Showing papers by "Volker Schmidt published in 2015"

Degradation of Li/S Battery Electrodes On 3D Current Collectors Studied Using X-ray Phase Contrast Tomography.

Abstract: Lithium/sulphur batteries are promising candidates for future energy storage systems, mainly due to their high potential capacity. However low sulphur utilization and capacity fading hinder practical realizations. In order to improve understanding of the system, we investigate Li/S electrode morphology changes for different ageing steps, using X-ray phase contrast tomography. Thereby we find a strong decrease of sulphur loading after the first cycle, and a constant loading of about 15% of the initial loading afterwards. While cycling, the mean sulphur particle diameters decrease in a qualitatively similar fashion as the discharge capacity fades. The particles spread, migrate into the current collector and accumulate in the upper part again. Simultaneously sulphur particles lose contact area with the conducting network but regain it after ten cycles because their decreasing size results in higher surface areas. Since the capacity still decreases, this regain could be associated with effects such as surface area passivation and increasing charge transfer resistance.

Controlling the dominant length scale of liquid-liquid phase separation in spin-coated organic semiconductor film

Abstract: Organic electronic devices are often made by solution processing a multi-component ink. During solution processing, for example, via spin coating, the solvent evaporates and the solid components deposit on the substrate. The morphology of this layer can range from well-mixed to extensively phase separated. To optimize device performance, it is essential to control the degree and dominant length scale of phase separation. Currently, the mechanism of phase separation induced by solvent evaporation is poorly understood. It has been shown that length scales are influenced by spin speed, drying time, final layer thickness and the ratio between the solid components, but a complete experimental dataset and consistent theoretical understanding are lacking. In this contribution, in situ measurements during spin coating and a simple numerical model are used to understand the drying process. In addition, an advanced image analysis of transmission electron micrographs of films processed under a wide range of processing conditions is carried out. A normalized drying rate is proposed as the key parameter that controls the dominant length scale of phase separation.

Spatiotemporal distribution of Holocene populations in North America

Abstract: As the Cordilleran and Laurentide Ice Sheets retreated, North America was colonized by human populations; however, the spatial patterns of subsequent population growth are unclear. Temporal frequency distributions of aggregated radiocarbon (14C) dates are used as a proxy of population size and can be used to track this expansion. The Canadian Archaeological Radiocarbon Database contains more than 35,000 14C dates and is used in this study to map the spatiotemporal demographic changes of Holocene populations in North America at a continental scale for the past 13,000 y. We use the kernel method, which converts the spatial distribution of 14C dates into estimates of population density at 500-y intervals. The resulting maps reveal temporally distinct, dynamic patterns associated with paleodemographic trends that correspond well to genetic, archaeological, and ethnohistoric evidence of human occupation. These results have implications for hypothesizing and testing migration routes into and across North America as well as the relative influence of North American populations on the evolution of the North American ecosystem.

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

Abstract: We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al–Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.

3D microstructure effects in Ni-YSZ anodes : prediction of effective transport properties and optimization of redox stability

Abstract: This study investigates the influence of microstructure on the effective ionic and electrical conductivities of Ni-YSZ (yttria-stabilized zirconia) anodes. Fine, medium, and coarse microstructures are exposed to redox cycling at 950 °C. FIB (focused ion beam)-tomography and image analysis are used to quantify the effective (connected) volume fraction (Φeff), constriction factor (β), and tortuosity (τ). The effective conductivity (σeff) is described as the product of intrinsic conductivity (σ0) and the so-called microstructure-factor (M): σeff = σ0*M. Two different methods are used to evaluate the M-factor: (1) by prediction using a recently established relationship, Mpred = eβ0.36/τ5.17, and (2) by numerical simulation that provides conductivity, from which the simulated M-factor can be deduced (Msim). Both methods give complementary and consistent information about the effective transport properties and the redox degradation mechanism. The initial microstructure has a strong influence on effective conductivities and their degradation. Finer anodes have higher initial conductivities but undergo more intensive Ni coarsening. Coarser anodes have a more stable Ni phase but exhibit lower YSZ stability due to lower sintering activity. Consequently, in order to improve redox stability, it is proposed to use mixtures of fine and coarse powders in different proportions for functional anode and current collector layers.

Quantitative comparison of segmentation algorithms for FIB-SEM images of porous media.

Abstract: Focused ion beam tomography has proven to be capable of imaging porous structures on a nano-scale. However, due to shine-through artefacts, common segmentation algorithms often lead to severe dislocation of individual structures in z-direction. Recently, a number of approaches have been developed, which take into account the specific nature of focused ion beam-scanning electron microscope images for porous media. In the present study, we analyse three of these approaches by comparing their performance based on simulated focused ion beam-scanning electron microscope images. Performance is measured by determining the amount of misclassified voxels as well as the fidelity of structural characteristics. Based on this analysis we conclude that each algorithm has certain strengths and weaknesses and we determine the scenarios for which each approach might be the best choice.

Fitting Laguerre tessellation approximations to tomographic image data

Abstract: The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data.

A New Method for Quantitative Marking of Deposited Lithium by Chemical Treatment on Graphite Anodes in Lithium-Ion Cells

Abstract: A novel approach for the marking of deposited lithium on graphite anodes from large automotive lithium-ion cells (≥6 Ah) is presented. Graphite anode samples were extracted from two different formats (cylindrical and pouch cells) of pristine and differently aged lithium-ion cells. The samples present a variety of anodes with various states of lithium deposition (also known as plating). A chemical modification was performed to metallic lithium deposited on the anode surface due to previous plating with isopropanol (IPA). After this procedure an oxygenated species was detected by scanning electron microscopy (SEM), which later was confirmed as Li2 CO3 by Fourier transform infrared spectroscopy (FTIR) and X-ray powder diffraction (XRPD). A valuation of the covered area by Li2 CO3 was carried out with an image analysis using energy-dispersive X-ray spectroscopy (EDX) and quantitative Rietveld refinement.

First Passage Percolation on Random Geometric Graphs and an Application to Shortest-Path Trees

Abstract: We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry In particular, we establish a strong linear growth property for shortest-path lengths on random geometric graphs which are generated by point processes We consider the event that the growth of shortest-path lengths between two (end) points of the path does not admit a linear upper bound Our linear growth property implies that the probability of this event tends to zero sub-exponentially fast if the direct (Euclidean) distance between the endpoints tends to infinity Besides, for a wide class of stationary and isotropic random geometric graphs, our linear growth property implies a shape theorem for the Euclidean first passage model defined by such random geometric graphs Finally, this shape theorem can be used to investigate a problem which is considered in structural analysis of fixed-access telecommunication networks, where we determine the limiting distribution of the length of the longest branch in the shortest-path tree extracted from a typical segment system if the intensity of network stations converges to 0

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

Abstract: 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.

A dedicated compression device for high resolution X-ray tomography of compressed gas diffusion layers

Abstract: We present an experimental approach to study the three-dimensional microstructure of gas diffusion layer (GDL) materials under realistic compression conditions. A dedicated compression device was designed that allows for synchrotron-tomographic investigation of circular samples under well-defined compression conditions. The tomographic data provide the experimental basis for stochastic modeling of nonwoven GDL materials. A plain compression tool is used to study the fiber courses in the material at different compression stages. Transport relevant geometrical parameters, such as porosity, pore size, and tortuosity distributions, are exemplarily evaluated for a GDL sample in the uncompressed state and for a compression of 30 vol.%. To mimic the geometry of the flow-field, we employed a compression punch with an integrated channel-rib-profile. It turned out that the GDL material is homogeneously compressed under the ribs, however, much less compressed underneath the channel. GDL fibers extend far into the channel volume where they might interfere with the convective gas transport and the removal of liquid water from the cell.

Numerical simulation and comparison of a real Al–Si alloy with virtually generated alloys

Abstract: Mechanical stress–strain curves are estimated by means of numerical simulation in order to analyze and compare the mechanical properties of a real strontium-modified Al–Si alloy with virtually designed materials. The virtual materials are generated by a competitive stochastic growth model of the 3D coral-like morphology of the eutectic Si in Al–Si alloys. The experimental data for the real material were acquired using FEB/SEM tomography. The numerical simulations are based on finite element methods. The effects of coarsening the mesh size and using different degrees of the finite elements are discussed. The simulations show that there is high conformity between the mechanical properties of the real and virtual materials. Experiments are also performed to show that the mechanical behavior of the realizations of the stochastic model is sensitive to changes in the parameters that control the morphological characteristics of the Si component.

