Journal of Materials Science

, Volume 53, Issue 14, pp 10217–10230 | Cite as

Effect of strain on the intrinsic stacking fault energy of fcc Co: a first-principles study

  • Tria Laksana Achmad
  • Wenxiang Fu
  • Hao Chen
  • Chi Zhang
  • Zhi-Gang Yang


Although tailoring stacking fault energy (SFE) through the addition of suitable alloying element can improve mechanical properties, the effect of strain must also be included to account for the Co-based alloy design. Using first-principles density-functional-theory calculations, we revealed that there is a strong effect of the strain (volumetric strain, simple strain, and volume conserving) and external pressure on the intrinsic SFE of face-centered cubic (fcc) cobalt. This result indicated a new insight into the Co-based alloys design, especially for application at high pressure and severe plastic deformation. The intrinsic SFE decreased by increasing tensile strain or decreasing pressure, thus the tendency of forming stacking faults increases which improves the mechanical properties. Effect of volumetric (hydrostatic) strain is the strongest indicated that the volume is the dominant factor in determining the SFE and the strain-induced fcc–hcp phase transformation. Different strain methods give different charge transfer between adjacent atoms and then contribute to the variation of the atomic bonding at the specific direction and SFE behavior. Application of external pressure from 0 to 15 GPa increased the elastic constants and elastic modulus of fcc Co and then improved the ductility.



This work was supported by Tsinghua University Initiative Scientific Research Program and the National Magnetic Confinement Fusion Energy Research Project of China (2015GB118001). TLA thanks the CSC for the financial support and RKU.

Supplementary material

10853_2018_2320_MOESM1_ESM.docx (261 kb)
Supplementary material 1 (DOCX 261 kb)


