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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2025-16-6-802-811</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-1620</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>CHEMISTRY AND MATERIALS SCIENCE</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ХИМИЯ И НАУКА О МАТЕРИАЛАХ</subject></subj-group></article-categories><title-group><article-title>Thermodynamic analysis of nanocrystal formation in the TiO2–H2O (NaOH, HCl) system</article-title><trans-title-group xml:lang="ru"><trans-title>Термодинамический анализ формирования нанокристаллов в системе TiO2-H2O (NaOH, HCl)</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4345-6086</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Еловиков</surname><given-names>Д. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Elovikov</surname><given-names>D. P.</given-names></name></name-alternatives><bio xml:lang="en"><p>Dmitry P. Elovikov</p><p>St. Petersburg</p></bio><email xlink:type="simple">syncdima@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6132-4178</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Альмяшева</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Almjasheva</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="en"><p>Oksana V. Almjasheva</p><p>St. Petersburg</p></bio><email xlink:type="simple">almjasheva@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4375-6388</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гусаров</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Gusarov</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="en"><p>Victor V. Gusarov</p><p>St. Petersburg</p></bio><email xlink:type="simple">victor.vladimirovich.gusarov@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Branch of Petersburg Nuclear Physics Institute named by B. P. Konstantinov of National Research Centre “Kurchatov Institute” – Institute of Silicate Chemistry</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>06</day><month>01</month><year>2026</year></pub-date><volume>16</volume><issue>6</issue><fpage>802</fpage><lpage>811</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Elovikov D.P., Almjasheva O.V., Gusarov V.V., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Еловиков Д.П., Альмяшева О.В., Гусаров В.В.</copyright-holder><copyright-holder xml:lang="en">Elovikov D.P., Almjasheva O.V., Gusarov V.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/1620">https://nanojournal.ifmo.ru/jour/article/view/1620</self-uri><abstract><p>A thermodynamic analysis of the crystallization of titanium dioxide in the anatase, brookite, and rutile modifications from aqueous salt solutions was performed, taking into account the influence of medium pH, temperature, reagent concentration, and the specific surface energy (σ) of the phases. It was shown that the choice of the σ value for the thermodynamic analysis of anatase crystallization is decisive: at σA = 0.3 J/m2, the minimum particle size is determined by the crystallochemical criterion (lmin ∼5–7 nm), while at σA = 1.3 J/m2, it is determined by thermodynamic criteria (dcrit ∼8 nm, deq ∼12 nm). Using σ values most closely approximating the conditions of a hydrated TiO2 surface (σR = 1.79, σB = 1.0, σA = 1.13 J/m2), the regions of possible crystallization for each modification were determined. Rutile can crystallize in a relatively wide pH range of 0.8–14 (25 °C) and 1.1–10.2 (200 °C), and the minimum particle sizes of rutile under these conditions are determined by thermodynamic criteria – dcrit and deq. For brookite and anatase in acidic and alkaline conditions (pH ∼1–3 and 9–14), the minimum particle sizes, as for rutile, are also determined by thermodynamic criteria, whereas in the neutral region, they are determined by the crystallochemical criterion lmin. Based on the analysis of structural transitions, it was established that anatase can transform into rutile or brookite at particle sizes larger than ∼16 nm. The calculated size for the brookite → rutile transition is ∼712 nm.</p></abstract><trans-abstract xml:lang="ru"><p>В работе проведен термодинамический анализ кристаллизации диоксида титана в модификациях анатаза, брукита и рутила из водно-солевых растворов с учетом влияния pH среды, температуры, концентрации реагентов и удельной поверхностной энергии фаз (σ). Показано, что выбор величины σ для термодинамического анализа кристаллизации анатаза является определяющим: при σA = 0.3 Дж/м² минимальный размер частиц определяется кристаллохимическим критерием (lmin~5–7 нм), а при σA = 1.3 Дж/м² -термодинамическими критериями (dcrit ~ 8 нм, deq ~ 12 нм). С использованием значений σ, наиболее приближенных к условиям гидратированной поверхности TiO2 (σR = 1.79, σB = 1.0, σA = 1.13 Дж/м²) определены области возможной кристаллизации каждой модификации. Рутил может кристаллизоваться в относительно широком диапазоне величин pH 0.8-14 (25 °С) и 1.1-10.2 (200 °С), а минимальные размеры частиц рутила в этих условиях определяются термодинамическими критериями – dcrit и deq. Для брукита и анатаза в кислых и щелочных условиях (pH ~1–3 и 9–14) минимальные размеры также, как и для рутила определяются термодинамическими критериями, тогда как в нейтральной области – кристаллохимическим критерием lmin. На основе анализа структурных переходов установлено, что анатаз может трансформироваться в рутил или брукит при размерах частиц более ~16 нм. Рассчитанный размер перехода брукит → рутил составляет ~712 нм.