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

Published online by Cambridge University Press:  04 June 2019

Brandon Bocklund Open the ORCID record for Brandon Bocklund [Opens in a new window] ,
Richard Otis ,
Aleksei Egorov ,
Abdulmonem Obaied ,
Irina Roslyakova  and
Zi-Kui Liu
Brandon Bocklund*
Affiliation:
Department of Materials Science & Engineering, Pennsylvania State University, University Park, PA, 16802, USA
Richard Otis
Affiliation:
Engineering and Science Directorate, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
Aleksei Egorov
Affiliation:
ICAMS, Ruhr-University Bochum, Universitätstr. 150, 44801, Bochum, Germany
Abdulmonem Obaied
Affiliation:
ICAMS, Ruhr-University Bochum, Universitätstr. 150, 44801, Bochum, Germany
Irina Roslyakova
Affiliation:
ICAMS, Ruhr-University Bochum, Universitätstr. 150, 44801, Bochum, Germany
Zi-Kui Liu
Affiliation:
Department of Materials Science & Engineering, Pennsylvania State University, University Park, PA, 16802, USA
*
Address all correspondence to Brandon Bocklund <bjb54@psu.edu>
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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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Type
Artificial Intelligence Research Letters
Information
MRS Communications , Volume 9 , Issue 2 , June 2019 , pp. 618 - 627
Copyright
Copyright © Materials Research Society 2019 

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References

1.Andersson, J.O., Helander, T., Höglund, L., Shi, P. and Sundman, B.: Thermo-Calc & DICTRA, computational tools for materials science. Calphad 26, 273–312 (2002).Google Scholar
2.Cao, W., Chen, S.L., Zhang, F., Wu, K., Yang, Y., Chang, Y.A., Schmid-Fetzer, R. and Oates, W.A.: PANDAT software with PanEngine, PanOptimizer and PanPrecipitation for multi-component phase diagram calculation and materials property simulation. Calphad Comput. Coupling Phase Diagrams Thermochem. 33, 328–342 (2009).Google Scholar
3.Dinsdale, A.T.: SGTE data for pure elements. Calphad 15, 317–425 (1991).Google Scholar
4.Bigdeli, S., Mao, H. and Selleby, M.: On the third-generation Calphad databases: an updated description of Mn. Phys. Status Solidi. Basic Res. 252, 2199–2208 (2015).Google Scholar
5.Roslyakova, I., Sundman, B., Dette, H., Zhang, L. and Steinbach, I.: Modeling of Gibbs energies of pure elements down to 0 K using segmented regression. Calphad Comput. Coupling Phase Diagrams Thermochem. 55, 165–180 (2016).Google Scholar
6.Paulson, N.H., Jennings, E. and Stan, M.: Bayesian strategies for uncertainty quantification of the thermodynamic properties of materials, (2018). http://arxiv.org/abs/1809.07365.Google Scholar
7.Li, Z., Mao, H., Korzhavyi, P.A. and Selleby, M.: Thermodynamic re-assessment of the Co-Cr system supported by first-principles calculations. Calphad Comput. Coupling Phase Diagrams Thermochem. 52, 1–7 (2016).Google Scholar
8.Mathieu, R., Dupin, N., Crivello, J.-C., Yaqoob, K., Breidi, A., Fiorani, J.-M., David, N. and Joubert, J.-M.: CALPHAD description of the Mo–Re system focused on the Sigma phase modeling. Calphad 43, 18–31 (2013).Google Scholar
9.Choi, W.M., Jo, Y.H., Kim, D.G., Sohn, S.S., Lee, S. and Lee, B.J.: A thermodynamic modelling of the stability of Sigma phase in the Cr-Fe-Ni-V high-entropy alloy system. J. Phase Equilibria Diffus. 39, 694–701 (2018).Google Scholar
