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DOE OSTI2020

Enhanced thermoelectric efficiency in nanocrystalline bismuth telluride nanotubes

We report on the thermal and thermoelectric properties of individual nanocrystalline Bi 2 Te 3 nanotubes synthesized by the solution phase method using 3ω method and a microfabricated testbench. Measurements show that the nanotubes offer improved ZT compared to bulk Bi 2 Te 3 near room temperature due to an enhanced Seebeck coefficient and suppressed thermal conductivity. This improvement in ZT originates from the nanocrystalline nature and low dimensionality of the nanotubes. Domain boundary filtering of low-energy electrons provides an enhanced Seebeck coefficient. The scattering of phonons at the surface of the nanotube leads to suppressed thermal conductivity. These have been theoretically analyzed using the Boltzmann equation based on the relaxation time approximation and Landauer approach. This work clearly demonstrates the possibility of achieving enhancement in thermoelectric efficiency by combining nanocrystalline and low-dimensional systems.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

An Investigation of Thermal Properties of 2D Materials [Dissertation]

Studying the thermal conductivity of 2D materials is important due to the applications of 2D materials in fields such as thermal management, thermoelectricity, renewable energy, and sensors. As such, measurements of the thermal conductivity of these 2D materials become important to measure. Thermal conductivity is often difficult to measure for 2D materials due to their atomically thin nature and many experimental methods for doing so requiring contact with the sample, which can alter the thermal properties. A non-contact method for calculating the thermal conductivity of 2D materials supported on substrates in order to model the thermal conductivity of 2D materials for devices, is proposed and experimentally performed in this dissertation. The optothermal Raman technique is a useful non-contact diagnostic technique useful in determining the thermal conductivity of 2D materials. The optothermal Raman typically does not account for heat losses due to convection or radiation or substrate resistance, which are shown to be important factors to consider when developing an optothermal Raman model. Additionally, the calculation of the interfacial thermal conductance between the bottom surface of the sample and the top surface of the substrate, plays an important role in determining the final value of the thermal conductivity of a supported sample, and will yield differing results based on whether or not the conductance is calculated using an approach such as the Diffuse Mismatch Model (DMM) or calculated directly by varying the laser heating profile (usually done by changing the laser objective). This is shown to be the case for both graphene on Ni, graphene on Cu, and SnSe 2 on Cu. In addition to experimentally calculating the thermal conductivity of a 2D material with the optothermal Raman technique, the thermal conductivity of 2D materials can also be calculated using computational methods. The three-phonon method is a method which can be used to simulate phonon scattering processes and determine the thermal conductivity of semiconductors, wherein phonon scattering is the dominant mechanism which determines the thermal conductivity. The three-phonon method uses relaxation times for phonon scattering with other phonons, electrons, and other material system elements, such as isotopes or material defects, in order to create a single-mode relaxation time approximation (SMRTA), which is used to calculate the final value of the thermal conductivity. An important consideration when determining the thermal conductivity of a 2D material using this method is the device geometry, which is reflected in this work as the phonon-boundary scattering relaxation time. This inclusion is important along with the inclusion of phonon-electron scattering in accurately determining the thermal conductivity of a 2D material. In both the optothermal Raman experiments and the three-phonon method computations, strain is shown to have a demonstrable effect on the thermal conductivity of 2D materials. When a 1.1% strain was applied to the mechanical properties of SnSe, the three-phonon processes yielded a lower thermal conductivity than the no-strain case. For the optothermal Raman experiments, the strain induced in the Cu substrate and transferred to a single-layer graphene (SLG) sample yields a trend where the thermal conductivity of the SLG decreases with respect to strain applied. In the case where the interfacial thermal conductance was calculated directly, the conductance increased with respect to strain applied. This presents strain as a reliable and viable method for tuning the thermal properties of 2D materials for device applications.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Method of information entropy for convergence assessment of molecular dynamics simulations

