopowders become three-component and their chemical composition can be presented by formula TiO2−*<sup>x</sup>*D2*x*/*N*, which accounts for the presence of 2 deuterium atoms per one defect [2]. Moreover, oxygen vacancies are supposed to be prone to joining in clusters, and *N* designates the amount of vacancies in a cluster. This formula enables easily obtaining that concentrations *CO* and *Cd* are connected as follows

$$\frac{\mathbb{C}\_O}{\mathbb{C}\_O^0} = 1 - \frac{N+4}{3\mathbb{C}\_O^0} \mathbb{C}\_{d\prime} \tag{1}$$

where *C*<sup>0</sup> *<sup>O</sup>* is the oxygen concentration in a defectless oxide; herefrom, concentrations are expressed in fractions of the number of atoms in a nanoparticle. It is seen from Expression (1) that when treating the dependences *CO*(*Cd*), the number of vacancies in a defect *N* can be determined if oxygen vacancies are combined in complexes. Expression (1) is obtained for nanoparticles of arbitrary shape and does not depend on the spatial distribution of defects and mutual arrangement of vacancies in a cluster. For example, it is valid for cases when defects are distributed in a nanoparticle uniformly or only in its thin surface layer with vacancies forming in a cluster of both 2D and 3D complexes.

When using the method of LE, the average concentrations *CO* and *Cd* were varied via the synthesis of nanopowders with different specific surface areas *S*. This approach makes it possible to produce nanopowders with different *CO* and *Cd*, if the concentrations of defects in the bulk and near the surface are different. In the SG technology, nanopowders with different defect concentrations were produced using vacuum annealings. In the preliminary experiments, it was established that vacuum annealings are by no means a universal way of decreasing the oxygen concentration in the titanium dioxide nanopowders. In particular, in the case of undoped TiO2, vacuum annealings exert a poor effect on the concentrations of oxygen and defects, which did not allow the analysis of the *CO*(*Cd*) dependence with reliable accuracy. At the same time, Co-doped nanopowders of TiO2 with widely ranging oxygen concentrations were prepared using vacuum annealings. The same result was obtained in work [5], where it was shown that alloying of TiO2 with cobalt

leads to increasing vacancy concentration. In view of this, in the case of the SG method, investigation of the dependence *CO*(*Cd*) was performed on powders alloyed with cobalt, its concentration in the cation sublattice made up of 3 at. %. Vacuum annealings were carried out after completion of the synthesis routine at temperatures varying from 200 to 500 ◦C and holding time, 15 to 30 min, 500 ◦C.

To measure the defect concentration using the DP method, first, nanopowders are annealed in gaseous deuterium, and then, the concentration of dissolved deuterium *CD* is measured using the NRA technique. The DP method is shown in work [2] to be sensitive to defects bringing about oxygen deficiency in nanoparticles and is based on the existence of unambiguous relation of the *Cd* and *CD* concentrations, which is provided by the formation of nanoparticles annealed in deuterium of clusters of a strictly specified composition. In particular, in the TiO2 nanoparticles, one cluster consists of a defect and 2 deuterium atoms. The cluster composition was determined using the dependence of *CD* on the dose of deuterium irradiation. In the current work, such a procedure was applied to all powders after synthesis and vacuum annealings, and the cluster composition was the same. In general, nanoparticles can contain defects of different types simultaneously. For example, in study [2], in the TiO2 particles, along with defects detectable for the DP method, one more type of defect was observed, which consisted of Ti3+ ions and oxygen vacancies. The duration of deuterium annealing we used was, just as in [2], 1 h, with deuterium pressure being 0.6 atm. In the DP method, the determination of the defect concentration *Cd* is reduced to measuring the deuterium concentration *CD*. For this reason, the metrological characteristics of the NRA technique for the reaction 2H(d,p)3H controlled the accuracy and sensitivity in the determination of the defect concentration *Cd*: statistical error made up several percent of the measured value and measurement sensitivity was about 0.01 at. %.

