Phonon Mean Free Path Research Articles

Dual Crystal-Liquid Thermal Transport Behavior in MAPbCl3.

Phonon dynamics in organic-inorganic hybrid perovskites (OIHPs) exhibit inherent complexity driven by the intricate interactions between rotatable organic cations and dynamically disordered inorganic octahedra, mediated by hydrogen bonding. This study aims to address this complexity by investigating the thermal transport behavior of MAPbCl3 as a gateway to the OIHPs family. The results reveal that the ultralow thermal conductivity of MAPbCl3 arises from a synergistic interplay of exceptionally low phonon velocities, short phonon lifetimes, and phonon mean free paths approaching the Regel-Ioffe limit. Additionally, the thermal conductivity of MAPbCl3 approaches its theoretical amorphous limit across a broad temperature range, with its thermal transport behavior transitioning from crystal-like to more liquid-like during the orthorhombic-to-cubic phase transitions. Furthermore, a phonon drag effect is observed at 17K, with Umklapp scattering serving as the predominant phonon resistive mechanism in the orthorhombic phase. In contrast, dynamic lattice distortions caused by the jumping rotation of MA+ cations become the primary factors influencing thermal transport in the cubic phase.

Grain Shape Dependent Thermal Conductivity of Polycrystalline Nanostructure

ABSTRACT We employed phonon transport simulations to provide insights into the relation between the grain shape of polycrystalline nanostructures and their thermal conductivity. Two types of polycrystalline nanostructures were modeled by using space-filling structures: one comprised of only a single grain shape (body-centered cubic, face-centered cubic, and simple cubic), and the other featuring two grains of differing sizes constructed by truncating vertices of cubes and filling the resulting volume. For the latter structures, various polycrystalline structures were created by tuning the truncation volume. Our phonon transport simulations in polycrystalline structures consisting of only single shape grains revealed that the boundary-scattering phonon mean free path, which determines the thermal conductivity of nanostructured materials, can vary by up to 10% depending on the grain shape. In addition, the mean free path increases with greater disparities in grain size in the polycrystalline nanostructures, with variations reaching up to about 10%. Furthermore, we found that the mean free path derived from phonon transport simulations is quantitatively consistent with the grain volume-to-surface area ratio in modeled polycrystalline nanostructures. This consistency indicates that the mean free path in polycrystalline nanostructures can be predicted using descriptors based on their fundamental structural features, without the need for numerical simulations.

Phonon spectroscopy and features of low-temperature heat capacity of solid solutions of electrolytes

The kinetic characteristics of thermal frequency phonons in the region of helium temperatures in ceramic samples of the Ce1–xGdxO2–y electrolyte solid solution have been studied. To explain the temperature dependence of the phonon mean free path, we used the previously performed calculations of the energy of vacancy formation in the anion sublattice of a solid solution of zirconium dioxide stabilized by yttrium ZrO2:Y2O3 (YSZ) with a similar crystal structure. It is shown that in the Ce1–xGdxO2–y system under study, the formation of structural defects associated with the presence of vacancies in the anion sublattice with energy Δ = 8.53 K is possible. It has been established that analysis of the temperature dependences of the YSZ heat capacity allows one to trace the degree of disorder (amorphization) of the solid solution depending on its level of stabilization.

Unveiling the impact of four-phonon scattering on thermal transport properties of the bulk β-Ga2O3 and monolayer Ga2O3

In recent years, the role of four-phonon (4ph) scattering in thermal transport properties has been gradually revealed. However, the underlying scattering mechanisms of the bulk β-Ga2O3 and monolayer Ga2O3 remain unclear. Hence, we evaluate the effect of 4ph scattering on the thermal transport properties of the bulk β-Ga2O3 and monolayer Ga2O3 by utilizing first-principles calculations. It has been observed that the Young's modulus and lattice thermal conductivity (κ) of the bulk β-Ga2O3 are anisotropic, while the values of the monolayer Ga2O3 are isotropic. The κ of the bulk β-Ga2O3 along the three directions ([100], [010], and [001]) and monolayer Ga2O3 after adding 4ph scattering are decreased by 9.23%, 11.52%, 13.89%, and 29.24% at 300 K, respectively. Moreover, the effect of four-phonon scattering is more pronounced at the high temperature. Afterwards, based on the phonon behaviors, we can prove that the addition of 4ph scattering can increase the phonon scattering rate, decrease the phonon mean free path, and increase the phase space, which results in lower thermal conductivity. The findings can contribute to a better understanding of high-order phonon scattering mechanisms of the Ga2O3 materials.

