III. Second sound and the thermo-mechanical effect at very low temperatures

Ward, John; Wilks, J.

doi:10.1080/14786440108520965

Cited by 92 publications

(29 citation statements)

References 2 publications

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“…2b that the normalized deviation is linear to wavevector q x along the temperature gradient direction with the same slope for all three acoustic branches in a wide range of wavevectors. This indicates that the distribution is indeed displaced, giving the macroscopic motion of phonons with the same velocity as in equation (2). In usual cases without strong hydrodynamic transport features, the normalized deviation shows no correlation among phonon modes and phonons cannot exhibit any macroscopic collective motion (see Supplementary Note 1 and Supplementary Fig.…”

Section: Displaced Distribution Functionmentioning

confidence: 99%

“…as previously derived 2,48,49 . For graphene, we calculate the speed of second sound using equation (20) and the phonon dispersion of ZA branch from first principles.…”

Section: Methodsmentioning

confidence: 99%

“…The past studies theoretically estimated the speed of second sound in three-dimensional materials as v I ffiffi ffi 3 p where v I is the speed of acoustic sound in Debye model 2,48,49 . For graphene, however, its phonon dispersion cannot be described by Debye model because of the nearly quadratic ZA phonon branch.…”

Section: Methodsmentioning

confidence: 99%

“…The second sound peak can be distinguished from a ballistic pulse using the fact that the propagation of second sound is slower than the propagation of acoustic sound or ballistic phonon transport. For three-dimensional materials, it is theoretically estimated that the speed of second sound, v II , is v I ffiffi ffi 3 p where v I is the speed of acoustic sound in Debye model 2,48,49 . In past experiments, a clear peak in dT/dt was observed with a delay time that could be explained well with the theoretical prediction of the speed of second sound, v II $ v I ffiffi ffi 3 p .…”

Section: Displaced Distribution Functionmentioning

confidence: 99%

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Hydrodynamic phonon transport in suspended graphene

et al. 2015

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Recent studies of thermal transport in nanomaterials have demonstrated the breakdown of Fourier's law through observations of ballistic transport. Despite its unique features, another instance of the breakdown of Fourier's law, hydrodynamic phonon transport, has drawn less attention because it has been observed only at extremely low temperatures and narrow temperature ranges in bulk materials. Here, we predict on the basis of first-principles calculations that the hydrodynamic phonon transport can occur in suspended graphene at significantly higher temperatures and wider temperature ranges than in bulk materials. The hydrodynamic transport is demonstrated through drift motion of phonons, phonon Poiseuille flow and second sound. The significant hydrodynamic phonon transport in graphene is associated with graphene's two-dimensional features. This work opens a new avenue for understanding and manipulating heat flow in two-dimensional materials.

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Section: Displaced Distribution Functionmentioning

confidence: 99%

“…as previously derived 2,48,49 . For graphene, we calculate the speed of second sound using equation (20) and the phonon dispersion of ZA branch from first principles.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Displaced Distribution Functionmentioning

confidence: 99%

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Hydrodynamic phonon transport in suspended graphene

et al. 2015

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“…51,52 In ideal gases this gives the relationship between the thermal velocity and sound velocity. 51 In solids and liquids at low temperature the phenomenon is known as second sound, 53,54 where it has been studied by models [55][56][57] and experiments in helium 58 , NaF 59,60 , NaI This appendix extends the BTE solution from 1D velocity v 1D in Fig. 3(a) to the more general case in Fig.…”

Section: Appendix C: Relationship Between 3d and 1d Group Velocitymentioning

confidence: 99%

Heating-frequency-dependent thermal conductivity: An analytical solution from diffusive to ballistic regime and its relevance to phonon scattering measurements

Yang

Dames

2015

Phys. Rev. B

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The heating frequency dependence of the apparent thermal conductivity in a semi-infinite body with periodic planar surface heating is explained by an analytical solution to the Boltzmann transport equation. This solution is obtained using a two-flux model and gray mean free time approximation, and verified numerically with a lattice Boltzmann method and numerical results from the literature. Extending the gray solution to the non-gray regime leads to an integral transform and accumulation-function representation of the phonon scattering spectrum, where the natural variable is mean free time, rather than mean free path as often used in previous work. The derivation leads to an approximate cutoff conduction similar in spirit to that of Koh and Cahill [Phys. Rev. B 76, 075207 (2007)] except that the most appropriate criterion involves the heater frequency rather than thermal diffusion length. The non-gray calculations are consistent with Koh and Cahill's experimental observation that the apparent thermal conductivity shows a stronger heater-frequency dependence in a SiGe alloy than in natural Si. Finally these results are demonstrated using a virtual experiment, which fits the phase lag between surface temperature and heat flux to obtain the apparent thermal conductivity and accumulation function.

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