The lack of a reliable method to evaluate the convergence of molecular dynamics simulations has contributed to discrepancies in different areas of molecular dynamics. Here, the method of information entropy is introduced to molecular dynamics for stationarity assessment. The Shannon information entropy formalism is used to monitor the convergence of the atom motion to a steady state in a continuous spatial domain and is also used to assess the stationarity of calculated multidimensional fields such as the temperature field in a discrete spatial domain. It is demonstrated in this work that monitoring the information entropy of the atom position matrix provides a clear indicator of reaching steady state in radiation damage simulations, non-equilibrium molecular dynamics thermal conductivity computations, and simulations of Poiseuille and Couette flow in nanochannels. A main advantage of the present technique is that it is non-local and relies on fundamental quantities available in all molecular dynamics simulations. Unlike monitoring average temperature, the technique is applicable to simulations that conserve total energy such as reverse non-equilibrium molecular dynamics thermal conductivity computations and to simulations where energy dissipates through a boundary as in radiation damage simulations. The method is applied to simulations of iron using the Tersoff/ZBL splined potential, silicon using the Stillinger–Weber potential, and to Lennard–Jones fluid. Its applicability to both solids and fluids shows that the technique has potential for generalization to other areas in molecular dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Implications of phonon anisotropy on thermal conductivity of fluorite oxides

Abstract Fluorite oxides are attractive ionic compounds for a range of applications with critical thermal management requirements. In view of recent reports alluding to anisotropic thermal conductivity in this face-centered cubic crystalline systems, we perform a detailed analysis of the impact of direction-dependent phonon group velocities and lifetimes on the thermal transport of fluorite oxides. We demonstrate that the bulk thermal conductivity of this class of materials remains isotropic despite notable anisotropy in phonon lifetime and group velocity. However, breaking the symmetry of the phonon lifetime under external stimuli including boundary scattering present in nonequilibrium molecular dynamics simulations of finite size simulation cell gives rise to apparent thermal conductivity anisotropy. We observe that for accurate determination of thermal conductivity, it is important to consider phonon properties not only along high symmetry directions commonly measured in inelastic neutron or x-ray scattering experiments but also of those along lower symmetry. Our results suggests that certain low symmetry directions have a larger contribution to thermal conductivity compared to high symmetry ones.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Nanoscale Decoupling of Carrier-Phonon Transport in Carbon Nanotube-Halide Perovskite Heterostructures

In conventional semiconductors, electrical and thermal conductivity are typically coupled, posing a challenge in optimizing both simultaneously. Overcoming this inherent trade-off enables strategies for advancing electronic applications. Herein, a strategy is demonstrated to decouple electrical and thermal conductivity trade-off by creating heterostructures of highly conductive single-walled carbon nanotubes (SWCNTs) coated with low conductivity hybrid perovskites. Coating SWCNTs with methylammonium lead iodide perovskite results in an enhancement in electrical conductivity (408-1266 S cm-1) due to p-type doping followed by a threefold decrease of the in-plane thermal conductivity (3.3-1 W m-1 K-1), compared to pristine SWCNTs. Molecular dynamics simulations uncover phonon boundary scattering at the SWCNT/perovskite interface as well as localization of methylammonium-related and softening of the Pb-I-related phonon modes in methylammonium lead iodide perovskite decreasing the thermal conductivity.

14 SOLAR ENERGY↗

DOE OSTI2021

Simulation of the PBX 9501 Self-Ignited Heavily Confined Cookoff Test

The PBX 9501 self-ignited thermally damaged explosive (SITX) test was carried out by Holmes et al. A 6-inch diameter sphere made of the PBX 9501 was heated inside a steel confinement vessel until it underwent a thermal explosion. This test provided measured temperature data that was used to define a boundary condition to carry out post-experiment finite element (FE) thermal simulations and comparisons of the FE thermal response with the experimental time to thermal ignition and internal temperature measurements at the center of the PBX 9501 sphere. Finite element models of this experiment were constructed using the heat transfer code Aria. A cookoff model for PBX 9501 was used to simulate the thermal decomposition of PBX 9501 and to predict the time to thermal ignition. An inverse heat conduction scheme was designed and applied to estimate a 1D temperature boundary condition.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Expression of interfacial Seebeck coefficient through grain boundary engineering with multi-layer graphene nanoplatelets

Energy filtering has been a long-sought strategy to enhance a thermoelectric material's figure of merit zT through improving its power factor. Here we show a composite of multi-layer graphene nanoplatelets (GNP) and n-type Mg 3 Sb 2 leads to the expression of an energy filtering like effect demonstrated by an increase in the material's Seebeck coefficient and maximum power factor, without impact on the material's carrier concentration. We analyse these findings from the perspective of a heterogeneous material consisting of grain and grain boundary phases, instead of a more traditional and common analysis that assumes a homogeneously transporting medium. An important implication of this treatment is that it leads to the development of an interfacial Seebeck coefficient term, which can explain the observed increase in the material's Seebeck coefficient. The contribution of this interfacial Seebeck coefficient to the overall Seebeck coefficient is determined by the relative temperature drop across the grain boundary region compared to that of the bulk material. In Te doped Mg 3 Sb 2 we show the introduction of GNP increases the interfacial thermal resistance of grain boundaries, enhancing the contribution of the interfacial Seebeck coefficient arising from grain boundaries to the overall Seebeck coefficient. Without significant detriment to the electrical conductivity this effect results in a net increase in maximum power factor. This increased interfacial thermal resistance also leads to the synergistic reduction of the total thermal conductivity. As a result, we enhance zT of the Mg 3 Sb 2 to a peak value of 1.7 near 750 K. Considering the two-dimensional nature of the grain boundary interface, this grain boundary engineering strategy could be applied to a few thermoelectric systems utilizing various two-dimensional nanomaterials.

42 ENGINEERING↗

DOE OSTI2025

Grain Boundary-Limited Thermal Transport in Suspended Thin Graphite across an Unexplored Thickness Regime

Here, we present systematic thermal conductivity (κ) measurements of suspended thin graphite ribbons, 234–527 nm thick, using a four-probe 3ω method. Unlike recent reports of phonon hydrodynamics and exceptionally high κ in micrometer-thick graphite ( Science, 2020), we observe significantly lower κ and no signatures of collective phonon flow in this intermediate thickness regime. Instead, our measured κ lies between few-layer graphene and bulk graphite. These results agree with a first-principles-informed Peierls–Boltzmann transport model with spatially resolved Monte Carlo sampling. Additionally, the temperature for the peak κ shifts lower with increasing thickness, due to the interplay of phonon-boundary and phonon-isotope scattering. Incorporating grain boundary scattering into simulations is necessary to replicate the experimental trends. These findings delineate the boundary between ballistic, hydrodynamic, and diffusive transport regimes in graphite and underscore the dominant role of disorder and geometry in phonon transport in quasi-two-dimensional materials, offering insights for nanoscale thermal management.

Boltzmann transport model↗

DOE OSTI2023

Grain Boundary Phases in NbFeSb Half‐Heusler Alloys: A New Avenue to Tune Transport Properties of Thermoelectric Materials

Abstract Many thermoelectric materials benefit from complex microstructures. Grain boundaries (GBs) in nanocrystalline thermoelectrics cause desirable reduction in the thermal conductivity by scattering phonons, but often lead to unwanted loss in the electrical conductivity by scattering charge carriers. Therefore, modifying GBs to suppress their electrical resistivity plays a pivotal role in the enhancement of thermoelectric performance, zT . In this work, different characteristics of GB phases in Ti‐doped NbFeSb half‐Heusler compounds are revealed using a combination of scanning transmission electron microscopy and atom probe tomography. The GB phases adopt a hexagonal close‐packed lattice, which is structurally distinct from the half‐Heusler grains. Enrichment of Fe is found at GBs in Nb 0.95 Ti 0.05 FeSb, but accumulation of Ti dopants at GBs in Nb 0.80 Ti 0.20 FeSb, correlating to the bad and good electrical conductivity of the respective GBs. Such resistive to conductive GB phase transition opens up new design space to decouple the intertwined electronic and phononic transport in thermoelectric materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Lossless Phonon Transition Through GaN‐Diamond and Si‐Diamond Interfaces

