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Article Dans Une Revue Journal of Chemical Physics Année : 2020

Key role of retardation and non-locality in sound propagation in amorphous solids as evidenced by a projection formalism

Anaël Lemaître

Résumé

We investigate acoustic propagation in amorphous solids by constructing a projection formalism based on separating atomic vibrations into two, "phonon" (P) and "non-phonon" (NP), subspaces corresponding to large and small wavelengths. For a pairwise interaction model, we show the existence of a "natural" separation lengthscale, determined by structural disorder, for which the isolated P subspace presents the acoustic properties of a nearly homogenous (Debye-like) elastic continuum, while the NP one encapsulates all small scale non-affinity effects. The NP eigenstates then play the role of dynamical scatterers for the phonons. However, at variance with a conjecture of defect theories, their spectra present a finite low frequency gap, which turns out to lie around the Boson peak frequency, and only a small fraction of them are highly localized. We then show that small scale disorder effects can be rigorously reduced to the existence, in the Navierlike wave equation of the continuum, of a generalized elasticity tensor, which is not only retarded, since scatterers are dynamical, but also non-local. The full neglect of both retardation and non-locality suffices to account for most of the corrections to Born macroscopic moduli. However, these two features are responsible for sound speed dispersion and have quite a significant effect on the magnitude of sound attenuation. Although it remains open how they impact the asymptotic, large wavelength scaling of sound damping, our findings rule out the possibility of representing an amorphous solid by an inhomogeneous elastic continuum with the standard (i.e., local and static) elastic moduli.
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Dates et versions

hal-03942534 , version 1 (17-01-2023)

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Christiane Caroli, Anaël Lemaître. Key role of retardation and non-locality in sound propagation in amorphous solids as evidenced by a projection formalism. Journal of Chemical Physics, 2020, 153 (14), pp.144502. ⟨10.1063/5.0019964⟩. ⟨hal-03942534⟩
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