Semi-analytical models describing transport phenomena governed by the Laplace equation (like conduction of charge carriers or heat) are presented for the case of a porous composite with two solid phases and one pore-phase (i.e., two conducting and one insulating phase), closing the existing gap in the literature for fast and accurate predictions for this particular case. The models allow for an efficient screening of promising concepts and material combinations, as they are computationally much more efficient compared to numerical simulations on a 3D geometry. Three different semi-analytical models (Maxwell, Xu and MST models) are compared and validated using a microstructure dataset of perovskite-CGO solid oxide cell electrodes obtained by stochastic modeling. Based on the results from both numerical and semi-analytical models, the effects of the resulting composite transport properties are discussed for the application example of these fully ceramic electrodes. CGO and the used LSTN perovskite are both mixed ionic and electronic conductors (MIECs), which leads to different reaction mechanisms and associated requirements for the microstructure design compared to, e.g., Ni-YSZ. Due to the MIEC-property of both solid phases, the transport of neither electrons nor oxygen ions is limited to a single phase. Consequently, the composite conductivity, which is inherent to MIEC electrodes, opens a much larger design space for microstructure optimization compared to the single-phase conductivity of conventional electrodes, which are prone to percolation failure. The effect of composite conductivity and its implications for microstructure design are studied for a porous composite. Three semi-analytical models are suggested to predict the effective composite conductivity in an efficient and accurate way.

To significantly improve on the unavoidable degradation of state-of-the-art Solid oxide fuel cell (SOFC) anodes like Ni-YSZ, we elaborate on fully ceramic composite electrodes, which are based on mixed ionic and electronic conductors (MIEC) like doped ceria and perovskite materials. Thereby, a Digital Materials Design (DMD) framework is used for the systematic and model-based optimization of MIEC SOFC-electrodes. In our DMD approach we combine experimental methods, stochastic microstructure modeling, virtual testing of 3D microstructures and a multiscale-multiphysics electrode model. The electrode model developed in this contribution captures all the relevant physico-chemical processes involved like the transport of charge carriers in the two MIEC solid phases, transport of the gas species in the pore-phase and the reaction kinetics. A special emphasize is laid to the appropriate description of the microstructure effects, applying the previously reported DMD-methodologies. This model-based performance prediction enables to explore a much larger design space than it would be possible with experimental methods only.

AbstractMany different definitions of tortuosity can be found in literature. In addition, also many different methodologies are nowadays available to measure or to calculate tortuosity. This leads to confusion and misunderstanding in scientific discussions of the topic. In this chapter, a thorough review of all relevant tortuosity types is presented. Thereby, the underlying concepts, definitions and associated theories are discussed in detail and for each tortuosity type separately. In total, more than 20 different tortuosity types are distinguished in this chapter. In order to avoid misinterpretation of scientific data and misunderstandings in scientific discussions, we introduce a new classification scheme for tortuosity, as well as a systematic nomenclature, which helps to address the inherent differences in a clear and efficient way. Basically, all relevant tortuosity types can be grouped into three main categories, which are (a) the indirect physics-based tortuosities, (b) the direct geometric tortuosities and (c) the mixed tortuosities. Significant differences among these tortuosity types are detected, when applying the different methods and concepts to the same material or microstructure. The present review of the involved tortuosity concepts shall serve as a basis for a better understanding of the inherent differences. The proposed classification and nomenclature shall contribute to more precise and unequivocal descriptions of tortuosity.

A standardized microstructure characterization tool for solid oxide cell (SOC) electrodes is presented, allowing for the automatic determination of a large number of microstructure characteristics relevant for the cell performance.

This open access book provides a thorough review of tortuosity in porous materials and discusses the impact of the microstructure on materials properties

A workflow for the stochastic microstructure modeling of solid oxide cell electrodes is presented. Based on a few real microstructures, the design space can be virtually explored, allowing for a subsequent optimization of microstructure properties.

