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Cooperative atomic motion during shear deformation in metallic glass
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  • Published: 12 January 2026

Cooperative atomic motion during shear deformation in metallic glass

  • Yoshinori Shiihara  ORCID: orcid.org/0000-0001-7972-91331,
  • Takuya Iwashita  ORCID: orcid.org/0000-0002-0757-79322,
  • Nozumu Adachi3,
  • Yoshikazu Todaka  ORCID: orcid.org/0000-0002-0022-08933 &
  • …
  • Takeshi Egami  ORCID: orcid.org/0000-0002-1126-02764,5,6 

Nature Communications , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Computational methods
  • Glasses

Abstract

Elucidating mechanical deformation in glassy materials at the atomic level is challenging due to their disordered atomic structure. Using our frozen-atom analysis of the simulation data, we reveal that anelastic deformation in CuZr metallic glasses is fundamentally driven by cooperative atomic motions of tens of atoms elastically linked to one another, forming trigger groups. They initiate localized rearrangements, which can cascade into plastic flow. These cores show no clear structural or elastic precursors in the initial configuration, challenging the idea that deformation occurs in defective regions. Instead, deformation events are highly stochastic and transient, driven by collective atomic motion. This finding not only reshapes our understanding of glassy material deformation mechanisms but also highlights cooperative motion as a key factor in avalanche-like phenomena governing the behavior of disordered systems across multiple scales.

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Data availability

The data underlying the figures, including atomic structure data and associated derived quantities, have been deposited in Zenodo with DOI 10.5281/zenodo.1795899458. The complete set of atomic configurations exceeds 1 TB and cannot be deposited in a public repository due to size limitations. These data are preserved by the authors and may be accessed for non-commercial academic research by contacting the corresponding author (shiihara@toyota-ti.ac.jp). Requests will receive a response within 2 weeks, and the data will remain available for at least 5 years after publication.

Code availability

The implementations of the frozen-atom analysis are available in a Code Ocean capsule at DOI 10.24433/CO.2573501.v159.

References

  1. Greer, A., Cheng, Y. & Ma, E. Shear bands in metallic glasses. Mater. Sci. Eng. R: Rep. 74, 71 (2013).

    Google Scholar 

  2. Nicolas, A., Ferrero, E. E., Martens, K. & Barrat, J.-L. Deformation and flow of amorphous solids: insights from elastoplastic models. Rev. Mod. Phys. 90, 045006 (2018).

    Google Scholar 

  3. Richard, D. et al. Predicting plasticity in disordered solids from structural indicators. Phys. Rev. Mater. 4, 113609 (2020).

    Google Scholar 

  4. Hansen, N. Hall–Petch relation and boundary strengthening. Scr. Mater. 51, 801 (2004).

    Google Scholar 

  5. Meyers, M., Mishra, A. & Benson, D. Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 51, 427 (2006).

    Google Scholar 

  6. Johnson, W. L. & Samwer, K. A universal criterion for plastic yielding of metallic glasses with a \({(T/{T}_{g})}^{2/3}\) temperature dependence. Phys. Rev. Lett. 95, 195501 (2005).

    Google Scholar 

  7. Argon, A. & Kuo, H. Plastic flow in a disordered bubble raft (an analog of a metallic glass). Mater. Sci. Eng. 39, 101 (1979).

    Google Scholar 

  8. Delogu, F. Effects of compression cycles on the atomic mobility in metallic glasses. Phys. Rev. B 79, 064205 (2009).

    Google Scholar 

  9. Liu, Z. Y. et al. Temperature dependent dynamics transition of intermittent plastic flow in a metallic glass. II. Dynamics analysis. J. Appl. Phys. 114, 033521 (2013).

    Google Scholar 

  10. Shang, B. S., Li, M. Z., Yao, Y. G., Lu, Y. J. & Wang, W. H. Evolution of atomic rearrangements in deformation in metallic glasses. Phys. Rev. E 90, 042303 (2014).

    Google Scholar 

  11. L, M. & Sen Gupta, B. Characteristics and correlations of nonaffine particle displacements in the plastic deformation of athermal amorphous materials. Soft Matter 18, 8626 (2022).

    Google Scholar 

  12. Adam, G. & Gibbs, J. H. On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139 (1965).

    Google Scholar 

  13. Cohen, M. H. & Grest, G. S. The nature of the glass transition. J. Non-Cryst. Solids 61–62, 749 (1984).

    Google Scholar 

  14. Blackburn, F., Cicerone, M. T., Hietpas, G., Wagner, P. A. & Ediger, M. Cooperative motion in fragile liquids near the glass transition: probe reorientation in o-terphenyl and polystyrene. J. Non-Cryst. Solids 172–174, 256 (1994).

    Google Scholar 

  15. Donati, C. et al. Stringlike cooperative motion in a supercooled liquid. Phys. Rev. Lett. 80, 2338 (1998).

    Google Scholar 

  16. Zhang, H. et al. Role of string-like collective atomic motion on diffusion and structural relaxation in glass forming Cu–Zr alloys. J. Chem. Phys. 142, 164506 (2015).

