1
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Lerner E, Moriel A, Bouchbinder E. Enumerating low-frequency nonphononic vibrations in computer glasses. J Chem Phys 2024; 161:014504. [PMID: 38949282 DOI: 10.1063/5.0216351] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2024] [Accepted: 06/10/2024] [Indexed: 07/02/2024] Open
Abstract
In addition to Goldstone phonons that generically emerge in the low-frequency vibrational spectrum of any solid, crystalline or glassy, structural glasses also feature other low-frequency vibrational modes. The nature and statistical properties of these modes-often termed "excess modes"-have been the subject of decades-long investigation. Studying them, even using well-controlled computer glasses, has proven challenging due to strong spatial hybridization effects between phononic and nonphononic excitations, which hinder quantitative analyses of the nonphononic contribution DG(ω) to the total spectrum D(ω), per frequency ω. Here, using recent advances indicating that DG(ω)=D(ω)-DD(ω), where DD(ω) is Debye's spectrum of phonons, we present a simple and straightforward scheme to enumerate nonphononic modes in computer glasses. Our analysis establishes that nonphononic modes in computer glasses indeed make an additive contribution to the total spectrum, including in the presence of strong hybridizations. Moreover, it cleanly reveals the universal DG(ω)∼ω4 tail of the nonphononic spectrum, and opens the way for related analyses of experimental spectra of glasses.
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Affiliation(s)
- Edan Lerner
- Institute of Theoretical Physics, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands
| | - Avraham Moriel
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
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2
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Chakraborty S, Ramola K. Long-range correlations in elastic moduli and local stresses at the unjamming transition. SOFT MATTER 2024; 20:4895-4904. [PMID: 38860707 DOI: 10.1039/d4sm00328d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2024]
Abstract
We explore the behaviour of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic p2 dependence of the correlations as the pressure p approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.
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Affiliation(s)
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad 500046, India.
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3
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Jiang C, Baggioli M, Douglas JF. Stringlet excitation model of the boson peak. J Chem Phys 2024; 160:214505. [PMID: 38832741 DOI: 10.1063/5.0210057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Accepted: 05/20/2024] [Indexed: 06/05/2024] Open
Abstract
The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.
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Affiliation(s)
- Cunyuan Jiang
- School of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
- Wilczek Quantum Center, Shanghai Jiao Tong University, 200240 Shanghai, China
- Shanghai Research Center for Quantum Sciences, 200240 Shanghai, China
| | - Matteo Baggioli
- School of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
- Wilczek Quantum Center, Shanghai Jiao Tong University, 200240 Shanghai, China
- Shanghai Research Center for Quantum Sciences, 200240 Shanghai, China
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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4
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Cravero R, Tlili A, Paterson J, Tomelleri M, Marcello P, Debord R, Pailhès S, Bourgeois O, Hippert F, Le Qui D, Raty JY, Noe P, Giordano VM. Glass-Like Phonon Dynamics and Thermal Transport in a GeTe Nano-Composite at Low Temperature. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2024; 20:e2310209. [PMID: 38634392 DOI: 10.1002/smll.202310209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2023] [Revised: 01/29/2024] [Indexed: 04/19/2024]
Abstract
In this work, the experimental evidence of glass-like phonon dynamics and thermal conductivity in a nanocomposite made of GeTe and amorphous carbon is reported, which is of interest for microelectronics, and specifically phase change memories. It is shown that, the total thermal conductivity is reduced by a factor of three at room temperature with respect to pure GeTe, due to the reduction of both electronic and phononic contributions. This latter, similarly to glasses, is small and weakly increasing with temperature between 100 and 300 K, indicating a mostly diffusive thermal transport and reaching a value of 0.86(7) Wm-1K-1 at room temperature. A thorough investigation of the nanocomposite's phonon dynamics reveals the appearance of an excess intensity in the low energy vibrational density of states, reminiscent of the Boson peak in glasses. These features can be understood in terms of an enhanced phonon scattering at the interfaces, due to the presence of elastic heterogeneities, at wavelengths in the 2-20 nm range. The findings confirm recent simulation results on crystalline/amorphous nanocomposites and open new perspectives in phonon and thermal engineering through the direct manipulation of elastic heterogeneities.
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Affiliation(s)
- R Cravero
- Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, Villeurbanne cedex, F-69622, France
- Institut NEEL, CNRS, Université Grenoble Alpes, 25 avenue des Martyrs, Grenoble, F-38042, France
| | - A Tlili
- Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, Villeurbanne cedex, F-69622, France
| | - J Paterson
- CEA, LETI, Université Grenoble Alpes, Grenoble, 38000, France
| | - M Tomelleri
- CEA, LETI, Université Grenoble Alpes, Grenoble, 38000, France
| | - P Marcello
- Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, Villeurbanne cedex, F-69622, France
| | - R Debord
- Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, Villeurbanne cedex, F-69622, France
| | - S Pailhès
- Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, Villeurbanne cedex, F-69622, France
| | - O Bourgeois
- Institut NEEL, CNRS, Université Grenoble Alpes, 25 avenue des Martyrs, Grenoble, F-38042, France
| | - F Hippert
- CNRS, Grenoble INP, LMGP, Université Grenoble Alpes, Grenoble, F-38000, France
| | - D Le Qui
- FNRS and CESAM, Université de Liége, Sart-Tilman, 4000, Belgique
| | - J-Y Raty
- FNRS and CESAM, Université de Liége, Sart-Tilman, 4000, Belgique
| | - P Noe
- CEA, LETI, Université Grenoble Alpes, Grenoble, 38000, France
| | - V M Giordano
- Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, Villeurbanne cedex, F-69622, France
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5
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Pettinari T, During G, Lerner E. Elasticity of self-organized frustrated disordered spring networks. Phys Rev E 2024; 109:054906. [PMID: 38907496 DOI: 10.1103/physreve.109.054906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 04/23/2024] [Indexed: 06/24/2024]
Abstract
There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by studying a minimal model for structural glasses' elasticity in which the degree of mechanical disorder-as characterized by recently introduced dimensionless quantifiers-is readily tunable over a very large range. We comprehensively investigate a number of scaling laws observed for various macro, meso and microscopic elastic properties, and rationalize them using scaling arguments. Interestingly, we demonstrate that the model features the universal quartic glassy vibrational density of states as seen in many atomistic and molecular models of structural glasses formed by cooling a melt. The emergence of this universal glassy spectrum highlights the role of self-organization (toward mechanical equilibrium) in its formation, and elucidates why models featuring structural frustration alone do not feature the same universal glassy spectrum. Finally, we discuss relations to existing work in the context of strain stiffening of elastic networks and of low-energy excitations in structural glasses, in addition to future research directions.
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6
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Schirmacher W, Paoluzzi M, Mocanu FC, Khomenko D, Szamel G, Zamponi F, Ruocco G. The nature of non-phononic excitations in disordered systems. Nat Commun 2024; 15:3107. [PMID: 38600083 PMCID: PMC11258284 DOI: 10.1038/s41467-024-46981-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Accepted: 03/18/2024] [Indexed: 04/12/2024] Open
Abstract
The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of states g(ω) of these modes obeys an ωs scaling, where the exponent s, ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal. Here we show, using heterogeneous-elasticity theory, that in a marginally-stable glass sample g(ω) follows a Debye-like scaling (s = 2), and the associated excitations (type-I) are of random-matrix type. Further, using a generalisation of the theory, we demonstrate that in more stable samples, other, (type-II) excitations prevail, which are non-irrotational oscillations, associated with local frozen-in stresses. The corresponding frequency scaling exponent s is governed by the statistics of small values of the stresses and, therefore, depends on the details of the interaction potential.
