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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Atomic dynamics in 𝑀⁢Cr⁢𝑋 2 (𝑀=Ag, Cu; 𝑋 = S, Se) across magnetic and superionic transitions

Here, a systematic study of atomic dynamics and thermal properties of the family of layered chalcogenide compounds 𝑀⁢Cr⁢𝑋 2 (𝑀= Ag, Cu; 𝑋 = S, Se) was performed, including neutron and x-ray scattering, thermal characterization, and first-principles simulations. In all compounds, we observe a breakdown of specific phonon modes across the superionic phase transition, for phonons whose eigenvectors exhibit large contributions of mobile ions. In particular, the nondispersive portions of transverse acoustic (TA) branches at short-wavelengths and the low-energy optical phonons with large contributions from Ag + or Cu + become severely damped in the superionic phase. However, well-defined quasiparticles persist in the superionic state for long-wavelength TA phonons. In the case of AgCrS 2 , the coupling of lattice dynamics with its antiferromagnetic transition was also investigated. The magnetic ordering couples with the monoclinic–rhombohedral structural transition, and the Cr 3+ spin arrangement strongly affects the phonon dispersions. We qualitatively reproduce the magnetic and nuclear components of the INS measurement for antiferromagnetic AgCrS 2 by combining models of spin-waves and spin-polarized first-principles phonon simulations. Quasielastic magnetic fluctuations persist in the paramagnetic phase up to high temperature, but are clearly distinguished from the nuclear component through their momentum dependence. Finally, we report measurements of the thermal properties of the selenide compounds and find good agreement with our DFT simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Evaluation of Thermal Neutron Scattering Cross Section of Uranium Silicide with Ab Initio Lattice Dynamics

Uranium silicide (U 3 Si 2 ) is a candidate material for the high-density nuclear fuel in commercial light water reactors [1], [2]. Its higher uranium density, 11.3 g-U/cm3, compared to that of uranium dioxide (UO 2 ), 9.7 g-U/cm3, can improve the performance of a nuclear reactor while using low enriched uranium (LEU) and diversify the choice of cladding materials [1]–[3]. It also has a higher thermal conductivity than UO 2 , which can reduce the thermal stress on the material caused by a temperature gradient across the fuel pellet and provide a larger margin for some postulated accidents [1], [2], [4]. Furthermore, compared to U3Si, another high-density fuel candidate, it has better resistance to in-pile swelling due to less irradiation-induced rapid amorphization [1], [3]. Corresponding to its importance in nuclear engineering, many previous studies have reported the properties of U3Si2. Experiments showed that U 3 Si 2 is a paramagnetic (PM) metal, where a slight linear increase in magnetic susceptibility was measured with increasing temperature [5], [6]. In addition, thermodynamic quantities such as thermal expansion coefficient, heat capacity, and thermal conductivity were experimentally determined over a wide temperature range [1], [7], [8]. In several computational studies, ab initio atomistic simulations based on density functional theory (DFT) were performed to calculate various properties including elastic constants, electronic density of states (DOS), and phonon dispersion curves [9]–[12]. Nevertheless, thermal neutron scattering cross sections, which are critical to the prediction of the parameters in reactor physics that are ultimately related to reactor criticality, have not yet been evaluated for U3Si2. The scattering cross section can be calculated from the phonon DOS, or the energy spectrum of lattice vibrations, of the crystalline system [13], [14]. However, there is also no experimental data available for the phonon DOS of U 3 Si 2 . While some computational studies reported the phonon DOS and/or dispersion curves from ab initio simulations [9]–[12], the accuracy cannot be guaranteed because it is unclear whether the spin-polarization behavior of PM U 3 Si 2 was properly described. In the present study, the thermal neutron scattering cross section for U 3 Si 2 is evaluated for the first time by calculating the phonon DOS for U3Si2 from ab initio lattice dynamics (AILD) simulations based on DFT. First, U 3 Si 2 is modeled based on the experimental structure, and AILD simulations are performed on the modeled U3Si2 to optimize the structure. Next, AILD simulations are performed for supercells with atomic displacement to calculate Hellmann-Feynman forces. Based on the calculated forces, partial phonon DOSs for U and Si are obtained, and the thermal neutron scattering law (TSL) for U 3 Si 2 is finally evaluated. To verify the accuracy of the calculations in the present study, the calculation results are compared with experimental data on the structure and heat capacity of U3Si2 [1], [7], [8], [15].