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>нанокристаллы</kwd><kwd>оксид титана</kwd><kwd>критический зародыш</kwd></kwd-group><kwd-group xml:lang="en"><kwd>nanocrystals</kwd><kwd>titanium oxide</kwd><kwd>critical nucleus</kwd></kwd-group><funding-group><funding-statement xml:lang="en">The work was supported by state assignment No. 1023032900322-9-1.4.3.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Dachille F., Simons P.Y, Roy R. Pressure-temperature studies of anatase, brookite, rutile and TiO2-II. Am. Mineralogist, 1968, 53, P. 1929–1938.</mixed-citation><mixed-citation xml:lang="en">Dachille F., Simons P.Y, Roy R. Pressure-temperature studies of anatase, brookite, rutile and TiO2-II. Am. Mineralogist, 1968, 53, P. 1929–1938.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Wells A.F. Structural Inorganic Chemistry. Oxford University Press, London W1, 1975, P. 109.</mixed-citation><mixed-citation xml:lang="en">Wells A.F. Structural Inorganic Chemistry. Oxford University Press, London W1, 1975, P. 109.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Chemseddine A., Moritz T. Nanostructuring titania: control over nanocrystal structure, size, shape, and organization. Eur. J. Inorg. Chem., 1999, 2, P. 235–245.</mixed-citation><mixed-citation xml:lang="en">Chemseddine A., Moritz T. Nanostructuring titania: control over nanocrystal structure, size, shape, and organization. Eur. J. Inorg. Chem., 1999, 2, P. 235–245.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Rempel A.A. Nonstoichiometry and defect structure of titanium dioxide. Russian Chemical Reviews, 1994, 63(4), P. 303–326</mixed-citation><mixed-citation xml:lang="en">Rempel A.A. Nonstoichiometry and defect structure of titanium dioxide. Russian Chemical Reviews, 1994, 63(4), P. 303–326</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Hanaor D.A.H., Sorrell C.C. Review of the anatase to rutile phase transformation. Journal of Materials science, 2011, 46(4), P. 855–874.</mixed-citation><mixed-citation xml:lang="en">Hanaor D.A.H., Sorrell C.C. Review of the anatase to rutile phase transformation. Journal of Materials science, 2011, 46(4), P. 855–874.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Almjasheva O.V. Formation and structural transformations of nanoparticles in the TiO2–H2O system. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7(6), P. 1031–1049</mixed-citation><mixed-citation xml:lang="en">Almjasheva O.V. Formation and structural transformations of nanoparticles in the TiO2–H2O system. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7(6), P. 1031–1049</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Yamakata A., Vequizo J.J.M. Curious behaviors of photogenerated electrons and holes at the defects on anatase, rutile, and brookite TiO2 powders: A review. Journal of Photochemistry and Photobiology C: Photochemistry Reviews, 2019, 40, P. 234–243.</mixed-citation><mixed-citation xml:lang="en">Yamakata A., Vequizo J.J.M. Curious behaviors of photogenerated electrons and holes at the defects on anatase, rutile, and brookite TiO2 powders: A review. Journal of Photochemistry and Photobiology C: Photochemistry Reviews, 2019, 40, P. 234–243.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Manzoli M., Freyria F.S., Blangetti N., Bonelli B. Brookite, a sometimes under evaluated TiO2 polymorph. RSC Advances, 2022. 12(6), P. 3322– 3334.</mixed-citation><mixed-citation xml:lang="en">Manzoli M., Freyria F.S., Blangetti N., Bonelli B. Brookite, a sometimes under evaluated TiO2 polymorph. RSC Advances, 2022. 12(6), P. 3322– 3334.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Eddy D.R., Permana M.D., Sakti L.K., Sheha G.A.N., Solihudin, Hidayat S., Takei T., Kumada N., Rahayu I. Heterophase polymorph of TiO2 (Anatase, Rutile, Brookite, TiO2 (B)) for efficient photocatalyst: fabrication and activity. Nanomaterials, 2023, 13(4), P. 704.</mixed-citation><mixed-citation xml:lang="en">Eddy D.R., Permana M.D., Sakti L.K., Sheha G.A.N., Solihudin, Hidayat S., Takei T., Kumada N., Rahayu I. Heterophase polymorph of TiO2 (Anatase, Rutile, Brookite, TiO2 (B)) for efficient photocatalyst: fabrication and activity. Nanomaterials, 2023, 13(4), P. 704.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang H., Banfield J. Structural characteristics and mechanical and thermodynamic properties of nanocrystalline TiO2. Chemical Reviews, 2014. 114(19), P. 9613–9644.</mixed-citation><mixed-citation xml:lang="en">Zhang H., Banfield J. Structural characteristics and mechanical and thermodynamic properties of nanocrystalline TiO2. Chemical Reviews, 2014. 114(19), P. 9613–9644.