Solving the Hydrogen and Lithium Substructure of Poly(triazine imide)/LiCl Using NMR Crystallography.

Poly(triazine imide) with incorporated lithium chloride has recently attracted substantial attention due to its photocatalytic activity for water splitting. However, an apparent H/Li disorder prevents the delineation of structure-property relationships, for example, with respect to band-gap tuning. Herein, we show that through a combination of one- and two-dimensional, multinuclear solid-state NMR spectroscopy, chemical modelling, automated electron diffraction tomography, and an analysis based on X-ray pair distribution functions, it is finally possible to resolve the H/Li substructure. In each cavity, one hydrogen atom is bound to a bridging nitrogen atom, while a second one protonates a triazine ring. The two lithium ions within each cavity are positioned between two nitrogen atoms of neighbouring triazine rings. The thereby induced local dipole moments cause slight buckling of the framework and lateral displacements of the Cl- ions at a coherence length below 2 nm. Nevertheless, the average structure conforms to space group P21 21 21 . In this way, we demonstrate that, in particular, the above-mentioned techniques allow for smart interplay in delineating the real structure of PTI/LiCl.

Refining short-range order parameters from the three-dimensional diffuse scattering in single-crystal electron diffraction data.

Our study compares short-range order parameters refined from the diffuse scattering in single-crystal X-ray and single-crystal electron diffraction data. Nb0.84CoSb was chosen as a reference material. The correlations between neighbouring vacancies and the displacements of Sb and Co atoms were refined from the diffuse scattering using a Monte Carlo refinement in DISCUS. The difference between the Sb and Co displacements refined from the diffuse scattering and the Sb and Co displacements refined from the Bragg reflections in single-crystal X-ray diffraction data is 0.012 (7) Šfor the refinement on diffuse scattering in single-crystal X-ray diffraction data and 0.03 (2) Šfor the refinement on the diffuse scattering in single-crystal electron diffraction data. As electron diffraction requires much smaller crystals than X-ray diffraction, this opens up the possibility of refining short-range order parameters in many technologically relevant materials for which no crystals large enough for single-crystal X-ray diffraction are available.

Direct interpretation of the X-ray and neutron three-dimensional difference pair distribution functions (3D-ΔPDFs) of yttria-stabilized zirconia.

Three-dimensional difference pair distribution functions (3D-ΔPDFs) from X-ray and neutron diffraction experiments are reported for yttria-stabilized zirconia (Zr0.82Y0.18O1.91). 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) Šalong ⟨1, 0, 0⟩ towards the vacancy while metal ions neighbouring a vacancy shift by 0.465 (2) Šalong ⟨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.

Structural phase transition to disorder low-temperature phase in [Fe(ptz)6](BF4)2 spin-crossover compounds.

In the spin-crossover compound [Fe(ptz)(6)](BF(4))(2) (where ptz=1-n-propyltetrazole) six different phases are observed. When a single crystal is slowly cooled from high temperatures to those below 125 K, the reflections broaden into diffuse maxima and split into two maxima along the c* direction [Kusz, Gütlich & Spiering (2004). Top. Curr. Chem. 234, 129-153]. As both maxima are broad along the c* direction, the short-range order exists only along the c direction and in the ab plane the structure remains long-range ordered. In this disordered phase additional satellite reflections appear. Upon heating above 135 K, the diffuse maxima return to their previous shape and this process is completely reversible. Rapidly cooled samples, on the other hand, do not show such splitting and the symmetry remains R\bar 3, despite a jump in lattice parameters. We use a special technique to analyse the disorder model of the slowly cooled samples, which consists of layered domains shifted in the hexagonal ab plane. The low-spin disordered phase was solved in a novel approach to accommodate the very unusual twinning and refined in the non-standard space group C\bar 1. In contrast to the ordered low-spin phase, the Fe ion is in a non-centrosymmetric coordination polyhedron and two of the six propyl groups change their conformation.

Efficient solution of particle shape functions for the analysis of powder total scattering data.