Geometry Optimization↗
DOE OSTI2024

Manipulating Spin–Lattice Coupling in Layered Magnetic Topological Insulator Heterostructure via Interface Engineering

Induced magnetic order in a topological insulator (TI) can be realized either by depositing magnetic adatoms on the surface of a TI or engineering the interface with epitaxial thin film or stacked assembly of 2D van der Waals (vdW) materials. Herein, the observation of spin-phonon coupling in the otherwise non-magnetic TI Bi 2 Te 3 is reported, due to the proximity of FePS 3 (an antiferromagnet (AFM), T N ≈ 120 K), in a vdW heterostructure framework. Temperature-dependent Raman spectroscopic studies reveal deviation from the usual phonon anharmonicity originated from spin-lattice coupling at the Bi 2 Te 3 /FePS 3 interface at/below 60 K in the peak position (self-energy) and linewidth (lifetime) of the characteristic phonon modes of Bi 2 Te 3 (106 and 138 cm –1 ) in the stacked heterostructure. The Ginzburg-Landau (GL) formalism, where the respective phonon frequencies of Bi 2 Te 3 couple to phonons of similar frequencies of FePS 3 in the AFM phase, is adopted to understand the origin of the hybrid magneto-elastic modes. At the same time, the reduction of characteristic TN of FePS 3 from 120 K in isolated flakes to 65 K in the heterostructure, possibly due to the interfacial strain, which leads to smaller Fe-S-Fe bond angles as corroborated by computational studies using density functional theory (DFT). Besides, inserting hexagonal boron nitride within Bi 2 Te 3 /FePS 3 stacking regains the anharmonicity in Bi 2 Te 3 . As a result, controlling interfacial spin-phonon coupling in stacked heterostructure can have potential application in surface code spin logic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Dislocation-Limited Thermal Conductivity in LiF: Revisiting Perturbative Models

We revisit models to describe phonon-dislocation interactions and resulting dislocation-limited thermal conductivity (k), particularly as applied to describe the temperature-dependent k behavior of LiF with significant dislocation densities. Coupling semiempirical models of phonon scattering from dislocation strain fields provided by Klemens and Carruthers with density functional theory description of the phonons and input parameters, we find that both models significantly overpredict the measured k of LiF, as found previously. However, more direct application of the quantum perturbation theory description, from which the models were derived, gives significantly stronger phonon-dislocation scattering and strongly underpredicts the measured k data. We revisit the derivation of phonon-dislocation-strain field scattering and provide numerical details regarding its implementation. This work demonstrates that quantum perturbative calculations, now accessible to modern computational architectures, may provide a reasonable description of dislocation-limited k in materials as governed by phonon-strain field interactions provided that questions regarding the relevant strain field range can be resolved.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Microscopic mechanism of unusual lattice thermal transport in TlInTe 2

We investigate the microscopic mechanism of ultralow lattice thermal conductivity (κ l ) of TlInTe 2 and its weak temperature dependence using a unified theory of lattice heat transport, that considers contributions arising from the particle-like propagation as well as wave-like tunneling of phonons. While we use the Peierls–Boltzmann transport equation (PBTE) to calculate the particle-like contributions (κ l (PBTE)), we explicitly calculate the off-diagonal (OD) components of the heat-flux operator within a first-principles density functional theory framework to determine the contributions (κ l (OD)) arising from the wave-like tunneling of phonons. At each temperature, T, we anharmonically renormalize the phonon frequencies using the self-consistent phonon theory including quartic anharmonicity, and utilize them to calculate κ l (PBTE) and κ l (OD). With the combined inclusion of κ l (PBTE), κ l (OD), and additional grain-boundary scatterings, our calculations successfully reproduce the experimental results. Our analysis shows that large quartic anharmonicity of TlInTe 2 (a) strongly hardens the low-energy phonon branches, (b) diminishes the three-phonon scattering processes at finite T, and (c) recovers the weaker than T –1 decay of the measured κ l .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Anomalous thermal transport under high pressure in boron arsenide

