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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

The equilibrium-diffusion limit for radiation hydrodynamics

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy. Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2 ) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Understanding copper diffusion in CuInSe 2 with first-principles based atomistic and continuum models

We investigate the diffusion of copper in CuInSe 2 using thermodynamic and kinetic models based on density functional theory calculations, attempting to reconcile large differences in reported experimental diffusivities. We find that observations of rapid chemical diffusion can be explained by large thermodynamic factors, which we calculate using a compositionally constrained model of intrinsic point defect formation. We further characterize how copper diffusion coefficients depend on material synthesis conditions and exhibit their variation across the CuInSe 2 secondary phase diagram. In doing so, we identify stable off-stoichiometries that are dominated by either vacancy- or interstitial-mediated diffusion mechanisms. These results are employed in the development of a continuum reaction–diffusion model, which we use to simulate experimental depth profiles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A Finite Difference informed Random Walk solver for simulating radiation defect evolution in polycrystalline structures with strongly inhomogeneous diffusivity

Diffusivity of species and defects on grain boundaries is usually several orders of magnitude larger than that inside grains. Such strongly inhomogeneous diffusivity requires prohibitively high computational demands for modeling microstructural evolution. Here, this paper presents a highly-efficient numerical solver, combining the Finite Difference method and Random Walk model, designed for accurately modeling strongly inhomogeneous diffusion within polycrystalline structures. The proposed solver, termed Finite Difference informed Random Walk (FDiRW), integrates a customized Finite Difference (cFD) scheme tailored for fast diffusion along thin grain boundaries represented by a single-layer of nodes. Numerical experiments demonstrate that the FDiRW solver achieves an impressive efficiency gain of 1560x compared to traditional Finite Difference methods while maintaining accuracy, making it feasible for personal computer machines to handle diffusional systems with strongly inhomogeneous diffusivity across static polycrystalline microstructures. The model has been successfully applied to simulate radiation defect evolution, showcasing its scalability to engineering scales in both length and time dimensions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Effect of lithium diffusion into Ga 2 O 3 thin films

The integration of lithium based compounds (e.g., Li:NiO/Ga 2 O 3 , LiGa 5 O 8 /Ga 2 O 3 ) in Ga 2 O 3 based pn-heterojunctions raises concerns about interface stability, i.e., Li diffusion effects on Ga 2 O 3 properties. In this work the ex-situ diffusion of Li is investigated in three different Ga 2 O 3 epilayers systems [(001) κ-Ga 2 O 3 and (−201) β-Ga2O3 heteroepitaxy on (001) α-Al 2 O 3 , and (010) β-Ga 2 O 3 homoepitaxy] at relevant temperatures for the synthesis / processing of Li-based epilayers. It is here experimentally demonstrated and quantified the Li diffusion in all the investigated Ga 2 O 3 epilayers systems and Li bulk (D Li,bulk ) and 2D defects (D Li,2D ) diffusion coefficients are provided. In the case of the (010) β-Ga 2 O 3 homoepitaxial layer (nominally free of structural defects), hybrid functional theory calculations foresee a diffusion mechanism mediated by Ga vacancies (VGa). Moreover, in the (010) β-Ga 2 O 3 homo-layer a significant effect on its functional properties (e.g., additional Raman vibrational modes, induced conductivity in an otherwise insulating sample) upon the Li-diffusion process is experimentally highlighted and tentatively related to the passivation of acceptor defects (i.e., formation of V Ga -nLi complexes).

Defects↗
DOE OSTI2018

Effective gaseous diffusion coefficients of select ultra-fine, super-fine and medium grain nuclear graphite

Understanding “Where?” and “How much?” oxidation has occurred in a nuclear graphite component is critical to predicting any deleterious effects to physical, mechanical, and thermal properties. A key factor in answering these questions is characterizing the effective mass transport rates of gas species in nuclear graphites. Effective gas diffusion coefficients were determined for twenty-six graphite specimens spanning six modern grades of nuclear graphite. A correlation was established for the majority of grades examined allowing a reasonable estimate of the effective diffusion coefficient to be determined purely from an estimate of total porosity. The importance of Knudsen diffusion to the measured diffusion coefficients is also shown for modern grades. Furthermore, Knudsen diffusion has not historically been considered to contribute to measured diffusion coefficients of nuclear graphite.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties

Here we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive behaviors. To identify the subset of microcstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. Results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, this denoising diffusion algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. Numerical experiments are conducted on the open-source mechanical MNIST data set (Lejeune, 2020). Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media, but also learns the nonlinear structure–property map to quantitatively understand the multiscale interplay among the geometry, topology, and their effective macroscopic properties.

