Journal of Materials Science

, Volume 54, Issue 21, pp 13609–13618 | Cite as

When a defect is a pathway to improve stability: a case study of the L12 Co3TM superlattice intrinsic stacking fault

  • Ying Zhang
  • Jinshan Li
  • William Yi WangEmail author
  • Peixuan Li
  • Bin Tang
  • Jun Wang
  • Hongchao Kou
  • Shunli Shang
  • Yi Wang
  • Laszlo J. Kecskes
  • Xidong Hui
  • Qiang FengEmail author
  • Zi-Kui LiuEmail author
Computation & theory


Effect of solutes of transition metals (TM = Cr, Fe, Hf, Mn, Mo, Nb, Ni, Pt, Rh, Ru, Re, Ta, Ti, V, W, Y and Zr) on the local phase transition between the L12 and D019 structures in superlattice intrinsic stacking fault (SISF) of Co3TM has been investigated. All the models employed herein, i.e. (1) the SISF-containing supercell, (2) the axial nearest-neighbor Ising (ANNI) model, and (3) both the L12- and D019-containing (L12 + D019) supercell, yield the same result regarding the stability of SISF in L12-type Co3TM. In the view of bonding charge density, the atomic and electronic basis of local D019 phase transition in the SISF fault layers of Co3TM are revealed. Especially, the negative SISF energy predicted by the L12 + D019 model suggests that both the SISF fault layers (i.e. the local D019 structure) and the L12 phase of Co3TM can be stabilized through a coupling interaction between the fault layers and the solutes, paving a pathway to stabilize Co-base superalloys via Co3TM precipitate. Moreover, the consist results of ESISF via the ANNI model with the classical SISF-supercell method utilized in first-principles calculations supports the approach to efficiently distinguish various planar faults and predict their corresponding energies, such as SISF, superlattice intrinsic stacking fault, anti-phase boundaries, and so on.



This work was financially supported by National Natural Science Foundation of China (51771019 and 51690163), project of SKL-AMM-USTB (Grant No. 2016-Z07) and Fundamental Research Funds for the Central Universities in China (G2016KY0302). First-principles calculations were carried out on the clusters at the Northwestern Polytechnical University.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10853_2019_3884_MOESM1_ESM.docx (4.2 mb)
Supplementary material 1 (DOCX 4348 kb)