As was noted in Section 1, no experimental data on the spatial arrangement of defects in oxide nanoparticles are available in the literature. Such a task is objectively complicated because of the small size of nanoparticles. In the current work, a particular solution was obtained. It is based on an approach that involves the characterization of the defect structure using only two defect concentrations, namely, at the surface of nanoparticle *Cds* and average concentration in the nanoparticle bulk *Cdv*. For the powders synthesized using LE, we investigated the dependence of defect concentration on the specific surface area *Cd*(*S*), which allowed us to obtain, in the model with two concentration values *Cds* and *Cdv*, information on the spatial distribution of defects in nanoparticles. For example, the growth of *Cd* with increasing *S* means higher defect concentration near the surface then in the bulk and vice versa. If *Cds* = *Cdv*, the defect concentration *Cd* evidently is independent of *S*. In this work, of special interest was the case when defects to which the DP method is sensitive are localized near the nanoparticle surface. In this case, the chemical composition of nanopowders can be expressed by the formula (1 − Δ*ρS*)TiO2(Δ*ρS*) TiO2−*<sup>y</sup>* D2*y*/*<sup>N</sup>* , and the following relationship works:

$$\mathcal{C}\_d = \frac{\Delta y \rho S}{N(3 - \Delta y \rho S)}\,\text{}\tag{2}$$

where *ρ* is the oxide density, Δ is the thickness of the oxygen-deficient layer whose chemical composition is denoted as TiO2−y. Expression (2) is valid for particles of arbitrary shape. Hence, with equal parameters *N*, Δ, and *y*, in the powders with different specific area *S*, the dependence *Cd*(*S*) will be close to linear, with the extrapolated value *Cd*(0) = 0. Since the DP method provides a high accuracy in measuring the defect concentration, in some particular cases the study of *Cd*(*S*) can give reliable information on the ratio of defect concentrations in the bulk and near the nanoparticle surface. Note that application of this approach is bound to solely the case when powders are synthesized by LE technology. It favors independence of the parameters, Δ, and *y* of *S*, which will be considered in Section 3.2.

The average concentrations of oxygen *CO* and deuterium *CD* in nanopowders were determined by the NRA technique at a 2 MB van de Graaf accelerator using reactions 16O(d,p1) 17O\* and 2H(d,p)3H with the deuteron energy of 900 and 650 keV, respectively. In the majority of experiments in the accelerator, the samples were at room temperature and nanoparticles of powders were pressed into an indium plate. When the concentration *CO* was measured at the temperature of 400 ◦C, nanoparticles were pressed into copper powder. Using Rutherford backscattering spectroscopy, it was established that indium or copper atoms were absent in the zone under analysis. The sample surface was set perpendicular to the incident beam, nuclear reaction products were registered with the use of a silicon surface barrier detector. The angle of proton registration was 160◦, and the diameter of the incident beam was 1 or 2 mm. The irradiation dose was measured on the samples using a secondary monitor, with the statistical error being 0.2 to 1.0%. When mathematically processing the data, spectra from the samples under study were compared with those from reference samples having constant-in-depth isotope concentrations. For 16O, it was CuO, whereas for deuterium, ZrCr2D0.12. In more detail, the experimental setting and processing procedure are described in work [2].

When doing this, it was necessary to provide highly accurate measurements of concentrations *CO* and *CD*, which was not trivial as the data on *CO* depended on the presence on the nanoparticle surface of water molecules. With increasing the thickness of the water layer, the oxygen concentration in factions of the number of atoms in a nanoparticle decreases since the H2O molecule contains fewer oxygen atoms than TiO2. In view of this, the powders were dried under vacuum pumping-off. To monitor the oxygen concentration *CO*, sampling measurements of the powders were performed in the accelerator chamber at 400 ◦C, which allows the elimination of the adsorbed water molecules. The results of the concentration *CD* and *Cd*, unlike *CO*, were not changed when varying experimental conditions, temperature, pressure, and annealing time. In addition, these results did not depend on the conditions of storing the powders for a year and more, since the deuterium annealing provided the elimination of water molecules from the nanoparticle surface. Figure 2 shows the spectra of protons p for the nuclear reactions 16O(d,p1) 17O\* and 2H(d,p)3H, which were used to determine the oxygen and defect concentrations. The *CO* and *Cd* concentrations are directly proportional to the number of registered protons, the shape of the spectra does not depend on *CO* and *Cd*.

