The β1 Triad-Related Configurations in a Mg-RE Alloy


As the building block of a honeycomb precipitate network, the triadic arrangement of β1 strengthening precipitates is technologically important for the potential development of highly tuneable nanostructure in rare-earth (RE) containing Mg alloys. In this work, we provide systematic experimental observations of those impinged β1 variants in a Mg-Nd alloy, which are directly related to the characteristic triadic configuration. It is found that the isolated α-Mg crystal in a β1 triad has a 10.5 deg rotation when it has a perfect equilateral-triangular shape. This rotation angle decreases to ~ 9.4 deg when the isolated α-Mg crystal exhibits a non-equilateral shape. In this case, one or two of its lateral interfaces include a step with a height of 0.56 nm to reduce the lattice mismatch. Furthermore, the pre-stage prior to the formation of β1 triadic configuration is revealed for the first time. It originates from the implement of two β1 variants with the same sense of shear. The presence of such two variants, in the absence of the third variant, leads to a rotation of the α-Mg crystal in the small area close to the approaching ends of these two variants. A low-angle symmetrical tilt boundary around the [0001]α rotation axis is formed between the rotated and unrotated α-Mg crystals. Most of the tilt boundaries observed in this work have a tilt angle of ~ 4.7 deg. The atomic structure of such a tilt boundary is constructed using a crystallographic model and validated by molecular dynamics simulation. The unique distribution of Nd-rich solute clusters along the tilt boundary is qualitatively discussed based on crystallographic analysis.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. 1.

    T.M. Pollock: Science, 2010, vol. 328, pp. 986-7.

    CAS  Google Scholar 

  2. 2.

    A.A. Luo: Inter. Mater. Rev., 2004, vol. 49, pp. 13-30.

    CAS  Google Scholar 

  3. 3.

    M. Bamberger and G. Dhem: Ann. Rev. Mater. Res., 2008, vol. 38, pp. 505-33.

    CAS  Google Scholar 

  4. 4.

    A. Kelly and R.B. Nicholson: Prog. Mater. Sci., 1963, vol. 10, pp. 151-391.

    Google Scholar 

  5. 5.

    J.F. Nie: Scr. Mater., 2003, vol. 48, pp. 1009-15.

    CAS  Google Scholar 

  6. 6.

    J.F. Nie: Metall. Mater. Trans. A, 2012, vol. 43, pp. 3891-3939.

    Google Scholar 

  7. 7.

    Y.M. Zhu, A. J. Morton and J.F. Nie: Scr. Mater., 2008, vol. 58, pp. 525-8.

    CAS  Google Scholar 

  8. 8.

    P. Vostry, B. Solma, I. Stulikova, F. Buch and B.L. Mordike: Phys. Status. Solidi. A, 1999, vol. 175, pp. 491-500.

    CAS  Google Scholar 

  9. 9.

    I.A. Anyanwu, S. Kamado and Y. Kojima: Mater. Trans., 2001, vol. 42, pp. 1206-11.

    CAS  Google Scholar 

  10. 10.

    P.J. Apps, H. Karimzadeh, J.F. King and G.W. Lorimer: Scr. Mater., 2003, vol. 48, pp. 1023-8.

    CAS  Google Scholar 

  11. 11.

    T. Honma, T. Ohkubo, K. Hono and S. Kamado: Mater. Sci. Eng. A, 2005, vol. 395, pp. 301-6.

    Google Scholar 

  12. 12.

    J.F. Nie, X. Gao and S.M. Zhu: Scr. Mater., 2005, vol. 53, pp. 1049-53.

    CAS  Google Scholar 

  13. 13.

    M. Nishijima and K. Hiraga: Mater. Trans., 2007, vol. 48, pp. 10-5.

    CAS  Google Scholar 

  14. 14.

    M. Nishijima, K. Yubuta and K. Hiraga: Mater. Trans., 2007, vol. 48, pp. 84-7.

    CAS  Google Scholar 

  15. 15.

    X. Gao, S.M. He, X.Q. Zeng, L.M. Peng, W.J. Ding and J.F. Nie: Mater. Sci. Eng. A, 2006, vol. 431, pp. 322-7.

    Google Scholar 

  16. 16.

    K. Hono, C.L. Mendis, T.T. Sasaki and K. Oh-ishi: Scr. Mater., 2010, vol. 63, pp.710-5.

    CAS  Google Scholar 

  17. 17.

    K. Saito, A. Yasuhara, M. Nishijima and K. Hiraga: Mater. Trans., 2011, vol. 52, pp. 1009-15.

    CAS  Google Scholar 

  18. 18.

    K. Saito and K. Hiraga: Mater. Trans., 2011, vol. 52, pp. 1860-7.

    CAS  Google Scholar 

  19. 19.

