*3.3. Investigations with the Help of Computed Tomography*

To validate the measurements with the light band micrometer, computed tomography was used to determine battery cell thickness growth, as shown in Figure 8.

Therefore, images of the cell in a fully discharged state and in a fully charged state are generated, creating two three-dimensional models of the battery cell.

**Figure 8.** (**a**) Cross−section of the 3D CT image of the battery cell with magnified extent. Contraction of the battery cell is colored in pink; (**b**) representation of the absolute surface of the recorded battery volume, which changes over the charge according to the indicated expansion. The largest proportion of the battery surface expands between 10μm and 20 μm while charging.

By superposing these models, the difference in the shape of the outside of the casing between the two states of charge of the battery cell can be visualized. Figure 8a shows a sectional view of the three-dimensional scan of the cell and the 50-fold amplified change on the outer side of the cell. The figure confirms the clear expansion of the cell housing in the area of the anode current collector tab and at the opposite position of the cell (180◦ offset). The maximum absolute radius change at expanding regions of the cell is also of the same order of magnitude. In contrast to the measurements with the micrometer, the expansion in the area of the anode current collector tab does not go directly into a contraction of the surrounding positions around the circumference of the battery cell. Overall, there is a smaller number of contraction positions seen around the circumference of the cell. The absolute change in radius also lags well behind the maximum contraction that occurred in the micrometer. While the averaged radius change of the cell in the light band micrometer measurement is only about Δ*r*LBM = 1 μm, it is about Δ*r*CT = 12 μm in the computed tomography measurements. Nevertheless, the inhomogeneous expansion of the cell is clearly emphasized. The potato shape due to the increased expansion is also clearly recognizable. In addition to the differently expanding areas, a sinusoidal shape of the change of the cell housing can be seen in the images. It is possible that this is due to the manufacturing process of the cell housing. Confirmation of this effect by subsequent measurements is still to be conducted. Figure 8b shows how much area of the outer housing expands or contracts. It is clear that the largest proportion of the surface of the housing exhibits a radius change of Δ*r* = 20 μm during charging compared to the discharged state of the cell.

Figure 9a shows a representation of the 3D image of the cell including the analysis. The coloring clearly shows an area of contraction on the left side and areas of varying degrees of expansion on the remaining surface. The color scale can be found in Figure 8. Figure 9b shows the expansion of a cross-section over the height of the cell, proving that there is no significant change in cell thickness growth over height. Only the absolute expansion decreases in the direction of the poles. In addition, the left side of the plot shows that, even after the end of the current collector tab, there is a reduction in the absolute expansion of the cell over the height of the battery cell.

**Figure 9.** (**a**) 3D representation of the recorded battery volume analyzed for expansion; (**b**) longitudinal section through the battery cell over the recorded height with the corresponding expansion analysis.

#### **4. Discussion**

As shown in the section Results, the use of a light band micrometer is a stable and reliable method to study cell thickness growth. During the cycling of LG INR18650 M29, the change in radius of a single position could be measured with an accuracy of *a*acc = 99.67%. The operating temperature of the light band micrometer is between 0 ◦C ≤ *T* ≤ 50 ◦C, so, when measuring in a climatic chamber at a constant temperature of *T* = 25 ◦C, a temperature effect of the environment on the measuring device and the battery cell can be neglected.

The measurement of the volume change over the complete circumference of the battery cell shows that a non-uniform change in the shape of the cell takes place. Instead of the expected uniform expansion, the cell takes on a potato shape, putting it simply. The roundness of the cell decreases and bulges and valleys form around the circumference depending on the position and orientation of the jelly roll inside the housing. Where the negative current collector tab is located, the cell expands at an above-average rate, while it contracts more than average at points where the jelly roll is not directly against the housing and a cavity is created.

