Theory Of Thermal Transport Research Articles

Non‐Monotonic Variation of the Low Lattice Thermal Conductivity with Temperature in Penta‐HgO2 Sheet

AbstractInspired by the experimental synthesis of bulk HgO2 with the potential of exfoliation to form a penta‐HgO2 sheet composed entirely of pentagonal motifs, a detailed theoretical study on the lattice thermal conductivity by using first‐principles calculations combined with the unified theory of thermal transport is performed. It is found that the penta‐HgO2 sheet is semiconducting with an indirect bandgap of 1.18 eV and possesses a low lattice thermal conductivity of 2.07 W m−1 K−1 (3.28 W m−1 K−1) along the x (y)‐direction at 300 K. More interestingly, the variation of its thermal conductivity with temperature is non‐monotonic, different from most cases. The phonon dispersion, phonon scattering, and phonon coherence is further systematically investigated to understand the underlying physics. This results suggest that the strong intrinsic anharmonicity resulting from its unique atomic configuration with the buckled structure and the heavy element of Hg leads to a high scattering rate, resulting in the ultralow particle‐like thermal transport of 0.20 W m−1 K−1 (0.01 W m−1 K−1) in the x (y)‐direction, while the narrow average frequency interval and strong phonon linewidth are responsible for the dominant coherent thermal transport and non‐monotonic variation of the low lattice thermal conductivity of the penta‐HgO2 sheet.

Machine Learning for Predicting Ultralow Thermal Conductivity and High ZT in Complex Thermoelectric Materials.

Efficient and precise calculations of thermal transport properties and figures of merit, alongside a deep comprehension of thermal transport mechanisms, are essential for the practical utilization of advanced thermoelectric materials. In this study, we explore the microscopic processes governing thermal transport in the distinguished crystalline material Tl9SbTe6 by integrating a unified thermal transport theory with machine learning-assisted self-consistent phonon calculations. Leveraging machine learning potentials, we expedite the analysis of phonon energy shifts, higher-order scattering mechanisms, and thermal conductivity arising from various contributing factors, such as population and coherence channels. Our finding unveils an exceptionally low thermal conductivity of 0.31 W m-1 K-1 at room temperature, a result that closely correlates with experimental observations. Notably, we observe that the off-diagonal terms of heat flux operators play a significant role in shaping the overall lattice thermal conductivity of Tl9SbTe6, where the ultralow thermal conductivity resembles that of glass due to limited group velocities. Furthermore, we achieve a maximum ZT value of 3.17 in the c-axis orientation for p-type Tl9SbTe6 at 600 K and an optimal ZT value of 2.26 in the a-axis and b-axis direction for n-type Tl9SbTe6 at 500 K. The crystalline Tl9SbTe6 not only showcases remarkable thermal insulation but also demonstrates impressive electrical properties owing to the dual-degeneracy phenomenon within its valence band. These results not only elucidate the underlying reasons for the exceptional thermoelectric performance of Tl9SbTe6 but also suggest potential avenues for further experimental exploration.

Amorphous-Like Ultralow Thermal Transport in Crystalline Argyrodite Cu7PS6.

Due to their amorphous-like ultralow lattice thermal conductivity both below and above the superionic phase transition, crystalline Cu- and Ag-based superionic argyrodites have garnered widespread attention as promising thermoelectric materials. However, despite their intriguing properties, quantifying their lattice thermal conductivities and a comprehensive understanding of the microscopic dynamics that drive these extraordinary properties are still lacking. Here, an integrated experimental and theoretical approach is adopted to reveal the presence of Cu-dominated low-energy optical phonons in the Cu-based argyrodite Cu7PS6. These phonons yield strong acoustic-optical phonon scattering through avoided crossing, enabling ultralow lattice thermal conductivity. The Unified Theory of thermal transport is employed to analyze heat conduction and successfully reproduce the experimental amorphous-like ultralow lattice thermal conductivities, ranging from 0.43 to 0.58Wm-1 K-1, in the temperature range of 100-400 K. The study reveals that the amorphous-like ultralow thermal conductivity of Cu7PS6 stems from a significantly dominant wave-like conduction mechanism. Moreover, the simulations elucidate the wave-like thermal transport mainly results from the contribution of Cu-associated low-energy overlapping optical phonons. This study highlights the crucial role of low-energy and overlapping optical modes in facilitating amorphous-like ultralow thermal transport, providing a thorough understanding of the underlying complex dynamics of argyrodites.