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Pletnev R.N., Ivakin A.A., Kleshchev D.G., Denisova T.A., Burmistrov V.A. Hydrated Oxides of the Group IV and V Elements, 1986, P. 186.</mixed-citation><mixed-citation xml:lang="en">Pletnev R.N., Ivakin A.A., Kleshchev D.G., Denisova T.A., Burmistrov V.A. Hydrated Oxides of the Group IV and V Elements, 1986, P. 186.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Onorin S.A. Structure of X-ray-amorphous hydrated titanium dioxide. Russian Journal of Inorganic Chemistry, 1992, 37(6), P. 1228–1232.</mixed-citation><mixed-citation xml:lang="en">Onorin S.A. Structure of X-ray-amorphous hydrated titanium dioxide. Russian Journal of Inorganic Chemistry, 1992, 37(6), P. 1228–1232.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Reyes-Coronado D., Rodrıguez-Gattorno G., Espinosa-Pesqueira M.E., Cab C., de Coss R., Oskam G. Phase-pure TiO2 nanoparticles: anatase, brookite and rutile. Nanotechnology, 2008. 19(14), P. 145605.</mixed-citation><mixed-citation xml:lang="en">Reyes-Coronado D., Rodrıguez-Gattorno G., Espinosa-Pesqueira M.E., Cab C., de Coss R., Oskam G. Phase-pure TiO2 nanoparticles: anatase, brookite and rutile. Nanotechnology, 2008. 19(14), P. 145605.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang H., Banfield J. Understanding polymorphic phase transformation behavior during growth of nanocrystalline aggregates: insights from TiO2. The Journal of Physical Chemistry, 2000, 104(15), P. 3481–3487.</mixed-citation><mixed-citation xml:lang="en">Zhang H., Banfield J. Understanding polymorphic phase transformation behavior during growth of nanocrystalline aggregates: insights from TiO2. The Journal of Physical Chemistry, 2000, 104(15), P. 3481–3487.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Meskin P.E., Gavrilov A.I., Maksimov V.D., Ivanov V.K., Churagulov B.P. Hydrothermal/microwave and hydrothermal/ultrasonic synthesis of nanocrystalline titania, zirconia, and hafnia. Russian Journal of Inorganic Chemistry, 2007, 52(11), P. 1648–1656.</mixed-citation><mixed-citation xml:lang="en">Meskin P.E., Gavrilov A.I., Maksimov V.D., Ivanov V.K., Churagulov B.P. Hydrothermal/microwave and hydrothermal/ultrasonic synthesis of nanocrystalline titania, zirconia, and hafnia. Russian Journal of Inorganic Chemistry, 2007, 52(11), P. 1648–1656.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Dorosheva I.B., Valeeva A.A., Rempel A.A. Sol-gel synthesis of nanosized titanium dioxide at various pH of the initial solution. AIP Conference Proceedings, 2017, 1886(020006). [17] Zlobin V.V., Krasilin A.A., Almjasheva O.V. Effect of heterogeneous inclusions on the formation of TiO2 nanocrystals in hydrothermal conditions. Nanosystems: Physics, Chemistry, Mathematics., 2019, 10(6), P. 733–739.</mixed-citation><mixed-citation xml:lang="en">Dorosheva I.B., Valeeva A.A., Rempel A.A. Sol-gel synthesis of nanosized titanium dioxide at various pH of the initial solution. AIP Conference Proceedings, 2017, 1886(020006). [17] Zlobin V.V., Krasilin A.A., Almjasheva O.V. Effect of heterogeneous inclusions on the formation of TiO2 nanocrystals in hydrothermal conditions. Nanosystems: Physics, Chemistry, Mathematics., 2019, 10(6), P. 733–739.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Rempel A.A., Valeeva A.A., Vokhmintsev A.S., Weinstein I.A. Titanium dioxide nanotubes: Synthesis, structure, properties and applications. Russian Chemical Reviews, 2021, 90(11), P. 1397–1414.</mixed-citation><mixed-citation xml:lang="en">Rempel A.A., Valeeva A.A., Vokhmintsev A.S., Weinstein I.A. Titanium dioxide nanotubes: Synthesis, structure, properties and applications. Russian Chemical Reviews, 2021, 90(11), P. 1397–1414.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Zlobin V.V., Nevedomskiy V.N., Almjasheva O.V. Formation and growth of anatase TiO2 nanocrystals under hydrothermal conditions. Materials Today Communications, 2023, 36, P. 106436.</mixed-citation><mixed-citation xml:lang="en">Zlobin V.V., Nevedomskiy V.N., Almjasheva O.V. Formation and growth of anatase TiO2 nanocrystals under hydrothermal conditions. Materials Today Communications, 2023, 36, P. 106436.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Onorin S.A., Khodyashev M.B., Denisova T.A., Zakharov N.D. Effect of synthesis conditions on structure and ion-exchange properties of hydrous titanium dioxide. Russian Journal of Inorganic Chemistry, 1992, 37(6), P. 612–615.</mixed-citation><mixed-citation xml:lang="en">Onorin S.A., Khodyashev M.B., Denisova T.A., Zakharov N.D. Effect of synthesis conditions on structure and ion-exchange properties of hydrous titanium dioxide. Russian Journal of Inorganic Chemistry, 1992, 37(6), P. 612–615.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Onorin S.A., Khodyashev M.B., Zakharov N.D. Physicochemical studies of hydrated titanium dioxide and products of sorption of As and Na ions on it. Russian Journal of Inorganic Chemistry, 1992, 37(6), P. 1223–1227.