The measured change in radius, caused by the intercalation and deintercalation of Li-ions in the electrodes, is up to a maximum of Δ*r*max,ex = 27 μm on expansion of the cell (as seen in Figure 6a) and up to Δ*r*max,con = −25 μm on contraction (as seen in Figure 6c). A SoC dependent volume change behavior was observed at all locations of the battery cell. The averaged diameter of the battery cell with a low SoC is *d*SoC=<sup>0</sup> = 18.15 mm. The change in radius over charge averages Δ*r*mean = 1.1 μm for each position by the circumference of the cell, respectively Δ*d*mean = 2.2 μm, resulting in an averaged diameter of the battery cell in the fully charged state of *d*SoC=<sup>1</sup> = 18.152 mm. As shown by the small difference between the average diameter when fully discharged and the average diameter when fully charged, the volume change of the battery cell is non-uniform because the areas of expansion and the areas of contraction compensate each other. The actual change of radius of different zones around the circumference of the cell is up to 12 times higher than the average expansion. Since the expansion of the individual positions was investigated in 36 consecutive cycles, deviations due to forming processes, aging processes, and possibly existing influences due to different relaxation of expansion and pressure are to be expected. The absolute values are therefore to be considered critically and must be validated elsewhere with an extended setup that allows the investigation of all of the different positions within a single cycle for multiple samples and different cell chemistries. In addition, the influence of the current and the ambient temperature on the uniformity of the expansion still need to be considered in future studies.

The CT scan could confirm the non-uniform change in the shape of the cell and the potato-shaped expansion. The absolute maximum radius change of both measurement methods is between 29 μm < Δ*r*max < 37 μm. However, there is a significant difference between the absolute surface area expanding and the absolute surface area contracting. It should be noted that the resolution of computer tomography is much higher than that of manual measurement or rotation by α = 10◦ in the light band micrometer. In addition, there is a risk that peaks or valleys near the area of interest will falsify the measurement due to the arrangement of the measurement area with the light band micrometer. Therefore, optimization of the measurement setup is mandatory for further investigations.

By analyzing a section of a battery cell with a height of *h* = 1 cm, computed tomography is able to confirm the initial assumption that the change in radius of the cell does not change significantly with height. Only the absolute value of the expansion or contraction decreases in the direction of the poles.

As shown in Figures 6 and 7, a correlation of the radius change with the SoC is very well possible. This correlation between the lithiation of the electrodes and the change in radius can be established regardless of whether the cell expands or contracts at the corresponding position. The characteristic points, for example, the end of the CC charging and discharging phase, as well as the influence of the temperature rise and the relaxation at the respective CV phases, can be seen over almost all of the examined positions. However, this correlation is much clearer for positions where the absolute value of the change in radius is higher. Figure 7 also shows that the intercalation and deintercalation of Li-ions result in different swelling and contraction, which leads to a visible hysteresis. The variation in the slope of the radius change in Figure 6 is probably related to the stage formation during the lithiation of graphite. Further investigation of this will be reported elsewhere. In addition, investigation of the influence of the SoH on the expansion at various locations is still outstanding.

## **5. Conclusions**

It has been shown that spatially resolved measurement of the expansion of battery cells is limited with a light band micrometer and very feasible with the aid of computed tomography. The investigated battery cells show significant deviations from the expected uniform expansion and form areas of expansion and contraction over their circumference, depending on the orientation of the jelly roll in the case.

Hence, the use of volume change to study aging or predict SoC, as indicated by different authors [9,12], requires special caution, since the expansion varies significantly depending on the measurement position and the measurement results may be biased depending on the measurement method.

**Author Contributions:** Conceptualization, J.H.; methodology, J.H., F.D., and J.G.; investigation, J.H., F.D., and J.G.; CT images, J.G.; writing—original draft preparation, J.H.; writing—original draft preparation CT part, J.G.; writing—review and editing, J.G., A.F., F.D., K.P.B., and J.H.; visualization, J.H. and A.F.; supervision, K.P.B.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Bundesministerium für Wirtschaft und Energie (BMWi - ZF4370703LT9).

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors are thankful to Tina Kreher, Maike Lambarth, and Martin Kühnemund for reviewing the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
