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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="other" 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">569</article-id><article-id pub-id-type="doi">10.18323/2782-4039-2022-3-2-90-98</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></subject></subj-group></article-categories><title-group><article-title xml:lang="en">Planar superstructural defects in the alloys with L10 superstructure</article-title><trans-title-group xml:lang="ru"><trans-title>Планарные сверхструктурные дефекты в сплавах сверхструктуры L10</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3663-784X</contrib-id><name-alternatives><name xml:lang="en"><surname>Khalikov</surname><given-names>Albert R.</given-names></name><name xml:lang="ru"><surname>Халиков</surname><given-names>Альберт Рашитович</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>PhD (Physics and Mathematics), Associate Professor</p></bio><bio xml:lang="ru"><p>кандидат физико-математических наук, доцент</p></bio><email>khalikov.albert.r@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8366-4819</contrib-id><name-alternatives><name xml:lang="en"><surname>Bebikhov</surname><given-names>Yuri V.</given-names></name><name xml:lang="ru"><surname>Бебихов</surname><given-names>Юрий Владимирович</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="ru"><p>кандидат физико-математических наук, доцент</p></bio><email>bebikhov.yura@mail.ru</email><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5975-4849</contrib-id><name-alternatives><name xml:lang="en"><surname>Korznikova</surname><given-names>Elena A.</given-names></name><name xml:lang="ru"><surname>Корзникова</surname><given-names>Елена Александровна</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Doctor of Sciences (Physics and Mathematics), Professor</p></bio><bio xml:lang="ru"><p>доктор физико-математических наук, профессор</p></bio><email>elena.a.korznikova@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6744-4445</contrib-id><name-alternatives><name xml:lang="en"><surname>Dmitriev</surname><given-names>Sergey V.</given-names></name><name xml:lang="ru"><surname>Дмитриев</surname><given-names>Сергей Владимирович</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Doctor of Sciences (Physics and Mathematics), Professor, leading researcher</p></bio><bio xml:lang="ru"><p>доктор физико-математических наук, профессор, ведущий научный сотрудник</p></bio><email>dmitriev.sergey.v@gmail.com</email><xref ref-type="aff" rid="aff3"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Ufa State Aviation Technical University, Ufa</institution></aff><aff><institution xml:lang="ru">Уфимский государственный авиационный технический университет, Уфа</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Mirny Polytechnic Institute (branch) of North-Eastern Federal University, Mirny</institution></aff><aff><institution xml:lang="ru">Политехнический институт (филиал) Северо-Восточного федерального университета им. М.К. Аммосова в г. Мирном, Мирный</institution></aff></aff-alternatives><aff-alternatives id="aff3"><aff><institution xml:lang="en">Institute of Physics of Molecules and Crystals of Ufa Federal Research Center of the Russian Academy of Sciences, Ufa</institution></aff><aff><institution xml:lang="ru">Институт физики молекул и кристаллов Уфимского научного центра Российской академии наук, Уфа</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2022-09-30" publication-format="electronic"><day>30</day><month>09</month><year>2022</year></pub-date><issue>3-2</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>90</fpage><lpage>98</lpage><history><date date-type="received" iso-8601-date="2022-09-30"><day>30</day><month>09</month><year>2022</year></date></history><permissions><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/></permissions><self-uri xlink:href="https://vektornaukitech.ru/jour/article/view/569">https://vektornaukitech.ru/jour/article/view/569</self-uri><abstract xml:lang="en"><p>Planar superstructural defects have a great influence on the mechanical, functional properties of binary ordered alloys of the <italic>L</italic>1<sub>0</sub> superstructure based on the fcc lattice, but there is no complete analysis of their structure and energy in the literature. For the <italic>L</italic>1<sub>0</sub> superstructure alloys of the stoichiometric composition <italic>AB</italic>, the paper gives the expressions for calculating the sublimation energy and the energy of a planar superstructural defect in the model of hard coordination spheres and pair interatomic interactions. The crystal lattice