Volume 220, Issue 12 - Diffuse Scattering

Using complementary X-ray reflectivity (XR) and grazing incidence X-ray diffraction (GIXD), we report structural studies of supported thin-organic layers in contact with water and air. Using a monochromatic synchrotron beam to penetrate 10 mm of liquid, we have characterized buried films composed of 12.5 repeating bilayers of arachidic acid (C 20 H 40 O 2 ) complexed with cadmium ions (cadmium arachidate, CdAr 2 ). We found that the layered structure of the CdAr 2 multilayers do not exhibit rearrangement after exposure to water with negligible water penetration into the inner layers when compared to their dry state. These findings are consistent with the formation of extremely robust CdAr 2 multilayers that can withstand multiple rinses in strong organic solvents, acid, and mechanical wear. The second goal was to demonstrate the feasibility of similar experiments to study much thinner single bilayer bio-membranes. These studies are the first successful GIXD experiments of ultra thin-organic film composed of a few layers at the solid-liquid interface.

Mesoscopic features, such as thick twin walls, surface relaxations, or haloes around metamict regions in crystals have a lengthscale of the order of 1–100 Å. Such features are studied experimentally using diffuse scattering signals; either between pairs of twin-related Bragg peaks (for twin walls) or around Bragg peaks (for features such as metamict haloes). Study of such features by X-ray diffraction has a number of advantages over the use of electron microscopy, many related to the reduced need for invasive sample preparation. The weak intensity of diffraction from mesostructures requires careful attention to experimental design, either using extremely strong incident radiation, or optimised collection geometry. Measurements of twin wall widths in a range of ferroelastic and co-elastic materials and minerals and their temperature dependence are reviewed, and found to be consistent with theoretical predictions and the results of other experimental methods. Determination of the size of metamict regions in zircon from diffuse scattering agree with the results of microscopy experiments.

The atomic pair distribution function (PDF) approach has been used to study the local structure of liquids, glasses and disordered crystalline materials. In this paper, we demonstrate the use of the PDF method to investigate systems containing a crystalline and an amorphous structural phase. We present two examples: Bulk metallic glass with crystalline reinforcements and Fontainebleau sandstone, where an unexpected glassy phase was discovered. In this paper we also discuss the refinement methods used in detail.

Thermal diffuse scattering (TDS) of X-rays from crystals contains information on phonons. This paper reviews the general theory of TDS and some recent experiments aimed at further developing TDS into a useful and efficient method for studying phonon dispersion relations.

Diffuse scattering in zirconia is reviewed mainly for yttria- and calcia-stabilized material. Common general disorder features are explained by rhombohedral-type and/or tetragonal-type short-range and long-range ordered clusters or “domains”. Differences are comparatively discussed on the basis of available experimental data and theoretical work.

A review of the application of electron microscopy to disordered materials exhibiting sharp, highly structured diffuse intensity distributions is given from a modulation wave approach perspective. Structurally useful diffraction phenomena such as polarization, overall diffuse distribution shape and pseudo-extinction conditions are highlighted. The dangers of multiple scattering are emphasized before two particular such systems, substitutionally disordered solid solutions and inherently flexible framework structures are considered in more detail.

This work is part of an extended study of benzil (C 14 H 10 O 2 ) and some of its derivatives which aims to understand the role of molecular flexibility in crystal packing and polymorphism. Significant steps have been made in modelling the structured thermal diffuse scattering from 3,3′-dimethoxybenzil, C 16 H 14 O 4 . It appears that the structure can be considered as a stack of layers of molecules in which interactions are strongest within the layers. The layers interact weakly along the a direction but more strongly along c , so shearing of the planes relative to each other is energetically likely. The molecule must be treated as flexible for a good model to be found.

We review results obtained in the study of the diffuse scattering in the i-AlPdMn quasicrystal. Most of the diffuse scattering is the result of long wavelength phason modes. The shape and intensity distribution of the diffuse scattering is well reproduced using the generalised elasticity theory and two phason elastic constants. The temperature dependence of the diffuse scattering indicates a softening of the phason elastic constant as the temperature is lowered. Using coherent X-rays and photo-correlation X-ray spectroscopy, it is shown that phason modes are collective diffusive modes, in agreement with the hydrodynamic theory of long wavelength fluctuations in quasicrystals.

