Facilitated the discovery of new γ/γ′ Co-based superalloys by combining first-principles and machine learning
Source abstract
Abstract
Superalloys are indispensable materials for the fabrication of high-temperature components in aircraft engines. The discovery of a novel class of γ/γ′ Co-Al-W alloys has ignited a surge of interest in Co-based superalloys, with the aspiration to transcend the inherent constraints of their Ni-based counterparts. However, the conventional methodologies utilized in the design and advancement of new γ/γ′ Co-based superalloys are frequently characterized by their laborious and resource-intensive nature. In this study, we employed a coupled Density Functional Theory (DFT) and machine learning (ML) approach to predict and analyze the stability of the crucial γ′ phase, which is instrumental in expediting the discovery of γ/γ′ Co-based alloys. A dataset comprised of thousands of reliable formation ( H f ) and decomposition ( H d ) energies was obtained through high-throughput DFT calculations. Through regression model selection and feature engineering, our trained Random Forest (RF) model achieved prediction accuracies of 98.07% for H f and 97.05% for H d . Utilizing the well-trained RF model, we predicted the energies of over 150,000 ternary and quaternary γ′ phases within the Co-Ni-Fe-Cr-Al-W-Ti-Ta-V-Mo-Nb system. The energy analyses revealed that the presence of Ni, Nb, Ta, Ti, and V significantly reduced the H f and the H d of γ′, while Mo and W deteriorate the stability by increasing both energy values. Interestingly, although Al reduces the H f , it increases H d , thereby adversely affecting the stability of γ′. Applying domain-specific screening based on our knowledge, we identified 1049 out of >150,000 compositions likely to form stable γ′ phases, predominantly distributed across 11 Al-containing systems and 25 Al-free systems. Combining the analysis of CALPHAD method, we experimentally synthesized two new Co-based alloys with γ/γ′ dual-phase microstructures, corroborating the reliability of our theoretical prediction model.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: High Temperature Alloys and Creep · Advanced Materials Characterization Techniques · Intermetallics and Advanced Alloy Properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (81)
Show source-provided references
1. Sims, C. T., Stoloff, N. S. & Hagel, W. C. In New York: John Wiley and Sons (1987).
2. Reed, R. C. In Cambridge: Cambridge University Press (2006).
3. Feng, Q., Nandy, T. K., Tin, S. & Pollock, T. M. Solidification of high-refractory ruthenium-containing superalloys. Acta Mater. 51, 269 (2003).10.1016/S1359-6454(02)00397-X ↗
4. Mackay, R. A., Gabb. T. P., Smialek. J. L. & Nathal, M. V. Alloy Design Challenge: Development of Low Density Superalloys for Turbine Blade Applications. Natl. Aero. Space Admin. 2009–215819 (2009).
5. Pollock, T. M. & Tin, S. Nickel-Based Superalloys for Advanced Turbine Engines: Chemistry, Microstructure and Properties. J. Propulsion Power, 22, 361–374, https://doi.org/10.2514/1.18239 (2006).10.2514/1.18239 ↗
6. Pollock, T. M. Alloy design for aircraft engines. Nat. Mater. 15, 809–815, https://doi.org/10.1038/nmat4709 (2016).10.1038/nmat4709 ↗
7. Sato, J. et al. Cobalt-base high-temperature alloys. Science 312, 90–91, https://doi.org/10.1126/science.1121738 (2006).10.1126/science.1121738 ↗
8. Selvaraj, S. K. et al. Recent advancements in the field of ni-based superalloys. Adv. Mater. Sci. Eng. 2021, 1–60, https://doi.org/10.1155/2021/9723450 (2021).10.1155/2021/9723450 ↗
9. Makineni, S., Nithin, B. & Chattopadhyay, K. Synthesis of a new tungsten-free γ-γ′ Cobalt-based superalloy by tuning alloying additions. Acta Materialia 85, https://doi.org/10.1016/j.actamat.2014.11.016 (2015).10.1016/j.actamat.2014.11.016 ↗
10. Makineni, S. K., Nithin, B. & Chattopadhyay, K. A new tungsten-free γ–γ’ Co–Al–Mo–Nb-based superalloy. Scr. Mater. 98, 36–39, https://doi.org/10.1016/j.scriptamat.2014.11.009 (2015).10.1016/j.scriptamat.2014.11.009 ↗
11. Makineni, S. K. et al. A new class of high strength high temperature Cobalt based γ–γ′ Co–Mo–Al alloys stabilized with Ta addition. Acta Mater. 97, 29–40, https://doi.org/10.1016/j.actamat.2015.06.034 (2015).10.1016/j.actamat.2015.06.034 ↗
12. Pandey, P., Mukhopadhyay, S., Srivastava, C., Makineni, S. K. & Chattopadhyay, K. Development of new γ′-strengthened Co-based superalloys with low mass density, high solvus temperature and high temperature strength. Mater. Sci. Eng.: A 790, https://doi.org/10.1016/j.msea.2020.139578 (2020).10.1016/j.msea.2020.139578 ↗
13. Reyes Tirado, F. L., Taylor, S. & Dunand, D. C. Effect of Al, Ti and Cr additions on the γ-γ’ microstructure of W-free Co-Ta-V-Based superalloys. Acta Mater. 172, 44–54, https://doi.org/10.1016/j.actamat.2019.04.031 (2019).10.1016/j.actamat.2019.04.031 ↗
14. Ruan, J. et al. Accelerated design of novel W-free high-strength Co-base superalloys with extremely wide γ/γʹ region by machine learning and CALPHAD methods. Acta Mater. 186, 425–433, https://doi.org/10.1016/j.actamat.2020.01.004 (2020).10.1016/j.actamat.2020.01.004 ↗
15. Chen, Y. et al. High-strength Co–Al–V-base superalloys strengthened by γ′-Co3(Al,V) with high solvus temperature. Acta Mater. 170, 62–74, https://doi.org/10.1016/j.actamat.2019.03.013 (2019).10.1016/j.actamat.2019.03.013 ↗
16. Chen, Y. et al. Development of low-density γ/γ′ Co–Al–Ta-based superalloys with high solvus temperature. Acta Mater. 188, 652–664, https://doi.org/10.1016/j.actamat.2020.02.049 (2020).10.1016/j.actamat.2020.02.049 ↗
17. Cao, B. X. et al. L12-strengthened multicomponent Co-Al-Nb-based alloys with high strength and matrix-confined stacking-fault-mediated plasticity. Acta Mater. 229, https://doi.org/10.1016/j.actamat.2022.117763 (2022).10.1016/j.actamat.2022.117763 ↗
18. Hart, G. L. W., Mueller, T., Toher, C. & Curtarolo, S. Machine learning for alloys. Nat. Rev. Mater. 6, 730–755, https://doi.org/10.1038/s41578-021-00340-w (2021).10.1038/s41578-021-00340-w ↗
19. Li, Y., Zhu, R., Wang, Y., Feng, L. & Liu, Y. Center-environment deep transfer machine learning across crystal structures: from spinel oxides to perovskite oxides. NPJ Comput. Mater. 9, https://doi.org/10.1038/s41524-023-01068-7 (2023).10.1038/s41524-023-01068-7 ↗
20. Zhang, J., Cai, C., Kim, G., Wang, Y. & Chen, W. Composition design of high-entropy alloys with deep sets learning. NPJ Comput. Mater. 8, https://doi.org/10.1038/s41524-022-00779-7 (2022).10.1038/s41524-022-00779-7 ↗
21. Vazquez, G. et al. Efficient machine-learning model for fast assessment of elastic properties of high-entropy alloys. Acta Mater. 232, https://doi.org/10.1016/j.actamat.2022.117924 (2022).10.1016/j.actamat.2022.117924 ↗
22. Liu, P. et al. Machine learning assisted design of γ′-strengthened Co-base superalloys with multi-performance optimization. NPJ Comput. Mater. 6, https://doi.org/10.1038/s41524-020-0334-5 (2020).10.1038/s41524-020-0334-5 ↗
23. Faber, F. A., Lindmaa, A., von Lilienfeld, O. A. & Armiento, R. Machine Learning Energies of 2 Million Elpasolite(ABC2D6)Crystals. Phys. Rev. Lett. 117, https://doi.org/10.1103/PhysRevLett.117.135502 (2016).10.1103/PhysRevLett.117.135502 ↗
24. Zhou, Z. et al. Machine learning guided appraisal and exploration of phase design for high entropy alloys. NPJ Comput. Mater. 5, https://doi.org/10.1038/s41524-019-0265-1 (2019).10.1038/s41524-019-0265-1 ↗
25. Mao, Y. et al. Prediction and classification of formation energies of binary compounds by machine learning: an approach without crystal structure information. ACS Omega 6, 14533–14541, https://doi.org/10.1021/acsomega.1c01517 (2021).10.1021/acsomega.1c01517 ↗
26. Zhang, M., Hua, F. & Zhao, W. Research on phase prediction of high-entropy alloys based on machine learning. Mater. Rep. 35, 331–335 (2021).
27. Hu, H. Stability prediction of perovskite structure based on sisso and machine learning method: establishment and verification of a new admissible factor. Chin. J. Nonferrous Met. 30, 8, https://doi.org/10.11817/j.ysxb.1004.0609.2020-35838 (2020).10.11817/j.ysxb.1004.0609.2020-35838 ↗
28. Zhao, W. et al. Study on prediction of formation enthalpy of laves phase alloys based on machine learning. Materuals Rep. 36, 21120179 (2022).
29. Rengaraj, V. et al. A Two-step machine learning method for predicting the formation energy of ternary compounds. Computation 11, https://doi.org/10.3390/computation11050095 (2023).10.3390/computation11050095 ↗
30. Levämäki, H. et al. Predicting elastic properties of hard-coating alloys using ab-initio and machine learning methods. NPJ Comput. Mater. https://doi.org/10.1038/s41524-022-00698-7 (2022).10.1038/s41524-022-00698-7 ↗
31. Wu, T.-T. et al. Structural design of organic battery electrode materials: from DFT to artificial intelligence. Rare Met. 42, 3269–3303, https://doi.org/10.1007/s12598-023-02358-1 (2023).10.1007/s12598-023-02358-1 ↗
32. Chen, D. et al. Machine learning assisted discovering of new M2X3-type thermoelectric materials. Rare Met. 41, 1543–1553, https://doi.org/10.1007/s12598-021-01911-0 (2022).10.1007/s12598-021-01911-0 ↗
33. Wang, W. Y. et al. Artificial intelligence enabled smart design and manufacturing of advanced materials: the endless Frontier in AI+ era. Mater. Genome Eng. Adv. e56, https://doi.org/10.1002/mgea.56 (2024).10.1002/mgea.56 ↗
