Abstract
Defects in crystals influence and control many relevant material properties. It is essential to employ multiscale modeling to understand structure and evolution of crystal defects. Most multiscale modeling schemes are hierarchical in nature, typically passing results from modeling conducted at each successive length/time scale to the next higher scale(s), with the intent to inform model parameters or instruct the form of reduced-order models. Here, we briefly review some pertinent hierarchical multiscale modeling advances for fundamentals of crystal defects.
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The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
J.D. Clayton, D.J. Bammann, D.L. McDowell, Philos. Mag. 85, 3983 (2005)
C.G. Van de Walle, J. Neugebauer, J. Appl. Phys. 95, 3851 (2004)
C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, C.G. Van de Walle, Rev. Mod. Phys. 86, 253 (2014)
P. Olsson, C. Domain, J. Wallenius, Phys. Rev. B 75, 014110 (2007)
M.C. Marinica, F. Willaime, J.P. Crocombette, Phys. Rev. Lett. 108, 025501 (2012)
T. Seletskaia, Y. Osetsky, R.E. Stoller, G.M. Stocks, Phys. Rev. Lett. 94, 046403 (2005)
C.-C. Fu, F. Willaime, Phys. Rev. B 72, 064117 (2005)
W.A. Counts, C. Wolverton, R. Gibala, Acta Mater. 58, 4730 (2010)
K. Heinola, T. Ahlgren, K. Nordlund, J. Keinonen, Phys. Rev. B 82, 094102 (2010)
M. Muzyk, D. Nguyen-Manh, K.J. Kurzydłowski, N.L. Baluc, S.L. Dudarev, Phys. Rev. B 84, 104115 (2011)
X.-S. Kong, X. Wu, Y.-W. You, C.S. Liu, Q.F. Fang, J.-L. Chen, G.N. Luo, Z. Wang, Acta Mater. 66, 172 (2014)
S.K. Nayak, C.J. Hung, V. Sharma, S.P. Alpay, A.M. Dongare, W.J. Brindley, R.J. Hebert, NPJ Comput. Mater. 4, 11 (2018)
S. Zhao, G.M. Stocks, Y. Zhang, Phys. Chem. Chem. Phys. 18, 24043 (2016)
W. Chen, X. Ding, Y. Feng, X. Liu, K. Liu, Z.P. Lu, D. Li, Y. Li, C.T. Liu, X.-Q. Chen, J. Mater. Sci. Technol. 34, 355 (2018)
O. El-Atwani, N. Li, M. Li, A. Devaraj, J.K.S. Baldwin, M.M. Schneider, D. Sobieraj, J.S. Wróbel, D. Nguyen-Manh, S.A. Maloy, E. Martinez, Sci. Adv. 5, eaav2002 (2019)
G. Henkelman, B.P. Uberuaga, H. Jónsson, J. Chem. Phys. 113, 9901 (2000)
G. Henkelman, H. Jónsson, J. Chem. Phys. 113, 9978 (2000)
A. Heyden, A.T. Bell, F.J. Keil, J. Chem. Phys. 123(22), 224101 (2005)
G. Henkelman, H. Jónsson, J. Chem. Phys. 111, 7010 (1999)
Q. Xu, A. Sharma, B. Comer, H. Huang, E. Chow, A.J. Medford, J.E. Pask, P. Suryanarayana, SoftwareX 15, 100709 (2021)
N. Anento, A. Serra, Y. Osetsky, Acta Mater. 132, 367 (2017)
D. Smirnova, A.Y. Kuksin, S. Starikov, J. Nucl. Mater. 458, 304 (2015)
D.S. Aidhy, C. Lu, K. Jin, H. Bei, Y. Zhang, L. Wang, W.J. Weber, Acta Mater. 99, 69 (2015)
D. Bacon, A. Calder, F. Gao, V. Kapinos, S. Wooding, Nucl. Instrum. Methods Phys. Res. B 102, 37 (1995)
R. Stoller, G. Odette, B. Wirth, J. Nucl. Mater. 251, 49 (1997)
Y.N. Osetsky, L.K. Béland, A.V. Barashev, Y. Zhang, Curr. Opin. Solid State Mater. Sci. 22, 65 (2018)
M.I. Mendelev, S. Han, W.-J. Son, G.J. Ackland, D.J. Srolovitz, Phys. Rev. B 76, 214105 (2007)
I.J. Beyerlein, M.J. Demkowicz, A. Misra, B. Uberuaga, Prog. Mater. Sci. 74, 125 (2015)
M. Demkowicz, L. Thilly, Acta Mater. 59, 7744 (2011)
W. Han, M.J. Demkowicz, N.A. Mara, E. Fu, S. Sinha, A.D. Rollett, Y. Wang, J.S. Carpenter, I.J. Beyerlein, A. Misra, Adv. Mater. 25, 6975 (2013)
J. Huang, M. Meyer, V. Pontikis, Philos. Mag. A 63, 1149 (1991)
X.-M. Bai, A.F. Voter, R.G. Hoagland, M. Nastasi, B.P. Uberuaga, Science 327, 1631 (2010)
X.-M. Bai, L.J. Vernon, R.G. Hoagland, A.F. Voter, M. Nastasi, B.P. Uberuaga, Phys. Rev. B 85, 214103 (2012)
O. Senninger, F. Soisson, E. Martínez, M. Nastar, C.-C. Fu, Y. Brechet, Acta Mater. 103, 1 (2016)
J. Hao, L. Casillas-Trujillo, H. Xu, Curr. Opin. Solid State Mater. Sci. 26, 101021 (2022)
Z. Yu, H. Xu, Commun. Mater. 4, 29 (2023)
H. Xu, R.E. Stoller, Y.N. Osetsky, D. Terentyev, Phys. Rev. Lett. 110, 265503 (2013)
A. Stukowski, D. Cereceda, T.D. Swinburne, J. Marian, Int. J. Plast. 65, 108 (2015)
C. Domain, C. Becquart, L. Malerba, J. Nucl. Mater. 335, 121 (2004)
H. Xu, Y.N. Osetsky, R.E. Stoller, J. Nucl. Mater. 423, 102 (2012)
S. Hayakawa, H. Xu, Comput. Mater. Sci. 200, 110785 (2021)
S. Hayakawa, J. Isaacs, H.R. Medal, H. Xu, Comput. Mater. Sci. 194, 110390 (2021)
H. Xu, R.E. Stoller, L.K. Béland, Y.N. Osetsky, Comput. Mater. Sci. 100, 135 (2015)
J. Chai, S. Jin, Z. Yu, H. Xu, G.-H. Lu, J. Mater. Sci. Technol. 93, 169 (2021)
V. Vitek, Philos. Mag. 84, 415 (2004)
D.L. Medlin, N. Yang, C.D. Spataru, L. Hale, Y. Mishin, Nat. Commun. 10, 1820 (2019)
C. Woodward, D. Trinkle, L. Hector Jr., D. Olmsted, Phys. Rev. Lett. 100, 045507 (2008)
S. Yadav, R. Ramprasad, A. Misra, X.-Y. Liu, Acta Mater. 74, 268 (2014)
Y. Si, Y. Zhang, D. Chen, J.L. Wormald, B.S. Anglin, D.L. McDowell, T. Zhu, J. Mech. Phys. Solids 178, 105359 (2023)
F. Nabarro, Proc. Phys. Soc. 59, 256 (1947)
V. Vitek, F. Kroupa, Philos. Mag. 19, 265 (1969)
A.S.K. Mohammed, O.K. Celebi, H. Sehitoglu, Acta Mater. 233, 117989 (2022)
V.V. Bulatov, E. Kaxiras, Phys. Rev. Lett. 78, 4221 (1997)
G. Liu, X. Cheng, J. Wang, K. Chen, Y. Shen, Int. J. Plast. 90, 156 (2017)
W. Ren, E. Vanden-Eijnden, J. Chem. Phys. 126, 164103 (2007)
