Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder

Cui, Bingyu; Zaccone, Alessio

doi:10.1039/d0sm00814a

Cited by 14 publications

(27 citation statements)

References 32 publications

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“…According to the theoretical analysis in ref. [57], such enhancement to the Rayleigh scattering of phonons in amorphous solids originates from long-range power-law spatial correlations of elastic constants or internal stress. For example, the shear stress tensor, σ(r) = σ 0 + Δσ(r) is expressed in terms of its mean value plus a random fluctuation, i.e.…”

Section: Theory For Longitudinal Excitations In 2dmentioning

confidence: 99%

“…a e-mail: alessio.zaccone@unimi.it peak shows up in a frequency range where the broadening of the acoustic excitations becomes of the order of magnitude of resonance frequency, states near the boson peak frequency are neither actually propagating nor localized, and the boson peak itself appears to be closely related to an underlying Ioffe-Regel crossover from ballistic phonon propagation to diffusive excitations, the so-called diffusons [51][52][53][54]. Among previous theories, the heterogeneous elasticity theory (HET) [42,[55][56][57][58] uses a field-theoretical scheme to derive the DOS, by assuming Gaussian uncorrelated spatial fluctuations in the elastic constants of the system [4]. The theory provides a quantitative relation between the boson peak and the Brillouin width (sound attenuation coefficient) Γ , and reproduces the Rayleigh scattering law Γ ∼ ω d+1 .…”

Section: Introductionmentioning

confidence: 99%

“…The theory provides a quantitative relation between the boson peak and the Brillouin width (sound attenuation coefficient) Γ , and reproduces the Rayleigh scattering law Γ ∼ ω d+1 . However, following numerical evidence of a logarithmic enhancement correction of the form Γ (k) ∼ −k d+1 ln(k) to the Rayleigh scattering law (with wavenumber k, in d-dimension) [59], it has been shown analytically that long-ranged power-law spatial correlations in elasticity, or equivalently in the internal stresses, are the cause of such enhancement [57].…”

Section: Introductionmentioning

confidence: 99%

“…In ref. [57], by finding the rigorous solution to the self-consistent anistropic wave propagation problem, it was possible to derive the logarithmic Rayleigh scattering law, which is ubiquitously observed in experiments and simulations [61][62][63][64][65][66][67][68], and to show that it is the direct result of the power-law correlation in internal stresses or elastic constants.…”

Section: Introductionmentioning

confidence: 99%

“…The answer is presented in this paper, where we exploit the successful framework of ref. [57] for the acoustic attenuation, and apply it to study the properties of the DOS. We reveal that the boson peak picks up a logarithmic correction which is most evident in the excess DOS.…”

Section: Introductionmentioning

confidence: 99%

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Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity

Cui

Zaccone

2020

Eur. Phys. J. E

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Abstract. A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D($\omega$ ω ) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form $ \sim -\omega^{2}\ln\omega$ ∼ - ω 2 ln ω is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a $ \sim\omega^{4}$ ∼ ω 4 regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory. Graphical abstract

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Section: Theory For Longitudinal Excitations In 2dmentioning

confidence: 99%