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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="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">blackmet</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений. Черная Металлургия</journal-title><trans-title-group xml:lang="en"><trans-title>Izvestiya. Ferrous Metallurgy</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0368-0797</issn><issn pub-type="epub">2410-2091</issn><publisher><publisher-name>National University of Science and Technology "MISIS"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17073/0368-0797-2022-4-268-277</article-id><article-id custom-type="elpub" pub-id-type="custom">blackmet-2298</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="ru"><subject>ФИЗИКО-ХИМИЧЕСКИЕ ОСНОВЫ МЕТАЛЛУРГИЧЕСКИХ ПРОЦЕССОВ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICO-CHEMICAL BASICS OF METALLURGICAL PROCESSES</subject></subj-group></article-categories><title-group><article-title>Термодинамика восстановления щелочноземельных металлов из шлаковых расплавов</article-title><trans-title-group xml:lang="en"><trans-title>Thermodynamics of alkaline-earth metals reduction from slag melts</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Якушевич</surname><given-names>Н. Ф.</given-names></name><name name-style="western" xml:lang="en"><surname>Yakushevich</surname><given-names>N. F.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Николай Филиппович Якушевич, д.т.н., профессор-консультант кафедры металлургии цветных металлов и химической технологии</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Nikolai F. Yakushevich, Dr. Sci. (Eng.), Prof.-Consultant of the Chair of Non-Ferrous Metallurgy and Chemical Engineering</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">Yakushevich@cmet.sibsiu</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7554-2168</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Протопопов</surname><given-names>Е. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Protopopov</surname><given-names>E. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Евгений Валентинович Протопопов, д.т.н., профессор кафедры металлургии черных металлов</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Evgenii V. Protopopov, Dr. Sci. (Eng.), Prof. of the Chair of Ferrous Me­tallurgy</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">protopopov@sibsiu.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/0000-0001-7985-5666</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Темлянцев</surname><given-names>М. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Temlyantsev</surname><given-names>M. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михаил Викторович Темлянцев, д.т.н., профессор, проректор по учебной и воспитательной работе</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Mikhail V. Temlyantsev, Dr. Sci. (Eng.), Prof., Vice-Rector for Educational and Tutorial Work</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">uchebn_otdel@sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Павлов</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Pavlov</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Вячеслав Владимирович Павлов, соискатель степени к.т.н. кафедры металлургии черных металлов</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Vyacheslav V. Pavlov, Candidates for a degree of Cand. Sci. (Eng.) of the Chair of Ferrous Metallurgy</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">maxtroshkin93@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Абина</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Abina</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Анастасия Александровна Абина, аспирант кафедры металлургии черных металлов</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Anastasiya A. Abina, Postgraduate