Revealing the Quantitative Connection between Electrode-level Cracks and Capacity Fading of Silicon Electrodes in Lithium-ion Battery

Abstract

For the coupling problems of lithium-ion batteries, a key issue at hand is that it is still unclear which mechanical failures can cause degradation and how, which is particularly salient at the electrode level. In this work, the correlation between electrode-level cracks and cycling capacity of silicon electrodes is investigated. Unexpectedly, for cracks in active layers, the capacity decreases with the increase of crack width, while the connection of other crack features to the capacity is weaker or even absent. Meanwhile, the modeling results, however, suggest that the increase in crack width cannot directly cause the capacity fading. To explain these results, the relationship between electrode debonding and active layer crack opening is also described quantitatively. By combining the debonding model and the porous electrode model, the connection between crack widths of active layers and capacity fading is clarified, and accurate predictions are obtained. These results indicate that the easily measurable width of active layer cracks is qualified to evaluate degradation, while the electrode debonding is in fact the direct cause of capacity fading. The findings in this work provide a more precise understanding of the degradation mechanism in lithium-ion battery electrodes.

1. Introduction

Lithium-ion batteries (LIBs) are currently one of the most important energy storage technologies and are the key component of various electronic devices, electric vehicles, and large-scale energy storage devices.^1,2 As a typical complex system problem, the aging behavior in LIBs still has much to be investigated.² Qualitatively, the coupled mechanical-electrochemical degradation behavior has been regarded as one of the key mechanisms of LIB failure.^3,4 However, potentially, all types of mechanical failure of the components from the particle level to the cell level can relate to the fading of battery performance. The correspondence between specific types of mechanical failure and the resulting degradation in electrochemical performance is still not clearly understood.⁵ This has become one of the biggest obstacles in investigating the coupled mechanical-electrochemical problem of LIBs.³

In particular, the electrode-level fracture behavior in composite electrodes, which has been widely observed in many different systems, is commonly considered in general terms to be related to battery fading. Most of the related studies roughly connected the crack pattern of the active layer with the electrochemical performance.^6–11 For instance, the qualitative evolution of widths,^12–14 numbers,^15–18 depths,^19,20 opening areas,²¹ and lengths^12,14 of electrode-level cracks has been employed to characterize the structural stability in composite electrodes, particularly in high-capacity ones where mechanical failure is often more severe. However, these delicate but divergent works still did not quantify electrode-level cracks, let alone establish a precise link between cracks and battery performance at the electrode level.

Recently, efforts have been made to more precisely describe in-plane cracks of active layers, which are easy to observe. For instance, Su et al.²² and He et al.²³ quantitatively extracted the width and the depth of the cracks in the active layer of composite electrodes, respectively, to describe the electrode structure stability, while Kumberg et al.²⁴ and Li et al.²⁵ extracted the opening area of the cracks. However, even if these works quantify the electrode-level cracks, they still cannot answer the relationship between mechanical damage and electrochemical performance fading. It is also worth mentioning that not all types of electrode-level cracks are easily observable and quantifiable. For example, it has been widely acknowledged that the electrode-level debonding is a key factor affecting battery performance,²⁶ but such a phenomenon of debonding between the active layer and the current collector is commonly invisible and difficult to detect directly.^27,28 Meanwhile, it should be emphasized that similar mud crack problems in classic fracture/damage mechanics commonly focus on the crack density as well,^29,30 although this quantity has been rarely mentioned in the field of LIBs. In any case, it is evident that there is a problem with non-standard and inconsistent descriptions of electrode-level cracks in LIBs.

