Inhomogeneous Elastic Response of Silica Glass

Léonforte, Fabien; Tanguy, Anne; Wittmer, J. P.; Barrat, Jean‐Louis

doi:10.1103/physrevlett.97.055501

Cited by 211 publications

(213 citation statements)

References 38 publications

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“…A similar conclusion was drawn from molecular-dynamics simulations of quenched Lennard-Jones Argon and SiO 2 [13]. In the latter study it emerged that these correlations exist over an extended number of inter-atomic distances.…”

Section: -1supporting

confidence: 59%

Sound attenuation and anharmonic damping in solids with correlated disorder

Schirmacher¹,

Tomaras

Schmid³

et al. 2010

Condens. Matter Phys.

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We study via self-consistent Born approximation a model for sound waves in a disordered environment, in which the local fluctuations of the shear modulus G are spatially correlated with a certain correlation length ξ. The theory predicts an enhancement of the density of states over Debye's ω 2 law (boson peak) whose intensity increases for increasing correlation length, and whose frequency position is shifted downwards as 1/ξ. Moreover, the predicted disorder-induced sound attenuation coefficient Γ(k) obeys a universal scaling law ξΓ(k) = f (kξ) for a given variance of G. Finally, the inclusion of the lowest-order contribution to the anharmonic sound damping into the theory allows us to reconcile apparently contradictory recent experimental data in amorphous SiO 2 . 63.50.-x, 43.20.+g, 65.60.+a The vibrational properties of disordered solids at THz frequencies are subject of an enormous attention both from the experimental and from the theoretical side [1], due to the related anomalies observed in the specific heat and thermal conductivity of glasses [2]. The origin of an excess of the vibrational density of states (DOS) over the Debye prediction ("boson peak") at THz frequencies and its relation to the rather anomalous sound attenuation in the same frequency regime is in focus of a lively debate [3][4][5]. In particular, the origin of the dispersion and attenuation of sound-like excitation in the THz frequency range has been a matter of controversy quite recently [6,7]. In spite of this debate, nowadays many authors agree that the boson peak and the frequency dependence of the sound attenuation are the related phenomena dictated by the structural disorder, rather than by anharmonic interactions, and occur at frequencies at which the wavevector k looses its significance for labeling the transverse vibrational states (Ioffe-Regel regime) [8]. Key words: sound attenuation, vibrational properties of disordered solids, boson peak, anharmonic interactions PACS:The way the disorder controls the thermophysical properties, however, is still not fully understood, and the experimental phenomenology is not completely reproduced by the current fluctuating-elastic-constant (FE) approaches [6,9,10], which are based on zero-range correlations.The FE approach has been recently applied to low-frequency Raman scattering and for the first time accounted for the experimentally observed frequency dependence, which is different from incoherent neutron scattering [11]. In this study and in a recent comparison of a scalar FE model with a simulation of a simple model having correlated disorder [12] it was realized that the finite

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Section: -1supporting

confidence: 59%

Sound attenuation and anharmonic damping in solids with correlated disorder

Schirmacher¹,

Tomaras

Schmid³

et al. 2010

Condens. Matter Phys.

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“…This peak is called the Boson peak. We have seen 36 that it is approximately located at the transition frequency 2pc/n. It is shown in Fig.…”

Section: Vibration Modesmentioning

confidence: 86%

Vibration Modes and Characteristic Length Scales in Amorphous Materials

Tanguy

2015

JOM

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The numerical study of the mechanical responses of amorphous materials at the nanometer scale shows characteristic length scales that are larger than the intrinsic length of the microstructure. In this article, we review the different scales appearing upon athermal elastoplastic mechanical load and we relate it to a detailed study of the vibrational response. We compare different materials with different microstructures and different bond directionality (from Lennard-Jones model materials to amorphous silicon and silicate glasses). This work suggests experimental measurements that could help to understand and, if possible, to predict plastic deformation in glasses.

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“…That such a length-scale exists has been pointed out by many researchers in various classes of disordered materials. [42][43][44][45] This characteristic length may very well have important implications for both elastic and plastic deformation of metallic glasses. In particular, it may be related to the size of shear transformation zones (the fundamental units of plastic deformation in metallic glasses), which are thought to contain about 20 to 100 atoms corresponding to a diameter of about 4 to 6Å [46].…”

Section: Discussionmentioning

confidence: 99%

Length-scale dependence of elastic strain from scattering measurements in metallic glasses

et al. 2012

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Several recent studies have reported that the elastic strain in metallic glasses, as measured from peak shifts in the pair correlation functions of samples under load, increases with distance from an average atom, approaching the macroscopic strain at large distances. We have verified this behavior using high-energy x-ray scattering on metallic glasses loaded under uniaxial compression, uniaxial tension, and pure shear, and show that the apparent length-scale dependence of elastic strain is not an artifact of the assumption of structural isotropy in the data analysis. Molecular dynamics simulations of a binary Lennard-Jones glass loaded in uniaxial tension reproduce, qualitatively, the behavior observed in the experiments when the elastic strain is calculated from the shifts in the peaks of the pair correlation function. Under hydrostatic loading, however, the length-scale dependence of elastic strain observed in the simulations is greatly reduced. This suggests that non-affine atomic displacements, which are smaller under hydrostatic loading than under uniaxial loading, may play a key role in the length-scale dependence of elastic strain. Furthermore, no length-scale dependence is observed in simulations, for either uniaxial or hydrostatic loading, when the elastic strain is calculated from the average local deformation gradient tensor. We explain this apparent contradiction and show that the atomic displacements resulting from elastic loading are largest in the low density regions between atomic shells around an average atom. Finally, we present an analysis of length-scale dependence of elastic strain calculated from the pair correlation function for the case of homogeneous deformation, which is in good agreement with the simulations conducted under hydrostatic loading. For uniaxial loading, however, the analysis diverges from both the experimental and simulated results in the first two near-neighbor atomic shells. This suggests, in agreement with our observations from the molecular dynamics simulations, that the observed length-scale dependence of elastic strain from scattering measurements reflects the nature of the non-affine atomic displacements in the glass.

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Inhomogeneous Elastic Response of Silica Glass

Cited by 211 publications

References 38 publications

Sound attenuation and anharmonic damping in solids with correlated disorder

Sound attenuation and anharmonic damping in solids with correlated disorder

Vibration Modes and Characteristic Length Scales in Amorphous Materials

Length-scale dependence of elastic strain from scattering measurements in metallic glasses

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