Machine learning-accelerated first-principles predictions of the stability and mechanical properties of L1₂-strengthened cobalt-based superalloys

Abstract

As promising next-generation candidates for applications in aero-engines, L1₂-strengthened cobalt (Co)-based superalloys have attracted extensive attention. However, the L1₂ strengthening phase in first-generation Co-Al-W-based superalloys is metastable, and both its solvus temperature and mechanical properties still need improvement. Therefore, it is necessary to discover new L1₂-strengthened Co-based superalloy systems with a stable L1₂ phase by exploring the effect of alloying elements on their stability. Traditional first-principles calculations are capable of providing the crystal structure and mechanical properties of the L1₂ phase doped by transition metals but suffer from low efficiency and relatively high computational costs. The present study combines machine learning (ML) with first-principles calculations to accelerate crystal structure and mechanical property predictions, with the latter providing both the training and validation datasets. Three ML models are established and trained to predict the occupancy of alloying elements in the supercell and the stability and mechanical properties of the L1₂ phase. The ML predictions are evaluated using first-principles calculations and the accompanying data are used to further refine the ML models. Our ML-accelerated first-principles calculation approach offers more efficient predictions of the crystal structure and mechanical properties for Co-V-Ta- and Co-Al-V-based systems than the traditional counterpart. This approach is applicable to expediting crystal structure and mechanical property calculations and thus the design and discovery of other advanced materials beyond Co-based superalloys.

Keywords

Co-based superalloys / first-principles calculations / site occupancy / phase stability / mechanical properties / machine learning

References

[1] Sims C. , Stoloff N., Hagel W. Superalloys II: High-temperature materials for aerospace and industrial power; 1987. Available from: https://www.researchgate.net/profile/James-Smialek/publication/283993132_High_Temperature_Oxidation_in_Superalloy/links/5829db5e08ae138f1bf2f305/High-Temperature-Oxidation-in-Superalloy.pdf [Last accessed on 14 Sep 2022]

[2] Ruan J,Yang T.Accelerated design of novel W-free high-strength Co-base superalloys with extremely wide γ/γʹ region by machine learning and CALPHAD methods.Acta Materialia2020;186:425-33.

[3] Zhao S,Smith GD.Research and Improvement on structure stability and corrosion resistance of nickel-base superalloy INCONEL alloy 740.Mater Des2006;27:1120-7

[4] Sahay S.Recent developments in co-base alloys.SSP2009;150:197-219

[5] Zhu J,Pollock TM.Experimental investigation and thermodynamic modeling of the Co-rich region in the Co-Al-Ni-W quaternary system.J Phase Equilib Diffus2014;35:595-611.

[6] Sato J,Oikawa K,Kainuma R.Cobalt-base high-temperature alloys.Science2006;312:90-1

[7] Miura S,Mohri T.Mechanical properties of Co-based L1₂ intermetallic compound Co₃(Al,W).Mater Trans2007;48:2403-8

[8] Kobayashi S,Takasugi T.Determination of phase equilibria in the Co-rich Co-Al-W ternary system with a diffusion-couple technique.Intermetallics2009;17:1085-9.

[9] Yu Y,Liu X,Kainuma R.Experimental determination of phase equilibria in the Co-Ti-Mo ternary system.Intermetallics2008;16:1199-205.

[10] Yao Q,Hu Y.First-principles investigation of phase stability, elastic and thermodynamic properties in L1₂Co₃(Al,Mo,Nb) phase.Intermetallics2016;78:1-7.

[11] Qiang Y,Kang W.Phase stability, elastic, and thermodynamic properties of the L1₂(Co,Ni)₃(Al,Mo,Nb) phase from first-principles calculations.J Mater Res2017;32:1-9.

