Thermodynamic model for deoxidation of liquid steel considering strong metal–oxygen interaction in the quasichemical model framework

Yong-Min Cho; Youn-Bae Kang

doi:10.1007/s12613-023-2766-7

Volume 31 Issue 5

May 2024

Turn off MathJax

Article Contents

Article Navigation > International Journal of Minerals, Metallurgy and Materials > 2024 > 31(5): 988-1002

Yong-Min Cho and Youn-Bae Kang, Thermodynamic model for deoxidation of liquid steel considering strong metal–oxygen interaction in the quasichemical model framework, Int. J. Miner. Metall. Mater., 31(2024), No. 5, pp. 988-1002. https://doi.org/10.1007/s12613-023-2766-7

Cite this article as:

Yong-Min Cho and Youn-Bae Kang, Thermodynamic model for deoxidation of liquid steel considering strong metal–oxygen interaction in the quasichemical model framework, Int. J. Miner. Metall. Mater., 31(2024), No. 5, pp. 988-1002. https://doi.org/10.1007/s12613-023-2766-7

Citation:

PDF( 2447 KB)

Research Article

Thermodynamic model for deoxidation of liquid steel considering strong metal–oxygen interaction in the quasichemical model framework

Yong-Min Cho^{1, 2} and
Youn-Bae Kang^{1, 3,}

+ Author Affiliations

Corresponding author:
Youn-Bae Kang E-mail: ybkang@postech.ac.kr
Received: 18 July 2023; Revised: 13 October 2023; Accepted: 20 October 2023; Available online: 25 October 2023

Abstract

Abstract

Herein, a thermodynamic model aimed at describing deoxidation equilibria in liquid steel was developed. The model provides explicit forms of the activity coefficient of solutes in liquid steel, eliminating the need for the minimization of internal Gibbs energy preliminarily when solving deoxidation equilibria. The elimination of internal Gibbs energy minimization is particularly advantageous during the coupling of deoxidation equilibrium calculations with computationally intensive approaches, such as computational fluid dynamics. The model enables efficient calculations through direct embedment of the explicit forms of activity coefficient in the computing code. The proposed thermodynamic model was developed using a quasichemical approach with two key approximations: random mixing of metallic elements (Fe and oxidizing metal) and strong nonrandom pairing of metal and oxygen as nearest neighbors. Through these approximations, the quasichemical approach yielded the activity coefficients of solutes as explicit functions of composition and temperature without requiring the minimization of internal Gibbs energy or the coupling of separate programs. The model was successfully applied in the calculation of deoxidation equilibria of various elements (Al, B, C, Ca, Ce, Cr, La, Mg, Mn, Nb, Si, Ti, V, and Zr). The limitations of the model arising from these assumptions were also discussed.
- deoxidation equilibria;
- thermodynamics;
- quasichemical approach;
- computational fluid dynamics

FullText(HTML)

Supplements(1)

Supplementary Information-s12613-023-2766-7.docx.docx

References(108)

