## 3 Results
### Validity of Impedance Spectra  
The TI criterion for a valid impedance value was defined based on the difference between measured and calculated impedance amplitude using the _zHit_ method. The maximum difference allowed here is 0.15 m\(\Omega\), which is around 5% of the smallest impedance amplitude measured on the test cells. For the analysis, only parts of the spectra can be considered, which fulfills this criterion, as only these parts describe a time-invariant system. In Figure 5, impedance spectra are presented. They were recorded on \(TC1\) during _hard AK3.4_ with discharging superimposed DC-currents after the first cycling phase of the aging test (after 15 FCE). In the Nyquist diagrams, the time-invariant impedance values are marked with squares. Additionally, the measured and calculated impedance amplitudes are shown together with their absolute difference. For superimposed discharge currents, all measured points pass the criterion at frequencies above 0.1 Hz. For \(-\)4.5I\({}_{20}\), impedance spectra were recorded only down to this frequency (see Section 2.2). The impedance values of lower frequencies do not correspond to a time-invariant system. Figure 6 shows the impedance spectra with charging DC-currents. The same measurement points of the \(+\)1I\({}_{20}\) spectrum are invalid as of the \(-\)1I\({}_{20}\) spectrum. In the first \(+\)4.5I\({}_{20}\) spectrum, points until 1 Hz are valid. The repeated \(+\)4.5I\({}_{20}\) spectrum and the \(+\)6I\({}_{20}\) spectrum recorded at the end of the check-up have invalid measurement points also at high frequencies around 100 Hz. These observations can be made for the other test cells as well (presented as supplementary material). In general, it can be said that, for high charging currents, a significant part of the spectrum, which also comprises the negative electrode, is invalid. Toward smaller charging currents and discharging currents, this part of the negative electrode can be used for analysis. Most values of the positive electrode spectrum part are invalid--regardless of which DC-current was used. Figure 5: Impedance spectra measured on \(TC1\) of _hard AK3.4_ at the end of the first cycling phase (after 15 FCE). Impedance spectra with discharging DC-currents are presented as a Nyquist diagram at the top. The impedance values, which pass the LTI criterion, are marked with squares. The impedance amplitudes measured and calculated with the _zHit_ method are shown over the frequency at the bottom. The absolute difference between the amplitudes is presented as well with its own _y_-axis on the right side. Figure 6: _Cont._  
In Figures 7 and 8, impedance spectra of _TC_1 aged in _hard AK3.4_ are presented, which were recorded after the cycling (graphs on the top) and after the recharging phase (graphs on the bottom) at the end of the aging test (120 FCE). All spectra with discharging DC-currents shown in these figures have enough valid points to analyze the ohmic resistance and the charge-transfer process of the negative electrode. In all spectra with charging DC-currents, compared with spectra with discharging DC-currents, independently of previous cycling or charging treatment, more points infringe on the TI criterion. Further noticeable is that the \(+8\)I\({}_{20}\) spectrum has a higher number of valid measurement points than the \(+6\)I\({}_{20}\) spectrum recorded after the cycling and charging phase. For all check-ups, it could be observed that, toward the end of the check-up, fewer points in the spectra with charging DC-current satisfy the TI criterion. In the spectrum with \(-8\)I\({}_{20}\) DC-current recorded after cycling, the first half-cycle is not fully visible. With this shape, the fitting of \(R_{ct}\) and \(C_{dl}\) does not provide a distinct result. Single spectra with \(-6\)I\({}_{20}\) and \(-4.5\)I\({}_{20}\) DC-current had a similar shape, so the spectra of these DC-currents could not be used for the entire aging test. Spectra measured after recharging show a different shape than the spectra measured after cycling.