Two-dimensional Diffraction Patterns Research Articles

Local structural modelling and local pair distribution function analysis for Zr–Pt metallic glass

In disordered glass structures, the structural modelling and analyses based on local experimental data are not yet established. Here we investigate the icosahedral short-range order (SRO) in a Zr–Pt metallic glass using local structural modelling, which is a reverse Monte Carlo simulation dedicated to two-dimensional angstrom-beam electron diffraction (ABED) patterns, and local pair distribution function (PDF) analysis. The local structural modelling invariably leads to the icosahedral SRO atomic configurations that are similarly distorted by starting from some different initial configurations. Furthermore, the SRO configurations with 11–13 coordination numbers reproduce almost identical ABED patterns, indicating that these SRO structures are similar to each other. Further local PDF analysis explicitly indicates the presence of the wide distribution of atomic bond distances, which is comparable to the global PDF profile, even at the SRO level. The SRO models based on the conventional MD simulation can be strengthened by comparison with those obtained by the present local structural modelling and local PDF analysis based on the ABED data.

Voltage-controlled two-dimensional Fresnel diffraction pattern in quantum dot molecules

This study explores the influence of inter-dot tunneling effects within a quantum dot molecule on the Fresnel diffraction phenomenon. Our findings indicate that the Fresnel diffraction of the output probe Gaussian field can be manipulated by adjusting the inter-dot tunneling parameter’s strength and the characteristics of the coupling field. The inter-dot tunneling effect establishes a closed-loop system, setting conditions for the interference of the applied fields. We specifically examine a Laguerre–Gaussian (LG) coupling field, investigating how its properties-such as strength, value, and sign of the orbital angular momentum (OAM)-impact the Fresnel diffraction of the output probe field. Increasing the inter-dot tunneling parameter and the coupling LG field’s strength allows for control over the spatial distribution of the Fresnel diffraction pattern. Notably, the inter-dot tunneling parameter can disturb the symmetry of the diffraction patterns. Additionally, considering a negative OAM for the coupling LG field transforms the diffraction pattern into its inverse shape. This suggests that, in the presence of the inter-dot tunneling effect, the Fresnel diffraction pattern is contingent on the direction of rotation of the helical phase front of the coupling LG field. Our results offer insights into quantum control of Fresnel diffraction patterns and the identification of OAM in LG beams, presenting potential applications in quantum technologies.

Efficient two-dimensional Fraunhofer diffraction pattern via electron spin coherence

In this letter, we have discussed the two-dimensional diffraction pattern via electron spin coherence in a GaAs quantum dot. Impulsive stimulated Raman excitation utilizing coherent optical fields is employed for the purpose of regulating the electron spin coherence within a charged ensemble of GaAs quantum dots, by means of an intermediate charged exciton (trion) state. We show that for the coupling two-dimensional standing wave (SW) field in the x and y directions, the two-dimensional Fraunhofer pattern can be formed for a weak probe light. By using the experimental parameters and controlling the Rabi frequency of the SW field and relative phase between applied lights, the symmetry and asymmetry diffraction pattern are obtained for the weak probe light due to the four-wave mixing mechanism. Our proposed model may have potential applications in high-capacity optical communications and quantum information technologies.

Enhancing Mechanical Properties of Poly(p-phenylene sulfide) by Biaxial Deformation Using Cross-Rolling and Subsequent Annealing

The effect of thermal treatment on the mechanical performance of biaxially oriented poly(p-phenylene sulfide) by cold roll milling was studied. It was found that the ductility of the cross-rolled material could be further enhanced by annealing at temperatures above Tg and the yield strength could be enhanced by annealing at temperatures below Tg with a partial loss in ductility. Two-dimensional wide-angle X-ray diffraction patterns suggested a reduced crystallinity in the rolled material and showed that the crystal structure of the unrolled material could be partially recovered by annealing above Tg; however, scattering patterns adjacent to the crystalline reflections persisted with heat treatment. Modulated differential scanning calorimetry (MDSC) and broadband dielectric spectroscopy indicated that cross-rolling altered the kinetics of the cold-crystallization process. MDSC and dynamic mechanical analysis measured a reduction in Tg suggesting enhanced molecular mobility as an outcome of cross-rolling. After annealing at temperatures well beyond Tg, a large reduction in elongation to failure was observed, and the material could not cold draw. These results suggest that a two-stage process involving plastic deformation by roll milling followed by annealing treatment may be used to commercially produce high toughness and yield strength sheet products from commercially available resins.

