<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">10.17073/0368-0797-2025-2-139-147</article-id><article-id custom-type="elpub" pub-id-type="custom">blackmet-2858</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>МАТЕРИАЛОВЕДЕНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATERIAL SCIENCE</subject></subj-group></article-categories><title-group><article-title>Инициация плавления на границах зерен наклона в аустените в зависимости от угла разориентации</article-title><trans-title-group xml:lang="en"><trans-title>Initiation of melting at tilt grain boundaries in austenite depending on the misorientation angle</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5748-813X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Зоря</surname><given-names>И. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Zorya</surname><given-names>I. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ирина Васильевна Зоря, д.ф.-м.н., доцент, заведующий кафедрой теплогазоводоснабжения, водоотведения и вентиляции</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Irina V. Zorya, Dr. Sci. (Phys.-Math.), Prof., Head of the Chair of Heat-Gas-Water Supply, Water Disposal and Ventilation</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">zorya.i@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/0000-0002-5252-2455</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Полетаев</surname><given-names>Г. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Poletaev</surname><given-names>G. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Геннадий Михайлович Полетаев, д.ф.-м.н., профессор, ведущий научный сотрудник</p><p>Россия, 656038, Алтайский край, Барнаул, пр. Ленина, 46</p></bio><bio xml:lang="en"><p>Gennadii M. Poletaev, Dr. Sci. (Phys.-Math.), Prof., Leading Researcher</p><p>46 Lenina Ave., Barnaul, Altai Territory 656038, Russian Federation</p></bio><email xlink:type="simple">gmpoletaev@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8366-4819</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бебихов</surname><given-names>Ю. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Bebikhov</surname><given-names>Yu. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Юрий Владимирович Бебихов, д.ф.-м.н., доцент</p><p>Россия, 678170, Рес­публика Саха (Якутия), Мирный, ул. Тихонова, 5</p></bio><bio xml:lang="en"><p>Yurii V. Bebikhov, Dr. Sci. (Phys.-Math.), Assist. Prof.</p><p>5 Tikhonova Str., Mirnyi, Republic of Sakha (Yakutia) 678170, Russian Federation</p></bio><email xlink:type="simple">bebikhov.yura@mail.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9940-3915</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Семенов</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Semenov</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Александр Сергеевич Семенов, д.ф.-м.н., директор института</p><p>Россия, 678170, Рес­публика Саха (Якутия), Мирный, ул. Тихонова, 5</p></bio><bio xml:lang="en"><p>Aleksandr S. Semenov, Dr. Sci. (Phys.-Math.), Director of the Institute</p><p>5 Tikhonova Str., Mirnyi, Republic of Sakha (Yakutia) 678170, Russian Federation</p></bio><email xlink:type="simple">as.semenov@s-vfu.ru</email><xref ref-type="aff" rid="aff-3"/></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><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Алтайский государственный технический университет им. И.И. Ползунова</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Polzunov Altai State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Политехнический институт Северо-Восточного федерального университета им. М.К. Аммосова</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Mirny Polytechnic Institute (branch) of North-Eastern Federal University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>21</day><month>04</month><year>2025</year></pub-date><volume>68</volume><issue>2</issue><fpage>139</fpage><lpage>147</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Зоря И.В., Полетаев Г.М., Бебихов Ю.В., Семенов А.С., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Зоря И.В., Полетаев Г.М., Бебихов Ю.В., Семенов А.С.</copyright-holder><copyright-holder xml:lang="en">Zorya I.V., Poletaev G.M., Bebikhov Y.V., Semenov A.S.