Density of states below the first sound mode in 3D glasses

Wang, Lijin; Fu, Licun; Nie, Yunhuan

doi:10.1063/5.0102081

Cited by 11 publications

(19 citation statements)

References 65 publications

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“…[3,5] Finally, it is worth noting that we assume a power law as a good description of the low-frequency spectrum or sound attenuation, in line with what was usually done in many previous studies. [37][38][39][40][41][42][43][44][45][46][47][48][49][50] However, the available data due to current computational capacity is insufficient to confirm the accuracy of the power laws down to much lower frequencies, in particular, over several decades of frequency, which represents the big challenge inevitably encountered in recent simulation studies of low-frequency vibrations.…”

Section: Discussionmentioning

confidence: 99%

“…To avert the binning issue [5,37,38] encountered frequently in the numerical calculation of D(ω), we calculate instead the total cumulative density of states, which reads…”

Section: Models and Methodsmentioning

confidence: 99%

“…This thus exposes a low-frequency window below ω 1 where phonon-like modes are not allowed and hence there are only excess modes. A large amount of simulation work [37][38][39][40][41][42][43][44][45][46][47][48][49][50] following this line suggests that γ could depend on the system size, [38,39,41] glass stability, [42,47] spatial dimensions, [38,45] stress distribution, [29,46] fraction of pinned particles [48,50] or even the frequency range examined. [37,38] However, to date, consensus is still lacking regarding the value of γ in simulations.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we refer to Refs. [37][38][39] for the latest study of the low-frequency spectrum in the density of excess modes not hybridizing with phonon-like modes.…”

Section: Introductionmentioning

confidence: 99%

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Low-frequency hybridized excess vibrations of two-dimensional glasses

Fu 付,

Zheng 郑,

Wang 王

2024

Chinese Phys. B

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One hallmark of glasses is the existence of excess vibrational modes at low frequencies $\omega$ beyond the Debye's prediction. Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses. However, it is still under intensive debate on the frequency dependence of the population of low-frequency excess vibrations. In particular, excess modes could hybridize with phonon-like modes, and the density of hybridized excess modes has been reported to follow $D_{\rm exc}(\omega) \sim \omega^{2}$ in 2D glasses with an inverse-power-law potential. Yet, it remains to check the universality of the quadratic scaling since recent work suggested that the interaction potentials could influence the scaling of vibrational spectrum. Here, we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant difference in the density or the interparticle repulsion. Moreover, we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion, which is accompanied by a suppression in the strength of the sound attenuation. Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.

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Section: Discussionmentioning

confidence: 99%

“…To avert the binning issue [5,37,38] encountered frequently in the numerical calculation of D(ω), we calculate instead the total cumulative density of states, which reads…”

Section: Models and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Here, we refer to Refs. [37][38][39] for the latest study of the low-frequency spectrum in the density of excess modes not hybridizing with phonon-like modes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Low-frequency hybridized excess vibrations of two-dimensional glasses

Fu 付,

Zheng 郑,

Wang 王

2024

Chinese Phys. B

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“…[17,33,34] Moreover, it has also been argued that the quartic scaling could be generalized to 2D and four-dimensional (4D) glasses. [41,43,45] However, the universality of the quartic scaling of the excess-mode spectrum below ω 1 has recently been challenged by some simulation studies [17,42,43,[46][47][48][49][50][51] in both 2D and 3D glasses. Of these studies reporting the deviations from the low-frequency ω 4 distribution, in Refs.…”

Section: Introductionmentioning

confidence: 99%

Density of excess modes below the first phonon mode in four-dimensional glasses

Wang 王,

Xu 胥,

Zhang 张

2024

Chinese Phys. B

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Glasses are known to possess low-frequency excess modes beyond the Debye prediction. For decades, it has been assumed the evolution of the low-frequency density of excess modes $D(\omega)$ with the frequency $\omega$ follows a power-law scaling: $D(\omega)\sim \omega^{\gamma}$. However, it remains debated on the value of $\gamma$ at low frequencies below the first phonon-like mode in finite-size glasses. Early simulation studies reported $\gamma=4$ at low frequencies in two- (2D), three- (3D) and four-dimensional (4D) glasses, whereas recent observations in 2D and 3D glasses suggested $\gamma=3.5$ in a lower-frequency regime. It's uncertain whether the low-frequency scaling of $D(\omega)\sim \omega^{3.5}$ could be generalized to 4D glasses. Here, we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses. We find the system size dependence of $D(\omega)$ below the first phonon-like mode varies with spatial dimensions: $D(\omega)$ increases in 2D glasses but decreases in 3D and 4D glasses as the system size increases. Furthermore, we demonstrate that the $\omega^{3.5}$ scaling, rather than the $\omega^{4}$ scaling, works in the lowest-frequency regime accessed in 4D glasses, regardless of interaction potentials and system sizes examined. Therefore, our findings in 4D glasses, combined with previous results in 2D and 3D glasses, suggest a common low-frequency scaling of $D(\omega)\sim \omega^{3.5}$ below the first phonon-like mode across different spatial dimensions, which would inspire further theoretical studies.

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Low-frequency vibrational density of states of ordinary and ultra-stable glasses

Xu,

Zhang,

Tong

et al. 2024

Nat Commun

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A remarkable feature of disordered solids distinct from crystals is the violation of the Debye scaling law of the low-frequency vibrational density of states. Because the low-frequency vibration is responsible for many properties of solids, it is crucial to elucidate it for disordered solids. Numerous recent studies have suggested power-law scalings of the low-frequency vibrational density of states, but the scaling exponent is currently under intensive debate. Here, by classifying disordered solids into stable and unstable ones, we find two distinct and robust scaling exponents for non-phononic modes at low frequencies. Using the competition of these two scalings, we clarify the variation of the scaling exponent and hence reconcile the debate. Via the study of both ordinary and ultra-stable glasses, our work reveals a comprehensive picture of the low-frequency vibration of disordered solids and sheds light on the low-frequency vibrational features of ultra-stable glasses on approaching the ideal glass.

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Density of states below the first sound mode in 3D glasses

Cited by 11 publications

References 65 publications

Low-frequency hybridized excess vibrations of two-dimensional glasses

Low-frequency hybridized excess vibrations of two-dimensional glasses

Density of excess modes below the first phonon mode in four-dimensional glasses

Low-frequency vibrational density of states of ordinary and ultra-stable glasses

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