C.R. Weinberger, A.T. Jennings, K. Kang, J.R. Greer, J. Mech. Phys. Solids 60, 84 (2012)
T. Zhu, J. Li, A. Samanta, A. Leach, K. Gall, Phys. Rev. Lett. 100, 025502 (2008)
M. Guziewski, H. Yu, C.R. Weinberger, “Modeling Dislocation Nucleation in Nanocrystals,” in Multiscale Materials Modeling for Nanomechanics, ed. by C.R. Weinberger, G.J. Tucker (Springer, Cham, 2016), p. 373
R. Zhang, J. Wang, I. Beyerlein, A. Misra, T. Germann, Acta Mater. 60, 2855 (2012)
R. Zhang, J. Wang, I. Beyerlein, T. Germann, Scr. Mater. 65, 1022 (2011)
A.M.Z. Tan, Z. Li, H. Gao, Phys. Rev. Mater. 7, 053601 (2023)
P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)
S. Ryu, K. Kang, W. Cai, J. Mater. Res. 26, 2335 (2011)
T. Zhu, J. Li, S. Yip, “Atomistic Reaction Pathway Sampling: The Nudged Elastic Band Method and Nanomechanics Applications,” in Nano and Cell Mechanics: Fundamentals and Frontiers, 1st edn., chap. 12, Microsystem and Nanotechnology Series, ed. by H.D. Espinosa, G. Bao (Wiley, Chichester, 2013), p. 311
V.G. Sursaeva, S. Protasova, B.B. Straumal, Defect Diffus. Forum 192, 15 (2001)
G. Esteban-Manzanares, R. Santos-Güemes, I. Papadimitriou, E. Martínez, J. LLorca, Acta Mater. 184, 109 (2020)
S. Saroukhani, L. Nguyen, K. Leung, C. Singh, D. Warner, J. Mech. Phys. Solids 90, 203 (2016)
Y. Wang, W. Cai, Proc. Natl. Acad. Sci. U.S.A. 120, e2222039120 (2023)
Q. Pan, H. Zhou, Q. Lu, H. Gao, L. Lu, Nature 551, 214 (2017)
J. Zhang, S. Chakraborty, S. Ghosh, Int. J. Multiscale Comput. Eng. 15(2), 99 (2017)
L. Xiong, G. Tucker, D.L. McDowell, Y. Chen, J. Mech. Phys. Solids 59, 160 (2011)
Z. Cheng, H. Zhou, Q. Lu, H. Gao, L. Lu, Science 362, eaau1925 (2018)
J. Wang, JOM 67, 1515 (2015)
R. Miller, E. Tadmor, R. Phillips, M. Ortiz, Model. Simul. Mater. Sci. Eng. 6, 607 (1998)
T. Shimokawa, T. Kinari, S. Shintaku, Phys. Rev. B 75, 144108 (2007)
L. Shilkrot, R.E. Miller, W. Curtin, Phys. Rev. Lett. 89, 025501 (2002)
M. Dewald, W. Curtin, Philos. Mag. 87, 4615 (2007)
S. Xu, R. Che, L. Xiong, Y. Chen, D.L. McDowell, Int. J. Plast. 72, 91 (2015)
S. Xu, L. Xiong, Y. Chen, D.L. McDowell, NPJ Comput. Mater. 2, 15016 (2016)
S. Xu, L. Xiong, Y. Chen, D.L. McDowell, Acta Mater. 122, 412 (2017)
S. Xu, L. Xiong, Y. Chen, D.L. McDowell, JOM 69, 814 (2017)
S. Xu, D.L. McDowell, I.J. Beyerlein, Acta Mater. 174, 160 (2019)
L. Xiong, J. Rigelesaiyin, X. Chen, S. Xu, D.L. McDowell, Y. Chen, Acta Mater. 104, 143 (2016)
X. Chen, W. Li, L. Xiong, Y. Li, S. Yang, Z. Zheng, D.L. McDowell, Y. Chen, Acta Mater. 136, 355 (2017)
V.V. Bulatov, L.L. Hsiung, M. Tang, A. Arsenlis, M.C. Bartelt, W. Cai, J.N. Florando, M. Hiratani, M. Rhee, G. Hommes, Nature 440, 1174 (2006)
