Comparative structural and electrochemical analysis of cubic and Na-rich rhombohedral Prussian blue analogues for sodium-ion batteries

Prussian blue analogues (PBAs) are prominent cathode materials for sodium-ion batteries (SIBs) owing to their low cost and tunable frameworks. In this study, we systematically evaluate the structure-performance relationships of two iron-based PBAs: cubic (c-PBA) and rhombohedral (r-PBA). The N 2 -protected co-precipitation route yields a Na-rich r-PBA (11.64 wt% Na), whereas the acid-mediated route yields a Na-deficient c-PBA (5.97 wt% Na). r-PBA delivers an initial discharge capacity of 94.20 mAh g −1 with 96.62% retention after 125 cycles and 57.70 mAh g −1 at 5.0C. Computational analysis indicates a substantially smaller calculated electronic gap and a lower Na-ion migration barrier for r-PBA than for c-PBA. The idealized MACE-ML/CI-NEB model gives a migration barrier of 0.147 eV for r-PBA; calculations including representative vacancy/water-containing environments yield higher absolute barriers while preserving the lower-barrier trend for r-PBA. These results establish correlations among synthesis conditions, Na content, lattice symmetry, and electrochemical behavior, while avoiding attribution of the observed differences to any single synthesis variable.