Формирование базы данных по физическим свойствам компонентов оксидной окалины для теоретической оценки эффективности лазерной очистки углеродистых сталей и родственных технологий

В настоящее время в машиностроительных производствах имеется потребность в автоматизации технологий, в частности лазерных, для удаления оксидных слоев – окалины, ржавчины – со стальных изделий с целью улучшения энергоэффективности обработки. При этом можно использовать теоретическую оценку интенсивности нагрева оксидного слоя и фазового перехода в нем для оптимизации лазерной очистки (ЛО) поверхности стали. Для нее требуются специальный сбор и верификация данных по зависящим от температуры свойствам железосодержащих конденсированных фаз как возможных компонентов, содержащихся, в частности, в окалине, распространенной в металлоизделиях. В связи с этим в качестве задачи данной работы было принято формирование базы данных по характеристикам компонентов оксидной окалины путем подбора сведений по физическим свойствам ее компонентов и стальной основы, требующихся для надежного оценивания теплотехнических параметров эффективности технологии лазерной очистки углеродистых сталей, а также активно внедряемых родственных технологий – лазерной резки, сверления, оплавления покрытий и др. Аналитический обзор опубликованных экспериментальных данных позволил систематизировать сведения по ряду переносных и других свойств железосодержащих компонентов при атмосферном давлении в области от 298 К до температур плавления металлических и оксидных фаз и выше них. При этом предварительная расчетная термохимическая оценка показала существование таких термодинамически стабильных конденсированных фаз в пятне нагрева окалины при ее ЛО в точке плавления и выше, как Fe₃O₄, FeO и Fe, что согласуется и с известными опытными данными. Сравнение определенных нами (по опубликованным значениям k, ρ и теплоемкости и с применением экстраполяции в высокотемпературной области) значений a для рассматриваемых видов компонентов окалины с набором имеющихся в современной литературе опытных велечин этого параметра выявило наличие отличий как для оксидных, так и металлических фаз. Новые значения заполняют пробел в области температур 1600–1800 К, имевшийся к данному моменту по температуропроводности. Также нами получено значение a = (0,83–0,92) × 10^–6 м²/с для расплава оксида двухвалентного железа при температуре T ≈ 1800 К, не определявшееся ранее экспериментально, что мешало проведению корректного численного моделирования как лазерных процессов поверхностной термообработки, плавления и очистки сталей, так и расчетам в области металлургических и иных технологий, для которых характерно наличие зон с железооксидными расплавами в ходе нагрева.

1. Xie X., Huang Q., Long J., Ren Q., Hu W., Liu S. (2020) A New Monitoring Method for Metal Rust Removal States in Pulsed Laser Derusting Via Acoustic Emission Techniques. Journal of Materials Processing Technology, 275, 116321. https://doi.org/10.1016/j.jmatprotec.2019.116321.

2. Sofronov V.L., Kartashov E.Yu., Tkachuk S.A., Pak A.D., Tinin V.V., Galata A.A. (2022) Research on Laser Deactivation Cleaning of Metal Surfaces Contaminated with Radioactive Materials. Izvestiya Tomskogo Politekhnicheskogo Universiteta. Inzhiniring Georesursov = Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 333 (11), 171–182 (in Russian). https://doi.org/10.18799/24131830/2022/11/3734.

3. Ma M., Wang L., Li J., Jia X., Wang X., Ren Y., Zhou Y. (2020) Investigation of the Surface Integrity of Q345 Steel After Nd:YAG Laser Cleaning of Oxidized Mining Parts. Coatings, 10 (8), 716. https://doi.org/10.3390/coatings10080716.

4. Deschênes J. M., Fraser A. (2020). Empirical Study of Laser Cleaning of Rust, Paint, and Mill Scale from Steel Surface. Lee J., Wagstaff S., Lambotte G., Allanore A., Tesfaye F. (eds) Materials Processing Fundamentals 2020. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-030-36556-1_17.

5. Ren Y., Wang L., Ma M., Cheng W., Li B., Lou Y., Li J., Ma X. (2022) Stepwise Removal Process Analysis Based on Layered Corrosion Oxides. Materials, 15 (21), 7559. https://doi.org/10.3390/ma15217559.

6. Zhou Z., Sun W., Wu J., Chen H., Zhang F., Wang S. (2023) The Fundamental Mechanisms of Laser Cleaning Technology and Its Typical Applications in Industry. Processes, 11 (5), 1445. https://doi.org/10.3390/pr11051445.

