Ballistic Thermal Transport Research Articles

Modeling heat conduction with dual-dissipative variables: A mechanism-data fusion method.

Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.

Introduction of Asymmetry to Enhance Thermal Transport in Porous Metamaterials at Low Temperature

Introducing porosity with different degrees of disorder has been widely used to regulate thermal properties of materials, which generally results in decrease of thermal conductivity. We investigate the thermal conductivity of porous metamaterials in the ballistic transport region by using the Lorentz gas model. It is found that the introduction of asymmetry and Gaussian disorder into porous metamaterials can lead to a strong enhancement of thermal conductivity. By dividing the transport process into ballistic transport, non-ballistic transport, and unsuccessful transport processes, we find that the enhancement of thermal conductivity originates from the significant increase ballistic transport ratio. The findings enhance the understanding of ballistic thermal transport in porous materials and may facilitate designs of high-performance porous thermal metamaterials.

Real-time imaging of acoustic waves in bulk materials with X-ray microscopy

The dynamics of lattice vibrations govern many material processes, such as acoustic wave propagation, displacive phase transitions, and ballistic thermal transport. The maximum velocity of these processes and their effects is determined by the speed of sound, which therefore defines the temporal resolution (picoseconds) needed to resolve these phenomena on their characteristic length scales (nanometers). Here, we present an X-ray microscope capable of imaging acoustic waves with subpicosecond resolution within mm-sized crystals. We directly visualize the generation, propagation, branching, and energy dissipation of longitudinal and transverse acoustic waves in diamond, demonstrating how mechanical energy thermalizes from picosecond to microsecond timescales. Bulk characterization techniques capable of resolving this level of structural detail have previously been available on millisecond time scales-orders of magnitude too slow to capture these fundamental phenomena in solid-state physics and geoscience. As such, the reported results provide broad insights into the interaction of acoustic waves with the structure of materials, and the availability of ultrafast time-resolved dark-field X-ray microscopy opens a vista of new opportunities for 3D imaging of materials dynamics on their intrinsic submicrosecond time scales.

Ballistic Thermal Transport at Sub‐10 nm Laser‐Induced Hot Spots in GaN Crystal (Adv. Sci. 2/2023)

Ballistic Thermal Transport In this article number 2204777, Yanan Yue and co-workers develop a tip-enhanced Raman thermometry to study ballistic thermal transport within 10 nm in GaN, simultaneously achieving local laser heating and temperature probing. The phonon mean free path is predicted which can find wide application in the thermal management of GaN-based electronics.

Ballistic Thermal Transport at Sub-10nm Laser-Induced Hot Spots in GaN Crystal.

Ballistic thermal transport at nanoscale hotspots will greatly reduce the performance of a Gallium nitride (GaN) device when its characteristic length reaches the nanometer scale. In this work, the authors develop a tip-enhanced Raman thermometry approach to study ballistic thermal transport within the range of 10nm in GaN, simultaneously achieving laser heating and measuring the local temperature. The Raman results show that the temperature increase from an Au-coated tip-focused hotspot up to two times higher (40 K) than that in a bare tip-focused region (20 K). To further investigate the possible mechanisms behind this temperature difference, the authors perform electromagnetic simulations to generate a highly focused heating field, and observe a highly localized optical penetration, within a range of 10nm. The phonon mean free path (MFP) of the GaN substrate can thus be determined by comparing the numerical simulation results with the experimentally measured temperature increase which is in good agreement with the average MFP weighted by the mode-specific thermal conductivity, as calculated from first-principles simulations. The results demonstrate that the phonon MFP of a material can be rapidly predicted through a combination of experiments and simulations, which can find wide application in the thermal management of GaN-based electronics.

The ballistic and diffusive thermal transport in low-dimensional structures

The thermal transport property in low-dimensional structures has been studied theoretically taking into account the effect of temperature on phonon–phonon coupling. New thermal-transport equations are developed to discriminatively treat the ballistic and diffusive thermal transport in quantum structures. Using the new thermal transport equations, the thermal transport properties in GaAs nanowire and zigzag graphene nanoribbon are investigated to demonstrate the crossover from ballistic to diffusive thermal transport.