42 ENGINEERING↗
DOE OSTI2017

A curved pathway for oxygen interstitial diffusion in aluminum

Here, the diffusion of interstitial oxygen (O) in fcc aluminum (Al) has been studied using first-principles and the diffusion coefficient has been calculated. Whereas interstitial atoms in fcc systems are typically found to hop directly between interstitial centres, the diffusion pathway for interstitial O in fcc Al was calculated to have a curved minimum energy pathway with an energy barrier of 0.95 eV. The barrier was found to be off-centre of a neighboring octahedral site. Also unlike the majority of fcc metals, O prefers to sit in the tetrahedral interstitial site as opposed to the octahedral site. The calculated O diffusion coefficient is on the same order of magnitude of the diffusion coefficient of O in other fcc metals. The preferred interstitial site, diffusion pathway and vacancy binding energy were found to be related to the bond length of O with neighboring Al atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2021

First-principles studies of the concentration-dependent tritium diffusion in the zirconium hydrides with and without Sn impurity

We performed first-principles calculations to study the 3 H diffusion in the zirconium hydrides with or without Sn impurity. Our results show that the formation of Zr 3 H x becomes preferable as the 3 H concentration increases. Based on the most stable configurations of Zr 3 H x (x = 0.5, 1.0, 1.5, 2.0), we studied the interstitial 3 H diffusion with or without Sn impurity. The results show that the interstitial 3 H diffusion becomes less probable in the hydrides with a higher 3 H concentration. When introducing a substitutional Sn impurity, the diffusion barriers increase. Therefore, the substitutional Sn in the diffusion pathway hampers the 3 H diffusion in Zr hydrides.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗
DOE OSTI2020

Persistent compositions of non-stoichiometric compounds with low bulk diffusivity: A theory and application to Nb3Sn superconductors

Non-stoichiometric compounds may develop a composition gradient when they are formed by reactive diffusional processes. This paper reports an interesting phenomenon that in compounds with low bulk diffusivities, which rely mainly on grain boundary diffusion for their growth, the final bulk compositions may be far from equilibrium, with a very low bulk diffusivity leading to fixed (persistent) compositions – one such example is Nb 3 Sn, a superconductor. We investigated the microchemistry at the reactive interface using atom probe tomography to clarify the diffusion reaction mechanism for this low-bulk-diffusivity case and thus propose a theory for what determines the compound composition, using Nb 3 Sn as an example for concreteness. Using certain approximations, we derive an explicit analytical equation that illustrates what factors determine its composition profile. We compare our model with the known facts of Nb 3 Sn and see good agreement. In particular, this model predicts that internal oxidation may lead to higher Sn contents than conventional, non-oxidized Nb 3 Sn. Our measurements show that this is indeed true, and that the internally-oxidized Nb 3 Sn also has higher upper critical fields, achieving up to 28.2 T at 4.2 K. We discuss the general applicability of this model to non-stoichiometric compounds with low bulk diffusivity, and propose it as a tool to help in the design and processing of such materials for compositional control.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Diffusion behaviors between metallic fuel alloys with Pd addition and Fe

Fission product lanthanides (Lns) in metallic fuel is the primary cause of fuel-cladding chemical interaction (FCCI). Palladium (Pd) is being explored as a potential additive to reduce or mitigate FCCI by forming stable Pd-Ln compounds. The current study is an investigation of diffusion behaviors between UZrPd, UZrPdLn, UPuZrPd, and UPuZrPdLn alloys (Ln = 53Nd-25Ce-16Pr-6La wt. %) and iron (Fe). Diffusion couple tests were performed followed by microstructural analysis using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It is found that the diffusion of Fe into the fuel is reduced by PdZr2 precipitates randomly dispersed throughout the fuel matrix. Ln-Pd compounds form in UZrPdLn alloys, and (Ln,Pu)Pd forms in the UPuZrPdLn alloy. In both diffusion couples with Ln, small amounts of Lns are diffusing into the Fe. This could be due to small amounts of dissolved Lns in the precipitates, or could be due to the Ln-Pd compounds decomposing. In either case, diffusion caused by Lns is greatly reduced.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Radiation driven diffusion in γU-Mo

