Science China Materials

, Volume 61, Issue 3, pp 409–416 | Cite as

Spherical periodicity as structural homology of crystalline and amorphous states

  • Shuang Zhang (张爽)
  • Dandan Dong (董丹丹)
  • Zijian Wang (王子鉴)
  • Chuang Dong (董闯)
  • Peter Häussler


It has been widely accepted that spherical periodicity generally dominates liquid and amorphous structure formation, where atoms tend to gather near spherically periodic shells according to Friedel oscillation. Here we revealed that the same order is just hidden in the atomic global packing modes of the crystalline phases relevant to bulk metallic glasses. Among the nearest-neighbor clusters developed from all the non-equivalent atomic sites in a given phase, there always exists a principal a principal cluster, centered by which the spherical periodicity, both topologically and chemically, is the most distinct. Then the principal clusters plus specific glue atoms just constitute the cluster-plus-glue-atom structural units shared by both metallic glasses and the corresponding crystalline phases. It is further pointed out that the spherical periodicity order represents a common structural homology of crystalline and amorphous states in the medium-range through scrutinizing all binary bulk-glass-relevant phases in Cu-(Zr, Hf), Ni-(Nb, Ta), Al-Ca, and Pd-Si systems.


spherical periodicity order Friedel oscillation metallic glasses cluster-plus-glue-atom model principal cluster 



球周期在液体与非晶的结构形成过程中占有主要地位, 根据Friedel振荡理论, 原子倾向于聚集在球周期壳层上. 本文提出在非晶晶体相结构中依然隐藏着球周期序列. 在一个给定的相中, 所有非等效原子占位皆衍生出相应的最近邻团簇, 其中必然存在一个具有代表性的主团簇, 以其为中心时, 球周期最明显. 该主团簇加上特定的连接原子组成了对应非晶态的团簇加连接原子结构单元. 本文通过全面分析Cu-(Zr, Hf), Ni-(Nb, Ta), Al-Ca与Pd-Si二元块体非晶形成体系中的晶化相, 进一步指出球周期序代表了晶态与非晶态在中程序的结构同源性.



This work was supported by the Science Challenge Program (JCKY2016212A504) and the National Natural Science Foundation of China (11674045).


  1. 1.
    Häussler P. Interrelations between atomic and electronic structures —liquid and amorphous metals as model systems. Phys Rep, 1992, 222: 65–143CrossRefGoogle Scholar
  2. 2.
    Friedel J. Electronic structure of primary solid solutions in metals. Adv Phys, 1954, 3: 446–507CrossRefGoogle Scholar
  3. 3.
    Häussler P, Barzola-Quiquia J. Spherical periodicity, an intermediate step to long-range order. J Non-Crystalline Solids, 2002, 312-314: 498–501CrossRefGoogle Scholar
  4. 4.
    Han G, Qiang J, Li F, et al. The e/a values of ideal metallic glasses in relation to cluster formulae. Acta Mater, 2011, 59: 5917–5923CrossRefGoogle Scholar
  5. 5.
    Luo L, Chen H, Wang Y, et al. 24 electron cluster formulas as the ‘molecular’ units of ideal metallic glasses. Philos Mag, 2014, 94: 2520–2540CrossRefGoogle Scholar
  6. 6.
    Liu X, Xu Y, Hui X, et al. Metallic liquids and glasses: atomic order and global packing. Phys Rev Lett, 2010, 105: 155501CrossRefGoogle Scholar
  7. 7.
    Wu Z, Li M, Wang W, et al. Hidden topological order and its correlation with glass-forming ability in metallic glasses. Nat Commun, 2015, 6: 6035CrossRefGoogle Scholar
  8. 8.
    Dong C, Wang Q, Qiang J, et al. From clusters to phase diagrams: composition rules of quasicrystals and bulk metallic glasses. J Phys D-Appl Phys, 2007, 40: R273–R291CrossRefGoogle Scholar
  9. 9.
    Häussler P. A new hume-rothery phase with an amorphous structure in noble-metal/simple-metal alloys. J Phys Colloques, 1985, 46: C8–361–C8–365CrossRefGoogle Scholar
  10. 10.
    Bernal J. Geometry of the structure of monatomic liquids. Nature, 1960, 185: 68–70CrossRefGoogle Scholar
  11. 11.
    Gaskell P. A new structural model for transition metal–metalloid glasses. Nature, 1978, 276: 484–485CrossRefGoogle Scholar
  12. 12.
    Miracle D. The efficient cluster packing model–an atomic structural model for metallic glasses. Acta Mater, 2006, 54: 4317–4336CrossRefGoogle Scholar
  13. 13.
    Chen J, Wang Q, Wang Y, et al. Cluster formulae for alloy phases. Philos Mag Lett, 2010, 90: 683–688CrossRefGoogle Scholar
  14. 14.
    Du J, Wen B, Melnik R, et al. Determining characteristic principal clusters in the “cluster-plus-glue-atom” model. Acta Mater, 2014, 75: 113–121CrossRefGoogle Scholar
  15. 15.
    Dong D, Zhang S, Wang Z, et al. Composition interpretation of binary bulk metallic glasses via principal cluster definition. Mater Des, 2016, 96: 115–121CrossRefGoogle Scholar
  16. 16.
    Harrison WA. Solid State Theory. New York: McGraw-Hill, Inc., 1970Google Scholar
  17. 17.
    Ziman JM. Principles of the Theory of Solids. Cambridge: Cambridge university press, 1972CrossRefGoogle Scholar
  18. 18.
    Hafner J, Heine V. The crystal structures of the elements: pseudopotential theory revisited. J Phys F-Met Phys, 1983, 13: 2479–2501CrossRefGoogle Scholar
  19. 19.
    Kroha J, Huck A, Kopp T. Coulomb interaction and disorder at q=2kF: a novel instability of the Fermi sea and implications for amorphous alloys. Phys Rev Lett, 1995, 75: 4278–4281CrossRefGoogle Scholar
  20. 20.
    Zallen R. The Physics of Amorphous Solids. New York: John Wiley & Sons, Inc., 1983CrossRefGoogle Scholar
  21. 21.
    Wang Z, Qiang J, Wang Y, et al. Composition design procedures of Ti-based bulk metallic glasses using the cluster-plus-glue-atom model. Acta Mater, 2016, 111: 366–376CrossRefGoogle Scholar
  22. 22.
    Wang Z, Dong D, Zhang S, et al. Characteristics of cluster formulas for binary bulk metallic glasses. J Alloys Compd, 2016, 654: 340–343CrossRefGoogle Scholar
  23. 23.
    Zhang S, Dong D, Wang Z, et al. Composition formulas of Ni-(Nb, Ta) bulk metallic glasses. Intermetallics, 2017, 85: 176–179CrossRefGoogle Scholar
  24. 24.
    Huang B, Corbett J. Two new binary calcium-aluminum compounds: Ca13Al14, with a novel two-dimensional aluminum network, and Ca8Al3, an Fe3Al-type analogue. Inorg Chem, 1998, 37: 5827–5833CrossRefGoogle Scholar
  25. 25.
    Hong H, Wang Q, Dong C, et al. Understanding the Cu-Zn brass alloys using a short-range-order cluster model: significance of specific compositions of industrial alloys. Sci Rep, 2014, 4: 7065CrossRefGoogle Scholar
  26. 26.
    Hong H, Wang Q, Dong C. Composition formulas of Cu-Ni industrial alloy specifications. Sci China Mater, 2015, 58: 355–362CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Shuang Zhang (张爽)
    • 1
  • Dandan Dong (董丹丹)
    • 2
  • Zijian Wang (王子鉴)
    • 1
  • Chuang Dong (董闯)
    • 1
  • Peter Häussler
    • 3
  1. 1.Key Laboratory for Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology (DUT)), Ministry of EducationDalianChina
  2. 2.College of Physical Science and TechnologyDalian UniversityDalianChina
  3. 3.Physics InstituteChemnitz University of TechnologyChemnitzGermany

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