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We use in situ synchrotron X-ray diffraction measurements to monitor the solvothermal crystallization mechanism of the aperiodic metal-organic framework TRUMOF-1. Following an initial incubation period, TRUMOF-1 forms as a metastable intermediate that subsequently transforms into an ordered product with triclinic crystal symmetry. We determine the structure of this ordered phase, which we call msw-TRUMOF-1, and show that it is related to TRUMOF-1 through topotactic reorganization of linker occupancies. Our results imply that the connectivity of TRUMOF-1 can be reorganized, as required for data storage and manipulation applications.

The pair distribution function (PDF) is an important metric for characterising structure in complex materials, but it is well known that meaningfully different structural models can sometimes give rise to equivalent PDFs. In this paper, we discuss the use of model likelihoods as a general approach for discriminating between such homometric structure solutions. Drawing on two main case studies-one concerning the structure of a small peptide and the other amorphous calcium carbonate-we show how consideration of model likelihood can help drive robust structure solution, even in cases where the PDF is particularly information-poor. The obvious thread of these individual case studies is the potential role for machine-learning approaches to help guide structure determination from the PDF, and our paper finishes with some forward-looking discussion along these lines.

By virtue of their open network structures and low densities, metal-organic frameworks (MOFs) are soft materials that exhibit elastic instabilities at low applied stresses. The conventional strategy for improving elastic stability is to increase the connectivity of the underlying MOF network, which necessarily increases the material density and reduces the porosity. Here we demonstrate an alternative paradigm, whereby elastic stability is enhanced in a MOF with an aperiodic network topology. We use a combination of variable-pressure single-crystal X-ray diffraction measurements and coarse-grained lattice-dynamical calculations to interrogate the high-pressure behaviour of the topologically aperiodic system TRUMOF-1, which we compare against that of its ordered congener MOF-5. We show that the topology of the former quenches the elastic instability responsible for pressure-induced framework collapse in the latter, much as irregularity in the shapes and sizes of stones acts to prevent cooperative mechanical failure in drystone walls. Our results establish aperiodicity as a counter-intuitive design motif in engineering the mechanical properties of framework structures that is relevant to MOFs and larger-scale architectures alike., (© 2024. The Author(s).)

Background: Data sharing in developmental science is increasingly encouraged, supported by funder and publisher mandates for open data access. Data sharing can accelerate discovery, link researchers with high quality analytic expertise to researchers with large datasets and democratise the research landscape to enable researchers with limited funding to access large sample sizes. However, there are also significant privacy and security concerns, in addition to conceptual and ethical considerations. These are particularly acute for developmental science, where child participants cannot consent themselves. As we move forward into a new era of data openness, it is essential that we adequately represent the views of stakeholder communities in designing data sharing efforts., Methods: We conducted a comprehensive survey of the opinions of 195 parents on data sharing in developmental science. Survey themes included how widely parents are willing to share their child's data, which type of organisations they would share the data with and the type of consent they would be comfortable providing., Results: Results showed that parents were generally supportive of curated, but not open, data sharing. In addition to individual privacy and security concerns, more altruistic considerations around the purpose of research were important. Parents overwhelmingly supported nuanced consenting models in which preferences for particular types of data sharing could be changed over time. This model is different to that implemented in the vast majority of developmental science research and is contrary to many funder or publisher mandates., Conclusions: The field should look to create shared repositories that implement features such as dynamic consent and mechanisms for curated sharing that allow consideration of the scientific questions addressed. Better communication and outreach are required to build trust in data sharing, and advanced analytic methods will be required to understand the impact of selective sharing on reproducibility and representativeness of research datasets., Competing Interests: No competing interests were disclosed., (Copyright: © 2024 Begum Ali J et al.)

We use a combination of X-ray pair distribution function (PDF) measurements, lattice dynamical calculations, and ab initio density functional theory (DFT) calculations to study the local structure and dynamics in various MPt(CN) 6 Prussian blue analogues. In order to link directly the local distortions captured by the PDF with the lattice dynamics of this family, we develop and apply a new "interaction-space" PDF refinement approach. This approach yields effective harmonic force constants, from which the (experiment-derived) low-energy phonon dispersion relations can be approximated. Calculation of the corresponding Grüneisen parameters allows us to identify the key modes responsible for negative thermal expansion (NTE) as arising from correlated tilts of coordination octahedra. We compare our results against the phonon dispersion relations determined using DFT calculations, which identify the same NTE mechanism., Competing Interests: The authors declare no competing financial interest., (© 2024 The Authors. Published by American Chemical Society.)

