Conversion cathode materials are gaining interest for secondary batteries due to their high theoretical energy and power density. However, practical application as a secondary battery material is currently limited by practical issues such as poor cyclability. To better understand these materials, we have, for this study, developed a pseudo-two-dimensional model for conversion cathodes. We apply this model to FeS2 – a material that undergoes intercalation followed by conversion during discharge. The model is derived from the half-cell Doyle–Fuller–Newman model with additional loss terms added to reflect the converted shell resistance as the reaction progresses. We also account for polydisperse active material particles by incorporating a variable active surface area and effective particle radius. Using the model, we show that the leading loss mechanisms for FeS2 are associated with solid-state diffusion and electrical transport limitations through the converted shell material. The polydisperse simulations are also compared to a monodisperse system, and we show that polydispersity has very little effect on the intercalation behavior yet leads to capacity loss during the conversion reaction. Finally, we provide the code as an open-source Python Battery Mathematical Modeling (PyBaMM) model that can be used to identify performance limitations for other conversion cathode materials.
Cooper, Samuel J.; Roberts, Scott A.; Liu, Zhao L.; Winiarski, Bartlomiej W.
The mesostructure of porous electrodes used in lithium-ion batteries strongly influences cell performance. Accurate imaging of the distribution of phases in these electrodes would allow this relationship to be better understood through simulation. However, imaging the nanoscale features in these components is challenging. While scanning electron microscopy is able to achieve the required resolution, it has well established difficulties imaging porous media. This is because the flat imaging planes prepared using focused ion beam milling will intersect with the pores, which makes the images hard to interpret as the inside walls of the pores are observed. It is common to infiltrate porous media with resin prior to imaging to help resolve this issue, but both the nanoscale porosity and the chemical similarity of the resins to the battery materials undermine the utility of this approach for most electrodes. In this study, a technique is demonstrated which uses in situ infiltration of platinum to fill the pores and thus enhance their contrast during imaging. Reminiscent of the Japanese art of repairing cracked ceramics with precious metals, this technique is referred to as the kintsugi method. The images resulting from applying this technique to a conventional porous cathode are presented and then segmented using a multi-channel convolutional method. We show that while some cracks in active material particles were empty, others appear to be filled (perhaps with the carbon binder phase), which will have implications for the rate performance of the cell. Energy dispersive X-ray spectroscopy was used to validate the distribution of phases resulting from image analysis, which also suggested a graded distribution of the binder relative to the carbon additive. The equipment required to use the kintsugi method is commonly available in major research facilities and so we hope that this method will be rapidly adopted to improve the imaging of electrode materials and porous media in general.
Conversion cathodes represent a viable route to improve rechargeable Li+ battery energy densities, but their poor electrochemical stability and power density have impeded their practical implementation. Here, we explore the impact cell fabrication, electrolyte interaction, and current density have on the electrochemical performance of FeS2/Li cells by deconvoluting the contributions of the various conversion and intercalation reactions to the overall capacity. By varying the slurry composition and applied pressure, we determine that the capacity loss is primarily due to the large volume changes during (de)lithiation, leading to a degradation of the conductive matrix. Through the application of an external pressure, the loss is minimized by maintaining the conductive matrix. Further, we determine that polysulfide loss can be minimized by increasing the current density (>C/10), thus reducing the sulfur formation period. Analysis of the kinetics determines that the conversion reactions are rate-limiting, specifically the formation of metallic iron at rates above C/8. While focused on FeS2, our findings on the influence of pressure, electrolyte interaction, and kinetics are broadly applicable to other conversion cathode systems.
Electrode-scale heterogeneity can combine with complex electrochemical interactions to impede lithium-ion battery performance, particularly during fast charging. This study investigates the influence of electrode heterogeneity at different scales on the lithium-ion battery electrochemical performance under operational extremes. We employ image-based mesoscale simulation in conjunction with a three-dimensional electrochemical model to predict performance variability in 14 graphite electrode X-ray computed tomography data sets. Our analysis reveals that the tortuous anisotropy stemming from the variable particle morphology has a dominating influence on the overall cell performance. Cells with platelet morphology achieve lower capacity, higher heat generation rates, and severe plating under extreme fast charge conditions. On the contrary, the heterogeneity due to the active material clustering alone has minimal impact. Our work suggests that manufacturing electrodes with more homogeneous and isotropic particle morphology will improve electrochemical performance and improve safety, enabling electromobility.
