Acoustic Wave Propagation through a Supercooled Liquid: A Normal Mode Analysis

Matsuoka, Yuki; Mizuno, Hideyuki; Yamamoto, Ryōichi

doi:10.1143/jpsj.81.124602

Cited by 7 publications

(19 citation statements)

References 35 publications

(62 reference statements)

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“…This observation seems to indicate that moduli heterogeneities impact the spatial structure of the normal modes 56,57,62 rather than simply reducing their life-times. Since acoustic plane waves are superpositions of different normal modes 14,15 , we conclude that these modifications are the main reason for the important frequency attenuation of the acoustic-like excitations ( Fig. 12(k)).…”

Section: B Life-times Of the Vibrational Excitationsmentioning

confidence: 79%

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Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

2016

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In crystals, molecules thermally vibrate around the periodic lattice sites. Vibrational motions are well understood in terms of phonons, which carry heat and control heat transport. The situation is notably different in disordered solids, where vibrational excitations are not phonons and can be even localized. Recent numerical work has established the concept of elastic heterogeneity: Disordered solids show inhomogeneous local mechanical response. Clearly, the heterogeneous nature of elastic properties strongly influences vibrational and thermal properties, and it is expected to be the origin of anomalous features, including boson peak, vibrational localization, and temperature dependence of thermal conductivity. These are all crucial long-standing problems in material physics, which we address in the present work. We have considered a toy model able to stabilize different states of matter, by introducing an increasing amount of size disorder. The phase diagram generated by Molecular Dynamics simulation encompasses the perfect crystalline state with spatially homogeneous elastic moduli distribution, multiple defective phases with increasing moduli heterogeneities, and eventually a series of amorphous states. We have established clear correlations among heterogeneous local mechanical response, vibrational states, and thermal conductivity. We provide evidence that elastic heterogeneity controls both vibrational and thermal properties, and is a key concept to understand the anomalous puzzling features of disordered solids.

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Section: B Life-times Of the Vibrational Excitationsmentioning

confidence: 79%

“…The life-times can be therefore calculated from the auto-correlation function of the energy δE Xq (t), from relations analogous to Eqs. (15) and (16). Note that, since the acoustic waves are not genuine normal modes in the disordered states, the energy equipartition does not hold and E Xq (t) = T .…”

Section: B Life-times Of the Vibrational Excitationsmentioning

confidence: 96%

Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

2016

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“…Many authors 6,16,21,22,[53][54][55][56] have calculated the vibrational modes in glasses in the periodic boundary condition. We can examine them with boundary walls by including the last term in Eq.…”

Section: B Inherent State and Quasi-equilibrium In Glassmentioning

confidence: 99%

Theory of Shear Modulus in Glasses

Onuki,

Kawasaki

2018

Preprint

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We construct a linear response theory of applying shear deformations from boundary walls in the film geometry in Kubo's theoretical scheme. Our method is applicable to any solids and fluids. For glasses, we assume quasi-equilibrium around a fixed inherent state. Then, we obtain linearresponse expressions for any variables including the stress and the particle displacements, even though the glass interior is elastically inhomogeneous. In particular, the shear modulus can be expressed in terms of the correlations between the interior stress and the forces from the walls. It can also be expressed in terms of the inter-particle correlations, as has been shown in the previous literature. Our stress relaxation function includes the effect of the boundary walls and can be used for inhomogeneous flow response. We show the presence of long-ranged, long-lived correlations among the fluctuations of the forces from the walls and the displacements of all the particles in the cell. We confirm these theoretical results numerically in a two-dimensional model glass. As an application, we describe propagation of transverse sounds after boundary wall motions using these time-correlation functions We also find resonant sound amplification when the frequency of an oscillatory shear approaches that of the first transverse sound mode.

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“…41,42 In particular, localized soft modes predicted by the "normal mode analysis" have been revealed to be a good predictor of the dynamic heterogeneity; from a single and instantaneous snapshot of the particle configuration, information regarding the spatial heterogeneity of dynamics can be extracted with the use of the distribution of localized low-frequency phonons. 37,38 Similar methods are also employed to predict yielding spots in a jammed system at zero temperature. 43,44 To compare the distribution of the free volumes with the high-propensity region determined from a static configuration, we perform the normal mode analysis for our system along the lines of Ref.…”

Section: Normal Mode Analysismentioning

confidence: 99%

“…In spite of difficulties in studying the local density fluctuations, one method has recently enabled the possibility of capturing the "inherent structure" as a localized soft mode, which can be calculated from a static configuration of particles in a supercooled liquid with the use of normal mode analysis. 37,38 Since this approach is, to our knowledge, the only established approach to predict tendencies of heterogeneity of dynamic propensity from a momentary configuration of the particles, it can be the bridge between dynamical heterogeneity and its origin. In this study, we examine the heterogeneities of the local density distributions and dynamics by capturing and tracing weakly existing density fluctuations in a constructive manner, and subsequently, we investigate its relationship to the inherent structure to clarify the probable role of the density fluctuation in dynamical heterogeneity.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal heterogeneity of local free volumes in highly supercooled liquid

Shiba

Kawasaki

2013

The Journal of Chemical Physics

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We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions. To trace voids heterogeneously existing with lower local densities, which move along with the structural relaxation, we employ the minimum local density for each particle in a time window whose width is set along with the structural relaxation time. Particles subject to free volumes correspond well to the configuration rearranging region of dynamical heterogeneity. While the correlation length for dynamical heterogeneity grows with temperature decrease, no growth in the correlation length of heterogeneity in the minimum local density distribution takes place. A comparison of these results with those of normal mode analysis reveals that superpositions of lower-frequency soft modes extending over the free volumes exhibit spatial correlation with the broken bonds. This observation suggests a possibility that long-ranged vibration modes facilitate the interactions between fragile regions represented by free volumes, to induce dynamical correlations at a large scale.

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Acoustic Wave Propagation through a Supercooled Liquid: A Normal Mode Analysis

Cited by 7 publications

References 35 publications

Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

Theory of Shear Modulus in Glasses

Spatiotemporal heterogeneity of local free volumes in highly supercooled liquid

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