  1. 1.
    Krasheninnikov AV (2018) When defects are not defects. Nat Mater 17:757–758CrossRefGoogle Scholar
  2. 2.
    Li X, Lu K (2017) Playing with defects in metals. Nat Mater 16:700–701CrossRefGoogle Scholar
  3. 3.
    Kosterlitz JM (2017) Nobel lecture: topological defects and phase transitions. Rev Mod Phys 89:040501CrossRefGoogle Scholar
  4. 4.
    Wang WY, Wang Y, Shang SL, Darling KA, Kim H, Tang B, Kou HC, Mathaudhu SN, Hui XD, Li JS, Kecskes LJ, Liu Z-K (2017) Strengthening Mg by self-dispersed nano-lamellar faults. Mater Res Lett 5:415–425CrossRefGoogle Scholar
  5. 5.
    Kumar M, Schuh CA (2006) Preface to the viewpoint set on grain boundary engineering. Scr Mater 54:961–962CrossRefGoogle Scholar
  6. 6.
    Beyerlein IJ, Demkowicz MJ, Misra A, Uberuaga BP (2015) Defect-interface interactions. Prog Mater Sci 74:125–210CrossRefGoogle Scholar
  7. 7.
    Ma XL, Huang CX, Xu WZ, Zhou H, Wu XL, Zhu YT (2015) Strain hardening and ductility in a coarse-grain/nanostructure laminate material. Scr Mater 103:57–60CrossRefGoogle Scholar
  8. 8.
    Ball P (2013) Four decades of materials developments transform society. MRS Bull 38:873–885CrossRefGoogle Scholar
  9. 9.
    Wang WY, Darling KA, Wang Y, Shang S-L, Kecskes LJ, Hui XD, Liu Z-K (2016) Power law scaled hardness of Mn strengthened nanocrystalline AlMn non-equilibrium solid solutions. Scr Mater 120:31–36CrossRefGoogle Scholar
  10. 10.
    Wang WY, Zhang Y, Li J, Zou C, Tang B, Wang H, Lin D, Wang J, Kou H, Xu D (2018) Insight into solid-solution strengthened bulk and stacking faults properties in Ti alloys: a comprehensive first-principles study. J Mater Sci 53:7493–7505. CrossRefGoogle Scholar
  11. 11.
    Wang WY, Tang B, Shang S-L, Wang J, Li S, Wang Y, Zhu J, Wei S, Wang J, Darling KA, Mathaudhu SN, Wang Y, Ren Y, Hui XD, Kecskes LJ, Li J, Liu Z-K (2019) Local lattice distortion mediated formation of stacking faults in Mg alloys. Acta Mater 170:231–239CrossRefGoogle Scholar
  12. 12.
    Sato J, Omori T, Oikawa K, Ohnuma I, Kainuma R, Ishida K (2006) Cobalt-base high-temperature alloys. Science 312:90–91CrossRefGoogle Scholar
  13. 13.
    Titus MS, Eggeler YM, Suzuki A, Pollock TM (2015) Creep-induced planar defects in L12-containing Co- and CoNi-base single-crystal superalloys. Acta Mater 82:530–539CrossRefGoogle Scholar
  14. 14.
    Titus MS, Mottura A, Babu Viswanathan G, Suzuki A, Mills MJ, Pollock TM (2015) High resolution energy dispersive spectroscopy mapping of planar defects in L12-containing Co-base superalloys. Acta Mater 89:423–437CrossRefGoogle Scholar
  15. 15.
    Eggeler YM, Muller J, Titus MS, Suzuki A, Pollock TM, Spiecker E (2016) Planar defect formation in the gamma’ phase during high temperature creep in single crystal CoNi-base superalloys. Acta Mater 113:335–349CrossRefGoogle Scholar
  16. 16.
    Smith TM, Esser BD, Antolin N, Carlsson A, Williams REA, Wessman A, Hanlon T, Fraser HL, Windl W, McComb DW, Mills MJ (2016) Phase transformation strengthening of high-temperature superalloys. Nat Commun 7:13434CrossRefGoogle Scholar
  17. 17.
    Wang L, Oehring M, Lorenz U, Yang J, Pyczak F (2018) Influence of alloying additions on L12 decomposition in γ–γ′ Co–9Al–9W–2X quaternary alloys. Scr Mater 154:176–181CrossRefGoogle Scholar
  18. 18.
    Suzuki A, Inui H, Pollock TM (2015) L12-strengthened cobalt-base superalloys. Annu Rev Mater Res 45:345–368CrossRefGoogle Scholar
  19. 19.
    Wang WY, Xue F, Zhang Y, Shang S-L, Wang Y, Darling KA, Kecskes LJ, Li J, Hui X, Feng Q, Liu Z-K (2018) Atomic and electronic basis for solutes strengthened (010) anti-phase boundary of L12 Co3(Al, TM): a comprehensive first-principles study. Acta Mater 145:30–40CrossRefGoogle Scholar