Viscoelasticity-induced structure anisotropy in amorphous materials

Viscoelasticity-induced structural change in Zr55Cu30Ni5Al10 metallic glass (Zr-MG) and amorphous selenium (a-Se) is investigated using synchrotron X-ray diffraction. By analyzing the two-dimensional diffraction pattern, two types of structural anisotropy with the feature of the residual elastic strain or heterogeneous intensity of diffraction rings are revealed. The origin of the structural anisotropy is attributed to the topological rearrangement in the Zr-MG and conformation rearrangement in the a-Se. Our findings bring a structural identity to the phenomenological structureless deformation defect widely used in different amorphous materials.

Structural evolution and related physical properties of machine direction oriented poly(butylene succinate-co-adipate) films

This study sheds light on the microstructural change of uniaxially oriented poly(butylene succinate-co-adipate) (PBSA) copolymer, and the consequent gas permeabilities, as well as tensile and optical properties. Uniaxial stretching at 62 °C takes place by means of a machine direction orientation (MDO) with varied draw ratios and annealing near the melting temperature. The PBSA precursor sheet favorably melt-crystallizes in the form of α-PBS crystals with isotropic in-plane orientation. MDO-PBSA films with and without annealing exhibit preferential orientation of the α-PBS crystal parallel to the stretching direction (MD), with an increased degree of crystallinity according to the increased draw ratio and applied annealing. This was evident from two-dimensional wide-angle X-ray diffraction patterns and X-ray diffraction profiles. Additionally, MDO stretching above the crystallization temperature simultaneously induces rigid amorphous fraction, in particular, by a high draw ratio (5 × ) and chain relaxation during annealing near the melting temperature. From the determined Herman's orientation function, the c-axis of the α-PBS crystal is parallel to the MD, thereby resulting in decreased diffusion path tortuosity. Consequently, oxygen and water vapor permeation are promoted. Furthermore, Young's modulus and tensile strength of MDO-PBSA films drastically increase with high ductility, and are approximately two and four times higher than those of non-oriented PBSA, respectively. MDO-PBSA films exhibit high clarities above 94% while yielding low haze values.

Dynamic Surface Wrinkles for In Situ Light-Driven Dynamic Gratings.

Dynamic diffraction gratings (DDGs) are considered as one of the most promising technologies for application in smart optical devices because of their in situ dynamic regulation of light propagation on demand; however, it is still a challenge to fabricate dynamic periodic micro/nanostructures due to limited materials and processes. Here, a facile and feasible strategy to construct a near-infrared (NIR) radiation-driven DDG is developed based on a double-sided surface pattern, which is fabricated by dynamic wrinkles and/or soft-imprinted static wrinkles. Poly(dimethylsiloxane) (PDMS) containing carbon nanotubes (CNTs) serves as the substrate, and wrinkles are formed on both sides. The resulting double-sided wrinkle pattern can be used as a DDG to generate various adjustable two-dimensional (2D) diffraction patterns driven by NIR light. Furthermore, with various combinations of wrinkles, we demonstrated a single-sided responsive DDG and a double-sided responsive DDG to realize the evolution of diffraction patterns from 2D to one-dimensional (1D) and 2D to zero-dimensional (0D), respectively. The results provide an alternative for DDGs that will have wide applications in smart display, sensing, and imaging systems.

C-Perpendicular Orientation of Poly(ʟ-lactide) Films.