    Google Scholar 

  17. Jaiswal, A. et al. Onset of cooperative dynamics in an equilibrium glass-forming metallic liquid. J. Phys. Chem. B 120, 1142 (2016).

    Google Scholar 

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

    Google Scholar 

  19. Sethna, J. P., Dahmen, K. A. & Myers, C. R. Crackling noise. Nature 410, 242 (2001).

    Google Scholar 

  20. Antonaglia, J. et al. Bulk metallic glasses deform via slip avalanches. Phys. Rev. Lett. 112, 155501 (2014).

    Google Scholar 

  21. Antonaglia, J. et al. Tuned critical avalanche scaling in bulk metallic glasses. Sci. Rep. 4, 4382 (2014).

    Google Scholar 

  22. Malandro, D. L. & Lacks, D. J. Molecular-level mechanical instabilities and enhanced self-diffusion in flowing liquids. Phys. Rev. Lett. 81, 5576 (1998).

    Google Scholar 

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

    Google Scholar 

  24. Berthier, L. & Kob, W. Static point-to-set correlations in glass-forming liquids. Phys. Rev. E 85, 011102 (2012).

    Google Scholar 

  25. Barbot, A. et al. Local yield stress statistics in model amorphous solids. Phys. Rev. E 97, 033001 (2018).

    Google Scholar 

  26. Bhowmik, B. P., Chaudhuri, P. & Karmakar, S. Effect of pinning on the yielding transition of amorphous solids. Phys. Rev. Lett. 123, 185501 (2019).

    Google Scholar 

  27. Xu, D., Zhang, S., Liu, A. J., Nagel, S. R. & Xu, N. Discontinuous instabilities in disordered solids. Proc. Natl. Acad. Sci. USA 120, e2304974120 (2023).

    Google Scholar 

  28. Cheng, Y. & Ma, E. Atomic-level structure and structure–property relationship in metallic glasses. Prog. Mater. Sci. 56, 379 (2011).

    Google Scholar 

  29. Egami, T. & Srolovitz, D. Local structural fluctuations in amorphous and liquid metals: a simple theory of the glass transition. J. Phys. F: Met. Phys. 12, 2141 (1982).

    Google Scholar 

  30. Fan, Y., Iwashita, T. & Egami, T. Evolution of elastic heterogeneity during aging in metallic glasses. Phys. Rev. E 89, 062313 (2014).

    Google Scholar 

  31. Lieou, C. K. C. & Egami, T. Relevance of structural defects to the mechanism of mechanical deformation in metallic glasses. Sci. Rep. 13, 15979 (2023).

    Google Scholar 

  32. Iwashita, T., Nicholson, D. M. & Egami, T. Elementary excitations and crossover phenomenon in liquids. Phys. Rev. Lett. 110, 205504 (2013).

    Google Scholar 

  33. Langer, J. S. Dynamics of shear-transformation zones in amorphous plasticity: formulation in terms of an effective disorder temperature. Phys. Rev. E 70, 041502 (2004).

    Google Scholar 

  34. Iwashita, T. & Egami, T. Atomic mechanism of flow in simple liquids under shear. Phys. Rev. Lett. 108, 196001 (2012).

    Google Scholar 

  35. Wei, D. et al. Revisiting the structure–property relationship of metallic glasses: common spatial correlation revealed as a hidden rule. Phys. Rev. B 99, 014115 (2019).

    Google Scholar 

  36. Wei, D. et al. Assessing the utility of structure in amorphous materials. J. Chem. Phys. 150, 114502 (2019).

    Google Scholar 

  37. Bapst, V. et al. Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 16, 448 (2020).

    Google Scholar 

  38. Dahmen, K. A., Ben-Zion, Y. & Uhl, J. T. Micromechanical model for deformation in solids with universal predictions for stress–strain curves and slip avalanches. Phys. Rev. Lett. 102, 175501 (2009).

    Google Scholar 

  39. Dahmen, K. A., Ben-Zion, Y. & Uhl, J. T. A simple analytic theory for the statistics of avalanches in sheared granular materials. Nat. Phys. 7, 554 (2011).

    Google Scholar 

  40. Uhl, J. T. et al. Universal quake statistics: from compressed nanocrystals to earthquakes. Sci. Rep. 5, 16493 (2015).

    Google Scholar 

  41. Thompson, A. P. et al. LAMMPS—a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).

    Google Scholar 

  42. Cheng, Y. Q., Ma, E. & Sheng, H. W. Atomic level structure in multicomponent bulk metallic glass. Phys. Rev. Lett. 102, 245501 (2009).

    Google Scholar 

  43. Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511 (1984).

    Google Scholar 

  44. Hoover, W. G. Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31, 1695 (1985).

    Google Scholar 

  45. Nakamura, T., Kawamoto, S. & Shinoda, W. Precise calculation of the local pressure tensor in Cartesian and spherical coordinates in LAMMPS. Comput. Phys. Commun. 190, 120 (2015).

