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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Experimental Study of the Fundamental Properties of Warm Dense Mixtures

The aim of the proposed research was to provide a multi-scale study of the properties of warm dense hydrocarbons, by studying the thermodynamic properties through the equation of state and the microscopic properties by x-ray scattering. Understanding the fundamental properties of warm dense mixtures is an intellectual challenge due to the complexity of the system. Unlike liquids or gases, where constituent particle interactions occur through collisions or bonding between valence electrons, in these strongly coupled systems the atoms will be partially ionized and compressed so tightly together that interactions between the inner core electrons can play a role in the systems chemistry. Advances in computational capabilities and development of new theoretical models have been used to predict the properties of mixtures but there is currently no experimental data of the fundamental interaction between the particles in mixtures to test these predictions against. The proposed research was to experimentally investigate the interaction of the different species in hydrocarbons by measuring the compressibility of substances with different carbon and hydrogen ratios and the complexity of the microscopic interactions through elastic and inelastic x-ray scattering. To study the bulk properties of warm dense hydrocarbons we established the Warm Dense Matter Research Laboratory (WDMRL) in the Institute for Shock Physics at Washington State University. The goal was for experiments in the WDMRL to determine shock loading conditions of interest in the hydrocarbon mixtures. We planned on using Hugoniot EOS measurements and a range of carbon and hydrogen concentrations to determine conditions when the EOS of the mixture varied significantly from that of the classical mixing model. Even though shock transit measurements through aluminum foils suggested pressures upto 400GPa, the experiments in the WDMRL were unsuccessful in getting usable shockwave compression data above 100GPa in polystyrene which was below the pressure of interest for hydrocarbon mixtures (>200GPa). To complete the project, we tested a technique using x-ray phase contrast imaging to map the location of tracer layers in a test sample of polycarbonate to record the material motion in dynamically compressed samples. A technique that will be useful for future warm dense matter experiments. These experiments used <200nm gold layers in polycarbonate samples to measure the material velocity and shock speed using x-ray phase contrast imaging. These results were compared to continuum surface measurements performed at ISP and show that the tracer layer technique can measure hydrodynamic properties accurately in dynamically compressed materials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

First-Principles Simulation of Beam-Induced Processes Underlying Atomic Manipulation in Electron Microscopes

The development of experimental methods and apparatuses capable of promoting atomically precise material manipulations holds great promise for realizing the ultimate limit of feature miniaturization in materials and devices. The ability to modify materials atom by atom is anticipated to usher in new technologies in areas as diverse as separation science, medicine, and quantum information science. Historically, scanning probe-based techniques have been the most prominent approaches in this space. However, these methods are best suited for the manipulation of surface-exposed regions of materials, as the strong perturbations required for bond scission are delivered most effectively to atoms in the near-proximity to the scanning probe. In contrast, convergent electron beams with energies tuned slightly below the threshold for inducing irreversible knock-on damage have recently been employed (within scanning transmission electron microscopy) to promote atomic-scale bond rearrangements in various beam-stable solids. Currently, however, the efficiency and selectivity of beam-induced atomic manipulation processes with focused electron beams are such that long irradiation times are required to induce a desired atomic rearrangement. With a better understanding of the underlying physics dictating the outcome of a given irradiation event, methods can be devised to improve the efficiency of these techniques so that their promise can be fully realized through widespread adoption.To this end, this Account details our recent efforts to develop and apply tractable first-principles simulation approaches for studying the response of materials to electric beam-like external electric potentials applied in real space. We briefly review the concepts and capabilities in the area of atomically precise materials manipulation and review the early demonstrations of accomplishments in this area, focusing on studies using scanned convergent electron beam probes in particular. We expound upon the depth of the challenge and identify critical shortcomings of theoretical methods that have previously been employed in the simulation of beam-induced processes. We then describe the computational methods that we have generalized from the concepts and tools most commonly applied to the study of molecular photochemistry and how our adaptations of these methods can be employed to capture the relevant dynamical phenomena for beam-induced processes ranging from the initial electron scattering to the ensuing multistate reactions. Here, we contextualize these methods within the current state of the art in this area, which has historically focused primarily on the simulation of inelastic image formation in the electron microscope for the purpose of interpreting the results of quantitative electron microscopy experiments. We demonstrate that the spatial distribution of state-specific excitation rates due to the presence of an external (probe) electric charge is inhomogeneous, such that irradiation at particular locations in materials can favor specific electronic transitions (and disallow others). In addition to the potential for excited-state reaction pathways to be accessed through the initial inelastic scattering of the tightly focused electron beam from the targeted atoms, we also identify favorable conditions for the electronically nonadiabatic evolution of the highly vibrationally excited system to open complex multistate reaction pathways. Implications of the early results for understanding the mechanisms and potential routes to improved efficiency and selectivity in beam-induced reactions are discussed. We conclude with a summary of the current state of theory and modeling capabilities in this area and provide our perspective on future directions for theoretical and experimental developments that we view as crucial to advancing the use of convergent electron beams in mode-specific, atomically precise platforms for direct-write materials modifications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Uranium Carbide and Uranium-Metal Thermal Scattering Law Evaluations and Cross Sections [Slides]

