Distinguishing and Quantifying Reversible/Irreversible Lithium in Practical Lithium Metal Batteries


 Practical lithium metal batteries have been researched worldwide, but due to excessive “Li reservoir” in the anode, quantification of the authentic reversibility of practical cells remains unresolved. Quantitative method for assessing the reversibility and irreversibility of Li anode is thereby essentially needed. Here we propose an index system composed of several quantitative parameters to evaluate the reversibility of practical lithium metal batteries. Mathematical relationships between these parameters and cycle number are successfully established based on the mass of active and inactive Li in the cycled Li anode. By establishing a novel and universal analytical method, mass of active Li can be quantitatively distinguished from the inactive one of cycled lithium metal anode in Ah-level pouch cells. Through fitting quantified data of active and inactive Li under different cycles, values of parameters representing for the reversibility and irreversibility of Li are quantitatively decoupled. The quantitative analysis method presented in this work provides new criteria to accurately assess practical lithium metal batteries for more reliable degradation analysis and failure prediction.


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Currently, both academic and industrial attentions are focusing on practical lithium metal batteries (LMBs) with energy density beyond 500 Wh/kg. [1][2][3][4] But how to distinguish and separate reversible Li from the irreversible one in the cycled lithium metal anode (LMA) for accurate evaluation and quantification of the authentic reversibility of practical LMBs still remains a big challenge. 5,6 For anode-free cells without LMA, the irreversible capacity loss can be easily identified by the Coulombic inefficiency of the cell (CiEcell), and the cycling performance truly reflects cell degradation ( Supplementary Fig. 1a). 7,8 In contrast, in LMBs, LMA as "Li reservoir" will continuously compensate for the loss of lithium originating from the cathode, therefore the CiEcell does not precisely reflect the real Li loss during cycling. [9][10][11][12] In fact, degradation of LMBs is dominantly governed by LMA at present due to the much worse electrochemical reversibility of LMA than that of the cathode. [13][14][15] Therefore, quantitative parameters reflecting the authentic reversibility and irreversibility of LMA should be established as criteria to objectively assess the degradation behavior of LMBs for better battery design and failure prediction.
It is well known that the irreversible Li (also known as dead Li)in cycled LMA arises from the formation of (electro)chemically formed Li + compounds in the solid electrolyte interphase (SEI Li + ) and electrically isolated unreacted metallic Li (inactive Li). 16,17 The continuous formation and agglomeration of such ineluctable "dead Li" upon cycling will gradually accelerate the loss of active Li in LMA as they block the transportation of electrons and Li-ions. 18,19 The ever-changing irreversible loss of Li in LMA (IRLLi,n, n corresponds to the cycle number) during cycling can be mathematically expressed based on two parts ( Supplementary Fig. 1b), namely the intrinsic Li loss of the pristine LMA (IRLLi,0) which is determined by the specific parameters and working conditions of LMBs, and the cycle-number-dependent incremental part which reflects the cumulative effects of the "dead Li" formed within the (n-1) cycles on the irreversible Li loss at the n th cycle . Determination of IRLLi,0 and the related incremental part offers the criteria to evaluate and understand the degradation behavior of LMA hidden beneath the apparent CiEs for practical LMBs in a quantitative way. However, 4 both cannot be directly characterized by simply calculating the total charge flows. As cycled LMA is composed of reversible Li (termed as the active Li) and SEI encapsulated inactive Li (Figure 1a), quantifying active Li and inactive Li in LMA as a prerequisite to decouple reversible Li from the irreversible one makes the determination of two parts possible. 8,11,17,[20][21][22][23][24] However, there are still two obstacles to be surmounted to identify them through quantitative chemical analysis. One is how to separate active and inactive Li for independent identification of these species. Although inactive Li was quantified in anode-free coin cells by in situ nuclear magnetic resonance 20,21,[25][26][27] and hydrogen titration gas chromatography 17,28 , these methods can't distinguish active Li from inactive ones in cycled LMA due to their identical metallic nature. 29 The other issue is how to establish a mathematical relationship that can be used to determine the inherent Li loss and the cycle-number-dependent incremental part from the quantitative analysis results.
Herein we report a novel and universal chemical analytical methodology to quantitatively distinguish the active Li from the inactive one in cycled LMAs in Ahlevel LMB pouch cells. Biphenyl/THF solution is employed to dissolve the active Li through complexation but to preserve the completeness of SEI that encapsulates the inactive Li. The as-separated active and inactive Li can be independently quantified by atomic emission spectrometry and gas chromatography, respectively. Furthermore, by introducing an exponential function of cycle number to describe the incremental effect of "dead Li", values of IRLLi,0 and the incremental coefficient are decoupled and identified through fitting quantified results of active and inactive Li, which can be employed to analyze the authentic reversibility of LMA in practical LMBs. The variations of IRLLi,n suggest that high stack pressure suppresses inherent Li loss by minimizing the cracking possibility of SEI, and agglomeration of "dead Li" drives dendritic Li plating for more inactive Li. And the inherent Li loss is mainly governed by the electrolyte, charging rates and stack pressures rather than the kinds of cathodes.
By using this quantitative analytical method, the blindfold for the compositional and structural evolution of LMA beneath qualitative morphology characterizations can be 5 uncovered . Quantification of reversible/irreversible Li provides a variable-independent   and quantifiable criterion to reflect the magnitude of effects from different variables in   LMBs, including external variables (stack pressures, rates, charge voltages, temperatures, etc.) and internal variables (cathodes, anodes, binders, etc.), which can make a significant contribution to better and more efficient LMB cell design.

