Interplay between electrochemical reactions and mechanical responses in silicon–graphite anodes and its impact on degradation

Durability of high-energy throughput batteries is a prerequisite for electric vehicles to penetrate the market. Despite remarkable progresses in silicon anodes with high energy densities, rapid capacity fading of full cells with silicon–graphite anodes limits their use. In this work, we unveil degradation mechanisms such as Li+ crosstalk between silicon and graphite, consequent Li+ accumulation in silicon, and capacity depression of graphite due to silicon expansion. The active material properties, i.e. silicon particle size and graphite hardness, are then modified based on these results to reduce Li+ accumulation in silicon and the subsequent degradation of the active materials in the anode. Finally, the cycling performance is tailored by designing electrodes to regulate Li+ crosstalk. The resultant full cell with an areal capacity of 6 mAh cm−2 has a cycle life of >750 cycles the volumetric energy density of 800 Wh L−1 in a commercial cell format.

Silicon nanoparticles with lengths of 85 or 100 nm (denoted as 85-and 100-nm Si, respectively; see Table 1 for the average dimensions) were prepared by ball milling of micron-sized silicon powder. A chemical vapour deposition process was then used to deposit carbon on the surfaces of the silicon particles using a custom rotary kiln. An additional surface treatment was carried out with coal tar pitch as the carbon source, whereby the silicon particles and coal tar pitch were mixed in a powder mixer and heated at 900°C for 3 h to complete the carbonization reaction. This coated structure provides highly conductive percolation pathways and limits any unwanted reactions between the silicon particles and electrolyte. The difference in pellet density is related to the hardness of the graphite powder particles 1 . Typically, synthetic graphite is harder than natural graphite. To better understand the relationship between the type of graphite powder and pellet density, we measured the pressure-induced changes in volume of the HPD and LPD graphite powders, as well as two other graphite powders (denoted as graphite1 (Shanshan Technology) and graphite2 (JFE technology)), at different compaction pressures. The densities of the graphite pellets varied with the compaction pressure, as shown in Supplementary Fig. 2a.
In addition, the graphite type greatly affected the compact density. The higher density of the HPD-graphite compact compared to the LPD-graphite compact indicates that LPD-graphite is harder than HPD-graphite. The graphite1 and graphite2 compacts were both denser than the HPD-and LPD-graphite compacts.
To test the effect of graphite type on the cycling performance, anodes were prepared using graphite1, graphite2, HPD-graphite, and LPD-graphite (82. in a custom-made line. The electrode density of the cathode was 3.6 g cm -3 .

Supplementary Note 1. Quantification of Li + content in individual materials
X-ray diffraction (XRD) spectra and electrochemical data were measured simultaneously.
The diffraction spectra of graphite and the Cu current collector were extracted in the range of 1.45 < q < 2.0 Å -1 and then fitted using OriginPro ® to deconvolute the peaks of different graphite phases and determine the peak intensities. Here, q is the scattering wave vector. Previous crystallographic data for graphite 2-6 were referred to for the fitting.
The Coulombic efficiencies of the full cells were as high as 99.8%; thus, we ignored lithium loss due to solid electrolyte interphase (SEI) formation and electrode deterioration in a single cycle. Li + was therefore considered to be present only in the graphite and silicon components. We employed the following linear equation based on the assumption that the XRD intensity of each phase is linearly proportional to the Li + content of each phase.
where Ak, Bk, Ck, Dk, and Ek are the intensities of the peaks for stage 1, stage 2L, stage 2, stage 3L, and stage 4L, respectively, which are extracted from the fitting results of the XRD analysis; , , , , and  are the corresponding coefficients that convert the intensity of each phase into its capacity. k is the Li + content in silicon, and Capacityk is the capacity of a cell in the kth sequential data. The stages are named by the order of lithium ions in each nth interslab of graphite, and the letter L indicates 'liquid-like', without any in-plane order 7 . The lithium contents in stage 2L and stage 2 are summed and noted as stage 2 in the main text.  3c). Our only ansatz here is that the XRD intensity is proportional to the capacity of the graphite phase. The baselines were generated by the spline method and Gaussian multipeak fitting was conducted using a nonlinear curve fitting tool. The number of points for baseline generation was the only manually selected data and was approached with great caution within the series analysis.
This method was used to devise the amounts of Li + in each component, as shown in