10.Joubert, J.-M. and Crivello, J.-C.: Non-Stoichiometry and Calphad modeling of Frank-Kasper Phases. Appl. Sci. 2, 669–681 (2012). doi: 10.3390/app2030669.Google Scholar
11.Marker, C., Shang, S.L., Zhao, J.C. and Liu, Z.K.: Elastic knowledge base of bcc Ti alloys from first-principles calculations and CALPHAD-based modeling. Comput. Mater. Sci. 140, 121–139 (2017)Google Scholar
12.Thermo-Calc Software and Databases, (2015).Google Scholar
13.Tang, F. and Hallstedt, B.: Using the PARROT module of Thermo-Calc with the Cr–Ni system as example. Calphad Comput. Coupling Phase Diagrams Thermochem. 55, 260–269 (2016).Google Scholar
14.Cockayne, E. and van de Walle, A.: Building effective models from sparse but precise data: application to an alloy cluster expansion model. Phys. Rev. B. 81, 012104 (2010).Google Scholar
15.Honarmandi, P., Duong, T.C., Ghoreishi, S.F., Allaire, D. and Arroyave, R.: Bayesian uncertainty quantification and information fusion in CALPHAD-based thermodynamic modeling, ArXiv Prepr. ArXiv1806.05769. (2018).Google Scholar
16.Shang, S., Wang, Y. and Liu, Z.K.: ESPEI: extensible, self-optimizing phase equilibrium infrastructure for magnesium alloys, In: Agnew, S.R., Neelameggham, N.R., Nyberg, E.A., Sillekens, W.H. (Eds.), Magnes. Technol. 2010, The Minerals, Metals and Materials Society, Warrendale, PA, 2010; pp. 617–622.Google Scholar
17.Otis, R. and Liu, Z.-K.: Pycalphad: CALPHAD-based computational thermodynamics in python. J. Open Res. Softw. 5, 1 (2017).Google Scholar
18.Gelman, A., Stern, H.S., Carlin, J.B., Dunson, D.B., Vehtari, A. and Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC, New York, NY, 2013.Google Scholar
19.Hillert, M.: The compound energy formalism. J. Alloys Compd. 320, 161–176 (2001).Google Scholar
20.De Boer, F.R., Mattens, W.C.M., Boom, R., Miedema, A.R. and Niessen, A.K.: Cohesion in Metals, Philips Research Laboratories, Eindhoven, Netherlands, 1988.Google Scholar
21.Hautier, G., Fischer, C.C., Jain, A., Mueller, T. and Ceder, G.: Finding natures missing ternary oxide compounds using machine learning and density functional theory. Chem. Mater. 22, 3762–3767 (2010).Google Scholar
22.Liu, Z.K.: First-Principles calculations and CALPHAD modeling of thermodynamics. Calphad 30, 517–534 (2009).Google Scholar
23.Redlich, O. and Kister, A.T.: Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 40, 345–348 (1948).Google Scholar
24.Cavanaugh, J.E.: Unifying the derivations for the Akaike and corrected Akaike information criteria. Stat. Probab. Lett. 33, 201–208 (1997).Google Scholar
25.Akaike, H.: Information Theory and an Extension of the Maximum Likelihood Principle, Springer, New York, 1998.Google Scholar
26.Goodman, J. and Weare, J.: Ensemble samplers with affine invariance. Commun. Appl. Math. Comput. Sci. 5, 65–80 (2010).Google Scholar
27.Foreman-Mackey, D., Hogg, D.W., Lang, D. and Goodman, J.: Emcee: the MCMC hammer. Publ. Astron. Soc. Pacific. 125, 306–312 (2013).Google Scholar
28.Thermo-Calc Software AB: Thermo-Calc Documentation Set (2019), Database Manager User Guide. http://www.thermocalc.com.Google Scholar
29.Bocklund, B.: ESPEI Software Documentation, (2019). https://espei.org.Google Scholar
30.ECMA International: The JSON Data Interchange Syntax, 2017.Google Scholar