References

[1]	L.F. Zhang and B.G. Thomas, State of the art in evaluation and control of steel cleanliness, ISIJ Int., 43(2003), No. 3, p. 271. doi: 10.2355/isijinternational.43.271
[2]	Y. Sahai and T. Emi, Tundish Technology for Clean Steel Production, World Scientific, Singapore, 2007.
[3]	K. Wasai and K. Mukai, Thermodynamic analysis of Fe−Al−O liquid alloy equilibrated with α-Al₂O₃(s) by an associated solution model, J. Jpn. Inst. Met. Mater., 52(1988), No. 11, p. 1088. doi: 10.2320/jinstmet1952.52.11_1088
[4]	H. Suito, H. Inoue, and R. Inoue, Aluminium−oxygen equilibrium between CaO−Al₂O₃ melts and liquid iron, ISIJ Int., 31(1991), No. 12, p. 1381. doi: 10.2355/isijinternational.31.1381
[5]	T. Kimura and H. Suito, Calcium deoxidation equilibrium in liquid iron, Metall. Mater. Trans. B, 25(1994), No. 1, p. 33. doi: 10.1007/BF02663176
[6]	H. Itoh, M. Hino, and S. Ban-Ya, Assessment of Al deoxidation equilibrium in liquid iron, Tetsu-to-Hagané, 83(1997), No. 12, p. 773.
[7]	I.H. Jung, S.A. Decterov, and A.D. Pelton, A thermodynamic model for deoxidation equilibria in steel, Metall. Mater. Trans. B, 35(2004), No. 3, p. 493. doi: 10.1007/s11663-004-0050-4
[8]	T. Miki and M. Hino, Numerical analysis on Si deoxidation of molten Fe−Ni and Ni−Co alloys by quadratic formalism, ISIJ Int., 44(2004), No. 11, p. 1800. doi: 10.2355/isijinternational.44.1800
[9]	W.Y. Cha, T. Nagasaka, T. Miki, Y. Sasaki, and M. Hino, Equilibrium between titanium and oxygen in liquid Fe−Ti alloy coexisted with titanium oxides at 1873 K, ISIJ Int., 46(2006), No. 7, p. 996. doi: 10.2355/isijinternational.46.996
[10]	A. Hayashi, T. Uenishi, H. Kandori, T. Miki, and M. Hino, Aluminum deoxidation equilibrium of molten Fe–Ni alloy coexisting with alumina or hercynite, ISIJ Int., 48(2008), No. 11, p. 1533. doi: 10.2355/isijinternational.48.1533
[11]	M.K. Paek, J.J. Pak, and Y.B. Kang, Aluminum deoxidation equilibria in liquid iron: Part II. thermodynamic modeling, Metall. Mater. Trans. B, 46(2015), No. 5, p. 2224. doi: 10.1007/s11663-015-0369-z
[12]	C. Wagner, Thermodynamics of Alloys, Addison-Wesley Pub. Co., Reading, MA, 1951, p. 51.
[13]	C.H.P. Lupis and J. F. Elliott, The relationship between the interaction coefficients epsilon and e, Trans. Metall. Soc. AIME, 233(1965), p. 257.
[14]	C.H.P. Lupis, Chemical Thermodynamics of Materials, Simon & Schuster (Asia) Pte Ltd., Singapore, 1993.
[15]	L.S. Darken, Thermodynamics of binary metallic solutions, Trans. Metall. Soc. AlME, 239(1967), p. 80.
[16]	R. Schuhmann, Solute interactions in multicomponent solutions, Metall. Trans. B, 16(1985), No. 4, p. 807. doi: 10.1007/BF02667517
[17]	A.D. Pelton, The polynomial representation of thermodynamic properties in dilute solutions, Metall. Mater. Trans. B, 28(1997), No. 5, p. 869. doi: 10.1007/s11663-997-0015-5
[18]	Y.B. Kang, Thermodynamic modeling of liquid steel, ISIJ Int., 60(2020), No. 12, p. 2717. doi: 10.2355/isijinternational.ISIJINT-2020-101
[19]	Y.B. Kang, The uniqueness of a correction to interaction parameter formalism in a thermodynamically consistent manner, Metall. Mater. Trans. B, 51(2020), No. 2, p. 795. doi: 10.1007/s11663-020-01792-1
