Hexacyanometallates for sodium-ion batteries: insights into higher redox potentials using d electronic spin configurations

Abstract

A fundamental understanding of anomalous redox mechanisms in hexacyanometallate compounds, compared with conventional NaMO₂ systems (M: transition metals), is presented based on first-principles calculations and experimental validations. From theoretical calculations, we identified low-spin and high-spin states of Fe ions coordinated by the cyanide group (–CN) with the same oxidation state (Fe²⁺) in Na₂Fe₂(CN)₆. Considering the site dependency of d electronic spin configurations based on the crystal field theory (CFT) of transition metals (TMs), we calculated the thermodynamic mixing energy using Na₂Fe₂(CN)₆ and Na₂Mn₂(CN)₆ for obtaining a thermodynamically stable phase of Na₂FeMn(CN)₆. The phase stabilities of Na₂Fe_2−xMn_x(CN)₆ among many atomic configurations and lattice parameters originating from octahedral structures (i.e., Fe(CN)₆ and Mn(NC)₆) are highly dependent on the electronic structures of TMs with spin states. From partial density of states (PDOS) and spatial electron distributions, it was observed that Fe²⁺ in the low-spin state (t⁶_2g) and Mn²⁺ in the high-spin states (t³_2g and e²_g) in the stable phase lead to higher redox potentials (∼3.55 V vs. Na/Na⁺) with the removal of Na⁺ as compared to that of Na₂Fe₂(CN)₆. In addition, lattice parameters from x = 0 to x = 1 in Na₂Fe_2−xMn_x(CN)₆ are increased due to the larger ionic radius of Mn²⁺ in the high-spin states. On the other hand, Fe²⁺ in the high-spin states (t⁴_2g and e²_g) and Mn²⁺ in the low-spin state (t⁵_2g) in the most unstable phase of Na₂FeMn(CN)₆ would have lower redox potentials. Based on the fundamental correlation between redox potentials and CFT with spin configurations of TMs, we suggest a material design concept for intercalation compounds with higher energy densities for rechargeable battery systems.