Probing the Temperature-Dependent Thermal Conductivity of Violet Phosphorus via Optothermal Raman Spectroscopy.

The temperature-dependent thermal conductivity of violet phosphorus on a perforated SiO2/Si substrate has been investigated via optothermal Raman spectroscopy. The obtained temperature coefficients of the Tg mode and Ptub mode of the violet phosphorus sample are -0.01268 and -0.01789 cm-1 K-1, respectively. On the basis of the temperature coefficients and power coefficients, the thermal conductivity of the violet phosphorus has been calculated to be 44.642 ± 4.995 W/mK at room temperature, which is higher than that of other two-dimensional materials such as black phosphorus and MoS2 due to the effect of boundary scattering and the phonon mean free path. Additionally, the thermal conductivity of violet phosphorus decreases as a power exponential function of the temperature, which is primarily associated with the phonon mean free path and phonon group velocity. This work provides a scientific foundation for thermal management and heat dissipation in designing micro-nano devices with violet phosphorus.

Colloidal synthetic environmental design towards high-density twin boundaries and boosted thermoelectric performance in Cu5FeS4 icosahedrons

High-density twin boundaries can significantly influence materials’ functional and mechanical properties. In thermoelectrics, twin engineering is able to manipulate the carrier and phonon transport in semiconductors, leading to improved dimensionless figure of merit (zT). However, obtaining twin boundaries with tunable density and uniform distribution in thermoelectric semiconductors is rather challenging. Here, by precisely controlling the temperature of sulfur precursor, the particle size of synthesized Cu5FeS4 icosahedrons can be decreased to produce higher-density twin boundaries. Accordingly, the optimized average distance between two adjacent twin boundaries matches the mean free path of phonons but is much larger than that of carriers, thereby efficiently lowering the lattice thermal conductivity without affecting the carrier mobility significantly. In combination with the enhanced power factor caused by increased carrier concentration, a maximal zT of 0.95 is achieved at 773 K in a p-type Cu5FeS4 derivative material, which is one of the highest values among those in Earth-abundant, environmentally-friendly thermoelectric sulfides. This work uncovers the crucial role of high-density twin boundaries in decoupling the carrier and phonon transport for improved thermoelectric performance in Cu5FeS4-based materials.

Enhancing the thermal conductivity of semiconductor thin films via phonon funneling

The second law of thermodynamics asserts that energy diffuses from hot to cold. The resulting temperature gradients drive the efficiencies and failures in a plethora of technologies. However, as the dimensionalities of materials shrink to the nanoscale regime, proper heat dissipation strategies become more challenging since the mean free paths of phonons become larger than the characteristic length scales. This leads to temperature gradients that are dependent on interfaces and boundaries, which ultimately can lead to severe thermal bottlenecks. Herein, we uncover a phenomenon which we refer to as ‘phonon funneling’, that allows the control of phonon transport to preferentially direct phonon energy away from geometrically confined interfacial thermal bottlenecks and into localized colder regions. This phenomenon supersedes heat diffusion based on the macroscale temperature gradients, thus introducing a nanoscale regime in which boundary scattering increases the phonon thermal conductivity of thin films, an opposite effect than what is traditionally realized. This work advances the fundamental understanding of phonon transport at the nanoscale and the role of efficient scattering methods for enhancing thermal transport.

