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5 - Fundamentals of Computational Thermodynamics and the CALPHAD Method

Published online by Cambridge University Press:  29 June 2023

Yong Du ,
Rainer Schmid-Fetzer ,
Jincheng Wang ,
Shuhong Liu ,
Jianchuan Wang  and
Zhanpeng Jin
Yong Du
Affiliation:
Central South University, China
Rainer Schmid-Fetzer
Affiliation:
Clausthal University of Technology, Germany
Jincheng Wang
Affiliation:
Northwestern Polytechnical University, China
Shuhong Liu
Affiliation:
Central South University, China
Jianchuan Wang
Affiliation:
Central South University, China
Zhanpeng Jin
Affiliation:
Central South University, China
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Summary

Chapter 5 focuses on the CALPHAD approach and its thermodynamic basis with the crucial concept of “phase." The origins, development, and principles of the CALPHAD method are briefly explained and current software is compiled (Thermo-Calc, Pandat, FactSage, and more). Thermodynamic modeling of Gibbs energy is introduced, from simple pure substances to complex solution phases. Examples of how to establish a thermodynamic database are given, and key issues on the consistency, coherency, quality assurance, and safety of the database are emphasized. The most important application examples in the computational design of alloys and their processing are separated in two levels. In the first level, solely thermodynamic CALPHAD databases are required. It is shown which type of calculations have proved most useful to guide design. In the second level, applications using extended CALPHAD-type databases with kinetic and thermophysical material parameters are outlined for casting, solidification, and heat treatment processes. The use of advanced CALPHAD-type software packages is demonstrated. Finally, a case study on design of Al alloys with improved hot cracking resistance is presented with these tools.

Keywords

CALPHAD methodmulticomponent multiphase materialsthermodynamic softwarethermodynamic databasecalculated phase diagramsScheil solidification simulationheat treatment designalloy design
Type
Chapter
Information
Computational Design of Engineering Materials
Fundamentals and Case Studies
 , pp. 113 - 197
Publisher: Cambridge University Press
Print publication year: 2023

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References

Agarwal, R., Fries, S. G., Lukas, H. L., et al. (1992) Assessment of the Mg–Zn system. Zeitschrift für Metallkunde, 83(4), 216–223.Google Scholar
Agarwal, R., Fries, S. G., Lukas, H. L., et al. (1998) System Mg–Zn, in Ansara, I., Dinsdale, A. T., and Rand, M. H. (eds), COST507 – Definition of Thermochemical and Thermophysical Properties to Provide a Database for the Development of New Light Alloys, volume 2: Thermochemical Database for Light Metal Alloys. Luxembourg: European Commission, DG XII, 227–233.Google Scholar
Ågren, J., Cheynet, B., Clavaguera-Mora, M. T., et al. (1995) Workshop on thermodynamic models and data for pure elements and other endmembers of solutions: Schloβ Ringberg 1995, Group 2. CALPHAD, 19(4), 449–480.Google Scholar
Ågren, J., and Hillert, M. (2019) Thermodynamic modelling of vacancies as a constituent. CALPHAD, 67, 101666.CrossRefGoogle Scholar
Ågren, J., and Schmid-Fetzer, R. (2014) True phase diagrams. Metallurgical and Materials Transactions A, 45(11), 4766–4769.CrossRefGoogle Scholar
Aldinger, F., Fernandez Guillermet, A., Iorich, V. S., et al. (1995) Workshop on thermodynamic models and data for pure elements and other endmembers of solutions: Schloβ Ringberg 1995, Group 6. CALPHAD, 19(4), 555–571.Google Scholar
Andersson, J. O., Helander, T., Höglund, L., Shi, P., and Sundman, B. (2002) Thermo-Calc & DICTRA, computational tools for materials science. CALPHAD, 26(2), 273–312.CrossRefGoogle Scholar
Ansara, I., Burton, B., Chen, Q., et al. (2000) Models for composition dependence. CALPHAD, 24(1), 19–40.CrossRefGoogle Scholar