Graphite electrodes in the lithium-ion battery exhibit various particle shapes, including spherical and platelet morphologies, which influence structural and electrochemical characteristics. It is well established that porous structures exhibit spatial heterogeneity, and the particle morphology can influence transport properties. The impact of the particle morphology on the heterogeneity and anisotropy of geometric and transport properties has not been previously studied. This study characterizes the spatial heterogeneities of 18 graphite electrodes at multiple length scales by calculating and comparing the structural anisotropy, geometric quantities, and transport properties (pore-scale tortuosity and electrical conductivity). We found that the particle morphology and structural anisotropy play an integral role in determining the spatial heterogeneity of directional tortuosity and its dependency on pore-scale heterogeneity. Our analysis reveals that the magnitude of in-plane and through-plane tortuosity difference influences the multiscale heterogeneity in graphite electrodes.
Li metal anodes are enticing for batteries due to high theoretical charge storage capacity, but commercialization is plagued by dendritic Li growth and short circuits when cycled at high currents. Applied pressure has been suggested to improve morphology, and therefore performance. We hypothesized that increasing pressure would suppress dendritic growth at high currents. To test this hypothesis, here, we extensively use cryogenic scanning electron microscopy to show that varying the applied pressure from 0.01 to 1 MPa has little impact on Li morphology after one deposition. We show that pressure improves Li density and preserves Li inventory after 50 cycles. However, contrary to our hypothesis, pressure exacerbates dendritic growth through the separator, promoting short circuits. Therefore, we suspect Li inventory is better preserved in cells cycled at high pressure only because the shorts carry a larger portion of the current, with less being carried by electrochemical reactions that slowly consume Li inventory.
Image-based simulation, the use of 3D images to calculate physical quantities, relies on image segmentation for geometry creation. However, this process introduces image segmentation uncertainty because different segmentation tools (both manual and machine-learning-based) will each produce a unique and valid segmentation. First, we demonstrate that these variations propagate into the physics simulations, compromising the resulting physics quantities. Second, we propose a general framework for rapidly quantifying segmentation uncertainty. Through the creation and sampling of segmentation uncertainty probability maps, we systematically and objectively create uncertainty distributions of the physics quantities. We show that physics quantity uncertainty distributions can follow a Normal distribution, but, in more complicated physics simulations, the resulting uncertainty distribution can be surprisingly nontrivial. We establish that bounding segmentation uncertainty can fail in these nontrivial situations. While our work does not eliminate segmentation uncertainty, it improves simulation credibility by making visible the previously unrecognized segmentation uncertainty plaguing image-based simulation.
The galvanostatic intermittent titration technique (GITT) is widely used to evaluate solid-state diffusion coefficients in electrochemical systems. However, the existing analysis methods for GITT data require numerous assumptions, and the derived diffusion coefficients typically are not independently validated. To investigate the validity of the assumptions and derived diffusion coefficients, we employ a direct-pulse fitting method for interpreting the GITT data that involves numerically fitting an electrochemical pulse and subsequent relaxation to a one-dimensional, single-particle, electrochemical model coupled with non-ideal transport to directly evaluate diffusion coefficients. Our non-ideal diffusion coefficients, which are extracted from GITT measurements of the intercalation regime of FeS2 and independently verified through discharge predictions, prove to be 2 orders of magnitude more accurate than ideal diffusion coefficients extracted using conventional methods. We further extend our model to a polydisperse set of particles to show the validity of a single-particle approach when the modeled radius is proportional to the total volume-to-surface-area ratio of the system.
Mishra, Lubhani; Subramaniam, Akshay; Jang, Taejin; Shah, Krishna; Uppaluri, Maitri; Roberts, Scott A.; Subramanian, Venkat R.
Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. In this paper, using a motivating example of a moving boundary model in one dimension, we show how battery models need proper formulation for mass conservation, especially when simulated over multiple charge and discharge cycles. The article concludes with some thoughts on mass conservation and proper formulation for multiscale models.
Mistry, Aashutosh; Franco, Alejandro A.; Cooper, Samuel J.; Roberts, Scott A.; Viswanathan, Venkatasubramanian
Electrochemical systems function via interconversion of electric charge and chemical species and represent promising technologies for our cleaner, more sustainable future. However, their development time is fundamentally limited by our ability to identify new materials and understand their electrochemical response. To shorten this time frame, we need to switch from the trial-and-error approach of finding useful materials to a more selective process by leveraging model predictions. Machine learning (ML) offers data-driven predictions and can be helpful. Herein we ask if ML can revolutionize the development cycle from decades to a few years. We outline the necessary characteristics of such ML implementations. Instead of enumerating various ML algorithms, we discuss scientific questions about the electrochemical systems to which ML can contribute.
Macrohomogeneous battery models are widely used to predict battery performance, necessarily relying on effective electrode properties, such as specific surface area, tortuosity, and electrical conductivity. While these properties are typically estimated using ideal effective medium theories, in practice they exhibit highly non-ideal behaviors arising from their complex mesostructures. In this paper, we computationally reconstruct electrodes from X-ray computed tomography of 16 nickel-manganese-cobalt-oxide electrodes, manufactured using various material recipes and calendering pressures. Due to imaging limitations, a synthetic conductive binder domain (CBD) consisting of binder and conductive carbon is added to the reconstructions using a binder bridge algorithm. Reconstructed particle surface areas are significantly smaller than standard approximations predicted, as the majority of the particle surface area is covered by CBD, affecting electrochemical reaction availability. Finite element effective property simulations are performed on 320 large electrode subdomains to analyze trends and heterogeneity across the electrodes. Significant anisotropy of up to 27% in tortuosity and 47% in effective conductivity is observed. Electrical conductivity increases up to 7.5× with particle lithiation. We compare the results to traditional Bruggeman approximations and offer improved alternatives for use in cellscale modeling, with Bruggeman exponents ranging from 1.62 to 1.72 rather than the theoretical value of 1.5. We also conclude that the CBD phase alone, rather than the entire solid phase, should be used to estimate effective electronic conductivity. This study provides insight into mesoscale transport phenomena and results in improved effective property approximations founded on realistic, image-based morphologies.
The development of solid-state batteries has encountered a number of problems due to the complex interfacial contact conditions between lithium (Li) metal and solid electrolytes (SEs). Recent experiments have shown that applying stack pressure can ameliorate these problems. Here, we report a multi-scale three-dimensional time-dependent contact model for describing the Li-SE interface evolution under stack pressure. Our simulation considers the surface roughness of the Li and SEs, Li elastoplasticity, Li creep, and the Li metal plating/stripping process. Consistency between the very recent experiments from two different research groups indicates effective yield strength of the Li used in those experiments of 16 ± 2 MPa. We suggest that the preferred stack pressure be at least 20 MPa to maintain a relatively small interface resistance while reducing void volume.
Recent advancements in micro-scale additive manufacturing techniques have created opportunities for design of novel electrode geometries that improve battery performance by deviating from the traditional layered battery design. These 3D batteries typically exhibit interpenetrating anode and cathode materials throughout the design space, but the existing well-established porous electrode theory models assume only one type of electrode is present in each battery layer. We therefore develop and demonstrate a multielectrode volume-averaged electrochemical transport model to simulate transient discharge performance of these new interpenetrating electrode architectures. We implement the new reduced-order model in the PETSc framework and asses its accuracy by comparing predictions to corresponding mesoscale-resolved simulations that are orders of magnitude more computationally-intensive. For simple electrode designs such as alternating plates or cylinders, the volume-averaged model predicts performance within ∼2% for electrode feature sizes comparable to traditional particle sizes (5-10μm) at discharge rates up to 3C. When considering more complex geometries such as minimal surface designs (i.e. gyroid, Schwarz P), we show that using calibrated characteristic diffusion lengths for each design results in errors below 3% for discharge rates up to 3C. These comparisons verify that this novel model has made reliable cell-scale simulations of interpenetrating electrode designs possible.
Battery electrodes are composed of polydisperse particles and a porous, composite binder domain. These materials are arranged into a complex mesostructure whose morphology impacts both electrochemical performance and mechanical response. We present image-based, particle-resolved, mesoscale finite element model simulations of coupled electrochemical-mechanical performance on a representative NMC electrode domain. Beyond predicting macroscale quantities such as half-cell voltage and evolving electrical conductivity, studying behaviors on a per-particle and per-surface basis enables performance and material design insights previously unachievable. Voltage losses are primarily attributable to a complex interplay between interfacial charge transfer kinetics, lithium diffusion, and, locally, electrical conductivity. Mesoscale heterogeneities arise from particle polydispersity and lead to material underutilization at high current densities. Particle-particle contacts, however, reduce heterogeneities by enabling lithium diffusion between connected particle groups. While the porous composite binder domain (CBD) may have slower ionic transport and less available area for electrochemical reactions, its high electrical conductivity makes it the preferred reaction site late in electrode discharge. Mesoscale results are favorably compared to both experimental data and macrohomogeneous models. This work enables improvements in materials design by providing a tool for optimization of particle sizes, CBD morphology, and manufacturing conditions.
Deep learning segmentation models are known to be sensitive to the scale, contrast, and distribution of pixel values when applied to Computed Tomography (CT) images. For material samples, scans are often obtained from a variety of scanning equipment and resolutions resulting in domain shift. The ability of segmentation models to generalize to examples from these shifted domains relies on how well the distribution of the training data represents the overall distribution of the target data. We present a method to overcome the challenges presented by domain shifts. Our results indicate that we can leverage a deep learning model trained on one domain to accurately segment similar materials at different resolutions by refining binary predictions using uncertainty quantification (UQ). We apply this technique to a set of unlabeled CT scans of woven composite materials with clear qualitative improvement of binary segmentations over the original deep learning predictions. In contrast to prior work, our technique enables refined segmentations without the expense of the additional training time and parameters associated with deep learning models used to address domain shift.
Static structural finite element models of an aluminum-framed crystalline silicon (c-Si) photovoltaic (PV) module and a glass-glass thin film PV module were constructed and validated against experimental measurements of deflection under uniform pressure loading. Parametric analyses using Latin Hypercube Sampling (LHS) were performed to propagate simulation input uncertainties related to module material properties, dimensions, and manufacturing tolerances into expected uncertainties in simulated deflection predictions. This exercise verifies the applicability and validity of finite element modeling for predicting mechanical behavior of solar modules across architectures and enables computational models to be used with greater confidence in assessment of module mechanical stressors and design for reliability. Sensitivity analyses were also performed on the uncertainty quantification data sets using linear correlation coefficients to elucidate the key parameters influencing module deformation. This information has implications on which materials or parameters may be optimized to best increase module stiffness and reliability, whether the key optimization parameters change with module architecture or loading magnitudes, and whether parameters such as frame design and racking must be replicated in reduced-scale reliability studies to adequately capture full module mechanical behavior.
Zhang, Xin; Wang, Q.J.; Harrison, Katharine L.; Jungjohann, Katherine; Boyce, Brad B.; Roberts, Scott A.; Attia, Peter M.; Harris, Stephen J.
We offer an explanation for how dendrite growth can be inhibited when Li metal pouch cells are subjected to external loads, even for cells using soft, thin separators. We develop a contact mechanics model for tracking Li surface and sub-surface stresses where electrodes have realistically (micron-scale) rough surfaces. Existing models examine a single, micron-scale Li metal protrusion under a fixed local current density that presses more or less conformally against a separator or stiff electrolyte. At the larger, sub-mm scales studied here, contact between the Li metal and the separator is heterogeneous and far from conformal for surfaces with realistic roughness: the load is carried at just the tallest asperities, where stresses reach tens of MPa, while most of the Li surface feels no force at all. Yet, dendrite growth is suppressed over the entire Li surface. To explain this dendrite suppression, our electrochemical/mechanics model suggests that Li avoids plating at the tips of growing Li dendrites if there is sufficient local stress; that local contact stresses there may be high enough to close separator pores so that incremental Li+ ions plate elsewhere; and that creep ensures that Li protrusions are gradually flattened. These mechanisms cannot be captured by single-dendrite-scale analyses.
As computing power rapidly increases, quickly creating a representative and accurate discretization of complex geometries arises as a major hurdle towards achieving a next generation simulation capability. Component definitions may be in the form of solid (CAD) models or derived from 3D computed tomography (CT) data, and creating a surface-conformal discretization may be required to resolve complex interfacial physics. The Conformal Decomposition Finite Element Methods (CDFEM) has been shown to be an efficient algorithm for creating conformal tetrahedral discretizations of these implicit geometries without manual mesh generation. In this work we describe an extension to CDFEM to accurately resolve the intersections of many materials within a simulation domain. This capability is demonstrated on both an analytical geometry and an image-based CT mesostructure representation consisting of hundreds of individual particles. Effective geometric and transport properties are the calculated quantities of interest. Solution verification is performed, showing CDFEM to be optimally convergent in nearly all cases. Representative volume element (RVE) size is also explored and per-sample variability quantified. Relatively large domains and small elements are required to reduce uncertainty, with recommended meshes of nearly 10 million elements still containing upwards of 30% uncertainty in certain effective properties. This work instills confidence in the applicability of CDFEM to provide insight into the behaviors of complex composite materials and provides recommendations on domain and mesh requirements.
Typical lithium-ion battery electrodes are porous composites comprised of active material, conductive additives, and polymeric binder, with liquid electrolyte filling the pores. The mesoscale morphology of these constituent phases has a significant impact on both electrochemical reactions and transport across the electrode, which can ultimately limit macroscale battery performance. We reconstruct published X-ray computed tomography (XCT) data from a NMC333 cathode to study mesoscale electrode behavior on an as-manufactured electrode geometry. We present and compare two distinct models that computationally generate a composite binder domain (CBD) phase that represents both the polymeric binder and conductive additives. We compare the effect of the resulting CBD morphologies on electrochemically active area, pore phase tortuosity, and effective electrical conductivity. Both dense and nanoporous CBD are considered, and we observe that acknowledging CBD nanoporosity significantly increases effective electrical conductivity by up to an order of magnitude. Properties are compared to published measurements as well as to approximate values often used in homogenized battery-scale models. All reconstructions exhibit less than 20% of the standard electrochemically active area approximation. Order of magnitude discrepancies are observed between two popular transport simulation numerical schemes (finite element method and finite volume method), highlighting the importance of careful numerical verification.
The objective of this project is to improve the fidelity of battery-scale simulations of abuse scenarios through the creation and application of microscale (particle-scale) electrode simulations.
The overall goal of this work was to develop, establish the credibility of, and deliver to our NW users a multi-physics performance model of a single cell of a thermally activated battery.
Lithium-ion battery electrodes are composed of active material particles, binder, and conductive additives that form an electrolyte-filled porous particle composite. The mesoscale (particle-scale) interplay of electrochemistry, mechanical deformation, and transport through this tortuous multi-component network dictates the performance of a battery at the cell-level. Effective electrode properties connect mesoscale phenomena with computationally feasible battery-scale simulations. We utilize published tomography data to reconstruct a large subsection (1000+ particles) of an NMC333 cathode into a computational mesh and extract electrode-scale effective properties from finite element continuum-scale simulations. We present a novel method to preferentially place a composite binder phase throughout the mesostructure, a necessary approach due difficulty distinguishing between non-active phases in tomographic data. We compare stress generation and effective thermal, electrical, and ionic conductivities across several binder placement approaches. Isotropic lithiation-dependent mechanical swelling of the NMC particles and the consideration of strain-dependent composite binder conductivity significantly impact the resulting effective property trends and stresses generated. Our results suggest that composite binder location significantly affects mesoscale behavior, indicating that a binder coating on active particles is not sufficient and that more accurate approaches should be used when calculating effective properties that will inform battery-scale models in this inherently multi-scale battery simulation challenge.
