The MEM/Rietveld method with nano-applications – accurate charge-density studies of nano-structured materials by synchrotron-radiation powder diffraction

Structural Chemistry of Giant Metal Based Supramolecules

The review presents a bird-eye view on the state of research in the field of giant nonbiological discrete metal complexes and ions of nanometer size, which are structurally characterized by means of single-crystal X-ray diffraction, using the crystal structure as a common key feature. The discussion is focused on the main structural features of the metal clusters, the clusters containing compact metal oxide/hydroxide/chalcogenide core, ligand-based metal-organic cages, and supramolecules as well as on the aspects related to the packing of the molecules or ions in the crystal and the methodological aspects of the single-crystal neutron and X-ray diffraction of these compounds.

DevelopingWinXPRO: a software for determination of the multipole-model-based properties of crystals

The new release of the computer program packageWinXPRO v.3xfor determination of the crystal properties from parameters of the multipole-modeled experimental electron density and anharmonic atomic displacement coefficients is described. The set of properties is significantly extended by using the density functional and information theories. In addition, a built-in multi-functional viewer and programs to display the output data, including the mapping of the chosen functional bonding descriptors onto surfaces of the other properties, are included.

Contemporary X-ray electron-density studies using synchrotron radiation

Synchrotron radiation has many compelling advantages over conventional radiation sources in the measurement of accurate Bragg diffraction data. The variable photon energy and much higher flux may help to minimize critical systematic effects such as absorption, extinction and anomalous scattering. Based on a survey of selected published results from the last decade, the benefits of using synchrotron radiation in the determination of X-ray electron densities are discussed, and possible future directions of this field are examined.

Crystallographic studies of gas sorption in metal-organic frameworks

Metal-organic frameworks (MOFs) are a class of porous crystalline materials of modular design. One of the primary applications of these materials is in the adsorption and separation of gases, with potential benefits to the energy, transport and medical sectors. In situ crystallography of MOFs under gas atmospheres has enabled the behaviour of the frameworks under gas loading to be investigated and has established the precise location of adsorbed gas molecules in a significant number of MOFs. This article reviews progress in such crystallographic studies, which has taken place over the past decade, but has its origins in earlier studies of zeolites, clathrates etc. The review considers studies by single-crystal or powder diffraction using either X-rays or neutrons. Features of MOFs that strongly affect gas sorption behaviour are discussed in the context of in situ crystallographic studies, specifically framework flexibility, and the presence of (organic) functional groups and unsaturated (open) metal sites within pores that can form specific interactions with gas molecules.

Hierarchical dielectric orders in layered ferroelectrics Bi2SiO5

Electric dipole engineering is now an emerging technology for high electron-mobility transistors, ferroelectric random access memory and multiferroic devices etc. Although various studies to provide insight into dipole moment behaviour, such as phase transition, order and disorder states, have been reported, macroscopic spontaneous polarization has been mainly discussed so far. Here, visualization of the electric dipole arrangement in layered ferroelectrics Bi2SiO5 by means of combined analysis of maximum entropy charge density and electrostatic potential distribution analysis based on synchrotron radiation X-ray powder diffraction data is reported. It was found that the hierarchical dipole orders, the weak-ferroelectric and ferroelectric configurations, were observed in the Bi2O2 and the SiO3 layers, respectively, and the ferrielectric configuration was realised by the interlayer interaction. This discovery provides a new method to visualize the local polarization in ferroelectric materials.

Modulated anharmonic ADPs are intrinsic to aperiodic crystals: a case study on incommensurate Rb2ZnCl4