**Figure 2.** The spectra of products of the nuclear reactions 16O(d,p1) 17O\* and 2H(d,p)3H for the nanopowders synthesized by sol–gel method and annealed in vacuum. The temperatures and annealing times are shown in the figure.

#### **3. Results and Discussion**

#### *3.1. Number of Oxygen Vacancies in a Defect*

The dependence *CO*(*Cd*) shown in Figure 3 agrees with Expression (1), which testifies to the formation in the TiO2 nanoparticles of defects consisting of oxygen vacancies. Processing by the least-square method gave the number of vacancies in a defect *N* = 12.5 ± 0.9.

**Figure 3.** Dependence of the oxygen concentration *CO* in TiO2 nanopowders on the defect concentration *Cd*. Black points show results for powders synthesized by sol–gel method; red points, laser evaporation of ceramic target.

As follows from Figure 3, the formation in the dioxide titanium nanoparticles of defects containing *N* = 12 oxygen vacancies is invariant with respect to experimental conditions. First, it takes place in the nanopowders synthesized by different technologies and characterized by different mechanisms of defect formation. In the technology of SG method, in the as-synthesized powders of composition close to stoichiometric, the formation of defects occurs in the course of vacuum annealing through the oxygen depletion of nanoparticles. Upon LE, oxygen-deficient defects were formed directly in the course of synthesizing. Second, the powders strongly differ in the number of defects per unit volume of nanoparticles. This follows from Figure 2 since this parameter decreases with decreasing concentration *CO*. Finally, the powders under study differed in phase composition. In the case of the SG method, it was anatase, whereas upon LE, the mixture of TiO2 phases. In particular, in the powders with S > 200 m2/g, brookite with small additions of anatase and rutile predominates, whereas at S < 200 m2/g, quite the opposite, brookite was not observed at all, only anatase and rutile. Since the number of vacancies in a defect *N* = 12 does not depend on the synthesis technology, mechanism of defect formation, phase composition, and other characteristics of nanoparticles, one can suggest that the formation of such defects, denoted as Ti6, is conditioned by thermodynamic reasons. This question needs further investigation.

#### *3.2. Spatial Distribution of Defects Ti6 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 *Cd*(*S*) was studied for the powders synthesized by the LE. As is seen in Figure 4, the experimental dependence *Cd*(*S*) matches Expression (2) at constant parameters *N*, Δ, and *y*, which indicates that the defects consisting of 12 oxygen vacancies are located on the surface and absent in the bulk of TiO2 nanoparticles.

**Figure 4.** Dependence of the defect concentration *Cd* on the specific surface area *S* of TiO2 nanoparticles. Points are experimental data for the powders synthesized by laser evaporation of ceramic targets. Line is calculated by Expression (2) at *<sup>N</sup>* = 12 and <sup>Δ</sup>*<sup>ρ</sup>* y = 7.56 <sup>×</sup> <sup>10</sup>−<sup>8</sup> g/cm2.

The independence of the parameter *N* on *S* was experimentally shown in Section 3.1. As for the parameters Δ 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 TiO2 [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 Ti6 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 Ti6 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 Ti6 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 TiO2 particles, there are present two types of regions: (i) consisting of 6 titanium atoms and (ii) having composition close to stoichiometric TiO2. 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 Ti6 defect, the fraction of nanoparticle surface occupied by regions consisting of 6 titanium atoms is expressed as

$$\infty = \frac{1 - \mathbb{C}\_{\mathcal{O}} / \mathbb{C}\_{\mathcal{O}}^{0}}{\Delta \rho \mathbb{S} (1 - \mathbb{C}\_{\mathcal{O}})} \le 1. \tag{3}$$