Unraveling High Thermal Conductivity with In-Plane Anisotropy Observed in Suspended SiP2.

The anisotropic thermal transport properties of low-symmetry two-dimensional materials play an important role in understanding heat dissipation and optimizing thermal management in integrated devices. Examples of efficient energy dissipation and enhanced power sustainability have been demonstrated in nanodevices based on materials with anisotropic thermal transport properties. However, the exploration of materials with high thermal conductivity and strong in-plane anisotropy remains challenging. Herein, we demonstrate the observation of anisotropic in-plane thermal conductivities of few-layer SiP2 based on the micro-Raman thermometry method. For suspended SiP2 nanoflake, the thermal conductivity parallel to P-P chain direction (κ∥b) can reach 131 W m-1 K-1 and perpendicular to P-P chain direction (κ⊥b) is 89 W m-1 K-1 at room temperature, resulting in a significant anisotropic ratio (κ∥b/κ⊥b) of 1.47. Note that such a large anisotropic ratio mainly results from the higher phonon group velocity along the P-P chain direction. We also found that the thermal conductivity can be effectively modulated by increasing the SiP2 thickness, reaching a value as high as 202 W m-1 K-1 (120 W m-1 K-1) for κ∥b (κ⊥b) at 111 nm thickness, which is the highest among layered anisotropic phosphide materials. Notably, the anisotropic ratio always remains at a high level between 1.47 and 1.68, regardless of the variation of SiP2 thickness. Our observation provides a new platform to verify the fundamental theory of thermal transport and a crucial guidance for designing efficient thermal management schemes of anisotropic electronic devices.

The differences in bonding properties and electrical, thermal conductivity between the preferred crystallographic orientation interface of Cu3Sn/Cu

First-principles calculations based on Density-Functional theory and Semi-classical Boltzmann thermal transport theory have been applied to research the interfacial stability, electronic structures, bonding properties, and thermoelectric transport properties of different preferred crystallographic orientation interface of Cu3Sn/Cu. All interface models proved to have stable structures, the interfacial ideal adhesion of works of Cu3Sn (02¯5)/Cu (042) interface, Cu3Sn (100)/Cu (100) interface, and Cu3Sn <010>⊥Cu (100) interface are 1.956 J/m2, 1.182 J/m2, and 2.126 J/m2, respectively. The newly formed chemical bonds at the interface exhibit ionic and covalent properties. Moreover, the electrical conductivity and thermal conductivity of 16.787 × 108 S · m−1 and 1.136 × 104 W · m−1 · K−1 at 300 K for the Cu3Sn <010>⊥Cu (100) interface are superior than the other two Cu3Sn/Cu interfaces.

Recent progress and frontier issues in thermal transport theory of metals

Metal is one of the most widely used engineering materials. In contrast to the extensive research dedicated to their mechanical properties, studies on the thermal conductivity of metals remain relatively rare. The understanding of thermal transport mechanisms in metals is mainly through the Wiedemann-Franz Law established more than a century ago. The thermal conductivity of metal is related to both the electron transport and the lattice vibration. An in-depth understanding of the thermal transport mechanism in metal is imperative for optimizing their practical applications. This review first discusses the history of the thermal transport theory in metals, including the Wiedemann-Franz law and models for calculating phonon thermal conductivity in metal. The recently developed first-principles based mode-level electron-phonon interaction method for determining the thermal transport properties of metals is briefly introduced. Then we summarize recent theoretical studies on the thermal conductivities of elemental metals, intermetallics, and metallic ceramics. The value of thermal conductivity, phonon contribution to total thermal conductivity, the influence of electron-phonon interaction on thermal transport, and the derivation of the Lorenz number are comprehensively discussed. Moreover, the thermal transport properties of metallic nanostructures are summarized. The size effect of thermal transport and the Lorenz number obtained from experiments and calculations are compared. Thermal transport properties including the phonon contribution to total thermal conductivity and the Lorenz number in two-dimensional metals are also mentioned. Finally, the influence of temperature, pressure, and magnetic field on thermal transport in metal are also discussed. The deviation of the Lorenz number at low temperatures is due to the different electron-phonon scattering mechanisms for thermal and electrical transport. The difference in thermal conductivity among metals is induced by the difference in pressure among different metals and is related to the electron state at the Fermi level as well. The effect of magnetic field on thermal transport is related to the coupling between the electron and the magnetic field, therefore the electron distribution in the Brillouin zone is an important factor. In addition, this review also looks forward to the future research directions of metal thermal transport theory.

