Two-dimensional Diffraction Patterns Research Articles

CRAFS: a model to analyze two-dimensional X-ray diffraction patterns of plant cellulose

Cellulose from higher plants is a vast renewable resource organized as crystals. Analysis of these crystals by X-ray diffraction poses very specific challenges, including ubiquitous crystallite texture and substantial overlapping of diffraction peaks. In this article, a tailor-made model named Cellulose Rietveld Analysis for Fine Structure (CRAFS) is developed to analyze two-dimensional X-ray diffraction patterns from raw and processed plant cellulose. One-dimensional powder diffractograms are analyzable as a particular case. The CRAFS model considers cellulose Iβ crystal structure, fibrillar crystal shape, paracrystalline peak broadening, pseudo-Voigt peak profiles, harmonic crystallite orientation distribution function and diffraction in fiber geometry. Formulated on the basis of the Rietveld method, CRAFS is presently written in the MATLAB computing language. A set of meaningful coefficients are output from each analyzed pattern. To exemplify model applicability, representative samples are analyzed, bringing some general insights and evidencing the model's potential for systematic parameterization of the fine structure of raw and processed plant celluloses.

Phase diffraction gratings based on a Si(400) crystal

The X-ray optical properties of diffraction gratings fabricated on the basis of a Si(400) crystal with a period of D = 1 μm are studied by triple-crystal X-ray diffractometry. The diffraction gratings are manufactured both by silicon profiling during the process of plasma chemical etching and by forming a phase-shift grating on the surface of a Si crystal. The principal difference in the diffraction properties of these gratings is demonstrated. The presence of an Au phase-shift grating is shown to lead to the formation of a two-dimensional diffraction pattern, whereas Si profiling leads to the formation of only a one-dimensional diffraction pattern.

Concentration and Strain Fields inside a Ag/Au Core–Shell Nanowire Studied by Coherent X-ray Diffraction

Three-dimensional coherent diffraction patterns of an isolated, single-crystalline Ag/Au core-shell nanowire were recorded at different X-ray beam energies close to the Au LIII absorption edge. Two-dimensional slices of the three-dimensional diffraction pattern, with the diffraction vector oriented perpendicular to the wire axis, were investigated in detail. In reciprocal space, facet streaks with thickness fringes were clearly observed in the two-dimensional diffraction patterns, from which the shape and size of the corresponding cross sections of the nanowire could be revealed. Comparison with simulated diffraction patterns exhibited the coherency strain field in the nanowire. During in situ annealing at temperatures which would lead to significant intermixing by volume diffusion in bulk material, according to literature data, a core-shell morphology was preserved; that is, intermixing in the nanowire was pronouncedly decelerated compared to bulk diffusion.

<i>In Situ</i> X-Ray Diffraction Study of Thermal Stability of Cu and Cu-Zr Samples Processed by ECAP

X-ray diffraction (XRD) studies of ECAP (equal-channel angular pressing) materials were performed after annealing and by in-situ measurements in XRD high-temperature chamber for samples prepared by different number of passes and number of revolutions, respectively. Main attention was given to Cu and Cu-Zr samples. Significant dependence on number of passes was found for ECAP samples. In-situ measurements were focused not only on temperature dependence but also on time evolution of the diffraction line profiles. Evaluation in terms of dislocation densities, correlation and crystallite size and its distribution was performed by our own software MSTRUCT developed for total powder diffraction pattern fitting. Abnormal growth of some grains with annealing is well-known for copper and leads to the creation of bimodal microstructure. Therefore a special care must be given to the evaluation and a model of two Cu components (larger and smaller crystallites) was fitted to the data if an indication of some crystallite growth appears either in the XRD line profile shape or in two-dimensional diffraction patterns.

Transition from fast to slow atom diffraction

For energetic atomic beams grazingly incident at a surface along low-index directions, the fast motion of the projectile in the surface plane and the slow motion in the direction perpendicular to the surface appear nearly decoupled. Fast-atom diffraction (FAD) experiments reveal two-dimensional (2D) diffraction patterns associated with exchange of the reciprocal vector perpendicular to the low-index direction of fast motion. These results are usually interpreted within the axial-channeling approximation, where the effective 2D potential experienced by the projectile is set as an average of the 3D surface potential along the atomic strings forming the channel. In this work, using the example of grazing scattering of He atoms at a LiF(001) surface, we address theoretically the range of validity of the axial-channeling approximation. Full quantum wave-packet-propagation calculations are used to study the transition from the 2D (fast atom) to the 3D diffraction pattern characteristic for low-energy atomic and molecular projectiles scattered from surfaces. Along with exact calculations, a semianalytical perturbative treatment based on the Lippmann-Schwinger equation allows an explanation of why the diffraction processes involving the exchange of reciprocal-lattice vectors along the fast-motion direction are exponentially small in typical FAD conditions.

Classifying and assembling two-dimensional X-ray laser diffraction patterns of a single particle to reconstruct the three-dimensional diffraction intensity function: resolution limit due to the quantum noise.

A new two-step algorithm is developed for reconstructing the three-dimensional diffraction intensity of a globular biological macromolecule from many experimentally measured quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The first step is classification of the two-dimensional patterns into groups according to the similarity of direction of the incident X-rays with respect to the molecule and an averaging within each group to reduce the noise. The second step is detection of common intersecting circles between the signal-enhanced two-dimensional patterns to identify their mutual location in the three-dimensional wavenumber space. The newly developed algorithm enables one to detect a signal for classification in noisy experimental photon-count data with as low as ~0.1 photons per effective pixel. The wavenumber of such a limiting pixel determines the attainable structural resolution. From this fact, the resolution limit due to the quantum noise attainable by this new method of analysis as well as two important experimental parameters, the number of two-dimensional patterns to be measured (the load for the detector) and the number of pairs of two-dimensional patterns to be analysed (the load for the computer), are derived as a function of the incident X-ray intensity and quantities characterizing the target molecule.

The biaxial lamello-columnar liquid crystalline structure of a tetrathiafulvalene sanidic molecule

A macroscopically oriented lamello-columnar mesophase was obtained from a newly designed and synthesized symmetric tetrathiafulvalene-based molecule (symTTF11) containing four flexible alkyl chains chemically attached to the periphery of TTF mesogens (L. Wang, et al., J. Mater. Chem., 2011, 21, 60), and its phase behaviors and physical properties were investigated by the combined experimental techniques. Based on the experimental results and structure analyses, it was revealed that there are two ordered columnar phases below the isotropic phase: a columnar crystalline phase (ColK) and a columnar smectic liquid crystal phase (ColL). From two-dimensional wide angle X-ray diffraction patterns of the macroscopically oriented samples, phase structures of ColK and ColL were identified and their biaxial molecular packing structures were also proposed. Since the assembled symTTF11 columns were well organized in the ordered layer structures over a macroscopic domain, symTTF11 exhibited a good charge carrier mobility in the ColL phase.

Nano-structuring of solid surface by extreme ultraviolet Ar8+ laser

AbstractThis work demonstrates the patterning of polymethylmethacrylate (PMMA) by ablation with Ar8+ ion laser (λ = 46.9 nm) pumped by pulse, high-current, capillary-discharge. For focusing a long-focal spherical mirror (R = 2100 mm) covered by 14 double-layer Sc-Si coating was used. The ablated focal spots demonstrate not only that the energy of our laser is sufficient for such experiments, but also that the design of focusing optics must be more sophisticated: severe aberrations were revealed — an irregular spot shape and strong astigmatism with astigmatic difference as large as 16 mm. In some cases, on the bottom of ablated spots a laser-induced periodic surface structure appeared. Finally, an illumination of the sample through quadratic hole 7.5 × 7.5 µm, standing in contact with PMMA substrate ablated from the surface a strongly developed two-dimensional diffraction pattern (period in the center about 125 nm).

Formation of quasi-regular diffraction patterns in the nonlinear photorefractive Fabry-Perot interferometer

Formation of optical inhomogeneities under self-action of light fields in photorefractive Fabry-Perot interferometers has been experimentally investigated using the samples of Y — and Z-cut lithium niobate. For the interferometer with the Z-cut sample, it is demonstrated that spiral-shaped inhomogeneities and two-dimensional quasi-regular diffraction patterns are formed under the effect of the Gaussian beam about 1mm in diameter and the light field with a homogeneous intensity distribution.

Compositional and Quantitative Microtextural Characterization of Historic Paintings by Micro-X-ray Diffraction and Raman Microscopy

This work shows the benefits of characterizing historic paintings via compositional and microtextural data from micro-X-ray diffraction (μ-XRD) combined with molecular information acquired with Raman microscopy (RM) along depth profiles in paint stratigraphies. The novel approach was applied to identify inorganic and organic components from paintings placed at the 14th century Islamic University-Madrasah Yusufiyya-in Granada (Spain), the only Islamic University still standing from the time of Al-Andalus (Islamic Spain). The use of μ-XRD to obtain quantitative microtextural information of crystalline phases provided by two-dimensional diffraction patterns to recognize pigments nature and manufacture, and decay processes in complex paint cross sections, has not been reported yet. A simple Nasrid (14th century) palette made of gypsum, vermilion, and azurite mixed with glue was identified in polychromed stuccos. Here also a Christian intervention was found via the use of smalt, barite, hematite, Brunswick green and gold; oil was the binding media employed. On mural paintings and wood ceilings, more complex palettes dated to the 19th century were found, made of gypsum, anhydrite, barite, dolomite, calcite, lead white, hematite, minium, synthetic ultramarine blue, and black carbon. The identified binders were glue, egg yolk, and oil.