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Affiliation(s)
- Walter Schirmacher
- Institut für Physik, Staudinger Weg 7, Universität Mainz, D-55099, Mainz, Germany.
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 291 Viale Regina Elena, I-00161, Roma, Italy.
| | - Matteo Paoluzzi
- Istituto per le Applicazioni del Calcolo del Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, 80131, Napoli, NA, Italy
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028, Barcelona, Spain
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy
| | - Felix Cosmin Mocanu
- Dept. of Materials, Univ. of Oxford, Parks Road, Oxford, OX13PH, UK
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
| | - Dmytro Khomenko
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy
| | - Grzegorz Szamel
- Dept. of Chemistry, Colorado State University, Fort Collins, CO, 80523, USA
| | - Francesco Zamponi
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
| | - Giancarlo Ruocco
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 291 Viale Regina Elena, I-00161, Roma, Italy.
- Dipartimento di Fisica, Universita' di Roma "La Sapienza", P'le Aldo Moro 5, I-00185, Roma, Italy.
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7
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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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8
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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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9
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Mossa S, Bryk T, Ruocco G, Schirmacher W. Heterogeneous-elasticity theory of instantaneous normal modes in liquids. Sci Rep 2023; 13:21442. [PMID: 38052816 DOI: 10.1038/s41598-023-46248-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 10/30/2023] [Indexed: 12/07/2023] Open
Abstract
Since decades, the concept of vibrational density of states in glasses has been mirrored in liquids by the instantaneous-normal-mode spectrum. In glasses instantaneous configurations are believed to be situated close to minima of the potential-energy hypersurface and all eigenvalues of the associated Hessian matrix are positive. In liquids this is no longer true, and modes corresponding to both positive and negative eigenvalues exist. The instantaneous-normal-mode spectrum has been numerically investigated in the past, and it has been demonstrated to bring important information on the liquid dynamics and transport properties. A systematic deeper theoretical understanding is now needed. Heterogeneous-elasticity theory has proven to be particularly successful in explaining many details of the low-frequency excitations in glasses, ranging from the thoroughly studied boson peak, to other anomalies related to the crossover between wave-like and random-matrix-like excitations. Here we present an extension of heterogeneous-elasticity theory to the liquid state, and show that the outcome of the theory agrees well to the results of extensive molecular-dynamics simulations of a model liquid at different temperatures. We find that the spectrum of eigenvalues [Formula: see text] has a sharp maximum close to (but not at) [Formula: see text], and decreases monotonically with [Formula: see text] on both its stable and unstable side. We show that the spectral shape strongly depends on temperature, being symmetric at high temperatures and becoming rather asymmetric at low temperatures, close to the dynamical critical temperature. Most importantly, we demonstrate that the theory naturally reproduces a surprising phenomenon, a zero-energy spectral singularity with a cusp-like character developing in the vibrational spectra upon cooling. This feature, known from a few previous numerical studies, has been generally overlooked in the past due to a misleading representation of the data. We provide a thorough analysis of this issue, based on both very accurate predictions of our theory, and computational studies of model liquid systems with extended size.
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Affiliation(s)
- Stefano Mossa
- CEA, IRIG-MEM-LSim, University Grenoble Alpes, 38054, Grenoble, France.
| | - Taras Bryk
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, 79011, Ukraine
- Institute of Applied Mathematics and Fundamental Sciences, Lviv National Polytechnic University, Lviv, 79013, Ukraine
| | - Giancarlo Ruocco
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 295 Viale Regina Elena, 00161, Roma, Italy.
- Dipartimento di Fisica, Universitá di Roma "La Sapienza", P.le Aldo Moro 5, 00185, Roma, Italy.
| | - Walter Schirmacher
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 295 Viale Regina Elena, 00161, Roma, Italy
- Institut für Physik, Universität Mainz, Staudinger Weg 7, 55099, Mainz, Germany
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10
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El Hamdaoui A, Ghardi EM, Atila A, Jabraoui H, Badawi M, Hasnaoui A, Ouaskit S. The boson peak in silicate glasses: insight from molecular dynamics. Phys Chem Chem Phys 2023; 25:31270-31280. [PMID: 37955301 DOI: 10.1039/d3cp02912c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
In the low-frequency regime, ≈1 THz, glasses show an anomalous excess in their vibrational density of states called the boson peak (BP). The origin of BP has been a subject of debate since its first discovery a few decades ago. Although BP has been the focus of numerous studies, no conclusive answers have been found about its origins, which remained elusive to date. Here, we present results based on molecular dynamics of several binary and ternary silicate glasses with different network intermediates and modifier oxides. The vibrational density of states and the BP are reported for all the studied glasses. Their correlation with the elastic constant C44, structural, and dynamical properties are extensively discussed in terms of Voronoi atomic volume and the vibrational mean square displacement of Q4 species specifically. We also question the classical classification of alkali oxides as modifiers, and we suggest that Li2O plays the role of pseudo-intermediate oxide in lithium silicate glasses. This claim is supported by the effect of Li on various vibrational modes, and this effect differs from the other alkali metals. Furthermore, we demonstrate a correlation between the BP intensities and both the Voronoi volume of the Q4 and Q3 units and vibrational mean square displacements.
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Affiliation(s)
- Ahmed El Hamdaoui
- Laboratoire de Physique de la Matière Condensée, Faculté des Sciences Ben M'sik, University Hassan II of Casablanca, B.P. 7955, Av Driss El Harti, Sidi Othmane, Casablanca, Morocco.
| | - El Mehdi Ghardi
- Nuclear Futures Institute, Bangor University, Gwynedd, LL57 2DG, UK.
| | - Achraf Atila
- Department of Material Science and Engineering, Saarland University, Saarbrücken, 66123, Germany
| | - Hicham Jabraoui
- Université Paris-Saclay, NIMBE, CEA, CNRS, F-91191 Gif-sur-Yvette Cedex, France
- LAAS-CNRS, University of Toulouse, 31077 Toulouse, France
| | | | - Abdellatif Hasnaoui
- LS2ME, Faculté Polydisciplinaire Khouribga, Sultan Moulay Slimane University of Beni Mellal, B.P. 145, 25000 Khouribga, Morocco
| | - Said Ouaskit
- Laboratoire de Physique de la Matière Condensée, Faculté des Sciences Ben M'sik, University Hassan II of Casablanca, B.P. 7955, Av Driss El Harti, Sidi Othmane, Casablanca, Morocco.
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11
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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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12
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Shiraishi K, Mizuno H, Ikeda A. Non-phononic density of states of two-dimensional glasses revealed by random pinning. J Chem Phys 2023; 158:2887555. [PMID: 37125708 DOI: 10.1063/5.0142648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Accepted: 04/17/2023] [Indexed: 05/02/2023] Open
Abstract
The vibrational density of states of glasses is considerably different from that of crystals. In particular, there exist spatially localized vibrational modes in glasses. The density of states of these non-phononic modes has been observed to follow g(ω) ∝ ω4, where ω is the frequency. However, in two-dimensional systems, the abundance of phonons makes it difficult to accurately determine this non-phononic density of states because they are strongly coupled to non-phononic modes and yield strong system-size and preparation-protocol dependencies. In this article, we utilize the random pinning method to suppress phonons and disentangle their coupling with non-phononic modes and successfully calculate their density of states as g(ω) ∝ ω4. We also study their localization properties and confirm that low-frequency non-phononic modes in pinned systems are truly localized without far-field contributions. We finally discuss the excess density of states over the Debye value that results from the hybridization of phonons and non-phononic modes.
