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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Data on the comprehensive first-principles diffusion study of the aluminum-magnesium system

First-principles calculation of diffusion coefficients between Mg and Al is investigated comprehensively using density functional theory (DFT). The effect of different uncertainty sources arising from first principles calculations has been investigated systematically. These sources include the diffusion model, energetic, entropic and attempt frequency calculations. Variation in self and impurity diffusion coefficients of Mg and Al in stable phases are quantified using different DFT settings and compared with the experiments. Using the optimal DFT settings, diffusion coefficients in metastable phases of Al and Mg are predicted. The dataset refers to “An integrated experimental and computational study of diffusion and atomic mobility of the aluminum-magnesium system” [1].

36 MATERIALS SCIENCE↗
DOE OSTI2026

Multi-Objective design of interlocking metasurfaces using conditional diffusion models

Unit cell design remains a major challenge for interlocking metasurfaces, a promising joining technology for dissimilar materials, due to the complex, competing, multivariate design space and the need for rapid adaptation to varying performance requirements. This study explores Conditional Diffusion Models as a design optimization tool for interlocking metasurfaces. Given the complex, competing, multivariate design space for interlocking metasurfaces, unit cell design remains a major challenge for this joining technology. We trained a conditional diffusion model on 25,000 finite element analysis-simulated interlocking metasurface unit cells to generate designs with tailored thermo-mechanical properties (tensile strength, shear strength, and thermal conductivity) based on specified performance criteria. The model demonstrated a success rate of approximately 72 % in producing designs that met specified property bounds. The conditional diffusion model generated both thermally resistive and conductive designs, revealing clear trends in design characteristics: taller, dendritic structures were advantageous for tensile loads, while shorter, robust designs excelled in shear applications. Our findings indicate that the model's performance is more influenced by the breadth of the design space than by the quantity of training data, highlighting the importance of expansive design domains for generating innovative solutions. This work establishes conditional diffusion models as a highly efficient and adaptable tool for rapid interlocking metasurface unit cell design, paving the way for advancements in multi-material joining technologies, as well as highlighting the justification to leverage conditional diffusion models as design tools across complex design domains.

Conditional diffusion models↗
DOE OSTI2017

Neon diffusion kinetics and implications for cosmogenic neon paleothermometry in feldspars

Observations of cosmogenic neon concentrations in feldspars can potentially be used to constrain the surface exposure duration or surface temperature history of geologic samples. The applicability of cosmogenic neon to either application depends on the temperature-dependent diffusivity of neon isotopes. Here in this work, we investigate the kinetics of neon diffusion in feldspars of different compositions and geologic origins through stepwise degassing experiments on single, proton-irradiated crystals. To understand the potential causes of complex diffusion behavior that is sometimes manifest as nonlinearity in Arrhenius plots, we compare our results to argon stepwise degassing experiments previously conducted on the same feldspars. Many of the feldspars we studied exhibit linear Arrhenius behavior for neon whereas argon degassing from the same feldspars did not. This suggests that nonlinear behavior in argon experiments is an artifact of structural changes during laboratory heating. However, other feldspars that we examined exhibit nonlinear Arrhenius behavior for neon diffusion at temperatures far below any known structural changes, which suggests that some preexisting material property is responsible for the complex behavior. In general, neon diffusion kinetics vary widely across the different feldspars studied, with estimated activation energies (E a ) ranging from 83.3 to 110.7 kJ/mol and apparent pre-exponential factors (D 0 ) spanning three orders of magnitude from 2.4 ×10 -3 to 8.9 × 10 -1 cm 2 s -1 . Finally, as a consequence of this variability, the ability to reconstruct temperatures or exposure durations from cosmogenic neon abundances will depend on both the specific feldspar and the surface temperature conditions at the geologic site of interest.

