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

Abstract

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Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects

“…[39], where Caroli and Lemaître considered separately the effects of the long-wavelength, elastic continuum-like, and small-scale, primarily non-affine, motions with the small-scale motions being the scatterers for the long-wavelength ones. Reference [39] analyzed sound propagation and attenuation in two-dimensional amorphous solids, which are somewhat special in that almost all of their low frequency modes are extended [40,41]. In 3D amorphous solids there is a clear distinction between low-frequency quasilocalized and extended modes [30,40].…”

Coupling of quasi-localized and phonon modes in glasses at low frequency

“…4 have frequencies slightly lower than the calculated phonon bands in Table 2, resulting from the reduction of frequencies caused by coupling effects as suggested in some theories. [22,23] Figure 4(a) displays that the calculated Debye level remains unchanged; see the data given in Table 2. A gap replacing the Debye level occurs near zero frequency in the reduced VDOS and becomes shorter with increasing sample size.…”

“…Despite much controversy in various viewpoints, it is generally accepted that BP originates from the coupling of localized non-phonon modes and transverse phonon modes, which causes a complete reconstruction of vibrational density of states (VDOS) at low frequencies. [14,22,23] A localized mode centers at a disordered core with length scale approaching ten atoms, and decays away from it in the form of ∼ r −2 , where r denotes the distance from the core. [24] These disordered cores are loosely packed [25] and highly distorted.…”

“…Recently, Lerner and Bouchbinder [35] clearly observed these hybridized patterns and produced an original method to successfully extract the localized contribution from the highly-hybridized BP modes. By separating atomic vibrations into phonon subspace and non-phonon subspace, Caroli and Lemaitre [23] found that the coupling between phonon subspace and non-phonon subspace is necessary to account for the property of acoustic propagation and attenuation. But for finite sample size, phonon modes and localized modes at low frequencies may not couple sufficiently to each other, indicated by the well-identified localized modes by participation ratio [36] and the discrete set of phonon bands.…”

Theory of sound attenuation in amorphous solids from nonaffine motions

“…In this sense, the heterogeneous elasticity theory (HET) has provided a derivation of this Rayleigh type damping based on the assumption of Gaussian spatial fluctuations of the shear modulus [11]. This theory, however, is entirely at the continuum level (its starting point is the elastic modulus, which is a continuum quantity, while the modulus' dependence on microphysics, particle displacements, interactions etc is neglected), hence it does not account for the microscopic structural order/disorder [12] nor for the underlying microscopic (nonaffine) particle dynamics [13][14][15].…”