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NASA NTRS2013

Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, Linda Neergaard↗

NASA NTRS2013

Modeling of Particle Acceleration at Multiple Shocks via Diffusive Shock Acceleration: Preliminary Results

Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box. We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (E(sub max)) appropriate for quasi-parallel and quasi-perpendicular shocks and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, L. Neergaard↗

NASA NTRS2013

THEMIS Observations of the Magnetopause Electron Diffusion Region: Large Amplitude Waves and Heated Electrons

We present the first observations of large amplitude waves in a well-defined electron diffusion region based on the criteria described by Scudder et al at the subsolar magnetopause using data from one Time History of Events and Macroscale Interactions during Substorms (THEMIS) satellite. These waves identified as whistler mode waves, electrostatic solitary waves, lower hybrid waves, and electrostatic electron cyclotron waves, are observed in the same 12 s waveform capture and in association with signatures of active magnetic reconnection. The large amplitude waves in the electron diffusion region are coincident with abrupt increases in electron parallel temperature suggesting strong wave heating. The whistler mode waves, which are at the electron scale and which enable us to probe electron dynamics in the diffusion region were analyzed in detail. The energetic electrons (approx. 30 keV) within the electron diffusion region have anisotropic distributions with T(sub e(right angle))/T(sub e(parallel)) > 1 that may provide the free energy for the whistler mode waves. The energetic anisotropic electrons may be produced during the reconnection process. The whistler mode waves propagate away from the center of the "X-line" along magnetic field lines, suggesting that the electron diffusion region is a possible source region of the whistler mode waves.

magnetopause and boundary layers↗

NASA NTRS2014

A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation

Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double-strand breaks.

Plante, Ianik↗

NASA NTRS1960

Heat Diffusion in Gases, Including Effects of Chemical Reaction

The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.

Hansen, C. Frederick↗

NASA NTRS2017

Kinetic Monte Carlo Simulations of Oxygen Diffusion in Environmental Barrier Coating Materials

Ceramic Matrix Composite (CMC) materials are of interest for use in next-generation turbine engine components, offering a number of significant advantages, including reduced weight and high operating temperatures. However, in the hot environment in which such components operate, the presence of water vapor can lead to corrosion and recession, limiting the useful life of the components. Such degradation can be reduced through the use of Environmental Barrier Coatings (EBCs) that limit the amount of oxygen and water vapor reaching the component. Candidate EBC materials include Yttrium and Ytterbium silicates. In this work we present results of kinetic Monte Carlo (kMC) simulations of oxygen diffusion, via the vacancy mechanism, in Yttrium and Ytterbium disilicates, along with a brief discussion of interstitial diffusion. An EBC system typically includes a bond coat located between the EBC and the component surface. Bond coat materials are generally chosen for properties other than low oxygen diffusivity, but low oxygen diffusivity is nevertheless a desirable characteristic, as the bond coat could provide some additional component protection, particularly in the case where cracks in the coating system provide a direct path from the environment to the bond coat interface. We have therefore performed similar kMC simulations of oxygen diffusion in this material.

Good, Brian S.↗

NASA NTRSDate not supplied

Zircon (U-TH)/He Impact Crater Thermochronometry and the Effects of Shock Microstructures on Helium Diffusion Kinetics

Accurate age determinations of hyper-velocity impact and cratering events remains difficult and often controversial, while less than half of all known impact craters are regarded as accurately and precisely dated. Besides 40Ar/39Ar and U-Pb methods, zircon (U-Th)/He dating of impactites is a burgeoning technique to date large- to medium-sized impact structures. Zircon (U-Th)/He ages can be fully reset in minutes at 1000°C, T commonly reached in and directly adjacent to impact melt domains, whereas complete resetting of zircon (U-Th)/He at <300°C, which might be encountered near the crater margins or persist in post-impact hydrothermal systems, may take >103-4 years. However, there is a critical need to test the reliability of (U-Th)/He impact dating in shock deformed zircon, and to quantify helium diffusion kinetics in well-characterized grains with a broad spectrum of shock-induced defect substructures. For this purpose, we investigated samples from two impact structures, the 66 Ma Chicxulub multi-ring basin and the 15 Ma Ries complex crater, to compare zircon diffusion kinetics from impact structures with varying parameters, including size, age, and hydrothermal system longevity. Shock microstructures were characterized by backscattered-electron (BSE) imaging prior to determination of diffusion step-heating fractional release experiments using light-bulb furnace with prograde and retrograde incrementally 10°C steps from 300°C to 600°C. We find that zircon with low-level shock microstructures exhibit no significant deviation from helium diffusion kinetics of undamaged zircon. In contrast, zircon grains with planar deformation features and granular textures classified by SEM are characterized by a dramatic decrease in helium retentivity, similar to radiation damage, due to the reduction in the effective domain size and the introduction of fast diffusion pathways. This likely renders shocked grains more susceptible to impact-induced hydrothermal resetting. Hence, characterization of impact microstructure is critical for determining accurate impact ages, but also offers the opportunity to determine the magnitude and duration of post-impact hydrothermal circulation.

Catherine Ross↗

NASA NTRS2020

The Effect of UV and Solar Wind Exposure on the Reflectance of Two Black Diffuse Materials

The Bidirectional Reflectance Distribution Function (BRDF) and Total Hemispherical Reflectance (THR) of two candidate black diffuse materials for the dim calibration targets of the NASA GSFC PACE Ocean Color Instrument (OCI)were reported in the SPIE conference last year. In this paper, we present new BRDF and THR results of the two black diffuse materials following additional UV exposure and solar wind tests. The BRDF measurements for five samples of each two black diffuse material were made at incident angles of 0° and 45° and at the wavelengths of 360 nm, 600 nm, and 1600 usi ng the Table-top Goniometer (TTG) located in the Diffuser Calibration Laboratory (DCL) at NASA GSFC. The THR of the samples, 15 mm in diameter, was measured using a commercial UV-VIS-NIR spectrophotometer from 200 nm to 2500 nm. The spectral THR results of the two black diffuse materials exposed to UV and solar wind show an approximate 10 % higher reflectivity than the unexposed samples. The spectral profiles of the THR of the exposed and unexposed samples are relatively similar. The BRDF results at the incident angle of 45° show different trends in the forward and backward scattering regions, while those at normal incident angle are consistent with the THR results. We will also present the details of the samples’ surface features and the comparison of the 0°/45° BRDF and THR results, demonstrate the significance of background subtraction in the THR measurements for small, low reflectance samples, and discuss validation of BRDF scale, measurement repeatability, and major contributions of uncertainty.

Jinan Zeng↗

DOE OSTI2025

Diffusion and phase formation in the γ-uranium-technetium system

Phase formation in the U-Tc binary system at 800 °C was investigated using a diffusion couple experiment. Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) identified four novel potential intermetallic phases - U 7 Tc 3 , U 13 Tc 12 , U 3 Tc 5 , and UTc 4 . Diffusion coefficients were calculated for the intermetallic phases using the Boltzmann-Matano method and were respectively found to be – 120, 38.2, 15.6, and 1.51 × 10 −18 m 2 /s. Tc also exhibits a solid-solution phase with high penetration into the U with a diffusion coefficient of ∼ 10 −14 m 2 /s. Furthermore, these findings expand the number of known U-Tc phases and provide the first diffusion coefficients for the U-Tc system, and contribute valuable data to the broader field of actinide metallurgy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Multiscale, mechanistic modeling of irradiation-enhanced silver diffusion in TRISO particles

Tristructural isotropic (TRISO) particles are under consideration for use in several proposed advanced nuclear reactor concepts. The silicon carbide (SiC) layer in TRISO acts as a barrier to prevent the release of the fission products. However, despite remarkable retention, silver (Ag) release has been observed from intact particles, which requires investigation since the Ag isotope ( 110m Ag) has a long half-life. Previous work focused on developing a multiscale, mechanistic model for Ag diffusion accounting for temperature and microstructure effect and has been successfully validated. In this work, we expand the previous model to account for irradiation-enhanced Ag diffusivity in SiC and improve its accuracy over a wider grain size and temperature ranges relevant for advanced reactor conditions. A temperature, grain size, and flux dependent diffusivity is therefore derived using the mesoscale code MARMOT and implemented in the fuel performance code BISON. The irradiation-enhanced Ag diffusivity in SiC is compared against experimental data and validated using BISON against Ag release measurements from the Advanced Gas Reactor Fuel Development and Qualification Program (AGR-1 and AGR-2). Herein, we quantify the impact of SiC grain size, irradiation, and temperature on Ag release. In agreement with previous studies, we find accounting for SiC grain size improves agreement between BISON predictions and experimental observations for most cases. In conclusion, we also find that accounting for irradiation improves agreement for cases where Ag release was underestimated, but the impact was less significant than accounting for microstructure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion

The motion of dopants in magnetic spin lattices has received tremendous attention for at least four decades due to its connection to high-temperature superconductivity. Despite these efforts, we lack a complete understanding of their behavior, especially out of the equilibrium and at nonzero temperatures. In this paper, we take a significant step towards a much deeper understanding based on state-of-the-art matrix-product-state calculations. In particular, we investigate the nonequilibrium dynamics of a dopant in two-leg 𝑡−𝐽 ladders with antiferromagnetic XXZ spin interactions. In the Ising limit, we find that the dopant is localized for all investigated nonzero temperatures due to an emergent disordered potential, with a localization length controlled by the underlying correlation length of the spin lattice, which increases exponentially with decreasing temperature. The dopant, hereby, only delocalizes asymptotically in the zero temperature limit. This greatly generalizes the localization effect discovered recently in Hilbert space fragmented models [Phys. Rev. Res. 6, 023325 (2024), SciPost Phys. Core 7, 054 (2024)]. In the presence of spin-exchange processes at rate 𝛼, the dopant diffuses with a diffusion coefficient, 𝐷 ℎ , depending nonmonotonically on 𝛼. It initially increases linearly as 𝐷 ℎ ∝ 𝛼 for 𝛼 ≪ 1 before dropping off as 𝛼 −1 for 𝛼 > 1. Moreover, we show that the underlying spin dynamics at infinite temperature behaves qualitatively the same, albeit with important quantitative differences. We substantiate these findings by showing that the dynamics features self-similar scaling behavior, which strongly deviates from the Gaussian behavior of regular diffusion, especially for weak spin exchange. Finally, we show that the diffusion coefficient 𝐷 ℎ follows an Arrhenius relation at high temperatures, whereby it is exponentially suppressed upon cooling.

Anomalous diffusion↗

DOE OSTI2024

Interpenetrated Structures for Enhancing Ion Diffusion Kinetics in Electrochemical Energy Storage Devices

The architectural design of electrodes offers new opportunities for next-generation electrochemical energy storage devices (EESDs) by increasing surface area, thickness, and active materials mass loading while maintaining good ion diffusion through optimized electrode tortuosity. However, conventional thick electrodes increase ion diffusion length and cause larger ion concentration gradients, limiting reaction kinetics. We demonstrate a strategy for building interpenetrated structures that shortens ion diffusion length and reduces ion concentration inhomogeneity. This free-standing device structure also avoids short-circuiting without needing a separator. The feature size and number of interpenetrated units can be adjusted during printing to balance surface area and ion diffusion. Starting with a 3D-printed interpenetrated polymer substrate, we metallize it to make it conductive. This substrate has two individually addressable electrodes, allowing selective electrodeposition of energy storage materials. Using a Zn//MnO 2 battery as a model system, the interpenetrated device outperforms conventional separate electrode configurations, improving volumetric energy density by 221% and exhibiting a higher capacity retention rate of 49% compared to 35% at temperatures from 20 to 0 °C. Our study introduces a new EESD architecture applicable to Li-ion, Na-ion batteries, supercapacitors, etc.

25 ENERGY STORAGE↗

DOE OSTI2025

Diffusion behavior of lanthanide fission products in bcc Fe cladding: A first-principles study

Fuel-cladding chemical interaction poses significant challenges in nuclear reactors, where fission products generated from nuclear fuel interact with Fe-based cladding materials, potentially compromising their structural integrity. This study investigates the diffusion behavior of lanthanide fission products, Lanthanum (La), Cerium (Ce), Praseodymium (Pr), and Neodymium (Nd), within body-centered cubic (bcc) Fe cladding using the density functional theory, nudged elastic band method, and self-consistent mean field theory. Our results reveal significant vacancy binding energies, particularly with the 1st and 2nd nearest neighbors, which diminish beyond the 5th nearest neighbor, with La exhibiting the strongest binding affinity, followed by Nd, Ce, and Pr. The nudged elastic band calculations indicate significant high barriers for the dissociation of 1st nearest neighbor vacancy-solute pairs for all fission products. The tracer diffusion coefficients of these fission products were derived in an Arrhenius form, with a magnetic correction that accounts for the high-temperature paramagnetic state. The significant trapping effect of vacancies caused by a very dilute concentration of fission products reduces vacancy mobility, potentially leading to modifications in point defect supersaturation, void nucleation, and swelling under irradiation. These represent critical challenges for irradiated cladding materials. The tracer diffusion coefficients indicate that Nd diffuses the fastest, followed by La, Ce, and Pr. Furthermore, this study provides essential insights for understanding fission product transport in cladding materials and informs future design strategies to mitigate fuel-cladding chemical interaction, ultimately enhancing nuclear reactor safety and performance.

Diffusion↗

DOE OSTI2025

Radiation-reduced diffusion of Nd in bcc Fe

Here, this study combines ab initio calculations and kinetic Monte Carlo simulations to investigate the bulk diffusion of Nd, an exemplar lanthanide element, in bcc Fe. Contrary to the conventional belief that irradiation accelerates diffusion processes, our study reveals that irradiation can unexpectedly reduce the diffusion of Nd due to the strong binding between substitutional Nd atoms and vacancies in bcc Fe. Combined with the high concentration of nonequilibrium vacancies, this promotes the abundant formation of Nd+3Va defect complexes containing a single Nd substitutional atom and three vacancies, accompanied by the depletion of Nd-vacancy pairs that mediate the diffusion of Nd.

