3D Diffraction Research Articles

Orientational distribution functions and order parameters in "de Vries"-type smectics: A simulation study.

Simple smectic A liquid crystal phases with different types of prescribed orientational distribution functions have been simulated and compared in order to study the possibility to distinguish between the Maier-Saupe type and cone-like orientational distributions using the popular method of Davidson et al. [J. Phys. II 5, 113 (1995)]. This method has been used to extract the orientational distribution functions from simulated diffraction patterns, and the results have been compared with actual distribution functions which have been prescribed during simulations. It has been shown that it is indeed possible to distinguish between these two qualitatively different types of orientational distribution already from the shape of the 2D diffraction pattern. Moreover, typical experimental diffraction patterns for "de Vries"-type smectic liquid crystals appear to be close to the ones which have been simulated using the prescribed Maier-Saupe orientational distribution function.

Direct observation of grain rotations during coarsening of a semisolid Al–Cu alloy

Sintering is a key technology for processing ceramic and metallic powders into solid objects of complex geometry, particularly in the burgeoning field of energy storage materials. The modeling of sintering processes, however, has not kept pace with applications. Conventional models, which assume ideal arrangements of constituent powders while ignoring their underlying crystallinity, achieve at best a qualitative description of the rearrangement, densification, and coarsening of powder compacts during thermal processing. Treating a semisolid Al-Cu alloy as a model system for late-stage sintering-during which densification plays a subordinate role to coarsening-we have used 3D X-ray diffraction microscopy to track the changes in sample microstructure induced by annealing. The results establish the occurrence of significant particle rotations, driven in part by the dependence of boundary energy on crystallographic misorientation. Evidently, a comprehensive model for sintering must incorporate crystallographic parameters into the thermodynamic driving forces governing microstructural evolution.

Possibilities of surface-sensitive X-ray methods for studying the molecular mechanisms of interaction of nanoparticles with model membranes

The processes of structural rearrangement in a model membrane, i.e., an arachic acid monolayer formed on a colloidal solution of cerium dioxide or magnetite, are studied in situ in real time by the methods of X-ray standing waves and 2D diffraction. It is shown that the character of the interaction of nanoparticles with the monolayer is determined by their nature and sizes and depends on the conditions of nanoparticle synthesis. In particular, the structure formation in the monolayer–particle system is greatly affected by the stabilizer (citric acid), which is introduced into the colloidal solution during synthesis.

TPCO single-crystal optical devices equipped with one-dimensional diffraction gratings

ABSTRACTWe have formed one-dimensional (1D) diffraction gratings on a photoresist polymer (SU-8) by interference exposure using a Lloyd mirror. A single crystal of thiophene/phenylene co-oligomers (TPCOs) grown in a vapor phase was placed on the 1D diffraction grating. Excitation of the single crystal by an ultraviolet light of a mercury lamp produced spectrally-narrowed fluorescence. On the basis of the grating periods and emission peak locations, we evaluated effective refractive indices and diffraction orders. The relevant information enables us to design and fabricate the 1D diffraction gratings that cause the spectrally-narrowed emission lines to superimpose inherently occurring high-intensity fluorescence peaks.

Quantifying Interparticle Forces and Heterogeneity in 3D Granular Materials.

Interparticle forces in granular materials are intimately linked to mechanical properties and are known to self-organize into heterogeneous structures, or force chains, under external load. Despite progress in understanding the statistics and spatial distribution of interparticle forces in recent decades, a systematic method for measuring forces in opaque, three-dimensional (3D), frictional, stiff granular media has yet to emerge. In this Letter, we present results from an experiment that combines 3D x-ray diffraction, x-ray tomography, and a numerical force inference technique to quantify interparticle forces and their heterogeneity in an assembly of quartz grains undergoing a one-dimensional compression cycle. Forces exhibit an exponential decay above the mean and partition into strong and weak networks. We find a surprising inverse relationship between macroscopic load and the heterogeneity of interparticle forces, despite the clear emergence of two force chains that span the system.

In-situ structural identification of Zr3Al2 type metastable phase during crystallization of a Zr-based MG

A metastable phase was detected using higher energy synchrotron radiation when Zr-based metallic glass (MG) was annealed under vacuum in Linkam hot stage at 848K. The formation and transformation processes of metastable phase were recorded by synchrotron radiation method. The metastable phase during crystallization was identified as Zr3Al2 structure type according to powder diffraction and TEM analysis. The structure of Zr3Al2 type MCP was experimentally evidenced by 3D diffraction patterns and mathematically described. The identification of Zr3Al2 MCP could be helpful for the understanding of cluster structure of MG.

Microfluidic Generation of Monodisperse and Photoreconfigurable Microspheres for Floral Iridescence–Inspired Structural Colorization

Flowering plants have evolved their structural coloration strategies exquisitely to split various vivid colors into a spatially distributed sequence by using the 2D diffraction elements, confined onto a curved surface. Herein, A new strategy of artificially mimicking floral-inspired grating diffractive motifs onto the monodisperse and smooth microspheres is reported, developed by microfluidics; thus, the accessible design space of structural colorization can be greatly expanded.

Algorithms of Two-Dimensional X-Ray Diffraction

ABSTRACTX-ray diffraction pattern collected with two-dimensional detector contains the scattering intensity distribution as a function of two orthogonal angles. One is the Bragg angle 2θ and the other is the azimuthal angle about the incident x-ray beam, denoted by γ. A 2D diffraction pattern can be integrated to a conventional diffraction pattern and evaluated by most exiting software and algorithms for conventional applications, such as, phase identification, structure refinement and 2θ-profile analysis. However, the materials structure information associated to the intensity distribution along γ direction is lost through the integration. The diffraction vector approach has been approved to be the genuine theory in 2D data analysis. The unit diffraction vector used for 2D analysis is a function of both 2θ and γ. The unit diffraction vector for all the pixels in the 2D pattern can be expressed either in the laboratory coordinates or in the sample coordinates. The vector components can then be used to derive fundamental equations for many applications, including stress, texture, crystal orientation and crystal size evaluation.

Organic light-emitting transistors with a thin metal layer covering a diffraction grating

ABSTRACTWe fabricated organic light-emitting transistors (OLETs) characterized by an Ag layer deposited on a one-dimensional (1D) or two-dimensional (2D) diffraction grating that acts as a combined gate insulator with SiO2. The Ag layer was entirely covered with an organic crystal. Upon photoexcitation that crystal showed narrow linewidth emissions (NLEs) parallel to the substrate plane. The narrowed lines were either redshifted or blueshifted with rotation of the crystal around a normal to its surface with respect to the grating wave vector. Strong emissions (∼104–106 cd m−2) accompanied by current-injected NLEs were observed from the 1D and 2D grating OLETs.

A pnCCD-based, fast direct single electron imaging camera for TEM and STEM

We report on a new camera that is based on a pnCCD sensor for applications in scanning transmission electron microscopy. Emerging new microscopy techniques demand improved detectors with regards to readout rate, sensitivity and radiation hardness, especially in scanning mode. The pnCCD is a 2D imaging sensor that meets these requirements. Its intrinsic radiation hardness permits direct detection of electrons. The pnCCD is read out at a rate of 1,150 frames per second with an image area of 264 x 264 pixel. In binning or windowing modes, the readout rate is increased almost linearly, for example to 4000 frames per second at 4× binning (264 x 66 pixel). Single electrons with energies from 300 keV down to 5 keV can be distinguished due to the high sensitivity of the detector. Three applications in scanning transmission electron microscopy are highlighted to demonstrate that the pnCCD satisfies experimental requirements, especially fast recording of 2D images. In the first application, 65536 2D diffraction patterns were recorded in 70 s. STEM images corresponding to intensities of various diffraction peaks were reconstructed. For the second application, the microscope was operated in a Lorentz-like mode. Magnetic domains were imaged in an area of 256 x 256 sample points in less than 37 seconds for a total of 65536 images each with 264 x 132 pixels. Due to information provided by the two-dimensional images, not only the amplitude but also the direction of the magnetic field could be determined. In the third application, millisecond images of a semiconductor nanostructure were recorded to determine the lattice strain in the sample. A speed-up in measurement time by a factor of 200 could be achieved compared to a previously used camera system.

Two-dimensional electromagnetically induced grating via gain and phase modulation in a two-level system

A scheme for two-dimensional (2D) electromagnetically induced grating via spatial gain and phase modulation is presented in a two-level atomic system. Based on the interactions of two orthogonal standing-wave fields, the atom could diffract the weak probe beam into high-order directions and a 2D diffraction grating is generated. It is shown that the diffraction efficiency of the grating can be efficiently manipulated by controlling the Rabi frequencies of control fields, the detunings of the control and probe fields, and interaction length. Different from 2D cross-grating via electromagnetically induced transparency in a four-level atomic system, the present scheme results from the spatial modulation of gain and phase in a simple two-level system, which could lead to 2D gain-phase grating with larger diffraction intensities in the diffraction directions. The studies we present may have potential applications in developing photon devices for optical-switching, optical imaging and quantum information processing.

Hybrid approach for structural modeling of biological systems from X-ray free electron laser diffraction patterns.

We present a new hybrid approach for structural modeling using X-ray free electron laser (XFEL) diffraction patterns from non-crystalline biological samples. Reconstruction of a 3D structure requires a large number of diffraction patterns; however, in the current XFEL experiments with biological systems, the analysis often relies on a small number of 2D diffraction patterns. In this study, we explore the strategies to identify plausible 3D structural models by combining the 2D analysis of such diffraction patterns with computational modeling (normal mode analysis or molecular dynamics simulations). As the first step toward such hybrid modeling, we established a protocol to assess the agreement between the model structure and the target XFEL diffraction pattern and showed that XFEL data can be used to study the conformational transitions of biological molecules. We tested the proposed algorithms using data of three biomolecular complexes of different sizes (elongation factor 2, CCM virus, and ribosome) and examined the experimental conditions that are required to perform such studies, in particular the XFEL beam intensity requirements. The results indicate that the current beam intensity is close to a strength that enables us to study conformational transitions of macromolecules, such as ribosomes. The proposed algorithm can be combined with molecular mechanics approaches, such as molecular dynamics simulations and normal mode analysis, to generate a large number of candidate structures to perform hybrid structural modeling.

Nonreciprocal microwave devices based on magnetic nanocomposites made of opal matrices

Microwave circulators based on magnetic nanocomposites made of opal matrices are mathematically simulated and experimentally studied. Mathematical models are based on the solution of the 3D diffraction problems using the projection method and the decomposition computational algorithm that employs autonomous units with magnetic nanoinclusions and virtual Floquet channels. The computational algorithm developed using the projection method with effective parameters of the magnetic nanocomposite is used to calculate the S parameters of the scattering matrix of the microwave Y circulator based on the opal-matrix magnetic nanocomposite. The S parameters (real loss, isolation between arms, and reflection coefficient) of the Y circulator are measured for several nanocomposites made of opal matrices with magnetic nanoparticles (Co0.5Zn0.5Fe2O4 and Ni0.5Zn0.5Fe2O4) and compared with the parameters of the circulator based on magnesium–manganese ferrite in a frequency interval of 14–18 GHz. The simulated results are compared with the experimental dependences.

New exact solutions of nonlinear fractional acoustic wave equations in ultrasound

In this paper, new exact solutions of fractional nonlinear acoustic wave equations have been devised. The travelling periodic wave solutions of fractional Burgers–Hopf equation and Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation have obtained by first integral method. Nonlinear ultrasound modelling is found to have an increasing number of applications in both medical and industrial areas where due to high pressure amplitudes the effects of nonlinear propagation are no longer negligible. Taking nonlinear effects into account, the ultrasound beam analysis makes more accurate in these applications. The Burgers–Hopf equation is one of the extensively studied models in mathematical physics. In addition, the KZK parabolic nonlinear wave equation is one of the most widely employed nonlinear models for propagation of 3D diffraction sound beams in dissipative media. In the present analysis, these nonlinear equations have solved by first integral method. As a result, new exact analytical solutions have been obtained first time ever for these fractional order acoustic wave equations. The obtained results are presented graphically to demonstrate the efficiency of this proposed method.

Theoretical study of surface plasmons coupling in transition metallic alloy 2D binary grating

The excitation of a surface plasmon polariton (SPP) wave on a metal–air interface by a 2D diffraction grating is numerically investigated. The grating consists of homogeneous alloys of two metals of a formula AxB1−x, or three metals of a formula AxByCz, where A, B and C could be silver (Ag), copper (Cu), gold (Au) or aluminum (Al).It is observed that all the alloys of two metals present a very small change of surface plasmon resonance (SPR) irrespective of composition x. Moreover, the addition of 25% of Al to two metals alloy is insufficient to change the SPR curves. The influence of the different grating parameters is discussed in details using rigorous coupled-wave analysis (RCWA) method. Furthermore, the SPR is highly dependent on grating periods (dx and dy) and the height of the grating h. The results reveal that dx= dy= 700nm, h=40nm and duty cycle w=0.5 are the optimal parameters for exciting SPP.

Visualization of defects in single components of thin composite elements with 1D diffraction structure

Specific features of the implementation of a method for individual monitoring of the quality of components of thin composite diffraction elements with a 1D periodic structure are considered. Several optical schemes for visualization of defects of single components are proposed and analyzed. A composite diffraction element that represents a set of optical components (thin transparent plate with curved surfaces and 1D periodic microstructure) is used as an example to demonstrate a possibility of separate visualization of the defects of substrate and periodic structure. Interference patterns that characterize the quality of the thin substrate and periodic structure of the composite element are presented. The periodic structure represents an amplitude grating that is recorded in a thin photosensitive layer located between two glass substrates.