    A. Sanaty-Zadeh, A. A. Luo and D. S. Stone: Acta Mater., 2015, vol. 94, pp. 294-306.

    CAS  Google Scholar 

  20. 20.

    X.Y. Xia, W.H. Sun, A.A. Luo and D.S. Stone: Acta Mater., 2016, vol. 111, pp. 335-47.

    CAS  Google Scholar 

  21. 21.

    D. Choudhuri, S.G. Srinivasan, M.A. Gibson, Y.F. Zheng, D.L. Jaeger, H.L. Fraser and R. Banerjee: Nat. Commun., 2017, vol. 8, 2000.

    Google Scholar 

  22. 22.

    Y. Zhang, Y.M. Zhu, W. Rong, Y. Wu, L.M. Peng, J.F. Nie and N. Birbilis: Metall. Mater. Trans. A, 2018, vol. 49, pp. 673-94.

    Google Scholar 

  23. 23.

    M.A. Easton, M.A. Gibson, D. Qiu, S.M. Zhu, J. Gröbner, R. Schmid-Fetzer, J.F. Nie and M.-X. Zhang: Acta Mater., 2012, vol. 60, pp. 4420-30.

    CAS  Google Scholar 

  24. 24.

    Y.Z. Ji, A. Issa, T.W. Heo, J.E. Saal, C. Wolverton and L.Q. Chen: Acta Mater., 2014, vol. 76, pp. 259-71.

    CAS  Google Scholar 

  25. 25.

    A. Issa, J.E. Saal and C. Wolverton: Acta Mater., 2014, vol. 65, pp. 240-50.

    CAS  Google Scholar 

  26. 26.

    P. Hidalgo-Manrique, J.D. Robson and M.T. Pérez-Prado: Acta Mater., 2017, vol. 124, pp. 456-467.

    CAS  Google Scholar 

  27. 27.

    R. Wilson, C.J. Bettles, B.C. Muddle and J.F. Nie: Mater. Sci. Forum, 2003, vol. 419-422, pp. 267-72.

    Google Scholar 

  28. 28.

    W. Lefebvre, V. Kopp and C. Pareige: Appl. Phys. Lett., 2012, vol. 100, 141906.

    Google Scholar 

  29. 29.

    Y.M. Zhu, H. Liu, Z. Xu, Y. Wang and J.F. Nie: Acta Mater., 2015, vol. 83, pp. 239-47.

    CAS  Google Scholar 

  30. 30.

    J.P. Hadorn and S.R. Agnew: Mater. Sci. Eng. A, 2012, vol. 533, pp. 9-16.

    CAS  Google Scholar 

  31. 31.

    H. Liu, Y. Gao, Y.M. Zhu, Y. Wang and J.F. Nie: Acta Mater., 2014, vol. 77, pp. 133-50.

    CAS  Google Scholar 

  32. 32.

    J.Z. Peng, Y.F. Wang and M.F. Gray: Physica B, 2008, vol. 403, pp. 2344-8.

    CAS  Google Scholar 

  33. 33.

    Z. Xu, M. Weyland and J. F. Nie: Acta Mater., 2014, vol. 81, pp. 58-70.

    CAS  Google Scholar 

  34. 34.

    A. Issa, J.E. Saal and C. Wolverton: Acta Mater., 2015, vol. 83, pp. 75–83.

    CAS  Google Scholar 

  35. 35.

    M. Paliwai, S.K. Das, J. Kim and I. Jung: Scr. Mater., 2015, vol. 108, pp. 11-4.

    Google Scholar 

  36. 36.

    Y.M. Zhu, K. Ohishi, N.C. Wilson, K. Hono, A.J. Morton and J.F. Nie: Metall. Mater. Trans. A, 2016, vol. 47, pp. 927-40.

    CAS  Google Scholar 

  37. 37.

    J.F. Nie, N.C. Wilson, Y.M. Zhu and Z. Xu: Acta Mater., 2016, vol. 106, pp. 260-71.

    CAS  Google Scholar 

  38. 38.

    A.R. Natarajan, E.L.S. Solomon, B. Puchala, E.A. Marquis and A.Van der Ven: Acta Mater., 2016, vol. 108, pp. 367-79.

    CAS  Google Scholar 

  39. 39.

    H. Liu, Y.M. Zhu, N.C. Wilson and J.F. Nie: Acta Mater., 2017, vol. 133, pp. 408-26.

    CAS  Google Scholar 

  40. 40.

    A.R. Natarajan and A. Van der Ven: Acta Mater., 2017, vol. 124, pp. 620-32.

    CAS  Google Scholar 

  41. 41.

