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DOE OSTI2017

A semi-analytical method for simulating matrix diffusion in numerical transport models

We report a semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

CO 2 -Induced displacement and diffusive transport of shale geofluids in silica nanopores of varying sizes

The need to recover our energy resources in a sustainable manner necessitates the development of technological approaches to reduce water use and enhance the use and storage of alternative processing fluids such as CO 2 . These societal and technological needs require a fundamental understanding of the pore-scale organization and transport behaviors of confined fluids. Therefore, the aim of this study is to establish a molecular-scale basis for evaluating CO 2 -induced selective adsorption and diffusive transport behavior of hydrocarbon fluids such as propane and toluene in silica nanopores with sizes in the range of 2–10 nm. The studied fluids are composed of CO 2 -propane, CO 2 -propane-toluene, and CO 2 -toluene. CO 2 was found to adsorb preferentially to the silica surfaces by forming hydrogen bonds with the surface hydroxyl (–OH) groups. The selective adsorption of CO 2 over propane was significantly higher compared to toluene at the pore sizes in the range of 2–10 nm. Increasing pore size reduces the extent of CO 2 , propane and toluene adsorbed on the silica surfaces while the corresponding diffusivities increased. Anisotropic diffusivities of the confined molecules were noted. More polar and higher molecular weight constituents of the oil such as toluene diffuse more slowly in confinement. These studies provide detailed scientific insights into the role of CO 2 in enhancing hydrocarbon recovery from unconventional and complex porous environments. These molecular-scale investigations suggest that CO 2 has a higher tendency to displace lighter aliphatic hydrocarbon molecules such as propane away from the surface as opposed to heavier hydrocarbon molecules such as toluene.

42 ENGINEERING↗

DOE OSTI2014

A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

A moving mesh finite difference method for equilibrium radiation diffusion equations

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Acceleration of diffusive molecular dynamics simulations through mean field approximation and subcycling time integration

Highlights: • Two numerical methods are presented to accelerate DMD simulations. • The methods greatly reduce the computation time without much loss of accuracy. • The accelerated DMD model is capable of simulating long-term mass transport at atomistic length scales. • Demonstrated for the propagation of an atomically sharp phase boundary over 30 seconds. - Abstract: Diffusive Molecular Dynamics (DMD) is a class of recently developed computational models for the simulation of long-term diffusive mass transport at atomistic length scales. Compared to previous atomistic models, e.g., transition state theory based accelerated molecular dynamics, DMD allows the use of larger time-step sizes, but has a higher computational complexity at each time-step due to the need to solve a nonlinear optimization problem at every time-step. This paper presents two numerical methods to accelerate DMD based simulations. First, we show that when a many-body potential function, e.g., embedded atom method (EAM), is employed, the cost of DMD is dominated by the computation of the mean of the potential function and its derivatives, which are high-dimensional random variables. To reduce the cost, we explore both first- and second-order mean field approximations. Specifically, we show that the first-order approximation, which uses a point estimate to calculate the mean, can reduce the cost by two to three orders of magnitude, but may introduce relatively large error in the solution. We show that adding an approximate second-order correction term can significantly reduce the error without much increase in computational cost. Second, we show that DMD can be significantly accelerated through subcycling time integration, as the cost of integrating the empirical diffusion equation is much lower than that of the optimization solver. To assess the DMD model and the numerical approximation methods, we present two groups of numerical experiments that simulate the diffusion of hydrogen in palladium nanoparticles. In particular, we show that the computational framework is capable of capturing the propagation of an atomically sharp phase boundary over a time window of more than 30 seconds. The effects of the proposed numerical methods on solution accuracy and computation time are also assessed quantitatively.

