*2.3. Computed Tomography*

In order to verify the measurements with the light band micrometer, a 3D nondestructive measurement was needed with high spatial resolution. X-ray computed tomography is one such method with the capability of providing high resolution 3D scans of objects. The combination of non-destructive methodology and high resolution makes it apt for analyzing the non-uniform expansions of Li-ion cells. A cone-beam X-ray computed tomography is used specifically in our experiment as shown in Figure 3. In this setup, at one end is an X-ray source radiating a cone shaped beam and on the other end there is a flat-panel X-ray detector. The object to be scanned is placed on a high precision rotation stage between the source and the detector. During the scan, the object is rotated slowly over 360° and, in this duration, several thousand 2D images called the projections are captured by the detector. This stack of 2D projections of the object to be measured is then fed into a tomographic reconstruction algorithm to generate the 3D volume of the scanned object. The resolution of the scan depends on how close the object is to the source. Like a shadow approach, the closer the object is to the source, the higher is the scan resolution; however, the field of view is smaller. If we move away from the source, we have a greater field of view but at the cost of resolution.

**Figure 3.** Computed tomography setup for 3D measurement of the battery cell for different loading conditions to compare the mechanical structure of the cylindrical cell.

The Li-ion cell is scanned in two states, once with SoC = 0 and once with SoC = 1. In both of the cases, the resolution of the 3D reconstructed volume was 10 μm. This was followed by a surface determination on the 3D volume data to determine the surface of the cell in the two states. These generated surfaces from both scans were then used to calculate the non-uniform expansion of the cell walls in 3D. In order to have an absolute co-relation between the two states, a reference metal tube was fixed to the setup, which was used to register the 3D volumes of both scans. This would ensure that there is no geometric shift or rotation influencing the measurement of the non-uniform expansion of the cells. Although CT has been used to study various effects in batteries [9,18–20], to the best of the author's knowledge, a 3D non-uniform expansion of Li-ion cells measured with CT is investigated for the first time in this work. Figure 3 shows the setup of the computed tomography for the 3D measurement of the battery cell with the source for the X-rays and the detector.

In order to be able to evaluate which local expansions belong to which geometrical influences within the cell later on also during the measurements with the light band micrometer, a picture of the cell examined in the light band micrometer was also taken with the computed tomography. In addition, the position of the anode current collector was marked on the housing of the battery cell to assign the corresponding positions.
