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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">10.17073/0368-0797-2025-1-69-75</article-id><article-id custom-type="elpub" pub-id-type="custom">blackmet-2842</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>Построение поверхности ликвидус пятикомпонентной схемы диаграммы Fe – B – Mn – C – Cr</article-title><trans-title-group xml:lang="en"><trans-title>Construction of liquidus surface of Fe – B – Mn – C – Cr five-component diagram</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0007-1542-979X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Казакевич</surname><given-names>Г. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kazakevich</surname><given-names>G. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Григорий Алексеевич Казакевич, аспирант кафедры «Технология транспортного машиностроения и ремонта подвижного состава»</p><p>Москва, 127994, ул. Образцова, 9, стр. 9</p></bio><bio xml:lang="en"><p>Grigorii A. Kazakevich, Postgraduate of the Chair “Technology of Transport Engineering and Repair of Rolling Stock”</p><p>9, bld. 9 Obraztsova Str., Moscow 127994, Russian Federation</p></bio><email xlink:type="simple">KazakevichG@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/0000-0002-3397-9484</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Попов</surname><given-names>А. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Popov</surname><given-names>A. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Юрьевич Попов, к.т.н., доцент кафедры «Технология транспортного машиностроения и ремонта подвижного состава»</p><p>Москва, 127994, ул. Образцова, 9, стр. 9</p></bio><bio xml:lang="en"><p>Aleksei Yu. Popov, Cand. Sci. (Eng.), Assist. Prof. of the Chair “Techno­logy of Transport Engineering and Repair of Rolling Stock”</p><p>9, bld. 9 Obraztsova Str., Moscow 127994, Russian Federation</p></bio><email xlink:type="simple">madrat@inbox.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Российский университет транспорта</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Russian University of Transport</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>23</day><month>02</month><year>2025</year></pub-date><volume>68</volume><issue>1</issue><fpage>69</fpage><lpage>75</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Казакевич Г.А., Попов А.Ю., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Казакевич Г.А., Попов А.Ю.</copyright-holder><copyright-holder xml:lang="en">Kazakevich G.A., Popov A.Y.</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/2842">https://fermet.misis.ru/jour/article/view/2842</self-uri><abstract><p>Для построения поверхности ликвидус пятикомпонентной системы Fe – B – Mn – C – Cr применялась методика построения в традиционных координатах «температура – концентрация» схем многокомпонентных диаграмм (n &gt; 3), основанием которых являют­ся n-угольники с дивергентной координатной сеткой при n &gt; 4. Выбор системы обусловлен необходимостью упрочнения поверхнос­тей деталей, изготовленных из большого количества низколегированных сталей борированием. Критическими точками поверхности ликвидус являлись температуры плавления химических элементов сплава, боридов и эвтектик двойных диаграмм состояния, которые являются сторонами пятигранной призмы. Принимались во внимание также отдельные экспериментальные температуры плавления сталей и рассчитанные температуры плавления новых эвтектик, образующихся при взаимодействии эвтектик двойных диаграмм состоя­ния. Последние определялись по правилу эвтектической реакции, предусматривающему использование при расчете только температур плавления исходных эвтектик. Одновременно определялся и фазовый состав многокомпонентных боридных эвтектик системы. Полученная поверхность ликвидус показывает температуру начала кристаллизации и фазовый состав слоя при проведении борирования из обмазок литейных форм для поверхностного упрочнения отливок. Рассчитанные температуры плавления эвтектик образуют поверхности солидус системы. В соответствии с концентрационными значениями элементов, и особенно бора, в системе образуются пять поверхностей солидус при 1571, 1451, 1394, 1105 и 978 °С. Данные температуры плавления эвтектик являются границами между диффузионным и диффузионно-кристаллизационным механизмами формирования борированных слоев в твердом и затвердевающем состояниях обрабатываемых поверхностей. Следовательно, они определяют механизм формирования борированных слоев, их фазовый состав, структурную морфологию и свойства.</p></abstract><trans-abstract xml:lang="en"><p>The authors used the technique of constructing the schemes of multicomponent diagrams (n &gt; 3) in traditional coordinates “temperature – concentration”, the basis of which are n – angles with a divergent coordinate grid at n &gt; 4, to construct the liquidus surface of the Fe – B – Mn – C – Cr five-component system. Choice of the system was determined by the need to harden the surfaces of parts made from a large number of low-alloy steels by boriding. The critical points of the liquidus surface were melting points of the alloy chemical elements, melting points of borides and melting temperatures of eutectics of the phase diagrams, which are the sides of a pentahedral prism. Individual experimental melting temperatures of the steels and calculated melting temperatures of new eutectics during the interaction of eutectics of double phase diagrams were also taken into account. The latter were determined according to the eutectic reaction rule, which provides for the use of only melting temperatures of the initial eutectics in the calculation. At the same time, phase composition of the multicomponent boride eutectics of the system was determined. The resulting liquidus surface shows the temperature at which crystallization begins and the phase composition of the layer during boriding of casting mold coa­tings for surface hardening of castings. The calculated melting temperatures of eutectics form the solidus surfaces of the system. In accordance with the concentration values ​​of the elements, especially boron, five solidus surfaces are formed in the system at 1571, 1451, 1394, 1105 and 978 °C. These melting temperatures of eutectics are the boundaries between the diffusion and diffusion-crystallization mechanisms of formation of boronized layer in solid and solidifying states of treated surfaces, therefore, they determine the mechanism of formation of boronized layer, their phase composition, structural morphology and properties.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>поверхность ликвидус</kwd><kwd>пятикомпонентная система</kwd><kwd>расчет эвтектических температур</kwd><kwd>дивергентная сетка</kwd><kwd>диаграммы состояния</kwd><kwd>стали</kwd><kwd>борирование</kwd></kwd-group><kwd-group xml:lang="en"><kwd>liquidus surface</kwd><kwd>five-component system</kwd><kwd>calculation of eutectic temperatures</kwd><kwd>divergent grid</kwd><kwd>phase diagram</kwd><kwd>steel</kwd><kwd>boriding</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">Лахтин Ю.М., Леонтьева В.П. 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