Hidden diversity of vacancy networks in Prussian blue analogues

Prussian blue analogues (PBAs) are a diverse family of microporous inorganic solids, famous for their gas storage,(1) metal-ion immobilization,(2) proton conduction,(3) and stimuli-dependent magnetic,(4,5) electronic,(6) and optical(7) properties. The family includes the double-metal cyanide (DMC) catalysts(8,9) and the hexacyanoferrate/hexacyanomanganate (HCF/HCM) battery materials.(10,11) Central to the various physical properties of PBAs is the ability to transport mass reversibly, a process enabled by structural vacancies. Normally presumed random,(12,13) vacancy arrangements are crucial because they control micropore network characteristics, and hence diffusivity and adsorption profiles.(14,15) The long-standing obstacle to characterising PBA vacancy networks is the inaccessibility of single crystals.(16) Here we report the growth of single crystals of a range of PBAs. By measuring and interpreting their X-ray diffuse scattering patterns, we identify a striking diversity of non-random vacancy arrangements that is hidden from conventional crystallographic analysis of powders. Moreover, we rationalise this unexpected phase complexity in terms of a simple microscopic model based on local rules of electroneutrality and centrosymmetry. The hidden phase boundaries that emerge demarcate vacancy-network polymorphs with profoundly different micropore characteristics. Our results establish a foundation for correlated defect engineering in PBAs as a means of controlling storage capacity, anisotropy, and transport efficiency.