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DOE OSTI2021

Simulating Dopant Diffusion in a Detalied Porous Structure

The National Ignition Facility (NIF) at Lawrence Livermore National Laboratory (LLNL) uses highpowered lasers to explore cutting edge fusion technology. Specialized optics, known as fiber lasers, generate and amplify the NIF’s high-powered lasers that facilitate fusion experiments. Fiber lasers are glass fibers that are doped with heavy elements to stimulate light emission. The fiber laser doping processing uses a predeposited layer of porous silica nanoparticles on the surface of the glass to absorb a dopant rich salt solution. Our project simulated the diffusion of dopants into porous silica with prescribed colloidal stacking geometries using COMSOL Multiphysics. With these simulations we identified the porosity and tortuosity of the porous nanoparticle structures as the primary parameters that will dictate how the dopants will diffusive into the porous surface of the glass. Porosity and Tortuosity are geometric parameters that can easily be input into more detailed simulations to estimate an effective diffusivity within the porous layer. Future work should account for surface reactions to accurately simulate the full-scale diffusion of the solution doping process.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Fundamental Studies of Tritium Diffusivity in Irradiation Defective Lithium Aluminate and Lithium Zirconates Pellets Used in TPBAR

Due to its excellent irradiation behavior at elevated temperatures, lithium aluminate (LiAlO 2 ) is used in the form of annular ceramic pellets enriched with the 6Li isotope in tritium producing burnable absorber rod (TPBAR). To simulate the nuclear characteristics and produce tritium (T), TPBAR is irradiated by a neutron flux in a pressurized water reactor (PWR). The T diffuses through the pellets and is captured by the metal getter where it chemically reacts and leads to formation of metal hydride. The transport of T in radiation damaged pellets that contain defects and impurities is not clearly understood due to the lack of fundamental studies of T solubility and diffusivity. The other candidate material possessing a similar physical and chemical properties and can be potentially useful as a tritium breading blanket in the future is Lithium Zirconates (Li 2 ZrO 3 ). In FY2017, we investigated the diffusion and solubility properties in irradiation defective LiAlO 2 and Li 2 ZrO 3 crystals with different level of tritium concentration. In FY2018 we continued to explore the diffusivity and solubility properties extensively in those candidate materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Hydrogen Diffusion Coefficient Measures on Thin Film Uranium Oxide

Thin films of uranium oxides, putatively UO 2 and U 3 O 8 , were deposited on palladium/silver (75/25) foil discs (10 μm thick, 10 mm diameter). Methodology for sealing these foils, applying a hydrogen pressure (~ 1 atm) to the oxide side, and measuring the pressure on the permeate side (opposite side of foil) is reported. The experimental apparatus is held at 100 °C to speed diffusion, aided by the pressure differential across the foil (~1 atm (750 torr) on oxide side, initially low vacuum on permeate side, ~1x 10 -4 torr). Early results indicate an effective diffusion coefficient of roughly 7.66 x 10 -17 +/- 2.22 x 10 -17 cm 2 /sec for UO 2 . These values are in line with expectations and prior measures relative to large lag times for system baseline (substrate only). Evaluation of the technique for U 3 O 8 thin films suggests further development will be needed to extend the technique to more oxidized films (U 3 O 8 , UO 3 ). Characterization of the foils (thickness and speciation) post diffusion experiments will be carried out by SIGMA (Eric Tegtmeier and Andy Richards) in FY24 which will sharpen the uncertainty quantification for UO 2 diffusion coefficients, aiding the nucleation model for DRACO.

36 MATERIALS SCIENCE↗

DOE OSTI2024

First-Principles Studies of Tritium Species Diffusivity Across the Interface of Nickel-Plated Zircaloy-4

In this study, we will calculate the 3H2 and 3H2O diffusion mechanism in the Ni coated layer and the dominant 3H species dissolution into the Zircaloy-4 getter. We will optimize the Ni/Zr interface and introduce Sn and O impurities. To achieve the objectives, we will perform the investigation by using spin-polarized density functional theory (DFT) methods to capture the effects of Ni magnetic properties on 3H diffusion. We will introduce NiO/Ni(OH) on the Ni side closer to the interface. Then, the 3H diffusion pathways and barriers from Ni side to the zircalory-4 will be explored. We will investigate how NiO/Ni(OH) affects the 3H diffusion across the interface.

