, Volume 69, Issue 11, pp 2107–2112 | Cite as

Thermal Expansion, Elastic and Magnetic Properties of FeCoNiCu-Based High-Entropy Alloys Using First-Principle Theory

  • Shuo Huang
  • Ádám Vida
  • Anita Heczel
  • Erik Holmström
  • Levente Vitos


The effects of V, Cr, and Mn on the magnetic, elastic, and thermal properties of FeCoNiCu high-entropy alloy are studied by using the exact muffin-tin orbitals method in combination with the coherent potential approximation. The calculated lattice parameters and Curie temperatures in the face-centered-cubic structure are in line with the available experimental and theoretical data. A significant change in the magnetic behavior is revealed when adding equimolar V, Cr, and Mn to the host composition. The three independent single-crystal elastic constants are computed using a finite strain technique, and the polycrystalline elasticity parameters including shear modulus, Young’s modulus, Pugh ratio, Poisson’s ratio, and elastic anisotropy are derived and discussed. The effects of temperature on the structural parameters are determined by making use of the Debye–Grüneisen model. It is found that FeCoNiCuCr possesses a slightly larger thermal expansion coefficient than do the other alloys considered here.



This work was supported by the Swedish Research Council, the Swedish Foundation for Strategic Research, the Swedish Foundation for International Cooperation in Research and Higher Education, the Carl Tryggers Foundation, the Sweden’s Innovation Agency (VINNOVA Grant No. 2014-03374), the China Scholarship Council, and the Hungarian Scientific Research Fund (OTKA 109570). We acknowledge the Swedish National Supercomputer Centre in Linköping for computer resources.


