Hydrodynamic Phonon Transport Research Articles

Ultrafast electron diffuse scattering as a tool for studying phonon transport: Phonon hydrodynamics and second sound oscillations.

Hydrodynamic phonon transport phenomena, like second sound, have been observed in liquid helium more than 50 years ago. More recently second sound has been observed in graphite at over 200 K using transient thermal grating (TG) techniques. In this work, we explore signatures of phonon hydrodynamic transport and second sound oscillations in ultrafast electron diffuse scattering patterns, which can provide time, momentum, and branch resolved information on the state-of-excitation of the phonon system beyond that available through TG experiments. We use the density functional theory and solve the Boltzmann transport equation to determine time-resolved non-equilibrium phonon populations and model phonon transport in graphite. This model also provides the information necessary to calculate the time evolution of one-phonon structure factors and diffuse scattering patterns during thermal transport covering ballistic, diffusive, and hydrodynamic regimes where the effect of a second sound oscillation on the phonon distribution is observed. Direct measurements of how the phonon distribution varies in time and space in various thermal transport regimes should yield new insights into the fundamental physics of the underlying processes.

Effect of atomic substitution and structure on thermal conductivity in monolayers H-MN and T-MN (M = B, Al, Ga).

Finding materials with suitable thermal conductivity (κ) is crucial for improving energy efficiency, reducing carbon emissions, and achieving sustainability. Atomic substitution and structural adjustments are commonly used methods. By comparing the κ of two different structures of two-dimensional (2D) IIIA-nitrides and their corresponding carbides, we explored whether atomic substitution has the same impact on κ in different structures. All eight materials exhibit normal temperature dependence, with κ decreasing as the temperature rises. Both structures are single atomic layers of 2D materials, forming M-N bonds, with the difference being that H-MN consists of hexagonal rings, while T-MN consists of tetragonal and octagonal rings. 2D IIIA-nitrides provide a good illustration of the impact of atomic substitution and structure on κ. On a logarithmic scale of κ, it approximates two parallel lines, indicating that different structures exhibit similar trends of κ reduction under the same conditions of atomic substitution. We analyzed the mechanisms behind the decreasing trend in κ from a phonon mode perspective. The main reason for the decrease in κ is that heavier atoms lower lattice vibrations, reducing phonon frequencies. Electronegativity increases, altering bonding characteristics and increasing anharmonicity. Reduced symmetry in complex structures decreases phonon group velocities and enhances phonon anharmonicity, leading to decreased phonon lifetimes. It's noteworthy that we found that atomic substitution and structure significantly affect hydrodynamic phonon transport as well. Both complex structures and atomic substitution simultaneously reduce the effects of hydrodynamic phonon transport. By comparing the impact of κ on two different structures of 2D IIIA-nitrides and their corresponding carbides, we have deepened our understanding of phonon transport in 2D materials. Heavier atomic substitution and more complex structures result in reduced κ and decreased hydrodynamic phonon transport effects. This research is likely to have a significant impact on the study of micro- and nanoscale heat transfer, including the design of materials with specific heat transfer properties for future applications.

Ab initio investigations on hydrodynamic phonon transport: From diffusion to convection

In classical theory, heat conduction in solids is regarded as a diffusion process driven by a temperature gradient, whereas fluid transport is understood as convection process involving the bulk motion of the liquid or gas. In the framework of ab initio theory, which is directly built upon quantum mechanics without relying on measured parameters or phenomenological models, we observed and investigated the fluid-like convective transport of energy carriers in solid heat conduction. Thermal transport, carried by phonons, is simulated in graphite by solving the Boltzmann transport equation using a Monte Carlo algorithm. To capture convective transport, with phonon distributions deviating significantly from equilibrium Bose-Einstein distribution, we determined phonon interactions using ab initio approaches that go beyond relaxation time approximations. The presence of strong momentum-conserved Normal scatterings in graphite introduces a regime for hydrodynamic phonon transport. Fluid-like features, such as vortex and jet flow, are visualized and compared with classical theories on heat diffusion and fluid convection. Our study on phonon convection enhances fundamental understandings of heat conduction in solids from both atomic scale and quantum aspects, innovating thermal designs for future microelectronic devices and other thermal management applications. This potentially offers solutions for heat dissipation challenges in the post-Moore era.

