Abstract
Thermodynamic modeling of Fe-Mn-C and Fe-Mn-Al ternary systems was performed in order to develop a thermodynamically consistent database of a Fe-Mn-Al-C quaternary system. The system is a core system of high Mn-high Al steels for various applications including automotive, cryogenic, electrical steels, etc., and ferromanganese alloy production. Most previous thermodynamic modeling results were reviewed. In order to treat strong chemical interaction between metals (Fe and Mn) and non-metal (C), the modified quasichemical model in the pair approximation was employed for the liquid phase. A number of solid solutions were modeled using the compound energy formalism. Gibbs energy descriptions in sub-binary systems were taken from previous literatures, except for the Mn-Al binary system. Liquid phase in the Mn-Al system was re-optimized in the present study, while the model parameters for other solid phases were adopted from a literature. By merging the Gibbs energies for relevant phases in sub-binary systems, thermodynamic calculations were carried out for each ternary system. Optimization results of the Fe-Mn-C system in the present study showed improved descriptions for both liquid and solid phases. Solubilities of C in the liquid and the fcc phases were reproduced well, and phase diagram information (liquidus, invariant reactions) was also in good agreement with the experimental data. Thermodynamic assessment of the Fe-Mn-Al system with consideration of A2/B2 order-disorder transition for the bcc phase also showed satisfactory representations for the experimental data. The model parameters derived in the present study can be utilized for further thermodynamic modeling of the Fe-Mn-Al-C quaternary system.
Similar content being viewed by others
References
S.-H. Kim, H.-S. Kim, N.-J. Kim, Brittle intermetallic compound makes ultrastrong low-density steel with large ductility. Nature 518, 77-79 (2015)
D.-W. Suh, S.-J. Park, T.-H. Lee, C.-S. Oh, S.-J. Kim, Influence of Al on the microstructural evolution and mechanical behavior of low-carbon, manganese transformation-induced-plasticity steel. Metall. Mater. Trans. A 41, 397-408 (2010)
K.-G. Chin, H.-J. Lee, J.-H. Kwak, J.-Y. Kang, B.-J. Lee, Thermodynamic calculation on the stability of (Fe, Mn)\(_3\)AlC carbide in high aluminum steels. J. Alloys Compd. 505, 217-223 (2010)
K. Shubhank, Y.-B. Kang, Critical evaluation and thermodynamic optimization of Fe-Cu, Cu-C, Fe-C binary systems and Fe-Cu-C ternary system. CALPHAD 45, 127-137 (2014)
M.-K. Paek, J.-J. Pak, Y.-B. Kang, Phase equilibria and thermodynamics of Mn-C, Mn-Si, Si-C binary systems and Mn-Si-C ternary system by critical evaluation, combined with experiment and thermodynamic modeling. CALPHAD 46, 92-102 (2014)
A.D. Pelton, Y.-B. Kang, Modeling short-range ordering in solutions. Int. J. Mater. Res. 98, 907-917 (2007)
Y.-B. Kang, A.D. Pelton, Modeling short-range ordering in liquids: the Mg-Al-Sn system. CALPHAD 34, 180-188 (2010)
A.D. Pelton, S. Decterov, G. Eriksson, C. Robelin, Y. Dessureault, The modified quasichemical model I—binary solutions. Metall. Mater. Trans. B 31, 651-659 (2000)
M.-K. Paek, Ph.D. Thesis, Hanyang University, Ansan, Republic of Korea (2014)
A.T. Phan, M.-K. Paek, Y.-B. Kang, Phase equilibria and thermodynamics of the Fe-Al-C system: critical evaluation. Experiment and thermodynamic optimization. Acta Mater. 79, 1-15 (2014)
A. Shukla, A.D. Pelton, Thermodynamic assessment of the Al-Mn and Mg-Al-Mn systems. J. Phase Equilib. Diff. 30, 28-39 (2008)
P. Chartrand, Private communication (École Polytechnique, Montreal, 2004)
