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Non-affine atomic rearrangement of glasses through stress-induced structural anisotropy

Nature Physics volume 19, pages 1896–1903 (2023)Cite this article

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Abstract

The atomic-scale structural rearrangement of glasses on applied stress is central to the understanding of their macroscopic mechanical properties and behaviour. However, experimentally resolving the atomic-scale structural changes of a deformed glass remains challenging due to the disordered nature of the glass structure. Conventional structural analyses such as X-ray diffraction are based on the assumption of structural isotropy and hence cannot discern the subtle atomic-scale structural rearrangement induced by deformation. Here we show that structural anisotropy correlates with non-affine atomic displacements—meaning those that do not preserve parallel lines in the atomic structure—in various types of glass. This serves as an approach for identifying the atomic-scale non-affine deformation in glasses. We also uncover the atomic-level mechanism responsible for plastic flow, which differs between metallic glasses and covalent glasses. The non-affine structural rearrangements in metallic glasses are mediated through the stretching or contraction of atomic bonds. The non-affinity of covalent glasses that occurs in a less localized manner is mediated through the rotation of atomic bonds or chains without changing the bond length. These findings provide key ingredients for exploring the atomic-scale process governing the macroscopic deformation of amorphous solids.

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Fig. 1: Illustration of detecting and characterizing the anisotropic structure for glasses after creep.
Fig. 2: Comparison of experimentally observed anisotropic PDF to theoretically fitted anisotropic PDF, and to observed isotropic PDF for the studied glasses after creep deformation.
Fig. 3: Correlations of structural anisotropy with non-affine deformation and changes in bonds for deformed metallic and polymer glasses in simulations.
Fig. 4: Unveiled deformation mechanisms of metallic and polymer glasses in simulations.

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Data availability

The data that support the findings of this study are available via Figshare at https://doi.org/10.6084/m9.figshare.23515368. Source data are provided with this paper.

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Code data are available from the corresponding authors upon reasonable request.

References

  1. Bourhis, E. L. Glass: Mechanics and Technology (John Wiley & Sons, 2014).

  2. Ernsberger, F. M. Mechanical properties of glass. J. Non-Cryst. Solids 25, 293–321 (1977).

    ADS  Google Scholar 

  3. Morgan, R. J. & O’Neal, J. E. The mechanical properties of polymer glasses. Polym. Plast. Technol. 5, 173–197 (1975).

    Google Scholar 

  4. Schuh, C. A., Hufnagel, T. C. & Ramamurty, U. Mechanical behavior of amorphous alloys. Acta Mater. 55, 4067–4109 (2007).

    ADS  Google Scholar 

  5. Greer, A. L., Cheng, Y. Q. & Ma, E. Shear bands in metallic glasses. Mat. Sci. Eng. R 74, 71–132 (2013).

    Google Scholar 

  6. Yavari, A. R., Lewandowski, J. J. & Eckert, J. Mechanical properties of bulk metallic glasses. MRS Bull. 32, 635–638 (2011).

    Google Scholar 

  7. Wondraczek, L. Overcoming glass brittleness. Science 366, 804–805 (2019).

    ADS  Google Scholar 

  8. Hofmann, D. C. et al. Designing metallic glass matrix composites with high toughness and tensile ductility. Nature 451, 1085–1089 (2008).

    ADS  Google Scholar 

  9. Sarac, B. & Schroers, J. Designing tensile ductility in metallic glasses. Nat. Commun. 4, 2158 (2013).

    ADS  Google Scholar 

  10. Hirata, A. et al. Direct observation of local atomic order in a metallic glass. Nat. Mater. 10, 28–33 (2011).

    ADS  Google Scholar 

  11. Chen, D. Z. et al. Fractal atomic-level percolation in metallic glasses. Science 349, 1306–1310 (2015).

    ADS  Google Scholar 

  12. Yang, Y. et al. Determining the three-dimensional atomic structure of an amorphous solid. Nature 592, 60–64 (2021).

    ADS  Google Scholar 

  13. Falk, M. L. The flow of glass. Science 318, 1880–1881 (2007).

    Google Scholar 

  14. Cubuk, E. D. et al. Structure-property relationships from universal signatures of plasticity in disordered solids. Science 358, 1033–1037 (2017).