H.M. Zbib, T.A. Khraishi, “Dislocation Dynamics,” in Handbook of Materials Modeling: Methods, ed. by S. Yip (Springer, Dordrecht, 2005), p. 1097
N. Ghoniem, S.-H. Tong, L. Sun, Phys. Rev. B 61, 913 (2000)
J.R. Mianroodi, B. Svendsen, J. Mech. Phys. Solids 77, 109 (2015)
V. Taupin, L. Capolungo, C. Fressengeas, M. Upadhyay, B. Beausir, Int. J. Solids Struct. 71, 277 (2015)
T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, J. Mech. Phys. Solids 63, 167 (2014)
S. Xia, A. El-Azab, Model. Simul. Mater. Sci. Eng. 23, 055009 (2015)
J.P. Hirth, G. Hirth, J. Wang, Proc. Natl. Acad. Sci. U.S.A. 117, 196 (2020)
J.P. Hirth, D. Xie, G. Hirth, J. Wang, Proc. Natl. Acad. Sci. U.S.A. 120, e2215085120 (2023)
L. Capolungo, V. Taupin, Mater. Theory 3, 2 (2019)
C. Fressengeas, V. Taupin, Metals 10, 1517 (2020)
J. Hirth, J. Wang, C. Tomé, Prog. Mater. Sci. 83, 417 (2016)
M. Gong, S. Xu, D. Xie, S. Wang, J. Wang, C. Schuman, J.-S. Lecomte, Acta Mater. 164, 776 (2019)
M. Gong, H. Ma, K. Yang, Y. Liu, J.-F. Nie, J. Wang, NPJ Comput. Mater. 8, 168 (2022)
G. Liu, H. Mo, J. Wang, Y. Shen, Acta Mater. 202, 399 (2021)
J. Hirth, R. Pond, R. Hoagland, X.-Y. Liu, J. Wang, Prog. Mater. Sci. 58, 749 (2013)
J. Wang, R. Zhang, C. Zhou, I.J. Beyerlein, A. Misra, J. Mater. Res. 28, 1646 (2013)
J. Wang, R. Zhang, C. Zhou, I.J. Beyerlein, A. Misra, Int. J. Plast. 53, 40 (2014)
I.J. Beyerlein, J. Wang, R. Zhang, Acta Mater. 61, 7488 (2013)
J. Wang, A. Misra, R. Hoagland, J. Hirth, Acta Mater. 60, 1503 (2012)
M.D. Sangid, T. Ezaz, H. Sehitoglu, I.M. Robertson, Acta Mater. 59, 283 (2011)
H.J. Chu, J. Wang, I.J. Beyerlein, E. Pan, Int. J. Plast. 41, 1 (2013)
O.K. Celebi, A.S.K. Mohammed, J.A. Krogstad, H. Sehitoglu, Int. J. Plast. 148, 103141 (2022)
Q. Zhu, Q. Huang, C. Guang, X. An, S.X. Mao, W. Yang, Z. Zhang, H. Gao, H. Zhou, J. Wang, Nat. Commun. 11, 3100 (2020)
J. Wang, A. Misra, J. Hirth, Phys. Rev. B 83, 064106 (2011)
Y. Gu, Z. Li, H. Gao, JOM 75, 1405 (2023)
S. Shao, C. Zhou, A. Misra, J. Wang, “Mesoscale Modeling of Dislocation-Interactions in Multilayered Materials,” in Handbook of Materials Modeling: Methods: Theory and Modeling, ed. by W. Andreoni, S. Yip (Springer, Cham, 2020), p. 1049
G. Liu, D. Xie, S. Wang, A. Misra, J. Wang, Int. J. Plast. 121, 134 (2019)
J. Wang, S. Yadav, J. Hirth, C. Tomé, I. Beyerlein, Mater. Res. Lett. 1, 126 (2013)
J. Wang, J. Hirth, C. Tomé, Acta Mater. 57, 5521 (2009)
M. Gong, J.P. Hirth, Y. Liu, Y. Shen, J. Wang, Mater. Res. Lett. 5, 449 (2017)
L. Jiang, M. Gong, J. Wang, Z. Pan, X. Wang, D. Zhang, Y.M. Wang, J. Ciston, A.M. Minor, M. Xu, Nat. Commun. 13, 20 (2022)