M.-S. Kim, Y.-B. Kang, Development of thermodynamic database for High Mn—high Al steels: phase equilibria in the Fe-Mn-Al-C system: experiment and thermodynamic modeling. CALPHAD (2015). doi:10.1016/j.calphad.2015.08.004
V.G. Rivlin, 14: critical review of constitution of carbon-chromium-iron and carbon-iron-manganese systems. Int. Met. Rev. 29, 299-328 (1984)
G. Raynor, V. Rivlin, “Al-Fe-Mn” in phase equilibria in iron ternary alloys (Institute of Metals, London, 1988), pp. 98-106
V. Raghavan, Al-Fe-Mn (aluminum-iron-manganese). J. Phase Equilib. 15, 410-411 (1994)
V. Raghavan, Al-Fe-Mn (aluminum-iron-manganese). J. Phase Equilib. Diff. 26, 65-67 (2005)
W. Huang, A thermodynamic assessment of the Fe-Mn-C system. Metall. Mater. Trans. A 21, 2115-2123 (1990)
B.-J. Lee, D.-N. Lee, A thermodynamic study on the Fe-Mn-C system. CALPHAD 13, 355-365 (1989)
D. Djurovic, B. Hallstedt, J. Appen, R. Dronskowski, Thermodynamic assessment of the Fe-Mn-C system. CALPHAD 35, 479-491 (2011)
R. Umino, X.J. Liu, Y. Sutou, C.P. Wang, I. Ohnuma, R. Kainuma, K. Ishida, Experimental determination and thermodynamic calculation of phase equilibria in the Fe-Mn-Al system. J. Phase Equilib. Diff. 27, 54-62 (2006)
B.B. Lindahl, M. Selleby, The Al-Fe-Mn system revisited—an updated thermodynamic description using the most recent binaries. CALPHAD 43, 86-93 (2013)
P. Gustafson, A thermodynamic evaluation of the Fe-C system. Scand. J. Metall. 14, 259-267 (1985)
B. Hallstedt, D. Djurovic, Modelling of interstitials in the bcc phase. CALPHAD 33, 233-236 (2009)
B. Hallstedt, D. Djurovic, J. Appen, R. Dronskowski, A. Dick, F. Körmann, T. Hickel, J. Neugebauer, Thermodynamic properties of cementite (Fe\(_3\)C). CALPHAD 34, 129-133 (2010)
R. Naraghi, M. Selleby, J. Ågren, Thermodynamics of stable and metastable structures in Fe-C system. CALPHAD 46, 148-158 (2014)
W. Huang, An assessment of the Fe-Mn system. CALPHAD 11, 183-186 (1989)
V. Witusiewicz, F. Sommer, E. Mittemeijer, Enthalpy of formation and heat capacity of Fe-Mn alloys. Metall. Mater. Trans. B 34, 209-223 (2003)
W. Huang, Thermodynamic assessment of the Mn-C system. Scand. J. Metall. 19, 26-32 (1990)
D. Djurovic, B. Hallstedt, J. Appen, R. Dronskowski, Thermodynamic assessment of the Mn-C system. CALPHAD 34, 279-285 (2010)
U. Kattner, B. Burton, Phase Diagrams of Binary Iron Alloys (ASM International, Materials Park, 1993)
B. Sundman, I. Ohnuma, N. Dupin, U. Kattner, S. Fries, An assessment of the entire Al-Fe system including D0\(_3\) ordering. Acta Mater. 57, 2896-2908 (2009)
M. Jacobs, R. Schmid-Fetzer, Phase behavior and thermodynamic properties in the system Fe-Al. CALPHAD 33, 170-178 (2009)
M. Seiersten, SINTEF report STF-28F93051, Oslo, Norway, 1993
F. Woolley, J.F. Elliott, Heats of solution of aluminum, copper, and silicon in liquid iron. Trans. AIME 239, 1872-1883 (1967)
M.S. Petrushevskiy, Y.O. Esin, P.V. Gel’d, V.M. Sandakov, Concentration dependence of the enthalpy of formation of iron-aluminum molten alloys. Izv. Akad. Nauk SSSR Metall. 6, 193-197 (1972)
A. McAlister, J. Murray, The (Al-Mn) aluminum-manganese system. Bull. Alloy Phase Diagrams 8, 438-447 (1987)
Y. Du, J. Wang, J. Zhaoa, J. Schuster, F. Weitzer, R. Schmid-Fetzer, M. Ohno, H. Xu, Z.-K. Liu, S. Shang, W. Zhang, Reassessment of the Al-Mn system and a thermodynamic description of the Al-Mg-Mn system. Int. J. Mat. Res. 98, 855-871 (2007)
A. Jansson, A thermodynamic evaluation of the Al-Mn system. Metall. Mater. Trans. A 23, 2953-2962 (1992)
X. Liu, I. Ohnuma, R. Kainuma, K. Ishida, Thermodynamic assessment of the aluminum-manganese (Al-Mn) binary phase diagram. J. Phase Equilib. 20, 45-56 (1999)
V. Rivlin, 12: critical review of constitution of aluminum-iron-manganese and iron-manganese-silicon systems. Int. Met. Rev. 28, 309-337 (1983)
