Electrochemical Modeling of Linear and Nonlinear Aging of Lithium-Ion Cells

The current density i of the lithium de-/intercalation reaction is calculated by the Butler-Volmer equation

$$\begin{eqnarray}&&{i}_{n}={i}_{0,n}\left(\exp \left(\displaystyle \frac{{\alpha }_{a,n}F}{{RT}}{\eta }_{n}\right)-\exp \left(-\displaystyle \frac{{\alpha }_{c,n}F}{{RT}}{\eta }_{n}\right)\right)\end{eqnarray} \tag{ 3 }$$

where the index n symbolizes the negative or positive electrode, i₀ is the exchange current density, α_a and α_c are the anodic and cathodic charge-transfer coefficients, F, R and T represent Faraday's constant, the universal gas constant and the cell temperature, respectively. The overpotential η_neg of the main reaction at the negative electrode is obtained by the solid phase potential Φ_s, the liquid phase potential Φ_l, the negative electrode equilibrium potential E_Eq,neg and the potential drop ${i}_{\mathrm{neg}}{R}_{{{Li}}^{+}}$²⁹

$$\begin{eqnarray}&&{\eta }_{\mathrm{neg}}={{\rm{\Phi }}}_{s}-{{\rm{\Phi }}}_{l}-{E}_{\mathrm{Eq},\mathrm{neg}}-{i}_{\mathrm{neg}}{R}_{{{Li}}^{+}}\end{eqnarray} \tag{ 4 }$$

The potential drop by a cathode electrolyte interphase (CEI) at the positive electrode is left out of consideration in this work. Therefore, the overpotential η_pos is defined as

$$\begin{eqnarray}&&{\eta }_{\mathrm{pos}}={{\rm{\Phi }}}_{s}-{{\rm{\Phi }}}_{l}-{E}_{\mathrm{Eq},\mathrm{pos}}\end{eqnarray} \tag{ 5 }$$

with the positive electrode equilibrium potential E_Eq,pos. Table I shows the chosen parameters—measured, taken from the literature and estimated—for the above introduced model at 25 °C.

Table I.  Electrochemical model parameters measured from a Sanyo UR18650E cell labeled with superscript m. The superscript e indicates estimated values.

Parameter	Negative electrode	Separator	Positive electrode
Geometry
Thickness l	70 μm m	20 μm m	60 μm m
Mean particle radius rp	10 μm m		4 μm m
Solid phase fraction εs	0.59 e		0.61 e
Liquid phase fraction εl	0.3 e	0.45 e	0.3 e
Thermodynamics
Equilibrium voltage EEq	see Fig. A·1 m		see Fig. A·1 m
Maximum Li+ concentration cs,max	31 370 mol m−3 33		51 385 mol m−3 7
Initial state of charge $\displaystyle \frac{{c}_{s,0}}{{c}_{s,\max }}$	0.8 e		0.4 e
Kinetics
Reaction rate constant kn	1.5 × 10−11 m s−1 e		1.5 × 10−11 m s−1 e
Activation energy ${{Ea}}_{{k}_{n}}$	1 × 104 J mol−1 e		1 × 104 J mol−1 e
Anodic charge-transfer coefficientαa	0.5 e		0.5 e
Cathodic charge-transfer coefficient αc	0.5 e		0.5 e
Transport
Solid diffusivity Ds	9 × 10−11 m2 s−1 e		2.6 × 10−13 m2 s−1 e
Activation energy ${{Ea}}_{{D}_{s}}$	5 × 104 J mol−1 34		2.5 × 104 J mol−1 34
Solid conductivity σ	100 S m−1 e		3.8 S m−1 e
Parameter		Electrolyte
Electrolyte concentration cl		1000 mol m−3 e
Electrolyte diffusivity Dl		see Eq. 23 35
Electrolyte conductivity κ		see Eq. 24 35
Activity dependency $\displaystyle \frac{\partial \mathrm{ln}{f}_{\pm }}{\partial \mathrm{ln}{c}_{l}}$		see Eq. 25 35
Transport number t+		0.3835
Parameter		Cell
Nominal capacity CN		2.05 Ah m
Radius rcell		9 mm m
Height hcell		65 mm m
Mass mcell		45 g m
Cell surface area Acell		4.1846 × 10−3 m2
Cell volume Vcell		1.654 × 10−5 m3