Supplementary Note 2. Origin of abrupt changes in XRD signals
The differential capacity (dQ/dV) plots of Li-Si alloys typically exhibit much broader peaks than those of graphite, which indicates that various alloy phases exist The amount of Li + , n, vs. the potential of silicon, E, near the phase-transition point, is a step function, so that the asymptotic form of n vs.
E is tan -1 x. The average amount of Li + in the Li-Si alloy, 〈n〉, can be described as Sudden changes in the individual SOCs were clearly observed in our XRD results for the following reasons. When a silicon phase transition occurs, the amount of Li + in the Li-Si alloy changes abruptly. According to this argument, the change in the amount of Li + is more abrupt than the change in potential that occurs near the phase transition.
Furthermore, the amount of Li + is directly associated with the diffraction peaks measured by XRD.

Supplementary Note 3. Calculation of pressure on graphite
When lithiation in stage 1 graphite is relatively small, the fitting error of the peak's position is larger because the signal is small. From the XRD peak shift, the pressure applied on the graphite (P) can be calculated using the following equation: where c is the compressibility of the c-axis of LiC6, reported to be 1/cₒ(∂c/∂P)Pₒ = 1.344 × 10 -2 GPa -1 ; c is the c-axis constant; and c0 is the c-axis lattice constant at the reference pressure, P0 (9) .

Supplementary Note 4. Thermodynamic calculations for internal redox reaction
The LixC6 phase can be determined from the amount of Li + in graphite, while the phase of the silicon particle shell can be identified using the position of the phase transition from the XRD results. It is difficult for Li + in the shell of the silicon particles to move into the core because of an increase in pressure due to volume expansion of the lithiated shell 10 .
Thus, the chemical potential of the silicon component reduces more slowly than that of the graphite 11 . For this reason, we assume in this work that graphite interacts only with the shell of the silicon particles. The difference in chemical potentials () at a constant temperature and pressure can therefore be described by the following equation: where i and Gi are the chemical potentials and Gibbs free energies of the components, respectively (i = LixSishell, LiyC6, and metallic Li) 12,13 . Herein, LixSishell is the lithium silicide phase of the shell of the silicon particles.
The chemical potential is the change in Gibbs free energy that occurs as the amount of Li + changes. In the case of charging Cell B at 0.5C (see Fig. 1b), the third phase transition (red triangle at 65% SOC) corresponds to the phase transition from Li2.3Si to Li3.25Si 14,15 , which occurs mostly on the surface of silicon due to the two-phase lithiation.
The ratio of the electrochemically active volume (presumably the surface) to the total volume of the silicon particle can be calculated as 92.3% from the difference between the Li + content in the surface phase (Li3.25Si) and the measured total Li + content in silicon during the third phase transition. Assuming that the reacted volume is maintained after the third phase transition, the lithiated state of the silicon particle shell can be estimated, and subsequently, the chemical potentials of the LixSishell and LiyC6 phases can be calculated using previously reported thermodynamic values [15][16][17] . Here, the pressure and temperature of this system were set to 1 atm and 297 K, respectively. In order to correct for the pressure effect, we assume that the changes in the internal energy and entropy owing to the volume change can be ignored. Therefore, the change in the chemical potential can be described by the following equation: where P, V, and x are pressure, volume, and number of lithium ions, respectively.
In graphite, the change in the c-axis dimension owing to applied pressure is smaller than the difference between the c-axes of LiC6 and graphite; thus, the maximum of (∂V/∂x)P,T can be calculated. If the increase in pressure is 0.4 Gpa, the difference in the chemical potential of LiyC6 owing to the increase in pressure can be calculated as follows: where NA is Avogadro's constant.
In the same manner, the maximum of (∂V/∂x)P,T can be described as (∂V/∂x)P,T = In the half-cell experiments, no internal redox couples were observed. Lithiation in the working electrode is regulated by a constant current until a set potential (0.01 V), at which point the lithium content in LixSi reaches x = 3.75 (20) . Lithiation in the anode of the full cell, however, is regulated by the overall potential difference between the cathode and anode. The minimum potential of the anode (~0.1 V) during full-cell charging, as measured using a three-electrode set-up, was higher than that measured in the half-cell experiment, as shown in Fig. 2a. Therefore, the electric potential applied to the anode in the full cell during charging was higher than that in the half cell.