A probabilistic approach to the prediction of area weather events, applied to precipitation

Abstract: In meteorology it is important to compute the probabilities of certain weather events occurring. There are a number of numerical and statistical methods for estimating the probability that a weather event occurs at a fixed location (a point). However, there are no widely applicable techniques for estimating the probability of such an event occurring in a geographical region (an area). In this paper, we propose a model-based approach for the computation of area probabilities using point probabilities. We develop this approach in the context of estimating the probability of the meteorological event ‘occurrence of precipitation’. We treat the point and area probabilities as coverage probabilities of a germ–grain model, where the grains can roughly be interpreted as precipitation cells. The germ–grain model is completely characterized by a sequence of local intensities and a grain size. We compute these model characteristics using available point probabilities. A non-negative least-squares approach is used to determine the local intensities and a semivariogram estimation technique is used to find the grain size. We are then able to determine area probabilities either analytically or by repeated simulation of the germ–grain model. We validate our model, using radar observations to assess the precision of the computed probabilities.

Joint distributions for total lengths of shortest-path trees in telecommunication networks

Abstract: Shortest-path trees play an important role in the field of optimising fixed-access telecommunication networks with respect to costs and capacities. Distributional properties of the corresponding two half-trees originating from the root of such a tree are of special interest for engineers. In the present paper, we derive parametric approximation formulas for the marginal density functions of the total lengths of both half-trees. Besides, a parametric copula is used in order to combine the marginal distributions of these functionals to a bivariate joint distribution as, naturally, the total lengths of the half-trees are not independent random variables. Asymptotic results for infinitely sparse and infinitely dense networks are discussed as well.

Asymptotic Properties of Collective-Rearrangement Algorithms

Abstract: We analyze asymptotic properties of collective-rearrangement algorithms being a class of dense packing algorithms. Traditionally, they transform finite systems of (possibly overlapping) particles into non-overlapping configurations by collective rearrangement of particles in finitely many steps. We consider the convergence of such algorithms for not necessarily finite input data, which means that the configuration of particles in any bounded sampling window remains unchanged after finitely many rearrangement steps. More precisely, we derive sufficient conditions implying the convergence of such algorithms when a stationary process of particles is used as input. We also provide numerical results and present an application in computational materials science.

Neue Dialektometrie mit Methoden der stochastischen Bildanalyse

Abstract: Vorrangiger Zweck ist die Entwicklung neuer Methoden zur quantitativen sowie qualitativen Auswertung großer Korpora areallinguistischer Daten. Zielpunkt ist die Bereitstellung der im Projekt entwickelten und erprobten Methoden in einem kompakten und anwenderfreundlichen Softwarepaket namens GeoLing, das es anderen Nutzern ermöglicht, mit ihren eigenen Daten entsprechende Analysen eigenständig durchzuführen. Die Software ist komplett in Java geschrieben und nicht nur plattformübergreifend lauffähig, sondern vom Benutzer bei Bedarf auch individuell anpassbar. Ein erster Ausgangspunkt für die Arbeiten im Projekt war die „klassische“ Dialektometrie (Séguy 1971, 1973; Goebl 1982, 1984), die bislang in der Hauptsache mittels Aggregation versucht, der Variationsvielfalt in Sprachatlanten Herr zu werden. Während diese aggregativen Vorgehensweisen (die weiterhin die Basis vieler quantitativer Zugänge zur Sprachgeographie sind, vgl. für einen Überblick etwa Heeringa 2004: 14–24; Nerbonne 2010; Nerbonne & Kretzschmar 2013) zweifelsohne die „dominanten“ (d.h. „möglichst hochrangige[n]“; Goebl 1986: 43) Strukturen der Variation gut abbilden können, werden schwächere oder weniger hochrangige Aspekte der Variation ausgeblendet. Einher geht damit oftmals auch eine starre Sicht auf „Areale“, die implizit als einheitliche Dialekträume konzeptualisiert werden, die sich scheinbar klar an Grenzen voneinander scheiden, statt fließend ineinander überzugehen. Darüber hinaus blieben (und bleiben bis heute) eventuell auftretende Mehrfachbelege an einem Ort in diesen Herangehensweisen unberücksichtigt. 2

Stochastic 3D Models for the Micro-structure of Advanced Functional Materials

Abstract: Optimization of functional materials is a challenging task. Thereby, stochastic morphology models can provide helpful methods. Three classes of stochastic models are presented describing different micro-structures of functional materials by means of methods from stochastic geometry, graph theory and time series analysis. The structures of these materials strongly differ from each other, where we consider organic solar cells being an anisotropic composite of two materials, nonwoven gas-diffusion layers in proton exchange membrane fuel cells consisting of a system of curved carbon fibers, and graphite electrodes in Li-ion batteries which are built up by an isotropic two-phase system (i.e., consisting of a pore and a solid phase). The goal is to give an overview how the stochastic modeling of functional materials can be organized and to provide an outlook how these models can be used for material optimization with respect to functionality.