Exponential approximation of the coherence contribution to the thermal conductivity of complex clathrate-type crystals

The low-temperature properties of guest-host crystals, such as clathrates and skutterudites, offer a rich playground for discovering novel physical phenomena and developing new materials with unique properties. The temperature dependence of thermal conductivity in these materials can exhibit both crystal-like and glass-like behavior, which reflects the properties of the phonon excitations and various scattering mechanisms. The ultra-low thermal conductivity of clathrate crystals is closely related to the concept of minimal thermal conductivity, which is determined by the intrinsic phonon scattering in the material. In this work, the temperature dependence of thermal conductivity for both crystal-like and glass-like behavior of different structural types of clathrates and skutterudites was analyzed using the ”Unified theory of thermal transport in crystals and glasses” of M. Simoncelli, N. Marzari & F. Mauri. A method was proposed and tested for the coherence contribution related to wave-like tunneling and loss of coherence between different vibrational eigenstates. The temperature dependence of the coherence contribution to thermal conductivity was approximated by the exponential function of an Arrhenius type with characteristic energy E and characteristic minimal thermal conductivity parameter κ0. The coherence contribution is intertwined with other phonon scattering mechanisms, and over a wide temperature range, its temperature dependence is universal with parameters depending on the crystal structure, positional disorder, and impurity doping. This work provides insights into the temperature dependence of thermal conductivity in guest-host materials and its importance for designing and optimizing their properties for various applications, such as thermoelectric generators.

Hydrodynamic finite-size scaling of the thermal conductivity in glasses

In the past few years, the theory of thermal transport in amorphous solids has been substantially extended beyond the Allen-Feldman model. The resulting formulation, based on the Green-Kubo linear response or the Wigner-transport equation, bridges this model for glasses with the traditional Boltzmann kinetic approach for crystals. The computational effort required by these methods usually scales as the cube of the number of atoms, thus severely limiting the size range of computationally affordable glass models. Leveraging hydrodynamic arguments, we show how this issue can be overcome through a simple formula to extrapolate a reliable estimate of the bulk thermal conductivity of glasses from finite models of moderate size. We showcase our findings for realistic models of paradigmatic glassy materials.

On/off switchable interfacial thermal resistance in graphene/fullerene/graphene heterostructures

Switchable thermal devices are attracting significant research interest as a basic thermal management component. In this work, taking graphene/fullerene/graphene sandwiches as an example, we demonstrate that the interfacial thermal resistance can show a switchable, step-like change by varying the number of fullerenes in the sandwich structure. Changing the number of fullerenes causes a structural transition between the graphene layers from adhered to separated, resulting in an enhancement of about a factor of two in the interfacial thermal resistance during this on/off switchable phenomenon, which we analyze using analytic expressions based on the thermal transport theory. We further illustrate that the switchable phenomenon can also be realized by applying mechanical strain or by varying the temperature of the sandwich structure. This work demonstrates that the sandwich-liked nanoscale heterostructures can exhibit hysteretic changes in heat transport, and thus have promise for potential applications in switchable thermal devices.