Supplementary Note 5. Increase in CV charging time in cells using a silicongraphite anode
The internal redox reaction in the silicon-graphite anode leads to an increase in the CV charging time. After CC charging is terminated, the highly concentrated lithium at the anode-electrolyte interface diffuses into the bulk of the anode. Moreover, CV charging is terminated when the concentration gradient within the active material is minimised 21 .
There is a distinctive pathway for minimizing the concentration gradient, namely Li + mass transport from silicon to graphite via the internal redox reaction. During CV charging, this pathway delays the end of charging because Li + diffusivity in silicon is two orders less than that in graphite 22,23 . Consequently, the time for CV charging increases, and the delithiated cathode experiences a high cut-off voltage during the extended CV charging time.

Supplementary Note 6. Change in thickness of cell and compression force on cell during CV charging
As shown in Fig. 1, Li + transfers from silicon to graphite during CV charging. Thus, the thickness of the anode, which increases during CC charging, must decrease from a certain point during CV charging owing to the large variation in the size of (de)lithiated silicon.
We monitored the variation in thickness over a cycle by measuring the thickness in situ (see Methods in the main text for details). During the CV charging and rest stages, which correspond to the voltage plateaus in Fig. 1d, the thickness of the cell using the silicongraphite anode (upper panel of Fig. 1d) starts to reduce after 251 min, whereas the thickness of the graphite-only anode (lower panel of Fig. 1d) plateaus after 255 min.
Simultaneously, the force on the cell with the silicon-graphite anode (upper panel of The thickness and force variation during CV charging do not originate from particle rearrangement, as this would be illustrated in the cross-sectional images at 0% and 100% SOC every 50 cycles shown in Supplementary Fig. 7. Supplementary Fig. 7 demonstrates that graphite is in a compacted state; that is, the space between the SSC and graphite remains unfilled in the 0% SOC images.

Supplementary Note 7. Calculation of Li + penetration into silicon core during CV charging
Here, free energy of Li + penetrating into the silicon core during CV charging is calculated by using an analytical solution based on two-phase lithiation, which describes the effect of stress on the driving force for the reaction 24 . At the interface between the LixSi shell and core of a spherical silicon particle, the net change in free energy is described as where Gr is the free energy of the reaction in which one lithium atom and 1/ (ii) during CV: Gr = −30.79 kJ mol -1 , e = 9.65 kJ mol -1 , β = 2.807, and x = 2.6. Gr was calculated using previously reported thermodynamic values [15][16][17] ; eϕ was obtained from the three-electrode data in Fig. 2a; and β and VSi were calculated using previously reported values 18 .
Before CV charging, the value of a/b is 0.2047 when G is zero. During CV charging, G becomes negative when a/b equals 0.2047, which indicates that Li + can penetrate into the depressurized silicon core during CV charging owing to Li + crosstalk.

Supplementary Note 8. Determination of lithium contents
The amounts of lithium in the electrodes and electrolyte were traced every 50 cycles by the following process. After discharging, the cells were disassembled in an Ar-filled glovebox. All electrodes were rinsed with DMC for 5 min and dried under vacuum for 6 h, and the remaining electrolyte was collected. After chemical treatment 26 , the amounts of lithium in the electrodes and electrolyte were determined using ICP-AES. Their weights were calculated using the loading level (g cm -2 ) and area of the electrodes, and the amounts of lithium were converted into capacities. The weight of lithium in the electrolyte was calculated using the weight of electrolyte in the cell.
To measure the amount of electrochemically inactive lithium, a half cell assembled using the disassembled anode was fully delithiated to a cut-off voltage of 1.5 V at 0.05C.
Then, the half cell was disassembled in an Ar-filled glovebox, and the amount of lithium in the anode (i.e. the electrochemically inactive lithium) was determined using ICP-AES.
The difference in the amounts of lithium between the discharged anode and the reassembled-and-delithiated anode corresponds to the amount of Li + remaining in the anode. After the first and 250th cycles of Cell B, we measured the amounts of total lithium (black), inactive lithium (red), and remaining Li + (blue) in the anode, as shown in Supplementary Fig. 8. Here, inactive lithium corresponds to the lithium consumed during the formation of the SEI. The loading (g cm -2 ) of the anode; the molar masses of carbon, silicon, and lithium; and the atomic composition of the anode were used to calculate the SOCs of anode after the first and 250th cycles, which were 3.5% and 14.3%, respectively.
Supplementary Table 1 describes these data sets. Supplementary Fig. 9 shows and dark red areas, as shown in Supplementary Fig. 12b. The bright part surrounds the pitch, and consists mainly of LiF ( Supplementary Fig. 12d), similarly to that on the SSC particles after the first cycle ( Supplementary Fig. 11e). The dark part is lithium silicide ( Supplementary Fig. 12d). Therefore, Li + had accumulated inside the silicon particles by  Table 1). Then, the roughly estimated lithium losses by SEI on SSC at first and 250th cycles are 6.0 and 6.5 mAh, respectively. The specific properties of SEIs on different components as well as the ratios of volumes and surfaces of materials could affect the calculation result, but might not significantly change the estimation.