A major cause for the inconsistencies in the physical quantities describing electrode-level cracks is the lack of sufficient understanding of the degradation mechanisms connecting electrode cracking to battery fading. In general, it is known that electrode-level cracks can qualitatively and potentially correspond to many different degradation mechanisms, e.g., the loss of active materials, the block of electron and ion transport paths, the newly exposed surfaces, and extra solid electrolyte interphase (SEI) formation, etc.³ However, investigations in this field are generally inconclusive and muddled, and further clarification is crucial.^1,3

In this paper, the silicon composite electrode, which generally suffers from extremely severe electrode-level mechanical failure due to the large volume expansion of silicon, is selected to demonstrate the connection between electrode-level crack evolution and capacity fading. By processing the scanning electron microscope (SEM) images, features of in-plane cracks in active layers, such as the density, opening area, and width, are first captured. The relationship between these features and cycling capacity is analyzed. Furthermore, by combining the electrode debonding model and the porous electrode model, the mechanism of the electrode-level cracks affecting electrochemical performance is discussed.

2. Experimental Section

2.1 Electrode preparation

Silicon composite electrodes were made by mixing 50 wt% silicon powders (size 100 nm, Alorich), 25 wt% carbon nanotubes (CNT, TCI), and 25 wt% sodium alginate (SA, Alorich) to form a slurry, while deionized water was used as the solvent. This formula ensures a relatively stable cycling performance of silicon electrodes.^17,31 Meanwhile, electrode-level cracks can be constantly observed in electrodes of this formula.^17,31 The slurry was stirred by a mixer (ARE-310, Thinky) for 2.5 h, and the mixed slurry was cast onto a battery-grade Cu foil (12 µm thickness, Kejing) using a doctor blade (Kejing). The coated electrode was then dried in a vacuum drying oven (Shanghai Feiyue) at 70 °C for 12 h. Finally, the electrode was punched to roundness with a diameter of 10 mm and further dried for 12 h in a vacuum chamber (MIKROUNA). The average thickness and mass loading of the prepared electrodes were 24–26 µm and 0.56–0.59 mg/cm², respectively. The silicon electrode, separator (Celgard 2400), and lithium disk (thickness of 1 mm, Sigma-Aldrich) were assembled into CR2032 coin cells in an argon-filled glovebox (H₂O <0.1 ppm, O₂ <0.1 ppm, MIKROUNA). The solution of 1 M LiPF₆ dissolving in ethylene carbonate/ethyl methyl carbonate (EC/EMC, 3 : 7 by volume) with 10 % fluoroethylene carbonate (FEC) was employed as the electrolyte, and each cell used 90 µL of electrolyte.

2.2 Cycling tests

Electrochemical tests were performed by a charge-discharge instrument (CT-4000-mA, NEWARE) at room temperature. The cells were charged and discharged repeatedly under a constant current of C/10, where the theoretical capacity of 3600 mA h/g was used to calculate the C-rate. The upper and lower cut-off voltages were set to 1 V and 0.01 V, respectively. The cycled electrodes were obtained by disassembling the cells inside an argon-filled glovebox, and were rinsed thoroughly with the dimethyl carbonate (DMC, Gotion).

3. Results and Discussion

Figure 1a shows the averaged cycling performance of the silicon electrodes for 100 cycles. The initial unstable performance for approximately five cycles is due to the SEI formation, and the cycling performance of the rest cycles is consistent with the results reported in the literature.^32–34 It is worth mentioning that the first five cycles are commonly used as the formation stage for silicon composite electrodes.³¹ In other words, the degradation mechanism of the first five cycles is different from that of the subsequent ones. In order to exclude the effect of the formation stage, we will focus mainly on the performance evolution after the 5th cycle hereafter. The detailed cycling performance of all involved electrodes can be found in Fig. S1, in which the performance of different samples has a relatively good consistency.

Figure 1.

(a) The averaged cycling performance of the silicon electrodes. The SEM images of Si composite electrodes at (b) the pristine state and at the end of the (c) 5th, (d) 10th, (e) 30th, and (f) 100th cycle.

