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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.

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.

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.

ConspectusThe structural degrees of freedom of a solid material are the various distortions most straightforwardly activated by external stimuli such as temperature, pressure, or adsorption. One of the most successful design strategies in materials chemistry involves controlling these individual distortions to produce useful collective functional responses. In a ferroelectric such as lead titanate, for example, the key degree of freedom involves asymmetric displacements of Pb 2+ and Ti 4+ cations; it is by coupling these together that the system as a whole interacts with external electric fields. Collective rotations of the polyhedral units in oxide ceramics are another commonly exploited distortion, driving anomalous behavior such as negative thermal expansion-the counterintuitive phenomenon of volume contraction on heating. An exciting development in the field has been to take advantage of the interplay between different distortion types: generating polarization by combining two different polyhedral rotations, for example. In this way, degrees of freedom act as geometric "elements" that can themselves be combined to engineer materials with new and interesting properties. Just as the discovery of new chemical elements quite obviously diversified chemical space, we might expect that identifying new and different types of structural degrees of freedom to be an important strategy for developing new kinds of functional materials. In this context, the broad family of molecular frameworks is emerging as an extraordinarily fertile source of new and unanticipated distortion types, the vast majority of which have no parallel in the established families of conventional solid-state chemistry.Framework materials are solids whose structures are assembled from two fundamental components: nodes and linkers. Quite simply, linkers join the nodes together to form scaffolding-like networks that extend from the atomic to the macroscopic scale. These structures usually contain cavities, which can also accommodate additional ions for charge balance. In the well-established systems-such as lead titanate-node, linker, and extra-framework ions are all individual atoms (Ti, O, and Pb, respectively). But in molecular frameworks, at least one of these components is a molecule.In this Account, we survey the unconventional degrees of freedom introduced through the simple act of replacing atoms by molecules. Our motivation is to understand the role these new distortions play (or might be expected to play) in different materials properties. The various degrees of freedom themselves-unconventional rotational, translational, orientational, and conformational states-are summarized and described in the context of relevant experimental examples. The much-improved prospect for generating emergent functionalities by combining these new distortion types is then discussed. We highlight a number of directions for future research-including the design and application of hierarchically structured phases of matter intermediate to solids and liquid crystals-which serve to highlight the extraordinary possibilities for this nascent field.

The negative thermal expansion material potassium cadmium dicyanoargentate, KCd[Ag(CN) 2 ] 3 , is studied at high pressure using a combination of X-ray single-crystal diffraction, X-ray powder diffraction, infrared and Raman spectroscopy, and density functional theory calculations. In common with the isostructural manganese analogue, KMn[Ag(CN) 2 ] 3 , this material is shown to exhibit very strong negative linear compressibility (NLC) in the crystallographic c direction due to structure hinging. We find increased structural flexibility results in enhanced NLC and NTE properties, but this also leads to two pressure-induced phase transitions-to very large unit cells involving octahedral tilting and shearing of the structure-below 2 GPa. The presence of potassium cations has an important effect on the mechanical and thermodynamic properties of this family, while the chemical versatility demonstrated here is of considerable interest to tune unusual mechanical properties for application., Competing Interests: The authors declare no competing financial interest., (Copyright © 2020 American Chemical Society.)

We report the synthesis and structural characterization of the ABX 3 perovskite frameworks [C(NH 2 ) 3 ]Mn 1- x 2+ (Fe 2 x /3 3+ ,□ x /3 )(HCOO) 3 (□ = B-site vacancy). For large x , the vacancies order, lowering the crystal symmetry. This system establishes B-site vacancies as a new type of defect in formate perovskites, with important chemical, structural, and functional implications. Monte Carlo simulations driven by nearest-neighbor vacancy repulsions show checkerboard vacancy order to emerge for x > 0.6, in accord with experiment.

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" (Hf 12 O 8 (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.

The manipulation of distortions in perovskite structures is critical to tailoring the properties of these materials for a variety of applications. Here we demonstrate a violation of established octahedral tilt rules in the double perovskite analogue (NH4)2SrFe(CN)6·2H2O. The forbidden tilt pattern we observe arises through coupling to hydration-driven Jahn-Teller-like distortions of the Sr coordination environment. Access to novel distortion mechanisms and the ability to switch these distortions on and off through chemical modification fundamentally expands the toolbox of techniques available for engineering symmetry-breaking processes in solid materials.

We study the compositional dependence of molecular orientation (multipolar) and orbital (quadrupolar) order in the perovskite-like metal-organic frameworks [C(NH2)3]CuxCd1-x(HCOO)3. Upon increasing the fraction x of Jahn-Teller-active Cu(2+), we observe an orbital disorder/order transition and a multipolar reorientation transition, each occurring at distinct critical compositions xo = 0.45(5) and xm = 0.55(5). We attribute these transitions to a combination of size, charge distribution, and percolation effects. Our results establish the accessibility in formate perovskites of novel structural degrees of freedom beyond the familiar dipolar terms responsible for (anti)ferroelectric order. We discuss the implications of cooperative quadrupolar and multipolar states for the design of relaxor-like hybrid perovskites.

