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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↗

NASA NTRS1974

A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

Tenney, D. R.↗

NASA NTRS1985

Diffusion welding of MA 6000 and a conventional nickel-base superalloy

A feasibility study of diffusion welding the oxide dispersion strengthened (ODS) alloy MA 6000 to itself and to conventional Ni-base superalloy Udimet 700 was conducted. Butt joints between MA 6000 pieces and lap joints between Udimet 700 and the ODS alloy were produced by hot pressing for 1.25 hr at temperatures ranging from 1000 to 1200 C (1832-2192 F) in vacuum. Following pressing, all weldments were heat treated and machined into mechanical property test specimens. While three different combinations of recrystallized and unrecrystallized MA 6000 butt joints were produced, the unrecrystallized to unrecrystallized joint was most successful as determined by mechanical properties and microstructural examination. Failure to weld the recrystallized material probably related to a lack of adequate deformation at the weld interface. While recrystallized MA 6000 could be diffusion welded to Udimet 700 in places, complete welding over the entire lap joint was not achieved, again due to the lack of sufficient deformation at the faying surfaces. Several methods are proposed to promote the intimate contact necessary for diffusion welding MA 6000 to itself and to superalloys.

Moore, T. J.↗

DOE OSTI2024

Onset of kinetic effects on Rayleigh–Taylor instability: Advective–diffusive asymmetry

In nature and engineering applications, the Rayleigh–Taylor instability (RTI) occurs over a wide range of Atwood, Reynolds, Mach, and Knudsen numbers. At low Atwood, Mach, and Knudsen numbers, the classic advective instability causes quasi-symmetric bubble and spike growth on the two sides of the interface. However, recent findings suggest that at high degrees of rarefaction, advective effects are suppressed and molecular diffusion leads to planar growth of the density fronts on either side of the interface. This study aims to investigate the flow physics of the transition from advective to diffusive behavior, focusing on the onset of the kinetic effects. Using the gas kinetic methodology, RTI is simulated over a range of Knudsen and Mach numbers in the transition regime. The simulation results reveal the various stages of transformation from advective instability to diffusive transport. For the first time, the study demonstrates the existence of a Knudsen–Mach parameter regime where the bubble side exhibits advective instability, while the other side shows a planar density front due to molecular diffusion, rather than the canonical advective spike shape. The dominance of different mechanisms on the two sides of the interface leads to the advective–diffusive asymmetry. In conclusion, the findings of this study can lead to a more comprehensive understanding of RTI over a wide range of Mach and Knudsen numbers.

42 ENGINEERING↗

DOE OSTI2021

Molecular dynamics of the early stages of high-temperature corrosion

In this work, we performed molecular dynamics simulations of the high-temperature oxidation of metal alloys composed of Al, Cr, and Fe and compared their behavior with that of pure Fe. The metal alloy elements (Al and Cr) segregated to the surface during oxidation, producing a lower stress gradient at the metal/environment interface compared to pure Fe. We have found that the lowered stress gradients produced in the alloy material appear to play a key role in the development of corrosion. Interfaces with lower stress gradients have reduced rates of H 2 O adsorption, especially for the ferritic (bcc) alloys. The diffusivity of oxygen and hydrogen drops more rapidly for the interfaces with reduced stress gradients. The stress gradient is also diminished when the gas pressure is increased, indicating that the Fe-Cr-Al alloy system is more resistant to oxidation than pure Fe at higher pressures. Therefore, we conclude that the lower stress gradients at the alloy/environment interface reduce the stress concentration and can slow down the rate of the initial oxide scale growth. We also compared bcc and fcc alloys with pure Fe based on our three evaluation criteria (peak stress, stress gradient, and summation of stress in the oxide scale). We found that the alloys have lower values under the three criteria compared to pure Fe. The bcc alloy has the best score under a water rich environment and the fcc alloy is proven to be better for peak stress and summation of stress in the oxide scale under an oxygen rich environment. For surface segregation to occur, we find that a minimum content of Al or Cr in the near-surface region must be achieved. We also learned that the role of Al is more important than that of Cr in terms of corrosion resistant behavior at relatively higher temperatures for the Fe-Cr-Al ternary alloys.