</mixed-citation><mixed-citation xml:lang="en">Onorin S.A., Khodyashev M.B., Zakharov N.D. Physicochemical studies of hydrated titanium dioxide and products of sorption of As and Na ions on it. Russian Journal of Inorganic Chemistry, 1992, 37(6), P. 1223–1227.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Roy P., Berger S., Schmuki P. TiO2 nanotubes: synthesis and applications. Angewandte Chemie International Edition, 2011, 50(13), P. 2904–2939.</mixed-citation><mixed-citation xml:lang="en">Roy P., Berger S., Schmuki P. TiO2 nanotubes: synthesis and applications. Angewandte Chemie International Edition, 2011, 50(13), P. 2904–2939.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Nakata K., Fujishima A. TiO2 photocatalysis: Design and applications. Journal of photochemistry and photobiology C: Photochemistry Reviews, 2012, 13(3), P. 169–189.</mixed-citation><mixed-citation xml:lang="en">Nakata K., Fujishima A. TiO2 photocatalysis: Design and applications. Journal of photochemistry and photobiology C: Photochemistry Reviews, 2012, 13(3), P. 169–189.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Lebedev V.A., Kozlov D.A., Kolesnik I.V., Poluboyarinov A.S., Becerikli A.E., Grunert W., Garshev A.V. The amorphous phase in titania and its ¨ influence on photocatalytic properties. Applied Catalysis B: Environmental, 2016, 195, P. 39–47.</mixed-citation><mixed-citation xml:lang="en">Lebedev V.A., Kozlov D.A., Kolesnik I.V., Poluboyarinov A.S., Becerikli A.E., Grunert W., Garshev A.V. The amorphous phase in titania and its ¨ influence on photocatalytic properties. Applied Catalysis B: Environmental, 2016, 195, P. 39–47.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Noman M.T., Ashraf M.A., Ali A. Synthesis and applications of nano-TiO2: a review. Environmental Science and Pollution Research, 2019, 26(4), P. 3262–3291.</mixed-citation><mixed-citation xml:lang="en">Noman M.T., Ashraf M.A., Ali A. Synthesis and applications of nano-TiO2: a review. Environmental Science and Pollution Research, 2019, 26(4), P. 3262–3291.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Kolesnik I.V., Lebedev V.A., Garshev A.V. Optical properties and photocatalytic activity of nanocrystalline TiO2 doped by 3d-metal ions. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9(3), P. 401–409.</mixed-citation><mixed-citation xml:lang="en">Kolesnik I.V., Lebedev V.A., Garshev A.V. Optical properties and photocatalytic activity of nanocrystalline TiO2 doped by 3d-metal ions. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9(3), P. 401–409.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Rempel A.A., Valeeva A.A. Nanostructured titanium dioxide for medicinal chemistry. Russian Chemical Bulletin, 2019, 68(12), P. 2163–2171.</mixed-citation><mixed-citation xml:lang="en">Rempel A.A., Valeeva A.A. Nanostructured titanium dioxide for medicinal chemistry. Russian Chemical Bulletin, 2019, 68(12), P. 2163–2171.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Rempel A.A. Functional nanomaterials based on modified titanium dioxide. Russian Chemical Bulletin, 2024, 73(8), P. 2144–2151.</mixed-citation><mixed-citation xml:lang="en">Rempel A.A. Functional nanomaterials based on modified titanium dioxide. Russian Chemical Bulletin, 2024, 73(8), P. 2144–2151.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Kumar A., Pandey G. Different methods used for the synthesis of TiO2 based nanomaterials: A review. Am. J. Nano Res. Appl., 2018. 6(1), P. 1-10.</mixed-citation><mixed-citation xml:lang="en">Kumar A., Pandey G. Different methods used for the synthesis of TiO2 based nanomaterials: A review. Am. J. Nano Res. Appl., 2018. 6(1), P. 1-10.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Mironyuk I.F., Soltys L.M., Tatarchuk T.R., Savka K.O. Methods of titanium dioxide synthesis. Physics and Chemistry of Solid State, 2020, 21(3), P. 462–477.</mixed-citation><mixed-citation xml:lang="en">Mironyuk I.F., Soltys L.M., Tatarchuk T.R., Savka K.O. Methods of titanium dioxide synthesis. Physics and Chemistry of Solid State, 2020, 21(3), P. 462–477.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Wang Z., Liu S., Cao X., et al. Preparation and characterization of TiO2 nanoparticles by two different precipitation methods. Ceramics International, 2020, 46(10), P. 15333–15341.</mixed-citation><mixed-citation xml:lang="en">Wang Z., Liu S., Cao X., et al. Preparation and characterization of TiO2 nanoparticles by two different precipitation methods. Ceramics International, 2020, 46(10), P. 15333–15341.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Hu Y., Pan D., Zhang Z., et al. Preparation of CunCo1Ox catalysts by co-precipitation method for catalytic oxidation of toluene. Journal of Molecular Structure, 2025, 1326, P. 141139.</mixed-citation><mixed-citation xml:lang="en">Hu Y., Pan D., Zhang Z., et al. Preparation of CunCo1Ox catalysts by co-precipitation method for catalytic oxidation of toluene. Journal of Molecular Structure, 2025, 1326, P. 141139.