Super-Ballistic Width Dependence of Thermal Conductivity in Graphite Nanoribbons and Microribbons.

The super-ballistic temperature dependence of thermal conductivity, facilitated by collective phonons, has been widely studied. It has been claimed to be unambiguous evidence for hydrodynamic phonon transport in solids. Alternatively, hydrodynamic thermal conduction is predicted to be as strongly dependent on the width of the structure as is fluid flow, while its direct demonstration remains an unexplored challenge. In this work, we experimentally measured thermal conductivity in several graphite ribbon structures with different widths, from 300 nm to 1.2 µm, and studied its width dependence in a wide temperature range of 10-300 K. We observed enhanced width dependence of the thermal conductivity in the hydrodynamic window of 75 K compared to that in the ballistic limit, which provides indispensable evidence for phonon hydrodynamic transport from the perspective of peculiar width dependence. This will help to find the missing piece to complete the puzzle of phonon hydrodynamics, and guide future attempts at efficient heat dissipation in advanced electronic devices.

How Hydrodynamic Phonon Transport Determines the Convergence of Thermal Conductivity in Two-Dimensional Materials.

The phonon Boltzmann transport equation combined with first-principles calculation has achieved great success in exploring the lattice thermal conductivity () of various materials. However, the convergence of the predicted is a critical issue, leading to quite scattered results recorded in the literature, even for the same material. In this paper, we explore the origin for the convergence of thermal conductivity in two-dimensional (2D) materials. Two kinds of typical 2D materials, graphene and silicene, are studied, and the bulk silicon is also compared as a control system for a three-dimensional material. The effect of the cutoff radius () in the third-order interatomic force constants on is studied for these three materials. It is found that that of these three materials exhibits diverse convergence behaviors with respect to , which coincides very well with the strength of hydrodynamic phonon transport. By further analyzing the phonon lifetime and scattering rates, we reveal that the dominance of the normal scattering process gives rise to the hydrodynamic phonon transport in both graphene and silicene, which results in long-range interaction and a large lifetime of low-frequency flexural acoustic phonons, while the same phenomenon is absent in bulk silicon. Our study highlights the importance of long-range interaction associated with hydrodynamic phonon transport in determining the thermal conductivity of 2D materials.

Hydrodynamically enhanced thermal transport due to strong interlayer interactions: A case study of strained bilayer graphene

Manipulating interlayer interactions in two-dimensional (2D) materials is a widely used and effective method for regulating heat transport, which is important for thermal management of electronics. In this paper, we find that thermal transport can be enhanced by strong interlayer interactions. For instance, 2D bilayer materials with interlayer bonding have larger thermal conductivity than their monolayer counterparts. To further verify the conjecture, we take bilayer graphene (BLG) as a study case to gradually strengthen the interlayer interactions in BLG by applying a series of compressive strains along the out-of-plane direction. It is found that the thermal conductivity of BLG first decreases and then anomalously increases when the strain is larger than the threshold of 12%. For the decreasing trend, it is mainly due to the strain-induced reduction of phonon group velocity and lifetime. While at larger strain (>12%), the anomalous increase of thermal conductivity is found to be caused by hydrodynamic phonon transport and weak phonon anharmonicity. Thus, enhanced interlayer interactions can enhance the hydrodynamic phonon transport and thus improve the heat transfer performance. In this paper, we not only report the hydrodynamic enhancement of thermal transport through enhanced interlayer interactions but also provide solid evidence. These findings will deepen the understanding of thermal transport in layered materials and heterostructures, which will benefit the applications in thermal management.