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Affiliation(s)
- Kumpei Shiraishi
- Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
- Research Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Komaba, Tokyo 153-8902, Japan
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13
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Ishima D, Saitoh K, Otsuki M, Hayakawa H. Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime. Phys Rev E 2023; 107:054902. [PMID: 37328994 DOI: 10.1103/physreve.107.054902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 03/23/2023] [Indexed: 06/18/2023]
Abstract
Using the Jacobian matrix, we obtain a theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. We find that there are two modes in the density of states for sufficiently small k_{T}/k_{N}, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in k_{T}/k_{N} and becomes indistinguishable from the translational band for large k_{T}/k_{N}.
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Affiliation(s)
- Daisuke Ishima
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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14
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Zhang S, Jin W, Wang D, Xu D, Zhang J, Shattuck MD, O'Hern CS. Local and global measures of the shear moduli of jammed disk packings. Phys Rev E 2023; 107:054903. [PMID: 37329065 DOI: 10.1103/physreve.107.054903] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1-F_{-})〈G_{+}〉+F_{-}〈G_{-}〉, where F_{-} is the fraction of jammed packings with negative shear moduli and 〈G_{+}〉 and 〈G_{-}〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G_{+}〉 and 〈|G_{-}|〉 obey different power-law scaling relations above and below pN^{2}∼1. For pN^{2}>1, both 〈G_{+}〉N and 〈|G_{-}|〉N∼(pN^{2})^{β}, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN^{2})^{β^{'}} with β^{'}≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}≪1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r[over ⃗]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over ⃗]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}≳10^{-2}.
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Affiliation(s)
- Shiyun Zhang
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Weiwei Jin
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Dong Wang
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Ding Xu
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jerry Zhang
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- Graduate Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA
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15
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Papadopoulos AG, Tagiara NS, Stavrou E, Li F, Yang G, Kamitsos EI. Pressure-Induced Structural Transformations and Electronic Transitions in TeO 2 Glass by Raman Spectroscopy. J Phys Chem Lett 2023; 14:387-394. [PMID: 36622290 DOI: 10.1021/acs.jpclett.2c03612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
TeO2 glass has been studied by Raman spectroscopy up to the record pressure of 70 GPa. The boson peak frequency ωb exhibits a decrease of the ∂ωb/∂P slope at 5-6 GPa and saturates above 30 GPa with a practically constant value up to 70 GPa. Experiment and theory indicate that pressures up to 20 GPa induce the transformation of single Te-O-Te bridges to double Te-O2-Te bridges, leading to a more compact structure, while Raman activity developing at higher pressures around 580 cm-1 signals the increase of Te coordination from 4- to 6-fold. Natural bond orbital analysis shows that double Te-O2-Te bridges favor the s → d transition and promote the increase of Te coordination through d2sp3 hybridization. This transition leads to the formation of TeO6 octahedra, in strict difference with crystalline TeO2 at the same pressure range, and to the development of a 3D network that freezes the medium range order.
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Affiliation(s)
- Anastasios G Papadopoulos
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, 116 35Athens, Greece
| | - Nagia S Tagiara
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, 116 35Athens, Greece
| | - Elissaios Stavrou
- Materials Science and Engineering Program, Guangdong Technion-Israel Institute of Technology, Shantou, Guangdong515063, China
- Department of Materials Science and Engineering, Technion-Israel Institute of Technology, Haifa32000, Israel
| | - Fei Li
- State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for Microstructural Materials Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao066004, China
| | - Guochun Yang
- State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for Microstructural Materials Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao066004, China
| | - Efstratios I Kamitsos
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, 116 35Athens, Greece
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16
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González-Jiménez M, Barnard T, Russell BA, Tukachev NV, Javornik U, Hayes LA, Farrell AJ, Guinane S, Senn HM, Smith AJ, Wilding M, Mali G, Nakano M, Miyazaki Y, McMillan P, Sosso GC, Wynne K. Understanding the emergence of the boson peak in molecular glasses. Nat Commun 2023; 14:215. [PMID: 36639380 PMCID: PMC9839737 DOI: 10.1038/s41467-023-35878-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 01/05/2023] [Indexed: 01/15/2023] Open
Abstract
A common feature of glasses is the "boson peak", observed as an excess in the heat capacity over the crystal or as an additional peak in the terahertz vibrational spectrum. The microscopic origins of this peak are not well understood; the emergence of locally ordered structures has been put forward as a possible candidate. Here, we show that depolarised Raman scattering in liquids consisting of highly symmetric molecules can be used to isolate the boson peak, allowing its detailed observation from the liquid into the glass. The boson peak in the vibrational spectrum matches the excess heat capacity. As the boson peak intensifies on cooling, wide-angle x-ray scattering shows the simultaneous appearance of a pre-peak due to molecular clusters consisting of circa 20 molecules. Atomistic molecular dynamics simulations indicate that these are caused by over-coordinated molecules. These findings represent an essential step toward our understanding of the physics of vitrification.
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Affiliation(s)
| | - Trent Barnard
- Department of Chemistry, University of Warwick, Warwick, UK
| | - Ben A Russell
- School of Chemistry, University of Glasgow, Glasgow, UK
| | | | - Uroš Javornik
- Slovenian NMR Centre, National Institute of Chemistry, Ljubljana, Slovenia
| | | | | | - Sarah Guinane
- School of Chemistry, University of Glasgow, Glasgow, UK
| | - Hans M Senn
- School of Chemistry, University of Glasgow, Glasgow, UK
| | - Andrew J Smith
- Diamond Light Source, Harwell Science and Innovation Campus, Harwell, UK
| | | | - Gregor Mali
- Department of Inorganic Chemistry and Technology, National Institute of Chemistry, Ljubljana, Slovenia
| | - Motohiro Nakano
- Research Center for Thermal and Entropic Science, Osaka University, Osaka, Japan
| | - Yuji Miyazaki
- Research Center for Thermal and Entropic Science, Osaka University, Osaka, Japan
| | - Paul McMillan
- Department of Chemistry, University College London, London, UK
| | | | - Klaas Wynne
- School of Chemistry, University of Glasgow, Glasgow, UK.
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17
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Extensive study on the optical and structural characteristics of Nd3+ doped Lead-Borate-Strontium-Tungsten glass system: Judd–Ofelt analysis. RESULTS IN CHEMISTRY 2023. [DOI: 10.1016/j.rechem.2023.100869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/02/2023] Open
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18
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Fu L, Wang L. Sound attenuation in two-dimensional glasses at finite temperatures. Phys Rev E 2022; 106:054605. [PMID: 36559469 DOI: 10.1103/physreve.106.054605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Accepted: 10/24/2022] [Indexed: 06/17/2023]
Abstract
The thermal conductivity of glasses exhibits an unusual temperature dependence compared to their crystalline counterparts. Sound attenuation due to disorder in glasses was proposed to be important in rationalizing this special behavior. Simulation studies suggest that in the harmonic approximation, the sound attenuation follows Rayleigh scattering scaling at small wave vector in both two-dimensional (2D) and 3D glasses. The influence of the anharmonicity on sound attenuation has very recently been investigated numerically, but only in 3D glasses. Hence, it remains unknown in simulations how sound attenuation changes with the wave vector in 2D glasses when the anharmonicity comes into play. Here, we address this issue by performing computer simulations in low-temperature 2D glasses over a large range of glass stabilities. We find that the way the anharmonicity affects sound attenuation in 2D glasses is the same as that in 3D, thus revealing that numerically the influence of the anharmonicity on sound attenuation does not rely on the spatial dimension.
