## 4 Discussion
Since NMC 622 has a molar mass of 203.5 g/mol and a bulk density of 4.76 g/cm\({}^{3}\), the Li concentration \(C_{0}\) was calculated to be 0.0234 mol/cm\({}^{3}\). According to the study from [PERSON] et al. [22], in order to calculate the chemical diffusion coefficient of lithium-ion in LiFeO\({}_{4}\) (LFP), electrode area \(A\) in Equation (2) was substituted by 1/3 of the of the total Brunauer-Emmett-Teller (BET) surface area, because the lithium-ion diffusion path in LFP is one-dimensional. Since NMC 622 has a two-dimensional diffusion path for lithium-ion along (111) plane [23], the electrode area \(A\) is calculated as two-third of the total BET surface area for structured and unstructured electrodes. The BET surface equals the specific surface area multiplied by the mass of active material in the electrode, thus the electrode area is calculated with following equation:  
\[A=A_{BET}\cdot\frac{2}{3}=A_{spec}\cdot m_{active}\cdot\frac{2}{3} \tag{3}\]  
The chemical diffusion coefficients of cells with different cathodes were calculated combining the Equations (2) and (3), as well as the slope from Figure 6, and are shown in Table 3. The diffusion coefficient of lithium-ions in NMC 622 electrode during discharge at room temperature varies from \(2.7\times 10^{-13}\) cm\({}^{2}\)/s to \(8.6\times 10^{-13}\) cm\({}^{2}\)/s. However, the values are lower compared to the diffusion coefficient acquired from galvanostatic intermittent titration technique (GITT) of \(8\times 10^{-11}\) cm\({}^{2}\)/s [24]. Table 3 shows that the diffusion coefficients of lithium-ions during charge process are higher comparing to discharge process, indicating that the during deintercalation, lithium-ions require less activation energy to diffuse from one octahedral site to the next site through an intermediate tetrahedral site [24]. The lithium-ion diffusivity in the NMC 622 electrode decreases with increasing electrode  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Thickness** & **Pitch Distance** & \multicolumn{2}{c}{\(\Delta\)**P\({}^{\text{/}}\)/\(\Delta\)v\({}^{\text{/}2}\) [A-s\({}^{\text{/}2}\cdot\)V\({}^{\text{-}1/2}\)]**} & \multicolumn{2}{c}{**D\({}_{\text{CV}}\) [cm\({}^{2}\)/s]**} \\ \cline{2-6}
**(\(\mu\)m)** & **(\(\mu\)m)** & **Charge** & **Discharge** & **Charge** & **Discharge** \\ \hline
91 & - & 0.41 & \(-\)0.30 & \(1.62\times 10^{-12}\) & \(8.65\times 10^{-13}\) \\
91 & 200 & 0.37 & \(-\)0.22 & \(1.84\times 10^{-12}\) & \(6.52\times 10^{-13}\) \\
91 & 400 & 0.41 & \(-\)0.25 & \(1.85\times 10^{-12}\) & \(6.90\times 10^{-13}\) \\
91 & 600 & 0.44 & \(-\)0.29 & \(1.94\times 10^{-12}\) & \(8.43\times 10^{thickness, which corresponds to the deterioration of rate capability for thick electrodes. Although structured cathodes show higher discharge capacity at C/2 to 2C in galvanostatic measurement, the diffusion coefficients of structured and unstructured cathodes are at the same level (Table 3). However, it should be pointed out that the electrode area \(A\) can only be controversially discussed. In recent research from [PERSON] et al., it was shown that the sidewalls of laser generated patterns play a dominant role regarding lithium-ion diffusion [14]. Therefore, it is justified to replace the electrode area \(A\) (Equation (3)) by the electrode surface-shell envelope, assuming that the direct contact area of active material to free liquid electrolyte provides the main contribution to lithium-ion diffusion kinetics. After laser structuring, the surface of electrode can expand 100-300%. The generated surface leads to a shortened diffusion path for lithium-ions inside the bulk electrode, and therefore improves energy at high power. In addition, the electrode wetting ability of laser structured electrodes with liquid electrolytes can be accelerated and become more homogeneous due to the capillary effect, which is a benefit regarding cell production costs and safety issues [25].