Research of the impact of uniaxial tension on the thermoelectric properties of NbCoX (X=Ge, Sn, Pb) compounds

Half-Heusler materials have been confirmed as excellent thermoelectric materials. To simulate the stress conditions in engineering applications, we adopt uniaxial tensile strain to assess the impact of lattice changes on NbCoX (X=Ge, Sn, Pb) compound's thermoelectric performance. The research reveals that when NbCoX compounds are stretched by 1.5 %, the material almost does not decrease the power factor but significantly reduces thermal conductivity, thereby enhancing the ZT value. At a carrier concentration of 1E22 cm−3 and a temperature of 873 K, the predicted ZT values for p-type NbCoSn compound reach 0.359 and 0.354 after stretching by 1.5 % in the x-y and z directions, respectively. Compared to the previous original values, this improvement is approximately 1.5 times, highlighting the significant role of tensile strain in enhancing thermoelectric performance. This may be attributed to changes in compound lattice symmetry induced by strain, leading to increased defects and interfaces, which complicate phonon transport paths, resulting in a decrease in the average phonon mean free path and consequently lowering thermal conductivity. Additionally, with the increase in atomic number of Ge, Sn, and Pb, their thermoelectric figure of merit also increases continuously, with ZT values remaining higher under stretching than compression. Such research provides a new avenue for designing and optimizing high-performance thermoelectric materials and offers insights into strain engineering for future exploration of thermoelectric materials.

Anomalously strong size effect on thermal conductivity of diamond microparticles

Diamond has the known highest thermal conductivity of around 2000 W m−1 K−1 and is, therefore, widely used for heat dissipation. In practical applications, synthetic diamond microparticles are usually assumed to have similar thermal conductivity to that of bulk diamond because the particle size is larger than the theoretical phonon mean free path, so that boundary scattering of heat-carrying phonons is absent. In this report, we find that the thermal conductivity of diamond microparticles anomalously depends on their sizes. The thermal conductivity of diamond microparticles increases from 400 to 2000 W m−1 K−1 with the size growing from 20 to 300 μm. We attribute the abnormally strong size effect to the long-range defects during the growth process based on analysis of point defects, dislocations, and thermal penetration depth dependence of thermal conductivity. Our results play a vital role in the design of diamond composites and in the improvement of the thermal conductivity of synthetic diamonds.

Investigation of the thermal conductivity of SiO2 glass using molecular dynamics simulations

AbstractA recent study showed that generating local crystalline paths within a glassy matrix provides only a moderate increase in thermal conductivity until the path fills most of the total volume. It was indicated that percolation theory governs the thermal conductivity in such crystalline‐implanted glass composites. In this study, we use computer simulations to investigate the effect of partial vitrification by breaking structural order of silica crystals by local vitrification. Such locally vitrified crystal structures are made by the bond‐transposition method, where the extent of vitrification can be tuned. Also, we test melt‐quenching of three SiO2 crystalline structures (α‐quartz, coesite, and stishovite) to make silica glasses with different densities. The cooling rates and pressures were varied during the melting process in order to obtain glass structures with varied degrees of order. Our results show that the thermal conductivity of silica glasses calculated using Green–Kubo relation decreases rapidly as soon as the crystallinity is disturbed by bond transition or generated local glassy phase. This implies the phonon mean free path rapidly shrinks with even a small number of scatterers, regardless of the original polymorph. Through the investigation of the pressure effect, a strong proportional relation between the thermal conductivity and the density is found among all silica samples. Such correlation can be accounted by assuming a constant integral term in the Green–Kubo relation without the volume scaling, which is reasonable based on a weak dependence of κV on the density of silica glass except with a slight increase at low quench pressures. We hypothesize that when the quench pressure increases moderately, an increase of characteristic ring size tends to generate a more flexible SiO2 structure which results more phonon scattering. Green–Kubo modal analysis further shows that the contribution from modes at low frequencies is suppressed when SiO2 is melt‐quenched at higher pressure and vice versa.

