2.1.1. Set-Up

The alkaline-manganese battery consists of a steel shell into which the hollow cylinder of the cathode material—consisting of manganese dioxide and an electrolyte—was inserted by the manufacturer. The anode was made of a mixture of zinc powder and an electrolyte, and it was injected into the shell. Between the anode and the cathode, a separator is located. A metallic nail at the bottom of the battery acts as the negative pole of the battery. It protrudes into the anode and acts as a charge collector. Between the bottom and the cathode, a seal prevents leakage of the cell.

#### 2.1.2. Chemical Processes in an Alkaline-Manganese Battery

During the initial discharge, a reduction reaction takes place at the cathode; see Equations (1) and (2) [1]:

$$\rm{MnO\_2 + H\_2O + \varepsilon^- \to MnCOH + OH^-},\tag{1}$$

$$\text{C}3\text{MnOOH}\_2 + e^- \rightarrow \text{Mn}\_3\text{O}\_4 + \text{OH}^- + \text{H}\_2\text{O} \tag{2}$$

Due to the formation of MnOOH, the cathode expands in volume by about 17%. At the anode, as given in Equation (3), zinc initially forms zincate. After the electrolyte is supersaturated with zincate, the reaction product changes to zinc hydroxide, see Equation (4), which is then slowly dehydrated to zinc oxide, see Equation (5):

$$\text{Zn} + 4\text{OH}^- \rightarrow \left[\text{Zn(OH)}\_4\right]^{2-} + 2e^- \tag{3}$$

$$\text{Zn} + 2\text{OH}^- \rightarrow \text{Zn(OH)}\_2 + 2e^- \tag{4}$$

$$\text{Zn(OH)}\_{2} \rightarrow \text{ZnO} + \text{H}\_{2}\text{O} \tag{5}$$

The overall discharge redox reaction is shown in Equation (6) [1]:

$$2\text{MnO}\_2 + \text{Zn} + 2\text{H}\_2\text{O} \rightarrow 2\text{MnOOH} + \text{Zn}(\text{OH})\_2\tag{6}$$

For a small to medium discharge, the reaction in Equation (7) predominantly takes place in alkaline-manganese batteries [8]:

$$2\text{MnO}\_2 + 2\text{Zn} \rightarrow 2\text{Mn}\_3\text{O}\_4 + 2\text{ZnO} + \text{Zn}(\text{OH})\_2\tag{7}$$

#### 2.1.3. Setup for Charge and Discharge of Alkaline-Manganese Batteries

The batteries were discharged with a VOLTCRAFT Multicharger VC 1506 that was connected to a computer. The batteries were charged using the charger type ACP62 PowerSet AA. For measuring the behavior of the charger, an oscilloscope was connected in parallel to a battery. To avoid damage, the conventional primary cells were charged in a pulsed mode and not to above 1.72 V. RAM were discharged to 0.9 V at currents of 100 mA, 200 mA, and 400 mA. The primary cell was discharged at 200 mA current.

#### 2.1.4. X-ray Tomography System and Measurement Procedure

The setup consisted of a fixed Hamamatsu microfocus X-ray tube (L8121-3) with a stable spot size of 7 μm and a Hamamatsu flat panel detector (C7942SK-05). The X-ray tube had an operational voltage range of 40 kV to 150 kV, and the target spot had a diameter of 7 μm [39]. The detector comprised a gadolinium oxysulfide (Gadox)-based scintillator on a 2316 × 2316 pixel detector array with a pixel size of 50 μm. On a goniometer, a sample can be mounted and moved with 5 degrees of freedom.

To avoid image analysis on large zinc-free spaces, cells with a homogenous zinc distribution inside the field of view were preferred. For that, multiple RAM and multiple primary cells were radiographed. Batteries were discarded if air inclusions were visible. Eventually, one primary cell and three RAM were selected. Before and after the first, second, third, fifth, 10th and if possible, 15th, charging step a tomogram was recorded.

For tomography, a source–object distance of 58 mm, and a source–detector distance of 350 mm were selected, which resulted in an effective pixel size of 8.3 μm, and thus a special resolution of 16.6 μm. The magnification chosen in this way was the largest that projected the entire image onto the detector, and not just a part of it. To achieve maximum contrast and the best signal-to-noise ratio, the X-ray tube was operated at 130 kV and 76 μA with a 0.5 mm copper filter. Furthermore, an exposure time of 1.6 s for each of the in total 1500 projections over 360◦ was applied, resulting in a total scanning time of 1.8 hr per tomogram. After image acquisition, the images were reconstructed using the software 'Octopus' (version 8, XRE, Gent, Belgium).

#### *2.2. Data Processing*

For particle analysis, it is usually necessary to filter the data, because otherwise individual particles touching each other would be counted as a single particle, or noise artefacts would be interpreted as small particles. The choice of the filter thus had a strong impact on the significance of particle analysis. The reconstructed 3D data were filtered with the Software 'Fiji' (version 1.52a) [40,41], and then analyzed with the software 'Avizo' (version 8.1, Thermo Fisher Scientific, Waltham, MA, USA). Figure 1 demonstrates some of the main steps of the measurement and image analysis procedure schematically.

#### 2.2.1. Median Filter

Median filtering consists of first sorting all voxels to be analyzed, and their neighbors with respect to their grey values, and then lining them up in a list. The voxel to be analyzed then receives the grey level located in the middle of this list (i.e., the median value of all voxels in the neighborhood). With this method, noise is partially eliminated.

**Figure 1.** Sketch illustrating the reconstruction and data preparation process. After capturing all 1500 radiographic projection images—one shown in (**a**)—a tomographic 3D data set is reconstructed in (**b**). After binarization (**c**), the individual zinc particles are labelled (and, for example, color-coded as in (**d**)), which allows for a shape analysis of each individual particle.

#### 2.2.2. Threshold Filter/Binarization

The 3D data sets were binarized with a threshold filter [42]. If a voxel of the dataset belonged to a zinc particle, the value 1 was assigned to it, whereas all other voxels received the value 0. After setting a threshold, all voxels above this value were set to 1 and all others to 0. The choice of the threshold value was crucial in this stage. The larger this threshold was chosen, the higher the X-ray absorption of a voxel had to be, to qualify as belonging to a particle.