7. Avdeev Ya. G., Gorichev I. G., Luchkin А. Yu. (2012) Effect of IFKhAN-92 Inhibitor on Scale Removal during Sulfuric Acid Pickling of Steel. International Journal of Corrosion and Scale Inhibition, 1 (1), 26–37. https://doi.org/10.17675/2305-6894-2012-1-1-026-037.

8. Mourao R., Marquesi A. R., Gorbunov A. V., Filho G. P., Halinouski A. A., Otani C. (2015). Thermochemical Assessment of Gasification Process Efficiency of Biofuels Industry Waste with Different Plasma Oxidants. IEEE Transactions on Plasma Science, 43 (10), 3760–3767. https://doi.org/10.1109/TPS.2015.2416129.

9. Gorbunov A. V., Devoino O. G., Gorbunova V. A., Yatskevitch O. K., Koval V. A. (2021) Thermodynamic Estimation of the Parameters for C-H-O-N-Me-Systems as Operating Fluid Simulants for New Processes of Powder Thermal Spraying and Spheroidizing. Nauka i Tehnika = Science and Technique, 20 (5), 390–398. https://doi.org/10.21122/2227-1031-2021-20-5-390-398.

10. Carslaw H. S., Jaeger J. C. (1986) Conduction of Heat in Solids. Oxford University Press. 2nd ed. 520.

11. Pinsker V. A. (2006). Unsteady-State Temperature Field in a Semi-Infinite Body Heated by a Disk Surface Heat Source. High Temperature, 44 (1), 129–138. https://doi.org/10.1007/s10740-006-0015-1.

12. Pinsker V. A. (2008) Quasi-Static Thermoelastic Stresses in a Half-Space Heated by a Circular Surface Heat Source. VI Minskii Mezhdunarodnyi Forum po Teplo- i Massoobmenu, 19–23 Maya 2008 g.: Tezisy Dokladov i Soobshchenii. T. 2 [VI Minsk Medunarodny Forum for Heat and Mass, 19–23 May 2008: These are the Documents and the Information]. Minsk, HMTI of NAS of Belarus. 10 pp. (in Russian).

13. CRC Handbook of Chemistry and Physics, 95th ed.; Haynes W. M. (Editor); CRC Press, USA, 2014–2015, 2704 p. ISBN-10:‎ 1482208679, ISBN-13:‎ 978-1482208672.

14. Gas Phase Thermochemistry Data. Available at: https://webbook.nist.gov/cgi/cbook.cgi?ID=C74828&Units=SI&Mask=1#Thermo-Gas.

15. Okumu H. W. (2022) Cleaning of Metal Surfaces by Laser Irradiation; Mathematical Modeling and Experimental Analysis. Tesis de Maestría en Ciencias. Centro de Investigaciones en Óptica, León, Guanajuato, Mexico. 91.

16. Kermanpur A., Mahmoudi Sh., Hajipour A. (2008). Numerical Simulation of Metal Flow and Solidification in the Multi-Cavity Casting Moulds of Automotive Components. Journal of Materials Processing Technology, 206 (1–3), 62–68. https://doi.org/10.1016/j.jmatprotec.2007.12.004.

17. Schneider S. (1963) Compilation of the Melting Points of the Metal Oxides. National Bureau of Standards Monograph 68. Gaithersburg, MD. https://doi.org/10.6028/NBS.MONO.68.

18. Chen Z., Qu Y., Zeilstra C., Van Der Stel J., Sietsma J., Yang Y. (2019) Prediction of Density and Volume Variation of Hematite Ore Particles during In-Flight Melting and Reduction. Journal of Iron and Steel Research International, 26, 1285–1294. https://doi.org/10.1007/s42243-019-00265-3.

19. Qu Y., Yang Y., Zou Z., Zeilstra C., Meijer K., Boom R. (2014). Thermal Decomposition Behaviour of Fine Iron Ore Particles. ISIJ International, 54 (10), 2196–2205. https://doi.org/10.2355/isijinternational.54.2196.

20. Iron (II) Oxide. Available at: https://ceramica.fandom.com/wiki/Iron(II)_oxide.

21. Cotton F. A., Wilkinson G., Murillo C. A., Bochmann M. (1999). Advanced Inorganic Chemistry. 6th Ed. New York, Wiley-Interscience.

22. Zou W.F., Xie Y.M., Xiao X., Zeng X.Z., Luo Y. (2014). Application of Thermal Stress Model to Paint Removal by Q-Switched Nd:YAG Laser. Chinese Physics B, 23 (7), 074205. https://doi.org/10.1088/1674-1056/23/7/074205.