Smectic‐Layer Alignments of Surface‐Modified Gold Nanoparticles in the Nanocomposite Induced by a Hydrogen‐Bonded Bent‐Core Liquid Crystalline Host under Electric Fields

There has been great interest recently in the fabrication of highly ordered metal nanoparticle (NP) assemblies. Large scale periodical arrangements of NPs are fascinating systems for the development of nanostructural materials exhibiting new electronic, magnetic, optical, and photonic properties. Many examples of the application of templates have appeared for the generation of ordered assemblies of NPs, by using, for example, surfacemodified polymers, self-assembled monolayers, lipid films, and DNA. In addition, the self-organization behavior of gold NPs surface-modified with rod-like, bent-core, and discotic liquid crystal (LC) surfactants has been reported. Moreover, several strategies have been proposed to template arrays of NPs by using block copolymer systems, in which the spatial arrangements are directed through self-assembly of the block copolymers. LC materials possessing a variety of mesomorphic structures can be aligned in a straightforward manner through the application of electric fields, magnetic fields, and polymer networks. The self-organization of LC molecules is determined by the characteristic arrangements of the mesophasic types, including the nematic, cholesteric, smectic, and columnar phases. Herein, we describe the synthesis of the novel hydrogenbonded bent-core LC host VPy-SiA (bearing a flexible carbosilane chain) and the gold nanocomposite (VPy-SiA/ AuNPs-S) by adding 5 wt% the surface-modified gold NPs (AuNPs-S) to the self-assembled LC host (VPy-SiA; Scheme 1). We developed a novel in situ technique for alignment of the nanocomposite VIPy-SiA/AuNPs-S under (DC/AC) electric fields, and examined the orientation behavior of the smectic layer structures using two-dimensional X-ray diffraction patterns and frozen transmission electron microscopy (FTEM). To the best of our knowledge, no previous reports have described the ordered layer arrangements of NPs in a nanocomposite—induced by compatibility of the NPs in the phase of the LC hosts—that could then be further aligned under electric fields. [a] W.-H. Chen, Y.-T. Chang, Prof. H.-C. Lin Department of Materials Science and Engineering National Chiao Tung University, Hsinchu 300 (Taiwan) Fax: (+8863)5724727 E-mail : linhc@cc.nctu.edu.tw [b] J.-J. Lee, W.-T. Chuang National Synchrotron Radiation Research Center Hsinchu, 30076 (Taiwan) Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201102607. Scheme 1. Chemical structures of the hydrogen-bonded bent-core LC host VPy-SiA (containing the hydrogen bond acceptor VPy and the hydrogen bond donor SiA) and the surface-modified gold NPs AuNPs-S presenting the covalently bonded bent-core surfactant S.

DIIS: A cross-platform program for the reduction of X-ray diffraction data from a cylindrical area detector

A new program capable of rapidly and accurately reducing a two-dimensional X-ray diffraction pattern obtained from a Debye–Scherrer or Gandolfi camera to a quantitative digital diffractogram is described. By implementing geometric optimization routines based on the symmetry and sharpness of diffraction lines, the optimal configuration of the camera, X-ray path, and sample can be determined, thus providing the best possible set of integration parameters. Results for NIST standard reference materials 640c (Si) and 676 (Al 2O 3) are included to illustrate program functionality.

X rays from a free-electron laser resolve the structures of complex biomolecules

A new imaging technique merges thousands of two-dimensional diffraction patterns from a stream of single particles to construct a high-resolution 3D map of electron density.

The software packageANAELUfor X-ray diffraction analysis using two-dimensional patterns

A new software package for interpreting two-dimensional diffraction diagrams is presented. The application capabilities include representation of single- and polycrystal structures with an inverse pole figure treatment of texture phenomena, measurement and analysis of diffraction signals, and different approaches to the modelling of two-dimensional diffraction patterns obtained from both single-crystal and polycrystalline samples. Particular consideration is given to the effect of axially symmetric textures on two-dimensional diffraction patterns. An example showing the capabilities of the software is presented.

Data preparation and evaluation techniques for x-ray diffraction microscopy

The post-experiment processing of X-ray Diffraction Microscopy data is often time-consuming and difficult. This is mostly due to the fact that even if a preliminary result has been reconstructed, there is no definitive answer as to whether or not a better result with more consistently retrieved phases can still be obtained. We show here that the first step in data analysis, the assembly of two-dimensional diffraction patterns from a large set of raw diffraction data, is crucial to obtaining reconstructions of highest possible consistency. We have developed software that automates this process and results in consistently accurate diffraction patterns. We have furthermore derived some criteria of validity for a tool commonly used to assess the consistency of reconstructions, the phase retrieval transfer function, and suggest a modified version that has improved utility for judging reconstruction quality.

X-Ray Diffraction Study of Micro Amounts of Polycrystalline Samples

With the use of reference polycrystalline 6h-Al2O3 (NIST SRM- 1976) and MoO3 samples we consider the most significant geometric and physical factors affecting the accuracy of X-ray diffraction data obtained on a diffractometer equipped with a flat two-dimensional detector (Debye-Scherrer scheme). A general strategy to measure polycrystalline samples in the amount of 20–30 fug is proposed. By the example of SRM-1976 it is shown that with the proper processing of two-dimensional diffraction patterns and the introduction of certain corrections the angles 2θ can be measured with the accuracy not less than ±0.01°. Even with a strong tendency of particles towards preferred orientation the relative intensities of diffraction reflections are shown to be obtained with the accuracy not less than ±10%.

Stress relaxation experiments of olivine under conditions of subducted slab in Earth's deep upper mantle

Stress relaxation experiments of olivine were conducted under high-pressure and high-temperature conditions up to 10GPa and 1273K using a Kawai-type multi-anvil apparatus. A pre-sintered San Carlos olivine sample rod was inserted between two dense Al2O3 pistons to yield high stress at high-pressure within an octahedral pressure medium. Stress was determined from the two-dimensional diffraction pattern taken using monochromatic X-rays and an imaging-plate, and sample length was determined from an X-ray radiograph. In these experiments, pressure was first increased at room temperature, and then the temperature was increased and kept at 673, 873, 1073, and 1273K. Four relaxation cycles, in total, were carried out in two experimental runs. The magnitude of deviatoric stress was calculated from five diffraction peaks with the following hkls: 021, 101, 130, 131, and 112. The calculated deviatoric stress was significantly different depending on which diffraction peak was used (up to a factor of ∼2) due to plastic deformation within the polycrystalline sample. The deviatoric stress decreased with increasing temperature in all of relaxation cycles. At given temperatures, the final-state value of deviatoric stress increased with increasing pressure. The upper bound for the plastic strain rate in the final-state was determined to be 10−7s−1 based on a comparison between the total sample length determined from the radiograph and the d-spacings along the piston direction determined from X-ray diffraction. Present results suggest a positive activation volume for the low-temperature rheology of olivine.

One-shot structure determination

By sampling a two-dimensional diffraction pattern on a spherical detector, three-dimensional structure determination of single molecules should be possible from a single measurement.

In Situ Observation of Dynamic Recrystallization in the Bulk of Zirconium Alloy

Dynamic recrystallization and related effects have been followed in situ and in real time while a metal undergoes rapid thermo-mechanical processing. Statistics and orientation correlations of embedded/bulk material grains were deduced from two-dimensional X-ray diffraction patterns and give deep insight into the formation of the microstructure. Applications are relevant in materials design, simulation, and in geological systems.

Refinement of the 200 structure factor for GaAs using parallel and convergent beam electron nanodiffraction data

We present a new method to measure structure factors from electron spot diffraction patterns recorded under almost parallel illumination in transmission electron microscopes. Bloch wave refinement routines have been developed to refine the crystal thickness, its orientation and structure factors by comparison of experimentally recorded and calculated intensities. Our method requires a modicum of computational effort, making it suitable for contemporary personal computers. Frozen lattice and Bloch wave simulations of GaAs diffraction patterns are used to derive optimised experimental conditions. Systematic errors are estimated from the application of the method to simulated diffraction patterns and rules for the recognition of physically reasonable initial refinement conditions are derived. The method is applied to the measurement of the 200 structure factor for GaAs. We found that the influence of inelastically scattered electrons is negligible. Additionally, we measured the 200 structure factor from zero loss filtered two-dimensional convergent beam electron diffraction patterns. The precision of both methods is found to be comparable and the results agree well with each other. A deviation of more than 20% from isolated atom scattering data is observed, whereas close agreement is found with structure factors obtained from density functional theory [A. Rosenauer, M. Schowalter, F. Glas, D. Lamoen, Phys. Rev. B 72 (2005), 085326-1], which account for the redistribution of electrons due to chemical bonding via modified atomic scattering amplitudes.