of the Chair of Ferrous Metallurgy</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">Yakushevich@cmet.sibsiu</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бивол</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Bivol</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ольга Владимировна Бивол, аспирант кафедры теплоэнергетики и экологии</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Ol’ga V. Bivol, Postgraduate of the Chair “Thermal Power and Ecology”</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">kuznetsova_ov@sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Сибирский государственный индустриальный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Siberian State Industrial University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>05</day><month>05</month><year>2022</year></pub-date><volume>65</volume><issue>4</issue><fpage>268</fpage><lpage>277</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Якушевич Н.Ф., Протопопов Е.В., Темлянцев М.В., Павлов В.В., Абина А.А., Бивол О.В., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Якушевич Н.Ф., Протопопов Е.В., Темлянцев М.В., Павлов В.В., Абина А.А., Бивол О.В.</copyright-holder><copyright-holder xml:lang="en">Yakushevich N.F., Protopopov E.V., Temlyantsev M.V., Pavlov V.V., Abina A.A., Bivol O.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://fermet.misis.ru/jour/article/view/2298">https://fermet.misis.ru/jour/article/view/2298</self-uri><abstract><p>На основе диаграмм состояния двухкомпонентных силикатных систем SrO – SiO2 , BaO – SiO2 , CaO – SiO2 определены активности компонентов в инвариантных (эвтектических и монотектических) точках рассматриваемых систем. Процессы кристаллизации в инвариантных эвтектических точках l1 и l2 рассматриваются как химические реакции жe1 (KSiO2 (ж) + lMeO(ж)) → CSiO2 (тв) + α(MeO·SiO2 )(тв), жe2 (mSiO2 (ж) + nMeO(ж)) → (MeO·SiO2 )(тв) + b(2MeO·SiO2 )(тв), для которых определяются значения ΔG°T и константы равновесия. При заданных температурах и известных значениях активностей компонентов в равновесных с шлаком металлических расплавах определены значения aMeO в шлаках. В гомогенных шлаковых расплавах активности оксидов щелочноземельных металлов (ЩЗМ) определялись из констант равновесных реакций восстановления этих металлов из шлаков кремнием железокремниевых металлических расплавов. В области гомогенных шлаковых расплавов построены зависимости aSiO2 = f (x(SiO2 )) при температурах 1600 и 1700 °С, а при использовании данных по активностям ЩЗМ (Sr, Ba, Ca) в металлических высококремнистых расплавах определены зависимости lga(SrO) = f (x(SiO2 ) , x(Si)) при 1493 °С и lga(BaO) = f (x(SiO2 ) , x(Si)) при 1450 °С. На трехпараметрической диаграмме в координатах a[Si] – a(SiO2 ) – a(MeO) (для щелочноземельных металлов) построены зависимости a(SrO) = f (a[Si] , a(SiO2 ) ) при 1493 °С и a(BaO) = f(a[Si] , a(SiO2 ) ) при 1450 °С. Показано, что низкие равновесные значения a(SrO) и a(BaO) , lga(SrO) = f (a(SiO2 ) , a[Si] ) ≤ (–4) и lga(BaO) = f (a(SiO2 ) , a[Si] ) ≤ (–3), могут достигаться при равновесных значениях активности кремния в металлических расплавах a[Si] &gt; 0,5 при восстановлении стронция и a[Si] &gt; 0,7 при восстановлении бария.</p></abstract><trans-abstract xml:lang="en"><p>Based on the state diagrams of two–component silicate systems SrO – SiO2 , BaO – SiO2 , CaO – SiO2 , the authors have determined the activity of components in invariant (eutectic and monotectic) points of the systems under consideration. Crystallization processes at invariant eutectic points l1 and l2 are considered as chemical reactions le1 (KSiO2 (l) + lMeO(l)) → CSiO2 (sol) + α(MeO·SiO2 )(sol), le2 (mSiO2 (l) + nMeO(l)) → (MeO·SiO2 )(sol) + b(2MeO·SiO2 )(sol), for which the values ΔG°T and the equilibrium constants were established. The values of aMeO