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Low stacking fault energy governs deformation mechanisms in the γ matrix of Co-based superalloys

Yingchun Tang1,*, Song Lu2, Wei Li3, Anssi Laukkanen2, Levente Vitos3,4,†, and Florian Pyczak1,5

  • *Contact author: yingchun.tang@hereon.de
  • †Contact author: levente@kth.se

Phys. Rev. Materials 10, 106203 – Published 13 October, 2026

DOI: https://doi.org/10.1103/lzf5-2v51

Abstract

Understanding plastic deformation mechanisms in the γ matrix is essential for the development of next-generation Co-based superalloys. Since magnetic transitions in Co-based matrices can occur within service temperature ranges, stacking fault energies (SFEs) must be evaluated with explicit consideration of magnetic state effects. In this work, SFEs of pure Co and Co-rich alloys are calculated to quantify their compositional and temperature dependences in both ferromagnetic (FM) and paramagnetic (PM) states. The predicted values show good agreement with available experimental and theoretical data. For pure Co, the SFE increases with temperature in the FM state and decreases in the PM state; when the magnetic contribution is considered, the PM (Mag.) SFE exhibits the same trend as its FM counterpart. Co-rich alloys, by contrast, display a distinct temperature response, highlighting the dominant role of magnetic entropy in the PM state. Low SFEs predicted for Co-rich alloys at elevated temperatures favor deformation twinning, consistent with experimental observations. These results demonstrate that magnetic-state-dependent SFE calculations provide a robust framework for predicting plastic deformation modes and guiding the alloying design of Co-based alloys.

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References (96)

  1. J. Sato, T. Omori, K. Oikawa, I. Ohnuma, R. Kainuma, and K. Ishida, Cobalt-base high-temperature alloys, Science 312, 90 (2006).
  2. A. Bezold, N. Volz, M. Lenz, N. Karpstein, C. H. Zenk, E. Spiecker, M. Göken, and S. Neumeier, Quantification of the temperature-dependent evolution of defect structures in a CoNi-base superalloy, Acta Mater. 227, 117702 (2022).
  3. M. Lenz, Y. M. Eggeler, J. Müller, C. H. Zenk, N. Volz, P. Wollgramm, G. Eggeler, S. Neumeier, M. Göken, and E. Spiecker, Tension/compression asymmetry of a creep deformed single crystal Co-base superalloy, Acta Mater. 166, 597 (2019).
  4. Y. Tang, W. Li, C. Li, S. Lu, L. Vitos, and F. Pyczak, First-principles calculations of elastic and thermodynamic properties for multi-component Co-based superalloys, Metall. Mater. Trans. A 54, 1635 (2023).
  5. Y. Tang, C. Li, S. Lu, W. Li, L. Vitos, and F. Pyczak, Magneto-chemical effects in the elastic properties of Co3Al-based compounds, Mater. Today Commun. 41, 110507 (2024).
  6. S. K. Makineni, M. Lenz, S. Neumeier, E. Spiecker, D. Raabe, and B. Gault, Elemental segregation to antiphase boundaries in a crept CoNi-based single crystal superalloy, Scr. Mater. 157, 62 (2018).
  7. L. P. Freund, O. M. Messé, J. S. Barnard, M. Göken, S. Neumeier, and C. M. Rae, Segregation assisted microtwinning during creep of a polycrystalline L12-hardened Co-base superalloy, Acta Mater. 123, 295 (2017).
  8. F. Pyczak, A. Bauer, M. Göken, U. Lorenz, S. Neumeier, M. Oehring, J. Paul, N. Schell, A. Schreyer, A. Stark, and F. Symanzik, The effect of tungsten content on the properties of L12-hardened Co–Al–W alloys, J. Alloys Compd. 632, 110 (2015).
  9. F. Pyczak, B. Devirent, and H. Mughrabi, The effects of different alloying elements on the thermal expansion coefficients, lattice constants and misfit of nickel-based superalloys investigated by x-ray diffraction, Superalloys 2004, 827 (2004).
