Abstract
The design of next-generation alloys through the integrated computational materials engineering (ICME) approach relies on multiscale computer simulations to provide thermodynamic properties when experiments are difficult to conduct. Atomistic methods such as density functional theory (DFT) and molecular dynamics (MD) have been successful in predicting properties of never before studied compounds or phases. However, uncertainty quantification (UQ) of DFT and MD results is rarely reported due to computational and UQ methodology challenges. Over the past decade, studies that mitigate this gap have emerged. These advances are reviewed in the context of thermodynamic modeling and information exchange with mesoscale methods such as the phase-field method (PFM) and calculation of phase diagrams (CALPHAD). The importance of UQ is illustrated using properties of metals, with aluminum as an example, and highlighting deterministic, frequentist, and Bayesian methodologies. Challenges facing routine uncertainty quantification and an outlook on addressing them are also presented.
Similar content being viewed by others
References
R. Darolia, JOM 43, 44 (1991).
G. Hanko, H. Antrekowitsch, and P. Ebner, JOM 54, 51 (2002).
B.O. Iddins, D.E. Graham, M.H. Waugh, T. Robbins, J. Cunningham III, and M.T. Finn, J. Occup. Environ. Med. 62, 287 (2020).
P. Honarmandi and R. Arróyave, Integr. Mater. Manuf. Innov. 9, 103 (2020).
A.V. Chernatynskiy, S.R. Phillpot, and R.A. LeSar, Annu. Rev. Mater. Res. 43, 157 (2013).
Y. Wang and D. McDowell, Uncertainty Quantification in Multiscale Materials Modeling (Elsevier Science and Technology: San Diego, 2020).
D.V. Malakhov, Calphad 21, 391 (1997).
E. Königsberger and G. Eriksson, Calphad 19, 207 (1995).
T.C. Duong, A. Talapatra, W. Son, M. Radovic, and R. Arróyave, Sci. Rep. 7, 5138 (2017).
R.G. Hennig, A. Wadehra, K.P. Driver, W.D. Parker, C.J. Umrigar, and J.W. Wilkins, Phys. Rev. B. 82, 014101 (2010).
M. Stan, Mater. Today 12, 20 (2009).
W. Kohn, A.D. Becke, and R.G. Parr, J. Phys. Chem. 100, 12974 (1996).
M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (Oxford: Clarendon, 1987).
B.S.D. Frenkel, Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed. (San Diego: Academic, 2002).
D.C. Rapaport, The Art of Molecular Dynamics Simulation, 2nd ed. (New York: Cambridge University Press, 2004).
J. Haile, Molecular Dynamics Simulation: Elementary Methods (New York: Wiley-Interscience, 1997).
J. Hoyt, M. Asta, and A. Karma, Mater. Sci. Eng. R 41, 121 (2003).
J. Sun, R. Haunschild, B. Xiao, I.W. Bulik, G.E. Scuseria, and J.P. Perdew, J. Chem. Phys. 138, 044113 (2013).
J. Sun, A. Ruzsinszky, and J.P. Perdew, Phys. Rev. Lett. 115, 036402 (2015).
J. Wellendorff, K.T. Lundgaard, K.W. Jacobsen, and T. Bligaard, J. Chem. Phys. 140, 144107 (2014).
F. Tran, J. Stelzl, and P. Blaha, J. Chem. Phys. 144, 204120 (2016).
P. Janthon, S.A. Luo, S.M. Kozlov, F. Viñes, J. Limtrakul, D.G. Truhlar, and F. Illas, J. Chem. Theory Comput. 10, 3832 (2014).
K. Choudhary, G. Cheon, E. Reed, and F. Tavazza, Phys. Rev. B. 98, 014107 (2018).
P.E. Blöchl, Phys. Rev. B. 50, 17953 (1994).
J.J. Mortensen, L.B. Hansen, and K.W. Jacobsen, Phys. Rev. B. 71, 035109 (2005).