36 MATERIALS SCIENCE↗

NASA NTRS1989

Finite element modeling of frictionally restrained composite interfaces

The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.

Ballarini, Roberto↗

NASA NTRS1976

On the kinetics of the pack - Aluminization process

An investigation has been made of the aluminization of unalloyed Ni in fluoride-activated packs of varying Al activity. In packs of low Al activity, in which the ratio of Al to Ni was less than 50 at. pct, the specimen surface quickly came to equilibrium with the pack and remained close to equilibrium for the duration of normal coating runs. In these packs the kinetics of aluminization was controlled by diffusion in the solid. In packs of higher Al activity the surface of the specimen did not come to equilibrium with the pack and the kinetics of the process was governed by a combination of solid and gas diffusion rates. Under most conditions however, the surface composition was time-invariant and a steady-state appeared to exist at the pack-coating interface. By combining Levine and Caves' model for gaseous diffusion in pure-Al packs with calculations of solid diffusion rates some success has been achieved in explaining the results.

Sivakumar, R.↗

NASA NTRS2013

Oxygen Permeability and Grain-Boundary Diffusion Applied to Alumina Scales

High-temperature oxygen permeability measurements had determined grain-boundary diffusivities (deltaD(sub gb)) in bulk polycrystalline alumina (Wada, Matsudaira, and Kitaoka). They predict that oxygen deltaD(sub gb,O) varies with oxygen pressure as P(O2)(sup -1/6) at low pressure whereas aluminum deltaD(sub gb),Al varies with P(O2)(sup +3/16) at high pressure. These relations were used to evaluate alumina scale growth in terms of diffusivity and grain size. A modified Wagner treatment for dominant inward oxygen growth produces the concise solution: П(sub i) = k(sub p,i)×G(sub i) = 12 deltaD(sub gb,O,int), where П(sub i) is a constant and k(sub p,i) and G(sub i) refer to instantaneous values of the scale parabolic growth constant and grain size, respectively. A commercial FeCrAl(Zr) alloy was oxidized at 1100 to 1400 degC to determine k(sub p,i), interfacial grain size, П, and thus deltaD(sub gb,O,int). The deltaD(sub gb,O,int) values predicted from oxidation at (375 kJ/mole) were about 20 times less than those obtained above (at 298 kJ/mole), but closer than extrapolations from high-temperature bulk measurements. The experimental oxidation results agree with similar FeCrAl(X) studies, especially where both k(sub p,i) and G(sub i) were characterized. This complete approach accounts for temperature-sensitive oxidation effects of grain enlargement, equilibrium interface pressure variation, and grain-boundary diffusivity.

Smialek, James L.↗

DOE OSTI2021

Time-Resolved Evolution of the 3D Nanoporous Structure of Sintered Ag by X-Ray Nanotomography: Role of the Interface with a Copper Substrate

Here, the evolution of the nanoporous structure of cylindrical sintered silver samples during high temperature aging, ranging from 200 to 350 °C for 350 min, is studied through in situ computed X-ray tomography. Investigations are carried out for two types of specimens: pure sintered silver and specimens containing a silver-copper interface. It is shown that the overall pore evolution is driven by the evolution of very few large ones. The smaller pores, although being more numerous, do not really evolve before being absorbed by the few bigger ones. In pure silver, pore evolution is driven by diffusion (Ostwald ripening) but the presence of an interface promotes faster growth kinetics until the aging time reaches a threshold value, after which a deviation from Ostwald ripening occurs. The transition is a function of the aging temperature. This behavior is associated with the competition between elastic relaxation and surface energy minimization.

