The cells are built using Graphite (1506T) and NMC532 (Toda America), fabricated at the Cell Analysis, Modeling, and Prototyping (CAMP) Facility at Argonne National Laboratory. The cells were designed using two different electrode active material loadings (denoted as L_moderate and L_low), and were tested under various charge profiles. More details about the cell materials, designs, numberings, and charge profiles can be found in Supplementary Tables S1–S3 in Supporting Information 1.

The cells were tested using a MACCOR series 4000 Automated Test System at 30°C ± 1°C. During each life cycle, the cells were charged between 10 and 15 min with different charging protocols. All the cells were charged to 4.1 V, except in 2 cells lower cut-off voltages of 3.78 or 3.66 V were applied. Reference performance tests (RPTs) were conducted every 25–50 cycles initially, and every 100–125 cycles in the later stages over the course of aging. An RPT test includes a C/20 charge-discharge test between 3.0 and 4.1 V separated by 1 h rest time, followed by EIS measurement at selected RPTs. Before the EIS test, cells were charged to 3.8 V at C/1 and rested for 15 min. EIS was measured with an AC voltage amplitude of 10 mV over a frequency range of 500 kHz to 0.01 Hz. A Solartron 1287 potentiostat and analyzer (Model 1260) were used for EIS measurements. The cells were subjected to different numbers of aging cycles. The L_moderate cells were cycled to 450 cycles. The L_low cells went up to 600 cycles, except two of them were charged to a lower cut-off voltage and cycled to 1000 cycles. Selected cells were disassembled for secondary post-testing characterizations to determine predominant aging modes. Detailed information about charging protocols can be referred to Supplementary Table S2 in Supporting Information 1.

The EIS data collected are processed using the ECM approach as a comparison to the mathematical quick-fitting approach that will be discussed later in this article. An basic ECM contains electrical components, i.e., resistors and capacitors, to simulate bulk, surface-interphase, and diffusion behaviors (Westerhoff et al., 2016). The model used in this article, as shown in Figure 1A is based on the most widely-accepted LiB system with minimized circuit elements for practical impedance analysis (Choi et al., 2020; Iurilli et al., 2021). The bulk resistance (R_Ohm) is a combined resistant effect from current collector, electrode, electrolyte, and separator. The constant phase elements (CPEs) are used to simulate non-ideal capacitances of LiBs to make the model more accurate. The CPE_SEI and CPE_DL represent the capacitances of solid electrolyte interface (SEI) layer and double layer, respectively. R_SEI and R_CT represent the resistances of SEI layer and charge-transfer process, respectively. Warburg impedance describes diffusional effects of lithium-ion on the host material. Figure 1B shows a comparison between an experimental Nyquist plot from one of the graphite/NMC532 cells at 600 cycle and the fitting results. The result shows good match between measured data and fitted data. More discussion about the fitting approach, mathematical expressions, and quality of fitting can be found in Supporting Information 2.

A typical Nyquist plot of the graphite/NMC532 cells in this study is shown in Figure 2. The Nyquist plot consists of two arcs located at higher (frequency range 10⁵—10³ Hz, referred as the first arc) and lower frequency domains (frequency range 10³–1 Hz, referred as the second arc), followed by a tail. This type of EIS curve is common in LiBs (Choi et al., 2020; Iurilli et al., 2021). The impedance arc at higher frequency comes from the solid electrolyte interface (SEI) layer (R_SEI), which is related to the resistance of anode materials and SEI layer. The arc at lower frequency is the response from charge transfer (R_CT), which is linked to the kinetics of electrochemical reactions. R_CT is heavily dependent on material properties such as phase transition, bandgap structure, particle integrity and size, and surface coating, making it an effective indicator to interpret reaction mechanisms in a cell. The longer tail following the arcs originates from Warburg diffusional effects.

In our approach, the arcs in the EIS data (x, y files) are fitted directly to partial circles as a mathematical proxy to describe the shape of the Nyquist plot. The fitting algorithm is built using Python. We referenced an optimized least squares approach under the scipy package (Virtanen et al., 2020) to search the least square circle fit for the data. The input data range is changed along with the datapoints in the arc to determine the best fits and uncertainties. Detailed information regarding the fitting process and methods are discussed in Supporting Information 3. There are several mathematical features that can be extracted from the least square circle fitting, including the chord lengths of the semi-arcs, and intersection point with -Z′′ = 0. The chord length, determined by the radius and center of the fitted circle, will be an approximation for R_SEI (chord length 1) and R_CT (chord length 2). The -Z″ intersection represent the R_Ohm. In the following demonstrations, the chord length will be compared to the resistance obtained using ECM fitting.

The major aging modes of the cells in this study align with loss of Li inventory (LLI) and loss of active materials in the cathode (LAM_PE). The aging behaviors were previously identified using various non-destructive (e.g., incremental capacity (IC) analysis) and destructive methods (e.g., optical and electron microscopy, ex situ X-ray scattering) (Paul et al., 2021a; Tanim et al., 2021a; Chinnam et al., 2021; Tanim et al., 2022). LLI is confirmed using both incremental capacity (IC) analysis (Dubarry et al., 2012) and disassembly of cell at the end of lifetime. The diagnosis of LAM_PE is based on SEM images showing secondary particle cracking and on half-cells assembled from cathodes harvested after cycling, as well as IC analysis (Tanim et al., 2021a). Loss of active materials in the anode (LAM_NE) was not included in the discussion because aging in the anode is minor.

IC analysis was performed to quantify the amounts of LLI and LAM_PE of representative L_moderate and L_low cells at the end of cycling life, and the amounts of LAM_PE and LLI are summarized in Figure 3. The primary aging behavior can be correlated with the design of the cells and charging rates. In the L_low cases, cathode cracking induced LAM_PE is the most significant aging mode (Tanim et al., 2021a) because of its higher charge acceptance and cathode utilization, causing more stress during cycling. When the charging cutoff voltage is reduced to 3.78 or 3.66 V, the amount of cracking and thus LAM_PE is reduced even at 9C rate. In contrast, the L_moderate series, in which the anode loading is higher, the dominant aging behavior becomes higher in LLI with less amount of LAM_PE (Chinnam et al., 2021). For L_moderate cells cycled with greater than 4.5C protocol, the cells suffer from Li plating, a severe form of LLI; whereas those cycled at 4C only exhibit minor LLI caused by SEI growth (Paul et al., 2021a; Paul et al., 2021b). This phenomenon is attributed to more severe electrolyte depletion at the anode during high C-rate, causing sluggish Li ion transport.

EIS data of five representative cells are selected based on their dominant aging modes (LLI or LAM_PE) and the percentage of LAM_PE and LLI are listed in Table 1. The cells and aging behaviors include:

• LAM_PE dominated (L_low 1C and 9C)

The EIS as a function of cycle numbers are presented in Figure 4. Across the two electrode loadings and various cycling conditions, one common feature is that the first arc grows steadily over the course of aging, while the second arc evolves distinctively with higher or lower amount of LAM_PE. As shown in Figures 4A, B, which are the high LAM_PE cases, the second arc not only moves to the right, but the size also grows significantly at 600 cycles (as marked by the arrows). In contrast, when a lower cutoff voltage of (3.78 V) instead of 4.1 V is applied to the cell during charging, the second arc does not grow obviously even after 1000 cycles (Figure 4C). The link between growth of the second arc and LAM_PE can be further rationalized by the behavior in Figures 4D, E. Both cells exhibit low amount of LAM_PE and higher LLI, and the latter is caused by two different mechanisms, namely SEI-growth and Li plating. 4(d) ages through SEI-growth, a mild form of LLI, in which the capacity fade remains below 10%. The case in 4(e) suffered from heavy Li plating due to the interplay between a higher C-rate and greater anode thickness. In this case, Li plating causes ∼15% of capacity fade in the initial 100 cycles and close to ∼20% at the end of 450 cycles. Whether LLI is severe or not, the second arc in Figures 4D, E evolve similarly and does not exhibit significant growth at later stages of aging. Therefore, the growth of the second arc can be exclusively attributed to LAM_PE instead of LLI. From an angle of electrochemical reactions, as LAM_PE occurs in the form of cathode cracking, the overpotential for charge transfer reactions increases and therefore leads to an increased R_CT For this reason, R_CT is concluded to be exclusively correlated to LAM_PE.

To validate our EIS fitting approach’s capability in catching the trend of aging, the fitting results are compared against the resistance values obtained using ECM. In the quick-fitting approach, the Zʹ-intersection and chord lengths are used as a proxy of resistances, as shown in Figure 5. The progression of Zʹ-intersection and cord lengths of the first and the second arc are consistent with the growth trend of R_Ohm, R_SEI and R_CT, respectively. Whether the cells are low or high in LAM_PE, the first chord length and R_SEI grows steadily along with aging cycles (red trends). In the high LAM_PE cases, the second chord length and R_CT stay around the same level before 225 cycles but increase almost by four times from 225 to 600 cycles (blue trends). In contrast, for the LAM_PE cells, the chord length or R_CT does not exhibit very significant growth trends. The trends in the 1^st and 2^nd chord lengths are also consistent with the percentages of LLI and LAM_PE, respectively (Chinnam et al., 2021).

To investigate the mathematical correlation between the geometric metrices and resistances, R_Ohm, R_SEI, and R_CT are plotted against their corresponding features for all of the EIS data (16 cells in total) taken at different cycle numbers. As shown in Figures 6A, B, The Zʹ -intersection and R_Ohm exhibits a proportional trend (R² = 0.949), as indicated by the regression results (see Supplementary Figure S6 in Supporting information 4). Similar relationship exists between the 1^st chord length and R_SEI (R² = 0.989). However, the correlation between 2^nd chord length and R_CT in Figure 6C is not as obvious (R² = 0.667), especially when 2^nd chord length or R_CT < 0.6 Ω cm². This is due to the ill-defined second arcs especially at early stages of aging (less than 125 cycles), where the arcs are relatively flat due to insignificant LAM_PE. Most of the fitted chord lengths fall in a range between 0.3 and 0.5 Ω cm² compared to the corresponding R_CT ranges roughly at the same scale between 0.2 and 0.4 Ω cm². There also exists a few outliers as marked by black arrows in Figure 6C from early stages of aging at 0 or 25 cycles, where the shape of second arc is not yet well developed. As the arcs developed more defined shapes in later stages of aging (chord length >0.5 Ω cm² or R_CT > 0.4 Ω cm²) the linear correlation between the chord length and R_CT can be seen more clearly. The consistency between the trends of geometric metrics and the resistances allows our EIS-fitting algorithm to quickly gauge the growth trend of resistance without the need of sophisticated ECM analysis. As discussed above, whether the arc is well-defined or not will be a limitation of the quick-fitting approach estimating the resistance values.