58 GEOSCIENCES↗
DOE OSTI2014

Stress and Diffusion in Stored Pu ZPPR Fuel from Alpha Generation

ZPPR (Zero Power Physics Reactor) is a research reactor that has been used to investigate breeder reactor fuel designs. The reactor has been dismantled but its fuel is still stored there. Of concern are its plutonium containing metal fuel elements which are enclosed in stainless steel cladding with gas space filled with helium–argon gas and welded air tight. The fuel elements which are 5.08 cm by 0.508 cm up to 20.32 cm long (2 in × 0.2 in × 8 in) were manufactured in 1968. A few of these fuel elements have failed releasing contamination raising concern about the general state of the large number of other fuel elements. Inspection of the large number of fuel elements could lead to contamination release so analytical studies have been conducted to estimate the probability of failed fuel elements. This paper investigates the possible fuel failures due to generation of helium in the metal fuel from the decay of Pu and its possible damage to the fuel cladding from metal fuel expansion or from diffusion of helium into the fuel gas space. This paper (1) calculates the initial gas loading in a fuel element and its internal free volume after it has been brought into the atmosphere at ZPPR, (2) shows that the amount of helium generated by decay of Pu over 46 years since manufacture is significantly greater than this initial loading, (3) determines the amount of fuel swelling if the helium stays fixed in the fuel plate and estimates the amount of helium which diffuses out of the fuel plate into the fuel plenum assuming the helium does not remain fixed in the fuel plate but can diffuse to the plenum and possibly through the cladding. Since the literature is not clear as to which possibility occurs, as with Schroedinger’s cat, both possibilities are analyzed. The paper concludes that (1) if the gas generated is fixed in the fuel, then the fuel swelling it can cause would not cause any fuel failure and (2) if the helium does diffuse out of the fuel (in accordance diffusivities estimated from the literature), then it is unlikely that fuel element bulging will occur.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2019

Concentration dependence of hydrogen diffusion in α-iron from atomistic perspectives

Evaluation of hydrogen diffusion in structural materials is essential to predict the leakage and embrittlement of hydrogen storage applications. Here, we investigate the atomic-scale diffusion of interstitial hydrogen (H) in α-iron (Fe) over a temperature range from 350 to 900 K with different H concentrations (0.01–5%), employing classical molecular dynamics (MD) simulations. The self-diffusivity of H atoms increases with increasing temperature and decreasing concentration. With low concentrations, the calculated diffusion properties agree well with prior experiments. However, with a higher concentration (≥1%), the H diffusivity at low temperatures deviates from a high-temperature Arrhenius behavior. Through the energetic and structural analysis, we suggest that this deviation is attributed to a reduced mobility due to increased energy barrier by other H interstitials. This work contributes to the effective design of H storage applications by identifying temperature and concentration effects on permeability and addressing possible microstructural transformation.

08 HYDROGEN↗
DOE OSTI2012

Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

A large class of radiative transfer and particle transport problems contain highly diffusive regions. It is possible to reduce computational costs by solving a diffusion problem in diffusive subdomains instead of the transport equation. This enables one to decrease the dimensionality of the transport problem. In this paper we present a methodology for decomposition of a spatial domain of a transport problem into transport and diffusion subregions. We develop methods for solving one-group problems in 1D slab geometry. To identify and locate diffusive regions, we develop metrics for measuring transport effects that are based on the quasidiffusion (Eddington) factor. We present the results of test problems that demonstrate the accuracy of the proposed methodology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2023

Pore connectivity influences mass transport in natural rocks: Pore structure, gas diffusion and batch sorption studies

For this work, six rocks (one granodiorite, one limestone, two chalks, one mudstone, and one dolostone) with different extents of heterogeneity at six different particle sizes (from 75 to 8000 μm) were studied to describe the effects of pore connectivity on mass transport. The methods applied were (i) porosity measurement of granular rocks, (ii) analyses of gas-phase diffusive transport in a bed of packed particles, along with a solid quartz method at these six particle sizes being developed to identify the contribution of intraparticle diffusion, and (iii) batch sorption tests of multiple ions (anions and cations) with subsequent analyses of inductively coupled plasma-mass spectrometry. Granular porosity measurement results reveal that with decreasing particle sizes, the effective porosities for the “heterogenous” group of rocks (Grimsel granodiorite and Edwards limestone) increase, whereas the porosities of another “homogeneous” group (two Israel chalk samples, Japan mudstone, and Wyoming dolostone) remain constant. Gas diffusion results show that the intraparticle gas diffusion coefficient among these two sample groups, varying in the magnitude of 10 -8 to 10 -6 m 2 /s, are not directly correlated to the porosity differences. Moreover, the batch sorption work displays a different affinity of rocks for various tracers. For Grimsel granodiorite, Japan mudstone, and Wyoming dolostone, the adsorption capacity of Sm 3+ and Eu 3+ increases as the particle size decreases. In general, this integrated research of grain size distribution, granular rock porosity, intraparticle diffusivity, and ionic sorption capacity gives insights into the pore connectivity effect on both physical and chemical transport behaviors for different lithologies and/or different particle sizes.

