The performance of all-solid-state battery (ASSB) cathodes strongly depends on their microstructure. Optimizing the cathode morphology can therefore enhance effective macroscopic properties such as ionic and electronic conductivity. The search for optimized microstructures can be facilitated by virtual materials testing, i.e., by integrating image analysis and stochastic microstructure modeling to generate a wide range of realistic 3D microstructures and evaluate their effective macroscopic properties by means of numerical simulations, thereby reducing the need for extensive physical experiments. This approach allows for the investigation of structure-property relationships through parametric regression models that incorporate relevant geometric descriptors of 3D microstructures such as volume fractions, mean geodesic tortuosities, specific surface areas, and constrictivities. By linking these geometric descriptors to effective macroscopic properties, virtual materials testing provides quantitative insight into how microstructure influences material performance. In this paper, this framework is applied to ASSB cathodes. In addition, by systematically varying model parameters, a broad range of 3D microstructures can be generated, which remain close to the original cathode morphology while inducing targeted changes in selected geometric descriptors. The resulting database enables the calibration of regression models whose predictive performance is assessed by comparing predicted and simulated effective properties such as the ionic and electronic conductivity, thereby quantifying how accurately combinations of geometric descriptors can explain and predict variations in effective macroscopic properties.

Precise control over nanoparticle synthesis in gas-phase processes such as flame and plasma reactors remains a significant challenge because of the complex, non-linear particle formation dynamics governed by coagulation and sintering. This paper presents a computational methodology that combines a Monte Carlo (MC) simulation framework and a convolutional neural network (CNN)-based surrogate model to accelerate predictions of bivariate particle descriptor vector distributions. The MC framework, optimized for computational efficiency, predicts the evolution of the particle surface area and volume distributions over time under isothermal conditions. This bivariate description enables accurate representation of particle morphology, which in turn influences formation dynamics and final product performance. Evaluation against established models demonstrates high agreement, emphasizing its precision in capturing particle formation dynamics. Indications and restrictions are identified for the achievement of a self-preserving size distribution (SPSD) for both aggregate volume and surface area, offering the potential to simplify and facilitate bivariate modeling approaches. The CNN-based surrogate model leverages bivariate histograms to predict time-dependent distributions for variable temperatures, achieving a 15 000-fold reduction in computation time compared to the MC framework and thus reaching real-time capability, while maintaining sufficient accuracy. In addition, the differentiable nature of the model enables the optimization of temperature profiles. This paper demonstrates the potential for integrating advanced MC frameworks with neural networks to balance computational efficiency and predictive accuracy.

A novel stereological framework to generate synthetic three-dimensional cellular material structures using Voronoi tessellations is presented. While conventional investigations of microstructural features rely on costly and often destructive three-dimensional imaging techniques, our method enables the reconstruction of 3D cellular structures from two-dimensional planar-sectional image data. By representing 3D cell architectures through Voronoi tessellations, we obtain an analytical representation requiring only three parameters per cell, ensuring efficient storage and computational processing. Our framework employs a differentiable approximation of Voronoi tessellations combined with a discriminator neural network in an adversarial learning context, enabling gradient-based optimization of tessellation parameters to generate random 3D cellular structures with statistically similar 2D planar sections as observed in measured 2D image data. We demonstrate the framework on image data of various cellular materials including metallic alloys, biological cells, and foam structures. The presented framework shows state-of-the-art capability of stereologically reconstructing 3D cellular microstructures, while introducing a low-parameter representation, preserving physical interpretability, and ensuring computational efficiency.

The microstructural degradation of Ni–CGO anodes in solid oxide fuel cells affects both electrochemical and mechanical properties. This study presents an automated workflow to quantify the evolution of geometrical descriptors and their influence on effective mechanical properties. Three-dimensional anode microstructures were aged up to 35,000 h using phase-field and stochastic modeling, followed by mechanical loading simulations. Aging caused microstructural coarsening as the mean pore diameter increased, while pore specific surface area and triple-phase boundary density decreased. Effective elastic moduli also decreased with aging. While the average von Mises stress remained nearly constant, the critical volume fraction increased with aging. Within the studied microstructures, the effective Hill modulus was strongly related to pore volume fraction and pore specific surface area. The critical volume fraction related positively with pore diameter and inversely with pore specific surface area and triple-phase boundary density.