New Uranium Carbide and Uranium Metal evaluations have been developed using the FLASSH platform. Ab initio LD/MD models converged electronic, magnetic, and dynamical properties and demonstrate good agreement with experimental data. Thermal scattering cross sections generate inelastic and elastic thermal neutron scattering libraries in FLASSH . New TSL evaluations occurred in the production of ENDF File 7 data for Uranium Carbide and Uranium Metal submitted to NNDC for ENDF/B-VIII.1 release.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Generalized quasiharmonic approximation via space group irreducible derivatives

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature-dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. In this work we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second-order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO 2 ) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time-domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data-driven applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Coupled Hydromechanical Modeling and Assessment of Induced Seismicity at FWU: Utilizing Time-Lapse VSP and Microseismic Data

The objective of this work is to utilize integrated geomechanics, field vertical seismic profile (VSP) and microseismic data to characterize the complex subsurface stress conditions at the Farnsworth Unit (FWU). The model is based on a five-spot sector model extracted from a primary geomechanical model. The five-spot well injection pattern is characterized by extensive reservoir characterization data, such well logs, extracted cores and borehole geophone data, to facilitate the detailed examination of stress changes and microseismic event occurrences. The study utilizes field vertical seismic volumes acquired from the injection well 13-10A. The seismic volumes successfully provided snapshots of the behavior of the reservoir at distinct times. The use of VSP and microseismic data provided direct and indirect estimates of the dynamic stress changes occurring in the overburden, reservoir and underburden rock formations. In order to illuminate the stress regions and identify rocks that have undergone inelastic failure, microseismic event occurrences were utilized. Microseismic activity has been detected at the FWU; further study of its locations, timing, and magnitude was needed to deduce the nature of the changing stress state. The results of the study revealed that microseismic events were successfully modeled within the Morrow B formation. Moment magnitudes of seismic events were within the same magnitudes for events in the reservoir, suggesting the suitability of the model. The results of the study showed that the computed moment magnitudes for seismic events were insignificant to warrant safety concerns. The study findings showed the usefulness of coupled hydromechanical models in predicting the subsurface stress changes associated with CO 2 injection. The knowledge gained from this study will serve as a guideline for industries planning to undertake underground CO 2 storage, and characterize the subsurface stress changes.

02 PETROLEUM↗
DOE OSTI2026

Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. II. Deuteron and spectator nucleon tagging

We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (previous article), we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. In Part II (this article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. Methods of light-front quantization are employed to separate nuclear and hadronic structure in the high-energy process and achieve a composite description. The light-front wave function of the polarized deuteron is obtained from a rotationally covariant three-dimensional wave function in the center-of-mass frame of the proton-neutron system. The tagged structure functions are computed in the impulse approximation. The momentum and spin distribution of the active nucleon are controlled by the deuteron polarization and the detected spectator momentum (𝐷/𝑆 wave ratio). The cross section and spin asymmetries are evaluated for general deuteron polarization (vector and tensor, longitudinal and transverse) as functions of the spectator momentum. Tensor-polarized spin asymmetries of order unity are achieved for spectator momenta of approximately 300 MeV, which select configurations with a large 𝐷 wave. Sum rules for the tagged spin structure functions are derived. The results can be used for simulations of spectator tagging in future polarized fixed-target experiments (Jefferson Lab) or at the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Linear Boltzmann transport for jet propagation in the quark-gluon plasma: Inelastic processes and jet modification