[20]	C.W. Bale, E. Bélisle, P. Chartrand, et al., FactSage thermochemical software and databases—Recent developments, Calphad, 33(2009), No. 2, p. 295. doi: 10.1016/j.calphad.2008.09.009
[21]	C.W. Bale, E. Bélisle, P. Chartrand, et al., FactSage thermochemical software and databases, 2010–2016, Calphad, 54(2016), p. 35. doi: 10.1016/j.calphad.2016.05.002
[22]	J.O. Andersson, T. Helander, L. Höglund, P.F. Shi, and B. Sundman, Thermo-Calc & DICTRA, computational tools for materials science, Calphad, 26(2002), No. 2, p. 273. doi: 10.1016/S0364-5916(02)00037-8
[23]	S. Petersen and K. Hack, The thermochemistry library ChemApp and its applications, Int. J. Mater. Res., 98(2007), No. 10, p. 935. doi: 10.3139/146.101551
[24]	Y. Cho, H. Cho, S. Han, et al., A chemical reaction-fluid dynamics coupled model for Al reoxidation in tundish by open eye formation, [in] 8th International Congress on the Science and Technology of Steelmaking, Warredale, PA, 2022, p. 167.
[25]	M.K. Paek, K.H. Do, Y.B. Kang, I.H. Jung, and J.J. Pak, Aluminum deoxidation equilibria in liquid iron: Part III—Experiments and thermodynamic modeling of the Fe–Mn–Al–O system, Metall. Mater. Trans. B, 47(2016), No. 5, p. 2837. doi: 10.1007/s11663-016-0728-4
[26]	G.K. Sigworth and J.F. Elliott, The thermodynamics of liquid dilute iron alloys, Met. Sci., 8(1974), No. 1, p. 298. doi: 10.1179/msc.1974.8.1.298
[27]	L. S. Darken, Thermodynamics of ternary metallic solutions, Trans. Metall. Soc. AlME, 239(1967), p. 90.
[28]	C.W. Bale and A.D. Pelton, The unified interaction parameter formalism: Thermodynamic consistency and applications, Metall. Trans. A, 21(1990), No. 7, p. 1997. doi: 10.1007/BF02647247
[29]	D. Bouchard and C.W. Bale, Thermochemical properties of iron-rich liquid solutions containing oxygen and aluminum, J. Phase Equilib., 16(1995), No. 1, p. 16. doi: 10.1007/BF02646244
[30]	A.D. Pelton, S.A. Degterov, G. Eriksson, C. Robelin, and Y. Dessureault, The modified quasichemical model I—Binary solutions, Metall. Mater. Trans. B, 31(2000), No. 4, p. 651. doi: 10.1007/s11663-000-0103-2
[31]	A.D. Pelton, P. Chartrand, and G. Eriksson, The modified quasi-chemical model: Part IV. Two-sublattice quadruplet approximation, Metall. Mater. Trans. A, 32(2001), No. 6, p. 1409. doi: 10.1007/s11661-001-0230-7
[32]	J. Lehmann and L. Zhang, The generalized central atom for metallurgical slags and high alloyed steel grades, Steel Res. Int., 81(2010), No. 10, p. 875. doi: 10.1002/srin.201000137
[33]	E.A. Guggenheim, Statistical thermodynamics of mixtures with non-zero energies of mixing, Proc. R. Soc. Lond. A, 183(1944), No. 993, p. 213. doi: 10.1098/rspa.1944.0033
[34]	Y.B. Kang, Pelton A.D., P. Chartrand, and C.D Fuerst, Critical evaluation and thermodynamic optimization of the Al–Ce, Al–Y, Al–Sc and Mg–Sc binary systems, Calphad, 32(2008), No. 2, p. 413. doi: 10.1016/j.calphad.2008.03.002
[35]	Y.B. Kang and Pelton A.D, Modeling short-range ordering in liquids: The Mg–Al–Sn system, Calphad, 34(2010), No. 2, p. 180. doi: 10.1016/j.calphad.2010.02.003
