Effective-medium approximation for a percolation network: The structure factor and the Ioffe-Regel criterion

Polatsek, G.; Entin‐Wohlman, O.

doi:10.1103/physrevb.37.7726

Cited by 53 publications

(11 citation statements)

References 17 publications

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“…We recall here that more generally in the effective medium approximation, for a percolating network, the Rayleigh law becomes ∝ν d + 1 where d is the Euclidean dimensionality. 69,70 Considering the crossover in longitudinal damping occurring at 0.22 Å −1 found by Monaco et al, it remains fully comparable to our findings of a cross-over in damping at frequency close to 1 THz (see Figure 6 for q − ν correspondence). In the same time, the value of damping itself falls in fair agreement with our values.…”

Section: Current Correlationssupporting

confidence: 92%

“…For the lowest frequencies studied, a strong damping process is present which can be understood in terms of Rayleigh elastic scattering on structural heterogeneities of nanometer size and consequently there is no formal reason for the Debye model to hold in this case. We note that, as stated in different works, 9,69,70 the negative dispersion of sound velocity occurring in glassy state is directly related to the variation of the power-law in damping via Kramers-Kronig relation and is not a manifestation of mode softening. Rayleigh regime will have to cease when half the wavelength will be smaller than the characteristic size of structural inhomogeneities, which in turn corresponds to the IR criterion 69 and the crossover from strong to weak scattering regime.…”

Section: Discussionsupporting

confidence: 61%

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Structural heterogeneities at the origin of acoustic and transport anomalies in glycerol glass-former

Busselez

Pézeril

Gusev

2014

The Journal of Chemical Physics

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By means of large scale molecular dynamics simulations, we explore mesoscopic properties of prototypical glycerol glass-former above and below the glass transition. The model used, in excellent agreement with various experimental techniques, permits to carefully study the structure and the vibrational dynamics. We find that a medium range order is present in glycerol glass-former and arises from hydrogen bond network extension. The characteristic size of the structural heterogeneities is related to the anomalous properties of acoustic vibrations (Rayleigh scattering, "mode softening," and Boson Peak) in the glassy state. Finally the characteristic size of these heterogeneities, nearly constant in temperature, is also connected to the cross-over between structural relaxation and diffusion in liquid glycerol.

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Section: Current Correlationssupporting

confidence: 92%

Section: Discussionsupporting

confidence: 61%

Structural heterogeneities at the origin of acoustic and transport anomalies in glycerol glass-former

Busselez

Pézeril

Gusev

2014

The Journal of Chemical Physics

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“…This relationship is often seen to hold up to frequencies above the IR crossover. The second of these models (see, e.g., (15)) is based on an effective-medium approximation (EMA) (16) and asserts that, in the region of the IR crossover, a DHO function is not a valid fit to S L (k, ω), and that the scattering becomes much stronger (see, e.g., (15)). A functional form for S L (k, ω) is used which imposes Γ ∝ k 4 by construction, and this has given good fits of the dynamical structure factor at frequencies close to the IR crossover (14).…”

Section: Introductionmentioning

confidence: 99%

Vibrational behavior of a realistic amorphous-silicon model

Christie

Taraskin

Elliott

2007

Journal of Non-Crystalline Solids

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The vibrational properties of a high-quality realistic model of amorphous silicon are examined. The longitudinal and transverse dynamical structure factors are calculated, and fitted to a damped harmonic oscillator (DHO) function. The width Γ of the best-fit DHO to the longitudinal dynamical structure factor scales approximately as k 2 for wavevectors k 0.55Å −1 , which is above the Ioffe-Regel crossover frequency separating the propagating and diffusing regimes, occurring at k = 0.38 ± 0.03Å −1 . Using the DHO function as a fitting function for the transverse dynamical structure factor (without theoretical justification), gives a dependence of Γ ∝ k α with α ∼ 2.5 for wavevectors k 0.7Å −1 . There was no evidence for Γ ∝ k 4 behaviour for either polarization.

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“…The first contribution in this direction has been the phonon-fracton approach [26,27], in which harmonic vibrational excitations on a percolating lattice were considered. However, a numerical simulation of this model [27] showed that the crossover from propagating modes (phonons) to localized fractal excitations (fractons) does not lead to an excess DOS, although calculations using the coherent potential approximation (CPA) [28,29] had predicted such an excess. Moreover, there is no experimental evidence for spatially fractal behaviour of bulk glasses.…”

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confidence: 99%

Harmonic Vibrational Excitations in Disordered Solids and the “Boson Peak”

1998

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We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearestneighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states g(ω) are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states g(ω)/ω 2 as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states. 63.50.+xA ubiquitous and rather intriguing feature in the physics of glasses is the anomalous behavior of the low-frequency part of the vibration spectrum and the corresponding thermal properties [1][2][3]. While the origin of the linear lowtempature specific heat is commonly attributed to the existence of double-well potentials or two-level systems [4], there is still considerable debate about the so-called "boson peak". This peak shows up in the density of states (DOS) g(ω) as an excess contribution, compared to the usual Debye behaviour ( g(ω) ∝ ω 2 ). It is taken as being responsible for a number of features observed in specific heat and thermal conductivity measurements, as well as in Raman or neutron scattering data [1-3,5-8]. The boson peak seems also to persist at elevated temperatures. Here its relation to the liquid-glass transition and the corresponding relaxation dynamics is a matter of discussion [9][10][11][12][13]. Due to the development of new experimental techniques allowing to perform Brillouin scattering measurements in the THz range [14][15][16][17], as well as pertinent molecular dynamics simulations [18][19][20][21][22] the question concerning the nature of the modes in the boson peak region has gained much additional interest recently.Several models have been formulated to explain the physical origin of the boson peak. In the soft-potential model [23,24] the existence of anharmonic localized vibrations is postulated to be an intrinsic and essential property of amorphous systems. The scattering of propagating phonons by these modes is then taken as the origin for the excess DOS in the boson peak region.Another, almost orthogonal approach considers harmonic degrees of freedom solely. Here the scattering of phonons is associated with the disorder in the force constants, or, equivalently, spatially fluctuating elastic constants [25]. The first contribution in this direction has been the phonon-fracton approach [26,27], in which harmonic vibrational excitations on a percolating lattice were considered. However, a numerical simulation of this model [27] showed that the crossover from propagating modes (phonons) to localized fractal excitations (fractons) does not lead t...

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Effective-medium approximation for a percolation network: The structure factor and the Ioffe-Regel criterion

Cited by 53 publications

References 17 publications

Structural heterogeneities at the origin of acoustic and transport anomalies in glycerol glass-former

Structural heterogeneities at the origin of acoustic and transport anomalies in glycerol glass-former

Vibrational behavior of a realistic amorphous-silicon model

Harmonic Vibrational Excitations in Disordered Solids and the “Boson Peak”

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