X. Liu, S. Hao, A thermodynamic calculation of the Fe-Mn-Al ternary system. CALPHAD 17, 79-91 (1993)
D. Chakrabarti, Phase stability in ternary systems of transition elements with aluminum. Metall. Trans. B 8, 121-123 (1977)
C. Müller, H. Stadelmaier, B. Reinsch, G. Petzow, Constitution of Mn-Al-(Cu, Fe, Ni or C) alloys near the magnetic \(\tau\) phase. Z. Metallkd. 88, 620-624 (1997)
X. Liu, S. Hao, Phase equilibria and \(\alpha\) (BCC) phase region continuity at 1000 \(^\circ\)C in the Fe-Mn-Al system. Scr. Metall. Mater. 28, 611-616 (1993)
W. Pearson, Handbook of Lattice Spacings and Stuctures of Metals and Alloys (Pergamon, New York, 1967)
E.-J. Kim, B.-D. You, J.-J. Pak, Thermodynamics of carbon in liquid manganese and ferromanganese alloys. Metall. Mater. Trans. B 34, 51-59 (2003)
H. Enokido, A. Moro-Oka, E. Ichise, Thermochemical activities of liquid Fe-Mn-C alloy. Tetsu-to-Hagane 81, 619-624 (1995)
C.W. Bale, P. Chartrand, S. Degterov, G. Eriksson, K. Hack, R.B. Mahfoud, J. Melancon, A.D. Pelton, S. Petersen, FactSage thermochemical software and databases. CALPHAD 26, 189-228 (2006)
C.W. Bale, E. Bélisle, P. Chartrand, S. Decterov, G. Eriksson, K. Hack, I.-H. Jung, Y.-B. Kang, J. Melançon, A.D. Pelton, C. Robelin, S. Petersen, FactSage thermochemical software and databases—recent developments. CALPHAD 33, 295-311 (2009)
A. Dinsdale, SGTE data for pure elements. CALPHAD 15, 317-425 (1991)
A.D. Pelton, P. Chartrand, The modified quasichemical model: part II. multicomponent solutions. Metall. Mater. Trans. A 32, 1409-1416 (2001)
M.K. Paek, J.J. Pak, Y.-B. Kang, Aluminum deoxidation equilibria in liquid iron: part II. thermodynamic modeling, Metall. Mater. Trans. B (2015). doi:10.1007/s11663-015-0369-z
M. Hillert, The compound energy formalism. J. Alloys Compd. 320, 161-176 (2001)
M. Hillert, M. Jarl, A model for alloying effects in ferromagnetic metals. CALPHAD 2, 227-238 (1978)
G. Inden, The role of magnetism in the calculation of phase diagrams. Physica B+C 103, 82-100 (1981)
J. Chipman, R. Alfred, L. Gott, R. Small, D. Wilson, C. Thomson, D. Gue, The solubility of carbon in molten iron and iron-silicon and iron-manganese alloys. Trans. ASM 44, 1215-1232 (1952)
E. Turkdogan, R. Hancock, S. Herlitz, J. Dentan, Thermodynamics of carbon dissolved in iron alloys, part V: solubility of graphite in iron-manganese, iron-cobalt, and iron-nickel melts. J. Iron Steel Inst. 183, 69-72 (1956)
R. Ni, Z. Ma, S. Wei, Thermodynamics of Mn-Fe-C and Mn-Si-C system. Steel Res. 61, 113-116 (1990)
J. Fenstad, Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 2000
M.-K. Paek, W.-K. Lee, J. Jin, J.-M. Jang, J.-J. Pak, Thermodynamic interactions among carbon, silicon and iron in carbon saturated manganese melts. Korea J. Met. Mater. 50, 45-51 (2012)
S. Saxena, H. Midtagaard, SINTEF Report No. STF-34F79017, Trondheim, Norway, 1979
F. Schürmann, I. Geissler, Melting equilibria of the ternary system iron-manganese-carbon. Giessereiforschung 29, 153-159 (1977)
K. Kuo, L. Persson, A contribution to the constitution of the ternary system Fe-Mn-C isothermal sections at 1050 \(^\circ\)C, 910 \(^\circ\)C, and 690 \(^\circ\)C. J. Iron Steel Inst. 178, 39-44 (1954)
W. Koch, H. Keller, Equilibrium investigations in the system iron-manganese-carbon as an example for the use of separating methods for establishing and checking constitutional diagrams (in German). Arch. Eisenhüttenwes 35, 1173-1180 (1964)
T. Nishizawa, An experimental study of the Fe-Mn-C and Fe-Cr-C systems at 1000 \(^\circ\)C. Scand. J. Metall. 6, 74-78 (1977)
R. Benz, J. Elliott, J. Chipman, Thermodynamics of the solid phases in the system Fe-Mn-C. Metall. Mater. Trans. B 4, 1975-1986 (1973)
