Designing High-Entropy Alloys With Low Stacking Fault Energy Through Interpretable Machine Learning

Shuai Nie , Yixuan He , Haoxiang Liu , Xudong Liu , Haifeng Wang , Ziqing He , Menghao Yang

Materials Genome Engineering Advances ›› 2026, Vol. 4 ›› Issue (1) : e70043

PDF (5115KB)
Materials Genome Engineering Advances ›› 2026, Vol. 4 ›› Issue (1) :e70043 DOI: 10.1002/mgea.70043
RESEARCH ARTICLE
Designing High-Entropy Alloys With Low Stacking Fault Energy Through Interpretable Machine Learning
Author information +
History +
PDF (5115KB)

Abstract

Low stacking fault energy (SFE) CoCrFeNiMn-based high entropy alloys (HEAs) have garnered widespread attention due to their excellent mechanical properties. These outstanding mechanical properties result from multiple deformation mechanisms during tensile deformation, such as stacking faults, deformation twinning, and martensitic transformation. However, the vast and complex compositional space presents a significant challenge for the design of low SFE HEAs. To address this issue, this study developed an interpretable machine learning (ML) ensemble algorithm framework that integrates three high-accuracy ML models (multilayer perceptron regressor, support vector regressor, extreme gradient boosting regressor, R2 > 0.9). In the alloy composition screening stage, the Valence Electron Concentration (VEC) and the proposed ML scoring parameter (Score = A*Mean + B*Std) were employed to constrain the phase composition and screen for low SFE alloy compositions. Ultimately, multiple No-BCC phase CoCrFeNiMn-based HEAs with twinning-induced plasticity/transformation-induced plasticity effects were successfully designed. To overcome the challenge of insufficient model accuracy in data-driven design, correlation-based and importance-based feature selection methods were combined. This approach efficiently processed additional descriptors generated from atomic compositions, improving model accuracy by 13%. Furthermore, the Shapley additive explanation method revealed the influence of individual elements on the SFE, providing valuable guidance for designing low-SFE HEAs.

Cite this article

Download citation ▾
Shuai Nie, Yixuan He, Haoxiang Liu, Xudong Liu, Haifeng Wang, Ziqing He, Menghao Yang. Designing High-Entropy Alloys With Low Stacking Fault Energy Through Interpretable Machine Learning. Materials Genome Engineering Advances, 2026, 4 (1) : e70043 DOI:10.1002/mgea.70043

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

J. W. Yeh, S. K. Chen, S. J. Lin, et al., “Nanostructured High-Entropy Alloys With Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes,” Advanced Engineering Materials 6, no. 5 (2004): 299–303, https://doi.org/10.1002/adem.200300567.

[2]

B. Cantor, I. T. H. Chang, P. Knight, and A. Vincent, “Microstructural Development in Equiatomic Multicomponent Alloys,” Materials Science and Engineering A 375–377 (2004): 213–218, https://doi.org/10.1016/j.msea.2003.10.257.

[3]

O. El-Atwani, N. Li, M. Li, et al., “Outstanding Radiation Resistance of Tungsten-Based High-entropy Alloys,” Science Advances 5, no. 3 (2019): eaav2002, https://doi.org/10.1126/sciadv.aav2002.

[4]

Y. Ren, X. Shao, J. Liu, et al., “Friction-Driven Surface Segregation of (AlCrZrMoV-Ti-B-C)Nx Crystal-Amorphous Nanocomposites Enables Wear Reduction,” Nano Research 18, no. 8 (2025): 94907444, https://doi.org/10.26599/nr.2025.94907444.

[5]

H. Liu, Y. He, M. Li, et al., “Promoting Strength-ductility Synergy Through Sequential Martensitic Transformation in a Hierarchical Heterostructured Eutectic High-Entropy Alloy,” International Journal of Plasticity 190 (2025): 104374, https://doi.org/10.1016/j.ijplas.2025.104374.