  20. 20.
    Xue F, Zhou HJ, Shi QY, Chen XH, Chang H, Wang ML, Feng Q (2015) Creep behavior in a γ′ strengthened Co–Al–W–Ta–Ti single-crystal alloy at 1000 °C. Scr Mater 97:37–40CrossRefGoogle Scholar
  21. 21.
    Xue F, Zhou HJ, Feng Q (2014) Improved high-temperature microstructural stability and creep property of novel Co-base single-crystal alloys containing Ta and Ti. JOM 66:2486–2494CrossRefGoogle Scholar
  22. 22.
    Carvalho PA, Bronsveld PM, Kooi BJ, De Hosson JTM (2002) On the fcc-D019 transformation in Co-W alloys. Acta Mater 50:4511–4526CrossRefGoogle Scholar
  23. 23.
    Reyes Tirado FL, Perrin Toinin J, Dunand DC (2018) γ + γ′ microstructures in the Co–Ta–V and Co–Nb–V ternary systems. Acta Mater 151:137–148CrossRefGoogle Scholar
  24. 24.
    Cheong B, Feng YC, Laughlin DE (1994) L12 to D019 structural ordering during the fcc to hcp transformation in a CoCrTa alloy. Scr Metall Mater 30:1419–1424CrossRefGoogle Scholar
  25. 25.
    Li Y, Pyczak F, Oehring M, Wang L, Paul J, Lorenz U, Yao Z (2017) Thermal stability of γ′ phase in long-term aged Co–Al–W alloys. J Alloy Compd 729:266–276CrossRefGoogle Scholar
  26. 26.
    Wang WY, Shang SL, Wang Y, Darling KA, Mathaudhu SN, Hui XD, Liu ZK (2012) Electron localization morphology of the stacking faults in Mg: a first-principles study. Chem Phys Lett 551:121–125CrossRefGoogle Scholar
  27. 27.
    Wang WY, Shang SL, Wang Y, Darling KA, Kecskes LJ, Mathaudhu SN, Hui XD, Liu Z-K (2014) Electronic structures of long periodic stacking order structures in Mg: a first-principles study. J Alloy Compd 586:656–662CrossRefGoogle Scholar
  28. 28.
    Vamsi KV, Karthikeyan S (2018) High-throughput estimation of planar fault energies in A3B compounds with L12 structure. Acta Mater 145:532–542CrossRefGoogle Scholar
  29. 29.
    Titus MS, Rhein RK, Wells PB, Dodge PC, Viswanathan GB, Mills MJ, Van der Ven A, Pollock TM (2016) Solute segregation and deviation from bulk thermodynamics at nanoscale crystalline defects. Sci Adv 2:e1601796–e1601796CrossRefGoogle Scholar
  30. 30.
    Chandran M, Sondhi SK (2011) First-principle calculation of stacking fault energies in Ni and Ni–Co alloy. J Appl Phys 109:103525CrossRefGoogle Scholar
  31. 31.
    Denteneer PJH, Haeringen WV (1987) Stacking-fault energies in semiconductors from first-principles calculations. J Phys C: Solid State Phys 20:L883–L887CrossRefGoogle Scholar
  32. 32.
    Jordan RG, Liu Y, Qiu SL, Xu X, Durham PJ, Guo GY (1993) Origin of long-period superlattices in Ag–Mg alloys. Phys Rev B 47:16521–16524CrossRefGoogle Scholar
  33. 33.
    Colinet C, Pasturel A (2002) Structural stability of one-dimensional long-period structures in the TiAl3 compound. J Phys: Condens Matter 14:6713Google Scholar
  34. 34.
    Denteneer PJH, Haeringen WV (1987) Stacking-fault energies in semiconductors from first-principles calculations. J Phys C: Solid State Phys 20:L883CrossRefGoogle Scholar
  35. 35.
    Kresse G, Furthmuller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186CrossRefGoogle Scholar
  36. 36.
    Kresse G, Furthmuller J (1996) Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp Mater Sci 6:15–50CrossRefGoogle Scholar
  37. 37.
    Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758–1775CrossRefGoogle Scholar
  38. 38.
    Wang Y, Perdew JP (1991) Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. Phys Rev B 44:13298–13307CrossRefGoogle Scholar
  39. 39.
    Wang Y, Chen LQ, Liu ZK, Mathaudhu SN (2010) First-principles calculations of twin-boundary and stacking-fault energies in magnesium. Scr Mater 62:646–649CrossRefGoogle Scholar
  40. 40.