</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/2858">https://fermet.misis.ru/jour/article/view/2858</self-uri><abstract><p>С помощью молекулярно-динамического моделирования проведено исследование влияния угла разориентации и энергии границ зерен наклона с осями разориентации \(\left\langle {100} \right\rangle\), \(\left\langle {110} \right\rangle\) и \(\left\langle {111} \right\rangle\) на температуру плавления и характер начальной инициации плавления на границе зерен в аустените. Показано, что при постепенном нагревании плавление начинается от границ зерен, там, где имеются нарушения кристаллической структуры и, соответственно, атомы находятся в менее глубоких потенциальных ямах. В случае больше­угловых границ плавление начинается одновременно вдоль всей границы, в случае малоугловых ‒ в ядрах зернограничных дислокаций. Получены зависимости температуры плавления моделируемых расчетных ячеек от угла разориентации зерен и избыточной энергии. Для осей разориентации \(\left\langle {100} \right\rangle\), \(\left\langle {110} \right\rangle\) и \(\left\langle {111} \right\rangle\) результаты оказались аналогичными. В области малых углов разориентации (менее 15°) температура плавления с ростом угла падает почти линейно, затем, для большеугловых границ, снижение становится менее интенсивным. Эти зависимости коррелируют c энергией образования границ зерен или со связанной с ней величиной избыточной энергии расчетной ячейки. Главным количественным критерием, определяющим влияние дефектов на снижение температуры плавления, является избыточная энергия, то есть разность энергий рассматриваемой структуры и идеального кристалла, которую еще можно интерпретировать как энергию образования рассматриваемой структуры. Температура плавления линейно уменьшается с ростом избыточной энергии. Очевидно, что данный эффект, то есть влияние границ зерен на температуру плавления, становится существенным только для материалов с очень высоким содержанием границ зерен, например, для материалов с нанокристаллической структурой.</p></abstract><trans-abstract xml:lang="en"><p>Using molecular dynamics simulation, the authors studied the influence of misorientation angle and energy of tilt grain boundaries with the misorientation axes \(\left\langle {100} \right\rangle\), \(\left\langle {110} \right\rangle\) and \(\left\langle {111} \right\rangle\) on the melting temperature and nature of early initiation of melting at grain boundaries in austenite. It is shown that with gradual heating, melting begins from the grain boundaries, where there is a violation of the crystal structure and, accordingly, the atoms are located in less deep potential wells. In the case of large‒angle boundaries, melting begins simultaneously along the entire boundary, in the case of small-angle boundaries – in the cores of grain-boundary dislocations. Dependences of the melting temperature of the simulated calculation cells on the angle of grain misorientation and excess energy were obtained. For the misorientation axes \(\left\langle {100} \right\rangle\), \(\left\langle {110} \right\rangle\) and \(\left\langle {111} \right\rangle\), the results were similar. In the region of small misorientation angles (less than 15°), the melting point decreases almost linearly with increasing angle, then, for large-angle boundaries, the decrease becomes less intense. These dependences correlate with the energy of grain boundary formation or with the associated excess energy of the calculation cell. The main quantitative criterion determining the effect of defects on a decrease in melting temperature is excess energy, that is, the energy difference between the considered structure and the ideal crystal, which can also be interpreted as the energy of the consi­dered structure formation. The melting point decreases linearly with increasing excess energy. Obviously, the effect of grain boundaries on the melting point becomes significant only for materials with a very high content of grain boundaries, for example, for materials with a nanocrystalline structure. </p></trans-abstract><kwd-group xml:lang="ru"><kwd>молекулярная динамика</kwd><kwd>плавление</kwd><kwd>граница зерен</kwd><kwd>угол разориентации</kwd><kwd>аустенит</kwd></kwd-group><kwd-group xml:lang="en"><kwd>molecular dynamics</kwd><kwd>melting</kwd><kwd>grain boundary</kwd><kwd>misorientation angle</kwd><kwd>austenite</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при финансовой поддержке Министерства науки и высшего образования Российской Федерации (проект FZMM-2023-0003) и Российского научного фонда (проект № 24-22-00092).