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ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

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Abstract

The software package ESPEI has been developed for efficient evaluation of thermodynamic model parameters within the CALPHAD method. ESPEI uses a linear fitting strategy to parameterize Gibbs energy functions of single phases based on their thermochemical data and refines the model parameters using phase equilibrium data through Bayesian parameter estimation within a Markov Chain Monte Carlo machine learning approach. In this paper, the methodologies employed in ESPEI are discussed in detail and demonstrated for the Cu–Mg system down to 0 K using unary descriptions based on segmented regression. The model parameter uncertainties are quantified and propagated to the Gibbs energy functions.

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Acknowledgments

The authors thank Jiong Wang, ShunLi Shang, and Yi Wang for their help in testing ESPEI. B.B. was supported by a NSF National Research Trainee Fellowship grant DGE-1449785. This work was also supported by a NASA Space Technology Research Fellowship grant number 80NSSC18K1168 and used the NSF Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant number ACI-1548562. R.O. acknowledges financial support from NASA’s Science Mission Directorate and Space Technology Mission Directorate through the Game Changing Development program under Prime Contract #80NM0018D0004, and the Space Technology Office at the Jet Propulsion Laboratory, California Institute of Technology. The financial support from the Collaborative Research Center “Superalloys Single Crystal” (TR-103 project C6) of the German Research Foundation (DFG) and the Sino-German Cooperation Group is acknowledged.

Author information

Authors and Affiliations

  1. Department of Materials Science & Engineering, Pennsylvania State University, University Park, PA, 16802, USA

    Brandon Bocklund & Zi-Kui Liu

  2. Engineering and Science Directorate, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109, USA

    Richard Otis

  3. ICAMS, Ruhr-University Bochum, Universitätstr. 150, 44801, Bochum, Germany

    Aleksei Egorov, Abdulmonem Obaied & Irina Roslyakova

Authors
  1. Brandon Bocklund
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  2. Richard Otis
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  3. Aleksei Egorov
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  4. Abdulmonem Obaied
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  5. Irina Roslyakova
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  6. Zi-Kui Liu
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Corresponding author

Correspondence to Brandon Bocklund.

ESPEI Documentation

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The supplementary material for this article can be found at https://doi.org/10.1557/mrc.2019.59

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Bocklund, B., Otis, R., Egorov, A. et al. ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg. MRS Communications 9, 618–627 (2019). https://doi.org/10.1557/mrc.2019.59

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