23. Beygelzimer E., Beygelzimer Y. (2021) Generalized Estimates for the Density of Oxide Scale in the Range From 0 C to 1300 C [Preprints]. Arxiv. Available at: https://arxiv.org/abs/2110.09791.ttps://doi.org/10.48550/arXiv.2110.09791.

24. Beygelzimer E., Beygelzimer Y. (2021) Thermal Conductivity of Oxide Scale and its Components in the Range from 0 °C to 1300 °C: Generalized Estimates with Account for Movability of Phase Transitions [Preprints]. Arxiv. Available at: https://arxiv.org/abs/2110.11632. https://doi.org/10.48550/arXiv.2110.11632.

25. Beygelzimer E., Beygelzimer Y. (2021) Heat Capacity of Oxide Scale in the Range from 0 C to 1300 C: Generalized Estimates with Account for Movability of Phase Transitions. [Preprints]. Arxiv. Available at: https://arxiv.org/abs/2110. 11101.https://doi.org/10.48550/arXiv.2110.11101.

26. Max Metal Surface Cleaning Tyre Mold Portable 200w Pulse Laser Cleaning Machine. Available at: https://www.alibaba.com/product-detail/Max-Metal-Surface-Cleaning-Tyre-Mold_1600762853557.html.

27. Vil’danov S. K. (2021) Calculation of Viscosity and Thermal Conductivity at a High Temperature for Glasses Based on the SiO2–Al2O3–R2O System (R = Na, K) and Doped with CaO, MgO, and FeO. Glass Physics and Chemistry, 47, 235–244. https://doi.org/10.1134/S1087659621030135.

28. Hara S., Irie K., Gaskell D. R., Ogino K. (1988) Densities of Melts in the FeO-Fe2O3-CaO and FeO-Fe2O3-2CaO•SiO2 Systems. Transactions of the Japan Institute of Metals, 29 (12), 977–989. Available at: https://www.jsta ge.jst.go.jp/article/matertrans1960/29/12/29_12_977/_pdf/- char/en.

29. Li G., Wang P. (2013) Properties of Steel at Elevated Temperatures. Advanced Analysis and Design for Fire Safety of Steel Structures. Advanced Topics in Science and Technology in China. Springer, Berlin, Heidelberg, 37–65. https://doi.org/10.1007/978-3-642-34393-3_3.

30. Bergström D., Powell J., Kaplan A.F.H. (2007). The Absorptance of Steels to Nd:YLF and Nd:YAG Laser Light at Room Temperature. Applied Surface Science, 253 (11), 5017–5028. https://doi.org/10.1016/j.apsusc.2006.11.018.

31. Henning T., Mutschke H. (1997) Low-Temperature Infrared Properties of Cosmic Dust Analogues. Astronomy and Astrophysics, 327, 743–754.

32. Marusak L.A., Messier R., White W. B. (1980). Optical Absorption Spectrum of Hematite, αFe2O3 Near IR to UV. Journal of Physics and Chemistry of Solids, 41 (9), 981–984. https://doi.org/10.1016/0022-3697(80)90105-5.

33. Schlegel A., Alvarado S.F., Wachter P. (1979) Optical Properties of Magnetite (Fe3O4). Journal of Physics C: Solid State Physics, 12 (6), 1157–1164. https://doi.org/10.1088/0022-3719/12/6/027.

34. Frewin M. R. (1997) Experimental and Theoretical Investigation of Tandem Laser Welding. Doctor of Philosophy Thesis. Department of Materials Engineering, University of Wollongong, Australia. 179. Available at: https://core. ac.uk/download/pdf/37028176.pdf.

35. Mich J., Braig D., Gustmann T., Hasse C., Scholtissek A. (2023) A Comparison of Mechanistic Models for the Combustion of Iron Microparticles and Their Application to Polydisperse Iron-Air Suspensions. Combustion and Flame, 256, 112949. https://doi.org/10.1016/j.combustflame.2023.112949.

36. Mi X. C., Fujinawa A., Bergthorson J. M. (2022) A Quantitative Analysis of the Ignition Characteristics of Fine Iron Particles. Combustion and Flame, 240, 112011. https://doi.org/10.1016/j.combustflame.2022.112011

37. Jones J. M., Mason P. E., Williams A. (2019). A Compilation of Data on the Radiant Emissivity of Some Materials at High Temperatures. Journal of the Energy Institute, 92 (3), 523–534. https://doi.org/10.1016/j.joei.2018.04.006.