42 ENGINEERING↗

DOE OSTI2025

Extending the capillary wave model to include the effect of bending rigidity: X-ray reflectivity and diffuse scattering

The surface roughness of a thin film at a liquid interface exhibits contributions of thermally excited fluctuations. This thermal roughness depends on temperature (𝑇), surface tension (𝛾), and elastic material properties, specifically the bending modulus (𝜅) of the film. A nonzero 𝜅 suppresses the thermal roughness at small length scales compared to an interface with zero 𝜅, as expressed by the power spectral density of the thermal roughness. The description of the x-ray scattering of the standard capillary wave model (CWM), which is valid for zero 𝜅, is extended to include the effect of 𝜅. The extended CWM (eCWM) provides a single analytical form for both the specular x-ray reflectivity (XRR) and the diffuse scattering around the specular reflection, and recovers the expression of the CWM at its zero 𝜅 limit. This theoretical approach enables the use of single-shot grazing incidence x-ray off-specular scattering (GIXOS) measurements for characterizing the structure of thin films on a liquid surface. The eCWM analysis approach decouples the thermal roughness factor from the surface scattering signal, providing direct access to the intrinsic surface-normal structure of the film and its bending modulus. Moreover, the eCWM facilitates the calculation of reflectivity at any desired resolution (pseudo-XRR approach). The transformation into pseudo-XRR provides the benefit of using widely available XRR software to perform GIXOS analysis. The extended range of the vertical scattering vector (𝑄 𝑧 ) available with the GIXOS pseudo-XRR approach allows for a higher spatial resolution than with conventional XRR. Experimental results are presented for various lipid systems, showing strong agreement between conventional specular XRR and pseudo-XRR methods. This agreement validates the proposed approach and highlights its utility for analyzing soft, thin films.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Effect of diffusion constant on the morphology of dendrite growth in lithium metal batteries

Lithium dendrites can lead to a short circuit and battery failure, and developing strategies for their suppression is of considerable importance. In this work, we study the growth of dendrites in a simple model system where the solvent is a continuum and the lithium ions are hard spheres that can deposit by sticking to existing spheres or the electrode surface. Using stochastic dynamics simulations, we investigate the effect of applied voltage and diffusion constant on the growth of dendrites. We find that the diffusion constant is the most significant factor, and the inhomogeneity of the electric field does not play a significant role. Additionally, the growth is most pronounced when the applied voltage and diffusion constant are both low. We observe a structural change from broccoli to cauliflower shape as the diffusion constant is increased. The simulations suggest that a control of electrolyte parameters that impact lithium diffusion might be an attractive route to controlling dendrite growth.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1993

A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Lenardic, A.↗

DOE OSTI2020

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗

DOE OSTI2021

Working Principle of an Ionic Liquid Interlayer During Pressureless Lithium Stripping on Li 6.25 Al 0.25 La 3 Zr 2 O 12 (LLZO) Garnet‐Type Solid Electrolyte

Abstract Solid‐state‐batteries employing lithium metal anodes promise high theoretical energy and power densities. However, morphological instability occurring at the lithium/solid–electrolyte interface when stripping and plating lithium during cell cycling needs to be mitigated. Vacancy diffusion in lithium metal is not sufficiently fast to prevent pore formation at the interface above a certain current density during stripping. Applied pressure of several MPa can prevent pore formation, but this is not conducive to practical application. This work investigates the concept of ionic liquids as “self‐adjusting” interlayers to compensate morphological changes of the lithium anode while avoiding the use of external pressure. A clear improvement of the lithium dissolution process is observed as it is possible to continuously strip more than 70 μm lithium (i. e., 15 mAh cm −2 charge) without the need for external pressure during assembly and electrochemical testing of the system. The impedance of the investigated electrodes is analyzed in detail, and contributions of the different interfaces are evaluated. The conclusions are corroborated with morphology studies using cryo‐FIB‐SEM and chemical analysis using XPS. This improves the understanding of the impedance response and lithium stripping in electrodes employing liquid interlayers, acting as a stepping‐stone for future optimization.

Fuchs, Till↗

DOE OSTI2021

A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems

We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share “nonlocal” interfaces of the size of the nonlocal horizon. This system of nonlocal equations is first rewritten in terms of minimization of a nonlocal energy, then discretized with a meshfree approximation and finally solved via a Lagrange multiplier approach in a way that resembles the finite element tearing and interconnect method. Specifically, we propose a distributed projected gradient algorithm for the solution of the Lagrange multiplier system, whose unknowns determine the nonlocal interface conditions between subdomains. Several two-dimensional numerical tests on problems as large as 191 million unknowns illustrate the strong and the weak scalability of our algorithm, which outperforms the standard approach to the distributed numerical solution of the problem. Finally, this work is the first rigorous numerical study in a two-dimensional multi-domain setting for nonlocal operators with finite horizon and, as such, it is a fundamental step towards increasing the use of nonlocal models in large scale simulations.