[36]	Y.B. Kang and A.D. Pelton, The shape of liquid miscibility gaps and short-range-order, J. Chem. Thermodyn., 60(2013), p. 19. doi: 10.1016/j.jct.2013.01.003
[37]	Y.B. Kang, I.H. Jung, S.A. Decterov, A.D. Pelton, and H.G. Lee, Critical thermodynamic evaluation and optimization of the CaO−MnO−SiO₂ and CaO−MnO−Al₂O₃ systems, ISIJ Int., 44(2004), No. 6, p. 965. doi: 10.2355/isijinternational.44.965
[38]	Y.B. Kang, I.H. Jung, and H.G. Lee, Critical thermodynamic evaluation and optimization of the MnO–“TiO₂” –“Ti₂O₃” system, Calphad, 30(2006), No. 3, p. 235. doi: 10.1016/j.calphad.2006.05.001
[39]	Y.B. Kang, I.H. Jung, and H.G. Lee, Critical thermodynamic evaluation and optimization of the MnO–SiO₂–“TiO₂” –“Ti₂O₃” system, Calphad, 30(2006), No. 3, p. 226. doi: 10.1016/j.calphad.2006.05.002
[40]	Y.B. Kang and J.H. Lee, Reassessment of oxide stability diagram in the Fe–Al–Ti–O system, ISIJ Int., 57(2017), No. 9, p. 1665. doi: 10.2355/isijinternational.ISIJINT-2017-182
[41]	Y.B. Kang and A.D. Pelton, Thermodynamic model and database for sulfides dissolved in molten oxide slags, Metall. Mater. Trans. B, 40(2009), No. 6, p. 979. doi: 10.1007/s11663-009-9283-6
[42]	R. Piao, D.H. Woo, H.G. Lee, and Y.B. Kang, A thermodynamic model and database for oxysulfide inclusions containing Ca−Mn−Si−Al−O−S and its application to prediction of inclusions evolution in steels, AIST Trans., 11(2014), No. 5, p. 218.
[43]	D.G. Kim, M.A. Van Ende, C. van Hoek, C. Liebske, S. van der Laan, and I.H. Jung, A critical evaluation and thermodynamic optimization of the CaO−CaF₂ system, Metall. Mater. Trans. B, 43(2012), No. 6, p. 1315. doi: 10.1007/s11663-012-9733-4
[44]	C.B. Alcock and F.D. Richardson, Dilute solutions in alloys, Acta Metall., 8(1960), No. 12, p. 882. doi: 10.1016/0001-6160(60)90157-7
[45]	I. Barin, O. Knacke, and O. Kubaschewski, Thermochemical Properties of Inorganic Substances, Springer Berlin Heidelberg, Berlin, Heidelberg, 1977.
[46]	A.T. Dinsdale, SGTE data for pure elements, Calphad, 15(1991), No. 4, p. 317. doi: 10.1016/0364-5916(91)90030-N
[47]	R.J. Fruehan, Activities in liquid Fe–Al–O and Fe–Ti–O alloys, Metall. Trans., 1(1970), No. 12, p. 3403. doi: 10.1007/BF03037871
[48]	S. Dimitrov, A. Weyl, and D. Janke, Control of the aluminium-oxygen reaction in pure iron melts, Steel Res., 66(1995), No. 1, p. 3. doi: 10.1002/srin.199501762
[49]	D. Janke and W.A. Fischer, Desoxidationsgleichgewichte von titan, aluminium und zirconium in eisenschmelzen Bei 1600°C, Archiv für das Eisenhüttenwesen, 47(1976), No. 4, p. 195.
[50]	L.E. Rohde, A. Choudhury, and M. Wahlster, Neuere untersuchungen über das aluminium-sauerstoff-gleichgewicht in eisenschmelzen, Archiv für das Eisenhüttenwesen, 42(1971), No. 3, p. 165.
[51]	V. Shevtsov, Thermodynamics of oxygen solutions in the Fe–Al system, Russ. Metall., (1981), No. 1, p. 52.
[52]	J.D. Seo, S.H. Kim, and K.R. Lee, Thermodynamic assessment of the Al deoxidation reaction in liquid iron, Steel Res., 69(1998), No. 2, p. 49. doi: 10.1002/srin.199801342
[53]	J. Swisher, Note on the aluminum-oxygen interaction in liquid iron, AIME Met. Soc. Trans., 239(1967), No. 1, p. 123.