We distinguish between SEI formation due to its non-ideal insulating properties and SEI re-formation due to cracking of the layer. Both are modeled as irreversible side reactions by cathodic Tafel equations. The current density for SEI formation is calculated by

$$\begin{eqnarray}&&{i}_{\mathrm{SEI},\mathrm{form}}=-{i}_{0,\mathrm{SEI}}\exp \left(-\displaystyle \frac{{\alpha }_{c,\mathrm{SEI}}F}{{RT}}{\eta }_{\mathrm{SEI},\mathrm{form}}\right)\end{eqnarray} \tag{ 6 }$$

with the SEI's exchange current density i_0,SEI and cathodic charge-transfer coefficient α_c,SEI. The overpotential η_SEI,form is calculated by

$$\begin{eqnarray}&&{\eta }_{\mathrm{SEI},\mathrm{form}}={{\rm{\Phi }}}_{s}-{{\rm{\Phi }}}_{l}-{E}_{\mathrm{Eq},\mathrm{SEI}}-{i}_{\mathrm{SEI},\mathrm{form}}{R}_{{e}^{-}}\end{eqnarray} \tag{ 7 }$$

where ${i}_{\mathrm{SEI},\mathrm{form}}{R}_{{e}^{-}}$ symbolizes the potential drop due to the insulating conductivity of the SEI for electrons. Due to its non-ideal insulating properties, the solid electrolyte interphase grows continuously. However, this formation slows down over time or with cycles due to the increasing potential drop caused by the growth of the film.

SEI re-formation considers an expansion factor f_exp dependent on the stoichiometry x as depicted in Fig. 2. This expansion factor is the gradient of a graphite expansion curve as previously introduced and as already implemented in an electrochemical SEI model by Kindermann et al.²⁹

$$\begin{eqnarray}&&{i}_{\mathrm{SEI},\mathrm{re}-\mathrm{form}}=-{i}_{0,\mathrm{SEI}}\,{f}_{\exp }(x)\,\exp \left(-\displaystyle \frac{{\alpha }_{c,\mathrm{SEI}}F}{{RT}}{\eta }_{\mathrm{SEI},\mathrm{re}-\mathrm{form}}\right)\end{eqnarray} \tag{ 8 }$$

The overpotential η_{SEI,re−form} considers no iR drop

$$\begin{eqnarray}&&{\eta }_{\mathrm{SEI},\mathrm{re}-\mathrm{form}}={{\rm{\Phi }}}_{s}-{{\rm{\Phi }}}_{l}-{E}_{\mathrm{Eq},\mathrm{SEI}}\end{eqnarray} \tag{ 9 }$$

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The current density of the lithium plating side reaction is calculated by a Butler-Volmer equation, as reported by Arora et al.³⁶

$$\begin{eqnarray}&&{i}_{\mathrm{lpl}}={i}_{0,\mathrm{lpl}}\left(\exp \left(\displaystyle \frac{{\alpha }_{a,\mathrm{lpl}}F}{{RT}}{\eta }_{\mathrm{lpl}}\right)-\exp \left(\displaystyle \frac{-{\alpha }_{c,\mathrm{lpl}}F}{{RT}}{\eta }_{\mathrm{lpl}}\right)\right),{\eta }_{\mathrm{lpl}}\leqslant 0\,{\rm{V}}\end{eqnarray} \tag{ 10 }$$

with the lithium plating exchange current density i_0,lpl and the anodic and cathodic charge-transfer coefficients α_a,lpl and α_c,lpl. This equation is valid as long as the overpotential η_lpl is less than or equal to 0 V. Once the overpotential becomes positive again and as long as reversibly plated lithium exists, lithium stripping takes place

$$\begin{eqnarray}\begin{array}{rcl}{i}_{\mathrm{lst}} & = & {i}_{0,\mathrm{lst}}\left(\exp \left(\displaystyle \frac{{\alpha }_{a,\mathrm{lst}}F}{{RT}}{\eta }_{\mathrm{lst}}\right)-\exp \left(\displaystyle \frac{-{\alpha }_{c,\mathrm{lst}}F}{{RT}}{\eta }_{\mathrm{lst}}\right)\right)\\ & & \times \ f\left(\displaystyle \frac{\xi {q}_{\mathrm{lpl}}-{q}_{\mathrm{lst}}}{{q}_{\mathrm{cor}}}\right),{\eta }_{\mathrm{lst}}\gt 0\,{\rm{V}}\end{array}\end{eqnarray} \tag{ 11 }$$

