Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Atomic packing and short-to-medium-range order in metallic glasses

Abstract

Unlike the well-defined long-range order that characterizes crystalline metals, the atomic arrangements in amorphous alloys remain mysterious at present. Despite intense research activity on metallic glasses and relentless pursuit of their structural description, the details of how the atoms are packed in amorphous metals are generally far less understood than for the case of network-forming glasses. Here we use a combination of state-of-the-art experimental and computational techniques to resolve the atomic-level structure of amorphous alloys. By analysing a range of model binary systems that involve different chemistry and atomic size ratios, we elucidate the different types of short-range order as well as the nature of the medium-range order. Our findings provide a reality check for the atomic structural models proposed over the years, and have implications for understanding the nature, forming ability and properties of metallic glasses.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Reverse Monte Carlo modelling to reproduce the experimental X-ray diffraction and absorption data.
Figure 2: The evolution of partial RRDFs of the Ni 80 P 20 liquid observed in ab initio molecular dynamics simulations.
Figure 3: CN distribution of the solute atoms in several representative MGs, obtained from ab initio calculations.
Figure 4: The occurrences of different coordination polyhedra (with different Voronoi indices) of the solute atoms in the MGs.
Figure 5: The packing of the solute-centred quasi-equivalent clusters, showing their MRO.
Figure 6: Configurations of solute atoms at increasing solute concentrations.

References

  1. Bernal, J. D. Geometry of the structure of monatomic liquids. Nature 185, 68–70 (1960)

    ADS  Article  Google Scholar 

  2. Bernal, J. D. The structure of liquids. Proc. R. Soc. Lond. A 280, 299–322 (1964)

    ADS  CAS  Article  Google Scholar 

  3. Greer, A. L. Intermetallic Compounds—Principles and Practice Vol. 1 (eds Westbrook, J. H. & Fleischer, R. L.) 731–754 (Wiley, New York, 1995)

    Google Scholar 

  4. Gaskell, P. H. A new structural model for transition metal–metalloid glasses. Nature 276, 484–485 (1978)

    ADS  CAS  Article  Google Scholar 

  5. Gaskell, P. H. A new structural model for amorphous transition metal silicides, borides, phosphides and carbides. J. Non-Cryst. Solids 32, 207–224 (1979)

    ADS  CAS  Article  Google Scholar 

  6. Elliott, S. R. Physics of Amorphous Materials 2nd edn, 139–151 (Longman, London, 1990)

    Google Scholar 

  7. Gaskell, P. H. Amorphous Metals (eds Matyja, H. & Zielinski, P. G.) 35–57 (World Scientific Publishing, Singapore, 1985)

    Google Scholar 

  8. Gaskell, P. H. Medium-range structure in glasses and low-Q structure in neutron and X-ray scattering data. J. Non-Cryst. Solids 351, 1003–1013 (2005)

    ADS  CAS  Article  Google Scholar 

  9. Miracle, D. B. A structural model for metallic glasses. Nature Mater. 3, 697–702 (2004)

    ADS  CAS  Article  Google Scholar 

  10. Miracle, D. B., Sanders, W. S. & Senkov, O. N. The influence of efficient atomic packing on the constitution of metallic glasses. Phil. Mag. A 83, 2409–2428 (2003)

    CAS  Article  Google Scholar 

  11. McGreevy, R. L. Reverse Monte Carlo modeling. J. Phys. Cond. Matter 13, R877–R913 (2001)

    ADS  CAS  Article  Google Scholar 

  12. Luo, W. K. et al. Icosahedral short-range order in amorphous alloys. Phys. Rev. Lett. 92, 145502 (2004)

    ADS  CAS  Article  Google Scholar 

  13. Lamparter, P. Reverse Monte-Carlo simulation of amorphous Ni80P20 and Ni81B19 . Phys. Scr. T57, 72–78 (1995)

    ADS  CAS  Article  Google Scholar 

  14. Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A. & Joannopoulos, J. D. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045–1097 (1992)