Structural characterization of powder samples via total scattering methods, in either real or reciprocal space, must take into account the effect of particle shape. Here, the shape contribution of a set of ideally isolated particles to the small-angle scattering (SAS) component of the intensity profile is modelled using the shape function [Svergun & Koch (2003). Rep. Prog. Phys. 66, 1735-1782]. The shape function is obtained by orientational averaging of common volume functions (CVFs) for a discrete set of directions. The effects of particle size and size dispersity are accounted for via scaling of the CVFs and their convolution with the underlying probability distribution. The method is applied to shapes with CVFs expressed analytically or by using discrete tables. The accurate calculation of SAS particle shape contributions up to large momentum transfer demonstrates the reliability and flexibility of modelling shape functions from sets of CVFs. The algorithm presented here is computationally efficient and can be directly incorporated into existing routines for analysis of powder total scattering data.

Quantitative analysis of diffuse electron scattering in the lithium-ion battery cathode material Li1.2Ni0.13Mn0.54Co0.13O2.

In contrast to perfectly periodic crystals, materials with short-range order produce diffraction patterns that contain both Bragg reflections and diffuse scattering. To understand the influence of short-range order on material properties, current research focuses increasingly on the analysis of diffuse scattering. This article verifies the possibility to refine the short-range order parameters in submicrometre-sized crystals from diffuse scattering in single-crystal electron diffraction data. The approach was demonstrated on Li1.2Ni0.13Mn0.54Co0.13O2, which is a state-of-the-art cathode material for lithium-ion batteries. The intensity distribution of the 1D diffuse scattering in the electron diffraction patterns of Li1.2Ni0.13Mn0.54Co0.13O2 depends on the number of stacking faults and twins in the crystal. A model of the disorder in Li1.2Ni0.13Mn0.54Co0.13O2 was developed and both the stacking fault probability and the percentage of the different twins in the crystal were refined using an evolutionary algorithm in DISCUS. The approach was applied on reciprocal space sections reconstructed from 3D electron diffraction data since they exhibit less dynamical effects compared with in-zone electron diffraction patterns. A good agreement was achieved between the calculated and the experimental intensity distribution of the diffuse scattering. The short-range order parameters in submicrometre-sized crystals can thus successfully be refined from the diffuse scattering in single-crystal electron diffraction data using an evolutionary algorithm in DISCUS.

Ensemble modeling of very small ZnO nanoparticles.

The detailed structural characterization of nanoparticles is a very important issue since it enables a precise understanding of their electronic, optical and magnetic properties. Here we introduce a new method for modeling the structure of very small particles by means of powder X-ray diffraction. Using thioglycerol-capped ZnO nanoparticles with a diameter of less than 3 nm as an example we demonstrate that our ensemble modeling method is superior to standard XRD methods like, e.g., Rietveld refinement. Besides fundamental properties (size, anisotropic shape and atomic structure) more sophisticated properties like imperfections in the lattice, a size distribution as well as strain and relaxation effects in the particles and-in particular-at their surface (surface relaxation effects) can be obtained. Ensemble properties, i.e., distributions of the particle size and other properties, can also be investigated which makes this method superior to imaging techniques like (high resolution) transmission electron microscopy or atomic force microscopy, in particular for very small nanoparticles. For the particles under study an excellent agreement of calculated and experimental X-ray diffraction patterns could be obtained with an ensemble of anisotropic polyhedral particles of three dominant sizes, wurtzite structure and a significant relaxation of Zn atoms close to the surface.

Exact and fast calculation of the X-ray pair distribution function.

A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

New zeolite-like RUB-5 and its related hydrous layer silicate RUB-6 structurally characterized by electron microscopy.