Mathematical hypothesis
For conventional lithium-ion batteries, the capacity retention after n cycles equals to (CEcell) n owing to nearly unchanged value of the Coulombic efficiency of the cell. 30 In contrast, the CiEcell,n of anode-free cells, which corresponds to IRLLi,n, changes along with the cycle number. Figure 1b confirms the gradual increase of CiEcell,n of a 0.5 Ah anode-free pouch cell when cycling. Fitting result demonstrates that the proportion of the irreversible Li loss in each cycle is a time-variable exponential function closely related to the cycle number (n). In other words, "dead Li" formed in former cycles will bring accumulative effects to the proliferation of "dead Li" in the latter cycles. 31 Mathematically, the ever-changing IRLLi,n can be expressed in Equation 1 as the inherent irreversibility of LMA (IRLLi,0) multiplied by an exponential function of Euler's number with variables of the cycle number (n) and the incremental coefficient The same mathematical expression can be applied to understand the irreversibility of LMAs, but sufficient "Li reservoir" of LMA determines that the total irreversible Li loss after a certain cycle number in LMB follows a mathematical addition relationship. (mathematical illustration in Figure 1c, details in Methods).
More specifically, IRLLi,n of LMB can be divided into two parts, IRLinactive Li,n and IRLSEI,n (Figure 1d) Table 1. This index system can be used to quantitatively describe the authentic reversibility and irreversibility of a specific LMB, thus, to scientifically evaluate the effects of key materials, cell parameters and testing protocols on the performance of practical LMBs.
Assuming no capacity loss in the cathode, failure prediction of LMBs based on ideal (no accumulative effects) and calibrated (considering agglomeration of "dead Li") conditions are shown in Figure 1e to demonstrate the significance of RLi,0 and KIRL.
With the same value of RLi,0, the lifetime of the cell is largely shortened when the cumulative effects from "dead Li" (K) is taken into consideration. The calibrated lifetime is much closer to the reality of practical LMBs, demonstrating the validity of this mathematical hypothesis. When RLi,0 is increased along with decreasing of KIRL, the reversibility of LMB is evidently improved to deliver hundreds even thousands of cycles. A very small increment in RLi,0 and/or decrement in KIRL will cause huge differences in the cyclic stability of the cells. The requirements for RLi,0 and KIRL to reach specific cycle numbers under certain conditions are simulated in Figure 1f, which can be used for lifetime prediction when knowing the specific values. 32 The above predictions are also consistent with the data published by the Battery500 Consortium.
As previously mentioned, CE cannot be directly used to predict the cycle life. Either the SEI growth or accumulation of dead Li should be considered as the build-up effect for the degradation of the LMB. 33 Moreover, in the recently published results with optimized N/P ratio and electrolyte system, the LMB's cycle was extended to more than 600 cycles without the sudden drop, indicating that the well-controlled LMB could demonstrate a K value even smaller than 0.005 (orange line in Figure 1e). 12

Methodology for quantifying active and inactive Li
Active Li, inactive Li and Li composites (from electrolyte or electrodes) in SEI are three major components in cycled LMA (Figure 2a). As active and inactive Li are both metallic Li in terms of their composition, the only difference between them is that inactive Li is the SEI-encapsulated particles. 34 Although bulk Li foil is also covered by 8 SEI, punching LMAs to small pieces in an Ar-filled glove box for quantitative analysis will expose fresh surface of bulk Li without SEI coverage. Considering the high chemical stability of SEI in organic solvents, 35,36 it is possible to convert active Li to Li-ions by organic solvent 37   Active Li in cycled LMAs was firstly dissolved in biphenyl/THF (6.0 wt.% of biphenyl), and its content was quantified by ICP-AES (termed as Li-ion atomic emission spectrometer titration, Li-AEST). Residual inactive Li encapsulated by SEI was then reacted with deionized water. Hydrogen as the reaction product was collected and 9 quickly injected to gas chromatography (GC) for quantifying the content of inactive Li (termed as hydrogen gas chromatography titration, H2-GCT). The accuracy and sensitivity of Li-AEST and H2-GCT were measured before quantitative analysis. As shown in Figure 2h, theoretical Li concentrations of standard biphenyl/THF solutions prepared by fully dissolving Li foils with pre-designed masses (Supplementary Fig. 7 and Table 4

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The variations of RLi,n, IRLinactive Li,n and IRLSEI,n (Figure 3g-i) along with cycling demonstrate that the reversibility of LMAs upon cycling are jointly determined by the inherent irreversibility and its related incremental coefficient. IRLinactive Li at 400 kPa and 800 kPa only slightly increases when compared to that at 100 kPa, suggesting that high stack pressure mainly avoids the deterioration of electron and ion transportation owing to less dendritic electro-deposition morphology. However, its function for minimizing SEI cracking possibilities is inconspicuous. It is believed that stack pressure can no longer suppress dendritic morphology from the mechanicalelectrochemical perspective when thick and porous "dead Li" layer is formed.
According to the small increment of inactive Li (0.1 mg, Supplementary  38 . Long-term cycling will also be benefited from re-utilization of inactive Li from dense "dead Li" layer. 29,43 Except for that, according to the mathematical hypothesis, knowing values of IRLLi,0 and KIRL theoretically enables failure prediction for practical LMBs. As shown in Supplementary Fig. 11, a 0.9Ah Li/NCM811 pouch cell cycled under C/5 and 100 kPa encounters sudden capacity drop at the 69 th cycle. The thickness of the residual active Li is 37 μm (theoretically calculated to be near 3.0 mg of active Li remaining) as determined by SEM. The mathematical modeling based on the quantitative analysis results of this cell predicts that critical failure occurs after ~80 cycles ( Supplementary Fig. 12), which is in good agreement with the realistic test results and reflects the practicality of this method in assessing the potential level of LMBs without long-term cycling.