  10. K. Tanaka, M. Ooshima, N. Tsuno, A. Sato, and H. Inui, Creep deformation of single crystals of new Co–Al–W-based alloys with fcc/L12 two-phase microstructures, Philos. Mag. 92, 4011 (2012).
  11. Y. M. Wang-Koh, Understanding the yield behaviour of L12 -ordered alloys, Mater. Sci. Technol. 33, 934 (2017).
  12. T. M. Pollock and A. S. Argon, Creep resistance of CMSX-3 nickel base superalloy single crystals, Acta Metall. Mater. 40, 1 (1992).
  13. Y. M. Eggeler, J. Müller, M. S. Titus, A. Suzuki, T. M. Pollock, and E. Spiecker, Planar defect formation in the γ′ phase during high temperature creep in single crystal CoNi-base superalloys, Acta Mater. 113, 335 (2016).
  14. K. V. Vamsi and S. Karthikeyan, Yield anomaly in L12Co3AlxW1−x vis-à-vis Ni3Al, Scr. Mater. 130, 269 (2017).
  15. T. M. Smith, B. D. Esser, N. Antolin, A. Carlsson, R. E. A. A. Williams, A. Wessman, T. Hanlon, H. L. Fraser, W. Windl, D. W. McComb, and M. J. Mills, Phase transformation strengthening of high-temperature superalloys, Nat. Commun. 7, 13434 (2016).
  16. D. Wen and M. S. Titus, First-principles study of Suzuki segregation at stacking faults in disordered face-centered cubic Co-Ni alloys, Acta Mater. 221, 117358 (2021).
  17. T. L. Achmad, W. Fu, H. Chen, C. Zhang, and Z. G. Yang, Effect of strain on the intrinsic stacking fault energy of fcc Co: A first-principles study, J. Mater. Sci. 53, 10217 (2018).
  18. S. Ma, L. Carroll, and T. M. Pollock, Development of γ phase stacking faults during high temperature creep of Ru-containing single crystal superalloys, Acta Mater. 55, 5802 (2007).
  19. Y. Zhang, Y. Zhang, Y. Cao, S. Lu, S. Zhu, J. Zhu, H. Fu, and J. Xie, Role of planar defects interactions within γ channels on creep resistance enhancement in a novel Co-Ni based superalloy, Acta Mater. 305, 121833 (2026).
  20. L. Rémy and A. Pineau, Twinning and strain-induced f.c.c. →h.c.p. transformation on the mechanical properties of Co Ni Cr Mo alloys, Mater. Sci. Eng. 26, 123 (1976).
  21. R. p. Singh and R. D. Doherty, Strengthening in MULTIPHASE (MP35N) alloy: Part I. ambient temperature deformation and recrystallization, Metall. Mater. Trans. A 23, 307 (1992).
  22. M. Jo, Y. M. Koo, B.-J. J. Lee, B. Johansson, L. Vitos, and S. K. Kwon, Theory for plasticity of face-centered cubic metals, Proc. Natl. Acad. Sci. USA 111, 6560 (2014).
  23. S. Kibey, J. B. Liu, D. D. Johnson, and H. Sehitoglu, Energy pathways and directionality in deformation twinning, Appl. Phys. Lett. 91, 181916 (2007).
  24. S. Kibey, J. B. Liu, D. D. Johnson, and H. Sehitoglu, Generalized planar fault energies and twinning in Cu–Al alloys, Appl. Phys. Lett. 89, 191911 (2006).
  25. C. Niu, C. R. LaRosa, J. Miao, M. J. Mills, and M. Ghazisaeidi, Magnetically-driven phase transformation strengthening in high entropy alloys, Nat. Commun. 9, 1363 (2018).