Ansara, I., Dinsdale, A., and Rand, M. (1998) COST 507 Definition of Thermochemical and Thermophysical Properties to Provide a Database for the Development of New Light Alloys, volume 2: Thermochemical Database for Light Metal Alloys. Luxembourg: European Commission. DG XII.Google Scholar
Ansara, I., Dupin, N., and Sundman, B. (1997) Reply to the paper: “When is a compound energy not a compound energy? A critique of the 2-sublattice order/disorder model”: Of Nigel Saunders, Calphad 20 (1996) 491–499. CALPHAD, 21(4), 535–542.CrossRefGoogle Scholar
Bale, C. W., Bélisle, E., Chartrand, P., et al. (2009) FactSage thermochemical software and databases – recent developments. CALPHAD, 33(2), 295–311.CrossRefGoogle Scholar
Cacciamani, G., Dinsdale, A., Palumbo, M., and Pasturel, A. (2010) The Fe–Ni system: thermodynamic modelling assisted by atomistic calculations. Intermetallics, 18(6), 1148–1162.CrossRefGoogle Scholar
Cai, Q., Mendis, C. L., Chang, I. T., and Fan, Z. (2020) Microstructure evolution and mechanical properties of new die-cast Al–Si–Mg–Mn alloys. Materials and Design, 187, 108394.CrossRefGoogle Scholar
Campbell, C. E., Kattner, U. R., and Liu, Z.-K. (2014) The development of phase-based property data using the CALPHAD method and infrastructure needs. Integrating Materials and Manufacturing Innovation, 3(1), 12.CrossRefGoogle Scholar
Cao, G., Zhang, C., Cao, H., Chang, Y. A., and Kou, S. (2010) Hot-tearing susceptibility of ternary Mg–Al–Sr alloy castings. Metallurgy and Materials Transactions A, 41(3), 706–716.CrossRefGoogle Scholar
Cao, W., Chen, S. L., Zhang, F., Wu, K., Yang, Y., Chang, Y. A., Schmid-Fetzer, R., and Oates, W. A. (2009) PANDAT software with PanEngine, PanOptimizer and PanPrecipitation for multi-component phase diagram calculation and materials property simulation. CALPHAD, 33(2), 328–342.CrossRefGoogle Scholar
Cao, W., Zhang, F., Chen, S.-L., et al. (2016) Precipitation modeling of multi-component nickel-based alloys. Journal of Phase Equilibria and Diffusion, 37(4), 491–502.CrossRefGoogle Scholar
Cao, W., Zhang, F., Chen, S. L., Zhang, C., and Chang, Y. A. (2011) An integrated computational tool for precipitation simulation. JOM, 63(7), 29–34.CrossRefGoogle Scholar
Chang, A., Colinet, C., Hillert, M., Moser, Z., Sanchez, J. M., Saunders, N., Watson, R. E., and Kussmaul, A. (1995) Workshop on thermodynamic models and data for pure elements and other endmembers of solutions: Schloβ Ringberg 1995, Group 3. CALPHAD, 19(4), 481–498.Google Scholar
Chang, Y. A., Chen, S., Zhang, F., Yan, X., Xie, F., Schmid-Fetzer, R., and Oates, W. A. (2004) Phase diagram calculation: past, present and future. Progress in Materials Science, 49(3), 313–345.CrossRefGoogle Scholar
Chang, Y. A., and Oates, W. A. (2010) Materials Thermodynamics. Hoboken: John Wiley & Sons.Google Scholar
Chartrand, P., and Pelton, A. D. (2001) The modified quasi-chemical model: Part III. Two sublattices. Metallurgical and Materials Transactions A, 32(6), 1397–1407.CrossRefGoogle Scholar
Chase, M. W. (1998) NIST-JANAF Thermochemical Tables, fourth edition. New York: The American Chemical Society, and The American Institute of Physics for the National Institute of Standards and Technology.Google Scholar
Chase, M. W., Ansara, I., Dinsdale, A., et al. (1995) Workshop on thermodynamic models and data for pure elements and other endmembers of solutions: Schloβ Ringberg 1995, Group 1. CALPHAD, 19(4), 437–447.Google Scholar
Chen, H.-L., Chen, Q., and Engström, A. (2018) Development and applications of the TCAL aluminum alloy database. CALPHAD, 62, 154–171.CrossRefGoogle Scholar
Chen, L., Zhang, Z., Huang, Y., Cui, J., Deng, Z., Zou, H., and Chang, K. (2019) Thermodynamic description of the Fe–Cu–C system. CALPHAD, 64, 225–235.CrossRefGoogle Scholar