Reexamination of hydrodynamic phonon transport in thin graphite

The recent hydrodynamic phonon transport theory for graphitic materials has been supported by the measurements of the second sound at temperatures up to about 100 K. When boundary scattering becomes comparable to momentum-conserving normal phonon scattering processes that are responsible for phonon hydrodynamics, Poiseuille phonon flow phenomena can emerge to give rise to unique size-dependent thermal conductivity in thin graphite. Here, we examine the thickness range for the Poiseuille phonon flow to become observable in thin graphite with the use of both deviational Monte Carlo simulation of the Peierls-Boltzmann transport equation and four-probe thermal transport measurements. As the basal-plane thermal conductivity calculated by prior first-principles theories saturates to the graphite value when the thickness is increased to five graphene layers, the phonon dispersion of graphite is used in the current calculations of thin graphite of micrometer thickness and a 23-layer thick ultrathin graphite (UTG) sample. The calculations show that diffuse surface scattering by surface defects can lead to Poiseuille phonon flow at 50 K in thin graphite with the thickness close to several micrometers but not in the 65 μm thin graphite and 23-layer UTG, where phonon scattering by the top and bottom surfaces become, respectively, much less and more frequent than the normal processes. In addition, the calculation results with the bulk graphite dispersion and diffuse surface scattering show decreased basal-plane thermal conductivity with decreasing thickness, opposite to recent thermocouple measurements of thin graphite samples. In comparison, the calculation results reveal that partially diffuse surface defect scattering can yield the four-probe measurement results of UTG samples, which are prepared here with an improved process to minimize surface contamination.

A transient heat conduction phenomenon to distinguish the hydrodynamic and (quasi) ballistic phonon transport

Previous studies have predicted the failure of Fourier’s law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regimes only by this phenomenon. In this work, the transient heat propagation in homogeneous thermal system is studied based on the phonon Boltzmann transport equation (BTE) under the Callaway model. Given a quasi-one or quasi-two (three) dimensional simulation with homogeneous environment temperature, at initial moment, a heat source is added suddenly at the center with high temperature, then the heat propagates from the center to the outer. Numerical results show that in quasi-two (three) dimensional simulations, the transient temperature will be lower than the lowest value of initial temperature in the hydrodynamic regime within a certain range of time and space. This phenomenon appears only when the normal scattering dominates heat conduction. Besides, it disappears in quasi-one dimensional simulations. Similar phenomenon is also observed in thermal systems with time varying heat source. This transient heat propagation phenomenon of hydrodynamic phonon transport distinguishes it well from (quasi) ballistic phonon transport.

Transient Hydrodynamic Lattice Cooling by Picosecond Laser Irradiation of Graphite

Recent theories and experiments have suggested hydrodynamic phonon transport features in graphite at unusually high temperatures. Here, we report a picosecond pump-probe thermal reflectance measurement of heat-pulse propagation in graphite. The measurement results reveal transient lattice cooling near the adiabatic center of a 15-μm-diameter ring-shape pump beam at temperatures between 80 and 120K. While such lattice cooling has not been reported in recent diffraction measurements of second sound in graphite, the observation here is consistent with both hydrodynamic phonon transport theory and prior heat-pulse measurements of second sound in bulk sodium fluoride.

A perspective on the hydrodynamic phonon transport in two-dimensional materials

Thermal transport in two-dimensional (2D) materials has attracted great attention since the discovery of high thermal conductivity in graphene, which is closely related to the hydrodynamic phonon transport. In this Perspective, we briefly summarize the recent progresses in studying hydrodynamic phonon transport in 2D materials, including both theoretical and experimental works. First, the criterion and numerical methods for studying hydrodynamic phonon transport are reviewed. We then discuss the physical mechanism and peculiar phenomena related to hydrodynamic phonon transport in 2D materials and finally present the challenge for future studies. This Perspective aims to provide the physical understanding of the hydrodynamic phonon transport, which might be beneficial to the exploration of novel thermal transport behaviors in 2D materials.