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Affiliation(s)
- Licun Fu
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
| | - Lijin Wang
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
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19
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Wang L, Fu L, Nie Y. Density of states below the first sound mode in 3D glasses. J Chem Phys 2022; 157:074502. [DOI: 10.1063/5.0102081] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses’ unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes D( ω) depends on the frequency ω has been debated for decades. Recent simulation studies of 3D glasses suggest that D( ω) scales universally with ω4 in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated D( ω) below the first sound mode in 3D glasses over a wide range of frequencies. We find D( ω) scales with ω β with β < 4 at very low frequencies examined, while the ω4 law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The ω4 law of D( ω) below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.
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Affiliation(s)
- Lijin Wang
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
| | - Licun Fu
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
| | - Yunhuan Nie
- Beijing Computational Science Research Center, Beijing 100193, China
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20
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Mizuno H, Hachiya M, Ikeda A. Phonon transport properties of particulate physical gels. J Chem Phys 2022; 156:204505. [DOI: 10.1063/5.0090233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Particulate physical gels are sparse, low-density amorphous materials in which clusters of glasses are connected to form a heterogeneous network structure. This structure is characterized by two length scales, ξ s and ξ G: ξ s measures the length of heterogeneities in the network structure and ξ G is the size of glassy clusters. Accordingly, the vibrational states (eigenmodes) of such a material also exhibit a multiscale nature with two characteristic frequencies, [Formula: see text] and ω G, which are associated with ξ s and ξ G, respectively: (i) phonon-like vibrations in the homogeneous medium at [Formula: see text], (ii) phonon-like vibrations in the heterogeneous medium at [Formula: see text], and (iii) disordered vibrations in the glassy clusters at ω > ω G. Here, we demonstrate that the multiscale characteristics seen in the static structures and vibrational states also extend to the phonon transport properties. Phonon transport exhibits two distinct crossovers at frequencies ω* and ω G (or at wavenumbers of [Formula: see text] and [Formula: see text]). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at [Formula: see text] and diffusive damping at [Formula: see text]. Remarkably, the Ioffe–Regel limit is located at the very low frequency of ω*. Thus, phonon transport is localized above ω*, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.
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Affiliation(s)
- Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Makoto Hachiya
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
- Research Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo, Tokyo 153-8902, Japan
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21
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Modeling the instantaneous normal mode spectra of liquids as that of unstable elastic media. Proc Natl Acad Sci U S A 2022; 119:2119288119. [PMID: 35169078 PMCID: PMC8872781 DOI: 10.1073/pnas.2119288119] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/18/2022] [Indexed: 11/18/2022] Open
Abstract
We present a theory, based on an unstable elasticity model with thermally fluctuating elastic constants, which explains the salient features of the instantaneous normal mode (INM) spectrum of a numerically simulated liquid over a large range of temperatures. The INM spectrum of a liquid is obtained in a molecular dynamics (MD) simulation by considering the harmonic eigenvalue spectrum of the potential energy, taken at a given instant (snapshot). Because the INM spectrum records the curvatures of the fluctuating potential landscape of the liquid, an understanding of this spectrum may pave the way toward understanding the liquid to glass transformation process. We study the instantaneous normal mode (INM) spectrum of a simulated soft-sphere liquid at different equilibrium temperatures T. We find that the spectrum of eigenvalues ρ(λ) has a sharp maximum near (but not at) λ=0 and decreases monotonically with |λ| on both the stable and unstable sides of the spectrum. The spectral shape strongly depends on temperature. It is rather asymmetric at low temperatures (close to the dynamical critical temperature) and becomes symmetric at high temperatures. To explain these findings we present a mean-field theory for ρ(λ), which is based on a heterogeneous elasticity model, in which the local shear moduli exhibit spatial fluctuations, including negative values. We find good agreement between the simulation data and the model calculations, done with the help of the self-consistent Born approximation (SCBA), when we take the variance of the fluctuations to be proportional to the temperature T. More importantly, we find an empirical correlation of the positions of the maxima of ρ(λ) with the low-frequency exponent of the density of the vibrational modes of the glasses obtained by quenching to T=0 from the temperature T. We discuss the present findings in connection to the liquid to glass transformation and its precursor phenomena.
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22
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Zhong J, Nakagawa S, Kaczmarska K, Terao W, Grabowska B, Fujii Y, Koreeda A, Kohara S, Tanimoto H, Tokoro H, Ohkoshi SI, Ko JH, Duan Y, Mori T. Investigation of the vibrational density of states of sodium carboxymethyl starch glass via terahertz time-domain spectroscopy. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2022; 266:120414. [PMID: 34619511 DOI: 10.1016/j.saa.2021.120414] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Revised: 09/16/2021] [Accepted: 09/19/2021] [Indexed: 06/13/2023]
Abstract
We investigated the vibrational density of states of sodium carboxymethyl starch (CM-starch) by terahertz (THz) time-domain spectroscopy. The CM-starch showed a broad peak at ∼3 THz. The structure of the peak was similar to those corresponding to glucose-based polymer glasses possessing hydrogen bonds. The boson peak (BP) appeared at 1.16 THz at the lowest temperature and disappeared because of the existence of excess wing at higher temperatures. However, based on our novel BP frequency determination method using the inflection point of the extinction coefficient, the BP frequency showed almost no dependence on temperature. Further, the chain length dependence of the BP frequency of the glucose-based glasses showed that the BP frequency of the polymer glass was slightly lower than that of the monomer glass. The power law behaviour of the absorption coefficient suggested the existence of fractons, and the fractal dimension was estimated to be 2.33.
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Affiliation(s)
- Junlan Zhong
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Shin Nakagawa
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Karolina Kaczmarska
- AGH - University of Science and Technology, Faculty of Foundry Engineering, Reymonta 23, 30 059 Krakow, Poland
| | - Wakana Terao
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Beata Grabowska
- AGH - University of Science and Technology, Faculty of Foundry Engineering, Reymonta 23, 30 059 Krakow, Poland
| | - Yasuhiro Fujii
- Department of Physical Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
| | - Akitoshi Koreeda
- Department of Physical Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
| | - Shinji Kohara
- Quantum Beam Field, Research Center for Advanced Measurement and Characterization, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
| | - Hisanori Tanimoto
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Hiroko Tokoro
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Shin-Ichi Ohkoshi
- Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Jae-Hyeon Ko
- School of Nano Convergence Technology, Hallym University, 1 Hallymdaehakgil, Chuncheon, Gangwondo 24252, Republic of Korea
| | - Yu Duan
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Tatsuya Mori
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan.
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23
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Abnormal specific heat at low temperatures and transport properties in Mg-Cu-Ag-Gd bulk metallic glass. J RARE EARTH 2022. [DOI: 10.1016/j.jre.2022.02.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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24
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Shukla P. Average density of states of amorphous Hamiltonians: role of phonon mediated coupling of nano-clusters. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:135701. [PMID: 34996057 DOI: 10.1088/1361-648x/ac4938] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
Based on a description of an amorphous solid as a collection of coupled nanosize molecular clusters referred as basic blocks, we analyse the statistical properties of its Hamiltonian. The information is then used to derive the ensemble averaged density of the vibrational states (non-phonon) which turns out to be a Gaussian in the bulk of the spectrum and an Airy function in the low frequency regime. A comparison with experimental data for six glasses confirms validity of our theoretical predictions.
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Affiliation(s)
- Pragya Shukla
- Department of Physics, Indian Institute of Technology, Kharagpur-721302, India
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25
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Benzine O, Pan Z, Calahoo C, Bockowski M, Smedskjaer MM, Schirmacher W, Wondraczek L. Vibrational disorder and densification-induced homogenization of local elasticity in silicate glasses. Sci Rep 2021; 11:24454. [PMID: 34961778 PMCID: PMC8712522 DOI: 10.1038/s41598-021-04045-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Accepted: 12/14/2021] [Indexed: 11/13/2022] Open
Abstract
We report the effect of structural compaction on the statistics of elastic disorder in a silicate glass, using heterogeneous elasticity theory with the coherent potential approximation (HET-CPA) and a log-normal distribution of the spatial fluctuations of the shear modulus. The object of our study, a soda lime magnesia silicate glass, is compacted by hot-compression up to 2 GPa (corresponding to a permanent densification of ~ 5%). Using THz vibrational spectroscopic data and bulk mechanical properties as inputs, HET-CPA evaluates the degree of disorder in terms of the length-scale of elastic fluctuations and the non-affine part of the shear modulus. Permanent densification decreases the extent of non-affine elasticity, resulting in a more homogeneous distribution of strain energy, while also decreasing the correlation length of elastic heterogeneity. Complementary 29Si magic angle spinning NMR spectroscopic data provide a short-range rationale for the effect of compression on glass structure in terms of a narrowing of the Si-O-Si bond-angle and the Si-Si distance.
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Affiliation(s)
- Omar Benzine
- Otto Schott Institute of Materials Research, University of Jena, 07743, Jena, Germany
| | - Zhiwen Pan
- Otto Schott Institute of Materials Research, University of Jena, 07743, Jena, Germany
| | - Courtney Calahoo
- Otto Schott Institute of Materials Research, University of Jena, 07743, Jena, Germany
| | - Michal Bockowski
- Institute of High-Pressure Physics, Polish Academy of Sciences, 01-142, Warsaw, Poland
| | - Morten M Smedskjaer
- Department of Chemistry and Bioscience, Aalborg University, 9220, Aalborg, Denmark
| | | | - Lothar Wondraczek
- Otto Schott Institute of Materials Research, University of Jena, 07743, Jena, Germany.
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26
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Affiliation(s)
- Zhehua Jiang
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, and Department of Physics, University of Science and Technology of China Hefei 230026 P. R. China
| | - Ning xu
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, and Department of Physics, University of Science and Technology of China Hefei 230026 P. R. China
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27
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Wang L, Szamel G, Flenner E. Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses. PHYSICAL REVIEW LETTERS 2021; 127:248001. [PMID: 34951818 DOI: 10.1103/physrevlett.127.248001] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 11/09/2021] [Indexed: 06/14/2023]
Abstract
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency ω as ω^{4} in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows D_{exc}(ω)∼ω^{2} up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D_{exc}(ω) correlates with the stability dependence of low-frequency sound attenuation. However, we also find that, in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode, there are excess modes with a system size independent density of states that scales as ω^{3}.
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Affiliation(s)
- Lijin Wang
- School of Physics and Optoelectronics Engineering, Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, People's Republic of China
| | - 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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28
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Mahajan S, Ciamarra MP. Unifying Description of the Vibrational Anomalies of Amorphous Materials. PHYSICAL REVIEW LETTERS 2021; 127:215504. [PMID: 34860101 DOI: 10.1103/physrevlett.127.215504] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Revised: 08/19/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
The vibrational density of states D(ω) of solids controls their thermal and transport properties. In crystals, the low-frequency modes are extended phonons distributed in frequency according to Debye's law, D(ω)∝ω^{2}. In amorphous solids, phonons are damped, and at low frequency D(ω) comprises extended modes in excess over Debye's prediction, leading to the so-called boson peak in D(ω)/ω^{2} at ω_{bp}, and quasilocalized ones. Here we show that boson peak and phonon attenuation in the Rayleigh scattering regime are related, as suggested by correlated fluctuating elasticity theory, and that amorphous materials can be described as homogeneous isotropic elastic media punctuated by quasilocalized modes acting as elastic heterogeneities. Our numerical results resolve the conflict between theoretical approaches attributing amorphous solids' vibrational anomalies to elastic disorder and localized defects.
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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
- CNRS@CREATE LTD, 1 Create Way, #08-01 CREATE Tower, Singapore 138602
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy
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29
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Kapteijns G, Bouchbinder E, Lerner E. Unified quantifier of mechanical disorder in solids. Phys Rev E 2021; 104:035001. [PMID: 34654186 DOI: 10.1103/physreve.104.035001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Accepted: 08/18/2021] [Indexed: 11/07/2022]
Abstract
Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature: one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related to the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.
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Affiliation(s)
- Geert Kapteijns
- Institute of Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Edan Lerner
- Institute of Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands
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Ren S, Zong HX, Tao XF, Sun YH, Sun BA, Xue DZ, Ding XD, Wang WH. Boson-peak-like anomaly caused by transverse phonon softening in strain glass. Nat Commun 2021; 12:5755. [PMID: 34599172 PMCID: PMC8486772 DOI: 10.1038/s41467-021-26029-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Accepted: 09/14/2021] [Indexed: 11/09/2022] Open
Abstract
Strain glass is a glassy state with frozen ferroelastic/martensitic nanodomains in shape memory alloys, yet its nature remains unclear. Here, we report a glassy feature in strain glass that was thought to be only present in structural glasses. An abnormal hump is observed in strain glass around 10 K upon normalizing the specific heat by cubed temperature, similar to the boson peak in metallic glass. The simulation studies show that this boson-peak-like anomaly is caused by the phonon softening of the non-transforming matrix surrounding martensitic domains, which occurs in a transverse acoustic branch not associated with the martensitic transformation displacements. Therefore, this anomaly neither is a relic of van Hove singularity nor can be explained by other theories relying on structural disorder, while it verifies a recent theoretical model without any assumptions of disorder. This work might provide fresh insights in understanding the nature of glassy states and associated vibrational properties.
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Affiliation(s)
- Shuai Ren
- Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China
| | - Hong-Xiang Zong
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, 710049, Xi'an, China
| | - Xue-Fei Tao
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, 710049, Xi'an, China
| | - Yong-Hao Sun
- Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China
| | - Bao-An Sun
- Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China
| | - De-Zhen Xue
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, 710049, Xi'an, China
| | - Xiang-Dong Ding
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, 710049, Xi'an, China.
| | - Wei-Hua Wang
- Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China.
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31
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Leishangthem P, Ahmad F, Das SP. Localization, Disorder, and Entropy in a Coarse-Grained Model of the Amorphous Solid. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1171. [PMID: 34573796 PMCID: PMC8468715 DOI: 10.3390/e23091171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Revised: 08/29/2021] [Accepted: 08/30/2021] [Indexed: 11/16/2022]
Abstract
We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle system used in the classical density functional model. We demonstrate that intermediate localization of the particles results in a change of the entropy from what is obtained from a microscopic approach using for sharply localized vibrational modes following a Debye distribution. An additional contribution is included in the density of vibrational states g(ω) to account for this excess entropy. A corresponding peak in g(ω)/ω2 vs. frequency ω matches the characteristic boson peak seen in amorphous solids. In the present work, we also compare the shear modulus for the inhomogeneous solid having localized density profiles with the corresponding elastic response for the uniform liquid in the limit of high frequencies.
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Affiliation(s)
| | | | - Shankar P. Das
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India; (P.L.); (F.A.)