Chen, Q., Hillert, M., Sundman, B., Oates, W. A., Fries, S. G., and Schmid-Fetzer, R. (1998) Phase equilibria, defect chemistry and semiconducting properties of CdTe(s) – thermodynamic modeling. Journal of Electronics Materials, 27(8), 961–971.CrossRefGoogle Scholar
Chen, S. L., Daniel, S., Zhang, F., Chang, Y. A., Yan, X. Y., Xie, F. Y., Schmid-Fetzer, R., and Oates, W. A. (2002) The PANDAT software package and its applications. CALPHAD, 26(2), 175–188.CrossRefGoogle Scholar
Chuang, Y.-Y., Chang, Y. A., Schmid, R., and Lin, J.-C. (1986) Magnetic contributions to the thermodynamic functions of alloys and the phase equilibria of Fe–Ni system below 1200 K. Metallurgical Transactions A, 17(8), 1361–1372.CrossRefGoogle Scholar
Chuang, Y. Y., Schmid, R., and Chang, Y. A. (1985) Magnetic contributions to the thermodynamic functions of pure Ni, Co, and Fe. Metallurgical Transactions A, 16(2), 153–165.CrossRefGoogle Scholar
Costa e Silva, A., Ågren, J., Clavaguera-Mora, M. T., et al. (2007) Applications of computational thermodynamics – the extension from phase equilibrium to phase transformations and other properties. CALPHAD, 31(1), 53–74.CrossRefGoogle Scholar
de Fontaine, D. d., Fries, S. G., Inden, G., Miodownik, P., Schmid-Fetzer, R., and Chen, S.-L. (1995) Workshop on thermodynamic models and data for pure elements and other endmembers of solutions: Schloβ Ringberg 1995, Group 4. CALPHAD, 19(4), 499–536.Google Scholar
Desai, P. (1987) Thermodynamic properties of nickel. International Journal of Thermophysics, 8(6), 763–780.CrossRefGoogle Scholar
Dinsdale, A., Khvan, A., Smirnova, E. A., Ponomareva, A. V., and Abrikosov, I. A. (2021) Modelling the thermodynamic data for Hcp Zn and Cu–Zn alloys –an ab initio and CALPHAD approach. CALPHAD, 72, 102253.CrossRefGoogle Scholar
Dinsdale, A. T. (1991) SGTE data for pure elements. CALPHAD, 15(4), 317–425.CrossRefGoogle Scholar
Dupin, N., and Ansara, I. (1999) On the sublattice formalism applied to the B2 phase. Zeitschrift für Metallkunde, 90(1), 76–85.Google Scholar
Dupin, N., Ansara, I., and Sundman, B. (2001) Thermodynamic re-assessment of the ternary system Al–Cr–Ni. CALPHAD, 25(2), 279–298.CrossRefGoogle Scholar
Easton, M. A., and StJohn, D. H. (2001) A model of grain refinement incorporating alloy constitution and potency of heterogeneous nucleant particles. Acta Materialia, 49(10), 1867–1878.CrossRefGoogle Scholar
Eriksson, G. (1975) SOLGASMIX, a computer program for calculation of equilibrium compositions in multiphase systems. Chemica Scripta, 8, 100–103.Google Scholar
Fang, H., Tang, Q., Zhang, Q., Gu, T., and Zhu, M. (2019) Modeling of microstructure and microsegregation formation during solidification of Al–Si–Mg alloys. International Journal of Heat Mass Transfer, 133, 371–381.CrossRefGoogle Scholar
Fernández Guillermet, A., Gustafson, P., and Hillert, M. (1985) The representation of thermodynamic properties at high pressures. Journal of Physics and Chemistry of Solids, 46(12), 1427–1429.CrossRefGoogle Scholar
Fu, P., Peng, L., Jiang, H., Chang, J., and Zhai, C. (2008) Effects of heat treatments on the microstructures and mechanical properties of Mg–3Nd–0.2Zn–0.4Zr (wt.%) alloy. Materials Science and Engineering A, 486(1), 183–192.Google Scholar
Gibbs, J. W. (1874) On the equilibrium of heterogeneous substances, I. Transactions of the Connecticut Academy of Arts and Sciences, 3(96), 108–248.Google Scholar
Gibbs, J. W. (1878) On the equilibrium of heterogeneous substances, II. Transactions of the Connecticut Academy of Arts and Sciences, 3(96), 343–524.Google Scholar
Gröbner, J., and Schmid-Fetzer, R. (2013) Key issues in a thermodynamic Mg alloy database. Metallurgical and Materials Transactions A, 44(7), 2918–2934.CrossRefGoogle Scholar
Gulliver, G. H. (1913) The quantitative effect of rapid cooling upon the constitution of binary alloys. Journal of the Institute of Metals, 9, 120–157.Google Scholar
Gustafson, P. (1985) A thermodynamic evaluation of the Fe–C system. Scandinavian Journal of Metallurgy, 14(5), 259–267.Google Scholar