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Tian Z.M., Yuan S.L., He J.H., et al. Structure and magnetic properties in Mn doped SnO2 nanoparticles synthesized by chemical co-precipitation method. Journal of Alloys and Compounds, 2008, 466(1-2), P. 26–30.</mixed-citation><mixed-citation xml:lang="en">Tian Z.M., Yuan S.L., He J.H., et al. Structure and magnetic properties in Mn doped SnO2 nanoparticles synthesized by chemical co-precipitation method. Journal of Alloys and Compounds, 2008, 466(1-2), P. 26–30.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Yapryntsev A.D., Baranchikov A.E., Ivanov V.K. Layered rare-earth hydroxides: a new family of anion-exchangeable layered inorganic materials. Russian Chemical Reviews, 2020, 89(6), P. 629–666.</mixed-citation><mixed-citation xml:lang="en">Yapryntsev A.D., Baranchikov A.E., Ivanov V.K. Layered rare-earth hydroxides: a new family of anion-exchangeable layered inorganic materials. Russian Chemical Reviews, 2020, 89(6), P. 629–666.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Enikeeva M.O., Proskurina O.V., Levin A.A., Smirnov A.V., Nevedomskiy V.N., Gusarov V.V. Structure of Y0.75La0.25PO4 · 0.67H2O rhabdophane nanoparticles synthesized by the hydrothermal microwave method. Journal of Solid State Chemistry, 2023, 319, P. 123829.</mixed-citation><mixed-citation xml:lang="en">Enikeeva M.O., Proskurina O.V., Levin A.A., Smirnov A.V., Nevedomskiy V.N., Gusarov V.V. Structure of Y0.75La0.25PO4 · 0.67H2O rhabdophane nanoparticles synthesized by the hydrothermal microwave method. Journal of Solid State Chemistry, 2023, 319, P. 123829.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Bugrov A.N., Almjasheva O.V. Effect of hydrothermal synthesis conditions on the morphology of ZrO2 nanoparticles. Nanosystems: Physics, Chemistry, Mathematics, 2013, 4(6), P. 810.</mixed-citation><mixed-citation xml:lang="en">Bugrov A.N., Almjasheva O.V. Effect of hydrothermal synthesis conditions on the morphology of ZrO2 nanoparticles. Nanosystems: Physics, Chemistry, Mathematics, 2013, 4(6), P. 810.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Lomakin M.S., Proskurina O.V., Sergeev A.A., Buryanenko I.V., Semenov V.G., Voznesenskiy S.S., Gusarov V.V. Crystal Structure and Optical Properties of the Bi–Fe–W–O Pyrochlore Phase Synthesized via a Hydrothermal Method. J. Alloys Compd., 2021, 889, P. 161598.</mixed-citation><mixed-citation xml:lang="en">Lomakin M.S., Proskurina O.V., Sergeev A.A., Buryanenko I.V., Semenov V.G., Voznesenskiy S.S., Gusarov V.V. Crystal Structure and Optical Properties of the Bi–Fe–W–O Pyrochlore Phase Synthesized via a Hydrothermal Method. J. Alloys Compd., 2021, 889, P. 161598.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Elovikov D.P., Proskurina O.V., Gusarov V.V. Formation of Alunite-type Compounds in the Bi2O3–Al2O3–Fe2O3–P2O5–H2O System under Hydrothermal Conditions. Russian Journal of Inorganic Chemistry, 2025, 70(7), P. 960–967.</mixed-citation><mixed-citation xml:lang="en">Elovikov D.P., Proskurina O.V., Gusarov V.V. Formation of Alunite-type Compounds in the Bi2O3–Al2O3–Fe2O3–P2O5–H2O System under Hydrothermal Conditions. Russian Journal of Inorganic Chemistry, 2025, 70(7), P. 960–967.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Tabesh S., Davar F., Loghman-Estarki M.R. Preparation of γ-Al2O3 nanoparticles using modified sol-gel method and its use for the adsorption of lead and cadmium ions. J. Alloys Comp., 2018, 730, P. 441–449.</mixed-citation><mixed-citation xml:lang="en">Tabesh S., Davar F., Loghman-Estarki M.R. Preparation of γ-Al2O3 nanoparticles using modified sol-gel method and its use for the adsorption of lead and cadmium ions. J. Alloys Comp., 2018, 730, P. 441–449.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang H., Ke H., Ying P., Luo H., Zhang L., Wang W., Jia D., Zhou Y. Crystallisation process of Bi5Ti3FeO15 multiferroic nanoparticles synthesized by a sol–gel method. J. Sol-Gel Sci. Technol., 2018, 85(1), P. 132–139.</mixed-citation><mixed-citation xml:lang="en">Zhang H., Ke H., Ying P., Luo H., Zhang L., Wang W., Jia D., Zhou Y. Crystallisation process of Bi5Ti3FeO15 multiferroic nanoparticles synthesized by a sol–gel method. J. Sol-Gel Sci. Technol., 2018, 85(1), P. 132–139.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">El-Cheikh A.Z.F., Kwapinski W., Ahmad M.N., Leahy J.J., El-Rassy H. Nanoporous ZnO/SiO2 aerogel and xerogel composites via a one-pot sol–gel process at room temperature. RSC Adv RSC Advances, 2025, 15(47), P. 39566–39577.</mixed-citation><mixed-citation xml:lang="en">El-Cheikh A.Z.F., Kwapinski W., Ahmad M.N., Leahy J.J., El-Rassy H. Nanoporous ZnO/SiO2 aerogel and xerogel composites via a one-pot sol–gel process at room temperature. RSC Adv RSC Advances, 2025, 15(47), P. 39566–39577.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Belghiti M., El Mersly L., Tanji K., Belkodia K., Lamsayety I., Ouzaouit K., Foqir H., Benzakour I., Rofqah S., Outzourhit A. Sol-gel combined mechano-thermal synthesis of Y2O3, CeO2, and PdO partially coated ZnO for sulfamethazine and basic yellow 28 photodegradation under UV and visible light. Optical Materials, 2023, 136, P. 113458.