4.1.2. EIS

Figures 5 and 6 present the results of the impedance spectroscopy conducted on half of the cells built from the aged negative electrodes. The results are for a cell charged at 60%. EIS spectra can be fitted by an equivalent circuit:

$$L\_1 + R\_1 + Q\_2 // R\_2 + Q\_3 // R\_3 \tag{29}$$


Values are summarised in Table 1.

Figure 5 represents the results in the Nyquist plan of the different cells. Figure 6 presents the parameter values of the fitted models on each plot.

**Figure 5.** Nyquist plot of the different cells at SOC = 60%.

No ageing cell has the same resistance and capacitance, which reflects a difference in the morphology of the "electrodes".

The cells aged at −20 ◦C, 0 ◦C, and by calendar ageing at CV keep an interface resistance (*R*1) in the same order as the fresh cells. These cells may not have developed extra SEI, or the thickness of the SEI has not increased.

**Figure 6.** EIS results based on equivalent circuit *L*<sup>1</sup> + *R*<sup>1</sup> + *Q*2//*R*<sup>2</sup> + *Q*3//*R*<sup>3</sup> at SOC = 60%. (**a**) Comparison of inductance values. (**b**) Comparison of ohmic resistances. (**c**) Comparison of the interface resistance according to the interface capacitance. (**d**) Comparison of the charge transfer resistance according to the charge transfer capacitance.


**Table 1.** EIS results based on equivalent circuit *L*<sup>1</sup> + *R*<sup>1</sup> + *Q*2//*R*<sup>2</sup> + *Q*3//*R*<sup>3</sup> at SOC = 60%.

The interface capacitance *Q*<sup>2</sup> of the fresh cells and the cells aged at −20 ◦C are quite the same, which confirms the results of GD-OES: no extra SEI has been formed.

The interface capacitance of cells aged at 0 ◦C and by calendar ageing at OCV is more important than that of the fresh cells, but the resistance is in the same order of value. It induces a transformation in the morphology of the SEI for these cells. The SEI is less compact.

EIS confirms that cells aged at 25 ◦C and 45 ◦C have the same kind of SEI morphology. The resistance and capacitance interfaces are closed (Figure 6c).

Cells aged by a calendar process at *CV* have a resistance *R*<sup>2</sup> and *Q*<sup>2</sup> close to the one of cells aged at 25 ◦C and 45 ◦C. GD-OES has shown that the extra SEI developed is not of the same nature. One growth is due to salt degradation, the other to solvent degradation. Compared to cells aged at OCV the resistance is higher, which means that the thickness developed by the CV process is greater than the one developed by an OCV process. This is confirmed by GD-OES.

Regarding charge transfer resistance *R*3, cells aged at 25 ◦C, 45 ◦C, and by calendar ageing keep the same order of value as the fresh cells. However, charge transfer capacitances (*Q*3) are lower than for the fresh cells. The interface film solution might be less porous certainly due to the growth of SEI.

The cells aged by calendar ageing at constant voltage tend to have the same morphology as cells aged at 25 ◦C and 45 ◦C regarding the values of *R*3, *R*2, *Q*2, *Q*3.

Nevertheless, the ohmic resistance (Figure 6b) is more important, which means that the properties of the electrolyte are different. The GD-OES shows that the processes of SEI generation are not similar. One is based on the decomposition of salt and the other on the degradation of the solvents. Components present in the electrolyte might be different.

Cells aged at −20 ◦C and 0 ◦C have an important resistance charge transfer *R*3. The growth of the resistance value, in the case of the cells aged at −20 ◦C, can be explained by the development of metallic lithium. In the case of the cells aged at 0 ◦C, the GD-OES analysis exhibits the presence of lithium (Figure 4a). The analyses show that lithium is not contained in the SEI layer and is not in a metallic state. It is as if lithium was blocked on the the film interface.