Hallstedt, B., Dupin, N., Hillert, M., Höglund, L., Lukas, H. L., Schuster, J. C., and Solak, N. (2007) Thermodynamic models for crystalline phases. Composition dependent models for volume, bulk modulus and thermal expansion. CALPHAD, 31(1), 28–37.CrossRefGoogle Scholar
Hertzman, S., and Sundman, B. (1982) A thermodynamic analysis of the Fe–Cr system. CALPHAD, 6(1), 67–80.CrossRefGoogle Scholar
Hillert, M. (1981) Some viewpoints on the use of a computer for calculating phase diagrams. Physica B, 103(1), 31–40.CrossRefGoogle Scholar
Hillert, M. (2001) The compound energy formalism. Journal of Alloys and Compounds, 320(2), 161–176.CrossRefGoogle Scholar
Hillert, M. (2008) Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis, second edition. New York and London: Cambridge University Press.Google Scholar
Hillert, M., and Jarl, M. (1978) A model for alloying in ferromagnetic metals. CALPHAD, 2(3), 227–238.CrossRefGoogle Scholar
Hillert, M., Selleby, M., and Sundman, B. (2009) An attempt to correct the quasichemical model. Acta Materialia, 57(17), 5237–5244.CrossRefGoogle Scholar
Hillert, M., and Staffansson, L. (1970) Regular-solution model for stoichiometric phases and ionic melts. Acta Chemica Scandinavica, 24(10), 3618–3626.CrossRefGoogle Scholar
Huang, D., Liu, S., Du, Y., and Sundman, B. (2015) Modeling of the molar volume of the solution phases in the Al–Cu–Mg system. CALPHAD, 51, 261–271.CrossRefGoogle Scholar
Hutchinson, C., Nie, J., and Gorsse, S. (2005) Modeling the precipitation processes and strengthening mechanisms in a Mg–Al–(Zn) AZ91 alloy. Metallurgy and Materials Transactions A, 36(8), 2093–2105.CrossRefGoogle Scholar
Ilatovskaia, M., Savinykh, G., and Fabrichnaya, O. (2017) Thermodynamic description of the ZrO2–TiO2–Al2O3 system based on experimental data. Journal of the European Ceramics Society, 37(10), 3461–3469.CrossRefGoogle Scholar
Inden, G. (1981) The role of magnetism in the calculation of phase diagrams. Physica B, 103(1), 82–100.CrossRefGoogle Scholar
Janz, A., and Schmid-Fetzer, R. (2005) Impact of ternary parameters. CALPHAD, 29(1), 37–39.CrossRefGoogle Scholar
Jung, J.-G., Cho, Y.-H., Lee, J.-M., Kim, H.-W., and Euh, K. (2019) Designing the composition and processing route of aluminum alloys using CALPHAD: case studies. CALPHAD, 64, 236–247.CrossRefGoogle Scholar
Kampmann, R., and Wagner, R. (1984) Kinetics of precipitation in metastable binary alloys – theory and application to Cu-1.9 at % Ti and Ni-14 at % Al, in Haasen, P., Gerold, V., Wagner, R., and Ashby, M. F. (eds), Decomposition of Alloys: The Early Stages: Proceedings of the 2nd Acta-Scripta Metallurgica Conference. Sonnenberg, Germany, 19-23/09/1983. Oxford: Pergamon, 91–103.Google Scholar
Kattner, U. R., and Seifert, H. J. (2010) Integrated computational materials engineering, CALPHAD and Hans Leo Lukas. CALPHAD, 34, 385–386.CrossRefGoogle Scholar
Kaufman, L., and Ågren, J. (2014) CALPHAD, first and second generation – birth of the materials genome. Scripta Materialia, 70(Supplement C), 3–6.CrossRefGoogle Scholar
Kaufman, L., and Bernstein, H. (1970) Computer Calculation of Phase Diagrams – with Special Reference to Refractory Metals. New York: Academic Press.Google Scholar
Kevorkov, D., Schmid-Fetzer, R., and Zhang, F. (2004) Phase equilibria and thermodynamics of the Mg–Si–Li system and remodeling of the Mg–Si system. Journal of Phase Equilibria and Diffusion, 25(2), 140–151.CrossRefGoogle Scholar
Kou, S. (2015) A criterion for cracking during solidification. Acta Materialia, 88, 366–374.CrossRefGoogle Scholar
Lee, B. D., Kim, E. J., Baek, U. H., and Han, J. W. (2013) Precipitate prediction model of Mg–xAl(x=3,6,9) alloys. Metals and Materials International, 19(2), 135–145.CrossRefGoogle Scholar
Li, S., and Apelian, D. (2011) Hot tearing of aluminum alloys. International Journal of Metalcasting, 5(1), 23–40.CrossRefGoogle Scholar