38. Touloukian Y. S., DeWitt D. P. (1970) Thermal Radiative Properties: Metallic Elements and Alloys. Vol. 7. New York, IFI/Plenum Press.

39. Touloukian Y.S., DeWitt D.P. (1971) Thermal Radiative Properties. Non-Metallic Solids. Vol. 8. New York, IFI/Plenum Press.

40. Ratanapupech P., Bautista R. G. (1981) Normal Spectral Emissivities of Liquid Iron, Liquid Nickel and Liquid Iron-Nickel Alloys. High Temperature Science, 14 (4), 269–283.

41. Li M., Endo R., Akoshima M., Susa M. (2017). Temperature Dependence of Thermal Diffusivity and Conductivity of FeO Scale Produced on Iron by Thermal Oxidation. ISIJ International, 57 (12), 2097–2106. https://doi.org/10. 2355/isijinternational.ISIJINT-2017-301.

42. Iron Oxide (Wustite) Fe0.947O (c, l; wustite)). Available at: https://www.chem.msu.su/Zn/Fe/print-Fe0.947O_c.html (in Russian).

43. Wilson J. (August 2007) Materials Data. Available at: http://www.electronics-cooling.com/2007/08/thermal-diffusivity/.

44. Gaskell D. R., Laughlin D. E. (2017) Introduction to the Thermodynamics of Materials. 6th Ed. Boca Raton, USA, CRC Press. 714. https://doi.org/10.1201/9781315119038.

45. Lienhard J. H. IV, Lienhard J. H. V. (2019) A Heat Transfer Textbook. 5th ed. Dover Publications. 715.

46. Grinchuk P. S., Dmitriev S. I., Khina B. B. (2012). Modeling of the Reduction of Iron Oxide by Methane-Conversion Products in a Plasma Jet. II. Heat and Mass Transfer. Journal of Engineering Physics and Thermophysics, 85 (2), 265–273. https://doi.org/10.1007/s10891-012-0649-2.

47. Susa M., Endo R. K. (2009) Emissivities of High Temperature Metallic Melts. Fukuyama H, Waseda Y. (eds.) High Temperature Measurements of Materials. Berlin, Springer, 111–129. https://doi.org/10.1007/978-3-540-85918-5.

48. Chen R. Y., Yeun W. Y. D. (2003) Review of the High-temperature Oxidation of Iron and Carbon Steels in Air or Oxygen. Oxidation of Metals, 59 (5–6), 433–468. https://doi.org/10.1023/A:1023685905159.

49. Nishi T., Shibata H., Waseda Y., Ohta H. (2003). Thermal Conductivities of Molten Iron, Cobalt, and Nickel by Laser Flash Method. Metallurgical & Materials Transactions – A, 34 (12), 2801–2807. https://doi.org/10.1007/s11661-003-0181-2.

50. Nishi T., Shibata H., Tsutsumi K., Ohta H., Waseda Y. (2002). Measurement of Thermal Diffusivity of Steels at Elevated Temperature by a Laser Flash Method. ISIJ International, 42 (5), 498–503. https://doi.org/10.2355/isijinternational.42.498.

51. Li M., Akoshima M., Endo R., Ueda M., Tanei H., Susa M. (2022) Thermal Diffusivity and Conductivity of Fe3O4 Scale Provided by Oxidation of Iron. ISIJ International, 62 (1), 275–277. https://doi.org/10.2355/isijinternational.ISIJINT-2021-326.

52. Pottlacher G., Boboridis K., Cagran C., Hüpf T., Seifter A., Wilthan B. (2013) Normal Spectral Emissivity Near 680 nm at Melting and in the Liquid Phase for 18 Metallic Elements. AIP Conference Proceedings, 1552 (1), 704–709. https://doi.org/10.1063/1.4819628.

53. Endo R., Hayashi H., Li M., Akoshima M., Okada H., Tanei H., Hayashi M., Susa M. (2020) Determination of Thermal Diffusivity/conductivity of Oxide Scale Formed on Steel Plate by Laser Flash Method through Thermal Effusivity Measurement by Transient Hot-strip Method. ISIJ International, 60 (12), 2773–2779. https://doi.org/10.2355/isijinternational.ISIJINT-2020-163.

