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CALPHAD Modeling of High-Entropy Alloys

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Abstract

Phase diagrams are the key to understanding of high-entropy alloy formation. This chapter first presents the basics of CALPHAD (acronym of Calculation of Phase Diagrams) methodology and then details the procedures used in developing self-consistent thermodynamic databases tailored for HEA systems. A self-consistent thermodynamic database (PanHEA) has been developed for the Al-Co-Cr-Fe-Ni system that covers the complete compositional ranges for all its constituent binaries and ternaries, and it will be useful for future HEA design and processing optimization. HEA formation from the thermodynamic point of view is then illustrated for three HEA systems using TCNI7 database: FCC-forming Co-Cr-Fe-Mn-Ni, FCC- and BCC-forming Al-Co-Cr-Fe-Ni, and BCC-forming Mo-Nb-Ta-Ti-V-W systems. The FCC system shows large positive excess entropy while the BCC system shows small negative excess entropy, and these results are consistent with their vibrational entropies of mixing predicted from first-principle calculations presented in Chap. 10 “Applications of Special Quasi-random Structures to High-Entropy Alloys.” Addition of Al to CoCrFeNi stabilizes the BCC phase via the dominating enthalpy effect. The present study demonstrates that configurational entropy does not always dominate, and enthalpy and competing phases need to be considered in terms of phase stability. Applications of CALPHAD to high-entropy alloy design and microstructure development are then presented for the case of several alloys and satisfactory agreement between modeling calculations and experimental results is observed. Various isotherms and isopleths of the Al-Co-Cr-Fe-Ni system are predicted. Future perspectives on CALPHAD development including short-range ordering and kinetic database development pertaining to HEAs conclude this chapter.

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Acknowledgments

M.C.G. acknowledges the financial support by the Crosscutting Technology Research Program at the National Energy Technology Laboratory (NETL) – Strategic Center for Coal – managed by Robert Romanosky (Technology Manager) and Charles Miller (Technology Monitor). The research was executed through NETL’s Office of Research and Development’s Innovative Process Technologies (IPT) Field Work Proposal under the RES contract DE-FE-0004000. The authors thank Prof. P.K. Liaw’s group for providing experimental support. C.Z. thanks Fan Zhang and Shuanglin Chen for inspiring discussions on CALPHAD modeling. M.C.G. thanks Mike Widom, Jeffrey A. Hawk, David E. Alman, and Bryan Morreale for their general discussion on HEAs.

Disclaimer

This chapter co-authored by M.C.G. was funded by the Department of Energy, National Energy Technology Laboratory, an agency of the United States Government, through a support contract with AECOM. Neither the United States Government nor any agency thereof, nor any of their employees, nor AECOM, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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  1. CompuTherm, LLC, Madison, WI, 53719, USA

    Chuan Zhang

  2. National Energy Technology Laboratory/AECOM, Albany, OR, 97321, USA

    Michael C. Gao

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Editors and Affiliations

  1. National Energy Technology, Laboratory & AECOM, Albany, Oregon, USA

    Michael C. Gao

  2. Department of Materials Science and Eng, National Tsing Hua University, Hsinchu, Taiwan

    Jien-Wei Yeh

  3. Department of Materials Science and Eng, The University of Tennessee, KNOXVILLE, Tennessee, USA

    Peter K. Liaw

  4. State Key Laboratory for Advanced Metal, University of Science and Technology, Beijing, China

    Yong Zhang

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Zhang, C., Gao, M.C. (2016). CALPHAD Modeling of High-Entropy Alloys. In: Gao, M., Yeh, JW., Liaw, P., Zhang, Y. (eds) High-Entropy Alloys. Springer, Cham. https://doi.org/10.1007/978-3-319-27013-5_12

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