Simulation domain size requirements for elastic response of 3D polycrystalline materials

A fast Fourier transform (FFT) based spectral algorithm is used to compute the full field mechanical response of polycrystalline microstructures. The field distributions in a specific region are used to determine the sensitivity of the method to the number of surrounding grains through quantification of the divergence of the field values from the largest simulation domain, as successively smaller surrounding volumes are included in the simulation. The analysis considers a mapped 3D structure where the location of interest is taken to be a particular pair of surface grains that enclose a small fatigue crack, and synthetically created statistically representative microstructures to further investigate the effect of anisotropy, loading condition, loading direction, and texture. The synthetic structures are generated via DREAM3D and the measured material is a cyclically loaded, Ni-based, low solvus high refractory (LSHR) superalloy that was characterized via 3D high energy x-ray diffraction microscopy (HEDM). Point-wise comparison of distributions in the grain pairs shows that, in order to obtain a Pearson correlation coefficient larger than 99%, the domain must extend to at least the third nearest neighbor. For an elastic FFT calculation, the stress–strain distributions are not sensitive to the shape of the domain. The main result is that convergence can be specified in terms of the number of grains surrounding a region of interest.

<i>In Situ</i> Testing and Heterogeneity of UFG Cu at Elevated Temperatures

Experiments were conducted to investigate deformation-induced processes during in-situ tensile test at elevated temperature. Consequently the microstructure after creep loading was examined by 3D Electron Back Scatter Diffraction (EBSD) technique. The billets of coarse-grained copper were processed by equal-channel angular pressing (ECAP) at room temperature using a die that had an internal angle of 90° between the two parts of the channel and an outer arc of curvature of ~ 20°, where these two parts intersect. The pressing speed was 10 mm/min. To obtain an ultrafine-grained (UFG) material, the billets were subsequently pressed by route Bc by 8 ECAP passes to give the mean grain size ~ 0.7 μm. The constant strain-rate test in tension was performed at 473 K using testing GATAN stage Microtest 2000EW with EH 2000 heated grips which is configured for in-situ electron back scatter diffraction (EBSD) observations. Microstructure was examined by FEG-SEM TESCAN MIRA 3 XM equipped by EBSD detector HKL NordlysMax from OXFORD INSTRUMENT. The tensile test was interrupted by fast stress reductions after different deformation step and observation of microstructure changes was performed. Despite of a considerable interest in ECAP processing method, there are not many works documenting microstructure evolution and changes during creep testing and determining creep mechanisms of ultrafine-grained materials processed by ECAP. It was found that creep resistance of UFG pure Al and Cu is considerably improved after one ECAP pass in comparison with coarse grained material, however, further repetitive pressing leads to a noticeable deterioration in creep properties of ECAP material. Recently it was observed the coarsening of the grains in microstructure of ECAP copper during creep at elevated temperature. It was suggested that creep behaviour is controlled by storage and dynamic recovery of dislocations at high-angle boundaries. In the present work was found that ultrafine-grained microstructure is instable and significant grain growth has already occurred during heating to the testing temperature. Static recrystallization during heating led to the formation of high fraction of special boundaries Σ3 and Σ9. The tensile deformation at 473 K led to the additional grain growth and formation of new grains. Microstructure was investigated also by 3D EBSD.

Wood anomalies in the vicinity of 3D Bragg diffraction from hybrid opaline photonic crystals

For hybrid chalcogenide/opal photonic crystals the optical reflection spectra demonstrating the interplay of diffraction resonances such as 3D Bragg diffraction and resonant Wood anomaly have been studied. The coupling coefficient of the Wood and Bragg waves has been estimated on the basis of the coupled-waves approach and the concept of the effective refractive index of the wave-guiding surface layer of the hybrid structure. A phenomenological expression for the coefficient of reflection from a hybrid photonic crystal allowing one to investigate the interference of the Wood anomalies has been proposed.

Towards quantitative, atomic-resolution reconstruction of the electrostatic potential via differential phase contrast using electrons

Differential phase contrast images in scanning transmission electron microscopy can be directly and quantitatively related to the gradient of the projected specimen potential provided that (a) the specimen can be treated as a phase object and (b) full 2D diffraction patterns as a function of probe position can be obtained. Both are challenging to achieve in atomic resolution imaging. The former is fundamentally limited by probe spreading and dynamical electron scattering, and we explore its validity domain in the context of atomic resolution differential phase contrast imaging. The latter, for which proof-of-principle experimental data sets exist, is not yet routine. We explore the extent to which more established segmented detector geometries can instead be used to reconstruct a quantitatively good approximation to the projected specimen potential.