Poly(ʟ-lactide) (PLLA) films, even of high thickness, exhibiting co-crystalline and crystalline α phases with their chain axes preferentially perpendicular to the film plane (c⊥ orientation) have been obtained. This c⊥ orientation, unprecedented for PLLA films, can be achieved by the crystallization of amorphous films as induced by low-temperature sorption of molecules being suitable as guests of PLLA co-crystalline forms, such as N,N-dimethylformamide, cyclopentanone or 1,3-dioxolane. This kind of orientation is shown and quantified by two-dimensional wide-angle X-ray diffraction (2D-WAXD) patterns, as taken with the X-ray beam parallel to the film plane (EDGE patterns), which present all the hk0 arcs centered on the meridian. PLLA α-form films, as obtained by low-temperature guest-induced crystallization, also exhibit high transparency, being not far from those of the starting amorphous films.

Functional Bionanocomposite Fibers of Chitosan Filled with Cellulose Nanofibers Obtained by Gel Spinning.

Extremely high mechanical performance spun bionanocomposite fibers of chitosan (CHI), and cellulose nanofibers (CNFs) were successfully achieved by gel spinning of CHI aqueous viscous formulations filled with CNFs. The microstructural characterization of the fibers by X-ray diffraction revealed the crystallization of the CHI polymer chains into anhydrous chitosan allomorph. The spinning process combining acidic–basic–neutralization–stretching–drying steps allowed obtaining CHI/CNF composite fibers of high crystallinity, with enhanced effect at incorporating the CNFs. Chitosan crystallization seems to be promoted by the presence of cellulose nanofibers, serving as nucleation sites for the growing of CHI crystals. Moreover, the preferential orientation of both CNFs and CHI crystals along the spun fiber direction was revealed in the two-dimensional X-ray diffraction patterns. By increasing the CNF amount up to the optimum concentration of 0.4 wt % in the viscous CHI/CNF collodion, Young’s modulus of the spun fibers significantly increased up to 8 GPa. Similarly, the stress at break and the yield stress drastically increased from 115 to 163 MPa, and from 67 to 119 MPa, respectively, by adding only 0.4 wt % of CNFs into a collodion solution containing 4 wt % of chitosan. The toughness of the CHI-based fibers thereby increased from 5 to 9 MJ.m−3. For higher CNFs contents like 0.5 wt %, the high mechanical performance of the CHI/CNF composite fibers was still observed, but with a slight worsening of the mechanical parameters, which may be related to a minor disruption of the CHI matrix hydrogel network constituting the collodion and gel fiber, as precursor state for the dry fiber formation. Finally, the rheological behavior observed for the different CHI/CNF viscous collodions and the obtained structural, thermal and mechanical properties results revealed an optimum matrix/filler compatibility and interface when adding 0.4 wt % of nanofibrillated cellulose (CNF) into 4 wt % CHI formulations, yielding functional bionanocomposite fibers of outstanding mechanical properties.

DATAD: a Python-based X-ray diffraction simulation code for arbitrary texture and arbitrary deformation

DATAD, a Python-based X-ray diffraction simulation code, has been developed for simulating one- and two-dimensional diffraction patterns of a polycrystalline specimen with an arbitrary texture under an arbitrary deformation state and an arbitrary detection geometry. Pixelated planar and cylindrical detectors can be used. The basic principles and key components of the code are presented along with the usage of DATAD. As validation and application cases, X-ray diffraction patterns of single-crystal and polycrystalline specimens with or without texture, or applied strain, on a planar or cylindrical detector are simulated.

