Quantitative Analysis of Time-Domain Supported Electrochemical Impedance Spectroscopy Data of Li-Ion Batteries: Reliable Activation Energy Determination at Low Frequencies
Authors: Mertens Andreas , Vinke Izaak C. , Tempel Hermann , Kungl Hans , de Haart L.G.J. , Eichel Rüdiger-Albrecht , Granwehr Josef 
Published: February 2020

Physico-chemical processes in batteries are taking place on a broad time scale from fractions of seconds to the order of days [1]. Thus, for an accurate characterization of transport and mobility processes in batteries using electrochemical impedance spectroscopy (EIS), a large frequency range of up to ten decades must be covered. This implies measurement durations on the order of days for low frequency measurements, yielding the risk of distorting electrochemical instabilities in the battery and a considerable change of its state of charge (SOC) due to the probing ac current excitation. It is shown that the SOC change is frequency dependent and with 10-15% of the nominal battery capacity for the sub-millihertz range hardly a small perturbation. Nevertheless, these obstacles can be mitigated by the time domain measurement (TDM) technique [2-4]. TDM is limited to impedance measurements at low frequencies, with a small and frequency-independent SOC change. The combination of TDM and EIS, called time-domain supported electrochemical impedance spectroscopy (TD-EIS), opens up the possibility for a time-efficient implementation of impedance spectroscopy over a large frequency range down to microhertz frequencies [5].
In this work, TD-EIS at varying temperatures in combination with data fitting using an electrical equivalent circuit battery model, is used for the high-accuracy quantification of low-frequency mobility parameters in lithium-ion batteries. It is experimentally demonstrated, for the first time, that the phase of the impedance measurements converges in the sub-millihertz range, which permits a reliable quantification of diffusion kinetics. Moreover, it is shown that with TD-EIS time savings of up to 80% compared to the standard EIS measurement are feasible.
From the electrical equivalent circuit battery model fit, an accurate estimate of charge transfer resistance and, in particular, also solid-state diffusion rate are obtained. Both processes follow an Arrhenius law, allowing the determination of activation energies with small variance. The results for the charge transfer process and for the solid-state diffusion process are within the range of literature values measured for similar systems.
This work has been published in JECS [6].

References

[1] A. Jossen, “Fundamentals of battery dynamics”, Journal of Power Sources 154 (2) (2006) 530-538
[2] S. C. Creason, J. W. Hayes, D. E. Smith, “Fourier transform faradaic admittance measurements - III. Comparison of measurement efficiency for various test signal waveforms”, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 47 (1) (1973) 9-46
[3] J.-S. Yoo, S.-M. Park, “An electrochemical impedance measurement technique employing Fourier transform”, Analytical Chemistry 72 (9) (2000) 2035-2041
[4] D. Klotz, M. Schönleber, J. Schmidt, E. Ivers-Tiffée, “New approach for the calculation of impedance spectra out of time domain data”, Electrochimica Acta 56 (24) (2011) 8763-8769
[5] J. Illig, J. Schmidt, M. Weiss, A. Weber, E. Ivers-Tiffée, “Understanding the impedance spectrum of 18650 LiFePO4-cells”, Journal of Power Sources 239 (2013) 670-679
[6] A. Mertens, I.C. Vinke, H. Tempel, H. Kungl, L.G.J. de Haart, R.-A. Eichel, J. Granwehr, "Quantitative Analysis of Time-Domain Supported Electrochemical Impedance Spectroscopy Data of Li-Ion Batteries: Reliable Activation Energy Determination at Low Frequencies", Journal of the Electrochemical Society 163 (7) (2016) H521-H527

Figure caption: Arrhenius plot of the solid-state diffusion rate obtained from battery model fits of impedance data from three batteries measured at different temperatures. The activation energies are determined from the gradients.

Figure 1