    Methfessel M, Paxton AT (1989) High-precision sampling for Brillouin-zone integration in metals. Phys Rev B 40:3616–3621CrossRefGoogle Scholar
  41. 41.
    Blochl PE, Jepsen O, Andersen OK (1994) Improved tetrahedron method for Brillouin-zone integrations. Phys Rev B 49:16223–16233CrossRefGoogle Scholar
  42. 42.
    Birch F (1978) Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high-pressures and 300°K. J Geophys Res 83:1257–1268CrossRefGoogle Scholar
  43. 43.
    Shang SL, Saengdeejing A, Mei ZG, Kim DE, Zhang H, Ganeshan S, Wang Y, Liu ZK (2010) First-principles calculations of pure elements: equations of state and elastic stiffness constants. Comp Mater Sci 48:813–826CrossRefGoogle Scholar
  44. 44.
    Nakashima PNH, Smith AE, Etheridge J, Muddle BC (2011) The bonding electron density in aluminum. Science 331:1583–1586CrossRefGoogle Scholar
  45. 45.
    Wang WY, Shang SL, Wang Y, Han F, Darling KA, Wu Y, Xie X, Senkov ON, Li J, Hui XD, Dahmen KA, Liaw PK, Kecskes LJ, Liu Z-K (2017) Atomic and electronic basis for the serrations of refractory high-entropy alloys. NPJ Comput Mater 3:23CrossRefGoogle Scholar
  46. 46.
    Momma K, Izumi F (2011) VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J Appl Crystallogr 44:1272–1276CrossRefGoogle Scholar
  47. 47.
    Breidi A, Allen J, Mottura A (2018) First-principles modeling of superlattice intrinsic stacking fault energies in Ni3Al based alloys. Acta Mater 145:97–108CrossRefGoogle Scholar
  48. 48.
    Choudhuri D, Srinivasan SG, Gibson MA, Zheng Y, Jaeger DL, Fraser HL, Banerjee R (2017) Exceptional increase in the creep life of magnesium rare-earth alloys due to localized bond stiffening. Nat Commun 8:2000CrossRefGoogle Scholar
  49. 49.
    Xu WW, Han JJ, Wang Y, Wang CP, Liu XJ, Liu ZK (2013) First-principles investigation of electronic, mechanical and thermodynamic properties of L12 ordered Co3(M, W) (M = Al, Ge, Ga) phases. Acta Mater 61:5437–5448CrossRefGoogle Scholar
  50. 50.
    Ellner M, Kek S, Predel B (1992) Zur Existenz einer Phase Co3Al vom Cu3Au-Strukturtyp. J Alloy Compd 189:245–248CrossRefGoogle Scholar
  51. 51.
    Xu WW, Han JJ, Wang ZW, Wang CP, Wen YH, Liua XJ, Zhu ZZ (2013) Thermodynamic, structural and elastic properties of Co3X (X = Ti, Ta, W, V, Al) compounds from first-principles calculations. Intermetallics 32:303–311CrossRefGoogle Scholar
  52. 52.
    Jin M, Miao N, Zhao W, Zhou J, Du Q, Sun Z (2018) Structural stability and mechanical properties of Co3(Al, M) (M = Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, W) compounds. Comp Mater Sci 148:27–37CrossRefGoogle Scholar
  53. 53.
    Omori T, Oikawa K, Sato J, Ohnuma I, Kattner UR, Kainuma R, Ishida K (2013) Partition behavior of alloying elements and phase transformation temperatures in Co–Al–W-base quaternary systems. Intermetallics 32:274–283CrossRefGoogle Scholar
  54. 54.
    Saal JE, Wolverton C (2016) Energetics of antiphase boundaries in γ′ Co3(Al, W)-based superalloys. Acta Mater 103:57–62CrossRefGoogle Scholar
  55. 55.
    Yang S, Kiraly B, Wang WY, Shang S, Cao B, Zeng H, Zhao Y, Li W, Liu Z-K, Cai W, Huang TJ (2012) Fabrication and characterization of beaded SiC quantum rings with anomalous red spectral shift. Adv Mater 24:5598–5603CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.State Key Laboratory of Solidification ProcessingNorthwestern Polytechnical UniversityXi’anChina
  2. 2.State Key Laboratory for Advanced Metals and MaterialsUniversity of Science and Technology BeijingBeijingChina
  3. 3.Department of Materials Science and EngineeringThe Pennsylvania State UniversityUniversity ParkUSA
  4. 4.Hopkins Extreme Materials InstituteJohns Hopkins UniversityBaltimoreUSA

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