Heat vortices of ballistic and hydrodynamic phonon transport in two-dimensional materials

Heat conduction in solid materials may behave like fluid dynamics when normal (N) scattering dominates phonon transport. In this hydrodynamic regime, the heat vortices have been predicted with frequency-independent relaxation time. So can this phenomena appear in other regimes? And what are the differences? In order to answer these questions, in this work, the heat vortices in two-dimensional materials are investigated based on the frequency-dependent phonon Boltzmann transport equation (BTE) under the Callaway model. We find that apart from the hydrodynamic regime, the heat vortices can appear in the ballistic and other transition regimes, which is a wider window of heat vortices compared to previous study (Fig. 1). The differences of heat vortices in the ballistic and hydrodynamic regime are investigated. In ribbon structure, the vortices sizes increase with system length in the ballistic regime but are confined by the system width in the hydrodynamic regime. In porous structures, the critical values of τR (or τN) about when the heat vortices disappear (or when the vortices size starts to become smaller) are found.

Phonon vortex dynamics in graphene ribbon by solving Boltzmann transport equation with ab initio scattering rates

In this work, we study thermal phonon vortex in graphene ribbon by a discrete-ordinate solution of phonon Boltzmann equation under Callaway's dual relaxation model. The phonon scattering rates of normal and resistive processes are acquired from ab initio calculation without need of any empirical input parameters. The temperature, size and isotope effects on transition from phonon vortex transport to conventional Fourier's heat conduction in both simple and complex geometries are investigated. The physical mechanism for the evolution of phonon vortex is declared by wide phonon mean free path distribution of resistive processes. A hierarchical vortex series is obtained with primary, secondary and terniary vortexes in a complicated geometry. The present work provides an accurate and efficient multi-scale numerical framework for modeling hydrodynamic phonon transport in high-thermal-conductivity materials and also sheds light on the heat dissipation applications.

Phonon transport in graphene based materials.

Graphene, due to its atomic layer structure, has the highest room temperature thermal conductivity k for all known materials. Thus, it is expected that graphene based materials are the best candidates for thermal management in next generation electronic devices. In this perspective, we first review the in-plane k of monolayer graphene and multilayer graphene obtained using experimental measurements, theoretical calculations and molecular dynamics (MD) simulations. Considering the importance of four-phonon scattering in graphene, we also compare the effects of three-phonon and four-phonon scattering on phonon transport in graphene. Then, we review phonon transport along the cross-plane direction of multilayer graphene and highlight that the cross-plane phonon mean free path is several hundreds of nanometers instead of a few nanometers as predicted using classical kinetic theory. Recently, hydrodynamic phonon transport has been observed experimentally in graphitic materials. The criteria for distinguishing the hydrodynamic from ballistic and diffusive regimes are discussed, from which we conclude that graphene based materials with a high Debye temperature and high anharmonicity (due to ZA modes) are excellent candidates to observe the hydrodynamic phonon transport. In the fourth part, we review how to actively control phonon transport in graphene. Graphene and graphite are often adopted as additives in thermal management materials such as polymer nanocomposites and thermal interface materials due to their high k. However, the enhancement of the composite's k is not so high as expected because of the large thermal resistance between graphene sheets as well as between the graphene sheet and matrix. In the fifth part, we discuss the interfacial thermal resistance and analyze its effect on the thermal conductivity of graphene based materials. In the sixth part, we give a brief introduction to the applications of graphene based materials in thermal management. Finally, we conclude our review with some perspectives for future research.