Meanwhile, as clearly shown in Fig. 1a, the silicon composite electrodes experienced a relatively rapid performance fading. Considering a potential relationship between cycling performance and electrode-level cracks in silicon electrodes,³ a qualitative evaluation of active layer cracks is carried out initially. A scanning electron microscope (SEM, Zeiss Sigma 300) was used to capture the crack patterns of active layers. Figure 1b presents the surface morphology of the pristine electrode, in which cracks are already present. This is a very common phenomenon for silicon composite electrodes.²⁵ The crack pattern evolves further with the cycling, as shown in Figs. 1b to 1f. Intuitively, cracks in the electrode with more cycles are easier to observe. With an increase in the cycle number, the width of remaining cracks increases, but unexpectedly, the number/density of observed cracks seems to decrease. These qualitative results will be further verified in the subsequent quantitative analysis. Meanwhile, notably, the out-of-plane displacement is observed after the 30th cycle, indicating that the mechanical damage inside the electrode gradually becomes more complex. It is also worth mentioning that, in Figs. 1e and 1f, there are numerous randomly distributed microcracks can be observed. These microcracks can be identified as gaps between silicon particles or particle clusters. Considering that these are particle-level or sub-electrode-level mechanical damages, they are not included in the investigation of electrode-level cracks.

3.1 Active layer cracks

The active layer cracks, which are easier to observe than the electrode debonding, are first focused in this section. It should be noted that the SEM magnification should be carefully selected. A too-low magnification causes blurred crack images and distorted information, while a too-high one results in the extraction of basically random information. In this study, 500X of magnification was implemented to obtain precise and reliable crack information. Additionally, three electrodes as one set were examined parallelly, and SEM images of three different locations on each electrode were captured. Considering the possible in-plane distribution of active layer cracks, these locations were randomly selected near the electrode centers. In total, 24 electrodes and 72 images were involved. Each SEM image was then digitally analyzed to determine the density, opening area, and width of active layer cracks.

For demonstration, a representative SEM image of the silicon composite electrode is presented in Fig. 2a. Apparently, some cracks can be observed in this raw image. In order to conduct digital analysis of the image, further pre-processing of the image is required. The discrete Gaussian filter and mean filter were employed for the processing, and threshold segmentation was performed on the processed image to separate the target crack from the image and generate a binary mask. The processed binary image is shown in Fig. 2b. Figure 2c is the stacked image of Figs. 2a and 2b to demonstrate the effectiveness of pre-processing. Further, by converting the pixel length of the SEM image to the real length,³⁵ the features of active layer cracks can be directly obtained from the processed binary images. The demonstration of the opening area, width, and length of active layer cracks is shown in Fig. 2d. The crack opening area S is directly calculated by extracting the total area of the pixels describing cracks. The contour line is synthesized from the edges of the binary mask, and then the total length of the contour line, denoted by D, can be extracted. The total crack length L can be further obtained by L = D/2. Moreover, the average crack width W can also be expressed as W = S/L. Meanwhile, the crack density is denoted by ρ = L/S_a, where S_a is the actual area of the image.²⁴ Due to the proportional relationship between L and ρ, the crack length L will not be discussed separately hereafter. For simplicity, we ignore the process of crack penetration due to the low thickness of active layers²⁰ and simply assume that it is penetrated. Such an assumption is actually quite common in related investigations^3,4,17,36 and will be justified in Section 3.2.

Figure 2.

Image processing: (a) the raw SEM image, (b) pre-processed and binarized image, and (c) stacked image. (d) Demonstration of the length, opening area and width of electrode cracks.

Although the density, opening area, and width of active layer cracks are defined above, they have vastly different magnitudes and numerical values. To solve this issue, all the crack information is normalized. Meanwhile, the evolution of cracks is focused, which is expressed as the density variation $\Delta \rho_{i} = (\rho_{i} - \bar{\rho }_{0})/\bar{\rho }_{0}$, opening area variation $\Delta S_{i} = (S_{i} - \bar{S}_{0})/\bar{S}_{0}$, and width variation $\Delta W_{i} = (W_{i} - \bar{W}_{0})/\bar{W}_{0}$, respectively, where the subscript i represents the ith cycle and $\bar{x}_{0}$ represents the averaged initial value of physical quantity x. According to the image processing method provided above, all SEM images were processed and the features of active layer cracks were extracted. To minimize measurement uncertainty as much as possible, the features of a sample were calculated as the average corresponding to the three SEM images taken at random locations.

