A Low Diffusion Verified Conforming Transient h-r Unstructured Adaptive Mesh Refinement (cThruAMR) Method for Coupled Interface Problems
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Noble, David Ronald↗
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Numerical Diffusion (Mixing) of Material in Numerical Simulations of Hydrodynamics [Slides]
It is often assumed that a material interface between two materials is spread over a few numerical cells in numerical simulations for hydrodynamics. Also, we have the impression that higher order methods introduce less numerical diffusion (mixing) of material. As we know one of the purposes of adaptive mesh refinement (AMR) is to resolve interfaces between materials, but we would like to know how effective AMR is to reduce numerical diffusion of material. We will present our investigation about numerical diffusion (mixing) of material in xRage. The result of the investigation indicates that the assumptions mentioned above are not always valid. In this talk, we will also demonstrate the effectiveness of numerical techniques to reduce numerical diffusion of material, including contact discontinuity steepening, isotropic interface steepening, max interface steepening, material interface reconstruct.
36 MATERIALS SCIENCE↗
Anomalous nanoparticle surface diffusion in LCTEM is revealed by deep learning-assisted analysis
Significance Liquid cell transmission electron microscopy (LCTEM) is an emerging technique, which enables nanoscale visualization and tracking of single nanoparticles near interfaces with unprecedented spatial resolution. Here, we studied the diffusion of nanoparticles in LCTEM experiments using techniques powered by deep neural networks and statistical tests. We observed two underlying regimes of diffusive behavior which are governed by the interaction of the electron beam, the nanoparticle, the nearby substrate, and the liquid environment. This understanding forms the foundation to use LCTEM for single-nanoparticle tracking for a broad range of nanoparticles, interfaces, and liquids.
Jamali, Vida↗
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↗
Phase-Field Modeling of Materials Interfaces and Nanostructures
Nanostructured materials offer unique properties for a wide range of energy applications. Among various known processing methods, liquid metal dealloying (LMD)—the selective dissolution of a base alloy element into a metallic melt—has emerged as a powerful technique to produce a new class of nano-/meso-scale open porous and bicontinuous composite structures with ultra-high interfacial area. LMD has recently been complemented by the advent of vapor phase dealloying (VPD), a novel technique that exploits the selective evaporation of one element from a parent alloy containing elements with very different vapor pressures, thereby enabling to fabricate open nanoporous structures of various elements from less-noble metals to inorganic elements regardless of their chemical activity without requiring high LMD temperatures and chemical etching. Together LMD and VPD have greatly expanded the scope of dealloying techniques, limited by traditional electrochemical means to noble metals, and boosted the design of new functional and structural materials that combine a wide variety of elements. Topologically-connected open porous structures with ultra-high surface area allow mass transport within the structure while preserving structural integrity, enabling them to serve as catalysts, fuel cells, supercapacitors, or high-capacity battery materials. Bicontinuous composite structures in turn can display high strength and high ductility or superior radiation-damage resistance due to the ultra-high interface area between interpenetrating solid phases. This research program makes use of state-of-the-art computational methods to understand at a basic level the self-organizing dealloying process with main focus on dealloying kinetics and interfacial pattern formation at the dealloying front controlling initial structure size, topology, and phase compositions. Phase-field simulation studies of LMD focus on solid solutions, line compounds, and intermetallic systems that can form ternary composites by nucleation and growth of a new phase. Studies of VPD employ phase-field modeling and a hybrid method combining a kinetic Monte Carlo (KMC) model of evaporation and surface diffusion with molecular dynamics for vapor-phase transport inside nanopores. Simulations explore mechanisms of interface- and diffusion-controlled dealloying kinetics, both observed in VPD but not fundamentally understood. In addition, our newly developed multi-physics phase-field approach of large-volume-change phase transformations is being used to model novel 3D anode geometries based on dealloyed nanoporous structures including novel sandwiched graphene/Si/silica for highrate Li ion battery. Those studies are aimed at elucidating geometric design principles that improve mechanical stability. We expect this research to enhance the capability to tailor nano-/mesoscale structures for a wide range of energy-related materials applications and to yield further advances in computational methodologies that benefit a broad materials research community.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Ultrahigh-Rate and Long-Life Zinc–Metal Anodes Enabled by Self-Accelerated Cation Migration
Aqueous zinc ion batteries are receiving unprecedented attention owing to their markedly high safety and sustainability, yet their lifespan particularly at high rates is largely limited by the poor reversibility of zinc (Zn) metal anodes, due to the random ion diffusion and sluggish ion replenishment at reaction interface. In this work, we propose a tunnel-rich and corona-poled ferroelectric thin film coating for Zn metal anode to tackle above conundra. It is demonstrated that the poled ferroelectric coating can better deconcentrate and self-accelerate ion migration at coating/Zn interface upon electroplating process than untreated ferroelectric coating and bare Zn, thus enabling a compact and horizontally-aligned Zn morphology even at ultrahigh rates. Notably, a maximal cumulative plating capacity of over 6500 mAh cm -2 (at 10 mA cm -2 ) is achieved for the surface-modified Zn metal anode, showing extraordinary reversibility of Zn plating/stripping. This work provides new insights in stabilizing Zn metal electrodeposition at the scale of interfacial ion diffusion.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
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↗
Lamination of >21% Efficient Perovskite Solar Cells with Independent Process Control of Transport Layers and Interfaces
Transport layer and interface optimization is critical for improving the performance and stability of perovskite solar cells (PSCs) but is restricted by the conventional fabrication approach of sequential layer deposition. While the bottom transport layer is processed with minimum constraints, the narrow thermal and chemical stability window of the halide perovskite (HP) layer severely restricts the choice of top transport layer and its processing conditions. To overcome these limitations, we demonstrate lamination of HPs—where two transport layer-perovskite half-stacks are independently processed and diffusion-bonded at the HP-HP interface—as an alternative fabrication strategy that enables self-encapsulated solar cells. Power conversion efficiencies (PCE) of >21% are realized using cells that incorporate a novel transport layer combination along with dual-interface passivation via self-assembled monolayers, both of which are uniquely enabled by the lamination approach. This is the highest reported PCE for any laminated PSC encapsulated between glass substrates. We further show that this approach expands the processing window beyond traditional fabrication processes and is adaptable for different transport layer compositions. The laminated PSCs retained >75% of their initial PCE after 1000 h of 1-sun illumination at 40 °C in air using an all-inorganic transport layer configuration without additional encapsulation. Furthermore, a laminated 1 cm 2 device maintained a V oc of 1.16 V. Finally, the scalable lamination strategy in this study enables the implementation of new transport layers and interfacial engineering approaches for improving performance and stability.
14 SOLAR ENERGY↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