Non-Monotonic Thickness Dependent Hydrodynamic Phonon Transport in Layered Titanium Trisulphide: First-Principles Calculation and Improved Callaway Model Fitting

Non-Monotonic Thickness Dependent Hydrodynamic Phonon Transport in Layered Titanium Trisulphide: First-Principles Calculation and Improved Callaway Model Fitting

Hydrodynamic phonon transport in bulk crystalline polymers

Hydrodynamic phonon transport in solids exhibits unique thermal transport behaviors, such as second sound, the Poiseuille flow, and ultrahigh thermal conductivity. However, those have been limited up to the cryogenic temperature ($\ensuremath{\sim}1$ K) for a few materials. In this work, by employing the phonon Boltzmann transport equation, we demonstrate hydrodynamic phonon transport in organic systems such as bulk crystalline polymers. Remarkable hydrodynamic phonon transport up to 50 K is demonstrated for both polyacene ${(\ensuremath{-}{\mathrm{C}}_{4}{\mathrm{H}}_{2}\ensuremath{-})}_{n}$ and polyacetylene ${(\ensuremath{-}{\mathrm{C}}_{2}{\mathrm{H}}_{2}\ensuremath{-})}_{n}$ crystals. More interestingly, a weak phonon hydrodynamic behavior takes place in crystalline polyethylene ${(\ensuremath{-}{\mathrm{C}}_{2}{\mathrm{H}}_{4}\ensuremath{-})}_{n}$ in the intermediate-temperature range around 120 K, different from the observed hydrodynamics in most systems. The spectral phonon analysis reveals that the torsional motion of the ${A}_{2}$ mode causes this unique hydrodynamic behavior. A modified criterion for the emergence of hydrodynamic phonon transport is proposed which agrees quantitatively with the results from thermal conductivity and phonon drifting component calculations. This study provides physical insights into the understanding of phonon hydrodynamics in organic materials and also a reliable criterion to probe the hydrodynamic phonon transport in complex systems.

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation with the Callaway model approximation, we derive a 2D Guyer-Krumhansl-like equation describing hydrodynamic phonon transport, taking into account the quadratic dispersion of flexural phonons. In addition to Poiseuille flow, second sound propagation, the equation predicts heat current vortices and negative non-local thermal conductance in 2D materials, which are common in classical fluids but have not yet been considered in phonon transport. Our results also illustrate the universal transport behaviors of hydrodynamics, independent of the type of quasi-particles and their microscopic interactions.

Direct simulation of second sound in graphene by solving the phonon Boltzmann equation via a multiscale scheme

The direct simulation of the dynamics of second sound in graphitic materials remains a challenging task due to lack of methodology for solving the phonon Boltzmann equation in such a stiff hydrodynamic regime. In this work, we aim to tackle this challenge by developing a multiscale numerical scheme for the transient phonon Boltzmann equation under Callaway's dual relaxation model which captures well the collective phonon kinetics. Comparing to traditional numerical methods, the present multiscale scheme is efficient, accurate and stable in all transport regimes attributed to avoiding the use of time and spatial steps smaller than the relaxation time and mean free path of phonons. The formation, propagation and composition of ballistic pulses and second sound in graphene ribbon in two classical paradigms for experimental detection are investigated via the multiscale scheme. The second sound is declared to be mainly contributed by ZA phonon modes, whereas the ballistic pulses are mainly contributed by LA and TA phonon modes. The influence of temperature, isotope abundance and ribbon size on the second sound propagation is also explored. The speed of second sound in the observation window is found to be at most 20 percentages smaller than the theoretical value in hydrodynamic limit due to the finite umklapp, isotope and edge resistive scattering. The present study will contribute to not only the solution methodology of phonon Boltzmann equation, but also the physics of transient hydrodynamic phonon transport as guidance for future experimental detection.