G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
K. Lejaeghere, G. Bihlmayer, T. Björkman, P. Blaha, S. Blügel, V. Blum, D. Caliste, I.E. Castelli, S.J. Clark, A. Dal Corso, S.D. Gironcoli, T. Deutsch, J.K. Dewhurst, I.D. Marco, C. Draxl, M. Dulak, O. Eriksson, J.A. Flores-Livas, K.F. Garrity, L. Genovese, P. Giannozzi, M. Giantomassi, S. Goedecker, X. Gonze, O. Grånäs, E.K.U. Gross, A. Gulans, F. Gygi, D.R. Hamann, P.J. Hasnip, N.A.W. Holzwarth, D. Iuşan, D.B. Jochym, F. Jollet, D. Jones, G. Kresse, K. Koepernik, E. Küçükbenli, Y.O. Kvashnin, I.L.M. Locht, S. Lubeck, M. Marsman, N. Marzari, U. Nitzsche, L. Nordström, T. Ozaki, L. Paulatto, C.J. Pickard, W. Poelmans, M.I.J. Probert, K. Refson, M. Richter, G.-M. Rignanese, S. Saha, M. Scheffler, M. Schlipf, K. Schwarz, S. Sharma, F. Tavazza, P. Thunström, A. Tkatchenko, M. Torrent, D. Vanderbilt, M.J. van Setten, V.V. Speybroeck, J.M. Wills, J.R. Yates, G.-X. Zhang, and S. Cottenier, Science 351, 1415 (2016).
K. Choudhary and F. Tavazza, Comput. Mater. Sci. 161, 300 (2019).
J.J. Gabriel, F.Y.C. Congo, A. Sinnott, K. Mathew, T.C. Allison, F. Tavazza, and R.G. Hennig. arXiv preprint arXiv:2001.01851 (2020).
N.L. Anderson, R.P. Vedula, and A. Strachan, Comput. Mater. Sci. 109, 124 (2015).
J. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
A. Jain, S.P. Ong, G. Hautier, W. Chen, W.D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K.A. Persson, APL Mater. 1, 011002 (2013).
S. Curtarolo, W. Setyawan, S. Wang, J. Xue, K. Yang, R.H. Taylor, G.L. Hart, S. Sanvito, M.B. Nardelli, N. Mingo, and O. Levy, Comput. Mater. Sci. 58, 227 (2012).
J.E. Saal, S. Kirklin, M. Aykol, B. Meredig, and C. Wolverton, JOM 65, 1501 (2013).
K. Choudhary, I. Kalish, R. Beams, and F. Tavazza, Sci. Rep. 7, 5179 (2017).
K. Lejaeghere, V.V. Speybroeck, G.V. Oost, and S. Cottenier, Crit. Rev. Solid State Mater. Sci. 39, 1 (2014).
K. Lejaeghere, J. Jaeken, V.V. Speybroeck, and S. Cottenier, Phys. Rev. B. 89, 014304 (2014).
P.-W. Guan, G. Houchins, and V. Viswanathan, J. Chem. Phys. 151, 244702 (2019).
G.A.D. Wijs, G. Kresse, and M.J. Gillan, Phys. Rev. B 57, 8223 (1998).
H.J. Monkhorst and J.D. Pack, Phys. Rev. B 13, 5188 (1976).
G. Petretto, S. Dwaraknath, H.P.C. Miranda, D. Winston, M. Giantomassi, M.V. Setten, X. Gonze, K.A. Persson, G. Hautier, and G.-M. Rignanese, Sci. Data 5, 180065 (2018).
R. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K.A. Persson, and S.P. Ong, Sci. Data 3, 160080 (2016).
M.I. Mendelev, M.J. Kramer, C.A. Becker, and M. Asta, Philos. Mag. 88, 1723 (2008).
C.A. Becker and M.J. Kramer, Model. Simul. Mater. Sci. Eng. 18, 74001 (2010).
B. Grabowski, T. Hickel, and J. Neugebauer, Phys. Rev. B 76, 24309 (2007).
C.A. Becker, F.M. Tavazza, Z.T. Trautt, and R.A.B. de Macedo, Curr. Opin. Solid State Mater. Sci. 17, 277 (2013).
L. Alzate-Vargas, M.E. Fortunato, B. Haley, C. Li, C.M. Colina, and A. Strachan, Model. Simul. Mater. Sci. Eng. 26, 65007 (2018).
J. Mullins, Y. Ling, S. Mahadevan, L. Sun, and A. Strachan, Reliab. Eng. Syst. Saf. 147, 49 (2016).
Z.T. Trautt, F. Tavazza, and C.A. Becker, Model. Simul. Mater. Sci. Eng. 23, 74009 (2015).