High pressure represents extreme environments and provides opportunities for materials discovery. Thermal transport under high hydrostatic pressure has been investigated for more than 100 years and all measurements of crystals so far have indicated a monotonically increasing lattice thermal conductivity. Here we report in situ thermal transport measurements in the newly discovered semiconductor crystal boron arsenide, and observe an anomalous pressure dependence of the thermal conductivity. We use ultrafast optics, Raman spectroscopy and inelastic X-ray scattering measurements to examine the phonon bandstructure evolution of the optical and acoustic branches, as well as thermal conductivity under varied temperatures and pressures up to 32 gigapascals. Using atomistic theory, we attribute the anomalous high-pressure behaviour to competitive heat conduction channels from interactive high-order anharmonicity physics inherent to the unique phonon bandstructure. Our study verifies ab initio theory calculations and we show that the phonon dynamics—resulting from competing three-phonon and four-phonon scattering processes—are beyond those expected from classical models and seen in common materials. In conclusion, this work uses high-pressure spectroscopy combined with atomistic theory as a powerful approach to probe complex phonon physics and provide fundamental insights for understanding microscopic energy transport in materials of extreme properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Advanced Modeling and Simulation Methods for Evaluation of Thermal Neutron Scattering Materials

With the rise of interest in thermal neutron scattering data for advanced reactor, criticality safety, and shielding applications, new experimental data are required for evaluation of new materials or for re-evaluation (or validations) of previously evaluated materials. New experimental data are evaluated in a three-step process: (1) computing the phonon characteristics, (2) computing the dynamic structure factor (DSF) from the data, and (3) using the experimental setup to simulate the experimental data. All three steps have challenges, ranging from the need for a sufficiently general material simulation code—a processing code that can compute the corresponding DSF—to having a detailed layout of the instrument/beamline/facility where the data were measured. Whereas phonon characteristics of materials can be computed using various methods (molecular dynamics, density functional theory, etc.), a high-fidelity computation of the DSF and the simulation of the experiment based on the DSF is vital to the accuracy of the evaluation. The latter two steps can be achieved by using the two corresponding code systems developed by instrument scientists at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory: (1) OCLIMAX, a program that calculates the dynamic structure factor from DFT and MD simulation results, and (2) MCViNE, a Monte Carlo neutron ray-tracing program designed to simulate neutron scattering experiments. Recently, polyethylene and yttrium hydride were measured at the Wide Angular-Range Chopper (ARCS) and SEQUOIA instrument stations of the SNS. These experiments are simulated using the density functional theory code, the Cambridge Serial Total Energy Package (CASTEP), to compute its phonon characteristics (eigenvalues/vectors and PDOS), which is then processed using OCLIMAX to yield the DSF, and finally the data at each instrument station are simulated by the MCViNE for comparison to the measured data for evaluation. For comparison to conventional evaluation methods, the scattering data processed from OCLIMAX are compared against those processed from the LEAPR module of NJOY, and the results from MCViNE simulations are compared against previously used simplified beamline models implemented in the Monte Carlo N-Particle (MCNP) code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors

Though YB 6 and LaB 6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB 6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB 2 . LaB 6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB 6 ’s greater Fermi-level (E f ) density of states and higher electron–phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB 6 , hybridize with π B–B bonds and bring this π-system lower in energy than the σ B–B bonds otherwise at E f . This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB 6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB 6 . These phonons in YB 6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB 6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB 6 , introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB 6 and YB 6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

Science & Technology - Other Topics↗
DOE OSTI2020

Charge-density-wave melting in the one-dimensional Holstein model

We study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the real-time evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photoinduced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state density-matrix renormalization group method for electron-phonon systems using local basis optimization. In our examples, we account for up to M ph =40 bare phonons per site by working with O(10) optimal phonon modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Hybridization-driven strong anharmonicity in Yb-filled skutterudites

A high-pressure study of the structural and thermal transport properties is carried out on one of the most efficient filled skutterudites, $\mathrm{Yb_{0.3}Co_4Sb_{12}}$, to understand the relatively low thermal conductivity behavior in this family. By combining x-ray diffraction and Raman scattering measurements, we detect a phase transition at around 12.4 GPa. The mode Grüneisen parameters of the observed phonon modes are obtained from the determined bulk modulus and the phonon frequency shifts with pressure. The strong anharmonicity in this material is demonstrated by the obtained large average Grüneisen parameter. We also find the depressed group velocity within the low-frequency range, the flat guest mode avoided crossing with the acoustic-phonon mode, and the significant contribution of optical phonons. The hybridization of the guest atom and host lattice and the related enhanced anharmonicity are suggested to account for the low lattice thermal conductivity in the studied system. So, these findings provide new insight into how phonon-phonon interactions lower lattice thermal conductivity in this important thermoelectric family.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Thermal Hall conductivity of electron-doped cuprates

