Observation of second sound in graphite at temperatures above 100 K

Huberman, Samuel; Duncan, R. A.; Chen, K.; Song, Bai; Chiloyan, Vazrik; Ding, Zhiwei; Maznev, A. A.; Chen, G.; Nelson, Keith A.

doi:10.1126/science.aav3548

Cited by 217 publications

(215 citation statements)

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“…However at micro-and nanoscale this theory faces significant difficulties, because macroscopic constitutive relations can be inapplicable at lower length scales. For example, recent theoretical [2-4] and experimental studies [5][6][7][8][9] show that at micro-and nanoscale the Fourier law of heat conduction can be violated. In particular, ballistic regime of heat transport is observed [10,11].A convenient model for investigation of thermomechanical processes at micro-and nanoscale is the Fermi-Pasta-Ulam (FPU) chain [12].…”

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confidence: 99%

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Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature

Kuzkin

Кривцов

2020

Phys. Rev. E

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We study conversion of thermal energy to mechanical energy and vice versa in α-FPU chain with spatially sinusoidal profile of initial temperature. We show analytically that thermal expansion and temperature oscillations, caused by quasiballistic heat transport, excite mechanical vibrations with growing amplitude. This new phenomenon is referred to as "ballistic resonance". At large times, the mechanical vibrations decay monotonically. No recurrence, typical for the original FPU problem, is observed. We assume that the absence of recurrence is due to finite initial temperature of the chain.Energy of an isolated solid body can be converted from a mechanical form to a thermal form and vice versa. Conversion of mechanical energy to thermal energy leads, for example, to damping of mechanical vibrations (or waves). Thermal expansion and heat transport cause an opposite process, i.e. conversion of thermal energy to mechanical energy.In macroscopic continuum theories, the conversion is modeled by coupling between the equation of momentum balance and the equation of energy balance. An example of a continuum theory, describing the conversion, is the linear thermoviscoelasticity. Macroscopic theory of linear thermoviscoelasticity is well-developed [1]. However at micro-and nanoscale this theory faces significant difficulties, because macroscopic constitutive relations can be inapplicable at lower length scales. For example, recent theoretical [2-4] and experimental studies [5][6][7][8][9] show that at micro-and nanoscale the Fourier law of heat conduction can be violated. In particular, ballistic regime of heat transport is observed [10,11].A convenient model for investigation of thermomechanical processes at micro-and nanoscale is the Fermi-Pasta-Ulam (FPU) chain [12]. Despite the apparent simplicity of the model, analytical description of thermoelasticity, heat transport and energy conversion in the FPU chain remains a serious challenge for theoreticians.Several anomalies of thermomechanical behavior are observed for the FPU chain. The heat transport in the FPU model is anomalous, i.e. the Fourier law is not satisfied [13][14][15]. The Maxwell-Cattaneo-Vernotte law also fails to describe the heat transport in FPU chains [16,17]. Harmonic approximation allows to derive equations [18,19] and closed-form solutions [20, 21] describing heat transport in chains. However the question arises wether temperature field, obtained in harmonic approximation, can be used for estimation of thermoelastic effects (e.g. excitation of mechanical vibrations due to thermal expansion). We address this question below.Conversion of mechanical energy to thermal energy is even more challenging. Studies of this process have a long history, starting from the pioneering work of Fermi, Pasta, and Ulam [12]. In paper [12], initial conditions, corresponding to the first normal mode of a chain, were considered. It was shown numerically that energy of this normal mode demonstrates almost periodic behavior, i.e. the system does not reach thermal equilibrium...