A monolithic fuel design based on a U-Mo alloy has been selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). A critical phenomenon of interest with U-Mo monolithic fuel is the large amount of swelling that takes place during operation, particularly at high fission densities. The accurate prediction of fuel evolution under irradiation requires implementation of correct thermodynamic and kinetic properties into mesoscale and continuum level fuel performance modeling codes. One such property where there exists incomplete data is the diffusion of relevant species under irradiation. Fuel performance swelling predictions rely on an accurate representation of diffusion in order to determine the rate of fission gas swelling and the local microstructural evolution. In this work, we present molecular dynamics simulations of the radiation driven diffusion of U, Mo and Xe in U-Mo nuclear fuels. Diffusion coefficients for each species are determined over a range of temperatures and compositions. In this work, updated diffusion coefficients are presented that are applicable under irradiation that incorporate both intrinsic and radiation driven diffusion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Thermal diffusivity of irradiated tungsten and tungsten-rhenium alloys

The Japan-US PHENIX project irradiated tungsten materials in the RB-19J capsule experiment in the High Flux Isotope Reactor (HFIR). A gadolinium (Gd) shielding was used to absorb the thermal neutrons and reduce rhenium and osmium generation in tungsten. Pure tungsten and K-doped W-3% Re samples were irradiated at 532 – 662 °C to dose of 0.21-0.46 dpa, with the grain orientation perpendicular or parallel to the disk surface. Thermal diffusivity measurements were performed from 100 °C to 500 °C. Furthermore, additional measurements followed after annealing up to 900 °C. Irradiated pure tungsten specimens showed similar thermal diffusivity results compared with an unirradiated W-1% Re specimen in another study. The transmutation amount of Re was calculated to be about 0.52% for those specimens that showed good agreement with this study. Specimens irradiated in this study to different doses presented almost the same thermal diffusivity. Annealing up to 800 °C resulted in no recovery of thermal diffusivity. These results show that the contribution of crystalline defects to degradation of thermal diffusivity is quite limited. In addition, the thermal diffusivity of the irradiated specimens was getting close to that of the unirradiated specimens at elevated temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Modeling fission product diffusion in TRISO fuel particles with BISON

Diffusion of fission products in intact TRISO particles depends on particle geometry, fission product source rates, time, temperature, and temperature-dependent diffusion coefficients. Simulating this diffusion process requires models for source rates and diffusion coefficients, plus computation of the temperature field if not prescribed. In addition, simulation quality depends on discretization of the geometry, appropriate time stepping, and the accuracy of the solution method. In this paper, we explore the simulation of fission product diffusion in TRISO fuel particles using the finite element method via the fuel performance code Bison. Recent material model development has occurred in Bison for each material present in tri-structural isotropic (TRISO) fuel particles: the buffer, inner pyrolytic carbon, silicon carbide, and outer pyrolytic carbon layers, as well as the fuel kernel. Also, new mesh generation and fission product release fraction capabilities have been added. Diffusion capabilities are shown to converge to the correct solution via formal verification tests. A large number of code benchmarking problems are also given, with good results, showing that Bison’s computed release fractions closely match those of other software tools. Finally, a significant validation effort is detailed in which fission product release, measured as part of the AGR-1 capsule experiments, is compared to Bison outputs. Bison outputs compare very well to the experimental data and to PARFUME results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Europium diffusion in IG-110 nuclear graphite

Europium diffusion in graphite has been recognized to be of interest in high-temperature gas reactor safety analysis, particularly as an indicator of strontium diffusion. However, no measurements of europium diffusion coefficients have been reported in the literature. In this work, the effective diffusion coefficient of europium was measured using a time-release method. Natural europium was loaded into pre-milled unirradiated IG-110 graphite spheres using a pressurized acid digestion vessel. The time-release experiments were performed in the temperature range 1823 K – 1973 K using a SiC diffusion cell connected to an inductively-coupled plasma mass spectrometer (ICP-MS) via a He gas line. Finally, the results of this work are: D Eu, IG-110 = (1.5 x 10 -3 m 2 /s) exp $(\frac{-2.87\mathrm{x}10^{5} J/mol}{RT})$ This effective diffusion coefficient can be used to aid in predictive modelling of europium transport in HTGRs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Effect of Mg and Ni impurities on tritium diffusion in lithium ceramics through cluster dynamics simulations