Li, S., Sadayappan, K., and Apelian, D. (2011) Characterisation of hot tearing in Al cast alloys: methodology and procedures. International Journal of Cast Metals Research, 24(2), 88–95.CrossRefGoogle Scholar
Liang, P., Su, H. L., Donnadieu, P., et al. (1998a) Experimental investigation and thermodynamic calculation of the central part of the Mg–Al phase diagram. Zeitschrift für Metallkunde, 89(8), 536–540.Google Scholar
Liang, P., Tarfa, T., Robinson, J. A., et al. (1998b) Experimental investigation and thermodynamic calculation of the Al–Mg–Zn system. Thermochimica Acta, 314(1), 87–110.CrossRefGoogle Scholar
Liang, S.-M., Hsiao, H.-M., and Schmid-Fetzer, R. (2015) Thermodynamic assessment of the Al–Cu–Zn system, part I: Cu–Zn binary system. CALPHAD, (51), 224–232.CrossRefGoogle Scholar
Liang, S.-M., and Schmid-Fetzer, R. (2013) Thermodynamic assessment of the Al–P system based on original experimental data. CALPHAD, 42(0), 76–85.CrossRefGoogle Scholar
Liang, S.-M., and Schmid-Fetzer, R. (2014) Corrigendum to “thermodynamic assessment of the Al–P system based on original experimental data”[Calphad 42 (2013) 76–85]. CALPHAD, 100(45), 251–253.CrossRefGoogle Scholar
Liang, S.-M., and Schmid-Fetzer, R. (2015) Thermodynamic assessment of the Al–Cu–Zn system, part II: Al–Cu binary system. CALPHAD, 51, 252–260.CrossRefGoogle Scholar
Liang, S.-M., and Schmid-Fetzer, R. (2016) Thermodynamic assessment of the Al–Cu–Zn system, part III: Al–Cu–Zn ternary system. CALPHAD, 52, 21–37.CrossRefGoogle Scholar
Liang, S.-M., Taubert, F., Kozlov, A., Seidel, J., Mertens, F., and Schmid-Fetzer, R. (2017) Thermodynamics of Li–Si and Li–Si–H phase diagrams applied to hydrogen absorption and Li–ion batteries. Intermetallics, 81, 32–46.CrossRefGoogle Scholar
Lima, J., Barbosa, C., Magno, I., et al (2018) Microstructural evolution during unsteady-state horizontal solidification of Al–Si–Mg (356) alloy. Transactions of the Nonferrous Metals Society, 28(6), 1073–1083.CrossRefGoogle Scholar
Liu, J., and Kou, S. (2017) Susceptibility of ternary aluminum alloys to cracking during solidification. Acta Materialia, 125, 513–523.CrossRefGoogle Scholar
Liu, Y., Zhang, C., Du, C., et al. (2020) CALTPP: a general program to calculate thermophysical properties. Journal of Materials Science and Technology, 42, 229–240.Google Scholar
Liu, Z.-K. (2018) Ocean of data: integrating first-principles calculations and CALPHAD modeling with machine learning. Journal of Phase Equilibria and Diffusion, 39(5), 635–649.CrossRefGoogle Scholar
Liu, Z.-K. (2020) Computational thermodynamics and its applications. Acta Materialia, 200, 745–792.CrossRefGoogle Scholar
Liu, Z.-K., and Wang, Y. (2016) Computational Thermodynamics of materials. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Löffler, A., Gröbner, J., Hampl, M., Engelhardt, H., Schmid-Fetzer, R., and Rettenmayr, M. (2012) Solidifying incongruently melting intermetallic phases as bulk single phases using the example of Al2Cu and Q-phase in the Al–Mg–Cu–Si system. Journal of Alloys and Compounds, 515(Supplement C), 123–127.CrossRefGoogle Scholar
Löffler, A., Zendegani, A., Gröbner, J., Hampl, M., Schmid-Fetzer, R., Engelhardt, H., Rettenmayr, M., Körmann, F., Hickel, T., and Neugebauer, J. (2016) Quaternary Al–Cu–Mg–Si Q phase: sample preparation, heat capacity measurement and first-principles calculations. Journal of Phase Equilibria and Diffusion, 37(2), 119–126.CrossRefGoogle Scholar
Lu, X.-G., Selleby, M., and Sundman, B. (2005a) Assessments of molar volume and thermal expansion for selected Bcc, Fcc and Hcp metallic elements. CALPHAD, 29(1), 68–89.CrossRefGoogle Scholar
Lu, X.-G., Selleby, M., and Sundman, B. (2005b) Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc. CALPHAD, 29(1), 49–55.CrossRefGoogle Scholar
Lu, X.-G., Selleby, M., and Sundman, B. (2005c) Theoretical modeling of molar volume and thermal expansion. Acta Materialia, 53(8), 2259–2272.CrossRefGoogle Scholar