</funding-statement><funding-statement xml:lang="en">The research was supported by the Ministry of Science and Higher Education of the Russian Federation (project FZMM-2023-0003) and the Russian Science Foundation (project No. 24-22-00092).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Gleiter H. Nanostructured materials: Basic concepts and microstructure. Acta Materialia. 2000;48(1):1‒29. https://doi.org/10.1016/S1359-6454(99)00285-2</mixed-citation><mixed-citation xml:lang="en">Gleiter H. Nanostructured materials: Basic concepts and microstructure. Acta Materialia. 2000;48(1):1‒29. https://doi.org/10.1016/S1359-6454(99)00285-2</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Meyers M.A., Mishra A., Benson D.J. Mechanical properties of nanocrystalline materials. Progress in Materials Science. 2006;51(4):427–556. https://doi.org/10.1016/j.pmatsci.2005.08.003</mixed-citation><mixed-citation xml:lang="en">Meyers M.A., Mishra A., Benson D.J. Mechanical properties of nanocrystalline materials. Progress in Materials Science. 2006;51(4):427–556. https://doi.org/10.1016/j.pmatsci.2005.08.003</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Kumar K.S., Van Swygenhoven H., Suresh S. Mechanical behavior of nanocrystalline metals and alloys. Acta Materialia. 2003;51(19):5743–5774. https://doi.org/10.1016/j.actamat.2003.08.032</mixed-citation><mixed-citation xml:lang="en">Kumar K.S., Van Swygenhoven H., Suresh S. Mechanical behavior of nanocrystalline metals and alloys. Acta Materialia. 2003;51(19):5743–5774. https://doi.org/10.1016/j.actamat.2003.08.032</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Nazarov A.A., Murzaev R.T. A method for the construction of initial structures for molecular dynamics simulations of nanocrystals with nonequilibrium grain bounda­ries containing extrinsic dislocations. Letters on Materials. 2018;8(1):5‒10. https://doi.org/10.22226/2410-3535-2018-1-5-10</mixed-citation><mixed-citation xml:lang="en">Nazarov A.A., Murzaev R.T. A method for the construction of initial structures for molecular dynamics simulations of nanocrystals with nonequilibrium grain boundaries containing extrinsic dislocations. Letters on Materials. 2018;8(1):5‒10. https://doi.org/10.22226/2410-3535-2018-1-5-10</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Castro T., Reifenberger R., Choi E., Andres R.P. Size-dependent melting temperature of individual nanometer-sized metallic clusters. Physical Review B. 1990;42:8548‒8556. https://doi.org/10.1103/PhysRevB.42.8548</mixed-citation><mixed-citation xml:lang="en">Castro T., Reifenberger R., Choi E., Andres R.P. Size-dependent melting temperature of individual nanometer-sized metallic clusters. Physical Review B. 1990;42:8548‒8556. https://doi.org/10.1103/PhysRevB.42.8548</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Dick K., Dhanasekaran T., Zhang Z., Meisel D. Size-denpendent melting of silica-encapsulated gold nanoparticles. Journal of the American Chemical Society. 2002;124(10): 2312‒2317. https://doi.org/10.1021/ja017281a</mixed-citation><mixed-citation xml:lang="en">Dick K., Dhanasekaran T., Zhang Z., Meisel D. Size-denpendent melting of silica-encapsulated gold nanoparticles. Journal of the American Chemical Society. 2002;124(10): 2312‒2317. https://doi.org/10.1021/ja017281a</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Hirasawa M., Orii T., Seto T. Size-dependent crystallization of Si nanoparticles. Applied Physics Letters. 2006;88(9): 093119. https://doi.org/10.1063/1.2182018</mixed-citation><mixed-citation xml:lang="en">Hirasawa M., Orii T., Seto T. Size-dependent crystallization of Si nanoparticles. Applied Physics Letters. 2006;88(9): 093119. https://doi.org/10.1063/1.2182018</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Tang S., Zhu S., Lu H., Meng X. Shape evolution and thermal stability of Ag nanoparticles on spherical SiO2 substrates. Journal of Solid State Chemistry. 2008;181(3):587‒592. https://doi.org/10.1016/j.jssc.2008.01.014</mixed-citation><mixed-citation xml:lang="en">Tang S., Zhu S., Lu H., Meng X. Shape evolution and thermal stability of Ag nanoparticles on spherical SiO2 substrates. Journal of Solid State Chemistry. 