<?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">10.17073/0368-0797-2018-2-135-139</article-id><article-id custom-type="elpub" pub-id-type="custom">blackmet-1245</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>МОДЕЛЬ ЭЛЕКТРОЭРОЗИОННОГО РАЗРУШЕНИЯ КОМПОЗИЦИОННЫХ ЭЛЕКТРОВЗРЫВНЫХ ПОКРЫТИЙ В УСЛОВИЯХ ИСКРОВОЙ ЭРОЗИИ</article-title><trans-title-group xml:lang="en"><trans-title>MODEL OF ELECTROEROSION DESTRUCTION OF COMPOSITE ELECTROEXPLOSIVE COATINGS IN THE CONDITIONS OF SPARK EROSION</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Романов</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Romanov</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Кандидат технических наук, доцент кафедры естественнонаучных дисциплин им. профессора В.М. Финкеля.</p><p> </p></bio><bio xml:lang="en"><p>Cand. Sci. (Eng.), Assist. Professor of the Chair of Scien­ce named after V.M. Finkel.</p><p>Novokuznetsk</p></bio><email xlink:type="simple">romanov_da@physics.sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Протопопов</surname><given-names>Е. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Protopopov</surname><given-names>E. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Доктор технических наук, профессор кафедры металлургии черных металлов.</p><p> </p></bio><bio xml:lang="en"><p>Dr. Sci. (Eng.), Professor of the Chair of Ferrous Metallurgy.</p><p> </p><p> </p></bio><email xlink:type="simple">protopopov@sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></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><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>07</day><month>03</month><year>2018</year></pub-date><volume>61</volume><issue>2</issue><fpage>135</fpage><lpage>139</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Романов Д.А., Протопопов Е.В., 2018</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="ru">Романов Д.А., Протопопов Е.В.</copyright-holder><copyright-holder xml:lang="en">Romanov D.A., Protopopov E.V.</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/1245">https://fermet.misis.ru/jour/article/view/1245</self-uri><abstract><p>Предложена модель электроэрозионного разрушения композиционных электровзрывных покрытий систем W – Cu, Mo – Cu, W – C – Cu, Mo – C – Cu, Ti – B – Cu и TiB2 – Cu в условиях искровой эрозии, происходящей при размыкании электрических контактов. Модель рассматривает испарение электродов под действием теплового потока, который возникает вследствие искрообразования при размыкании электрических контактов. При построении этой модели сопротивление электрических контактов во время испытаний находилось в  интервале 40  –  50  мкОм. Модель строится в рамках задачи нагрева полупространства поверхностным нормальным импульсным источником тепла, равномерно распределенным по площади определенного радиуса и с определенной длительностью воздействия. Распределение энергии импульса во времени аппроксимировали прямоугольным импульсом. Решали уравнение теплопроводности в цилиндрической системе координат для плоского мгновенного источника тепла с учетом конечного времени импульса. По температуре поверхности определяли давление паров металла. В расчетах принимали напряжение на контактах 380  В, силу тока 3  А, время искрового разряда 150  мкс, радиус пятна контакта искрового разряда с поверхностью 152  мкм. В результате расчета определены температура поверхности электродов из чистого материала, температура поверхности электродов из композиционных покрытий, глубина слоя испарения электродов из чистых материалов, потеря массы композиционного покрытия после единичного импульса разряда, относительное изменение объемной электро-эрозионной стойкости электродов из чистых материалов, относительное изменение массовой электроэрозионной стойкости электродов из чистых материалов, относительное изменение объемной электроэрозионной стойкости электровзрывных композиционных покрытий, относительное изменение массовой электроэрозионной стойкости электровзрывных композиционных покрытий. Произведен расчет парциального состава элементов, входящих в композиционное покрытие. Полученные результаты хорошо совпадают с экспериментальными, особенно в тройных системах W – C – Cu, Mo – C – Cu и Ti – B – Cu. При сравнении с литературными данными наблюдается достаточно хорошая корреляция. Для двойных систем W – Cu, Mo – Cu причины отклонения состоят в приближениях модели.