This study made use of a recently developed combination of advanced methods to reveal the atomic structure of a disordered nanocrystalline zeolite using exit wave reconstruction, automated diffraction tomography, disorder modelling and diffraction pattern simulation. By applying these methods, it was possible to determine the so far unknown structures of the hydrous layer silicate RUB-6 and the related zeolite-like material RUB-5. The structures of RUB-5 and RUB-6 contain the same dense layer-like building units (LLBUs). In the case of RUB-5, these building units are interconnected via additional SiO4/2 tetrahedra, giving rise to a framework structure with a 2D pore system consisting of intersecting 8-ring channels. In contrast, RUB-6 contains these LLBUs as separate silicate layers terminated by silanol/sil-oxy groups. Both RUB-6 and RUB-5 show stacking disorder with intergrowths of different polymorphs. The unique structure of RUB-6, together with the possibility for an interlayer expansion reaction to form RUB-5, make it a promising candidate for interlayer expansion with various metal sources to include catalytically active reaction centres.

Towards quantitative treatment of electron pair distribution function.

The pair distribution function (PDF) is a versatile tool to describe the structure of disordered and amorphous materials. Electron PDF (ePDF) uses the advantage of strong scattering of electrons, thus allowing small volumes to be probed and providing unique information on structure variations at the nano-scale. The spectrum of ePDF applications is rather broad: from ceramic to metallic glasses and mineralogical to organic samples. The quantitative interpretation of ePDF relies on knowledge of how structural and instrumental effects contribute to the experimental data. Here, a broad overview is given on the development of ePDF as a structure analysis method and its applications to diverse materials. Then the physical meaning of the PDF is explained and its use is demonstrated with several examples. Special features of electron scattering regarding the PDF calculations are discussed. A quantitative approach to ePDF data treatment is demonstrated using different refinement software programs for a nanocrystalline anatase sample. Finally, a list of available software packages for ePDF calculation is provided.

Ab initio structure determination and quantitative disorder analysis on nanoparticles by electron diffraction tomography.

Nanoscaled porous materials such as zeolites have attracted substantial attention in industry due to their catalytic activity, and their performance in sorption and separation processes. In order to understand the properties of such materials, current research focuses increasingly on the determination of structural features beyond the averaged crystal structure. Small particle sizes, various types of disorder and intergrown structures render the description of structures at atomic level by standard crystallographic methods difficult. This paper reports the characterization of a strongly disordered zeolite structure, using a combination of electron exit-wave reconstruction, automated diffraction tomography (ADT), crystal disorder modelling and electron diffraction simulations. Zeolite beta was chosen for a proof-of-principle study of the techniques, because it consists of two different intergrown polymorphs that are built from identical layer types but with different stacking sequences. Imaging of the projected inner Coulomb potential of zeolite beta crystals shows the intergrowth of the polymorphs BEA and BEB. The structures of BEA as well as BEB could be extracted from one single ADT data set using direct methods. A ratio for BEA/BEB = 48:52 was determined by comparison of the reconstructed reciprocal space based on ADT data with simulated electron diffraction data for virtual nanocrystals, built with different ratios of BEA/BEB. In this way, it is demonstrated that this smart interplay of the above-mentioned techniques allows the elaboration of the real structures of functional materials in detail - even if they possess a severely disordered structure.

Diffuse single-crystal scattering corrected for molecular form factor effects.

This paper shows that chemical short-range order in two-component molecular crystals can be solved directly by separating the influence of the molecular form factor from the diffraction pattern. This novel technique is demonstrated by analysing the diffuse scattering of tris-tert-butyl-1,3,5-benzene tricarboxamide.

Close-packed structures with finite-range interaction: computational mechanics of layer pair interaction.

The stacking problem is approached by computational mechanics, using an Ising next-nearest-neighbour model. Computational mechanics allows one to treat the stacking arrangement as an information processing system in the light of a symbol-generating process. A general method for solving the stochastic matrix of the random Gibbs field is presented and then applied to the problem at hand. The corresponding phase diagram is then discussed in terms of the underlying ℇ-machine, or optimal finite-state machine. The occurrence of higher-order polytypes at the borders of the phase diagram is also analysed. The applicability of the model to real systems such as ZnS and cobalt is discussed. The method derived is directly generalizable to any one-dimensional model with finite-range interaction.

Atomic-level structural correlations across the morphotropic phase boundary of a ferroelectric solid solution: xBiMg1/2Ti1/2O3-(1 - x)PbTiO3.