This study investigates the impact of Mg and Ni doping on tritium diffusion in LiAlO 2 and LiAl 5 O 8 ceramics, that are used in tritium-producing burnable absorber rods (TPBARs). Utilizing Centipede simulations across a broad temperature range (500 K to 1250 K), we explore the interplay between defect dynamics, cluster formation, and tritium mobility. In LiAlO 2 , Mg doping significantly enhances tritium diffusivity by increasing tritium interstitial concentrations and diffusion coefficients of key species, thereby doubling the overall tritium diffusivity. Ni doping, while shifting the dominant defect to Li vacancies, maintains high tritium mobility due to the low binding energy of Li vacancy-tritium complexes, which ensures effective tritium migration. In LiAl 5 O 8 , Mg and Ni doping results in a slight reduction in the diffusion coefficients of key species, yet the dramatic increase in tritium interstitial concentrations compensates, leading to a net small increase in tritium diffusivity. In conclusion, the findings highlight the critical role of defects in tritium transport and the effect of Mg and Ni defects on the performance of these ceramics in demanding nuclear environments.

Cluster dynamics↗
DOE OSTI2025

First-principles investigation of cerium and neodymium diffusion in BCC chromium and vanadium via vacancy-mediated transport

Lanthanide transport plays a crucial role in the performance and longevity of metallic nuclear fuels. This study examines the diffusion behavior of Ce and Nd—two major fission products—in body-centered cubic (BCC) Cr and V, which are potential liner or coating materials for mitigating fuel-cladding chemical interactions (FCCI). Using density functional theory (DFT) calculations and self-consistent mean-field (SCMF) analysis, the vacancy-mediated diffusion coefficients are evaluated. Our findings reveal that Ce and Nd act as oversized solutes and are strongly bound to vacancies in BCC Cr and V, with diffusivities in Cr significantly lower than in V and in hexagonal closed-packed (HCP) Zr, as investigated in our previous work. The activation energies for Ce and Nd diffusion are 3.39 and 3.32 eV, respectively, in BCC Cr, and 2.56 and 2.33 eV, respectively, in BCC V. Analysis of vacancy drag and partial diffusion coefficient ratios indicates a strong tendency for lanthanide enrichment at vacancy sinks in BCC Cr, and to a lesser extent in BCC V, with this effect persisting up to the melting point in Cr and remaining substantial for Nd in V at high temperatures. Under irradiation, the increase in vacancy concentration is expected to enhance lanthanide transport, potentially accelerating interactions at liner-cladding interfaces. Although BCC Cr exhibits relatively low lanthanide diffusivities under equilibrium conditions, the expected segregation tendencies under irradiation suggest that Zr liners may be a more favorable option. Further investigations using rate theory, cluster dynamics, and phase-field modeling are required to quantitatively assess the performance of these materials in reactor environments.

36 - MATERIALS SCIENCE↗
DOE OSTI2023

Tensile behavior of diffusion bonded AA6061 - AA6061 with variation in cooling method

Hot isostatically pressed AA6061 cladding is an important structural component of the high performance, Zr-laminated U-10Mo monolithic fuel system for the application in research and test reactors. In this study, the mechanical behavior of two diffusion bonded aluminum alloy, AA6061, was examined using tensile testing. Solid-to-solid diffusion bonding between two pieces of AA6061 was performed by isothermal annealing at 560 °C for 1.5 h, and diffusion couples were subsequently cooled via three different cooling methods: furnace cooling, air cooling, and water quenching. Dog-bone shaped tensile specimens, with 10 mm in gauge length (with diffusion bonded interface in the middle), and 1.5 × 1.5 mm 2 gauge cross-sections, were fabricated from the diffusion bonded AA6061 by electro-discharge machining. Yield strength (% EL at failure) of furnace cooled, air cooled and water quenched tensile specimens determined was 82 ~ 89 MPa (10 ~ 30%), 112 ~ 116 MPa (10 ~ 14%), and 149 ~ 164 MPa (10 ~ 17%), respectively. This variation in mechanical behavior was examined with cooling-rate dependent, concentrated precipitation of Mg 2 Si at the diffusion bonded interface, with due respect for mechanical properties of the AA6061 alloy that inherently vary as a function of cooling rate from 560 °C. Finite element analysis using ABAQUS was employed to augment experimental findings with the appropriate microstructural constituents and alloy properties. Results suggest that the strength is dominated by matrix/bulk properties of AA6061, while ductility is strongly influenced by the cooling method dependent presence of Mg 2 Si precipitates at the interface.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