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Anomalous phonon scattering and elastic correlations in amorphous solids

Nature Materials volume 15, pages 1177–1181 (2016)Cite this article

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Abstract

A major issue in materials science is why glasses present low-temperature thermal and vibrational properties that sharply differ from those of crystals. In particular, long-wavelength phonons are considerably more damped in glasses, yet it remains unclear how structural disorder at atomic scales affects such a macroscopic phenomenon. A plausible explanation is that phonons are scattered by local elastic heterogeneities that are essentially uncorrelated in space, a scenario known as Rayleigh scattering, which predicts that the damping of acoustic phonons scales with wavenumber k as kd+1 (in dimension d). Here we demonstrate that phonon damping scales instead as − kd+1 ln k, with this logarithmic enhancement originating from long-range spatial correlations of elastic disorder caused by similar stress correlations. Our work suggests that the presence of long-range spatial correlations of local stress and elasticity may well be the crucial feature that distinguishes amorphous solids from crystals.

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Figure 1: Response to a transverse excitation.
Figure 2: Sound properties.
Figure 3: Departures from Rayleigh scaling.
Figure 4: Correlations of elastic stiffnesses.

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Acknowledgements

We are grateful to C. Caroli for pointing us to Velicky’s course30, and for her comments on the role of disorder correlations in scattering. S.G. acknowledges the financial support from Specially Promoted Research from the Japan Society for the Promotion of Science (JSPS) for his stay at Institute of Industrial Science (IIS), University of Tokyo. A.L. acknowledges the support for his stay in IIS from the Foundation for the Promotion of Industrial Science (Shorei kai). H.T. acknowledges the support from Grants-in-Aid for Scientific Research (S) (21224011) and Specially Promoted Research (25000002) from JSPS.

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Authors and Affiliations

  1. NAVIER, UMR 8205, École des Ponts, IFSTTAR, CNRS, UPE, 77420 Champs-sur-Marne, France

    Simon Gelin & Anaël Lemaître

  2. Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

    Simon Gelin & Hajime Tanaka

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  1. Simon Gelin
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A.L. and H.T. conceived the project, S.G. and A.L. performed numerical simulations and data analysis. All the authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to Hajime Tanaka or Anaël Lemaître.

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Gelin, S., Tanaka, H. & Lemaître, A. Anomalous phonon scattering and elastic correlations in amorphous solids. Nature Mater 15, 1177–1181 (2016). https://doi.org/10.1038/nmat4736

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