[6]

Z. Jiao, H. Liu, Y. Dong, et al., “Self-Generating Hierarchical Lubricious Phase for Superior High-Temperature Tribological Performance in Multi-Principal Element Alloys,” Scripta Materialia 268 (2025): 116843, https://doi.org/10.1016/j.scriptamat.2025.116843.

[7]

B. Gwalani, A. Martin, E. Kautz, et al., “Mechanistic Understanding of Speciated Oxide Growth in High Entropy Alloys,” Nature Communications 15, no. 1 (2024): 5026, https://doi.org/10.1038/s41467-024-49243-8.

[8]

Z. An, S. Mao, Y. Liu, et al., “Inherent and Multiple Strain Hardening Imparting Synergistic Ultrahigh Strength and Ductility in a Low Stacking Faulted Heterogeneous High-Entropy Alloy,” Acta Materialia 243 (2023): 118516, https://doi.org/10.1016/j.actamat.2022.118516.

[9]

C. Wagner and G. Laplanche, “Effects of Stacking Fault Energy and Temperature on Grain Boundary Strengthening, Intrinsic Lattice Strength and Deformation Mechanisms in CrMnFeCoNi High-Entropy Alloys With Different Cr/Ni Ratios,” Acta Materialia 244 (2023): 118541, https://doi.org/10.1016/j.actamat.2022.118541.

[10]

F. Otto, A. Dlouhý, C. Somsen, et al., “The Influences of Temperature and Microstructure on the Tensile Properties of a CoCrFeMnNi High-Entropy Alloy,” Acta Materialia 61 (2013): 5743–5755, https://doi.org/10.1016/j.actamat.2013.06.018.

[11]

B. Gludovatz, A. Hohenwarter, D. Catoor, E. H. Chang, E. P. George, and R. O. Ritchie, “A Fracture-Resistant High-Entropy Alloy for Cryogenic Applications,” Science 345, no. 6201 (2014): 1153–1158, https://doi.org/10.1126/science.1254581.

[12]

Z. An, S. Mao, C. Jiang, et al., “Achieving Superior Combined Cryogenic Strength and Ductility in a High-Entropy Alloy via the Synergy of Low Stacking Fault Energy and Multiscale Heterostructure,” Scripta Materialia 239 (2024): 115809, https://doi.org/10.1016/j.scriptamat.2023.115809.

[13]

M. Shih, J. Miao, M. Mills, and M. Ghazisaeidi, “Stacking Fault Energy in Concentrated Alloys,” Nature Communications 12, no. 1 (2021): 3590, https://doi.org/10.1038/s41467-021-23860-z.

[14]

R. Su, D. Neffati, Y. Zhang, et al., “The Influence of Stacking Faults on Mechanical Behavior of Advanced Materials,” Materials Science and Engineering A 803 (2021): 140696, https://doi.org/10.1016/j.msea.2020.140696.

[15]

C. Wagner, A. Ferrari, J. Schreuer, et al., “Effects of Cr/Ni Ratio on Physical Properties of Cr-Mn-Fe-Co-Ni High-Entropy Alloys,” Acta Materialia 227 (2022): 117693, https://doi.org/10.1016/j.actamat.2022.117693.

[16]

S. F. Liu, Y. Wu, H. T. Wang, et al., “Stacking Fault Energy of Face-Centered-Cubic High Entropy Alloys,” Intermetallics 93 (2018): 269–273, https://doi.org/10.1016/j.intermet.2017.10.004.

[17]

M. Ghiasabadi Farahani, M. Barati Rizi, M. Aghaahmadi, et al., “Activation of Different Twinning Mechanisms and Their Contributions to Mechanical Behavior of a Face-Centered Cubic Co-Based High-Entropy Alloy,” Acta Materialia 285 (2025): 120665, https://doi.org/10.1016/j.actamat.2024.120665.

[18]

S. Yoshida, R. Fu, W. Gong, et al., “Characteristic Deformation Microstructure Evolution and Deformation Mechanisms in Face-Centered Cubic High/Medium Entropy Alloys,” Acta Materialia 283 (2025): 120498, https://doi.org/10.1016/j.actamat.2024.120498.

[19]

C. Wagner, E. P. George, and G. Laplanche, “Effects of Grain Size and Stacking Fault Energy on Twinning Stresses of Single-Phase CrXMn20Fe20Co20Ni40-X High-Entropy Alloys,” Acta Materialia 282 (2025): 120470, https://doi.org/10.1016/j.actamat.2024.120470.

[20]

M. J. Sohrabi, M. S. Mehranpour, A. Heydarinia, et al., “Deformation-Induced Martensitic Transformation Kinetics in TRIP-Assisted Steels and High-Entropy Alloys,” Acta Materialia 280 (2024): 130354, https://doi.org/10.1016/j.actamat.2024.120354.

[21]

S. F. Liu, Y. Wu, H. T. Wang, et al., “Transformation-Reinforced High-Entropy Alloys With Superior Mechanical Properties via Tailoring Stacking Fault Energy,” Journal of Alloys and Compounds 792 (2019): 444–455, https://doi.org/10.1016/j.jallcom.2019.04.035.

[22]

Z. Fan, L. Li, Z. Chen, et al., “Temperature-Dependent Yield Stress of Single Crystals of Non-Equiatomic Cr-Mn-Fe-Co-Ni High-Entropy Alloys in the Temperature Range 10-1173 K,” Acta Materialia 246 (2023): 118712, https://doi.org/10.1016/j.actamat.2023.118712.

[23]

A. Samanta, P. Balaprakash, S. Aubry, and B. K. Lin, “Machine-Learning-Aided Density Functional Theory Calculations of Stacking Fault Energies in Steel,” Scripta Materialia 241 (2024): 115862, https://doi.org/10.1016/j.scriptamat.2023.115862.

[24]

C. Shang, D. Zhu, H. Wu, et al., “A Quantitative Relation for the Ductile-Brittle Transition Temperature in Pipeline Steel,” Scripta Materialia 244 (2024): 116023, https://doi.org/10.1016/j.scriptamat.2024.116023.

[25]

Z. Rao, P. Tung, R. Xie, et al., “Machine Learning-Enabled High-Entropy Alloy Discovery,” Science 378, no. 6615 (2022): 78–85, https://doi.org/10.1126/science.abo4940.

[26]

X. Jin, H. Luo, X. Wang, et al., “Data Mining Accelerated the Design Strategy of High-Entropy Alloys With the Largest Hardness Based on Genetic Algorithm Optimization,” Materials Genome Engineering Advances 2 (2024): e49, https://doi.org/10.1002/mgea.49.

[27]

C. Shang, H. Wu, K. Wang, et al., “High-Throughput Identification of the Martensite Start Temperature in Mixed-Grain Structures,” Review of Materials Research 1, no. 5 (2025): 100105, https://doi.org/10.1016/j.revmat.2025.100105.

[28]

S. Zhao, J. Li, W. Liao, and R. Yuan, “Machine Learning-Guided Plasticity Model in Refractory High-Entropy Alloys,” Materials Genome Engineering Advances 3, no. 2 (2025): e70022, https://doi.org/10.1002/mgea.70022.

[29]

C. Shang, C. Wang, H. Wu, et al., “Improved Data-Driven Performance of Charpy Impact Toughness via Literature-Assisted Production Data in Pipeline Steel,” Science China Technological Sciences 66, no. 7 (2023): 2069–2079, https://doi.org/10.1007/s11431-023-2372-x.

[30]

Y. Zhang, S. Xin, W. Zhou, X. Wang, Y. Xu, and Y. Su, “A Multi-Objective Feature Optimization Strategy for Developing High-Entropy Alloys With Optimal Strength and Ductility,” Materials Genome Engineering Advances 3, no. 1 (2025): e70000, https://doi.org/10.1002/mgea.70000.

[31]

M. Wang, H. L. Yu, Y. Chen, and M. Huang, “Machine Learning Assisted Screening of Non-Rare-Earth Elements for Mg Alloys With Low Stacking Fault Energy,” Computational Materials Science 196 (2021): 110544, https://doi.org/10.1016/j.commatsci.2021.110544.

[32]

Z. Li, K. Li, J. Zhou, and Z. Sun, “Understanding Stacking Fault Energy of NbMoTaW Multi-Principal Element Alloys by Interpretable Machine Learning,” Journal of Alloys and Compounds 1004 (2024): 175751, https://doi.org/10.1016/j.jallcom.2024.175751.

[33]

T. Z. Khan, T. Kirk, G. Vazquez, et al., “Towards Stacking Fault Energy Engineering in FCC High Entropy Alloys,” Acta Materialia 224 (2022): 117472, https://doi.org/10.1016/j.actamat.2021.117472.

[34]

H. Meng, R. Yu, Z. Tang, Z. Wen, and Y. Chu, “Formation Ability Descriptors for High-Entropy Diborides Established Through High-Throughput Experiments and Machine Learning,” Acta Materialia 256 (2023): 119132, https://doi.org/10.1016/j.actamat.2023.119132.

[35]

A. Roy, T. Babuska, B. Krick, and G. Balasubramanian, “Machine Learned Feature Identification for Predicting Phase and Young's Modulus of Low-Medium- and High-Entropy Alloys,” Scripta Materialia 185 (2020): 152–158, https://doi.org/10.1016/j.scriptamat.2020.04.016.

[36]

W. Liu, C. Wang, C. Liang, et al., “Optimal Design of γʹ-Strengthened High-Entropy Alloys via Machine Learning Multilayer Structural Model,” Materials Science and Engineering A 871 (2023): 144852, https://doi.org/10.1016/j.msea.2023.144852.

[37]

W. Gou, Z. Shi, Y. Zhu, et al., “Multi-Objective Optimization of Three Mechanical Properties of Mg Alloys Through Machine Learning,” Materials Genome Engineering Advances 2, no. 3 (2024): e54, https://doi.org/10.1002/mgea.54.

[38]

J. A. Castañeda, O. A. Zambrano, G. A. Alcázar, S. A. Rodríguez, and J. J. Coronado, “Stacking Fault Energy Determination in Fe-Mn-Al-C Austenitic Steels by X-Ray Diffraction,” Metals 11, no. 11 (2021): 1701, https://doi.org/10.3390/met11111701.

[39]

C. Tantardini and A. R. Oganov, “Thermochemical Electronegativities of the Elements,” Nature Communications 12, no. 1 (2021): 2087, https://doi.org/10.1038/s41467-021-22429-0.

[40]

S. M. Lundberg and S. Lee, “A Unified Approach to Interpreting Model Predictions,” in Neural Information Processing Systems (2017).

[41]

R. Shen, Z. Ni, S. Peng, H. Yan, and Y. Tian, “Effects of V Addition on the Deformation Mechanism and Mechanical Properties of Non-Equiatomic CoCrNi Medium-Entropy Alloys,” Materials 16, no. 14 (2023): 5167, https://doi.org/10.3390/ma16145167.

[42]

P. Patra, S. Dey, N. Gayathri, and P. Mukherjee, “Influence of Alloying Elements on Stacking Fault Energy in Ni and Ni-Based Alloy: A Firstprinciples Study,” Computational and Theoretical Chemistry 1240 (2024): 114815, https://doi.org/10.1016/j.comptc.2024.114815.

[43]

X. Zhang, B. Grabowski, F. Körmann, et al., “Temperature Dependence of the Stacking-Fault Gibbs Energy for Al, Cu, and Ni,” Physical Review B 98, no. 22 (2018): 224106, https://doi.org/10.1103/physrevb.98.224106.

[44]

S. Qiu, X.-C. Zhang, J. Zhou, et al., “Influence of Lattice Distortion on Stacking Fault Energies of CoCrFeNi and Al-CoCrFeNi High Entropy Alloys,” Journal of Alloys and Compounds 846 (2020): 156321, https://doi.org/10.1016/j.jallcom.2020.156321.

[45]

X. Zhao, K. Song, H. Huang, Y. Yan, Y. Su, and P. Qian, “Effect of Alloying Elements on the Stacking Fault Energy and Ductility in Mg2Si Intermetallic Compounds,” ACS Omega 6, no. 31 (2021): 20254–20263, https://doi.org/10.1021/acsomega.1c02099.

[46]

S. Yang, J. Lu, F. Xing, L. Zhang, and Y. Zhong, “Revisit the VEC Rule in High Entropy Alloys (HEAs) With High-Throughput CALPHAD Approach and Its Applications for Material Design-A Case Study With Al-Co-Cr-Fe-Ni System,” Acta Materialia 192 (2020): 11–19, https://doi.org/10.1016/j.actamat.2020.03.039.

[47]

G. Zhao, X. Li, and N. Petrinic, “Materials Information and Mechanical Response of TRIP/TWIP Ti Alloys,” Npj Computational Materials 7, no. 1 (2021): 91, https://doi.org/10.1038/s41524-021-00560-2.

[48]

W. Wang, Z. Cao, H. Chen, et al., “Effects of Fe and Cr on the Microstructure and Mechanical Properties of FexCr72-xNi14Al14 High-Entropy Alloys,” Journal of Alloys and Compounds 973 (2024): 172861, https://doi.org/10.1016/j.jallcom.2023.172861.

[49]

D. Cui, X. Liu, Z. Yang, et al., “Uniting Superior Mechanical Properties With Oxidation Resistance in a Refractory High-Entropy Alloy via Cr and Al Alloying,” Scripta Materialia 244 (2024): 116031, https://doi.org/10.1016/j.scriptamat.2024.116031.

[50]

S. Guo, C. Ng, J. Lu, and C. T. Liu, “Effect of Valence Electron Concentration on Stability of Fcc or Bcc Phase in High Entropy Alloys,” Journal of Applied Physics 109, no. 10 (2011): 103505, https://doi.org/10.1063/1.3587228.

[51]

M. Schneider, J.-P. Couzinié, A. Shalabi, et al., “Effect of Stacking Fault Energy on the Thickness and Density of Annealing Twins in Recrystallized FCC Medium and High-Entropy Alloys,” Scripta Materialia 240 (2024): 115844, https://doi.org/10.1016/j.scriptamat.2023.115844.

[52]

M. Rajkowski, A. B. Parsa, A. S. Tirunilai, et al., “Stacking Fault Energy, Thermal Expansion Behavior, and Elastic Coefficients of a Single-Crystalline CrFeNi Medium-Entropy Alloy,” Scripta Materialia 248 (2024): 116147, https://doi.org/10.1016/j.scriptamat.2024.116147.

[53]

A. I. Salimon, A. M. Korsunsky, and A. N. Ivanov, “The Character of Dislocation Structure Evolution in Nanocrystalline FCC Ni-Co Alloys Prepared by High-Energy Mechanical Milling,” Materials Science and Engineering A 271, no. 1–2 (1999): 196–205, https://doi.org/10.1016/s0921-5093(99)00205-1.

[54]

C. B. Carter and S. M. Holmes, “The Stacking-Fault Energy of Nickel,” Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics 35, no. 5 (1977): 1161–1172, https://doi.org/10.1080/14786437708232942.

[55]

N. Hashimoto, T. Fukushi, E. Wada, and W. Y. Chen, “Effect of Stacking Fault Energy on Damage Microstructure in Ion-Irradiated CoCrFeNiMn Concentrated Solid Solution Alloys,” Journal of Nuclear Materials 545 (2021): 152642, https://doi.org/10.1016/j.jnucmat.2020.152642.

[56]

K. V. Werner, M. Naeem, F. Niessen, et al., “Experimental and Computational Assessment of the Temperature Dependency of the Stacking Fault Energy in Face-Centered Cubic High-Entropy Alloys,” Acta Materialia 278 (2024): 120271, https://doi.org/10.1016/j.actamat.2024.120271.

