## 3 Results and Discussion
### Effect of the Cathode Current Density on the Microstructure of Carbon Cathodes  
As indicated in Figure 3, despite the penetration of the sodium and melt, the lattice fringes in the carbon cathode presented in an orderly permutation (Figure 3a) after aluminum electrolysis with normal current densities, showing the maintaining of perfect layer structure in the graphite. However, at higher current densities, the whole outline of the structure in Figure 3b appears to be similar with that of a tube. The appearance of sharp curves, as in Figure 3b, and other discontinuities, indicate that the carbon cathode has experienced substantial mechanical damage. Obviously, the higher current density may have an adverse effect on the carbon cathode performance. When discussing the influence of an electric current on the structure of graphite, it is interesting to note the recent works of a group of researchers at Cambridge University, who presented in situ Joule heating of graphite 'nanoribbons' inside a TEM. The project team called these structures zigzag and armchair edges [12]. In order to further observe the morphologies and the atomic arrangement of the carbon cathodes with a high current density, Figure 4 shows the microstructures of the semigraphic cathode at testing time 120 min with a cathode current density of 0.7 A/cm\({}^{2}\). Figure 3: HRTEM image of carbon cathodes at testing 20 min with various current densities (**a**) 0.45 A/cm\({}^{2}\) (**b**) 0.7 A/cm\({}^{2}\). As shown in Figure 4, higher current densities led to the formation of zigzag and armchair edges (Figure 4a,b), disordered carbon (Figure 4c), and the exfoliation of graphite flakes (Figure 4d). The microstructural changes of carbon cathodes resulted as a consequence of Joule heating and electrostatic charging, and the latter was the main reason [20]. While the electronic states of graphite are localized along the edges, zigzag-edged graphene ribbons are unique graphene structures. Because the electronic distribution in the carbon cathode is rather extensive at higher current densities, the electronic stream in zigzag-edged zones goes down mostly these zigzag edges. When a zigzag edge runs into another edge, the electronic movement is decreased significantly, and a large resistance is produced at the junction in the system. Therefore, heating will promote an electron stream away from the edge junction or, if sufficient energy is consumed at the junction, will lead to a change in the microstructure [10]. In this case, if sufficient energy is consumed this way, the carbon atom will rearrange partly until electronic flow is rebuilt again. Beginning from a zigzag edge, this can develop if the microstructure is transformed into a zigzag edge. Therefore, zigzag-zigzag junctions are the preferred form. The kink that can form from anywhere on the zigzag edges will develop along the same edges easily. After these kinks sweep through, 1 or a few zigzag atomic rows will slowly go away. This renders graphene with mainly zigzag edges, joined by small armchair edge fragments [21]. Figure 4: Microstructures of the carbon cathode at testing time 120 min with a cathode current density of 0.7 A/cm\({}^{2}\) (**a**) and (**d**) TEM image (**b**) and (**c**) HRTEM image. With the evolution of the diffusion-induced stresses in the carbon cathode, there was a remarkable change in the arrangement of the carbon atoms. As demonstrated by Figure 4c, the microstructure of the carbon cathode was characterized as less organized carbon, which was consistent with the results of creep deformation investigation [22]. This showed that better-ordered carbons in the bulk changed to disordered carbons at high temperatures and under sodium expansion. When an electric field applied to the carbon cathodes, the van der Waals forces between adjacent graphene layers could be reduced dramatically.