Paudel, Hari P.↗

DOE OSTI2015

Spatial and Temporal Correlates of Greenhouse Gas Diffusion from a Hydropower Reservoir in the Southern United States

Emissions of CO 2 and CH 4 from freshwater reservoirs constitute a globally significant source of atmospheric greenhouse gases (GHGs), but knowledge gaps remain with regard to spatiotemporal drivers of emissions. We document the spatial and seasonal variation in surface diffusion of CO 2 and CH 4 from Douglas Lake, a hydropower reservoir in Tennessee, USA. Monthly estimates across 13 reservoir sites from January to November 2010 indicated that surface diffusions ranged from 236 to 18,806 mg m -2 day -1 for CO 2 and 0 to 0.95 mg m -2 day -1 for CH 4 . Next, we developed statistical models using spatial and physicochemical variables to predict surface diffusions of CO 2 and CH 4 . Models explained 22.7 and 20.9% of the variation in CO 2 and CH4 diffusions, respectively, and identified pH, temperature, dissolved oxygen, and Julian day as the most informative important predictors. These findings provide baseline estimates of GHG emissions from a reservoir in eastern temperate North America a region for which estimates of reservoir GHGs emissions are limited. Our statistical models effectively characterized non-linear and threshold relationships between physicochemical predictors and GHG emissions. Further refinement of such models will aid in predicting current GHG emissions in unsampled reservoirs and forecasting future GHG emissions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Diffuse Bands 9577 and 9633: Relations to Other Interstellar Features

We study, for the first time, the relations of two strong diffuse bands (DIBs) at 9633 and 9577 Å, commonly attributed to C{sub 60}{sup +}, to other interstellar features seen in optical and UV spectra including H i, Ca i, Fe ii, Na i, Ti ii, CN, CH, CH{sup +}, and C{sub 2} and DIBs 5780, 5797, 6196, 6269, 6284, and 6614. We analyzed 62 lines of sight where the stellar contamination by Mg ii was corrected or found negligible for DIB 9633. Equivalent widths of DIB 9577 were measured in 62 lines of sight. Poor mutual correlation between the strengths of the above features and the major diffuse bands (5780 and 5797) as well as with other DIBs (with some exceptions) were revealed. The considered DIBs are also poorly correlated with the features of neutral hydrogen, molecular carbon, and those of simple interstellar radicals. Perhaps this phenomenon can be explained if the diffuse band 9577 is an unresolved blend of two or more interstellar features. There are indications that 9633 and 9577 diffuse bands are stronger in σ-type clouds, i.e., these features resemble the behavior of reasonably broad DIBs, which are strong in the lines of sight where the UV flux from the very hot nearby stars plays an important role.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

The burrell schmidt deep virgo survey: tidal debris, galaxy halos, and diffuse intracluster light in the virgo cluster

We present the results of a deep imaging survey of the Virgo cluster of galaxies, concentrated around the cores of Virgo subclusters A and B. The goal of this survey was to detect and study very low surface brightness features present in Virgo, including discrete tidal features, the faint halos of luminous galaxies, and the diffuse intracluster light (ICL). Our observations span roughly 16 degrees{sup 2} in two filters, reaching a 3σ limiting depth of μ{sub B} = 29.5 and μ{sub V} = 28.5 mag arcsec{sup −2}. At these depths, our limiting systematic uncertainties are astrophysical: variations in faint background sources as well as scattered light from galactic dust. We show that this dust-scattered light is well traced by deep far-infrared imaging, making it possible to separate it from true diffuse light in Virgo. We use our imaging to trace and measure the color of the diffuse tidal streams and ICL in the Virgo core near M87, in fields adjacent to the core including the M86/M84 region, and to the south of the core around M49 and subcluster B, along with the more distant W{sup ′} cloud around NGC 4365. Overall, the bulk of the projected ICL is found in the Virgo core and within the W{sup ′} cloud; we find little evidence for an extensive ICL component in the field around M49. The bulk of the ICL we detect is fairly red in color (B − V = 0.7–0.9), indicative of old, evolved stellar populations. Based on the luminosity of the observed ICL features in the cluster, we estimate a total Virgo ICL fraction of 7%–15%. This value is somewhat smaller than that expected for massive, evolved clusters, suggesting that Virgo is still in the process of growing its extended ICL component. We also trace the shape of M87's extremely boxy outer halo out to ∼150 kpc, and show that the current tidal stripping rate from low luminosity galaxies is insufficient to have built M87's outer halo over a Hubble time. We identify a number of previously unknown low surface brightness structures around galaxies projected close to M86 and M84. The extensive diffuse light seen in the infalling W{sup ′} cloud around NGC 4365 is likely to be subsumed in the general Virgo ICL component once the group enters the cluster, illustrating the importance of group infall in generating ICL. Finally, we also identify another large and extremely low surface brightness ultradiffuse galaxy, likely in the process of being shredded by the cluster tidal field. With the survey complete, the full imaging data set is now available for public release.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Detection of Extraplanar Diffuse Ionized Gas in M83

