To examine the impact of sodium insertion on the average interlayer spacing for each HC, the relative changes in interlayer spacing are determined from wide-angle X-ray scattering (WAXS) measurements capturing the (002) and (100) reflections during sodiation. The (002) reflection was fitted to determine the interlayer spacing, with the detailed fits provided in Figures . Figure shows systematic shifts in the interlayer spacing throughout the sodiation process across all HCs. For HC-1100 and HC-1400, during the first gradient of the slope region, the interlayer spacing decreases slightly due to localized contraction instigated by sodium adsorption at defect sites on the HC surface, observable by the high surface area. Subsequently, during the second gradient of the slope region, the interlayer spacing increases for all HCs. For HC-1100, this increase occurs between 32% and 52% SoS. This phenomenon, along with the increase in the C-C bond distance (Figure (c)), DFT calculations (Figure )), and supporting evidence from Raman studies, aligns with the "defect-assisted intercalation" mechanism. It is important to note that both "defect-assisted intercalation" and conventional intercalation mechanisms result in an increase in d002, making it challenging to distinguish between these two mechanisms based on d002.