Volker Schmidt’s research while affiliated with Ulm University and other places

Solid oxide fuel cells (SOFCs) are becoming increasingly important due to their high electrical efficiency, the flexible choice of fuels and relatively low emissions of pollutants. However, the increasingly growing demands for electrochemical devices require further performance improvements. Since it is well known that the 3D morphology of the electrodes, which is significantly influenced by the underlying manufacturing process, has a profound impact on the resulting performance, a deeper understanding for the structural changes caused by modifications of the manufacturing process or degradation phenomena is desirable. In the present paper, we investigate the influence of the operating time and the operating temperature on the 3D morphology of SOFC anodes using 3D image data obtained by focused-ion beam scanning electron microscopy, which is segmented into gadolinium-doped ceria, nickel and pore space. In addition, structural differences caused by manufacturing the anode via infiltration or powder technology, respectively, are analyzed quantitatively by means of various geometrical descriptors such as specific surface area, length of triple phase boundary per unit volume, mean geodesic tortuosity, and constrictivity. The computation of these descriptors from 3D image data is carried out both globally as well as locally to quantify the heterogeneity of the anode structure.

The conductive additive and binder domain (CBD) is an essential component of lithium-ion battery electrodes. It enhances the electrical connectivity and mechanical stability within the solid electrode matrix. Migration of the binder during electrode drying can lead to an inhomogeneous distribution of the CBD, impeding transport of lithium ions into the electrodes, and diminishing the electronic pathways between solid particles and the current collector. This is especially prominent in thick electrodes at high drying rates. Therefore, we investigate the effect of a non-uniform CBD distribution on the electrochemical performance of NMC622 electrodes via microstructure-resolved three-dimensional (3D) simulations on virtual electrodes, based on tomographic image data, and compare them with experimental results. The valuable information derived by combining microstructure-resolved models with electrochemical impedance spectroscopy measurements on symmetric cells under blocking electrolyte conditions is used to characterize the lithium-ion transport in the electrode pore space, including the contributions of the CBD. The effect of this inhomogeneity on electrode performance is then gauged via galvanostatic discharge simulations under changing discharge currents and for varying electrode densities. Through our work, we demonstrate the significance of the CBD distribution and enable predictive simulations for future battery design.

Li-ion battery performance is strongly influenced by their cathodes' properties and consequently by the 3D microstructure of the particles the cathodes are comprised of. During calendaring and cycling, cracks develop within cathode particles, which may affect performance in multiple ways. On the one hand, cracks reduce internal connectivity such that electron transport within cathode particles is hindered. On the other hand, intra-particle cracks can increase the cathode reactive surface. Due to these contradictory effects, it is necessary to quantitatively investigate how battery cycling effects cracking and how cracking in-turn influences battery performance. Thus, it is necessary to characterize the 3D particle morphology with structural descriptors and quantitatively correlate them with effective battery properties. Typically, 3D structural characterization is performed using image data. However, informative 3D imaging techniques are time-consuming, costly and rarely available, such that analyses often have to rely on 2D image data. This paper presents a novel stereological approach for generating virtual 3D cathode particles that exhibit crack networks that are statistically equivalent to those observed in 2D sections of experimentally measured particles. Consequently, more easily available 2D image data suffices for deriving a full 3D characterization of cracked cathodes particles. In future research, the virtually generated 3D particles will be used as geometry input for spatially resolved electro-chemo-mechanical simulations, to enhance our understanding of structure-property relationships of cathodes in Li-ion batteries.

A stochastic 3D modeling approach for the nanoporous binder-conductive additive phase in hierarchically structured cathodes of lithium-ion batteries is presented. The binder-conductive additive phase of these electrodes consists of carbon black, polyvinylidene difluoride binder and graphite particles. For its stochastic 3D modeling, a three-step procedure based on methods from stochastic geometry is used. First, the graphite particles are described by a Boolean model with ellipsoidal grains. Second, the mixture of carbon black and binder is modeled by an excursion set of a Gaussian random field in the complement of the graphite particles. Third, large pore regions within the mixture of carbon black and binder are described by a Boolean model with spherical grains. The model parameters are calibrated to 3D image data of cathodes in lithium-ion batteries acquired by focused ion beam scanning electron microscopy. Subsequently, model validation is performed by comparing model realizations with measured image data in terms of various morphological descriptors that are not used for model fitting. Finally, we use the stochastic 3D model for predictive simulations, where we generate virtual, yet realistic, image data of nanoporous binder-conductive additives with varying amounts of graphite particles. Based on these virtual nanostructures, we can investigate structure-property relationships. In particular, we quantitatively study the influence of graphite particles on effective transport properties in the nanoporous binder-conductive additive phase, which have a crucial impact on electrochemical processes in the cathode and thus on the performance of battery cells.