in the slags were determined at given temperatures and known values of the component activities in metal melts in equilibrium with slag. In homogeneous slag melts, the activity of alkaline-earth metal (AEM) oxides was defined from the constants of equilibrium reactions of reduction of these metals from slags by silicon of iron-silicon metal melts. In the zone of homogeneous slag melts, the dependences aSiO2 = f (x(SiO2 )) were constructed at temperatures of 1600 and 1700 °C, and when using data on the activities of AEM (Sr, Ba, Ca) in metallic high-silicon melts, the dependences lga(SrO) = f (x(SiO2 ) , x(Si)) at 1493 °C and lga(BaO) = f (x(SiO2 ) , x(Si)) at 1450 °C were determined. On a three-parameter diagram in coordinates a[Si] – a(SiO2 ) – a(MeO) (for AEM), the dependencies a(SrO) = f (a[Si] , a(SiO2 ) ) at 1493 °C and a(BaO) = f (a[Si] , a(SiO2 ) ) at 1450 °C were constructed. It is shown that low equilibrium values of a(SrO) and a(BaO) , lga(SrO) = f (a(SiO2 ) , a[Si] ) ≤ (–4) and lga(BaO) = f (a(SiO2 ) , a[Si] ) ≤ (–3), can be achieved at equilibrium values of silicon activity in metal melts a[Si] &gt; 0,5 during strontium reduction and a[Si] &gt; 0,7 during barium reduction.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>щелочноземельные металлы (ЩЗМ)</kwd><kwd>оксиды ЩЗМ</kwd><kwd>активности оксидов ЩЗМ</kwd><kwd>активности оксидов в шлаковых расплавах</kwd></kwd-group><kwd-group xml:lang="en"><kwd>alkaline-earth metals (AEM)</kwd><kwd>AEM oxides</kwd><kwd>activity of AEM oxides</kwd><kwd>activity of oxides in slag melts</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Якушевич Н.Ф., Протопопов Е.В., Темлянцев М.В., Павлов В.В., Абина А.А., Кузнецова О.В. Термодинамика восстановления щелочноземельных металлов и оксидов и условия кристаллизации сплавов в системе Fe – Si – Me (ЩЗМ) // Проб­лемы черной металлургии и материаловедения. 2020. № 2. С. 5–15.</mixed-citation><mixed-citation xml:lang="en">Yakushevich N.F., Protopopov E.V., Temlyantsev M.V., Pavlov V.V., Abina A.A., Kuznetsova O.V. Thermodynamics of alkaline-earth metals reduction from oxides and conditions of alloys crystallization in the system Fe – Si – Me (AEM). Problemy chernoi metallurgii i materialovedeniya. 2020, no. 2, pp. 5–15. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Эллиот Д., Глейзер М., Рамакришна В. Термохимия сталеплавильных процессов / Пер. с англ. С.Н. Расиной; под ред. Ю.Л. Плинера, Н.С. Смирнова. М.: Металлургия, 1969. 252 с.</mixed-citation><mixed-citation xml:lang="en">Elliott J.F., Gleiser M., Ramakrishna V. Thermochemistry for Steelmaking. Addison – Wesley Inc. 1963. (Russ. ed.: Elliott J., Gleiser  M., Ramakrishna V. Termokhimiya staleplavil’nykh protsessov. Moscow: Metallurgiya, 1969, 252 p.).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Якушевич Н.Ф., Галевский Г.В. Взаимодействие углерода с оксидами кальция, кремния, алюминия. Новокузнецк: ИЦ СибГИУ, 1999. 250 с.</mixed-citation><mixed-citation xml:lang="en">Yakushevich N.F., Galevskii G.V. Interaction of Carbon with Calcium Oxide, Silicon, Aluminum. Novokuznetsk: izd. SibSIU, 1999, 250 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Атлас шлаков. Справочник. М.: Металлургия, 1985. 208 с.</mixed-citation><mixed-citation xml:lang="en">Schlackenatlas. Verein Deutscher Eisenhüttenleute, Verlag Stahleisen, 1981, 282 p. (Russ. ed.: Atlas shlakov. Sprav. Moscow: Metallurgiya, 1985, 208 p.).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Рябчиков И.В. Модификаторы и технологии внепечной обработки железоуглеродистых сплавов. М.: Экомет, 2008. 400 с.</mixed-citation><mixed-citation xml:lang="en">Ryabchikov I.V. Modifiers and Technologies of Extra-Furnace Processing of Iron-Carbon Alloys. Moscow: Ekomet, 2008, 400 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Кожевников Г.Н., Зайко В.П., Рысс М.