## 3 Results and Discussion
### Focused Ion Beam/Scanning Electron Microscopy Tomography
The size of the extracted volume (Figure 8a and Figure S3) was 24.2 \(\times\) 14.7 \(\times\) 17.9 \(\upmu\)m (width \(\times\) height \(\times\) depth) with a voxel edge length of 37.2 nm in each direction. The statistical digital twin enabled a better in-depth understanding of the microstructure and the simulation or calculation of the electrochemical and mechanical electrode properties. Figure 8: FIB/SEM tomography of a positive electrode with a porosity \(<\) 20%. Transfer of the SEM image in (**b**) to a digital model in (**a**). (**c**) Shows the results for MIP of the experiment described in Section 3.4. and of the digital model plus the granulometry from the latter. In the model, the mercury intruded either from all sides (except from the bottom) or only from the top. The CBD was simulated on basis of the PSD from the MIP experiment (\(\epsilon=18\%\)) (see Figures 5 and 8c) and the ratio of the volumetric amount of AM to CBD in the electrode recipe (see Table 1). As the binder also covers the AM in the real composite electrodes, the volume of the CBD in the model could be overestimated. Other research groups adjusted the CBD structure to fit Li-ion or electronic conductivity measurements [36; 37; 53]. In the literature, the porosity of CBD varies from 47% (nanoporosity [53]) via 50% [36] to 58% [27]. The porosity of the digitally created CBD in this study was 50.2% with a minimal pore diameter of 37.2 nm, limited by the voxel length. When simulating CBD, the distribution in the electrode could be random, contact, or surface oriented [36], and the connections within the CBD in blocking, fully open, and partially open configurations for Li-ion diffusion [37]. In this study, the distribution of CBD was controlled by decreasing the surface energy and considering an open configuration for the channels within the CBD. Since simulating the CBD cannot be achieved by applying a singular correct model, the best model for the respective application has to be identified, fitting the measurements of the microstructure or the electrochemical experiments (herein MIP). To compare the porosity and PSD within the digital model with the previous results, GeoDict can perform a simulated MIP or granulometry experiment. The processes of the MIP were simulated as in the experiment with Hg intruding from all sides except the electrode bottom, close to the non-porous current collector, or only from the surface of the electrode considering larger electrode areas as in commercial applications [38; 39]. The simulated CBD determined the PSD (see Figure 8c) in the significant range from 19 to 1000 nm. Larger pores between AM secondary particles that were not filled with CBD had only a minor influence on the results of the MIP simulation in this pore size region. Thus, the relevance of the CBD and of the correct CBD simulation increase with lower electrode porosity (here 18%). Since a few larger pores were created by the simulation, differences in the results can be identified depending on how the PSD was determined. If Hg was only allowed to intrude from the sample surface, as in most of the experiments, the pore volume of larger pores (>1 \(\upmu\)m) was filled through smaller pore entries (<1 \(\upmu\)m) at the dense electrode surface as shown in Figure 5c. If Hg could intrude from all sides except from the current collector side or if granulometry was used, the larger pores were also depicted by modeling of the PSD. The MIP simulation and MIP experiment both had a D50 of the pores in the range of 200-260 nm. Using granulometry instead of MIP resulted in a shift of the PSD to higher values. This suggests that the pores had a smaller entrance than diameter or even a complete pore shielding effect occurred. In the MIP experiments, a conical model of the pores was used to calculate the PSD.