34. Wang, W.-Y. et al. Big data-assisted digital twins for the smart design and manufacturing of advanced materials: from atoms to products. J. Mater. Inform., https://doi.org/10.20517/jmi.2021.11 (2022).10.20517/jmi.2021.11 ↗
35. Kumar, R. & Singh, A. K. Chemical hardness-driven interpretable machine learning approach for rapid search of photocatalysts. NPJ Comput. Mater. 7, https://doi.org/10.1038/s41524-021-00669-4 (2021).10.1038/s41524-021-00669-4 ↗
36. Swetlana, S., Khatavkar, N. & Singh, A. K. Development of Vickers hardness prediction models via microstructural analysis and machine learning. J. Mater. Sci. 55, 15845–15856, https://doi.org/10.1007/s10853-020-05153-w (2020).10.1007/s10853-020-05153-w ↗
37. Guo, J. et al. Machine learning aided first-principles studies of structure stability of Co3(Al, X) doped with transition metal elements. Comput. Mater. Sci. 200, https://doi.org/10.1016/j.commatsci.2021.110787 (2021).10.1016/j.commatsci.2021.110787 ↗
38. Guo, J. et al. Element-configuration dependent first-principles machine learning studies of multiple alloying effects on the structure stability of Co3(Al, W). Comput. Mater. Sci. 233, https://doi.org/10.1016/j.commatsci.2023.112767 (2024).10.1016/j.commatsci.2023.112767 ↗
39. Khatavkar, N., Swetlana, S. & Singh, A. K. Accelerated prediction of Vickers hardness of Co- and Ni-based superalloys from microstructure and composition using advanced image processing techniques and machine learning. Acta Mater. 196, 295–303, https://doi.org/10.1016/j.actamat.2020.06.042 (2020).10.1016/j.actamat.2020.06.042 ↗
40. Xi, S. et al. Predicting atomic structure and mechanical properties in quinary L12-Strengthened cobalt-based superalloys using machine learning-driven first-principles calculations. Mater. Today Commun. 38, https://doi.org/10.1016/j.mtcomm.2023.107774 (2024).10.1016/j.mtcomm.2023.107774 ↗
41. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).10.1103/PhysRevLett.77.3865 ↗
42. Tian, L.-Y. et al. Exchange-correlation catastrophe in Cu-Au: a challenge for semilocal density functional approximations. Phys. Rev. Lett. 117, https://doi.org/10.1103/PhysRevLett.117.066401 (2016).10.1103/PhysRevLett.117.066401 ↗
43. Levämäki, H., Punkkinen, M. P. J., Kokko, K. & Vitos, L. Flexibility of the quasi-non-uniform exchange-correlation approximation. Phys. Rev. B 115107, 86 (2014).
44. Levämäki, H., Punkkinen, M. P. J., Kokko, K. & Vitos, L. Quasi-non-uniform gradient-level exchange-correlation approximation for metals and alloys. Phys. Rev. B 86, https://doi.org/10.1103/PhysRevB.86.201104 (2012).10.1103/PhysRevB.86.201104 ↗
45. Tian, L.-Y. et al. CPA descriptions of random Cu-Au alloys in comparison with SQS approach. Comput. Mater. Sci. 128, 302–309, https://doi.org/10.1016/j.commatsci.2016.11.045 (2017).10.1016/j.commatsci.2016.11.045 ↗
46. Xu, W. W. et al. Thermodynamic, structural and elastic properties of Co3X (X = Ti, Ta, W, V, Al) compounds from first-principles calculations. Intermetallics 32, 303–311, https://doi.org/10.1016/j.intermet.2012.08.022 (2013).10.1016/j.intermet.2012.08.022 ↗
47. Xiong, Z. Y. et al. Accelerating optimization of IN718 by mapping alloying effects on phase stabilities and mechanical properties using high-throughput calculations. Materi. Design 217, https://doi.org/10.1016/j.matdes.2022.110603 (2022).10.1016/j.matdes.2022.110603 ↗