  1. 1.
    J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, and S.Y. Chang, Adv. Eng. Mater. 6, 299 (2004).CrossRefGoogle Scholar
  2. 2.
    B. Cantor, I.T.H. Chang, P. Knight, and A.J.B. Vincent, Mater. Sci. Eng. A 375–377, 213 (2004).CrossRefGoogle Scholar
  3. 3.
    J.W. Yeh, JOM 65, 1759 (2013).CrossRefGoogle Scholar
  4. 4.
    M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang, High-Entropy Alloys: Fundamentals and Applications (Switzerland: Springer, 2016).CrossRefGoogle Scholar
  5. 5.
    C.J. Tong, M.R. Chen, J.W. Yeh, S.J. Lin, S.K. Chen, T.T. Shun, and S.Y. Chang, Metall. Mater. Trans. A 36, 1263 (2005).CrossRefGoogle Scholar
  6. 6.
    C.Y. Hsu, C.C. Juan, W.R. Wang, T.S. Sheu, J.W. Yeh, and S.K. Chen, Mater. Sci. Eng. A 528, 3581 (2011).CrossRefGoogle Scholar
  7. 7.
    M.H. Tsai, C.W. Wang, C.W. Tsai, W.J. Shen, J.W. Yeh, J.Y. Gan, and W.W. Wu, J. Electrochem. Soc. 158, H1161 (2011).CrossRefGoogle Scholar
  8. 8.
    Y.L. Chou, Y.C. Wang, J.W. Yeh, and H.C. Shih, Corros. Sci. 52, 3481 (2010).CrossRefGoogle Scholar
  9. 9.
    Y.F. Kao, T.D. Lee, S.K. Chen, and Y.S. Chang, Corros. Sci. 52, 1026 (2010).CrossRefGoogle Scholar
  10. 10.
    M.H. Chuang, M.H. Tsai, W.R. Wang, S.J. Lin, and J.W. Yeh, Acta Mater. 59, 6308 (2011).CrossRefGoogle Scholar
  11. 11.
    B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, and R.O. Ritchie, Science 345, 1153 (2014).CrossRefGoogle Scholar
  12. 12.
    Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, and C.C. Tasan, Nature 534, 227 (2016).CrossRefGoogle Scholar
  13. 13.
    Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, and Z.P. Lu, Prog. Mater. Sci. 61, 1 (2014).CrossRefGoogle Scholar
  14. 14.
    Y.F. Kao, T.J. Chen, S.K. Chen, and J.W. Yeh, J. Alloys Compd. 488, 57 (2009).CrossRefGoogle Scholar
  15. 15.
    H.P. Chou, Y.S. Chang, S.K. Chen, and J.W. Yeh, Mater. Sci. Eng. B 163, 184 (2009).CrossRefGoogle Scholar
  16. 16.
    W.H. Liu, J.Y. He, H.L. Huang, H. Wang, Z.P. Lu, and C.T. Liu, Intermetallics 60, 1 (2015).CrossRefGoogle Scholar
  17. 17.
    L. Liu, J.B. Zhu, C. Zhang, J.C. Li, and Q. Jiang, Mater. Sci. Eng. A 548, 64 (2012).CrossRefGoogle Scholar
  18. 18.
    J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).CrossRefGoogle Scholar
  19. 19.
    L. Vitos, Computational Quantum Mechanics for Materials Engineers (London: Springer, 2007).Google Scholar
  20. 20.
    P. Soven, Phys. Rev. 156, 809 (1967).CrossRefGoogle Scholar
  21. 21.
    B.L. Győrffy, A.J. Pindor, J. Staunton, G.M. Stocks, and H. Winter, J. Phys. F: Met. Phys. 15, 1337 (1985).CrossRefGoogle Scholar
  22. 22.
    S. Huang, W. Li, S. Lu, F. Tian, J. Shen, E. Holmström, and L. Vitos, Scr. Mater. 108, 44 (2015).CrossRefGoogle Scholar
  23. 23.
    S. Huang, W. Li, X. Li, S. Schönecker, L. Bergqvist, E. Holmström, L.K. Varga, and L. Vitos, Mater. Des. 103, 71 (2016).CrossRefGoogle Scholar
  24. 24.
    S. Huang, Á. Vida, D. Molnár, K. Kádas, L.K. Varga, E. Holmström, and L. Vitos, Appl. Phys. Lett. 107, 251906 (2015).CrossRefGoogle Scholar
  25. 25.
    S. Huang, Á. Vida, W. Li, D. Molnár, S.K. Kwon, E. Holmström, B. Varga, L.K. Varga, and L. Vitos, Appl. Phys. Lett. 110, 241902 (2017).CrossRefGoogle Scholar
  26. 26.
    V.L. Moruzzi, J.F. Janak, and K. Schwarz, Phys. Rev. B 37, 790 (1988).CrossRefGoogle Scholar
  27. 27.
    R. Hill, Proc. Phys. Soc. Sect. A 65, 349 (1952).CrossRefGoogle Scholar
  28. 28.
    Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, and P.K. Liaw, Adv. Eng. Mater. 10, 534 (2008).CrossRefGoogle Scholar
  29. 29.
    C.J. Tong, Y.L. Chen, J.W. Yeh, S.J. Lin, S.K. Chen, T.T. Shun, C.H. Tsau, and S.Y. Chang, Metall. Mater. Trans. A 36, 881 (2005).CrossRefGoogle Scholar
  30. 30.
    X.F. Wang, Y. Zhang, Y. Qiao, and G.L. Chen, Intermetallics 15, 357 (2007).CrossRefGoogle Scholar
  31. 31.
    L. Liu, J.B. Zhu, L. Li, J.C. Li, and Q. Jiang, Mater. Des. 44, 223 (2013).CrossRefGoogle Scholar
  32. 32.
    S. Praveen, B.S. Murty, and R.S. Kottada, Mater. Sci. Eng. A 534, 83 (2012).CrossRefGoogle Scholar
  33. 33.
    S. Guo and C.T. Liu, Prog. Nat. Sci. Mater. Int. 21, 433 (2011).CrossRefGoogle Scholar
  34. 34.
    K. Sato, L. Bergqvist, J. Kudrnovský, P.H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G. Bouzerar, H. Katayama-Yoshida, V.A. Dinh, T. Fukushima, H. Kizaki, and R. Zeller, Rev. Mod. Phys. 82, 1633 (2010).CrossRefGoogle Scholar
  35. 35.
    F. Körmann, D. Ma, D.D. Belyea, M.S. Lucas, C.W. Miller, B. Grabowski, and M.H.F. Sluiter, Appl. Phys. Lett. 107, 142404 (2015).CrossRefGoogle Scholar
  36. 36.
    D.C. Wallace, Thermodynamics of Crystals (New York: Wiley, 1972).Google Scholar
  37. 37.
    D.G. Pettifor, Mater. Sci. Technol. 8, 345 (1992).CrossRefGoogle Scholar
  38. 38.
    J.F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (New York: Oxford University Press, 1985).MATHGoogle Scholar
  39. 39.
    S. Huang, C.H. Zhang, R.Z. Li, J. Shen, and N.X. Chen, Intermetallics 51, 24 (2014).CrossRefGoogle Scholar
  40. 40.
    X.Q. Chen, H.Y. Niu, D.Z. Li, and Y.Y. Li, Intermetallics 19, 1275 (2011).CrossRefGoogle Scholar
  41. 41.
    S.F. Pugh, Philos. Mag. 45, 823 (1954).CrossRefGoogle Scholar
  42. 42.
    G. Wang, S. Schönecker, S. Hertzman, Q.M. Hu, B. Johansson, S.K. Kwon, and L. Vitos, Phys. Rev. B 91, 224203 (2015).CrossRefGoogle Scholar
  43. 43.
    K. Jin, S. Mu, K. An, W.D. Porter, G.D. Samolyuk, G.M. Stocks, and H. Bei, Mater. Des. 117, 185 (2017).CrossRefGoogle Scholar
  44. 44.
    G. Laplanche, P. Gadaud, O. Horst, F. Otto, G. Eggeler, and E.P. George, J. Alloys Compd. 623, 348 (2015).CrossRefGoogle Scholar
  45. 45.
    L. Vitos and B. Johansson, Phys. Rev. B 79, 024415 (2009).CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Shuo Huang
    • 1
  • Ádám Vida
    • 2
    • 3
  • Anita Heczel
    • 3
  • Erik Holmström
    • 4
  • Levente Vitos
    • 1
    • 2
    • 5
  1. 1.Applied Materials Physics, Department of Materials Science and EngineeringRoyal Institute of TechnologyStockholmSweden
  2. 2.Institute for Solid State Physics and OpticsWigner Research Centre for PhysicsBudapestHungary
  3. 3.Department of Materials PhysicsEötvös UniversityBudapestHungary
  4. 4.Sandvik Coromant R&DStockholmSweden
  5. 5.Department of Physics and Astronomy, Division of Materials TheoryUppsala UniversityUppsalaSweden

Personalised recommendations