Breakdown of the Debye approximation for the acoustic modes with nanometric wavelengths in glasses

Abstract

On the macroscopic scale, the wavelengths of sound waves in glasses are large enough that the details of the disordered microscopic structure are usually irrelevant, and the medium can be considered as a continuum. On decreasing the wavelength this approximation must of course fail at one point. We show here that this takes place unexpectedly on the mesoscopic scale characteristic of the medium range order of glasses, where it still works well for the corresponding crystalline phases. Specifically, we find that the acoustic excitations with nanometric wavelengths show the clear signature of being strongly scattered, indicating the existence of a cross-over between well-defined acoustic modes for larger wavelengths and ill-defined ones for smaller wavelengths. This cross-over region is accompanied by a softening of the sound velocity that quantitatively accounts for the excess observed in the vibrational density of states of glasses over the Debye level at energies of a few milli-electronvolts. These findings thus highlight the acoustic contribution to the well-known universal low-temperature anomalies found in the specific heat of glasses.disordered systems | elastic properties | inelastic X-ray scattering | vibrational density of states G lasses display a set of universal low-temperature properties (1). In particular, at a temperature of ∼10 K the specific heat is characterized by an excess over the level predicted by the continuum Debye model. This excess, absent in the corresponding crystalline phases, is related to the so-called boson peak, an excess over the Debye level that appears at energies of a few milli-electronvolts in the vibrational density of states. The physical origin of this universal property has been livelily discussed in the literature for many decades; however, an agreed on solution is still lacking. For example, one interpretation supports the idea that the boson peak is produced by soft vibrations that would be present in glasses in addition to the acoustic ones (2-4). Another interpretation is mainly based on models for the vibrational dynamics of glasses in terms of harmonic oscillators with disorder in the force constants: it supports the idea that the boson peak marks the transition between acoustic-like excitations and a disorder-dominated regime for the vibrational spectrum (5-7). Qualitatively similar results appear as well in recently developed theories for the vibrational spectrum of model systems with random spatial variations in the elastic moduli (8). In another interpretation, the boson peak is related to the characteristic vibrations of nanometric clusters (9, 10) that would exist in the glass as a consequence, for example, of a spatially inhomogeneous cohesion and that would hybridize with the acoustic modes (11). The idea of an inhomogeneous elastic response has been recently reconsidered by using a different approach: numerical studies show that the classical elasticity description breaks down in glasses on the mesoscopic length scale (12)(13)(14), and the boson peak woul...

Collective modes and thermodynamics of the liquid state

“…PSD, with the relative magnitude of few per cent, was observed in a model harmonic glass and attributed to the "instantaneous relaxation" due to fast decay and dissipation of shortwavelength phonons in a disordered system [86]. Later work demonstrated that starting from mesoscopic wavelengths, the effective speed of the longitudinal sound can also decrease [87][88][89]. Different mechanisms and contributions to PSD were subsequently discussed [76,90].…”

Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation

“…The VDOS asymptotically approaches g D (ω) = ω 2 /(2π It remains an open question whether or not the VDOS further approaches the Debye asymptote at lower frequencies. It is notable that a previous experiment also shows a few times larger VDOS than the Debye asymptote [26].…”

“…Simulations [17][18][19][20][21][22][23] and experiments [24][25][26][27][28] indicate an abundance of acoustic excitations in amorphous solids, exhibiting the so-called boson peak. For frequencies far lower than the boson peak, the Debye model can be supposed because the microscopic details are irrelevant to long-wavelength modes [26,29]. Several attempts have been made to verify the Debye model description on the microscopic basis by using molecular simulations [21,30], but no conclusive simulation data have been provided on the asymptotic behaviors at low frequencies.…”

Low temperature specific heats of permanently densified glassy GeO2

“…The BP and the broad hump in C/T 3 are considered as a manifestation of the enhanced low-energy vibrational dynamics having as a common origin an excess density of vibrational states (DVS), whose nature is a topic, at present very debated [8,9].…”