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Xu D, Zhang S, Tong H, Wang L, Xu N. Low-frequency vibrational density of states of ordinary and ultra-stable glasses. Nat Commun 2024; 15:1424. [PMID: 38365816 PMCID: PMC11258317 DOI: 10.1038/s41467-024-45671-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 02/01/2024] [Indexed: 02/18/2024] Open
Abstract
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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Affiliation(s)
- Ding Xu
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Shiyun Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Hua Tong
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Lijin Wang
- School of Physics and Optoelectronic Engineering, Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei, 230601, P. R. China.
| | - Ning Xu
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China.
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China.
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Mahajan S, Pica Ciamarra M. Heterogeneous attenuation of sound waves in three-dimensional amorphous solids. Phys Rev E 2024; 109:024605. [PMID: 38491599 DOI: 10.1103/physreve.109.024605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2023] [Accepted: 01/15/2024] [Indexed: 03/18/2024]
Abstract
Sound waves are attenuated as they propagate in amorphous materials. We investigate the mechanism driving sound attenuation in the Rayleigh scattering regime by resolving the dynamics of an excited phonon in time and space via numerical simulations. We find sound attenuation is spatiotemporally heterogeneous. It starts in localized regions, which identify soft regions within the material and correlate with low-frequency vibrational modes. As time progresses, the regions where sound is primarily attenuated invade the system via an apparent diffusive process.
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Affiliation(s)
- Shivam Mahajan
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Naples, Italy
- CNRS@CREATE LTD, 1 Create Way, 08-01 CREATE Tower, Singapore 138602
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Giannini JA, Lerner E, Zamponi F, Manning ML. Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition. J Chem Phys 2024; 160:034502. [PMID: 38226824 DOI: 10.1063/5.0176713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 12/15/2023] [Indexed: 01/17/2024] Open
Abstract
Under decompression, disordered solids undergo an unjamming transition where they become under-coordinated and lose their structural rigidity. The mechanical and vibrational properties of these materials have been an object of theoretical, numerical, and experimental research for decades. In the study of low-coordination solids, understanding the behavior and physical interpretation of observables that diverge near the transition is of particular importance. Several such quantities are length scales (ξ or l) that characterize the size of excitations, the decay of spatial correlations, the response to perturbations, or the effect of physical constraints in the boundary or bulk of the material. Additionally, the spatial and sample-to-sample fluctuations of macroscopic observables such as contact statistics or elastic moduli diverge approaching unjamming. Here, we discuss important connections between all of these quantities and present numerical results that characterize the scaling properties of sample-to-sample contact and shear modulus fluctuations in ensembles of low-coordination disordered sphere packings and spring networks. Overall, we highlight three distinct scaling regimes and two crossovers in the disorder quantifiers χz and χμ as functions of system size N and proximity to unjamming δz. As we discuss, χX relates to the standard deviation σX of the sample-to-sample distribution of the quantity X (e.g., excess coordination δz or shear modulus μ) for an ensemble of systems. Importantly, χμ has been linked to experimentally accessible quantities that pertain to sound attenuation and the density of vibrational states in glasses. We investigate similarities and differences in the behaviors of χz and χμ near the transition and discuss the implications of our findings on current literature, unifying findings in previous studies.
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Affiliation(s)
- Julia A Giannini
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam 1098 XH, The Netherlands
| | - Francesco Zamponi
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
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Baumgärtel P, Vogel F, Fuchs M. Properties of stable ensembles of Euclidean random matrices. Phys Rev E 2024; 109:014120. [PMID: 38366508 DOI: 10.1103/physreve.109.014120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 12/13/2023] [Indexed: 02/18/2024]
Abstract
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as a model for the low temperature vibrational properties of glass. Exact numerical diagonalization is performed in three and two spatial dimensions, which is accompanied by a detailed finite size analysis. It reveals a low-frequency regime of sound waves that are damped by Rayleigh scattering. At large frequencies localized modes exist. In between, the central peak in the vibrational density of states is well described by Wigner's semicircle law for not too large disorder, as is expected for simple random matrix systems. We compare our results with predictions from two recent self-consistent field theories.
