**1. Introduction**

The mechanical properties of commercial Li-ion cells are increasingly coming into focus, especially considering the steadily growing requirements. Higher energy and power densities, less space consumption, and longer service life—these are the challenges that need to be overcome. However, many promising material combinations are limited by their mechanical properties or are not suitable for real applications. For example, silicon has a significantly higher energy density and specific capacity (*Q*Si = 4200 mAh g−<sup>1</sup> [1]) than graphite (*Q*C6 <sup>=</sup> <sup>372</sup> mAh g−<sup>1</sup> [1]), is available in sufficient quantities in nature, and is reasonably priced [1,2]. However, the volume change of 100% ≤ Δ*V*SoC ≤ 300% compared to the initial volume due to lithium intercalation is problematic. This can lead to cracking in the lattice structure and thus to delamination of the active material from the current collector [3], which leads to a faster aging. For this reason, an alloy or a compound of different materials is usually used to combine the most favorable properties [1–5].

In order to understand which underlying mechanical processes take place inside the battery cell, suitable measurement methods are necessary for recording and analyzing parameters such as electrode thickness and volume change of the cell components. Various methods of measuring electrode thickness have already been implemented and show a volume change of electrode materials and battery cells caused by the intercalation and

**Citation:** Hemmerling, J.; Guhathakurta, J.; Dettinger, F.; Fill, A.; Birke, K.P. Non-Uniform Circumferential Expansion of Cylindrical Li-Ion Cells—The Potato Effect. *Batteries* **2021**, *7*, 61. https:// doi.org/10.3390/batteries7030061

Academic Editor: Manickam Minakshi

Received: 26 July 2021 Accepted: 31 August 2021 Published: 6 September 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

deintercalation of Li-ions [6–9]. Depending on the material, the electrodes expand differently with lithium migration. Compared to silicon, graphite as an anode material is significantly inferior when considering the specific capacity, but it expands only up to Δ*V*SoC = 12% [6,7,10] of the initial volume during lithiation and delithiation and thus exerts significantly less mechanical pressure on the cell components. Cathode materials, metal oxides frequently, also show a volume change due to lithiation and delithiation. In this process, Nickel Cobalt Manganese Oxide (NCM) expands by up to 1% ≤ Δ*V*SoC ≤ 2% [7,8,10] and Nickel Cobalt Aluminium Oxide (NCA) by up to Δ*V*SoC = 5% [10] of the initial volume.

Other factors influencing the cell volume are the Solid Electrolyte Interface (SEI) layer thickness growth due to electrolyte decomposition products forming a covering layer on the electrodes [11,12] and Li-plating (especially for Lithium Metal cells) [8,11]. These effects lead to a reduction in volume due to irreversible layer thickness growth and, together with the gassing that takes place due to side reactions [13,14], leads to an increase in pressure inside the cell on the housing, resulting in a measurable change of the cell thickness. This was measured using dilatometry [7,8], imaging techniques such as computed tomography [6] and neutron imaging [15], or strain gauges glued to the cells [9], among other methods. In some cases, besides reversible expansion due to the migration of lithium ions, irreversible expansion was also shown, which also correlates with the loss of cyclizable lithium.

In addition, measurement of the internal gas pressure has already been realized for different cell formats [13,14,16]. Aiken et al. [13] performed tests according to the Archimedes principle on clamped and unclamped pouch cells and demonstrated reversible volume expansion as a function of SoC for initial cycling of battery cells with different electrolytes. In unstrained cells, the volume change built up via charge could be dissipated upon discharge and was thus almost completely reversible. In the case of clamped cells, the pressure no longer decreased completely, since the gas collects on the outer sides of the electrode stack due to the static pressure caused by the clamping. The results obtained from the measurements suggest that, depending on the electrolyte, reversible gas formation is also possible, with the gas formed as the reactant in the chemical reactions taking place. Schmitt et al. [14] showed for the first time that internal gas pressure measurement is possible with commercial pressure sensors on large-sized cells. The results show that during formation the gas pressure in the cell increases irreversibly. Afterwards, a clear SoC dependence can be seen, from which a correlation between the expansion and the graphite stages (pressure increase correlates with the calculated volume change due to lithiation of the graphite and stagnates with restructuring of the crystal lattice) can also be established. Schmitt et al. [14] also showed the irreversible increase in internal gas pressure with decreasing State of Health (SoH). This is also evident in work by Schiele et al. [16], which shows an irreversible increase of internal pressure with increasing number of cycles because of gas evolution attributed to the thermal decomposition of the conducting salt LiPF6 using a multichannel in situ pressure measurement system.

