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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">Physics of Metals and Metallography</journal-id><journal-title-group><journal-title xml:lang="en">Physics of Metals and Metallography</journal-title><trans-title-group xml:lang="ru"><trans-title>Физика металлов и металловедение</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0015-3230</issn><issn publication-format="electronic">3034-6215</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">695555</article-id><article-id pub-id-type="doi">10.31857/S0015323025070096</article-id><article-categories><subj-group subj-group-type="toc-heading"><subject>СТРУКТУРА, ФАЗОВЫЕ ПРЕВРАЩЕНИЯ И ДИФФУЗИЯ</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">MODELING OF THE DIFFUSION PROCESS IN A COPPER–ALUMINUM BIMATERIAL</article-title><trans-title-group xml:lang="ru"><trans-title>МОДЕЛИРОВАНИЕ ПРОЦЕССА ДИФФУЗИИ В БИМАТЕРИАЛЕ “МЕДЬ–АЛЮМИНИЙ”</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Starostina</surname><given-names>Ekaterina S.</given-names></name><name xml:lang="ru"><surname>Старостина</surname><given-names>Екатерина Сергеевна</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio><p>Лаборант НИФТИ</p></bio><email>good113luck@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Berendeyev</surname><given-names>Nikolai N.</given-names></name><name xml:lang="ru"><surname>Берендеев</surname><given-names>Николай Николаевич</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>berendeyev@nifti.unn.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">National Research Lobachevsky State University of Nizhny Novgorod</institution></aff><aff><institution xml:lang="ru">ФГОУ ВО “Национальный исследовательский Нижегородский государственный университет им. Н.И. Лобачевского”</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-10-30" publication-format="electronic"><day>30</day><month>10</month><year>2025</year></pub-date><volume>126</volume><issue>7</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>817</fpage><lpage>825</lpage><history><date date-type="received" iso-8601-date="2025-10-30"><day>30</day><month>10</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Russian Academy of Sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Российская академия наук</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Russian Academy of Sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/" start_date="2026-10-30"/></permissions><self-uri xlink:href="https://transsyst.ru/0015-3230/article/view/695555">https://transsyst.ru/0015-3230/article/view/695555</self-uri><abstract xml:lang="en"><p>The study is devoted to the numerical modeling of diffusion processes in aluminum-copper bimetals using the finite element method. The focus is on the peculiarities of interdiffusion during the heat treatment of Al–Cu bimetallic materials and on the processes of formation and growth of intermetallic compounds in the Al–Cu system under elevated temperatures. The application of a migration diffusion model made it possible to account for the influence of temperature and stress concentration on the annealing processand on the interaction of materials and compounds under heating – an aspect unattainable with the standard diffusion model. This approach also enabled the construction of concentration distribution curves for copper and aluminum at different annealing temperatures and durations. A computational algorithm was developed for the formation and growth of intermetallic compounds in the sample, taking into account annealing temperature and the concentration of diffusing elements in accordance with the Al–Cu phase equilibrium diagram. As a result, intermetallic layers forming at the metal–metal interface during interdiffusion of copper and aluminum were obtained, which is consistent with experimental findings. It is shown that the numerical experiment demonstrates good qualitative and quantitative agreement with experimental data onthe thickness of the diffusion layer at the Al–Cu interface, with the simulated phase dimensions matching those observed experimentally within the margin of error.</p></abstract><trans-abstract xml:lang="ru"><p>Работа посвящена вопросам численного моделирования процессов диффузии в биметалле “алюминий–медь” методом конечных элементов. Основное внимание уделено описанию особенностей взаимной диффузии в процессе термообработки биметаллических алюминиево-медных материалов и процессу образования и роста интерметаллидных соединений в системе “алюминий–медь” при воздействии повышенной температуры. Использование миграционной модели диффузии позволило учесть влияние температуры и концентрации напряжений на процесс отжига и взаимодействие материалов и соединений при нагреве, что невозможно реализовать с применением стандартной диффузионной модели, а также получить графики распределения концентрации меди и алюминия при различных температурах и времени отжигов. Реализован программный алгоритм образования и роста интерметаллидных соединений в образце с учетом температуры отжига и концентрации диффундирующих элементов согласно диаграмме фазового равновесия “алюминий–медь”. Благодаря этому были получены слои интерметаллидов, возникающих на границе раздела металлов в процессе взаимной диффузии меди и алюминия, что наблюдали и в экспериментах. Показано, что численный эксперимент дает хорошее качественное и количественное совпадение с экспериментальными значениями толщины диффузионного слоя, на границе раздела “алюминий–медь” показывает совпадающие с натурным экспериментом впределах погрешности размеры возникших фаз.</p></trans-abstract><kwd-group xml:lang="en"><kwd>aluminum</kwd><kwd>copper</kwd><kwd>interdiffusion</kwd><kwd>numerical simulation</kwd><kwd>intermetallic compounds</kwd><kwd>finite element method</kwd><kwd>migration-based diffusion model</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>алюминий</kwd><kwd>медь</kwd><kwd>взаимная диффузия</kwd><kwd>численное моделирование</kwd><kwd>интерметаллические соединения</kwd><kwd>метод конечных элементов</kwd><kwd>миграционная модель</kwd></kwd-group><funding-group><award-group><funding-source><institution-wrap><institution xml:lang="ru">Грант РНФ</institution></institution-wrap></funding-source><award-id>№20-19-00672-П</award-id></award-group></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Wadsworth J., Lesuer D.R. 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