Recent experiments suggest that the interstitial site occupation of cations in Prussian Blue analogues (PBAs), a promising electrode material for alkali-ion batteries, is restricted by the local distribution of charge. These results imply that cation diffusion in PBAs is unlikely to follow a random walk, and atomic-scale understanding of cation ordering is critical to understand how diffusion occurs in these systems. Because intercalant disorder leads to capacity fade in certain PBAs, an investigation of cation arrangement within PBAs could aid in the design of electrodes with improved rate capability. Inspired by this idea, we performed density functional theory (DFT) calculations on symmetrically inequivalent configurations in a supercell of [Na1+xNiFe(CN)6]4. We found that nearest-neighbor vacancy pairs (NNVPs, see Fig. 1c) play a critical role in deciding the energy difference among the configurations. For a certain number of interstitial vacancies, the configurations free of NNVPs (VPFCs, see Fig. 1b) produce lower energy than the configurations with NNVPs (VPCs, see Fig. 1a). As it is computationally expensive to investigate cation ordering in a large supercell using DFT, we proposed a grand canonical ensemble (GCE) theory based on a vacancy pair free (VPF) model to obtain the time-averaged macrostates of an open Na1+xNiFe(CN)6 supercell by calculating the average over possible intercalant configurations. The VPF model assumes that configurations with NNVPs are inaccessible at room temperature and only includes VPFCs in the GCE. To sample VPFCs in the GCE effectively, we used a hybrid Markov method (HMM) to generate VPFCs. Three types of VPFCs were found during the microstate sampling. We applied the expectation theorem to our GCE to calculate equilibrium potential curve for intercalation into Na1+xNiFe(CN)6 and compared it with experimental data in Fig. 1e. The maximum discrepancy between the two curves was only 30meV. A similar analysis was performed for a non-interacting solution (NIS) to obtain equilibrium potential. The significant disagreement between the NIS and the experiment demonstrates the importance of cation ordering in the equilibrium behavior of PBAs.

Intercalated cation disorder in Prussian blue analogues: First principles and grand canonical analyses

2019 Fall National Meeting

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.