Multiscale Reciprocal Space Mapping of Magnetite Mesocrystals.

Mesocrystals are a class of nanostructured material, where a multiple-length-scale structure is a prerequisite of many interesting phenomena. Resolving the mesocrystal structure is quite challenging due to their structuration on different length scales. The combination of small- and wide-angle X-ray scattering (SAXS and WAXS) techniques offers the possibility of non-destructively probing mesocrystalline structures simultaneously, over multiple length scales to reveal their microscopic structure. This work describes how high dynamical range of modern detectors sheds light on the weak features of scattering, significantly increasing the information content. The detailed analysis of X-ray diffraction (XRD) from the magnetite mesocrystals with different particle sizes and shapes is described, in tandem with electron microscopy. The revealed features provide valuable input to the models of mesocrystal growth and the choice of structural motif; the impact on magnetic properties is discussed.

Correction: Exploring the 3D structure and defects of a self-assembled gold mesocrystal by coherent X-ray diffraction imaging.

Correction for 'Exploring the 3D structure and defects of a self-assembled gold mesocrystal by coherent X-ray diffraction imaging' by Jerome Carnis et al., Nanoscale, 2021, DOI: 10.1039/D1NR01806J.

Exploring the 3D structure and defects of a self-assembled gold mesocrystal by coherent X-ray diffraction imaging.

Mesocrystals are nanostructured materials consisting of individual nanocrystals having a preferred crystallographic orientation. On mesoscopic length scales, the properties of mesocrystals are strongly affected by structural heterogeneity. Here, we report the detailed structural characterization of a faceted mesocrystal grain self-assembled from 60 nm sized gold nanocubes. Using coherent X-ray diffraction imaging, we determined the structure of the mesocrystal with the resolution sufficient to resolve each gold nanoparticle. The reconstructed electron density of the gold mesocrystal reveals its intrinsic structural heterogeneity, including local deviations of lattice parameters, and the presence of internal defects. The strain distribution shows that the average superlattice obtained by angular X-ray cross-correlation analysis and the real, "multidomain" structure of a mesocrystal are very close to each other, with a deviation less than 10%. These results will provide an important impact to understanding the fundamental principles of structuring and self-assembly including ensuing properties of mesocrystals.

On Cayley graphs of {\bb Z}4.

The generating sets of {\bb Z}^4 have been enumerated which consist of integral four-dimensional vectors with components -1, 0, 1 and allow Cayley graphs without edge intersections in a straight-edge embedding in a four-dimensional Euclidean space. Owing to computational restrictions the valency of enumerated graphs has been fixed to 10. Up to isomorphism 58 graphs have been found and characterized by coordination sequences, shortest cycles and automorphism groups. To compute automorphism groups, a novel strategy is introduced that is based on determining vertex stabilizers from the automorphism group of a sufficiently large finite ball cut out from an infinite graph. Six exceptional, rather `dense' graphs have been identified which are locally isomorphic to a five-dimensional cubic lattice within a ball of radius 10. They could be built by either interconnecting interpenetrated three- or four-dimensional cubic lattices and therefore necessarily contain Hopf links between quadrangular cycles. As a consequence, a local combinatorial isomorphism does not extend to a local isotopy.

Isotopy classes for 3-periodic net embeddings.

Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. Periodic isotopy classifications are obtained for various families of embedded nets with small quotient graphs. The 25 periodic isotopy classes of depth-1 embedded nets with a single-vertex quotient graph are enumerated. Additionally, a classification is given of embeddings of n-fold copies of pcu with all connected components in a parallel orientation and n vertices in a repeat unit, as well as demonstrations of their maximal symmetry periodic isotopes. The methodology of linear graph knots on the flat 3-torus [0,1)3 is introduced. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.

Covalent Organic Framework (COF-1) under High Pressure.

COF-1 has a structure with rigid 2D layers composed of benzene and B3 O3 rings and weak van der Waals bonding between the layers. The as-synthesized COF-1 structure contains pores occupied by solvent molecules. A high surface area empty-pore structure is obtained after vacuum annealing. High-pressure XRD and Raman experiments with mesitylene-filled (COF-1-M) and empty-pore COF-1 demonstrate partial amorphization and collapse of the framework structure above 12-15 GPa. The ambient pressure structure of COF-1-M can be reversibly recovered after compression up to 10-15 GPa. Remarkable stability of highly porous COF-1 structure at pressures at least up to 10 GPa is found even for the empty-pore structure. The bulk modulus of the COF-1 structure (11.2(5) GPa) and linear incompressibilities (k[100] =111(5) GPa, k[001] =15.0(5) GPa) were evaluated from the analysis of XRD data and cross-checked against first-principles calculations.

On the origin of crystallinity: a lower bound for the regularity radius of Delone sets.

The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular. The universal abstract models of any atomic arrangements are Delone sets, which are uniformly distributed discrete point sets in Euclidean d space. An ideal crystal is a regular or multi-regular system, that is, a Delone set, which is the orbit of a single point or finitely many points under a crystallographic group of isometries. The local theory of regular or multi-regular systems aims at finding sufficient local conditions for a Delone set X to be a regular or multi-regular system. One of the main goals is to estimate the regularity radius \hat{\rho}_d for Delone sets X in terms of the radius R of the largest `empty ball' for X. The celebrated `local criterion for regular systems' provides an upper bound for \hat{\rho_d} for any d. Better upper bounds are known for d ≤ 3. The present article establishes the lower bound \hat{\rho_d}\geq 2dR for all d, which is linear in d. The best previously known lower bound had been \hat{\rho}_d\geq 4R for d ≥ 2. The proof of the new lower bound is accomplished through explicit constructions of Delone sets with mutually equivalent (2dR - ℇ)-clusters, which are not regular systems. The two- and three-dimensional constructions are illustrated by examples. In addition to its fundamental importance, the obtained result is also relevant for the understanding of geometrical conditions of the formation of ordered and disordered arrangements in polytypic materials.

Generating carbon schwarzites via zeolite-templating.

Zeolite-templated carbons (ZTCs) comprise a relatively recent material class synthesized via the chemical vapor deposition of a carbon-containing precursor on a zeolite template, followed by the removal of the template. We have developed a theoretical framework to generate a ZTC model from any given zeolite structure, which we show can successfully predict the structure of known ZTCs. We use our method to generate a library of ZTCs from all known zeolites, to establish criteria for which zeolites can produce experimentally accessible ZTCs, and to identify over 10 ZTCs that have never before been synthesized. We show that ZTCs partition space into two disjoint labyrinths that can be described by a pair of interpenetrating nets. Since such a pair of nets also describes a triply periodic minimal surface (TPMS), our results establish the relationship between ZTCs and schwarzites-carbon materials with negative Gaussian curvature that resemble TPMSs-linking the research topics and demonstrating that schwarzites should no longer be thought of as purely hypothetical materials.

Balancing Mechanical Stability and Ultrahigh Porosity in Crystalline Framework Materials.

A new mesoporous metal-organic framework (MOF; DUT-60) was conceptually designed in silico using Zn4 O6+ nodes, ditopic and tritopic linkers to explore the stability limits of framework architectures with ultrahigh porosity. The robust ith-d topology of DUT-60 provides an average bulk and shear modulus (4.97 GPa and 0.50 GPa, respectively) for this ultra-porous framework, a key prerequisite to suppress pore collapse during desolvation. Subsequently, a cluster precursor approach, resulting in minimal side product formation in the solvothermal synthesis, was used to produce DUT-60, a new crystalline framework with the highest recorded accessible pore volume (5.02 cm3 g-1 ) surpassing all known crystalline framework materials.

Multilayered intercalation of 1-octanol into Brodie graphite oxide.

Multilayered intercalation of 1-octanol into the structure of Brodie graphite oxide (B-GO) was studied as a function of temperature and pressure. Reversible phase transition with the addition/removal of one layer of 1-octanol was found at 265 K by means of X-ray Diffraction (XRD) and Differential Scanning Calorimetry (DSC). The same transition was observed at ambient temperature upon a pressure increase above 0.6 GPa. This transition was interpreted as an incongruent melting of the low temperature/high pressure B-GO intercalated structure with five layers of 1-octanol parallel to GO sheets (L-solvate), resulting in the formation of a four-layered structure that is stable under ambient conditions (A-solvate). Vacuum heating allows the removal of 1-octanol from the A-solvate layer by layer, while distinct sets of (00l) reflections are observed for three-, two-, and one-layered solvate phases. Step by step removal of the 1-octanol layers results in changes of distance between graphene oxide planes by ∼4.5 Å. This experiment proved that both L- and A-solvates are structures with layers of 1-octanol parallel to GO planes. Unusual intercalation with up to five distinct layers of 1-octanol is remarkably different from the behaviour of small alcohol molecules (methanol and ethanol), which intercalate B-GO structure with only one layer under ambient conditions and a maximum of two layers at lower temperatures or higher pressures. The data presented in this study make it possible to rule out a change in the orientation of alcohol molecules from parallel to perpendicular to the GO planes, as suggested in the 1960s to explain larger expansion of the GO lattice due to swelling with larger alcohols.

On the group-theoretical approach to the study of interpenetrating nets.

Using group-subgroup and group-supergroup relations, a general theoretical framework is developed to describe and derive interpenetrating 3-periodic nets. The generation of interpenetration patterns is readily accomplished by replicating a single net with a supergroup G of its space group H under the condition that site symmetries of vertices and edges are the same in both H and G. It is shown that interpenetrating nets cannot be mapped onto each other by mirror reflections because otherwise edge crossings would necessarily occur in the embedding. For the same reason any other rotation or roto-inversion axes from G \ H are not allowed to intersect vertices or edges of the nets. This property significantly narrows the set of supergroups to be included in the derivation of interpenetrating nets. A procedure is described based on the automorphism group of a Hopf ring net [Alexandrov et al. (2012). Acta Cryst. A68, 484-493] to determine maximal symmetries compatible with interpenetration patterns. The proposed approach is illustrated by examples of twofold interpenetrated utp, dia and pcu nets, as well as multiple copies of enantiomorphic quartz (qtz) networks. Some applications to polycatenated 2-periodic layers are also discussed.

Microwave-Assisted Synthesis of Defects Metal-Imidazolate-Amide-Imidate Frameworks and Improved CO2 Capture.

In this work, we report three isostructural 3D frameworks, named IFP-11 (R = Cl), IFP-12 (R = Br), and IFP-13 (R = Et) (IFP = Imidazolate Framework Potsdam) based on a cobalt(II) center and the chelating linker 2-substituted imidazolate-4-amide-5-imidate. These chelating ligands were generated in situ by partial hydrolysis of 2-substituted 4,5-dicyanoimidazoles under microwave (MW)-assisted conditions in DMF. Structure determination of these IFPs was investigated by IR spectroscopy and a combination of powder X-ray diffraction (PXRD) with structure modeling. The structural models were initially built up from the single-crystal X-ray structure determination of IFP-5 (a cobalt center and 2-methylimidazolate-4-amide-5-imidate linker based framework) and were optimized by using density functional theory calculations. Substitution on position 2 of the linker (R = Cl, Br, and Et) in the isostructural IFP-11, -12, and -13 allowed variation of the potential pore window in 1D hexagonal channels (3.8 to 1.7 Å). The potential of the materials to undergo specific interactions with CO2 was measured by the isosteric heat of adsorption. Further, we resynthesized zinc based IFPs, namely IFP-1 (R = Me), IFP-2 (R = Cl), IFP-3 (R = Br), and IFP-4 (R = Et), and cobalt based IFP-5 under MW-assisted conditions with higher yield. The transition from a nucleation phase to the pure crystalline material of IFP-1 in MW-assisted synthesis depends on reaction time. IFP-1, -3, and -5, which are synthesized by MW-assisted conditions, showed an enhancement of N2 and CO2, compared to the analogous conventional electrical (CE) heating method based materials due to crystal defects.

Hydrogen storage in high surface area graphene scaffolds.

Using an optimized KOH activation procedure we prepared highly porous graphene scaffold materials with SSA values up to 3400 m(2) g(-1) and a pore volume up to 2.2 cm(3) g(-1), which are among the highest for carbon materials. Hydrogen uptake of activated graphene samples was evaluated in a broad temperature interval (77-296 K). After additional activation by hydrogen annealing the maximal excess H2 uptake of 7.5 wt% was obtained at 77 K. A hydrogen storage value as high as 4 wt% was observed already at 193 K (120 bar H2), a temperature of solid CO2, which can be easily maintained using common industrial refrigeration methods.

From zeolite nets to sp(3) carbon allotropes: a topology-based multiscale theoretical study.

We present a comprehensive computational study of sp(3)-carbon allotropes based on the topologies proposed for zeolites. From ≈600,000 zeolite nets we identified six new allotropes, lying by at most 0.12 eV per atom above diamond. The analysis of cages in the allotropes has revealed close structural relations to diamond and lonsdaleite phases. Besides the energetic and mechanical stability of new allotropes, three of them show band gaps by ca. 1 eV larger than that of diamond, and therefore represent an interesting technological target as hard and transparent materials. A structural relation of new allotropes to continuous random networks is pointed out and possible engineering from diamond thin films and graphene is suggested.

Interconnection of nanoparticles within 2D superlattices of PbS/oleic acid thin films.

Make it connected! 2D close-packed layers of inorganic nanoparticles are interconnected by organic fibrils of oleic acid as clearly visualized by electron holography. These fibrils can be mineralised by PbS to transform an organic-inorganic framework to a completely interconnected inorganic semiconducting 2D array.

Zeolitic imidazolate framework-71 nanocrystals and a novel SOD-type polymorph: solution mediated phase transformations, phase selection via coordination modulation and a density functional theory derived energy landscape.

We report a rapid additive-free synthesis of nanocrystals (NCs) of RHO-type ZIF-71 () of composition [Zn(dcim)2] (dcim = 4,5-dichloroimidazolate) in 1-propanol as solvent at room temperature. NC- has a size of 30-60 nm and exhibits permanent microporosity with a surface area (SBET = 970 m(2) g(-1)) comparable to that of microcrystalline material. When kept under the mother solution NC- undergoes transformation into a novel SOD-type polymorph (), which in turn converts into known ZIF-72 () with lcs topology. It is shown that microcrystals (MCs) of can be favourably synthesised using 1-methylimidazole as a coordination modulator. NC- with size <200 nm was prepared using NC-ZIF-8 as a template with SOD topology in a solvent assisted ligand exchange-related process. DFT-assisted Rietveld analysis of powder XRD data revealed that novel polymorph possesses an unusual SOD framework conformation. was further characterised with regard to microporosity (SBET = 597 m(2) g(-1)) and thermal as well as chemical stability. DFT calculations were performed to search for further potentially existing but not-yet synthesised polymorphs in the [Zn(dcim)2] system.

Gate effects in a hexagonal zinc-imidazolate-4-amide-5-imidate framework with flexible methoxy substituents and CO2 selectivity.

A new imidazolate-4-amide-5-imidate based MOF, IFP-7, is generated, having flexible methoxy groups, which act as molecular gates for guest molecules. This allows highly selective CO2 sorption over N2 and CH4 gases.

Novel metastable metallic and semiconducting germaniums.

Group-IVa elements silicon and germanium are known for their semiconducting properties at room temperature, which are technologically critical. Metallicity and superconductivity are found at higher pressures only, Ge ß-tin (tI4) being the first high-pressure metallic phase in the phase diagram. However, recent experiments suggest that metallicity in germanium is compatible with room conditions, calling for a rethinking of our understanding of its phase diagram. Missing structures can efficiently be identified based on structure prediction methods. By means of ab initio metadynamics runs we explored the lower-pressure region of the phase diagram of germanium. A monoclinic germanium phase (mC16) with four-membered rings, less dense than diamond and compressible into ß-tin phase (tI4) was found. Tetragonal bct-5 appeared between diamond and tI4. mC16 is a narrow-gap semiconductor, while bct-5 is metallic and potentially still superconducting in the very low pressure range. This finding may help resolving outstanding experimental issues.