А. Электротермия лигатур щелочноземельных металлов с кремнием. М.: Наука, 1978. 224 с.</mixed-citation><mixed-citation xml:lang="en">Kozhevnikov G.N., Zaiko V.P., Ryss M.A. Electrothermy of Ligatures of Alkaline-Earth Metals with Silicon. Moscow: Nauka, 1978, 224 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Зубов В.Л., Гасик М.И. Электрометаллургия ферросилиция. Днепропетровск: Системные технологии, 2002. 704 с</mixed-citation><mixed-citation xml:lang="en">Zubov V.L., Gasik M.I. Electrometallurgy of Ferrosilicon. Dnepropetrovsk: Sistemnye tekhnologii, 2002, 704 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Li M., Li L., Zhang B., Li Q., Wu W., Zou Z. Numerical analysis of the particle-induced effect on gas flow in a supersonic powder-laden oxygen jet // Metallurgical and Materials Transactions B. 2020. Vol. 51. No. 4. P. 1718–1730. http://doi.org/10.1007/s11663-020-01855-3</mixed-citation><mixed-citation xml:lang="en">Li M., Li L., Zhang B., Li Q., Wu W., Zou Z. Numerical analysis of the particle-induced effect on gas flow in a supersonic powder-la­den oxygen jet. Metallurgical and Materials Transactions B. 2020, vol.  51, no. 4, pp. 1718–1730.  http://doi.org/10.1007/s11663-020-01855-3</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Wang B., Shen S., Ruan Y., Сheng S., Peng W., Zhang J. Simulation of gas-liquid two-phase flow in metallurgical process // Acta Metallurgica Sinica. 2020. Vol. 56. No. 4. P. 619–632. http://doi.org/10.11900/0412.1961.2019.00385</mixed-citation><mixed-citation xml:lang="en">Wang B., Shen S., Ruan Y., Сheng S., Peng W., Zhang J. Simulation of gas-liquid two-phase flow in metallurgical process. Acta Metallurgica Sinica. 2020, vol. 56, no. 4, pp. 619–632. http://doi.org/10.11900/0412.1961.2019.00385</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Barella S., Mapelli C., Mombelli D., Gruttadauria A., Laghi E., Ancona V., Valentino G. Model for the final decarburisation of the steel bath through a self-bubbling effect // Ironmaking and Steelmaking. 2019. Vol. 46. No. 8. P. 721–724. http://doi.org/10.1080/03019233.2017.1405179</mixed-citation><mixed-citation xml:lang="en">Barella S., Mapelli C., Mombelli D., Gruttadauria A., Laghi E., An-cona V., Valentino G. Model for the final decarburisation of the steel bath through a self-bubbling effect. Ironmaking and Steelmaking. 2019, vol. 46, no. 8, pp. 721–724. http://doi.org/10.1080/03019233.2017.1405179</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Pariser H.H., Backeberg N.R., Masson O.C.M., Bedder J.C.M. Changing nickel and chromium stainless steel markets – A review // Journal of the Southern African Institute of Mining and Metallurgy. 2018. Vol. 118. No. 6. P. 563–568. https://doi.org/10.17159/2411-9717/2018/V118N6A1</mixed-citation><mixed-citation xml:lang="en">Pariser H.H., Backeberg N.R., Masson O.C.M., Bedder J.C.M. Changing nickel and chromium stainless steel markets – A review. Journal of the Southern African Institute of Mining and Metallurgy. 2018, vol. 118, no. 6, pp. 563–568. https://doi.org/10.17159/2411-9717/2018/V118N6A1</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Zhuchkov V.I., Zayakin O.V., Zhdanov A.V. Utilization of substandard and offgrade raw materials for chromium and manganese ferroalloys production // Proceedings of the 12th Int. Ferroalloys Congress: Sustainable Future. INFACON 2010. Helsinki, Finland: Outotec Oyj, 2010. Р. 311–315.</mixed-citation><mixed-citation xml:lang="en">Zhuchkov V.I., Zayakin O.V., Zhdanov A.V. Utilization of substandard and offgrade raw materials for chromium and manganese ferroalloys production. In: Proceedings of the 12th Int. Ferroalloys Congress: Sustainable Future. INFACON 2010. Helsinki, Finland: Outotec Oyj, 2010, pp. 311–315.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Irons G.A., Tong X.