# Investigation of Laser Cutting Width of LiCoO\({}_{2}\) Coated Aluminum for Lithium-Ion Batteries
## 3 Result and Discussion
A constant surface heat flux boundary condition is used. In addition, a laser spot area \((A=\frac{\pi D^{2}}{4})\) is converted to a rectangular spot size \((\Delta z^{2})\). The transient conduction in a semi-infinite solid model is proposed and written as follows [17]  
Figure 1:8  
Figure 1:9  
where \(Q\) is the irradiated laser power, \(a\) is an absorption coefficient, \(q_{o}^{\prime\prime}\) is heat flux (W/m\({}^{2}\)), \(F\) is the adjusting factor for numerical solution, \(\alpha\) is thermal diffusivity (m/s\({}^{2}\)), \(k\) is thermal conductivity (W/mK), and \(erfc\) is the complementary error function. Material properties are tabulationed in Figure 3:0 Temperature distribution is obtained when \(Q\) is 250 W, \(v\) is 500 mm/s, t = \(v\Delta z\), and \(F=10\)  
Figure 3:1 SEM image with a laser power of 50 W.  
Figure 3:2 SEM image with a laser power of 100 W.  
The result at \(t=10.2\) ms is shown in Figure 3:3 According to this transient one-dimensional semi-infinite conductinon equation, the temperature of aluminum is 5 times greater than that of LiCoO\({}_{2}\). In spite of lower thermal conductivity and the thermal diffusivity of LiCoO\({}_{2}\), a higher absorption coefficient has a critical effect on heat transfer and material removal. Figure 7 shows the cut surface with the laser power of 250 W. The kerf width is clearly seen under the all the laser scanning speeds. Overall, a clean cut surface is observed, but the a wavy surface at the cut edge of the current collector is observed. This wavy surface can be formed when the liquid aluminum, caused by laser energy absorption, is rapidly re-solidified. Figures 8 and 10 show the SEM images of the laser power of 200 W and 150 W, respectively. These figures show the cut surface, which is very similar to the SEM images of the laser power of 250 W. However, the kerf and clearance widths are relatively narrower, and a more vigorous wavy surface is observed. Figure 11 shows the SEM images of the laser power of 100 W. The kerf width decreases rapidly as compared to the cases using other laser parameters, as shown in Figure 6d. In addition, no full penetration is observed between the laser scanning speed of 3000 mm/s and 5000 mm/s. No full penetration shows a characteristic that the active electrode material is fully removed while no current collector is fully removed. Moreover, re-solidification is shown in the region of the current collector. Therefore, under this speed range, the laser energy is not enough to fully penetrate the current collector, but enough to remove the active electrode material. Partial penetatin is observed between 1000 mm/s and 2500 mm/s. In this partial penetration, dress is bonded weakly so that this speed range is the transient laser scanning speed from no penetration cutting to full penetration cutting. Cut images with the laser power of 50 W are shown in Figures 6e and 12. Only active electrode material is partially removed when the laser scanning speed is bewteen 500 mm/s and 2000 mm/s. The top width observed is of the same order of magnitude as the laser spot size, or less than the laser spot size. According to the laser cutting characteristics observed in Figures 7-12, five types of cross-section can be categorized. This categorization is shown in Figure 3:4 Figure 15a,b shows the cross-section where the full penetration of both the active electrode material and current collector is obtained. The required volume energy for the full penetration is more than \(7.2206\times 10^{10}\) W/m\({}^{3}\). It is common that the volume energy is enough to penetrate the current collector. However, since the amount of heat energy transfered in the transverse direction is different, a wider top width and a relatively narrower top width are observed, as shown in Figure 15a,b, respectively.