Figures 3a to 3c illustrate the evolution of density, opening area, and width of active layer cracks with respect to the cycle number. Interestingly, the density variation Δρ constantly shows negative values, and even presents a certain degree of decrease after long-term cycles (Fig. 3a). This quantitative result is consistent with the qualitative evaluation of Figs. 1b to 1f, indicating that the unexpected phenomenon of crack closure is not coincidental. By carefully observing the SEM images of the large cycle number (such as Fig. 1f), it can be found that a few cracks grow dramatically to form primary cracks and lead to an increase in crack width and opening area. In fact, the similar phenomenon has also been observed by Wang et al.¹⁷ This phenomenon is most likely caused by the growth of SEI and the irreversible expansion of lithiated silicon, which occupy the space of cracks.^4,5

Figure 3.

Evolution of the (a) density variation Δρ, (b) opening area variation ΔS and (c) width variation ΔW of active layer cracks, in which the hollowed marks represent the averaged values. (d) Δρ, (e) ΔS and (f) ΔW versus capacity retention.

On the other hand, notably, the opening area variation ΔS (Fig. 3b) and width variation ΔW (Fig. 3c) are basically positive and show a clear trend of growth, indicating that the crack opening is repeatedly enhanced cycle by cycle. In other words, the crack opening and crack closure occur simultaneously. The only explanation for such results is that some cracks grow to form primary cracks, while the remained cracks close and become unobservable. In the SEM images of Fig. 1, primary cracks expand and become more visible as the cycle number increases; on the other hand, the remaining cracks become less visible which means closure occurred. To some extent, since the mechanical energy is released in the primary cracks, the remained cracks no longer open and become unobservable. Nevertheless, it can be concluded that the results in Figs. 3a to 3c provide quantitative support for the qualitative analysis of the SEM images in Figs. 1b to 1f.

Figures 3d to 3f demonstrate the relationship between the extracted crack features and the capacity retention. It can be observed that the density variation Δρ has a weak positive correlation with the capacity retention, while interestingly and more importantly, the other two crack features show strong negative correlations to the capacity retention. A more detailed analysis of the correlation³⁷ between the crack features and the cycling performance can be found in Figs. S2 and S3. The quantitative correlation analysis suggests that the connection with the electrochemical performance is strongest for the crack width and weakest for the crack density (Fig. S3). By reviewing the literature, it is found that the high correlation on the crack width is a relatively unexpected result, since the crack width is rarely measured or addressed in the battery field, while the crack density is a more common physical quantity to characterize structural damage.^28,29 This also means that battery degradation may not be described simply by traditional structural failure methods, but requires a deeper incorporation of electrochemical mechanisms.

Additionally, it can be found that the growth trend of the crack width (Fig. 3c) is more stable than that of the opening area (Fig. 3b), and the correlation of cycling performance to crack width is also higher than that to the opening area (Fig. S3). This is because the crack opening area is a combination of width and density, according to their mathematical expressions. Therefore, in the subsequent discussion, we will focus more on the crack width.

Although certain correlations are found for widths of active layer cracks and capacity retention, it should be noted that correlation does not imply causation. The correlation is not sufficient to explain how active layer cracks cause capacity fading. To solve this issue, a porous electrode model is employed here,^38,39 whose details can be found in Section S4. Two possible conditions of active layer cracks are evaluated, as shown in Figs. 4a and 4b, respectively. In the former case (Fig. 4a), the electrolyte is filled in the crack; while in the latter one (Fig. 4b), the electrolyte is absent within the crack. However, surprisingly, the electrochemical performance of the electrodes is hardly affected regardless of the crack opening degree and the presence/absence of electrolyte, as shown in Fig. 4c. This is, in fact, an understandable result, since the ion and electron pathways in the thickness direction are not altered by the presence of active layer cracks. Unfortunately, however, this causes the correlation between crack width growth and capacity decrease to be unexplained. This implies that the crack width growth may not be the direct cause of the cycling performance fading and that there may be other hidden mechanisms.

