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Register a new userHeat conduction in one dimensional systems: Fourier law, chaos, and heat control
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In this paper we give a brief review of the relation between microscopic dynamical properties and the Fourier law of heat conduction as well as the connection between anomalous conduction and anomalous diffusion. We then discuss the possibility to control the heat flow.
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Heat conduction experiments are performed in order to identify effects beyond Fourier. Two experimental setups are discussed. First, a simple experiment by a heterogeneous material is investigated from the point of view of generalized heat conduction, then the classical laser flash method is analysed.
In the hydrodynamic regime, phonons drift with a nonzero collective velocity under a temperature gradient, reminiscent of viscous gas and fluid flow. The study of hydrodynamic phonon transport has spanned over half a century but has been mostly limited to cryogenic temperatures (~1 K) and more recently to low-dimensional materials. Here, we identify graphite as a three-dimensional material that supports phonon hydrodynamics at significantly higher temperatures (~100 K) based on first-principles calculations. In particular, by solving the Boltzmann equation for phonon transport in graphite ribbons, we predict that phonon Poiseuille flow and Knudsen minimum can be experimentally observed above liquid nitrogen temperature. Further, we reveal the microscopic origin of these intriguing phenomena in terms of the dependence of the effective boundary scattering rate on momentum-conserving phonon-phonon scattering processes and the collective motion of phonons. The significant hydrodynamic nature of phonon transport in graphite is attributed to its strong intralayer sp2 hybrid bonding and weak van der Waals interlayer interactions. As a boundary-sensitive transport regime, phonon hydrodynamics opens up new possibilities for thermal management and energy conversion.
We study heat conduction in one dimensional (1D) anharmonic lattices analytically and numerically by using an effective phonon theory. It is found that every effective phonon mode oscillates quasi-periodically. By weighting the power spectrum of the total heat flux in the Debye formula, we obtain a unified formalism that can explain anomalous heat conduction in momentum conserved lattices without on-site potential and normal heat conduction in lattices with on-site potential. Our results agree very well with numerical ones for existing models such as the Fermi-Pasta-Ulam model, the Frenkel-Kontorova model and the $phi^4$ model etc.
For an one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long, slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our study is illustrated by the 1D diatomic gas model, with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.
Aluminum scandium nitride alloy (Al1-xScxN) is regarded as a promising material for high-performance acoustic devices used in wireless communication systems. Phonon scattering and heat conduction processes govern the energy dissipation in acoustic resonators, ultimately determining their performance quality. This work reports, for the first time, on phonon scattering processes and thermal conductivity in Al1-xScxN alloys with the Sc content (x) up to 0.26. The thermal conductivity measured presents a descending trend with increasing x. Temperature-dependent measurements show an increase in thermal conductivity as the temperature increases at temperatures below 200K, followed by a plateau at higher temperatures (T> 200K). Application of a virtual crystal phonon conduction model allows us to elucidate the effects of boundary and alloy scattering on the observed thermal conductivity behaviors. We further demonstrate that the alloy scattering is caused mainly by strain-field difference, and less by the atomic mass difference between ScN and AlN, which is in contrast to the well-studied Al1-xGaxN and SixGe1-x alloy systems where atomic mass difference dominates the alloy scattering. This work studies and provides the quantitative knowledge for phonon scattering and the thermal conductivity in Al1-xScxN, paving the way for future investigation of materials and design of acoustic devices.
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