Measurements of the thermal Hall conductivity in hole-doped cuprates have shown that phonons acquire chirality in a magnetic field both in the pseudogap phase and in the Mott insulator state. The microscopic mechanism at play is still unclear. A number of theoretical proposals are being considered including skew scattering of phonons by various defects, the coupling of phonons to spins, and a state of loop-current order with the appropriate symmetries, but more experimental information is required to constrain theoretical scenarios. Here we present our study of the thermal Hall conductivity κ xy in the electron-doped cuprates Nd 2–x Ce x CuO 4 and Pr 2–x Ce x CuO 4 for dopings across the phase diagram, from x = 0 in the insulating antiferromagnetic phase up to x = 0.17 in the metallic phase above optimal doping. We observe a large negative thermal Hall conductivity at all dopings in both materials. Since heat conduction perpendicular to the CuO 2 planes is dominated by phonons, the large thermal Hall conductivity we observe in electron-doped cuprates for a heat current in that direction must also be due to phonons, as in hole-doped cuprates. However, the degree of chirality, measured as the ratio |κ xy /κ xx | where κ xx is the longitudinal thermal conductivity, is much larger in the electron-doped cuprates. Here, we discuss various factors that may be involved in the mechanism that confers chirality to phonons in cuprates, including short-range spin correlations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Vibrational properties and thermal transport in quaternary chalcogenides: The case of Te-based compositions

Vibrational thermal properties of CuZn 2 InTe 4 , AgZn 2 InTe 4 , and Cu 2 CdSnTe 4 , derived from binary II-VI zinc-blendes, are reported based on first-principles calculations. While the chalcogenide atoms in these materials have the same lattice positions, the cation atom arrangements vary, resulting in different crystal symmetries and subsequent properties. The compositional differences have important effects on the vibrational thermal characteristics of the studied materials, which demonstrate that low-frequency optical phonons hybridize with acoustic phonons and lead to enhanced phonon-phonon scattering and low lattice thermal conductivities. The phonon density of states, mode Grüneisen parameters, and phonon scattering rates are also calculated, enabling deeper insight into the microscopic thermal conduction processes in these materials. Compositional variations drive differences among the three materials considered here; nonetheless, their structural similarities and generally low thermal conductivities (0.5–4 W/m K at room temperature) suggest that other similar II-VI zinc-blende derived materials will also exhibit similarly low values, as also corroborated by experimental data. Finally, this, combined with the versatility in designing a variety of motifs on the overall structure, makes quaternary chalcogenides interesting for thermal management and energy conversion applications that require low thermal conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Development Status of the KIPM Detector Consortium

A kinetic inductance phonon-mediated detector is a calorimeter that uses kinetic inductance detectors (KIDs) to read out phonon signals from the device substrate. We have established a consortium comprising university and national lab groups dedicated to advancing the state of the art in these detectors, with the ultimate goal of designing a detector with sub-eV threshold on energy deposited in the substrate, enabling searches for both light dark matter and low-energy neutrino interactions. This consortium brings together experts in KID design, phonon and quasi-particle dynamics, and noise modeling, along with specialized fabrication facilities, test platforms, and unique calibration capabilities. Recently, our consortium has demonstrated a resolution on energy absorbed by the sensor of 2.1 eV, the current record for phonon-sensitive KIDs. However, due to ∼ 1% phonon collection efficiency, the overall detector resolution was limited to 320 eV. Finally, the current focus of the consortium is modeling and improving the phonon collection efficiency and implementing low-T c superconductors, both of which serve to improve the overall energy resolution and threshold of the detectors.

