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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Frontier Materials &amp; Technologies</journal-id><journal-title-group><journal-title xml:lang="en">Frontier Materials &amp; Technologies</journal-title><trans-title-group xml:lang="ru"><trans-title>Frontier Materials &amp; Technologies</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2782-4039</issn><issn publication-format="electronic">2782-6074</issn><publisher><publisher-name xml:lang="en">Togliatti State University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">1026</article-id><article-id pub-id-type="doi">10.18323/2782-4039-2025-1-71-5</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Calculation of the effective solidification range and its relationship with hot brittleness of alloys based on Mg–Al and Mg–Zn systems</article-title><trans-title-group xml:lang="ru"><trans-title>Расчет эффективного интервала кристаллизации и его связь с горячеломкостью сплавов на основе систем Mg–Al и Mg–Zn</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3116-5057</contrib-id><name-alternatives><name xml:lang="en"><surname>Pozdniakov</surname><given-names>Andrey V.</given-names></name><name xml:lang="ru"><surname>Поздняков</surname><given-names>Андрей Владимирович</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>PhD (Engineering), Associate Professor</p></bio><bio xml:lang="ru"><p>кандидат технических наук, доцент</p></bio><email>pozdniakov@misis.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">University of Science and Technology MISIS</institution></aff><aff><institution xml:lang="ru">Университет науки и технологий МИСИС</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-03-31" publication-format="electronic"><day>31</day><month>03</month><year>2025</year></pub-date><issue>1</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>59</fpage><lpage>68</lpage><history><date date-type="received" iso-8601-date="2025-03-31"><day>31</day><month>03</month><year>2025</year></date><date date-type="accepted" iso-8601-date="2025-03-31"><day>31</day><month>03</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Pozdniakov A.V.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Поздняков А.В.</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Pozdniakov A.V.</copyright-holder><copyright-holder xml:lang="ru">Поздняков А.В.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://vektornaukitech.ru/jour/article/view/1026">https://vektornaukitech.ru/jour/article/view/1026</self-uri><abstract xml:lang="en"><p>Magnesium alloys of the Mg–Al and Mg–Zn systems have a wide effective solidification range (ESR), and as a result, have the tendency to hot brittleness during casting. There are several methods for analyzing and calculating the hot brittleness of magnesium alloys, but they are very labor-intensive. In this regard, the objective of the study is to develop a model for calculating the hot brittleness index (HBI) based on the value of the calculated effective solidification range, identifying and analyzing their relationship in binary and multicomponent alloys based on the Mg–Al and Mg–Zn systems. The ESR was calculated using the Thermo-Calc program (TTMG3 database). The ESR was calculated as the difference between the temperature of formation of a given amount of solid phases and the nonequilibrium solidus temperature. The study showed a good correlation between the calculated values of ESR and hot brittleness index in both binary and multicomponent magnesium alloys. In the Mg–Al system alloys, the calculated dependences of the ESR at 90 % of solid phases (ESR<sub>90</sub>) show the best correlation with the experimental values of HBI. In the binary alloys of the Mg–Zn system, a qualitatively similar dependence is observed. However, no clear correlation was noted between the ESR and HBI. The ESR<sub>65</sub> and ESR<sub>80</sub> dependences demonstrate the closest nature. According to the relationship between HBI and ESR, the considered multicomponent alloys are divided into two groups as a first approximation: the first one is the Mg–Al–Zn system alloys; the second one is the Mg–Zn–Zr and Mg–Nd–Zr alloys. Within these groups, the dependence of hot brittleness index and ESR has a nature close to a linear one. To describe the dependence of all alloys, a single equation can be applied if ESR<sub>65</sub> is used in the calculations for Mg–Al–Zn alloys and ESR<sub>90</sub> – for Mg–Zn–Zr and Mg–Nd–Zr alloys. The proposed model will allow for easy and quick calculation of the HBI, which is very important in the development of new high-tech magnesium alloys.</p></abstract><trans-abstract xml:lang="ru"><p>Магниевые сплавы систем Mg–Al и Mg–Zn имеют широкий эффективный интервал кристаллизации (ЭИК) и, как следствие, склонны к горячеломкости при литье. Существует несколько методик анализа и расчета горячеломкости магниевых сплавов, но они являются очень трудоемкими. В связи с этим цель исследования – разработать модель расчета показателя горячеломкости (ПГ) по величине расчетного эффективного интервала кристаллизации, установив и проанализировав их связь в двойных и многокомпонентных сплавах на основе систем Mg–Al и Mg–Zn. Расчет ЭИК проведен с использованием программы Thermo-Calc (база данных TTMG3). ЭИК рассчитывался как разница между температурой образования заданного количества твердых фаз и температурой неравновесного солидуса. Показана хорошая корреляция рассчитанных значений ЭИК с ПГ как в двойных, так и в многокомпонентных магниевых сплавах. В сплавах системы Mg–Al расчетные зависимости ЭИК при 90 % твердых фаз (ЭИК<sub>90</sub>) показывают наилучшую корреляцию с экспериментальными значениями ПГ. В двойных сплавах системы Mg–Zn наблюдается качественно такая же зависимость. Однако четкой корреляции между ЭИК и ПГ не отмечено. Наиболее близкий характер демонстрируют зависимости ЭИК<sub>65</sub> и ЭИК<sub>80</sub>. По связи ПГ и ЭИК рассмотренные многокомпонентные сплавы в первом приближении разделены на 2 группы: первая – сплавы системы Mg–Al–Zn, вторая – Mg–Zn–Zr и Mg–Nd–Zr. В пределах этих групп зависимость ПГ и ЭИК имеет близкий к линейному характер. Для описания зависимости всех сплавов можно применить одно уравнение при условии использования в расчетах ЭИК<sub>65</sub> для сплавов Mg–Al–Zn и ЭИК<sub>90</sub> для сплавов Mg–Zn–Zr и Mg–Nd–Zr. Предложенная модель позволит легко и быстро произвести расчет ПГ, что весьма актуально при разработке новых высокотехнологичных магниевых сплавов.</p></trans-abstract><kwd-group xml:lang="en"><kwd>magnesium alloys</kwd><kwd>hot brittleness</kwd><kwd>effective solidification range</kwd><kwd>thermodynamic calculation</kwd><kwd>nonequilibrium solidification</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>магниевые сплавы</kwd><kwd>горячеломкость</kwd><kwd>эффективный интервал кристаллизации</kwd><kwd>термодинамические расчеты</kwd><kwd>неравновесная кристаллизация</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Pan Fusheng, Yang Mingbo, Chen Xianhua. A Review on Casting Magnesium Alloys: Modification of Commercial Alloys and Development of New Alloys. Journal of Materials Science &amp; Technology, 2016, vol. 32, no. 12, pp. 1211–1221. 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