2008;181(3):587‒592. https://doi.org/10.1016/j.jssc.2008.01.014</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Kim H.K., Huh S.H., Park J.W., Jeong J.W., Lee G.H. The cluster size dependence of thermal stabilities of both molybdenum and tungsten nanoclusters. Chemical Physics Letters. 2002;354(1-2):165‒172. https://doi.org/10.1016/S0009-2614(02)00146-X</mixed-citation><mixed-citation xml:lang="en">Kim H.K., Huh S.H., Park J.W., Jeong J.W., Lee G.H. The cluster size dependence of thermal stabilities of both molybdenum and tungsten nanoclusters. Chemical Physics Letters. 2002;354(1-2):165‒172. https://doi.org/10.1016/S0009-2614(02)00146-X</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Qi Y., Cagin Т., Johnson W.L., Goddard III W.A. Melting and crystallization in Ni nanoclusters: The mesoscale regime. The Journal of Chemical Physics. 2001;115:385‒394. https://doi.org/10.1063/1.1373664</mixed-citation><mixed-citation xml:lang="en">Qi Y., Cagin Т., Johnson W.L., Goddard III W.A. Melting and crystallization in Ni nanoclusters: The mesoscale regime. The Journal of Chemical Physics. 2001;115:385‒394. https://doi.org/10.1063/1.1373664</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Shim J.-H., Lee B.-J., Cho Y.-W. Thermal stability of unsupported gold nanoparticle: A molecular dynamics study. Surface Science. 2002;512(3):262‒268. https://doi.org/10.1016/S0039-6028(02)01692-8</mixed-citation><mixed-citation xml:lang="en">Shim J.-H., Lee B.-J., Cho Y.-W. Thermal stability of unsupported gold nanoparticle: A molecular dynamics study. Surface Science. 2002;512(3):262‒268. https://doi.org/10.1016/S0039-6028(02)01692-8</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Li X. Modeling the size- and shape- dependent cohesive energy of nanomaterials and its applications in heterogeneous systems. Nanotechnology. 2014;25(18):185702. https://doi.org/10.1088/0957-4484/25/18/185702</mixed-citation><mixed-citation xml:lang="en">Li X. Modeling the size- and shape- dependent cohesive energy of nanomaterials and its applications in heterogeneous systems. Nanotechnology. 2014;25(18):185702. https://doi.org/10.1088/0957-4484/25/18/185702</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Chepkasov I.V., Gafner Yu.Ya., Vysotin M.A., Redel′ L.V. A study of melting of various types of Pt-Pd nanoparticles. Physics of the Solid State. 2017;59:2076‒2081. https://doi.org/10.1134/S1063783417100109</mixed-citation><mixed-citation xml:lang="en">Chepkasov I.V., Gafner Yu.Ya., Vysotin M.A., Redel′ L.V. A study of melting of various types of Pt-Pd nanoparticles. Physics of the Solid State. 2017;59:2076‒2081. https://doi.org/10.1134/S1063783417100109</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Poletaev G.M., Gafner Y.Y., Gafner S.L. Molecular dynamics study of melting, crystallization and devitrification of nickel nanoparticles. Letters on Materials. 2023; 13(4):298‒303.</mixed-citation><mixed-citation xml:lang="en">Poletaev G.M., Gafner Y.Y., Gafner S.L. Molecular dynamics study of melting, crystallization and devitrification of nickel nanoparticles. Letters on Materials. 2023; 13(4):298‒303.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Nanda K.K., Sahu S.N., Behera S.N. Liquid-drop model for the size-dependent melting of low-dimensional systems. Physical Review A. 2002;66:013208. https://doi.org/10.1103/PhysRevA.66.013208</mixed-citation><mixed-citation xml:lang="en">Nanda K.K., Sahu S.N., Behera S.N. Liquid-drop model for the size-dependent melting of low-dimensional systems. Physical Review A. 2002;66:013208. https://doi.org/10.1103/PhysRevA.66.013208</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Qi W.H., Wang M.P., Zhou M., Shen X.Q., Zhang X.F. Modeling cohesive energy and melting temperature of nanocrystals. Journal of Physics and Chemistry of Solids. 2006;67(4):851‒855. https://doi.org/10.1016/j.jpcs.2005.12.003</mixed-citation><mixed-citation xml:lang="en">Qi W.H., Wang M.P., Zhou M., Shen X.Q., Zhang X.F. Modeling cohesive energy and melting temperature of nanocrystals. Journal of Physics and Chemistry of Solids. 