Towards Quantification of Local Electrochemical Parameters in Microstructures of Solid Oxide Fuel Cell Electrodes using High Performance Computations

X-ray nanotomography and focused ion beam scanning electron microscopy (FIB-SEM) provide unique opportunities interrogate the 3D microstructure of solid oxide fuel cell (SOFC) electrodes with unprecedented spatial resolution with elemental specificity. Using x-ray nanotomography with differential absorption imaging across the Mn K-absorption edge (6539 eV), and energy selected backscatter detection for FIB-SEM, these two techniques have been applied to obtain 3D elemental mapping of the LSM, YSZ and pore phases in the cathode microstructure. Measurements taken by non-destructive x-ray imaging and FIB-SEM serial sectioning include three-phase boundary areas (nominal and effective); phase volume fraction; and phase contiguity. The results presented demonstrate the viability of nanotomography as a characterization technique and provide key insights into the SOFC cathode microstructure. The effects of instrument resolution on microstructural characterization are addressed and the roles of FIB-SEM and x-ray nanotomography in future SOFC microstructural characterization efforts are discussed.

Integration of a scanning electron microscope (SEM) and focused ion beam (FIB) technology into a single FIB/SEM system permits use of the FIB as a nano-scalpel to reveal site-specific subsurface microstructures which can be examined in great detail by SEM. The FIB/SEM technology is widely used in the semiconductor industry and material sciences, and recently its use in the life sciences has been initiated. Samples for FIB/SEM investigation can be either embedded in a plastic matrix, the traditional means of preparation of transmission electron microscopy (TEM) specimens, or simply dried as in samples prepared for SEM imaging. Currently, FIB/SEM is used in the life sciences for (a) preparation by the lift-out technique of lamella for TEM analysis, (b) tomography of samples embedded in a matrix, and (c) in situ site-specific FIB milling and SEM imaging using a wide range of magnifications. Site-specific milling and imaging has attracted wide interest as a technique in structural research of single eukaryotic and prokaryotic cells, small animals, and different animal tissue, but it still remains to be explored more thoroughly. In the past, preparation of samples for site-specific milling and imaging by FIB/SEM has typically adopted the embedding techniques used for TEM samples, and which have been very well described in the literature. Sample preparation protocols for the use of dried samples in FIB/SEM have been less well investigated. The aim of this chapter is to encourage application of FIB/SEM on dried biological samples. A detailed description of conventional dried sample preparation and FIB/SEM investigation of dried biological samples is presented. The important steps are described and illustrated, and direct comparison between embedded and dried samples of same tissues is provided. The ability to discover links between gross morphology of the tissue or organ, surface characteristics of any selected region, and intracellular structural details on the nanometer scale is an appealing application of electron microscopy in the life sciences and merits further exploration.

