Journal of Phase Equilibria and Diffusion

, Volume 28, Issue 1, pp 101–106 | Cite as

CALPHAD and Phase-Field Modeling: A Successful Liaison

  • I. SteinbachEmail author
  • B. Böttger
  • J. Eiken
  • N. Warnken
  • S. G. Fries
Basic and Applied Research


The connection between CALPHAD models and Phase-Field models is discussed against the background of minimization of the total Gibbs energy of a system. Both methods are based on separation of a multiphase system into individual contributions of the bulk phases, which are described by appropriate models in composition, temperature, and pressure. While the CALPHAD method uses a global minimization of the total Gibbs energy, the Phase-Field method introduces local interactions, interfaces, and diffusion and allows for non-equilibrium situations. Thus, the Phase-Field method is much more general by its concept, however, it can profit a lot if realistic thermodynamic descriptions, as provided by the CALPHAD method, are incorporated. The present paper discusses details of a direct coupling between the Multiphase-Field method and the CALPHAD method. Examples are presented from solidification of technical Mg and Ni base alloys and some problems arising from common practice concerning thermodynamic descriptions in order-disorder systems.


CALPHAD metastable phases microstructure phase transitions Phase-Field modeling 



We like to thank Dr. N. Dupin for providing information for the Ni database and the German research foundation (DFG) for financial support under the integrated project SPP1168 and the collaborative research center SFB370.