The Effect of Electrode Morphology on Solid Oxide Fuel Cell Performance

Abstract: Three different electrode morphologies are generated from three different starting powders, spheres representing non aggregated powders, agglomerates of spheres and high aspect ratio cylinders modelling splats formed in plasma sprays. Electrodes from each morphology are analysed using finite volumes to predict the effective transport coefficients, the triple phase boundary length and the performance of the electrode. The same structures are also analysed using morphological characterization which can be much more efficient. It was found that high aspect ratio base particles are favourable, and that constrictivity correlates best with the finite volume transport calculations.

Stationary Apollonian Packings

Abstract: The notion of stationary Apollonian packings in the d-dimensional Euclidean space is introduced as a mathematical formalization of so-called random Apollonian packings and rotational random Apollonian packings, which constitute popular grain packing models in physics. Apart from dealing with issues of existence and uniqueness in the entire Euclidean space, asymptotic results are provided for the growth durations and it is shown that the packing is space-filling with probability 1, in the sense that the Lebesgue measure of its complement is zero. Finally, the phenomenon is studied that grains arrange in clusters and properties related to percolation are investigated.

Parametric Modeling of Sparse Random Trees Using 3D Copulas

Abstract: We provide a parametric modeling approach suitable for various kinds of hierarchical networks based on random geometric graphs. In these networks, we have two kinds of components, so-called high-level components (HLC) and low-level components (LLC). Each HLC is associated with a serving zone and all LLC within this area are connected to the corresponding HLC. So-called sparse LLC networks, where only a few LLC occur in the typical serving zone, are a non-negligible subdomain when investigating hierarchical networks. Therefore, we supply distributional results for structural characteristics where two LLC are independently and uniformly distributed along the segment system of the typical serving zone. In particular, we are interested in the joint distribution of three quantities, namely the length of the joint part of the shortest paths from the LLC to the HLC as well as the lengths of the corresponding disjoint remaining parts. In order to provide a parametric, three-dimensional distribution function for t...

Methods Based on Spatial Processes

Abstract: We present methods of cluster analysis to identify and classify patterns which are formed by stationary point processes and used e.g. in the modeling of human cartilage cells. In particular, we consider a generalization of the single-linkage approach which has been appropriately adapted to deal with inhomogeneous data and describe how the random-forest methodology can be applied to the classification of the previously identified clusters. Furthermore, we show how statistical techniques for spatial point processes can be used to validate the methods of cluster identification and cluster classification considered in this chapter.

Statistical Inference for Curved Fibrous Objects in 3D – Based on Multiple Short Observations of Multivariate Autoregressive Processes

Abstract: Summary This paper deals with statistical inference on the parameters of a stochastic model, describing curved fibrous objects in three dimensions, that is based on multivariate autoregressive processes. The model is fitted to experimental data consisting of a large number of short independently sampled trajectories of multivariate autoregressive processes. We discuss relevant statistical properties (e.g. asymptotic behaviour as the number of trajectories tends to infinity) of the maximum likelihood (ML) estimators for such processes. Numerical studies are also performed to analyse some of the more intractable properties of the ML estimators. Finally the whole methodology, i.e., the fibre model and its statistical inference, is applied to appropriately describe the tracking of fibres in real materials.

Estimating hitting probabilities of an interacting particle system on a graph

Abstract: We consider the problem of estimating hitting probabilities related to a class of interacting particle systems. These systems, in which two types of particles — ‘electrons’ and ‘holes’ — move on a graph, are simplified versions of models describing charge transport in disordered materials. The probability of interest is the probability that an electron reaches a certain region of the graph before colliding with a hole. We provide a detailed description of our model and explain how it can be simulated. Next, we give a brief introduction to importance sampling, which we use to improve the efficiency of our estimators. To our knowledge, importance sampling has not yet been used to estimate probabilities related to interacting particle systems. We describe how importance sampling can be used to improve the efficiency of estimators of hitting time probabilities involving discrete time Markov chains. We then use importance sampling to estimate the probability that we are interested in. In doing so, we observe that there are a number of complexities that arise when working with interacting particle systems. We describe some simple heuristics for implementing importance sampling. These heuristics make minimal changes to the probability measure under which the original system evolves. We consider a specific example of our problem and investigate the effectiveness of the importance sampling approach. We show that our estimators outperform standard Monte Carlo estimators. Finally, we describe possible future work, which includes a more sophisticated importance sampling approach that uses ‘locally optimal’ changes of measure.