tetragonality was not taken into account. The authors presented the ordered alloy structure as a union of four monoatomic simple cubic lattices, two of which are occupied by <italic>A</italic> atoms, and the other two by <italic>B</italic> atoms. This approach allows calculating the sublimation energy required for crystal evaporation. The first eight coordination spheres were taken into account in the work. The paper shows an algorithm for determining all possible geometrically different representations of the <italic>L</italic>1<sub>0</sub> superstructure with the same sublimation energy, gives an expression for finding the planes of occurrence of all possible conservative antiphase boundaries. The study identified that the conservative and nonconservative antiphase boundaries, as well as conservative and nonconservative boundaries of <italic>C</italic>-domains are observed in the binary ordered alloys of the <italic>L</italic>1<sub>0</sub> superstructure based on the fcc lattice. The algorithms described in this work make it possible to carry out a crystal-geometric analysis of planar defects in both binary and multicomponent ordered alloys with various superstructures.</p></abstract><trans-abstract xml:lang="ru"><p>Планарные сверхструктурные дефекты оказывают большое влияние на механические и функциональные свойства бинарных упорядоченных сплавов сверхструктуры <italic>L</italic>1<sub>0</sub> на основе ГЦК решетки, но полный анализ их структуры и энергии сублимации в литературе отсутствует. В данной работе для сплавов сверхструктуры <italic>L</italic>1<sub>0</sub> стехиометрического состава <italic>АВ</italic> приведены выражения для расчета энергии сублимации и энергии планарного сверхструктурного дефекта в модели твердых координационных сфер и парных межатомных взаимодействий. Тетрагональность кристаллической решетки не учитывалась. Структура упорядоченного сплава была представлена в виде объединения четырех моноатомных простых кубических решеток, две из которых заняты атомами <italic>A</italic>, а две другие – атомами <italic>B</italic>. Такой подход позволяет рассчитать энергию сублимации, необходимую для испарения кристалла. В работе учитывались первые восемь координационных сфер. Показан алгоритм определения всех возможных геометрически различных представлений сверхструктуры <italic>L</italic>1<sub>0</sub>, имеющих одинаковую энергию сублимации. Приведено выражение для нахождения плоскостей залегания всех возможных консервативных антифазных границ. Установлено, что в бинарных упорядоченных сплавах сверхструктуры <italic>L</italic>1<sub>0</sub> на основе ГЦК решетки присутствуют консервативные и неконсервативные антифазные границы, а также консервативные и неконсервативные границы <italic>C</italic>-доменов. Алгоритмы, описанные в данной работе, позволяют проводить кристаллогеометрический анализ планарных дефектов как в бинарных, так и в многокомпонентных упорядоченных сплавах с различными сверхструктурами.</p></trans-abstract><kwd-group xml:lang="en"><kwd>planar superstructural defects</kwd><kwd>L10 superstructure</kwd><kwd>C-domains</kwd><kwd>antiphase boundaries</kwd><kwd>fcc lattice</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>планарные сверхструктурные дефекты</kwd><kwd>сверхструктура L10</kwd><kwd>C-домены</kwd><kwd>антифазные границы</kwd><kwd>ГЦК решетка</kwd></kwd-group><funding-group><funding-statement xml:lang="en">The study was financially supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the state assignment of the Federal State Budgetary Educational Institution of Higher Education “USATU” (agreement No. 075-03-2022-318/1) “Youth Research Laboratory of the REC “Metals and Alloys under the Extreme Conditions” for E.A. Korznikova (calculations), grant NSh-4320.2022.1.2 for E.A. Korznikova (analysis, discussion of the results), grant RSF 21-12-00229 for S.V. Dmitriev (problem setting, research conceptualization).</funding-statement><funding-statement xml:lang="ru">Исследование выполнено при финансовой поддержке Министерства науки и высшего образования РФ в рамках государственного задания ФГБОУ ВО «УГАТУ» (соглашение № 075-03-2022-318/1) «Молодежная научно-исследовательская лаборатория НОЦ "Металлы и сплавы при экстремальных воздействиях"» для Е.А. Корзниковой (проведение расчетов), гранта НШ-4320.2022.1.2 для Е.А. Корзниковой (анализ и обсуждение полученных результатов), гранта РНФ 21-12-00229 для С.В. Дмитриева (постановка задачи, концептуализация исследования).</funding-statement></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Starostenkov M.D., Dmitriev S.V., Bakaldin A.V. 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