**4. Discussion**

To study and track the reasons leading to lithium plating, starting from cycle 116 in our cell, we plotted the ionic conductivity of solid particles, the electrolyte, and electrode/separator interface over the constant current (CC) charge period for the anode and cathode, as shown in Figure 5 and 6 respectively. Figure 5A shows calculated ionic conductivity for region A which are the solid active particles of the negative electrode from start until end of the CC charge period for the 116th cycle. Two points of X=1 and X = 0.9 are chosen to be shown. X = 1 for the anode means the separator side. X = 0.9 is also displayed as it is the furthest point of the anode from the separator that shows lithium deposition over the whole simulated cycle life. As expected, the ionic conductivity of the particles declined while the SOC increased. At the end of the charge, particles closer to the separator side were at a higher SOC and therefore showed poorer ionic conductivity in comparison to particles with a higher distance to the separator. The beginning of Li-plating is where a short plateau is observable in the conductivity trend at the end of CC charge. Effective electrolyte ionic conductivity in Figure 5B is showing a similar trend. It displayed a higher value during early charge stages in comparison to the end of the charge as well as poorer particle ionic conductivity closer to the separator. This is explainable as the side reactions and surface layer formation was happening more at the separator side, leading to more porosity reduction which is equal to less electrolyte volume fraction. The last transport region of the anode that we include in this study is the electrolyte/solid particles interface. As shown in Figure 5C, the ionic conductivity increased while charging until a local SOC of 50%. By continuing the CC charge process we can observe a decline in conductivity values followed by a plateau which is the start of lithium plating. Comparing *<sup>σ</sup>s*,*<sup>a</sup>* to the corresponding Figure 6A, shows that anode active particles are having a better ionic conductivity, except for the end of the charge process which were slightly smaller than the cathode particle conductivity values. Figure 6B shows that electrolyte had a better effective ionic conductivity of factor 8 at the cathode side. It is the same when we compare their interface conductivity as well. Figure 6C shows that *<sup>σ</sup>i*,*<sup>c</sup>* is one order of magnitude bigger than *<sup>σ</sup>i*,*a*.

**Figure 5.** Ionic conductivity of the simulated cell at cycle 116 for the negative electrode side. Start of Li-plating is when a plateau is formed. ( **A**) Is the calculated ionic conductivity for region A over start until end of CC (current) charge period of the 116th cycle. X = 1 is at the separator side and X = 0.9 is at 0.9 of anode thickness closer to the separator. (**B**) is the effective ionic conductivity of electrolyte in the negative electrode over start until end of CC charge period of the 116th cycle. Data comes from the model. ( **C**) Is the calculated ionic conductivity for region B over start until end of the CC charge period of the 116th cycle.

**Figure 6.** Ionic conductivity of the simulated cell at cycle 116 for the positive electrode side. ( **A**) Is the calculated ionic conductivity for region E over start until end of the CC charge period of the 116th cycle. X = 0 is at separator side and X = 1 is at the current collector of the cathode. (**B**) Is the effective ionic conductivity of the electrolyte in the positive electrode over start until end of the CC charge period of the 116th cycle. Data comes from the model. ( **C**) Is the calculated ionic conductivity for region D over start until end of the CC charge period of the 116th cycle.

For comparison, the same is plotted in Figures 7 and 8 for the ionic conductivity results of the cell at cycle 10 where the cell is not aged and shows no trace of lithium plating. Looking at Figures 7A and 8A, we can see that values neither for the cathode nor the anode change significantly. In comparison to cycle 10, the final value at the end of charge of cycle 116 for both cathode and anode at the separator side declined. For the positive electrode, the cathode particles could not de-intercalate fully during the 10th cycle. To explain the anode behavior, listed data in Table 3 is helpful. Considering the *<sup>σ</sup>s*,*<sup>a</sup>* at different cycles, it is observable that by aging, the anode distribution of lithium ions becomes deficient so that by increasing the cycle number *<sup>σ</sup>s*,*<sup>a</sup>* at the current collector side shows higher values. This means by increasing the cycle number, during a charge process, particles atX=0 only charged to the lower SOCs. The reverse is observable for the particles at the separator side of the anode. This can lead the cell to favorable conditions for Li deposition. Figures 7B and 8B show that although electrolyte conductivity does not show a significant change at the cathode, the anode values declined by factor of 4. A similar behavior is observable for the anode interface ionic conductivity. Figure 7C shows that conductivity values of the 10th cycle are about 4 times bigger than those at cycle 116. However no significant variation is shown in Figure 8C in comparison to cycle 116. These two behaviors are another factor that cause Li-plating.


**Table 3.** Ionic conductivity for solid particles of active materials *σs*, electrolyte in the porous electrodes *<sup>σ</sup>l*, and electrode/electrolyte interface *σi* at cycle number 10, 50, 100, 116, 150, and 230. Cycle 116 is the start of Li-P and cycle 230 is the start of nonlinear aging behavior of the cell. *σs* and *σi* are calculated from Nernst–Einstein relation. *σl*is calculated directly through the model.

**Figure 7.** Ionic conductivity of the simulated cell at cycle 10 for the negative electrode side. (**A**) Is the calculated ionic conductivity for region A over start until end of the CC charge period of the 10th cycle. X = 1 is at the separator side and X = 0.9 is at 0.9 of relative anode thickness closer to the separator. (**B**) Is the effective ionic conductivity of the electrolyte in the negative electrode over start until end of the CC charge period of the 10th cycle. Data comes from the model. (**C**) Is the calculated ionic conductivity for region B over start until the end of the CC charge period of the 10th cycle.

**Figure 8.** Ionic conductivity of the simulated cell at cycle 10 for the positive electrode side. (**A**) Is the calculated ionic conductivity for region E over start until end of the CC charge period of the 10th cycle. X=0 is at the separator side and X = 1 is at the current collector of the cathode. (**B**) Is the effective ionic conductivity of electrolyte in the positive electrode over start until end of the CC charge period of 10th cycle. Data comes from the model. (**C**) Is the calculated ionic conductivity for region D over start until end of the CC charge period of the 10th cycle.