  26. K. Oikawa, G.-W. Qin, T. Ikeshoji, R. Kainuma, and K. Ishida, Direct evidence of magnetically induced phase separation in the fcc phase and thermodynamic calculations of phase equilibria of the Co–Cr system, Acta Mater. 50, 2223 (2002).
  27. S. Zhao, G. M. Stocks, and Y. Zhang, Stacking fault energies of face-centered cubic concentrated solid solution alloys, Acta Mater. 134, 334 (2017).
  28. L.-Y. Tian, R. Lizárraga, H. Larsson, E. Holmström, and L. Vitos, A first principles study of the stacking fault energies for fcc Co-based binary alloys, Acta Mater. 136, 215 (2017).
  29. K. Ishida, Direct estimation of stacking fault energy by thermodynamic analysis, Phys. Stat. Sol. (a) 36, 717 (1976).
  30. P.-A. Dubos, J. Fajoui, N. Iskounen, M. Coret, S. Kabra, J. Kelleher, B. Girault, and D. Gloaguen, Temperature effect on strain-induced phase transformation of cobalt, Mater. Lett. 281, 128812 (2020).
  31. A. Chiba, X. G. Li, and M. S. Kim, High work-hardening rate and deformation twinning of Co-Ni-based superalloy at elevated temperatures, Philos. Mag. A 79, 1533 (1999).
  32. S. Lu, X. Sun, Y. Tian, X. An, W. Li, Y. Chen, H. Zhang, and L. Vitos, Theory of transformation-mediated twinning, PNAS Nexus 2, pgac282 (2023).
  33. G. Grimvall, Spin disorder in paramagnetic fcc iron, Phys. Rev. B 39, 12300 (1989).
  34. W. Li, S. Lu, Q. M. Hu, B. Johansson, S. K. Kwon, M. Grehk, J. Y. Johnsson, and L. Vitos, Generalized stacking fault energy of γ -Fe, Philos. Mag. 96, 524 (2016).
  35. X. Sun, S. Lu, R. Xie, X. An, W. Li, T. Zhang, C. Liang, X. Ding, Y. Wang, H. Zhang, and L. Vitos, Can experiment determine the stacking fault energy of metastable alloys? Mater. Des. 199, 109396 (2021).
  36. S. Lu, R. Li, K. Kádas, H. Zhang, Y. Tian, S. K. Kwon, K. Kokko, Q. M. Hu, S. Hertzman, and L. Vitos, Stacking fault energy of C-alloyed steels: The effect of magnetism, Acta Mater. 122, 72 (2017).
  37. L. Vitos, Computational Quantum Mechanics for Materials Engineers, Engineering Materials and Processes (Springer, London, 2007), pp. 83–94.
  38. L. Vitos, H. L. Skriver, B. Johansson, and J. Kollár, Application of the exact muffin-tin orbitals theory: The spherical cell approximation, Comput. Mater. Sci. 18, 24 (2000).
  39. B. L. Gyorffy, Coherent-potential approximation for a nonoverlapping-muffin-tin-potential model of random substitutional alloys, Phys. Rev. B 5, 2382 (1972).
  40. P. Soven, Coherent-potential model of substitutional disordered alloys, Phys. Rev. 156, 809 (1967).
  41. L. Vitos, Total-energy method based on the exact muffin-tin orbitals theory, Phys. Rev. B 64, 014107 (2001).
  42. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  43. B. L. Gyorffy, A. J. Pindor, J. Staunton, G. M. Stocks, and H. Winter, A first-principles theory of ferromagnetic phase transitions in metals, J. Phys. F: Met. Phys. 15, 1337 (1985).
  44. A. J. Pindor, J. Staunton, G. M. Stocks, and H. Winter, Disordered local moment state of magnetic transition metals: A self-consistent KKR CPA calculation, J. Phys. F: Met. Phys. 13, 979 (1983).
  45. J. Staunton, B. L. Gyorffy, A. J. Pindor, G. M. Stocks, and H. Winter, The “disordered local moment” picture of itinerant magnetism at finite temperatures, J. Magn. Magn. Mater. 45, 15 (1984).
