**5. Discussion**

In the context of the aging study, the method introduced has proven to be advantageous for investigating processes with time constants in the range of minutes to hours. In addition to the more precise resolution of the low-frequency processes compared to the DRT, which is derived from frequency domain data, the time required for the measurements is significantly lower. Besides higher resolution and lower time efforts, the steady state criterion with regard to the SOC is not violated during the relaxation period. In order to avoid a change in the SOC during the EIS at low frequencies, the excitation current must be limited, which leads to a comparatively poor signal-to-noise ratio.

However, high sampling rates are required in order to investigate frequency-dependent processes with characteristic time constants in the range of a few seconds or even milliseconds such as charge transfer and SEI. According to the Shannon theorem, time constants in the range of milliseconds should theoretically be able to be evaluated with a sampling rate of 10 Hz, which is realistic for an online application. In contrast to this, the aging study has shown that only the parameters of processes with time constants of almost two decades higher (*τ* ≥ 1.6 s) can be quantified with sufficient accuracy using the aforementioned sampling rate. In many applications, and especially in most online applications, the method presented is therefore limited to the aging monitoring of processes with time constants in the range of seconds to several hours, such as solid state diffusion.

Therefore, for applications in which both pulse tests and EIS are possible, a combined use of both techniques is proposed. By merging the impedance data obtained through time and frequency domain data as suggested by [19], the impedance spectrum and DRT can be determined for a wide frequency range.

Using the DRT derived from the time domain data, a correlation between the polarization contribution and LAMAn could be determined at low frequencies around 35 μHz. Due to the limited frequency range of the EIS, this connection could not be established using the frequency domain data. A correlation between a degradation mechanisms and the impedance of LIBs could already be established in earlier studies. In a comprehensive experimental study, the correlations between kinetic parameters of an LIB and degradation mechanisms could be derived [1]. Recently, a correlation between low frequency impedance and the LLI was found in [24] and Schindler et al. [37] confirmed a correlation between the low frequency impedance and LAM. Using cell kinetics to gain insights into the degradation mechanisms is beneficial because measuring impedances at high and moderate frequencies is fast compared to deriving the mechanisms by recording open circuit voltage curves [1]. However, EIS measurements suffer from long measurement durations for low-frequency impedances and a lack of availability in most state-of-the-art online applications. In contrast, relaxation periods occur in every online application. As a result, the introduced method enables a time-effective investigation that can be used online in order to obtain the relevant parameters of the processes with large time constants and thus enable an online estimate of the degradation mechanisms.

It is known that LIBs can suffer from accelerated capacity loss towards the end of life due to lithium plating originally caused by a lack of anodic material [35,36]. For online applications, an early detection of an increasing capacity reduction and lithium plating is of great importance for the reliability and safety of LIBs. Many publications like [38] have therefore dealt with the prediction of the sudden reduction in capacity. As a further outcome of this study, the correlation found could be used to identify an advanced LAMAn online and thus the risk of lithium plating and the resulting rapid loss of capacity at an early stage.

In summary, this work showed that the evaluation of the voltage relaxation after a current pulse is suitable for investigating the kinetic parameters of a LIB even without prior knowledge of the polarization processes involved. The DRT obtained from the time domain data offers a time-effective determination of processes with large characteristic time constants and enables the parameters to be estimated online. The correlations found provide insights into the degradation mechanisms both offline and online and thus support the future battery design and enable optimization of the operating strategies. The findings about the early detection of a potential risk of lithium plating are available for subsequent studies and contribute to improving the reliability and safety of LIBs.

In a future step, Post-Mortem analyses will be carried out to directly quantify the LAMAn and validate the assumptions made. In addition, the transferability of the results to other cell chemistries and formats must be checked.

**Author Contributions:** Conceptualization, E.G.; methodology, E.G.; software, E.G.; validation, E.G.; formal analysis, E.G.; investigation, E.G.; resources, J.K.; data curation, E.G.; writing—original draft preparation, E.G.; writing—review and editing, J.K. and E.G.; visualization, E.G.; supervision, J.K.; project administration, E.G.; funding acquisition, J.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Bundesministerium für Bildung und Forschung grant number 16EMO0262 (SiCWell).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
