###### Abstract
There is a need for systematic examination of the preparation procedures and characterization of electrodes, e.g., [15; 16; 17; 18] and the behavior of (porous) materials as it is strongly related to their microstructure and defines their contribution in phenomena related to fluids (liquid or gaseous) transportation. The main characteristics of a material's microstructure are its porosity and tortuosity. In a review, [PERSON] et al. [19] conclude that every characterization method, independent of being old or new, has its own features, making it strong for a certain characterization. There are different methods and techniques for obtaining information about a material's microstructural characteristics, as described below:  
Methods that permit the measure of these characteristics in three-dimensional (3D) samples but without optical observation of the material itself, like mercury intrusion porosimetry. In such cases with no possibility for visual observation and description of the real pore system, theoretical models that are based on idealistic pore models like spherical or cylindrical pores to describe the microstructure. Using this technique, the total porosity, the total pore cumulative volume, the total specific surface area, the average pore radius, the bulk density, and the tortuosity can be determined. Methods for measuring microstructural characteristics using microscope images of materials with suitable cross sections and software. Microscopic methods provide a detailed picture of the microstructure of the specimen's surface to which they are limited [20]. In this case, the actual pore network is described but with specific limitations in the simulation of the third dimension of samples. X-rays can penetrate materials in varying depths depending on the number of protons in the nucleus, and the transmitted intensity I of monochromatic X-rays passing through an object can be calculated using [PERSON]'s law [21]. X-ray tomography is a very promising technique that can fill the gap between the two cases described before. It produces 3D images of the internal structure of the respective material with spatial resolution of less than 1 \(\upmu\)m, depending on the device used. The technique complements the higher resolution 2D microscopy, the lower resolution 3D ultrasonic imaging, and also FIB-SEM techniques where the observed volume is much less than in the Micro-Computed Tomography (\(\upmu\)-CT) [22]. [PERSON] et al. [23] estimated the tortuosity by applying the diffusion equation in the reconstructed 3D-pore space of electrodes obtained by FIB-SEM [24; 25]. The \(\upmu\)-CT technique maps a 3D picture and porosity data between different sample parts. Phases and features can be identified because they of their different absorption properties. The rotation of the sample makes it possible to reconstruct the features from 2D pictures. Afterward, using mathematical operations, we reconstruct the images to a 3D object, where each voxel (volume element or 3D-Pixel) represents the X-ray absorption at this point [2; 26]. The \(\upmu\)-CT method enables us to obtain detailed characterization of microstructure, permeability at micro-scale, phase volume fractions and their connectivity, spatial distributions, orientations, alignment, and connectivity of microstructural features as well as to quantify the relationship between microstructure and transport properties. Further, \(\upmu\)-CT enables the upscaling of permeability using simulations as proposed, e.g., by [PERSON] et al. [27]. In a study of [PERSON] et al. [28] it was shown that the X-ray computed micro-tomography, as modern, non-invasive method provides information about the pore space properties of different rocks. The main advantage between FIB-SEM analysis [29; 20] and \(\upmu\)-CT lies in the huge volume difference that is observed as FIB samples are typically 10 \(\times\) 10 \(\times\) 10 \(\upmu\)m\({}^{3}\) (for example, 8000 \(\upmu\)m\({}^{3}\) in [30]) as compared to volumes of up to several mm\({}^{3}\) with \(\upmu\)-CT [31].