where f is a damping function (as shown in Fig. 3), q_lpl and q_lst describe the charge quantity of plated and stripped lithium, ξ is the ratio of reversibly plated lithium and q_cor denotes a correction variable to ensure valid units. The damping function enables the lithium stripping reaction to be stopped as soon as all reversibly plated lithium has been dissolved. In contrast to a step function, the damping function is based on a Sigmoid function to ensure a stable numeric solver. Irreversibly plated lithium has lost its electrical contact to the negative electrode and is also called dead lithium, as shown in Fig. 1. The overpotentials are defined as

$$\begin{eqnarray}&&{\eta }_{\mathrm{lpl}}={\eta }_{\mathrm{lst}}={{\rm{\Phi }}}_{s}-{{\rm{\Phi }}}_{l}-{E}_{\mathrm{Eq},\mathrm{lpl}/\mathrm{lst}}\end{eqnarray} \tag{ 12 }$$

with the equilibrium potentials E_Eq,lpl = E_Eq,lst = 0 V. Here, the potential drop iR is left out of consideration due to the aforementioned high conductivity of metallic lithium.

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We consider a surface film on the graphite particles that is composed of SEI and metallic lithium

$$\begin{eqnarray}&&{\delta }_{\mathrm{film}}={\delta }_{0,\mathrm{film}}-\displaystyle \frac{({q}_{\mathrm{SEI},\mathrm{form}}+{q}_{\mathrm{SEI},\mathrm{re}-\mathrm{form}}){M}_{\mathrm{SEI}}}{F{\rho }_{\mathrm{SEI}}}-\displaystyle \frac{({q}_{\mathrm{lpl}}+{q}_{\mathrm{lst}}){M}_{\mathrm{Li}}}{F{\rho }_{\mathrm{Li}}}\end{eqnarray} \tag{ 13 }$$

with their molar masses M_SEI and M_Li and densities ρ_SEI and ρ_Li. δ_0,film symbolizes the initial film thickness. The charge quantities q are calculated by integrating the side reaction current densities. Cathodic current densities (i_SEI,form, i_{SEI,re−form} and i_lpl) have a minus-sign and anodic current densities (i_lst) a plus-sign. Therefore, SEI formation, SEI re-formation and lithium plating cause the film to grow, whereas lithium stripping partly dissolves it.

Furthermore, we consider effective transport parameters for the electrolyte diffusion coefficient D_l, the ionic conductivity κ and the electronic conductivity σ

$$\begin{eqnarray}&&{D}_{l,\mathrm{eff}}=\displaystyle \frac{1}{{N}_{M}}\,{D}_{l}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&{\kappa }_{\mathrm{eff}}=\displaystyle \frac{1}{{N}_{M}}\,\kappa \end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&{\sigma }_{\mathrm{eff}}=\displaystyle \frac{1}{{N}_{M}}\,\sigma \end{eqnarray} \tag{ 16 }$$

where MacMullin's number N_M describes the influence of porosity and tortuosity changes in the negative and positive electrode. In the literature, MacMullin's number is mostly given as a function depending on the porosity. However, especially for small porosities caused by film growth and pore clogging, adequate experimental data is missing. Based on simulation results by Xu et al.,²⁷ we assume an almost linearly increasing function depending on the cycles. Figure 4 shows both the considered MacMullin's number and its reciprocal.

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Finally, Table II shows all parameters for the SEI re-/formation and lithium plating/stripping side reaction definitions.

The electrochemical model is coupled with a 0D thermal model that simulates an evenly distributed heat in the cell. The total heat generation $\dot{q}$ is comprised of ohmic heat ${\dot{q}}_{\mathrm{ohm}}$, reaction heat ${\dot{q}}_{\mathrm{reac}}$ and reversible heat ${\dot{q}}_{\mathrm{rev}}$

$$\begin{eqnarray}\begin{array}{rcl}\dot{q} & = & {\dot{q}}_{\mathrm{ohm}}+{\dot{q}}_{\mathrm{reac}}+{\dot{q}}_{\mathrm{rev}}={i}_{l}{\rm{\nabla }}{{\rm{\Phi }}}_{l}+{i}_{s}{\rm{\nabla }}{{\rm{\Phi }}}_{s}\\ & & +\ \displaystyle \sum _{i}{a}_{i}{i}_{i}\left({\eta }_{i}+T\displaystyle \frac{\partial {E}_{\mathrm{Eq},i}}{\partial T}\right)\end{array}\end{eqnarray} \tag{ 17 }$$

with the electrolyte current density i_l and electrode current density i_s. Index i symbolizes the partial reactions at the negative and positive electrode. The entropy for both electrodes is given in the Appendix (see Fig. A·2). The heat transfer is considered by convection

$$\begin{eqnarray}&&{\dot{Q}}_{\mathrm{conv}}={{hA}}_{\mathrm{cell}}\left(T-{T}_{\infty }\right)\end{eqnarray} \tag{ 18 }$$

with the heat transfer coefficient h, the cell's surface A_cell and temperature T as well as the ambient temperature T_∞. The radiation is calculated by

$$\begin{eqnarray}&&{\dot{Q}}_{\mathrm{rad}}={\varepsilon }_{{th}}{\sigma }_{B}{A}_{\mathrm{cell}}\left({T}^{4}-{T}_{\infty }^{4}\right)\end{eqnarray} \tag{ 19 }$$

in which ε_th describes the emissivity and σ_B the Stefan–Boltzmann constant. In addition, the cell's thermal mass is considered by

$$\begin{eqnarray}&&{\dot{Q}}_{{th}}={m}_{\mathrm{cell}}{c}_{p}\displaystyle \frac{\partial T}{\partial t}\end{eqnarray} \tag{ 20 }$$

with its mass m_cell and specific heat capacity c_p. Hence, the governing equation is given by

$$\begin{eqnarray}\begin{array}{rcl}{m}_{\mathrm{cell}}{c}_{p}\displaystyle \frac{\partial T}{\partial t} & = & {V}_{\mathrm{cell}}\displaystyle \frac{1}{l}{\displaystyle \int }_{x=0}^{l}\dot{q}\,{dx}-{{hA}}_{\mathrm{cell}}\left(T-{T}_{\infty }\right)\\ & & -\ {\varepsilon }_{{th}}{\sigma }_{B}{A}_{\mathrm{cell}}\left({T}^{4}-{T}_{\infty }^{4}\right)\end{array}\end{eqnarray} \tag{ 21 }$$

with the thickness of a cell layer l = l_neg + l_sep + l_pos. All cell design information is listed in Tables I, and Table III shows the parameters of the thermal model.

Table III.  Thermal model parameters. The superscript e indicates estimated values.

Parameter	Value
Specific heat capacity cp	1000 J kg−1 K−1 7
Heat transfer coefficient h	10 W m−2 K−1 e
Emissivity εth	0.8 39
Ambient temperature T∞	298 K
Entropy $\tfrac{\partial {E}_{\mathrm{Eq}}}{\partial T}$	see Fig. A·2 40,41

The temperature dependency of the anodic and cathodic reaction rate constants k_a and k_c and the diffusion coefficients in the negative and positive active material D_s,neg and D_s,pos are described by the Arrhenius equation

$$\begin{eqnarray}&&{\rm{\Psi }}={{\rm{\Psi }}}_{\mathrm{ref}}\exp \left(\displaystyle \frac{{E}_{a,{\rm{\Psi }}}}{R}\left(\displaystyle \frac{1}{{T}_{\mathrm{ref}}}-\displaystyle \frac{1}{T}\right)\right)\end{eqnarray} \tag{ 22 }$$

with ${{E}_{a}}_{,{\rm{\Psi }}}$ as the activation energy. Ψ marks the dependent variable and Ψ_ref its reference value at the reference temperature T_ref.

The temperature dependency of the diffusion coefficient in the electrolyte D_l, the liquid phase conductivity κ and the thermodynamic factor $\tfrac{\partial \mathrm{ln}{f}_{\pm }}{\partial \mathrm{ln}{c}_{l}}$ are given by Valøen et al.³⁵ in Eqs. 23, 24 and 25.

