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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗
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.↗
DOE OSTI2022

First-principles ionized-impurity scattering and charge transport in doped materials

Scattering of carriers with ionized impurities governs charge transport in doped semiconductors. However, electron interactions with ionized impurities cannot be fully described with quantitative first-principles calculations, so their understanding relies primarily on simplified models. Here we show an ab initio approach to compute the interactions between electrons and ionized impurities or other charged defects. It includes the short- and long-range electron-defect (e-d) interactions on equal footing and allows for efficient interpolation of the e-d matrix elements. Here we combine the e-d and electron-phonon interactions in the Boltzmann transport equation to compute the carrier mobilities in doped silicon over a wide range of temperature and doping concentrations, seamlessly spanning the defect- and phonon-limited transport regimes. The individual contributions of the defect- and phonon-scattering mechanisms to the carrier relaxation times and mean-free paths are analyzed. Our method provides a powerful tool to study electronic interactions in doped materials. It broadens the scope of first-principles transport calculations, enabling studies of a wide range of doped semiconductors and oxides with application to electronics, energy, and quantum technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Electron-phonon drag enhancement of transport properties from a fully coupled ab initio Boltzmann formalism

We present a combined treatment of the nonequilibrium dynamics and transport of electrons and phonons by carrying out ab initio calculations of the fully coupled electron and phonon Boltzmann transport equations. We find that the presence of mutual drag between the two carriers causes the thermopower to be enhanced and dominated by the transport of phonons, rather than electrons as in the traditional semiconductor picture. Drag also strongly boosts the intrinsic electron mobility, thermal conductivity and the Lorenz number. Impurity scattering is seen to suppress the drag enhancement of the thermal and electrical conductivities, while having weak effects on the enhancement of the Lorenz number and thermopower. We demonstrate these effects in n-doped 3C-SiC at room temperature, and explain their origins. This work establishes the roles of microscopic scattering mechanisms in the emergence of strong drag effects in the transport of the interacting electron-phonon gas.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Ab initio electron dynamics in high electric fields: Accurate prediction of velocity-field curves

Electron dynamics in external electric fields governs the behavior of solid-state electronic devices. First-principles calculations enable precise predictions of charge transport in low electric fields. However, studies of high-field electron dynamics remain elusive due to a lack of accurate and broadly applicable methods. In this work, we develop an efficient approach to solve the real-time Boltzmann transport equation with both the electric field term and ab initio electron-phonon collisions. These simulations provide field-dependent electronic distributions in the time domain, allowing us to investigate both transient and steady-state transport in electric fields ranging from low to high (> 10 kV/cm). The broad capabilities of our approach are shown by computing nonequilibrium electron occupations and velocity-field curves in Si, GaAs, and graphene, obtaining results in quantitative agreement with experiment. Our approach sheds light on microscopic details of transport in high electric fields, including the dominant scattering mechanisms and valley occupation dynamics. Our results demonstrate quantitatively accurate calculations of electron dynamics in low to high electric fields, with broad application to power and micro-electronics, optoelectronics, and sensing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Space-time dependent thermal conductivity in nonlocal thermal transport

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A First Principles Approach to Spectral Phonon Transport in Heterostructures

