## 2 Experimental
### GDE Testing during Operando XAS  
For operando XAS experiments, XAS data were collected using the electrochemical cell illustrated in Figure 1b. The setup is equipped with two parallel Zn-GDE cells, which can be used independently, hence reducing the time needed to switch from one measurement/experiment to another and better exploiting the available beamtime. The setup also includes a channel for the insertion of a reference electrode, which enables to monitor simultaneously the evolution of cathode and anode potentials of one of the two cells. The cell design optimized the XAS spectral quality for the GDE materials, while minimizing the absorption from the other battery (Zn electrode, current collector, electrolyte) and structural materials. Prior to the introduction of the electrolyte (6.0 M KOH) into the cell, a set of XAS measurements was performed on the electrode in the pristine state, scanning the beam over the whole optical window, in order to gain positive information regarding the homogeneity of X-ray absorption across the measured area. After wetting the electrode with the electrolyte, again, several spectra were acquired in the same positions mentioned above, in order to ensure that no signal distortion occurred. After these preliminary steps, XAS measurements were performed, starting with a pristine GDE, under a series of electrochemical conditions, representative of practical battery operation: oxygen reduction (ORR) and oxygen evolution reaction (OER). All operando XAS measurements were carried out in ambient air and by applying a cathodic (for ORR) and an anodic (for OER) current density of j = 5 mA\(\cdot\)cm\({}^{-2}\), unless otherwise specified. After each change in current density level or sign, the system was allowed to equilibrate for 10 min (to ensure that the system reached a steady-state potential) before starting the acquisition of XAS spectra.  
With a ring electron energy of 2.0 GeV and an average current of 310 mA of the Elettra synchrotron light source, yielding a photon flux of \(\sim\)10\({}^{10}\) photon\(\cdot\)s\({}^{-1}\) from the bending magnet feeding the XAFS beamline, X-ray absorption spectra (XAS) were recorded [7]. A double-crystal Si (111) monochromator was used to monochromatize the light. The beam size was 20 mm \(\times\) 1.5 mm (H \(\times\) V). The XAS data were recorded in transmission mode during electrochemical experiments. An ion chamber in front of the sample was filled with a proper mixture of gases according to the energy of the incidence X-rays, which was used to measure the intensity I\({}_{0}\) of the incident X-rays. After the sample, a second ionization chamber was employed to gather the transmitted intensity I\({}_{1}\). The absorption edge of a Mn foil, which was also measured at the same time, was used to calibrate the energy.  
Figure 1: (a) X-ray adsorption characteristics at the Mn K-edge energy of the fabricated GDE, together with a raw spectrum acquired operando during ORR. (b) Sketch of the operando XAS setup, with the GDE side facing the incoming X-ray beam. Upon transmission through the entire sample, consisting of the GDE, the 6 M KOH electrolyte, and the Zn electrode, part of the X-rays is absorbed by the different materials.  
All of the data were obtained at room temperature and at atmospheric pressure. The software Athena [8] was used to carry out data reduction, alignment, merging, deglitching, normalization, and background removal. ARTEMIS [9] was used to perform the EXAFS analysis. The scattering paths for all spectra were produced using the FEFF6 code [10], which used crystallographic data for cryptomelane K\({}_{1.33}\)Mn\({}_{8}\)O\({}_{16}\)[11].