Skip to main content
SpringerLink
Log in

CALPHAD Uncertainty Quantification and TDBX

  • Augmenting Physics-based Models in ICME with Machine Learning and Uncertainty Quantification
  • Published:
JOM Aims and scope Submit manuscript

Abstract

CALPHAD uncertainty quantification (UQ) is the foundation of materials design with quantified confidence. We report a framework and software packages to enable CALPHAD UQ assessment and calculation using commercial CALPHAD software (Thermo-Calc). This Bayesian inference framework is coupled with a Markov chain Monte Carlo algorithm to establish uncertainty traces with a given thermodynamic database file (TDB) and corresponding experimental data points. This general framework is demonstrated with the Ni–Cr binary system. The algorithm is firstly validated on synthetic data with known ground truth. Then it is applied to real experimental data to generate posterior traces. We develop a file format named TDBX, which provides a single source of truth by combining the original TDB content and the traces for each assessed Gibbs energy parameter. CALPHAD UQ calculations are performed based on the TDBX file, from which uncertainties for phase boundaries, enthalpy curves, and solidification range are collected as examples of basic design parameters. This TDBX file with corresponding scripts are made open-source. The combination of CALPHAD UQ assessments and calculations connected by TDBX supports uncertainty-assisted modeling, enabling the integrated application of modern design with uncertainty methodologies to computational materials design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. G.B. Olson, Science 277(5330), 1237 (1997). https://doi.org/10.1126/science.277.5330.1237. https://science.sciencemag.org/content/277/5330/1237.

  2. D.V. Malakhov, Calphad 21(3), 391 (1997).

    Article  MathSciNet  Google Scholar 

  3. E. Königsberger, Calphad 15(1), 69 (1991).

    Article  Google Scholar 

  4. W. Olbricht, N.D. Chatterjee, and K. Miller, Phys. Chem. Min. 21(1–2), 36 (1994).

    Google Scholar 

  5. N.D. Chatterjee, K. Miller, and W. Olbricht, Phys. Chem. Min. 21(1–2), 50 (1994).

    Google Scholar 

  6. N.D. Chatterjee, R. Krüger, G. Haller, and W. Olbricht, Contrib. Mineral. Petrol. 133(1–2), 149 (1998).

    Article  Google Scholar 

  7. M. Stan and B. Reardon, Calphad 27(3), 319 (2003). https://doi.org/10.1016/j.calphad.2003.11.002.

    Article  Google Scholar 

  8. T.C. Duong, R.E. Hackenberg, A. Landa, P. Honarmandi, A. Talapatra, H.M. Volz, A. Llobet, A.I. Smith, G. King, S. Bajaj, et al., Calphad 55, 219–230 (2016). https://doi.org/10.1016/j.calphad.2016.09.006

    Article  Google Scholar 

  9. T.C. Duong, A. Talapatra, W. Son, M. Radovic, and R. Arróyave, Sci. Rep. 7(1), 1 (2017).

    Article  Google Scholar 

  10. P. Honarmandi, T.C. Duong, S.F. Ghoreishi, D. Allaire, and R. Arroyave, Acta Mater. 164, 636 (2019).

    Article  Google Scholar 

  11. B. Bocklund, R. Otis, A. Egorov, A. Obaied, I. Roslyakova, and Z.K. Liu, MRS Commun. 9, 618 (2019).

    Article  Google Scholar 

  12. R.A. Otis and Z.K. Liu, JOM 69(5), 886 (2017).

    Article  Google Scholar 

  13. N.H. Paulson, E. Jennings, and M. Stan, Int. J. Eng. Sci. 142, 74 (2019).

    Article  Google Scholar 

  14. N.H. Paulson, B.J. Bocklund, R.A. Otis, Z.K. Liu, and M. Stan, Acta Mater. 174, 9 (2019).

    Article  Google Scholar 

  15. N.H. Paulson, S. Zomorodpoosh, I. Roslyakova, and M. Stan, Calphad 68, 101728 (2020).

    Article  Google Scholar 

  16. R. Otis and Z.K. Liu, J. Open Res. Softw. 1 (2016). https://doi.org/10.5334/jors.140.

  17. G.B. Olson, H.J. Jou, J. Jung, J. Sebastian, A. Misra, I. Locci, and D.R. Hull, Superalloys pp. 923–932 (2008).

  18. A. Gelman, J. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin, Bayesian Data Analysis, 3rd edn. (CRC Press, Boca Raton, 2013).

    Book  Google Scholar 

  19. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, J. Chem. Phys. 21(6), 1087 (1953).

    Article  Google Scholar 

  20. W.K. Hastings, Biometrika 57(1), 97 (1970).

    Article  MathSciNet  Google Scholar 

  21. D.B. Dunson and J.E. Johndrow, Biometrika 107(1), 1 (2020). https://doi.org/10.1093/biomet/asz066.

    Article  MathSciNet  Google Scholar 

  22. J. Goodman and J. Weare, Commun. Appl. Math. Comput. Sci. 5(1), 65 (2010).

    Article  MathSciNet  Google Scholar 

  23. D. Foreman-Mackey, D.W. Hogg, D. Lang, and J. Goodman, Publ. Astron. Soc. Pac. 125(925), 306 (2013).

    Article  Google Scholar 

  24. https://github.com/questek/qt-tdbx-demo. Accessed 5 Oct 2020.

  25. F. Tang and B. Hallstedt, Calphad 55, 260 (2016). https://doi.org/10.1016/j.calphad.2016.10.003. http://www.sciencedirect.com/science/article/pii/S0364591616301638.

  26. J.E. Saal, I.S. Berglund, J.T. Sebastian, P.K. Liaw, and G.B. Olson, Scripta Mater. 146, 5 (2018). https://doi.org/10.1016/j.scriptamat.2017.10.027. http://www.sciencedirect.com/science/article/pii/S1359646217306231.

  27. H.J. Choi, D.L. Mcdowell, J.K. Allen, and F. Mistree, Eng. Optim. 40(4), 287 (2008). https://doi.org/10.1080/03052150701742201.

    Article  Google Scholar 

Download references

Acknowledgements

The work reported in this manuscript was made possible through support from the Office of Science of the US Department of Energy under SBIR Award DE-SC0017234. C.N. would like to acknowledge insightful conversations with Dr. Marius Stan and group members of the Uncertainty Quantification of Phase Equilibria and Thermodynamics (UQPET) group of the NIST-sponsored Center for Hierarchical Materials Design (CHiMaD). C.N. would also like to acknowledge Dr. Johan Jeppsson from Thermo-Calc Software for his help on TC-Python usage.

Author information

Author notes

  1. Ramón Frey

    Present address: ETH Zurich, Zurich, Switzerland

Authors and Affiliations

  1. QuesTek Innovations LLC, Evanston, IL, 60201, USA

    Yu Lin, Abhinav Saboo, Ramón Frey, Sam Sorkin, Jiadong Gong, Gregory B. Olson & Changning Niu

  2. Department of Statistics, Rice University, Houston, TX, 77005, USA

    Meng Li

Authors
  1. Yu Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abhinav Saboo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ramón Frey
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sam Sorkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jiadong Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Gregory B. Olson
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Meng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Changning Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changning Niu.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is supported by DOE SBIR Award DE-SC0017234.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, Y., Saboo, A., Frey, R. et al. CALPHAD Uncertainty Quantification and TDBX. JOM 73, 116–125 (2021). https://doi.org/10.1007/s11837-020-04405-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11837-020-04405-z

Search

Navigation