  46. P. A. Korzhavyi, A. V. Ruban, I. A. Abrikosov, and H. L. Skriver, Madelung energy for random metallic alloys in the coherent potential approximation, Phys. Rev. B 51, 5773 (1995).
  47. See Supplemental Material at http://link.aps.org/supplemental/10.1103/lzf5-2v51 for details of the CPA screening parameter in Fig. S1 and the effective chemical potential of W in Co-W alloys in Fig. S2, and for stacking fault energies of pure Co in Table S1, binary Co-W in Table S2, Co-Al in Table S3, and Co-Ni alloys in Table S4, Co and Co81.7Al9.3W9 in Table S5 at finite temperatures, and CoCrNi-based alloys in Table S6 in comparison with available experimental and theoretical data, which includes Refs. [16, 21, 22, 25, 27, 28, 31, 32, 53, 64, 65, 68, 70, 71, 72, 73, 74, 90, 91, 92, 93, 94, 95, 96].
  48. G. S. Wang, E. K. Delczeg-Czirjak, Q. M. Hu, K. Kokko, B. Johansson, and L. Vitos, The effect of long-range order on the elastic properties of Cu3Au, J. Phys.: Condens. Matter 25, 085401 (2013).
  49. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  50. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  51. W. B. Pearson, in A Handbook of Lattice Spacings and Structures of Metals and Alloys, edited by G. Raynor, International Series of Monographs on Metal Physics and Physical Metallurgy Vol. 4 (Pergamon Press, Oxford, 1958), pp. x+1044.
  52. T. Nishizawa and K. Ishida, The Co (Cobalt) system, Bull. Alloy Phase Diagrams 4, 387 (1983).
  53. T. L. Achmad, W. Fu, H. Chen, C. Zhang, and Z. G. Yang, First-principles calculations of generalized-stacking-fault-energy of Co-based alloys, Comput. Mater. Sci. 121, 86 (2016).
  54. F. Vincent and M. Figlarz, Refinement of lattice parameters and Debye-Scherrer line intensities for FCC and HCP cobalt, C. R. Hebd. Séances Acad. Sci. 264C, 1270 (1967).
  55. R. Kohlhaas, Ph. Dünner, and N. Schmitz-Pranghe, Über die Temperaturabhängigkeit der Gitterparameter von Eisen, Kobalt und Nickel im Bereich hoher Temperaturen, Z. Angew. Phys. 23, 245 (1967).
  56. S. Muller and P. Scholten, The lattice structure of cobalt at high temperatures, Z. Angew. Phys. 20, 498 (1966).
  57. B. Roebuck, E. A. Almond, and A. M. Cottenden, The influence of composition, phase transformation and varying the relative F.C.C. and H.C.P. phase contents on the properties of dilute Co W C alloys, Mater. Sci. Eng. 66, 179 (1984).
  58. T. Nishizawa and K. Ishida, The Co-Ni (Cobalt-Nickel) system, Bull. Alloy Phase Diagrams 4, 390 (1983).
  59. A. Taylor and R. W. Floyd, Precision measurements of lattice parameters of non-cubic crystals, Acta Cryst. 3, 285 (1950).
  60. M. Hnilička and L. Karmazin, New lattice parameter study of Ni Co alloys with respect to ordering in Ni3Co, Scr. Metall. 8, 1029 (1974).
  61. W. B. Pearson and L. T. Thompson, The lattice spacings of nickel solid solutions, Can. J. Phys. 35, 349 (1957).
  62. S. U. Jen and Y. R. Huang, Magnetization and transport properties of Co-Ni-Pd alloys, J. Appl. Phys. 69, 4674 (1991).
  63. P. Modak, A. K. Verma, R. S. Rao, B. K. Godwal, and R. Jeanloz, Ab initio total-energy and phonon calculations of Co at high pressures, Phys. Rev. B 74, 012103 (2006).
