K-ion slides in Prussian Blue Analogues

We study the phenomenology of cooperative off-centering of K+ ions in potassiated Prussian blue analogues. The principal distortion mechanism by which this off-centering occurs is termed a `K-ion slide', and its origin is shown to lie in the interaction between local electrostatic dipoles that couple through a combination of electrostatics and elastic strain. Using synchrotron X-ray powder diffraction measurements, we determine the crystal structures of a range of low-vacancy K2M[Fe(CN)6] PBAs (M = Mn, Co, Fe, Ni, Cd) and establish an empirical link between composition, temperature, and slide-distortion magnitude. Our results reflect a common underlying physics responsible for K-ion slides and their evolution with temperature and composition. Monte Carlo simulations driven by a simple model of dipolar interactions and strain coupling reproduce the general features of the experimental phase behaviour. We discuss the implications of our study for optimising the performance of PBA K-ion battery cathode materials, and also its relevance to distortions in other, conceptually related, hybrid perovskites.