[57]

T. Lam, M. Luo, T. Kawasaki, et al., “Tensile Response of As-Cast CoCrFeNi and CoCrFeMnNi High-Entropy Alloys,” Crystals 12, no. 2 (2022): 157, https://doi.org/10.3390/cryst12020157.

[58]

G. Laplanche, A. Kostka, O. M. Horst, G. Eggeler, and E. George, “Microstructure Evolution and Critical Stress for Twinning in the CrMnFeCoNi High-Entropy Alloy,” Acta Materialia 118 (2016): 152–163, https://doi.org/10.1016/j.actamat.2016.07.038.

[59]

G. Laplanche, A. Kostka, C. Reinhart, J. Hunfeld, G. Eggeler, and E. George, “Reasons for the Superior Mechanical Properties of Medium-Entropy CrCoNi Compared to High-Entropy CrMnFeCoNi,” Acta Materialia 128 (2017): 292–303, https://doi.org/10.1016/j.actamat.2017.02.036.

[60]

C. Wen, Y. Zhang, C. Wang, et al., “Machine Learning Assisted Design of High Entropy Alloys With Desired Property,” Acta Materialia 170 (2019): 109–117, https://doi.org/10.1016/j.actamat.2019.03.010.

[61]

B. Cao, T. Su, S. Yu, et al., “Active Learning Accelerates the Discovery of High Strength and High Ductility Lead-Free Solder Alloys,” Materials and Design 241 (2024): 112921, https://doi.org/10.1016/j.matdes.2024.112921.

[62]

F. Pedregosa, G. Varoquaux, A. Gramfort, et al., “Scikit-Learn: Machine Learning in Python,” Journal of Machine Learning Research 12 (2011): 2825–2830.

[63]

L. Breiman, “Random Forests,” Machine Learning 45, no. 1 (2001): 5–32, https://doi.org/10.1023/a:1010933404324.

[64]

R. Kruse, S. Mostaghim, C. Borgelt, et al., “Multi-Layer Perceptrons,” in Computational Intelligence: A Methodological Introduction (Springer International Publishing, 2022): 47–81.

[65]

J. Velthoen, C. Dombry, J.-J. Cai, and S. Engelke, “Gradient Boosting for Extreme Quantile Regression,” Extremes 26, no. 4 (2023): 639–667, https://doi.org/10.1007/s10687-023-00473-x.

[66]

T. Chen and C. Guestrin, “XGBoost: A Scalable Tree Boosting System,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2016): 785–794.

[67]

J. Ma, B. Cao, S. Dong, et al., “MLMD: A Programming-Free AI Platform to Predict and Design Materials,” Npj Computational Materials 10, no. 1 (2024): 59, https://doi.org/10.1038/s41524-024-01243-4.

[68]

D. R. Goldstein, “Analyzing Microarray Gene Expression Data,” Journal of the American Statistical Association 100, no. 472 (2005): 1464–1465, https://doi.org/10.1198/jasa.2005.s60.

[69]

Y. Wang, Y. Tian, T. Kirk, et al., “Accelerated Design of Fe-Based Soft Magnetic Materials Using Machine Learning and Stochastic Optimization,” Acta Materialia 194 (2020): 144–155, https://doi.org/10.1016/j.actamat.2020.05.006.

[70]

W. Zhao, C. Zheng, B. Xiao, et al., “Fine Optimization of 6061 Aluminum Alloy Composition Using a Bayesian Sampling Active Machine Learning Model,” Acta Metallurgica Sinica 57 (2021): 797–810, https://doi.org/10.11900/0412.1961.2020.00298.

RIGHTS & PERMISSIONS

2026 The Author(s). Materials Genome Engineering Advances published by Wiley-VCH GmbH on behalf of University of Science and Technology Beijing.

PDF (5115KB)

0

Accesses

0

Citation

Detail

Sections
Recommended

/