Experimental XRD-CT and micro-CT data XRD-CT measurements of a commercial AAA Li-ion NMC532 Trustfire battery cell were performed at beamline station P07 of the DESY synchrotron using a 103.5 keV (λ = 0.11979 Å) monochromatic X-ray beam focused to have a spot size of 20 × 3 μm (H x V). 2D powder diffraction patterns were collected also using the Pilatus3 X CdTe 2 M hybrid photon counting area detector. The sample was mounted onto a goniometer which was placed on the rotation stage. The rotation stage was mounted perpendicularly to the hexapod; the hexapod was used to translate the sample across the beam. The XRD-CT scans were measured by performing a series of zigzag line scans in the z (vertical) direction using the hexapod and rotation steps. The XRD-CT scan was made with 550 translation steps (with a translation step size of 20 μm) covering 0-180 ° angular range, in 400 steps. The total acquisition time per point was 10 ms. XRD-CT measurements were also performed at beamline station ID15A of the ESRF 53 using a MnNaW/SiO2 catalyst 54 and a 92.8 keV monochromatic X-ray beam focused to a spot size of 25 μm × 25 μm. 2D powder diffraction patterns were collected using a Pilatus3 X CdTe 300 K (487 × 619 pixels, pixel size of 172 μm) hybrid photon counting area detector. The acquisition time per point was 50 ms. The tomographic measurements were made with 180 translation steps covering 0-180° angular range, in steps of 1.5° (i.e. 120 line scans). XRD-CT measurements were performed at beamline ID15A of the ESRF using a 3D printed SrNbO2N photocatalyst and a 100 keV monochromatic X-ray beam focused to have a spot size of ca. 40 × 20 μm (horizontal × vertical). 2D powder diffraction patterns were acquired using the Pilatus3 X CdTe 2 M hybrid photon counting area detector. The XRD-CT scans were measured by performing a series of zigzag line scans. An exposure time of 10 ms and an angular range of 0-180° with 300 projections in total were used for the XRD-CT dataset. A translation step size of 100 microns was applied; in total 330 translation steps were made per line scan. Finally, XRD-CT measurements were made at beamline station ID31 of the ESRF using a Ni-Pd/CeO2-ZrO2/Al2O3 catalyst and a 70 keV monochromatic X-ray beam focused to have a spot size of 20 × 20 μm. Here, the total acquisition time per point was 20 ms. Tomographic measurements were made with 225 translation steps (translation step size of 20 μm) covering 0-180° angular range, in steps of 1.125° (ie, 160 line scans). In each case, the detector calibration was performed using a CeO2 standard. Every 2D diffraction image was calibrated and azimuthally integrated to a 1D powder diffraction pattern with a 10 % trimmed mean filter using the pyFAI software package and the nDTomo software suite 55,56 . Sinograms of interest were extracted from the data volumes corresponding to the distribution of NMC532 and Cu battery cell components (AAA Li-ion NMC532), SrNbO2N (photocatalyst), NiO (Ni-Pd/CeO2-ZrO2/Al2O3 catalyst) and SiO2 cristobalite (MnNaW/SiO2 catalyst). Micro-CT measurements of the same commercial AAA Li-ion NMC532 Trustfire battery cell were performed at beamline station I12 of the Diamond Light Source using a 100 keV monochromatic X-ray beam. A PCO.edge X-ray imaging camera with 7.91 μm pixel size (beamline I12 module 2) was used for acquiring the radiographs during the CT scan. In total 1800 frames with an exposure time of 8 ms per frame during a 0-180° scan (angular step size of 0.1°). Each frame had a size of 2160 × 2560 pixels. Prior to the micro-CT scan, 50 dark current and flat field images were acquired which were used to normalise the radiographs prior to reconstruction. Two sinograms of interest were extracted from the data volume for the image reconstruction tests; each of these two sinograms was acquired after taking the mean of seven neighbouring sinograms (i.e. to increase the signalto-noise ratio in the sinograms).