42 ENGINEERING↗

DOE OSTI2023

Temperature-Dependent Morphological Evolution during Corrosion of the Ni-20Cr Alloy in Molten Salt Revealed by Multiscale Imaging

Understanding the mechanisms leading to the degradation of alloys in molten salts at elevated temperatures is significant for developing several key energy generation and storage technologies, including concentrated solar and next-generation nuclear power plants. Specifically, the fundamental mechanisms of different types of corrosion leading to various morphological evolution characteristics for changing reaction conditions between the molten salt and alloy remain unclear. Here, in this work, the three-dimensional (3D) morphological evolution of Ni–20Cr in KCl–MgCl 2 is studied at 600 °C by combining in situ synchrotron X-ray and electron microscopy techniques. By further comparing different morphology evolution characteristics in the temperature range of 500–800 °C, the relative rates between diffusion and reaction at the salt–metal interface lead to different morphological evolution pathways, including intergranular corrosion and percolation dealloying. In this work, the temperature-dependent mechanisms of the interactions between metals and molten salts are discussed, providing insights for predicting molten salt corrosion in real-world applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Impact of metal diffusion, lattice distortions, native defects, and ambient on dielectric breakdown in Ni–Ga 2 O 3 Schottky diodes

Ga 2 O 3 unipolar devices are of high interest due to their ~8 MV/cm predicted breakdown fields, which have not yet been achieved due to premature device failure. Pre- and post-failure defect analysis of Ni–Ga 2 O 3 Schottky diodes in ultrahigh vacuum (UHV) and air were performed using depth-resolved cathodoluminescence, high angle annular dark field scanning transmission electron microscopy, and energy dispersive x-ray analysis to understand the physical mechanisms that precede premature breakdown. The breakdown voltage in UHV was dramatically reduced by nearly 40% compared with the breakdown in air. This reduction in the breakdown voltage correlated with post-breakdown differences in Ni distribution, indicating that the coordination and bonding of Ni contribute strongly to electrical behavior in Ni–Ga 2 O 3 Schottky diodes. Breakdown studies in UHV revealed that Ni diffuses away more from the metal–semiconductor interface than with air breakdown, where Ni localizes more near the interface, indicative of the preferential formation of a Ni oxide under O-poor conditions. These measurements also identified the formation of divacancy-interstitial complexes and their characteristic luminescence signature ~150 nm from the interface, the densities of which correlated with breakdown fields. These findings show that electric-field-induced degradation occurs via the rearrangement of native point defects, which act as an additional precursor to device failure. Macroscopically, they show the impact of both vacuum conditions and metal reactivity on Ga 2 O 3 device fabrication.

36 MATERIALS SCIENCE↗

DOE OSTI2022

The Importance of a Moving Boundary Approach for Modeling the SEI Layer Growth to Predict Capacity Fade

One of the contributing factors to the aging of lithium-ion batteries is the growth of the solid-electrolyte interphase (SEI) layer. The growth of the SEI layer leads to the irreversible loss of lithium available for cycling and increases the resistance of the battery. Physics-based models in literature model the kinetically limited or solvent diffusion-limited growth. In such models, the interface resistance is a constant, and the contribution to the overpotential of the intercalation reaction from the SEI layer is considered to be ohmic. In this study, we propose a model that describes the growth of the SEI layer on the electrode surface as a moving interface. The transport of lithium ions and the solvent in the electrolyte are affected by this moving interface. The equations that govern the species transport and the potential drop across the SEI layer are derived from dilute solution theory and solved by transforming the coordinates of the moving boundary. The ion transport induces changes in the conductivity across the SEI layer, which affects the potential drop that arises due to its growth. The effects of this potential on capacity fade are studied over cycling the battery.

25 ENERGY STORAGE↗