[54]	Y. Kang, M. Thunman, S.C. Du, T. Morohoshi, K. Mizukami, and K. Morita, Aluminum deoxidation equilibrium of molten iron–aluminum alloy with wide aluminum composition range at 1 873 K, ISIJ Int., 49(2009), No. 10, p. 1483. doi: 10.2355/isijinternational.49.1483
[55]	Japan Society for the Promotion of Science, Steelmaking Data Sourcebook, Gordon & Breach Science, New York, 1988.
[56]	R. Inoue and H. Suito, Determination of oxygen in iron-aluminum alloy by inert gas fusion-infrared absorptiometry, Mater. Trans. JIM, 32(1991), No. 12, p. 1164. doi: 10.2320/matertrans1989.32.1164
[57]	LECO Corporation, ON836 Oxygen /Nitrogen Analyzer Instruction Manual, St. Joseph, MI, 2013.
[58]	R. Fruehan, L. Martonik, and E. Turkdogan, Development of a galvanic cell for the determination of oxygen in liquid steel, Trans. Met. Soc. AIME, 245(1969), No. 7, p. 1501.
[59]	A. McLean and H. Bell, Experimental study of the reaction Al₂O₃ + 3H₂ = 3H₂O + 2Al, J. Iron Steel Inst., 203(1965), p. 123.
[60]	N.A. Gokcen and J. Chipman, Aluminum-oxygen equilibrium in liquid iron, JOM, 5(1953), No. 2, p. 173. doi: 10.1007/BF03397469
[61]	R.J. Fruehan, The thermodynamic properties of liquid Fe–Si alloys, Metall. Trans., 1(1970), No. 4, p. 865. doi: 10.1007/BF02811766
[62]	N.A. Gokcen and J. Chipman, Silicon-oxygen equilibrium in liquid iron, JOM, 4(1952), No. 2, p. 171. doi: 10.1007/BF03397667
[63]	D.C. Hilty and W. Crafts, Solubility of oxygen in liquid iron containing silicon and manganese, JOM, 2(1950), No. 2, p. 425. doi: 10.1007/BF03399020
[64]	S.S. Shibaev, P.V. Krasovskii, and K.V. Grigorovitch, Solubility of oxygen in iron–silicon melts in equilibrium with silica at 1873 K, ISIJ Int., 45(2005), No. 9, p. 1243. doi: 10.2355/isijinternational.45.1243
[65]	S. Pindar and M.M. Pande, Assessment of Si–O equilibria and nonmetallic inclusion characteristics in high silicon steels, Steel Res. Int., 94(2023), art. No.2300115. doi: 10.1002/srin.202300115
[66]	Y. Kojima, M. Inouye, and J.I. Ohi, Titanoxyd im gleichgewicht mit eisen-titan-legierungen Bei 1600°C, Archiv für das Eisenhüttenwesen, 40(1969), No. 9, p. 667.
[67]	H. Chino, Y. Nakamura, E. Tsunetomi, and K. Segawa, The deoxidation with titanium in liquid iron, Tetsu-to-Hagané, 52(1966), No. 6, p. 959. doi: 10.2355/tetsutohagane1955.52.6_959
[68]	A.M. Smellie and H.B. Bell, Titanium deoxidation reactions in liquid iron, Can. Metall. Q., 11(1972), No. 2, p. 351. doi: 10.1179/cmq.1972.11.2.351
[69]	W.A. Fischer and D. Janke, Die aktivität des sauerstoffs in reinen und mangan-, titan-oder borhaltigen eisenschmelzen, Archiv für das Eisenhüttenwesen, 42(1971), No. 10, p. 691.
[70]	S. Dimitrov, A. Weyl, and D. Janke, Control of the manganese–oxygen reaction in pure iron melts, Steel Res., 66(1995), No. 3, p. 87. doi: 10.1002/srin.199501092
[71]	K. Takahashi and M. Hino, Equilibrium between dissolved Mn and Ο in molten high-manganese steel, High Temp. Mater. Process., 19(2000), No. 1, p. 1. doi: 10.1515/HTMP.2000.19.1.1