R. Gurry, J. Christakos, L. Darken, Size, manganese content, and curie point of carbides extracted from manganese steel. Trans. ASM 53, 187-198 (1961)
C.K. Ande, M.H.F. Sluiter, First-principles calculations on stabilization of iron carbides (Fe\(_3\)C, Fe\(_5\)C\(_2\), and \(\eta\)-Fe\(_2\)C) in steels by common alloying elements. Metall. Mater. Trans. A 43, 4436-4444 (2012)
C.M. Fang, M.H.F. Sluiter, M.A. van Huis, C.K. Ande, H.W. Zandbergen, Origin of predominance of cementite among iron carbides in steel at elevated temperature. Phys. Rev. Lett. 105, 055503 (2010)
K.O.E. Henriksson, N. Sandberg, J. Wallenius, Carbides in stainless steels: results from ab initio investigations. Appl. Phys. Lett. 93, 191912 (2008)
K.O.E. Henriksson, K. Nordlund, Simulations of cementite: an analytical potential for the Fe-C system. Phys. Rev. B 79, 144107 (2009)
M. Widom, M. Mihalkovic, Stability of Fe-based alloys with structure type C\(_6\)Cr\(_{23}\). J. Mater. Res. 20, 237-242 (2011)
I.R. Shein, N.I. Medvedeva, A.I. Ivanovskii, Electronic and structural properties of cementite-type M\(_3\)X (M=Fe Co, Ni; X=C or B) by first principles calculations. Physica B 371, 126-132 (2006)
X. Liu, R. Kainuma, H. Ohtani, K. Ishida, Phase equilibria in the Mn-rich portion of the binary system Mn-Al. J. Alloys Compd. 235, 256-261 (1996)
A. Koch, P. Hokkeling, M. Steeg, K. Devos, New material for permanent magnets on a base of Mn and Al. J. Appl. Phys. 31, 75S-77S (1960)
H. Phillips, The constitution of alloys of aluminium with manganese silicon and iron. J. Inst. Met. 69, 275-316 (1942)
E. Dix, W. Fink, L. Willey, Equilibrium relations in Al-Mn alloys of high purity II. Trans. AIME 104, 335-352 (1933)
C. Muller, H. Stadelmaier, B. Reinsch, G. Petzow, Metallurgy of the magnetic \(\tau\)-phase in Mn-Al and Mn-Al-C. Z. Metallkd. 87, 594-597 (1996)
J. Murray, A. McAlister, R. Schaefer, L. Bendersky, F. Biancaniella, D. Moffatt, Stable and metastable phase equilibria in the Al-Mn system. Metall. Trans. A 18, 385-392 (1987)
T. Godecke, W. Koster, A supplement to the constitution of the Al-Mn system. Z. Metallkd. 62, 727-732 (1971)
W. Koster, E. Watchtel, Magnetic investigation of Al-Mn alloys containing more than 25 at.%Mn. Z. Metallkd. 51, 271-280 (1960)
Y. Esin, N. Bobrov, M. Petrushevskii, P. Gel’d, Concentration variation of the enthalpies of formation of manganese-aluminium melts at 1626K. Russ. J. Phys. Chem. 47, 1103-1105 (1973)
R. Chastel, M. Saito, C. Bergman, Thermodynamic investigation on Al\(_{1-x}\)Mn\(_x\) melts by Knudsen cell mass spectrometry. J. Alloys Compd. 205, 39-43 (1994)
G. Batalin, E.A. Beloborodava, V. Stukalo, A. Chekhovskii, Thermodynamic properties of molten alloys of aluminum with manganese. Sov. Prog. Chem. 38, 83-84 (1972)
G. Batalin, T. Bondarenko, V. Sudavtsova, Enthalpies of mixing in the Fe-Mn-Al systems. Dopov. Nat. Akad. Nauk. Ukr. 4, 76-78 (1985)
X. Liu, S. Hao, L. Xu, Y. Guo, H. Chen, Experimental study of the phase equilibria in the Fe-Mn-Al system. Metall. Mater. Trans. A 27, 2429-2435 (1996)
D. Schmatz, Formation of beta manganese-type structure in iron-aluminum-manganese alloys. Trans. AIME 215, 112-114 (1959)
Acknowledgments
The present authors thank to Dr. Min-Kyu Paek, McGill University, Canada for valuable discussions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, MS., Kang, YB. Thermodynamic Modeling of the Fe-Mn-C and the Fe-Mn-Al Systems Using the Modified Quasichemical Model for Liquid Phase. J. Phase Equilib. Diffus. 36, 453–470 (2015). https://doi.org/10.1007/s11669-015-0401-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11669-015-0401-7