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confidence: 99%

“…Since the total energy of the system is conserved, the growth of mechanical energy is associated with a decrease of thermal energy. Initial growth is well-described by analytical solution (9).…”

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confidence: 99%

Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature

Kuzkin

Кривцов

2020

Phys. Rev. E

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“…The Q-factors for the localized temperature pulse in space and forced temperature oscillation in time are compared and, in the former case, the group velocity is addressed. Previous reports of temperature oscillations, among which the recently observed temperature oscillation in graphite at cryogenic temperatures [2], are revised at the light of the present formulation, together with the possibilities offered by quantum materials on the ultra-short and ultra-fast space and time scales respectively. Specifically, the possibility of observing electronic temperature wave-like behaviour in solidstate condensates and spin-temperature oscillations in magnetic materials opens the way to all-solid state thermal nanodevices, operating well above liquid helium temperature while tacking advantage of different excitations -i.e electrons, phonons and spins -and, possibly, of their mutual interplay.…”

Section: Introductionmentioning

confidence: 87%

Accessing temperature waves: A dispersion relation perspective

Gandolfi

Benetti

Glorieux

et al. 2019

International Journal of Heat and Mass Transfer

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c 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ In order to account for non-Fourier heat transport, occurring on short time and length scales, the often-praised Dual-Phase-Lag (DPL) model was conceived, introducing a causality relation between the onset of heat flux and the temper-arXiv:1908.07612v1 [cond-mat.mes-hall] 18 Aug 2019 ature gradient. The most prominent aspect of the first-order DPL model is the prediction of wave-like temperature propagation, the detection of which still remains elusive. Among the challenges to make further progress is the capability to disentangle the intertwining of the parameters affecting wave-like behaviour.This work contributes to the quest, providing a straightforward, easy-to-adopt, analytical mean to inspect the optimal conditions to observe temperature wave oscillations. The complex-valued dispersion relation for the temperature scalar field is investigated for the case of a localised temperature pulse in space, and for the case of a forced temperature oscillation in time. A modal quality factor is introduced showing that, for the case of the temperature gradient preceding the heat flux, the material acts as a bandpass filter for the temperature wave.The bandpass filter characteristics are accessed in terms of the relevant delay times entering the DPL model. The optimal region in parameters space is discussed in a variety of systems, covering nine and twelve decades in space and time-scale respectively. The here presented approach is of interest for the design of nanoscale thermal devices operating on ultra-fast and ultra-short time scales, a scenario here addressed for the case of quantum materials and graphite.

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“…It was therefore very surprising that very recently, a group of experimentalists found a clear evidence of second sound in graphite at relatively high temperature, namely, above 100 K. 5 Moreover, if, as they predict with confidence, the same phenomenon will be found in the high-performance relative of graphite that is graphene, and this at room or even higher temperatures, important practical implications to microelectronics and nanoelectronics are expected to occur.…”

Section: Introductionmentioning

confidence: 99%

“…There is an intermediate regime, that of the so-called phonons hydrodynamics, which seems to prevail, under certain conditions, in graphite and graphene. 5 Many of the numerous formulations proposed to describe mathematically thermal phenomena fail to satisfy the laws of thermodynamics. Some scholars, such as, eg, Coleman et al 14,25 and Morro and Ruggeri, 15 tried to develop models on the sound grounds of thermodynamics, eg, based on the so-called extended (irreversible) thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

More around Cattaneo equation to describe heat transfer processes

Spigler

2020

Math Methods in App Sciences

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We revisit Cattaneo's derivation of the equation describing heat transfer and bearing his name, finding a more elaborated model equation, that we will compare with the time-lagged model. This equation does not comply with the second law of thermodynamics, as well as Cattaneo equation. The latter, however, is known to have provided meaningful results in certain experiments conducted in some liquids and solids at very low temperature. These experiments also match the results given by a nonlinear model proposed by A. Morro and T. Ruggeri in 1988, which instead does meet the laws of thermodynamics. A comparison is made with such a model too. KEYWORDS Cattaneo-Maxwell-Vernotte equation, heat equation, heat transfer, heat waves, second sound, thermal lag MSC CLASSIFICATION 80A20 Math Meth Appl Sci. 2020;43:5953-5962.wileyonlinelibrary.com/journal/mma

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Observation of second sound in graphite at temperatures above 100 K

Cited by 217 publications

References 39 publications

Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature

Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature

Accessing temperature waves: A dispersion relation perspective

More around Cattaneo equation to describe heat transfer processes

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