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NASA NTRS1987

Studies of HZE particle interactions and transport for space radiation protection purposes

The main emphasis is on developing general methods for accurately predicting high-energy heavy ion (HZE) particle interactions and transport for use by researchers in mission planning studies, in evaluating astronaut self-shielding factors, and in spacecraft shield design and optimization studies. The two research tasks are: (1) to develop computationally fast and accurate solutions to the Boltzmann (transport) equation; and (2) to develop accurate HZE interaction models, from fundamental physical considerations, for use as inputs into these transport codes. Accurate solutions to the HZE transport problem have been formulated through a combination of analytical and numerical techniques. In addition, theoretical models for the input interaction parameters are under development: stopping powers, nuclear absorption cross sections, and fragmentation parameters.

Townsend, Lawrence W.↗

NASA NTRS1995

HZETRN: Description of a free-space ion and nucleon transport and shielding computer program

The high-charge-and energy (HZE) transport computer program HZETRN is developed to address the problems of free-space radiation transport and shielding. The HZETRN program is intended specifically for the design engineer who is interested in obtaining fast and accurate dosimetric information for the design and construction of space modules and devices. The program is based on a one-dimensional space-marching formulation of the Boltzmann transport equation with a straight-ahead approximation. The effect of the long-range Coulomb force and electron interaction is treated as a continuous slowing-down process. Atomic (electronic) stopping power coefficients with energies above a few A MeV are calculated by using Bethe's theory including Bragg's rule, Ziegler's shell corrections, and effective charge. Nuclear absorption cross sections are obtained from fits to quantum calculations and total cross sections are obtained with a Ramsauer formalism. Nuclear fragmentation cross sections are calculated with a semiempirical abrasion-ablation fragmentation model. The relation of the final computer code to the Boltzmann equation is discussed in the context of simplifying assumptions. A detailed description of the flow of the computer code, input requirements, sample output, and compatibility requirements for non-VAX platforms are provided.

Wilson, John W.↗

NASA NTRS2001

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Li, Jian-Zhong↗

DOE OSTI2022

Panoramic Mapping of Phonon Transport from Ultrafast Electron Diffraction and Scientific Machine Learning

Abstract One central challenge in understanding phonon thermal transport is a lack of experimental tools to investigate frequency‐resolved phonon transport. Although recent advances in computation lead to frequency‐resolved information, it is hindered by unknown defects in bulk regions and at interfaces. Here, a framework that can uncover microscopic phonon transport information in heterostructures is presented, integrating state‐of‐the‐art ultrafast electron diffraction (UED) with advanced scientific machine learning (SciML). Taking advantage of the dual temporal and reciprocal‐space resolution in UED, and the ability of SciML to solve inverse problems involving coupled Boltzmann transport equations, the frequency‐dependent interfacial transmittance and frequency‐dependent relaxation times of the heterostructure from the diffraction patterns are reliably recovered. The framework is applied to experimental Au/Si UED data, and a transport pattern beyond the diffuse mismatch model is revealed, which further enables a direct reconstruction of real‐space, real‐time, frequency‐resolved phonon dynamics across the interface. The work provides a new pathway to probe interfacial phonon transport mechanisms with unprecedented details.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Quarkonium Polarization Kinetic Equation from Open Quantum Systems and Effective Field Theories

Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of J/ψ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2002

Microscopic Foundation and Simulation of Coupled Carrier-Temperature Diffusions in Semiconductor Lasers