54. Akiyama T., Ohta H., Takahashi R., Waseda Y., Yagi J. (1992). Measurement and Modeling of Thermal Conductivity for Dense Iron Oxide and Porous Iron Ore Agglomerates in Stepwise Reduction. ISIJ International, 32 (7), 829–837. https://doi.org/10.2355/isijinternational.32.829.

55. Chen J. K., Chen S. F. (2011) On Thermal Conductivity of an in-situ metal matrix Composite–cast Iron / In: Cuppoletti J. (ed.) Metal, Ceramic and Polymeric Composites for Various Uses. Intech Open. Taiwan, 211–224. https://doi.org/10.5772/21537.

56. Helsing J., Grimvall G. (1991). Thermal Conductivity of cast Iron: Models and Analysis of Experiments. Journal of Applied Physics, 70 (3), 1198–1206. https://doi.org/10.1063/1.349573.

57. Endo R., Yagi T., Ueda M., Susa M. (2014). Thermal Diffusivity Measurement of Oxide Scale Formed on Steel during Hot-rolling Process. ISIJ International, 54 (9), 2084–2088. https://doi.org/10.2355/isijinternational. 54.2084.

58. Masdeu F., Carmona C., Horrach G., Muñoz J. (2021) Effect of Iron (III) Oxide Powder on Thermal Conductivity and Diffusivity of Lime Mortar. Materials, 14 (4), 998. https://doi.org/10.3390/ma14040998.

59. Samsonov G. V. (1982). The Oxide Handbook. 2nd ed. New York and London, IFI/Plenum. 463. https://doi.org/10.1007/978-1-4757-1613-9.

60. Sipkens T. A. Hadwin P. J. Grauer S. J., Daun K. J. (2018). Predicting the Heat of Vaporization of Iron at High Temperatures Using Time-Resolved Laser-Induced Incandescence and Bayesian Model Selection. Journal of Applied Physics, 123 (9), 095103. https://doi.org/10.1063/1.5016341.

61. Heat of Fusion and Vaporization. Chemistry 301. Data base of Texas University. Available at: https://ch301.cm. utexas.edu/data/section2.php?target=heat-transition.php.

62. Kaplan A. F. H. (2014). Laser Absorptivity on Wavy Molten Metal Surfaces: Categorization of Different Metals and Wavelengths. Journal of Laser Applications, 26 (1), 012007. https://doi.org/10.2351/1.4833936.

63. Mahrle A., Beyer E. (2009). Theoretical Aspects of Fibre Laser Cutting. Journal of Physics D: Applied Physics, 42 (17), 175507. https://doi.org/10.1088/0022-3727/42/17/175507.

64. Volpp J. (2023). Laser Beam Absorption Measurement at Molten Metal Surfaces. Measurement, 209, 112524. https://doi.org/10.1016/j.measurement.2023.112524.

65. Dausinger F., Shen J. (1993). Energy Coupling Efficiency in Laser Surface Treatment. ISIJ International, 33 (9), 925–933. https://doi.org/10.2355/isijinternational.33.925.

66. Gorewoda J., Scherer V. (2016). The Influence of Carbonate Decomposition on Normal Spectral Radiative Emittance in the Context of Oxy-Fuel Combustion. Energy & Fuels, 30 (11), 9752–9760. https://doi.org/10.1021/acs.energyfuels.6b0139.8.

67. Burgess G. K., Foote P. D. (1916) The Emissivity of Metals and Oxides. IV. Iron Oxide. Bulletin of the Bureau of Standards, 12 (1), 83–89. https://doi.org/10.6028/bulletin.273.

68. Yang Y., Watanabe H., Akoshima M., Hayashi M., Susa M., Tanei H., Okada H., Endo R. (2021) Determination of Thermal Diffusivity and Its Temperature Dependence of Fe1−xO Scale at High Temperature by Electrical-Optical Hybrid Pulse-Heating Method. ISIJ International, 61 (1), 26–32. https://doi.org/10.2355/isijinternational.isijint-2019-635.

69. Gahmousse A., Ferria K., Rubio J., Cornejo N., Tamayo A. (2020). Influence of Fe2O3 on the Structure and Near-infrared Emissivity of Aluminosilicate Glass Coatings. Applied Physics A, 126 (9), 732. https://doi.org/10.1007/s00339-020-03921-8.