The structure of amorphous silicon (a-Si) is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such "dangling-bond" and "floating-bond" defects, respectively, a unified understanding is still missing. Here, we use advanced computational chemistry methods to reveal the complex structural and energetic landscape of defects in a-Si. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and thousands of individual defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned atomic energies to develop a classification of the different types of defects in a-Si. The results suggest a revision of the established floating-bond model by showing that fivefold-bonded atoms in a-Si exhibit a wide range of local environments-analogous to fivefold centers in coordination chemistry. Furthermore, it is shown that fivefold (but not threefold) coordination defects tend to cluster together. Our study provides new insights into one of the most widely studied amorphous solids, and has general implications for understanding defects in disordered materials beyond silicon alone., (© 2024 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)

We report the magnetic behavior of the hybrid perovskites [Gua]Mn 1- x Fe 2 x /3 □ x /3 (HCOO) 3 (0 ≤ x ≤ 0.88), showing that vacancy ordering drives bulk ferrimagnetism for x > 0.6. The behavior is rationalized in terms of a simple microscopic model of percolation-induced ferrimagnetism. Monte Carlo simulations driven by this model reproduce the experimental dependence of magnetic susceptibility on x and show that, at intermediate compositions, domains of short-range vacancy order lead to the emergence of local magnetization. Our results open up a new avenue for the design of multiferroic hybrid perovskites.

Amorphous calcium carbonate is an important precursor for biomineralization in marine organisms. Key outstanding problems include understanding the structure of amorphous calcium carbonate and rationalizing its metastability as an amorphous phase. Here we report high-quality atomistic models of amorphous calcium carbonate generated using state-of-the-art interatomic potentials to help guide fits to X-ray total scattering data. Exploiting a recently developed inversion approach, we extract from these models the effective Ca⋯Ca interaction potential governing the structure. This potential contains minima at two competing distances, corresponding to the two different ways that carbonate ions bridge Ca 2+ -ion pairs. We reveal an unexpected mapping to the Lennard-Jones-Gauss model normally studied in the context of computational soft matter. The empirical model parameters for amorphous calcium carbonate take values known to promote structural complexity. We thus show that both the complex structure and its resilience to crystallization are actually encoded in the geometrically frustrated effective interactions between Ca 2+ ions., (© 2023. The Author(s).)

We explore the role and nature of torsional flexibility of carboxylate-benzene links in the structural chemistry of metal-organic frameworks (MOFs) based on Zn and benzenedicarboxlyate (bdc) linkers. A particular motivation is to understand the extent to which such flexibility is important in stabilising the unusual topologically aperiodic phase known as TRUMOF-1. We compare the torsion angle distributions of TRUMOF-1 models with those for crystalline Zn/1,3-bdc MOFs, including a number of new materials whose structures we report here. We find that both periodic and aperiodic Zn/1,3-bdc MOFs sample a similar range of torsion angles, and hence the formation of TRUMOF-1 does not require any additional flexibility beyond that already evident in chemically-related crystalline phases. Comparison with Zn/1,4-bdc MOFs does show, however, that the lower symmetry of the 1,3-bdc linker allows access to a broader range of torsion angles, reflecting a greater flexibility of this linker., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The sodium-rich antiperovskites (NaRAPs) with composition Na 3 OB (B=Br, Cl, I, BH 4 , etc.) are a family of materials that has recently attracted great interest for application as solid electrolytes in sodium metal batteries. Non-Arrhenius ionic conductivities have been reported for these materials, the origin of which is poorly understood. In this work, we combined temperature-resolved bulk and local characterisation methods to gain an insight into the origin of this unusual behaviour using Na 3 OBr as a model system. We first excluded crystallographic disorder on the anion sites as the cause of the change in activation energy; then identified the presence of a poorly crystalline impurities, not detectable by XRD, and elucidated their effect on ionic conductivity. These findings improve understanding of the processing-structure-properties relationships pertaining to NaRAPs and highlight the need to determine these relationships in other materials systems, which will accelerate the development of high-performance solid electrolytes., Competing Interests: The authors declare no conflict of interest., (© 2023 The Authors. Angewandte Chemie published by Wiley-VCH GmbH.)

We study the phenomenology of cooperative off-centering of K + ions in potassiated Prussian blue analogues (PBAs). 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 powder X-ray diffraction measurements, we determine the crystal structures of a range of low-vacancy K 2 M[Fe(CN) 6 ] PBAs (M = Ni, Co, Fe, Mn, Cd) and establish an empirical link between composition, temperature, and slide-distortion magnitude. Our results reflect the 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 behavior. We discuss the implications of our study for optimizing the performance of PBA K-ion battery cathode materials and also its relevance to distortions in other, conceptually related, hybrid perovskites.

Based on simple electrostatic and harmonic potential considerations, we derive a straightforward expression linking the composition of a Prussian blue analogue (PBA) to its propensity to undergo collective structural distortions. We demonstrate the existence of a threshold value, below which PBAs are undistorted and above which PBAs distort by a degree that is controlled by a geometric tolerance factor. Our analysis rationalizes the presence, absence, and magnitude of distortions in a wide range of PBAs and distinguishes their structural chemistry from that of other hybrid perovskites.

Structure-property relationships in ordered materials have long been a core principle in materials design. However, the introduction of disorder into materials provides structural flexibility and thus access to material properties that are not attainable in conventional, ordered materials. To understand disorder-property relationships, the disorder - i.e., the local ordering principles - must be quantified. Local order can be probed experimentally by diffuse scattering. The analysis is notoriously difficult, especially if only powder samples are available. Here, we combine the advantages of three-dimensional electron diffraction - a method that allows single crystal diffraction measurements on sub-micron sized crystals - and three-dimensional difference pair distribution function analysis (3D-ΔPDF) to address this problem. In this work, we compare the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia (Zr 0.82 Y 0.18 O 1.91 ) and demonstrate the reliability of the proposed approach., (© 2023. Springer Nature Limited.)

Zeolitic imidazolate frameworks are widely thought of as being analogous to inorganic AB 2 phases. We test the validity of this assumption by comparing simplified and fully atomistic machine-learning models for local environments in ZIFs. Our work addresses the central question to what extent chemical information can be "coarse-grained" in hybrid framework materials.

Disorder in crystals is rarely random, and instead involves local correlations whose presence and nature are hidden from conventional crystallographic probes. This hidden order can sometimes be controlled, but its importance for physical properties of materials is not well understood. Using simple models for electronic and interatomic interactions, we show how crystals with identical average structures but different types of hidden order can have very different electronic and phononic band structures. Increasing the strength of local correlations within hidden-order states can open band gaps and tune mode (de)localisation-both mechanisms allowing for fundamental changes in physical properties without long-range symmetry breaking. Taken together, our results demonstrate how control over hidden order offers a new mechanism for tuning material properties, orthogonal to the conventional principles of (ordered) structure/property relationships., (© 2023. The Author(s).)

Short-range ordering in cation-disordered cathodes can have a significant effect on their electrochemical properties. Here, we characterise the cation short-range order in the antiperovskite cathode material Li 2 FeSO, using density functional theory, Monte Carlo simulations, and synchrotron X-ray pair-distribution-function data. We predict partial short-range cation-ordering, characterised by favourable OLi 4 Fe 2 oxygen coordination with a preference for polar cis -OLi 4 Fe 2 over non-polar trans -OLi 4 Fe 2 configurations. This preference for polar cation configurations produces long-range disorder, in agreement with experimental data. The predicted short-range-order preference contrasts with that for a simple point-charge model, which instead predicts preferential trans -OLi 4 Fe 2 oxygen coordination and corresponding long-range crystallographic order. The absence of long-range order in Li 2 FeSO can therefore be attributed to the relative stability of cis -OLi 4 Fe 2 and other non-OLi 4 Fe 2 oxygen-coordination motifs. We show that this effect is associated with the polarisation of oxide and sulfide anions in polar coordination environments, which stabilises these polar short-range cation orderings. We propose that similar anion-polarisation-directed short-range-ordering may be present in other heterocationic materials that contain cations with different formal charges. Our analysis illustrates the limitations of using simple point-charge models to predict the structure of cation-disordered materials, where other factors, such as anion polarisation, may play a critical role in directing both short- and long-range structural correlations., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Three-dimensional difference pair distribution functions (3D-ΔPDFs) from X-ray and neutron diffraction experiments are reported for yttria-stabilized zirconia (Zr 0.82 Y 0.18 O 1.91 ). A quantitative analysis of the signatures in the three-dimensional difference pair distribution functions is used to establish that oxygen ions neighbouring a vacancy shift by 0.525 (5) Å along ⟨1, 0, 0⟩ towards the vacancy while metal ions neighbouring a vacancy shift by 0.465 (2) Å along ⟨1, 1, 1⟩ away from the vacancy. The neutron 3D-ΔPDF shows a tendency for vacancies to cluster along ⟨½, ½, ½⟩, which results in sixfold coordinated metal ions., (open access.)