2006;67(4):851‒855. https://doi.org/10.1016/j.jpcs.2005.12.003</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Luo W., Hu W., Xiao S. Size effect on the thermodynamic properties of silver nanoparticles. The Journal of Physical Chemistry C. 2008;112(7):2359‒2369. https://doi.org/10.1021/jp0770155</mixed-citation><mixed-citation xml:lang="en">Luo W., Hu W., Xiao S. Size effect on the thermodynamic properties of silver nanoparticles. The Journal of Physical Chemistry C. 2008;112(7):2359‒2369. https://doi.org/10.1021/jp0770155</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Luo W., Deng L., Su K., Li K., Liao G., Xiao S. Gibbs free energy approach to calculate the thermodynamic properties of copper nanocrystals. Physica B: Condensed Matter. 2011;406(4):859–863. https://doi.org/10.1016/j.physb.2010.12.014</mixed-citation><mixed-citation xml:lang="en">Luo W., Deng L., Su K., Li K., Liao G., Xiao S. Gibbs free energy approach to calculate the thermodynamic properties of copper nanocrystals. Physica B: Condensed Matter. 2011;406(4):859–863. https://doi.org/10.1016/j.physb.2010.12.014</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Li H., Han P.D., Zhang X.B., Li M. Size-dependent melting point of nanoparticles based on bond number calculation. Materials Chemistry and Physics. 2013;137(3):1007‒1011. https://doi.org/10.1016/j.matchemphys.2012.11.016</mixed-citation><mixed-citation xml:lang="en">Li H., Han P.D., Zhang X.B., Li M. Size-dependent melting point of nanoparticles based on bond number calculation. Materials Chemistry and Physics. 2013;137(3):1007‒1011. https://doi.org/10.1016/j.matchemphys.2012.11.016</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Zhu J., Fu Q., Xue Y., Cui Z. Accurate thermodynamic relations of the melting temperature of nanocrystals with diffe­rent shapes and pure theoretical calculation. Materials Chemistry and Physics. 2017;192:22‒28. http://dx.doi.org/10.1016/j.matchemphys.2017.01.049</mixed-citation><mixed-citation xml:lang="en">Zhu J., Fu Q., Xue Y., Cui Z. Accurate thermodynamic relations of the melting temperature of nanocrystals with different shapes and pure theoretical calculation. Materials Chemistry and Physics. 2017;192:22‒28. http://dx.doi.org/10.1016/j.matchemphys.2017.01.049</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Phillpot S.R., Lutsko J.F., Wolf D., Yip S. Molecular-dyna­mics study of lattice-defect-nucleated melting in silicon. Physical Review B. 1989;40:2831. https://doi.org/10.1103/PhysRevB.40.2831</mixed-citation><mixed-citation xml:lang="en">Phillpot S.R., Lutsko J.F., Wolf D., Yip S. Molecular-dynamics study of lattice-defect-nucleated melting in silicon. Physical Review B. 1989;40:2831. https://doi.org/10.1103/PhysRevB.40.2831</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Xiao S., Hu W., Yang J. Melting behaviors of nanocrystalline Ag. The Journal of Physical Chemistry B. 2005;109(43): 20339‒20342. https://doi.org/10.1021/jp054551t</mixed-citation><mixed-citation xml:lang="en">Xiao S., Hu W., Yang J. Melting behaviors of nanocrystalline Ag. The Journal of Physical Chemistry B. 2005;109(43): 20339‒20342. https://doi.org/10.1021/jp054551t</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Xiao S., Hu W., Yang J. Melting temperature: From nanocrystalline to amorphous phase. Journal of Chemical Phy­sics. 2006;125(18):184504. https://doi.org/10.1063/1.2371112</mixed-citation><mixed-citation xml:lang="en">Xiao S., Hu W., Yang J. Melting temperature: From nanocrystalline to amorphous phase. Journal of Chemical Physics. 2006;125(18):184504. https://doi.org/10.1063/1.2371112</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Wejrzanowski T., Lewandowska M., Sikorski K., Kurzyd­lowski K.J. Effect of grain size on the melting point of confined thin aluminum films. Journal of Applied Physics. 2014;116(16):164302. https://doi.org/10.1063/1.4899240</mixed-citation><mixed-citation xml:lang="en">Wejrzanowski T., Lewandowska M., Sikorski K., Kurzydlowski K.J. Effect of grain size on the melting point of confined thin aluminum films. Journal of Applied Physics. 2014;116(16):164302. https://doi.org/10.1063/1.4899240</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Noori Z., Panjepour M., Ahmadian M. Study of the effect of grain size on melting temperature of Al nanocrystals by molecular dynamics simulation. Journal of Materials Research. 2015;30:1648‒1660. https://doi.org/10.1557/jmr.2015.109</mixed-citation><mixed-citation xml:lang="en">Noori Z., Panjepour M., Ahmadian M. Study of the effect of grain size on melting temperature of Al nanocrystals by molecular dynamics simulation. Journal of Materials Research. 