The simulated cell voltages and temperatures of the electrochemical and thermal model are shown in Fig. 5 and compared to the experimental data for discharge with C/10, C/5, C/2, 1C and 2C at ambient temperatures of 25 °C and 0 °C. We calculated mean absolute errors (MAE) and root mean square errors (RMSE) to assess the deviation between model and experiment. At 25 °C, the maximum MAEs are 14 mV (2 C) and 0.2 °C (2 C) and the maximum RMSEs are 21 mV (2 C) and 0.25 °C (2 C). At 0 °C, the maximum MAEs are 19 mV (2 C) and 0.3 °C (2 C) and the maximum RMSEs are 23 mV (2 C) and 0.4 °C (2 C). Therefore, the simulation results are in very good agreement with the experimental data for all C-rates as well as for both temperatures.

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Figure 6 shows the measured cell's relative capacity determined in the checkup cycles of the aging experiment (symbols). In the early stage that is arising from the beginning of cycling to about cycle 500, an almost linear or square-root-shaped, decelerating capacity loss is seen. Thereafter, an accelerating, nonlinear capacity loss denotes the later stage with a relative capacity of 65% after 800 cycles. Usually, an end of life is defined by falling below a relative capacity of 80% that is reached for this cell after 600 cycles, already within the stage of accelerated capacity loss. In a former study,¹³ we showed that the loss of lithium inventory is the dominant aging mechanism within the scope of this aging experiment. Electrochemical characterization and post-mortem analysis revealed solid electrolyte interphase growth and lithium plating induced capacity loss.

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Based on our electrochemical modeling approach and by setting the ratio of reversibly plated lithium ξ to one, we are able to simulate sole SEI formation and re-formation. Lithium plating may still take place but is plated completely reversibly and will be stripped subsequently. The simulation result is shown by the green line in Fig. 6 that is an almost linear or square-root-shaped capacity loss during cycling. The slope of the curve is fitted by the SEI re-/formation exchange current density i_0,SEI.

In contrast, the entire irreversible lithium plating is modeled by setting the ratio of reversibly plated lithium ξ to zero. No lithium stripping side reaction takes place anymore. The blue line in Fig. 6 shows the simulation result that exhibits an early stage, linear capacity loss and an accelerating capacity loss, starting at about cycle 400. Compared to the measurements, the simulation results in an earlier and more intense capacity loss.

Finally, the black line in Fig. 6 shows the simulated relative capacity considering a changing ratio of reversibly plated lithium ξ over cycles. With this approach, we assume that the amount of reversibly plated lithium decreases with ongoing cycling. In other words, the more lithium is plated, the more lithium is irreversibly plated. With an MAE of 0.17% and an RMSE of 0.25%, the simulation results are in very good agreement with the experimental data. Based on our modeling approach, we are able to simulate both linear and nonlinear aging as well as to define the onset and slope of nonlinear aging. Differentiating between reversible and irreversible lithium plating and their impact on capacity loss is also consistent to operando lithium plating quantifications using incremental capacity analysis shown by Ansean et al.⁴²

The fitted ratio of reversibly plated lithium ξ over cycles is shown in Fig. 7. Up to cycle 306, no lithium plating and thus no lithium stripping side reactions take place, as the potential of the negative electrode is always positive vs Li/Li⁺. As soon as this potential becomes negative and lithium is plated, we assume ξ to be 0.99 since Howlett et al.⁴³ showed a cycling efficiency of greater than 99% for lithium metal electrodes. To obtain a linear aging behavior, the cycling efficiency remains constant for about one hundred cycles. However, the efficiency declines with ongoing cycling due to degradation mechanisms, inhomogeneous current and potential distributions, and deposit morphology changes.^12,13,43,44 The change in the ratio of reversibly plated lithium concurs with the onset and slope of nonlinear aging in Fig. 6. In the end, the ratio is of less than 80% which means that one fifth is irreversibly plated.

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Figure 8 shows the simulated cell voltages (lines) compared to experimental data (symbols) over discharge capacity obtained from checkup cycles. With minimum errors of 8 mV (MAE) and 12 mV (RMSE) for cycle 200 and maximum errors of 27 mV (MAE) and 44 mV (RMSE) for cycle 700, the results are in very good agreement. Furthermore, the simulation results show that the model considers capacity as well as power fade.