AbstractIt is generally assumed that transport resistance in porous media, which can also be expressed as tortuosity, correlates somehow with the pore volume fraction. Hence, mathematical expressions such as the Bruggeman relation (i.e., τ2 = ε−1/2) are often used to describe tortuosity (τ)—porosity (ε) relationships in porous materials. In this chapter, the validity of such mathematical expressions is critically evaluated based on empirical data from literature. More than 2200 datapoints (i.e., τ – ε couples) are collected from 69 studies on porous media transport. When the empirical data is analysed separately for different material types (e.g., for battery electrodes, SOFC electrodes, sandstones, packed spheres etc.), the resulting τ versus ε—plots do not show clear trend lines, that could be expressed with a mathematical expression. Instead, the datapoints for different materials show strongly scattered distributions in rather ill-defined ‘characteristic’ fields. Overall, those characteristic fields are strongly overlapping, which means that the τ – ε characteristics of different materials cannot be separated clearly. When the empirical data is analysed for different tortuosity types, a much more consistent pattern becomes apparent. Hence, the observed τ − ε pattern indicates that the measured tortuosity values strongly depend on the involved type of tortuosity. A relative order of measured tortuosity values then becomes apparent. For example, the values observed for direct geometric and mixed tortuosities are concentrated in a relatively narrow band close to the Bruggeman trend line, with values that are typically < 2. In contrast, indirect tortuosities show higher values, and they scatter over a much larger range. Based on the analysis of empirical data, a detailed pattern with a very consistent relative order among the different tortuosity types can be established. The main conclusion from this chapter is thus that the tortuosity value that is measured for a specific material, is much more dependent on the type of tortuosity than it is dependent on the material and its microstructure. The empirical data also illustrates that tortuosity is not strictly bound to porosity. As the pore volume decreases, the more scattering of tortuosity values can be observed. Consequently, any mathematical expression that aims to provide a generalized description of τ − ε relationships in porous media must be questioned. A short section is thus provided with a discussion of the limitations of such mathematical expressions for τ − ε relationships. This discussion also includes a description of the rare and special cases, for which the use of such mathematical expressions can be justified.

Titanium and its alloys consitute one of the main classes of materials utilized as non-biodegradable implants in the human body. The corrosion resistance of titanium is mainly due to the presence of a thin, compact and passive layer on its surface. However, this layer degrades in the presence of reactive oxygen species, such as oxygen peroxide (H2O2) [1,2]. This leads to the device degradation and the release of its constituents in the surrounding tissues, which may bring about serious health issues (peri-implantitis, osteolysis, neurotoxicity...) [3]. H2O2 is produced by the immune system during inflammatory episodes by specific enzymes, such as NADPH oxidase and superoxide dismutase [4]. It is also utilized by surgeons at high concentrations (ca. 1 M) during peri-implant tissue disinfection. Ti6Al4V (titanium grade 5, an α + β alloy) is a popular implant material because of its excellent mechanical properties. However, in recent years, Ti6Al4V with equiaxed α grains (and β phase located at the grain boundaries) was reported to undergo a significant degradation by H2O2 characterized by the growth of a thick oxide layer on the α grains and the development of porosity and cracks in the β phase [1]. Ti6Al4V could be susceptible to stress corrosion cracking (SCC) under mechanical load due to the β phase dissolution in H2O2-containing physiological solutions (Figure 1). However, no clear link has been established yet between the corrosive environment, the mechanical load and the microstructure of the Ti6Al4V alloy. This contribution will report about the influence of H2O2 concentration on the in vitro corrosion of Ti6Al4V simulating inflammation conditions (low concentration) as well as disinfection procedures (high concentrations). Results on the electrochemical behavior (monitored by impedance spectroscopy), the degraded microstructure (obtained with focused ion beam scanning electron microscopy and transmission electron microscopy) and the impact of the H2O2-driven degradation on the mechanical properties of the alloy will be presented and discussed. Acknowledgements: The authors gratefully acknowledge the financial support of the French National Research Agency (grant agreement ANR-22-CE93-0007-02) and that of the Swiss National Science Foundation (grant agreement 200021L_213161). References: [1] Prestat et al., Microstructural aspects of Ti6Al4V degradation in H2O2-containing phosphate buffered saline , Corros. Sci. 190 (2021) 109640. [2] S. Hedberg et al., Mechanistic insight on the combined effect of albumin and hydrogen peroxide on surface oxide composition and extent of metal release from Ti6Al4V , J. Biomed. Mater. Res. - Part B Appl. Biomater. 107 (2019) 858. [3] T. Kim et al., General review of titanium toxicity , Int. J. Impl. Dent. 5 (2019) 10. [4] Prestat et al., Corrosion of titanium under simulated inflammation conditions: clinical context and in vitro investigations , Acta Biomater. 136 (2021) 72. Figure 1: Typical post-mortem SEM top-view micrograph of a Ti6Al4V surface with β phase dissolution (at the grain boundaries) after 30 minutes of exposure at 37 °C in phosphate buffer saline containing 1 M of H2O2. Figure 1

Abstract100 years ago, the concept of tortuosity was introduced by Kozeny in order to express the limiting influence of the microstructure on porous media flow. It was also recognized that transport is hindered by other microstructure features such as pore volume fraction, narrow bottlenecks, and viscous drag at the pore surface. The ground-breaking work of Kozeny and Carman makes it possible to predict the macroscopic flow properties (i.e., permeability) based on the knowledge of the relevant microstructure characteristics. However, Kozeny and Carman did not have access to tomography and 3D image analysis techniques, as it is the case nowadays. So, their descriptions were developed by considering simplified models of porous media such as parallel tubes and sphere packings. This simplified setting clearly limits the prediction power of the Carman-Kozeny equations, especially for materials with complex microstructures. Since the ground-breaking work of Kozeny and Carman many attempts were undertaken to improve the prediction power of quantitative expressions that describe the relationship between microstructure characteristics (i.e., tortuosity τ, constrictivity β, porosity ε, hydraulic radius rh) and effective transport properties (i.e., conductivity σeff, diffusivity Deff, permeability к,). Due to the ongoing progress in tomography, 3D image-processing, stochastic geometry and numerical simulation, new possibilities arise for better descriptions of the relevant microstructure characteristics, which also leads to mathematical expressions with higher prediction power. In this chapter, the 100-years evolution of quantitative expressions describing the micro–macro relationships in porous media is carefully reviewed,—first, for the case of conduction and diffusion,—and second, for flow and permeability.The following expressions are the once with the highest prediction power:$$\sigma_{eff} \left( {or D_{eff} } \right) = \varepsilon^{1.15} \beta^{0.37} /\tau_{{dir_{geodesic} }}^{4.39} ,$$ σ eff o r D eff = ε 1.15 β 0.37 / τ d i r geodesic 4.39 , for conduction and diffusion, and$$\kappa_{I} = 0.54\left( {\frac{\varepsilon }{{S_{V} }}} \right)^{2} \frac{{\varepsilon^{3.56} \beta^{0.78} }}{{\tau_{dir\_geodesic}^{1.67} }},$$ κ I = 0.54 ε S V 2 ε 3.56 β 0.78 τ d i r _ g e o d e s i c 1.67 , $$\kappa_{II} = \frac{{\left( {0.94r_{min} + 0.06r_{max} } \right)^{2} }}{8} \frac{{\varepsilon^{2.14} }}{{\tau_{dir\_geodesic}^{2.44} }},$$ κ II = 0.94 r min + 0.06 r max 2 8 ε 2.14 τ d i r _ g e o d e s i c 2.44 , both, for permeability in porous media.

AbstractIn this chapter, modern methodologies for characterization of tortuosity are thoroughly reviewed. Thereby, 3D microstructure data is considered as the most relevant basis for characterization of all three tortuosity categories, i.e., direct geometric, indirect physics-based and mixed tortuosities. The workflows for tortuosity characterization consists of the following methodological steps, which are discussed in great detail: (a) 3D imaging (X-ray tomography, FIB-SEM tomography and serial sectioning, Electron tomography and atom probe tomography), (b) qualitative image processing (3D reconstruction, filtering, segmentation) and (c) quantitative image processing (e.g., morphological analysis for determination of direct geometric tortuosity). (d) Numerical simulations are used for the estimation of effective transport properties and associated indirect physics-based tortuosities. Mixed tortuosities are determined by geometrical analysis of flow fields from numerical transport simulation. (e) Microstructure simulation by means of stochastic geometry or discrete element modeling enables the efficient creation of numerous virtual 3D microstructure models, which can be used for parametric studies of micro–macro relationships (e.g., in context with digital materials design or with digital rock physics). For each of these methodologies, the underlying principles as well as the current trends in technical evolution and associated applications are reviewed. In addition, a list with 75 software packages is presented, and the corresponding options for image processing, numerical simulation and stochastic modeling are discussed. Overall, the information provided in this chapter shall help the reader to find suitable methodologies and tools that are necessary for efficient and reliable characterization of specific tortuosity types.