Structural evolution in propylene-based elastomer with γ form during stress relaxation

The stress relaxation and the structural evolution of a random propylene-ethylene copolymer of about 12 mol% of ethylene co-units with pure γ form (iPPcoE12-γ), which was pre-stretched to various strains at 30 °C, were investigated by means of in situ wide angle X-ray diffraction techniques. The two-dimensional X-ray diffraction patterns were decomposed into oriented and unoriented parts. It turned out that the unoriented fraction of the iPPcoE12-γ sample became oriented in the process of the relaxation. Due to the unique “cross-β” arrangement in the γ form, the fraction of elastic stress of iPPcoE12-γ was higher than that of iPPcoE12-α with pure α form at a small pre-stretched strain (εH = 0.27) and the increased fraction of oriented parts was much less than that of iPPcoE12-α at medium strains (εH = 0.71 and 1.27). A comparative analysis of the relaxation behavior of iPPcoE12-γ and iPPcoE12-α revealed that the elasticity and stability of iPPcoE12-γ were more attractive at smaller strains (smaller than critical strain C—the strain of the starting of the fragmentation of crystalline blocks), while at larger strains (larger than 1.27) iPPcoE12-α had its advantages in elasticity. In addition, it was found that the γ to α transition occurred during the relaxation, and the unoriented crystallites with γ form were more difficult to transform than the oriented one.

Stabilizing rock and roll

X-Ray Imaging Coherent diffraction imaging with x-rays is a powerful characterization technique for nanoparticles. Piecing together the two-dimensional Bragg diffraction patterns through slices of the sample provides a three-dimensional picture of the structure and strain. However, for nanoparticles, the x-ray beam can induce mechanical instabilities in the sample; the rotation, rocking, and rolling that occur tend to limit the resolution of the information obtained. Bjorling et al. adapted a diffractive volume assembly algorithm that mitigates for the uncontrolled mechanical instabilities and demonstrate that it can be used to reconstruct sharper images of shape-controlled 60-nanometer-sized gold nanoparticles. Phys. Rev. Lett. 125 , 246101 (2020).

A Finite Energy Bandwidth-Based Diffraction Simulation Framework for Thermal Processing Applications

We present a novel finite energy bandwidth-based diffraction simulation framework to aid the analysis of x-ray diffraction patterns gathered during in situ advanced manufacturing processes. The framework generates two-dimensional diffraction patterns that simulate the effects of x-ray energy distributions typical of monochromating optics, and uses microstructure and temperature fields from thermal processing simulations as input. As a demonstration of the capabilities of the framework, we model diffraction associated with selective laser melting of the nickel-based superalloy Inconel 625, employing a finite element thermal model for the input. The simulated diffraction patterns correspond to material volumes exhibiting large temperature gradients consistent with complex thermal processing environments, and we illustrate their utility for interpreting in situ data.

X-ray diffractive imaging of controlled gas-phase molecules: Toward imaging of dynamics in the molecular frame.

We report experimental results on the diffractive imaging of three-dimensionally aligned 2,5-diiodothiophene molecules. The molecules were aligned by chirped near-infrared laser pulses, and their structure was probed at a photon energy of 9.5 keV (λ ≈ 130 pm) provided by the Linac Coherent Light Source. Diffracted photons were recorded on the Cornell-SLAC pixel array detector, and a two-dimensional diffraction pattern of the equilibrium structure of 2,5-diiodothiophene was recorded. The retrieved distance between the two iodine atoms agrees with the quantum-chemically calculated molecular structure to be within 5%. The experimental approach allows for the imaging of intrinsic molecular dynamics in the molecular frame, albeit this requires more experimental data, which should be readily available at upcoming high-repetition-rate facilities.

Texture, 2D diffraction and piezoelectricity

A computer-aided methodology for the approximate prediction of axially textured polycrystals’ properties is presented. The input data for the developed application consist of: (a) the two-dimensional diffraction pattern of the material under investigation and (b) the tensors of the elasto-piezo-dielectric properties of the single crystal case. Program ANAELU 2.0 allows the determination of the fiber axis inverse pole figure by means of a Rietveld-type procedure. The Material Properties Open Database (MPOD, http://mpod.cimav.edu.mx) provides free access to the experimentally determined values of the tensor properties for several crystal species. Practical estimates of polycrystals’ properties may be obtained by averaging single crystals’ properties tensors, with the orientation distribution function (the symmetry-axis inverse pole figure, in fiber textures) as a weight factor. This treatment, with the application of the Voigt, Reuss and Hill approaches, requires special precautions when it comes to the coupling properties (e.g. piezoelectricity, magnetostriction, magnetoelectricity). Some key physical, mathematical and computational aspects related to the considered topic are discussed. Program GISELLE systematizes the calculation of polycrystal properties under the considered treatments. The application of the proposed methodology to real-world events is illustrated by means of a case study.

Two-Dimensional Diffraction Pattern by a Silk Cloth

Adiffraction grating is a plane surface having a large number of closely spaced slits running in parallel. When light of appropriate wavelength is incident on a diffraction grating it functions as a spectrometer, able to separate the light into its spectral components. Physical examples of interest for diffraction in the real world are numerous—for example, measuring the diameter of a human hair or fine thread-like material, diffraction due to razor blade, mesh, compact disc, banana stem as a natural grating, fabrics, and other materials. Students can also experiment with various materials—silk screen, cotton fabrics, a mesh made of closely aligned fibers (human hair, cat whiskers, and fur), and any other materials having microscale structures. In order to observe the wave nature of light, we should always choose the slit size and separation that is comparable to the wavelength of light. Here we revisit the wave nature of light by performing a simple diffraction experiment that required only a laser and a silk cloth (an approx. rectangular mesh).

Nanocrystal segmentation in scanning precession electron diffraction data.

Scanning precession electron diffraction (SPED) enables the local crystallography of materials to be probed on the nanoscale by recording a two-dimensional precession electron diffraction (PED) pattern at every probe position as a dynamically rocking electron beam is scanned across the specimen. SPED data from nanocrystalline materials commonly contain some PED patterns in which diffraction is measured from multiple crystals. To analyse such data, it is important to perform nanocrystal segmentation to isolate both the location of each crystal and a corresponding representative diffraction signal. This also reduces data dimensionality significantly. Here, two approaches to nanocrystal segmentation are presented, the first based on virtual dark-field imaging and the second on non-negative matrix factorization. Relative merits and limitations are compared in application to SPED data obtained from partly overlapping nanoparticles, and particular challenges are highlighted associated with crystals exciting the same diffraction conditions. It is demonstrated that both strategies can be used for nanocrystal segmentation without prior knowledge of the crystal structures present, but also that segmentation artefacts can arise and must be considered carefully. The analysis workflows associated with this work are provided open-source. LAY DESCRIPTION: Scanning precession electron diffraction is an electron microscopy technique that enables studies of the local crystallography of a broad selection of materials on the nanoscale. The technique involves the acquisition of a two-dimensional diffraction pattern for every probe position in an area of the sample. The four-dimensional dataset collected by this technique can typically comprise up to 500 000 diffraction patterns. For nanocrystalline materials, it is common that single diffraction patterns contain signals from overlapping crystals. To process such data, we use nanocrystal segmentation, where a representative diffraction pattern is constructed for each individual crystal, together with a real space image showing its morphology and location in the data. This reduces the dimensionality of the data and allows unmixing of signals from overlapping crystals. In this work, we demonstrate two methods for nanocrystal segmentation, one based on creating virtual dark-field images, and one based on unsupervised machine learning. A model system of partly overlapping nanoparticles is used to demonstrate the segmentation, and a demanding case for segmentation is highlighted, where some crystals are not discernible based on their diffraction patterns. To obtain a more complete nanocrystal segmentation, we add an image segmentation routine to both methods, and we discuss benefits and limitations of the two methods. The demonstration data and the used code are provided open-source, so that it can be used by everyone for analysis of nanocrystalline materials or as a starting point for further development of nanocrystal segmentation in scanning precession electron diffractiondata.

