Evolution of Distribution of Relaxation Times in the Impedance Spectra of NMC/Graphite Cylindrical Cells during Cycling
Authors: Tang Qiaochu , Wang Jiabin , Stimming Ulrich 
Published: May 2020

Electrochemical impedance spectroscopy (EIS) is a powerful tool for the non-destructive diagnosis of lithium ion batteries (LIBs). Thanks to the measurement over a wide frequency range, electrochemical processes of different kinetics are reflected in EIS, which contains rich information on battery aging and degradation.
Distribution of relaxation times (DRT) method has been increasingly utilised to interpret EIS data. Compared to conventional EIS presentations such as Nyquist plot and Bode plot, DRT isolates the processes with different time constants and gives an explicit showcase of timescales in the battery [1]. Another advantage of DRT is the possibility to separate contributions from cathode and anode without the meticulous work to make three-electrode cells, given that relaxation time peaks can be identified with half cells [2]. The information acquired through DRT can provide insight into battery degradation paths and help improve data-driven methods for battery diagnosis/prediction.
This work looks into the DRT evolution of commercial NMC/graphite cylindrical cells (Sony US14500VR2 with a nominal capacity of 715mAh) under various cycling conditions. Before the experiment starts, the cells are in shipping status i.e. undergone pre-aging and kept at approximately 70% state of charge (SoC). All cells then go through one 0.1C/0.1C cycle and 99 continuous cycles under various C-rates and temperatures (see table 1). The lower C-rates under 25ºC and 35ºC are scaled against 45ºC by Arrhenius relation. All charges are constant-current constant-voltage and all discharges are constant-current, between 3V and 4.2V. Impedance spectra are measured over 10kHz~0.1Hz range after being fully charged and fully discharged in each cycle.
The impedance spectra measured after every full charge of cells 1~5 are shown in Figure 1(a) ~ (e). The decrease of semicircle size as temperature increases can be seen. During continuous cycling, internal resistance and semicircle size grow monotonically as cycle number increases. While the semicircles in each EIS curve are overlapping, the impedance components with different relaxation times are clearly separated in the DRT plotted in Figure 2. In Figure 2(a) and (b), there are constantly four relaxation time peaks as cycle number increases in 25ºC. The feature time constant in lies tightly within 25ms~50ms range, corresponding to 20Hz~40Hz frequencies, regardless of C-rates. In Figure 2(c) and (d), relaxation time peaks differ with C-rates right after 35ºC cycling starts. With 0.5C/1C rate, the evolution trend of relaxation time is similar to 25ºC cases. With 1C/2C rate however, there are initially only three relaxation time peaks and the mid-frequency (between 0.1s and 1s) peak “splits” into two as cycle number approaches 100. This could be related to joule heating resulting from higher C-rate or kinetic factors, and is more similar to the 45ºC case as shown in Figure 2(e). In 45ºC with 1C/2C rate, the relaxation time peaks start with three and “split” into four around the 60th cycle.
While the evolution of DRT needs further interpretation and more long-term experiments, we can see the effective of time scale separation for EIS under various cycling conditions. The time scale features can be incorporated into data-driven methods e.g. machine learning to aim at accurate battery diagnosis/prediction. Also, the fact that feature relaxation times (may be battery-type specific) are distributed in a relatively narrow range suggests the EIS measurement can be done with reduced frequency points to save on-board resources for future system-level application.
This work is supported by Faraday Institution (EP/S003053/1) and North-East Centre of Energy Materials (EP/R021503/1) funded by EPSRC.
[1] Ciucci, F., & Chen, C. (2015). Analysis of electrochemical impedance spectroscopy data using the distribution of relaxation times: A Bayesian and hierarchical Bayesian approach. Electrochimica Acta, 167, 439-454.
[2] Sabet, P. S., Stahl, G., & Sauer, D. U. (2018). Non-invasive investigation of predominant processes in the impedance spectra of high energy lithium-ion batteries with Nickel-Cobalt-Aluminum cathodes. Journal of Power Sources, 406, 185-193.

Figure 1