Carbon steel samples covered with initially crack-free zinc-nickel coatings were polarized with a small anodic overpotential in moderately alkaline NaCl solution. Along with zinc dissolution, the coatings developed a mud-crack pattern due to tensile stress release, allowing the electrolyte to access the underlying steel surface. Simonkolleite grew on both the zinc-nickel coating and the steel substrate. The resulting current density, that was first strongly anodic, switched to small cathodic values when the coating surface was almost fully covered by a compact simonkolleite layer. (c) 2021 Elsevier B.V. All rights reserved.

Mixed ionic and electronic conducting (MIEC) materials recently gained much interest for use as anodes in solid oxide fuel cell (SOFC) applications. However, many processes in MIEC-based porous anodes are still poorly understood and the appropriate interpretation of corresponding electrochemical impedance spectroscopy (EIS) data is challenging. Therefore, a model which is capable to capture all relevant physico-chemical processes is a crucial prerequisite for systematic materials optimization. In this contribution we present a comprehensive model for MIEC-based anodes providing both the DC-behaviour and the EIS-spectra. The model enables one to distinguish between the impact of the chemical capacitance, the reaction resistance, the gas impedance and the charge transport resistance on the EIS-spectrum and therewith allows its appropriate interpretation for button cell conditions. Typical MIEC-features are studied with the model applied to gadolinium doped ceria (CGO) anodes with different microstructures. The results obtained for CGO anodes reveal the spatial distribution of the reaction zone and associated transport distances for the charge carriers and gas species. Moreover, parameter spaces for transport limited and surface reaction limited situations are depicted. By linking bulk material properties, microstructure effects and the cell design with the cell performance, we present a way towards a systematic materials optimization for MIEC-based anodes.

Ti6Al4V surfaces were exposed to simulated inflammation conditions in H2O2-containing phosphate buffered saline with and without FeCl3. Scanning electron microscopy analysis revealed significantly different degradation modes for the alpha and beta phases. While the a grains are covered by a ca. 400 nm thick protective nanostructured oxide layer, the attack of the beta phase generates a porous microstructure with microscaled cracks and a low polarization resistance. The beta phase is postulated to be sensitive to H2O2 reduction products and less able to generate a passive oxide film. The presence of FeCl3 enhances the cathodic activity and the beta phase degradation.

Effective conductivity and permeability of a versatile, graph-based model of random structures are investigated numerically. This model, originally introduced in Gaiselmann et al. (2014) allows one to simulate a wide class of realistic materials. In the present work, an extensive dataset of two-phase microstructures with wide-ranging morphological features is used to assess the relationship between microstructure and effective transport properties, which are computed using Fourier-based methods on digital images. Our main morphological descriptors are phase volume fractions, mean geodesic tortuosity, two "hydraulic radii" for characterizing the length scales of heterogeneities, and a "constrictivity" parameter that describes bottleneck effects. This additional parameter, usually not considered in homogenization theories, is an essential ingredient for predicting transport properties, as observed in Gaiselmann et al. (2014). We modify the formula originally developed in Stenzel et al. (2016) for predicting the effective conductivity and propose a formula for permeability. For the latter one, different geometrical definitions of the hydraulic radius are compared. Our predictions are validated using tomographic image data of fuel cells. (C) 2019 Elsevier Ltd. All rights reserved.