</mixed-citation><mixed-citation xml:lang="en">Belghiti M., El Mersly L., Tanji K., Belkodia K., Lamsayety I., Ouzaouit K., Foqir H., Benzakour I., Rofqah S., Outzourhit A. Sol-gel combined mechano-thermal synthesis of Y2O3, CeO2, and PdO partially coated ZnO for sulfamethazine and basic yellow 28 photodegradation under UV and visible light. Optical Materials, 2023, 136, P. 113458.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Tang H., Hu Q., Jiang F., Jiang W., Liu J., Chen T., Feng G., Wang T., Luo W. Size control of CZrSiO4 pigments via soft mechano-chemistry assisted non-aqueous sol-gel method and their application in ceramic glaze. Ceramics International, 2019, 45(8), P. 10756–10764.</mixed-citation><mixed-citation xml:lang="en">Tang H., Hu Q., Jiang F., Jiang W., Liu J., Chen T., Feng G., Wang T., Luo W. Size control of CZrSiO4 pigments via soft mechano-chemistry assisted non-aqueous sol-gel method and their application in ceramic glaze. Ceramics International, 2019, 45(8), P. 10756–10764.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Gurule A.C., Gaikwad S.S., Kajale D.D., Shinde V.S., Jadhav G.R., Gaikwad V.B. Synthesis of magnesium oxide nanoparticles via hydrothermal and sol-gel methods: Charaterization and their application for H2S and NO2 gas sensing. Journal of the Indian Chemical Society, 2025, 102(1), P. 101496.</mixed-citation><mixed-citation xml:lang="en">Gurule A.C., Gaikwad S.S., Kajale D.D., Shinde V.S., Jadhav G.R., Gaikwad V.B. Synthesis of magnesium oxide nanoparticles via hydrothermal and sol-gel methods: Charaterization and their application for H2S and NO2 gas sensing. Journal of the Indian Chemical Society, 2025, 102(1), P. 101496.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang H., Banfield J. Thermodynamic analysis of phase stability of nanocrystalline titania. J. Mater. Chem., 1998, 8, P. 2073–2076.</mixed-citation><mixed-citation xml:lang="en">Zhang H., Banfield J. Thermodynamic analysis of phase stability of nanocrystalline titania. J. Mater. Chem., 1998, 8, P. 2073–2076.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Almjasheva O.V. Formation of oxide nanocrystals and nanocomposites under hydrothermal conditions, structure and properties of materials based on them. Abstract of a dissertation for the degree of Doctor of Chemical Sciences: specialty 02.00.21, St. Petersburg, 2017 (in Russian)</mixed-citation><mixed-citation xml:lang="en">Almjasheva O.V. Formation of oxide nanocrystals and nanocomposites under hydrothermal conditions, structure and properties of materials based on them. Abstract of a dissertation for the degree of Doctor of Chemical Sciences: specialty 02.00.21, St. Petersburg, 2017 (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">Kalaivani T., Anilkumar P. Role of temperature on the phase modification of TiO2 nanoparticles synthesized by the precipitation method. Silicon, 2018, 10(4), P. 1679–1686.</mixed-citation><mixed-citation xml:lang="en">Kalaivani T., Anilkumar P. Role of temperature on the phase modification of TiO2 nanoparticles synthesized by the precipitation method. Silicon, 2018, 10(4), P. 1679–1686.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">Belov G.V., Iorish V.S., Yungman V.S. IVTANTHERMO for Windows-database on thermodynamic properties and related software. Calphad, 1999, 23(2), P. 173–180.</mixed-citation><mixed-citation xml:lang="en">Belov G.V., Iorish V.S., Yungman V.S. IVTANTHERMO for Windows-database on thermodynamic properties and related software. Calphad, 1999, 23(2), P. 173–180.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">Stull D.R. JANAF Thermochemical Tables. Clearinghouse, 1965, 1.</mixed-citation><mixed-citation xml:lang="en">Stull D.R. JANAF Thermochemical Tables. Clearinghouse, 1965, 1.</mixed-citation></citation-alternatives></ref><ref id="cit49"><label>49</label><citation-alternatives><mixed-citation xml:lang="ru">Roine A. HSC-software Ver. 3.0 for thermodynamic calculations. Proceedings of the international symposium on computer software in chemical and extractive metallurgy, 1989, P. 15–29.</mixed-citation><mixed-citation xml:lang="en">Roine A. HSC-software Ver. 3.0 for thermodynamic calculations. Proceedings of the international symposium on computer software in chemical and extractive metallurgy, 1989, P. 15–29.</mixed-citation></citation-alternatives></ref><ref id="cit50"><label>50</label><citation-alternatives><mixed-citation xml:lang="ru">Ranade M.R., Navrotsky A., Zhang. H.Z., Banfield J.F., Elder S.H., Zaban A., Borse P.H., Kulkarni S.K., Doran G.S., Whitfield H.J. Energetics of nanocrystalline TiO2. Proc. Natl. Acad. Sci., 2002, 99, P. 6476–6481.</mixed-citation><mixed-citation xml:lang="en">Ranade M.R., Navrotsky A., Zhang. H.Z., Banfield J.F., Elder S.H., Zaban A., Borse P.H., Kulkarni S.K., Doran G.S., Whitfield H.J. Energetics of nanocrystalline TiO2. Proc. Natl. Acad. Sci., 2002, 99, P. 6476–6481.