Lowest-Order Nonvanishing Contribution to Lattice Viscosity

DeVault, G.P.

doi:10.1103/physrev.155.875

Cited by 17 publications

(5 citation statements)

References 19 publications

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“…We indicate briefly why this approach fails. The physical picture underlying the calculation of viscous dissipation in (3D) insulating solids is due to Akhieser [1] -see also [8,15,30]. Imagine one of the low frequency phonons in a lattice system of phonons.…”

Section: B Phonons and The Boltzmann-peierls Equationmentioning

confidence: 99%

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Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains

2008

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We examine the thermal conductivity and bulk viscosity of a onedimensional (1D) chain of particles with cubic-plus-quartic interparticle potentials and no on-site potentials. This system is equivalent to the FPUαβ system in a subset of its parameter space. We identify three distinct frequency regimes which we call the hydrodynamic regime, the perturbative regime and the collisionless regime. In the lowest frequency regime (the hydrodynamic regime) heat is transported ballistically by long wavelength sound modes. The model that we use to describe this behaviour predicts that as ω → 0 the frequency dependent bulk viscosity,ζ(ω), and the frequency dependent thermal conductivity,κ(ω), should diverge with the same power law dependence on ω. Thus, we can define the bulk Prandtl number, P r ζ = kBζ(ω)/(mκ(ω)), where m is the particle mass and kB is Boltzmann's constant. This dimensionless ratio should approach a constant value as ω → 0. We use mode-coupling theory to predict the ω → 0 limit of P r ζ . Values of P r ζ obtained from simulations are in agreement with these predictions over a wide range of system parameters. In the middle frequency regime, which we call the perturbative regime, heat is transported by sound modes which are damped by four-phonon processes. This regime is characterized by an intermediate-frequency plateau in the value ofκ(ω). We find that the value ofκ(ω) in this plateau region is proportional to T −2 where T is the temperature; this is in agreement with the expected result of a four-phonon Boltzmann-Peierls equation calculation. The Boltzmann-Peierls approach fails, however, to give a nonvanishing bulk viscosity for all FPU-αβ chains. We call the highest frequency regime the collisionless regime since at these frequencies the observing times are much shorter than the characteristic relaxation times of phonons.

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Section: B Phonons and The Boltzmann-peierls Equationmentioning

confidence: 99%

“…For frequencies ωτ 1 Akhieser and others [1,8,15,30] have applied the Boltzmann-Peierls equation, with and without the single relaxation time approximation, to calculate 3D lattice viscosities (i.e. shear and bulk).…”

Section: B Phonons and The Boltzmann-peierls Equationmentioning

confidence: 99%

Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains

2008

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“…As pointed out in [48], this amounts to introducing an exponential decay in the time-dependent relaxation function. This is preferable to the expression (4.15) proposed in [49], as the latter does not have a finite KramersKronig transform.…”

Section: Network Viscositymentioning

confidence: 99%

“…As explained above, this result should be interpreted in terms of the Q −1 anh produced by anharmonicity. The theory of lattice viscosity was developed for crystals, in which case the calculation of correlation functions [48] or the sums over modes [11,49] could be carried out quite far. For glasses, only the fracton model has been pursued to the point of making analytic predictions for the acoustic linewidth [19,50].…”

Section: Network Viscositymentioning

confidence: 99%

Anharmonic versus relaxational sound damping in glasses. I. Brillouin scattering from densified silica

et al. 2005

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This series discusses the origin of sound damping and dispersion in glasses. In particular, we address the relative importance of anharmonicity versus thermally activated relaxation. In this first article, Brillouin-scattering measurements of permanently densified silica glass are presented. It is found that in this case the results are compatible with a model in which damping and dispersion are only produced by the anharmonic coupling of the sound waves with thermally excited modes. The thermal relaxation time and the unrelaxed velocity are estimated.

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“…The expression (56) is the general formula for a. If some assumptions are made as to y and 'G we can obtain results which have been derived by DeVault [16], Kishore [17], and Maris [18]. The first two of them assume y not to be dependent on the magnitude of q but only on its direction.…”

Section: B) Q ' Gmentioning

confidence: 95%

On Acoustic Attenuation in Dielectric Solids

Ožvold

1970

Physica Status Solidi (b)

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Starting from the general equation of motion for the atoms of the primitive lattice and using the Green function method the sound absorption coefficient is derived in the threephonon approximation. The here derived results hold for transverse waves in the whole frequency region and for longitudinal ones in the high frequency region ( Q t > 1). The frequency and temperature dependence of the absorption coefficient are discussed for the high and low frequencies (Q t > 1 and 9 t < 1). Using the dispersion relation, the change of elastic constants due to the three-phonon processes is determined.Ausgehend von den allgemeinen Bewegungsgleichungen der Atome in einem primitiven Kristallgitter und nnter Benutzung der Methode der Greenschen Funktionen werden die Koeffizienten der Schallabsorption im Rahmen einer Drei-Phonon-Approximation abgeleitet. Die so erhaltenen Ergebnisse sind gultig fur transversale Wellen im ganzen Frequenzbereich und fur longitudinale Wellen im Bereich der hohen Frequenzen (Q t > 1). Frequenz-und Temperaturabhiingigkeit der Absorptionskoeffizienten werden fur den Fall hoher nnd tiefer Frequenzen besprochen (Q t > 1 und Q z < 1). Unt,er Benutzung der Dispersionsrelationen werden die Anderungen der elastischen Konstanten, die durch den Drei-Phonon-ProzeB hervorgerufen werden, ermittelt.

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Lowest-Order Nonvanishing Contribution to Lattice Viscosity

Cited by 17 publications

References 19 publications

Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains

Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains

Anharmonic versus relaxational sound damping in glasses. I. Brillouin scattering from densified silica

On Acoustic Attenuation in Dielectric Solids

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