</p></abstract><trans-abstract xml:lang="en"><p>In this paper, the authors propose a model of electroerosion destruction of composite electroexplosive coatings of W – Cu, Mo – Cu, W – Cu – Cu, Mo – Cu – Cu, Ti – B – Cu, and TiB2 – Cu systems underspark erosion that occurs when electrical contacts are opened. The model is associated with the evaporation of electrodes under the influence of heat flow, which arises from sparking when electrical contacts are opened. In constructing this model, the resistance of electrical contacts during the tests was in the range from 40 to 50  μΩ. The model was constructed in the framework of the problem of heating a half-space by a surface normal pulsed heat source uniformly distributed over an area of a certain radius and with certain duration of action. Distribution of the pulse energy in time was approximated by a rectangular pulse. The heat equation was solved in a cylindrical coordinate system for a plane instantaneous source with allowance for a finite time of the pulse. The vapor pressure of the metal was determined from the surface temperature. The calculations were carried out at a voltage of 380  V, a current of 3  A, a spark discharge time of 150  μs and a radius of the contact spot of a spark discharge with a surface of 152  μm. As a result, there were determined: the surface temperature of electrodes from pure metal, the surface temperature of electrodes from composite coatings, the depth of the evaporation layer of electrodes from pure materials, the loss of mass of the composite coating after a single discharge pulse, the relative change in the volumetric electroerosion resistance of electrodes from pure materials, durability of electrodes from pure materials, relative change in volumetric erosion resistance of electroexplosive composite coatings and the relative change in mass spark resistance of electroexplosive composite coatings. The partial composition of the elements­ included in the composite coating was calculated. The obtained results are in good agreement with the experimental results, especially in the W – C – Cu, Mo – C – Cu and Ti – B – Cu ternary systems. Comparison with data from the literature has a fairly good degree of correlation. Deviations for the binary W – Cu, Mo – Cu systems have causes in the model approximations.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>математическая модель</kwd><kwd>искровая эрозия</kwd><kwd>покрытия</kwd><kwd>композит</kwd><kwd>вольфрам</kwd><kwd>молибден</kwd><kwd>углерод</kwd><kwd>титан</kwd><kwd>бор</kwd><kwd>диборид титана</kwd><kwd>медь</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical model</kwd><kwd>spark erosion</kwd><kwd>coatings</kwd><kwd>composite</kwd><kwd>tungsten</kwd><kwd>molybdenum</kwd><kwd>carbon</kwd><kwd>titanium</kwd><kwd>boron</kwd><kwd>titanium diboride</kwd><kwd>copper</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">РФФИ в  рамках научного проекта № 16-32-60032 мол_а_дк; Грант Президента Российской Федерации для государственной поддержки молодых российских ученых – кандидатов наук МК-1118.2017.2.</funding-statement><funding-statement xml:lang="en">The Russian Foundation for Basic Research within the framework of the scientific project no. 16-32-60032 Mol_a_dk; The Grant of the President of the Russian Federation for the state support of young Russian scientists  – candidates of sciences MK-1118.2017.2.</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">Panin V.E., Gromov V.E., Romanov D.A., Budovskikh E.A., Panin S.V. The Physical Basics of Structure Formation in Electroexplosive Coatings // Doklady Physics. 2017. Vol. 62. No. 2. P. 67 – 70.</mixed-citation><mixed-citation xml:lang="en">Panin V.E., Gromov V.E., Romanov D.A., Budovskikh E.A., Panin  S.V. The physical basics of structure formation in electroexplosive coatings. Doklady Physics. 2017, vol. 62, no. 2, pp. 67–70.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Romanov D.A., Gromov V.E., Glezer A.M., Panin S.V., Semin A.P. Structure of electroexplosion resistant coatings consisting of immiscible components // Materials Letters. 2017. Vol. 188. P. 25 – 28.</mixed-citation><mixed-citation xml:lang="en">Romanov D.A., Gromov V.E., Glezer A.M., Panin S.V., Semin A.P. Structure of electroexplosion resistant coatings consisting of immiscible components. Materials Letters. 2017, vol. 188, pp. 25–28.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Romanov D.A., Olesyuk O.V., Budovskikh E.A., Gromov V.E., Ivanov Yu.F., Teresov A.D. Structure of the molybdenum–carbon– copper composite coatings produced by electroexplosive spraying followed by electron-beam treatment // Russian Metallurgy (Me­ tally). 2015. No. 13. P. 1134 – 1138.</mixed-citation><mixed-citation xml:lang="en">Romanov D.A., Olesyuk O.V., Budovskikh E.A., Gromov V.E., Ivanov Yu.F., Teresov A.D. Structure of the molybdenum–carbon– copper composite coatings produced by electroexplosive spraying followed by electron-beam treatment. Russian Metallurgy (Metally). 2015, no. 13, pp. 1134–1138.