2015;30:1648‒1660. https://doi.org/10.1557/jmr.2015.109</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Poletaev G.M., Bebikhov Y.V., Semenov A.S. Molecular dynamics study of the formation of the nanocrystalline structure in nickel nanoparticles during rapid cooling from the melt. Materials Chemistry and Physics. 2023;309:128358. https://doi.org/10.1016/j.matchemphys.2023.128358</mixed-citation><mixed-citation xml:lang="en">Poletaev G.M., Bebikhov Y.V., Semenov A.S. Molecular dynamics study of the formation of the nanocrystalline structure in nickel nanoparticles during rapid cooling from the melt. Materials Chemistry and Physics. 2023;309:128358. https://doi.org/10.1016/j.matchemphys.2023.128358</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Lau T.T., Först C.J., Lin X., Gale J.D., Yip S., Van Vliet K.J. Many-body potential for point defect clusters in Fe–C alloys. Physical Review Letters. 2007;98:215501. https://doi.org/10.1103/PhysRevLett.98.215501</mixed-citation><mixed-citation xml:lang="en">Lau T.T., Först C.J., Lin X., Gale J.D., Yip S., Van Vliet K.J. Many-body potential for point defect clusters in Fe–C alloys. Physical Review Letters. 2007;98:215501. https://doi.org/10.1103/PhysRevLett.98.215501</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Oila A., Bull S.J. Atomistic simulation of Fe-C austenite. Computational Materials Science. 2009;45(2):235‒239. https://doi.org/10.1016/j.commatsci.2008.09.013</mixed-citation><mixed-citation xml:lang="en">Oila A., Bull S.J. Atomistic simulation of Fe-C austenite. Computational Materials Science. 2009;45(2):235‒239. https://doi.org/10.1016/j.commatsci.2008.09.013</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Зоря И.В., Полетаев Г.М., Бебихов Ю.В., Семенов А.С. Молекулярно-динамическое исследование влияния примеси углерода на процесс кристаллизации наночастиц аустенита при быстром охлаждении. Известия вузов. Черная металлургия. 2024;67(4):440‒448. https://doi.org/10.17073/0368-0797-2024-4-440-448</mixed-citation><mixed-citation xml:lang="en">Zorya I.V., Poletaev G.M., Bebikhov Yu.V., Semenov A.S. Molecular dynamics study of the influence of carbon impurity on austenite nanoparticles crystallization during rapid cooling. Izvestiya. Ferrous Metallurgy. 2024;67(4):440–448. https://doi.org/10.17073/0368-0797-2024-4-440-448</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Tsuzuki H., Branicio P.S., Rino J.P. Structural characterization of deformed crystals by analysis of common atomic neighborhood. Computer Physics Communications. 2007;177(6):518–523. https://doi.org/10.1016/j.cpc.2007.05.018</mixed-citation><mixed-citation xml:lang="en">Tsuzuki H., Branicio P.S., Rino J.P. Structural characterization of deformed crystals by analysis of common atomic neighborhood. Computer Physics Communications. 2007;177(6):518–523. https://doi.org/10.1016/j.cpc.2007.05.018</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Fortes M.A., Deus A.M. Effects of triple grain junctions on equilibrium boundary angles and grain growth kinetics. Materials Science Forum. 2004;455-456:648−652. https://doi.org/10.4028/www.scientific.net/MSF.455-456.648</mixed-citation><mixed-citation xml:lang="en">Fortes M.A., Deus A.M. Effects of triple grain junctions on equilibrium boundary angles and grain growth kinetics. Materials Science Forum. 2004;455-456:648−652. https://doi.org/10.4028/www.scientific.net/MSF.455-456.648</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Perevalova O.B., Konovalova E.V., Koneva N.A., Koz­lov E.V. Energy of grain boundaries of different types in fcc solid solutions, ordered alloys and intermetallics with L1(2) superstructure. Journal of Materials Science &amp; Technology. 2003;19(6):593−596.</mixed-citation><mixed-citation xml:lang="en">Perevalova O.B., Konovalova E.V., Koneva N.A., Kozlov E.V. Energy of grain boundaries of different types in fcc solid solutions, ordered alloys and intermetallics with L1(2) superstructure. Journal of Materials Science &amp; Technology. 2003;19(6):593−596.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Poletaev G., Gafner Y., Gafner S., Bebikhov Y., Semenov A. Molecular dynamics study of the devitrification of amorphous copper nanoparticles in vacuum and in a silver shell. Metals. 