Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale

Abstract

The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties that are, however, anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite a longstanding debate, remain poorly understood. By using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: The elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length scale of Ϸ10 interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This reduction turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of Ϸ1 THz in the vibrational density of states or at temperatures of Ϸ10 K in the specific heat. disordered systems ͉ molecular dynamics ͉ vibrational properties G lasses are structurally disordered systems. As common experience shows, in the macroscopic limit they support sound waves as corresponding crystalline materials do. In fact, averaging on a large enough length scale, the details of the microscopic arrangement become essentially irrelevant. This holds true for sound waves with long wavelengths of at least several hundreds of nanometers, corresponding to wavenumbers q in the 10 Ϫ2 -nm Ϫ1 range, as those probed with light scattering techniques (1). On further increasing q, the effect of the structural disorder must appear at one point. The much larger q scale of few nm Ϫ1 is also well known because it can be accessed experimentally with inelastic X-ray (2) and neutron (3) scattering techniques, and numerically with molecular dynamics simulations (4-11). These studies typically probe the dynamic structure factor S(q, ), that is, the space and time Fourier transform of the density-density correlation function. These studies clearly indicate the existence in glasses of excitations that appear in those spectra as very broad peaks whose position as a function of q is characterized by a sinusoidal-like dispersion curve. Thus, these excitations strongly recall the acoustic modes in (poly-)crystalline systems up to roughly one half of the pseudo-Brillouin zone (12), i.e., down to distances corresponding to the interatomic spacing. For this reason, they are often dubbed as acoustic-like. However, as their broadening clearly indicates, they are far from being...

The jamming scenario—an introduction and outlook

“…This leads to a plateau in the diffusivity consistent with the results of Fig.(1.8). This analysis predicts a drop in the speed of sound near ω * , a subtle effect recently observed numerically at the Boson peak frequency in model glasses [42]. In the case where the isostatic state is a square lattice [32], the Ioffe-Regel criterion is satisfied at the crossover frequency ω * and ℓ s is of order the lattice spacing.…”

Measuring spatial distribution of the local elastic modulus in glasses

“…The scale ξ of the elastic heterogeneities can be assessed by measuring the local elastic properties as a function of a coarse graining size, and monitoring the convergence towards macroscopic properties [3]. The elastic continuum approximation for the acoustic excitations breaks down on a mesoscopic wavelength comparable to ξ, where a marked reduction of the sound velocity and strong scattering were observed [10,11]. It has been suggested that the elastic heterogeneity is closely linked to several unusual properties of glasses, which include low-temperature thermal properties [12], an excess vibrational density of states, known as the "Boson peak" [13,14], and anomalous acoustic properties [10,11,[15][16][17].…”

“…The elastic continuum approximation for the acoustic excitations breaks down on a mesoscopic wavelength comparable to ξ, where a marked reduction of the sound velocity and strong scattering were observed [10,11]. It has been suggested that the elastic heterogeneity is closely linked to several unusual properties of glasses, which include low-temperature thermal properties [12], an excess vibrational density of states, known as the "Boson peak" [13,14], and anomalous acoustic properties [10,11,[15][16][17]. Theoretical models [18,19] have been proposed to relate the boson peak and the associated thermal and acoustic anomalies to a randomly fluctuating shear modulus.…”

Elastic anomalies at terahertz frequencies and excess density of vibrational states in silica glass

“…This frequency range is also at the lower edge of the region accessible to molecular dynamics simulations. 3 A variety of theoretical models has been proposed to explain these low-frequency (∼1 THz) vibrations. Among them we may recall the soft potential model, 4 the mode-coupling theory applied to the vibrations in glasses, 5 models on a lattice 6 or on the continuum 7 with randomly fluctuating elastic constants, and harmonic models where the atoms vibrate around topologically disordered configurations.…”

“…25 These experimental results have been confirmed by molecular dynamics simulations of a Lennard-Jones glass performed on an exceptionally large simulation box, containing 10 7 particles. 3 The observation of these elastic anomalies requires a very high accuracy which has been attained only in recent years, thanks to the continuous development of the IXS technique. The particular case of vitreous silica has been deeply studied by means of IXS in the past, [26][27][28][29][30][31][32][33][34][35] but these fine features of the dynamics were hidden by the noise in the first experiments.…”