Problems encountered in making measurements of diffuse X-ray scattering are discussed. These generally arise from the need to measure very weak scattering in the presence of very strong scattering (Bragg peaks) using multi-detectors of various kinds. The problems are not confined to synchrotron experiments but may even occur using a tube source in the home laboratory. Specific details are given of experiments using 80.725 keV X-rays and a mar345 Image Plate detector on the 1-ID beamline of XOR at the Advanced Photon Source. In these a severe ‘blooming’ artefact which occurred around some strong Bragg peaks was traced to fluorescence from a steel mounting plate in the detector when strong Bragg peaks were incident. Algorithms developed to remove these artefacts from the data are described.

In this review we present three representative examples of molecular disorder: substitution disorder for carbon nanotubes in zeolite, coupling between substitution disorder and displacements through the pinning of charge-density waves in one-dimensional molecular conductors, and the combination of random packing with orientational disorder in the C 60 —C 60 dimers systems.

X-ray diffractograms of tris(bicyclo[2.1.1]hexeno)benzene, crystallized at the interface between a benzene solution and a layer of acetonitrile, show hexagonal symmetry and streaks of diffuse scattering along c *. The heavily faulted layer stacking is analyzed qualitatively and quantitatively in terms of a systematic protocol. This protocol requires partitioning the crystal structure into layers in such a way that pairs of adjacent layers may be stacked in different, but geometrically equivalent ways, which are dictated by the layer group symmetry. This approach is shown to provide a consistent alternative for analysis of a number of related cases provided the layers are defined on the basis of geometrical criteria rather than chemical intuition.

The emergence of intense synchrotron X-ray sources, efficient focusing optics and high-performance X-ray sensitive area detectors allows for measurements of diffuse scattering from cubic micron-scale sample vol umes. Here we present an experiment that illustrates methods for studying the local structure and defect content of tiny sample volumes. In the experiment, an X-ray microbeam illuminating about ∼5 μm 3 of a Ni-based superalloy single crystal, is used to collect Laue patterns and reciprocal space volume maps around fundamental and a superstructure reflections. This measurement illustrates how diffuse reciprocal-space distributions can be collected with good spatial and momentum-transfer resolution from a tiny real-space sample volume. This example demonstrates that emerging diffuse scattering techniques can provide fundamentally new information about crystallographic organization and defect content over many length scales.

A review is given on the recent developments in the study of magnetic short-range order in disordered and ordered binary alloys. We describe the study of the correlation between atomic and magnetic short-range order, in which full use was made of the technique of simultaneous measurement of X-ray and neutron diffuse scattering from single crystals. The study of the effect of atomic order on magnetic fluctuation using the same technique is also described. These two studies cast new light in the understanding of the magnetic properties of the disordered and ordered alloys containing 3d-metals.

Single-crystal X-ray and neutron diffuse scattering techniques have been used to probe a variety of short-range displacive and magnetic orderings in the layered transition-metal perovskites which arise due to the intimate coupling of their structural, electronic and magnetic degrees of freedom. The present work reviews recent analyses that have successfully modeled short-range intralayer and/or interlayer correlations in these materials leading to useful physical insights, and describes the methods employed within a general formulation of the disordered structure function.

A new evolutionary algorithm for Monte Carlo modelling of disordered structures, called Cooperative Evolution (CE), is proposed. The functionality of this method is demonstrated by means of two series of refinements of different complexity. In both cases the CE method was capable of reproducing the known disordered structure to a reasonable degree. In order to test the perform ance of the CE method in comparison with other techniques, the refinements were repeated using Reverse Monte Carlo (RMC) modelling and the Monte Carlo/Differential Evolution (MC/DE) method. The tests have shown that the CE method leads to more reliable results than RMC modelling and that it is faster than the MC/DE technique in particular in case of complex problems.