Anharmonicity-induced phonon hardening and phonon transport enhancement in crystalline perovskite BaZrO3

We investigated the effects of cubic and quartic anharmonicity on lattice dynamics and thermal transport in highly anharmonic ${\mathrm{BaZrO}}_{3}$ crystal over a wide temperature range (300--2000 K) by combining the first-principles-based self-consistent phonon theory and a unified theory of thermal transport including population and coherence contributions. By considering the effects from bubble and loop diagrams, the contributions of both three-phonon (3ph) and four-phonon (4ph) interaction processes to phonon scattering rates and energy shifts were clarified. Anharmonic phonon renormalization is found to play a crucial role in determining the finite-temperature phonon energies and lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ in ${\mathrm{BaZrO}}_{3}$. Specifically, the lattice anharmonicity induces significant low-frequency optical phonon hardening at elevated temperatures, which is correlated with the U-shaped potential energy surfaces for these modes. The low-frequency optical phonon hardening significantly suppresses phonon scattering rates by altering the phonon weighted phase space of both 3ph and 4ph interaction processes, thereby leading to significant enhancement in the ${\ensuremath{\kappa}}_{\mathrm{L}}$ and weaker temperature dependence of ${\ensuremath{\kappa}}_{L}\ensuremath{\sim}{T}^{\ensuremath{-}0.75}$ than traditional harmonic treatments. Moreover, although the coherent thermal transport channel is suppressed by anharmonic phonon renormalization, it is enhanced by the 4ph scattering processes. The coherence contribution becomes nonnegligible at elevated temperatures and may contribute up to 17.38% of the total ${\ensuremath{\kappa}}_{\mathrm{L}}$ at 1500 K. In this paper, we highlight the strong influence of the lattice anharmonicity on thermal conductivity in severely anharmonic systems and the importance of coherent thermal transport channel at elevated temperatures.

High thermoelectric performance in metal phosphides MP2 (M = Co, Rh and Ir): a theoretical prediction from first-principles calculations.

Although metal phosphides have good electronic properties and high stabilities, they have been overlooked in general as thermoelectrics based on expectation of high thermal conductivity. Here we propose the metal phosphides MP2 (M = Co, Rh and Ir) as promising thermoelectrics through first-principles calculations of their thermoelectric properties. By using lattice dynamics calculations within unified theory of thermal transport in crystal and glass, we obtain the lattice thermal conductivities κl of MP2 as 0.63, 1.21 and 1.81 W m−1 K at 700 K for M = Co, Rh and Ir, respio ectively. Our calculations for crystalline structure, phonon dispersion, Grüneisen parameters and cumulative κl reveal that such low κl originates from strong rattling vibrations of M atoms and lattice anharmonicity, which significantly suppress heat-carrying acoustic phonon modes coupled with low-lying optical modes. Using mBJ exchange–correlation functional, we further calculate the electronic structures and transport properties, which are in good agreement with available experimental data, evaluating the relaxation time of charge carrier within deformation potential theory. We predict ultrahigh thermopower factors as 10.2, 7.1 and 6.4 mW m−1 K2 at 700 K for M = Co, Rh and Ir, being superior to the conventional thermoelectrics GeTe. Finally, we estimate their thermoelectric performance by computing figure of merit ZT, finding that upon n-type doping ZT can reach ∼1.7 at 700 K specially for CoP2. We believe that our work offers a novel materials platform to search for high-performance thermoelectrics using metal phosphides.

Industrial Thermal Insulation Properties above Sintering Temperatures.

Processing highly flammable products, the oil and gas (O&G) industry can experience major explosions and fires, which may expose pressurized equipment to high thermal loads. In 2020, oil fires occurred at two Norwegian O&G processing plants. To reduce the escalation risk, passive fire protection may serve as a consequence-reducing barrier. For heat or cold conservation, equipment and piping often require thermal insulation, which may offer some fire protection. In the present study, a representative thermal insulation (certified up to 700 °C) was examined with respect to dimensional changes and thermal transport properties after heat treatment to temperatures in the range of 700 °C to 1200 °C. Post heat treatment, the thermal conductivity of each test specimen was recorded at ambient temperature and up to 700 °C, which was the upper limit for the applied measurement method. Based on thermal transport theory for porous and/or amorphous materials, the thermal conductivity at the heat treatment temperature above 700 °C was estimated by extrapolation. The dimensional changes due to, e.g., sintering, were also analyzed. Empirical equations describing the thermal conductivity, the dimensional changes and possible crack formation were developed. It should be noted that the thermal insulation degradation, especially at temperatures approaching 1200 °C, is massive. Thus, future numerical modeling may be difficult above 1150 °C, due to abrupt changes in properties as well as crack development and crack tortuosity. However, if the thermal insulation is protected by a thin layer of more robust material, e.g., passive fire protection to keep the thermal insulation at temperatures below 1100 °C, future modeling seems promising.