Lukas, H., Henig, E. T., and Zimmermann, B. (1977) Optimization of phase diagrams by a least squares method using simultaneously different types of data. CALPHAD, 1(3), 225–236.CrossRefGoogle Scholar
Lukas, H. L., Fries, S. G., and Sundman, B. (2007) Computational Thermodynamics: The CALPHAD Method. New York: Cambridge University Press.CrossRefGoogle Scholar
Luo, A. A. (2015) Material design and development: from classical thermodynamics to CALPHAD and ICME approaches. CALPHAD, 50, 6–22.CrossRefGoogle Scholar
Ma, X., Li, C., Zhang, W., and Schmid-Fetzer, R. (2005) The influence of nitrogen fugacity on the phase equilibria of Me–N systems. CALPHAD, 29(3), 247–253.CrossRefGoogle Scholar
McDowell, M. T., Lee, S. W., Nix, W. D., and Cui, Y. (2013) 25th anniversary article: understanding the lithiation of silicon and other alloying anodes for lithium–ion batteries. Advanced Materials, 25(36), 4966–4985.CrossRefGoogle ScholarPubMed
Mirković, D., Gröbner, J., Schmid-Fetzer, R., Fabrichnaya, O., and Lukas, H. L. (2004) Experimental study and thermodynamic re-assessment of the Al–B system. Journal of Alloys and Compounds, 384(1), 168–174.CrossRefGoogle Scholar
Müller, M., Seebold, S., Wu, G., Yazhenskikh, E., Jantzen, T., and Hack, K. (2018) Experimental investigation and modeling of the viscosity of oxide slag systems. Journal of Sustainable Metallurgy, 4(1), 3–14.CrossRefGoogle Scholar
Oates, W. A., Chen, S. L., Cao, W., Zhang, F., Chang, Y. A., Bencze, L., Doernberg, E., and Schmid-Fetzer, R. (2008) Vacancy thermodynamics for intermediate phases using the compound energy formalism. Acta Materialia, 56(18), 5255–5262.CrossRefGoogle Scholar
Ohno, M., Kozlov, A., Arroyave, R., Liu, Z. K., and Schmid-Fetzer, R. (2006a) Thermodynamic modeling of the Ca–Sn system based on finite temperature quantities from first-principles and experiment. Acta Materialia, 54(18), 4939–4951.CrossRefGoogle Scholar
Ohno, M., Mirkovic, D., and Schmid-Fetzer, R. (2006b) Liquidus and solidus temperatures of Mg-rich Mg–Al–Mn–Zn alloys. Acta Materialia, 54(15), 3883–3891.CrossRefGoogle Scholar
Onderka, B., Unland, J., and Schmid-Fetzer, R. (2002) Thermodynamics and phase stability in the In–N system. Journal of Materials Research, 17(12), 3065–3083.CrossRefGoogle Scholar
Otis, R., and Liu, Z.-K. (2017) Pycalphad: CALPHAD-based computational thermodynamics in Python. JORS, 5(1), 1–11.CrossRefGoogle Scholar
Palumbo, M., Burton, B., Silva, A. C. E., et al. (2014) Thermodynamic modelling of crystalline unary phases. Physica Status Solidi B, 251(1), 14–32.CrossRefGoogle Scholar
Pelton, A. D. (2014) Thermodynamics and phase diagrams, in Laughlin, D. E., and Hono, K. (eds), Physical Metallurgy, fifth edition. Amsterdam: Elsevier, 203–303.CrossRefGoogle Scholar
Pelton, A. D., and Chartrand, P. (2001) The modified quasi-chemical model: part II. Multicomponent Solutions. Metallurgical and Materials Transactions A, 32(6), 1355–1360.CrossRefGoogle Scholar
Pelton, A. D., Chartrand, P., and Eriksson, G. (2001) The modified quasi-chemical model: part IV. Two-sublattice quadruplet approximation. Metallurgical and Materials Transactions A, 32(6), 1409–1416.CrossRefGoogle Scholar
Pelton, A. D., Degterov, S. A., Eriksson, G., Robelin, C., and Dessureault, Y. (2000) The modified quasichemical model I – binary solutions. Metallurgical and. Materials Transactions B, 31(4), 651–659.CrossRefGoogle Scholar
Povoden-Karadeniz, E., Cirstea, D., Lang, P., Wojcik, T., and Kozeschnik, E. (2013) Thermodynamics of Ti–Ni shape memory alloys. CALPHAD, 41, 128–139.CrossRefGoogle Scholar
Pumphrey, W., and Moore, D. (1948) Cracking during and after solidification in some aluminium copper magnesium alloys of high purity. Journal of the Institute of Metals, 74(9), 425–438.Google Scholar