    ADS  Google Scholar 

  15. Wang, Z., Sun, B. A., Bai, H. Y. & Wang, W. H. Evolution of hidden localized flow during glass-to-liquid transition in metallic glass. Nat. Commun. 5, 5823 (2014).

    ADS  Google Scholar 

  16. Huang, P. Y. et al. Imaging atomic rearrangements in two-dimensional silica glass: watching silica’s dance. Science 342, 224–227 (2017).

    ADS  Google Scholar 

  17. Spaepen, F. A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall. 25, 407–415 (1976).

    Google Scholar 

  18. Argon, A. S. Plastic deformation in metallic glasses. Acta Metall. 27, 47–58 (1979).

    Google Scholar 

  19. Falk, M. L. & Langer, J. S. Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 57, 7192–7205 (1998).

    ADS  Google Scholar 

  20. Johnson, W. L. & Samwer, K. A universal criterion for plastic yielding of metallic glasses with a (T/Tg)2/3 temperature dependence. Phys. Rev. Lett. 95, 195501 (2005).

    ADS  Google Scholar 

  21. Liu, A. C. Y. et al. Local symmetry predictors of mechanical stability in glasses. Sci. Adv. 8, eabn0681 (2022).

    Google Scholar 

  22. Schall, P., Weitz, D. A. & Spaepen, F. Structural rearrangements that govern flow in colloidal glasses. Science 318, 1895–1899 (2007).

    ADS  Google Scholar 

  23. Laurati, M., Masshoff, P., Mutch, K. J., Egelhaaf, S. U. & Zaccone, A. Long-lived neighbors determine the rheological response of glasses. Phys. Rev. Lett. 118, 018002 (2017).

    ADS  Google Scholar 

  24. Kong, D. J., Chen, W. R., Zeng, K. Q., Porcar, L. & Wang, Z. Localized elasticity governs the nonlinear rheology of colloidal supercooled liquids. Phys. Rev. X 12, 041006 (2022).

    Google Scholar 

  25. Demkowicz, M. J. & Argon, A. S. High-density liquidlike component facilitates plastic flow in a model amorphous silicon system. Phys. Rev. Lett. 93, 025505 (2004).

    ADS  Google Scholar 

  26. Wang, Y. et al. Tension–compression asymmetry in amorphous silicon. Nat. Mater. 20, 1371–1377 (2021).

    ADS  Google Scholar 

  27. Zaccone, A. & Scossa-Romano, E. Approximate analytical description of the nonaffine response of amorphous solids. Phys. Rev. B 83, 184205 (2011).

    ADS  Google Scholar 

  28. Ganguly, S., Sengupta, S. & Sollich, P. Statistics of non-affine defect precursors: tailoring defect densities in colloidal crystals using external fields. Soft Matter 11, 4517–4526 (2015).

    ADS  Google Scholar 

  29. Ganguly, S., Sengupta, S., Sollich, P. & Rao, M. Nonaffine displacements in crystalline solids in the harmonic limit. Phys. Rev. E 87, 042801 (2013).

    ADS  Google Scholar 

  30. DiDonna, B. A. & Lubensky, T. C. Nonaffine correlations in random elastic media. Phys. Rev. E 72, 066619 (2005).

    ADS  Google Scholar 

  31. Popli, P., Kayal, S., Sollich, P. & Sengupta, S. Exploring the link between crystal defects and nonaffine displacement fluctuations. Phys. Rev. E 100, 033002 (2019).

