Abstract
In general, the forward phase stability problem consists of mapping thermodynamic conditions (e.g., composition, temperature, pressure) to corresponding equilibrium states. In this paper, we instead focus on the generalized inverse phase stability problem (GIPSP) that deals with mapping a set of phase constitutions to a set of corresponding thermodynamic conditions. Specifically, we define the GIPSP as mapping of sets of phase constitution definitions in a multidimensional phase constitution search space to corresponding ranges of thermodynamic conditions. Mathematically, the solution to the GIPSP corresponds to all solutions to a continuous constraint satisfaction problem (CCSP). We present novel algorithms combining computational thermodynamics, evolutionary computation, and machine learning to approximate solution sets to the GIPSP as a CCSP. Some preliminary examples demonstrating the algorithms are presented. Moreover, the implications of the proposed framework for the larger problem of materials design are discussed, and future work is suggested.
Similar content being viewed by others
References
T. Pollock, J.E. Allison, D.G. Backman, M.C. Boyce, M. Gersh, E.A. Holm, R. LeSar, M. Long, A.C. Powell, J.J. Schirra, D.D. Whitis, and C. Woodward, Integrated Computational Materials Engineering: a Transformational Discipline for Improved Competitiveness and National Security (National Academies Press, Washington, DC, 2008)
N. Saunders and A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, vol. 1 (Elsevier, New York, 1998)
J.O. Andersson, T. Helander, L. Höglund, P. Shi, and B. Sundman, CALPHAD 26(2), 273 (2002)
W. Cao, S.L. Chen, F. Zhang, K. Wu, Y. Yang, Y. Chang, R. Schmid-Fetzer, and W. Oates, CALPHAD 33(2), 328 (2009)
B. Sundman, U.R. Kattner, M. Palumbo, and S.G. Fries, Integr. Mater. Manuf. Innov. 4(1), 1 (2015)
A.E. Gheribi, C. Audet, S. Le Digabel, E. Bélisle, C. Bale, and A. Pelton, CALPHAD 36, 135 (2012)
A.E. Gheribi, C. Robelin, S. Le Digabel, C. Audet, and A.D. Pelton, J. Chem. Thermodyn. 43(9), 1323 (2011)
T. Gomez-Acebo, M. Sarasola, and F. Castro, CALPHAD 27(3), 325 (2003)
H. Du and J. Morral, J. Alloys Compd. 247(1), 122 (1997)
E. Tsang, Foundations of Constraint Satisfaction (Academic, London, 1995)
J. Cruz, Proceedings of the 2005 Conference on Constraint Reasoning for Differential Models, (IOS Press, Amsterdam, 2005), pp. 1–216
E. Galvan, R.J. Malak, S. Gibbons, and R. Arroyave, ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (American Society of Mechanical Engineers, 2014), pp. V02BT03A010–V02BT03A010
M.L. Ginsberg and W.D. Harvey, Artif. Intell. 55(2), 367 (1992)
W.D. Harvey and M.L. Ginsberg, in IJCAI (1) (1995), pp. 607–615
S.W. Golomb and L.D. Baumert, J. ACM 12(4), 516 (1965)
D. Sam-Haroud and B. Faltings, Constraints 1(1–2), 85 (1996)
J. Hu, M. Aminzadeh and Y. Wang, J. Mech. Des. 136(3), 031002 (2014)
A.M. Zalzala and P.J. Fleming (eds.), Genetic Algorithms in Engineering Systems, Control Engineering Series 55 (Institution of Electrical Engineers, London, 1997)
D.M. Tax and R.P. Duin, Pattern Recognit. Lett. 20(11), 1191 (1999)
E. Galvan, S. Gibbons, R. Arroyave, and R.J. Malak, Texas A&M University, unpublished research, 2016
C.M. Fonseca, J.D. Knowles, L. Thiele, and E. Zitzler, Third International Conference on Evolutionary Multi-Criterion Optimization (EMO) (2005), Vol. 216, pp. 240
H. Kanoh, M. Matsumoto, and S. Nishihara, IEEE International Conference on Intelligent Systems for the 21st Century on Systems, Man and Cybernetics, 1995, Vol. 1 (IEEE, 1995), pp. 626–631
E. Galvan and R. Malak, ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (American Society of Mechanical Engineers, 2012), pp. 777–788
T. Poggio and G. Cauwenberghs, Adv. Neural Inform. Process Syst. 13, 409 (2001)
E. Roach, R.R. Parker, R.J. Malak, ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (American Society of Mechanical Engineers, 2011), pp. 741–751
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, IEEE Trans Evol. Comput. 6(2), 182 (2002)
K. Deb, Multi-objective Optimization Using Evolutionary Algorithms, vol. 16 (Wiley, New York, 2001)
K. Ishida, J. Alloys Compd. 220(1), 126 (1995)
M. Hillert, Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis (Cambridge University Press, Cambridge, 2007)
Acknowledgements
This work was partially supported by the National Science Foundation and the Air Force under Grant EFRI-1240483. The authors would like to thank Paul Mason from Thermo-Calc for providing the thermodynamic dataset. R.A. acknowledges the partial support of NSF under Grant NSF-CMMI-1534534.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Arróyave, R., Gibbons, S.L., Galvan, E. et al. The Inverse Phase Stability Problem as a Constraint Satisfaction Problem: Application to Materials Design. JOM 68, 1385–1395 (2016). https://doi.org/10.1007/s11837-016-1858-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11837-016-1858-5