Understanding thermal transport across interfaces which give rise to a thermal resistance (also known as Kapitza resistance) is a critical issue affecting the development of nanotechnologies. Much modern and emergent nanotechnology consist of adjacent materials, and phonon mediated heat transfer governs thermal behavior across internal interfaces in these devices. The physics of thermal transport in solids are governed both by phenomena occurring at the atomic scale and interactions with the material's microstructure. The forecasting of fundamental quantities such as temperature, heat flux and thermal conductivity typically employs the semi-classical Boltzmann transport equation to predict the macroscopic behavior of materials in terms of the microscopic dynamics of its heat carriers. Kapitza resistance was first discovered in liquid helium experiments and has led to a fundamental research thrust in micro and nano-scale heat transport, the behavior of thermal carriers across internal interfaces. Thermal interfacial resistance (TIR) is a widely studied phenomenon, first engaged by Swartz and Pohl through their development of the acoustic and diffuse mismatch methods, then continued through myriad efforts with varying methods and approaches in an attempt to resolve carrier behavior at thermal interfaces. Many of the fundamental approaches to TIR have been at the nanoscale, and research is conducted with molecular dynamics (MD) and density functional theory (DFT) methods. The limitations of these methods is system size; atomistic methods tend to be limited to system sizes of 100,000 atoms or less. Larger length-scale methods have also been pursued, based on the principles of acoustic or diffuse mismatch, but not all include simulation of TIR using a full phonon band spectrum, or temperature dependent methods. Our approach to enabling phonon transport in layered materials draws upon our previous work of demonstrating spectrally coupled phonon transport in homogeneous and heterogeneous materials. We use a semi-analytical approach in which the Bose-Einstein (B-E) statistics set the strength of the phonon radiance in a frequency group, but the B-E statistics are informed with information from the transport system. The B-E statistics in a single frequency group feels the influence of all the groups through the spatial temperature. We also include a new field term which is an indicator of the amount of non-equilibrium behavior of the phonon spectrum---this is added to the phonon source term in all groups to ensure closure and conservation of energy, as the phonon groups in the transport system and the analytical systems are coupled. This work builds upon our previous approach by adding a phonon coupling term at an internal interface, using the principles of the DMM through transmission and reflection coefficients. In this work, the coefficients are determined through computing a common temperature at the interface, influenced by the phonon band structure of both materials, in effect, providing mixing between the two material systems and using the common temperature to set the strength of the phonon radiance at the boundaries on either side of the interface. Our approach uses material properties computed along various crystallographic orientations, and while some isotropy is built into the interface condition, the material properties weight the phonon distributions in the proper crystalline direction. Greater resolution of phonon behavior in proximity to an interface, and more accurate predictions of TIR are obtained. While it is true the assumption of diffuse mismatch can yield inconsistent results compared to experiment especially at low temperatures, this work focuses on room temperature and beyond effects, for future applications in nuclear fuel, or thermoelectric devices; a modified mismatch approach may be feasible if applied properly. Additionally, our methods focus on bridging mesoscale to engineering scale

36 MATERIALS SCIENCE↗
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 OSTI2022

Combined Experimental and Computational Study of Molybdenum and Niobium for Nuclear Sensor Application

Due to their novel electromagnetic and thermal properties, molybdenum (Mo) and niobium (Nb) become optimal temperature sensor materials for nuclear energy applications. We leveraged voltage recorded during a heat ramp to tune a computational method to predict the Seebeck electromotive force (EMF) of Mo and Nb. Using a combined Density Functional Theory (DFT) and Boltzmann Transport Equations (BTE) method the voltage was predicted but did not include the effects of temperature on atomic structure. Combining Ab Initio Molecular Dynamics (AIMD) and BTE included temperature effects on structure optimization and yielded voltages in a good agreement with experiment. Lanthanum (La) and Phosphorus (P) additives in Mo and Nb, respectively, could increase the EMF compared to those of the pure metals. The presence of oxygen (O) in Mo increases the EMF while O in Nb slightly reduces the EMF. Furthermore, our studies suggested that heat treatment-induced structural changes that lead to a reduction in voltage occur not only at the mesoscale as previously understood but also at the atomic scale.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

A hybrid Monte Carlo-deterministic second moment method with efficient variance reduction

In this work, we present a hybrid method that combines Monte Carlo with deterministic finite element methods to solve a linear Boltzmann transport equation. Our hybrid method runs orders of magnitude faster than Monte Carlo, without sacrificing accuracy, for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material. We believe that this is the first demonstration of a hybrid Second Moment Method in more than one spatial dimension, the first to consider more than one material, and the first to use variance reduction. Our variance reduction approach arises from an asymptotic analysis in which we show that the magnitude of the scattering source grows without bound. We transform the problem to compute the deviation of the radiation intensity from isotropy. The magnitude of the source in the transformed problem is bounded, and the quality of the hybrid method solution is dramatically improved by a substantial reduction in the variance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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 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 OSTI2022

