THE COMPARISON OF ELECTROCHEMICAL IMPEDANCE BEHAVIORS OF LITHIUM-ION AND NICKEL-METAL HYDRIDE BATTERIES AT DIFFERENT STATE-OF-CHARGE CONDITIONS

In this study, impedance responses of a lithium-ion battery and a nickel metal-hydride battery were analyzed as a function of different state of charge conditions. The physical parameters of these widely used rechargeable batteries have been extracted through an equivalent circuit model by fitting impedance data. The fit was excellent. The regressed parameters explain the battery physics and dynamics well. Results show that the developed model could be utilized for the broadly used rechargeable batteries at their operational potentials. The electrochemical impedance spectroscopy is a beneficial technique to provide information regarding battery life, battery performance, and state of health of a battery.


Introduction
In recent years, to reduce the dependence on conventional energy sources, electric vehicles and hybrid electric vehicles are considered as the most popular technologies. These technologies also provide a solution to the environmental problems caused by transportation (Jaguemont, Boulon, & Dube, 2016a). The energy storage systems, especially batteries, are the most significant part of these technological systems (Jaguemont, Boulon, & Dube, 2016b). The applications of the battery rank among the most important systems of the world. Batteries are used in mobile phones, portable devices, hybrid and electric vehicles, and modern aircrafts. The types of the application determine battery dimension, battery capacity, power and energy * Sorumlu yazar; e-posta : esalim@ogu.edu.tr density (Fleischer, Waag, Heyn, & Sauer, 2014). It is important to recognize the battery capacity and its power density to conserve the battery performance during the operation and to get a longer cell life (Galeotti, Cinà, Giammanco, Cordiner, & Di Carlo, 2015).
A battery package typically consists of a negative electrode, electrolyte, a separator, current collectors, and a positive electrode. Several processes such as electrochemical reactions and mass transport occur when the battery is in operation. These processes determine the battery performance and remaining useful life, which can be considered as state of health of the battery (Leng, Wei, Tan, & Yazami, 2017). Different kinds of methods were developed by the scientists and researchers to understand these processes in the battery (Ecker et al., 2015). One of these methods is electrochemical impedance spectroscopy (EIS) that is widely used to specify electrochemical processes and to determine their effects (Xie, Li, & Yuan, 2014). EIS is a measurement technique based on alternating potential or current at various frequencies. It is possible to evaluate the physical and chemical properties in a battery without any destruction by using EIS (Ecker et al., 2015;Galeotti et al., 2015;Huang, Li, Liaw, & Zhang, 2016). Impedance analysis could be made by plotting different types of diagnostic graphs. There are two main plots, namely Nyquist plot and Bode plot. These plots are used to provide valuable information on the key performance parameters of a battery. Nyquist plots of batteries generally display a vertical line at high frequencies, semi-circles or depressed semi-circles at mid-frequencies, and a slopped line or curve at low frequencies (Raijmakers, Danilov, van Lammeren, Lammers, & Notten, 2014). These frequency regions of the Nyquist plot provide information for ohmic resistance at high frequencies, charge transfer resistance and double layer capacitance at midfrequencies, diffusion of the ions through electrolyte/electrode interphase at low frequencies (Itagaki, Honda, Hoshi, & Shitanda, 2015). To obtain battery parameters, a model that simulates characteristics of a battery was applied to the EIS data (Castano-Solis, Serrano-Jimenez, Gauchia, & Sanz, 2017). The battery models are designed as an equivalent circuit consisting of various kinds of elements such as electrolyte resistances, capacitances, inductances, charge transfer resistances, constant phase elements, Warburg elements, and so on. The configuration of the elements in the equivalent circuit influences the accuracy and stability of the model (Leng et al., 2017).
The impact of connecting cells in parallel on the energy imbalance was investigated by Bruen and Marco (Bruen & Marco, 2016). They used a validated model against EIS data for four 3 Ah 18650 lithium ion cells. Gong et al. studied the characteristics of battery packs with parallel-connected lithium-ion battery cells (Gong, Xiong, & Mi, 2015). Various battery packs were built with a group of degraded lithium-ion cells to explore the effect of the cell consistency in parallel-connected cells. This was achieved through the physical model simulating the operation of the battery packs. In another study, Ecker et al. studied on 7.5 Ah lithium-ion cell to determine the physical parameters through a electrochemical model (Ecker et al., 2015). The measured parameters were compared with the model results. In a different study, Hang et al. measured the impedance of the lithium-ion battery with Li4Ti5O12 anode at different states of charge and temperatures (Hang et al., 2013). They determined the reason of the capacity fade of the lithium-ion battery by using equivalent circuit model. They showed that the equivalent circuit model could be used for interpretation of the performance parameters of the battery. Gomez et al. proposed an equivalent circuit model for a Sony commercial Li-ion polymer battery at several states of charges (Gomez, Nelson, Kalu, Weatherspoon, & Zheng, 2011). Their model had a quite number of parameters including multiple double layer capacitances, charge transfer resistances, an inductance, a Warburg impedance, and an intercalation capacitance to fit the EIS data they collected. Cruz et al. analyzed the impedance spectroscopy of nickel metal hydride (Ni-MH) batteries at different SoC with a proposed equivalent circuit (Cruz-Manzo, Greenwood, & Chen, 2017). They model impedance response based on fundamental electrochemical theories and diffusion mechanisms. Nelatury and Singh suggested two different circuits to fit Ni-MH battery impedance (Nelatury & Singh, 2004). They inserted a Warburg element to the equivalent circuit model when SoC the battery gets lower. In a previous work, Morali and Erol analyzed and modeled the impedance response of commercial Li-ion and Ni-MH batteries at the same cell potential (Moralı & Erol, 2020). A number of models have been developed to characterize and simulate lithium-ion and nickel metal hydride cells. These models have already described the battery systems. However, they have been only valid for the modelled system. Further equivalent circuits can be improved for a recognized model simulating every types of battery.
The objective of this study is to introduce an effective model appropriate for through analysis of performance parameters of both Li-ion cell and Ni-MH battery. This was achieved through EIS method that was applied to commercially available 18650 Li-ion cells and 6HR61 Ni-MH cells at various SoC conditions. The contribution of this study is to extend the existing literature in terms of both simulation method and experimental data.

Materials and Methods
Electrochemical experiments were performed by a potentiostat on a 18650 Li-ion and a 6HR61 Ni-MH battery cells.

Materials
Experiments were carried out on commercial cylindrical 18650 lithium-ion cells (diameter: 18 mm, length: 65 mm, weight: 47 g average, capacity: 3000 mAh, Sony VTC6, Sony Energy, Japan) and commercial rectangular 6HR61 Ni-MH cells (horizontal length: 24.5 mm, vertical length: 46.5 mm, thickness: 17.5 mm, typical volume: 22.8 cm 3 , weight: 42 g average, capacity: 170 mAh, Duracell 6HR61, Duracell batteries, USA). The tested 18650 Li-ion cells exhibit a working potential between 3.0-4.2 V with a nominal voltage of 3.6V. The vendor supplies a potential range between 7.0-9.2 V for the 6HR61 Ni-MH cell. The tested 6HR61 Ni-MH cell exhibits a nominal potential of 8.4 V. The state of charge of 18650 Li-ion cell and 6HR61 Ni-MH battery was defined as 100% when their potentials reach 4.2 V and 9.2 V, respectively.

Instruments
All of the electrochemical experiments and impedance measurements were conducted by using a Gamry Reference 3000 Potentiostat/Galvanostat/ZRA from Gamry Instruments, USA. The cylindrical battery holder (Gamry Instruments) for 18650 size cells was used to eliminate additional impedances due to cable connections. Both cells were also placed in a commercial Gamry Faraday cage to prevent environmental magnetic effects on any electrochemical measurements.