Temples, Dylan J. [Fermi National Accelerator Labo↗
DOE OSTI2021

Atomic-Level, Energy-Conversion Heat Transfer

Abstract Heat is stored in quanta of kinetic and potential energies in matter. The temperature represents the equilibrium and excited occupation (boson) of these energy conditions. Temporal and spatial temperature variations and heat transfer are associated with the kinetics of these equilibrium excitations. During energy-conversion (between electron and phonon systems), the occupancies deviate from equilibria, while holding atomic-scale, inelastic spectral energy transfer kinetics. Heat transfer physics reaches nonequilibrium energy excitations and kinetics among the principal carriers, phonon, electron (and holes and ions), fluid particle, and photon. This allows atomic-level tailoring of energetic materials and energy-conversion processes and their efficiencies. For example, modern thermal-electric harvesters have transformed broad-spectrum, high-entropy heat into a narrow spectrum of low-entropy emissions to efficiently generate thermal electricity. Phonoelectricity, in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes a high-entropy heat. In particular, the suggested phonovoltaic cell generates phonoelectricity by employing the nonequilibrium, low-entropy, and elevated temperature optical-phonon produced population—for example, by relaxing electrons, excited by an electric field. A phonovoltaic material has an ultranarrow electronic bandgap, such that the hot optical-phonon population can relax by producing electron-hole pairs (and power) instead of multiple acoustic phonons (and entropy). Examples of these quanta and spectral heat transfer are reviewed, contemplating a prospect for education and research in this field.

Engineering↗
DOE OSTI2021

Generation of the TSL for Zirconium Hydrides from Ab Initio Methods

Zirconium hydride (ZrHx) is a moderator material used in TRIGA and other reactors that may exist in multiple phases with varying stoichiometry, which include the δ phase and the ϵ phase. Current ENDF/B-VIII.0 ZrHx thermal scattering law (TSL) evaluations do not distinguish between phases. These sub-libraries were generated with the LEAPR module of NJOY using historic phonon spectra derived from a central force model and assume incoherent elastic scattering for both bound hydrogen and zirconium, which neglects the effects of crystal structures important for scattering from zirconium bound in ZrHx. In this work, the TSLs for hydrogen and zirconium bound in δ-ZrHx and ϵ-ZrH2 were generated from phonon spectra derived from modern ab initio lattice dynamics methods and ab initio molecular dynamics. Subsequently, TSLs for hydrogen and zirconium in ZrHx and ZrH2 were generated using the Full Law Analysis Scattering System Hub (FLASSH) code. The built-in generalized coherent elastic routine was used to generate the previously neglected elastic contribution from zirconium for this material. The present TSLs provide both a re-evaluation of the current ZrH sub-libraries and expansion of the set of TSLs available for the examination of neutrons in systems with zirconium hydride, permitting explicit treatment of δ and ϵ phases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1985

Conducting a thermal conductivity survey

A physically transparent approximate theory of phonon decay rates is presented starting from a pair potential model of the interatomic forces in an insulator or semiconductor. The theory applies in the classical regime and relates the 3-phonon decay rate to the third derivative of the pair potential. Phonon dispersion relations do not need to be calculated, as sum rules relate all the needed quantities directly to the pair potential. The Brillouin zone averaged phonon lifetime turns out to involve a dimensionless measure of the anharmonicity multiplied by an effective density of states for 3-phonon decay. Results are given for rare gas and alkali halide crystals. For rare gases, the results are in good agreement with more elaborate perturbation calculations. Comparison to experimental data on phonon linewidths and thermal conductivity are made.

Allen, P. B.↗
NASA NTRS1991

A model for the high-temperature transport properties of heavily doped n-type silicon-germanium alloys

A model is presented for the high-temperature transport properties of large-grain-size, heavily doped n-type silicon-germanium alloys. Electron and phonon transport coefficients are calculated using standard Boltzmann equation expressions in the relaxation time approximation. Good agreement with experiment is found by considering acoustic phonon and ionized impurity scattering for electrons, and phonon-phonon, point defect, and electron-phonon scattering for phonons. The parameters describing electron transport in heavily doped and lightly doped materials are significantly different and suggest that most carriers in heavily doped materials are in a band formed largely from impurity states. The maximum dimensionless thermoelectric figure of merit for single-crystal, n-type Si(0.8)Ge(0.2) at 1300 K is estimated at ZT about 1.13 with an optimum carrier concentration of n about 2.9 x 10 to the 20th/cu cm.

Vining, Cronin B.↗
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↗