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Romanov D.A., Olesyuk O.V., Budovskikh E.A., Gromov V.E., Ivanov­ Yu.F., Teresov A.D. Structural-Phase States and Tribological Properties of Electroexplosive Composite Coatings on Copper after Electron-Beam Treatment // Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques. 2015. Vol. 9. No. 4. P. 699 – 705.</mixed-citation><mixed-citation xml:lang="en">Romanov D.A., Olesyuk O.V., Budovskikh E.A., Gromov V.E., Ivanov Yu.F., Teresov A.D. Structural-phase states and tribological properties of electroexplosive composite coatings on copper after electron-beam treatment. Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques. 2015. vol. 9, no. 4, pp. 699–705.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Veklich A., Lebid A., Minakova R., Kryachko L., Grechanyuk N. Peculiarities of interaction of electric arc plasma and composite electrodes’ working surface. – In: 21st Symposium on Physics of Switching Arc 2015. – Nove Mesto Na Morave, Czech Republic, 2015. P. 96 – 99.</mixed-citation><mixed-citation xml:lang="en">Veklich A., Lebid A., Minakova R., Kryachko L., Grechanyuk N. Peculiarities of interaction of electric arc plasma and composite electrodes’ working surface. In: 21st Symposium on Physics of Switching Arc 2015. Nove Mesto Na Morave, Czech Republic, 2015, pp. 96–99.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Bogdan M., Marcin H., Grechanyuk I.N., Grechanyuk N.I., Minakova R.V., Xu L.J. The actual state and prospects of a high power electron beam technology for metallic and non-metallic compositions used in electric contacts and electrodes // Advanced Materials Research. 2014. Vol. 875-877. P. 1437 – 1448.</mixed-citation><mixed-citation xml:lang="en">Bogdan M., Marcin H., Grechanyuk I.N., Grechanyuk N.I., Minakova R.V., Xu L.J. The actual state and prospects of a high power electron beam technology for metallic and non-metallic compositions used in electric contacts and electrodes. Advanced Materials Research. 2014, vol. 875-877, pp. 1437–1448.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Grechanyuk N.I., Minakova R.V., Kopylova, G.E. Current state and prospects of high-speed electron-beam evaporation and subsequent vacuum condensation of metals and nonmetals to produce electric contacts and electrodes // Powder Metallurgy and Metal Ceramics. 2013. Vol. 52. No. 3-4. P. 228 – 236.</mixed-citation><mixed-citation xml:lang="en">Grechanyuk N.I., Minakova R.V., Kopylova, G.E. Current state and prospects of high-speed electron-beam evaporation and subsequent vacuum condensation of metals and nonmetals to produce electric contacts and electrodes. Powder Metallurgy and Metal Ceramics. 2013, vol. 52, no. 3-4, pp. 228–236.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Bukhanovsky V., Rudnytsky M., Grechanyuk M., Minakova R., Zhang C. Vapour-phase condensed composite materials based on copper and carbon // Materiali in Tehnologije. 2016. Vol. 50. No. 4. pp.523 – 530.</mixed-citation><mixed-citation xml:lang="en">Bukhanovsky V., Rudnytsky M., Grechanyuk M., Minakova R., Zhang C. Vapour-phase condensed composite materials based on copper and carbon. Materiali in Tehnologije. 2016, vol. 50, no. 4, pp.523–530.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Khomenko E.V., Minakova R.V., Lesnik, N.D. Microstructural evolution­ of Cr-Cu composites in liquid-phase sintering // Powder Metallurgy and Metal Ceramics. 2013. Vol. 52. No. 1-2. P. 20 – 31.</mixed-citation><mixed-citation xml:lang="en">Khomenko E.V., Minakova R.V., Lesnik, N.D. Microstructural evolution of Cr-Cu composites in liquid-phase sintering. Powder Metallurgy and Metal Ceramics. 2013, vol. 52, no. 1-2, pp. 20–31.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Khomenko E.V., Minakova R.V., Naida Yu.I. Analyzing the quality of grinding and mixing of copper and chromium powders in a new-type mill // Powder Metallurgy and Metal Ceramics. 2012. Vol. 51. pp. 137 – 141.</mixed-citation><mixed-citation xml:lang="en">Khomenko E.V., Minakova R.V., Naida Yu.I. Analyzing the quality of grinding and mixing of copper and chromium powders in a new-type mill. Powder Metallurgy and Metal Ceramics. 2012, vol.  51, pp. 137–141.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Bukhanovsky V.V, Grechanyuk N.I., Minakova R.V., Mamuzich I., Kharchenko V.V., Rudnitsky N.P. Production technology, structure and properties of Cu-W layered composite condensed materials for electrical contacts // International Journal of Refractory Metals and Hard Materials. 2011. Vol. 29. No. 5. P. 561 – 644.</mixed-citation><mixed-citation xml:lang="en">Bukhanovsky V.V, Grechanyuk N.I., Minakova R.V., Mamuzich I., Kharchenko V.V., Rudnitsky N.P. Production technology, structure and properties of Cu – W layered composite condensed materials for electrical contacts. International Journal of Refractory Metals and Hard Materials. 