While measurable changes in cell thickness are obvious for pouch cells, having a flexible aluminum composite foil housing, reversible, and irreversible cell thickness growth can also be observed for cylindrical cells, although to a much lesser extent due to the rigid housing [9]. Considering all mentioned effects and investigations, as well as due to the rigid housing and the cylindricity of the commercial cylindrical battery cells, the assumption of a homogeneous expansion of the battery cell over the entire surface is reasonable. The irreversible cell thickness growth due to the mentioned causes and the increase of the internal gas pressure due to side reactions would thus have to lead to an increasing load on the cell housing. Figure 1a schematically shows the assumed cell thickness growth of a cylindrical cell with increasing SoC as a result of the lithiation of the anode, which expands much more than the cathode. The increase in the radius of the cell is shown in blue. During discharge, the cell completely returns to its original shape as the lithium delithiates completely from the graphite. In Figure 1b, the assumed cell thickness growth of the cylindrical battery cell with decreasing SoH (marked in green) is visualized. The red area marks the aging, which

increases with higher number of cycles over lifetime. The increase in battery cell radius Δ*r*SoH is directly related on the residual capacity, as already proven by Willenberg et al. [9]. Thus, by correlating with the SoC and the SoH, a state variable estimation can also be attempted by measuring the battery cell thickness change. However, a requirement for this is the uniform expansion of the battery cell over the entire circumference.

**Figure 1.** Theoretical schematic representation of (**a**) reversible and (**b**) irreversible cell thickness growth (Δ*r*SoC) compared to the initial diameter (*d*0). (**a**) As a result of the volume expansion of graphite with increasing lithiation, the radius of the battery cell increases over every single cycle. The battery cell returns to its original shape when discharged. (**b**) Due to SEI layer thickness growth, defects in graphite, and pressure rise due to side reactions over the lifetime of a cylindrical Li-ion cell, the radius of the battery cell increases irreversibly by Δ*r*SoH with decreasing SoH (green) and increasing irreversible aging (red) until the end-of-life (EoL) of the cell.

The central question of this work was whether the cell really expands uniformly as expected. Both manufacturing and geometric variables are important here – the position and thickness of the current collector tabs that connects the electrodes, the number of layers of electrodes, and the position in the housing. How these influence and what difficulties can arise in measuring battery cell thickness growth are discussed below. It remains to be tested whether cell thickness growth can be used for cell state estimation.

## **2. Materials and Methods**

The study of battery cell thickness growth is performed on a commercial cylindrical Li-Ion cell, LG INR18650 M29. The battery cell has a positive electrode made of nickelrich NCM active material and a negative electrode made of graphite. The specifications of the battery cell are listed in Table 1. The battery cell has a usable voltage range of 2.5 V ≤ *U* ≤ 4.2 V according to the producer's datasheet [17].


**Table 1.** Product specification of the cylindrical Li-ion battery cell applied [17].

#### *2.1. Experimental Setup*

To investigate the punctual radial expansion of the LG INR18650 M29 battery cell, an optoCONTROL ODC2600 light band micrometer with a high-resolution CCD camera for measuring geometric quantities from Micro-Epsilon Messtechnik GmbH & Co. KG (Ortenburg, Germany) is used. The light band micrometer is shown schematically in Figure 2. The measuring range (red band between laser and acquisition unit) has a total height of *l*range = 40 mm. The linearity *l*, i.e., the deviation between an ideal straight characteristic curve and the real characteristic curve, is max. *l* = 3 μm. The resolution *d*res of the measurement signal is *d*res = 0.1 μm, at a measurement rate *f* of up to *f* = 2.3 kHz. The micrometer operates on the principle of shading or light quantity measurement and thus detects the dimension and position of the object to be measured.

**Figure 2.** Schematic measurement setup with the light band micrometer from Micro-Epsilon Messtechnik GmbH & Co. KG for investigating the punctual expansion of the cylindrical Li-Ion cell (LG INR18650 M29) at the top edge of the cell located in the *l*range high light band marked in red. In fact, the distance between the LG INR18650 M29 and the end of the measuring range is measured (*l*meas). As the cell expands, the distance decreases and vice versa. The cell is cycled in the light band micrometer and rotated 10° after charge and discharge, until the complete circumference has been measured with a total of 36 cycles.

To examine the expansion of the battery cell, the cell is clamped at the poles in a holder for contacting so that it is free and orthogonal to the light band in the measuring area marked in red, as shown in Figure 2. The light band micrometer has different setting modes. The transition between the shading by the cell and the adjacent light edge of the laser is used as a reference point. Either the path between the upper edge of the battery cell and the lower edge of the measuring range, or the path between the lower edge of the battery cell and the upper edge of the measuring range can be measured. As the battery cell expands, the top edge of the cell shifts, resulting in increased shading and thus increased measurable distance. In addition, the diameter of the shading through the cell or a gap between two shadings can be determined. However, this mode is not suitable for the following investigations because the expansion of one position and a contraction at the opposite position can cancel each other out. Therefore, the change of the battery cell radius is always indicated in the following. The acquisition can only be performed for one position or one diameter at a time. To examine the cell thickness growth over the entire circumference, the battery cell must be rotated manually.