Efficient recovery of critical raw materials such as lithium from metallurgical slags requires optimized liberation of target phases during comminution. To determine effective mechanical process parameters for target phase recovery, an in-depth understanding of the characteristics of slag particles is crucial. For this purpose, modern tomography techniques, such as computed tomography (CT), can provide high-resolution 3D images of micrometer-sized slag particles. However, analysis of such CT images poses challenges, such as insufficient grayscale contrast between mineral phases and partial-volume effects. This paper presents a scalable workflow for accurate phase- and particle-wise 3D characterization of particle systems by correlating 3D CT images with 2D mineral maps. For this purpose, high-resolution scanning electron microscopy (SEM) slices are registered in 3D CT images and used as ground truth to train 3D convolutional neural networks (CNNs) for the segmentation of individual particles and mineral phases. This approach addresses the principal challenges of obtaining CT-based mineralogical characterizations, allowing for the particle-wise 3D characterization of complex slag systems with minimum manual labeling effort. The trained CNNs are then applied to CT images of particle systems with different particle sizes (from 63 μm to 100 μm and from 100 μm to 250 μm) of a lithium-bearing slag with LiAlO2 as the target phase. Although virtual cross-sections of the predicted 3D segmentations show excellent agreement with mineral liberation obtained from 2D validation SEM-EDS data, the derived 3D mineral liberation statistics differ significantly from 2D estimates. In particular, our results show that the 2D analyses significantly overestimate mineral liberation compared to the 3D characterization. By addressing this stereological bias, the correlative 3D characterization workflow provides essential insights required to tailor pyrometallurgical and mechanical processing parameters to improve the recovery of raw materials.

This study addresses the challenge of real-time detection of the weeds Colchicum autumnale and Rumex species on grassland sites, which is an inherently difficult problem because the predominantly green weed leaves provide little contrast to the similarly colored vegetation backgrounds. The resulting detector will be integrated into the SELBEWAG tool, a non-chemical, site-specific weed treatment device. We collected and annotated RGB video recordings from grassland sites in Southwest Germany and trained a quantized EfficientDet object detection model, which has been optimized for low latency on edge devices. The detection system achieved a mean average precision of 0.606 across both weed types (0.617 for Rumex and 0.595 for C. autumnale). With an optimal decision threshold, the model demonstrated precision values of 56.0

Organic electrode-active materials offer a sustainable pathway toward sodium-based batteries, yet their application is hindered by electrolyte dissolution, limited conductivity, and synthetic challenges. Herein, we present an efficient nickel-free synthesis of poly(pyrene-4,5,9,10-tetraone) (PPTO), a high-capacity organic carbonyl-based polymer, via oxidative Pd-catalyzed homopolymerization of propylene glycol-protected PTO boronic esters. Among different conductive carbon-based electrodes, a PPTO@CNTs@Ketjen Black composite electrode achieves a reversible capacity of 286 mAh g-1 at 1 A g-1, 72% capacity retention over 500 cycles, and delivers 201 mAh g-1 even at 10 A g-1. An energy density of 549 Wh kg-1 (at low rates) and 346 Wh kg-1 (at high rates) is achieved based on active-material mass under half-cell conditions (275 Wh kg-1 based on total electrode mass). Ex situ spectroscopy, combined with theoretical calculations, reveals a two-electron redox process of each PTO unit with possible intermolecular interactions stabilizing the reduced state. Kinetic studies demonstrate rapid Na+ transport (D Na + approximate to 10-10 cm2 s-1) and capacitive-dominated storage. Tomographic 3D image data reconstruction highlights the favorable microstructure of the CNT/Ketjen Black composite in hindering PPTO dissolution. This work provides insights into the interplay between polymer chemistry, electrode architecture, and ion transport, offering design principles for organic electrode materials for sodium-based batteries.

Random geometric graphs defined on Euclidean subspaces, also called Gilbert graphs, are widely used to model spatially embedded networks across various domains. In such graphs, nodes are located at random in Euclidean space, and any two nodes are connected by an edge if they lie within a certain distance threshold. Accurately estimating rare-event probabilities related to key properties of these graphs, such as the number of edges and the size of the largest connected component, is important in the assessment of risk associated with catastrophic incidents, for example. However, this task is computationally challenging, especially for large networks. Importance sampling offers a viable solution by concentrating computational efforts on significant regions of the graph. This paper explores the application of an importance sampling method to estimate rare-event probabilities, highlighting its advantages in reducing variance and enhancing accuracy. Through asymptotic analysis and numerical studies, we demonstrate the effectiveness of our methodology, contributing to improved analysis of Gilbert graphs and showcasing the broader applicability of importance sampling in complex network analysis.

Abstract The 3D microstructure of solid oxide fuel cell anodes significantly influences their electrochemical performance, but conventional methods for acquiring high-resolution microstructural 3D data, such as focused ion beam scanning electron microscopy, are costly in both time and resources. In contrast, obtaining 2D images, such as from scanning electron microscopy (SEM), is more accessible, though typically providing insufficient information to accurately characterize the 3D microstructure. To address this challenge, we propose a novel approach that predicts the 3D microstructure from 2D SEM images. The presented method utilizes a low-parametric stochastic geometry model to generate virtual 3D microstructures and employs a physics-based SEM simulation tool to obtain the corresponding 2D SEM images. By systematically varying the model parameters, a large dataset can be generated to train convolutional neural networks. By doing so, we can statistically reconstruct the 3D microstructure from 2D SEM images by drawing realizations from the stochastic 3D model using the predicted model parameters. This workflow is quantitatively validated by an error analysis on geometrical descriptors, which shows that 3D microstructures can be predicted with reasonably high accuracy from 2D SEM images. Thus, this approach is a valuable computational tool that additionally circumvents the typically time-consuming segmentation of image data.

We present methods for the geometric characterization of hierarchical 3D microstructures of continuously carbon fiber reinforced composites made from stacked woven textile preforms, using X-ray CT and statistical image analysis. As the representative volume of these composites is rather large (in-plane side length > 20 mm) and, simultaneously, contains very small details (< 10 µm), we propose to divide the characterization procedure into three steps, considering (1) single rovings, (2) single weave layers, and (3) full laminates. In this paper, we focus on the geometry of single rovings and a single weave layer. Special emphasis is put on deviations from idealized shapes, including deformation of the commonly assumed elliptical cross section of single rovings, which results from the interaction between the undulating orthogonal rovings. We show that roving cross sections exhibit periodic changes in shape corresponding to their position in the weave structure. Using a mathematical modeling approach, we quantify the variability between rovings.

Peptide nanofibrils (PNFs) and peptide amphiphiles (PAs) are promising tools for enhancing viral transduction and gene transfer. However, quantitative insight into how their supramolecular architecture governs virion-cell interactions is limited. Here, we introduce a framework for the acquisition, processing, and statistical analysis of scanning transmission electron microscopy (STEM) tomograms to objectively quantify peptide-virion-cell interactions. Using four transduction-enhancing peptides (D4, Vectofusin-1, palmitic acid-PA (pal-PA), and eicosapentaenoic-PA (eic-PA)), peptide aggregate morphology, interfacial contact areas, and the spatial organization of virions with respect to peptides and cells were analyzed using advanced geometric descriptors. All peptides efficiently captured virions, resulting in few free virions, but they differ in how strictly virions were spatially confined near the cell surface. These differences reflect alternative spatial organization strategies, which are likely crucial factors influencing transduction-enhancing efficacy. Our approach provides a novel, generalizable method to evaluate infection-enhancing nanomaterials and guides the rational design of next-generation peptide assemblies for therapeutic viral delivery.

Agglomeration is an industrially relevant process for the production of bulk materials in which the product properties depend on the morphology of the agglomerates, e.g., on the distribution of size and shape descriptors. Thus, accurate characterization and control of agglomerate morphologies is essential to ensure high and consistent product quality. This paper presents a pipeline for image-based inline agglomerate characterization and prediction of their time-dependent multivariate morphology distributions within a spray fluidized bed process with transparent glass beads. The framework classifies observed objects in image data into three distinct morphological classes-primary particles, chain-like agglomerates and raspberry-like agglomerates-using various size and shape descriptors. Therefore, a fast and robust random forest classifier is trained. Additionally, the fraction of primary particles belonging to each of these classes, either as individual primary particles or as part of a larger structure in the form of chain-like or raspberry-like agglomerates, is described using parametric regression functions. Finally, the temporal evolution of bivariate size and shape descriptor distributions of these classes is modeled using low-parametric regression functions and Archimedean copulas. This approach improves the understanding of agglomerate formation and allows the prediction of process kinetics, facilitating precise control over class fractions and morphology distributions.

Macroscopic effective transport properties of battery materials are predominantly influenced by the morphology of their microstructure. In order to bridge the gap between these different length-scales, a stochastic 3D microstructure model is combined with physical simulations on the electrode scale. More precisely, the stochastic model is used to generate virtual, but realistic microstructures of cathodes in lithium-ion batteries. The model is calibrated to tomographic image data and validated with respect to various geometric descriptors and effective transport properties. By systematically varying the parameters of the model, a database of artificial microstructures is created with varying volume fractions and size distributions of active material particles. Furthermore, a resistor network method is used to quickly compute the effective conductivity and effective diffusivity of these microstructures on the electrode scale, where the microstructure is represented by a simplified graph structure. Subsequently, the available database is used to investigate quantitative structure-property relationships, which link geometric descriptors of the microstructure to effective transport properties of the electrode. Finally, the results are used to validate a previously established empirical formula that uses geometric descriptors of the microstructure to predict the effective conductivity.

Recycling aluminum chips remains a major challenge in aluminum manufacturing because it is difficult to retain the original quality alloy properties while reducing the carbon footprint and ensuring a sustainable process. This work investigates the microstructural evolution and bonding quality of compacted AA6082 chips processed through friction extrusion/consolidation. The residual material left inside the extrusion container after processing at a high extrusion ratio was analyzed using SEM, EDS, and EBSD to understand bonding mechanisms and microstructure evolution in front of the die. The SEM results show that voids are still present between the chips in the initial compacted material which already shows bonding, while these voids are reducing towards the die interface, particularly related to the present severe plastic deformation. EDS analysis confirms the presence of Al (Fe,Mn)Si intermetallic particles, which break and disperse in the matrix because of shear deformation due to die rotation. EBSD analysis reveals that grains are coarser near the base material, and subdivisions of grains near the die interface are significant because of continuous dynamic recrystallization.

Understanding the mechanical behavior of lunar regolith under low-g conditions is essential for processing regolith in the lunar environment. While well understood for many granular materials on Earth, these properties have yet to be studied for lunar regolith. For ground-based experimental investigation of regolith properties, simulants are used, which mimic certain physical or chemical aspects of lunar regolith. However, rheology is significantly influenced by particle size and shape, which has not yet been thoroughly characterized for lunar regolith particles. Moreover, it remains unclear how well common simulants approximate the morphology of lunar regolith particles. In this paper, we quantify the multivariate distributions of size and shape descriptors of actual lunar regolith particles and seven commonly used mare and highlands regolith simulants, using 3D tomographic image data obtained via micro computed tomography. Quantitative analysis confirms that there are large differences in morphology within regolith simulants and between simulants and lunar regolith. This highlights the need to develop regolith simulants with accurate morphologies for experimental investigations of mechanical properties. Alternatively, statistically representative digital models of lunar regolith can be used as input for numerical simulations, enabling simulation studies of morphology-driven mechanical behavior under lunar conditions.

Predicting the macroscopic properties of thin fiber-based porous materials from their microscopic morphology remains challenging because of the structural heterogeneity of these materials. In this study, computational fluid dynamics simulations were performed to compute volume air flow based on tomographic image data of uncompressed and compressed paper sheets. To reduce computational demands, a pore network model was employed, allowing volume air flow to be approximated with less computational effort. To improve prediction accuracy, geometric descriptors of the pore space, such as porosity, surface area, median pore radius, and geodesic tortuosity, were combined with predictions of the pore network model. This integrated approach significantly improves the predictive power of the pore network model and indicates which aspects of the pore space morphology are not accurately represented within the pore network model. In particular, we illustrate that a high correlation among descriptors does not necessarily imply redundancy in a combined prediction.

