## 3 Results
To localize sample regions with specific compositions we apply two different methods. In the first, we produce maps of ratios between the components that clearly highlight local inhomogeneities. In the second method, we produce phase maps, consisting of the scatter plot obtained by directly correlating these components pixel by pixel on a xy graph, and then mapping regions with comparable spectral features. With this second approach  
Figure 2: Normalized O-K spectra obtained from the average intensity of valid pixels in the field of view. Coated and noncoated samples of the same point of charge have been grouped to favor comparison. Vertical blue bars mark the position of the three components \(A\), \(B\), \(C\) considered in our analysis, while the “O\({}_{2}\)” labels denote the position of the main features of molecular oxygen according to [PERSON] et al. (2018). Note that the O\({}_{2}\)\(\pi^{\prime}\) feature overlaps with component C.  
absorption artifacts are more easily recognized. Core-shell distributions are clearly shown in these samples. A statistically more proper representation of component ratio is using the arctangent of the ratio, as explained in Appendix B. When plotting distributions of ratio values, skewed shapes are obtained in general, while the arctangent allows avoiding intrinsically asymmetric representations of distributions and better discrimination of compositional heterogeneities that are reflected in deviations from the normal Gaussian shape. Figure 4 shows the detail of \(C\) vs. \(B\) maps and corresponding histograms that allow analyzing the spectra heterogeneity on the sample. As \(B\) is the most intense and dominant component of the sample, we use it to normalize changes in \(C\) and remove thickness effects. The choice of a nearby component for normalization reduces the impact of small misalignments and possible sample contractions that may then produce artifacts. The spectral variations along the charge-discharge cycle are reflected by the shifts in the average value, which increases slightly from P01 to P03, corresponding to the sloping part of the profile, where the main process is the Ni oxidation, and more strongly with P04 and further at P05, where the anion redox is expected to contribute in overlap to the partial Mn reduction, and component \(C\) emerges. With discharge the component \(C\) withdraws partially, leading to the decreased ratio. The delay caused by the VOx coating indeed is also evident at P04, because \(C\) does not move before this stage. The peak width also increases considerably at  
Figure 3: Images obtained from the pristine Vanadium-coated sample. (**a**) absorbance map averaged in the O-K pre-edge energy range (526.3–527.2 eV); (**b**) absorbance map averaged in the O-K prepeak energy range (C peak region, 530.3–530.1 eV); (**c**) composite image with following channels: red (**a**), and yellow (difference **b**-**a**); (**d**) composite image from the V-L region (516.8–525.9 eV), green channel, and (**b**), yellow channel. The background from the pre-edge has been subtracted from both oxide and vanadium components. Insets in (**c**,**d**) show a detail at increased magnification. P04, particularly with the uncoated sample. This looks not related to the value of the ratio, because the distribution becomes sharper again at P05. Not only can we infer an increased composition heterogeneity in this sample. At a closer look, the uncoated P04 distribution also becomes quite asymmetric, with increased intensity on the side of lower \(C\)/\(B\) ratios. This seems related to a larger relative number of regions with lower O\({}_{2}\) content, in some regions of the bulk, and generally at particle edges, which could be seen as a possible confirmation of the escape of molecular oxygen from macroscopic cracks or damages in the particles. The smaller width for the corresponding coated sample corresponds to a more homogenous composition, which could be mainly attributed to the delayed delithiation of the active material.