Abstract Advancing Silicon (Si) technology beyond Moore's law through 3D architectures requires highly efficient heat management methods compatible with foundry processes. While continued increases in transistor density can be achieved through 3D architectures, self‐heating in the upper tiers degrades the performance. Self‐heating is a critical problem for high‐power, high‐frequency, wide bandgap, and ultra‐wide bandgap devices as well. Diamond, known for its exceptional thermal conductivity, offers a viable solution in both these cases. Since thermal boundary resistance (between the channel/junction and diamond plays a crucial role in overall thermal resistance, this study investigates various dielectrics for interface engineering, such as Silicon dioxide (SiO 2 ), amorphous‐ Silicon Carbide (a‐SiC), and Silicon Nitride (SiN x ), to make a phonon bridge at gallium nitride (GaN)‐diamond and Si‐diamond interfaces. The a‐SiC interlayer reduces diamond/GaN (<5 m 2 K per GW) and diamond/Si (<2 m 2 K per GW) thermal boundary resistances by linking low‐ and high‐frequency phonons, boosting phonon transport through the interface. Engineered interfaces enhance heat spreading from the channel/junction and rule out premature failure.

Malakoutian, Mohamadali↗

DOE OSTI2026

Hierarchical microstructure of Yb-filled skutterudites through ultrasonically atomized spherical powders for enhanced thermoelectric performance

Hierarchical microstructures are widely explored as a strategy to reduce lattice thermal conductivity in thermoelectric materials while preserving favorable electronic transport. Here we demonstrate that ultrasonic atomization of precursor powders provides an intrinsic pathway to generate such architectures in n-type Yb0.3Co4Sb12 skutterudites. Materials were synthesized by both conventional sealed-ampoule and ultrasonic atomization routes, each yielding essentially single-phase skutterudite after densification. However, the atomized spherical powders undergo a distinct reaction-driven microstructural evolution during thermal treatment prior to densification. Electron microscopy reveals that the skutterudite phase within the particles induces swelling, cracking, and fragmentation of the droplets before consolidation. Multimodal structural and microstructural characterizations show that densification of these fragmented powders produces a hierarchical microstructure consisting of submicron grains, micrometer-scale faceted crystallites, and powder-derived domains separated by oxide-decorated boundaries. Comprehensive thermoelectric transport measurements evidence that this multiscale architecture lowers the lattice thermal conductivity while maintaining favorable electronic transport, leading to an average ~10% enhancement in the thermoelectric figure of merit. Complementary 121Sb Mössbauer spectroscopy further indicates lattice softening in the atomized material. These results demonstrate that ultrasonic atomization provides an effective route to engineer hierarchical microstructures in skutterudite thermoelectrics and offers a promising strategy for tailoring thermal transport in energy-conversion materials.

Bouteiller, Hugo [ORNL] (ORCID:0009000421322962)↗

DOE OSTI2022

Measuring sub-surface spatially varying thermal conductivity of silicon implanted with krypton

The thermal properties of semiconductors following exposure to ion irradiation are of great interest for the cooling of electronic devices; however, gradients in composition and structure due to irradiation often make the measurement difficult. Furthermore, the nature of spatial variations in thermal resistances due to spatially varying ion irradiation damage is not well understood. In this work, we develop an advancement in the analysis of time-domain thermoreflectance to account for spatially varying thermal conductivity in a material resulting from a spatial distribution of defects. We then use this method to measure the near-surface (≲1 μm) thermal conductivity of silicon wafers irradiated with Kr + ions, which has an approximate Gaussian distribution centered 260 nm into the sample. Our numerical analysis presented here allows for the spatial gradient of thermal conductivity to be extracted via what is fundamentally a volumetric measurement technique. We validate our findings via transmission electron microscopy, which is able to confirm the spatial variation of the sub-surface silicon structure, and provide additional insight into the local structure resulting from the effects of ion bombardment. Thermal measurements found the ion stopping region to have a nearly 50x reduction in thermal conductivity as compared to pristine silicon, while TEM showed the region was not fully amorphized. Our results suggest this drastic reduction in silicon thermal conductivity is primarily driven by structural defects in crystalline regions along with boundary scattering between amorphous and crystalline regions, with a negligible contribution being due to implanted krypton ions themselves.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Predicting mesoscale spectral thermal conductivity using advanced deterministic phonon transport techniques