Three-dimensional microstructure reconstruction is indispensable for understanding the performance and reliability of SOFC electrodes. Not only the microstructure parameters, but also SOFC electrochemical characteristics such as overpotentials can be calculated when combined with numerical simulations. The most common method to analyze 3-D structures with a feature size of 0.01 – 10 μm is a focused ion beam - scanning electron microscope (FIB-SEM). However, there’s a tradeoff between reconstruction volume size and resolution. Besides, in order to obtain high quality reconstruction, accumulation of know-hows for pre and post-processing is required. Therefore, fast screening of the microstructures is not easy for FIB-SEM due to the difficulty of measurement. On the other hand, a single SEM image can be obtained very easily. An arising question is if it is possible to extract properties of microstructures and numerically synthesize 3-D model directly from a single 2-D SEM image.In recent years, machine learning techniques have become a powerful tool for image processing. Nevertheless, applications of machine learning in the field of porous materials, in particular fuel cells and batteries are still limited. The previous works concentrated on relatively simple artificial neural networks (ANN), but the class of neural networks that can effectively analyze visual images is the convolutional neural network (CNN). Gayon-Lombardo et al. (1) demonstrated a successful application of generative adversarial network (GAN) based on CNN layers to fabricate synthetic 3-D SOFC microstructures. It is indicated that the GAN-based approach can be very effective, but the algorithm requires 3-D teaching data (GAN3Dto3D).In the scope of this research, a novel method for fabrication of synthetic 3-D microstructure directly from a 2-D SEM image is proposed (Fig. 1A). The GAN2Dto3D network consists of a 3-D microstructure generator and a discriminator which operate on 2-D data. Each microstructure fabricated by the generator is treated as a set of individual cross-sectional 2-D images. The discriminator checks the validity of each 2-D slice in the generated microstructure in all spatial directions (height, width and thickness). Patches extracted from a real 2-D cross-section image are used as training data. In each training iteration, new random patches are extracted to increase the number of available training data. Additionally, the training images are augmented by random horizontal and vertical flipping. As all of the cross-section of the newly generated microstructure has to be statistically equivalent to the real 2-D cross-section, the generated 3-D microstructure is smooth in all spatial directions.The GAN2Dto3D approach is tested on the dataset of real SOFC microstructures. For the real microstructure, a set of nickel (Ni) – gadolinium doped ceria (GDC) microstructures was fabricated. All composite anode samples were prepared with NiO (AGC Seimi, Japan) and GDC (Gd0.1Ce0.9O ShinEtsu, Japan) powders mixed in a designated proportion and sintered at 1350 oC. Differences in the structure are due to the initial anode slurry composition and packing density. The solid phase fractions were controlled by GDC share in the composite in the range of 30 – 70 vol.%, and their porosity was controlled by isostatic pressing (2). 3-D microstructures were reconstructed by FIB-SEM and used as the ground truth data for the validation of GAN2Dto3D model. The results of the GAN2Dto3D algorithm applied to generate two synthetic microstructures with different GDC share and the porosity are shown in Fig. 1B and 1C. The size of the generated microstructures is 64 × 64 × 64 voxels, which is equivalent to 6.4 × 6.4 × 6.4 µm. The real microstructures reconstructed with FIB-SEM are shown for comparison. The proposed GAN algorithm produces realistic microstructures, which indicates that GAN has a great potential to enable fast evaluation of various samples without carrying out complex FIB-SEM measurements.1. Gayon-Lombardo, L. Mosser, N. P. Brandon, and S. J. Cooper, npj Comput. Mater., 6, 1–11 (2020).2. Komatsu, A. Sciazko, and N. Shikazono, J. Power Sources, 485, 229317 (2021). Figure 1

The solid oxide fuel cell (SOFC) offers a great potential for stationary energy conversion applications because of its high combined heat and power efficiency. It is of great interest to understand performance relevant aspects of both material selection and manufacturing optimization. A design, which is made by co-sintering of inert substrate and functional layers, offers great possibilities for further methodological development. Findings can be transferred to different cell concepts. To understand and link fabrication parameters to the cell performance and identify aging mechanisms, sophisticated investigation of the 3D microstructure is necessary. This contribution will demonstrate how advanced correlative multiscale tomography can be used to identify microstructural parameters ranging from millimeter to nanometer scale. We combine optical microscopy (OM), X-ray computed tomography (μ-CT), focused ion beam – scanning electron microscopy (FIB-SEM) tomography and energy dispersive X-ray spectroscopy - scanning transmission electron microscopy (EDXS-STEM). The resulting microstructure data can be used to visualize performance critical cell areas such as inhomogeneities and secondary phases. In addition, pore and tortuosity distributions obtained from data of different length scales allow modeling of gas diffusion losses of all cell layers. This exemplifies how correlative tomography helps to understand specific contributions to overall cell performance. Figure 1

A new method to study representative volume element (RVE) size is developed based on three-dimensional (3D) fracture numerical network modelling and a stochastic mathematical model. A 3D fracture numerical network is established, and the network factors that affect RVE size, such as fracture density, diameter, strike, and dip angle, are collected. This paper utilizes these four factors to obtain the RVE size based on the contingency table method. It is concluded that the side length of the RVE is 2–8 times larger than the average trace length. Fracture frequency is chosen to validate the RVE size through 3D fracture numerical network modelling. RVE size calculated through fracture frequency is consistent with the contingency table method. It is proven that the method for calculating RVE size through the contingency table method is feasible and credible.