48. Erdmann, B. & Keller, C. Actinide(lanthanide)-noble metal alloy phases, preparation and properties. J. Solid State Chem. 7, 40–48 (1973).10.1016/0022-4596(73)90119-9 ↗
49. Bronger, W. & Klemm, W. Darstellung von Legierungen des Platins mit unedlen Metallen. Zeitschrift für Anorg. Allg. Chem. 319, 58–81, https://doi.org/10.1002/zaac.19623190110 (1962).10.1002/zaac.19623190110 ↗
50. Schnetder, A. & Esch, U. Das System Kupfer—Platin. Z. für. Elektrochem. Angew. Phys. Chem. 50, 290–301, https://doi.org/10.1002/bbpc.19440501109 (1944).10.1002/bbpc.19440501109 ↗
51. Schneider, A. & Esch, U. Das System Silber-Platin. Ein Beitrag zur Frage der Spannungskorrosion. Zeitschrift für Elektrochem. Angew. Phys. Chem. 49, 72–89, https://doi.org/10.1002/bbpc.19430490203 (1943).10.1002/bbpc.19430490203 ↗
52. Loebich, O. & Raub, E. Die Legierungen des Palladiums mit Yttrium, Samarium, Gadolinium, Dysprosium, Holmium und Erbium. J. Less Common Met. 30, 47–62 (1973).10.1016/0022-5088(73)90006-4 ↗
53. Jones, D. M. O. Experimental study of the variation of the degree of order with temperature in a Cu - Pd alloy. Proc. Phys. Soc. Lond. 67, 297–303, https://doi.org/10.1088/0370-1301/67/4/303 (1954).10.1088/0370-1301/67/4/303 ↗
54. Geballe, T. H. et al. Superconductivity in binary alloy systems of the rare earths and of thorium with Pt-Group metals. Phys. Rev. 137, A119–A127, https://doi.org/10.1103/PhysRev.137.A119 (1965).10.1103/PhysRev.137.A119 ↗
55. Guo, G. Y., Wang, Y. K. & Hsu, L. S. First-principles and experimental studies of the electronic structures and magnetism in Ni3Al, Ni3Ga and Ni3In. J. Magn. Magn. Mater. 239, 91–93 (2002).10.1016/S0304-8853(01)00564-9 ↗
56. Nepal, N. K., Adhikari, S., Neupane, B. & Ruzsinszky, A. Formation energy puzzle in intermetallic alloys: random phase approximation fails to predict accurate formation energies. Phys. Rev. B 102, https://doi.org/10.1103/PhysRevB.102.205121 (2020).10.1103/PhysRevB.102.205121 ↗
57. Kittel, C. Introduction to Solid State Physics. 7th ed. New York: John Wiley and Sons (1996).
58. Pearson, W. A handbook of lattice spacings and structures of metals and alloys. 4,123 (1958).10.1016/B978-1-4832-1318-7.50011-5 ↗
59. Otte, H. M., Montague, W. G. & Welch, D. O. X‐Ray diffractometer determination of the thermal expansion coefficient of aluminum near room temperature. J. Appl. Phys. 34, 3149–3150, https://doi.org/10.1063/1.1729148 (1963).10.1063/1.1729148 ↗
60. Rzyman, K. et al. Enthalpies of formation of Ni3Al: experiment versus theory. JPE 17, 173–178, https://doi.org/10.1007/BF02648485 (1996).10.1007/BF02648485 ↗
61. Ma, D., Grabowski, B., Körmann, F., Neugebauer, J. & Raabe, D. Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: importance of entropy contributions beyond the configurational one. Acta Mater. 100, 90–97, https://doi.org/10.1016/j.actamat.2015.08.050 (2015).10.1016/j.actamat.2015.08.050 ↗
62. Sasakura, H. & Masuda, S. K. Curie temperature in itinerant electron ferromagnetic Ni3Al system. J. Phys. Soc. Jpn. 53, 754–759 (2007).10.1143/JPSJ.53.754 ↗
63. Connelly, D. L., Loomis, J. S. & Mapother, D. E. Specific heat of nickel near the curie temperature. Phys. Rev. B 3, 924–934 (1971).10.1103/PhysRevB.3.924 ↗
