Theoretical estimation for correlations of diffraction patterns from objects differently oriented in space

Coherent diffraction imaging of single biomolecules is expected to open unique opportunities for studies of non-crystalline samples. There are, however, still many technical and physical issues that need to be resolved in a more quantitative manner, especially if one aims for structural information at high resolution. Signal recorded from an object after a single shot is low. As primarily proposed in Spence and Doak (2004) and Huldt et al. (2003) [1] and [2], averaging over the diffraction patterns from many different shots is necessary, in order to achieve a signal-to-noise ratio sufficient for image reconstruction. The images of the randomly oriented molecules have to be sorted out in order to identify those corresponding to the similar spatial orientations of the objects. This procedure is called the classification of diffraction images. Here we approach the classification in the framework of pattern-to-pattern correlations, and analyse theoretically the correlations between diffraction images of differently oriented objects.     

In situ electron backscattered diffraction of individual GaAs nanowires

We suggest and demonstrate that electron backscattered diffraction, a scanning electron microscope-based technique, can be used for non-destructive structural and morphological characterization of statistically significant number of nanowires in situ on their growth substrate. We obtain morphological, crystal phase, and crystal orientation information of individual GaAs nanowires in situ on the growth substrate GaAs(111) B. Our results, verified using transmission electron microscopy and selected area electron diffraction analyses of the same set of wires, indicate that most wires possess a wurtzite structure with a high density of thin structural defects aligned normal to the wire growth axis, while others grow defect-free with a zincblende structure. The demonstrated approach is general, applicable to other material systems, and is expected to provide important insights into the role of substrate structure on nanowire structure on nanowire crystallinity and growth orientation.     

The scanning low-energy electron microscope: First attainment of diffraction contrast in the scanning electron microscope

Using small Pb crystals deposited in situ on a partially contaminated Si (100) crystal, we demonstrate that a commercial scanning electron microscope (SEM) can easily be converted into a scanning low-energy electron microscope (SLEEM). Although the contrast mechanism is much more complicated than that in nonscanning LEEM because not only one diffracted monochromatic beam and its close environment are used for imaging, but several diffracted beams and a wide energy spectrum of electrons of different origin (secondary electrons, inelastically andelastically scattered electrons) are used, SLEEM is a valuable addition to the standard SEM because it provides an additional structure- and orientation-sensitive contrast mechanism in crystalline materials, a low sampling depth, and high intensity at low energies.     

10-kV diffractive imaging using newly developed electron diffraction microscope

A new electron diffraction microscope based on a conventional scanning electron microscope (SEM), for obtaining atomic-level resolution images without causing serious damage to the specimen, has been developed. This microscope in the relatively low-voltage region makes it possible to observe specimens at suitable resolution and record diffraction patterns. Using the microscope we accomplished 10-kV diffractive imaging with the iterative phase retrieval and reconstructed the structure of a multi-wall carbon nanotube with its finest feature corresponding to 0.34-nm carbon wall spacing. These results demonstrate the possibility of seamless connection between observing specimens by SEM and obtaining their images at high resolution by diffractive imaging.     

Towards sub-A atomic resolution electron diffraction imaging of metallic nanoclusters: a simulation study of experimental parameters and reconstruction algorithms

A simulation study is carried out to elucidate the effects of dynamical scattering, electron beam convergence angle and detection noise on atomic resolution diffraction imaging of small particles and to develop effective reconstruction procedures. Au nanoclusters are used as model because of their strong scattering. The results show that the dynamical effects of electron diffraction place a limit on the size of Au nanoclusters that can be reconstructed from the diffraction intensities with sufficient accuracy. For smaller Au nanoclusters, the simulations show that diffraction patterns recorded under the experimental conditions can be reconstructed using a combination of phase retrieval algorithms. The use of a low-resolution image is shown to be effective for reconstructing diffraction patterns without the central beam. A new algorithm for estimating the object support is proposed.     

Visualization and electron diffraction on cryosections of stratum corneum: a utopia?