Revelation of unequivocal structural information at the atomic level for complex systems is uniquely important for deeper and generic understanding of the structure property connections and a key challenge in materials science. Here we report an experimental study of the local structure by applying total elastic scattering and Raman scattering analyses to an important non-relaxor ferroelectric solid solution exhibiting the so-called composition-induced morphotropic phase boundary (MPB), where concomitant enhancement of physical properties have been detected. The powerful combination of static and dynamic structural probes enabled us to derive direct correspondence between the atomic-level structural correlations and reported properties. The atomic pair distribution functions obtained from the neutron total scattering experiments were analysed through big-box atom-modelling implementing reverse Monte Carlo method, from which distributions of magnitudes and directions of off-centred cationic displacements were extracted. We found that an enhanced randomness of the displacement-directions for all ferroelectrically active cations combined with a strong dynamical coupling between the A- and B-site cations of the perovskite structure, can explain the abrupt amplification of piezoelectric response of the system near MPB. Altogether this provides a more fundamental basis in inferring structure-property connections in similar systems including important implications in designing novel and bespoke materials.

Close-packed structure dynamics with finite-range interaction: computational mechanics with individual layer interaction.

This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status Solidi B (2000), 218, 425-430] avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hägg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close-packed structures is made for such a Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, are discussed. It is argued that the Ahmad & Khan model is simpler and predicts a larger set of polytypes than previous treatments.

Celebrating 100 years of the Debye scattering equation.

One hundred years of the Debye scattering equation are celebrated with a series of articles arising from the DSE 2015 conference.

Universal solvent restructuring induced by colloidal nanoparticles.

Colloidal nanoparticles, used for applications from catalysis and energy applications to cosmetics, are typically embedded in matrixes or dispersed in solutions. The entire particle surface, which is where reactions are expected to occur, is thus exposed. Here, we show with x-ray pair distribution function analysis that polar and nonpolar solvents universally restructure around nanoparticles. Layers of enhanced order exist with a thickness influenced by the molecule size and up to 2 nanometers beyond the nanoparticle surface. These results show that the enhanced reactivity of solvated nanoparticles includes a contribution from a solvation shell of the size of the particle itself.

Synthesis and characterisation of new MO(OH)2 (M = Zr, Hf) oxyhydroxides and related Li2MO3 salts.

Two new solid MO(OH)2 (M = Zr, Hf) oxyhydroxides have been synthesised by an ion-exchange reaction from Li2MO3 (M = Zr, Hf) precursors obtained by a citrate combustion technique. The crystal structure of the oxyhydroxides has been solved by direct methods and refined using Rietveld full profile fitting based on X-ray powder diffraction data. Both oxyhydroxides crystallize in a P2(1)/c monoclinic unit cell and have a structure resembling that of the related salts. Detailed characterisation of the fine-structure features and chemical bonding in precursors and oxyhydroxide powders has been performed using vibrational spectroscopy, nuclear magnetic resonance spectroscopy, scanning electron microscopy, pair distribution function analysis and quantum-chemical modelling.

Defect crystal structure of new TiO(OH)2 hydroxide and related lithium salt Li2TiO3.

Crystal structures of TiO(OH)(2) and Li(2)TiO(3) have been studied in detail and refined using X-ray powder diffraction data. Both compounds possess a high concentration of defects in the structure. The crystal structure of the Li(2)TiO(3) salt obtained at 700 degrees C reveals stacking faults of LiTi(2) metal layers, which leads to the appearance of short-range order in three possible space groups: C2/c, C2/m, P3(1)12. The possibility to stabilise this imperfect state increases the mobility of the Li(+) ions in the structure and allows the complete exchange of lithium by hydrogen in acid water solutions with formation of TiO(OH)(2). The crystal structure of TiO(OH)(2) belongs to the layered double hydroxide structure type with the 3R(1) sequence of oxygen layers and can be described as a stacking of charge-neutral metal oxyhydroxide slabs [(OH)(2)OTi(2)O(OH)(2)]. TiO(OH)(2) is the first layered double hydroxide structure formed by a cation with oxidation state +4 only.