Nonequilibrium Electrical, Thermal and Spin Transport in Open Quantum Systems of Topological Superconductors, Semiconductors and Metals

We study nonequilibrium transport in various open quantum systems whose systems and leads/baths are made of topological superconductors (TSs), semiconductors, and metals. Using quantum Langevin equations and Green’s function method, we derive exact expressions for steady-state electrical, thermal, and spin current at the junctions between a system and leads. We validate these current expressions by comparing them with the results from direct time-evolution simulations. We then show how an electrical current injected in TS wires divides into two parts carried by single electronic excitations and Cooper pairs. We further show ballistic thermal transport in an open TS wire in the topological phase under temperature or voltage bias. The thermal current values grow significantly near the topological phase transition, where thermal conductance displays a sharp quantized peak as predicted earlier. We relate the quantized thermal conductance to the zero-frequency thermoelectric transmission coefficient of the open TS wire. We also observe a large thermoelectric current near the topological transition of the TS wires. We introduce a differential spin conductance which displays a quantized zero-bias peak at zero temperature for a spinful TS wire in the topological phase. The role of superconducting baths in transport is demonstrated by thoroughly examining the features of zero-temperature differential electrical conductance and thermal conductance in open systems with TS baths. Our new thermoelectric and spin transport findings in various two-terminal geometries are beneficial to the present challenges in probing the emergence of Majorana quasi-particles in experiments.

Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source

In the paper we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The dynamics of the lattice is described by an infinite system of stochastic ordinary differential equations with white noise in the right-hand side, which models the point heat source. On the base of the previous analytical unsteady analysis an analytical formula in continuum approximation is suggested, which allows one to describe a steady-state kinetic temperature distribution in the graphene lattice in continuum approximation. The obtained solution is in a good agreement with numerical results obtained for the discrete system everywhere excepting a neighbourhood of six singular rays with the origin at the heat source location. The continuum solution becomes singular at these rays, unlike the discrete one, which appears to be localized in a certain sense along the rays. The factors, which cause such a directional localization and the mismatch between the continuum and discrete solutions are discussed. We expect that the suggested formula is applicable for various damped polyatomic lattices where all particles have equal masses in the case of universal for all particles external viscosity.

Ballistic heat conduction in semiconductor nanowires

Ballistic thermal transport is a remarkable nanoscale phenomenon with possible applications in microelectronics. In the past decade, research on ballistic thermal transport focused on the measurements of length-dependent thermal conductivity in semiconductor nanowires. In this Perspective article, we review the experimental demonstrations of this phenomenon in nanowires of various materials and sizes and at different temperatures. Our literature analysis reveals a controversy between works reporting two distinct pictures of ballistic conduction: perfectly ballistic conduction even at room temperature and weak quasi-ballistic conduction mainly below room temperature. Simulations seem to support the weaker version of the effect. Thus, future experiments are expected to resolve this controversy.

Ballistic magnetic thermal transport coupled to phonons

Motivated by thermal conductivity experiments in spin chain compounds, we propose a phenomenological model to account for a ballistic magnetic transport coupled to a diffusive phononic one, along the line of the seminal two-temperature diffusive transport Sanders-Walton model. Although the expression for the effective thermal conductivity is identical to that of Sanders-Walton, the interpretation is entirely different, as the "magnetic conductivity" is replaced by an "effective transfer conductivity" between the magnetic and phononic component. This model also reveals the fascinating possibility of visualizing the ballistic character of magnetic transport, for appropriately chosen material parameters, as a two peak counter-propagating feature in the phononic temperature. It is also appropriate for the analysis of any thermal transport experiment involving a diffusive component coupled to a ballistic one.

Ballistic thermal rectification in asymmetric homojunctions.

Ballistic thermal rectification is of significance for the management of thermal transport at the nanoscale since the size of thermal devices shrinks down to the phonon mean free path. By using the single-particle Lorentz gas model, the ballistic thermal transport in asymmetric homojunctions is investigated. The ballistic thermal rectification of the asymmetric rectangular homojunction is enhanced by the increasing structural asymmetry. A hyperbolic tangent profile is introduced to the interface to study the effect of interface steepness on thermal transport. We find that the thermal rectification ratio increases with the decreasing interface steepness, indicating that a gradual interface is of benefit to increase the thermal rectification. Moreover, the thermal rectification of the asymmetric homojunction can be improved by either increasing the temperature gradient or decreasing the average temperature of two heat sources.

