Metallurgical and Materials Transactions A

, Volume 49, Issue 9, pp 4167–4172 | Cite as

First-Principles Modeling of the Temperature Dependence for the Superlattice Intrinsic Stacking Fault Energies in L1\(_2\) Ni\(_{75-x}\)X\(_x\)Al\(_{25}\) Alloys

  • J. D. T. Allen
  • A. Mottura
  • A. BreidiEmail author
Topical Collection: Superalloys and Their Applications
Part of the following topical collections:
  1. Third European Symposium on Superalloys and their Applications


Stronger and more resistant alloys are required in order to increase the performance and efficiency of jet engines and gas turbines. This will eventually require planar faults engineering, or a complete understanding of the effects of composition and temperature on the various planar faults that arise as a result of shearing of the \(\gamma ^\prime \) precipitates. In the current study, a combined scheme consisting of the density functional theory, the quasi-harmonic Debye model, and the axial Ising model, in conjunction with a quasistatic approach is used to assess the effects of composition and temperature of a series of pseudo-binary alloys based on the \(({\mathrm{Ni}}_{75-x}{\mathrm{X}}_{x}){\mathrm{Al}}_{25}\) system using distinct relaxation schemes to assess observed differences. Our calculations reveal that the (111) superlattice intrinsic stacking fault energies in these systems decline modestly with temperature between \(0\,\)K and \(1000\,\)K.



This study made use of these computational facilities: (a) the University of Birmingham’s BlueBEAR HPC service (, (b) MidPlus Regional HPC Center (, and (c) Beskow cluster ( The authors are therefore very much grateful and would like to thank them for making this study possible. The authors would like, as well, to thank the EPSRC (Grant EP/M021874/1) and EU FP7 (Grant GA109937) for their financial support. Part of this study (A. Breidi) has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under the Grant Agreement No. 633053 and from the RCUK Energy Programme [Grant Number EP/P012450/1]. The views and opinions expressed herein do not necessarily reflect those of the European Commission.


  1. 1.
    C.M.F. Rae and R.C. Reed.: Acta Mater. 55(3):1067–81 (2007). Scholar
  2. 2.
    L. Vitos, J. O. Nilsson and B. Johansson: Acta Mater. 54:3821–26 (2006). Scholar
  3. 3.
    Y. Qi and R. K. Mishra: Phys. Rev. B, 75:224105–10, 2007. Scholar
  4. 4.
    C. B. Carter and S. M. Holmes: Philos. Mag., 35:1161–72, 1977. Scholar
  5. 5.
    H. Suzuki: J. Phys. Soc. Jpn., 17:322--25, 1962. Scholar
  6. 6.
    V. A. Vorontsov, L. Kovarik, M. J. Mills, and C. M. F. Rae: Acta Mater., 60(12):4866–78, 2012. Scholar
  7. 7.
    G. B. Viswanathan, R. Shi, A. Genc, V. A. Vorontsov, L. Kovarik, C. M. F. Rae, and M. J. Mills: Scripta Mater., 94:5–8, 2015. Scholar
  8. 8.
    K. V. Vamsi and S. Karthikeyan: in Superalloys 2012, pp. 521--530. Wiley (2012). Scholar
  9. 9.
    K. V. Vamsi and S. Karthikeyan: in Superalloys 2012. Wiley, 2012, pp. 521–30.
  10. 10.
    P.J.H. Denteneer and W. van Haeringen: J. Phys. C, 20(32):L883, 1987.CrossRefGoogle Scholar
  11. 11.
    A. Breidi, J. Allen, and A. Mottura: Acta Mater., 145:97–108, 2018. Scholar
  12. 12.
    A. Breidi, J. Allen, and A. Mottura: Phys. Status Solidi (b), 2017. Scholar
  13. 13.
    M.A. Blanco, E. Francisco, and V. Luaña.: Comput. Phys. Commun., 158(1):57–72, 2004. Scholar
  14. 14.
    Y. Mishima, S. Ochiai, and T. Suzuki: Acta Metall., 33(6):1161–69, 1985. Scholar
  15. 15.
    A. V. Ruban, V.A. Popov, V.K. Portnoi, and V.I. Bogdanov. Philos. Mag., 94(1):20--34, 2014. Scholar
  16. 16.
    C. Jiang and B. Gleeson: Scripta Mater., 55(5):433–36, 2006. Scholar
  17. 17.
    A. V. Ruban and H. L. Skriver: Phys. Rev. B, 55:856–74, 1997. Scholar
  18. 18.
    J. M. Cowley: J. Appl. Phys., 21(1):24–30, 1950. Scholar
  19. 19.
    B. E. Warren: X-ray Diffraction. New York, Dover, 1990.Google Scholar
  20. 20.
    P. Hohenberg and W. Kohn.: Phys. Rev., 136(3B):B864–71, 1964. Scholar
  21. 21.
    W. Kohn and L. J. Sham.: Phys. Rev., 140(4A):A1133–38, 1965. Scholar
  22. 22.
    G. Kresse and D. Joubert.: Phys. Rev. B, 59:1758–1775, 1999. Scholar
  23. 23.
    G. Kresse and J. Furthmüller.: Comput. Mater. Sci., 6(1):15–50, 1996. Scholar
  24. 24.
    P. E. Blöchl: Phys. Rev. B, 50:17953–79, 1994. Scholar
  25. 25.
    J. P. Perdew, K. Burke, and M. Ernzerhof.: Phys. Rev. Lett., 77(18):3865–68, 1996. Scholar
  26. 26.
    W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery: Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, Cambridge, 2007. ISBN 9780521880688.Google Scholar
  27. 27.
    C. A. Swenson: J. Phys. Chem. Solids, 29(8):1337–48, 1968. Scholar
  28. 28.
    E. F. Wasserman: in Handbook of Ferromagnetic Materials, Handbook of Ferromagnetic Materials, vol. 5. Elsevier, 1990, pp. 237–322.
  29. 29.
    O.L. Anderson and D.G. Isaak: Elastic Constants of Mantle Minerals at High Temperature. American Geophysical Union, 2013, pp. 64–97. ISBN 9781118668191.
  30. 30.
    Y. Wang, J. J. Wang, H. Zhang, V. R. Manga, S. L. Shang, L.-Q. Chen, and Z.-K. Liu: J. Phys., 2010, vol. 22(22), art. no. 225404.Google Scholar
  31. 31.
    S.-L. Shang, H. Zhang, Y. Wang, and Z.-K. Liu: J. Phys., 2010, vol. 22(37), art. no. 375403.Google Scholar
  32. 32.
    O. Gülseren and R. E. Cohen.: Phys. Rev. B, 2002, vol. 65, art. no. 064103,
  33. 33.
    I. Bleskov, T. Hickel, J. Neugebauer, and A. Ruban.: Phys. Rev. B, 2016, vol. 93, art. no. 214115,
  34. 34.
    V. I. Razumovskiy, A. Reyes-Huamantinco, P. Puschnig, and A. V. Ruban.: Phys. Rev. B, 2016, vol. 93, art. no. 054111,
  35. 35.
    C. Kittel: Introduction to Solid State Physics, 7th edition. Wiley, New York, 1996Google Scholar
  36. 36.
    Y.-K. Kim, D. Kim, H.-K. Kim, C.-S. Oh, and B.-J. Lee: Int. J. Plast., 79:153–175, 2016. Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  1. 1.School of Metallurgy and MaterialsUniversity of BirminghamEdgbastonUK
  2. 2.UK Atomic Energy AuthorityCulham Science CentreOxfordshireUK

Personalised recommendations