Nanoscale fluctuation of stacking fault energy strengthens multi-principal element alloys

doi:10.1016/j.jmst.2023.01.042

Abstract

Abstract: Chemical randomness and the associated energy fluctuation are essential features of multi-principal element alloys (MPEAs). Due to these features, nanoscale stacking fault energy (SFE) fluctuation is a natural and independent contribution to strengthening MPEAs. However, existing models for conventional alloys (i.e., alloys with one principal element) cannot be applied to MPEAs. The extreme values of SFEs required by such models are unknown for MPEAs, which need to calculate the nanoscale volume relevant to the SFE fluctuation. In the present work, we developed an analytic model to evaluate the strengthening effect through the SFE fluctuation, profuse in MPEAs. The model has no adjustable parameters, and all parameters can be determined from experiments and ab initio calculations. This model explains available experimental observations and provides insightful guidance for designing new MPEAs based on the SFE fluctuation. It generally applies to MPEAs in random states and with chemical short-range order.

Key words: Nanoscale energy fluctuation, Staking fault energy, Chemical short-range order, Multi-principal element alloy, Mechanism

Zongrui Pei, Markus Eisenbach, Peter K. Liaw, Mingwei Chen. Nanoscale fluctuation of stacking fault energy strengthens multi-principal element alloys[J]. J. Mater. Sci. Technol., 2023, 158: 218-225.

References

[1] X. Liu, J. Zhang, Z. Pei, Prog. Mater. Sci. 131(2022) 101018.
[2] E.P. George, D. Raabe, R.O. Ritchie, Nat. Rev. Mater. 4 (8) (2019) 515-534.
[3] J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, C.-H. Tsau, S.-Y. Chang, Adv. Eng. Mater. 6 (5) (2004) 299-303.
[4] B. Cantor, I. Chang, P. Knight, A. Vincent, Mater. Sci. Eng.A 375-377(2004) 213-218.
[5] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Prog. Mater. Sci. 61(2014) 1-93.
[6] M.C. Gao, J.-W. Yeh, P.K. Liaw, Y. Zhang, High-Entropy Alloys, Springer Interna- tional Publishing, 2016.
[7] E.P. George, W. Curtin, C.C. Tasan, Acta Mater. 188(2020) 435-474.
[8] Q.-J. Li, H. Sheng, E. Ma, Nat. Commun. 10 (1) (2019) 1-11.
[9] X. Liu, Z. Pei, M. Eisenbach, Mater. Des. 180(2019) 107955.
[10] R. Zhang, S. Zhao, J. Ding, Y. Chong, T. Jia, C. Ophus, M. Asta, R.O.Ritchie A. M. Minor, Nature 581 (7808) (2020) 283-287.
[11] Q. Ding, Y. Zhang, X. Chen, X. Fu, D. Chen, S. Chen, L. Gu, F. Wei, H. Bei, Y. Gao M. Wen, J. Li, Z. Zhang, T. Zhu, R.O. Ritchie, Q. Yu, Nature 574 (7777) (2019) 223-227.
[12] X. Chen, Q. Wang, Z. Cheng, M. Zhu, H. Zhou, P. Jiang, L. Zhou, Q. Xue, F. Yuan, J. Zhu, X. Wu, E. Ma, Nature 592 (7856) (2021) 712-716.
[13] H. Suzuki, J. Phys. Soc. Jpn. 17 (2) (1962) 322-325.
[14] G. Gottstein, Springer Science & Business Media, 2013.
[15] J.A. Yasi, L.G. Hector Jr, D.R. Trinkle, Acta Mater. 58 (17) (2010) 5704-5713.
[16] Z. Pei, B. Dutta, F. Körmann, M. Chen, Phys. Rev. Lett. 126 (25) (2021) 255502.
[17] Y. Zeng, X. Cai, M. Koslowski, Acta Mater. 164(2019) 1-11.
[18] L. Zhang, Y. Xiang, J. Han, D.J. Srolovitz, Acta Mater. 166(2019) 424-434.
[19] B. Yin, S. Yoshida, N. Tsuji, W. Curtin, Nat. Commun. 11 (1) (2020) 1-7.
[20] N.L. Okamoto, S. Fujimoto, Y. Kambara, M. Kawamura, Z.M. Chen, H. Mat- sunoshita, K.Tanaka, H. Inui, E.P. George, Sci. Rep. 6(2016) 35863.
[21] Z. Pei, Scr. Mater. 162(2019) 503-506.
[22] Q. Ding, Y. Zhang, X. Chen, X. Fu, D. Chen, S. Chen, L. Gu, F. Wei, H. Bei, Y. Gao, M. Wen, J. Li, Z. Zhang, T. Zhu, R.O. Ritchie, Q. Yu, Nature 574 (7777) (2019) 223-227.
[23] Y. Wu, F. Zhang, X. Yuan, H. Huang, X. Wen, Y. Wang, M. Zhang, H. Wu, X. Liu H. Wang, S. Jiang, Z. Lu, J. Mater. Sci.Technol. 62(2021) 214-220.
[24] M. Shih, J. Miao, M. Mills, M. Ghazisaeidi, Nat. Commun. 12 (1) (2021) 1-10.
[25] S. Chen, Z.H. Aitken, S. Pattamatta, Z. Wu, Z.G. Yu, D.J. Srolovitz, P.K. Liaw, Y.-W. Zhang, Nat. Commun. 12 (1) (2021) 1-11.
[26] S. Yin, Y. Zuo, A. Abu-Odeh, H. Zheng, X.-G. Li, J. Ding, S.P. Ong, M. Asta, R.O. Ritchie, Nat. Commun. 12 (1) (2021) 1-14.
[27] S. Chen, Z.H. Aitken, S. Pattamatta, Z. Wu, Z.G. Yu, R. Banerjee, D.J. Srolovitz, P.K. Liaw, Y.-W. Zhang, Acta Mater. 206(2021) 116638.
[28] E. Antillon, C. Woodward, S. Rao, B. Akdim, T. Parthasarathy, Acta Mater. 190(2020) 29-42.
[29] S.D. Wang, X.J. Liu, Z.F. Lei, D.Y. Lin, F.G. Bian, C.M. Yang, M.Y. Jiao, Q. Du, H. Wang, Y. Wu, S.H. Jiang, Z.P. Lu, Phys. Rev. B 103 (2021) 104107.
[30] X. Liu, H. Zhao, H. Ding, D.-Y. Lin, F. Tian, Appl. Phys. Lett. 119 (13) (2021) 131904.
[31] P.B. Hirsch, A. Kelly, Philos. Magaz. A 12 (119) (1965) 881-900.
[32] E. Nembach, Scr. Metall. 20 (5) (1986) 763-768.
[33] C. Varvenne, A. Luque, W.A. Curtin, Acta Mater. 118(2016) 164-176.
[34] P. Hohenberg, W. Kohn, Phys. Rev. 136(1964) B864.
[35] W. Kohn, L.J. Sham, Phys. Rev. 140(1965) A1133.
[36] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169-11186.
[37] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77(1996) 3865-3868.
[38] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953-17979.
[39] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188-5192.
[40] S.S. Sohn, A. Kwiatkowski da Silva, Y. Ikeda, F. Körmann, W. Lu, W.S. Choi, B. Gault, D. Ponge, J. Neugebauer, D. Raabe, Adv. Mater. 31 (8) (2019) 1807142.
[41] A. Zaddach, C. Niu, C. Koch, D. Irving, JOM 65 (12) (2013) 1780-1789.
[42] G. Laplanche, A. Kostka, C. Reinhart, J. Hunfeld, G. Eggeler, E. George, Acta Mater 128 (2017) 292-303.
[43] S. Rao, B. Akdim, E. Antillon, C. Woodward, T. Parthasarathy, O. Senkov, Acta Mater. 168(2019) 222-236.
[44] J. Ding, Q. Yu, M. Asta, R.O. Ritchie, Proc. Natl. Acad. Sci. 115 (36) (2018) 8919-8924.
[45] Z. Pei, M. Eisenbach, S. Mu, G.M. Stocks, Comput. Phys. Commun. 235(2019) 95-101.
[46] S.N. Khan, M. Eisenbach, Phys. Rev. B 93 (2016) 024203.
[47] S. Zhao, Y. Osetsky, G.M. Stocks, Y. Zhang, npj Comput. Mater. 5(1) (2019) 1-7.
[48] A. Zunger, S.-H. Wei, L.G. Ferreira, J.E. Bernard, Phys. Rev. Lett. 65 (3) (1990) 353.
[49] D. Ma, M. Friák, J. von Pezold, J.Neugebauer, D. Raabe, Acta Mater. 98(2015) 367-376.
[50] G.P.M. Leyson, W.A. Curtin, L.G. Hector, C.F. Woodward, Nat. Mater. 9 (9) (2010) 750-755.
[51] A. Tehranchi, B. Yin, W. Curtin, Acta Mater. 151(2018) 56-66.
[52] C. Varvenne, G.P.M. Leyson, M. Ghazisaeidi, W.A. Curtin, Acta Mater 124 (2017) 660-683.
[53] Z. Pei, S. Zhang, Y. Lei, F. Zhang, M. Chen, Proc. Natl. Acad. Sci. 118 (51) (2021) e2114167118.
[54] P.M. Anderson, J.P. Hirth, J. Lothe, Theory of Dislocations, Cambridge University Press, 2017.
[55] D.C. Yang, Y.H. Jo, Y. Ikeda, F. Körmann, S.S. Sohn, J. Mater. Sci.Technol. 90(2021) 159-167.
[56] V. Gerold, H. Karnthaler, Acta Metall. 37 (8) (1989) 2177-2183.
[57] T. Neeraj, M. Mills, Mater. Sci. Eng. A 319 (2001) 415-419.
[58] I. Toda-Caraballo, P.E.R.-D. del Castillo, Acta Mater. 85(2015) 14-23.