</mixed-citation></citation-alternatives></ref><ref id="cit51"><label>51</label><citation-alternatives><mixed-citation xml:lang="ru">Ryzhenko B.N., Kovalenko N.I., Prisyagina N.I. Titanium complexation in hydrothermal systems. Geochemistry International, 2006, 44(9), P. 879– 895.</mixed-citation><mixed-citation xml:lang="en">Ryzhenko B.N., Kovalenko N.I., Prisyagina N.I. Titanium complexation in hydrothermal systems. Geochemistry International, 2006, 44(9), P. 879– 895.</mixed-citation></citation-alternatives></ref><ref id="cit52"><label>52</label><citation-alternatives><mixed-citation xml:lang="ru">Knauss K.G., Dibley M.J., Bourcier W.L., Shaw H.F. Ti (IV) hydrolysis constants derived from rutile solubility measurements made from 100 to 300 C. Applied Geochemistry, 2001, 16(9-10), P. 1115–1128.</mixed-citation><mixed-citation xml:lang="en">Knauss K.G., Dibley M.J., Bourcier W.L., Shaw H.F. Ti (IV) hydrolysis constants derived from rutile solubility measurements made from 100 to 300 C. Applied Geochemistry, 2001, 16(9-10), P. 1115–1128.</mixed-citation></citation-alternatives></ref><ref id="cit53"><label>53</label><citation-alternatives><mixed-citation xml:lang="ru">Schmidt J., Vogelsberger W. Aqueous long-term solubility of titania nanoparticles and titanium (IV) hydrolysis in a sodium chloride system studied by adsorptive stripping voltammetry. Journal of solution chemistry, 2009, 38(10), P. 1267–1282.</mixed-citation><mixed-citation xml:lang="en">Schmidt J., Vogelsberger W. Aqueous long-term solubility of titania nanoparticles and titanium (IV) hydrolysis in a sodium chloride system studied by adsorptive stripping voltammetry. Journal of solution chemistry, 2009, 38(10), P. 1267–1282.</mixed-citation></citation-alternatives></ref><ref id="cit54"><label>54</label><citation-alternatives><mixed-citation xml:lang="ru">Li Y., Ishigaki T. Thermodynamic analysis of nucleation of anatase and rutile from TiO2 melt. Journal of Crystal Growth, 2002, 242(3-4), P. 511– 516.</mixed-citation><mixed-citation xml:lang="en">Li Y., Ishigaki T. Thermodynamic analysis of nucleation of anatase and rutile from TiO2 melt. Journal of Crystal Growth, 2002, 242(3-4), P. 511– 516.</mixed-citation></citation-alternatives></ref><ref id="cit55"><label>55</label><citation-alternatives><mixed-citation xml:lang="ru">Molea A., Popescu V., Rowson N.A., Dinescu A.M. Influence of pH on the formulation of TiO2 nano-crystalline powders with high photocatalytic activity. Powder Technology, 2014, 253, P. 22–28.</mixed-citation><mixed-citation xml:lang="en">Molea A., Popescu V., Rowson N.A., Dinescu A.M. Influence of pH on the formulation of TiO2 nano-crystalline powders with high photocatalytic activity. Powder Technology, 2014, 253, P. 22–28.</mixed-citation></citation-alternatives></ref><ref id="cit56"><label>56</label><citation-alternatives><mixed-citation xml:lang="ru">Razak K.A., Halin D.C., Abdullah M.M.A., Salleh M.M., Mahmed N., Azani A., Chobpattana V. Factors of controlling the formation of titanium dioxide (TiO2) synthesized using sol-gel method–A short review. Journal of Physics: Conference Series. IOP Publishing, 2022, 2169(1), P. 012018.</mixed-citation><mixed-citation xml:lang="en">Razak K.A., Halin D.C., Abdullah M.M.A., Salleh M.M., Mahmed N., Azani A., Chobpattana V. Factors of controlling the formation of titanium dioxide (TiO2) synthesized using sol-gel method–A short review. Journal of Physics: Conference Series. IOP Publishing, 2022, 2169(1), P. 012018.</mixed-citation></citation-alternatives></ref><ref id="cit57"><label>57</label><citation-alternatives><mixed-citation xml:lang="ru">Mehranpour H., Askari M., Ghamsari M. Nucleation and growth of TiO2 nanoparticles. Nanomaterials, 2011, 22, P. 3–26.</mixed-citation><mixed-citation xml:lang="en">Mehranpour H., Askari M., Ghamsari M. Nucleation and growth of TiO2 nanoparticles. Nanomaterials, 2011, 22, P. 3–26.</mixed-citation></citation-alternatives></ref><ref id="cit58"><label>58</label><citation-alternatives><mixed-citation xml:lang="ru">Gribb A.A., Banfield J.F. Particle size effects on transformation kinetics and phase stability in nanocrystalline TiO2. American Mineralogist, 1997, 82(7-8), P. 717–728.</mixed-citation><mixed-citation xml:lang="en">Gribb A.A., Banfield J.F. Particle size effects on transformation kinetics and phase stability in nanocrystalline TiO2. American Mineralogist, 1997, 82(7-8), P. 717–728.</mixed-citation></citation-alternatives></ref><ref id="cit59"><label>59</label><citation-alternatives><mixed-citation xml:lang="ru">Levchenko A.A., Li G., Boerio-Goates J., Woodfield B.F., Navrotsky A. TiO2 stability landscape: Polymorphism, surface energy, and bound water energetics. Chemistry of Materials, 2006, 18(26), P. 6324–6332.</mixed-citation><mixed-citation xml:lang="en">Levchenko A.A., Li G., Boerio-Goates J., Woodfield B.F., Navrotsky A. TiO2 stability landscape: Polymorphism, surface energy, and bound water energetics. Chemistry of Materials, 2006, 18(26), P. 6324–6332.</mixed-citation></citation-alternatives></ref><ref id="cit60"><label>60</label><citation-alternatives><mixed-citation xml:lang="ru">Oliver P.M., Watson G.W., Kelsey E.T., Parker S.C. Atomistic simulation of the surface structure of the TiO2 polymorphs rutile and anatase. Journal of Materials Chemistry, 1997, 7(3), P. 563–568.