64. Buschow, K. H. J. Encyclopedia of materials : science and technology. Elsevier, Amsterdam (2001).
65. Jarlborg, T. Electronic structure, magnetism and curie temperatures in Fe, Co and Ni. J. Magn. Magn. Mater. 42, 89–99, https://doi.org/10.1016/0304-8853(84)90293-2 (1984).10.1016/0304-8853(84)90293-2 ↗
66. Bartel, C. J., Weimer, A. W., Lany, S., Musgrave, C. B. & Holder, A. M. The role of decomposition reactions in assessing first-principles predictions of solid stability. npj Comput. Mater. 5, https://doi.org/10.1038/s41524-018-0143-2 (2019).10.1038/s41524-018-0143-2 ↗
67. Furness, J. W., Kaplan, A. D., Ning, J., Perdew, J. P. & Sun, J. Accurate and numerically efficient r2SCAN meta-generalized gradient approximation. J. Phys. Chem. Lett. 11, 8208–8215, https://doi.org/10.1021/acs.jpclett.0c02405 (2020).10.1021/acs.jpclett.0c02405 ↗
68. Chen, T. & Guestrin, C. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 785–794 (2016).10.1145/2939672.2939785 ↗
69. Sarker, I. H. Machine learning: algorithms, real-world applications and research directions. SN Comput. Sci. 2, https://doi.org/10.1007/s42979-021-00592-x (2021).10.1007/s42979-021-00592-x ↗
70. Breiman, L. Random forests. Mach. Learn. 45, 5–32 (2001).10.1023/A:1010933404324 ↗
71. Shinagawa, K. et al. Phase Equilibria and Microstructure on γ′; Phase in Co-Ni-Al-W System. Mater. Trans. 49, 1474–1479, https://doi.org/10.2320/matertrans.MER2008073 (2008).10.2320/matertrans.MER2008073 ↗
72. Xu, W. W. et al. Accelerating the discovery of novel γ/γ‘ Co-based superalloys by probing temperature and alloying effects on the γ‘ precipitates. Materialia 18, https://doi.org/10.1016/j.mtla.2021.101171 (2021).10.1016/j.mtla.2021.101171 ↗
73. Feng, G., Li, H., Li, S. S. & Sha, J. Effect of Mo additions on microstructure and tensile behavior of a Co–Al–W–Ta–B alloy at room temperature. Scr. Mater. 67, 499–502, https://doi.org/10.1016/j.scriptamat.2012.06.013 (2012).10.1016/j.scriptamat.2012.06.013 ↗
74. Qu, S. S. et al. Microstructural evolution and compression property of a novel γ‘-strengthened directionally solidified CoNi-base superalloy. Mater. Sci. Eng. A 761, 1–9 (2019).10.1016/j.msea.2019.138034 ↗
75. Li, W., Li, L., Antonov, S. & Feng, Q. Effective design of a Co-Ni-Al-W-Ta-Ti alloy with high γ′ solvus temperature and microstructural stability using combined CALPHAD and experimental approaches. Mater. Design 180, https://doi.org/10.1016/j.matdes.2019.107912 (2019).10.1016/j.matdes.2019.107912 ↗
76. Abrikosov, I. & Johansson, Börje Anisotropic lattice distortions in random alloys from first-principles theory. Phys. Rev. Lett. 8715, 6401 (2001).
77. Vitos, L. Total-energy method based on the exact muffin-tin orbitals theory. Phys. Rev. Lett. B 64, 167–173 (2001).
78. Hohenberg, P. K. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).10.1103/PhysRev.136.B864 ↗
79. Soven, P. Coherent-potential model of substitutional disordered alloys. Phys. Rev. 156, 809–813, https://doi.org/10.1103/PhysRev.156.809 (1967).10.1103/PhysRev.156.809 ↗
80. Gyorffy, B. L. Coherent-potential approximation for a nonoverlapping-muffin-tin-potential model of random substitutional alloys. Phys. Rev. B 5, 2382–2384, https://doi.org/10.1103/PhysRevB.5.2382 (1972).10.1103/PhysRevB.5.2382 ↗
81. Gyorffy, B. L., Pindor, A. J., Staunton, J., Stocks, G. M. & Winter, H. A first-principles theory of ferromagnetic phase transitions in metals. J. Phys. F: Metal Phys. (1985).10.1088/0305-4608/15/6/018 ↗