70. Timoshpolsky V. I., Samoilovich Yu. A., Trusova I. A., Khopova O. G. (2001) Calculation Analysis of the Occurrence of “Dark Spots” During Thermal Interaction of heated wares with Supporting Devices of Reheating/ Continuous Furnaces. Metallurgiya: Respublikanskiy Mezhvedomstvennyy Sbornik Nauchnykh Trudov [Metallurgy. Republican Interdepartmental Collection of Scientific Works]. Minsk, Vysshaya Shkola Publ., Iss. 25, 12–23 (in Russian).

71. van Gool C. E. A. G., Thijs L. C., Ramaekers W. J. S., van Oijen J. A., de Goey P. (2023). Particle Equilibrium Composition Model for Iron Dust Combustion. Applications in Energy and Combustion Science, 13, 100115. https://doi.org/10.1016/j.jaecs.2023.100115.

72. Schöpp H; Sperl A; Kozakov R; Gött G; Uhrlandt D; Wilhelm G (2012). Temperature and Emissivity Determination of Liquid Steel S235. Journal of Physics D: Applied Physics, 45 (23), 235203. https://doi.org/10.1088/0022-3727/45/23/235203.

73. Muller M., El-Rabii H., Fabbro R. (2015). Liquid Phase Combustion of Iron in an Oxygen Atmosphere. Journal of Materials Science, 50 (9), 3337–3350. https://doi.org/10.1007/s10853-015-8872-9.

74. Teulet P., Girard L., Razafinimanana M., Gleizes A., Bertrand P., Camy-Peyret F., Baillot E., Richard F. (2006) Experimental Study of an Oxygen Plasma Cutting Torch: II. Arc–Material Interaction, Energy Transfer and Anode Attachment. Journal of Physics D: Applied Physics, 39 (8), 1557–1573. https://doi.org/10.1088/0022-3727/39/8/01.

75. Zaitsev A. V., Ermolaev G. V., Polyanskiy T. A., Gurin A. M. (2018). Calculation of Intrinsic Absorption Coefficient in High Power Laser Material Processing. Journal of Physics: Conference Series, 1109, 012011. https://doi.org/10.1088/1742-6596/1109/1/012011.

76. Seibold G., Dausinger F., Hügel H. (2000) Absorptivity of Nd: YAG-Laser Radiation on Iron and Steel Depending on Temperature and Surface Conditions. International Congress on Applications of Lasers & Electro-Optics, 89, 125–132. https://doi.org/10.2351/1.5059485.

77. Muller M., El-Rabii H., Fabbro R., Coste F., Rostaing J.-C., Ridlova M., Colson A., Barthelemy H. (2016) Detailed Investigation of the Sequence of Mechanisms Participating in MetalsIgnition in Oxygen Using Laser Heating and In Situ, Real-Time Diagnostics. Flammability and Sensitivity of Materials in Oxygen-Enriched Atmospheres. Vol. 14. ASTM International, 308–325. https://doi.org/10.1520/STP159620150065.

78. Krishnan S., Yugawa K., Nordine P. (1997). Optical Properties of Liquid Nickel and Iron. Physical Review B - Condensed Matter and Materials Physics, 55 (13), 8201–8206. https://doi.org/10.1103/physrevb.55.8201.

79. Sugie K., Kobatake H., Uchikoshi M., Isshiki M., Sugioka K.-I., Tsukada T., Fukuyama H. (2011) Noncontact Laser Modulation Calorimetry for High-Purity Liquid Iron. Japanese Journal of Applied Physics. 50, 11RD04. https://doi.org/10.1143/JJAP.50.11RD04.

80. Makovsky V. A., Lavrentik I. I. (1977) Heating Furnace Control Algorithms. Moscow, Metallurgiya Publ. 183 (in Russian).

81. Watanabe M., Adachi M., Uchikoshi M., Fukuyama H. (2019). Thermal Conductivities of Fe-Ni Melts Measured by Non-Contact Laser Modulation Calorimetry. Metallurgical and Materials Transactions A, 50, 3295–3300. https://doi.org/10.1007/s11661-019-05250-9.

82. Lee G. W., Jeon S., Kang D. H. (2013). Crystal–Liquid Interfacial Free Energy of Supercooled Liquid Fe Using a Containerless Technique. Crystal Growth & Design, 13 (4), 1786–1792. https://doi.org/10.1021/cg4001889.

83. Korell J. A., French M., Steinle-Neumann G., Redmer R. (2019). Paramagnetic-to-Diamagnetic Transition in Dense Liquid Iron and Its Influence on Electronic Transport Properties. Physical Review Letters, 122 (8), 086601. https://doi.org/10.1103/PhysRevLett.122.086601.