  64. T. Ericsson, The temperature and concentration dependence of the stacking fault energy in the Co-Ni system, Acta Metall. 14, 853 (1966).
  65. E. B. Tadmor, A first-principles measure for the twinnability of FCC metals, J. Mech. Phys. Solids 52, 2507 (2004).
  66. M. Lenz, M. Wu, and E. Spiecker, Segregation-assisted climb of Frank partial dislocations: An alternative route to superintrinsic stacking faults in L12-hardened superalloys, Acta Mater. 191, 270 (2020).
  67. S. K. Makineni, A. Kumar, M. Lenz, P. Kontis, T. Meiners, C. Zenk, S. Zaefferer, G. Eggeler, S. Neumeier, E. Spiecker, D. Raabe, and B. Gault, On the diffusive phase transformation mechanism assisted by extended dislocations during creep of a single crystal CoNi-based superalloy, Acta Mater. 155, 362 (2018).
  68. M. Chandran and S. K. Sondhi, First-principle calculation of stacking fault energies in Ni and Ni-Co alloy, J. Appl. Phys. 109, 103525 (2011).
  69. P. Chowdhury, H. Sehitoglu, W. Abuzaid, and H. J. Maier, Mechanical response of low stacking fault energy Co–Ni alloys–Continuum, mesoscopic and atomic level treatments, Int. J. Plast. 71, 32 (2015).
  70. A. Howie and P. R. Swann, Direct measurements of stacking-fault energies from observations of dislocation nodes, Philos. Mag. 6, 1215 (1961).
  71. E. H. Köster, A. R. Thölén, and A. Howie, Stacking fault energies of Ni–Co–Cr alloys, Philos. Mag. 10, 1093 (1964).
  72. F. Häussermann and M. Wilkens, Bestimmung der Stapelfehlerenergie kubisch-flächenzentrierter Metalle aus der Analyse des elektronenmikroskopischen Beugungskontrastes von Stapelfehlerdipolen, Phys. Status Solidi (b) 18, 609 (1966).
  73. B. E. P. Beeston, I. L. Dillamore, and R. E. Smallman, The stacking-fault energy of some nickel-cobalt alloys, Met. Sci. J. 2, 12 (1968).
  74. M. H. Loretto, L. M. Clarebrough, and R. L. Segall, Stacking-fault tetrahedra in deformed face-centred cubic metals, Philos. Mag. 11, 459 (1965).
  75. R. Lizárraga, F. Pan, L. Bergqvist, E. Holmström, Z. Gercsi, and L. Vitos, First principles theory of the hcp-fcc phase transition in cobalt, Sci. Rep. 7, 3778 (2017).
  76. K. V. Werner, F. Niessen, M. Villa, and M. A. J. Somers, Experimental validation of negative stacking fault energies in metastable face-centered cubic materials, Appl. Phys. Lett. 119, 141902 (2021).
  77. F. Niessen, W. Li, K. V. Werner, S. Lu, L. Vitos, M. Villa, and M. A. Somers, Ab initio study of the effect of interstitial alloying on the intrinsic stacking fault energy of paramagnetic γ -Fe and austenitic stainless steel, Acta Mater. 253, 118967 (2023).
  78. H. L. Skriver, Crystal structure from one-electron theory, Phys. Rev. B 31, 1909 (1985).
  79. X. Zhang, B. Grabowski, F. Körmann, A. V. Ruban, Y. Gong, R. C. Reed, T. Hickel, and J. Neugebauer, Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni, Phys. Rev. B 98, 224106 (2018).
  80. S. F. Matar, A. Houari, and M. A. Belkhir, Ab initio studies of magnetic properties of cobalt and tetracobalt nitride Co4N, Phys. Rev. B 75, 245109 (2007).
