Skip to main content Accessibility help
×
×
Home

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

  • Brandon Bocklund (a1), Richard Otis (a2), Aleksei Egorov (a3), Abdulmonem Obaied (a3), Irina Roslyakova (a3) and Zi-Kui Liu (a1)...

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.

Copyright

Corresponding author

Address all correspondence to Brandon Bocklund <bjb54@psu.edu>

References

Hide All
1.Andersson, J.O., Helander, T., Höglund, L., Shi, P. and Sundman, B.: Thermo-Calc & DICTRA, computational tools for materials science. Calphad 26, 273312 (2002).
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, 328342 (2009).
3.Dinsdale, A.T.: SGTE data for pure elements. Calphad 15, 317425 (1991).
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, 21992208 (2015).
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, 165180 (2016).
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.
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, 17 (2016).
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, 1831 (2013).
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, 694701 (2018).
10.Joubert, J.-M. and Crivello, J.-C.: Non-Stoichiometry and Calphad modeling of Frank-Kasper Phases. Appl. Sci. 2, 669681 (2012). doi: 10.3390/app2030669.
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, 121139 (2017)
12.Thermo-Calc Software and Databases, (2015).
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, 260269 (2016).
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).
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).
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. 617622.
17.Otis, R. and Liu, Z.-K.: Pycalphad: CALPHAD-based computational thermodynamics in python. J. Open Res. Softw. 5, 1 (2017).
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.
19.Hillert, M.: The compound energy formalism. J. Alloys Compd. 320, 161176 (2001).
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.
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, 37623767 (2010).
22.Liu, Z.K.: First-Principles calculations and CALPHAD modeling of thermodynamics. Calphad 30, 517534 (2009).
23.Redlich, O. and Kister, A.T.: Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 40, 345348 (1948).
24.Cavanaugh, J.E.: Unifying the derivations for the Akaike and corrected Akaike information criteria. Stat. Probab. Lett. 33, 201208 (1997).
25.Akaike, H.: Information Theory and an Extension of the Maximum Likelihood Principle, Springer, New York, 1998.
26.Goodman, J. and Weare, J.: Ensemble samplers with affine invariance. Commun. Appl. Math. Comput. Sci. 5, 6580 (2010).
27.Foreman-Mackey, D., Hogg, D.W., Lang, D. and Goodman, J.: Emcee: the MCMC hammer. Publ. Astron. Soc. Pacific. 125, 306312 (2013).
28.Thermo-Calc Software AB: Thermo-Calc Documentation Set (2019), Database Manager User Guide. http://www.thermocalc.com.
29.Bocklund, B.: ESPEI Software Documentation, (2019). https://espei.org.
30.ECMA International: The JSON Data Interchange Syntax, 2017.
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.
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, 111 (2004).
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, 317329 (1998).
34.Coughanowr, C.A., Ansara, I., Luoma, R., Hamalainen, M. and Lukas, H.L.: Assessment of the Cu–Mg system. Z. Meterol. 82, 574581 (1991).
35.Zuo, Y. and Chang, Y.A.: Thermodynamic calculation of the Mg-Cu phase diagram. Z. Meterol. 84, 662667 (1993).
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, 158166 (2007).
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, 196210 (2014).
38.Preston-Werner, T.: Semantic Versioning 2.0.0, (n.d.). https://semver.org/spec/v2.0.0.html.
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. 109118 (2018).
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, 126138 (2017). doi: 10.1016/j.calphad.2016.12.004.
41.Pfeif, E.A. and Kroenlein, K.: Perspective: data infrastructure for high throughput materials discovery. APL Mater. 4, 053203 (2016).
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, 4254 (1995).
43.King, R. and Kleppa, O.: A thermochemical study of some selected laves phases. Acta Metall. 12, 8797 (1964).
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, 2931 (1987).
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.
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, 196210 (2014).
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, 915 (2019). doi:10.1016/j.actamat.2019.05.017.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

MRS Communications
  • ISSN: 2159-6859
  • EISSN: 2159-6867
  • URL: /core/journals/mrs-communications
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
Type Description Title
PDF
Supplementary materials

Bocklund et al. supplementary material
Bocklund et al. supplementary material 1

 PDF (2.2 MB)
2.2 MB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed