Use of Electrochemical Impedance Spectroscopy, Capacity, and Electrochemical Noise Measurements to Study Aging of Lithium-Ion Batteries

Abstract

Aging studies of lithium-ion batteries are essential for understanding material degradation, which impacts performance and, consequently, battery lifespan. In this paper, we propose the use of electrochemical impedance spectroscopy, differential capacity analysis, and electrochemical noise measurements to evaluate the effects of different C-rates (2C, C/2, and C/20) on a cell. We study aging up to 800 charge/discharge cycles. We demonstrate that aging is associated with a linear increase in electrode resistance, which correlates with capacity fading. Additionally, noise measurements indicate a rise in noise levels at low frequencies following a ${1/f}^{\gamma }$ trend with $1<\gamma <2$.

1. Introduction

Lithium-based batteries are undoubtedly among the most promising electrochemical systems for energy storage [1,2]. With their broad range of materials and versatile applications [2], they have been developed for over three decades to meet the needs of diverse sectors, including electronics, transportation, stationary energy storage, and medical devices [1,2,3,4,5,6]. Lithium-ion batteries (LiBs) operate on a ‘rocking chair’ principle, storing and releasing electrical energy through the reversible movement of lithium ions between the anode and cathode during charge and discharge cycles. Their performance is highly dependent on the chemistry of the materials used in the electrodes, particularly the anode and cathode. Variations in materials, such as the use of LiCoO₂ for the cathode, significantly influence factors like energy density, cycle life, and overall efficiency, making them suitable for 3C devices [7]. However, as cycling progresses, some lithium ions engage in secondary reactions, which reduce the overall capacity [8,9]. These undesired reactions can also consume active electrode materials, leading to the formation of passivation layers, specifically the solid electrolyte interphase (SEI) [10,11] on the anode and the cathode electrolyte interphase (CEI) [12,13] on the cathode, which consume active lithium and contribute to aging.

Aging mechanisms in lithium-ion batteries are strongly influenced by the nature of the electrode materials, particularly the composition and structure of both the cathode and anode. They involve complex interactions between chemical, mechanical, and thermal processes that degrade performance over time [14,15]. Mattieu Dubarry was the first to classify these processes into the following three categories [16]: the loss of active material (LAM), the loss of lithium inventory (LLI), and Conductivity Loss (CL) These are the critical contributors to fading capacity. For instance, LAM occurs due to the detachment or isolation of active materials from the conductive network, often caused by particle cracking, electrode swelling, or the dissolution of transition metals [8,17]. This reduces the effective amount of material available for electrochemical reactions. On the other hand, LLI results from the consumption of lithium ions in irreversible side reactions, such as the formation and growth of the solid electrolyte interphase (SEI) on the anode or lithium plating during charging. LLI leads to a reduction in the pool of lithium ions available for cycling, diminishing the overall capacity of the battery [8]. Dubarry et al. [16] reported that these degradation modes can be correlated, meaning that LLI can be influenced by LAM. This further complicates the identification of aging origins. Rui XIONG et al. [18] linked LLI and LAM to eleven battery aging effects in electrical terms occurring in cathode active materials, anode materials, and inactive materials. Furthermore, they connected these effects both to an increase in battery resistance and a decrease in its capacity.

Aging is a complex phenomenon that remains challenging to fully understand, despite the various physicochemical techniques used to study it [15]. Electrochemical impedance spectroscopy (EIS) is a valuable method for analyzing electrochemical phenomena, lithium-ion diffusion, the electrical double layer, charge transfer resistance R_ct, and polarization resistance R_P. It can also assess the state-of-health (SoH) of LiBs by tracking changes within the internal resistance of electrodes and interphases [19,20,21,22,23]. EIS is based on modeling the cell with an equivalent circuit model (ECM), which can be challenging when precise system characterization is required [24]. One critical factor often influencing the accuracy of EIS analysis is the thickness of the electrode, as this affects the diffusion pathways of ions. Ogihara et al. [25] demonstrated that thicker electrodes increase ionic resistance, leading to delayed electrochemical responses and a reduced power performance in LiBs. Many researchers have attempted to combine EIS with other methods to enhance accuracy [22]. Many studies have been conducted to investigate the aging mechanisms using EIS [20,21,22,26,27,28]. For example, Pastor-Fernández et al. [27] proved that the cell impedance in mid-frequencies is primarily affected by LLI mode, while, at the same time, LAM is reflected by an increase in $Z\left(\omega \right)$ in low frequencies.

Electrochemical noise measurement is another technique for inspecting the aging of LiBs. It is widely used to measure corrosion in materials. To our knowledge, there are very few articles on the noise measurement of Li-ion batteries in general and LiCoO₂ batteries in particular. In 1999, S. Martinet et al. [29] were the first to exploit electrochemical noise measurements of Li-ion (LiCoO₂) batteries by showing the detection of overcharge and the estimation of gas evolution rate during overcharge, which can be an important indicator for determining the state of health of batteries. E. A. Astafev [30] exploited the evolution of the electrochemical noise level of Li-ion batteries in discharge, i.e., at different values of SoC. He observed the presence of excess noise at low frequencies, which decreased with the relaxation time to reach a noise level corresponding to the real part of the measured impedance. The highest excess noise level was observed at 0% SoC. In another work [31], E.A. Astafev applied the method of measuring electrochemical noise in LiCoO₂ batteries during charge and discharge cycles to visualize the evolution of power spectral density levels during aging and compared these results with the spectra obtained by the method of electrochemical impedance spectroscopy. This result showed that the amplitude of electrochemical noise increased by a factor of 5.81 after 1300 cycles, while the real part of the impedance increased by 1.21 after the same number of cycles.

In this work, we apply three non-invasive approaches to study LiB aging. The first is EIS, in which we calculate the complex impedance using an optimized experimental protocol. The second is differential capacity analysis (DCA), which evaluates the derivative of cell capacity with respect to the terminal voltage in the absence of load resistance [32,33]. Lastly, we use electrochemical noise measurement (ECN) derived from voltage noise spectral density. Our primary objective from this work is improving the correlations between noise, capacity, and impedance measurements, aiming for a better understanding of LiB aging.

2. Materials and Methods

2.1. Materials

In this study, commercial coin cells composed of a LiCoO₂ cathode and a graphite-based anode, characterized by a nominal voltage of 3.6 V and a theoretical capacity of 45 mAh, were studied. Their maximum charging voltage and discharge cutoff were 4.2 V and 2.75 V, respectively. Important information given by the manufacturer on the cycling conditions of these batteries included the maximum C-rate in charge and discharge. The maximum C-rate for discharge was C/2 (2 h of discharge), and for charge, it was 1C (1 h of charge). The chemical composition of the positive electrode was deduced from the X-Ray Diffraction technique at room temperature by a Brucker D8 Advance diffractometer equipped with a Cu anode $(\lambda =1.5406 Å)$ and a LynxEye Detector, indicating LiCoO₂ as the cathode active material (see Figure 1).

2.2. Methods

Coin cell cycling was performed with a BCS-805 cycler from BioLogic. (Grenoble, France). The galvanostatic cycling with potential limitation (GCPL) protocol was adopted to charge and discharge the cells to 4.2 V and 2 V, respectively. Measurements were made at two different C-rates and at various state-of-charge (SOC) values on several coin cells. All the cells were cycled initially at C/20 for 40h to determine the residual capacity. Some of them were cycled at C/2 (4 h) and the others at 2C (1 h). Figure 2A shows the different discharge cycles of the commercial cells at the C/2 rate. After cycling, EIS measurements were carried out at room temperature after reaching the full-charging state, followed by ECN measurements. Figure 2B represents the evolution of the Nyquist diagram of the battery after C/2 cycles.

EIS was performed with the SP300 potentiostat–galvanostat from BioLogic (Grenoble, France) between 0.01 Hz and 7 MHz, with 10 points per decade. To ensure linear conditions, the AC signal magnitude was optimized to 10 mV. In these conditions, the duration of the measurement to record an EIS spectrum was about 35 min. The validity of the measurements was checked by the proposed quality indicators proposed by BioLogic [34,35], as well as the mathematical Kramers–Kronig test established by B. Boukamp [36].

The ECN setup used to measure the noise spectra is shown in Figure 3. The voltage signal delivered by the DUT (battery) was amplified by an EG&G 5184 low-noise voltage amplifier before being applied to the input of a Vector Signal Analyzer HP 89410A (Agilent, Longmont, CO, USA. Typically, Li-ion coin cell impedance is less than 1 Ω for frequencies below 1 MHz. Thus, the sample noise source can be lower than the amplifier’s one. Then, we performed a cross-correlation between the pre-amplified signals from the sample along two parallel channels. This allowed us to measure a noise level equivalent to 2 Ω. This level corresponds to the detection threshold for the noise measurement, which we will represent as a dotted line on the noise measurement graphs. The Li-ion coin cells were placed in a holder connected directly to the input of the preamplifiers. The device and the preamplifiers were placed inside a shielded box. The frequency measurement range was 4 Hz–4 MHz. Note that electrochemical noise measurements were performed immediately after each cycle for cells that were cycled by 2C. Over the frequency range from 4 Hz to 1 MHz, the duration of a noise measurement was less than 3 min.

3. Results and Discussions

3.1. Electrochemical Impedance Spectroscopy

The complex impedance $Z^{*}=Z^{\prime }+i{Z}^{″}$ is measured at room temperature between 0.01 Hz and 7 MHz. Figure 4A presents the Nyquist diagram $-Z^{″}$ as a function of $Z^{\prime }$ with frequency as a parameter for a fresh cell. Different resistance values can be deduced from this diagram: the low-frequency resistance R_LF corresponds to the difference in Z’ values between 0.16 Hz and 1.6 Hz, whereas the medium-frequency resistance R_MF corresponds to the difference in Z’ values between 26 Hz and 86 Hz. The sum of these two resistances is called the polarization resistance R_P, so R_P = R_LF + R_MF. This is shown in Figure 4A along with the ohmic resistance R₀: it is well known that this resistance is mainly that of the electrolyte. The value of R₀ is much lower than that of R_P. Figure 4B shows the evolution of R₀, R_LF, and R_MF as a function of cycling at C/2 up to 200 cycles. The resistance R₀ remains constant during cycling, and, therefore, it can be deduced that the electrolyte does not age up to 200 cycles. On the other hand, R_LF increases almost linearly with cycling (R² = 0.96), which shows that the electrodes are aging. In the literature, it is acknowledged that aging is mainly due to the concentration of Li⁺ ions moving between both electrodes, causing mechanical damage to their crystallographic structure, as well as the consumption of electrode active materials (LAM) [26,28]. Since we are working with commercial Li-ion cells, this increase in R_LF can originate from a contribution to the aging of both electrodes during cycling at C/2. The resistance R_MF is constant throughout cycling, and can be attributed to the stabilization of the anode–electrolyte interface [26,37], commonly associated with the formation of the SEI. This stable behavior over 200 cycles serves as evidence of the high quality of these commercial cells. Figure 4C shows the evolution of the resistance R_p with cycling: a linear increase is observed with a value multiplied by 2.5 after 200 cycles. This is related mainly to the increase in R_LF resistance caused by LAM, as was explained above.

While this study employs an equivalent circuit model (ECM) to interpret EIS data and identify key degradation phenomena, it is important to note that physics-based models, such as the Newman pseudo two-dimensional (P2D) model, can provide deeper mechanistic insights [38]. Unlike ECMs, which offer empirical fits to observed behaviors, the Newman model accounts for spatial variations in lithium concentration, reaction kinetics, and transport processes within electrodes and electrolyte. Such models can more accurately capture degradation modes like lithium plating, SEI growth, and active material loss. However, they require detailed cell parameters and computational resources, which limit their practical application in commercial cell studies.

Another way to represent EIS measurements is by the distribution function of relaxation times (DRT), which is a complementary method to the electrochemical circuit model (ECM) [39]. This approach consists of transferring the data from the frequency domain to a spectrum of time constants $\left(\tau \right)$ using discretization [39,40,41,42,43,44,45] of the following equation:

$$Z\left(\omega \right)=R_{\infty }+{\int }_{-\infty }^{\infty }{\displaystyle \frac{\gamma \left(\tau \right)}{1+j\omega \tau }}\hspace{0.17em}dln(\tau )$$

where Z(ω) is the complex impedance, $R_{\infty } = Z\left(\omega \to \infty \right)$ is the high-frequency resistance, and γ(τ) is the DRT function. The chosen discretization function and regularization method are Gaussian with a shape factor of 0.5 and Tikhonov discretization with λ = 0.1.

Figure 5A shows the curves of the distribution function of relaxation time obtained using the DRTtools software developed by Ciuccislab [45] and their evolution during charging over 200 cycles at C/2. By using the deconvolution of EIS data, we identify two well-separated peaks, labeled τ_LF and τ_MF, referring to charge transfer reactions and SEI polarization, respectively. [26]. Figure 5B shows the evolution of τ_LF area throughout cycling.

As the number of cycles increases, the amplitude of the τ_LF peak increases, as does its area, which is equal to R_LF [39], and the peaks shift toward higher τ values. In contrast, the amplitude of the τ_MF peaks remains constant, as does their area, which is equal to R_MF; moreover, their positions do not change to a first approximation over the 200 cycles. No τ_HF values are identified with DRTtools because the high-frequency peak is masked by the overlapping medium-frequency peak τ_MF. This behavior can be explained by the nearly constant ohmic resistance observed in Figure 5B, which reflects the stability of the SEI, as mentioned above. On the other hand, during repeated charge/discharge cycling, the main DRT peak progressively increases in amplitude, indicating a higher diffusion resistance of lithium ions within the electrodes. As reported by Sohaib et al. [26] and confirmed by [28], this increase is primarily attributed to electrode degradation processes, including structural changes, particle fracture, and a loss of active material. Furthermore, the increased R_LF affects the peak position by shifting to higher relaxation times. This can be explained by the proportionality relationship between $\tau$ and resistance.

3.2. Capacity Measurements

Another electrical measurement used to characterize aging is capacity measurement. Figure 6A shows that the capacity Q decreases linearly with cycling: it declines from 45 mAh, a nominal value, to 34 mAh after 200 cycles, which is a decrease of about 24%. Figure 6B shows the evolution of the polarization resistance R_p as a function of capacity. We can clearly see a correlation between these two parameters with R² = 0.97. So, the capacity fading as the polarization resistance increases is linked, at first approximation, to the [14] combined effects of both LLI and LAM. However, as observed in the frequency deconvolution of the EIS measurements, only the low-frequency resistance changes significantly, indicating that LAM has a greater contribution to this degradation, as previously stated.

This correlation between capacity fading and polarization resistance can be further explored using electrochemical analyses based on derivatives, such as $dQ/dV$, the differential capacity analysis (DCA). It is also known as incremental capacity analysis (ICA), derived from the voltage response of the battery during charge/discharge cycles at a constant current. The derivation process gives curves with clear variations, making them straightforward to measure and compare. These variations are directly related to the material chemistry, providing critical thermodynamic information about its internal state [32,33,46]. Dubarry et al. [8] proposed an improved DCA method for analyzing the aging of Li-ion batteries. This approach involves tracking changes in battery capacity over time by performing $dQ/dV$ measurements at various C-rates and comparing the results to reference models.

Figure 7A shows the differential capacity $(dQ/dV)$ curves during charging as a function of voltage for cycles 2, 54, 93, 145, and 200 at C/2. After two cycles at C/2, two peaks are observed during charging, located at approximately 3.8 V and 3.9 V [47]. The progressive changes observed in these peaks reflect alterations in the electrochemical behavior of the battery due to aging [46,48]. The attenuation of the main peak at ~3.9 V is particularly significant, as it corresponds to a key lithiation/delithiation equilibrium of the LCO cathode. This reduction in peak intensity with cycling, as shown in Figure 7B, is commonly attributed to electrode degradation, SEI growth, and a loss of active material (LAM) at the cathode, which diminishes the number of redox-active sites contributing to the charge storage process [47,48]. Additionally, the shifting of peak positions toward higher voltages suggests a loss of lithium inventory (LLI), which induces electrode slippage and displaces the equilibrium potentials of electrodes in the full-cell configuration, causing an increase in cell impedance [48].

3.3. Electrochemical Noise Measurements

First, we try a fast cycle 2C on a battery. This 2C rate is high for the tested cell, because it is not designed to support such a high current value. In this first study, the objective is to observe the evolution of the noise level $S_V\left(f\right)$ caused by an unconventional cycling procedure. Figure 8A presents the results of the measurements obtained. The electrochemical noise measurements are first carried out on a fresh cell and then after various cycles at 2C. The excess noise level increases with the number of cycles from C200 to C800. The fresh cell curve is at the same level as the threshold line. The excess noise at low frequencies is due to the $1/f$ noise of the preamplifiers used for the measurement. This excess noise is, therefore, not significant. With rapid cycling, lithium ions move from the cathode to the anode and vice versa very quickly. As a result, this movement creates reactions between the moving lithium ions and the electrolyte layer, which produces gas evolution. Thus, the increase in the excess noise level $1/f^{\gamma }$ observed for the battery at cycle 800 is due to the fluctuation of the gases during discharge and charge phenomena [29]. Therefore, it can be said that ECN can be considered a characterization method to study the aging of Li-ion batteries in a degraded charge/discharge mode. Then, we study the evolution of the noise level of the cell according to the SOC at 2C after 100 cycles.

Figure 8B shows the evolution of the excess noise level at 10 Hz with increasing SOC values. A decrease in the noise level at 10 Hz of a factor of 300 is observed when the SOC increases from 20% to 100%.

We perform noise measurements as a function of relaxation time, with the aim of obtaining more information about the behavior of ECN under different C-rates. Figure 9A,B, respectively, show the evolution of ECN spectra during relaxation times after 50 cycles at 2C and after a cycle at C/2 on the same cell. After cycling, the noise spectrum shows excess noise in $1/f^{\gamma }$. As can be seen, this noise level gradually decreases to the level of the detection threshold of the noise measurement bench. The time to reach this threshold is longer for cycling at 2C than for cycling at C/2. Therefore, the applied current (C-rate) is dependent on the relaxation time. It seems that the relaxation phenomena in the ECN measurement corresponds to the diffusion of the electrode in the active material. Thus, over-concentrations or under-concentrations on the active electrodes are created during cycling, and they return to their quasi-equilibrium state after a certain relaxation time [49]. This study shows that it is necessary to perform noise measurements immediately after the end of cycling in order to obtain information on the aging of the cells using ECN measurement.

4. Conclusions and Perspectives

Electrochemical impedance spectroscopy and capacity and electrochemical noise measurements were performed on commercial LCO battery coin cells after cycling at different C-rates. With moderate cycling at C/2, gradual aging was highlighted up to 200 cycles from complex impedance and capacity measurements. This aging was attributed to the loss of active lithium in the cathode. It was also shown that with fast cycling at 2C, the excess noise level increased rapidly. Moreover, the excess noise level decreased with an increase in SOC values. To obtain information on aging by using the ECN method, we showed that the measurement must be made just after cycling.

In this study, we focused on Lithium Cobalt Oxide (LCO) due to its abundance and well-established performance in the lithium-ion battery market, particularly for 3C devices. Although the experiments were conducted at room temperature, it is important to note that LCO-based batteries, like those used in portable electronics and electric vehicles, often operate at elevated temperatures due to internal heat generation during cycling. Temperature can significantly influence electrochemical behavior, aging mechanisms, and the characteristics of electrochemical noise. Therefore, assessing the reliability and sensitivity of noise measurement techniques under various thermal conditions is essential.

The perspective is to extend this research to other chemistries, such as Nickel Manganese Cobalt (NMC) and Lithium Iron Phosphate (LFP), which are increasingly used in applications like electric vehicles (EVs) and energy storage systems (ESSs). By investigating noise measurements in these materials under realistic thermal and operational conditions, we aim to better understand their behavior and optimize their performance for these advanced applications.