  81. H. Zhang, B. Johansson, and L. Vitos, Density-functional study of paramagnetic iron, Phys. Rev. B 84, 140411 (2011).
  82. Y. H. Zhang, Y. Zhuang, A. Hu, J. J. Kai, and C. T. Liu, The origin of negative stacking fault energies and nano-twin formation in face-centered cubic high entropy alloys, Scr. Mater. 130, 96 (2017).
  83. W. M. Choi, Y. H. Jo, S. S. Sohn, S. Lee, and B. J. Lee, Understanding the physical metallurgy of the CoCrFeMnNi high-entropy alloy: An atomistic simulation study, npj Comput. Mater. 4, 1 (2018).
  84. J. Miao, C. E. Slone, T. M. Smith, C. Niu, H. Bei, M. Ghazisaeidi, G. M. Pharr, and M. J. Mills, The evolution of the deformation substructure in a Ni-Co-Cr equiatomic solid solution alloy, Acta Mater. 132, 35 (2017).
  85. C. E. Slone, S. Chakraborty, J. Miao, E. P. George, M. J. Mills, and S. R. Niezgoda, Influence of deformation induced nanoscale twinning and FCC-HCP transformation on hardening and texture development in medium-entropy CrCoNi alloy, Acta Mater. 158, 38 (2018).
  86. Y. W. Qi, Z. P. Luo, B. Zhang, and X. Y. Li, Plastic deformation induced strong and stable nanograined face-centered cubic Co, Acta Mater. 286, 120691 (2025).
  87. S. Chu, F. Zhang, D. Chen, M. Chen, and P. Liu, Atomic-scale in situ observations of reversible phase transformation assisted twinning in a CrCoNi medium-entropy alloy, Nano Lett. 24, 3624 (2024).
  88. P. Pandey, M. Heczko, N. Khatavkar, N. Mazumder, A. Sharma, A. Singh, M. J. Mills, and K. Chattopadhyay, On the faulting and twinning mediated strengthening and plasticity in a γ′ strengthened CoNi-based superalloy at room temperature, Acta Mater. 252, 118928 (2023).
  89. S. Kibey, J. B. Liu, D. D. Johnson, and H. Sehitoglu, Predicting twinning stress in fcc metals: Linking twin-energy pathways to twin nucleation, Acta Mater. 55, 6843 (2007).
  90. S. Wei and C. C. Tasan, Deformation faulting in a metastable CoCrNiW complex concentrated alloy: A case of negative intrinsic stacking fault energy? Acta Mater. 200, 992 (2020).
  91. Z. Z. Zhang, H. Sheng, Z. Wang, B. Gludovatz, Z. Z. Zhang, E. P. George, Q. Yu, S. X. Mao, and R. O. Ritchie, Dislocation mechanisms and 3D twin architectures generate exceptional strength-ductility-toughness combination in CrCoNi medium-entropy alloy, Nat. Commun. 8, 14390 (2017).
  92. P. Humble, M. H. Loretto, and L. M. Clarebrough, The nature of defects in quenched nickel, Philos. Mag. 15, 297 (1967).
  93. C. B. Carter and S. M. Holmes, The stacking-fault energy of nickel, Philos. Mag. 35, 1161 (1977).
  94. J. Ding, Q. Yu, M. Asta, and R. O. Ritchie, Tunable stacking fault energies by tailoring local chemical order in CrCoNi medium-entropy alloys, Proc. Natl. Acad. Sci. USA 115, 8919 (2018).
  95. S. F. Liu, Y. Wu, H. T. Wang, J. Y. He, J. B. Liu, C. X. Chen, X. J. Liu, H. T. Wang, and Z. P. Lu, Stacking fault energy of face-centered-cubic high entropy alloys, Intermetallics 93, 269 (2018).
  96. G. Laplanche, A. Kostka, C. Reinhart, J. Hunfeld, G. Eggeler, and E. P. George, Reasons for the superior mechanical properties of medium-entropy CrCoNi compared to high-entropy CrMnFeCoNi, Acta Mater. 128, 292 (2017).

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