Background: Previous research has suggested that there is an association between impulsivity, assessed via self-report measures and behaviourally, and disinhibited eating patterns, but it remains unclear which specific dimension of impulsivity is the most salient in this relationship. Furthermore, it remains uncertain whether any such associations would extend to actual eating behaviours and food consumption., Aims: The present study aimed to examine whether impulsivity, assessed both behaviourally and via self-report, is associated with self-reported disinhibited and actual eating behaviour in a controlled eating task., Method: 70 women from a community sample (aged 21-35) completed the Disinhibition subscale of the Three Factor Eating Questionnaire (TFEQ), the Barratt Impulsiveness Scale (BIS-11), the Matching Familiar Figures Task (MFFT-20), and a behavioural food consumption task., Results: Bivariate correlational analyses revealed significant associations between self-report measure of impulsivity, the scores on the MFFT-20 (assessing reflection impulsivity), and self-report measure of disinhibited eating. All these measures were associated with overall food consumption in a taste task, with reflection impulsivity, that is poor ability to reflect on information before making a decision, having the strongest association with the amount of food consumed. Self-reported impulsivity was most strongly associated with disinhibited eating. Partial correlations controlling for BMI and age did not diminish any significant correlations within these relationships., Conclusions: Significant associations between both trait and behavioural (reflection) impulsivity, and self-reported disinhibited eating and actual eating behaviour were demonstrated. The implications of these findings on uncontrolled eating patterns in real life are discussed., Competing Interests: Declaration of competing interest We confirm that there are no financial/personal interests or beliefs that could affect the objectivity of our work. There are no competing interests to declare., (Copyright © 2023 The Authors. Published by Elsevier Ltd.. All rights reserved.)

When tiles decorated to lower their symmetry are joined together, they can form aperiodic and labyrinthine patterns. Such Truchet tilings offer an efficient mechanism of visual data storage related to that used in barcodes and QR codes. We show that the crystalline metal-organic framework [OZn 4 ][1,3-benzenedicarboxylate] 3 (TRUMOF-1) is an atomic-scale realization of a complex three-dimensional Truchet tiling. Its crystal structure consists of a periodically arranged assembly of identical zinc-containing clusters connected uniformly in a well-defined but disordered fashion to give a topologically aperiodic microporous network. We suggest that this unusual structure emerges as a consequence of geometric frustration in the chemical building units from which it is assembled.

Single-crystal X-ray diffuse scattering measurements are reported of the compositional series KCl 1-x Br x , a model system for the broader family of disordered rocksalts. Using a combination of Monte Carlo simulations and lattice dynamical calculations, we show that the observed diffuse scattering is well described in terms of (i) non-statistical anion distributions, (ii) local lattice relaxations accompanying Cl/Br substitution, and (iii) the contribution from low-energy phonons. It is found that a tendency for compositional domain formation broadens the thermal diffuse scattering by splitting and softening the acoustic phonon branches. This effect, which is strongest for intermediate compositions, is seen in both experiment and calculation alike. These results establish a link between local compositional order and unconventional lattice dynamics in this system, and reinforce emerging design principles of exploiting compositional fluctuations to tailor physical properties, such as thermal conductivity, that depend on phonon broadening., (open access.)

In the dense metal-organic framework Na[Mn(HCOO)_{3}], Mn^{2+} ions (S=5/2) occupy the nodes of a "trillium" net. We show that the system is strongly magnetically frustrated: the Néel transition is suppressed well below the characteristic magnetic interaction strength; short-range magnetic order persists far above the Néel temperature; and the magnetic susceptibility exhibits a pseudo-plateau at 1/3-saturation magnetization. A simple model of nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions accounts quantitatively for all observations, including an unusual 2-k magnetic ground state. We show that the relative strength of dipolar interactions is crucial to selecting this particular ground state. Geometric frustration within the classical spin liquid regime gives rise to a large magnetocaloric response at low applied fields that is degraded in powder samples as a consequence of the anisotropy of dipolar interactions.