MCBTE: A variance-reduced Monte Carlo solution of the linearized Boltzmann transport equation for phonons

MCBTE solves the linearized Boltzmann transport equation for phonons in three-dimensions using a variance-reduced Monte Carlo solution approach. The algorithm is suited for both transient and steady-state analysis of thermal transport in structured materials with size features in the nanometer to hundreds of microns range. The code is portable and integrated with both first-principles density functional theory calculations and empirical relations for the input of phonon frequency, group velocity, and mean free path required for calculating the thermal properties. The program outputs space- and time-resolved temperature and heat flux for the transient study. For the steady-state simulations, the frequency-resolved contribution of phonons to temperature and heat flux is written to the output files, thus allowing the study of cumulative thermal conductivity as a function of phonon frequency or mean free path. We provide several illustrative examples, including ballistic and quasi-ballistic thermal transport, the thermal conductivity of thin films and periodic nanostructures, to demonstrate the functionality and to benchmark our code against available theoretical/analytical/computational results from the literature. Moreover, we parallelize the code using the Matlab Distributed Computing Server, providing near-linear scaling with the number of processors. Program summaryProgram Title:MCBTECPC Library link to program files:https://doi.org/10.17632/rzn86w7t3p.1Developer's repository link:https://github.com/abhipath90/MCBTECode Ocean capsule:https://codeocean.com/capsule/7196257Licensing provisions: GPLv3Programming language: MATLABNature of problem: Calculation of time- and space-dependent temperature and heat flux profiles, and frequency-resolved effective thermal conductivity in structured systems where heat is carried by phonons.Solution method: Solution of linearized Boltzmann transport equation for phonons, variance-reduced Monte Carlo approach.Additional comments including restrictions and unusual features: Runtime about 1 to 10 hours on a personal computer.

Mean Free Path Suppression of Low-Frequency Phonons in SiGe Nanowires.

Accurate measurements of the size-dependent lattice thermal conductivity (κl) of alloy nanostructures are challenging but help to address outstanding questions on the effects of atomic disorder and surface roughness on low-frequency vibrational modes in functional materials. Here, we report sensitive κl measurements of multiple segments of the same individual SiGe nanowires. In contrast to a previous report of ballistic thermal transport over several microns in SiGe nanowires, the obtained κl are nearly independent of the segment length from 2 to 10 μm and the temperature between 150 and 300 K. The results are in agreement with a theoretical calculation based on the virtual crystal approximation of the vibrational modes as phonons with mean free paths suppressed by purely diffuse surface scattering. The findings inform continuing theoretical efforts for understanding the roles of different types of vibrational modes in thermal transport in disordered thermoelectric and electronic materials.

Ballistic thermal transport in asymmetric Y-branch three terminal junction

The thermal transport properties of Y-branch three terminal junction are studied by using the scattering-matrix method for in-plane waves. The mode conversion has been considered for two transmitted components (P wave and SV wave). The results show that the phonon mode separation behavior exists not only at low incident frequencies but also at high incident frequencies. The non-integer quantization thermal conductance has been found. Furthermore, the transmission coefficients of acoustic phonon in both branches can be modulated by the phonon nanocavity length L. The work suggests that such Y-branch structure can be act as a thermal shunt.

Semiballistic thermal conduction in polycrystalline SiGe nanowires

Ballistic heat conduction remains a controversial nanoscale phenomenon because of its occurrence and strength depending on the material, alloy composition, and temperature. Here, we discuss the impact of ballistic thermal conduction and compare the results with theoretical predictions. We experimentally investigate ballistic thermal transport in SiGe polycrystalline nanowires by measuring the length dependence of thermal conductivity for different alloy compositions and temperatures. At room temperature, our experiments show that ballistic effects are negligible in nanowires made of pure polycrystalline Si but become stronger as the Ge composition increases. As we decreased the temperature, we observed that ballistic contribution becomes even stronger.

Strained effects on the thermal conductance of flexural and in-plane modes in graphene nanoribbons

Ballistic thermal transport properties in graphene nanoribbon modulated with strain are investigated by non-equilibrium Green’s function approach. The results show that the strain can suppress the phonon transport of flexural phonon mode (FPM) and enhance the phonon transport of in-plane mode (IPM) in low-frequency region, leading to the reduction in the thermal conductance of FPM and the enhancement in the thermal conductance of IPM. The total thermal conductance is decreased by strain as the reduction in the thermal conductance of FPM overcomes the enhancement in the thermal conductance of IPM.

