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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.

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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.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  ADS  CAS  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)

    Article  ADS  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  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)

    Article  ADS  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  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)

    Article  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  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)

    Article  ADS  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  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)

    Article  ADS  CAS  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)

    Article  ADS  CAS  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)

    Article  ADS  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)

    Article  ADS  CAS  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.

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

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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)

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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

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