A typical semiconductor-based optoelectronic device, such as a diode laser, consists of three subsystems: an optical field, an electron-hole plasma (EHP), and a host crystal lattice. The physics of such a device involves the interplay of optical, electrical and thermal processes. A proper description of such a device requires that all three processes are treated on equal footing and in a self-consistent fashion. Furthermore, since a semiconductor laser has intrinsic spatial inhomogeneity, such a self-consistency naturally leads to a set of partial differential equations in space and time. There is a significant lacking of research interest and results on the transport aspects of optical devices in the literature with only a few exceptions. Even the most important carrier diffusion coefficient has not been properly derived and studied so far for optically excited plasma, while most of the work adopted results from electronics community where heavily doped semiconductors with mainly one type of carriers are dealt with. The corresponding transport equation for plasma energy or temperature has received even less attention. In this talk we describe our recent results on such a self-consistent derivation of temperature and carrier-density diffusion equations coupled with the lasing process. Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field. The equations derived above are implemented in various limiting cases to a typical diode laser to study the consequences of nonlinear diffusion and the cross diffusion terms on laser behavior, especially the dynamic behavior of a diode laser under modulation. Detailed results will be presented by comparing with the standard rate equation results.

Li, J.↗

NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗

DOE OSTI2025

Kohn anomalies and phonon anharmonicity in iridium

Elemental iridium presents surprising challenges for both inelastic neutron scattering (INS) and theoretical thermal transport calculations due to its high neutron absorption cross-section and strong electron-phonon interactions, respectively. Here, in this study, we overcome these challenges to measure temperature-dependent phonon dispersion curves, compare these with calculations based on density functional theory (DFT), and ultimately examine the electron-phonon limited transport behaviors of this material. Our DFT calculations demonstrate Kohn anomalies, near the 𝐾 point of the iridium Brillouin zone, indicating coupling between electrons and phonons. Strong electron-phonon coupling can compete with anharmonic effects to determine electrical and thermal transport behaviors and make the Kohn anomalies challenging to observe. Nonetheless, our INS measurements map these anomalies and other dispersion features over the Brillouin zone from 100 to 700 K. These measurements also uncover unexpectedly large mode specific Grüneisen parameters obtained from the temperature-dependent phonon energies, highlighting strong anharmonicity in iridium. DFT-based Boltzmann transport calculations demonstrate how anharmonicity and electron-phonon couplings determine electronic and lattice transport behaviors. Furthermore, we correlate the Kohn anomalies with calculated electron-phonon nesting functions, Fermi surfaces, and DFT-derived coupling strengths. This study provides detailed insights into the temperature-dependent mode-resolved lattice dynamics and anharmonicity, transport behavior, and electron-phonon interactions.

DFT↗

DOE OSTI2025

Magnon thermal conductivity in multiferroics with spin cycloids

Multiferroic materials, characterized by the occurrence of two or more ferroic properties, hold potential in future technological applications and also exhibit intriguing phenomena caused by the interplay of multiple orders. One such example is the formation of spin-cycloid structures within multiferroic materials, which we investigate in this work by focusing on their magnon excitations and transport based on a general multiferroic Hamiltonian with an antiferromagnetic order. More specifically, we identify the ground state and explore the dynamics of magnon modes, revealing distinct in-plane and out-of-plane modes with anisotropic dispersion relations. The magnon modes include a massless excitation, known as the Goldstone boson, originating from the spontaneous breaking of the translational symmetry by the formation of the cycloid structures. By employing the Boltzmann transport formalism, the magnonic thermal conductivity with spin cycloids and low-temperature anisotropic behaviors is discussed. This work provides pathways to envision the spin-textured multiferroics, which may serve as a fertile ground to look for novel thermal and spin transport with the rich interplay of quasiparticles such as magnons and phonons.

Park, Hyeon Woo↗

DOE OSTI2022

First principles thermal transport modeling in GaN and related materials

Gallium nitride is a wide bandgap material utilized in a variety of technologies, including high-power electronics and light-emitting diodes, partly due to its favorable thermal properties. This chapter describes modern first-principles-based modeling of phonons and lattice thermal conductivity (k) of GaN, III-nitrides and related materials. In particular, we describe the theoretical underpinnings of calculating phonon dispersions, intrinsic phonon interactions, and other lattice dynamical properties from quantum perturbation theory and density functional theory (DFT) methods. Description of how these methods are then coupled with the Peierls-Boltzmann transport (PBT) equation to determine phonon distributions and lifetimes relevant for thermal transport is given. These theoretical and numerical methods have demonstrated quantitative accuracy and predictive power for calculating pristine k and defect-limited k from first principles for a variety of materials. We present a review of the literature utilizing DFT-PBT methods to understand novel k behaviors in III-nitrides and related materials.

Lindsay, Lucas↗

NASA NTRS1991

Transport of photons produced by lightning in clouds

The optical effects of the light produced by lightning are of interest to atmospheric scientists for a number of reasons. Two techniques are mentioned which are used to explain the nature of these effects: Monte Carlo simulation; and an equivalent medium approach. In the Monte Carlo approach, paths of individual photons are simulated; a photon is said to be scattered if it escapes the cloud, otherwise it is absorbed. In the equivalent medium approach, the cloud is replaced by a single obstacle whose properties are specified by bulk parameters obtained by methods due to Twersky. Herein, Boltzmann transport theory is used to obtain photon intensities. The photons are treated like a Lorentz gas. Only elastic scattering is considered and gravitational effects are neglected. Water droplets comprising a cuboidal cloud are assumed to be spherical and homogeneous. Furthermore, it is assumed that the distribution of droplets in the cloud is uniform and that scattering by air molecules is neglible. The time dependence and five dimensional nature of this problem make it particularly difficult; neither analytic nor numerical solutions are known.

Solakiewicz, Richard↗

DOE OSTI2024

Phonon modal analysis of thermal transport in ThO 2 with point defects using equilibrium molecular dynamics

Defects can significantly degrade the thermal conductivity of ThO 2 , an advanced nuclear fuel material as well as a surrogate for other fluorite-structured materials. Here, we investigate how point defects in ThO 2 impact phonon mode-resolved thermal transport. By incorporating phonon modes from lattice dynamics, we decompose the trajectory and heat flux to phonon normal mode space and extract key phonon properties, including phonon relaxation times and their contributions to thermal conductivity. We implement two methods. The first method is based on the Green Kubo formalism to resolve the contribution of each phonon mode to thermal conductivity. The second resolves the lifetime of individual phonon modes and the thermal conductivity is calculated using the Boltzmann transport equation within relaxation time approximation. Notably, a lower contribution of acoustic modes is revealed compared to perturbative approaches considering only three-phonon scattering processes. The effects of four types of point defects are evaluated. The strongest impact on a reduction in thermal conductivity is from Th interstitials, followed by Th vacancies. O interstitials/vacancies have a similar impact, albeit smaller than defects on the thorium sublattice. These observations are consistent with previous studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

A computational approach to complex junctions and interfaces

Molecular- and nano- junctions, surfaces, interfaces, and interfacial processes have been the subjects of this DOE supported program for about 20 years. We have investigated electronic and magnetic structure, spin-dependent charge transport, and emerging phenomena at surfaces and interfaces in a number of physical systems ranging from nano-clusters, to nanowires, to two-dimensional (2D) crystals and their interactions, to bulk matter. Eighty-four refereed papers were published [1-84], with a majority effort from the group led by the PI, and over a hundred presentations were made at international conferences. We use first-principles methods in the framework of density functional theory in conjunction with nano-equilibrium Green function techniques, semi-empirical Boltzmann transport theory, tight-binding models, and the Hubbard model and many-body wavefunction approaches. In pursuing our scientific goals, we have also developed a number of computational algorithms and computational packages.