Supplementary Note 10. X-ray photoelectron spectroscopy (XPS)
For ex situ XPS measurements (PHI Quantera-II), the core-level spectra were measured using Al Kα as the excitation source (1486.6 eV) at an accelerating voltage of 1 kV. All spectra were referenced to the C 1s peak at 284.8 eV. The cells were dissembled in an Ar-filled glovebox and rinsed in DMC for 5 min, followed by 30 min drying under vacuum. Subsequently, the electrodes were loaded into an in-house airtight vessel and transferred to the instrument without exposure to ambient air.
The chemical composition of the SEI in Cell B was investigated using XPS. The results are shown in Supplementary Fig. 13. The SEI surface consists of organic compounds such as ROLi (where R is a hydrogen, hydrocarbon side chain, or group of atoms) and inorganic compounds such as LiF, Li2CO3, and Li2O. Supplementary Fig. 13 also exhibits a tendency for the LiF (684.8 eV), Li2CO3 (531.8 eV), and C-O-C (286.4 eV) components to increase with cycling. In addition, all the C 1s XPS spectra ( Supplementary Fig. 13c) exhibit a peak at ~284 eV, which corresponds to the underlying graphite component of the anodes (the penetration depth of XPS is several nanometres).
This suggests that the SEI layer is still thinner than the maximum XPS penetration depth of ca. 10 nm (28) after 250 cycles. Thus, the growth of the SEI was well controlled, which is in good agreement with the ICP results.
The formation of LiF is attributed to the decomposition of FEC (a component of the electrolyte). LiF forms on the outside of the SSC particles, where the coal tar pitch is situated. However, LiF is not observed inside the SSC particles, as shown in the TEM results in Supplementary Note 9. Thus, the SSC structure effectively hinders the electrolyte from penetrating into the silicon particles.

Supplementary Note 11. Electron probe micro-analysis (EPMA)
The SEI was visualised by measuring the distribution of P originating from the 3b, c, e, and f.

Supplementary Note 12. Effect of C-rate on anode lithiation
The internal redox reaction also occurs at higher C-rates of 1C and 2C, as shown in Supplementary Fig. 15. At a low C-rate of 0.5C (Fig. 1b), the experimental individual SOCs are in good agreement with the calculated values. When the C-rate increases to 1C and 2C (Supplementary Fig. 8a and b), the sudden changes in the amount of Li + due to LiyC6 phase transitions become less distinct, and the silicon SOC decreases, while those of graphite become higher at SOCs of below 67%. This behaviour might be because silicon has a poorer C-rate capability than graphite 30 .

Supplementary Note 13. Retardation of Li + transfer to silicon
The calculated silicon SOCs (red line, Supplementary Fig. 16) indicate the intrinsic lithiation behaviour of the silicon component. The experimentally determined silicon SOCs for the 250th cycle (red circles, Supplementary Fig. 16) are in good agreement with the calculated values between 0% and 15%. However, at SOCs of 15%-34%, the experimental data deviate discontinuously from the calculated SOCs, and do not follow the intrinsic lithiation behaviour of silicon.

Supplementary Note 14. Image analysis
The features corresponding to the silicon boundaries were extracted from the grey-scale SEM micrographs using image analysis. First, the grey-scale SEM images were converted to binary images, and the coordinates associated with the boundaries were estimated. To preserve the silicon boundaries and edges where there were large changes in intensity while selectively removing uncertain lines with small intensity fluctuations, L0 gradient minimisation 29 (with a weighting factor of 0.009) was used, which is particularly effective for highlighting silicon boundaries. Furthermore, morphological processing 32 (dilation/erosion) was used to preserve the original object shapes. Otsu's method 33 was used to segment silicon (white, '1') and others (black, '0'). When silicon regions overlapped in the image, the silicon particles were partially manually divided.
Finally, the MATLAB ® 2018a built-in function 'regionprops' was applied to calculate the average particle area and diameter. All algorithms were implemented using MATLAB ® 2018a (MathWorks, Inc.).

