We show how different aspects of a model of the complex disordered structure of wüstite, Fe1−xO, affect the pair distribution function (PDF) and powder diffraction pattern. The aim is to assess the efficacy of using these techniques to determine details of local structure. The different aspects include the nature of the individual defect clusters, the nature of the paracrystalline superlattice on which they are distributed and the ‘size-effect’ relaxation of the basic rocksalt FeO matrix around the defects. The results show that PDF data are sensitive to those aspects of the models that have a significant effect on the populations of interatomic spacings but are less able to determine correlation structures in the samples if these do not have a substantial interaction with interatomic separations.

Different experimental conditions at a versatile high-energy beamline equipped with a two-dimensional detector have been compared for powder diffraction and pair distribution function (PDF) experiments. In particular, sample size and sample to detector distances have been evaluated on a standard sample, to evaluate their effects in both Q and real space. Two illustrative cases are also discussed. The average structure and local distortions in a BaTiO3 powder with 100 nm particle size show that spurious ripples in the PDF are suppressed by increased counting statistics. Effects of small amounts of a crystalline impurity phase on a SiO2.Al2O3.Na2O.CaO glass have been quantified.

Two examples of anionic complexes having vapochromic behavior are investigated: [K(H2O)][Pt(ppy)(CN)2] “Pt(ppy)” and [K(H2O)][Pt(bzq)(CN)2] “Pt(bzq)”, where ppy = 2-phenylpyridinate and bzq = 7,8-benzoquinolate. These monohydrate-potassium salts exhibit a change in color from purple to yellow [Pt(ppy)] and from red to yellow [Pt(bzq)] upon heating to 110 °C, and they transform back into the original color upon absorption of water molecules from the environment. Available only in the form of polycrystalline samples, no structural information on such compounds is accessible, due to highly overlapping peaks in powder diffraction profiles. We use in situ Pair Distribution Function measurements on powder samples to investigate the dynamics of the structural changes induced by temperature variations. By means of a multivariate approach, we were able to extract dynamic structural information from collected profiles without using prior knowledge on the static crystal structure of the compounds. The critical temperature and the characteristics of the vapochromic transition have been identified, as well as the main structural changes causing it.

Ion-exchanged Aurivillius materials form perovskite nanosheet booklets wherein well-defined bi-periodic sheets, with ~11.5 Å thickness, exhibit extensive stacking disorder. The perovskite layer contents were defined initially using combined synchrotron X-ray and neutron Rietveld refinement of the parent Aurivillius structure. The structure of the subsequently ion-exchanged material, which is disordered in its stacking sequence, is analyzed using both pair distribution function (PDF) analysis and recursive method simulations of the scattered intensity. Combined X-ray and neutron PDF refinement of supercell stacking models demonstrates sensitivity of the PDF to both perpendicular and transverse stacking vector components. Further, hierarchical ensembles of stacking models weighted by a standard normal distribution are demonstrated to improve PDF fit over 1–25 Å. Recursive method simulations of the X-ray scattering profile demonstrate agreement between the real space stacking analysis and more conventional reciprocal space methods. The local structure of the perovskite sheet is demonstrated to relax only slightly from the Aurivillius structure after ion exchange.

The size of dopant-rich nanodomains was assessed in four samples of Ce1−μ Yμ O2−μ/2 through systematic pair distribution function (PDF) refinements. Experimental G(r) curves were fitted by different structural models with the aim of finding a description which balanced precise structure parameterization and reasonable number of parameters. The most reliable model was a single Y2O3-like phase, which best accommodated to the close relationship between the fluorite (CeO2-like) and C-type (Y2O3-like) structures. In this model, a refined cation coordinate, x(M2), measured the relative occurrence in the G(r) of the chemical environment of Y and Ce at any value of r. The r-value at which x(M2) vanished, i.e. at which the refined C-type cell becomes a redundant, low-symmetry description of a fluorite cell, was assumed as the size of a C-type domain. Subtle features in G(r) could be attributed to the fluorite or C-type phase up to ~500 Å thanks to the narrow instrumental resolution function of the ID31 beamline (now ID22) at the ESRF, which allows us to get high resolution PDF data.

The crystal structure of a new hafnium oxyhydroxide obtained by an ion-exchange reaction from a Li2HfO3 precursor has been solved by a direct method and refined using Rietveld full profile fitting based on X-ray powder diffraction data. HfO(ОН)2 crystallizes in a P21/c monoclinic unit cell (a = 5.5578(5) Å, b = 9.0701(10) Å, c = 5.7174(5) Å, β = 119.746(5)°); its structure can be described as a framework formed by edge-sharing HfO6 octahedra connected to each other via vertices. In addition, an analysis of the atomic pair distribution function obtained using synchrotron radiation was used to confirm the model and to describe fine-structure features.

The method of high-energy total elastic X-ray scattering to determine the atomic structure of nanocrystalline, highly disordered, and amorphous materials is presented. The current state of the technique, its potential, and limitations are discussed with two successful studies on the pressure induced phase transition in mackinawite (FeS) and the high-pressure behavior of liquid gallium.

We examine simulated electron microdiffraction patterns from models of thin polycrystalline silicon. The models are made by a Voronoi tessellation of random points in a box. The Voronoi domains are randomly selected to contain either a randomly-oriented cubic crystalline grain or a region of continuous random network material. The microdiffraction simulations from coherent probes of different widths are computed at the ideal kinematical limit, ignoring inelastic and multiple scattering. By examining the normalized intensity variance that is obtained in fluctuation electron microscopy experiments, we confirm that intensity fluctuations increase monotonically with the percentage of crystalline grains in the material. However, anomalously high variance is observed for models that have 100% crystalline grains with no imperfections. We confirm that the reduced normalized variance, V(k,R) − 1, that is associated with four-body correlations at scattering vector k, varies inversely with specimen thickness. Further, for probe sizes R larger than the mean grain size, we confirm that the reduced normalized variance obeys the predicted form given by Gibson et al. [Ultramicroscopy, 83, 169–178 (2000)] for the kinematical coherent scattering limit.