The measurement of electrochemical noise of a Li-ion battery during charge-discharge cycling

Journal Pre-proofs The measurement of electrochemical noise of a Li-ion battery during chargedischarge cycling E.A. Astafev PII: DOI: Reference:

S0263-2241(20)30029-4 https://doi.org/10.1016/j.measurement.2020.107492 MEASUR 107492

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Measurement

Received Date: Revised Date: Accepted Date:

5 August 2019 18 October 2019 7 January 2020

Please cite this article as: E.A. Astafev, The measurement of electrochemical noise of a Li-ion battery during chargedischarge cycling, Measurement (2020), doi: https://doi.org/10.1016/j.measurement.2020.107492

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The measurement of electrochemical noise of a Li-ion battery during charge-discharge cycling

E.A. Astafev*

Institute of Problems of Chemical Physics RAS, Acad. Semenov av. 1, Chernogolovka 142432, Russia

*Corresponding author. E-mail: [email protected], tel. +7 903 7203152.

Abstract For the first time electrochemical noise of a commercial Li-ion battery was measured during discharge via a constant value resistor for 1500 cycles. Spectral and statistical analyses were carried out. Both the power spectral density frequency dependence level and noise amplitude were increasing during battery cycling. Distribution diagrams, skewness and kurtosis values demonstrated unchanged normal noise distribution during cycling. Linear dependencies of the current power spectral density values on cycle number were found in the low-frequency band. Dependencies of the power spectral density on the DC-current value were measured at different stages of charge-discharge cycling. The total progress of electrochemical noise growth during cycling was divided into three stages with different prevalent battery degradation types: film growth, active material exfoliation, and structural changes.

Keywords: Electrochemical noise; Li-ion battery; Battery state of health.

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1. Introduction At present, an urgent task is a means for ensuring the accurate assessment of the state of health (SOH) of electrochemical power sources [1, 2]. In this connection, due to their widespread popularity as a portable electrochemical power source, particular attention is paid to rechargeable Li-ion batteries. Typically, the SOH of Li-ion batteries is evaluated by various electrochemical techniques,

including

DC-measurements,

charge-discharge

cycling

and

impedance

measurements [3-5]. However, despite the fact that these techniques are already well developed, novel methods for evaluating the SOH of chemical power sources continue to be of considerable research interest [2, 6]. One such novel methodological approach is electrochemical noise (ECN) measurement and analysis [7, 8]. ECN has been applied as a means of SOH measurement for various types of batteries [9-11] and fuel-cells [12-13]. The majority of the cited works conclude that the ECN method has the potential to support useful and wide-ranging diagnostic applications for evaluating electrochemical power sources. The problem here is the very small number of researchers having attempted to investigate ECN during chemical power source cycling. Only a very few works can be cited in the case of Li-ion batteries [14, 15]. However, no direct chargedischarge cycling for Li-ion battery has yet been performed to investigate ECN. Such an attempt has been made in the case of Ni-Cd batteries [16]; however, probably due to the instrumentation limitations, it was not very successful. Since ECN amplitudes of chemical power sources are very small, precise measurements require specially-designed instruments [17]. The second major problem associated with the ECN method is the choice of data processing technique. Various approaches have so far been used, including statistical and spectral analysis [18-20], new techniques based on discrete polynomial decomposition [21], as well as flicker-noise spectroscopy [22, 23]. In our own previous investigations, we employed a spectral analysis approach. The advantage of this technique is that it allows the ECN spectrum to be modelled using electrochemical impedance spectroscopy (EIS) data [24, 25]. When investigating the ECN behaviour of the commercial Li-ion battery during discharge process [26], we observed that no significant changes in ECN behaviour take place during the first 50% of the discharge process. At the same time, it is recommended that the battery condition be fully charged for SOH estimation when carrying out EIS measurements due 2

to the very significant changes taking place in impedance spectra when the battery reaches the end of the discharge process [27]. For this reason, it becomes harder to distinguish the various discharge and cycling effects in the case of a discharged battery as compared with the single ageing (cycling) effect for a fully charged battery. Thus, the main aim of the current work was to measure the ECN of a commercial Li-ion battery over a series of consecutive charge-discharge cycles. A secondary aim was to investigate the collected ECN data and try to find any correlations between the cycle number and the degree of battery capacity degradation.

2. Experimental Commercial Li-ion batteries (EEMB LIR1220) were used as test objects. Their characteristics are as follows: nominal voltage 3.6 V; nominal capacity 12 mAh; minimum capacity 8 mAh; charging voltage 4.2 V; discharge cut-off voltage 2.75 V; form-factor 1220. Cathode material is LiCoO2. The measurements with the several batteries were performed and they all have demonstrated the same tendencies in ECN behaviour evolution during chargedischarge cycling. The current work represents one of them. A NM-5-10K instrument (Electrochemical Instruments, Russia) was used for the ECN measurement. This device, which is described in detail in work [28], was also used as the primary measurement instrument in a number of our previous works [26]. Its validation in the current configuration was carried out in our previous work in which the ECN of the same type Li-ion battery was evaluated during a single discharge cycle [29-30]. It is important that the instrument is validated under the current configuration, which has the best fit for the chosen type of the battery ECN measurements, taking its impedance, capacity characteristics and the ECN level it demonstrates under the chosen discharge rate into account. The configuration of the instrument was as follows: main ECN amplifier – 4 parallel ADA4898 low-noise operational amplifiers; main amplifier gain – 250; load resistor value – 6.34 kΩ (low-noise, thin film resistor); analogue-to-digital converter data rates – 10 kHz, and 500 Hz. It took 60 s of timelength to collect the low-frequency data of 30000 points. In the present work, the DC-blocking high-pass filter cut-off frequency was 0.02 Hz. All other experimental conditions were the same as in work [30]. 3

Compared with the standard validation procedures [28], the instrument was additionally validated by replacing our battery under test (having a capacity of 12 mAh) with a Samsung ICR18650-30B battery (2950 mAh corresponding to C/450 discharge rate with the load resistor of 6.34 kΩ). With a current load resistor of 6.34 kΩ, this fully-charged battery does not provide ECN capable of being measured by our instrumentation. By performing the measurement, it was found that the thus-obtained power spectral density (PSD) spectra coincide with the instrument noise ones with a shorted input at all frequency ranges considered in the current work. This means that no excess noise is involved in the applied load resistors under the experiment conditions (with flowing battery discharge current); consequently, no electrical noise measured in the current work can be attributed to these factors. Such validation tests should be performed because different types of resistors (for example carbon ones) can posses flicker noise caused by the contact resistances oscillations between carbon grains. Metal foil resistors are considered to be free of such effects but it is necessary to check it before the precision experiments with extremely low-signals as in the current work are performed. The validation result is shown in Fig. 1. The spectrum corresponding to the validation measurement with a large battery is several Ω higher than the short-input measurement due to the shot noise presence in this case. Moreover, even this difference cannot be responsible for the ECN spectrum levels further observed in the current work, as well as in previous studies [26, 29, 30]. Reproducible electrochemical noise behaviour was observed in these and other works [24, 25]. It possessed distinctive individual PSD spectra for different types of the batteries been tested. These spectra were reproducible changing during battery (Li-Ion, Li-SOCl2 or other primary ones) discharge. Thus, the observed electrochemical noise cannot be attributed to the noise of the load resistor. The ECN of Li-ion battery investigated in works [26, 29, 30] possessed quite low amplitude but reproducible linear frequency dependencies of the ECN PSD. Directly after the load resistor removing, the relaxation noise of the Li-Ion battery demonstrated the same PSD spectrum behaviour (close level and slope) as for the ECN under this load. This experimental fact was investigated in details in work [30] for the different SOC values. It additionally proves that observed noise is not caused by the resistors nature but produced by the Li-ion battery.

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Fig. 1. Instrument validation spectra: 1 – shorted input measurement (black curve); 2 – measurement with the large Li-ion 2950 mAh battery loaded by the 6.34 kΩ resistor (red curve). Vertical axis is recalculated into values of equivalent noise resistance (Ω) with the use of Nyquist formula from the PSD values (V2/Hz).

The data processing part of the work included ECN power spectral density (PSD) calculations. Along with trend removal procedures, these calculations were performed the same way as in work [26]. For this, the entire 30000-point data array was divided into several segments. The trend removal procedure included a local linear approximation technique applied individually in each segment of ECN data array. Discrete Fourier-transform was used to calculate the ECN PSD frequency dependence in each segment and they were averaged after that. Two types of ECN PSD spectra were used in the current work. The first comprised the evolution of the PSD spectrum during charge-discharge cycling. These spectra were measured by means of a single ADC sample rate of 500 Hz. Individual segment length was 300 points and segments amount (PSD averaging factor) was 100. The second type of ECN spectra was discharge rate variation PSD. This was calculated using two ADC sample rates – 10 kHz and 500 Hz. Each individual segment length was 300 points; their total number was 100. In this way, final spectra were obtained across a wide frequency band. This was necessary in order to compare the behaviour of the ECN under different load conditions, since at small load currents the ECN level diminishes when reducing the ECN PSD spectrum towards to the thermal noise spectrum of the battery under zero load current [30]. The time-length of a single segment of 300 data points is 0.6 s if the ADC data rate of 500 Hz is used. It is lower than 0.003% of the time5