In Figure 5, the dependences ∝ *CO*/*C*<sup>0</sup> *O* calculated by Expression (3) for several values of *S* are shown. Points in Figure 5 show sampling experimental results, data on *y*  *CO*/*C*<sup>0</sup> *O* are also given. It is easy to show that the values of ∝ and *y* obey the expression *y =* 2∝. Bends on the dependences ∝ *CO*/*C*<sup>0</sup> *O* correspond to the formation on the nanoparticle surface of a solid monolayer in which oxygen atoms are absent. The horizontal portions of the dependences ∝ *CO*/*C*<sup>0</sup> *O* correspond to the formation in nanoparticles of one more monolayer deficient in oxygen. It follows from Figure 5 that the fraction ∝ that is taken by regions consisting of 6 titanium atoms can be an easily controlled parameter. In particular, this refers to nanoparticles of TiO2 produced by the SG method. In the as-synthesized state, they are virtually stoichiometric (∝≈ 0), and by vacuum annealings and alloying with cobalt, this value can be increased to 1.

**Figure 5.** Dependence of the parameters ∝ and *y* for the surface monolayer of the titanium dioxide nanoparticles on the oxygen concentration *CO*/*C*<sup>0</sup> *<sup>O</sup>* in nanopowders. Lines show the calculation results by Expression (3): green—for nanopowders with the specific area 222 m2/g; black, 156 m2/g, red, 130 m2/g, and blue, 70 m2/g. Points are sampling results for the nanoparticles under study: filled ones refer to the powders synthesized by the sol–gel method; empty, laser evaporation of ceramic target.

It is shown that under certain conditions, in the TiO2 nanoparticles there form twodimensional defects consisting of 6 titanium atoms and localized on the nanoparticle surface, which results in a significant deviation of the chemical composition from the stoichiometry. Since, as noted in Section 1, in the TiO2 nanoparticles there are present defects of other types, of interest is to compare the data on the concentration of surface two-dimensional defects with those obtained in previous studies. Unfortunately, in view of the absence of such information in works on oxide nanoparticles, we have to restrict ourselves to rough estimates. In a general case, defects of almost all types cause changes in the chemical composition of nanoparticles and their presence in the samples gives rise to a deviation from the linear dependence in Figure 3. Since in the work no deviations beyond the statistical experimental errors were registered, one can conclude that the concentration of other defects was far smaller than that of defects consisting of 6 titanium atoms.

#### **4. Conclusions**

Thus, new data on the defects that condition the oxygen deficit in the oxide nanoparticles of TiO2 have been gained. The formed two-dimensional defects of atomic thickness are established to consist of six titanium atoms. They are free of oxygen atoms and located on the nanoparticle surface. The presence of such defects is detected in two cases: in the cobalt-doped nanoparticles of TiO2 synthesized by the sol–gel method and subjected to vacuum annealings and undoped nanoparticles synthesized by laser evaporation of ceramic target. The data on the defect structure were obtained by the method of deuterium probes, DP, which was applied to measure the defect concentrations, and by nuclear reactions, NRA, to determine the oxygen concentration in nanopowders. The concentration of the

defects under study can be varied in wide limits; in particular, using vacuum annealings can provide gradual growth from 0 to 1.5 at. %, including the formation of a solid film of titanium atoms on the nanoparticle surface. The concentration of defects of other types in the nanoparticles under study was lower than that of two-dimensional defects located on the nanoparticle surface.

**Author Contributions:** Conceptualization, V.B.V.; Investigation, T.E.K. and E.V.V.; Writing—original draft, V.B.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was carried out within the state assignment of the Ministry of Science and Higher Education of the Russian Federation (theme "Function" no. AAAA-A19-119012990095-0).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** Authors are very grateful to A.S. Minin, A.E. Yermakov, and M.A. Uimin for useful discussion and valuable remarks and to A.S. Minin for the synthesis of nanopowders by the sol–gel method.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