36 MATERIALS SCIENCE↗

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 OSTI2023

A diffusion–deformation model with damage for polymer undergoing rapid decompression failure

Green hydrogen is emerging as one of the most promising alternatives to replace fossil fuels. While hydrogen gas has a good energy density by weight, its poor energy density by volume requires it to be stored under high pressure for commercial use. The hydrogen infrastructure developed to handle this high pressure hydrogen contains multiple components made of polymers as sealing agents. Although polymers do not react chemically with hydrogen gas, they undergo a mechanical failure when high pressure hydrogen gas is suddenly depressurized. This phenomenon known as 'rapid decompression failure' occurs due to the diffusion of hydrogen through polymer and getting trapped inside pre-existing cavities or voids. Here, in this paper, a continuum mechanics-based coupled diffusion-deformation-damage model was developed to predict the hydrogen distribution, stress distribution, and damage propagation inside the polymer while it undergoes rapid decompression failure. The polymer was modeled as a hyperelastic material because it represents the nonlinear material response observed in uniaxial tensile tests perfectly. The effects of hydrogen diffusivity, pre-existing cavity size, cavity location, applied hydrogen pressure, and depressurization rate on damage initiation were studied. It was found that the coefficient of diffusion plays an important role in damage initiation and damage was mostly concentrated in the inside areas rather than near the surface. Experiments were conducted with EPDM polymer which agreed well with the predicted trends using the given model. The effect of adding carbon black and silica filler particles and plasticizer to the pure EPDM polymer was also studied. It was found that damage during RDF decreases with the addition of fillers, but increases with the addition of the plasticizer. Finally, the damage evolution in the presence of two cavities was also studied, and was found that the interaction of stress fields around the cavities alters the damage occurring during RDF.

36 MATERIALS SCIENCE↗

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↗

DOE OSTI2022

A Robust Numerical Treatment of Solid-Phase Diffusion in Pseudo Two-Dimensional Lithium-Ion Battery Models

Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of discretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).

battery modeling↗

DOE OSTI2025

Effect of high scandium doping in barium zirconate on nickel diffusion and performance of proton-conducting solid oxide electrolyzer cells

Proton-conducting solid oxide electrolyzer cells (p-SOECs) are emerging but promising technologies for hydrogen production. However, due to the lack of a robust electrolyte, p-SOECs struggle simultaneously to display high performance, Faradaic efficiency, and durability. Motivated by its high proton concentrations and stability as a barium zirconate, we have investigated BaZr 0.6 Sc 0.4 O 3-δ (BZSc40) as a potential next-generation p-SOEC electrolyte. Here, we found elevated levels of NiO diffusion through BZSc40 electrolytes during high-temperature sintering, attributed to the large oxygen vacancy concentrations present in BZSc40, as revealed by first-principle computational results. Controlling NiO diffusion is critical, as it can facilitate densification and grain size growth, but it may also detrimentally impact performance by causing electronic leakage. By optimizing sintering temperature when fabricating BZSc40 cells, we successfully controlled NiO diffusion, achieving sufficient electrolyte densification along with high performance and Faradaic efficiency. BZSc40 cells reached −0.99 A/cm 2 at 1.3 V and 600 °C and exhibited enhanced durability with a 3.37 mV/kh degradation rate at −0.8 A/cm 2 over a 200-h testing period. BZSc40 electrolytes demonstrated superior performance over BaZr 0.8 Y 0.2 O 3-δ (BZY20). In addition to elevated current densities and grain sizes, BZSc40 cells achieved Faradaic efficiencies of 76 % compared to 54 % for BZY20 at −0.2 A/cm 2 and 600 °C. This work lays the foundation for BZSc40 as a potential electrolyte due to its advantages over BZY20 while demonstrating the significance of controlling NiO diffusion when fabricating p-SOECs.

Electrolyzer↗

DOE OSTI2012

Local structure of Rb{sub 2}Li{sub 4}(SeO{sub 4}){sub 3}{center_dot}2H{sub 2}O by the modeling of X-ray diffuse scattering - from average-structure to microdomain model

Local structure of dirubidium tetralithium tris(selenate(VI)) dihydrate - Rb{sub 2}Li{sub 4}(SeO{sub 4}){sub 3}{center_dot} 2H{sub 2}O has been determined basing on the modeling of X-ray diffuse scattering. The origin of observed structured diffuse streaks is SeO{sub 4} tetrahedra switching between two alternative positions in two quasi-planar layers existing in each unit cell and formation of domains with specific SeO{sub 4} tetrahedra configuration locally fulfilling condition for C-centering in the 2a Multiplication-Sign 2b Multiplication-Sign c superstructure cell. The local structure solution is characterized by a uniform distribution of rather large domains (ca. thousand of unit cells) in two layers, but also monodomains can be taken into account. Inside a single domain SeO{sub 4} tetrahedra are ordered along ab-diagonal forming two-string ribbons. Inside the ribbons SeO{sub 4} and LiO{sub 4} tetrahedra share the oxygen corners, whereas ribbons are bound to each other by a net of hydrogen bonds and fastened by corner sharing SeO{sub 4} tetrahedra of the neighboring layers. - Graphical abstract: Experimental sections of the reciprocal space showing diffraction effects observed for RLSO. Bragg spots are visible on sections with integer indices (1 kl section - on the left), streaks - on sections with fractional ones (1.5 kl section - on the right). At the center: resulting local structure of the A package modeled as a microdomain: two-string ribbons of ordered oxygen-corners-sharing SeO{sub 4} and LiO{sub 4} terahedra extended along ab-diagonal are seen; ribbons are bound by hydrogen bonds (shown in pink); the multiplied 2a Multiplication-Sign 2b unit cell is shown. Highlights: Black-Right-Pointing-Pointer X-ray diffuse scattering in RLSO was registered and modeled. Black-Right-Pointing-Pointer The origin of diffuse streaks is SeO{sub 4} tetrahedra switching in two structure layers. Black-Right-Pointing-Pointer The local structure is characterized by a uniform distribution of microdomains. Black-Right-Pointing-Pointer Inside a single domain SeO{sub 4} tetrahedra are ordered along ab-diagonal forming ribbons. Black-Right-Pointing-Pointer The ribbons are bound to each other by a net of hydrogen bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Electric field enhanced diffusion welding of alloy 617: Microstructural characteristics and mechanical properties

This study investigated the microstructural characteristics and mechanical behavior of diffusion welded nickel-based Alloy 617 obtained by electric field-assisted sintering (EFAS) using various parameters. The interfacial microstructure exhibited different characteristics including good grain boundary (GB) migration across the interface in the samples diffusion-welded at 1100 °C and a flat interface in the samples joined at 1000 °C and 1050 °C. The interface consisted of fine Al 2 O 3 oxides, while precipitation of interfacial M 23 C 6 carbides was not observed. Grain boundaries migrated across the Al 2 O 3 oxides, leaving these oxides within the grains. Graded grain size was observed, with grain coarsening being more significant near the sample surface due to the temperature gradient induced by EFAS. Tensile testing revealed that the specimens fractured in the matrix away from the interface, indicting strong diffusion-welded joints. Further, the peak tensile strength of 807 MPa was obtained in the samples welded at 1000 °C due to minimal grain growth. The materials obtained at 1100 °C exhibited reduced tensile strength but improved ductility. Strain maps revealed by digital image correlation showed alternating high and low strain segments in the samples produced at 1000 °C and 1050 °C, indicating that the flat interfaces with no GB migration were less ductile compared to the matrix. A greater strain uniformity was observed along the bond interfaces with improved GB migration. The hardness reduced near the sample surfaces due to enlarged grains induced by temperature gradient. This study demonstrates that GB migration and enhanced mechanical strength can be achieved in diffusion-welded Alloy 617.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Electroluminescence pulse shape and electron diffusion in liquid argon measured in a dual-phase TPC

Here, we report the measurement of the longitudinal diffusion constant in liquid argon with the DarkSide-50 dual-phase time projection chamber. The measurement is performed at drift electric fields of 100 V/cm, 150 V/cm, and 200 V/cm using high statistics $^{39}$Ar decays from atmospheric argon. We derive an expression to describe the pulse shape of the electroluminescence signal (S2) in dual-phase TPCs. The derived S2 pulse shape is fit to events from the uppermost portion of the TPC in order to characterize the radial dependence of the signal. The results are provided as inputs to the measurement of the longitudinal diffusion constant DL, which we find to be (4.12 $\pm$ 0.04) cm$^2$/s for a selection of 140keV electron recoil events in 200V/cm drift field and 2.8kV/cm extraction field. To study the systematics of our measurement we examine datasets of varying event energy, field strength, and detector volume yielding a weighted average value for the diffusion constant of (4.09 $\pm$ 0.09) cm$^2$ /s. The measured longitudinal diffusion constant is observed to have an energy dependence, and within the studied energy range the result is systematically lower than other results in the literature.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2018

Helium diffusivity in oxide nuclear fuel: Critical data analysis and new correlations

Helium is relevant in determining nuclear fuel behaviour. It affects the performance of nuclear fuel both in reactor and in storage conditions. Helium becomes important in reactor conditions when high burnups are targeted or MOX fuel is used, whereas for storage conditions it can represent a threat to the fuel rods integrity. The accurate knowledge of helium behaviour combined with predictive model capabilities is fundamental for the safe management of nuclear fuel, with helium diffusivity being a critical property. For this reason, a considerable number of separate effect experiments in the last fifty years investigated helium diffusivity in nuclear fuel. The aim of this work is to critically review and assess the experimental results concerning the helium diffusivity. Experimental results are critically analysed in terms of the helium introduction technique used (either infusion, implantation or doping) and of sample characteristics (single crystal, poly-crystal or powder). Accordingly, we derived two different correlations for the diffusivity. Clearly, each of the new correlations corresponds to a limited range of application conditions, depending on the experimental data used to derive it. We provide recommendations regarding the proper application conditions for each correlation (e.g., in reactor or storage conditions).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

Conditions for translation and scaling invariance of the neutron diffusion equation

Lie group methods are applied to the time-dependent, monoenergetic neutron diffusion equation in materials with spatial and time dependence. To accomplish this objective, the underlying 2nd order partial differential equation (PDE) is recast as an exterior differential system so as to leverage the isovector symmetry analysis approach. Some of the advantages of this method as compared to traditional symmetry analysis approaches are revealed through its use in the context of a 2nd order PDE. In this context, various material properties appearing in the mathematical model (e.g., a diffusion coefficient and macroscopic cross section data) are left as arbitrary functions of space and time. The symmetry analysis that follows is restricted to a search for translation and scaling symmetries; consequently the Lie derivative yields specific material conditions that must be satisfied in order to maintain the presence of these important similarity transformations. The principal outcome of this work is thus the determination of analytic material property functions that enable the presence of various translation and scaling symmetries within the time-dependent, monoenergetic neutron diffusion equation. The results of this exercise encapsulate and generalize many existing results already appearing in the literature. While the results contained in this work are primarily useful as phenomenological guides pertaining to the symmetry behavior of the neutron diffusion equation under certain assumptions, they may eventually be useful in the construction of exact solutions to the underlying mathematical model. Furthermore, the results of this work are also useful as a starting point or framework for future symmetry analysis studies pertaining to the neutron transport equation and its many surrogates.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Solute diffusion behavior during heat treatment and its impact in Sc-microalloyed Al-Cu system

Scandium (Sc) is a promising microalloying element that enhances the strength and thermal stability of aluminum (Al) alloys. However, these benefits are not fully realized in aluminum-copper (Al-Cu) systems, and corrosion resistance often declines due to the complex phase evolution and diffusion behavior of Cu and Sc. Here, to clarify this, solute diffusion behavior and Cu-Sc interaction during heat treatment (HT) were investigated using in situ synchrotron-based transmission x-ray microscopy (TXM), wide-angle x-ray scattering (WAXS), and x-ray absorption near-edge structure (XANES) spectroscopy. The results, supported by electron microscopy, reveal strong Cu-Sc bonding that significantly impedes solute diffusion, leading to inhomogeneous solute distribution and non-uniform precipitation. Moreover, the Al-Cu-Sc eutectic phase exhibits high thermal stability, resisting dissolution even near the matrix liquidus. These findings quantitatively elucidate the sluggish diffusion kinetics of Cu and Sc, which can help redesign HT schedules to improve both mechanical properties and corrosion resistance in Sc-microalloyed Al-Cu alloys.

36 MATERIALS SCIENCE↗