## 3 Results and Discussion
### Width, Removal Energy, and Cut Surface of the Compressed Cathode  
Figure 3a shows the kerf width with respect to scanning speed (left) and volume energy (right). The kerf width is not formed with the laser power of 50 W. When the scanning speed is faster than 2500 mm/s, the kerf width is not formed with the laser power of 100 W. Increasing scanning speed from 500 mm/s to 2500 mm/s decreases the kerf width with the laser power of 100 W. According to volume energy, volume energy greater than 9.628 \(\times 10^{10}\) J/m\({}^{3}\) is required to form the kerf width with the laser power of 100 W. The kerf width is not formed with the laser power of 150 W when the scanning speed is faster than 4000 mm/s so that it is noted that the volume energy greater than  
Figure 2: Definition of areas for cutting efficiency. \begin{table}
\begin{tabular}{l c c c c} \hline
**Property** & **Fe** & **P** & **Li** & **O** & **LiFePO\({}_{4}\)** \\ \hline Melting temperature & 1809.15 (K) & 317.3 (K) & 453.85 (K) & 54.36 (K) & 744.745 (K) \\ Normal boiling temperature & 3134.15 (K) & 553.65 (K) & 1609.15 (K) & 90.20 (K) & 1325.56 (K) \\ Critical point temperature & 8500 (K) & 994(K) & 3223 (K) & 154.59 (K) & 3408.62 (K) \\ Liquid density & 2986.5 (kg/m\({}^{3}\)) & 740 (kg/m\({}^{3}\)) & 512.5 (kg/m\({}^{3}\)) & 1141 (kg/m\({}^{3}\)) & 1687.91 (kg/m\({}^{3}\)) \\ Solid density & 7800 (kg/m\({}^{3}\)) & 1820 (kg/m\({}^{3}\)) & 5334 (kg/m\({}^{3}\)) & 1535 (kg/m\({}^{3}\)) & 3764.65 (kg/m\({}^{3}\)) \\ Latent heat of vaporization & 247,000 (kg) & 2120,00 (kg) & 27.3 (K) & 107 (kg) & 0.2131 \(\times\) 10\({}^{6}\) (J/kg) & 33.97 (kg) \\ Latent heat of fusion & 6,260,000 (J/kg) & 392,000 (J/kg) & 0.4339 \(\times\) 10\({}^{6}\) (J/kg) & 13.88 \(\times\) 10\({}^{5}\) (J/kg) & 116,362 (J/kg) \\ Liquid constant-pressure specific heat & 1642.35 (J/kgK) & 2542.41 (J/kgK) & 4225.8 (J/kgK) & 1675.062 (J/kgK) & 1946 (J/kgK) \\ Solid constant-pressure specific heat & 460.548 (J/kgK) & 770 (J/kgK) & 3514.6 (J/kgK) & 125.0046 (J/kgK) & 519.56 (J/kgK) \\ Atomic weight & 55.845 (g/mol) & 30.97(g/mol) & 6.941 (g/mol) & 31.9988 (g/mol) & 157.757 (g/mol) \\ \hline \end{tabular}
\end{table} 
Table 3: Material Properties of Fe, P, Li, O, and LiFePO\({}_{4}\). 9.026 \(\times 10^{10}\) J/m\({}^{3}\) is required to form the kerf width. For the laser power of 150 W, 200 W and 250 W, the average kerf widths are bounded between 19 \(\upmu\)m and 37 \(\upmu\)m whenever the kerf width is observed. For the laser power of 200 W and 250 W, the kerf width can be observed for all scanning speeds used in this study. The kerf width decreases almost linearly and two slopes are observed. One slope is observed from the scanning speed of 500 mm/s to 1500 mm/s and the other slope is observed from the scanning speed of 1500 mm/s to 5000 mm/s. Figure 3b shows the top width. Increasing scanning speed decreases the top width almost linearly with the laser power of 100 W, 150 W, 200 W, and 250 W, as well as the average top widths are bounded between 35 \(\upmu\)m and 70 \(\upmu\)m. The top widths with the laser power of 50 W are slightly lower than top widths obtained at other laser powers. In addition, increasing the scanning speed from 500 mm/s to 5000 mm/s exponentially decreases the top width at the laser power of 50 W.  
Figure 3 also shows trend lines of volume energy (right). The trend line is obtained by regression analysis, which shows the relationship between the volume energy and the kerf width as well as the volume energy and the top width. The kerf width and the top width are dependent on the volume energies. Furthermore, increasing volume energy causes a logarithmic increase of the kerf width and the top width. The correlation coefficient (\(r\)) of the kerf width and top width is 0.8350 and 0.8341, respectively. Since it is rather close to 1, it indicates that the variables are positively logarithmically related. Figure 4 shows the average values of energy required to remove materials. This remove energy is obtained by Equation (5).