We report the structures of eight new dicyanometallate frameworks containing molecular extra-framework cations. These systems include a number of hybrid inorganic-organic analogues of conventional ceramics, such as Ruddlesden-Popper phases and perovskites. The structure types adopted are rationalized in the broader context of all known dicyanometallate framework structures. We show that the structural diversity of this family can be understood in terms of (i) the charge and coordination preferences of the particular metal cation acting as framework node, and (ii) the size, shape, and extent of incorporation of extra-framework cations. In this way, we suggest that dicyanometallates form a particularly attractive model family of extended frameworks in which to explore the interplay between molecular degrees of freedom, framework topology, and supramolecular interactions.

Using a combination of single-crystal and powder X-ray diffraction measurements, we study temperature- and pressure-driven structural distortions in zinc(II) cyanide (Zn(CN)2) and cadmium(II) imidazolate (Cd(im)2), two molecular frameworks with the anticuprite topology. Under a hydrostatic pressure of 1.52 GPa, Zn(CN)2 undergoes a first-order displacive phase transition to an orthorhombic phase, with the corresponding atomic displacements characterized by correlated collective tilts of pairs of Zn-centered tetrahedra. This displacement pattern sheds light on the mechanism of negative thermal expansion in ambient-pressure Zn(CN)2. We find that the fundamental mechanical response exhibited by Zn(CN)2 is mirrored in the temperature-dependent behavior of Cd(im)2. Our results suggest that the thermodynamics of molecular frameworks may be governed by considerations of packing efficiency while also depending on dynamic instabilities of the underlying framework topology.

We show that KMn[Ag(CN)(2)](3) exhibits the strongest negative linear compressibility (NLC) effect over the largest pressure range yet observed. Variable pressure neutron powder diffraction measurements reveal that its crystal lattice expands along the c axis of its trigonal cell under increasing hydrostatic pressure, while contracting along the a axis. This corresponds to a "wine-rack"-like mechanism for NLC that we find also results in anisotropic negative thermal expansion (NTE) in the same material. Inclusion of extra-framework K(+) counterions has minimal effect on framework flexibility (and hence the magnitude of NTE/NLC) but selectively frustrates the soft phonon modes responsible for destroying NLC in the related material Ag(3)[Co(CN)(6)].

Reduction of La(1-x)Ca(x)MnO(3) (0.6 ≤ x ≤ 1) perovskite phases with sodium hydride yields materials of composition La(1-x)Ca(x)MnO(2+δ). The calcium-rich phases (x = 0.9, 1) adopt (La(0.9)Ca(0.1))(0.5)Mn(0.5)O disordered rocksalt structures. However local structure analysis using reverse Monte Carlo refinement of models against pair distribution functions obtained from neutron total scattering data reveals lanthanum-rich La(1-x)Ca(x)MnO(2+δ) (x = 0.6, 0.67, 0.7) phases adopt disordered structures consisting of an intergrowth of sheets of MnO(6) octahedra and sheets of MnO(4) tetrahedra. X-ray absorption data confirm the presence of Mn(I) centers in La(1-x)Ca(x)MnO(2+δ) phases with x < 1. Low-temperature neutron diffraction data reveal La(1-x)Ca(x)MnO(2+δ) (x = 0.6, 0.67, 0.7) phases become antiferromagnetically ordered at low temperature.

Tetramethylammonium copper(I) zinc(II) cyanide, which consists of N(CH(3))(4)(+) ions trapped within a cristobalite-like metal cyanide framework, has been studied by variable-temperature powder and single-crystal X-ray diffraction. Its coefficient of thermal expansion is approximately zero over the temperature range 200-400 K and comparable with the best commercial zero thermal expansion materials. The atomic displacement parameters, apparent bond lengths, and structure of a low-temperature, low-symmetry phase reveal that the low-energy vibrational modes responsible for this behavior maintain approximately rigid Zn coordination tetrahedra but involve significant distortion of their Cu counterparts.

The thermal expansion properties of two isostructural zinc dicyanometallates that crystallize with and without the inclusion of a weakly interacting secondary crystalline phase have been investigated using variable temperature single-crystal and powder X-ray diffraction. The guest-free Zn[Au(CN)(2)](2) framework was found to show very strong anisotropic positive and negative thermal expansion. In contrast, its cocrystal analogue Zn[Ag(CN)(2)](2) x xAgCN exhibited much more moderate behavior, such that the coefficient of thermal expansion for the host Zn[M(CN)(2)](2) framework now matched that of crystalline AgCN. It was proposed that this correlation points to a more general ability of highly flexible framework materials to "match" the thermal expansivity of adhered phases (e.g., substrates, sorbates, or cocrystallized species), suggesting a methodology of eliminating thermal strain in multicomponent assemblies.

The thermal expansion behavior of isostructural variants of the colossal thermal expansion material Ag3[CoIII(CN)6] has been investigated using variable temperature X-ray and neutron powder diffraction. It was found that substitution at the octahedral transition metal site did not strongly affect the thermal expansion behavior, giving Ag3[FeIII(CN)6] as a new colossal thermal expansion material. Substitution at the Ag site (by D) was shown to reduce the thermal expansion coefficients by an order of magnitude. It was proposed that this correlation between the presence of argentophilic interactions and extreme thermal expansion behavior may explain a variety of thermal effects in flexible framework materials containing metallophilic interactions.

The guest-dependent thermal expansion behavior of the nanoporous Prussian Blue analogues MIIPtIV(CN)6.x{H2O} (0