Multichannel thermal transport in crystalline Tl3VSe4

The validity of the particlelike phonon picture in describing the thermal transport physics in strongly anharmonic crystalline materials is a subject of recent debate. On the one hand, the Peierls-Boltzmann transport equation-based particlelike treatment of phonons was found to be insufficient in explaining the experimentally observed ultralow thermal conductivity of ${\text{Tl}}_{3}\text{V}{\text{Se}}_{4}$, and subsequently another thermal transport theory based on an additional thermal transport channel was proposed. On the other hand, the validity of this multichannel transport was questioned through a higher-level theory accounting for higher-order terms. Here, using the highest level of thermal transport theory with contributions from a temperature-dependent potential energy surface, lattice thermal expansion, force constant renormalization, long-range Coulombic interactions, and higher-order quartic phonon scattering processes, the validity of multichannel thermal transport is tested for ${\text{Tl}}_{3}\text{V}{\text{Se}}_{4}$. The particlelike transport channel is found to severely underpredict the experimentally measured thermal conductivity by a factor of 3 at a temperature of 300 K. The contribution of the wavelike coherent transport channel is found to be twice that of the particlelike channel, and the total thermal conductivity from multichannel transport theory is found to be in agreement with experimental measurements.

Quantum critical thermal transport in the unitary Fermi gas

Strongly correlated systems are often associated with an underlying quantum critical point which governs their behavior in the finite temperature phase diagram. Their thermodynamical and transport properties arise from critical fluctuations and follow universal scaling laws. Here, we develop a microscopic theory of thermal transport in the quantum critical regime expressed in terms of a thermal sum rule and an effective scattering time. We explicitly compute the characteristic scaling functions in a quantum critical model system, the unitary Fermi gas. Moreover, we derive an exact thermal sum rule for heat and energy currents and evaluate it numerically using the nonperturbative Luttinger-Ward approach. For the thermal scattering times we find a simple quantum critical scaling form. Together, the sum rule and the scattering time determine the heat conductivity, thermal diffusivity, Prandtl number and sound diffusivity from high temperatures down into the quantum critical regime. The results provide a quantitative description of recent sound attenuation measurements in ultracold Fermi gases.

Thermal accommodation in nanoporous silica for vacuum insulation panels

The thermal accommodation coefficient is a measure for the quality of thermal energy exchange between gas molecules and a solid surface. It is an important parameter to describe heat flow in rarefied gases, for example, in aerospace or vacuum technology. As special application, it plays a decisive role for the thermal transport theory in silica filled vacuum insulation panels. So far, no values have been available for the material pairings of silica and various gases. For that reason, this paper presents thermal conductivity measurements under different gas-pressure conditions for precipitated and fumed silica in combination with the following gases: helium, air, argon, carbon dioxide (CO$_{2}$), sulfur dioxide (SO$_{2}$), krypton, and sulfur hexafluoride (SF$_{6}$). Additionally, a calculation method for determining thermal accommodation coefficients from the thermal conductivity curves in combination with the pore size distribution of silica determined by mercury intrusion porosimetry is introduced. The results are compared with existing models.

Unified theory of thermal transport in crystals and glasses

Crystals and glasses exhibit fundamentally different heat conduction mechanisms: the periodicity of crystals allows for the excitation of propagating vibrational waves that carry heat, as first discussed by Peierls; in glasses, the lack of periodicity breaks Peierls' picture and heat is mainly carried by the coupling of vibrational modes, often described by a harmonic theory introduced by Allen and Feldman. Anharmonicity or disorder are thus the limiting factors for thermal conductivity in crystals or glasses; hitherto, no transport equation has been able to account for both. Here, we derive such equation, resulting in a thermal conductivity that reduces to the Peierls and Allen-Feldman limits, respectively, in anharmonic-and-ordered or harmonic-and-disordered solids, while also covering the intermediate regimes where both effects are relevant. This approach also solves the long-standing problem of accurately predicting the thermal properties of crystals with ultralow or glass-like thermal conductivity, as we show with an application to a thermoelectric material representative of this class.

Unified theory of thermal transport in crystals and disordered solids

Crystals and glasses exhibit fundamentally different heat conduction mechanisms: the periodicity of crystals allows for the excitation of propagating vibrational waves that carry heat, as first discussed by Peierls; in glasses, the lack of periodicity breaks Peierls' picture and heat is mainly carried by the coupling of vibrational modes, often described by a harmonic theory introduced by Allen and Feldman. Anharmonicity or disorder are thus the limiting factors for thermal conductivity in crystals or glasses; hitherto, no transport equation has been able to account for both. In the paper https://arxiv.org/abs/1901.01964, we derive such equation, resulting in a thermal conductivity that reduces to the Peierls and Allen-Feldman limits, respectively, in anharmonic-and-ordered or harmonic-and-disordered solids, while also covering the intermediate regimes where both effects are relevant. This approach also solves the long-standing problem of accurately predicting the thermal properties of crystals with ultralow or glass-like thermal conductivity, as we show with an application to a thermoelectric material representative of this class. This database contains the raw data related to the images reported in the paper https://arxiv.org/abs/1901.01964.

Emergence of Fourier's Law of Heat Transport in Quantum Electron Systems.

The microscopic origins of Fourier's venerable law of thermal transport in quantum electron systems has remained somewhat of a mystery, given that previous derivations were forced to invoke intrinsic scattering rates far exceeding those occurring in real systems. We propose an alternative hypothesis, namely, that Fourier's law emerges naturally if many quantum states participate in the transport of heat across the system. We test this hypothesis systematically in a graphene flake junction and show that the temperature distribution becomes nearly classical when the broadening of the individual quantum states of the flake exceeds their energetic separation. We develop a thermal resistor network model to investigate the scaling of the sample and contact thermal resistances and show that the latter is consistent with classical thermal transport theory in the limit of large level broadening.

A wave theory of heat transport with applications to Kapitsa resistance and thermal rectification.

We develop a theory of thermal transport in nanoscale-layered structures based on wave processes. The theory incorporates two fundamental principles, first, that the spectra of thermally excited waves are determined by the temperature differential and the heat flux, and second, that the wave fields in the heat exchanging domains are coupled. The developed method includes classical theories as special cases that are valid in larger scales, and it naturally explains such phenomena as interface thermal resistance (Kapitsa resistance) and thermal rectification (asymmetry of thermal transport). Numerical examples demonstrate the feasibility of the approach, and they show good agreement with measurements of Kapitsa resistance reported in the literature.

Probing the Thermodynamic Stability and Phonon Transport in Two-Dimensional Hexagonal Aluminum Nitride Monolayer

Discovery of graphene and its astonishing properties have drawn great interest in new two-dimensional (2D) materials for practical applications in micro- and nanodevices. 2D hexagonal aluminum nitride monolayer (h-AlN), a III–V group wide-bandgap semiconductor, has promising applications in optoelectronics and energy conversion. Unfortunately, their high temperature thermodynamic stability and thermal transport properties have not been reported. Here we investigate these properties, for the first time, of monolayer h-AlN using both equilibrium and nonequilibrium molecular dynamics simulations. We find that h-AlN has a very high melting point in the range of 3500–4000 K due to the strong Al–N covalent bonding. On the basis of the kinetic theory of thermal transport and quantum corrections, the intrinsic in-plane thermal conductivity of ∼264.1 W m–1 K–1 and phonon mean free path of ∼154 nm of h-AlN are estimated at quantum-corrected room temperature. The analysis of phonon transport properties demonstrates ...