90 91 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 within the corresponding vacancy networks. It is possible to calculate from these MC configurations the expected single-crystal diffuse scattering patterns and, by comparing these with experiment, propose representative pore network geometries for each PBA sample.Two such networks are illustrated in Fig. 3. Both Finding order in disordered porous materials Related publication: Simonov A., De Baerdemaeker T., BoströmH. L. B., Ríos Gómez M. L., Gray H. J., Chernyshov D., Bosak A., Bürgi H. B. & Goodwin A. L. Hidden diversity of vacancy networks in Prussian blue analogues. Nature 578 , 256–260 (2020). DOI: 10.1038/s41586-020-1980-y Publication keywords: Prussian blue analogues; Porous materials; Correlated disorder P russian blue analogues (PBAs) are a family of solids used in batteries and hydrogen gas storage, and as catalysts to make high-value chemicals. These practical applications use a network of connected tunnels (pores) within the solids that allow ions or molecules to move in and out. This pore network is so disordered that no-one has ever been able towork out its structure. An international team of researchers investigated the disordered pore structures of a range of PBAs to determine their characteristics ( e.g. howwell connected they are) and the extent to which they vary frommaterial to material. They used Diamond Light Source’s Small-Molecule Single-Crystal Diffraction beamline (I19), which allowed them to measure the single-crystal X-ray diffuse scattering patterns of various PBA crystals. The diffuse scattering is extremely weak continuous scattering between the Bragg peaks typically used for structure determination, and contains information about the disordered structure. Their results show that the pore networks of all PBAs—although disordered—are far from random. The patterns that persist within these non-randomnetwork structures affect the physical properties of thematerials, such as their ability to store gases or the rate at which ions can bemoved in and out. Tuning the type of disorder present by varying the composition and synthesis route of the PBAs could produce improved materials, for example battery cathodes. Prussian blue analogues (PBAs) are a broad family of materials used as cathode materials, heterogeneous catalysts, and in gas-storage applications. 1 Chemically they are obtained as the insoluble hexacyanometallate salts of transition metals, and they crystallise with structures related to the simple cubic net (Fig. 1). A general formula is M[M´(CN) 6 ] 2/ 3 1/3 , where M and M´ denote, respectively, a divalent and trivalent transition metal, and represents a hexacyanometallate vacancy. The vacancies create large (~5 Å-sized) voids in the network structure that connect to form an internal three-dimensional pore network.This network is what allows PBAs to reversibly store gases, for example; it also facilitates the transport of ions in PBA battery materials. A longstanding problem in the field has been to determine the structure of these PBA pore networks: it has long been known they are disordered, but the extent to which this disorder is correlated or randomwas unknown. Single-crystal X-ray diffuse scattering measurements, such as those performed on the I19 beamline, are sensitive to the existence and nature of correlations within disordered states. 2 Because PBAs are so insoluble, they are usually obtained as extremely fine powders, and while the diffraction patterns of these powder samples in principle also contain diffuse scattering signatures, in practice this information is buried in the background and has been essentially impossible to interpret. Using slow-diffusion techniques, a series of PBA single crystals have now been grown and their three-dimensional diffuse scattering patterns measured (Fig. 2a). In all cases this scattering is highly structured — a sign that the disorder from which it arises is strongly-correlated rather than random—and variable as a function of PBA composition. There are many possible methods of interpreting diffuse scattering patterns, but one particularly interesting recent approach is to focus on their Fourier transform, known as the three-dimensional difference pair distribution function (3D- D PDF). 