Origins of significant reduction of lattice thermal conductivity in graphene allotropes

Coherent wave effects of thermal phonons hold promise of transformative opportunities in thermal transport control but remain largely unexplored due to the small wavelength of thermal phonons, typically below a few nanometers. This small length scale indicates that, instead of artificial phononic crystals, a more promising direction is to examine the coherent phonon effects in natural materials with hierarchical superstructures matching the thermal phonon wavelength. In this work, we use first-principles simulations to characterize the previously unstudied thermal properties of D-graphene and T-graphene, two-dimensional carbon allotropes based upon the traditional graphene structure but containing a secondary, in-plane periodicity. We find that despite very similar atomic structure and bonding strength, D-graphene and T-graphene possess significantly different thermal properties than that of pristine graphene. At room temperature, the calculated thermal conductivity of D-graphene and T-graphene is 600 Wm-1K-1 and 800 Wm-1K-1 compared to over 3000 Wm-1K-1 for graphene. We attribute these distinct properties to the presence of naturally occurring, low frequency optical phonon modes that display characteristics of phonon coherence and arise from a folding of the acoustic modes and the associated frequency gap opening, a phenomenon also found in superlattices where an out of plane periodicity is introduced. Furthermore, we observe significantly enhanced Umklapp scatterings in D- and T-graphene that largely suppress the hydrodynamic phonon transport in pristine graphene. Our study presents D-graphene and T-graphene as ideal model systems to explore the coherent phonon effects in 2D and demonstrates the potential of using coherent phonon effects to significantly modify thermal transport of 2D materials without making drastic changes to their fundamental compositions.

Crossover of ballistic, hydrodynamic, and diffusive phonon transport in suspended graphene

Hydrodynamic phonon transport was recently predicted as an important regime for phonon transport in graphitic materials. Many of past studies on hydrodynamic phonon transport have focused on the cases where the hydrodynamic regime predominates over other regimes such that hydrodynamic features can be clearly observed. However, this often requires stringent conditions of temperature and sample size. In many cases, a single regime does not dominate other regimes, but all three regimes - ballistic, hydrodynamic, and diffusive regimes - exist to some extent. Here we assess the extent of three regimes by comparing momentum destruction rates by three different mechanisms, each of which represents a different regime: diffuse boundary scattering without internal phonon scattering (ballistic regime), diffuse boundary scattering combined with normal scattering (hydrodynamic regime), and umklapp scattering (diffusive regime). We solve the Peierls-Boltzmann equation with an ab initio full scattering matrix using a deviational Monte Carlo method. We sample distribution functions of ballistic and scattered particles separately, and thereby compare the momentum destruction rates by the three different mechanisms. Using this framework, we discuss a well-known phenomenon of ballistic-to-hydrodynamic crossover, called phonon Knudsen minimum.

Role of hydrodynamic viscosity on phonon transport in suspended graphene

When phonon transport is in the hydrodynamic regime, the thermal conductivity exhibits peculiar dependences on temperatures ($T$) and sample widths ($W$). These features were used in the past to experimentally confirm the hydrodynamic phonon transport in three-dimensional bulk materials. Suspended graphene was recently predicted to exhibit strong hydrodynamic features in thermal transport at much higher temperature than the three-dimensional bulk materials, but its experimental confirmation requires quantitative guidance by theory and simulation. Here we quantitatively predict those peculiar dependences using the Monte Carlo solution of the Peierls-Boltzmann equation with an ab initio full three-phonon scattering matrix. Thermal conductivity is found to increase as ${T}^{\ensuremath{\alpha}}$ where $\ensuremath{\alpha}$ ranges from 1.89 to 2.49 depending on a sample width at low temperatures, much larger than 1.68 of the ballistic case. The thermal conductivity has a width dependence of ${W}^{1.17}$ at 100 K, clearly distinguished from the sublinear dependence of the ballistic-diffusive regime. These peculiar features are explained with a phonon viscous damping effect of the hydrodynamic regime. We derive an expression for the phonon hydrodynamic viscosity from the Peierls-Boltzmann equation, and discuss the fact that the phonon viscous damping explains well those peculiar dependences of thermal conductivity at 100 K. The phonon viscous damping still causes significant thermal resistance when a temperature is 300 K and a sample width is around 1 \textmu{}m, even though the hydrodynamic regime is not dominant over other regimes at this condition.