A.P. Bartok, M.C. Payne, R. Kondor, and G. Csanyi, Phys. Rev. Lett. 104, 136403 (2010).
R. Jinnouchi, J. Lahnsteiner, F. Karsai, G. Kresse, and M. Bokdam, Phys. Rev. Lett. 122, 225701 (2019).
M. Vohra, A.Y. Nobakht, S. Shin, and S. Mahadevan, Int. J. Heat Mass Transf. 127, 297 (2018).
R.A. Messerly, M.R. Shirts, and A.F. Kazakov, J. Chem. Phys. 149, 114109 (2018).
S.L. Frederiksen, K.W. Jacobsen, K.S. Brown, and J.P. Sethna, Phys. Rev. Lett. 93, 165501 (2004).
A. Mishra, S. Hong, P. Rajak, C. Sheng, K. Nomura, R.K. Kalia, A. Nakano, and P. Vashishta, NPJ Comput. Mater. 4, 42 (2018).
F. Rizzi, H.N. Najm, B.J. Debusschere, K. Sargsyan, M. Salloum, H. Adalsteinsson, and O.M. Knio, Multiscale Model. Simul. 10, 1428 (2012).
P. Zhang and D.R. Trinkle, Model. Simul. Mater. Sci. Eng. 23, 65011 (2015).
P. Angelikopoulos, C. Papadimitriou, and P. Koumoutsakos, J. Chem. Phys. 137, 144103 (2012).
S. Longbottom and P. Brommer, Model. Simul. Mater. Sci. Eng. 27, 44001 (2019).
S.T. Reeve and A. Strachan, J. Comput. Phys. 334, 207 (2017).
F. Rizzi, H.N. Najm, B.J. Debusschere, K. Sargsyan, M. Salloum, H. Adalsteinsson, and O.M. Knio, Multiscale Model. Simul. 10, 1460 (2012).
J. Wang, S. Olsson, C. Wehmeyer, A. Pérez, N.E. Charron, G. de Fabritiis, F. Noé, and C. Clementi, ACS Cent. Sci. 5, 755 (2019).
F. Grogan, M. Holst, L. Lindblom, and R. Amaro, J. Chem. Phys. 147, 234106 (2017).
K.L. Joshi and S. Chaudhuri, Phys. Chem. Chem. Phys. 17, 18790 (2015).
K. Joshi and S. Chaudhuri, Combust. Flame 184, 20 (2017).
K. Joshi and S. Chaudhuri, J. Phys. Chem. C 122, 14434 (2018).
K. Lee, K. Joshi, S. Chaudhuri, and D. Stewart, Combust. Flame 215, 352 (2020).
K. Lee, K. Joshi, S. Chaudhuri, and D.S. Stewart, J. Chem. Phys. 144, 184111 (2016).
G. Dhaliwal, P.B. Nair, and C.V. Singh, Carbon 142, 300 (2019).
A.V. Tran and Y. Wang, Comput. Mater. Sci. 127, 141 (2017).
D. Zhang and S. Chaudhuri, Comput. Mater. Sci. 160, 222 (2019).
A. Tran, D. Liu, H. Tran, and Y. Wang, Model. Simul. Mater. Sci. Eng. 27, 64005 (2019).
H. Lukas, S.G. Fries, and B. Sundman, Computational Thermodynamics: The Calphad Method (Oxford: Cambridge University Press, 2007).
M. Stan and B. Reardon, Calphad 27, 319 (2003).
Z.-K. Liu, J. Phase Equilib. Diffus. 30, 517 (2009).
S. Bigdeli, L.-F. Zhu, A. Glensk, B. Grabowski, B. Lindahl, T. Hickel, and M. Selleby, Calphad 65, 79 (2019).
J. Pavlů, P. Řehák, J. Vřešťál, and M. Šob, Calphad 51, 161 (2015).
B. Hu, S. Sridar, L. Hao, and W. Xiong, Intermetallics 122, 106791 (2020).
M. Hillert, J. Alloys Compd. 320, 161 (2001).
G. Cacciamani, A.T. Dinsdale, M. Palumbo, and A. Pasturel, Intermetallics 18, 1148 (2010).
T.C. Duong, R.E. Hackenberg, A. Landa, P. Honarmandi, A. Talapatra, H.M. Volz, A.M. Llobet, A.I. Smith, G.M. King, S. Bajaj, A. Ruban, L. Vitos, P.E.A. Turchi, and R. Arroyave, Calphad 55, 219 (2016).
