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Length-scale dependence of the anomalous atomic motion in metallic glasses

Nature Physics (2026)Cite this article

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Abstract

Establishing microscopic structure–dynamics relations in glasses is essential for developing a comprehensive theory yet remains challenging owing to limited access to the relevant time and length scales. Here we probe density fluctuations in three metallic glasses and describe a complex organization of the dynamics that provides a framework of the anomalous compressed relaxation universally observed in metallic glasses at the atomic level. We demonstrate that this faster-than-exponential motion occurs only at length scales characterized by medium-range order and originates from internal stresses stored during the freezing of rigid domains across the glass transition. At larger length scales, the dynamics becomes stationary and heterogeneous, with stretched exponential relaxations reflecting the statistically averaged motions of different domains. We also identify a second independent relaxation, associated with persistent liquid-like motions, whose strength increases at large wavelengths. These findings reveal the cooperative, multiscale nature of relaxations in glasses.

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Fig. 1: Length-scale dependence of the dynamics.
Fig. 2: Modelling of the double decay of the ISFs and temporal evolution of the dynamics.
Fig. 3: Temperature and q dependence of the relaxation times and KWW exponents of the two processes.
Fig. 4: Thermal-history dependence of the fast and slow relaxation processes.
Fig. 5: q dependence of relaxation behaviour in Pt42.5Cu27Ni9.5P21 and Pd42.5Cu27Ni9.5P21 MGs.

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The data that support the plots within this paper are available within the Article and its Supplementary Information. Additional data concerning this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We acknowledge the European Synchrotron Radiation Facility (ESRF, Grenoble, France) and Deutsches Elektronen-Synchrotron (DESY, Hamburg, Germany) for providing beamtime. The related experiments were carried out on the ID10 and ID15A beamlines at ESRF and the P10 beamline at PETRA III (DESY). The Partnership for Soft Condensed Matter (PSCM) at the ESRF is also acknowledged for providing support facilities for sample characterization. We thank K. Lhoste for assistance on the ID10 beamline and J.-L. Barrat for useful discussions. E.P. acknowledges María de Maeztu CEX 2023-001300-M/AEI/10.13039/501100011033. This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 948780).

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Authors and Affiliations

  1. University Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    Jie Shen, Antoine Cornet, Irene Festi, Alberto Ronca & Beatrice Ruta

  2. ESRF—The European Synchrotron, Grenoble, France

    Jie Shen, Antoine Cornet, Yuriy Chushkin, Federico Zontone, Marco Cammarata, Marco di Michiel, Gavin Vaughan & Beatrice Ruta

  3. Institute for Frontier Materials on Earth and in Space, German Aerospace Center (DLR), Cologne, Germany

    Fan Yang

  4. Department of Physics, Institute of Energy Technologies, Barcelona Research Centre in Multiscale Science and Engineering, Universitat Politècnica de Catalunya—BarcelonaTech, Barcelona, Spain

    Eloi Pineda

  5. Université Grenoble Alpes, CNRS, LIPhy, Grenoble, France

    Kirsten Martens

  6. Chair of Metallic Materials, Saarland University, Saarbrucken, Germany

    Nico Neuber, Maximilian Frey & Ralf Busch

  7. GOETTFERT GmbH, Buchen, Germany

    Maximilian Frey

  8. Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

    Michael Sprung

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Contributions

J.S., F.Y., A.C., A.R., E.P., I.F., N.N., M.C., Y.C., F.Z., M.S., M.F. and B.R. carried out the XPCS experiments. J.S., A.C., B.R., M.d.M. and G.V. were responsible for the XRD measurements. J.S., F.Y., Y.C., K.M. and B.R. performed the data analysis. The paper was written by J.S. and B.R., with all authors contributing to revisions. B.R. conceived the research idea and led the overall project.

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Correspondence to Jie Shen or Beatrice Ruta.

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Nature Physics thanks Takeshi Egami, Yoshio Kono and Raghavan Ranganathan for their contribution to the peer review of this work.

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Shen, J., Yang, F., Cornet, A. et al. Length-scale dependence of the anomalous atomic motion in metallic glasses. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03228-0

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