Battery performance, while observed at the macroscale, is primarily governed by the bicontinuous mesoscale network of the active particles and a polymeric conductive binder in its electrodes. Manufacturing processes affect this mesostructure, and therefore battery performance, in ways that are not always clear outside of empirical relationships. Directly studying the role of the mesostructure is difficult due to the small particle sizes (a few microns) and large mesoscale structures. Mesoscale simulation, however, is an emerging technique that allows the investigation into how particle-scale phenomena affect electrode behavior. In this manuscript, we discuss our computational approach for modeling electrochemical, mechanical, and thermal phenomena of lithium-ion batteries at the mesoscale. We review our recent and ongoing simulation investigations and discuss a path forward for additional simulation insights.
As LiCoO2 cathodes are charged, delithiation of the LiCoO2 active material leads to an increase in the lattice spacing, causing swelling of the particles. When these particles are packed into a bicontinuous, percolated network, as is the case in a battery electrode, this swelling leads to the generation of significant mechanical stress. In this study we performed coupled electrochemical-mechanical simulations of the charging of a LiCoO2 cathode in order to elucidate the mechanisms of stress generation and the effect of charge rate and microstructure on these stresses. Energy dispersive spectroscopy combined with scanning electron microscopy imaging was used to create 3D reconstructions of a LiCoO2 cathode, and the Conformal Decomposition Finite Element Method is used to automatically generate computational meshes on this reconstructed microstructure. Replacement of the ideal solution Fickian diffusion model, typically used in battery simulations, with a more general non-ideal solution model shows substantially smaller gradients of lithium within particles than is typically observed in the literature. Using this more general model, lithium gradients only appear at states of charge where the open-circuit voltage is relatively constant. While lithium gradients do affect the mechanical stress state in the particles, the maximum stresses are always found in the fully-charged state and are strongly affected by the local details of the microstructure and particle-to-particle contacts. These coupled electrochemical-mechanical simulations begin to yield insight into the partitioning of volume change between reducing pore space and macroscopically swelling the electrode. Finally, preliminary studies that include the presence of the polymeric binder suggest that it can greatly impact stress generation and that it is an important area for future research.
Electrical conductivity is key to the performance of thermal battery cathodes. In this work we present the effects of manufacturing and processing conditions on the electrical conductivity of Li/FeS2 thermal battery cathodes. We use finite element simulations to compute the conductivity of three-dimensional microcomputed tomography cathode microstructures and compare results to experimental impedance spectroscopy measurements. A regression analysis reveals a predictive relationship between composition, processing conditions, and electrical conductivity; a trend which is largely erased after thermally-induced deformation. The trend applies to both experimental and simulation results, although is not as apparent in simulations. This research is a step toward a more fundamental understanding of the effects of processing and composition on thermal battery component microstructure, properties, and performance.
The polymer-composite binder used in lithium-ion battery electrodes must both hold the electrodes together and augment their electrical conductivity while subjected to mechanical stresses caused by active material volume changes due to lithiation and delithiation. We have discovered that cyclic mechanical stresses cause significant degradation in the binder electrical conductivity. After just 160 mechanical cycles, the conductivity of polyvinylidene fluoride (PVDF):carbon black binder dropped between 45-75%. This degradation in binder conductivity has been shown to be quite general, occurring over a range of carbon black concentrations, with and without absorbed electrolyte solvent and for different polymer manufacturers. Mechanical cycling of lithium cobalt oxide (LiCoO2 ) cathodes caused a similar degradation, reducing the effective electrical conductivity by 30-40%. Mesoscale simulations on a reconstructed experimental cathode geometry predicted the binder conductivity degradation will have a proportional impact on cathode electrical conductivity, in qualitative agreement with the experimental measurements. Finally, ohmic resistance measurements were made on complete batteries. Direct comparisons between electrochemical cycling and mechanical cycling show consistent trends in the conductivity decline. This evidence supports a new mechanism for performance decline of rechargeable lithium-ion batteries during operation - electrochemically-induced mechanical stresses that degrade binder conductivity, increasing the internal resistance of the battery with cycling.