Thermal properties of In2O3 and α-Ga2S3 compounds

We investigate the thermal conductivity of In₂O₃ and α-Ga₂S₃ lattices using simulations based on the Boltzmann phonon transport equation (BTE) and first-principles calculations. The study employs a real-space finite displacement method to determine the second- and third-order interatomic force constants (IFCs), which are critical for solving the BTE iteratively. Our findings indicate that In₂O₃ and α-Ga₂S₃ exhibit relatively low thermal conductivities compared to other wide-bandgap semiconductors. At room temperature (300 K), the calculated isotropic thermal conductivity of cubic In₂O₃ is 16.2 Wm−1K⁻1. For monoclinic α-Ga₂S₃, the three principal components of thermal conductivity are 17.0, 20.7, and 15.2 W m⁻1 K⁻1, depending on the crystallographic direction. This low thermal conductivity is primarily attributed to significant phonon scattering via three-phonon processes. Furthermore, we estimate the phonon mean free path (MFP) to be approximately 56 nm for In₂O₃ and between 198 and 231 nm for α-Ga₂S₃, varying with crystal orientation. These findings offer valuable insights into the thermal transport properties of In₂O₃ and α-Ga₂S₃, highlighting their potential for thermoelectric applications while delineating the constraints these properties impose on their use in electronic devices.

In-Plane Overdamping and Out-Plane Localized Vibration Contribute to Ultralow Lattice Thermal Conductivity of Zintl Phase KCdSb.

Zintl phases typically exhibit low lattice thermal conductivity, which are extensively investigated as promising thermoelectric candidates. While the significance of Zintl anionic frameworks in electronic transport properties is widely recognized, their roles in thermal transport properties have often been overlooked. This study delves into KCdSb as a representative case, where the [CdSb4/4]- tetrahedrons not only impact charge transfer but also phonon transport. The phonon velocity and mean free path, are heavily influenced by the bonding distance and strength of the Zintl anions Cd and Sb, considering the three acoustic branches arising from their vibrations. Furthermore, the weakly bound Zintl cation K exhibits localized vibration behaviors, resulting in strong coupling between the high-lying acoustic branch and the low-lying optical branch, further impeding phonon diffusion. The calculations reveal that grain boundaries also contribute to the low lattice thermal conductivity of KCdSb through medium-frequency phonon scattering. These combined factors create a glass-like thermal transport behavior, which is advantageous for improving the thermoelectric merit of zT. Notably, a maximum zT of 0.6 is achieved for K0.84Na0.16CdSb at 712 K. The study offers both intrinsic and extrinsic strategies for developing high-efficiency thermoelectric Zintl materials with extremely low lattice thermal conductivity.

Insight into the TiO2 on transport behavior and heat transfer of the CaO–SiO2–FeO–MgO system at different basicities: Molecular dynamics simulation and thermodynamics

In order to promote the resource utilization of Ti-containing converter slag and reduce the loss of metallic Ti, it is necessary to clarify the relationship between the oxygen network structure and thermophysical properties of the slag. The present work uses classical molecular dynamics (CMD) simulation to study the effects of basicity (1.0–3.0) and TiO2 content (0%–10 %) on the local structural properties, viscosity, and thermal conductivity of the CaO–SiO2–FeO–MgO–TiO2 (CSFMT) system at 1873 K. The M − O (M = Ca, Si, Fe, Mg, and Ti) bond length calculated based on CMD is consistent with the experimental results, and the [SiO4] tetrahedron and [TiO6] octahedron are the basic structural units of the CSFMT system. The increase in basicity promotes the break of bridging oxygen (BO) Si–O–Si and the formation of non-bridging oxygen Si–O-M. The increase in TiO2 content promotes the formation of Ti–O–Si in the system. The basicity and TiO2 content affect the thermophysical properties of the CSFMT system by promoting and inhibiting the depolymerization of the oxygen network structure, respectively. The diffusion abilities of different atoms in the CSFMT system are in descending order of Fe > Mg > Ca > O > Si > Ti. The viscosity of the CSFMT system decreases with increasing basicity and increases with increasing TiO2 content. Increasing the proportion of BOs can weaken the anharmonicity in the polyhedral structural units and reduce phonon scattering. With increasing basicity and TiO2 content, the effective phonon mean free path decreases and increases, respectively, resulting in a decrease and an increase in the thermal conductivity of the CSFMT system. The changes in the microstructure properties of the CSFMT system can be reasonably explained by the changes in its thermodynamic properties such as enthalpy. It is worth noting that the basicity has a greater effect on the viscosity, while the TiO2 content has a more significant impact on the thermal conductivity of the CSFMT system.