    Google Scholar 

  46. Lobzenko, I., Shiihara, Y., Iwashita, T. & Egami, T. Shear softening in a metallic glass: first-principles local-stress analysis. Phys. Rev. Lett. 124, 085503 (2020).

    Google Scholar 

  47. Yang, Z.-Y., Wei, D., Zaccone, A. & Wang, Y.-J. Machine-learning integrated glassy defect from an intricate configurational-thermodynamic-dynamic space. Phys. Rev. B 104, 064108 (2021).

    Google Scholar 

  48. Cubuk, E. D. et al. Identifying structural flow defects in disordered solids using machine-learning methods. Phys. Rev. Lett. 114, 108001 (2015).

    Google Scholar 

  49. Baggioli, M., Kriuchevskyi, I., Sirk, T. W. & Zaccone, A. Plasticity in amorphous solids is mediated by topological defects in the displacement field. Phys. Rev. Lett. 127, 015501 (2021).

    Google Scholar 

  50. Wakeda, M., Shibutani, Y., Ogata, S. & Park, J. Relationship between local geometrical factors and mechanical properties for Cu–Zr amorphous alloys. Intermetallics 15, 139 (2007).

    Google Scholar 

  51. Jin, W., Datye, A., Schwarz, U. D., Shattuck, M. D. & O’Hern, C. S. Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids. Soft Matter 17, 8612 (2021).

    Google Scholar 

  52. Lobzenko, I., Tsuru, T., Shiihara, Y. & Iwashita, T. First-principles atomic level stresses: application to a metallic glass under shear. Mater. Res. Express 10, 085201 (2023).

    Google Scholar 

  53. Tsamados, M., Tanguy, A., Goldenberg, C. & Barrat, J.-L. Local elasticity map and plasticity in a model Lennard–Jones glass. Phys. Rev. E 80, 026112 (2009).

    Google Scholar 

  54. Şopu, D., Stukowski, A., Stoica, M. & Scudino, S. Atomic-level processes of shear band nucleation in metallic glasses. Phys. Rev. Lett. 119, 195503 (2017).

    Google Scholar 

  55. Richard, D., Kapteijns, G., Giannini, J. A., Manning, M. L. & Lerner, E. Simple and broadly applicable definition of shear transformation zones. Phys. Rev. Lett. 126, 015501 (2021).

    Google Scholar 

  56. Dasgupta, R., Hentschel, H. G. E. & Procaccia, I. Microscopic mechanism of shear bands in amorphous solids. Phys. Rev. Lett. 109, 255502 (2012).

    Google Scholar 

  57. Fan, Z. & Ma, E. Predicting orientation-dependent plastic susceptibility from static structure in amorphous solids via deep learning. Nat. Commun. 12, 1506 (2021).

    Google Scholar 

  58. Shiihara, Y., Iwashita, T., Todaka, T., Adachi, N. & Egami, T. Data for: cooperative atomic motion during shear deformation in metallic glass. Zenodo https://doi.org/10.5281/zenodo.17958994 (2025).

  59. Shiihara, Y., Iwashita, T., Todaka, T., Adachi, N. & Egami, T. Frozen-atom analysis code. Code Ocean https://doi.org/10.24433/CO.2573501.v1 (2025).

  60. Stukowski, A. Visualization and analysis of atomistic simulation data with OVITO—the open visualization tool. Model. Simul. Mater. Sci. Eng. 18, 015012 (2009).

    Google Scholar 

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Acknowledgements

This work was supported by Grant-in-Aid for Transformative Research Areas B, “Rheology of disordered structures: establishing Anankeon dynamics", JSPS KAKENHI Grant Numbers 22B206, 22H05041, 22H05042, 22H05040, and 23K28105. T.E. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.

Author information

Authors and Affiliations

  1. Graduate School of Engineering, Toyota Technological Institute, Nagoya, Aichi, Japan

    Yoshinori Shiihara

  2. Department of Science and Technology, Oita University, Oita, Japan

    Takuya Iwashita

  3. Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi, Aichi, Japan

    Nozumu Adachi & Yoshikazu Todaka

  4. University of Tennessee, Knoxville, TN, USA

    Takeshi Egami

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

    Takeshi Egami

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

    Takeshi Egami

Authors
  1. Yoshinori Shiihara
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Contributions

Y.S. and T.I. conceived the research. Y.S. developed the modeling framework. Y.S. and T.I. performed the simulations and conducted the data analysis. Y.S. and T.E. developed further interpretation of the data and wrote the manuscript. N.A. and Y.T. provided advice on the physics of the system. All the authors discussed the results and contributed to the manuscript.

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Correspondence to Yoshinori Shiihara, Takuya Iwashita or Takeshi Egami.

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Shiihara, Y., Iwashita, T., Adachi, N. et al. Cooperative atomic motion during shear deformation in metallic glass. Nat Commun (2026). https://doi.org/10.1038/s41467-026-68308-4

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  • Received: 03 April 2025

  • Accepted: 03 January 2026

  • Published: 12 January 2026

  • DOI: https://doi.org/10.1038/s41467-026-68308-4

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