    S. DeWitt, E.L.S. Solomon, A.R. Natarajan, V. Araullo-Peters, S. Rudraraju, L.K. Aagesen, B. Puchala, E.A. Marquis, A. van der Ven, K. Thornton and J.E. Allison: Acta Mater., 2017, vol. 136, pp. 378-89.

    CAS  Google Scholar 

  42. 42.

    J.F. Nie and B.C. Muddle: Acta Mater., 2000, vol. 48, pp. 1691-1703.

    CAS  Google Scholar 

  43. 43.

    H. Liu, Y. Gao, Z. Xu, Y.M. Zhu, Y. Wang and J.F. Nie: Sci. Rep., 2015, vol. 5, 16530.

    CAS  Google Scholar 

  44. 44.

    Z. Xu, M. Weyland and J.F. Nie: Acta Mater., 2014, vol. 75, pp. 122-33.

    CAS  Google Scholar 

  45. 45.

    Y. Gao, H. Liu, R. Shi, N. Zhou, Z. Xu, Y.M. Zhu, J.F. Nie and Y. Wang: Acta Mater., 2012, vol. 60, pp. 4819-32.

    CAS  Google Scholar 

  46. 46.

    S. Plimpton: J. Comput. Phys., 1995, vol. 117, pp. 1-19.

    CAS  Google Scholar 

  47. 47.

    M.A. Tschopp and D.L. McDowell: Philos. Mag., 2007, vol. 87, pp. 3147-73.

    CAS  Google Scholar 

  48. 48.

    D.Y. Sun, M.I. Mendelev, C.A. Becker, K. Kudin, T. Haxhimali, M. Asta, J.J. Hoyt, A. Karma and D.J. Srolovitz: Phys. Rev. B, 2006, vol. 73, 024116.

    Google Scholar 

  49. 49.

    J.F. Nie: Acta Mater., 2008, vol. 56, pp. 3169-76.

    CAS  Google Scholar 

  50. 50.

    W.-Z. Zhang and G.C. Weatherly: Prog. Mater. Sci., 2005, vol. 50, pp. 181-292.

    CAS  Google Scholar 

  51. 51.

    M.X. Zhang and P.M. Kelly: Prog. Mater. Sci., 2009, vol. 54, pp. 1101-70.

    CAS  Google Scholar 

  52. 52.

    J.P. Hirth and R.C. Pond: Acta Mater., 1996, vol. 44, pp. 4749-63.

    CAS  Google Scholar 

  53. 53.

    W. Bollmann: Crystal Defects and Crystalline Interfaces, Springer, Berlin, 1970.

    Google Scholar 

  54. 54.

    R.W. Balluffi, A. Brokman and A.H. King: Acta Metall., 1982, vol. 30, pp. 1453-70.

    CAS  Google Scholar 

  55. 55.

    W.-Z. Zhang and G.R. Purdy: Phil. Mag. A, 1993, vol. 68, pp. 279-90.

    Google Scholar 

  56. 56.

    W.-Z. Zhang and G.R. Purdy: Phil. Mag. A, 1993, vol. 68, pp. 291-303.

    Google Scholar 

  57. 57.

    N. Cherkashin, O. Kononchuk, S. Reboh and M. Hÿtch: Acta Mater., 2012, vol. 60, pp. 1161-73.

    CAS  Google Scholar 

  58. 58.

    F.C. Frank: Report of the Symposium on the Plastic Deformation of Crystalline Solids, Carnegie Institute of Technology, Pittsburgh PA, 1950.

    Google Scholar 

  59. 59.

    J.P. Hirth and J. Lothe: Theory of Dislocations, 2nd ed., Wiley, New York, 1982.

    Google Scholar 

  60. 60.

    J. Wang and I.J. Beyerlein: Model. Simul. Mater. Sci. Eng., 2012, vol. 20, 024002.

    Google Scholar 

  61. 61.

    H.A. Khater, A. Serra, R.C. Pond and J.P. Hirth: Acta Mater., 2012, vol. 60, pp. 2007-20.

    CAS  Google Scholar 

  62. 62.

    Y.M. Zhu, M.Z. Bian and J.F. Nie: Acta Mater., 2017, vol. 127, pp. 505-18.

    CAS  Google Scholar 

Download references


The authors wish to acknowledge gratefully financial supports by the Australian Research Council and Baosteel-Australia Joint Research and Development Centre, and the access to the facilities of the Monash Centre for Electron Microscopy.

Author information



Corresponding author

Correspondence to J. F. Nie.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Manuscript submitted August 8, 2019.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhu, Y.M., Zhang, H., Xu, S.W. et al. The β1 Triad-Related Configurations in a Mg-RE Alloy. Metall Mater Trans A 51, 1887–1896 (2020).

Download citation