High intrinsic ZT in InP3 monolayer at room temperature

Two-dimensional thermoelectric (TE) materials which have the figure of merit ZT that is greater than 1.5 at room temperature would be highly desirable in energy conversion since the efficiency is competitive to conventional energy conversion techniques. Here, we report that the indium triphosphide (InP3) monolayer shows a large ZT of 1.92 at 300 K, based on the quantum calculations within the ballistic thermal transport region. A remarkably low and isotropic phononic thermal conductivity is found due to the flat lattice vibration modes, which takes a major responsibility for the impressively high ZT at room temperature. Moreover, a large ZT of 1.67 can still be achieved even under a 1% mechanical tension on the lattice. These results suggest that the InP3 monolayer is a promising candidate for low dimensional TE applications.

Graphite gets a second sound

Thermal Transport Between the two extremes of ballistic and diffusive lattice thermal transport is the potential for an exotic wave-like state known as second sound. Huberman et al. used fast, transient thermal grating measurements to show the existence of second sound in graphite between 85 and 125 kelvin (see the Perspective by Shi). Previous observations of second sound have been rare, confined to isotopically pure materials at very low temperatures. The observation of second sound in graphite is likely due to its layered nature, suggesting that this thermal transport mode may be accessible in other two-dimensional materials. Science , this issue p. [375][1]; see also p. [332][2] [1]: /lookup/doi/10.1126/science.aav3548 [2]: /lookup/doi/10.1126/science.aax2319

Observation of second sound in graphite at temperatures above 100 K.

Wavelike thermal transport in solids, referred to as second sound, is an exotic phenomenon previously limited to a handful of materials at low temperatures. The rare occurrence of this effect restricted its scientific and practical importance. We directly observed second sound in graphite at temperatures above 100 kelvins by using time-resolved optical measurements of thermal transport on the micrometer-length scale. Our experimental results are in qualitative agreement with ab initio calculations that predict wavelike phonon hydrodynamics. We believe that these results potentially indicate an important role of second sound in microscale transient heat transport in two-dimensional and layered materials in a wide temperature range.

Theoretical study of interface thermodynamic properties of 1,3,5-triamino-2,4,6-trinitrobenzene based polymer bonded explosives

The thermodynamic properties of insensitive high explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) based polymer bonded explosives (PBXs) are investigated by using first principle calculation and molecular dynamics simulation. The results include the phonon dispersion relations, interface thermal conductances, and thermal conductivities of TATB based PBXs. Both TATB and PVDF structures are optimized, in which the optimized lattice constants accord with previous results. The phonon dispersion relation of TATB and PVDF are calculated based on lattice dynamics. All interatomic force constants are calculated by the finite displacement method (numerical derivatives from perturbed supercells). The calculated phonon dispersion relation of TATB and heat capacity are in general agreement with experimental and theoretical results. The imaginary frequencies are observed in both TATB and PVDF dispersion relation. The imaginary frequencies are mainly due to the smaller calculated supercell size and temperature effect. The phonon mode of TATB and PVDF are assigned at Γ point. Based on the calculated phonon dispersion, some information including heat capacity, phonon density of states and phonon mode assignment is derived. The TATB possesses 144 phonon modes including 3 acoustic-phonon modes and 141 optical phonon modes. The anylized phonon mode of TATB shows that -NO<sub>2</sub> dominates the phonon DOS in low frequency zone, phenyl rings dominate in middle frequency zone and -NH<sub>2</sub> dominates in high frequency zone. By analyzing the phonon density of states and capacity, both TATB and PVDF imply that low-frequency vibration dominates the thermal conductivity. The thermal conductivity is determined for TATB by using the equlibrium molecular dynamics method and an established TATB force field. The TATB model is built with 2880 atoms. The structure of TATB is optimized by using molecular mechanics, then this system is relaxed by using a Nose-Hoover thermostat and barostat with a damping factor of 50 fs cin time steps of 0.1 fs. The calcultated thermal conductivity at room temperature shows good agreement with experimental result. The interface thermal conductance of TATB-PVDF is calculated by using a diffusive mismatch model. The interface thermal transport still follows Fourier’s law of heat conduction, and ballistic thermal transport mechanism is not involved. By using the above results, the thermal conductivity of mixture TATB-PVDF system is analized with a simple series model. The particle size smaller than 100 nm significantly suppresses the mixture system thermal conductivity.