Figure 4.

Schematic diagrams of the electrode with an active layer crack: (a) presence and (b) absence of electrolyte within the crack. (c) Impact of the crack width and the presence/absence of electrolyte on voltage profiles. L_A is the representative width of cracked active layer.

3.2 Electrode debonding

The correlation, but not causation, between the width increase of active layer cracks and the capacity fading implies that there may be another mechanism that associates with the former and causes the latter, and this hidden mechanism is likely to be another type of mechanical failure. By reviewing the mechanical failure types at the electrode level, the electrode debonding is not involved in Section 3.1, although its potential presence is in fact implied in Fig. 1. Therefore, the electrode debonding is likely to be the missing piece of the puzzle and will be focused on in this section.

To prove the existence of the electrode debonding, the electrode was prepared by ion milling (Hitachi IM 4000 Plus), and the cross-section images were captured using a matching SEM (Hitachi Regulus 8100), as shown in Fig. 5. Before cycling, the initial crack does not completely penetrate the active layer, and no debonding is observed at the interface between the current collector and the active layer. After the first cycle, the crack penetrates the active layer, and the slight but observable debonding can be observed at the interface. With further cycling, the electrode debonding increases along with the opening of the active layer crack. In other words, in addition to demonstrating the existence of electrode debonding, Fig. 5 also reveals a correlation between the opening of active layer cracks and the electrode debonding. In fact, this correlation has also been reported in Refs. 4 and 17.

Figure 5.

Cross-section images of the electrode at (a) the pristine state and at the end of the (b) 1st and (c) 30th cycle. The marked area is the area of cracks. The interface between the active layer and the current collector is also demonstrated.

It is worth noting that electrode debonding evolves at the electrode interface and cannot be quantitatively described solely through the analysis of electrode cross-sections. A feasible alternative is to describe the debonding degree indirectly through an easily measurable quantity. Fact, according to the analytical model for electrode debonding developed in our previous work,^40–42 a simple relationship between the opening of the active layer crack and the electrode debonding can be given as follows (details in Section S5):

  

\begin{equation} \frac{L_{d}}{R} = \begin{cases} 0 & \text{$W < 2\delta_{\text{tc}}$}\\ 1 - \dfrac{2\delta_{\text{tc}}}{W} & \text{$W \geq 2\delta_{\text{tc}}$} \end{cases} \end{equation} (1)

where L_d is the averaged debonding length, δ_tc = 2Γ/σ_tc is the cohesive sliding displacement limit, Γ is the interface fracture energy, σ_tc is the shear cohesive strength and W is the averaged width of active layer cracks. Considering the fractured active layer as consisting of multiple islands, R stands for the average radius of the islands, as shown in Fig. 6a. In this work, R = 3 × 10⁻⁵ m, σ_tc = 40 MPa, and Γ = 5 J/m² are employed.^40,43,44 This equation can describe the phenomenon that the electrode debonding size increases along with the width of active layer cracks (Fig. 5), as shown in Fig. 6b. Meanwhile, the crack width is obviously an easily measurable quantity.

Figure 6.

Electrode debonding: (a) a schematic diagram of the model, (b) the relationship between active layer crack opening and electrode debonding, and (c) impact of electrode debonding on voltage profiles.

Using the porous electrode model on the initial configuration^4,26,45–48 provided in Section S4 and assuming that the debonded interface is insulating, the effect of debonding on the electrochemical performance can be obtained, as shown in Fig. 6c. Due to the blockage of the electron pathway by electrode debonding, the capacity gradually decreases as the size of debonding increases. For a low degree of debonding, the impact is insignificant. However, once the debonding length exceeds half the radius of the active layer island, the capacity rapidly decreases.