A linear Boltzmann transport (LBT) Monte Carlo model has been developed to describe jet propagation and interaction with the quark-gluon plasma (QGP) in relativistic heavy-ion collisions. A complete set of elastic-scattering processes and medium-induced gluon emissions based on the higher-twist formalism are incorporated for both jet shower and medium recoil partons. It has been employed to describe experimental data on large transverse momentum hadron and jet spectra, correlation and jet substructures in high-energy heavy-ion collisions. Here, we document in detail the structure of the model and validation of the Monte Carlo implementations of the physics processes in LBT, in particular, the inelastic process of medium-induced gluon radiation. We carry out a comprehensive examination of the jet-medium interaction as implemented in LBT through energy loss and momentum broadening of a single hard parton, the energy and transverse momentum transfer from leading partons to medium-induced gluons and jet-induced medium excitation, and medium modification of reconstructed jets in a static and uniform medium. With realistic and event-by-event hydrodynamic medium in heavy-ion collisions, we compute and compare with experimental data on the jet cone-size dependence of the single inclusive jet suppression at both the BNL Relativistic Heavy-Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), the dijet asymmetry at the LHC and γ-jet correlation at RHIC. Effects of medium-induced gluon emissions and jet-induced medium excitation on jet observables are systematically examined. Rescatterings of the radiated gluons and recoil partons with the QGP are found essential to account for the enhancement of soft particle yield toward the edge of the jet cone.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Anisotropic inelastic materials milestone 2021

The focus on new fuel and cladding models are drivers for several new capabilities at the MOOSE and BISON levels. Since these materials are anisotropic, they require an extension of our inelastic mechanics capabilities, which currently heavily rely on radial return mapping and the assumption of isotropic stiffness. We plan to add additional code paths to support fully anisotropic materials, without degrading the performance for modeling isotropic materials.

42 ENGINEERING↗
DOE OSTI2025

Dynamical structure factors of warm dense matter from time-dependent orbital-free and mixed-stochastic-deterministic density functional theory

Abstract We present the first calculations of the inelastic part of the dynamical structure factor (DSF) for warm dense matter (WDM) using time-dependent orbital-free density functional theory (TD-OF-DFT) and mixed-stochastic-deterministic (mixed) Kohn Sham TD-DFT (KS TD-DFT). WDM is an intermediate phase of matter found in planetary cores and laser-driven experiments, where the accurate calculation of the DSF is critical for interpreting x-ray Thomson scattering measurements. Traditional TD-DFT methods, while highly accurate, are computationally expensive, motivating the exploration of TD-OF-DFT and mixed TD-KS-DFT as more efficient alternatives. We applied these methods to experimentally measured WDM systems, including solid-density aluminum and beryllium, compressed beryllium, and carbon–hydrogen mixtures. Our results show that TD-OF-DFT requires a dynamical kinetic energy potential in order to qualitatively capture the plasmon response. Additionally, it struggles with capturing bound electron contributions. In contrast, mixed TD-KS-DFT offers greater accuracy in distinguishing bound and free electron effects, aligning well with experimental data, though at a higher computational cost. This study highlights the trade-offs between computational efficiency and accuracy, demonstrating that TD-OF-DFT remains a valuable tool for rapid scans of parameter space, while mixed TD-KS-DFT should be preferred for high-fidelity simulations. Our findings provide insight into the future development of DFT methods for WDM and suggest potential improvements for TD-OF-DFT.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Software Verification and Validation Guidelines for Non-Linear Soil-Structure Interaction Analysis