[12] Kobayashi S,Takasugi T.Phase equilibria in the Co-rich Co-Al-W-Ti quaternary system.Intermetallics2011;19:1908-12

[13] Kobayashi S,Takasugi T.The effects of alloying elements (Ta, Hf) on the thermodynamic stability of γ′-Co₃(Al,W) phase.Intermetallics2012;31:94-8

[14] Makineni S,Rojhirunsakool T.A new class of high strength high temperature Cobalt based γ-γ′ Co-Mo-Al alloys stabilized with Ta addition.Acta Materialia2015;97:29-40

[15] Makineni S,Chattopadhyay K.A new tungsten-free γ-γ’ Co-Al-Mo-Nb-based superalloy.Scripta Materialia2015;98:36-9

[16] Makineni S,Chattopadhyay K.Synthesis of a new tungsten-free γ-γ′ cobalt-based superalloy by tuning alloying additions.Acta Materialia2015;85:85-94

[17] Makineni SK,Palanisamy D.Phase evolution and crystallography of precipitates during decomposition of new “tungsten-free” Co(Ni)-Mo-Al-Nb γ-γ′ superalloys at elevated temperatures.J Mater Sci2016;51:7843-60.

[18] Chinen H,Oikawa K,Kainuma R.Phase Equilibria and Ternary Intermetallic Compound with L1₂ Structure in Co-W-Ga System.J Phase Equilib Diffus2009;30:587-94.

[19] Chinen H,Omori T.New ternary compound Co₃(Ge,W) with L1₂ structure.Scripta Materialia2007;56:141-3

[20] Zenk CH,Li R.A novel type of Co-Ti-Cr-base γ/γ′ superalloys with low mass density.Acta Materialia2017;135:244-51

[21] Im HJ,Gault B,Raabe D.Elemental partitioning and site-occupancy in γ/γ′ forming Co-Ti-Mo and Co-Ti-Cr alloys.Scripta Materialia2018;154:159-62

[22] Chen M.First-principles investigation of the site preference and alloying effect of Mo, Ta and platinum group metals in γ′-Co₃(Al,W).Scri Mater2009;60:659-62

[23] Chen M.First-principle investigation of 3d transition metal elements in γ′-Co₃(Al,W).J Appl Phys2010;107:093705

[24] Mao Z,Sudbrack CK,Seidman DN.Interfacial free energies, nucleation, and precipitate morphologies in Ni-Al-Cr alloys: calculations and atom-probe tomographic experiments.Acta Materialia2019;166:702-14

[25] Xu W,Wang C.Accelerating exploitation of Co-Al-based superalloys from theoretical study.Mater Des2018;142:139-48.

[26] Yu J,Chen Y,Liu X.Accelerated design of L1₂-strengthened Co-base superalloys based on machine learning of experimental data.Mater Des2020;195:108996.

[27] Nosengo N.Can artificial intelligence create the next wonder material?.Nature2016;533:22-5

[28] Raccuglia P,Adler PD.Machine-learning-assisted materials discovery using failed experiments.Nature2016;533:73-6

[29] Pilania G.Machine learning in materials science: From explainable predictions to autonomous design.Comp Mater Sci2021;193:110360

[30] Yu J,Pan S.Machine learning-guided design and development of metallic structural materials.J Mater Inf2021;1:9

[31] Liu P,Antonov S.Machine learning assisted design of γ′-strengthened Co-base superalloys with multi-performance optimization.npj Comput Mater2020;6

[32] Swetlana S,Singh AK.Development of Vickers hardness prediction models via microstructural analysis and machine learning.J Mater Sci2020;55:15845-56

[33] Ruan J,Yang S.Novel Co-Ti-V-base superalloys reinforced by L1₂-ordered γ′ phase.Intermetallics2018;92:126-32

[34] Zou M,Li L,Feng Q.Machine learning assisted design approach for developing γ′-strengthened Co-Ni-base superalloys. 2020.

[35] Li W,Antonov S,Zhao J.High-throughput exploration of alloying effects on the microstructural stability and properties of multi-component CoNi-base superalloys.J Alloys Compd2021;881:160618

[36] Tamura R,Minagawa K.Machine learning-driven optimization in powder manufacturing of Ni-Co based superalloy.Mater Des2021;198:109290

[37] Guo J,Li Y.Machine learning aided first-principles studies of structure stability of Co₃(Al, X) doped with transition metal elements.Comp Mater Sci2021;200:110787.