58 GEOSCIENCES↗
DOE OSTI2021

Molecular dynamics studies of lattice defect effects on tritium diffusion in zirconium

Tritium diffusion in α-Zr containing point defects such as vacancies or self-interstitial atoms (SIAs) is simulated using molecular dynamics. Point defects rapidly aggregate to form extended defects, such as 3D nanoclusters and Frank loops. The geometry of extended defects is affected by the presence of tritium. At low temperature and in the absence of tritium, vacancies aggregate to form stacking fault pyramids. Addition of tritium at these temperatures promotes aggregation of vacancies to form 3D nanoclusters, within which the tritium concentration can be sufficiently high to suggest that these defects may serve as nucleation sites for hydride precipitation. Trapping of tritium in vacancy nanocluster reduces the calculated bulk diffusivity by an amount proportional to the vacancy concentration. At high temperature, vacancy clusters change shape to form planar basal dislocation loops, which bind tritium less strongly, leading to a sharp reduction in the fraction of trapped tritium and a corresponding increase in tritium diffusivity at high temperature. In contrast, SIAs increase tritium diffusion through α-Zr. Analysis of atomic trajectories shows that tritium does not interact directly with SIAs. In conclusion, diffusion enhancement is instead related to expansion of the lattice.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Diffusion behavior of copper atoms under Cu(II) reduction in Cucurbit[8]uril cavity at elevated temperatures

In this paper we describe copper clusters and nanoparticles formation by the reduction of copper (II) ions inside cavities of macrocycle molecules using supramolecular compound [Cu(Cyclen)(H{sub 2}O)@CB[8]](NO{sub 3}){sub 2}·12H{sub 2}O followed by Cu atoms diffusion between macrocycle CB[8] molecules. To understand the copper cluster genesis and nanoparticles formation x-ray powder diffraction (XRD), electron paramagnetic resonance (EPR), FTIR-spectroscopies, HRTEM and thermal analysis were used. It was found that atomic Cu(0) was not fixed in the cavity under heating, and Cu clusters and nanoparticles were formed by heating of supramolecular compound powder at 200–340 °C in He, but more preferably in H{sub 2}. The process was partially reversible after heating the powder up to 300 °C for 15 min and air exposure for a few months. The process was irreversible after heating of the sample at temperatures higher than 340 °C due to CB[8] cavitand decomposition. In general, exposure of the samples to air leads to oxidation and hydration clusters of Cu. Nanoparticles up to 600 nm in size formed on the surface of agglomerated polycrystalline powder at temperatures lower than 200 °C. The clusters less than 7 nm and 40 nm in size were formed at 300 °C inside and outside agglomerating polycrystalline powder, respectively. The diffusion coefficient of copper atoms inside polycrystalline CB[8] agglomerates equal to 10{sup −10} cm{sup 2}/s by heating the samples at 300 °C was found. - Graphical abstract: Copper nanoparticles and clusters are formed by the reduction of copper (II) ions inside cavities of macrocycle molecules at 200–340 °C in He, but more preferably in H{sub 2} using supramolecular compound [Cu(Cyclen)(H{sub 2}O)@CB[8]](NO{sub 3}){sub 2}·12H{sub 2}O followed by Cu atoms diffusion between macrocycle CB[8] molecules. Nanoparticles up to 600 nm in size formed on the surface of agglomerated polycrystalline powder at temperatures lower than 200 °C. The clusters less than 7 nm and 40 nm in size were formed at 300 °C inside and outside agglomerating polycrystalline powder, respectively. - Highlights: • We considered Cu NP's formation at CuCyclen thermolysis in H{sub 2} and He. • Initial complex CuCyclen was located inside cavitand CB[8]. • Cu(0) reduced in cavities diffuse between CB[8] molecules and Cu nuclei appear. • NPs less than 7 and 50 nm were formed inside and outside the CB[8] powder. • Coefficient of Cu(O) diffusion is 10{sup −10} cm{sup 2}/s for temperature at 300 °C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

An investigation on microstructure evolution and mechanical properties during liquid state diffusion bonding of Al2024 to Ti–6Al–4V

Joining mechanism of Ti/Al dissimilar alloys was studied during liquid state diffusion bonding process using Cu/Sn/Cu interlayer at 510 °C under vacuum of 7.5 × 10{sup −5} Torr for various bonding times. The microstructure and compositional changes in the joint zone were analyzed by scanning electron microscopy equipped with energy dispersive spectroscopy and X-ray diffraction. Microhardness and shear strength tests were also applied to study the mechanical properties of the joints. It was found that with an increase in bonding time, the elements of interlayer diffused into the parent metals and formed various intermetallic compounds at the interface. Diffusion process led to the isothermal solidification and the bonding evolution in the joint zone. The results from mechanical tests showed that microhardness and shear strength values have a straight relation with bonding time so that the maximum shear strength of joint was obtained for a bond made with 60 min bonding time. - Highlights: • Liquid state diffusion bonding of Al2024 to Ti–6Al–4V was performed successfully. • Diffusion of the elements caused the formation of various intermetallics at the interface. • Microhardness and shear strength values have a straight relation with bonding time. • The maximum shear strength reached to 36 MPa in 60 min bonding time.