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Affiliation(s)
| | - Florian Vogel
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
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Richard D, Kapteijns G, Lerner E. Detecting low-energy quasilocalized excitations in computer glasses. Phys Rev E 2023; 108:044124. [PMID: 37978582 DOI: 10.1103/physreve.108.044124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 09/15/2023] [Indexed: 11/19/2023]
Abstract
Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow one to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abundance, typical frequencies, and other important micromechanical properties. Here we present an efficient algorithm to detect the field of quasilocalized excitations in structural computer glasses. The algorithm introduced takes a computer-glass sample as input and outputs a library of QLEs embedded in that sample. We demonstrate the power of the algorithm by reporting the spectrum of glassy excitations in two-dimensional computer glasses featuring a huge range of mechanical stability, which is inaccessible using conventional harmonic analyses due to phonon hybridizations. Future applications are discussed.
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Affiliation(s)
- David Richard
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Geert Kapteijns
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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Vogel F, Fuchs M. Vibrational Phenomena in Glasses at Low Temperatures Captured by Field Theory of Disordered Harmonic Oscillators. PHYSICAL REVIEW LETTERS 2023; 130:236101. [PMID: 37354405 DOI: 10.1103/physrevlett.130.236101] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2022] [Accepted: 05/04/2023] [Indexed: 06/26/2023]
Abstract
We investigate the vibrational properties of topologically disordered materials by analytically studying particles that harmonically oscillate around random positions. Exploiting classical field theory in the thermodynamic limit at T=0, we build up a self-consistent model by analyzing the Hessian utilizing Euclidean random matrix theory. In accordance with earlier findings [T. S. Grigera et al.J. Stat. Mech. (2011) P02015.JSMTC61742-546810.1088/1742-5468/2011/02/P02015], we take nonplanar diagrams into account to correctly address multiple local scattering events. By doing so, we end up with a first principles theory that can predict the main anomalies of athermal disordered materials, including the boson peak, sound softening, and Rayleigh damping of sound. In the vibrational density of states, the sound modes lead to Debye's law for small frequencies. Additionally, an excess appears in the density of states starting as ω^{4} in the low frequency limit, which is attributed to (quasi-) localized modes.
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Lerner E, Bouchbinder E. Disordered Crystals Reveal Soft Quasilocalized Glassy Excitations. PHYSICAL REVIEW LETTERS 2022; 129:095501. [PMID: 36083650 DOI: 10.1103/physrevlett.129.095501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 08/04/2022] [Indexed: 06/15/2023]
Abstract
Structural glasses formed by quenching a melt are known to host a population of low-energy quasilocalized (nonphononic) excitations whose frequencies ω follow a universal ∼ω^{4} distribution as ω→0, independently of the glass formation history, the interparticle interaction potential, or spatial dimension. Here, we show that the universal quartic law of nonphononic excitations also holds in disordered crystals featuring finite long-range order, which is absent in their glassy counterparts. We thus establish that the degree of universality of the quartic law extends beyond structural glasses quenched from a melt. We further find that disordered crystals, whose level of disorder can be continuously controlled, host many more quasilocalized excitations than expected based on their degree of mechanical disorder-quantified by the relative fluctuations of the shear modulus-as compared to structural glasses featuring a similar degree of mechanical disorder. Our results are related to glasslike anomalies experimentally observed in disordered crystals. More broadly, they constitute an important step toward tracing the essential ingredients necessary for the emergence of universal nonphononic excitations in disordered solids.
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Affiliation(s)
- E Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - E Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
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Szamel G, Flenner E. Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects. J Chem Phys 2022; 156:144502. [DOI: 10.1063/5.0085199] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Sound attenuation in low-temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here, we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient. We verify that the sound damping coefficients calculated from our expression agree very well with results from independent simulations of sound attenuation. Small wavevector analysis of our expression shows that sound attenuation is primarily determined by the non-affine displacements’ contribution to the sound wave propagation coefficient coming from the frequency shell of the sound wave. Our expression involves only quantities that pertain to solids’ static configurations. It can be used to evaluate the low-temperature sound damping coefficients without directly simulating sound attenuation.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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