[38] Zunger A,Ferreira LG.Special quasirandom structures.Phys Rev Lett1990;65:353-6

[39] Jiang C.First-principles study of Co₃(Al,W) alloys using special quasi-random structures.Scr Mater2008;59:1075-8

[40] Asta M,Woodward C.A first-principles approach to modeling alloy phase equilibria.JOM2001;53:16-9

[41] de Walle A, Asta M, Ceder G. The alloy theoretic automated toolkit: a user guide.Calphad2002;26:539-53

[42] Kresse G.Ab initio molecular dynamics for liquid metals.Phys Rev B Condens Matter1993;47:558-61

[43] Kresse G.Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium.Phys Rev B Condens Matter1994;49:14251-69

[44] Kresse G.Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set.Comp Mater Sci1996;6:15-50

[45] Kresse G.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.Phys Rev B Condens Matter1996;54:11169-86

[46] Kresse G.From ultrasoft pseudopotentials to the projector augmented-wave method.Phys Rev B1999;59:1758-75

[47] Dang H,Shu X.Electronic structure of edge dislocation of core-doped Ti in Fe.Prog Nat Sci2004;14:477-82.

[48] Freysoldt C,Hickel T.First-principles calculations for point defects in solids.Rev Mod Phys2014;86:253-305

[49] Xi S,Bao L.Effects of alloying elements on the atomic structure, elastic and thermodynamic properties of L1₂-Co₃(V, Ti) compound.Mater Today Comm2022;30:102931

[50] Xu W,Wang C,Liu Z.Alloying effects of Ta on the mechanical properties of γ’ Co₃(Al, W): A first-principles study.Scr Mater2015;100:5-8.

[51] Saal JE.Thermodynamic stability of Co-Al-W L12 γ′.Acta Materialia2013;61:2330-8

[52] Wang S.Ab initio elastic constants for the lonsdaleite phases of C, Si and Ge.J Phys Condens Matter2003;15:5307

[53] Shang S,Liu Z.First-principles elastic constants of α- and θ-Al2O3.Appl Phys Lett2007;90:101909

[54] Chung D.Elastic moduli of single crystal and polycrystalline MgO.Philos Mag1963;8:833-41

[55] Anderson OL.A simplified method for calculating the debye temperature from elastic constants.J Phys Chem Sol1963;24:909-17.

[56] Chung DH.The Voigt-Reuss-Hill (VRH) approximation and the elastic moduli of polycrystalline ZnO, TiO₂ (Rutile), and α-Al₂O₃.J Appl Phys1968;39:2777-82.

[57] Liu X,Xu W,Wang C.Effects of transition elements on the site preference, elastic properties and phase stability of L1₂ γ′-Co₃(Al, W) from first-principles calculations.J Alloys Compd2020;820:153179.

[58] Ho Y.Simple explanation of the No-Free-Lunch theorem and its implications.J Optimiz The Appl2002;115:549-70

[59] Goldstein D.Analyzing microarray gene expression data.J Am Stat Assoc2005;100:1464-5

[60] Yu J,Chen Y.A two-stage predicting model for γ′ solvus temperature of L12-strengthened Co-base superalloys based on machine learning.Intermetallics2019;110:106466

[61] Belhumeur P,Kriegman D.Eigenfaces vs. fisherfaces: recognition using class specific linear projection.IEEE Trans patt analys mach intell1997;19:711-720

[62] Wang C,Wang Y.Effects of transition elements on the structural, elastic properties and relative phase stability of L1₂ γ′-Co₃Nb from first-principles calculations.Metals2021;11:933

[63] Sanyal S,Hanlon T.Ni/boride interfaces and environmental embrittlement in Ni-based superalloys: a first-principles study.Mater Sci Engineer: A2011;530:373-7

[64] Geng P,Zhang X.A theoretical model for yield strength anomaly of Ni-base superalloys at elevated temperature.J Alloys Compd2017;706:340-3

[65] Wang CP,Xu WW.Effects of alloying elements on relative phase stability and elastic properties of L1₂Co₃V from first-principles calculations.J Mater Sci2018;53:1204-16

[66] Bauer A,Pyczak F.Microstructure and creep strength of different γ/γ′-strengthened Co-base superalloy variants.Scr Mater2010;63:1197-200

[67] Ruan J,Yang S.Experimental investigations of microstructures and phase equilibria in the Co-V-Ta ternary system.J Alloys Compd2016;664:141-8

[68] Chen Y,Ruan J.High-strength Co-Al-V-base superalloys strengthened by γ′-Co₃(Al,V) with high solvus temperature.Acta Materialia2019;170:62-74