First-principles study of solid solution strengthening in Mg–X (X=Al, Er) alloys

  • Xiqin Liu
  • Zili LiuEmail author
  • Guodong Liu
  • Wenjing Wang
  • Jian Li


To study the solid solution strengthening effect on magnesium (Mg)–X (X = Al, Er) alloys, supercell models of Mg, \(\hbox {Mg}_{35}\hbox {Er}\) and \(\hbox {Mg}_{35}\hbox {Al}\) are established to perform the first-principles pseudopotential plane wave calculations based on density functional theory. The calculated cohesive energy of \(\hbox {Mg}_{35}\hbox {Er}\) is lower than that of \(\hbox {Mg}_{35}\hbox {Al}\). This indicates that \(\hbox {Mg}_{35}\hbox {Er}\) has better structural stability than \(\hbox {Mg}_{35}\hbox {Al}\). The bulk modulus, Young’s modulus and shear modulus of the solid solutions increases simultaneously when Al and Er are doped into the Mg matrix. Moreover, the solid solution strengthening of Er is much higher than the Al containing alloy. The order of toughness of the three solutions from the highest to the lowest is Mg, \(\hbox {Mg}_{35}\hbox {Er}\) and \(\hbox {Mg}_{35}\hbox {Al}\), while the order of increasing elastic anisotropy is in the reverse order. The number of bonding electrons of \(\hbox {Mg}_{35}\hbox {Er}\) in the low-energy region of the Fermi level is much higher than that of \(\hbox {Mg}_{35}\hbox {Al}\), and the density of states of \(\hbox {Mg}_{35}\hbox {Er}\) at the Fermi level is higher than that of \(\hbox {Mg}_{35}\hbox {Al}\). Compared with Al atoms, Er atoms share more electric charges with Mg atoms, which leads to an increasingly uniform charge distribution around Er atoms.


First-principles Mg solid solution solid solution strengthening Er Al 



This work was supported by the National Key Research and Development Program of China (no. 2016YFB0301002), the Special Fund of Jiangsu Province for the Transformation of Scientific and Technological Achievements (BA2016039), Six Peak Talent Project of Jiangsu Province (2014-XCL-005) and Suzhou Science and Technology Development Project (SGC201534).


  1. 1.
    Azzeddine H, Abdessameud S and Alili B 2011 Bull. Mater. Sci. 34 1417CrossRefGoogle Scholar
  2. 2.
    Gao L, Zhou J, Sun Z M, Chen R S and Han E H 2011 Chin. Sci. Bull. 56 1038CrossRefGoogle Scholar
  3. 3.
    Liu G, Zhang J and Dou Y 2015 Comput. Mater. Sci103 97Google Scholar
  4. 4.
    Liu Y, Ren H, Hu W C, Li D J, Zeng X Q and Wang K G 2016 J. Mater. Sci. Technol12 1222CrossRefGoogle Scholar
  5. 5.
    Ganeshan S, Shang S L, Wang Y and Liu Z K 2009 Acta Mater. 57 3876CrossRefGoogle Scholar
  6. 6.
    Vassiliki K T 2012 Phys. arXiv:1205.0928
  7. 7.
    Wu Y and Hu W Y 2014 Phys. Res. Int2008 4Google Scholar
  8. 8.
    Wang W J, Liu Z L, Liu X Q, Zhang Z D and Wang Q D 2014 Chin. J. Nonferr. Met. 24 343Google Scholar
  9. 9.
    Rokhlin L L, Nikitina N I and Zolina Z K 1978 Met. Sci. Heat Treat20 529CrossRefGoogle Scholar
  10. 10.
    Payne M C, Teter M P and Allan D C 1992 Rev. Mod. Phys64 1045CrossRefGoogle Scholar
  11. 11.
    Khan A, Ali Z and Khan I 2016 Bull. Mater. Sci. 39 1861CrossRefGoogle Scholar
  12. 12.
    Kohn W and Sham L J 1965 Phys. Rev. 140 A1133CrossRefGoogle Scholar
  13. 13.
    Blöchl P E 1994 Phys. Rev. B 50 17953CrossRefGoogle Scholar
  14. 14.
    Kresse G and Joubert D 1999 Phys. Rev. B 59 1758CrossRefGoogle Scholar
  15. 15.
    Fischer T H and Almlof J 1992 J. Phys. Chem. 96 9768CrossRefGoogle Scholar
  16. 16.
    Bendaif S, Boumaza A and Nemiri O 2015 Bull. Mater. Sci. 38 365CrossRefGoogle Scholar
  17. 17.
    Vanderbilt D 1990 Phys. Rev. B 41 7892CrossRefGoogle Scholar
  18. 18.
    Monkhorst H J and Pack J D 1976 Phys. Rev. B 13 5188CrossRefGoogle Scholar
  19. 19.
    Feng J, Xiao B, Zhou R, Pan W and Clarke D R 2012 Acta Mater. 60 3380CrossRefGoogle Scholar
  20. 20.
    Von-Batchelder F W and Raeuchle R F 1957 Phys. Rev. 105 59CrossRefGoogle Scholar
  21. 21.
    Hardie D and Parkins R N 1959 Philos. Mag. 4 815CrossRefGoogle Scholar
  22. 22.
    Raynor G V 1942 Proc. R. Soc. A 180 107Google Scholar
  23. 23.
    Barrett C and Massalski T B 1987 Structure of metals (New York: Pergamon Press)Google Scholar
  24. 24.
    Shein I R and Ivanovskii A L 2008 J. Phys20 415218Google Scholar
  25. 25.
    Nye J F 1964 Physical properties of crystals (Oxford: Clarendon Press)Google Scholar
  26. 26.
    Wazzan A R and Robinson L B 1967 Phys. Rev. 155 586CrossRefGoogle Scholar
  27. 27.
    Slutsky L J and Garland C W 1957 Phys. Rev. 107 972CrossRefGoogle Scholar
  28. 28.
    Yang F, Fan T W, Wu J, Tang B Y, Peng L M and Ding W J 2011 Phys. Status Solidi B 248 2809CrossRefGoogle Scholar
  29. 29.
    Voigt W 1928 Lehrbuch der Kristallphysik (Leipzig, Teubner)Google Scholar
  30. 30.
    Reuss A 1929 Z. Angew. Math. Mech9 49CrossRefGoogle Scholar
  31. 31.
    Frantsevich I N, Voronov F F and Bokuta S A 1983 Elastic constants and elastic moduli of metals and insulators handbook (Kiev: Naukova Dumka) 60Google Scholar

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© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.College of Materials Science and TechnologyNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China
  2. 2.Jiangsu Favour Automotive New Stuff Sci-Tech Co., Ltd.ChangshuPeople’s Republic of China

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