*3.1. Position-Dependent Volume Change*

Figure 4a shows the schematic illustration of a Li-ion cell as well as the examined positions over the circumference of the cell, starting at pos. 0, where the negative current collector (marked A in Figure 4b) is located inside the cell. Each further position is offset by <sup>α</sup> <sup>=</sup> <sup>10</sup>◦ from the previous one (pos. 1 <sup>=</sup> <sup>10</sup>◦, pos. 2 <sup>=</sup> <sup>20</sup>◦, ...).

**Figure 4.** (**a**) Schematic drawing of a cylindrical Li-Ion cell, marked with the points measured in the light band micrometer, which are located at an angle of *α* = 10◦ to each other. The start position from the measurement (position 0) corresponds to the position of the negative current collector tab, which was marked in the CT (marked A in Figure 4b; (**b**) 100-fold amplified expansion of the cell thickness in steps of ΔSoC = 2.5% at the corresponding positions including a CT image of the cell to assign the corresponding positions on the cell circumference. A marks the negative current collector tab, B the positive current collector tab. C highlights one of two spots, where a small gap between the jelly role and the housing is located, where the jelly role is not pressed against the housing. D marks the end of the jelly roll.

Figure 4b shows the change of the radius of the respective position Δ*r*Pos over the circumference of the battery cell per SoC change of ΔSoC = 2.5% amplified by a factor of 100. Between positions 0 and 5, a clear expansion of the cell is evident, which continues to flatten and reverses at position 7. The battery cell also shows significant expansion directly opposite the negative current collector tab and at the position of the positive current collector tab (marked B). The marks C (associated measurement positions: 30–35) and D (associated measurement positions: 8–11) each highlight locations where the jelly roll is not as tight as at the other locations and thus does not press against the housing. Both locations show a contraction of the cell over a wide range. Whether the cell wrap is more densely or less densely packed is determined by the distance between the cell wrap and the housing. If the cell coil lies directly against the housing, a denser packing can be assumed then if there is still a cavity between the cell coil and the housing (as in mark C in Figure 4b).

The results of the change in radius over the circumference of the battery cell suggest that, in particular, expansion occurs at those locations where the packing of the jelly roll is significantly tighter than normal due to the current collector tabs. Contraction occurs mostly at locations where the jelly roll is significantly looser. This ultimately leads to a potato-shaped cell form, also visualized in Figure 5.

Figure 5a shows the radial change Δ*r* (amplified by a factor of 100) over time *t* added to a fixed cell radius *r*mean to visualize the change in cell volume of each circumferential position over time. Each line reflects the recorded expansion or contraction of the battery cell Δ*r* in the light band micrometer at that point. The contraction at the bottom of the cell and the bulge near the negative current collector tab can be seen particularly clearly. The plane in gray shows the section plane applied at different states of charge to study the volume change of the battery cell for different states of charge.

Figures 5b–e show the sectional views at different states of charge (SoC = 0.25 ... 0.5 ... 0.75 ... 1), which once more clearly show the potato-shaped form of the battery cell. The change in radius at the position of the negative current collector tab is marked in green. The top view of the battery cell in gray reflects the initial shape of the cell.

**Figure 5.** (**a**) 100-fold amplified change of cell thickness growth over the time *t* in h of charge and discharge cycle in *α* = 10◦ steps added to a fixed cell radius (mean diameter of the cell with SoC = 0) for each position measured in the light band micrometer over the circumference of LG INR18650 M29. The gray area is the intersection for plots (**b**–**e**), showing sectional views of relevant SoCs (SoC = 0.25 ... 0.5 ... 0.75 ... 1). The current collector position is marked by a green line/dot in every plot. The blue dots belong to the charge of the battery cell, the red marks to the discharge, revealing a visible hysteresis of the volume change of the cell.

The change in radius during charging is shown in blue, and the change when the corresponding SoC is reached during discharging is shown in red.

An increase in the extreme points over the SoC can be clearly seen: the expansion becomes larger as the charge increases, but the contraction also becomes stronger as other regions expand. The hysteresis of the voltage due to the applied load has already been investigated many times [21–23]. However, the expansion also has a hysteresis, recognizable by the non-overlapping points especially at the extreme points.