We present a review, demonstration and simulation of phonon transport for the purposes of predicting materials performance at the mesoscale. We focus primarily on the development and implementation of a unified methodology to enable predictive heat transport. We report on the current state of the art as it pertains to deterministic phonon transport methodologies, discussing various topics concerning phonons. In application, we focus on the Self-Adjoint Angular Flux (SAAF) formulation of the Boltzmann transport equation for phonons, and develop the spatial, angular, and material property discretization required to accurately simulate the predictive physics of heat transport in dielectrics. We discuss thermal interfacial resistance and present our formulation of the diffuse mismatch model for simulating phonon interactions at internal boundaries. We have recently developed a deterministic, spectral phonon transport method for predicting effective thermal conductivity ($\kappa_{\textrm{eff}}$), using Bose-Einstein source terms coupled through an average material temperature. In this method, we introduce a closure term to the phonon transport system which acts as a redistribution function for the total energy of the system, and serves as a guide for the amount of non-equilibrium behavior occurring in the system. This method predicts thermal conductivity and equilibrium temperature distributions in homogeneous and heterogeneous materials using data generated by ab initio density functional theory methods. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. The equations associated with this method are solved via a modification of traditional source iteration. We compare the performance of source iteration applied to an existing uncoupled, traditional SAAF method to our new method and comment on the iterative performance of each. We observe ballistic and diffusive phonon scattering as acoustic thickness of the domain changes, and are able to make comparisons between the accuracy and efficiency of both methods.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Experimental confirmation of first-principles thermal conductivity in Zirconium-doped ThO 2

The degradation of thermal conductivity in advanced nuclear fuels due to the accumulation of fission products and irradiation-induced defects is inevitable, and must be considered as part of safety and efficiency analyses of nuclear reactors. Here, this study examines the thermal conductivity of a zirconium-doped ThO 2 crystal, synthesized via the hydrothermal method using a spatial domain thermoreflectance technique. Zirconium is one of the soluble fission products in oxide fuels that can effectively scatter heat-carrying phonons in the crystalline lattice of fuel. Thus, thermal property measurements of zirconium-doped ThO 2 single crystals provide insights into the effects of substitutional zirconium doping, isolated from extrinsic factors such as grain boundary scattering. The experimental results are compared with first-principles calculations of the lattice thermal conductivity of ThO 2 , employing an iterative solution of the Peierls-Boltzmann transport equation. Additionally, the non-perturbative Green's function methodology is utilized to compute phonon-point defect scattering rates, accounting for local distortions around point defects, including mass difference changes, interatomic force constants, and structural relaxation. The congruence between the predicted results from first-principles calculations and the measured temperature-dependent thermal conductivity validates the computational methodology. Furthermore, the methodologies employed in this study enable systematic investigations of thermal conductivity reduction by fission products, potentially leading to the development of more accurate fuel performance codes.

36 - MATERIALS SCIENCE↗

DOE OSTI2024

Numerical Evaluation of Effective Thermal Conductivity of PCM with Metal Foam Incorporating Buoyancy Effects for Thermal Energy Storage

The thermal energy storage (TES) system has the capability to efficiently preserve thermal energy directly derived from the energy source, minimizing any conversion losses. Especially latent heat storage offers distinct advantages, including a substantial increase in energy storage density and minimization of temperature fluctuations within the plants. However, the phase change material (PCM) employed in latent heat storage has low thermal conductivity. Consequently, various studies are being conducted to enhance heat transfer. One approach to enhance heat transfer involves utilizing metal foam to maximize the heat transfer area. However, modeling metal foam with its intricate structure is a challenging task in numerical analysis. For this reason, ongoing research focuses on simplifying the modeling of metal foam. Nevertheless, fully encompassing all the characteristics of actual metal foam proves to be a challenging task for the simplified analytical model. The objective of this paper is to interpret the simple lattice metal foam analysis model from the perspective of behavior induced by buoyancy. When comparing the analysis results of solid PCM and liquid PCM with the same thermal conductivity under changes in porosity and gravity direction, we conducted an analysis to discern the trends in effective thermal conductivity that are overestimated due to convection. In the analysis, a constant heat flux of 10 kW and a constant surface boundary condition of 350 K were applied, and a sensitivity study regarding the mesh was conducted. The results indicate that, from the perspective of gravity in the simple lattice model, the solid analysis yields an effective thermal conductivity 29-47% higher compared to the liquid analysis. Additionally, as porosity increases, there is an observed increase of 24-33% in effective thermal conductivity.