2023;13(10):1664. https://doi.org/10.3390/met13101664</mixed-citation><mixed-citation xml:lang="en">Poletaev G., Gafner Y., Gafner S., Bebikhov Y., Semenov A. Molecular dynamics study of the devitrification of amorphous copper nanoparticles in vacuum and in a silver shell. Metals. 2023;13(10):1664. https://doi.org/10.3390/met13101664</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Poletaev G.M., Sannikov A.V., Gafner Y.Y., Gafner S.L. Molecular dynamics study of the effect of structural defects, impurities, and the presence of a shell on the melting temperature of metallic nanoparticles. Letters on Materials. 2024;14(4):332‒339. https://doi.org/10.48612/letters/2024-4-332-339</mixed-citation><mixed-citation xml:lang="en">Poletaev G.M., Sannikov A.V., Gafner Y.Y., Gafner S.L. Molecular dynamics study of the effect of structural defects, impurities, and the presence of a shell on the melting temperature of metallic nanoparticles. Letters on Materials. 2024;14(4):332‒339. https://doi.org/10.48612/letters/2024-4-332-339</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Poletaev G.M., Bebikhov Yu.V., Semenov A.S., Sitni­­kov A.A. Molecular dynamics investigation of the effect of the interface orientation on the intensity of titanium dissolution in crystalline and amorphous aluminum. Journal of Experimental and Theoretical Physics. 2023;136(4):477‒483. https://doi.org/10.1134/S1063776123040118</mixed-citation><mixed-citation xml:lang="en">Poletaev G.M., Bebikhov Yu.V., Semenov A.S., Sitnikov A.A. Molecular dynamics investigation of the effect of the interface orientation on the intensity of titanium dissolution in crystalline and amorphous aluminum. Journal of Experimental and Theoretical Physics. 2023;136(4):477‒483. https://doi.org/10.1134/S1063776123040118</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Chan W.-L., Averback R.S., Cahill D.G., Ashkenazy Y. Solidiﬁcation velocities in deeply undercooled silver. Physical Review Letters. 2009;102:095701. https://doi.org/10.1103/PhysRevLett.102.095701</mixed-citation><mixed-citation xml:lang="en">Chan W.-L., Averback R.S., Cahill D.G., Ashkenazy Y. Solidiﬁcation velocities in deeply undercooled silver. Physical Review Letters. 2009;102:095701. https://doi.org/10.1103/PhysRevLett.102.095701</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang H.Y., Liu F., Yang Y., Sun D.Y. The molecular dyna­mics study of vacancy formation during solidification of pure metals. Scientific Reports. 2017;7:10241. https://doi.org/10.1038/s41598-017-10662-x</mixed-citation><mixed-citation xml:lang="en">Zhang H.Y., Liu F., Yang Y., Sun D.Y. The molecular dynamics study of vacancy formation during solidification of pure metals. Scientific Reports. 2017;7:10241. https://doi.org/10.1038/s41598-017-10662-x</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Li S., Yang L., Lai C. Atomistic simulations of energies for arbitrary grain boundaries. Part I: Model and validation. Computational Materials Science. 2019;161:330‒338. https://doi.org/10.1016/j.commatsci.2019.02.003</mixed-citation><mixed-citation xml:lang="en">Li S., Yang L., Lai C. Atomistic simulations of energies for arbitrary grain boundaries. Part I: Model and validation. Computational Materials Science. 2019;161:330‒338. https://doi.org/10.1016/j.commatsci.2019.02.003</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Olmsted D.L., Foiles S.M., Holm E.A. Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy. Acta Materialia. 2009; 57(13):3694‒3703. https://doi.org/10.1016/j.actamat.2009.04.007</mixed-citation><mixed-citation xml:lang="en">Olmsted D.L., Foiles S.M., Holm E.A. Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy. Acta Materialia. 2009; 57(13):3694‒3703. https://doi.org/10.1016/j.actamat.2009.04.007</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Van Beers P.R.M., Kouznetsova V.G., Geers M.G.D., Tschopp M.A., McDowell D.L. A multiscale model of grain boundary structure and energy: From atomistics to a conti­nuum description. Acta Materialia. 2015;82:513‒529. https://doi.org/10.1016/j.actamat.2014.08.045</mixed-citation><mixed-citation xml:lang="en">Van Beers P.R.M., Kouznetsova V.G., Geers M.G.D., Tschopp M.A., McDowell D.L. A multiscale model of grain boundary structure and energy: From atomistics to a continuum description. Acta Materialia. 2015;82:513‒529. https://doi.org/10.1016/j.actamat.2014.08.045</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>