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The capacity loss over cycles is depicted in Fig. 9. SEI formation shows a decelerated, square-root-shaped behavior over cycles, as the potential drop increases due to the growth of the film. However, SEI re-formation considers no influencing film and potential drop, and thus results in an almost linear capacity loss. Only by cause of capacity loss and shortened charge/discharge cycles, SEI re-formation decelerates. In contrast, irreversible lithium plating is unobtrusive over many cycles, but subsequently causes the nonlinear capacity fade between 500 and 800 cycles. After 800 cycles, about two thirds of the capacity loss are caused by SEI re-/formation and one third by irreversible lithium plating.

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The following subsection shows the characteristics of SEI re-/formation and lithium plating/stripping over cycling based on simulation results. Figure 10 depicts the cyclic cell voltage (a) and main reaction current density (b). With ongoing aging, the total cycle time decreases as the cell's capacity fades. Moreover, the resistance rise causes higher polarization that shortens the CC phase and extends the CV phase during charging. Both capacity and power loss—which in turn cause the energy loss of the cell—are clearly recognizable based on the cell voltage.

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Figure 10c depicts the side reaction current density of SEI formation (solid lines) and re-formation (dotted lines). For both, the current density declines while discharging and rises again while charging the cell. The maximum of current density corresponds to the transition from CC to CV charging, as the driving overpotentials are at a maximum. With ongoing aging, less SEI formation occurs because the total cycle time is getting shorter, but mainly because of the increasing potential drop caused by the growth of the film. In contrast, no iR drop is considered for SEI re-formation. As expected, SEI re-/formation is characterized by a decelerating behavior over cycling. In addition, the results show a higher SEI re-/formation for higher cell voltages, which means for higher SOCs.

The lithium plating and lithium stripping side reaction densities are shown in Fig. 10d. As soon as the local potential of the graphite anode becomes negative vs Li/Li⁺, lithium plating takes place, which reveals its maximum at the transition from the CC to the CV charging phase as well. Due to the decreasing main reaction current density in the CV charging phase, the cell's polarization also decreases. Once the driving overpotential becomes positive vs Li/Li⁺, subsequent lithium stripping dissolves the reversibly plated lithium. The lithium stripping side reaction density forms a maximum and diminishes towards the end of charging. In the subsequent discharging phase, the remaining amount of reversibly plated lithium is dissolved which causes a characteristic voltage plateau if the amount is big enough.³⁰ Furthermore, lithium plating firstly appears after a few hundred cycles and increases and then declines again with ongoing cycling. Finally, this is caused by the capacity loss, the increasing polarization, the shortened CC and extended CV phases—and therefore the reduced time when lithium plating can occur—and the transition from a stage I to a stage II potential plateau in the negative electrode caused by LLI (see Fig. 12).

Integrating the side reaction current densities results in surface charge quantities, which are shown in Fig. 11 over the thickness of the negative electrode. SEI formation and re-formation (solid and dotted lines in Fig. 11a, respectively) take place in the entire electrode. However, the SEI grows faster at the negative electrode/separator interface. In contrast, irreversible lithium plating occurs on the outer edge of the negative electrode at its interface to the separator,^5,24 as shown in Fig. 11b. At the interface of the negative electrode and its current collector, the overpotential vs Li/Li⁺ is always positive and no lithium is deposited. Finally, much more lithium is spatially deposited compared to SEI re-/formation, that is based on the difference in the magnitude of the side reaction current densities, as depicted in Figs. 10c and 10d.

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Figure 12 shows the shifts in stoichiometry—which is the intercalation degree—over cycles of the negative and positive electrode at end-of-charge (EOC) and end-of-discharge (EOD) as a consequence of capacity fade. As expected, the stoichiometry of the negative electrode at EOC decreases with ongoing aging due to LLI. The declining change in stoichiometry up to cycle 500, which increases subsequently, reveals the linear and nonlinear aging behavior. While the LLI effects a transition from a stage I to a stage II potential plateau in the negative electrode, the potential of the positive electrode slightly increases at EOC, which is defined by the cutoff-voltage of the cell at 4.2 V, which is the difference between the negative and positive electrode potential. As a result of the transition of the potential plateaus, the lithium plating side reaction diminishes with ongoing aging.

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At the EOD, the stoichiometry of the positive electrode decreases with ongoing aging based on the LLI as the dominant aging mechanism. Again, the change in stoichiometry results from the decelerating capacity loss due to SEI re-/formation and the subsequent accelerated capacity loss caused by irreversible lithium plating. Furthermore, the stoichiometry is a relative but not absolute variable and thus the shifts are not equidistant for the negative and positive electrode.