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Register a new userEffective phonons in anharmonic lattices: anomalous vs normal heat conduction
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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.
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We study anomalous heat conduction and anomalous diffusion in low dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is $sigma^2(t)equiv <Delta x^2> =2Dt^{alpha} (0<alphale 2)$, then the thermal conductivity can be expressed in terms of the system size $L$ as $kappa = cL^{beta}$ with $beta=2-2/alpha$. This result predicts that a normal diffusion ($alpha =1$) implies a normal heat conduction obeying the Fourier law ($beta=0$), a superdiffusion ($alpha>1$) implies an anomalous heat conduction with a divergent thermal conductivity ($beta>0$), and more interestingly, a subdiffusion ($alpha <1$) implies an anomalous heat conduction with a convergent thermal conductivity ($beta<0$), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.
We study thermal rectifying effect in two dimensional (2D) systems consisting of the Frenkel Kontorva (FK) lattice and the Fermi-Pasta-Ulam (FPU) lattice. It is found that the rectifying effect is related to the asymmetrical interface thermal resistance. The rectifying efficiency is typically about two orders of magnitude which is large enough to be observed in experiment. The dependence of rectifying efficiency on the temperature and temperature gradient is studied. The underlying mechanism is found to be the match and mismatch of the spectra of lattice vibration in two parts.
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.
Understanding microscopic heat conduction in thin films is important for nano/micro heat transfer and thermal management for advanced electronics. As the thickness of thin films is comparable to or shorter than a phonon wavelength, phonon dispersion relations and transport properties are significantly modulated, which should be taken into account for heat conduction in thin films. Although phonon confinement and depletion effects have been considered, it should be emphasized that surface-localized phonons (surface phonons) arise whose influence on heat conduction may not be negligible due to the high surface-to-volume ratio. However, the role of surface phonons in heat conduction has received little attention thus far. In the present work, we performed anharmonic lattice dynamics calculations to investigate the thickness and temperature dependence of in-plane thermal conductivity of silicon thin films with sub-10-nm thickness in terms of surface phonons. Through systematic analysis of the influences of surface phonons, we found that anharmonic coupling between surface and internal phonons localized in thin films significantly suppresses overall in-plane heat conduction in thin films. We also discovered that specific low-frequency surface phonons significantly contribute to surface--internal phonon scattering and heat conduction suppression. Our findings are beneficial for the thermal management of electronics and phononic devices and may lead to surface phonon engineering for thermal conductivity control.
We have investigated the anisotropic thermal expansion of graphite using ab-initio calculation of lattice dynamics and anharmonicity of the phonons, which reveal that the negative thermal expansion (NTE) in the a-b plane below 600 K and very large positive thermal expansion along the c-axis up to high temperatures arise due to various phonons polarized along the c-axis. While the NTE arises from the anharmonicity of transverse phonons over a broad energy range up to 60 meV, the large positive expansion along the c-axis occurs largely due to the longitudinal optic phonon modes around 16 meV and a large linear compressibility along the c-axis. The hugely anisotropic bonding in graphite is found to be responsible for wide difference in the energy range of the transverse and longitudinal phonon modes polarized along the c-axis, which are responsible for the anomalous thermal expansion behavior. This behaviour is in contrast to other nearly isotropic hexagonal structures like water-ice, which show anomalous thermal expansion in a small temperature range arising from a narrow energy range of phonons.
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