The skin acts as an effective barrier to protect the body against penetration of substances from the environment and against desiccation. The main barrier function resides in the stratum corneum, and more specifically in the intercellular lipid domains. Several techniques have been used to elucidate the local lipid crystal arrangements in these domains, but they either needed an extensive pretreatment of the skin with the risk of damaging the native structure, or were not suited to obtain local structure information as bulk quantities of stratum corneum were required. In this paper a method of performing local structure analysis (electron diffraction) on cryo-fixed specimens is described. Therefore a cold chain procedure was used to obtain cryosections of stratum corneum. On these sections visualization and electron diffraction at low temperature were carried out.
Using a so-called tape sandwich method, cryosections were prepared in which corneocytes and lipid matrix could easily be distinguished. Moreover, detailed cellular components such as desmosomes and intracellular lipid domains were observed. However, probably due to the limited amount of intercellular lipids in the stratum corneum, electron diffraction on cryosections did not result in diffraction patterns that were undoubtedly originating from the intercellular lipids. In the electron diffraction patterns of a skin lipid model system reflections were present that were indicative of hexagonal and orthorhombic sublattices. The d-spacings of these reflections were similar to the spacings of the high-intensity reflections of the X-ray diffraction pattern of the same mixture. This showed agreement between a bulk and a local technique, X-ray and electron diffraction.     

Analytical transmission electron microscopy and electron diffraction for characterization of multiphase Ni-P-Ti surface layer on Ti-6Al-4V alloy

The microstructure, chemical and phase composition of the hard Ni‐P‐Ti layer formed on the Ti‐6Al‐4V alloy after duplex surface treatment were investigated by light microscopy, X‐ray diffraction, scanning electron microscopy and analytical/high‐resolution transmission electron microscopy. These investigations showed that the improved mechanical and tribological properties of the surface‐treated alloy were related to the presence of a multilayered microstructure containing several phases from the Ni‐Ti‐P‐Al system.     

Construction of an organic crystal structural model based on combined electron and powder X-ray diffraction data and the charge flipping algorithm

The structure of an organic dye 1,5-diaminoanthraquinone (DAAQ) nanowire was studied by both electron diffraction and X-ray powder diffraction. The unit cell of the crystal was determined from a series of tilted selected area electron diffraction patterns (monoclinic: a=3.78 Å, b=9.73 Å, c=15.01 Å and β=82.4°). By using precession electron diffraction, the following extinction conditions were determined, 0k0: k=2n and 00l: l=2n, which give the space group as P2₁/C (no. 14). The powder charge flipping algorithm was applied to resolve the phase problem and the structural model of the DAAQ crystal was built.     

Distinguishing crystallographic misorientations of lanthanum zirconate epilayers on nickel substrates by electron backscatter diffraction

Electron backscatter diffraction (EBSD) was used for distinguishing crystallographic orientations and local lattice misfits of a La₂Zr₂O₇ (LZO) buffer layer epitaxially grown on a cube textured Ni-5.%W (Ni-W) substrate for a YBCO superconductor film. Orientation data were obtained from the LZO epilayer using low energy primary electrons (5 keV) and from the Ni-W substrate by increasing the voltage to 15 keV. In-plane and out-of-plane orientations of the LZO epilayer were revealed with respect to its Ni-W substrate. A strong {1 0 0} 〈0 1 1〉 rotated-cube texture in the LZO epilayer was formed on the {1 0 0} 〈0 0 1〉 cube-textured Ni-W substrates. LZO and Ni in-plane crystallographic axes are related by an expected 45° rotation. The step-misorientations and the local misfit strains between the LZO epilayer and the substrate were also analyzed.     

The weighted Burgers vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials

The Weighted Burgers Vector (WBV) is defined here as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) × (Burgers vector)]. Here we show that it can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has three advantages over other measures of local lattice distortion: it is a vector and hence carries more information than a scalar quantity, it has an explicit mathematical link to the individual Burgers vectors of dislocations and, since it is derived via tensor calculus, it is not dependent on the map coordinate system. If a sub-grain wall is included in the WBV calculation, the magnitude of the WBV becomes dependent on the step size but its direction still carries information on the Burgers vectors in the wall. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations.