journal article·2025-12-11Open access

Bayesian Optimization of Grain-Boundary Segregation in High-Entropy Alloys

Shimanta Das, Noah Oyeniran, Joshua Walter, Aidan Gesch, Chongze Hu

npj Computational Materials· Volume 11· Issue 1

Abstract

Abstract The concurrent segregation of multiple solute elements at grain boundaries (GBs), also known as co-segregation, is a pervasive interfacial behavior that governs microstructural evolution and influences many properties of high-entropy alloys (HEAs). However, accurately predicting co-segregation behavior in HEAs is a challenging task due to the vast compositional space and complex interactions among multiple solute elements. In this paper, we developed a scalarization-based Bayesian optimization (SBO) framework integrated with high-throughput atomistic simulations to efficiently explore and optimize the large compositional space of CrMnFeCoNi HEAs for targeted co-segregation behavior and other desirable interfacial properties. Specifically, Thompson sampling is adopted to explore the input compositional space and identify HEA candidates representing two extremes: the strongest and weakest co-segregation of Cr and Mn at CrMnFeCoNi GBs. These SBO-predicted segregation extremes are subsequently validated by hybrid molecular dynamics/Monte Carlo simulations and first-principles calculations. Furthermore, electronic structure calculations demonstrate that the co-segregation of Cr and Mn can be ascribed to the hybridization of their d valence electrons promoted by the presence of Fe. While this SBO framework focuses on segregation behavior, it can be easily extended to optimize a wide range of interfacial properties in multicomponent systems. This study establishes a new paradigm for designing advanced HEAs through interfacial property optimization.
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Research context

OpenAlex topics: High Entropy Alloys Studies · Additive Manufacturing Materials and Processes · High Temperature Alloys and Creep

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (87)

Show source-provided references
1. George, E. P., Raabe, D. & Ritchie, R. O. High-entropy alloys. Nat. Rev. Mater. 4, 515–534 (2019).10.1038/s41578-019-0121-4 ↗
2. Ye, Y. F., Wang, Q., Lu, J., Liu, C. T. & Yang, Y. High-entropy alloy: challenges and prospects. Mater. Today 19, 349–362 (2016).10.1016/j.mattod.2015.11.026 ↗
3. Yeh, J.-W. Recent progress in high entropy alloys. Ann. Chim. Sci. Mat. 31, 633–648 (2006).10.3166/acsm.31.633-648 ↗
4. Cantor, B., Chang, I. T. H., Knight, P. & Vincent, A. J. B. Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 375–377, 213–218 (2004).10.1016/j.msea.2003.10.257 ↗
5. Zhang, Y. et al. Microstructures and properties of high-entropy alloys. Prog. Mater. Sci. 61, 1–93 (2014).10.1016/j.pmatsci.2013.10.001 ↗
6. Dada, M., Popoola, P., Adeosun, S. & Mathe, N. High entropy alloys for aerospace applications. In Aerodynamics (2021).10.5772/intechopen.84982 ↗
7. Dixit, S. et al. Refractory high-entropy alloy coatings for high-temperature aerospace and energy applications. J. Therm. Spray. Technol. 31, 1021–1031 (2022).10.1007/s11666-022-01324-0 ↗
8. Xie, P. et al. Highly efficient decomposition of ammonia using high-entropy alloy catalysts. Nat. Commun. 10, 4011 (2019).10.1038/s41467-019-11848-9 ↗
9. Sun, Y. & Dai, S. High-entropy materials for catalysis: A new frontier. Sci. Adv. 7, eabg1600 (2021).10.1126/sciadv.abg1600 ↗
10. Liu, Y.-H. et al. Toward controllable and predictable synthesis of high-entropy alloy nanocrystals. Sci. Adv. 9, eadf9931 (2023).10.1126/sciadv.adf9931 ↗
11. Wang, X., Guo, W. & Fu, Y. High-entropy alloys: emerging materials for advanced functional applications. J. Mater. Chem. A 9, 663–701 (2021).10.1039/D0TA09601F ↗
12. Bai, J., Jin, X., Yang, H. & Qiao, J. A low melting high entropy alloy with conformal electroconductivity for flexible electronic circuits. J. Alloy. Compd. 919, 165736 (2022).10.1016/j.jallcom.2022.165736 ↗
13. Ahmady, A. R. et al. High entropy alloy coatings for biomedical applications: A review. Smart Mater. Manuf. 1, 100009 (2023).
14. Castro, D., Jaeger, P., Baptista, A. C. & Oliveira, J. P. An overview of high-entropy alloys as biomaterials. Metals 11, 648 (2021).10.3390/met11040648 ↗
15. Wang, W. et al. Novel Ti-Zr-Hf-Nb-Fe refractory high-entropy alloys for potential biomedical applications. J. Alloy. Compd. 906, 164383 (2022).10.1016/j.jallcom.2022.164383 ↗
16. Yeh, J. W., Chen, Y. L., Lin, S. J. & Chen, S. K. High-entropy alloys-A new era of exploitation. Materials science forum. 560, 1–9 (2007).10.4028/www.scientific.net/MSF.560.1 ↗
17. Lu, P. et al. Computational design and initial corrosion assessment of a series of non-equimolar high entropy alloys. Scr. Mater. 172, 12–16 (2019).10.1016/j.scriptamat.2019.07.003 ↗
18. Gorsse, S., Couzinié, J.-P. & Miracle, D. B. From high-entropy alloys to complex concentrated alloys. Compt. Rend. Phys. 19, 721–736 (2018).10.1016/j.crhy.2018.09.004 ↗
19. Gorsse, S., Miracle, D. B. & Senkov, O. N. Mapping the world of complex concentrated alloys. Acta Mater. 135, 177–187 (2017).10.1016/j.actamat.2017.06.027 ↗
20. Oh, H. S. et al. Engineering atomic-level complexity in high-entropy and complex concentrated alloys. Nat. Commun. 10, 2090 (2019).10.1038/s41467-019-10012-7 ↗
21. Chen, Y. et al. A focused review on engineering application of multi-principal element alloy. Front. Mater. 8, 816309 (2022).10.3389/fmats.2021.816309 ↗
22. Wang, L. & Ouyang, B. Phase selection rules of multi-principal element alloys. Adv. Mater. 36, 2307860 (2024).10.1002/adma.202307860 ↗
23. Borg, C. K. H. et al. Expanded dataset of mechanical properties and observed phases of multi-principal element alloys. Sci. Data 7, 430 (2020).10.1038/s41597-020-00768-9 ↗
24. Cantwell, P. R. et al. Grain boundary complexion transitions. Annu. Rev. Mater. Res. 50, 465–492 (2020).10.1146/annurev-matsci-081619-114055 ↗
25. Cantwell, P. R. et al. Grain boundary complexions. Acta Mater. 62, 1–48 (2014).10.1016/j.actamat.2013.07.037 ↗
26. Dillon, S. J., Tang, M., Carter, W. C. & Harmer, M. P. Complexion: A new concept for kinetic engineering in materials science. Acta Mater. 55, 6208–6218 (2007).10.1016/j.actamat.2007.07.029 ↗
27. Han, J., Thomas, S. L. & Srolovitz, D. J. Grain-boundary kinetics: A unified approach. Prog. Mater. Sci. 98, 386–476 (2018).10.1016/j.pmatsci.2018.05.004 ↗
28. Hu, C., Dingreville, R. & Boyce, B. L. Computational modeling of grain boundary segregation: A review. Comput. Mater. Sci. 232, 112596 (2024).10.1016/j.commatsci.2023.112596 ↗
29. Lei, T., Hu, C., Zhang, Q. & Wang, X. Elemental segregation and solute effects on mechanical properties and processing of vanadium alloys: A review. Metals 15, 96 (2025).10.3390/met15010096 ↗
30. Hu, C. & Luo, J. First-order grain boundary transformations in Au-doped Si: Hybrid Monte Carlo and molecular dynamics simulations verified by first-principles calculations. Scr. Mater. 158, 11–15 (2019).10.1016/j.scriptamat.2018.08.017 ↗
31. Zhou, N., Hu, C. & Luo, J. Grain boundary segregation transitions and critical phenomena in binary regular solutions: A systematics of complexion diagrams with universal characters. Acta Mater. 221, 117375 (2021).10.1016/j.actamat.2021.117375 ↗
32. Yang, S., Zhou, N., Zheng, H., Ong, S. P. & Luo, J. First-order interfacial transformations with a critical point: Breaking the symmetry at a symmetric tilt grain boundary. Phys. Rev. Lett. 120, 085702 (2018).10.1103/PhysRevLett.120.085702 ↗
33. Tang, M., Carter, W. C. & Cannon, R. M. Grain boundary transitions in binary alloys. Phys. Rev. Lett. 97, 075502 (2006).10.1103/PhysRevLett.97.075502 ↗
34. Luo, J. & Zhou, N. High-entropy grain boundaries. Commun. Mater. 4, 7 (2023).10.1038/s43246-023-00335-w ↗
35. Raabe, D. et al. Grain boundary segregation engineering in metallic alloys: A pathway to the design of interfaces. Curr. Opin. Solid State Mater. Sci. 18, 253–261 (2014).10.1016/j.cossms.2014.06.002 ↗
36. Wang, L. & Kamachali, R. D. Calphad integrated grain boundary co-segregation design: Towards safe high-entropy alloys. J. Alloy. Compd. 933, 167717 (2023).10.1016/j.jallcom.2022.167717 ↗
37. Xing, W., Kalidindi, A. R., Amram, D. & Schuh, C. A. Solute interaction effects on grain boundary segregation in ternary alloys. Acta Mater. 161, 285–294 (2018).10.1016/j.actamat.2018.09.005 ↗
38. Maldonado, A. J., Misra, K. P. & Misra, R. D. K. Grain boundary segregation in a high entropy alloy. Mater. Tech. 38, 2221959 (2023).10.1080/10667857.2023.2221959 ↗
39. Li, L., Kamachali, R. D., Li, Z. & Zhang, Z. Grain boundary energy effect on grain boundary segregation in an equiatomic high-entropy alloy. Phys. Rev. Mater. 4, 053603 (2020).10.1103/PhysRevMaterials.4.053603 ↗
40. Li, Y. J., Savan, A., Kostka, A., Stein, H. S. & Ludwig, A. Accelerated atomic-scale exploration of phase evolution in compositionally complex materials. Mater. Horiz. 5, 86–92 (2018).10.1039/C7MH00486A ↗
41. Ming, K., Li, L., Li, Z., Bi, X. & Wang, J. Grain boundary decohesion by nanoclustering Ni and Cr separately in CrMnFeCoNi high-entropy alloys. Sci. Adv. 5, eaay0639 (2019).10.1126/sciadv.aay0639 ↗
42. Wynblatt, P. & Chatain, D. Modeling grain boundary and surface segregation in multicomponent high-entropy alloys. Phys. Rev. Mater. 3, 054004 (2019).10.1103/PhysRevMaterials.3.054004 ↗
43. Ma, S. et al. Mechanism of elemental segregation around extended defects in high-entropy alloys and its effect on mechanical properties. Acta Mater. 264, 119537 (2024).10.1016/j.actamat.2023.119537 ↗
44. Yu, Z. et al. Segregation-induced ordered superstructures at general grain goundaries in a nickel-bismuth alloy. Science 358, 97–101 (2017).10.1126/science.aam8256 ↗
45. Yang, C. et al. Interfacial superstructures and chemical bonding transitions at metal-ceramic interfaces. Sci. Adv. 7, eabf6667 (2021).10.1126/sciadv.abf6667 ↗
46. Luo, Z. et al. A highly asymmetric interfacial superstructure in WC: Expanding the classic grain boundary segregation and new complexion theories. Mater. Horiz. 7, 173–180 (2020).10.1039/C9MH00969H ↗
47. Luo, J. Grain boundary segregation models for high-entropy alloys: Theoretical formulation and application to elucidate high-entropy grain boundaries. J. Appl. Phys.135 (2024).10.1063/5.0200669 ↗
48. Zhou, N., Hu, T. & Luo, J. Grain boundary complexions in multicomponent alloys: Challenges and opportunities. Curr. Opin. Solid State Mater. Sci. 20, 268–277 (2016).10.1016/j.cossms.2016.05.001 ↗
49. Wagih, M. & Schuh, C. A. Learning grain-boundary segregation: From first principles to polycrystals. Phys. Rev. Lett. 129, 046102 (2022).10.1103/PhysRevLett.129.046102 ↗
50. Huber, L., Hadian, R., Grabowski, B. & Neugebauer, J. A machine learning approach to model solute grain boundary segregation. npj Comput. Mater. 4, 64 (2018).10.1038/s41524-018-0122-7 ↗
51. Scheiber, D., Razumovskiy, V., Peil, O. & Romaner, L. High-throughput first-principles calculations and machine learning of grain boundary segregation in metals. Adv. Eng. Mater. 26, 2400269 (2024).10.1002/adem.202400269 ↗
52. Wagih, M., Naunheim, Y., Lei, T. & Schuh, C. A. Designing for cooperative grain boundary segregation in multicomponent alloys. Proc. Natl. Acad. Sci. U.S.A. 122, e2511930 (2025).10.1073/pnas.2511930122 ↗
53. Wagih, M., Larsen, P. M. & Schuh, C. Learning grain boundary segregation energy spectra in polycrystals. Nat. Commun. 11, 6376 (2020).10.1038/s41467-020-20083-6 ↗
54. Hu, C., Li, Y., Yu, Z. & Luo, J. Computing grain boundary diagrams of thermodynamic and mechanical properties. npj Comput. Mater. 7, 1–12 (2021).10.1038/s41524-021-00625-2 ↗
55. Das, S. & Hu, C. Deciphering grain-boundary composition-structure-mechanical property relationships via interfacial property diagrams. Mech. Mater. 105362 (2025).10.1016/j.mechmat.2025.105362 ↗
56. Hu, C., Zuo, Y., Chen, C., Ong, S. & Luo, J. Genetic algorithm-guided deep learning of grain boundary diagrams: Addressing the challenge of five degrees of freedom. Mater. Today 38, 49–57 (2020).10.1016/j.mattod.2020.03.004 ↗
57. Hu, C., Medlin, L. D. & Dingreville, R. Stability and mobility of disconnections in solute atmospheres: Insights from interfacial defect diagrams. Phys. Rev. Lett. 134, 016202 (2025).10.1103/PhysRevLett.134.016202 ↗
58. Hu, C. & Luo, J. Data-driven prediction of grain boundary segregation and disordering in high-entropy alloys in a 5D space. Mater. Horiz. 9, 1023–1035 (2022).10.1039/D1MH01204E ↗
59. Mclean, D.Grain Boundary in Metals, vol. 181 (Oxford University Press, 1958).10.1038/181976b0 ↗
60. Khatamsaz, D. et al. A physics informed bayesian optimization approach for material design: application to niti shape memory alloys. npj Computational Mater. 9, 221 (2023).10.1038/s41524-023-01173-7 ↗
61. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).10.1006/jcph.1995.1039 ↗
62. Thompson, A. P. et al. LAMMPS-A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).10.1016/j.cpc.2021.108171 ↗
63. Ogawa, H. Gbstudio: A builder software on periodic models of csl boundaries for molecular simulation. Mater. Trans. 47, 2706–2710 (2006).10.2320/matertrans.47.2706 ↗
64. Grimmer, H., Bollmann, W. T. & Warrington, D. H. Coincidence-site lattices and complete pattern-shift in cubic crystals. Acta Cryst. 30, 197–207 (1974).10.1107/S056773947400043X ↗
65. Choi, W.-M., Jo, Y. H., Sohn, S. S., Lee, S. & Lee, B.-J. Understanding the physical metallurgy of the CoCrFeMnNi high-entropy alloy: an atomistic simulation study. npj Comput. Mater. 4 (2018).10.1038/s41524-017-0060-9 ↗
66. Wynblatt, P. & Chatain, D. Modeling grain boundary and surface segregation in multicomponent high-entropy alloys. Phys. Rev. Mater. 3 (2019).10.1103/PhysRevMaterials.3.054004 ↗
67. Stukowski, A. Visualization and analysis of atomistic simulation data with OVITO-the open visualization tool. Model Simul. Mater. Sci. Eng. 18, 015012 (2009).10.1088/0965-0393/18/1/015012 ↗
68. Jones, D. R., Schonlau, M. & Welch, W. J. Efficient global optimization of expensive black-box functions. J. Glob. Opt. 13, 455–492 (1998).10.1023/A:1008306431147 ↗
69. Kotthoff, L., Wahab, H. & Johnson, P. Bayesian optimization in materials science: A survey. arXiv (2021). 2108.00002.
70. Xu, P. et al. Multi-objective optimization in machine learning assisted materials design and discovery. J. Mater. Inf. 5, N–A (2025).10.20517/jmi.2024.108 ↗
71. Startt, J., McCarthy, M. J., Wood, M. A., Donegan, S. & Dingreville, R. Bayesian blacksmithing: discovering thermomechanical properties and deformation mechanisms in high-entropy refractory alloys. npj Computat. Mater. 10, 164 (2024).10.1038/s41524-024-01353-z ↗
72. Shahriari, B., Swersky, K., Wang, Z., Adams, R. P. & de Freitas, N. Taking the human out of the loop: A review of bayesian optimization. Proc. IEEE 104, 148–175 (2016).10.1109/JPROC.2015.2494218 ↗
73. Rasmussen, C. E. & Williams, C. K. I.Gaussian Processes for Machine Learning (The MIT Press, 2005).10.7551/mitpress/3206.001.0001 ↗
74. Thompson, W. R. On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika 25, 285 (1933).10.1093/biomet/25.3-4.285 ↗
75. Chapelle, O. & Li, L. An empirical evaluation of thompson sampling. In Advances in Neural Information Processing Systems, vol. 24, 2249 (2011).
76. Agrawal, S. & Goyal, N. Analysis of thompson sampling for the multi-armed bandit problem. In Proceedings of the 25th Annual Conference on Learning Theory, vol. 23 of Proceedings of Machine Learning Research, 39.1–39.26 (2012).
77. Chugh, T. Scalarizing functions in bayesian multiobjective optimization. In 2020 IEEE Congress on Evolutionary Computation (CEC), 1–8 (2020).10.1109/CEC48606.2020.9185706 ↗
78. Satria Palar, P., Rizki Zuhal, L. & Shimoyama, K. Gaussian process surrogate model with composite kernel learning for engineering design. AIAA J. 58, 1864–1880 (2020).10.2514/1.J058807 ↗
79. Ghoreishi, S. F., Molkeri, A., Srivastava, A., Arroyave, R. & Allaire, D. Multi-information source fusion and optimization to realize icme: Application to dual-phase materials. J. Mech. Des.140 (2018).10.1115/1.4041034 ↗
80. Ghoreishi, S. F. & Allaire, D. Multi-information source constrained bayesian optimization. Struct. Multidis. Optim. 59, 977–991 (2018).10.1007/s00158-018-2115-z ↗
81. Liu, Q., Du, S., van Wyk, B. J. & Sun, Y. Niching particle swarm optimization based on euclidean distance and hierarchical clustering for multimodal optimization. Nonlinear Dyn. 99, 2459–2477 (2019).10.1007/s11071-019-05414-7 ↗
82. Dudani, S. A. The distance-weighted k-nearest-neighbor rule. IEEE Trans. Syst. Man. Cybern. SMC-6, 325–327 (1976).10.1109/TSMC.1976.5408784 ↗
83. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).10.1016/0927-0256(96)00008-0 ↗
84. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).10.1103/PhysRevB.47.558 ↗
85. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).10.1103/PhysRevB.50.17953 ↗
86. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).10.1103/PhysRevLett.77.3865 ↗
87. Grimme, S. Semiempirical gga-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).10.1002/jcc.20495 ↗