Contents: This dataset contains 3D image stacks acquired with FIB-tomography from Ni-YSZ cermet anodes for Solid Oxide Fuel Cells (SOFC). The data was collected from three different Ni-YSZ anodes (fine-, medium- and coarse-grained). Each of these anodes was investigated first in pristine state (after sintering and reduction) and then also in degraded state (after exposure to 8 redox cycles). The 6 tomographs are then presented as stacks of 2D-tiff-images in 2 different versions: as gray-scale images (raw data) and as segmented images (Ni=white, YSZ=gray and pores=black). In total this gives 12 image stacks. Further details, such as the voxel resolutions and image window sizes are listed in the downloadable excel file (2_3D_Data_Info.xlsx). Scientific Context: The microstructures of the cermet anodes were investigated for the purpose of optimizing the anode performance, which depends on effective transport properties (i.e. conductivity of ions in YSZ and of electrons in Ni, as well as diffusivity of fuel/gas in the pores). Furthermore the anode performance also depends on the catalytic/electrochemical activity (i.e. Ni-surface area and three phase boundary length TPBL). The microstructure characteristics have a strong influence on effective properties, electrochemical activity and associated anode performance. Furthermore, microstructure degradation (e.g. by Ni-coarsening) may lead to performance loss over time. Hence, the investigations focus on a fundamental, quentitative understanding of the relationships between microstructure characteristics and effective properties. The study reveals quantitative descriptions of all relevant microstructure characteristics (porosity, tortuosity, constrictivity, surface/interface areas, TPBL) and of the corresponding effective transport porperties (electric and ionic.conductivities). The corresponding anode performance was characterized by impedance spectroscopy. The quantitative results of the microstructure investigation were published in: Pecho et al 2015a (doi:10.3390/ma8095265), Pecho et al 2015b (doi:10.3390/ma8105370), Holzer et al 2013 (doi: 10.1016/j.jpowsour.2013.05.047), Holzer et al 2011a (doi: 10.1016/j.jpowsour.2010.08.017) and Holzer et al 2011b (doi: 10.1016/j.jpowsour.2010.08.006).

The degradation of sputtered columnar ZnO layers under DC polarization was studied by using electrochemical impedance spectroscopy and electron microscopy. It was found that the structure of the as-deposited ZnO film was dense at the nanoscale. An equivalent circuit model including de Levie impedance accounted for the localized propagation of microscale cracks towards the copper substrate. This generates a capacitance (C-ZnO) that represents the crack surface area in contact with the electrolyte. C-ZnO is small enough not to be obscured by the double layer capacitance at the top of the layers and increases with increasingly negative potential and time. These results were compared to nanoporous ZnO layers that behave differently and exhibit a large C-ZnO. The combination of in situ EIS analysis with the ex situ structural information provided by electron microscopy proved to be an efficient methodology to characterize very different microstructures of conductive coatings.

The perovskite-type mixed oxide La0.3Sr0.55Ti0.95Ni0.05O3-delta (LSTN) is demonstrated to exhibit the remarkable property of structural regeneration, where Ni can be reversibly exsoluted from the host perovskite lattice resulting in a regenerable Ni catalyst for solid oxide fuel cell anode applications. Results of catalytic tests for the water gas shift reaction and electrochemical investigations on a button sized fuel cell demonstrate the redox stability of LSTN, its potential application in solid oxide fuel cells, and its ability to recover catalytic activity completely after sulfur poisoning: Nickel segregation was characterized and quantified on powder samples by means of electron microscopy, X-ray diffraction, X-ray absorption spectroscopy, and temperature-programmed reduction-reoxidation cycles. Catalyst stability was much improved compared to impregnated Ni/La0.3Sr0.55TiO3-delta and Ni/Y0.08Zr0.92O2 anode materials. A full cell was tested under both open circuit voltage and polarized conditions, showing a stable cell voltage over redox cycles as well as periods of reverse potential and current overload. The area-specific resistance of the anode layer was as low as 0.58 Omega cm(2) at 850 degrees C. This allows LSTN to be applied in redox-stable solid oxide fuel cell anodes and reversible segregation of Ni to be exploited for fast recovery from sulfur poisoning.

Zinc oxide (ZnO) films with nano-granular structure were deposited by radio-frequency magnetron sputtering. The absence of preferred orientation was verified by XRD. HAADF-STEM images revealed a nanoporous structure with pore and grain sizes around 10 nm. The narrowness of the pores enabled to approximate that oxygen reduction takes place at the surface of the layers. During cathodic polarization, the surface of the electrodes became rougher due to the development of nodules on the surface. The ZnO electrodes exhibit a high activity towards oxygen reduction in KOH solution (pH=10). Rotating ring-disk electrode measurements coupled with reaction modelling allowed to quantitatively demonstrate that the direct reduction prevailed with the indirect pathway being active as well.