Prussian blue analogues (PBAs) are a broad and important family of microporous inorganic solids, famous for their gas storage (1,2,3,4,5), metal-ion immobilisation (6,7), proton conduction (8,9), and stimuli-dependent magnetic (10, 11, 12), electronic (13) and optical (14) properties. The family also includes the widely-used double-metal cyanide (DMC) catalysts (15,16,17) and the topical hexacyanoferrate/hexacyanomanganate arXiv:1908.10596v1 [cond-mat.mtrl-sci] PBAs is the ability to transport mass reversibly, a process made possible by structural vacancies. Normally presumed random (21,22,23), vacancy arrangements are actually crucially important because they control the connectivity of the micropore network, and hence diffusivity and adsorption profiles (24,25). The long-standing obstacle to characterising PBA vacancy networks has always been the relative inaccessibility of single-crystal samples (26). 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 for the first time a striking diversity of non-random vacancy arrangements that is hidden from conventional crystallographic analysis of powder samples. Moreover, we show that this unexpected phase complexity can be understood in terms of a remarkably 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 clear foundation for correlated defect engineering in PBAs as a means of controlling storage capacity, anisotropy, and transport efficiency.The true crystal structures of PBAs-as of Prussian Blue itself-have long posed a difficult and important problem in solid-state chemistry because their ostensibly simple powder diffraction patterns [ Fig. 1(a)] belie a remarkable complexity at the atomic scale (27,28,29). The common parent structure is based on the cubic lattice and corresponds to the idealised composition M[M (CN) 6 ]. Atoms of type M and M (usually transition-metal cations) occupy alternate lattice vertices and are octahedrally coordinated by bridging cyanide ions (CN − ) at the lattice edges [ Fig. 1(b)]. There is a close conceptual parallel to the double perovskite structure (30); indeed the key considerations of covalency and octahedral coordination geometry that stabilise perovskites amongst oxide ceramics (31) also favour this same architecture for transition-metal cyanides, which accounts for the chemical diversity of PBAs (32). Charge balance
Abstract. Theory and principles of the three-dimensional pair distribution function analysis of disordered single crystals are introduced. The mathematical framework is presented and the appearance of pair distribution function patterns is discussed on the examples of some basic disorder models. It is further demonstrated how pair distribution function maps are affected by typical experimental problems. Approaches for a better understanding of such effects and strategies for a proper handling of artifacts in diffuse scattering experiments are proposed.
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