Furthermore, by combining the electrode debonding model (Eq. 1 and Fig. 6b) and the porous electrode model (Section S4 and Fig. 6c), it is possible to theoretically predict the relationship between the crack width of active layers and the capacity retention, as shown in Fig. 7. The experimental data in Fig. 7 are replotted according to Fig. 3f. The modeling result matches the experimental data well. When the crack width exceeds 1 µm, the capacity retention drops rapidly. Between W = 1 µm and 4 µm, the capacity retention decreases approximately linearly. Since the capacity retention is already very low, further increasing the crack width no longer significantly reduces the capacity. This result supports that the relationship between the crack width of active layers and the electrode capacity is not random but rather influenced by debonding.

Figure 7.

Impact of crack width in active layers on capacity retention: modeling and experiments. The symbols represent the experimental data, while the solid line stands for the simulation result.

Although the cause of crack opening is not the focus of this work, it should be noted that such a phenomenon is expected to be related to the plastic deformation and the concentration-dependent volume change of silicon electrodes.^2,47,49–51 Combining the results in Sections 3.1 and 3.2, it can be concluded that the easily measurable crack width of active layers can serve as a significant indicator of electrode degradation, but it does not directly lead to cycling performance fading. The deformation of active layers simultaneously leads to the opening of active layer cracks and the electrode interface failure, while the latter causes capacity fading.

4. Conclusions

In this study, the relationship between cycling performance and electrode-level cracks in silicon composite electrodes has been investigated. First, for the active layer cracks, the crack density, opening area, and width have been extracted from the SEM images of the electrodes. It is found that the connection between the crack width and electrochemical cycling performance is the strongest. Further, the effect of crack opening on the capacity has been evaluated by a porous electrode model. It is revealed that the crack width growth in active layers does not directly affect the electrochemical performance.

By capturing the electrode cross-sections, a link between crack width and electrode debonding has been identified. By incorporating the debonding model with the porous electrode model, the connection between the increase in the crack width of active layers and the decrease in capacity retention has been explained. The deformation of active layers simultaneously induces the crack opening of active layers and the electrode interface debonding, and the debonding causes capacity fading. However, since it is commonly difficult to quantitatively measure the debonding degree at the electrode interface, measuring the crack width of active layers provides a useful indicator for characterizing the structural stability of LIB electrodes.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12072183 and 12172205).

Data Availability Statement

The data that support the findings of this study are openly available under the terms of the designated Creative Commons License in J-STAGE Data at https://doi.org/10.50892/data.electrochemistry.24523261.

• 1) For the coupling problems of lithium-ion batteries, a key issue at hand is that it is still unclear which mechanical failures can cause degradation and how, which is particularly salient at the electrode level. In this work, the correlation between electrode-level cracks and cycling capacity of silicon electrodes is investigated. Unexpectedly, for cracks in active layers, the capacity decreases with the increase of crack width, while the connection of other crack features to the capacity is weaker or even absent. Meanwhile, the modeling results, however, suggest that the increase in crack width cannot directly cause the capacity fading. To explain these results, the relationship between electrode debonding and active layer crack opening is also described quantitatively. By combining the debonding model and the porous electrode model, the connection between crack widths of active layers and capacity fading is clarified, and accurate predictions are obtained. These results indicate that the easily measurable width of active layer cracks is qualified to evaluate degradation, while the electrode debonding is in fact the direct cause of capacity fading. The findings in this work provide a more precise understanding of the degradation mechanism in lithium-ion battery electrodes.

CRediT Authorship Contribution Statement

Shanshan Zhu: Data curation (Lead), Investigation (Lead), Methodology (Lead), Writing – original draft (Lead)

Bo Lu: Conceptualization (Lead), Project administration (Lead), Writing – review & editing (Lead)

Bo Rui: Writing – review & editing (Equal)

Yicheng Song: Methodology (Equal)

Junqian Zhang: Supervision (Equal)

Conflict of Interest

The authors declare no conflict of interest in the manuscript.

Funding

National Natural Science Foundation of China: 12072183

National Natural Science Foundation of China: 12172205

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