Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

Abstract

The understanding of hydrodynamic heat transport in finite-sized graphitic materials remains elusive due to the lack of an efficient methodology. In this paper, we develop a computational framework enabling an accurate description of heat transport in anisotropic graphite ribbons by a kinetic theory approach with full quantum mechanical first-principles input. A unified analysis of the size scaling of the thermal conductivity in the longitudinal and transverse directions of the system is made within the computational framework complemented with a macroscopic hydrodynamic approach. As a result, we demonstrate a strong end effect on the phonon Knudsen minimum, as a hallmark of the transition from ballistic to hydrodynamic heat transports, along a rectangular graphite ribbon with finite length and width. The phonon Knudsen minimum is found to take place only when the ribbon length is ∼5-10 times the upper limit of the width range in the hydrodynamic regime. This paper contributes to a unique methodology with high efficiency and a deeper understanding of the size effect on phonon hydrodynamics, which would open opportunities for its theoretical and experimental investigation in graphitic micro-and nanostructures.

Observation of phonon Poiseuille flow in isotopically-purified graphite ribbons

“…3a, is mainly attributed to the anisotropic nature and special phonon dispersion of graphite. The hydrodynamic phonon transport is mainly contributed by the bending acoustic (BA) modes in graphite 17,33 , the group velocity of which increases with frequency due to the quadratic dispersion curve 13,56 . As expressed in equation ( 1), G ballistic is determined by both the heat capacity term and the group velocity term (v(k)).…”

“…Besides, another important aspect to evidence the phonon hydrodynamic flow is the super-ballistic width dependence of thermal conductivity, as clearly indicated by the effective mean free path l ∼ W 2 /l N . The suspended microstructure system built up in this work provides a good platform for further experiments to investigate the extraordinary super-linear width dependence of thermal conduction in the hydrodynamic regime or the phonon Knudsen minimum phenomenon 17,32,33,57 .…”

“…We modelled the hydrodynamic heat transport through finite-size graphite ribbons by directly solving the phonon Boltzmann transport equation (BTE) with fully first-principles inputs using the methodology developed in our recent work 33 . The required input of phonon properties (including phonon dispersion relations and scattering rates) are calculated in the open-source package SHENGBTE 64 , with the harmonic and anharmonic (third-order) force constants obtained by the first-principles calculations implemented in the package QUANTUM ESPRESSO 65 .…”

“…The required input of phonon properties (including phonon dispersion relations and scattering rates) are calculated in the open-source package SHENGBTE 64 , with the harmonic and anharmonic (third-order) force constants obtained by the first-principles calculations implemented in the package QUANTUM ESPRESSO 65 . To accurately describe the inter-layer interaction in graphite, we adopted the most advanced van der Waals non-local density functional theory, with all the numerical details and validation of the first-principle calculations provided in our previous work 33 . The first-principles phonon properties were also used in the calculation of the ballistic thermal conductance in equation (1).…”

“…The second sound has been recently observed in highly oriented pyrolytic graphite (HOPG) using transient thermal measurement techniques at recording high temperatures 14,15,31 . Despite the numerous theoretical investigations of phonon Poiseuille flow in graphitic materials 17,20,32,33 , the experimental observation remains challenging owing to its more stringent observation window condition compared to that of the second sound, as to be elucidated in this work. It requires a special temperature range to realise the dominance of normal scattering and well-designed suspended microstructures to establish the hydrodynamic phonon flow.…”