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Kapteijns G, Richard D, Bouchbinder E, Schrøder TB, Dyre JC, Lerner E. Does mesoscopic elasticity control viscous slowing down in glassforming liquids? J Chem Phys 2021; 155:074502. [PMID: 34418936 DOI: 10.1063/5.0051193] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase in the activation barrier ΔE(T) with decreasing temperature T. A class of theoretical frameworks-known as elastic models-attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus G∞(T). While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose and test the possibility that viscous slowing down is controlled by a mesoscopic elastic stiffness κ(T), defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent structures. First, we show that κ(T)-which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses-increases more strongly with decreasing T than the macroscopic inherent structure shear modulus G(T) [the glass counterpart of liquids' G∞(T)] in several computer liquids. Second, we show that the simple relation ΔE(T) ∝ κ(T) holds remarkably well for some computer liquids, suggesting a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the ΔE(T) ∝ κ(T) relation holds from those in which it does not is that the latter feature highly fragmented/granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. Under such conditions, it appears that the sub-basins do not properly represent the landscape properties relevant for structural relaxation.
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Affiliation(s)
- Geert Kapteijns
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - David Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Thomas B Schrøder
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C Dyre
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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33
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Richard D, Rainone C, Lerner E. Finite-size study of the athermal quasistatic yielding transition in structural glasses. J Chem Phys 2021; 155:056101. [PMID: 34364355 DOI: 10.1063/5.0053303] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Affiliation(s)
- David Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Corrado Rainone
- 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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Tomoshige N, Goto S, Mizuno H, Mori T, Kim K, Matubayasi N. Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:274002. [PMID: 33930889 DOI: 10.1088/1361-648x/abfd51] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 04/30/2021] [Indexed: 06/12/2023]
Abstract
Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak (BP). For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige,et al2019,Sci. Rep.919514], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the BP scales only with that of the global shear modulus. This observation suggests that the spatial heterogeneity of the local shear modulus distribution is insensitive to changes in the bending rigidity. Here, we demonstrate the insensitivity of elastic heterogeneity by directly measuring the local shear modulus distribution. We also study transverse sound wave propagation, which is also shown to scale only with the global shear modulus. Through these analyses, we conclude that the bending rigidity does not alter the spatial heterogeneity of the local shear modulus distribution, which yields vibrational and acoustic properties that are controlled solely by the global shear modulus of a polymer glass.
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Affiliation(s)
- Naoya Tomoshige
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Shota Goto
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Tatsuya Mori
- Department of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan
| | - Kang Kim
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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35
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Mahajan S, Chattoraj J, Ciamarra MP. Emergence of linear isotropic elasticity in amorphous and polycrystalline materials. Phys Rev E 2021; 103:052606. [PMID: 34134343 DOI: 10.1103/physreve.103.052606] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Accepted: 04/22/2021] [Indexed: 11/07/2022]
Abstract
We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale ξ_{E}, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size. The stiffness matrix of systems of finite size L>ξ_{E} is obtained, adding to that predicted by linear isotropic elasticity a random one of spectral norm (L/ξ_{E})^{-3/2} in three spatial dimensions. We further demonstrate that the elastic length scale corresponds to that of structural correlations, which in polycrystals reflect the typical size of the grain boundaries and length scales characterizing correlations in the stress field. We finally demonstrate that the elastic length scale affects the decay of the anisotropic long-range correlations of locally defined shear modulus and shear stress.
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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, Singapore
| | - Joyjit Chattoraj
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.,Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore 138632, Singapore
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.,CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy
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36
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Saitoh K, Mizuno H. Sound damping in soft particle packings: the interplay between configurational disorder and inelasticity. SOFT MATTER 2021; 17:4204-4212. [PMID: 33881038 DOI: 10.1039/d0sm02018d] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We numerically investigate sound damping in disordered two-dimensional soft particle packings. We simulate evolution of standing waves of particle displacements and analyze time correlation functions of particle velocities and power spectra. We control the strength of inelastic interactions between the particles in contact to show how the inelasticity affects anomalous sound characteristics of disordered systems: Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) attenuation coefficients exhibit a transition from the Rayleigh law to quadratic growth. We also report (iii) how the Ioffe-Regel limit frequencies depend on the strength of inelasticity as useful information for experiments and applications of the sound in disordered media. Our findings suggest that sound damping in soft particle packings is determined by the interplay between elastic heterogeneities and inelasticity.
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Affiliation(s)
- Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan.
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
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37
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Kapteijns G, Richard D, Bouchbinder E, Lerner E. Elastic moduli fluctuations predict wave attenuation rates in glasses. J Chem Phys 2021; 154:081101. [DOI: 10.1063/5.0038710] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Geert Kapteijns
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - David Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
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38
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González-López K, Shivam M, Zheng Y, Ciamarra MP, Lerner E. Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions. Phys Rev E 2021; 103:022605. [PMID: 33736046 DOI: 10.1103/physreve.103.022605] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 01/13/2021] [Indexed: 11/07/2022]
Abstract
Recent literature indicates that attractive interactions between particles of a dense liquid play a secondary role in determining its bulk mechanical properties. Here we show that, in contrast with their apparent unimportance to the bulk mechanics of dense liquids, attractive interactions can have a major effect on macro- and microscopic elastic properties of glassy solids. We study several broadly applicable dimensionless measures of stability and mechanical disorder in simple computer glasses, in which the relative strength of attractive interactions-referred to as "glass stickiness"-can be readily tuned. We show that increasing glass stickiness can result in the decrease of various quantifiers of mechanical disorder, on both macro- and microscopic scales, with a pair of intriguing exceptions to this rule. Interestingly, in some cases strong attractions can lead to a reduction of the number density of soft, quasilocalized modes, by up to an order of magnitude, and to a substantial decrease in their core size, similar to the effects of thermal annealing on elasticity observed in recent works. Contrary to the behavior of canonical glass models, we provide compelling evidence indicating that the stabilization mechanism in our sticky-sphere glasses stems predominantly from the self-organized depletion of interactions featuring large, negative stiffnesses. Finally, we establish a fundamental link between macroscopic and microscopic quantifiers of mechanical disorder, which we motivate via scaling arguments. Future research directions are discussed.
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Affiliation(s)
- Karina González-López
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - Mahajan Shivam
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yuanjian Zheng
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.,CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Naples, Italy
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
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Role of Anharmonic Interactions for Vibration Density of States in α-Cristobalite. MATERIALS 2021; 14:ma14030617. [PMID: 33572842 PMCID: PMC7866241 DOI: 10.3390/ma14030617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2020] [Revised: 01/25/2021] [Accepted: 01/27/2021] [Indexed: 11/29/2022]
Abstract
The vibrational density of states (VDOS) of solids in the low-energy regime controls the thermal and transport properties of materials, such as heat capacity, heat conduction, free energy and entropy. In α-Cristobalite, the low-frequency part of vibration density of states (VDOS) has many common features with the Boson peak in silica glass of matched densities. Recent theoretical work reported that anharmonic phonon–phonon interactions were critical for the low-frequency part of VDOS in α-Cristobalite. Therefore, it is urgent to identify the role of different anharmonic interactions from first principles. In this paper, we focus on the main peak of the low-frequency part of VDOS in α-Cristobalite. Calculated by our own developed codes and first principles, we find that the quartic anharmonic interaction can increase the frequency of the peak, while the cubic anharmonic can reduce the frequency and change the shape of the peak. Meanwhile, the anharmonic interactions are critical for the temperature effect. Therefore, we calculated the temperature-dependent property of the peak. We find that the frequency of the peak is directly proportional to the temperature. The atomic displacement patterns of different temperatures also confirm the above conclusion. All our calculations converged well. Moreover, our basic results agree well with other published results. Finally, we highlight that our codes offer a general and reliable way to calculate the VDOS with temperature.