Seismic analysis of structures, systems, and components (SSCs), including the consideration of soil-structure interaction (SSI) effects, is an important and required step in the design and licensing of nuclear power plant SSCs important to safety. Historically, the SSI analysis of nuclear structures has been performed using equivalent linear methods. However, there has been considerable industry investment in alternative seismic design and analysis approaches to reduce the construction cost of new reactors. Toward that goal and in alignment with the Licensing Modernization Project (LMP) framework, the Nuclear Regulatory Commission (US NRC) has proposed a risk-informed, performance-based approach to seismic design that allows inelastic response in those nuclear plant structures not required for confinement. As a complementary effort, reactor designers are exploring nonlinear seismic analysis methods to optimize structural designs and reduce construction costs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Improved control of electron computer-generated holographic grating groove profiles using ion beam gas-assisted etching

In a transmission electron microscope, electrons are described by matter-waves with wavelengths five orders of magnitude smaller than optical electromagnetic waves. Analogous to optical holography, electron wavefronts can be shaped using nanoscale holographic gratings. Here we demonstrate a novel, scalable nanofabrication method for creating off-axis holographic gratings that demonstrate near ideal diffraction efficiencies for binary, sinusoidal, and blazed grating groove profiles. We show that this method can produce up to 50 µm diameter area gratings that diffract up to 68% of the transmitted electron wave into a desired diffraction order with less than 7% into any other order. Additionally, we find that the amount of inelastically scattered electrons from the material gratings remaining in the coherent diffraction orders from the gratings is negligible in the far field.

Johnson, Cameron W.↗
DOE OSTI2022

Magnetic excitations, nonclassicality, and quantum wake spin dynamics in the Hubbard chain

Recent work has demonstrated that quantum Fisher information (QFI), a witness of multipartite entanglement, and magnetic Van Hove correlations G(r,t), a probe of local real-space real-time spin dynamics, can be successfully extracted from inelastic neutron scattering on spin systems through accurate measurements of the dynamical spin structure factor S(k,ω). In this work, we apply theoretically these ideas to the half-filled Hubbard chain with nearest-neighbor hopping, away from the strong-coupling limit. This model has nontrivial redistribution of spectral weight in S(k,ω) going from the noninteracting limit (U = 0) to strong coupling (U→∞), where it reduces to the Heisenberg quantum spin chain. We use the density matrix renormalization group to find S(k,ω), from which QFI is then calculated. We find that QFI grows with U. With realistic energy resolution it becomes capable of witnessing bipartite entanglement above U=2.5 (in units of the hopping), where it also changes slope. This point is also proximate to slope changes of the bandwidth W(U) and the half-chain von Neumann entanglement entropy. We compute G(r,t) by Fourier transforming S(k,ω). The results indicate a crossover in the short-time short-distance dynamics at low U characterized by ferromagnetic light-cone wavefronts, to a Heisenberg-type behavior at large U featuring antiferromagnetic light cones and spatially period-doubled antiferromagnetism. We find this crossover has largely been completed by U=3. Our results thus provide evidence that, in several aspects, the strong-coupling limit of the Hubbard chain is reached qualitatively already at a relatively modest interaction strength. We discuss experimental candidates for observing the G(r,t) dynamics found at low U.

1-dimensional systems↗
DOE OSTI2020

Temperature-dependent phonon lifetimes and thermal conductivity of silicon by inelastic neutron scattering and ab initio calculations

In this paper, inelastic neutron scattering on a single crystal of silicon was performed at temperatures from 100 to 1500 K. These experimental data were reduced to obtain phonon spectral intensity at all wave vectors $\overset{→}{Q}$ and frequencies ω in the first Brillouin zone. Thermal broadenings of the phonon peaks were obtained by fitting and by calculating with an iterative ab initio method that uses thermal atom displacements on an ensemble of superlattices. Agreement between the calculated and experimental broadenings was good, with possible discrepancies at the highest temperatures. Distributions of phonon widths versus phonon energy had similar shapes for computation and experiment. These distributions grew with temperature but maintained similar shapes. Parameters from the ab initio calculations were used to obtain the thermal conductivity from the Boltzmann transport equation, which was in good agreement with experimental data. Despite the high group velocities of longitudinal acoustic phonons, their shorter lifetimes reduced their contribution to the thermal conductivity, which was dominated by transverse acoustic modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

SHIVER - Spectroscopy HIstogram Visualizer for Event Reduction

Visualizing data from neutron scattering experiments is the first step in understanding the physics. The program is intended to generate and plot cuts and slices, through the four dimensional single crystal inelastic datasets, measured on direct geometry neutron spectrometers at the Spallation Neutron Source (ARCS, CNCS, HYSPEC, SEQUOIA).