Weak-Bonding Elements Lead to High Thermoelectric Performance in BaSnS 3 and SrSnS 3 : A First-Principles Study

SnS2, an earth-abundant and ecofriendly material, is limited as a thermoelectric material because of the high lattice thermal conductivity κ L and low carrier mobility μ. By introducing weak-bonding elements Ba or Sr into the SnS 2 framework, we discovered two SnS 2 -based materials BaSnS3 and SrSnS3 with the calculated low κL values of 0.15 and 0.17 W m -1 K -1 , respectively, along the a-axis. The low group velocity and high lattice anharmonicity originating from the weakened and distorted Sn–S bonding network are found in both systems. Moreover, the vibrations of Ba and Sr induce low-lying optical phonons, which strongly couple with the acoustic phonons and strengthen the phonon scattering rates. Compared to SnS 2 , both compounds present lower single-band effective masses, smaller deformation potential constants, and better band convergence, which enhance μ with an insignificantly reduced effective mass. By solving the linearized Boltzmann transport equation with a nonempirical carrier lifetime, we predict excellent ZT values of 2.89 and 2.77 along the a-axis at 900 K in BaSnS 3 and SrSnS 3 , respectively. Further phase diagram calculations of Ba 1–x Sr x SnS 3 solid solutions propose a new compound, Ba 0.5 Sr 0.5 SnS 3 , with an even higher ZT of 3.0. Our work analyzes explicitly how weak-bonding elements enhance μ and suppress κL simultaneously in SnS 2 -analogous systems with a series of compounds nominated as potential high-performance thermoelectric materials.

36 MATERIALS SCIENCE↗
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 OSTI2020

Vibrational hierarchy leads to dual-phonon transport in low thermal conductivity crystals

Many low-thermal-conductivity ( κ L ) crystals show intriguing temperature ( T ) dependence of κ L : κ L ∝ T -1 (crystal-like) at intermediate temperatures whereas weak T -dependence (glass-like) at high temperatures. It has been in debate whether thermal transport can still be described by phonons at the Ioffe-Regel limit. In this work, we propose that most phonons are still well defined for thermal transport, whereas they carry heat via dual channels: normal phonons described by the Boltzmann transport equation theory, and diffuson-like phonons described by the diffusion theory. Three physics-based criteria are incorporated into first-principles calculations to judge mode-by-mode between the two phonon channels. Case studies on La 2 Zr 2 O 7 and Tl 3 VSe 4 show that normal phonons dominate low temperatures while diffuson-like phonons dominate high temperatures. Our present dual-phonon theory enlightens the physics of hierarchical phonon transport as approaching the Ioffe-Regel limit and provides a numerical method that should be practically applicable to many materials with vibrational hierarchy.

42 ENGINEERING↗
DOE OSTI2023

Wide-range continuous tuning of the thermal conductivity of La0.5Sr0.5CoO3-δ films via room-temperature ion-gel gating

Abstract Solid-state control of the thermal conductivity of materials is of exceptional interest for novel devices such as thermal diodes and switches. Here, we demonstrate the ability to continuously tune the thermal conductivity of nanoscale films of La 0.5 Sr 0.5 CoO 3- δ (LSCO) by a factor of over 5, via a room-temperature electrolyte-gate-induced non-volatile topotactic phase transformation from perovskite (with δ ≈ 0.1) to an oxygen-vacancy-ordered brownmillerite phase (with δ = 0.5), accompanied by a metal-insulator transition. Combining time-domain thermoreflectance and electronic transport measurements, model analyses based on molecular dynamics and Boltzmann transport equation, and structural characterization by X-ray diffraction, we uncover and deconvolve the effects of these transitions on heat carriers, including electrons and lattice vibrations. The wide-range continuous tunability of LSCO thermal conductivity enabled by low-voltage (below 4 V) room-temperature electrolyte gating opens the door to non-volatile dynamic control of thermal transport in perovskite-based functional materials, for thermal regulation and management in device applications.

42 ENGINEERING↗
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↗