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40
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Shimada M, Mizuno H, Ikeda A. Novel elastic instability of amorphous solids in finite spatial dimensions. SOFT MATTER 2021; 17:346-364. [PMID: 33164008 DOI: 10.1039/d0sm01583k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Recently, progress has been made in the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency without any frequency gap. This gapless vibrational density of states (vDOS) suggests that glasses are on the verge of instability. This feature of marginal stability is now highlighted as a key concept in the theories of glasses. In particular, the elasticity theory based on marginal stability predicts the gapless vDOS. However, this theory yields a quadratic law and not the quartic law. To address this inconsistency, we presented a new type of instability, which is different from the conventional one, and proposed that amorphous solids are marginally stable considering the new instability in the preceding study [M. Shimada, H. Mizuno and A. Ikeda, Soft Matter, 2020, 16, 7279]. In this study, we further extend and detail the results for these instabilities. By analyzing various examples of disorder, we demonstrate that real glasses in finite spatial dimensions can be marginally stable by the proposed novel instability.
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Affiliation(s)
- Masanari Shimada
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan.
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan.
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan. and Research Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo, Tokyo 153-8902, Japan
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41
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Li D, Chen H, Qu B, Zhang F, Zhou R, Zhang B. The dependence of the boson peak on the thickness of Cu 50Zr 50 film metallic glasses. Phys Chem Chem Phys 2021; 23:982-989. [PMID: 33399595 DOI: 10.1039/d0cp05327a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this study, intensive calculations were performed to investigate the behavior of the low-temperature excess heat capacity of Cu50Zr50 ultrathin film metallic glasses. Our results show that there is a well-defined boson peak in the film metallic glasses and that the boson peak height exhibits an obvious size-dependent feature. Furthermore, there is a critical thickness dc in the curves between the boson peak height and the thickness, where the boson peak height changes abruptly. Through structural analysis, we found that the low-temperature excess heat capacity of the film metallic glasses is correlated with the density layering structure near the surface. The structural parameter S is defined by atomic density and it was found that the boson peak height is highly correlated with S. Our investigation of ultrathin film metallic glasses provides a deeper understanding about the structural origin of the boson peak in metallic glasses.
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Affiliation(s)
- Dongdong Li
- Engineering Research Center of High Performance Copper Alloy Materials and Processing, Ministry of Education, Hefei University of Technology, Hefei 230009, China. and School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, China
| | - Heng Chen
- School of Electronic Science & Applied Physics, Hefei University of Technology, Hefei 230009, China
| | - Bingyan Qu
- Engineering Research Center of High Performance Copper Alloy Materials and Processing, Ministry of Education, Hefei University of Technology, Hefei 230009, China. and School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, China
| | - Fabao Zhang
- Engineering Research Center of High Performance Copper Alloy Materials and Processing, Ministry of Education, Hefei University of Technology, Hefei 230009, China. and School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, China
| | - Rulong Zhou
- Engineering Research Center of High Performance Copper Alloy Materials and Processing, Ministry of Education, Hefei University of Technology, Hefei 230009, China. and School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, China
| | - Bo Zhang
- Engineering Research Center of High Performance Copper Alloy Materials and Processing, Ministry of Education, Hefei University of Technology, Hefei 230009, China. and School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, China
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42
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Casella L, Baggioli M, Mori T, Zaccone A. Physics of phonon-polaritons in amorphous materials. J Chem Phys 2021; 154:014501. [PMID: 33412881 DOI: 10.1063/5.0033371] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The nature of bosonic excitations in disordered materials has remained elusive due to the difficulties in defining key concepts such as quasi-particles in the presence of disorder. We report on an experimental observation of phonon-polaritons in glasses, including a prominent boson peak (BP), i.e., excess of THz modes over the Debye law. A theoretical framework based on the concept of diffusons is developed to describe the broadening linewidth of the polariton due to disorder-induced scattering. It is shown here for the first time that the BP frequency and the Ioffe-Regel (IR) crossover frequency of the polariton collapse onto the same power-law decay with the diffusivity of the bosonic excitation. This analysis dismisses the hypothesis of the BP being caused by a relic of the van Hove singularity. The presented framework establishes a new methodology to analyze bosonic excitations in amorphous media, well beyond the traditional case of acoustic phonons, and establishes the IR crossover as the fundamental physical mechanism behind the BP.
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Affiliation(s)
- Luigi Casella
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133 Milan, Italy
| | - Matteo Baggioli
- Instituto de Fisica Teorica UAM/CSIC, c/Nicolas Cabrera 13-15, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain
| | - Tatsuya Mori
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133 Milan, Italy
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43
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Cui B, Zaccone A. Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:72. [PMID: 33242169 DOI: 10.1140/epje/i2020-11995-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 11/02/2020] [Indexed: 06/11/2023]
Abstract
A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D([Formula: see text]) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form [Formula: see text] is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a [Formula: see text] regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory.
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Affiliation(s)
- Bingyu Cui
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE, Cambridge, UK
| | - Alessio Zaccone
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE, Cambridge, UK.
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133, Milano, Italy.
- Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, CB3 0AS, Cambridge, UK.
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44
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Mizuno H, Tong H, Ikeda A, Mossa S. Intermittent rearrangements accompanying thermal fluctuations distinguish glasses from crystals. J Chem Phys 2020; 153:154501. [PMID: 33092390 DOI: 10.1063/5.0021228] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Glasses exhibit vibrational and thermal properties that are markedly different from those of crystals. While recent works have advanced our understanding of vibrational excitations in glasses in the harmonic approximation limit, efforts in understanding finite-temperature anharmonic processes have been limited. In crystals, phonon-phonon coupling provides an extremely efficient mechanism for anharmonic decay that is also important in glasses. By using extensive molecular dynamics simulation of model atomic systems, here we first describe, both numerically and analytically, the anharmonic couplings in the crystal and the glass by focusing on the temperature dependence of the associated decay rates. Next, we show that an additional anharmonic channel of different origin emerges in the amorphous case, which induces unconventional intermittent rearrangements of particles. We have found that thermal vibrations in glasses trigger transitions among numerous different local minima of the energy landscape, which, however, are located within the same wide (meta)basin. These processes generate motions that are different from both diffusive and out-of-equilibrium aging dynamics. We suggest that (i) the observed intermittent rearrangements accompanying thermal fluctuations are crucial features distinguishing glasses from crystals and (ii) they can be considered as relics of the liquid state that survive the complete dynamic arrest taking place at the glass transition temperature.
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Affiliation(s)
- Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Hua Tong
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Stefano Mossa
- Univ. Grenoble Alpes, CEA, IRIG-MEM, 38000 Grenoble, France
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Pérez-Cota F, La Cavera III S, Naznin S, Fuentes-Domínguez R, Smith RJ, Clark M. Apparent attenuation by opto-acoustic defocus in phonon microscopy. PHOTOACOUSTICS 2020; 19:100180. [PMID: 32489857 PMCID: PMC7262445 DOI: 10.1016/j.pacs.2020.100180] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Revised: 01/10/2020] [Accepted: 03/30/2020] [Indexed: 05/20/2023]
Abstract
Understanding the mechanical properties of biological cells is a challenging problem for the life sciences partly because there are limited methods for mapping elasticity with high resolution. Phonon microscopy is a form of Brillouin light scattering which uses coherent phonons for imaging with elasticity-related contrast, phonon resolution and without labels. It can measure material properties such as sound velocity, acoustic impedance and attenuation. To use it as a contrast mechanism in microscopy, high numerical aperture (NA) lenses are key to high resolution. However, increasing NA induces apparent attenuation, a premature decay of the detected signal. To reduce signal decay and quantify the sound attenuation coefficient in cells, it is necessary to understand the mechanisms that affect signal decay. Here we define opto-acoustic defocus as a signal decay mechanism and propose methods to achieve quantitative sound attenuation measurements, and to optimise in-depth imaging at high resolution which is crucial for cell imaging.
