Data-driven site occupancy statistics in cubic Prussian Blue

Sodium-ion batteries are emerging as a cost-effective and sustainable alternative to lithium-ion technology. Prussian blue compounds are demonstrating considerable potential as cathode materials, offering exceptional structural stability and rapid sodium-ion diffusion capabilities. However, in spite of the importance of Prussian Blue for the emerging technology of sodium-ion batteries, surprisingly many atomistic details of the structural changes upon charging and dis-charging are not yet clarified. This study aims to assess stable sodium configurations and derive reliable site occupancy statistics. We employ periodic density functional theory (DFT) to construct the first complete convex hull for the cubic system, encompassing all 24d sites, thereby exploring the entire configurational space available within these compounds. We identify a new, more stable sodium arrangement within the fully sodiated, cubic Prussian Blue structure, which has to be considered for reliable atomistic modeling. The convex hull identifies a single stable intermediate sodium concentration (x = 1), which aligns with observed voltage plateaus in open-circuit voltage measurements. Furthermore, a comparative analysis of the cubic phase and its rhombohedral counterpart is conducted, demonstrating qualitative consistency with phase transition for higher sodium concentrations (x $>$ 1). These results strengthen the evidence that Prussian Blue compounds offer exceptional potential as cathode materials, providing valuable insights into their intricate sodium orderings.