1
|
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 DOI: 10.1038/s41467-024-46981-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [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.
Collapse
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.
| |
Collapse
|
2
|
Xu D, Zhang S, Tong H, Wang L, Xu N. Low-frequency vibrational density of states of ordinary and ultra-stable glasses. Nat Commun 2024; 15:1424. [PMID: 38365816 DOI: 10.1038/s41467-024-45671-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 02/01/2024] [Indexed: 02/18/2024] Open
Abstract
A remarkable feature of disordered solids distinct from crystals is the violation of the Debye scaling law of the low-frequency vibrational density of states. Because the low-frequency vibration is responsible for many properties of solids, it is crucial to elucidate it for disordered solids. Numerous recent studies have suggested power-law scalings of the low-frequency vibrational density of states, but the scaling exponent is currently under intensive debate. Here, by classifying disordered solids into stable and unstable ones, we find two distinct and robust scaling exponents for non-phononic modes at low frequencies. Using the competition of these two scalings, we clarify the variation of the scaling exponent and hence reconcile the debate. Via the study of both ordinary and ultra-stable glasses, our work reveals a comprehensive picture of the low-frequency vibration of disordered solids and sheds light on the low-frequency vibrational features of ultra-stable glasses on approaching the ideal glass.
Collapse
Affiliation(s)
- Ding Xu
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Shiyun Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Hua Tong
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Lijin Wang
- School of Physics and Optoelectronic Engineering, Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei, 230601, P. R. China.
| | - Ning Xu
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China.
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China.
| |
Collapse
|
3
|
Baumgärtel P, Vogel F, Fuchs M. Properties of stable ensembles of Euclidean random matrices. Phys Rev E 2024; 109:014120. [PMID: 38366508 DOI: 10.1103/physreve.109.014120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 12/13/2023] [Indexed: 02/18/2024]
Abstract
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as a model for the low temperature vibrational properties of glass. Exact numerical diagonalization is performed in three and two spatial dimensions, which is accompanied by a detailed finite size analysis. It reveals a low-frequency regime of sound waves that are damped by Rayleigh scattering. At large frequencies localized modes exist. In between, the central peak in the vibrational density of states is well described by Wigner's semicircle law for not too large disorder, as is expected for simple random matrix systems. We compare our results with predictions from two recent self-consistent field theories.
Collapse
Affiliation(s)
| | - Florian Vogel
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| |
Collapse
|
4
|
Chakraborty S, Krishnan VV, Ramola K, Karmakar S. Enhanced vibrational stability in glass droplets. PNAS NEXUS 2023; 2:pgad289. [PMID: 37746327 PMCID: PMC10516527 DOI: 10.1093/pnasnexus/pgad289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 08/28/2023] [Indexed: 09/26/2023]
Abstract
We show through simulations of amorphous solids prepared in open-boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the D ( ω ) ∼ ω 4 law changes to D ( ω ) ∼ ω δ with δ ≈ 5 in two dimensions and δ ≈ 4.5 in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system, which are absent in the unconfined system and find that the D ( ω ) ∼ ω 4 behavior is recovered.
Collapse
Affiliation(s)
| | - Vishnu V Krishnan
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
| |
Collapse
|
5
|
Mocanu FC, Berthier L, Ciarella S, Khomenko D, Reichman DR, Scalliet C, Zamponi F. Microscopic observation of two-level systems in a metallic glass model. J Chem Phys 2023; 158:014501. [PMID: 36610958 DOI: 10.1063/5.0128820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.
Collapse
Affiliation(s)
- Felix C Mocanu
- Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Ludovic Berthier
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Simone Ciarella
- Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Dmytro Khomenko
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Camille Scalliet
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Francesco Zamponi
- Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| |
Collapse
|
6
|
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.
Collapse
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
| |
Collapse
|