36 MATERIALS SCIENCE↗
DOE OSTI2017

On extreme points of the diffusion polytope

Here, we consider a class of diffusion problems defined on simple graphs in which the populations at any two vertices may be averaged if they are connected by an edge. The diffusion polytope is the convex hull of the set of population vectors attainable using finite sequences of these operations. A number of physical problems have linear programming solutions taking the diffusion polytope as the feasible region, e.g. the free energy that can be removed from plasma using waves, so there is a need to describe and enumerate its extreme points. We also review known results for the case of the complete graph Kn, and study a variety of problems for the path graph Pn and the cyclic graph Cn. Finall, we describe the different kinds of extreme points that arise, and identify the diffusion polytope in a number of simple cases. In the case of increasing initial populations on Pn the diffusion polytope is topologically an n-dimensional hypercube.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Diffusion and migration in polymer electrolytes

Mixtures of neutral polymers and lithium salts have the potential to serve as electrolytes in next-generation rechargeable Li-ion batteries. The purpose of this review is to expose the delicate interplay between polymer-salt interactions at the segmental level and macroscopic ion transport at the battery level. Since complete characterization of this interplay has only been completed in one system: mixtures of poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl)imide (PEO/LiTFSI), we focus on data obtained from this system. We begin with a discussion of the activity coefficient, followed by a discussion of six different diffusion coefficients: the Rouse motion of polymer segments is quantified by D seg , the self-diffusion of cations and anions is quantified by D self,+ and D self,- , and the build-up of concentration gradients in electrolytes under an applied potential is quantified by Stefan-Maxwell diffusion coefficients, D 0+ , D 0- , and D +- . The Stefan-Maxwell diffusion coefficients can be used to predict the velocities of the ions at very early times after an electric field is applied across the electrolyte. The surprising result is that D 0- is negative in certain concentration windows. A consequence of this finding is that at these concentrations, both cations and anions are predicted to migrate toward the positive electrode at early times. We describe the controversies that surround this result. Knowledge of the Stefan-Maxwell diffusion coefficients enable prediction of the limiting current. We argue that the limiting current is the most important characteristic of an electrolyte. Excellent agreement between theoretical and experimental limiting current is seen in PEO/LiTFSI mixtures. What sequence of monomers that, when polymerized, will lead to the highest limiting current remains an important unanswered question. It is our hope that the approach presented in this review will guide the development of such polymers.

25 ENERGY STORAGE↗
DOE OSTI2017

Numerical method for angle-of-incidence correction factors for diffuse radiation incident photovoltaic modules

Here, a numerical method is provided for solving the integral equation for the angle-of-incidence (AOI) correction factor for diffuse radiation incident photovoltaic (PV) modules. The types of diffuse radiation considered include sky, circumsolar, horizon, and ground-reflected. The method permits PV module AOI characteristics to be addressed when calculating AOI losses associated with diffuse radiation. Pseudo code is provided to aid users in the implementation, and results are shown for PV modules with tilt angles from 0° to 90°. Diffuse AOI losses are greatest for small PV module tilt angles. Including AOI losses associated with the diffuse irradiance will improve predictions of PV system performance.

14 SOLAR ENERGY↗
DOE OSTI2015

A comparative study of microstructural stability and sulphur diffusion in CdS/CdTe photovoltaic devices

The role of CdCl2 activation in the production of high quality CdTe-based photovoltaic devices remains a subject of much debate. In this study, CdTe-based cells produced in three independent laboratories using different device fabrication technologies are investigated before and after CdCl2 activation with regard to structural changes (recrystallisation and grain growth) and sulphur out-diffusion. Using scanning transmission electron microscopy (STEM) and x-ray diffraction it is demonstrated that CdCl2 activation of the investigated cells produces no statistical structural changes to the CdTe. Additionally, energy dispersive spectrometry (EDS) performed in the STEM on the same samples illustrates that the change in sulphur diffusion following activation is more limited than expected from previous studies; no change is detectable when the thermal budget for CdTe deposition is significantly greater than that for activation. This suggests that the efficiency enhancement during CdCl2 treatment is not due to sulphur out-diffusion. Lastly, cathodoluminescence microscopy is used to demonstrate in two dimensions how sulphur diffuses into a model sample and the results are found to be consistent with STEM-EDS. Some spectroscopic evidence for enhanced sulphur diffusion along grain boundaries is also observed.

14 SOLAR ENERGY↗