A new cohesive phase-field (CPF) interface fracture model is proposed on the basis of the Euler-Lagrange equation of the phase-field theory and the interface fracture energy check w.r.t. that of the cohesive zone model. It employs an exponential function for the interpolation of fracture energy between the bulk phase and the interface, while the effective interface fracture energy $\tilde{G}_i$ is derived in such a way that the integrated phase-field fracture energy across the diffusive interface region remains consistent with the sharp interface fracture energy $G_i$ defined in the classical cohesive zone model. This consistency is the key to ensure that the numerical results remain insensitive to the choice of length-scale parameters, particularly the regularized interface thickness L and the regularized fracture surface thickness b. By employing this energy consistency check, various CPF interface models in the literature are reviewed. Besides the length-scale insensitivity, the proposed CPF interface model offers further advantages. Thanks to the fact that the exponential interpolation function can be obtained conveniently from the relaxation solution of an Allen-Cahn equation, the proposed CPF model is advantageous over other models with high flexibility in handling structures containing complicated interface topology. In order to demonstrate this merit and to check the length-scale insensitivity in multiphysics context, the proposed CPF interface model is employed further to derive a thermodynamically consistent chemo-mechanical model relevant to Lithium-ion battery materials. Finite element simulation results of the concurrent bulk and interface fracture in polycrystalline electrode particles, reconstructed from images with segmented interfaces, confirm the expected computational advantages and the length-scale insensitivity in chemo-mechanical context.

Understanding structure-property relationships of Li-ion battery cathodes is crucial for optimizing rate-performance and cycle-life resilience. However, correlating the morphology of cathode particles, such as in NMC811, and their inner grain architecture with electrode performance is challenging, particularly, due to the significant length-scale difference between grain and particle sizes. Experimentally, it is currently not feasible to image such a high number of particles with full granular detail to achieve representivity. A second challenge is that sufficiently high-resolution 3D imaging techniques remain expensive and are sparsely available at research institutions. To address these challenges, a stereological generative adversarial network (GAN)-based model fitting approach is presented that can generate representative 3D information from 2D data, enabling characterization of materials in 3D using cost-effective 2D data. Once calibrated, this multi-scale model is able to rapidly generate virtual cathode particles that are statistically similar to experimental data, and thus is suitable for virtual characterization and materials testing through numerical simulations. A large dataset of simulated particles with inner grain architecture has been made publicly available.

Froth flotation predominantly separates particles according to their differences in wettability. However, other particle properties such as size, shape or density significantly influence the separation outcome as well. Froth flotation is most efficient for particles within a size range of about 20-200 µm, but challenges arise for very fine or coarse particles that are accompanied by low recoveries and poor selectivity. While the impact of particle size on the separation behavior in flotation is well known by now, the effect of particle shape is less studied and varies based on the investigated zone (suspension or froth) and separation apparatus used. Beyond these complexities, many particle properties are correlated, making it challenging to analyze the isolated impact of individual properties on the separation behavior. Therefore, a multidimensional perspective on the separation process, considering multiple particle properties, enhances the understanding of their collective influence. In this paper, the two-dimensional case is studied; i.e., a parametric modeling approach is applied to determine bivariate Tromp functions from scanning electron microscopy-based image data of the feed and the separated fractions. With these functions it is possible to characterize the separation behavior of particle systems. Using a model system of ultrafine (<10 µm) particles, consisting of either glass spheres or glass fragments with different wettability states as the floatable fraction and magnetite as the non-floatable fraction, allows for the investigation of the influence of descriptor vectors consisting of size, shape and wettability, on the separation. In this way, the present paper contributes to a better understanding of the complex interplay between certain descriptor vectors for the case of ultrafine particles. Furthermore, it demonstrates the benefits of using multivariate Tromp functions for evaluating separation processes and points out the limitations of SEM-based image measurements by means of mineral liberation analysis (MLA) for the studied particle size fraction.

Many post‐processing methods improve forecasts at individual locations but remove their correlation structure. However, this information is essential for forecasting larger‐scale events, such as the total precipitation amount over areas like river catchments, which are relevant for weather warnings and flood predictions. We propose a method to reintroduce spatial correlation into a post‐processed forecast using an R‐vine copula fitted to historical observations. The method rearranges predictions at individual locations and ensures that they still exhibit the post‐processed marginal distributions. It works similarly to well‐known approaches, like the “Schaake shuffle” and “ensemble copula coupling.” However, compared to these methods, which rely on a ranking with no ties at each considered location in their source for spatial correlation, the copula serves as a measure of how well a given arrangement compares with the observed historical distribution. Therefore, no close relationship is required between the post‐processed marginal distributions and the spatial correlation source. This is advantageous for post‐processed seamless forecasts in two ways. First, meteorological parameters such as the precipitation amount, whose distribution has an atom at zero, have rankings with ties. Second, seamless forecasts represent an optimal combination of their input forecasts and may spatially shifted from them at scales larger than the areas considered herein, leading to non‐reasonable spatial correlation sources for the well‐known methods. Our results indicate that the calibration of the combination model carries over to the output of the proposed model, that is, the evaluation of area predictions shows a similar improvement in forecast quality as the predictions for individual locations. Additionally, the spatial correlation of the forecast is evaluated with the help of object‐based metrics, for which the proposed model also shows an improvement compared to both input forecasts.