Ole Stenzel

3D Microstructure Effects in Ni-YSZ Anodes: Prediction of Effective Transport Properties and Optimization of Redox Stability

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 = εβ0.36/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.

Parametrization of Extended Gaussian Disorder Models from Microscopic Charge Transport Simulations.

Simulations of organic semiconducting devices using drift-diffusion equations are vital for the understanding of their functionality as well as for the optimization of their performance. Input parameters for these equations are usually determined from experiments and do not provide a direct link to the chemical structures and material morphology. Here we demonstrate how such a parametrization can be performed by using atomic-scale (microscopic) simulations. To do this, a stochastic network model, parametrized on atomistic simulations, is used to tabulate charge mobility in a wide density range. After accounting for finite-size effects at small charge densities, the data is fitted to the uncorrelated and correlated extended Gaussian disorder models. Surprisingly, the uncorrelated model reproduces the results of microscopic simulations better than the correlated one, compensating for spatial correlations present in a microscopic system by a large lattice constant. The proposed method retains the link to the material morphology and the underlying chemistry and can be used to formulate structure-property relationships or optimize devices prior to compound synthesis.

Nanoscale analysis of a hierarchical hybrid solar cell in 3D

A quantitative method for the characterization of nanoscale 3D morphology is applied to the investigation of a hybrid solar cell based on a novel hierarchical nanostructured photoanode. A cross section of the solar cell device is prepared by focused ion beam milling in a micropillar geometry, which allows a detailed 3D reconstruction of the titania photoanode by electron tomography. It is found that the hierarchical titania nanostructure facilitates polymer infiltration, thus favoring intermixing of the two semiconducting phases, essential for charge separation. The 3D nanoparticle network is analyzed with tools from stochastic geometry to extract information related to the charge transport in the hierarchical solar cell. In particular, the experimental dataset allows direct visualization of the percolation pathways that contribute to the photocurrent.

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.

Spatial modeling of the 3D morphology of hybrid polymer-ZnO solar cells, based on electron tomography data

A spatial stochastic model is developed which describes the 3D nanomorphology of composite materials, being blends of two different (organic and inorganic) solid phases. Such materials are used, for example, in photoactive layers of hybrid polymer zinc oxide solar cells. The model is based on ideas from stochastic geometry and spatial statistics. Its parameters are fitted to image data gained by electron tomography (ET), where adaptive thresholding and stochastic segmentation have been used to represent morphological features of the considered ET data by unions of overlapping spheres. Their midpoints are modeled by a stack of 2D point processes with a suitably chosen correlation structure, whereas a moving-average procedure is used to add the radii of spheres. The model is validated by comparing physically relevant characteristics of real and simulated data, like the efficiency of exciton quenching, which is important for the generation of charges and their transport toward the electrodes.

A General Framework for Consistent Estimation of Charge Transport Properties via Random Walks in Random Environments

A general framework is proposed for the study of the charge transport properties of materials via random walks in random environments (RWRE). The material of interest is modeled by a random environment, and the charge carrier is modeled by a random walker. The framework combines a model for the fast generation of random environments that realistically mimic materials morphology with an algorithm for efficient estimation of key properties of the resulting random walk. The model of the environment makes use of tools from spatial statistics and the theory of random geometric graphs. More precisely, the disordered medium is represented by a random spatial graph with directed edge weights, where the edge weights represent the transition rates of a Markov jump process (MJP) modeling the motion of the random walker. This MJP is a multiscale stochastic process. In the long term, it explores all vertices of the random graph model. In the short term, however, it becomes trapped in small subsets of the state space a...

Efficient simulation of charge transport in deep-trap media

This paper introduces a new approach to Monte Carlo estimation of the velocity of charge carriers drift-diffusing in a random medium. The random medium is modeled by a 1-dimensional lattice and the position of the charge carrier is modeled by a Markov jump process, whose state space is the set of lattice points. The transition rates of the Markov jump process are determined by the underlying energy landscape of the random medium. This energy landscape is modeled by a Gaussian process and contains regions of relatively low energy, in which charge carriers quickly become stuck. As a result, the state space is not adequately explored by the standard algorithms and the velocity of the charge carrier is poorly estimated. In addition, the conventional Monte Carlo estimators have very high variances. Our approach aims to reduce the number of simulation steps that are spent in the low energy problem regions. We do this by identifying the problem regions via a stochastic watershed algorithm. We then use a coarsened state space model, where the problem regions are treated as single states. In this way, we are able to simulate a semi-Markov process on the coarsened state space. This results in estimators that are unbiased and have considerably lower variance than the crude Monte Carlo alternatives.

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

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.