-P. Treatment of steel with alkaline-earth elements // ISIJ International. 1995. Vol. 35. No. 7. P. 838–844. https://doi.org/10.2355/isijinternational.35.838</mixed-citation><mixed-citation xml:lang="en">Irons G.A., Tong X.-P. Treatment of steel with alkaline-earth elements. ISIJ International. 1995, vol. 35, no. 7, pp. 838–844. https://doi.org/10.2355/isijinternational.35.838</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Bakin I.V., Mikhailov G.G., Golubtsov V.A., Ryabchikov I.V., Dresvyankina L.E. Methods for improving the efficiency of steel modifying // Material Science Forum. 2019. Vol. 946. P. 215–222. https://doi.org/10.4028/www.scientific.net/MSF.946.215</mixed-citation><mixed-citation xml:lang="en">Bakin I.V., Mikhailov G.G., Golubtsov V.A., Ryabchikov I.V., Dresvyankina L.E. Methods for improving the efficiency of steel modifying. Material Science Forum. 2019, vol. 946, pp. 215–222. https://doi.org/10.4028/www.scientific.net/MSF.946.215</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Якушевич Н.Ф., Полях О.А., Галевский Г.В., Тяжина А.А. Анализ фазово-химических равновесий в системе расплав (Fe – Si – C) – шлак (CaO – Al2O3 – SiO2 ) – газ (O2 – SiO – CO) // Известия вузов. Черная металлургия. 2015. Т. 58. № 5. С. 316–321. https://doi.org/10.15825/0368-0797-2015-5-316-321</mixed-citation><mixed-citation xml:lang="en">Yakushevich N.F., Polyakh O.A., Galevskii G.V., Tyazhina  A.A. Phase and chemical equilibria in melt (Fe – Si – C)–slag (CaO – Al2O3 – SiO2 )–gas (O2 – SiO – CO) system. Izvestiya. Ferrous Metallurgy. 2015, vol. 58, no. 5, pp. 316–321. (In Russ.). https://doi.org/10.15825/0368-0797-2015-5-316-321</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Якушевич Н.Ф., Кондратьев Д.В. Термодинамика первичных шлаков в системе CaO – Al2O3 – SiO2 // Известия вузов. Черная металлургия. 2000. Т. 43. № 2. С. 4–9.</mixed-citation><mixed-citation xml:lang="en">Yakushevich N.F., Kondrat’ev D.V. Thermodynamics of first slag in CaO – Al2O3 – SiO2 system. Izvestiya. Ferrous Metallurgy. 2000, vol. 43, no. 2, pp. 4–9. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Есин Ю.О., Сандаков В.Н., Гельд П.В. и др. Энтальпии смешения жидких кремния и бария при 1723 K // Журнал прикладной химии. 1973. Т. 46. № 11. С. 2402–2405.</mixed-citation><mixed-citation xml:lang="en">Esin Yu.O., Sandakov V.N., Gel’d P.V., etc. Enthalpies of mixing liquid silicon and barium at 1723 K. Zhurnal prikladnoi khimii. 1973, vol. 46, no. 11, pp. 2402–2405. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Есин Ю.О., Колесников С.П., Баев В.М. и др. Энтальпия образования сплавов стронция с кремнием // Журнал физической химии. 1979. Т. 53. № 6. С. 1624–1625.</mixed-citation><mixed-citation xml:lang="en">Esin Yu.O., Kolesnikov S.P., Baev V.M., etc. Enthalpy of formation of strontium-silicon alloys. Zhurnal fizicheskoi khimii. 1979, vol.  53, no. 6, pp. 1624–1625. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Turkdogan E.T. Phуsicochemical properties of slags and glasses // The Metal Soc. 1983. Vol. 10. No. 4. P. 113–117.</mixed-citation><mixed-citation xml:lang="en">Turkdogan E.T. Phуsicochemical properties of slags and glasses. The Metal Soc. 1983, vol. 10, no. 4, pp. 113–117.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Григорьев Ю.В., Рябчиков И.В., Рощин В.Е. Термодинамичес­кий анализ совместного восстановления кремния и бария углеродом // Известия вузов. Черная металлургия. 2005. Т. 48. № 7. С. 3–5.</mixed-citation><mixed-citation xml:lang="en">Grigor’ev Yu.V., Ryabchikov I.V., Roshchin V.E. Thermodynamic analysis of the co-reduction of silicon and barium with carbon. Izvestiya. Ferrous Metallurgy. 2005, vol. 48, no. 7, pp. 3–5. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Schei A., Tuset J.K., Tveit H. Production of High Silicon Alloys. Trondheim, Norway: Tapir Academic Press, 1998. 