Solid oxide fuel cells (SOFCs) are receiving increasing attention because of their ability to convert the chemical energy of fuels into electrical energy in an efficient and clean manner. It is generally accepted that electrode microstructure plays an important role in determining the performance and durability of SOFC electrodes because it has a significant influence on various transport phenomena and electrochemical reactions within the electrodes. In order to satisfy the growing demand for their performance and reliability, it is strongly required to understand the microstructure-performance relationships, and to optimize the microstructure.Here we focus on electrodes fabricated with nano-particle infiltration technique, where ceramics structure constructs a framework structure called scaffold, to which nickel particles are introduced in the form of nano particles. 3D microstructural analysis using the focused ion beam scanning electron microscopy (FIB-SEM) (e.g. Figure) revealed that the infiltration technique has a greater potential, compared with the conventional powder mixing and sintering approach, to control the electrode microstructure, which is significantly useful to satisfy the requirements for the electrode microstructure, such as transport properties and electrochemical activities. Numerical simulations for the electrochemical and mechanical analyses are also conducted using the acquired 3D microstructures, delivering a guideline to optimize the electrode microstructure.Figure. 3D reconstructed microstructure of an SOFC anode prepared using infiltration technique. A ceria scaffold (grey), infiltrated nickel particles (green) and extracted triple-phase boundary lines (red).

A numerical investigation has been conducted to determine the influence of Representative Volume Element (RVE) size and degree of irregularity of polymer foam microstructure on its compressive mechanical properties, including stiffness, plateau stress and onset strain of densification. Periodic two-dimensional RVEs have been generated using a Voronoi-based numerical algorithm and compressed. Importantly, self-contact of the foam’s internal microstructure has been incorporated through the use of shell elements, allowing simulation of the foam well into the densification stage of compression; strains of up to 80% are applied. Results suggest that the stiffness of the foam RVE is relatively insensitive to RVE size but tends to soften as the degree of irregularity increases. Both the shape of the plateau stress and the onset strain of densification are sensitive to both the RVE size and degree of irregularity. Increasing the RVE size and decreasing the degree of irregularity both tend to result in a decrease of the gradient of the plateau region, while increasing the RVE size and degree of irregularity both tend to decrease the onset strain of densification. Finally, a method of predicting the onset strain of densification to an accuracy of about 10%, while reducing the computational cost by two orders of magnitude is suggested.

Composite electrodes comprising a rare-earth nickelate phase and a doped rare-earth ceria phase with a high level of rare-earth doping have been studied as oxygen electrodes. While rare-earth nickelates have shown great promise as oxygen electrodes in both solid oxide fuel cells (SOFC) and solid oxide electrolysis cells (SOECs), they become unstable in contact with rare-earth doped ceria. In this work we describe a strategy to eliminate this instability and enable the use of these electrodes as stable high performance oxygen electrodes in both SOFC and SOEC applications. The performance of such composite electrodes is explored using a symmetrical cell approach, and through the electrical conductivity relaxation (ECR) method and compare it to state-of-the-art oxygen electrodes comprising strontium doped lanthanum manganite (LSM) – yttria stabilized zirconia (YSZ) composite electrodes. The symmetrical cell tests which reveal the stabilized nickelate-ceria electrodes to be superior, are also well-correlated with the results of testing complete cells in both SOFC and SOEC modes. Based on these results we make the case for deploying these stabilized nickelate-ceria composite electrodes as oxygen electrodes in reversible SOFC-SOEC systems.

Three dimensional structures of the inner and outer pig petrous bone using FIB-SEM: Implications for development and ancient DNA preservation

Representative volume element (RVE) is a technique to determine and predict the mechanical and physical effective properties of any random homogeneous or heterogeneous composite material models. An optimal size of RVE model became a major objective in order to be statistically equivalent to the real composite material. In this paper, possible approaches to solving the RVE size problem is by developing a particles dispersion model in implementing microstructure of silver (Ag) micro-particle composite for electrical purpose. In this technique, a micro scale of scanning electronic microscope condition was observed for verification on Ag morphology in an epoxy matrix. The morphological analysis is used to guide the particles dispersion model that can be considered to repeat the whole macro-scale of the composite. In the RVE size study, the various composite model sizes were analyzed on the electrical conductivity for convergence study. The model size was determined by a ratio between width of RVE model and the particle size which given in ? = W/D. The numbers of RVE size (?) were set in a size of 3, 4, 5, 6, 7, 8 and 9. The efficiency of size that represents the precision of the estimation of the electrical purpose has been successfully determined by a particle dispersion model developed at model size of ? = 7. The predicted conductivity at model size of ? = 7 shows a good agreement with experimental data with the results presented at 5.06 × 10?1 and 2.69 × 10?1 S/cm for modeling and experiments, respectively.

Identification of RVE length scale in fiber composites via combined optical and SEM digital image correlation

An SOFC design based on co-sintering of functional layers on an inert substrate is investigated. Understanding the impact of cell fabrication parameters on cell performance as well as the identification of the key aging mechanisms are important issues. This contribution will demonstrate how advanced correlative multiscale tomography (such as X-ray computed tomography (μ-CT), focused ion beam – scanning electron microscopy (FIB-SEM) tomography and energy dispersive X-ray spectroscopy - scanning transmission electron microscopy (EDXS-STEM)) can be used to identify performance critical cell components and gas transport limitations. The resulting microstructure data can be linked to cell performance measured via electrochemical impedance spectroscopy (EIS). Impedance data from full cells are compared to cathode/anode measurements on symmetrical cell geometry to quantify the different contributions. This exemplifies how performance and microstructural data can help to understand specific contributions to overall cell performance and degradation.

Combined Focused Ion Beam – Scanning Electron Microscope and Synchrotron X-ray Fluorescence analysis of multi-solid and melt inclusions from the super-giant Grasberg Cu[sbnd]Au deposit, Indonesia

Solid Oxide Fuel Cells (SOFCs) are widely considered to be an ideal power source across a range of industries in the near future due to their high efficiency, high power density, and fuel flexibility. However, for widespread usage of SOFCs to be feasible, certain disadvantages, such as their high operating temperature, electrochemical losses, and high cost of manufacturing, must be solved. In particular, the field of materials research occupies a unique position of being able to quickly and simultaneously solve many of these issues through the development of material compositions and structures that do not currently exist in the industry. Especially relevant to solid oxide fuel cells in particular, is the impact that the electrodes’ geometries and compositions have on the operating performance. The electrodes’ ability to quickly move reactants to the interface of the electrolyte and remove products to the bulk flow comes into play as the fuel cell operates at higher current densities and concentration losses become prominent. Therefore, the microstructures present throughout the electrodes’ depth plays a vital role in improving overall cell performance. However, current fuel cell research has not yet effectively captured and defined the connections of the microstructure parameters and measured their impact on cell behavior. Additionally, homogeneous electrode design and implementation have dominated the research and commercial space thus far. The technique of functional material grading, which has begun to see wide research and commercial usage for such problems as acoustic impedance matching, thermal control, and mechanical design will be leveraged for the enhancement of SOFC electrodes. Functionally graded electrodes have been used in solid oxide fuel cell research in recent years in an effort to improve the cell performance by altering the microstructure including porosity, particle size, and composition of electronic and ionic conductors near the triple phase boundary region. Normally the functional grading process adds additional fabrication steps making it less desirable as an optimization process and easy manufacturing method. However, by using an additive manufacturing process it eliminates the need for multiple discrete graded layers to be deposited to obtain a graded electrode functional layer. This study seeks to explore the correlations of geometry and structure parameters from the meso-scale through to the micro-scale level, together with mass transfer, ionic and electronic transport, and gas-surface electrochemical reactions inside the electrodes to guide future additive manufacturing of SOFCs. Outlined is the development of an effective medium model for simulating the performance of fuel cell microstructures as a function of specific operating ranges in temperature, pressure, and in fuels used. Smooth and continuous linear and nonlinear functional gradation profiles of porosity and material composition are studied within the framework of an effective medium boundary value problem where the electrochemical relations, such as the Butler-Volmer equation, percolating conduction paths, and gas diffusion are solved using the finite difference method. The form of these relations for homogeneous electrodes was analyzed by Costamagna, et. al [1], who also defined outstanding problems with regards to optimizing SOFC electrodes [2]. Globally optimal linear and nonlinear gradation profiles and cell parameters are derived as a function of particle sizes, ratio of conductivities, and desired operating conditions and scored based on their reduction of cell overpotentials.[1] Costamagna, P., P. Costa, and V. Antonucci, Micro-modelling of solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(3-4), pp.375-394.[2] Costamagna, P., P. Costa, and E. Arato, Some more considerations on the optimization of cermet solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(8), pp.967-972. Figure 1

Study on size effect of jointed rock mass and influencing factors of the REV size based on the SRM method