Savici, AndreiT [Oak Ridge National Laboratory (OR↗
DOE OSTI2023

Validating ENDF/B-VIII.1beta1 with LLNL Pulsed-Sphere Neutron-Leakage Spectra [Slides]

In this presentation 6 Li Distinct changes are observed. 235 U Discussion shows Improvements (seen in VIII.1beta0) are coming from new PFNS informed by Chi-Nu experimental data. Additionally, 239 Pu large changes coming from inelastic scattering. 9 Be ENDF/B-VIII.0 shows to be better right after elastic peak while 16 O had slight changes. 19 F had small improvements in ENDF/B-VIII.1 and 56 Fe had noticeable changes in thicker spheres. Examples of negligible changes for the sake of completeness are given.

16-Oxygen↗
DOE OSTI2021

Application of Machine Learning Algorithms to Identify Problematic Nuclear Data

In this work we aim to show that Machine learning algorithms are promising tools for the identification of nuclear data that contribute to increased errors in transport simulations. We demonstrate this through an application of a machine learning algorithm (Random Forest) to the Whisper/MCNP6 criticality validation library to identify nuclear data that are associated with an increase of the bias (simulated - experimental $k_{eff}$) in the calculations. Specifically, the $k_{eff}$ sensitivity profiles (w.r.t. nuclear data) of 233 U solution benchmarks are used to predict the bias and Shapley Additive Explanations (SHAP) are used to explain how the sensitivities are related to the predicted bias. The SHAP values can be interpreted as sensitivity coefficients of the machine learning model to the $k_{eff}$ sensitivities which are used to make predictions of bias. Using the SHAP values we can identify specific subsets of nuclear data which have the highest probability of influencing bias. We demonstrate the utility of this method by showing how SHAP values were used to identify an inconsistency in the 19 F inelastic scattering nuclear data. The methodology presented here is not limited to transport problems and can be applied to other simulations if there are experimental measurements to compare against, simulations of those experimental measurements, and the ability to calculate sensitivities of the model output with respect to the data inputs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Prediction of Bi 2 Te 3 -Sb 2 Te 3 Interfacial Conductance and Superlattice Thermal Conductivity Using Molecular Dynamics Simulations

Bismuth telluride (Bi 2 Te 3 ) and its alloys with antimony telluride (Sb 2 Te 3 ) have long been considered to be the best room-temperature bulk thermoelectric (TE) materials. In recent decades, proof-of-concept demonstrations on Bi 2 Te 3 -Sb 2 Te 3 nanostructures have shown high TE performance due to reduction in lattice thermal conductivities. Particularly, ultra-low thermal conductivities have been observed in Bi 2 Te 3 -Sb 2 Te 3 1D superlattices, leading to thermoelectric figures of merit (ZT) as high as 2.4. In contrast, very few computational studies have been performed to provide insight into the phonon transport across these nanostructures. In this work, we use non-equilibrium molecular dynamics simulations with previously developed force fields to simulate thermal transport across Bi 2 Te 3 -Sb 2 Te 3 interfaces and superlattices. We first calculate the thermal conductance associated with a Bi 2 Te 3 -Sb 2 Te 3 interface across a temperature range of 200–400 K. Furthermore, the values are also compared with thermal conductances calculated by a modified Landauer transport formalism using phonon transmission coefficients obtained from the diffuse mismatch model. Our results show that inelastic scattering processes contribute to an increase in interfacial thermal conductance at higher temperatures. Finally, we calculate the thermal conductivities of Bi 2 Te 3 -Sb 2 Te 3 superlattices with varying period lengths from 2 to 18 nm. A minimum thermal conductivity of 0.27 W/mK is observed at a period length of 4 nm, which is attributed to the competition between incoherent and coherent phonon transport regimes. In comparison with previous experimental measurements in the literature, our results show good agreement with respect to the range of thermal conductivity values and the period length corresponding to the minimum superlattice thermal conductivity.

42 ENGINEERING↗