Figure 3. The heterogeneous fracturing pattern in the NMC electrode that has gone through fast cycles at a rate of 5C. Panels (a) and (c) are the same lateral slice over the particle layer that is close to the 10-cycles electrode surface (furthest from the aluminum current collector). Panels (b) and (d) are the same lateral slices over the first layer of particles close to the aluminum current collector (10-cycles electrode). The relative ratios over these two slices is shown in the corresponding pie charts. Panels (e) and (f) are the surface sensitive soft x-ray spectroscopic results over the front (red) and the back (blue) of the 10-cycles electrode in TEY and TFY modes, respectively. The comparison of the fracturing profiles of the 10-cycles (panels (g), (i), and (k)) and 50-cycles (panels (h), (j), and (l)) electrodes. Panels (g) and (h) are the depth dependence of the fracturing profile. Panels (i) and (j) are the 3D representation of the severely fractured network, with their top views shown in panels (k) and (l), respectively.
The single-voxel-thick slices shown in Figures 3a-3d cut through the particles at different depth due to the random arrangement of the particles in the electrode. For a more precise quantification of the cracking profile, here we develop a more advanced approach. As a first step, we apply mild median filtering to the 3D image for improve the signal to noise ratio before conducting the particle edge detection (Supplementary Figure S2) based on Canny edge detection algorithm\cite{Canny_1986} using the FeatureJ plugin\cite{edges} in ImageJ\cite{Rueden_2017} software. The image filtering trades the image resolution, which is less important for the purpose of automatic particle detection and segmentation, for the reduction of the noise. The detected particle boundary is then used to automatically isolate individual particles from the 3D representation of the whole electrode. We then sum the 3D volume in any given 10-microns-thick depth window in the Z direction. The projected image (Supplementary Figure S2) is then used for identification and labeling of particles based on their degree of fracturing (Supplementary Figure S3). This procedure is repeated for the data sub-volume in different Z windows. The cracking patterns’ depth profiles of a 10-cycles and a 50-cycles electrode are summarized in Supplementary Tables S1 and S2, with the plots shown in Figures 3g and 3h, respectively. The 10-cycles electrode demonstrates a clear depth dependence in its fracturing profile, in a good agreement with the soft XAS data shown in Figures 3e and 3f. The 50-cycles electrode, on the other hand, shows more severe morphological damage and, thus, breaks down the depth dependence. Generally speaking, the degree of particle fracturing is positively correlated with the degree of active material utilization. Our data in Figure 3g and 4h suggests that the electrode’s active materials at different depth contributes to the cell level chemistry differently in both time and location. In the early cycles, particles near the separator accounts for more of the charge compensation, possibly, due to their favorable lithium diffusion rates. The higher degree of reaction near the separator causes severe local degradation, which could partially deactivate the particles in this region by detaching the particles from the conductive carbon network (see Supplementary Figure S4). Similar effect is also observed in conversion type of Si anode electrode\cite{M_ller_2018}. Subsequently, the particles that are located deeper in the electrode take over the electrochemical activities in the later cycles, making the depth dependent fracturing profile less apparent as suggested by Figure 3h. 
In addition to the depth dependent fracturing profile, which is a 1D representation of the inhomogeneous degree of active material utilization at the electrode level, our imaging data could also offer valuable insights into the lateral and, more importantly, the 3D complexity. With the extraction of the 3D centroid coordinates of all the severely damaged particles, here we develop a method to extract the network that connects all these particles based on their spatial distribution. For every severely damaged particle, our method searches for three of its nearest particles of the same kind and uses color coded bounds to connect them (see Figures 3i to 3l and the relative color map in the inset of Figure 3k). As the degree of particle cracking is positively correlated to the degree of active particle usage, we conjecture that the extracted network represents the 3D distribution of the local current density. The perspective and the top views of the networks for 10-cycles and 50-cycles electrodes are shown in Figures 3i, 3j and 3k, 3l, respectively. After the first 10 cycles, the heavily used particles are sparsely scattered throughout the 3D volume of the electrode. This is likely due to their favorable and balanced electric and ionic conductivity. After 50 cycles, this network becomes denser because the activation of more particles upon prolonged battery operation. The particle to particle distance clearly becomes smaller as it can be seen in the topological representations in Figures 3j and 3l.