[72]	D. Janke and W. Fischer, Equilibria of chromium and manganese with oxygen in iron melts at 1600°C, Archiv für das Eisenhüttenwesen, 47(1976), No. 3, p. 147.
[73]	J. Chipman, J.B. Gero, and T.B. Winkler, The manganese equilibrium under simple oxide slags, JOM, 2(1950), No. 2, p. 341. doi: 10.1007/BF03399009
[74]	M. Heinz, K. Koch, and D. Janke, Oxygen activities in Cr-containing Fe and Ni-based melts, Steel Res., 60(1989), No. 6, p. 246. doi: 10.1002/srin.198901646
[75]	R. Fruehan, Activities in liquid Fe–Cr–O system, Met. Soc. AIME-Trans, 245(1969), No. 6, p. 1215.
[76]	J.K. Pargeter, The effect of additions of manganese, vanadium and chromium on the activity of oxygen in molten iron, Can. Metall. Q., 6(1967), No. 1, p. 21. doi: 10.1179/cmq.1967.6.1.21
[77]	H. Chen and J. Chipman, The chromium–oxygen equilibirum in liquid iron, Metall. Trans. ASM, 38(1947), p. 70.
[78]	E. Turkdogan, Chromium-oxygen equilibrium in liquid iron, J. Iron Steel Inst., 178(1954), No. 3, p. 278.
[79]	D.C. Hilty, W.D. Forgeng, and R.L. Folkman, Oxygen solubility and oxide phases in the Fe–Cr–O system, JOM, 7(1955), No. 2, p. 253. doi: 10.1007/BF03377489
[80]	S. Dimitrov, H. Wenz, K. Koch, and D. Janke, Control of the chromium–oxygen reaction in pure iron melts, Steel Res., 66(1995), No. 2, p. 39. doi: 10.1002/srin.199501085
[81]	S. Matoba, Equilibrium of carbon and oxygen in molten iron, Tetsu-to-Hagané, 20(1934), No. 12, p. 837.
[82]	S. Banya and S. Matoba, Activity of carbon and oxygen in liquid iron, Tetsu-to-Hagané Overseas, 3(1963), No. 1, p. 21.
[83]	H. Schenck, E. Steinmetz, and M. Gloz, Der sauerstoffgehalt in kohlenstoffreichem und kohlenstoffgesättigtem flüssigem eisen Bei 1600°C, Archiv für das Eisenhüttenwesen, 39(1968), No. 1, p. 69.
[84]	W.A. Fischer and D. Janke, Elektrochemische aufzeichnung des entkohlungsablaufs von eisenschmelzen, Archiv für das Eisenhüttenwesen, 42(1971), No. 4, p. 249.
[85]	H. Schenck and H. Hinze, Equilibriums of the iron-carbon-oxygen system in the temperature and concentration range of molten steel and the effect of phosphorus, manganese, and sulfur, Archiv für das Eisenhüttenwesen, 37(1966), No. 1, p. 545.
[86]	T. Fuwa and J. Chipman, Activity of carbon in liquid-iron alloys, Trans. Metall. Soc. AIME, 215(1959), p. 708.
[87]	T. Fuwa and J. Chipman, The carbon–oxygen equilibria in liquid iron, Trans. AIME, 218(1960), p. 887.
[88]	S. Gustafsson and P.O. Mellberg, On the free energy interaction between some strong deoxidizers, especially calcium and oxygen in liquid iron, Scand. J. Metall., 9(1980), p. 111.
[89]	M. Hillert and M. Selleby, Solubility of CaO and Al₂O₃ in liquid Fe, Scand. J. Metall., 19(1990), p. 23.
[90]	W.M. Huang, Oxygen solubility in Fe–Zr–O liquid, Calphad, 28(2004), No. 2, p. 153. doi: 10.1016/j.calphad.2004.07.007
[91]	H.M. Hong and Y.B. Kang, Simultaneous analysis of soluble and insoluble oxygen contents in steel specimens using inert gas fusion infrared absorptiometry, ISIJ Int., 61(2021), No. 9, p. 2464. doi: 10.2355/isijinternational.ISIJINT-2020-596
