Throughout much of condensed matter science, correlated disorder is key to material function. While structural and compositional defects are known to exist within a variety of metal–organic frameworks, the prevailing understanding is that these defects are only ever included in a random manner. Here we show—using a combination of diffuse scattering, electron microscopy, anomalous X-ray scattering, and pair distribution function measurements—that correlations between defects can in fact be introduced and controlled within a hafnium terephthalate metal–organic framework. The nanoscale defect structures that emerge are an analogue of correlated Schottky vacancies in rocksalt-structured transition metal monoxides and have implications for storage, transport, optical and mechanical responses. Our results suggest how the diffraction behaviour of some metal–organic frameworks might be reinterpreted, and establish a strategy of exploiting correlated nanoscale disorder as a targetable and desirable motif in metal–organic framework design.

This article describes a web‐based tool (PASCal; principal axis strain calculator; http://pascal.chem.ox.ac.uk) designed to simplify the determination of principal coefficients of thermal expansion and compressibilities from variable‐temperature and variable‐pressure lattice parameter data. In a series of three case studies, PASCal is used to reanalyse previously published lattice parameter data and show that additional scientific insight is obtainable in each case. First, the two‐dimensional metal–organic framework [Cu2(OH)(C8H3O7S)(H2O)]·2H2O is found to exhibit the strongest area negative thermal expansion (NTE) effect yet observed; second, the widely used explosive HMX exhibits much stronger mechanical anisotropy than had previously been anticipated, including uniaxial NTE driven by thermal changes in molecular conformation; and third, the high‐pressure form of the mineral malayaite is shown to exhibit a strong negative linear compressibility effect that arises from correlated tilting of SnO6 and SiO4 coordination polyhedra.

We report a hafnium-containing MOF, hcp UiO-67(Hf), which is a ligand-deficient layered analogue of the face-centered cubic fcu UiO-67(Hf). hcp UiO-67 accommodates its lower ligand:metal ratio compared to fcu UiO-67 through a new structural mechanism: the formation of a condensed “double cluster” (Hf12O8(OH)14), analogous to the condensation of coordination polyhedra in oxide frameworks. In oxide frameworks, variable stoichiometry can lead to more complex defect structures, e.g., crystallographic shear planes or modules with differing compositions, which can be the source of further chemical reactivity; likewise, the layered hcp UiO-67 can react further to reversibly form a two-dimensional metal–organic framework, hxl UiO-67. Both three-dimensional hcp UiO-67 and two-dimensional hxl UiO-67 can be delaminated to form metal–organic nanosheets. Delamination of hcp UiO-67 occurs through the cleavage of strong hafnium-carboxylate bonds and is effected under mild conditions, suggesting that defect-ordered MOFs could be a productive route to porous two-dimensional materials.

TiNb2O7 is a Wadsley–Roth phase with a crystallographic shear structure and is a promising candidate for high-rate lithium ion energy storage. The fundamental aspects of the lithium insertion mechanism and conduction in TiNb2O7, however, are not well-characterized. Herein, experimental and computational insights are combined to understand the inherent properties of bulk TiNb2O7. The results show an increase in electronic conductivity of seven orders of magnitude upon lithiation and indicate that electrons exhibit both localized and delocalized character, with a maximum Curie constant and Li NMR paramagnetic shift near a composition of Li0.60TiNb2O7. Square-planar or distorted-five-coordinate lithium sites are calculated to invert between thermodynamic minima or transition states. Lithium diffusion in the single-redox region (i.e., x ≤ 3 in Li x TiNb2O7) is rapid with low activation barriers from NMR and D Li = 10–11 m2 s–1 at the temperature of the observed T 1 minima of 525–650 K for x ≥ 0.75. DFT calculations predict that ionic diffusion, like electronic conduction, is anisotropic with activation barriers for lithium hopping of 100–200 meV down the tunnels but ca. 700–1000 meV across the blocks. Lithium mobility is hindered in the multiredox region (i.e., x > 3 in Li x TiNb2O7), related to a transition from interstitial-mediated to vacancy-mediated diffusion. Overall, lithium insertion leads to effective n-type self-doping of TiNb2O7 and high-rate conduction, while ionic motion is eventually hindered at high lithiation. Transition-state searching with beyond Li chemistries (Na+, K+, Mg2+) in TiNb2O7 reveals high diffusion barriers of 1–3 eV, indicating that this structure is specifically suited to Li+ mobility.

Amorphous silicon ( a-Si) is a widely studied noncrystalline material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained using a machine-learning-based interatomic potential. Our best a-Si network is obtained by simulated cooling from the melt at a rate of 10 K/s (that is, on the 10 ns time scale), contains less than 2% defects, and agrees with experiments regarding excess energies, diffraction data, and Si NMR chemical shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4096-atom system that correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with experiments to date. Our study demonstrates the broader impact of machine-learning potentials for elucidating structures and properties of technologically important amorphous materials.

Thermally-densified hafnium terephthalate UiO-66(Hf) is shown to exhibit the strongest isotropic negative thermal expansion (NTE) effect yet reported for a metal-organic framework (MOF). Incorporation of correlated vacancy defects within the framework affects both the extent of thermal densification and the magnitude of NTE observed in the densified product. We thus demonstrate that defect inclusion can be used to tune systematically the physical behaviour of a MOF.

We describe a conceptually novel ''accelerated aging'' approach for the synthesis of metal-organic materials. This approach, inspired by natural mineral weathering processes, enables the synthesis of metal-organic structures from simple and inexpensive solid reactants upon exposure to catalytic amounts of an ammonium salt under conditions of high humidity and mild temperatures (up to 45 C). Accelerated aging exploits the inherent mobility of molecules and is entirely different from solutionbased (precipitation, solvothermal synthesis) or other solvent-free (mechanochemical synthesis) approaches to metal-organic materials that require either bulk solvent and/or thermo-or mechanochemical intervention. The present proof-of-principle study of accelerated aging demonstrates the catalysed and topologically specific transformation of ZnO into unusual close-packed varieties of zeolitic imidazolate frameworks (ZIFs) in a static, non-agitated reaction mixture. The reactivity is readily scaled up, as demonstrated by performing selected syntheses of quartz-and diamondoidtopology close-packed ZIFs in ten gram amounts. The latter framework, previously obtained only by using a large excess of reagents under hydrothermal conditions, is transformed into the well-known open framework ZIF-8 by exposure to methanol vapours at room temperature, suggesting an alternative to both solvothermal and mechanochemical approaches to these materials. A tentative proton-transfer mechanism underpinning the catalytic effect in accelerated aging is proposed, involving protonated imidazole as an intermediate.

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