length of the full discharge process at C-rate close to C/7 as in our case. It makes it possible to treat the investigated signal to be close to stationary. The relative approach was used in work [19] for statistical ECN data analysis. It is necessary for the success trend removal procedure and PSD calculation technique. At the same time, this segment length makes possible to obtain quite a wide frequency range of consideration (about 4 orders wide totally for two ADC speeds). We tried to apply wider segments to extend low-frequency limit but have found this one providing the most reproducible and promising results. These additional load variation ECN measurements were performed to investigate the influence of the discharge current on the ECN behaviour. This was necessary due to the gradual fall of the capacity of the battery observed during charge-discharge cycling. As a consequence of this, using the same load resistor (with the same load current) results in formally different C – rates (relative discharge rate comparing to the absolute current value in mA which keeps the same) of discharge for the different cycle numbers. The aim of these measurements carried out under different loads was to investigate this effect, as well as to make corresponding corrections in the main cycling experiment. These measurements were performed with a fully charged battery using load resistances from 1.5 kΩ to 68 kΩ. The measurements were performed at a 100% state of charge (SOC) value. Although high-load currents resulted in going deeper into the discharge process, no strong changes take place in ECN behaviour during the first half of the discharge process for the battery under test, as already shown in previous studies [26]. Standard deviation (SD) and statistical calculations were also included in ECN investigation during charge-discharge cycling as a quantification of ECN amplitude evolution. These calculations were performed in the time domain. 20th order polynomial fitting was applied as a procedure for trend removal. This was followed by double moving average trend removal procedure by 1000 points prior to standard deviation calculations. Although various other types of trend removal procedure are discussed in the literature [31-34], the technique successfully tested and described our previous work [31] was used in the current work. Standard deviation values were calculated using low-frequency measurement data with an ADC sample rate of 500 Hz. Such measurement and trend-removal parameters result in standard deviation calculation for frequencies at around 1 Hz. The SD calculations were performed with the same data array of 30000 points as for the PSD calculations. Each standard deviation measurement was performed 6

with a fully charged battery. The measurement was repeated six times with relaxation pauses of 300 s between measurements for better reproducibility and standard deviation error estimation. Here, it was necessary to clarify the strength of changes in observed standard deviation values by obtaining the standard deviation confidence interval for each charge-discharge cycle. Then the mean standard deviation value was calculated using these six values to construct the final dependencies on the cycling number and the lost capacity percent. The same type of the trend removal procedure was thoroughly tested in the work [26] for the ECN PSD spectra calculation of the same type Li-Ion battery. It was shown that it does not affect the PSD frequency dependencies in the observed frequency range from 5 Hz to 5 kHz. Nevertheless, some additional explanation can be given to approve such high order polynomial validity for the ECN trend removal in our case. The polynomial of the 20th order function possesses 19 extremums. The lowest frequency of our interest is 5 Hz as it was in the work [26]. The low-frequency ADC data rate is 500 Hz. It means that the single period length is 100 data points. The length of our data array is 30000 data points. It means that we got 300 periods of the sinusoidal signal at the lowest frequency of our interest. Each period of the sinusoidal function possesses 2 extremums. So, we got 600 extremums (or more for the higher frequencies). It means that polynomial function with 19 (or even 50 for example) extremums cannot fit such sinusoidal function. Thus, the signal of our interest in the lowest frequency limit (and higher frequencies) cannot be suppressed by such polynomial trend removal procedure (it cannot remove the ECN of the battery been investigated in considered frequency range). Statistical analysis was performed after applying the 20th order polynomial trend removal procedure to the ECN data. Following the construction of ECN distribution diagrams, their characteristics – skewness and kurtosis values – were calculated using the same ECN data as for spectral analysis. Such an analysis approach is widely used in the ECN field [15, 35, 36]. Kurtosis values were not normalised to -3 value. A P-45X potentiostat-galvanostat with FRA-24M frequency response analyser (Electrochemical Instruments, Russia) was used for the EIS measurements. In order to construct the EIS spectra evolution during charge-discharge cycling, the EIS of a fully-charged battery was measured at the same charge-discharge cycles as the ECN. This measurement was carried out in