Lithium-ion battery particle-scale (non-porous electrode) simulations applied to resolved electrode geometries predict localized phenomena and can lead to better informed decisions on electrode design and manufacturing. This work develops and implements a fully-coupled finite volume methodology for the simulation of the electrochemical equations in a lithium-ion battery cell. The model implementation is used to investigate 3D battery electrode architectures that offer potential energy density and power density improvements over traditional layer-by-layer particle bed battery geometries. Advancement of micro-scale additive manufacturing techniques has made it possible to fabricate these 3D electrode microarchitectures. A variety of 3D battery electrode geometries are simulated and compared across various battery discharge rates and length scales in order to quantify performance trends and investigate geometrical factors that improve battery performance. The energy density and power density of the 3D battery microstructures are compared in several ways, including a uniform surface area to volume ratio comparison as well as a comparison requiring a minimum manufacturable feature size. Significant performance improvements over traditional particle bed electrode designs are observed, and electrode microarchitectures derived from minimal surfaces are shown to be superior. A reduced-order volume-averaged porous electrode theory formulation for these unique 3D batteries is also developed, allowing simulations on the full-battery scale. Electrode concentration gradients are modeled using the diffusion length method, and results for plate and cylinder electrode geometries are compared to particle-scale simulation results. Additionally, effective diffusion lengths that minimize error with respect to particle-scale results for gyroid and Schwarz P electrode microstructures are determined.
Li/FeS2 thermal batteries provide a stable, robust, and reliable power source capable of long-term electrical energy storage without performance degradation. These systems rely on the electrical conductivity of FeS2 cathodes for critical performance parameters such as power and lifetime, and on permeability of the electrolyte through the solid FeS2 particles for ion transfer. The effects of component composition, manufacturing conditions, and the mechanical deformation on conductivity and permeability have not been studied. We present simulation results from a finite element computer model compared with impedance spectroscopy electrical conductivity experiments. Our methods elucidate the combined effects of slumping, particle size distribution, composition, and pellet density on properties related to electrical conduction in Li/FeS2 thermal battery cathodes.
Temperature histories on the surface of a body that has been subjected to a rapid, highenergy surface deposition process can be di cult to determine, especially if it is impossible to directly observe the surface or attach a temperature sensor to it. In this report, we explore two methods for estimating the temperature history of the surface through the use of a sensor embedded within the body very near to the surface. First, the maximum sensor temperature is directly correlated with the peak surface temperature. However, it is observed that the sensor data is both delayed in time and greatly attenuated in magnitude, making this approach unfeasible. Secondly, we propose an algorithm that involves tting the solution to a one-dimensional instantaneous energy solution problem to both the sensor data and to the results of a one-dimensional CVFEM code. This algorithm is shown to be able to estimate the surface temperature 20 C.
Lithium-ion battery electrodes rely on a percolated network of solid particles and binder that must maintain a high electronic conductivity in order to function. Coupled mechanical and electrochemical simulations may be able to elucidate the mechanisms for capacity fade. We present a framework for coupled simulations of electrode mechanics that includes swelling, deformation, and stress generation driven by lithium intercalation. These simulations are performed at the mesoscale, which requires 3D reconstruction of the electrode microstructure from experimental imaging or particle size distributions. We present a novel approach for utilizing these complex reconstructions within a finite element code. A mechanical model that involves anisotropic swelling in response to lithium intercalation drives the deformation. Stresses arise from small-scale particle features and lithium concentration gradients. However, we demonstrate, for the first time, that the largest stresses arise from particle-to-particle contacts, making it important to accurately represent the electrode microstructure on the multi-particle scale. Including anisotropy in the swelling mechanics adds considerably more complexity to the stresses and can significantly enhance peak particle stresses. Shear forces arise at contacts due to the misorientation of the lattice structure. These simulations will be used to study mechanical degradation of the electrode structure through charge/discharge cycles.