## 3 Results and Discussion
### GITT--Chemical Diffusion Coefficient  
Figure 4 presents the typical behaviour of the transient and steady-state voltages for a reference-cell. As a function of square root of time, the transient voltage change shows usually a linear trend. While using these parameters, the diffusion coefficient for each change in stoichiometry is reported in Figure 5. The product of BET surface area and the active material mass can define the electrochemical active area. For the unstructured and structured electrodes values of 136 cm\({}^{2}\) and 93 cm\({}^{2}\) are achieved, respectively. The approach is valid for a description of the 2D surface area (dashed line in Figure 5). Further information regarding the composite electrodes, such as mass, density, and porosity, can be extracted from [31]. Very recent research results were achieved, in which it could be proven that during discharging the lithium concentration at cathode side is significantly increased on top and along the contour of free-standing microstructures, i.e., the side-walls of laser generated grid structures are getting activated to provide additional Li pathways [37]. Therefore, the impact of the free-standing structures on the electrode surface needs to be included in a three-dimensional (3D) description, for which their contribution relates to the top and surrounding walls of each single structure. Based on the laser parameters used for the 3D structure generation, a decrease of 36% in surface area (2D) is expected  
Figure 4: Measured variables in the galvanostatic intermittent titration technique (GITT) for the evaluation of diffusion coefficient: (**a**) transient \(E_{\tau}\) and (**b**) equilibrium \(E_{s}\) potentials. Insets are illustrating the shaded part of the measured current pulse, which is taken into account for the respective potential. Figure 5: Diffusion coefficient of Li-ions obtained by GITT as a function of stoichiometry. Inset is illustrating the measured diffusion coefficient (log scale) as a function of stoichiometry. along with an increase of over 300%, due to the lateral wall contribution (3D) for the structured cathode layer. The titration technique offers information in relation to the phase diagram, i.e., the existing phases in the system. The diffusion coefficient corresponding to the laser structured material tends to be more sensitive to the phase transitions. At \(x\)-0.94 a clear change in the slope is observed, which, according to [38; 39], is related to the first order insulator-metal transition. For the \(x\) range between 0.94-0.86, the diffusion coefficient is described by a plateau in quite good agreement with the two-phase region that was described in the previous electrochemical studies. The measurements by [PERSON] et al. [40] found this two-phase region in the \(x\) range from 0.95 to 0.83, whereas lower concentration for \(x\) = 0.75 or 0.80 was reported by [38; 41], respectively. Smaller titration steps are needed for a more precise determination of the phase boundaries composition. Nevertheless, in this region, the diffusion coefficients of the two different material types are the lowest achieved (insert graph in Figure 5). Below \(x\)-0.86 the diffusion coefficient determined for laser structured sample is five times higher than for the unstructured. This range in stoichiometry corresponds to the layered hexagonal single phase [40; 42], where the 3D structures seem to have an impact on the kinetic properties. Approaching a lower \(x\), i.e., the order-disorder transition known for \(x\)-0.5, the diffusion coefficient of the cell with structured electrode tends to be more sensitive and it shows a change in slope. The values of the diffusion coefficients are in the range that is given by previous studies [43], which are influenced by the measurements parameters, voltage range, electrolyte properties, etc. However, the goal of this work was to determine the relative values with respect to the specific design characteristics of reference cell and cell with structured electrode.