Quantitative measurement for degradation analysis of LMA in practical LMBs
Inactive Li is mostly originated from detached Li dendrites during root-preferred stripping process; thus, quantification of inactive Li will offer deeper understanding of the degradation mechanism of LMA. As shown in Figure 4a, both CEcell and the capacity of the cell under C/2 decay much faster than those under C/5 (both of them 12 have no constant voltage charging process), and the cell completely fails only after 25 cycles ( Supplementary Fig. 11a, b). This result is quite unusual, since the corresponding areal current density to the rate of C/5 and C/2 is 0.75 mA/cm 2 and 1.87 mA/cm 2 , respectively, both of which are quite mild testing conditions in the case of coin-type cells. The much worse rate capability of pouch cells than that of coin cells strongly suggest that the degradation behavior of LMAs in pouch cells can't be simply learned from that in coin cells. Applying the analytical method proposed in this work, it is revealed that the mass of inactive Li increases dramatically at the rate of C/2, which is the main cause of the rapid failure of the cell (Figure 4b). In contrast, the quantity of inactive Li after 50 cycles at the rate of C/5 is less than 40% of that at C/2, and all data points are located below the dash line, demonstrating significantly improved stability of the Li anode when the rate is reduced from C/2 to C/5. Also, the average error of the mass of inactive Li at C/2 (7%) is more than three times higher than that at C/5 (2%), implying the existence of large and unevenly distributed protrusions and pits over the entire anode after cycling at C/2 due to rapidly deteriorated stripping/plating behavior of Li in practical cells when the current density is enlarged. 44 Furthermore, both the values of IRLinactive Li,0 and Kinactive increases enormously when the rate is raised from C/5 to C/2 (Figure 4c and d, and Supplementary Fig. 13c). High IRLinactive Li,0 (2.01%) at the rate of C/2 demonstrates serious irreversibility of Li plating and stripping at each cycle, 45,46 while high Kinactive (~0.06) indicates the incremental part for irreversibility grows quickly due to accumulation of large quantities of "dead Li" particles, which in turn aggravates dendritic Li growth. As plotted in Figure 4e, the total thickness of the "dead Li" layer on both sides of the Li anode quickly exceeds 300 μm only after 25 cycles at C/2, which is almost twice than that at C/5. Even after 50 cycles, the thickness of the "dead Li" layer only reaches 230 μm at C/5. The average thickness increment for the "dead Li" layer under C/2 (~12.4 μm/cycle) is nearly three times larger than that of C/5 (4.6 μm/cycle) (Figure 4f). In addition, the mass of active Li measured by the quantitative analysis method is quite coincident with its thickness observed from the SEM images ( Supplementary Fig. 14-21), confirming the accuracy of this 13 quantification method, and suggesting fast consumption of active Li under C/2.
Furthermore, FIB-SEM image of the Li anode after 25 cycles at C/5 (Figure 4g) displays compact accumulation state of "dead Li", whereas that at C/2 (Figure 4h) shows loosely packed "dead Li" with obviously higher porosity, which explains the much more serious thickness expanding of the Li anode at higher rates.
Combining LMBs can be revealed in a more quantitative way. We believe that this method will become a powerful tool to deeply understand the electrochemical behavior of LMA, and set a new and universal criterion to assess the authentic reversibility of LMBs, which is extremely essential to the development of high performance LMBs towards practical applications.  to assess the reversibility and irreversibility of the Li anode in LMBs.

Abbreviation Representation
IRLLi  Not enough data have been obtained to verify whether this method can also be effectively applied for coin cells.
2) 10 mL of biphenyl/THF (with 6.0 wt.% of biphenyl) was added into the air-tight glass bottle containing a disk sample obtained in the first step to dissolve the active Li.
The cycled LMAs were punched to form smaller pieces (14 mm in diameter) for quantitative analysis, hence the fresh punching boundaries of active Li (Li bulks) was Therefore, the mass of dissolved inactive Li can be neglected. After a certain period at 26 25 ℃, the mass of the whole Li-biphenyl/THF solution was recorded as (gram as the unit). A given volume of Li-biphenyl/THF solution (2 mL) was then quickly sampled. To ensure the accuracy of the results measured by ICP-AES, the sampled liquid was quickly injected to pure THF ( , gram as the unit) and sealed.
The whole mass of Li-biphenyl/THF after diluting was precisely weighed using a microbalance and recorded as (gram as the unit). Each sampled solution was then used for two parallel digestions; the mass of the digestion liquid was precisely 3) A given amount (2.0 mL) of deionized water was injected into the same air-tight bottle used in step 2 by a 5.0 mL air-tight syringe ( Supplementary Fig. 4b). The generated gas was quickly sampled using a 25 mL air-tight syringe ( Supplementary Fig.   4c), followed by the injection into a vacuum and air-tight Al foil packing bag ( Supplementary Fig. 4d). The gas in the bag was then injected to the GC equipment for quantifying the mass of the inactive Li in "dead Li". Hydrogen is the only gas generated by the reaction of pure Li with water ( Supplementary Fig. 8a). But as shown in Supplementary Fig. 8d, the SEI formed in cycled LMAs will also react with water to release CO2, CH4, C2H4 and C2H6. The generation of additional gases besides hydrogen will affect the molar ratio of H2 in the sample gases, interfering the peak area related to hydrogen for further quantitative measurement of hydrogen. Therefore, the calibration 27 curve (such as the curve in Supplementary Fig. 9a) established using pure Li foil with known weight is not able to accurately measure the inactive Li from cycled LMAs.
Fortunately, we found that argon which has a fixed content amount in all samples, could be used as a reference gas for internal calibration. After sealing in the Ar-filled glove box, the volume of Ar in the gas sample is kept unchanged during the entire measuring process. The integral area of the peaks related to H2 ( ℎ − ) and that of Ar

Data availability
The datasets analyzed and generated during the current study are included in the paper and its Supplementary Information.