Rappaz, M., Drezet, J.-M., and Gremaud, M. (1999) A new hot-tearing criterion. Metallurgical and. Materials Transactions A, 30(2), 449–455.CrossRefGoogle Scholar
Redlich, O., and Kister, A. T. (1948) Algebraic representation of thermodynamic properties and the classification of solutions. Industrial and Engineering Chemistry Research, 40(2), 345–348.CrossRefGoogle Scholar
Saal, J. E., Berglund, I. S., Sebastian, J. T., Liaw, P. K., and Olson, G. B. (2018) Equilibrium high entropy alloy phase stability from experiments and thermodynamic modeling. Scripta Materialia., 146, 5–8.CrossRefGoogle Scholar
Saunders, N. (1990) A review and thermodynamic assessment of the Al–Mg and Mg–Li systems. CALPHAD, 14(1), 61–70.CrossRefGoogle Scholar
Saunders, N., Guo, U., Li, X., Miodownik, A., and Schillé, J.-P. (2003) Using JMatPro to model materials properties and behavior. JOM, 55(12), 60–65.CrossRefGoogle Scholar
Scheil, E. (1942) Bemerkungen zur Schichtkristallbildung. Zeitschrift für Metallkunde, 34, 70–72.Google Scholar
Schmid-Fetzer, R. (2014) Phase diagrams: the beginning of wisdom. Journal of Phase Equilibria and Diffusion, 35(6), 735–760, Open Access: https://doi.org/10.1007/s11669-014-0343-5.CrossRefGoogle Scholar
Schmid-Fetzer, R. (2022) Third generation of unary CALPHAD descriptions and the avoidance of re-stabilized solid phases and unexpected large heat capacity. Journal of Phase Equilibria and Diffusion, 43, 304–316, Open Access: https://doi.org/10.1007/s11669-022-00976-3.CrossRefGoogle Scholar
Schmid-Fetzer, R., Andersson, D., Chevalier, P. Y., et al. (2007) Assessment techniques, database design and software facilities for thermodynamics and diffusion. CALPHAD, 31(1), 38–52.CrossRefGoogle Scholar
Schmid-Fetzer, R., and Hallstedt, B. (2012) Is zinc HCP_ZN or HCP_A3? CALPHAD, 37(Supplement C), 34–36.CrossRefGoogle Scholar
Schmid-Fetzer, R., and Kozlov, A. (2011) Thermodynamic aspects of grain growth restriction in multicomponent alloy solidification. Acta Materialia, 59(15), 6133–6144.CrossRefGoogle Scholar
Schmid-Fetzer, R., and Zhang, F. (2018) The light alloy CALPHAD databases PanAl and PanMg. CALPHAD, 61, 246–263.CrossRefGoogle Scholar
Schmid, R. (1983) A thermodynamic analysis of the Cu–O system with an associated solution model. Metallurgical Transactions B, 14(3), 473–481.CrossRefGoogle Scholar
Schmid, R., and Chang, Y. A. (1985) A thermodynamic study on an associated solution model for liquid alloys. CALPHAD, 9(4), 363–382.CrossRefGoogle Scholar
Schmitz, G. J., and Prahl, U. (eds) (2016) Handbook of Software Solutions for ICME, first edition. Weinheim: John Wiley & Sons.CrossRefGoogle Scholar
Sommer, F. (1982) Association model for the description of the thermodynamic functions of liquid alloys, 1. Basic concepts, 2. Numerical treatment and results. Z. MetaIlkd., 73(2), 72–86.Google Scholar
Sonderegger, B., and Kozeschnik, E. (2009a) Generalized nearest-neighbor broken-bond analysis of randomly oriented coherent interfaces in multicomponent Fcc and Bcc structures. Metallurgical and Materials Transactions A, 40(3), 499–510.CrossRefGoogle Scholar
Sonderegger, B., and Kozeschnik, E. (2009b) Size dependence of the interfacial energy in the generalized nearest-neighbor broken-bond approach. Scripta Materialia, 60(8), 635–638.CrossRefGoogle Scholar
Song, J., Wang, Z., Huang, Y., Srinivasan, A., Beckmann, F., Kainer, K. U., and Hort, N. (2015) Hot tearing susceptibility of Mg–Ca binary alloys. Metallurgical and Materials Transactions A, 46(12), 6003–6017.CrossRefGoogle Scholar
Spencer, P. (2008) A brief history of CALPHAD. CALPHAD, 32(1), 1–8.CrossRefGoogle Scholar
Spencer, P. J., Burton, B., Chart, T. G., et al. (1995) Workshop on thermodynamic models and data for pure elements and other endmembers of solutions: Schloβ Ringberg 1995, Groups 5 and 6. CALPHAD, 19(4), 537–553.Google Scholar
StJohn, D. H., Qian, M., Easton, M. A., and Cao, P. (2011) The interdependence theory: the relationship between grain formation and nucleant selection. Acta Materialia, 59(12), 4907–4921.CrossRefGoogle Scholar
Sundman, B., and Ågren, J. (1981) A regular solution model for phases with several components and sublattices, suitable for computer applications. Journal of the Physics and Chemistry of Solids, 42(4), 297–301.CrossRefGoogle Scholar
Sundman, B., and Aldinger, F. (1995) The Ringberg workshop 1995 on unary data for elements and other end-members of solutions. CALPHAD, 19(4), 433–436.CrossRefGoogle Scholar
Sundman, B., Chen, Q., and Du, Y. (2018) A review of CALPHAD modeling of ordered phases. Journal of Phase Equilibria and Diffusion, 39(5), 678–693.CrossRefGoogle Scholar
Sundman, B., Kattner, U. R., Hillert, M., et al. (2020) A method for handling the extrapolation of solid crystalline phases to temperatures far above their melting point. CALPHAD, 68, 101737.CrossRefGoogle ScholarPubMed
Sundman, B., Kattner, U. R., Palumbo, M., and Fries, S. G. (2015) OpenCalphad – a free thermodynamic software. Integrating Materials Manufacturing Innovation, 4(1), 1–15.CrossRefGoogle Scholar
Tang, K., Du, Q., and Li, Y. (2018) Modelling microstructure evolution during casting, homogenization and ageing heat treatment of Al–Mg–Si–Cu–Fe–Mn alloys. CALPHAD, 63, 164–184.CrossRefGoogle Scholar
Tsonopoulos, C. (1974) An empirical correlation of second virial coefficients. AIChE Journal, 20(2), 263–272.CrossRefGoogle Scholar
Unland, J., Onderka, B., Davydov, A., and Schmid-Fetzer, R. (2003) Thermodynamics and phase stability in the Ga–N system. Journal of Crystal Growth, 256(1), 33–51.CrossRefGoogle Scholar
Wang, P. S., Kozlov, A., Thomas, D., Mertens, F., and Schmid-Fetzer, R. (2013) Thermodynamic analysis of the Li–Si phase equilibria from 0 K to liquidus temperatures. Intermetallics, 42, 137–145.CrossRefGoogle Scholar
Weiss, R. J., and Tauer, K. J. (1956) Theory of Alloy Phases. Cleveland: ASM.Google Scholar
Xia, X., Sanaty-Zadeh, A., Zhang, C., Luo, A. A., and Stone, D. S. (2018) Experimental investigation and simulation of precipitation evolution in Mg–3Nd-0.2Zn alloy. CALPHAD, 60, 58–67.CrossRefGoogle Scholar
Xiong, W., and Olson, G. B. (2016) Cybermaterials: materials by design and accelerated insertion of materials. NPJ Computational Materials, 2(1), 15009.CrossRefGoogle Scholar
Xiong, W., Zhang, H., Vitos, L., and Selleby, M. (2011) Magnetic phase diagram of the Fe–Ni system. Acta Materialia, 59(2), 521–530.CrossRefGoogle Scholar
Yao, Z., Berman, T., and Allison, J. (2020) An ICME method for predicting phase dissolution during solution treatment in advanced super vacuum die cast magnesium alloys. Integrating Materials Manufacturing Innovation, 9(3), 301–313.CrossRefGoogle Scholar
Zhang, C., Cao, W., Chen, S.-L., et al. (2014) Precipitation simulation of AZ91 alloy. JOM, 66(3), 389–396.CrossRefGoogle Scholar
Zhang, F., Cao, W., Zhang, C., Chen, S., Zhu, J., and Lv, D. (2018) Simulation of co-precipitation kinetics of and in superalloy 718, in Ott, E. e. a. (ed), Proceedings of the 9th International Symposium on Superalloy 718 and Derivatives: Energy, Aerospace, and Industrial Applications. Cham: Springer TMS, 147–161.Google Scholar
Zhang, F., Zhang, C., Liang, S. M., Lv, D. C., Chen, S. L., and Cao, W. S. (2020) Simulation of the composition and cooling rate effects on the solidification path of casting aluminum alloys. Journal of Phase Equilibria and Diffusion, 41, 793–803. https://doi.org/10.1007/s11669-020-00834-0.CrossRefGoogle Scholar
Zhang, Y., Liu, Y., Liu, S., et al. (2021) Assessment of atomic mobilities and simulation of precipitation evolution in Mg–X (X= Al, Zn, Sn) alloys. Journal of Materials Science and Technology, 62, 70–82.CrossRefGoogle Scholar
Zhou, X., Zhang, F., Liu, S., Du, Y., and Jin, B. (2020) Phase equilibria and thermodynamic investigation of the In–Li system. CALPHAD, 70, 101779.CrossRefGoogle Scholar

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