    ADS  Google Scholar 

  32. Nath, P. et al. On the existence of thermodynamically stable rigid solids. Proc. Natl Acad. Sci. USA 115, 4322–4329 (2018).

    Google Scholar 

  33. Zaccone, A. & Terentjev, E. M. Disorder-assisted melting and the glass transition in amorphous solids. Phys. Rev. Lett. 110, 178002 (2013).

    ADS  Google Scholar 

  34. Lemaître, A. & Maloney, C. Sum rules for the quasi-static and visco-elastic response of disordered solids at zero temperature. J. Stat. Phys. 123, 415–453 (2006).

    ADS  MathSciNet  MATH  Google Scholar 

  35. Palyulin, V. V. et al. Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics. Soft Matter 14, 8475–8482 (2018).

    ADS  Google Scholar 

  36. Milkus, R. & Zaccone, A. Local inversion-symmetry breaking controls the boson peak in glasses and crystals. Phys. Rev. B 93, 094204 (2016).

    ADS  Google Scholar 

  37. Hess, S. Shear-flow-induced distortion of the pair-correlation function. Phys. Rev. A 22, 2844–2848 (1980).

    ADS  Google Scholar 

  38. Huang, G. R., Wu, B., Wang, Y. Y. & Chen, W. R. Characterization of microscopic deformation through two-point spatial correlation functions. Phys. Rev. E 97, 012605 (2018).

    ADS  Google Scholar 

  39. Evans, D. J., Hanley, H. J. M. & Hess, S. Non-Newtonian phenomena in simple fluids. Phys. Today 37, 26–35 (1984).

    ADS  Google Scholar 

  40. Wang, Z. et al. Fingerprinting molecular relaxation in deformed polymers. Phys. Rev. X 7, 031003 (2017).

    Google Scholar 

  41. Dmowski, W., Iwashita, T., Chuang, C. P., Almer, J. & Egami, T. Elastic heterogeneity in metallic glasses. Phys. Rev. Lett. 105, 205502 (2010).

    ADS  Google Scholar 

  42. Suzuki, Y., Haimovich, J. & Egami, T. Bond-orientational anisotropy in metallic glasses observed by X-ray diffraction. Phys. Rev. B 35, 2162–2168 (1987).

    ADS  Google Scholar 

  43. Wang, H. et al. Nonaffine strains control ductility of metallic glasses. Phys. Rev. Lett. 128, 155501 (2022).

    ADS  Google Scholar 

  44. Egami, T., Iwashita, T. & Dmowski, W. Mechanical properties of metallic glasses. Metals 3, 77–113 (2013).

    Google Scholar 

  45. Dmowski, W. & Egami, T. Observation of structural anisotropy in metallic glasses induced by mechanical deformation. J. Mater. Res. 22, 412–418 (2011).

    ADS  Google Scholar 

  46. Ott, R. T. et al. Anelastic strain and structural anisotropy in homogeneously deformed Cu64.5Zr35.5 metallic glass. Acta Mater. 56, 5575–5583 (2008).

    ADS  Google Scholar 

  47. Choi, I. C. et al. Indentation size effect and shear transformation zone size in a bulk metallic glass in two different structural states. Acta Mater. 60, 6862–6868 (2012).

    ADS  Google Scholar 

  48. Fan, Y., Iwashita, T. & Egami, T. How thermally activated deformation starts in metallic glass. Nat. Commun. 5, 5083 (2014).

    ADS  Google Scholar 

  49. Maloney, C. E. & Lemaître, A. Amorphous systems in athermal, quasistatic shear. Phys. Rev. E 74, 016118 (2006).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  51. Sheng, H. W., Luo, W. K., Alamgir, F. M., Bai, J. M. & Ma, E. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006).

    ADS  Google Scholar 

  52. Lan, S. et al. A medium-range structure motif linking amorphous and crystalline states. Nat. Mater. 20, 1347–1352 (2021).