Supplementary Note 15. DC-IR measurements
The direct current-internal resistance (DC-IR) characteristics of the prismatic cells at 50% SOC were measured every 100 cycles. DC-IR measurements were conducted by applying a 10 s long negative current pulse of 1C to the cell after 1 h of rest at opencircuit voltage (OCV), and the resistance was calculated from the difference between the OCV and the potential at the end of the pulse, divided by the pulse current 34,35 . The increase in the DC-IR values for cells with HPD-graphite was larger than that for cells with LPD-graphite, as shown in Supplementary Fig. 20.

Supplementary Note 16. Improvement over existing electrode design
Thus far, the anode has been designed based on the assumption that the LixSi phase would be x = 3.75 at full lithiation. In conventional electrode design, the Li3.75Si phase is difficult to attain in full-cell operation conditions, as the internal redox reaction dominates the anode reaction during CV charging, as shown in Fig. 1. Li + crosstalk facilitates long-term degradation of the cell. However, we can directly relieve the longterm detrimental effects of Li + crosstalk by changing the design of the anode, maintaining a fixed graphite content, and increasing the SSC content to 111% relative to that in Cell D. Because Li-Si alloys have a convex Gibbs free energy landscape as a function of x in LixSi with a minimum at x = 2.33 15,16 , prevention of over-lithiation of silicon (x < 2.33) would directly reduce Li + crosstalk.
Based on the above consideration, a revised anode was prepared from 18 wt% SSC, 79 wt% LPD-graphite, and 3 wt% binder. With the revised design, which simply increased the SSC content to 111% compared to that in Cell D, the cross-points of the SSC and graphite SOCs increased from 72.9% to 78.8% anode SOC, as shown in Supplementary Fig. 22a. In addition, by changing the electrode design, the utilisation of active materials in the anode decreased from 87.3% to 82.8% (see detailed calculations in Supplementary Note 17). This change prevents over-lithiation of silicon, which is the origin of Li + crosstalk between silicon and graphite during CV charging.
Increasing the number of accommodation sites for lithium in silicon and the prevention of over-lithiation reduced Li + crosstalk during CV charging in the full cell.
Consequently, the ratio of the time for CV charging to the total charging time (CV ratio) was reduced, and the capacity retention enhanced, as shown in Supplementary Fig. 22b. With our new understanding of the Li + crosstalk degradation mechanism, we were able to enhance the cycling performance while minimizing adverse effects. The anode thicknesses in the previous and revised designs were 73.3 and 76.8 m, respectively.
Thus, the revised electrode design increases the electrode thickness by 5%. However, the change in thickness at full volume expansion decreases by 2.5% (from 123% to 120.5% vs. initial thickness). Simultaneously, the discharge capacity for the first cycle after the formation stage decreases by 0.9% (from 606 to 600.5 mAh), but the capacity retention ratio increases from 95.4% to 97.1% after 100 cycles.

Supplementary Note 17. Utilisation of active materials in anode
The discharge capacity of the full cell, Qc, is given as follows: where Q0 + , QI − , n/p, and  − are the initial cathode charge capacity, the irreversible capacity of the anode, the negative to positive capacity ratio, and the initial Coulombic efficiency of the anode, respectively. Because the cathode has a lower cut-off voltage, the utilisation of the anode, , can be expressed using the utilisation of the cathode, : where QR − is the reversible capacity of the anode 36 .
By changing the design of the electrode, the n/p ratio increases from 1.03 to 1.08, and the initial Coulombic efficiency (ICE) of the anode decreases from 88.9% to 88.7%.
After the initial formation stage, the discharge capacity of the full cell decreases from 88.57% to 87.8% of the initial cathode charge capacity. Given the lower cut-off potential of the cathode (3.35 V), the utilisation of the cathode is 90.3%. Therefore, the utilisation of the anode decreases from 87.3% to 82.8%.

Supplementary Note 18. Direct visualisation through in situ electrochemical TEM
Recent developments in in situ TEM have provided a new opportunity to directly observe Li + diffusion between carbon (or graphite) and silicon [37][38][39]