Density functional theory (DFT)↗

DOE OSTI2025

Parallel diffusion operator for magnetized plasmas with improved spectral fidelity

Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge for describing non-grid-aligned magnetic structures in Eulerian (grid-based) simulations. Here, the present paper describes and validates a new method for parallel diffusion in magnetized plasmas based on the anti-symmetry representation [Halpern and Waltz, Phys. Plasmas 25, 060703 (2018)]. In the anti-symmetry formalism, diffusion manifests as a flow operator involving the logarithmic derivative of the transported quantity. Qualitative plane wave analysis shows that the new operator naturally yields better discrete spectral resolution compared to its conventional counterpart. Numerical simulations comparing the new method against existing finite difference methods are carried out, showing significant improvement. In particular, we find that combining anti-symmetry with finite differences in diagonally staggered grids essentially eliminates the so-called “artificial numerical diffusion” that affects conventional finite difference and finite volume methods.

Anisotropic diffusion↗

DOE OSTI2025

A dynamic likelihood approach to filtering transport processes: advection-diffusion dynamics

A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems –waves–, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Preferential adsorption of noble gases in zeolitic tuff with variable saturation: A modeling study of counter-intuitive diffusive-adsorptive behavior

Noble gas transport through geologic media has important applications in the prediction and characterization of measured gas signatures related to underground nuclear explosions (UNEs). Retarding processes such as adsorption can cause significant species fractionation of radionuclide gases, which has implications for measured and predicted signatures used to distinguish radioxenon originating from civilian nuclear facilities or from UNEs. Accounting for the effects of variable water saturation in geologic media on tracer transport is one of the most challenging aspects of modeling gas transport because there is no unifying relationship for the associated tortuosity changes between different rock types, and reactive transport processes such as adsorption that are affected by the presence of water likewise behave differently between gas species. In this study, we perform numerical diffusive-adsorptive transport simulations to estimate gas transport parameters associated with bench-scale laboratory diffusion cell experiments measuring breakthrough in zeolitic and non-zeolitic rocks for a gaseous mixture of xenon, krypton, and SF 6 at varying degrees of water saturation (S w ). Counter-intuitive transport behavior was observed in the zeolitic rock experiments whereby breakthrough concentrations were significantly higher when the core was partially saturated (S w = 17 %) than under dry (S w = 0 %) conditions. Breakthrough of xenon was especially retarded in the dry core – likely due to comparatively high affinity of xenon for zeolitic adsorption sites – and estimated effective diffusion coefficients for all gases were approximately an order of magnitude lower than what is predicted by porosity-tortuosity models. We propose the counter-intuitive behavior observed is because water infiltration of zeolite nanopores reduces both the adsorptive capacity of the rock and the tortuosity of connected flow paths. We developed a two-site competitive kinetic Langmuir adsorption reaction for the porous media transport simulator in order to constrain transport parameters within zeolitic tuff, where differential adsorption to zeolite and non-zeolite pores was observed. We determined that liquid saturation-dependent diffusive-adsorptive transport is affected by subtle and at times competing processes that are specific to different gases, which have a significant overall influence on effective transport parameters.

58 GEOSCIENCES↗

DOE OSTI2025

Micro-tensile testing of neutron-irradiated Al/Zr and Zr/U-Mo diffusion bonds

This study focuses on micro-tensile testing of neutron-irradiated Al/Zr and Zr/U-Mo diffusion bonds, which are integral to the structure and performance of nuclear fuel plates used in the fuel being developed for U.S. high-power research reactors. During fabrication, two distinct diffusion bonds occur—one at the Zr/U-10Mo interface via roll bonding, and the Zr/Al interface via hot isostatic pressing at 833 K. This work utilizes micro-tensile testing specimens approximately 7 × 7 × 18 μm 3 , which are sufficiently large to encompass the identified diffusion zones to evaluate the failure strength and identify the failure location. For the Zr/Al interface, all failures occurred in the bulk aluminum. The average yield strength, ultimate strength, and strain at failure for the two parent samples were: 125 ± 10 MPa, 139 ± 24 MPa, 156 ± 21 MPa, 185 ± 14 MPa, 37.9 ± 5.6 %, and 29.7 ± 3.4 %, respectively. For specimens across the Zr/U-Mo interface, failures occurred either in the bulk Zr or U-Mo, with no failures observed in the diffusion region. For specimens that failed in the bulk Zr the failure strength and strain for the two parent samples were 570 MPa, 710 ± 131 MPa, and 43.3 %, 27.3 ± 6.6 % respectively. The specimens that failed in the bulk U-Mo had failure strengths and strains of 596 ± 32 MPa, 548 ± 124 MPa, and 2.2 ± 1.3 %, 1.5 ± 0.6 % respectively. In conclusion, these findings support the development of accurate thermo-mechanical models for irradiated fuel performance by identifying the mechanical limits and failure locations within the bonded regions.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