We survey the most important kinds of structural complexity in Prussian blue analogues, their implications for materials function, and how they might be controlled through judicious choice of composition. We focus on six particular aspects: octahedral tilts, A-site 'slides', Jahn-Teller distortions, A-site species and occupancy, hexacyanometallate vacancies, and framework hydration. The promising K-ion cathode material K x Mn[Fe(CN) 6 ] y serves as a recurrent example that illustrates many of these different types of complexity. Our article concludes with a discussion of how the interplay of various distortion mechanisms might be exploited to optimise the performance of this and other related systems, so as to aid in the design of next-generation PBA materials.

High pressure is a powerful thermodynamic tool for exploring the structure and the phase behaviour of the crystalline state, and is now widely used in conventional crystallographic measurements. High-pressure local structure measurements using neutron diffraction have, thus far, been limited by the presence of a strongly scattering, perdeuterated, pressure-transmitting medium (PTM), the signal from which contaminates the resulting pair distribution functions (PDFs). Here, a method is reported for subtracting the pairwise correlations of the commonly used 4:1 methanol:ethanol PTM from neutron PDFs obtained under hydro-static compression. The method applies a molecular-dynamics-informed empirical correction and a non-negative matrix factorization algorithm to recover the PDF of the pure sample. Proof of principle is demonstrated, producing corrected high-pressure PDFs of simple crystalline materials, Ni and MgO, and benchmarking these against simulated data from the average structure. Finally, the first local structure determination of α-quartz under hydro-static pressure is presented, extracting compression behaviour of the real-space structure., (© Anna Herlihy et al. 2021.)

With ever-growing numbers of metal-organic framework (MOF) materials being reported, new computational approaches are required for a quantitative understanding of structure-property correlations in MOFs. Here, we show how structural coarse-graining and embedding ("unsupervised learning") schemes can together give new insights into the geometric diversity of MOF structures. Based on a curated data set of 1262 reported experimental structures, we automatically generate coarse-grained and rescaled representations which we couple to a kernel-based similarity metric and to widely used embedding schemes. This approach allows us to visualize the breadth of geometric diversity within individual topologies and to quantify the distributions of local and global similarities across the structural space of MOFs. The methodology is implemented in an openly available Python package and is expected to be useful in future high-throughput studies., Competing Interests: The authors declare no competing financial interest., (© 2021 American Chemical Society.)

The diffraction patterns of crystalline materials with strongly correlated disorder are characterized by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either atomistically or in terms of pairwise (Warren-Cowley) correlation parameters. Here it is demonstrated how a mean-field methodology allows efficient fitting of diffuse scattering directly in terms of a microscopic interaction model. In this way the approach gives as its output the underlying physics responsible for correlated disorder. Moreover, the use of a very small number of parameters during fitting renders the approach surprisingly robust to data incompleteness, a particular advantage when seeking to interpret single-crystal diffuse scattering measured in complex sample environments. As the basis of this proof-of-concept study, a toy model is used based on strongly correlated disorder in diammine mercury(II) halides., (© Ella M. Schmidt et al. 2022.)

Using a non-negative matrix factorisation (NMF) approach, we show how the pair distribution function (PDF) of complex mixtures can be deconvolved into the contributions from the individual phase components and also the interface between phases. Our focus is on the model system Fe∥Fe 3 O 4 . We establish proof-of-concept using idealised PDF data generated from established theory-driven models of the Fe∥Fe 3 O 4 interface. Using X-ray total scattering measurements for corroded Fe samples, and employing our newly-developed NMF analysis, we extract the experimental interface PDF ('iPDF') for this same system. We find excellent agreement between theory and experiment. The implications of our results in the broader context of interface characterisation for complex functional materials are discussed.

The ultrahigh porosity and varied functionalities of porous metal-organic frameworks make them excellent candidates for applications that range widely from gas storage and separation to catalysis and sensing. An interesting feature of some frameworks is the ability to open their pores to a specific guest, enabling highly selective separation. A prerequisite for this is bistability of the host structure, which enables the framework to breathe, that is, to switch between two stability minima in response to its environment. Here we describe a porous framework DUT-8(Ni)-which consists of nickel paddle wheel clusters and carboxylate linkers-that adopts a configurationally degenerate family of disordered states in the presence of specific guests. This disorder originates from the nonlinear linkers arranging the clusters in closed loops of different local symmetries that in turn propagate as complex tilings. Solvent exchange stimulates the formation of distinct disordered frameworks, as demonstrated by high-resolution transmission electron microscopy and diffraction techniques. Guest exchange was shown to stimulate repeatable switching transitions between distinct disorder states.