    ADS  Google Scholar 

  53. Ye, J. C., Lu, J., Liu, C. T., Wang, Q. & Yang, Y. Atomistic free-volume zones and inelastic deformation of metallic glasses. Nat. Mater. 9, 619–623 (2010).

    ADS  Google Scholar 

  54. Wang, W. H., Yang, Y., Nieh, T. G. & Liu, C. T. On the source of plastic flow in metallic glasses: concepts and models. Intermetallics 67, 81–86 (2015).

    Google Scholar 

  55. Pan, D., Inoue, A., Sakurai, T. & Chen, M. W. Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses. Proc. Natl Acad. Sci. USA 105, 14769–14772 (2008).

    ADS  Google Scholar 

  56. Sun, Y. H. et al. Flow-induced elastic anisotropy of metallic glasses. Acta Mater. 112, 132–140 (2016).

    ADS  Google Scholar 

  57. Mendelev, M. I. et al. Development of suitable interatomic potentials for simulation of liquid and amorphous Cu-Zr alloys. Philos. Mag. 89, 967–987 (2009).

    ADS  Google Scholar 

  58. Rossi, G., Monticelli, L., Puisto, S. R., Vattulainen, I. & Ala-Nissila, T. Coarse-graining polymers with the MARTINI force-field: polystyrene as a benchmark case. Soft Matter 7, 698–708 (2011).

    ADS  Google Scholar 

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Acknowledgements

This research was supported by the National Key Research and Development Plan with grant no. 2018YFA0703603 (B.S.); the Guangdong Major Project of Basic and Applied Basic Research of China with grant nos. 2019B030302010 (W.W.) and 2020B1515120092 (B.S.); the National Natural Science Foundation of China (NSFC) with grant nos. 52192601 (H.B.), 52192602 (B.S.), 61888102 (W.W.) and 52001272 (Y.T.); and the Strategic Priority Research Program of Chinese Academy of Sciences with grant no. XDB30000000 (W.W.). W.D. and T.E. were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. H.P. acknowledges the computer resources provided by High Performance Computing Cluster (HPC) of Central South University.

Author information

Author notes

  1. These authors contributed equally: Jie Dong, Hailong Peng, Hui Wang.

Authors and Affiliations

  1. Institute of Physics, Chinese Academy of Sciences, Beijing, China

    Jie Dong, Yutian Wang, Baoan Sun, Weihua Wang & Haiyang Bai

  2. Songshan Lake Materials Laboratory, Dongguan, China

    Jie Dong, Baoan Sun, Weihua Wang & Haiyang Bai

  3. School of Materials Science and Engineering, Central South University, Changsha, China

    Hailong Peng

  4. Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, USA

    Hui Wang, Wojciech Dmowski & Takeshi Egami

  5. Institute for Advanced Studies in Precision Materials, Yantai University, Yantai, China

    Yang Tong

  6. College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing, China

    Yutian Wang, Baoan Sun, Weihua Wang & Haiyang Bai

  7. Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA

    Takeshi Egami

  8. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Takeshi Egami

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Contributions

H.B. and B.S. conceived and supervised the project. J.D. prepared the materials and performed the mechanical and thermal experiments. H.P. performed the MD simulations. H.W., Y.T. and W.D. performed the high-energy XRD experiments. J.D., Y.T., H.P., Y.W. and B.S. performed the data analysis and wrote the manuscript with input from all the other co-authors. T.E., W.W. and H.B. discussed the results and revised the manuscript.

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Correspondence to Hailong Peng, Yang Tong, Baoan Sun or Haiyang Bai.

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Supplementary Figs. 1–9 and Texts I and II.

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Unprocessed diffraction patterns.

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Statistical source data.

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Dong, J., Peng, H., Wang, H. et al. Non-affine atomic rearrangement of glasses through stress-induced structural anisotropy. Nat. Phys. 19, 1896–1903 (2023). https://doi.org/10.1038/s41567-023-02243-9

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