25 ENERGY STORAGE↗

DOE OSTI2024

Boosting Thermoelectric Performance in Nanocrystalline Ternary Skutterudite Thin Films through Metallic CoTe 2 Integration

Metal–semiconductor nanocomposites have emerged as a viable strategy for concurrently tailoring both thermal and electronic transport properties of established thermoelectric materials, ultimately achieving synergistic performance. In this investigation, a series of nanocomposite thin films were synthesized, embedding metallic cobalt telluride (CoTe 2 ) nanophase within the nanocrystalline ternary skutterudite (Co(Ge 1.22 Sb 0.22 )Te 1.58 or CGST) matrix. Our approach harnessed composition fluctuation-induced phase separation and in situ growth during thermal annealing to seamlessly integrate the metallic phase. The distinctive band structures of both materials have developed an ohmic-type contact characteristic at the interface, which raised carrier density considerably yet negligibly affected the mobility counterpart, leading to a substantial improvement in electrical conductivity. The intricate balance in transport properties is further influenced by the metallic CoTe 2 phase’s role in diminishing lattice thermal conductivity. The presence of the metallic phase instigates enhanced phonon scattering at the interface boundaries. Consequently, a 2-fold enhancement in the thermoelectric figure of merit (zT ~ 1.30) is attained with CGST-7 wt. % CoTe 2 nanocomposite film at 655 K compared to that of pristine CGST.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Concept of Dynamic Heat Insulation for Rotating Detonation Engines

This work introduces a new class of materials concept to dynamically reduce instantaneous heat fluxes in Rotating Detonation Engine (RDE) combustor chamber walls. The high-frequency and high-amplitude surface heat fluxes observed in RDEs arise from large instantaneous temperature differences between the detonation shockwave and chamber wall surface. These temperature gradients drive substantial energy loss and reduce the chamber gas pressure, ultimately limiting the cycle’s thermodynamic efficiency. This work introduces a concept for dynamically insulating the combustion chamber surfaces using surface layers or coatings with low thermal time scale. With such coatings, the surface temperature may follow the fluctuations of the cyclic detonation wave temperature, thus reducing the instantaneous heat flux therefore cycle-mean heat flux. To analyze these cyclic thermal phenomena, a one-dimensional analytical conduction solver was utilized with the capability to handle multilayered structures. Parametric modeling was performed using transient heat flux boundary conditions representative of a hydrogen–air RDE across a broad range of coating thermal properties and engine conditions. The coating effectiveness scaled with the product of thermal time constant and detonation wave frequency and the results were non-dimensionalized to guide future materials development. This strategy may offer benefits in increasing material survivability, reducing cooling requirements, and enhancing pressure gain.

heat transfer↗

DOE OSTI2023

Thickness-Dependent Cross-Plane Thermal Conductivity Measurements of Exfoliated Hexagonal Boron Nitride

Submicrometer-thick layers of hexagonal boron nitride (hBN) exhibit high in-plane thermal conductivity and useful optical properties, and serve as dielectric encapsulation layers with low electrostatic inhomogeneity for graphene devices. Despite the promising applications of hBN as a heat spreader, the thickness dependence of its cross-plane thermal conductivity is not known, and the cross-plane phonon mean free paths (MFPs) have not been measured. We measure the cross-plane thermal conductivity of hBN flakes exfoliated from bulk crystals. We find that submicrometer thick flakes exhibit thermal conductivities up to 8.1 ± 0.5 W m –1 K –1 at 295 K, which exceeds previously reported bulk values by more than 60%. Surprisingly, the average phonon mean free path is found to be several hundred nanometers at room temperature, a factor of 5 larger than previous predictions. When planar twist interfaces are introduced into the crystal by mechanically stacking multiple thin flakes, the cross-plane thermal conductivity of the stack is found to be a factor of 7 below that of individual flakes with similar total thickness, thus providing strong evidence that phonon scattering at twist boundaries limits the maximum phonon MFPs. These results have important implications for hBN integration in nanoelectronics and improve our understanding of thermal transport in twodimensional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