3 This function quantifies the difference between local correlations in occupation or position and the configurational averages. One two-dimensional slice of the 3D- D PDF for a representative PBA is shown in Fig. 2b. To first order, it is characterised by a set of cross-like features with alternating positive and negative values.These crosses correspond to the correlations within an individual [M´(CN) 6 ] 3– cluster, and so the function can be interpreted in terms of the local correlations in the occupation of entire clusters relative to those expected for a statistical distribution. The negative peak at (½,½,0), for example, indicates that cluster vacancies are less likely to occupy neighbouring sites of the face-centred cubic hexacyanometallate sublattice than expected if they were distributed randomly. By determining and interpreting the 3D-DPDFs for each PBA it is possible then to characterise the correlations in pore network structure for each system. The particular vacancy correlations measured in this way are consistent with a simple model based on just two considerations: (i) local electroneutrality – i.e. thatvacanciestendtobedistributeduniformly;and(ii)thepreferenceforthenon- vacant M 2+ site to adopt centrosymmetric or acentric coordination geometries. It can be shown, using Monte Carlo (MC) simulations for example, that these two factorsgiverisetoaparticularlycomplexphasespaceforthe1/3-vacancyfraction common to many PBAs; this complexity reflects an incompatibility between the quadripartitenatureoftheface-centredcubic latticeanda2:1ratioof[M´(CN) 6 ] 3– clusters and their vacancies. As the energetic balance between electroneutrality and centrosymmetry is varied in MC simulations, so too do the correlations Crystallography Group Beamline I19 are heavily disordered; neither one is random. And both have different physical characteristics, such as tortuosity (a measure of the internal curvature of the network structure) or accessible pore volume. Moreover, the distribution of PBA systems throughout MC phase space is consistent with chemical intuition: those with open-shell M 2+ electronic configurations tend to preserve centrosymmetry, and those based on closed-shell ( d 10 ) Zn 2+ or Cd 2+ adopt acentric vacancy distributions, consistent with the tetrahedral coordination geometries of their parent pseudobinary cyanides. 4 So, the important family of PBAs is in fact a system in which there is scope for genuine synthetic control over the nature of correlated disorder in order to optimise their physical properties. For example, the performance of PBA-based cathode materials might be improved by choosing compositions that give rise to pore networks with high internal connectivity and low tortuosity.The family also highlights the broader challenge of establishing disorder–property relationships in functional materials more generally, for which single-crystal X-ray diffuse scatteringmeasurements clearly have a central role to play. 5 References: 1. Kaye S. S. et al. Hydrogen storage in the dehydrated prussian blue analogues M 3[Co(CN)6]2 (M=Mn, Fe, Co, Ni, Cu, Zn). J. Am. Chem. Soc. 127 , 6506–6507 (2005). DOI: 10.1021/ja051168t 2. WelberryT. R. et al. One hundred years of diffuse scattering. Crystallogr. Rev. 22 , 2–78 (2016). DOI: 10.1080/0889311X.2015.1046853 3. WeberT. et al. The three-dimensional pair distribution function analysis of disordered single crystals: basic concepts. 227 , 238–247 (2012). DOI: doi:10.1524/zkri.2012.1504 4. Dunbar K. R. et al. Chemistry of transitionmetal cyanide compounds: Modern perspectives. in Progress in Inorganic Chemistry, Volume 45 283–391 (John Wiley & Sons, Ltd, 2007). DOI: 10.1002/9780470166468.ch4 5. Simonov A. et al. Designing disorder into crystalline materials. Nat. Rev. Chem. 4 , 657–673 (2020). DOI: 10.1038/s41570-020-00228-3 Funding acknowledgement: This research was supported by the LeverhulmeTrust UK (Research Grant RPG- 2015-292), the F.W.O.-Vlaanderen (Postdoctoral Fellowship), the Swiss National Science Foundation (Fellowships PZ00P2_180035, P2EZP2_155608), the Consejo Nacional de Ciencia yTechnología (Mexico), and the European Research Council (Starting Grant 279705 and Advanced Grant 788144). Corresponding author: Prof. Andrew Goodwin, University of Oxford,
[email protected] Figure 1: Representation of the structure of PBAs, M[M´(CN) 6 ] 2/3 1/3 . M 2+ and [M´(CN) 6 ] 3– ions (black and white spheres, respectively) occupy alternating nodes of a simple cubic net; the edges correspond to M–N–C–M´ linkages. Vacancies occupy one third of the hexacyanometallate sites, giving rise to internal voids (orange spheres). These voids connect to form the disordered PBA pore structure. Figure 2: (a) Single-crystal X-ray diffraction patterns (hk0 plane) for two representative PBAs showing the presence of highly-structured diffuse scattering and its variation with composition; (b) The 3D- D PDF (uv0 slice) of Co[Co(CN) 6 ] 2/3 generated from the corresponding data in (a): red and blue features correspond to pair correlations respectively stronger and weaker than the statistical limit. Figure 3: Representative pore network structures for two PBAs. While both are disordered, the distribution of pore node connectivity and pore geometries differs meaningfully between the two. Consequently, network characteristics that govern e.g. mass transport rates are determined by the nature of the correlations within these disordered states.