2D materials↗

DOE OSTI2022

Reexamination of hydrodynamic phonon transport in thin graphite

The recent hydrodynamic phonon transport theory for graphitic materials has been supported by the measurements of the second sound at temperatures up to about 100 K. When boundary scattering becomes comparable to momentum-conserving normal phonon scattering processes that are responsible for phonon hydrodynamics, Poiseuille phonon flow phenomena can emerge to give rise to unique size-dependent thermal conductivity in thin graphite. Here, we examine the thickness range for the Poiseuille phonon flow to become observable in thin graphite with the use of both deviational Monte Carlo simulation of the Peierls-Boltzmann transport equation and four-probe thermal transport measurements. As the basal-plane thermal conductivity calculated by prior first-principles theories saturates to the graphite value when the thickness is increased to five graphene layers, the phonon dispersion of graphite is used in the current calculations of thin graphite of micrometer thickness and a 23-layer thick ultrathin graphite (UTG) sample. The calculations show that diffuse surface scattering by surface defects can lead to Poiseuille phonon flow at 50 K in thin graphite with the thickness close to several micrometers but not in the 65 μm thin graphite and 23-layer UTG, where phonon scattering by the top and bottom surfaces become, respectively, much less and more frequent than the normal processes. In addition, the calculation results with the bulk graphite dispersion and diffuse surface scattering show decreased basal-plane thermal conductivity with decreasing thickness, opposite to recent thermocouple measurements of thin graphite samples. In comparison, the calculation results reveal that partially diffuse surface defect scattering can yield the four-probe measurement results of UTG samples, which are prepared here with an improved process to minimize surface contamination.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Deciphering yield modification of hadron-triggered semi-inclusive recoil jets in heavy-ion collisions

Jet quenching is recognized as critical evidence for the existence of the quark-gluon plasma (QGP) and serves as an essential probe to study its transport properties. Measurements of hadron-triggered semi-inclusive recoil jets have gained popularity due to its capability to probe jets over an extended phase space at low transverse momenta (p T ) and large radii. Recent ALICE measurements showed that the I AA , yield ratio of recoil jets between heavy-ion and p+p collisions, rises with jet p T and exceeds unity at high p T , contradicting conventional expectations that jet quenching should result in I AA values less than one. In this contribution, we re-examine the surface bias and study the effects of energy losses for both trigger hadrons and recoil jets on I AA , employing the Linear Boltzmann Transport (LBT) model to simulate jet-medium interactions. Our findings suggest that a large portion of hadrons used for the triggers undergoes substantial energy loss, despite surface bias. In particular, the energy loss of the trigger hadrons elevates the I AA baseline, corresponding to the case of no energy loss for recoil jets, to be greatly larger than unity. This enhancement of the baseline implies that the measured I AA values being larger than unity could still signal jet quenching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Unravelling ultralow thermal conductivity in perovskite Cs2AgBiBr6: dominant wave-like phonon tunnelling and strong anharmonicity

Abstract Understanding the lattice dynamics and heat transport physics in the lead-free halide double perovskites remains an outstanding challenge due to their lattice dynamical instability and strong anharmonicity. In this work, we investigate the microscopic mechanisms of anharmonic lattice dynamics and thermal transport in lead-free halide double perovskite Cs 2 AgBiBr 6 from first principles. We combine self-consistent phonon calculations with bubble diagram correction and a unified theory of lattice thermal transport that considers both the particle-like phonon propagation and wave-like tunnelling of phonons. An ultra-low thermal conductivity at room temperature (~0.21 Wm −1 K −1 ) is predicted with weak temperature dependence( ~ T −0.34 ), in sharp contrast to the conventional ~T −1 dependence. Particularly, the vibrational properties of Cs 2 AgBiBr 6 are featured by strong anharmonicity and wave-like tunnelling of phonons. Anharmonic phonon renormalization from both the cubic and quartic anharmonicities are found essential in precisely predicting the phase transition temperature in Cs 2 AgBiBr 6 while the negative phonon energy shifts induced by cubic anharmonicity has a significant influence on particle-like phonon propagation. Further, the contribution of the wave-like tunnelling to the total thermal conductivity surpasses that of the particle-like propagation above around 310 K, indicating the breakdown of the phonon gas picture conventionally used in the Peierls-Boltzmann Transport Equation. Importantly, further including four-phonon scatterings is required in achieving the dominance of wave-like tunnelling, as compared to the dominant particle-like propagation channel when considering only three-phonon scatterings. Our work highlights the importance of lattice anharmonicity and wave-like tunnelling of phonons in the thermal transport in lead-free halide double perovskites.