The low-temperature thermal conduction and millimeter-wave dielectric properties of β-Si3N4 as a heat-dissipation substrate

Increasing operating frequency is required in wireless communication systems. In use, this generates heat, which results in serious problems for semiconductor devices. Silicon nitride (Si3N4) has high thermal conductivity and fracture strength. Therefore, it is expected to be suitable for heat dissipation in active circuit substrates for wireless communication. In this study, Si3N4 with varying thermal conductivities were prepared by controlling starting material and sintering conditions and their low-temperature thermal conductivities were measured. The mean free path of phonons in β-Si3N4 influences its thermal conductivity. The temperature dependence of the Debye–Waller factor obtained by synchrotron radiation scattering supported the high thermal conductivity of the β-Si3N4. The degradation of thermal conductivity was interpreted in terms of the full width at half maximum of Raman spectra. Further, infrared reflectivity and first-principles calculation for β-Si3N4 confirmed their superior dielectric properties compared with other high thermal conductive materials.

Effects of ballistic transport on the thermal resistance and temperature profile in nanowires

Effects of ballistic transport on the temperature profiles and thermal resistance in nanowires are studied. Computer simulations of nanowires between a heat source and a heat sink have shown that in the middle of such wires the temperature gradient is reduced compared to Fourier’s law with steep gradients close to the heat source and sink. In this work, results from molecular dynamics and phonon Monte Carlo simulations of the heat transport in nanowires are compared to a radiator model which predicts a reduced gradient with discrete jumps at the wire ends. The comparison shows that for wires longer than the typical mean free path of phonons the radiator model is able to account for ballistic transport effects. The steep gradients at the wire ends are then continuous manifestations of the discrete jumps in the model.Graphical abstract

Structural characteristics, mechanical properties, electronic behavior, and lattice thermal conductivities for novel LaX phases (X = P, As, Sb)

Rare-earth-metal monopnictides have rich high-pressure structures, magnetism, and topological properties, but there is still relatively little research related to them, especially in recent years. We here predict a new group of LaX (X = P, As, Sb) phases (HR-type) by means of the particle swarm optimization method. Their stabilities can be verified by dynamic, thermodynamic, and mechanical calculations. By utilizing the density functional and semiclassical Boltzmann transport theory, we investigate their mechanic, electronic, and thermal transport properties. These HR-type LaX are rather soft with lower than 6 GPa of Vickers hardness, and exhibit the obvious mechanical anisotropy. These HR-type LaX also exhibit amazing topological properties, owning a mostly flat surface band between two bulk Dirac cones. Based on the calculations of gaps in energy dispersion planes and Z2 invariants, we prove that these HR-type LaX should be the nodal-line semimetals. We compute their lattice thermal conductivities, and find that HR-type LaAs own the largest lattice thermal conductivity of 6.34 (22.34) W/mK along x (y) direction at 300 K. This mean free path of the pertinent heat-carrying phonons in the HR-type LaX are also predicted. Our research might offer new perspectives on the various allotropes of rare-earth-metal monopnictides.

High-Entropy Strategy to Achieve Electronic Band Convergence for High-Performance Thermoelectrics.

Multiband convergence has attracted significant interest due to its positive effects on further improving thermoelectric performance. However, the current research mainly focuses on two- or three-band convergence in lead chalcogenides through doping and alloying. Therefore, exploring a new strategy to facilitate more-band convergence has instructive significance and practical value in thermoelectric research. Herein, we first propose a high-entropy strategy to achieve four-band convergence for optimizing thermoelectric performance. Taking high-entropy AgSbPbSnGeTe5 as an example, we found that the emergence of more-band convergence occurs as the configuration entropy increases; in particular, the four-band convergence occurs in high-entropy AgSbPbSnGeTe5. The overlap of multiatom orbitals in the high-entropy sample contributes to the convergence of four valence bands, promoting the improvement of electrical performance. Meanwhile, due to large lattice distortion and disordered atoms, the phonon mean free path is effectively compressed, resulting in low lattice thermal conductivity of high-entropy AgSbPbSnGeTe5. Consequently, AgSbPbSnGeTe5 achieved an intrinsically high ZT value of 1.22 at 673 K, providing a cornerstone for further optimizing thermoelectric performance. For example, by generally optimizing the carrier concentration, a peak ZT value of ∼1.75 at 723 K is achieved. These insights offer a comprehensive understanding of the band structure affected by unique structures of high-entropy materials and also shed useful light on innovation mechanisms and functionalities for future improvement of thermoelectric performance.

Super-Suppression of Long-Wavelength Phonons in Constricted Nanoporous Geometries.

In a typical semiconductor material, the majority of the heat is carried by long-wavelength, long-mean-free-path phonons. Nanostructuring strategies to reduce thermal conductivity, a promising direction in the field of thermoelectrics, place scattering centers of size and spatial separation comparable to the mean free paths of the dominant phonons to selectively scatter them. The resultant thermal conductivity is in most cases well predicted using Matthiessen's rule. In general, however, long-wavelength phonons are not as effectively scattered as the rest of the phonon spectrum. In this work, using large-scale molecular-dynamics simulations, non-equilibrium Green's function simulations, and Monte Carlo simulations, we show that specific nanoporous geometries that create narrow constrictions in the passage of phonons lead to anticorrelated heat currents in the phonon spectrum. This effect results in super-suppression of long-wavelength phonons due to heat trapping and reductions in the thermal conductivity to values well below those predicted by Matthiessen's rule.

Rare earth tantalate coating materials for thermal and oxidation protection of carbon-carbon composites

To protect carbon/carbon composites against thermal corrosion and high-temperature oxidation, the thermal/oxygen barrier properties and static oxidation behavior of rare earth tantalates (YbTaO4 and LuTaO4) are investigated here. Both samples with the m' phase are successfully fabricated. The formation of oxygen vacancies benefits from atomic substitution and valence variation and the widths of the domain boundaries (18–23 nm) are close to the phonon mean free path. Low thermal conductivity is caused by Umklapp phonon-phonon scattering, oxygen vacancies and domain walls, with LuTaO4 having a value of 1.903 W m−1 K−1 at 900 °C. Furthermore, LuTaO4 has decreased oxygen-ion conductivity due to a high activation energy and immobile vacancies. A LuTaO4/Si coating can efficiently prevent the oxidation of C/C composites at 1100 °C for 15 h. The coating failure results from oxygen penetrating along the microscopic cracks and mismatch of the thermal expansion coefficients.

Thermal conductivity reduction due to phonon geometrical scattering in nano-engineered epitaxial germanium

Nano-engineering crystalline materials can be used to tailor their thermal properties. By adding new nanoscale phonon scattering centers and controlling their size, one can effectively decrease the phonon mean free path, hence the thermal conductivity of a fully crystalline material. In this Letter, we use the 3ω method in the temperature range of 100–300 K to experimentally report on the more than threefold reduction of the thermal conductivity of an epitaxially grown crystalline germanium thin film with embedded polydispersed crystalline Ge3Mn5 nano-inclusions with diameters ranging from 5 to 25 nm. A detailed analysis of the structure of the thin film coupled with Monte Carlo simulations of phonon transport highlights the role of the nano-inclusions volume fraction in the reduction of the phononic contribution to the thermal conductivity, in particular its temperature dependence, leading to a phonon mean free path that is set by geometrical constraints.