    ADS  CAS  Article  Google Scholar 

  15. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993)

    ADS  CAS  Article  Google Scholar 

  16. Allen, M. P. & Tidesley, D. J. Computer Simulation of Liquids (Clarendon, Oxford, 1989)

    Google Scholar 

  17. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996)

    CAS  Article  Google Scholar 

  18. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994)

    ADS  Article  Google Scholar 

  19. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999)

    ADS  CAS  Article  Google Scholar 

  20. Wang, Y. & Perdew, J. P. Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. Phys. Rev. B 44, 13298–13307 (1991)

    ADS  CAS  Article  Google Scholar 

  21. Stillinger, F. H. & Weber, T. A. Packing structures and transitions in liquids and solids. Science 225, 983–989 (1984)

    ADS  CAS  Article  Google Scholar 

  22. Ankudinov, A. L., Ravel, B., Rehr, J. J. & Conradson, S. D. Real-space multiple-scattering calculation and interpretation of X-ray-absorption near-edge structure. Phys. Rev. B 58, 7565–7576 (1998)

    ADS  CAS  Article  Google Scholar 

  23. Finney, J. L. Random packing and the structure of simple liquids. Proc. R. Soc. A 319, 479–493 (1970)

    ADS  CAS  Article  Google Scholar 

  24. Finney, J. L. Modeling structures of amorphous metals and alloys. Nature 266, 309–314 (1977)

    ADS  CAS  Article  Google Scholar 

  25. Borodin, V. A. Local atomic arrangements in polytetrahedral materials. Phil. Mag. A 79, 1887–1907 (1999)

    ADS  CAS  Article  Google Scholar 

  26. Borodin, V. A. Local atomic arrangements in polytetrahedral materials. II. Coordination polyhedra with 14 and 15 atoms. Phil. Mag. A 81, 2427–2446 (2001)

    ADS  CAS  Article  Google Scholar 

  27. Pauling, L. The principles determining the structure of complex ionic crystals. J. Am. Chem. Soc. 51, 1010–1026 (1929)

    CAS  Article  Google Scholar 

  28. O'Keeffe, M. & Navrotski, A. (eds) Structure and Bonding in Crystals (Academic, New York, 1981)

  29. Qi, D. W. & Wang, S. Icosahedral order and defects in metallic liquids and glasses. Phys. Rev. B 44, 884–887 (1991)

    ADS  CAS  Article  Google Scholar 

  30. Doye, J. P. K. & Walse, D. J. The effect of the range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to C60 . J. Phys. B 29, 4859–4894 (1996)

    ADS  CAS  Article  Google Scholar 

  31. Nelson, D. R. Order, frustration, and defects in liquids and glasses. Phys. Rev. B 28, 5515–5535 (1983)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  32. Frank, F. C. & Kasper, J. S. Complex alloy structures regarded as sphere packings. I. Definitions and basic principles. Acta Crystallogr. 11, 184–190 (1958)

    CAS  Article  Google Scholar 

  33. Watson, R. E. & Bennett, L. H. Crystalline and glassy phases of transition-metal–metalloid systems. Phys. Rev. B 43, 11642–11652 (1991)

    ADS  CAS  Article  Google Scholar 

  34. Egami, T. & Waseda, Y. Atomic size effect on the formability of metallic glasses. J. Non-Cryst. Solids 64, 113–134 (1984)

    ADS  CAS  Article  Google Scholar 

  35. Hafner, J. Theory of the formation of metallic glasses. Phys. Rev. B 21, 406–426 (1980)

    ADS  CAS  Article  Google Scholar 

  36. Clarke, A. S. & Jónsson, H. Structural changes accompanying densification of random hard-sphere packings. Phys. Rev. E 47, 3975–3984 (1993)

    ADS  CAS  Article  Google Scholar 

  37. Jónsson, H. & Anderson, C. Icosahedral ordering in the Lennard-Jones liquid and glass. Phys. Rev. Lett. 60, 2295–2298 (1988)