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potentiostatic mode at open circuit voltage. The AC amplitude was 5 mV, while the frequency range was from 0.05 Hz to 100 kHz. A P-20X8 multichannel potentiostat-galvanostat was used for charge-discharge cycling of the batteries under test. A single cycle comprised four steps: galvanostatic discharge by 6 mA current with a voltage limit of 2.7 V; potentiostatic secondary discharge under a voltage of 2.7 V for 1000 s; galvanostatic charge with a current of 6 mA up to the voltage of 4.25 V; potentiostatic secondary charge at a voltage of 4.25 V for 3000 s. This charge-discharge cycle was repeated 50 times and the EIS and ECN values were measured. After that, the sequence was repeated resulting in ECN and EIS data measurements for the cycle numbers 50, 100, 150… 1500. The cycling was prolonged until 30% of the capacity of the battery under test had been depleted. Such charge-discharge cycling test procedure is common for investigation of Li-ion batteries during their oldering.

3. Results and discussion ECN behaviour at different cycles is shown in Fig. 2a. A clear rise in the amplitude is observed with an increase in the cycle number. ECN PSD frequency dependencies for the different charge-discharge cycle numbers are shown in Fig. 2b. All these spectra demonstrate a linear frequency dependence of 1/fn type, where n value is close to 1. It can be seen that the level of the spectrum gradually increases during the battery charge-discharge cycling when the spectrum type is left unchanged. Distribution diagrams are shown in Fig. 2c. The skewness and kurtosis values for the same cycle numbers as the ECN data given in Fig. 2 are summarised in Table 1. The values and shapes of their distribution diagrams indicate that the normal distribution of the ECN values remains unchanged for all cycle numbers.

8

Fig. 2. (a): ECN at different cycle numbers: 1 – 50, 2 – 300, 3 – 450, 4 – 700, 5 – 900. (b): ECN PSD spectra for different cycle numbers: 1 – 50, 2 – 300, 3 – 450, 4 – 700, 5 – 900. (c): ECN distribution diagrams for different cycle numbers: 1 – 50, 2 – 300, 3 – 450, 4 – 700, 5 – 900. 300 segments were used to calculate the distribution diagram. The instrument noise spectrum is subtracted for PSD spectra.

Table 1 Skewness and kurtosis values for the ECN at different cycle numbers. All values correspond to distribution diagrams shown in Fig. 2c. Cycle number

Kurtosis

Skewness

50

2.88

-0.13

300

3.04

0.00086

450

3.28

-0.069

700

3.05

-0.046

900

3.20

-0.045

Standard deviation calculations were used to numerically evaluate the ECN level changing during the charge-discharge cycling. Fig. 3a demonstrates the dependence of the standard deviation values on the cycle number. Six black points are shown for each cycle number under investigation (for the cycle number 200 for example). These correspond to six separate measurements taken one by one with a pause of 300 s. The presence of multiple points allows us 9

to estimate the confidence interval of standard deviation values for each cycle number. The averaged points, by which means the approximation curve is constructed, are shown in blue. It can be seen that this curve remains inside the confidence interval. The reduction of the battery's capacity (given as a percent of the initial value) during cycling, which corresponds to the right axis, is also shown in this Figure. It exhibits non-linear behaviour, with a gradual fall occurring from one cycle to the next.

Fig. 3. (a): ECN standard deviation values dependence on cycle number (left axis): 1 – measurement results for each cycle number, 6 measurements shown (black dots); 2 – averaged values for the 6 measurements and the approximation line (blue dots and line); 3 – capacity percent from initial value dependence on cycle number (right axis, red curve). (b): ECN standard deviation values dependence on the capacity of the battery loss: 4 – measurement results for each cycle number, 6 measurements shown (black dots); 5 – averaged values for the 6 measurements and the approximation line (blue dots and line); 6 – correction line for the C-rate increasing during cycling; 7 – corrected standard deviation averaged value dependence on the capacity loss percent (red line and dots). Instrument noise level is subtracted in a form of variance only for curve 6 calculation.

Fig. 3a demonstrates that the ECN standard deviation value gradually increases with the cycle number. This increase can be explained in terms of several effects (hypotheses to be checked). The first of these takes place due to the capacity fall under cycling processes. Applied load resistor provides the same load current (measured in mA) for both fresh and cycled batteries. But the cycled battery with lower capacitance formally is tested under a higher 10

discharge rate in C (relative capacity) units of the discharge current. This implies that, under the fixed discharge current in mA units, the discharge rate of a small-capacity battery (cycled one) is faster than for a high-capacity battery (fresh one). It can influence the ECN behaviour due to the higher current density applied to the cycled battery, for example. Thus, it seems logical that a stronger (faster) discharge would demonstrate higher ECN amplitudes, which could explain the dependencies observed in Figure 3a. This hypothesis (first type of effect) must be checked. Conversely, the second reason (second effect) of ECN amplitude increase may be caused by any other reason connected with the degradation of the battery during charge-discharge cycling. For this reason, the next step in the present work was to separate these two effects by thoroughly investigating the first type effect. The ECN was measured with different load resistors for this purpose to obtain the dependence of PSD on DC-current value. Fig. 4 demonstrates the corresponding ECN PSD spectra for the different load resistors (different load currents) for two cycle numbers – 50 and 1000 (for a fresh and a cycled battery). Each spectrum is constructed of a low-frequency part measured at the ADC data rate of 500 Hz and highfrequency part measured at a 10 kHz ADC data rate. It is possible to see that these parts coincide in the mid-frequency band. It means that applied drift removal procedure works correctly for all considered discharge rates and assumption of quasi-stationarity of short 300 points segment is correct for PSD calculations. It is also possible to see that the quality of low-level spectra (curves 5) is not as good as for the high-level spectra (curves 1). It is caused by the procedure of instrument noise spectrum subtraction. It increases the resolution but increases the dispersion of low-level spectra.

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Fig. 4. ECN PSD spectra for the different discharge currents: 1 – 2.73 mA; 2 – 1.37 mA; 3 – 0.41 mA; 4 – 0.17 mA; 5 – 0.06 mA. EIS real part impedance spectrum – 6 (measured at the DC current of 0 mA). (a) – cycle number 50; (b) – cycle number 1000. Instrument noise spectrum is subtracted.

Table 2 ECN PSD slope absolute values for the different DC load currents. Load resistance,

DC load current,

Slope absolute

Slope absolute

kΩ

mA

value, cycle 50

value, cycle 1000

68

0.06

-

1.08

24

0.17

0.89

1.17

10

0.41

1.04

1.25

3

1.37

1.12

1.28

1.5

2.73

1.12

1.28

It can be seen that the ECN level is raised with an increase in the discharge current. The ECN spectrum consists of two parts for each load current. The high-frequency part corresponds to the thermal noise since it coincides with the real part of the impedance (Curve 6). This observation is especially clear for the low DC load currents and is one of the best validation 12

procedures of the experimental setup and calculations due to its demonstration of the coincidence of the EIS and ECN methods results. The low-frequency parts of the ECN spectra demonstrate the 1/fn behaviour and correspond to the electrochemical noise under load. As Table 2 demonstrates, the exponent value n does not change significantly with changed load. However, the crosspoint frequency strongly decreases with reduced load current. The most interesting parameter of these spectra evolution is change of PSD level with load current. The corresponding results are shown in Fig. 5 as the dependence of ECN PSD values on DC load current for two frequencies. Two cycle numbers are considered – 50 and 1000. It can be seen that these dependencies demonstrate a linear behaviour. The corresponding approximation results and equations are also shown in Fig. 5. Here it may be seen that the proportionality coefficient increases from about 1.92 to 2 during cycling, which is practically the same value. These dependencies mean that the low-frequency ECN PSD value is proportional to the DC-current value in the power of two.

Fig. 5. ECN PSD values dependencies on DC-current for two frequencies – 5 and 20 Hz for two cycle numbers: (a) – 50; (b) – 1000.

For now, it is possible to construct the model curve capable to predict the growth of the ECN PSD value during capacity loss over charge-discharge cycling. It is important that this prediction model supposes that the capacity falling during cycling takes place due to the exfoliation (or another loss) of active electrode material of the battery. It results in higher current density been applied for the remaining active electrode material. Fig. 5 demonstrates that the 13

higher current density increases the ECN amplitude. We know the capacity of the fresh and cycled battery (for each cycle number). It means that we know the DC-current which is required to discharge the battery during one hour (it is measured in mA units and is called 1C discharge rate). As we use the same load current (measured in mA units) for all cycle numbers, we can calculate relative DC-load current for each cycle number (in C-units). It is possible to see that it increases during battery cycling due to capacity lowering. Knowing the dependence of the ECN PSD value on the DC-current shown in Fig. 5 it is possible to predict how the ECN level increases due to the relative DC-current growth (in C-units). The corresponding result is shown in Fig. 3 as Curve 6. Here, it seems logical to try to construct the dependence of ECN standard deviation value on the lost capacity percentage, but not the cycle number due to non-linear capacity loss with cycle number increase (Fig. 3b). It can be seen that the growth of the prediction Curve 6 in Fig. 3b during the battery cycling (due solely to the first type effect) demonstrates much a slower increase comparing to the experimentally observed Curves 4 and 5. Conversely, Curve 7 in Fig. 3b includes the correction due to the first type effect. It is possible to conclude that this first type effect looks comparable to (and even smaller than) the deviations of the experimental data from the approximation line. This means that the increase in ECN level during battery cycling is dominated by the second-type effect caused by some other changes taking place during the battery degradation with consecutive cycling. It is also possible to conclude that the linear approximation shown in the coordinates of Fig. 3b was successful only for the mid-cycle numbers. The coordinates of Fig. 3a fit much better for the linear standard deviation approximation of the whole cycling experiment data. Fig. 6a demonstrates how the ECN PSD spectrum slope absolute value depends on the cycle number. It can be seen that there is an almost linearly dependence on the cycle number in the range from 0 to 1000 cycles. This linear slope breaks when higher cycle numbers are reached. Fig.7 demonstrates the EIS spectra evolution during the charge-discharge cycling. Here, it can be seen that there is a small but gradual increase in impedance. These spectra were used to calculate the current PSD values from the voltage PSD. Corresponding results are shown in Fig. 6b as dependencies of the current PSD values on a cycle number for three frequencies: 5, 20, and 100 Hz. The closest frequencies in the EIS spectrum were: 99.58 Hz, 19.34 Hz, and 5.21 Hz. 14

Fig. 6. (a): ECN PSD slope absolute value dependence on cycle number. (b): ECN current PSD dependencies on charge-discharge cycle number for 3 frequencies: 2 – 5 Hz, 3 – 20 Hz, 4 – 100 Hz. Shot noise PSD value for considered DC-current value is 2.11·10-22 A2/Hz. Instrument noise is subtracted.

It can be seen that the low-frequency ECN current PSD values are linearly dependent on the cycle number. The proportionality coefficient is the same for both low frequencies – 5 and 20 Hz. However, the higher frequency has its own coefficient value. As Fig. 6b demonstrates, the ECN level growth cannot be explained solely in terms of changing impedance: if this were the case, the approximation lines would be horizontal. In fact, the impedance increases during cycling constitute a third type of effect, which explains the increasing ECN level during cycling with increases in impedance (Fig. 7). However, since this factor is excluded from the figure, it may be concluded that increased impedance is not a significant reason for the increased ECN level during battery cycling. Additionally, comparing Figures 3 and 7, it is possible to conclude that changes in ECN amplitude are much more significant than the impedance values if considering any particular frequency (the lowest 0.05 Hz in all spectra in Fig. 7 for example).

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Fig. 7. (a): EIS spectra for the different charge-discharge cycle numbers: 1 – 50; 2 – 150; 3 – 250; 4 – 350; 5 – 450; 6 – 550; 7 – 650; 8 – 750; 9 – 850; 10 – 950; 11 – 1050; 12 – 1250; 13 – 1450. Frequency band 0.05 Hz – 100 kHz. Spectra are shifted in vertical direction by 1 Ω one from each other for better visual presentation. (b): Comparison of impedance real part value at 5 Hz growth – 14 (left axis), with an increase of ECN SD value – 15 during the cycling process (right axis, instrument noise is subtracted).

Figures 3a and 6b demonstrate that the ECN technique can be used for estimating the SOH of Li-ion batteries, since quite strong changes in ECN amplitude and PSD slope value are observed during battery cycling. It should be noted that the effect of the ECN level growth is not caused by the first-type effect of decreasing capacity and increase in C-rate if the same load current is used for all cycle numbers. Here, the much stronger second-type effect is observed. Although both methods have demonstrated some deviations of their quantitative indicators from the true-linear behaviour during the battery cycling, this is a normal situation for any physical or chemical analysis method. These deviations would look not so pronounced if a higher step between considered cycle numbers had been be used (e.g. 100 or 200 instead of 50). Nevertheless, it is possible to say that the ECN method is superior to the EIS method when evaluating the SOH value of the battery. The direct comparison between the two methods results is shown graphically in Fig. 7b. It demonstrates how the impedance real part value at 5 Hz changes during the cycling process. 16

The ECN SD value growth process is also shown. The left and the right axis scales are selected in such a way that both curves demonstrate relative dispersion which influences the precision of potential SOH estimation. It is possible to see that the ECN SD value shows much stronger growth comparing to the impedance value. The ECN amplitude has grown in 5.81 times during 1300 charge-discharge cycles when 27% of the capacity was lost (the instrument noise vas subtracted in variance units. It was equal to 18.4 nV in SD units). Such effects are much more strongly pronounced as compared to the effects demonstrated by the traditional EIS method. Here, the real part of the impedance at the frequency of 5 Hz has increased only in 1.21 times. The linear approximation results are also shown in Fig. 7b. They demonstrate that the ECN effect is 3.07 times greater than EIS if calculations are performed in SD units (uV). The superior capabilities of the ECN method can probably be explained by the fact that the ECN test is performed under load condition and it tests the battery deeper. It looks like it provides much more information comparing to the EIS test which is performed under open circuit voltage without DC-current flowing through the battery under test. As the first and third type effects of the ECN amplitude growth during cycling were shown not to be the main ones, it is interesting to investigate the second type of effect. Considering the literature [37-40] about the degradation mechanisms of the Li-ion batteries, it is possible to distinguish several main ways of the degradation: 1. Passive film growth which lowers the active surface and covers small pores. It also reduces the amount of active Li. 2. Exfoliation of carbon anode material. 3. Exfoliation and deactivation of cathode material containing Li. 4. Structural changes of the cathode. 5. Li plating and dendrites formation. 6. Current collectors corrosion. There are some more degradation reasons but the main ones are listed here. Fig. 8a demonstrates how the ECN level changes during cycling in different regions of cycle numbers in coordinates of capacity loss percent. It is possible to distinguish 3 of them – the first one in the range of 0 to 250 cycles (slow ECN level growth), the second one in the range of 250 – 1000 cycles (faster ECN level growth) and the last one for the cycle numbers higher than 1000 (fast 17

ECN level growth with high ECN amplitude dispersion). Fig. 8b demonstrates how the efficiency of charge-discharge processes changes during cycling. It was calculated as the percent of the charge lost during one charge-discharge cycle. It is most probably that strong change of this curve is caused by structural changes of the cathode after cycle number 1000.

Fig. 8. (a): Averaged ECN standard deviation values dependence on capacity loss in 3 regions: 0 – 250 cycles, 250 – 1000 cycles, 1000 – 1500 cycles. (b): Charge loss dependence on cycle number. Instrument noise is subtracted in a form of variance.

Fig. 9 demonstrates the ECN behaviour for the different cycle numbers together with the corresponding discharge curves. It is possible to see that the basic ECN level of the most of the discharge process increases during cycling. A small drop of the discharge voltage is only observed when we move from the cycle number 50 to 300. It means that ohmic resistance increases in this cycle numbers range. It corresponds usually to the solid electrolyte interface (SEI) growth. No visual (qualitative) changing in discharge curve behaviour takes place during 550 cycles (only the scale of horizontal axis shrinks). A small difference in final behaviour can be seen at cycle number 1450. The final fall of the voltage happens more gradual. It is probably due to the structural changes in the cathode material.

18

Fig. 9. ECN evolutions during discharge (a) and corresponding discharge curves (b) for the different cycle numbers. 19

It is possible to see that the final growth of the ECN amplitude at the end of the discharge process takes place at the lower discharge voltages for higher cycle numbers. It is possible to see that coming down to the level of about 3 volts results in the disappearance of the final ECN level growth when we move from the cycle number 300 to 1450. The lower discharge voltage of about 2 volts is required to reach the final ECN level growth if we look at the cycle number 550 discharge curve. If we consider the impedance spectra evolution during the cycling (Fig. 7), it is possible to conclude that it is quite hard to select any part of it which would change stronger than the others. Spectra colours in this figure correspond to the ones in Fig. 8 with the same cycle numbers. The most part of the hodograph – high-frequency SIE impedance (frequencies higher than 1 kHz) [41], mid-frequency impedance (central semi-circle in the frequency band from 1 kHz to 0.2 Hz) corresponding to the charge transfer resistances with double layer capacitances of the cathode and anode (it is impossible to separate them in our case without reference electrode) – all of them gradually increase during cycling process [42]. Only the low-frequency diffusion impedance (the rise of the impedance at the frequencies lower than 0.2 Hz) stays without visible changes. Relative changes in impedance behaviour were observed in work [43]. It is possible to suppose that two final degradation reasons (numbers 5 and 6) do not take place during cycling because no strong self-discharge is observed to indicate the process number 5 (self-discharge speed is the same as for the fresh battery). The relaxation noise of cycled battery behaves the same way as for the fresh one. It indicates the absence of lithium plating [44]. In another case, it would be possible to identify the corrosion processes which would show additional noise (as under load so after removing of it). It is probably that qualitative changes in discharge curve behaviour at cycle number 1450 correspond to the structural changes. This assumption is in agreement with charge-discharge effectiveness fall after cycle number 1000. The ECN amplitude changes fast from cycle to cycle in this range of cycle numbers as Fig. 8a demonstrates. So, it is possible that structural changes of the cathode take place in the region of cycle numbers from 1000 to 1500. The first range with slow ECN amplitude growth (blue data points in Fig 8a) probably corresponds to the growth of the SEI film as the voltage drop of the discharge curve indicates it. The red region (Fig. 8a, cycle numbers from 300 to 1000) with 20

increased speed of ECN level growth probably corresponds to the exfoliation of electrode materials (the loss of active material). This conclusion is in agreement with work [45] where cycling of Li-ion battery was performed and it was shown that active lithium is lost over 300 cycles. The Li-ion battery was investigated in work [46] and the increase of ohmic resistance was the main increasing component of the impedance during the first 300 cycles. It is probably that the exfoliation process is accompanied by the formation of the spikes in the ECN which can be seen in the time domain (Fig. 9). They can look like transients and possess non-reproducible character. It is probably that the superposition of such effects increases the ECN level during the discharge process of the cycled battery. The ECN curve of Fig. 9 for cycle number 1450 demonstrated such behaviour. It stochastically changes the ECN amplitude as Fig. 9 (for cycle number 1450) and Fig 8a demonstrates (final black part). These spikes can also be attributed to the current collector corrosion effects [47] but in this case, the strong noise of the battery must be observed under OCV conditions. The exfoliation is caused by the expansioncontraction process of graphite particles during lithiation-delithiation process in the Li-ion battery [48]. In the current work, the ECN of a Li-ion battery during cycling was investigated. Interesting results were obtained, having the potential to be of practical benefit. These became possible due to the purpose-designed precision instrumentation for solving the problem of using ECN to evaluate power sources [17, 28]. ECN treatment ideas, experimental setup organisation and validation techniques developed by Tyagai [49, 50] were used as widely as possible in the current and previous works. Nevertheless, there are now additional problems to be solved and questions to be answered. While it is probable that a 3-electrode setup [51, 52] could provide direct information concerning which electrode (cathode or anode) provides the majority of the observed ECN, it is likely that the nature of the ECN can only be revealed with the use of additional methods combined with the electrochemical techniques [53-55]. Although carrying out such measurements, which represent a very complex experimental task requiring elaborate instrumentation in the case of ECN method, are among the most interesting ideas for the future investigations.

4. Conclusions 21

The electrochemical noise of the commercial Li-ion battery was measured during chargedischarge cycling for the first time. It was shown that power spectral density frequency dependencies increase during battery cycling, as well as that the 1/fn shape of the low-frequency part remains the same having a small n value increasing from 1 up to 1.35. Standard deviation calculations in the low-frequency band have shown that noise amplitude increases during chargedischarge cycling. The electrochemical noise of the battery was measured using different loads to construct the dependencies of the power spectral density values on the DC load current for a fresh and a cycled battery. It was shown that these dependencies are linear in bi-logarithmic coordinates, having slope values close to 2. Statistical analysis confirms that the nature of the ECN does not change during battery cycling since normal ECN distribution is observed both for the fresh and the cycled battery. All types of calculations performed in the current work – standard deviation, voltage PSD, current PSD and ECN PSD slope values – demonstrate that the ECN technique can potentially be used for SOH evaluation of the tested Li-ion battery as an alternative to the EIS method. The ECN amplitude has grown in 5.81 times during 1300 charge-discharge cycles comparing to an increase of impedance values in 1.21 times. ECN behaviour changing during Li-Ion battery cycling made it possible to separate 3 different lifetime periods of the battery aging. Each period corresponds to one main degradation reason as DC-data analysis demonstrates.

Acknowledgements This work was performed in accordance with the state task, state registration No ААААА19-119061890019-5.

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For the first time, electrochemical noise of Li-ion battery was measured during cycling The amplitude of electrochemical noise increases during battery cycling Noise technique can be used to evaluate the state of health of the Li-ion battery Electrochemical noise test demonstrates stronger effects compared to the impedance

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