Methods
In this study, research and publication ethics were followed. It is stated in this article that no legal/special permission is required. The state of charge values were calculated based on the integration of time and current, i.e., 0%-100% at the potential window of 3.0 V-4.2 V and 7.0 V-9.2 V for Li-ion cell and NiMH battery, respectively. Prior to the impedance measurements, 18650 Li-ion cell was charged to 4.2 V, and 6HR61 Ni-MH battery was charged to 9.2 V to reach at their 100% state of charge. The batteries were slowly discharged to reach intended SoC values (75%, 50%, 25%, and 0%) after the impedance measurement at fully charged condition. A potentiostatic EIS was conducted from 10 kHz to 10 mHz using a 10 mV ac sinusoidal perturbation at the open circuit potential (OCP) of 18650 Li-ion cell. A galvanostatic EIS measurement was performed on 6HR61 Ni-MH cell in galvanostatic mode from 10 kHz to 10 mHz. Here, the applied for perturbation current was 10 mA. After obtaining impedance data, impedance responses were examined with an equivalent circuit model to extract performance parameters of the batteries. The least-squares method and the Simplex algorithm were employed by using Echem Analyst Software that is connected to the potentiostat.
All of the experiments were performed at room temperature to minimize uncertainty of the results. Gamry software was also activated to reduce errors between the repeated experimental runs.

Results
The impedance responses of the 18650 Li-ion cell and 6HR61 Ni-MH cell are presented for 100% state of charge.

Impedance analysis
To extract the performance parameters of both the 18650 Li-ion cell and 6HR61 Ni-MH battery, the impedance analyses were performed in the frequency range of 100 kHz-10 mHz. The impedance response in Nyquist format for the 18650 Li-ion cell at different SoC is given in Fig. 1. Nyquist diagram shows the negative imaginary part of the impedance as a function of the real part of the impedance of a battery in a frequency range. The distinct electrochemical processes can be indicated by using Nyquist plot (Galeotti et al., 2015). An inductive behavior for 18650 Li-ion cell was determined in the frequency range of 100-2.5 kHz. The inductive behavior, the positive part of the imaginary impedance in Fig. 1, is attributed to result from the interconnections of the cell such as connecting lines and cables (Westerhoff, Kurbach, Lienesch, & Kurrat, 2016). To obtain the data only from the characteristics of a Li-ion cell, the impedance corresponding to 3 kHz can be selected as the highest frequency for the fitting. In the moderate frequency range (2.5 kHz-0.3 Hz), two capacitive loops were observed in Fig. 1. These capacitive loops correspond to the electrochemical reactions occurring in the cell. The first capacitive loop in the higher frequency range of the moderate frequency range indicates the reactions that occur at the negative electrode. The second loop in the lower frequency range corresponds the electrochemical reactions at the positive electrode. The capacitive loops also indicate the formation of the double layer capacitances at the electrolyte/electrode interface and correspond to the charge-transfer processes.
The reactions between Li + ions and the constituents in the electrolyte can cause formation of a layer on the negative electrode when the Li-ion cell is in the charge mode. This layer is called solid-electrolyte interphase (SEI). Thus, the charge transfer process can occur both from the electrolyte into the SEI and from the SEI into the electrodes. This additional layer on the negative electrode can cause an increase in the charge transfer resistance of the anode. The SEI layer becomes thicker, and the resistance gets larger while the amount of battery cycle increases. After cycling the battery, the higher charge transfer resistance indicates that the first loop is related to the negative electrode. The lowest frequency region of the impedance curve corresponds to mass transfer of lithium ions between the electrodes and the electrolyte. The slope of the straight line in the lowest frequency region reflects the behavior of the diffusion of ions in the electrode. If the angle between the straight line and the x-axis is 45°, showing that the value of the slope is 1, the diffusion mechanism of the ions in the electrode is given by the Fick's 2 nd law of diffusion. The impedance representation in Nyquist format for 6HR61 Ni-MH at different SoC is shown in Fig. 2. The impedance responses in the higher frequency region between 100 kHz-30 kHz can be attributed to the inductive behavior originated from the interconnections and cables of the potentiostat. The comparison of the impedance responses of both cells showed that the 6HR61 battery exhibited less inductive behavior in the selected frequency range. This showed that the frequency range between 100 kHz-10 mHz is more suitable for the battery characteristics of the 6HR61 battery. The Nyquist plot in Fig. 2 demonstrates that the impedance of the Ni-MH battery also consists of two capacitive loops as of the Li-ion in the frequency range of 30 kHz-1 Hz. To be consistent with the Li-ion battery impedance behavior, the first loop between 30 kHz-100 Hz is assumed as corresponding to the charge transfer process occurring on the negative electrode that is the oxidation reaction of hydrogen in the negative electrode. The second loop between 100 Hz-1 Hz indicated the electrochemical reaction taking place at positive electrode representing the reduction reaction of NiOOH occurring at the interface of the electrolyte and positive electrode. When the shape of these two loops is compared, it can be deduced that the low frequency loop is not a perfect semicircle. The depressed shape of this loop reflects the heterogeneity of current distribution at the positive electrode surface. The similar assumption was made for the impedance response corresponding to the reaction of the positive electrode in the Li-ion cell. The low frequency impedance can be attributed to the mass transfer of the hydride ions in the cathode. The angle between the straight line and the x-axis at different %SoC is between 45°-48°. This angle range indicated that the diffusion of hydride ions into the cathode could be thought as it obeys the Fick's second law.
(a) (b) Figure 2. Impedance response of 6HR61 Ni-MH cell at different % SoC: a) complete spectra and b) high frequency values corresponding to the box in (a).
The differences between the impedance responses of these two batteries show distinct electrochemical reaction mechanisms. As shown in Fig. 1 and 2, the comparison of the impedance responses also showed that the impedance of 6HR61 Ni-MH battery is much greater than that of 18650 Li-ion cell. Present-day technologies enable us high energy density power sources and numerous processes require high energy density energy storage materials. The impedance response of the batteries can provide an insight for the energy density of these energy storage materials. The higher impedance response of the Ni-MH battery implies its lower energy density. This result is in agreement with the energy characteristics of the preferred power sources.

Mathematical Modeling
Mathematical models are used to describe the characteristics of batteries. These models compose of simple electrical elements. In this section, the equivalent circuit model of the batteries is presented to extract battery dynamics features from the impedance responses.
Equivalent circuit models generally comprise electrical elements such as inductance, resistances, and capacitances. The employed equivalent circuit model for the batteries is shown in Figure 3. The developed equivalent circuit model contains an electrolyte resistance Re, a charge transfer resistance for negative electrode Rt,a, a double layer capacitance for anode Cdl,a, a constant phase element for cathode CPEc (Qc, αc), a charge transfer resistance Rt,c and an expression for diffusion in positive electrode Zw,c (Warburg impedance). In this circuit, the impedance response of the resistances of both electrolyte and separator are indicated by the ohmic resistance Re. The two parallel elements Rt,a and Cdl,a represent the electrochemical reactions taking place at the negative electrode/electrolyte interface. The constant phase element (CPE) describes the capacity between the electrolyte and the cathode. In the cathode side of the electric circuit, the charge transfer resistance Rt,c connected with the Zw,c serially are parallel to the CPE. Rt,c represents the resistance of the electrochemical reactions taking place at the electrolyte/positive electrode interface. The CPE presented in Figure 3 indicated by two terms, Qc and αc. Qc is the CPE coefficient associated with the double layer capacitance of the positive electrode. αc is the CPE exponent that is highly related to a degree of the surface heterogeneity of the electrode. The diffusion of the ions inside the positive electrode is shown by the Zw,c in the equivalent circuit model (Orazem & Tribollet, 2017).
The battery impedance (Z) consists of the main components of the battery, anode (Za), electrolyte (Re) and cathode (Zc) impedances. Since these impedances are connected in series, the Z value is expressed as the sum of these impedances in Equation 1.
The anodic impedance Za in Equation 1 is expressed in Equation 2 as the equivalent impedance of the circuit elements shown in the anode region in Fig. 3.
The cathodic impedance in Equation 1 is shown in Equation 3, where Zc is the impedance of the circuit elements shown in the cathode region in Fig. 3.
In equation 4, w,c Z is the Warburg impedance and is defined as where w,c A is Warburg impedance coefficient and is simply considered as a resistance.
The regression results obtained from equation 1 and the impedance data presented in Fig. 1 are shown in Fig. 4. The regression results obtained from equation 1 and the impedance data presented in Fig. 2 are shown in Fig. 5. The consistency of the model to the impedance responses for both 18650 Li-ion cell and 6HR61 Ni-MH battery is excellent as shown from Fig. 4 and 5. The impedance responses in Fig. 1 and Fig. 2 were fitted to the developed model in Fig. 3 by the Simplex method. The regressed parameters of the model are presented in Table 1.  Table 1: a) complete spectra and b) low impedance values corresponding to the box in (a). NiMH battery, the anodic resistance was higher than the cathodic resistance when the state-of-charge of the battery was at 100%. This implies that there was no SEI film formation on the anodes or the thickness of this layer was low. It proves that 6HR61 battery are fresh and was not cycled adequate quantity to form the SEI layer.
For all the %SoC levels, the anodic resistance, the electrolyte resistance and the cathodic resistance for the 6HR61 Ni-MH were higher than those of the 18650 Liion cell. The higher ohmic resistance of the Ni-MH battery than that of Li-ion cell indicated that the discharging capacity and the cycling performance was lower than those of the Li-ion cell. Compared with the 6HR61 NiMH battery, the 18650 Li-ion cell had a lower ohmic resistance over the SoC range. Additionally, the lower ohmic resistance of the Li-ion cell was indicative of the higher electrolyte performance. The value of CPE exponent, α, varies between 0.5 and 1 for the electrochemical systems. This parameter for the Li-ion cell is closer to 1 that of the Ni-MH battery. This implies that the current distribution is more uniform and the roughness of the electrode surface is lower in the Li-ion battery. It also indicates that the pores in the cathode exhibited more uniform pore structure. The CPE coefficient, Qc, is highly related to the capacity of a battery. In other words, the higher value of Qc represents the higher adsorption ability of the electrode surface for the mobile ions in the electrolyte. Therefore, the Li-ion cell revealed more adsorption capability over the potential range than that of the Ni-MH. The anodic charge transfer resistance of the 18650 Li-ion cell increased with the SoC increasing. This result could be attributed to the thickening SEI layers of the anode resulting higher resistance of Li+ insertion into the electrode. In contrast to the anodic resistance, the cathodic charge transfer resistance of 18650 Li-ion battery decreased in more cases at higher SoC. The cathodic charge transfer resistance of the 6HR61 NiMH battery decreased at higher SoC. However, the dependence of the anodic charge transfer resistance on the SoC could not be observed. The results in Table 1 showed that the cathodic and electrolyte resistances at 0% SoC (low cut-off potential) and 100% SoC (high cutoff potential), reflecting large potential polarization at low and high potentials. The results indicated that the CPE exponent (α) of Li-ion cell increased at higher SoC. Additionally, the higher SoC could provide a uniformly distributed current that is demonstrated as a higher cathodic CPE exponent. The formed SEI layer may provide a uniform electrode surface leading higher α value. Not like the 18650 Li-ion cell, the SoC dependence for the cathodic CPE exponent of 6HR61 NiMH cell was not observed. This could be attributed to the electrolyte solvents and electrode material in the 18650 Li-ion cell different from those in 6HR61 NiMH cell. Although the explanations and fitting models were not exactly conclusive, it can be deduced that the diffusion of the ions in the solid electrode in the low-frequency region was influenced by the electrode structure and composition.
The interpretation of all the results indicates that the Liion cell has many advantages over the Ni-MH battery in terms of performance and capacity.

Conclusion
The electrochemical impedance analysis was performed on the two rechargeable batteries. An equivalent circuit model was developed that is suitable for both batteries. This study provides useful guides for the interpretation of the impedance responses of both 18650 Li-ion cell and the 6HR61 Ni-MH battery. The applied equivalent circuit analysis can be used for modeling both Li-ion cell and 6HR61 Ni-MH battery, regardless of the chemistry of the cells. The main contribution of this study is that the model can be used to represent the impedance responses and to extract the physically meaningful parameters for Li-ion and Ni-MH batteries throughout operational potential and SoC.

Author Contributions
Uğur Moralı proposed the concept, designed the experiment, carried out the electrochemical work, analyzed the electrochemical data, wrote the manuscript, drew the figures, and discussed the results. Salim Erol jointly conceptualized the paper, developed the methodology, carried out the electrochemical experiments, performed data analysis, wrote the manuscript, discussed the results and reviewed the manuscript.