    ADS  Article  Google Scholar 

  38. Kelton, K. F. et al. First X-ray scattering studies on electrostatically levitated metallic liquids: demonstrated influence of local icosahedral order on the nucleation barrier. Phys. Rev. Lett. 90, 195504 (2003)

    ADS  CAS  Article  Google Scholar 

  39. Manoharan, V. N., Elsesser, M. T. & Pine, D. J. Dense packing and symmetry in small clusters of microspheres. Science 301, 483–487 (2003)

    ADS  CAS  Article  Google Scholar 

  40. Caspar, D. L. D. & Klug, A. Physical principles in the construction of regular viruses. Quant. Biol. 27, 1–24 (1962)

    CAS  Article  Google Scholar 

  41. Zandi, R., Reguer, D., Bruinsma, R. F., Gelbart, W. M. & Rudnick, J. Origin of icosahedral symmetry in viruses. Proc. Natl Acad. Sci. USA 101, 15556–15560 (2004)

    ADS  CAS  Article  Google Scholar 

  42. Greer, A. L. Metallic glasses. Science 267, 1947–1953 (1995)

    ADS  CAS  Article  Google Scholar 

  43. Lamparter, P. Structure of metallic glasses. Phys. Scr. T57, 45–63 (1995)

    ADS  CAS  Article  Google Scholar 

  44. Kramer, M. J. & Sordelet, D. J. Polymorphism in the short-range order of Zr70Pd30 metallic glasses. J. Non-Cryst. Solids 351, 1586–1593 (2005)

    ADS  CAS  Article  Google Scholar 

  45. Dubois, J. M., Gaskell, P. H. & Le Caer, G. A model for the structure of metallic glasses based on chemical twinning. Proc. R. Soc. A 402, 323–357 (1985)

    ADS  CAS  Article  Google Scholar 

  46. Ohkobu, T. & Hirotsu, Y. Electron diffraction and high-resolution electron microscopy study of an amorphous Pd82Si18 alloy with nanoscale phase separation. Phys. Rev. B 67, 094201 (2003)

    ADS  Article  Google Scholar 

  47. Kob, W. & Andersen, H. C. Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture: The van Hove correlation function. Phys. Rev. E 51, 4626–4641 (1995)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by US DoE-BES, with computational resources provided by NERSC. We also thank D. B. Miracle for discussions.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to H. W. Sheng or E. Ma.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Figure 1

Comparisons between the experimental XANES and the theoretical calculations for the Ni80P20 metallic glass. (PDF 89 kb)

Supplementary Figure 2

Comparisons of the RRDFs from the RMC fitting and that measured in experiments. (PDF 94 kb)

Supplementary Figure 3

Illustration of the Voronoi tessellation method to identify different atomic coordination environments. (PDF 376 kb)

Supplementary Figure 4

Bond angle distribution functions of the idealized hard-sphere polyhedra and the metallic glasses from ab initio MD simulations. (PDF 714 kb)

Supplementary Figure 5

The cluster connection in the Ni80P20 metallic glass for the RMC simulation. (PDF 1086 kb)

Supplementary Figure 6

Distribution of the nearest-neighbor cluster coordination number of the quasi-equivalent clusters in metallic glasses. (PDF 57 kb)

Supplementary Figure 7

Comparisons of the RRDFs of the metallic glasses from the ab initio MD simulations and that measured in experiments. (PDF 126 kb)

Supplementary Figure 8

Illustration of the cavities formed in metallic glasses as a result of the dense cluster packing. (PDF 1370 kb)

Supplementary Figure 9

RDF and the bond angle distribution function of the Zr70Pd30metallic glass, indicating the tendency to form string-like solute-solute connections. (PDF 361 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sheng, H., Luo, W., Alamgir, F. et al. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006). https://doi.org/10.1038/nature04421

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature04421

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing