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At least 883 records · Page 49

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

The problem of a spatially discontinuous diffusion coefficient (D(x)) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow properties. To date, mass-transfer particle-tracking (MTPT) methods, a family of Lagrangian methods in which diffusion is jointly simulated by random walk and diffusive mass transfers, have been unable to solve this problem. This manuscript presents a new mass-transfer (MT) algorithm that enables MTPT methods to accurately solve the problem of discontinuous D(x). To achieve this, we derive a semi-analytical solution to the discontinuous D(x) problem by employing a predictor-corrector approach, and we use this semi-analytical solution as the weighting function in a reformulated MT algorithm. Furthermore, this semi-analytical solution is generalized for cases with multiple 1D interfaces as well as for 2D cases, including a 2 × 2 tiling of 4 subdomains that corresponds to a numerically-generated diffusion field. The solutions generated by this new mass-transfer algorithm closely agree with an analytical 1D solution or, in more complicated cases, trusted numerical results, demonstrating the success of our proposed approach.

42 ENGINEERING↗

Data-driven methods for diffusivity prediction in nuclear fuels

The growth rate of structural defects in nuclear fuels under irradiation is intrinsically related to the diffusion rates of the defects in the fuel lattice. The generation and growth of atomistic structural defects can significantly alter the performance characteristics of the fuel. This alteration of functionality must be accurately captured to qualify a nuclear fuel for use in reactors. Predicting the diffusion coefficients of defects and how they impact macroscale properties such as swelling, gas release, and creep is therefore of significant importance in both the design of new nuclear fuels and the assessment of current fuel types. In this article, we apply data-driven methods focusing on machine learning (ML) to determine various diffusion properties of two nuclear fuels—uranium oxide and uranium nitride. We show that using ML can increase, often significantly, the accuracy of predicting diffusivity in nuclear fuels in comparison to current analytical models. We also illustrate how ML can be used to quickly develop fuel models with parameter dependencies that are more complex and robust than what is currently available in the literature. In conclusion, these results suggest there is potential for ML to accelerate the design, qualification, and implementation of nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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

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

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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

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

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Liquid–Solid Boundaries Dominate Activity of CO 2 Reduction on Gas-Diffusion Electrodes

Electrochemical CO 2 electrolysis to produce hydrocarbon fuels or material feedstocks offers a renewable alternative to fossilized carbon sources. Gas-diffusion electrodes (GDEs), composed of solid electrocatalysts on porous supports positioned near the interface of a conducting electrolyte and CO 2 gas, have been able to demonstrate the substantial current densities needed for future commercialization. These higher reaction rates have often been ascribed to the presence of a three-phase interface, where solid, liquid, and gas provide electrons, water, and CO 2 , respectively. Conversely, mechanistic work on electrochemical reactions implicates a fully two-phase reaction interface, where gas molecules reach the electrocatalyst’s surface by dissolution and diffusion through the electrolyte. Because the discrepancy between an atomistic three-phase versus two-phase reaction has substantial implications for the design of catalysts, gas-diffusion layers, and cell architectures, the nuances of nomenclatures and governing phenomena surrounding the three-phase-region require clarification. In this paper we outline the macro, micro, and atomistic phenomena occurring within a gas-diffusion electrode to provide a focused discussion on the architecture of the often-discussed three-phase region for CO 2 electrolysis. From this information, we comment on the outlook for the broader CO 2 electroreduction GDE cell architecture.

CO2 reduction↗

Effects of diffusion barriers on reaction wave stability in Co/Al reactive multilayers

Bimetallic, reactive multilayers are uniformly structured materials composed of alternating sputter-deposited layers that may be ignited to produce self-propagating mixing and formation reactions. These nanolaminates are most commonly used as rapid-release heat sources. The specific chemical composition at each metal/metal interface determines the rate of mass transport in a mixing and formation reaction. The inclusion of engineered diffusion barriers at each interface will not only inhibit solid-state mixing but also may impede the self-propagating reactions by introducing instabilities to wavefront morphology. Here, this work examines the effect of adding diffusion barriers on the propagation of reaction waves in Co/Al multilayers. The Co/Al system has been shown to exhibit a reaction propagation instability that is dependent on the bilayer thickness, which allows for the occurrence of unstable modes in otherwise stable designs from the inclusion of diffusion barriers. Based on the known stability criteria in the Co/Al multilayer system, the way in which the inclusion of diffusion barriers changes a multilayer's heat of reaction, thermal conductivity, and material mixing mechanisms can be determined. These factors, in aggregate, lead to changes in the wavefront velocity and stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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

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

Anomalous diffusion↗

The Riddle of Dark LLZO: Cobalt Diffusion in Garnet Separators of Solid‐State Lithium Batteries

Abstract Solid‐state batteries (SSBs) with a Li 7 La 3 Zr 2 O 12 (LLZO) garnet electrolyte are attracting much attention as robust and safe alternative to conventional lithium‐ion batteries. Technical challenges in the practical implementation of garnet SSBs are related to the need for high‐temperature sintering, which often leads to undesirable chemical reactions with the cathode material. While these reactions are well understood for composite cathodes, very little is known about similar processes between cathode and separator during battery fabrication. This work focuses on understanding the processes between the composite LiCoO 2 ‐LLZO cathode and the LLZO separator and how they affect the battery performance. The extensive diffusion of Co‐ions within LLZO, which leads to the often‐observed LLZO darkening, is shown to have a significant impact on ionic conductivity, electronic conductivity, and dendrite stability of the separator. Experimental data coupled with large‐scale molecular dynamics simulations uncover the diffusion mechanism for Co‐ions and identify secondary phases that form during these interactions. In addition to extensive Co‐ion diffusion within the grains, a non‐uniform segregation of Co‐ions at grain boundaries is found leading to the formation of three distinct Co‐containing phases. This work offers a general approach to studying the fundamental ion diffusion processes that occur during the fabrication of oxide SSBs.

electrochemical properties↗

Quantification of Sheet Resistance in Boron-Diffused Silicon Using Micro-Photoluminescence Spectroscopy at Room Temperature

A micro-photoluminescence-based technique is presented, to quantify and map sheet resistances of boron-diffused layers in silicon solar cell precursors with micron-scale spatial resolution at room temperature. The technique utilizes bandgap narrowing effects in the heavily-doped layers, yielding a broader photoluminescence spectrum at the long-wavelength side compared to the spectrum emitted from lightly doped silicon. By choosing an appropriate spectral range as a metric to assess the doping density, the impacts of photon reabsorption on the analysis can be avoided; thus, an accurate characterization of the sheet resistance can be made. This metric is demonstrated to be better representative of the sheet resistance than the surface doping density or the total dopant concentration of the diffused layer. The technique is applied to quantify sheet resistances of 12-um-wide diffused fingers in interdigitated back-contact solar cell precursors and large diffused areas. The results are confirmed by both 4-point probe and time-of-flight secondary-ion mass spectrometry measurements. Lastly, the practical limitations associated with extending the proposed technique into an imaging mode are presented and explained.

14 SOLAR ENERGY↗

An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action

The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ=0 to non-integrable for ϵ≠0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Hermite analogs of the lowest order Raviart–Thomas mixed method for convection–diffusion equations

The Raviart–Thomas mixed finite-element method of the lowest order (Raviart and Thomas in mixed finite-element methods for second-order elliptic problems, Lecture Notes in mathematics, Springer, New York, 1977) commonly known as the RT{sub 0} method, is a well-established and popular numerical tool to solve diffusion-like problems providing flux continuity across inter-element boundaries. Douglas and Roberts extended the method to the case of more general second-order boundary-value problems including the convection–diffusion equations (cf. this journal Douglas in Comput Appl Math 1:91–103; 1982). The main drawback of these methods, however, is the poor representation of the primal variable by piecewise constant functions. The Hermite analog of the RT{sub 0} method for treating pure diffusion phenomena proposed in Ruas (J Comput Appl Math, 246:234–242; 2013) proved to be a valid alternative to attain higher order approximation of the primal variable while keeping intact the matrix structure and the quality of the discrete flux variable of the original RT{sub 0} method. Non-trivial extensions of this method are studied here that can be viewed as Hermite analogs of the two Douglas and Roberts’ versions of the RT{sub 0} method, to solve convection–diffusion equations. A detailed convergence study is carried out for one of the Hermite methods, and numerical results illustrate the performance of both of them, as compared to each other and to the corresponding mixed methods.

97 MATHEMATICS AND COMPUTING↗

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

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

25 ENERGY STORAGE↗

Effect of nickel on point defects diffusion in Fe – Ni alloys

Iron-Nickel alloys are perspective alloys as nuclear energy structural materials because of their good radiation damage tolerance and mechanical properties. Understanding of experimentally observed features such as the effect of Ni content to radiation defects evolution is essential for developing predictive models of radiation. Recently an atomic-scale modelling study has revealed one particular mechanism of Ni effect related to the reduced mobility of clusters of interstitial atoms in Fe-Ni alloys. In this paper we present results of the microsecond-scale molecular dynamics study of point defects, i.e. vacancies and self-interstitial atoms, diffusion in Fe-Ni alloys. It is found that the addition of Ni atoms affects diffusion processes: diffusion of vacancies is enhanced in the presence of Ni, whereas diffusion of interstitials is reduced and these effects increase at high Ni concentration and low temperature. As a result, the role of Ni solutes in radiation damage evolution in Fe-Ni alloys is discussed.

36 MATERIALS SCIENCE↗

An accurate and asymptotically compatible collocation scheme for nonlocal diffusion problems

Here, in this paper, we develop and analyze a collocation scheme for solving the linear nonlocal diffusion problem with general kernels. To approximate the nonlocal diffusion operator, we take a classic trapezoidal rule based on the linear interpolation as the starting point, and then carefully derive a new improved quadrature rule, which is not only more accurate but also could avoid the evaluations of singular integrals. We then use this rule to construct a collocation scheme for solving the nonlocal diffusion equations, that produces a symmetric positive definite stiffness matrix with Toeplitz structure. The proposed scheme is rigorously shown to be of second order accurate with respect to the mesh size for the nonlocal problem with fixed horizon, and in particular, it can achieve higher order accuracy for the commonly used kernels in the literature. Furthermore, we also prove that the scheme is asymptotically compatible, i.e., the approximate solution of the nonlocal diffusion problem converges to the exact solution of the corresponding local PDE problem when the horizon and the mesh size both go to zero. Finally, numerical experiments are presented to verify the theoretical results.

97 MATHEMATICS AND COMPUTING↗

High efficiency screen-printed n-type silicon solar cell using co-diffusion of APCVD boron emitter and POCl 3 back surface field

We present the fabrication and analysis of Passivated Emitter and Rear Totally Diffused (PERT) solar cells on n-type silicon using a co-diffusion process. In a single high temperature step, a BSG/SiO x stack deposited by APCVD and a POCl 3 back surface field diffuse into the wafer to form the boron doped emitter and phosphorus doped back surface field. The SiO x layer on top of BSG acts as a masking layer to prevent cross-doping of phosphorus as well as a blocking layer for boron out-diffusion. This resulted in an initial sheet resistance of 76 Ω with good uniformity and a final p + emitter sheet resistance of 97 Ω after boron rich layer removal. Additionally, bulk lifetime was investigated before and after the high temperature step that resulted in an increase from 1.2 ms to 1.5 ms due to a POCl 3 gettering effect. Finally, a peak cell efficiency of 20.3% was achieved and each recombination component in terms of saturation current density was calculated and analyzed to understand the cell for further efficiency enhancement.

14 SOLAR ENERGY↗

Anisotropic thermal diffusivity and conductivity in SiC/SiC tubes studied by infrared imaging and X-ray computed tomography

Traditional flash diffusivity evaluation of thermal diffusivity/conductivity of composite tubes require machining of specimens. For a thin-wall tube, this method can only be used to obtain through-thickness transport property. A novel method to evaluate anisotropic thermal diffusivity in a composite tube has been developed. Braided SiC/SiC composite tubes were subjected to a xenon flash heating pulse. A high-speed, high-sensitivity infrared camera was used to measure surface temperature changes as a function of time and nondestructively detect subsurface defects/damages, such as macroscopic pores. Standard reference material (Pyroceram 9606) and curved SiC/SiC composite tube specimens were used to validate thermal diffusivity obtained from infrared imaging. Unlike the traditional method, there is no need prepare special specimens, and thermal diffusivity values in three orientations are obtained after a single flash. A finite element analysis model based on x-ray computed tomography scans was developed to simulate the heat transfer. In conclusion, this technique is significant in assessing thermal conductivity and inspecting the health of ceramic tubes during and after service.

36 MATERIALS SCIENCE↗

Migration energy barriers and diffusion anisotropy of point defects on tungsten surfaces

We report tungsten is one of the most promising candidates for plasma-facing materials in future fusion devices, owing to its high performance under extreme irradiation conditions. However, irradiation-induced surface morphology varies significantly, depending on the irradiation type, fluence, and flux. Therefore, it is critical to examine the dynamics of point defects on tungsten (W) surfaces to understand how irradiation affects surface morphology. In this study, we employ the Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC) method to search for potential migration paths of point defects on W (1 0 0), (1 1 0) and (1 1 1) surfaces. The first-principles calculations are then used to accurately determine the migration energy barriers. The obtained paths and barriers are incorporated into a kinetic Monte Carlo (KMC) model to determine trajectories and diffusivities, which are described by diffusion tensors to demonstrate their anisotropic features. Multiple diffusion mechanisms have been identified on different surfaces, with various anisotropy factors. Particularly, point defects on the W (1 1 0) surface have the highest diffusivities, with anisotropy factors independent of temperatures. In comparison, the anisotropy of the W (1 0 0) surface decreases as temperature increases, while the W (1 1 1) surface is isotropic for point defects. This study provides insights into defect transport properties on different surfaces, which are essential for understanding the early stages of irradiation-induced microstructural evolutions and surface morphology of tungsten.

36 MATERIALS SCIENCE↗