  1. 1.
    Montero-Ocampo C, Juarez R, Salinas A (2002) Effect of fcc–hcp phase transformation produced by isothermal aging on the corrosion resistance of a Co–27Cr–5Mo–0.05C alloy. Metall Mater Trans A 33:2229–2235. CrossRefGoogle Scholar
  2. 2.
    Lee BS, Koizumi Y, Matsumoto H, Chiba A (2014) Collective behavior of strain-induced martensitic transformation (SIMT) in biomedical Co–Cr–Mo–N alloy polycrystal: an ex situ electron backscattering diffraction study. Mater Sci Eng A 611:263–273. CrossRefGoogle Scholar
  3. 3.
    Cui X-Y, Yen H-W, Zhu S-Q, Zheng R, Ringer SP (2015) On the universality of Suzuki segregation in binary Mg alloys from first principles. J Alloys Compd 620:38–41. CrossRefGoogle Scholar
  4. 4.
    Hu J, Sun G, Zhang X, Wang G, Jiang Z, Han S, Zhang J, Lian J (2015) Effects of loading strain rate and stacking fault energy on nanoindentation creep behaviors of nanocrystalline Cu, Ni–20 wt% Fe and Ni. J Alloys Compd 647:670–680. CrossRefGoogle Scholar
  5. 5.
    Mahato B, Shee SK, Sahu T, Chowdhury SG, Sahu P, Porter DA, Karjalainen LP (2015) An effective stacking fault energy viewpoint on the formation of extended defects and their contribution to strain hardening in a Fe–Mn–Si–Al twinning-induced plasticity steel. Acta Mater 86:69–79. CrossRefGoogle Scholar
  6. 6.
    Branicio PS, Zhang JY, Srolovitz DJ (2013) Effect of strain on the stacking fault energy of copper: a first-principles study. Phys Rev B 88:064104. CrossRefGoogle Scholar
  7. 7.
    Zhang SH, Beyerlein IJ, Legut D, Fu ZH, Zhang Z, Shang SL, Liu ZK, Germann TC, Zhang RF (2017) First-principles investigation of strain effects on the stacking fault energies, dislocation core structure, and Peierls stress of magnesium and its alloys. Phys Rev B 95:224106. CrossRefGoogle Scholar
  8. 8.
    Achmad TL, Fu W, Chen H, Zhang C, Yang ZG (2016) First-principles calculations of generalized-stacking-fault-energy of Co-based alloys. Comput Mater Sci 121:86–96. CrossRefGoogle Scholar
  9. 9.
    Achmad TL, Fu W, Chen H, Zhang C, Yang ZG (2017) Effects of alloying elements concentrations and temperatures on the stacking fault energies of Co-based alloys by computational thermodynamic approach and first-principles calculations. J Alloy Compd 694:1265–1279. CrossRefGoogle Scholar
  10. 10.
    Zhang JY, Branicio PS, Srolovitz DJ (2014) Planar fault energies of copper at large strain: a density functional theory study. J Appl Phys 116:103512. CrossRefGoogle Scholar
  11. 11.
    Brandl C, Derlet PM, Swygenhoven HV (2007) General-stacking-fault energies in highly strained metallic environments: ab initio calculations. Phys Rev B 76:054124. CrossRefGoogle Scholar
  12. 12.
    Heino P, Perondi L, Kaski K, Ristolainen E (1999) Stacking-fault energy of copper from molecular-dynamics simulations. Phys Rev B 60:14625. CrossRefGoogle Scholar
  13. 13.
    Yeratapally SR, Glavicic MG, Hardy M, Sangid MD (2016) Microstructure based fatigue life prediction framework for polycrystalline nickel-base superalloys with emphasis on the role played by twin boundaries in crack initiation. Acta Mater 107:152–167. CrossRefGoogle Scholar
  14. 14.
    Achmad TL, Fu W, Chen H, Zhang C, Yang ZG (2018) Effect of solute segregation on the intrinsic stacking fault energy of Co-based binary alloys: a first-principles study. J Alloy Compd 748:328–337. CrossRefGoogle Scholar
  15. 15.
    Hu WC, Liu Y, Li DJ, Zeng XQ, Xu CS (2013) Mechanical and thermodynamic properties of Al3Sc and Al3Li precipitates in Al–Li–Sc alloys from first-principles calculations. Physica B 427:85–90. CrossRefGoogle Scholar
  16. 16.
    Nylén J, Garcia FJ, Mosel BD, Pöttgen R, Häussermann U (2004) Structural relationships, phase stability and bonding of compounds PdSnn (n = 2, 3, 4). Solid State Sci 6:147–155. CrossRefGoogle Scholar
  17. 17.
    Kioussis N, Herbranson M, Collins E, Eberhart ME (2002) Topology of electronic charge density and energetics of planar faults in fcc metals. Phys Rev Lett 88:125501. CrossRefGoogle Scholar
  18. 18.
    Ma D, Friak M, Von Pezold J, Neugebauer J, Raabe D (2015) Ab initio study of compositional trends in solid solution strengthening in metals with low Peierls stresses. Acta Mater 98:367–376. CrossRefGoogle Scholar
  19. 19.
    Clark SJ, Segall MD, Pickard CJ, Hasnip PJ, Probert MJ, Refson K, Payne MC (2005) First principles methods using CASTEP. Z Krist 220:567–570. Google Scholar
  20. 20.
    Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133. CrossRefGoogle Scholar
  21. 21.
    Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. CrossRefGoogle Scholar
  22. 22.
    Vanderbilt D (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 41:7892. CrossRefGoogle Scholar
  23. 23.
    Murnaghan FD (1937) Finite deformations of an elastic solid. Am J Math 59:235–260. CrossRefGoogle Scholar
  24. 24.
    Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13:5188. CrossRefGoogle Scholar
  25. 25.
    Taylor A, Floyd RW (1950) Precision measurements of lattice parameters of non-cubic crystals. Acta Cryst 3:285. CrossRefGoogle Scholar
  26. 26.
    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. Comput Mater Sci 48:813–826. CrossRefGoogle Scholar
  27. 27.
    Ericsson T (1966) The temperature and concentration dependence of the stacking fault energy in the Co-Ni system. Acta Metall 14:853–865. CrossRefGoogle Scholar
  28. 28.
    Ren S, Wen C, Wu X, Gong Y, Long Y, Cheng L, Zhu X (2013) Influence of stacking fault energy and strain rate on the mechanical properties in Cu and Cu–Al–Zn alloys. Mater Sci Eng, A 585:174–177. CrossRefGoogle Scholar
  29. 29.
    Tian C, Han G, Cui C, Sun X (2014) Effects of stacking fault energy on the creep behaviors of Ni-base superalloy. Mater Des 64:316–323. CrossRefGoogle Scholar
  30. 30.
    Wu XX, Wen CE, Gong YL, Ren SY, Tao JM, Chen LP, Long Y, Zhu XK (2013) Effect of stacking fault energy and strain rate on the mechanical properties of Cu and Cu alloys. J Alloy Compd 573:1–5. CrossRefGoogle Scholar
  31. 31.
    Rémy L, Pineau A (1976) Twinning and strain-induced f.c.c.–h.c.p. transformation on the mechanical properties of Co–Ni–Cr–Mo alloys. Mater Sci Eng 26:123–132. CrossRefGoogle Scholar
  32. 32.
    Wang C, Zhang HY, Wang HY, Liu GJ, Jiang QC (2013) Effects of doping atoms on the generalized stacking-fault energies of Mg alloys from first-principles calculations. Scr Mater 69:445–448. CrossRefGoogle Scholar
  33. 33.
    Shang SL, Wang WY, Zhou BC, Wang Y, Darling KA, Kecskes LJ, Mathaudhu SN, Liu ZK (2014) Generalized stacking fault energy, ideal strength and twinnability of dilute Mg-based alloys: a first-principles study of shear deformation. Acta Mater 67:168–180. CrossRefGoogle Scholar
  34. 34.
    Achmad TL, Fu W, Chen H, Zhang C, Yang ZG (2017) Co-based alloys design based on first-principles calculations: influence of transition metal and rare-earth alloying element on stacking fault energy. AIP Conf Proc 1805:060004. CrossRefGoogle Scholar
  35. 35.
    Achmad TL, Fu W, Chen H, Zhang C, Yang ZG (2018) Computational thermodynamic and first-principles calculation of stacking fault energy on ternary Co-based alloys. Comput Mater Sci 143:112–117. CrossRefGoogle Scholar
  36. 36.
    Kong B, Zeng TX, Xu HB, Chen DL, Zhou ZW, Fu ZJ (2015) Phase diagram, mechanical and thermodynamics properties of metallic Co under high temperature and high pressure. Comput Mater Sci 104:130–137. CrossRefGoogle Scholar
  37. 37.
    Yoo CS, Cynn H, Söderlind P, Iota V (2000) New β(fcc)-Cobalt to 210 GPa. Phys Rev Lett 84:4132. CrossRefGoogle Scholar
  38. 38.
    Nye JF (1985) Physical properties of crystals. Clarendon Press, OxfordGoogle Scholar
  39. 39.
    Hill R (1952) The elastic behaviour of a crystalline aggregate. Proc Phys Soc A 65:349–354. CrossRefGoogle Scholar
  40. 40.
    Liu Y, Hu WC, Li DJ, Zeng XQ, Xu CS, Yang XJ (2012) First-principles investigation of structural and electronic properties of MgCu2 Laves phase under pressure. Intermetallics 31:257–263. CrossRefGoogle Scholar
  41. 41.
    Pettiifor DG (1992) Theoretical predictions of structure and related properties of intermetallics. J Mater Sci Technol 8:345–349. CrossRefGoogle Scholar
  42. 42.
    Pugh SF (1954) Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos Mag 45:823–843. CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Tria Laksana Achmad
    • 1
    • 2
  • Wenxiang Fu
    • 1
  • Hao Chen
    • 1
  • Chi Zhang
    • 1
  • Zhi-Gang Yang
    • 1
  1. 1.Key Laboratory of Advanced Materials, Ministry of Education, Collaborative Innovation Center of Advanced Nuclear Energy Technology, School of Materials Science and EngineeringTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Department of Metallurgical EngineeringInstitute Technology of BandungBandungIndonesia

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