Vibrational anomalies and marginal stability of glasses

Handle URI:
http://hdl.handle.net/10754/562583
Title:
Vibrational anomalies and marginal stability of glasses
Authors:
Marruzzo, Alessia; Köhler, Stephan; Fratalocchi, Andrea ( 0000-0001-6769-4439 ) ; Ruocco, Giancarlo; Schirmacher, Walter
Abstract:
The experimentally measured vibrational spectrum of glasses strongly deviates from that expected in Debye's elasticity theory: The density of states deviates from Debye's ω2 law ("boson peak"), the sound velocity shows a negative dispersion in the boson-peak frequency regime, and there is a strong increase in the sound attenuation near the boson-peak frequency. A generalized elasticity theory is presented, based on the model assumption that the shear modulus of the disordered medium fluctuates randomly in space. The fluctuations are assumed to be uncorrelated and have a certain distribution (Gaussian or otherwise). Using field-theoretical techniques one is able to derive mean-field theories for the vibrational spectrum of a disordered system. The theory based on a Gaussian distribution uses a self-consistent Born approximation (SCBA),while the theory for non-Gaussian distributions is based on a coherent-potential approximation (CPA). Both approximate theories appear to be saddle-point approximations of effective replica field theories. The theory gives a satisfactory explanation of the vibrational anomalies in glasses. Excellent agreement of the SCBA theory with simulation data on a soft-sphere glass is reached. Since the SCBA is based on a Gaussian distribution of local shear moduli, including negative values, this theory describes a shear instability as a function of the variance of shear fluctuations. In the vicinity of this instability, a fractal frequency dependence of the density of states and the sound attenuation ∝ ω1+a is predicted with a ≲ 1/2. Such a frequency dependence is indeed observed both in simulations and in experimental data. We argue that the observed frequency dependence stems from marginally stable regions in a glass and discuss these findings in terms of rigidity percolation. © 2013 EDP Sciences and Springer.
KAUST Department:
PRIMALIGHT Research Group; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
EDP Sciences
Journal:
European Physical Journal: Special Topics
Issue Date:
Jan-2013
DOI:
10.1140/epjst/e2013-01731-5
Type:
Article
ISSN:
19516355
Appears in Collections:
Articles; PRIMALIGHT Research Group; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMarruzzo, Alessiaen
dc.contributor.authorKöhler, Stephanen
dc.contributor.authorFratalocchi, Andreaen
dc.contributor.authorRuocco, Giancarloen
dc.contributor.authorSchirmacher, Walteren
dc.date.accessioned2015-08-03T10:43:41Zen
dc.date.available2015-08-03T10:43:41Zen
dc.date.issued2013-01en
dc.identifier.issn19516355en
dc.identifier.doi10.1140/epjst/e2013-01731-5en
dc.identifier.urihttp://hdl.handle.net/10754/562583en
dc.description.abstractThe experimentally measured vibrational spectrum of glasses strongly deviates from that expected in Debye's elasticity theory: The density of states deviates from Debye's ω2 law ("boson peak"), the sound velocity shows a negative dispersion in the boson-peak frequency regime, and there is a strong increase in the sound attenuation near the boson-peak frequency. A generalized elasticity theory is presented, based on the model assumption that the shear modulus of the disordered medium fluctuates randomly in space. The fluctuations are assumed to be uncorrelated and have a certain distribution (Gaussian or otherwise). Using field-theoretical techniques one is able to derive mean-field theories for the vibrational spectrum of a disordered system. The theory based on a Gaussian distribution uses a self-consistent Born approximation (SCBA),while the theory for non-Gaussian distributions is based on a coherent-potential approximation (CPA). Both approximate theories appear to be saddle-point approximations of effective replica field theories. The theory gives a satisfactory explanation of the vibrational anomalies in glasses. Excellent agreement of the SCBA theory with simulation data on a soft-sphere glass is reached. Since the SCBA is based on a Gaussian distribution of local shear moduli, including negative values, this theory describes a shear instability as a function of the variance of shear fluctuations. In the vicinity of this instability, a fractal frequency dependence of the density of states and the sound attenuation ∝ ω1+a is predicted with a ≲ 1/2. Such a frequency dependence is indeed observed both in simulations and in experimental data. We argue that the observed frequency dependence stems from marginally stable regions in a glass and discuss these findings in terms of rigidity percolation. © 2013 EDP Sciences and Springer.en
dc.publisherEDP Sciencesen
dc.titleVibrational anomalies and marginal stability of glassesen
dc.typeArticleen
dc.contributor.departmentPRIMALIGHT Research Groupen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalEuropean Physical Journal: Special Topicsen
dc.contributor.institutionUniv Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italyen
dc.contributor.institutionJohannes Gutenberg Univ Mainz, Inst Phys, D-55099 Mainz, Germanyen
kaust.authorFratalocchi, Andreaen
kaust.authorMarruzzo, Alessiaen
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