Chemistry↗

DOE OSTI2025

Screening of Coulombic Interactions To Achieve a Higher Power Factor in Conjugated Polymers

Thermoelectric properties of conducting polymers typically suffer from molecular chain disordering, as charge transport is predominantly controlled by morphology. This is especially more problematic when counterions are introduced to tune the carrier concentration for optimal thermoelectric performance, which disturbs the morphology further. Here, in this work, we introduce a new avenue for enhancing thermoelectric properties without needing to regulate the morphology, namely, by controlling the coulombic interaction between polarons and counterions. We perform in situ de-doping thermoelectric experiments over 3 orders of magnitude change in electrical conductivity of three distinct thermoelectric polymers, namely, poly(3-hexylthiophene-2,5-diyl) (P3HT), poly[2,5-bis(3-dodecylthiophen-2-yl)thieno[3,2-b]thiophene] (PBTTT-C 12 ), and poly[2,5-(2-octyldodecyl)-3,6-diketopyrrolopyrrole-alt-5,5-(2,5-di(thien-2-yl)thieno[3,2-b]thiophene)] (OD-PDPP2T-TT) conjugated polymers, followed by grazing-incidence wide-angle X-ray scattering (GIWAXS) to study their respective morphologies. We demonstrate a 9-fold enhancement in the thermoelectric power factor in OD-PDPP2T-TT compared to PBTTT-C 12 and link it to the coulombic screening of charge carriers, including in the optimally doped regime. We support this hypothesis using Boltzmann transport equations and show that, in both P3HT and PBTTT-C 12 , as the polymer is doped, impurity scattering remains the dominant scattering mechanism, while in OD-PDPP2T-TT, the scattering mechanism changes from impurity to acoustic phonon limited, resulting in more effective screening of ionized counterions. Our results provide an additional knob to enhance the fundamental understanding of thermoelectric physics of conducting polymers and provide a pathway to achieve higher performance in the field of organic thermoelectrics.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Ultrafast low-temperature metal–insulator interface phonon dynamics and heat transport in a Pt/Gd 3 Fe 5 O 12 heterostructure

Interfacial thermal and acoustic phenomena have an important role in quantum science and technology, including in spintronic and spincaloritronic materials and devices. Simultaneous measurements of the low-temperature thermal and acoustic properties of a metal/insulator heterostructure reveal distinct dynamics in the characteristic phonon frequency ranges of acoustic and thermal transport. The measurements probed a heterostructure consisting of a thin film of Pt on the ferrimagnetic insulator gadolinium iron garnet (Gd 3 Fe 5 O 12 , GdIG) grown epitaxially on a gadolinium gallium garnet substrate. Ultrafast structural dynamics within the Pt layer were tracked using time-resolved ultrafast x-ray diffraction and analyzed to probe interfacial acoustic and thermal properties. The rapid heating of the Pt layer by a 400 nm wavelength femtosecond-duration optical pulse produced transient structural changes that provided the stimulus for these measurements. Rapid heating produced a broadband acoustic pulse that was partially reflected by the Pt/GdIG interface. Temporal frequencies up to 740 GHz, corresponding to angular frequencies of several THz, were detected in a wavelet analysis of the acoustic oscillations of the strain in the Pt layer. The structural results were analyzed to determine (i) the acoustic damping coefficient and phonon mean free path in Pt at frequencies of hundreds of GHz and (ii) the Grüneisen anharmonicity parameter. The thermal conductance of the Pt/GdIG interface was tracked using the slower, tens-of-picosecond-scale, dynamics of the initial cooling of the heated Pt layer. Analysis using a model based on the Boltzmann transport equation shows that the phonon transmission is lower at the phonon frequencies relevant to thermal transport than for subterahertz regime acoustics.

Acoustic phenomena↗