[92]	Y.B. Kang, Y.M. Cho, and H.M. Hong, Thermodynamic basis of isothermal carbothermic reduction of oxide in liquid steel for simultaneous analysis of soluble/insoluble oxygen contents in the steel specimens, Metall. Mater. Trans. B, 53(2022), No. 4, p. 1980. doi: 10.1007/s11663-022-02520-7
[93]	Y.M. Cho, D.J. Lee, H.J. Cho, W.Y. Kim, S.W. Han, and Y.B. Kang, Simultaneous analysis of soluble and insoluble oxygen contents in Al-killed steels of various C contents and supersaturation phenomena in the steel, ISIJ Int., 62(2022), No. 8, p. 1705. doi: 10.2355/isijinternational.ISIJINT-2022-059
[94]	J. Seo and S. Kim, Thermodynamic assessment of Al, Mg, and Ca deoxidation reaction for the control of alumina inclusion in liquid steel, Bull. Korean Inst. Metall. Mater. (Korea), 12(1999), No. 3, p. 402.
[95]	T. Ototani, Y. Kataura, and T. Degawa, Deoxidation of liquid iron and its alloys by calcium contained in lime crucible, Trans. Iron Steel Inst. Jpn., 16(1976), No. 5, p. 275. doi: 10.2355/isijinternational1966.16.275
[96]	Y. Miyashita and K. Nishikawa, The deoxidation of liquid iron with calcium, Tetsu-to-Hagané, 57(1971), No. 13, p. 1969.
[97]	Q.Y. Han, X.D. Zhang, D. Chen, and P.F. Wang, The calcium-phosphorus and the simultaneous calcium–oxygen and calcium–sulfur equilibria in liquid iron, Metall. Trans. B, 19(1988), No. 4, p. 617. doi: 10.1007/BF02659153
[98]	M. Ozawa, The Japan Society for the Promotion of Science , 19th Committee Paper No. 9837, Iron Steel Institute of Japan, Toyko, 1975, p. 6.
[99]	Y.B. Kang, Oxide solubility minimum in liquid Fe–M–O alloy, Metall. Mater. Trans. B, 50(2019), No. 6, p. 2942. doi: 10.1007/s11663-019-01663-4
[100]	R.J. Fruehan, The effect of zirconium, cerium, and lanthanum on the solubility of oxygen in liquid iron, Metall. Trans., 5(1974), No. 2, p. 345. doi: 10.1007/BF02644100
[101]	W.A. Fischer and H. Bertram, Die desoxydation, entschwefelung und entstickung sauerstoff-, schwefel- oder stickstoffhaltiger eisenschmelzen durch die seltenen erdmetalle cer und lanthan, Archiv für das Eisenhüttenwesen, 44(1973), No. 2, p. 87.
[102]	D. Janke and W.A. Fischer, Deoxidation equilibria of cerium, lanthanum, and hafnium in liquid iron, Archiv für das Eisenhüttenwesen, 49(1978), No. 9, p. 425.
[103]	J.H. Park, D.J. Kim, and D.J. Min, Characterization of nonmetallic inclusions in high-manganese and aluminum-alloyed austenitic steels, Metall. Mater. Trans. A, 43(2012), No. 7, p. 2316. doi: 10.1007/s11661-012-1088-6
[104]	Y. Ogasawara, T. Miki, and T. Nagasaka, Equilibrium of Al deoxidation in liquid Fe–Mn alloy, CAMP-ISIJ, 25(2012), p. 240.
[105]	R. Nishigaki and H. Matsuura, Al deoxidation equilibrium of Fe–10–30 mass%Mn melt at 1873 K, Tetsu-to-Hagané, 105(2019), No. 3, p. 369.
[106]	R. Nishigaki and H. Matsuura, Deoxidation equilibria of Fe–Mn–Al melt with Al₂O₃ or MnAl₂O₄ at 1873 and 1773 K, ISIJ Int., 60(2020), No. 12, p. 2787. doi: 10.2355/isijinternational.ISIJINT-2020-177
[107]	Y.B. Kang and S.H. Jung, Oxide stability diagram of liquid steels – Construction and utilization, ISIJ Int., 58(2018), No. 8, p. 1371. doi: 10.2355/isijinternational.ISIJINT-2018-198
[108]	ANSYS, Inc., Ansys Fluent 12.0 , Theory Guide, 2009, p. 67.