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Shimada M, Mizuno H, Ikeda A. Vibrational spectrum derived from local mechanical response in disordered solids. SOFT MATTER 2020; 16:7279-7288. [PMID: 32696792 DOI: 10.1039/d0sm00376j] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The low-frequency vibrations of glasses are markedly different from those of crystals. These vibrations have recently been categorized into two types: spatially extended vibrations, whose vibrational density of states (vDOS) follows a non-Debye quadratic law, and quasilocalized vibrations (QLVs), whose vDOS follows a quartic law. The former are explained by elasticity theory with quenched disorder and microscopic replica theory as being a consequence of elastic instability, but the origin of the latter is still debated. Here, we show that the latter can also be directly derived from elasticity theory with quenched disorder. We find another elastic instability that the theory encompasses but that has been overlooked so far, namely, the instability of the system against a local dipolar force. This instability gives rise to an additional contribution to the vDOS, and the spatial structure and energetics of the mode originating from this instability are consistent with those of the QLVs. Finally, we construct a model in which the additional contribution to the vDOS follows a quartic law.
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Affiliation(s)
- Masanari Shimada
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan.
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Richard D, González-López K, Kapteijns G, Pater R, Vaknin T, Bouchbinder E, Lerner E. Universality of the Nonphononic Vibrational Spectrum across Different Classes of Computer Glasses. PHYSICAL REVIEW LETTERS 2020; 125:085502. [PMID: 32909789 DOI: 10.1103/physrevlett.125.085502] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Revised: 07/09/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies ω follow a gapless, universal distribution D(ω)∼ω^{4}. While this universal nonphononic spectrum has been shown to be robust to varying the glass history and spatial dimension, it has so far only been observed in simple computer glasses featuring radially symmetric, pairwise interaction potentials. Consequently, the relevance of the universality of nonphononic spectra seen in simple computer glasses to realistic laboratory glasses remains unclear. Here, we demonstrate the emergence of the universal ω^{4} nonphononic spectrum in a broad variety of realistic computer glass models, ranging from tetrahedral network glasses with three-body interactions, through molecular glasses and glassy polymers, to bulk metallic glasses. Taken together with previous observations, our results indicate that the low-frequency nonphononic vibrational spectrum of any glassy solid quenched from a melt features the universal ω^{4} law, independently of the nature of its microscopic interactions.
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Affiliation(s)
- David Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Karina González-López
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Geert Kapteijns
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Robert Pater
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Talya Vaknin
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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Wang L, Szamel G, Flenner E. Sound attenuation in finite-temperature stable glasses. SOFT MATTER 2020; 16:7165-7171. [PMID: 32671375 DOI: 10.1039/d0sm00633e] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The temperature dependence of the thermal conductivity of amorphous solids is markedly different from that of their crystalline counterparts, but exhibits universal behaviour. Sound attenuation is believed to be related to this universal behaviour. Recent computer simulations demonstrated that in the harmonic approximation sound attenuation Γ obeys quartic, Rayleigh scattering scaling for small wavevectors k and quadratic scaling for wavevectors above the Ioffe-Regel limit. However, simulations and experiments do not provide a clear picture of what to expect at finite temperatures where anharmonic effects become relevant. Here we study sound attenuation at finite temperatures for model glasses of various stability, from unstable glasses that exhibit rapid aging to glasses whose stability is equal to those created in laboratory experiments. We find several scaling laws depending on the temperature and stability of the glass. First, we find the large wavevector quadratic scaling to be unchanged at all temperatures. Second, we find that at small wavevectors Γ∼k1.5 for an aging glass, but Γ∼k2 when the glass does not age on the timescale of the calculation. For our most stable glass, we find that Γ∼k2 at small wavevectors, then a crossover to Rayleigh scattering scaling Γ∼k4, followed by another crossover to the quadratic scaling at large wavevectors. Our computational observation of this quadratic behavior reconciles simulation, theory and experiment, and will advance the understanding of the temperature dependence of thermal conductivity of glasses.
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Affiliation(s)
- Lijin Wang
- School of Physics and Materials Science, Anhui University, Hefei 230601, P. R. China.
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Mori T, Jiang Y, Fujii Y, Kitani S, Mizuno H, Koreeda A, Motoji L, Tokoro H, Shiraki K, Yamamoto Y, Kojima S. Detection of boson peak and fractal dynamics of disordered systems using terahertz spectroscopy. Phys Rev E 2020; 102:022502. [PMID: 32942491 DOI: 10.1103/physreve.102.022502] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2020] [Accepted: 08/10/2020] [Indexed: 06/11/2023]
Abstract
The boson peak is a largely unexplained excitation found universally in the terahertz vibrational spectra of disordered systems; the so-called fracton is a vibrational excitation associated with the self-similar structure of monomers in polymeric glasses. We demonstrate that such excitations can be detected using terahertz spectroscopy. In the case of fractal structures, we determine the infrared light-vibration coupling coefficient for the fracton region and show that information concerning the fractal and fracton dimensions appears in the exponent of the absorption coefficient. Finally, using terahertz time-domain spectroscopy and low-frequency Raman scattering, we experimentally observe these universal excitations in a protein (lysozyme) system that has an intrinsically disordered and fractal structure and argue that the system should be considered a single supramolecule. These findings are applicable to amorphous and fractal objects in general and will be valuable for understanding universal dynamics of disordered systems via terahertz light.
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Affiliation(s)
- Tatsuya Mori
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Yue Jiang
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Yasuhiro Fujii
- Department of Physical Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
| | - Suguru Kitani
- Laboratory for Materials and Structures, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Akitoshi Koreeda
- Department of Physical Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
| | - Leona Motoji
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Hiroko Tokoro
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Kentaro Shiraki
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Yohei Yamamoto
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Seiji Kojima
- Division of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
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Zaccone A. Relaxation and vibrational properties in metal alloys and other disordered systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:203001. [PMID: 31962298 DOI: 10.1088/1361-648x/ab6e41] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The relaxation dynamics and the vibrational spectra of amorphous solids, such as metal alloys, have been intensely investigated as well separated topics in the past. The aim of this review is to summarize recent results in both these areas in an attempt to establish, or unveil, deeper connections between the two phenomena of relaxation and vibration. Theoretical progress in the area of slow relaxation dynamics of liquid and glassy systems and in the area of vibrational spectra of glasses and liquids is reviewed. After laying down a generic modelling framework to connect vibration and relaxation, the physics of metal alloys is considered where the emergence of power-law exponents has been identified both in the vibrational density of states (VDOS) as well as in density correlations. Also, theoretical frameworks which connect the VDOS to the relaxation behaviour and mechanical viscoelastic response in metallic glasses are reviewed. The same generic interpretative framework is then applied to the case of molecular glass formers where the emergence of stretched-exponential relaxation in dielectric relaxation can be put in quantitative relation with the VDOS by means of memory-function approaches. Further connections between relaxation and vibration are provided by the study of phonon linewidths in liquids and glasses, where a natural starting point is given by hydrodynamic theories. Finally, an agenda of outstanding issues including the appearance of compressed exponential relaxation in the intermediate scattering function of experimental and simulated systems (metal alloys, colloidal gels, jammed packings) is presented in light of available (or yet to be developed) mathematical models, and compared to non-exponential behaviour measured with macroscopic means such as mechanical spectroscopy/rheology.
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Affiliation(s)
- Alessio Zaccone
- Department of Physics 'A. Pontremoli', University of Milan, via Celoria 16, 20133 Milano, Italy. Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, CB3 0AS Cambridge, United Kingdom. Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB30HE Cambridge, United Kingdom
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