We present the first kinematic study of extraplanar diffuse ionized gas (eDIG) in the nearby, face-on disk galaxy M83 using optical emission-line spectroscopy from the Robert Stobie Spectrograph on the Southern African Large Telescope. We use a Markov Chain Monte Carlo method to decompose the [N ii]λλ 6548, 6583, Hα, and [S ii]λλ 6717, 6731 emission lines into H ii region and diffuse ionized gas emission. Extraplanar, diffuse gas is distinguished by its emission-line ratios ([N ii]λ6583/Hα ≳ 1.0) and its rotational velocity lag with respect to the disk (Δv=−24 km s{sup −1} in projection). With interesting implications for isotropy, the velocity dispersion of the diffuse gas, σ=96 km s{sup −1}, is a factor of a few higher in M83 than in the Milky Way and nearby, edge-on disk galaxies. The turbulent pressure gradient is sufficient to support the eDIG layer in dynamical equilibrium at an electron scale height of h{sub z}=1 kpc. However, this dynamical equilibrium model must be finely tuned to reproduce the rotational velocity lag. There is evidence of local bulk flows near star-forming regions in the disk, suggesting that the dynamical state of the gas may be intermediate between a dynamical equilibrium and a galactic fountain flow. As one of the first efforts to study eDIG kinematics in a face-on galaxy, this study demonstrates the feasibility of characterizing the radial distribution, bulk velocities, and vertical velocity dispersions in low-inclination systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Parallel Diffusion Coefficient of Energetic Charged Particles in the Inner Heliosphere from the Turbulent Magnetic Fields Measured by Parker Solar Probe

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ ∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ ∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ ∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ ∥ = (5.16 ± 1.22) × 10 18 r 1.17 ± 0.08 E 0.71 ± 0.02 (cm 2 s -1 ) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Preliminary Monte Carlo and Thermal Hydraulic Analysis using a Hybrid ETF-Corrected-Diffusion Prediction Block

This paper builds upon previous work to accelerate the Picard iteration (PI) method typically applied for coupled Monte Carlo-Thermal hydraulic (MC-TH) solutions. Previously, the use of the generalized transfer functions (GTFs) to predict variation in macroscopic cross sections following a perturbation in TH properties was demonstrated for a subset of simple 3D problems. In addition, the reduced-order transport prediction block relied on the first order perturbation (FOP) method, which was shown to have computational overheads. Recent work replaced the FOP block with a 1-group nodal diffusion solver to eliminate these overheads. While the use of diffusion is desirable for large-scale problems, the new solver introduces significant homogenization error. This work aims to address this issue by using the Jacobian-Free Newton Krylov (JFNK) method to generate a set of super homogenization (SPH) factors to improve the accuracy of the diffusion solution. The SPH factors will be used in conjunction with an improved cross section prediction method – the expanded transfer function (ETF) method – to produce a highly accurate flux prediction for an axial 1D boiling water reactor (BWR) pincell following a large perturbation in moderator density. The ETF-corrected diffusion (ETF-CD) block is shown to be highly accurate for the 1D test case. Future work will investigate the accuracy of the method for a realistic 3D pressurized water reactor core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Effective Lanthanide Diffusivity through U-Zr Metallic Fuel