Y. Liu, P. Tang, M. Gong, R. McCabe, J. Wang, C. Tomé, Nat. Commun. 10, 3308 (2019)
S. Wang, M. Gong, R.J. McCabe, L. Capolungo, J. Wang, C.N. Tomé, Sci. Adv. 6, eaaz2600 (2020)
H. Wang, P. Wu, J. Wang, C. Tomé, Int. J. Plast. 49, 36 (2013)
H. Babaei, V.I. Levitas, J. Mech. Phys. Solids 144, 104114 (2020)
A. Pineau, G. Guillemot, G. Reinhart, G. Regula, N. Mangelinck-Noël, C.-A. Gandin, Acta Mater. 191, 230 (2020)
D.E. Spearot, V. Taupin, K. Dang, L. Capolungo, Mech. Mater. 143, 103314 (2020)
J. Cheng, J. Shen, R.K. Mishra, S. Ghosh, Acta Mater. 149, 142 (2018)
E. Popova, Y. Staraselski, A. Brahme, R. Mishra, K. Inal, Int. J. Plast. 66, 85 (2015)
C. Liu, P. Shanthraj, M. Diehl, F. Roters, S. Dong, J. Dong, W. Ding, D. Raabe, Int. J. Plast. 106, 203 (2018)
H. Mo, G. Liu, Y. Mao, Y. Shen, J. Wang, Int. J. Plast. 158, 103441 (2022)
D.L. McDowell, “Multiscale Modeling of Interfaces, Dislocations, and Dislocation Field Plasticity,” in Mesoscale Models: From Micro-Physics to Macro-Interpretation, 1st edn., ed. by S. Mesarovic, S. Forest, H. Zbib (Springer, Cham, 2019), p. 195
D. Dragoni, T.D. Daff, G. Csányi, N. Marzari, Phys. Rev. Mater. 2, 013808 (2018)
V.L. Deringer, M.A. Caro, G. Csányi, Adv. Mater. 31, 1902765 (2019)
A. Venkatraman, D.L. McDowell, S.R. Kalidindi, Int. J. Plast. 154, 103289 (2022)
A. Venkatraman, S. Mohan, V.R. Joseph, D.L. McDowell, S.R. Kalidindi, Model. Simul. Mater. Sci. Eng. 31, 044001 (2023)
Q. Zhao, Q. Zhu, Z. Zhang, X. Li, Q. Huang, W. Yang, J. Wang, H. Gao, H. Zhou, J. Mech. Phys. Solids 181, 105455 (2023)
Acknowledgments
J.W. acknowledges support from US DOE, Office of Science, Office of Basic Energy Sciences with the Grant No. DE-SC0016808. H.G. acknowledges support from a startup grant from Nanyang Technological University, Singapore, and a Programmatic Programme Grant No. M22L2b0111 from A*STAR, Singapore.
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This study was funded by the Office of Science (Grant No. DE-SC0016808).
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H.X. drafted the section of Point defects; H.G., D.L.M., and J.W. drafted the other sections. All authors wrote the section of Perspective, as well as commented on and revised the whole manuscript.
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Wang, J., Xu, H., Gao, H. et al. Multiscale modeling of crystal defects in structural materials. MRS Bulletin 49, 224–235 (2024). https://doi.org/10.1557/s43577-023-00647-9
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DOI: https://doi.org/10.1557/s43577-023-00647-9