  1. 1.
    W. A. Oates, H. Wenzel, and T. Mohri, Putting More Physics into Calphad Solution Models, CalPhad-computer Coupling of Phase Diagrams and Thermochemistry, 1996, 20, p 37-45Google Scholar
  2. 2.
    B.P. Burton, N. Dupin, S.G. Fries, G. Grimvall, A.F. Guillermet, P. Miodownik, W.A. Oates, and V. Vinogred, Using ab initio calculations in the CALPHAD environment, Z. Mettallk (2007) 92:514-525Google Scholar
  3. 3.
    Elder K. R., Grant M., Modeling Elastic and Plastic Deformations in Nonequilibrium Processing using Phase-Field Crystals. Phys. Rev. E (2004) 70, 051605-1-051605-18CrossRefADSGoogle Scholar
  4. 4.
    Goldenfeld N., Athreya B. P., Dantzig J. A., Renormalization Group Approach to Multiscale Simulation of Polycrystalline Materials using the Phase-Field Crystal Model. Phys. Rev. E (2005) 72:020601-1-020601-4CrossRefADSGoogle Scholar
  5. 5.
    Tijssens M. G. A., James G. D, Towards an Improved Continuum Theory for Phase Transformations. Mat. Sci. Eng. A (2004) 378:453-458CrossRefGoogle Scholar
  6. 6.
    G. Caginalp, P. Fife, Phase-Field Methods for Interfacial Boundaries. Phys. Rev. B (1986) 33:7792-7794CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Wheeler A. A., Boettinger W. J., McFadden G. B., Phase-Field Model for Isothermal Phase Transitions in Binary Alloys. Phys. Rev. A (1992) 45 7424-7439CrossRefADSGoogle Scholar
  8. 8.
    Kim S. G., Kim W. T., Suzuki T. Phase-field Model for Binary Alloys. Phys. Rev. E (1999) 60, 7186-7197CrossRefADSGoogle Scholar
  9. 9.
    U. Grafe, B. Böttger, J. Tiaden, and S. G. Fries, Coupling of Multicomponent Thermodynamic Databases to a Phase-Field Model: Application to Solidification and Solid State Transformations of Superalloys, Scripta Mat., 2000, 42, p 1179-1186Google Scholar
  10. 10.
    Cha P. -R., Yeon D. -H., Yoon J. -K., A Phase-Field Model for Isothermal Solidification of Multicomponent Alloys. Acta Mat. (2001), 49, 3295-3307CrossRefGoogle Scholar
  11. 11.
    Zhu J. Z., Liu Z. K., Vaithyanathan V., Chen L.Q, Linking Phase-Field Model to CALPHAD: Application to Precipitate Shape Evolution in Ni-base Alloys. Acta Mat. (2002), 46, 401-406Google Scholar
  12. 12.
    Kobayashi H., Ode M., Kim S. G., Kim W. T., Suzuki T., Phase-Field Model for Solidification of Ternary Alloys Coupled with Thermodynamic Database. Scripta Mat. (2003), 48, 689-694CrossRefGoogle Scholar
  13. 13.
    Qin R. S., Wallach E. R., A Phase-Field Model Coupled with a Thermodynamic Database. Acta Mat., 51, (2003), 6199-6210CrossRefGoogle Scholar
  14. 14.
    Li D. Y., Choudhury S., Liu Z. K., Chen L. -Q., Effect of External Mechanical Constraints on the Phase Diagram of Epitaxial PbZr1−xTixO3 Thin Films – Thermodynamic Calculations and Phase-Field Simulations. Appl. Phys. Lett. (2003) , 83, 1608-1610CrossRefADSGoogle Scholar
  15. 15.
    Wu K., Chang Y. A., Wang Y., Simulating Interdiffusion Microstructures in Ni-Al-Cr Diffusion Couples: A Phase-Field Approach Coupled with Calphad Database. Scripta Mat. (2004), 50, 1145-1150CrossRefGoogle Scholar
  16. 16.
    Eiken J., Böttger B., Steinbach I., Multi Phase-Field Approach for Alloy Solidification. Rev. E (2006), 73, 066122-1-066122-9Google Scholar
  17. 17.
    Steinbach I., Pezzolla F., Nestler B., Seeelberg M., Prieler R., Schmitz G. J., Rezende J. L. L, A Phase-Field Concept for Multiphase Systems. Physica D (1996), 94, 135-147zbMATHCrossRefGoogle Scholar
  18. 18.
    Tiaden J., Nestler B., Diepers H. J, Steinbach I. The Multiphase-Field Model with an Integrated Concept for Modeling Solute Diffusion. Physica D (1998), 115, 73-86zbMATHCrossRefADSGoogle Scholar
  19. 19.
    Steinbach I., Pezzolla F., A Generalized Field Method for Multiphase Transformations using Interface Fields. Physica D (1999), 134, 385-393zbMATHCrossRefADSMathSciNetGoogle Scholar
  20. 20.
    Perepezko J. H., Wilde G., Alloy Metastability During Nucleation-Controlled Reactions. Ber. Bunsenges. Phys. Chem. (1998), 102, 1074-1082Google Scholar
  21. 21.
    Fries S. G., Sundman B., Development of Multicomponent Thermodynamic Databases for Use in Process Modelling and Simulations. J. Phys. Chem. Sol. 66, (2005) 226-230CrossRefADSGoogle Scholar
  22. 22.
    Schmid-Fetzer R., Janz A., Gröbner J., Ohno M., Aspects of Quality Assurance in a Thermodynamic Mg Alloy Database. Anv. Eng. Mater. (2005), 7, 1142-1149CrossRefGoogle Scholar
  23. 23.
    C. E. Campbel, W. J. Boettinger, and U. R. Kattner, Development of Diffusion Mobility Database for Ni-Base Super alloys, Acta Mat., (2002) 50:775-792 CrossRefGoogle Scholar
  24. 24.
    Warnken N., Ma D., Mathes M., Steinbach I., Investigation of Eutectic Island Formation in SX Superalloys. Mat. Sci. Eng. A (2005), 413-414, 267-271CrossRefGoogle Scholar
  25. 25.
  26. 26.
    Ohno M., Schmid-Fetzer R., Thermodynamic Assessment of Mg-Al-Mn Phase Equilibria, Focusing on Mg-rich Alloys. Z. Metallk. (2005) , 96, 857-869Google Scholar
  27. 27.
    Böttger B., Eiken J., Ohno M., Klaus G., Fehlbier M., Schmid-Fetzer R., Steinbach I., Bührig-Polazcek A., Controlling Microstructure in Magnesium Alloys: A Combined Thermodynamic, Experimental and Simulation Approach. Adv. Eng. Mat. (2006), 8(4), 241-247CrossRefGoogle Scholar
  28. 28.
    G. Klaus and A. Bührig-Polazcek, Unpublished research at Foundry Institute Aachen, 2005Google Scholar

Copyright information

© ASM International 2007

Authors and Affiliations

  • I. Steinbach
    • 1
    Email author
  • B. Böttger
    • 1
  • J. Eiken
    • 1
  • N. Warnken
    • 1
  • S. G. Fries
    • 2
    • 3
  1. 1.RWTH-Aachen, ACCESS e.V.AachenGermany
  2. 2.SGF Scientific ConsultancyAachenGermany
  3. 3.Equipe Physico-chimie des Matériaux Organisés FonctionnelsUniversité Montpellier II, Institut C. Gerhardt, UMR-CNRS 5253MontpellierFrance

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