363 p.</mixed-citation><mixed-citation xml:lang="en">Schei A., Tuset J.K., Tveit H. Production of High Silicon Alloys. Trondheim, Norway: Tapir Academic Press, 1998, 363 p.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Wang J., Mao Yu. Slag Figures. Berjing: Metallurgical Industry Press, 1989. P. 44–60.</mixed-citation><mixed-citation xml:lang="en">Wang J., Mao Yu. Slag Figures. Berjing: Metallurgical Industry Press, 1989, pp. 44–60.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Breitzmann M., Engell H.-J., Janke D. Refining of steel melts using alkaline earth metals // Steel Research. 1988. Vol. 59. No. 7. P. 289–294. https://doi.org/10.1002/srin.198801505</mixed-citation><mixed-citation xml:lang="en">Breitzmann M., Engell H.-J., Janke D. Refining of steel melts using alkaline earth metals. Steel Research. 1988, vol. 59, no. 7, pp.  289–294. https://doi.org/10.1002/srin.198801505</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Li S., Cheng G., Yang L., Chen L., Yan Q., Li C. A thermodynamic model to desing the equilibrium slag compositions during electroslag remelting process: Description and verification // ISIJ International. 2017. Vol. 57. No. 4. P. 713–722. https://doi.org/10.2355/isijinternational.ISIJINT-2016-655</mixed-citation><mixed-citation xml:lang="en">Li S., Cheng G., Yang L., Chen L., Yan Q., Li C. A thermodynamic model to desing the equilibrium slag compositions during electroslag remelting process: Description and verification. ISIJ International. 2017, vol. 57, no. 4, pp. 713–722. https://doi.org/10.2355/isijinternational.ISIJINT-2016-655</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Hou D., Jiang Z.H., Dong Y.W., Gong W., Cao Y.L., Cao H. Effect of slag composition on the oxidation kinetics of alloying elements during electroslag remelting of stainless steel: Part-1. Mass-transfer model // ISIJ International. 2017. Vol. 57. No. 8. P. 1400–1409. https://doi.org/10.2355/isijinternational.ISIJINT-2017-147</mixed-citation><mixed-citation xml:lang="en">Hou D., Jiang Z.H., Dong Y.W., Gong W., Cao Y.L., Cao H. Effect of slag composition on the oxidation kinetics of alloying elements during electroslag remelting of stainless steel: Part-1. Mass-transfer model. ISIJ International. 2017, vol. 57, no. 8, pp. 1400–1409. https://doi.org/10.2355/isijinternational.ISIJINT-2017-147</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Ozturk B., Fruehan R.J. Activity of silica in calcium-aluminate based slags // Metallurgical Transactions B. 1987. Vol. 18. No. 4. P. 746–751. https://doi.org/10.1007/BF02672895</mixed-citation><mixed-citation xml:lang="en">Ozturk B., Fruehan R.J. Activity of silica in calcium-aluminate based slags. Metallurgical Transactions B. 1987, vol. 18, no. 4, pp.  746–751. https://doi.org/10.1007/BF02672895</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Weiss T., Schwerdfeger K. Chemical equilibria between silicon and slag melts // Metallurgical and Materials Transactions B. 1994. Vol. 25. No. 4. P. 497–504. https://doi.org/10.1007/BF02650071</mixed-citation><mixed-citation xml:lang="en">Weiss T., Schwerdfeger K. Chemical equilibria between silicon and slag melts. Metallurgical and Materials Transactions B. 1994, vol.  25, no. 4, pp. 497–504. https://doi.org/10.1007/BF02650071</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang X.-B., Jiang G.C., Xu K.D. Prediction of component activities of quaternary systems using the sub-regular solution model // Acta Metallurgica Sinica. 1992. Vol. 5b. No. 6. P. 476 – 482.</mixed-citation><mixed-citation xml:lang="en">Zhang X.-B., Jiang G.C., Xu K.D. Prediction of component activities of quaternary systems using the sub-regular solution model. Acta Metallurgica Sinica. 1992, vol. 5b, no. 6, pp. 476 – 482.</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>