</mixed-citation><mixed-citation xml:lang="en">Oliver P.M., Watson G.W., Kelsey E.T., Parker S.C. Atomistic simulation of the surface structure of the TiO2 polymorphs rutile and anatase. Journal of Materials Chemistry, 1997, 7(3), P. 563–568.</mixed-citation></citation-alternatives></ref><ref id="cit61"><label>61</label><citation-alternatives><mixed-citation xml:lang="ru">Gong X.Q., Selloni A. First-principles study of the structures and energetics of stoichiometric brookite TiO2 surfaces. Physical Review B— Condensed Matter and Materials Physics, 2007, 76(23), P. 235307.</mixed-citation><mixed-citation xml:lang="en">Gong X.Q., Selloni A. First-principles study of the structures and energetics of stoichiometric brookite TiO2 surfaces. Physical Review B— Condensed Matter and Materials Physics, 2007, 76(23), P. 235307.</mixed-citation></citation-alternatives></ref><ref id="cit62"><label>62</label><citation-alternatives><mixed-citation xml:lang="ru">Almjasheva O.V., Lomanova N.A., Popkov V.I., Proskurina O.V., Tugova E.A., Gusarov V.V. The minimum size of oxide nanocrystals: phenomenological thermodynamic vs crystal-chemical approaches. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10(4), P. 428–437.</mixed-citation><mixed-citation xml:lang="en">Almjasheva O.V., Lomanova N.A., Popkov V.I., Proskurina O.V., Tugova E.A., Gusarov V.V. The minimum size of oxide nanocrystals: phenomenological thermodynamic vs crystal-chemical approaches. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10(4), P. 428–437.</mixed-citation></citation-alternatives></ref><ref id="cit63"><label>63</label><citation-alternatives><mixed-citation xml:lang="ru">Davies C.W. The extent of dissociation of salts in water. Part VIII. An equation for the mean ionic activity coefficient of an electrolyte in water, and a revision of the dissociation constants of some sulphates. Journal of the Chemical Society, 1938, P. 2093–2098.</mixed-citation><mixed-citation xml:lang="en">Davies C.W. The extent of dissociation of salts in water. Part VIII. An equation for the mean ionic activity coefficient of an electrolyte in water, and a revision of the dissociation constants of some sulphates. Journal of the Chemical Society, 1938, P. 2093–2098.</mixed-citation></citation-alternatives></ref><ref id="cit64"><label>64</label><citation-alternatives><mixed-citation xml:lang="ru">Helgeson H.C., Kirkham D.H. Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures; II, Debye-Huckel parameters for activity coefficients and relative partial molal properties. American Journal of Science, 1974, 274(10), P. 1199–1261.</mixed-citation><mixed-citation xml:lang="en">Helgeson H.C., Kirkham D.H. Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures; II, Debye-Huckel parameters for activity coefficients and relative partial molal properties. American Journal of Science, 1974, 274(10), P. 1199–1261.</mixed-citation></citation-alternatives></ref><ref id="cit65"><label>65</label><citation-alternatives><mixed-citation xml:lang="ru">Che X., Li L., Zheng J., Li G., Shi Q. Heat capacity and thermodynamic functions of brookite TiO2. The Journal of Chemical Thermodynamics, 2016, 93, P. 45–51.</mixed-citation><mixed-citation xml:lang="en">Che X., Li L., Zheng J., Li G., Shi Q. Heat capacity and thermodynamic functions of brookite TiO2. The Journal of Chemical Thermodynamics, 2016, 93, P. 45–51.</mixed-citation></citation-alternatives></ref><ref id="cit66"><label>66</label><citation-alternatives><mixed-citation xml:lang="ru">Shkol’Nikov E.V. Thermodynamics of the dissolution of amorphous and polymorphic TiO2 modifications in acid and alkaline media. Russian Journal of Physical Chemistry A, 2016, 90(3), P. 567–571.</mixed-citation><mixed-citation xml:lang="en">Shkol’Nikov E.V. Thermodynamics of the dissolution of amorphous and polymorphic TiO2 modifications in acid and alkaline media. Russian Journal of Physical Chemistry A, 2016, 90(3), P. 567–571.</mixed-citation></citation-alternatives></ref><ref id="cit67"><label>67</label><citation-alternatives><mixed-citation xml:lang="ru">Cromer D.T., Herrington K. The structures of anatase and rutile. Journal of the American Chemical Society, 1955, 77(18), P. 4708–4709.</mixed-citation><mixed-citation xml:lang="en">Cromer D.T., Herrington K. The structures of anatase and rutile. Journal of the American Chemical Society, 1955, 77(18), P. 4708–4709.</mixed-citation></citation-alternatives></ref><ref id="cit68"><label>68</label><citation-alternatives><mixed-citation xml:lang="ru">Manzoli M., Freyria F.S., Blangetti N., Bonelli B. Brookite, a sometimes under evaluated TiO2 polymorph. RSC Advances, 2022, 12(6), P. 3322– 3334.</mixed-citation><mixed-citation xml:lang="en">Manzoli M., Freyria F.S., Blangetti N., Bonelli B. Brookite, a sometimes under evaluated TiO2 polymorph. RSC Advances, 2022, 12(6), P. 3322– 3334.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