Fuel-cladding chemical interaction (FCCI) is one of the main concerns for the performance of U-Zr metallic fuels. Although FCCI results in complex phase transformations and morphological changes in both the fuel and cladding sides of the interface, the formation of a brittle layer in the cladding side of the interface (sometimes referred to as wastage) has one of the most significant impacts on the cladding mechanical integrity. This brittle layer is associated with the formation of intermetallic compounds between the cladding constituents Fe, Cr and the lanthanide fission product species. The formation of this cladding wastage layer has been the focus of recent efforts to develop a mechanistic modeling framework, including production of lanthanides in the fuel, transport through the fuel to the fuel-cladding interface, and phase transformation to form intermetallic phases. To calculate the rate of transport of lanthanides through the fuel, a multi-scale computational approach has been used. Atomistic calculations have been performed to determine the diffusivities of Nd, the most prevalent lanthanide species, through the solid fuel matrix and along pore surfaces. These diffusivities have been used as input parameters for a mesoscale model to determine an effective diffusion coefficient that accounts for the formation of porosity, its interconnection, and infiltration with bond sodium from the fuel-cladding gap. The effective diffusivity has been used in engineering-scale simulations using the BISON fuel performance code, and BISON simulations have been compared to representative validation cases from the EBR-II reactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems. - Highlights: • Calculation of the correlation function. • The correlation function is connected to the survival probability. • The model can be applied to the internal dynamics of proteins.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

An agent-based approach to study the diffusion rate and the effect of policies on joint placement of photovoltaic panels and green roof under climate change uncertainty

As two of the highest trending green technologies, photovoltaic panels and green roofs are proven to be effective practices for energy generation and energy saving. The achievable impact from the widespread installation of such technologies is, however, not clearly established. This is mainly because the degree of this impact highly depends on the inherently uncertain environmental and climate factors, as well as the unknown adoption rates of these technologies, which in turn depend on different characteristics of decision makers and interactions among them. To that end, this study aims to investigate the diffusion rate of these green technologies under uncertainties caused by climate change, characteristics of adopters, and their interactions. An integrated framework is developed to capture the interplay between financial and attitudinal aspects, as well as the uncertainties due to both the stochastic nature of system parameters and the interactions among agents involving human beings. Specifically, this framework consists of a integer programming model to optimize the green roof and/or photovoltaic panel installation settings for a given building under climate change uncertainty, and an agent-based model to factor in the role of human behavior and interactions. A case study for the city of Knoxville, TN, is presented to evaluate the effects of different policies on the diffusion rate of the green technologies of interest. The results show that the affordability of green technologies and public awareness are the key drivers of the adoption of these technologies, which highlight the important role of the decision makers in impacting the diffusion rate.

14 SOLAR ENERGY↗

DOE OSTI2015

Integral approximations to classical diffusion and smoothed particle hydrodynamics

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary. The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. An immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.

boundary conditions, smoothed particle hydrodynami↗

DOE OSTI2015

A sub-pore model for multi-scale reaction–diffusion problems in porous media

Applications of reaction–diffusion systems in porous media pose a challenging problem for computational modeling approaches due to their multi-physics and multi-scale nature. The length scales usually span 3–4 orders of magnitude while physical phenomena involved include heat and mass transfer processes, and surface reactions. In this paper, a novel methodology that accounts for all the length scales and physical phenomena involved in a single framework is described. A length scale based dual approach is proposed – the larger pore channels (macro-pores) are resolved using conventional numerical techniques and a novel ‘sub-pore’ model is used to account for the unresolved pore channels (sub-pores) and the important physics therein. The porous network in the sub-pore system is composed of a fractal-like hierarchical system of straight cylindrical pores. Simplified governing equations for mass and energy transport are solved within the sub-pore system along with a reaction kinetics model to account for surface adsorption. An implicit coupling strategy is used to couple the macro-pore and the sub-pore systems so as to ensure conservation. The developed methodology is then applied to a few test cases and it is established that the proposed framework is necessary for problems where the adsorption time scale is much smaller than (diffusion-limited) or comparable to the diffusion time scale. Furthermore, it is also demonstrated that the framework can be potentially used to model the network of porous channels in its entirety thus significantly reducing computational costs.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Simulation of stochastic diffusion via first exit times

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a method based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Finite-volume scheme for anisotropic diffusion

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Reduction of vanadium diffusivity within copper grain boundaries due to enhanced binding

We investigate permeation of vanadium (V) through copper (Cu) layers in V/Cu/niobium (Nb) and molybdenum (Mo)/Cu/V tri-layer composites and compare it with the permeation behavior of Nb. Despite their low solubility in single-crystal Cu, both V and Nb permeate readily due to short-circuit transport through Cu grain boundaries (GBs). However, Nb permeates preferentially to V. Atomistic simulations suggest that this difference is due to lower V diffusivity at general GBs in Cu, compared to Nb. Here, the lower V diffusivity, in turn, arises from stronger V binding to the boundary, which manifests as a greater equilibrium GB concentration as well as a higher activation energy for GB diffusion.

36 MATERIALS SCIENCE↗