A combination of structure refinements, analysis of the superspace MEM density and interpretation of difference-Fourier maps has been used to characterize the incommensurate modulation of rubidium tetrachlorozincate, Rb(2)ZnCl(4), at a temperature of T = 196 K, close to the lock-in transition at T(lock-in) = 192 K. The modulation is found to consist of a combination of displacement modulation functions, modulated atomic displacement parameters (ADPs) and modulated third-order anharmonic ADPs. Up to fifth-order Fourier coefficients could be refined against diffraction data containing up to fifth-order satellite reflections. The center-of-charge of the atomic basins of the MEM density and the displacive modulation functions of the structure model provide equivalent descriptions of the displacive modulation. Modulations of the ADPs and anharmonic ADPs are visible in the MEM density, but extracting quantitative information about these modulations appears to be difficult. In the structure refinements the modulation parameters of the ADPs form a dependent set, and ad hoc restrictions had to be introduced in the refinements. It is suggested that modulated harmonic ADPs and modulated third-order anharmonic ADPs form an intrinsic part, however small, of incommensurately modulated structures in general. Refinements of alternate models with and without parameters for modulated ADPs lead to significant differences between the parameters of the displacement modulation in these two types of models, thus showing the modulation of ADPs to be important for a correct description of the displacive modulation. The resulting functions do not provide evidence for an interpretation of the modulation by a soliton model.

Maximum entropy method and charge flipping, a powerful combination to visualize the true nature of structural disorder from in situ X-ray powder diffraction data

In a systematic approach, the ability of the Maximum Entropy Method (MEM) to reconstruct the most probable electron density of highly disordered crystal structures from X-ray powder diffraction data was evaluated. As a case study, the ambient temperature crystal structures of disordered alpha-Rb(2)[C(2)O(4)] and alpha-Rb(2)[CO(3)] and ordered delta-K(2)[C(2)O(4)] were investigated in detail with the aim of revealing the ;true' nature of the apparent disorder. Different combinations of F (based on phased structure factors) and G constraints (based on structure-factor amplitudes) from different sources were applied in MEM calculations. In particular, a new combination of the MEM with the recently developed charge-flipping algorithm with histogram matching for powder diffraction data (pCF) was successfully introduced to avoid the inevitable bias of the phases of the structure-factor amplitudes by the Rietveld model. Completely ab initio electron-density distributions have been obtained with the MEM applied to a combination of structure-factor amplitudes from Le Bail fits with phases derived from pCF. All features of the crystal structures, in particular the disorder of the oxalate and carbonate anions, and the displacements of the cations, are clearly obtained. This approach bears the potential of a fast method of electron-density determination, even for highly disordered materials. All the MEM maps obtained in this work were compared with the MEM map derived from the best Rietveld refined model. In general, the phased observed structure factors obtained from Rietveld refinement (applying F and G constraints) were found to give the closest description of the experimental data and thus lead to the most accurate image of the actual disorder.

Modulation functions of incommensurately modulated Cr2P2O7 studied by the maximum entropy method (MEM)

The maximum entropy method (MEM) has been used to determine electron density in superspace of incommensurately modulated chromium pyrophosphate from X-ray diffraction data measured by Palatinus et al. [(2006), Acta Cryst. B62, 556-566]. Chromium pyrophosphate, Cr(2)P(2)O(7), contains ordered regions (83% of the volume) and regions with disorder. Analysis of the MEM density has allowed the determination of the displacive modulation functions within ordered regions. The disordered regions can be described as the alternate occupation of two conformations of the pyrophosphate group and two positions of the chromium atom, with occupational probabilities that depend continuously on the phase of modulation t. A structure model based on the interpretation of the MEM density provides a fit to the diffraction data of the same quality as the model given by Palatinus et al. (2006). The failure to find a model that better fits the data is attributed to the intrinsic inaccuracy of approximately 0.01 A for positions derived from the MEM and to the difficulties in constructing an appropriate model for the anharmonic ADPs and their modulation functions from electron densities.

Does Gd@C82 have an anomalous endohedral structure? Synthesis and single crystal X-ray structure of the carbene adduct

We report here the results on single crystal X-ray crystallographic analysis of the Gd@C82 carbene adduct (Gd@C82(Ad), Ad = adamantylidene). The Gd atom in Gd@C82(Ad) is located at an off-centered position near a hexagonal ring in the C2v-C82 cage, as found for M@C82 (M = Sc and La) and La@C82(Ad). Theoretical calculation also confirms the position of the Gd atom in the X-ray crystal structure.