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Winterthur, Switzerland

Mangipudi K.R.,University of Gottingen | Radisch V.,University of Gottingen | Holzer L.,Institute of Computational Physics | Volkert C.A.,University of Gottingen
Ultramicroscopy | Year: 2016

We present an automated focused ion beam nanotomography method for nanoporous microstructures with open porosity, and apply it to reconstruct nanoporous gold (np-Au) structures with ligament sizes on the order of a few tens of nanometers. This method uses serial sectioning of a well-defined wedge-shaped geometry to determine the thickness of individual slices from the changes in the sample width in successive cross-sectional images. The pore space of a selected region of the np-Au is infiltrated with ion-beam-deposited Pt composite before serial sectioning. The cross-sectional images are binarized and stacked according to the individual slice thicknesses, and then processed using standard reconstruction methods. For the image conditions and sample geometry used here, we are able to determine the thickness of individual slices with an accuracy much smaller than a pixel. The accuracy of the new method based on actual slice thickness is assessed by comparing it with (i) a reconstruction using the same cross-sectional images but assuming a constant slice thickness, and (ii) a reconstruction using traditional FIB-tomography method employing constant slice thickness. The morphology and topology of the structures are characterized using ligament and pore size distributions, interface shape distribution functions, interface normal distributions, and genus. The results suggest that the morphology and topology of the final reconstructions are significantly influenced when a constant slice thickness is assumed. The study reveals grain-to-grain variations in the morphology and topology of np-Au. © 2016 Elsevier B.V.

Neumann M.,University of Ulm | Stanek J.,Charles University | Pecho O.M.,ETH Zurich | Pecho O.M.,Institute of Computational Physics | And 3 more authors.
Computational Materials Science | Year: 2016

A parametric stochastic 3D model for the description of complex three-phase microstructures is developed. Such materials occur for example in anodes of solid oxide fuel cells (SOFC) which consist of pores, nickel (Ni) and yttria-stabilized zirconia (YSZ). The model is constructed using tools from stochastic geometry. More precisely, we model the backbones of the three phases by a certain class of random geometric graphs called beta-skeletons. This allows us to reproduce complete connectivity of all three phases as observed in experimental image data of a pristine Ni-YSZ anode as well as the prediction of volume fractions by model parameters. Finally a slightly generalized version of this model enables a good fit to experimental image data with respect to transport relevant microstructure characteristics and the length of triple phase boundary. Model validation is performed by comparing effective transport properties from finite element (FE) simulations based on 3D-data from the stochastic model and from tomography of real Ni-YSZ anodes. Moreover, the virtual, but realistic Ni-YSZ microstructures can be used for investigating the quantitative influence of microstructure characteristics on various physical properties and consequently on the performance of the anode material. © 2016 Elsevier B.V. All rights reserved.

Gaiselmann G.,University of Ulm | Neumann M.,University of Ulm | Holzer L.,Institute of Computational Physics | Holzer L.,Empa - Swiss Federal Laboratories for Materials Science and Technology | And 4 more authors.
Computational Materials Science | Year: 2013

A stochastic microstructure model is developed in order to describe and simulate the 3D geometry of two-phase microstructures (solid and pore phase), where the solid phase consists of spherical particles being completely connected with each other. Such materials appear e.g. in La0.6Sr 0.4CoO3-δ (LSC) cathodes of solid oxide fuel cells, which are produced by screen printing and sintering of a paste consisting of LSC powder manufactured by flame spray synthesis. Thus, as a model type, we consider (fully parameterized) random sphere systems which are based on ideas from stochastic geometry and graph theory. In particular, the midpoints of spheres are modeled by random point processes. In order to assure the complete connectivity of the spheres, a modified version of the relative neighborhood graph is introduced. This graph controls the radii of spheres such that a completely connected sphere system is obtained. The model parameters are exemplarily fitted to three different materials for LSC cathodes, produced with sintering temperatures of 750, 850 and 950 °C, respectively. Finally, the goodness of fit is validated by comparing structural characteristics of real and simulated image data. © 2011 Elsevier B.V. All rights reserved.

Gaiselmann G.,University of Ulm | Neumann M.,University of Ulm | Schmidt V.,University of Ulm | Pecho O.,Institute of Computational Physics | And 3 more authors.
AIChE Journal | Year: 2014

The microstructure influence on conductive transport processes is described in terms of volume fraction ε, tortuosity τ, and constrictivity β. Virtual microstructures with different parameter constellations are produced using methods from stochastic geometry. Effective conductivities σeff are obtained from solving the diffusion equation in a finite element model. In this way, a large database is generated which is used to test expressions describing different micro-macro relationships such as Archie's law, tortuosity, and constrictivity equations. It turns out that the constrictivity equation has the highest accuracy indicating that all three parameters (ε,τ,β) are necessary to capture the microstructure influence correctly. The predictive capability of the constrictivity equation is improved by introducing modifications of it and using error-minimization, which leads to the following expression: σeff=σ02.03ε1.57β0.72/τ2 with intrinsic conductivity σ0. The equation is important for future studies in, for example, batteries, fuel cells, and for transport processes in porous materials. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1983-1999, 2014 © 2014 American Institute of Chemical Engineers.

Stenzel O.,Institute of Computational Physics | Pecho O.,Institute of Computational Physics | Holzer L.,Institute of Computational Physics | Neumann M.,University of Ulm | Schmidt V.,University of Ulm
AIChE Journal | Year: 2016

Empirical relationships between effective conductivities in porous and composite materials and their geometric characteristics such as volume fraction ε, tortuosity τ and constrictivity β are established. For this purpose, 43 virtually generated 3D microstructures with varying geometric characteristics are considered. Effective conductivities σeff are determined by numerical transport simulations. Using error-minimization the following relationships have been established: σeff=σ0ε1.15β0.37τgeod4.39 and σeff=σ0εβ0.36τgeod5.17 (simplified formula) with intrinsic conductivity σ0, geodesic tortuosity τgeod and relative prediction errors of 19% and 18%, respectively. We critically analyze the methodologies used to determine tortuosity and constrictivity. Comparing geometric tortuosity and geodesic tortuosity, our results indicate that geometric tortuosity has a tendency to overestimate the windedness of transport paths. Analyzing various definitions of constrictivity, we find that the established definition describes the effect of bottlenecks well. In summary, the established relationships are important for a purposeful optimization of materials with specific transport properties, such as porous electrodes in fuel cells and batteries. © 2016 American Institute of Chemical Engineers.

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