Daniel Westhoff

Quantifying microstructural dynamics and electrochemical activity of graphite and silicon-graphite lithium ion battery anodes

Despite numerous studies presenting advances in tomographic imaging and analysis of lithium ion batteries, graphite-based anodes have received little attention. Weak X-ray attenuation of graphite and, as a result, poor contrast between graphite and the other carbon-based components in an electrode pore space renders data analysis challenging. Here we demonstrate operando tomography of weakly attenuating electrodes during electrochemical (de)lithiation. We use propagation-based phase contrast tomography to facilitate the differentiation between weakly attenuating materials and apply digital volume correlation to capture the dynamics of the electrodes during operation. After validating that we can quantify the local electrochemical activity and microstructural changes throughout graphite electrodes, we apply our technique to graphite-silicon composite electrodes. We show that microstructural changes that occur during (de)lithiation of a pure graphite electrode are of the same order of magnitude as spatial inhomogeneities within it, while strain in composite electrodes is locally pronounced and introduces significant microstructural changes.

Graph-based simulated annealing: a hybrid approach to stochastic modeling of complex microstructures

A stochastic model is proposed for the efficient simulation of complex three-dimensional microstructures consisting of two different phases. The model is based on a hybrid approach, where in a first step a graph model is developed using ideas from stochastic geometry. Subsequently, the microstructure model is built by applying simulated annealing to the graph model. As an example of application, the model is fitted to a tomographic image describing the microstructure of electrodes in Li-ion batteries. The goodness of model fit is validated by comparing morphological characteristics of experimental and simulated data.

Stochastic modeling and predictive simulations for the microstructure of organic semiconductor films processed with different spin coating velocities

A parametric stochastic model of the morphology of thin polymer:fullerene films is developed. This model uses a number of tools from stochastic geometry and spatial statistics. The fullerene-rich phase is represented by random closed sets and the polymer-rich phase is given by their complement. The model has three stages. First, a point pattern is used to model the locations of fullerene-rich domains. Second, domains are formed at these points. Third, the domains are rearranged to ensure a realistic configuration. The model is fitted to polymer:fullerene films produced using seven different spin coating velocities and validated using a variety of morphological characteristics. The model is then used to simulate morphologies corresponding to spin velocities for which no empirical data exists. The viability of this approach is demonstrated using cross-validation.

3D reconstruction of grains in polycrystalline materials using a tessellation model with curved grain boundaries

A compact and tractable representation of the grain structure of a material is an extremely valuable tool when carrying out an empirical analysis of the material’s microstructure. Tessellations have proven to be very good choices for such representations. Most widely used tessellation models have convex cells with planar boundaries. Recently, however, a new tessellation model — called the generalised balanced power diagram (GBPD) — has been developed that is very flexible and can incorporate features such as curved boundaries and non-convexity of cells. In order to use a GBPD to describe the grain structure observed in empirical image data, the parameters of the model must be chosen appropriately. This typically involves solving a difficult optimisation problem. In this paper, we describe a method for fitting GBPDs to tomographic image data. This method uses simulated annealing to solve a suitably chosen optimisation problem. We then apply this method to both artificial data and experimental 3D electron backscatter diffraction (3D EBSD) data obtained in order to study the properties of fine-grained materials with superplastic behaviour. The 3D EBSD data required new alignment and segmentation procedures, which we also briefly describe. Our numerical experiments demonstrate the effectiveness of the simulated annealing approach (compared to heuristic fitting methods) and show that GBPDs are able to describe the structures of polycrystalline materials very well.

Algorithmic structural segmentation of defective particle systems: a lithium-ion battery study: ALGORITHMIC STRUCTURAL SEGMENTATION OF DEFECTIVE PARTICLE SYSTEMS

We describe a segmentation algorithm that is able to identify defects (cracks, holes and breakages) in particle systems. This information is used to segment image data into individual particles, where each particle and its defects are identified accordingly. We apply the method to particle systems that appear in Li‐ion battery electrodes. First, the algorithm is validated using simulated data from a stochastic 3D microstructure model, where we have full information about defects. This allows us to quantify the accuracy of the segmentation result. Then we show that the algorithm can successfully be applied to tomographic image data from real battery anodes and cathodes, which are composed of particle systems with very different morpohological properties. Finally, we show how the results of the segmentation algorithm can be used for structural analysis.

Analysis, Modeling and Simulation of Tomographic Image Data for the 3D Microstructure of Electrode Material in Lithium-Ion Batteries

Abstract This article describes stochastic 3D structure models for electrodes of lithium-ion batteries, which can be used for model-based optimization of the electrode morphology. First, a single particle model is presented which can be used to parametrically describe individual particles from 3D tomographic image data. By fitting parametrical distributions it is therefore also possible to simulate (statistically similar) particles. Hereafter, different approaches for the arrangement of individual particles in the observation window are presented, so that system-based properties of different electrode types can be approximately matched (e. g. the connectivity of the particle system as well as the structure of the pore space). Finally, algorithms for the automatic recognition of particle cracks in tomographic image data are presented which can be used to integrate ageing effects into the models.

MULTIBAT: Unified workflow for fast electrochemical 3D simulations of lithium-ion cells combining virtual stochastic microstructures, electrochemical degradation models and model order reduction

We present a simulation workflow for efficient investigations of the interplay between 3D lithium-ion electrode microstructures and electrochemical performance, with emphasis on lithium plating. Our approach addresses several challenges. First, the 3D microstructures of porous electrodes are generated by a parametric stochastic model, in order to significantly reduce the necessity of tomographic imaging. Secondly, we integrate a consistent microscopic, 3D spatially-resolved physical model for the electrochemical behavior of the lithium-ion cells taking lithium plating and stripping into account. This highly non-linear mathematical model is solved numerically on the complex 3D microstructures to compute the transient cell behavior. Due to the complexity of the model and the considerable size of realistic microstructures even a single charging cycle of the battery requires several hours computing time. This renders large scale parameter studies extremely time consuming. Hence, we develop a mathematical model order reduction scheme. We demonstrate how these aspects are integrated into one unified workflow, which is a step towards computer aided engineering for the development of more efficient lithium-ion cells.

3D Microstructure Modeling and Simulation of Materials in Lithium-ion Battery Cells

The microstructure of lithium-ion battery electrodes has a major influence on the performance and durability of lithium-ion batteries. In this paper, an overview of a general framework for the simulation of battery electrode microstructures is presented. A multistep approach is used for the generation of such particle-based materials. First, a ‘host lattice’ for the coarse structure of the material and the placement of particles is generated. Then, several application-specific rules, which, e.g., influence connectivity are implemented. Finally, the particles are simulated using Gaussian random fields on the sphere. To show the broad applicability of this approach, three different applications of the general framework are discussed, which allow to model the microstructure of anodes of energy and power cells as well as of cathodes of energy cells. Finally, the validation of such models as well as applications together with electrochemical transport simulation are presented.