Unsupervised machine learning applied to scanning precession electron diffraction data

Scanning precession electron diffraction involves the acquisition of a two-dimensional precession electron diffraction pattern at every probe position in a two-dimensional scan. The data typically comprise many more diffraction patterns than the number of distinct microstructural volume elements (e.g. crystals) in the region sampled. A dimensionality reduction, ideally to one representative diffraction pattern per distinct element, may then be sought. Further, some diffraction patterns will contain contributions from multiple crystals sampled along the beam path, which may be unmixed by harnessing this oversampling. Here, we report on the application of unsupervised machine learning methods to achieve both dimensionality reduction and signal unmixing. Potential artefacts are discussed and precession electron diffraction is demonstrated to improve results by reducing the impact of bending and dynamical diffraction so that the data better approximate the case in which each crystal yields a given diffraction pattern.

Synchrotron X-ray measurements of cellulose in wood cell wall layers of Pinus densiflora in the transmission and reflectance modes. Part 1: results without loading

Abstract Synchrotron radiation X-ray diffraction (XRD) was applied to determine the cellulose content in 5-mm-thick sections of the annual rings of Japanese red pine (Pinus densiflora). Recent samples (air-dried in the last few years) and aged samples (250 years old) were investigated; the cellulose content in the S2 layer was measured by the transmission (Trs) method and that in the S1 and S3 layers by the reflection (Ref) method. Measurements were performed in the cellulose (004) Ref plane. The two XRD methods resulted in very different two-dimensional (2D) diffraction patterns, indicating differences in the cellulose characteristics. Azimuthal angle profiles showed cellulose chains measured by the Trs and the Ref methods oriented at about 9° and 75°, respectively, in terms of the longitudinal axis of the specimens. Moreover, 2θ profiles obtained by the Ref method had full-width-at-half-maximum (FWHM) values ≈3.5 times greater than the corresponding Trs profiles, indicating large variations in the cellulose lattice spacing d 004. The 250 years of aging had no effect on the cellulose contents.

Preparation and Properties of High-performance Polyimide Copolymer Fibers Derived from 5-Amino-2-(2-hydroxy-5-aminobenzene)-benzoxazole

A series of polyamic acid copolymers (co-PAAs) with para-hydroxyl groups was synthesized using two diamine monomers, namely p-phenylenediamine (p-PDA) and 5-amino-2-(2-hydroxy-5-aminobenzene)-benzoxazole (m-pHBOA), of different molar ratios through copolymerization with 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA) in N,N-dimethyacetamine (DMAc). The co-PAA solutions were used to fabricate fibers by dry-jet wet spinning, and thermal imidization was conducted to obtain polyimide copolymer (co-PI) fibers. The effects of the m-pHBOA moiety on molecular packing and physical properties of the prepared fibers were investigated. Fourier transform infrared (FTIR) spectroscopic results confirmed that intra/intermolecular hydrogen bonds originated from the hydroxyl group and the nitrogen atom of the benzoxazole group and/or the hydroxyl group and the oxygen atom of the carbonyl group of cyclic imide. As-prepared PI fibers displayed homogenous and smooth surface and uniform diameter. The glass transition temperatures (Tgs) of PI fibers were within 311−337 °C. The polyimide fibers showed 5% weight loss temperature (T5%) at above 510 °C in air. Two-dimensional wide-angle X-ray diffraction (WXRD) patterns indicated that the homo-PI and co-PI fibers presented regularly arranged polymer chains along the fiber axial direction. The ordered molecular packing along the transversal direction was destroyed by introducing the m-pHBOA moiety. Moreover, the crystallinity and orientation factors increased with increasing draw ratio. Small-angle X-ray scattering (SAXS) results showed that it is beneficial to reduce defects in the fibers by increasing the draw ratio. The resultant PI fibers exhibited excellent mechanical properties with fracture strength and initial modulus of 2.48 and 89.73 GPa, respectively, when the molar ratio of p-PDA/m-pHBOA was 5/5 and the draw ratio was 3.0.