Fig. 5: Schematic illustrations showing the structural change of the hollow gradient-structured Fe3O4@C nanospheres during fast charging and discharging.

A Three-dimensional (3D) view for the structural change of the hollow gradient-structured Fe3O4@C nanospheres; B simplified 2D cross-section view for the structural change of the hollow gradient-structured Fe3O4@C nanospheres; and C volume change of single Fe3O4 nanoparticle. ~7% diameter expansion of the gradient-structured nanospheres can be evaluated from the full charging to full discharging state, which is considerably lower than the theoretical value of Fe3O4 particles (~22%). proving that the gradient-structure can gradually release the stress caused by the volume change.