Solid-oxide fuel cells (SOFCs) are a promising energy conversion technology, offering a low environmental impact, low costs and high flexibility regarding the choice of the fuel. However, electrochemical performance of SOFCs decreases with time as a result of complex structural aging mechanisms of their anodes that are not yet fully understood. An option to quantitatively investigate this aging behavior could be tomographic imaging of the 3D microstructure of SOFC anodes for different aging durations, which is expensive and time-consuming. To overcome this issue, physics-based aging simulations resolving the 3D microstructural evolution can be exploited, which use tomographic image data of pristine SOFC anodes consisting of nickel, gadolinium-doped ceria (GDC) and pore space, as initial state. This microstructure simulation method is based on a grand-chemical potential multi-phase-field approach including surface diffusion. Computations conducted with the simulation framework are capable to predict the coarsening of the multiphase polycrystalline electrode. A promising approach to further accelerate the quantitative investigation of SOFC degradation is to combine physics-based aging simulation with data-driven stochastic 3D microstructure modeling, which is typically less computationally intensive compared to phase-field simulations. More precisely, an excursion set model based on Gaussian random fields is used to characterize the 3D microstructure of SOFC anodes by means of a small number of interpretable model parameters. Moreover, the evolution of the parameter vector of the calibrated stochastic 3D model over time is modeled by analytical functions that make fast predictive simulations possible. The prediction robustness is investigated by first assuming that the evolution of the 3D microstructure is known up to a certain point in time. Then, in a second step, the 3D microstructure of SOFC anodes is predicted for further future points in time and, through geometrical descriptors, compared with the results of physics-based aging simulation.

In order to link the properties of a feed stream to those of a product in separation operations such as cake filtration, a comprehensive database is required which often cannot be achieved through laboratory measurements alone. For this reason, a stochastic 3D model for the generation of virtual filter cake structures is developed and calibrated to tomographic image data of experimentally built filter cake structures. In this way, digital twins of real particles can be simulated and spatially arranged to form a three-dimensional artificial filter cake. Its 3D morphology is validated with respect to geometric descriptors that were not used for model fitting, such as tortuosity, constrictivity and specific surface area of pore space. In future work, using the model developed in the present paper, a large database of systematically varied artificial filter cakes will be generated by adjusting interpretable model parameters, allowing for structure-property relationships to be statistically investigated.

The agglomeration of small poorly wetted alumina particles in a stirred tank is investigated. For different experimental conditions, two bivariate probability densities for the area-equivalent diameter and aspect ratio of primary particles and agglomerates, respectively, are determined, using 2D image data from an inline camera system. Throughout each experiment, these densities do not change since the geometries of primary particles are unaffected by the experimental conditions, while large agglomerates fragment into multiple smaller ones, which results in an equilibrium state regarding the distribution of agglomerate descriptors. Mixtures of these densities are used to model the contents of the stirred tank at each time step of the experiments. Analytical functions, whose parameters characterize the agglomeration dynamics, are fitted to the time-dependent weights of these mixtures. This enables a quantitative comparison of agglomeration processes, highlighting the impact of mixing intensity on the joint distribution of agglomerate descriptors.

An approach for deploying stochastic three-dimensional (3D) models to generate microstructural 3D image data for training super-resolution networks is investigated for three different scaling factors alpha is an element of{2,4,8}. The presented approach addresses the issue of scarcity in training data by training the networks only on artificial image data, generated by means of a stochastic 3D model that produces digital twins of the nanoporous inner structure of active particles in battery cathodes. In addition, the performance of super-resolution networks is investigated when complementing the input data, i.e. low-resolved microstructural 3D image data, with spatially resolved transport simulations. The performance of the trained networks is evaluated based on real tomographic image data, and quantified with respect to various geometric descriptors and effective transport properties. It turned out that the integration of transport simulations into the training of super-resolution networks showed an increase in performance for the scaling factors alpha is an element of{2,4}, but a decrease in performance for alpha = 8. However, training the networks on artificial image data was effective in all cases.