R.A. Otis and Z.-K. Liu, JOM 69, 886 (2017).
N.H. Paulson, B.J. Bocklund, R.A. Otis, Z.-K. Liu, and M. Stan, Acta Mater. 174, 9 (2019).
N.H. Paulson, E. Jennings, and M. Stan, Int. J. Eng. Sci. 142, 74 (2019).
N.H. Paulson, S. Zomorodpoosh, I. Roslyakova, and M. Stan, Calphad 68, 101728 (2020).
D.M. Blei, A. Kucukelbir, and J.D. McAuliffe, J. Am. Stat. Assoc. 112, 859 (2017).
M. Hoffman and A. Gelman, J. Mach. Learn. Res 15, 1593 (2014).
M. Girolami and B. Calderhead, J. R. Stat. Soc. B 73, 123 (2011).
J.W. Cahn and J.E. Hilliard, J. Chem. Phys. 28, 258 (1958).
V. Landau and L. Ginzburg, Zh. Eksp. Teor. Fiz. 20, 10641082 (1950).
J. Gunton, M. Miguel, and P. Sahni, The dynamics of first-order phase transitions.Phase Transitions and Critical Phenomena, Vol. 8, ed. C. Domb and J.L. Lebowitz (London: Academic, 1987), pp. 267–466.
P. Hohenberg and B. Halperin, Rev. Mod. Phys. 49, 435 (1977).
V. Attari, P. Honarmandi, T. Duong, D.J. Sauceda, D. Allaire, and R. Arroyave, Acta Mater. 183, 452 (2020).
N. Wang, S. Rokkam, T. Hochrainer, M. Pernice, and A. El-Azab, Comput. Mater. Sci. 89, 165 (2014).
P. Miles, L. Leon, R. Smith, and W. Oates, Proc. SPIE 10165, Behavior and Mechanics of Multifunctional Materials and Composites, 1016509 (2017).
L.S. Leon, R.C. Smith, P. Miles, and W.S. Oates, Proc. SPIE 10596, Behavior and Mechanics of Multifunctional Materials and Composites XII, 105960T (2018).
K. Karayagiz, L. Johnson, R. Seede, V. Attari, B. Zhang, X. Huang, S. Ghosh, T. Duong, I. Karaman, A. Elwany, and R. Arróyave, Acta Mater. 185, 320 (2020).
E.A.B. de Moraes, M. Zayernouri, and M.M. Meerschaert, Int. J. Numer. Methods Eng. vol. submitted.
R. Schmid-Fetzer, D. Andersson, P.-Y. Chevalier, L. Eleno, O. Fabrichnaya, U. Kattner, B. Sundman, C. Wang, A. Watson, L. Zabdyr, and M. Zinkevich, Calphad 31, 38 (2007).
M. Wood, M. Cusentino, B. Wirth, and A. Thompson, Phys. Rev. B 99, 184305 (2019).
I. Steinbach, L. Zhang, and M. Plapp, Acta Mater. 60, 2689 (2012).
S.G. Kim, W.T. Kim, and T. Suzuki, Phys. Rev. E 60, 7186 (1999).
P. Honarmandi, T. Duong, S.F. Ghoreishi, D. Allaire, and R. Arroyave, Acta Mater. 164, 636 (2019).
L. Chen and J. Shen, Comput. Phys. Commun. 108, 147 (1998).
D.E. Ricciardi, O.A. Chkrebtii, and S.R. Niezgoda, Integr. Mater. Manuf. Innov. 9, 181 (2020).
Acknowledgements
J.J.G., N.H.P., and M.S. gratefully acknowledge financial support from awards 70NANB14H012 and 70NANB19H005 from US Department of Commerce, National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD) in the Northwestern-Argonne Institute of Science and Engineering, and the Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the US Department of Energy under Contract No. DE-AC02-06CH11357. T.C.D. and S.C. thank the ARPA-E for its support under Contract Number PRJ1007310.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing financial interests in the writing of this manuscript.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Gabriel, J.J., Paulson, N.H., Duong, T.C. et al. Uncertainty Quantification in Atomistic Modeling of Metals and Its Effect on Mesoscale and Continuum Modeling: A Review. JOM 73, 149–163 (2021). https://doi.org/10.1007/s11837-020-04436-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11837-020-04436-6