31.Lukas, H., Fries, S.G. and Sundman, B., Computational Thermodynamics The Calphad Method. Cambridge University Press, New York, NY, 2007. doi: 10.1017/CBO9780511804137.Google Scholar
32.Bailey, N.P., Schiøtz, J. and Jacobsen, K.W.: Simulation of Cu–Mg metallic glass: thermodynamics and structure. Phys. Rev. B: Condens. Matter Mater. Phys. 69, 1–11 (2004).Google Scholar
33.Buhler, T., Fries, S.G., Spencer, P.J. and Lukas, H.L.: A thermodynamic assessment of the Al–Cu–Mg ternary system. J. Phase Equilibria. 19, 317–329 (1998).Google Scholar
34.Coughanowr, C.A., Ansara, I., Luoma, R., Hamalainen, M. and Lukas, H.L.: Assessment of the Cu–Mg system. Z. Meterol. 82, 574–581 (1991).Google Scholar
35.Zuo, Y. and Chang, Y.A.: Thermodynamic calculation of the Mg-Cu phase diagram. Z. Meterol. 84, 662–667 (1993).Google Scholar
36.Zhou, S., Wang, Y., Shi, F.G., Sommer, F., Chen, L.-Q., Liu, Z.-K. and Napolitano, R.E.: Modeling of thermodynamic properties and phase equilibria for the Cu–Mg binary system. J. Phase Equilibria Diffus. 28, 158–166 (2007).Google Scholar
37.Gao, Q., Wang, J., Shang, S., Liu, S., Du, Y. and Liu, Z.-K.: First-principles calculations of finite-temperature thermodynamic properties of binary solid solutions in the Al–Cu–Mg system. Calphad 47, 196–210 (2014).Google Scholar
38.Preston-Werner, T.: Semantic Versioning 2.0.0, (n.d.). https://semver.org/spec/v2.0.0.html.Google Scholar
39.Jiang, Y., Zomorodpoosh, S., Roslyakova, I. and Zhang, L.: Thermodynamic re-assessment of binary Cr-Nb system down to 0K. Calphad Comput. Coupling Phase Diagrams Thermochem. 62. 109–118 (2018).Google Scholar
40.Wilthan, B., Pfeif, E.A., Diky, V. V., Chirico, R.D., Kattner, U.R. and Kroenlein, K.: Data resources for thermophysical properties of metals and alloys, part 1: structured data capture from the archival literature. Calphad Comput. Coupling Phase Diagrams Thermochem. 56, 126–138 (2017). doi: 10.1016/j.calphad.2016.12.004.Google Scholar
41.Pfeif, E.A. and Kroenlein, K.: Perspective: data infrastructure for high throughput materials discovery. APL Mater. 4, 053203 (2016).Google Scholar
42.Feufel, H. and Sommer, F.: Thermodynamic investigations of binary liquid and solid Cu–Mg and Mg-Ni alloys and ternary liquid Cu–Mg-Ni alloys. J. Alloys Compd. 224, 42–54 (1995).Google Scholar
43.King, R. and Kleppa, O.: A thermochemical study of some selected laves phases. Acta Metall. 12, 87–97 (1964).Google Scholar
44.Batalin, G.I., Sudavtsova, V.S. and Mikhailovskaya, M.V.: Thermodynamic properties of liquid alloys of the Cu–Mg systems. Izv. Vyss. Ucheb. Zaved., Tsvetn. Met. 2, 29–31 (1987).Google Scholar
45.Shin, D.: Thermodynamic properties of solid solutions from special quasirandom structures and CALPHAD modeling: application to aluminum-copper-magnesium-silicon and hafnium-silicon-oxygen. The Pennsylvania State University, State College, PA, 2007.Google Scholar
46.Gao, Q.N., Wang, J., Shang, S.L., Liu, S.H., Du, Y. and Liu, Z.K.: First-principles calculations of finite-temperature thermodynamic properties of binary solid solutions in the Al–Cu–Mg system. Calphad 47, 196–210 (2014).Google Scholar
47.Paulson, N.H., Bocklund, B.J., Otis, R.A., Liu, Z.-K. and Stan, M.: Quantified Uncertainty in Thermodynamic Modeling for Materials Design. Acta Mater. 174, 9–15 (2019). doi:10.1016/j.actamat.2019.05.017.Google Scholar
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