2011, vol. 29, no. 5, pp. 561–644.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Bukhanovs’kyi V.V., Rudnyts’Kyi M.P., Kharchenko V.V., Minakova R.V., Grechanyuk M.I., Mamuzic, I. Relationship between composition, structure, and mechanical properties of a condensed composite of coppertungsten system // Strength of Materials. 2011. Vol. 43. No. 4. P. 426 – 437.</mixed-citation><mixed-citation xml:lang="en">Bukhanovs’kyi V.V., Rudnyts’Kyi M.P., Kharchenko V.V., Minakova R.V., Grechanyuk M.I., Mamuzic, I. Relationship between composition, structure, and mechanical properties of a condensed composite of copper-tungsten system. Strength of Materials. 2011, vol. 43, no. 4, pp. 426–437.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Bukhanovskii V.V., Minakova R.V., Grechanyuk I.N., Mamuziæ I., Rudnitskii N.P. Effect of composition and heat treatment on the structure and properties of condensed composites of the Cu – W system // Metal Science and Heat Treatment. 2011. Vol. 53. P. 14 – 23.</mixed-citation><mixed-citation xml:lang="en">Bukhanovskii V.V., Minakova R.V., Grechanyuk I.N., Mamuziæ  I., Rudnitskii N.P. Effect of composition and heat treatment on the structure and properties of condensed composites of the Cu – W system. Metal Science and Heat Treatment. 2011, vol. 53, pp. 14–23.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Babich I.L., Boretskij V.F., Kryachko L.A., Minakova R.V., Semenyshyn R.V., Veklich A.N. Thermal plasma of electric arc discharge with silver vapours: Peculiarities of spectroscopic investigations. In: Source of the Document 19th Symposium on Physics of Switching Arc 2011, FSO 2011. 2011. P. 101 – 104.</mixed-citation><mixed-citation xml:lang="en">Babich I.L., Boretskij V.F., Kryachko L.A., Minakova R.V., Semenyshyn R.V., Veklich A.N. Thermal plasma of electric arc discharge with silver vapours: Peculiarities of spectroscopic investigations. In: Source of the Document 19th Symposium on Physics of Switching Arc 2011, FSO 2011. 2011, pp. 101–104.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Babich I.L., Boretskij V.F., Kryachko L.A., Minakova R.V., Semenyshyn R.V., Veklich A.N. Plasma of electric arc between composite electrodes on silver base // Problems of Atomic Science and Technology. 2010. No. 6. P. 141 – 143.</mixed-citation><mixed-citation xml:lang="en">Babich I.L., Boretskij V.F., Kryachko L.A., Minakova R.V., Semenyshyn R.V., Veklich A.N. Plasma of electric arc between composite electrodes on silver base. Problems of Atomic Science and Techno­ logy. 2010, no. 6, pp. 141–143.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Ibragimov A.R., Ilinkova T.A., Shafigullin L.N., Saifutdinov A.I. Investigation of mechanical properties of thermal coatings obtained during plasma spraying of powder zirconium dioxide // IOP Conference Series: Journal of Physics: Conf. Series. 2017. Vol. 789, pp. 012022 .</mixed-citation><mixed-citation xml:lang="en">Ibragimov A.R., Ilinkova T.A., Shafigullin L.N., Saifutdinov A.I. Investigation of mechanical properties of thermal coatings obtained during plasma spraying of powder zirconium dioxide. IOP Conference Series: Journal of Physics: Conf. Series. 2017, vol. 789, pp.  012022 .</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Карлслоу Г., Егер Д. Теплопроводность твердых тел. – М.: Нау­ ка, 1964. – 488 с.</mixed-citation><mixed-citation xml:lang="en">Carslaw H.S., Jaeger J.C. Conduction of Heat in Solids. Oxford University Press, London, 1947. (Russ.ed.: Carslaw H., Jaeger J. Тeploprovodnost’ tverdykh tel. Moscow: Nauka, 1964, 488 p.)</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Лозанский Э.Д., Фирсов О.Б. Теория искры. – М.: Атомиздат, 1975. – 272 с.</mixed-citation><mixed-citation xml:lang="en">Lozanskii E.D., Firsov O.B. Teoriya iskry [Theory of spark]. Moscow: Atomizdat, 1975, 272 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Кесаев И.Г. Катодные процессы электрической дуги. – М.: Наука, 1968. – 244 с.</mixed-citation><mixed-citation xml:lang="en">Kesaev I.G. Katodnye protsessy elektricheskoi dugi [Cathodic processes of electric arc]. Moscow: Nauka, 1968, 244 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Курочкин В.Д., Минакова Р.В., Кресанова А.П. Состав и параметры искровой плазмы в воздухе с электродами из вольфрам-медной композиции // Теплофизика высоких температур. 1993. Т. 31. Вып. 5. С. 693 – 697.</mixed-citation><mixed-citation xml:lang="en">Kurochkin V.D., Minakova R.V., Kresanova A.P. Composition and parameters of spark plasma in air with electrodes of tungsten-copper composition. Teplofizika vysokikh temperatur. 1993, vol. 31, no. 5, pp. 693–697. (In Russ.).</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>
