Dynamical Diffraction Research Articles

Diffraction contrast of ferroelectric domains in DPC STEM images.

Differential phase contrast scanning transmission electron microscopy (DPC STEM) is a powerful technique for directly visualizing electromagnetic fields inside materials at high spatial resolution. Electric field observation within ferroelectric materials is potentially possible by DPC STEM, but concomitant diffraction contrast hinders the quantitative electric field evaluation. Diffraction contrast is basically caused by the diffraction-condition variation inside a field of view, but in the case of ferroelectric materials, the diffraction conditions can also change with respect to the polarization orientations. To quantitatively observe electric field distribution inside ferroelectric domains, the formation mechanism of diffraction contrast should be clarified in detail. In this study, we systematically simulated diffraction contrast of ferroelectric domains in DPC STEM images based on the dynamical diffraction theory, and clarify the issues for quantitatively observing electric fields inside ferroelectric domains. Furthermore, we conducted experimental DPC STEM observations for a ferroelectric material to confirm the influence of diffraction contrast predicted by the simulations.

Preparation and measurement of an x-ray Laue-type monochromator based on a WSi2/Si multilayer

The Laue-type multilayer monochromator (LMM) is a promising optical element with a small size and high efficiency in a synchrotron radiation facility. By the dynamical diffraction theory, using DC magnetron sputtering technology, an LMM with a total thickness of 47 µm and a periodic thickness of 4.7 nm WSi2/Si multilayer at 26 keV is designed and fabricated. During the preparation, the total number of layers is up to 20000, and every 300th layer of Si is replaced by WSi2 as the marker, so the multilayer is divided into 67 areas. The cross section of the multilayer is measured by a scanning electron microscope (SEM), and the marker region thickness error is 0.28% (RMS). The diffraction test experiment of the LMM is carried out at the Shanghai synchrotron radiation facility (SSRF). The 1st-order peak angle is 5.05 mrad, and the efficiency is 75.0%, which is close to the theoretical calculation result of 5.1 mrad and 79.1%. The Darwin width of the LMM is 0.17 mrad which is equal to the theoretical calculation. Based on the Bragg’s diffraction equation, the energy resolution (ΔE/E) is 3.3%.

Mechanochemical Synthesis and Three-Dimensional Electron Diffraction Structure Solution of a Novel Cu-Based Protocatechuate Metal-Organic Framework.

Mechanochemical synthesis is a powerful approach to obtain new materials, limiting costs, and times. However, defected and submicrometrical-sized crystal products make critical their characterization through classical single-crystal X-ray diffraction. A valid alternative is represented by three-dimensional (3D) electron diffraction, in which a transmission electron microscope is used, like a diffractometer. This work matches a green water-based mechanochemical synthesis and 3D electron diffraction to obtain and characterize a Cu-based protocatechuate metal-organic framework (PC-MOF). Its structure has been fully refined through dynamical diffraction theory, and free water molecules could be detected in the channels of the framework. Thermal characterization, focused on the dehydration profile determination, leads to the formation of a novel high-temperature 2D coordination polymer, fully solved with 3D electron diffraction data. At last, the strong activity of the PC-MOF against cationic dyes like methylene blue has been reported.

Structure solution and refinement of beam-sensitive nano-crystals

Radiation sensitive materials are among the most difficult materials to study, even more so if they exist only as nanometer-sized particles, where their size is either intentional because of enhanced properties at the nano-scale or it is unintentional because it is impossible to obtain bigger particles of the same structure. In both cases characterization methods need to be optimized to get the most information out of these particles before the radiation damages them to a point where their structure is altered. When the particles are crystallized, both characteristics, the small size and the beam sensitivity, call for electron diffraction as a privileged investigation tool. The strong interaction of electrons (as compared to X-rays) with matter allows single crystal diffraction experiments on nanometer-sized crystals and for the same amount of beam damage, electron diffraction yields more information than X-rays. These inherent advantages of electron diffraction are optimized in the recently developed low-dose electron diffraction tomography (LD-EDT) by minimizing the necessary dose for a complete data collection. In this contribution we show that in some cases even doses as low as 2 e-/Ų can induce damage in crystal structures that inhibit a correct structure refinement. However, by LD-EDT we can obtain data using extremely low doses that don’t alter the structure which make it then possible not only to solve crystal structures but also to refine them using dynamical diffraction theory. Here a synthetic oxide containing volatile Na and a metal-organic framework are given as examples. A dynamical refinement of the structures is possible with data sets requiring a dose of less than 0.15 e-/Ų.

Zeta Potential and Size Analysis of Zeolitic Imidazolate Framework-8 Nanocrystals Prepared by Surfactant-Assisted Synthesis.

The crystal nucleation and growth mechanism of monodispersed metal-organic framework nanoparticles were studied using time-resolved light dynamic, electrokinetic, and powder X-ray diffraction methods. We confirmed that zeolitic imidazolate framework-8 (ZIF-8) nanocrystals follow a nonclassical crystal growth pathway, where a fast nucleation occurs with dense liquid clusters or nanocrystals forming spontaneously when two precursors are mixed. We also explored the zeta potential and solvodynamic size changes of ZIF-8 prepared by a surfactant-assisted synthesis. Three modulators, including 1-methylimidazole (1-mIm), tris(hydroxymethyl)aminomethane (THAM), and (1-hexadecyl)trimethylammonium bromide (CTAB), were studied. We found that 1-mIm dramatically increases the rate of nucleation of ZIF-8. With an increasing amount of 1-mIm, which functions as a coordination modulator, the size increases, and the zeta potential of ZIF-8 decreases. Whereas THAM, as both a coordination and a deprotonation modulator, increases the size and zeta potential of ZIF-8 simultaneously, CTAB, as a long alkyl cationic surfactant, mainly adsorbs on the surface of ZIF-8, and the zeta potential of the formed ZIF-8 is controlled by the amount of CTAB in solution compared with its critical micelle concentration. Overall, we reveal that the modulator type and concentration can be used to control the size and zeta potential of the dispersed ZIF-8 nanocrystals in a colloid system. The experiments also enable identification of the nucleation and crystal growth processes of ZIF-8. The findings will be applicable to other nanocrystals in colloid systems, which are used for heterogeneous catalysis and guest molecular loadings.

Ultrafast Solid-State Electrochemical Imprinting Utilizing Polymer Electrolyte Membrane Stamps for Static/Dynamic Structural Coloration and Letter Encryption.

Micro and nanopatterned surfaces hold potential for various applications, such as wettability control, antibiofouling, and optical components. However, conventional patterning processes are characterized by complexity, high costs, and environmental burdens because of the use of resists. Therefore, this paper proposes facile and ultrafast electrochemical imprinting employing a polymer electrolyte membrane (PEM) stamp for achieving micro and nanoscale patterning on Si surfaces. The solid-state electrochemical process efficiently generates oxide and hydrated oxide (Si-OH) patterns within several seconds at room temperature in a dry ambient environment. The formed oxide pattern can be employed as an etching mask to prepare diffraction gratings with diverse high-resolution (≈100nm) patterns utilizing the dry PEM stamp. The resulting oxide pattern on the Si surface exhibits instantaneous structural coloration upon exposure to humid air, attributable to the formation of a water microdroplet array on the oxide pattern. The oxide pattern is successfully applied for dynamic diffraction grating and letter encryption. The proposed solid-state electrochemical oxidation scheme based on a PEM stamp, which eliminates the need for liquid electrolyte and resist, represents a simple and ultrafast process with a time cost of a few seconds, characterized by low processing costs and environmental impact.

Dynamical and kinematical X-ray diffraction in a bent crystal

Numerical modeling of kinematical and dynamical X-ray diffraction in a bent crystal was performed on the basis of two approaches to integrating the Takagi–Taupin equations, and using two-dimensional recurrence relations. Within the framework of kinematical diffraction, a new equation is obtained that describes the distribution of diffracted intensity inside a bent crystal. The time taken for numerical calculations based on this equation is significantly reduced in comparison with the use of algorithms of the dynamical diffraction theory. The simulation shows for the first time that, for strongly bent crystals, the maximum value of the diffraction intensity is formed inside the deformed structure and not on its surface. In the case of strong bending of the crystal structure, the deviation of the X-ray beam from the Bragg angle does not change the diffraction pattern but shifts it along the lateral direction. The results of calculations of diffraction in a strongly bent crystal based on the equations of dynamical and kinematical diffraction coincide, while the computations for weakly bent crystals differ. The possibility of estimating the primary extinction length of a bent crystal as a function of the bending radius is shown. In the case of kinematical diffraction in bent crystalline microsystems, a new method has been developed to calculate X-ray reciprocal-space mapping.

Study of phase objects by dynamical diffraction of a spherical X-ray wave in a crystal using a temperature gradient

The possibility of reconstructing the internal structure of a phase object by dynamical diffraction of a spherical X-ray wave in a crystal using a temperature gradient was investigated. It is shown that the use of a temperature gradient directed perpendicular to the crystal surface makes it possible to obtain a focal distribution of all point inhomogeneities in the phase object on the exit surface of the crystal. By moving the phase object along the direction of the diffraction vector and registering the entire map of obtained data, one can restore the additional phase of the wave and the internal structure of the phase object section.

Modelling dynamical 3D electron diffraction intensities. II. The role of inelastic scattering.

The strong interaction of high-energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave-Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low-loss regime, while the Bragg-diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime.

High precision orientation mapping from 4D-STEM precession electron diffraction data through quantitative analysis of diffracted intensities

The association of scanning transmission electron microscopy (STEM) and detection of a diffraction pattern at each probe position (so-called 4D-STEM) represents one of the most promising approaches to analyze structural properties of materials with nanometric resolution and low irradiation levels. This is widely used for texture analysis of materials using automated crystal orientation mapping (ACOM). Herein, we perform orientation mapping in InP nanowires exploiting precession electron diffraction (PED) patterns acquired by an axial CMOS camera. Crystal orientation is determined at each probe position by the quantitative analysis of diffracted intensities minimizing a residue comparing experiments and simulations in analogy to x-ray structural refinement. Our simulations are based on the two-beam dynamical diffraction approximation and yield a high angular precision (∼0.03°), much lower than the traditional ACOM based on pattern matching algorithms (∼1°). We anticipate that simultaneous exploration of both spot positions and high precision crystal misorientation will allow the exploration of the whole potentiality provided by PED-based 4D-STEM for the characterization of deformation fields in nanomaterials.

Double-slit asymmetrical dynamical diffraction of X-rays in ideal crystals.

The theoretical investigation of double-slit asymmetrical dynamical diffraction of X-rays in perfect crystals establishes that Young's interference fringes on the exit surface are formed. The position of the fringes in the cross section of the beam depends on deviation from the Bragg exact orientation and asymmetry angle. An equation for the period of the fringes is presented, according to which the period is polarization sensitive. The period increases with increasing the absolute value of the asymmetry angle. In its turn, the size of the interference region also increases with increasing the absolute value of the asymmetry angle. However, the ratio of interference region size to period, i.e. the number of observed fringes, decreases with increasing the absolute value of the asymmetry angle. The size of the interference region can be of the order of a few tens of mm, which can be used for obtaining Fourier dynamical diffraction holograms of a large size. This type of diffraction can also be used for obtaining double-slit dynamical diffraction contrast of defects and deformations. Due to the phase difference information, in comparison with single-slit diffraction, double-slit diffraction is more sensitive to the existence of objects and deformations in the path of the wave.

Solving the crystallographic phase problem by linearizing dynamical electron diffraction

Solving the crystallographic phase problem by linearizing dynamical electron diffraction

Determining alloy concentration by analyzing dynamic diffraction at strained semiconductor interfaces

Determining alloy concentration by analyzing dynamic diffraction at strained semiconductor interfaces

Synthesis of rhombohedral Hf0.5Zr0.5O2 and analysis by x-ray diffraction through dynamical diffraction simulations

The persistence of ferroelectricity down to nanometer scales in hafnia-based materials makes these compounds promising candidates for future, electronic applications. Moreover, theoretical calculations show the existence of several meta-stable phases...

Diffraction image of a narrow X-rays beam in crystals with weak deformation

The problem of the dynamic diffraction of X-rays from a point source on the spatial lattice of a crystal weakly deformed by a temperature gradient is considered. The Theoretical study is based on the asymptotic representation of the Green-Riemann function for a pair of Takagi equations of the hyperbolic type. The Experimental studies were carried out on the quartz crystals in the presence of a temperature gradient that is perpendicular to the reflecting planes. The conditions and characteristics of focusing are considered, taking into account the distances source-crystal-detector and the parameter of the deformation field.

Multi-exposure diffraction pattern fusion applied to enable wider-angle transmission Kikuchi diffraction with direct electron detectors

Diffraction pattern analysis can be used to reveal the crystalline structure of materials, and this information is used to nano- and micro-structure of advanced engineering materials that enable modern life. For nano-structured materials typically diffraction pattern analysis is performed in the transmission electron microscope (TEM) and TEM diffraction patterns typically have a limited angular range (less than a few degrees) due to the long camera length, and this requires analysis of multiple patterns to probe a unit cell. As a different approach, wide angle Kikuchi patterns can be captured using an on-axis detector in the scanning electron microscope (SEM) with a shorter camera length. These ‘transmission Kikuchi diffraction’ (TKD) patterns present a direct projection of the unit cell and can be routinely analysed using EBSD-based methods and dynamical diffraction theory. In the present work, we enhance this analysis significantly and present a multi-exposure diffraction pattern fusion method that increases the dynamic range of the detected patterns captured with a Timepix3-based direct electron detector (DED). This method uses an easy-to-apply exposure fusion routine to collect data and extend the dynamic range, as well as normalise the intensity distribution within these very wide (>95°) angle patterns. The potential of this method is demonstrated with full diffraction sphere reprojection and highlight potential of the approach to rapidly probe the structure of nano-structured materials in the scanning electron microscope.

Investigation of dynamical X-ray back diffraction at grazing incidence

We report a theoretical investigation of X-ray back diffraction at grazing incidence. Based on the framework of the dynamical theory of X-ray diffraction, the grazing incidence for Si (12 4 0) back diffraction is taken as an example to resolve the eigenvalue problem inside the crystal. The dispersion surface and the resulting diffraction intensities are strongly affected by the miscut angle as well as the diffraction geometry of grazing incidence. The kinematical relationship between the incident angle and the miscut angle is well explained by Snell’s law. While only the two-beam diffraction is considered, our treatment can be further extended to include the cases for multiple diffractions as well.

Biosynthesis of silver nanocatalyst and its application for the efficient hydrogenation of nitroarenes

The utilization of plant extracts for the synthesis of silver nanoparticles (Ag-NPs) has attracted attention from all over the world due to its unique physicochemical characteristics and significance in the field of environment. Here, Nepal pepper fruit extract was successfully employed to synthesize Ag-NPs. As obtained, Nepal pepper-mediated Ag-NPs were employed for the catalytic conversion of nitroarenes including 2-nitrophenol (2-NP), 4-nitrophenol (4-NP), 2-nitroaniline (2-NA), and 2,4,6-trinitrophenol (2,4,6-TNP), into their corresponding amino derivatives using sodium borohydride (NaBH4). The Ag-NPs were analyzed using UV–visible (UV-Vis) spectroscopy, Fourier-transform infrared (FTIR) spectroscopy, Scanning Electron Microscopy (SEM), Energy Dispersive X-rays (EDX), Transmission Electron Microscopy (TEM), Dynamic Light Scattering (DLS), X-rays Diffraction (XRD), and Zeta potential. TEM micrographs revealed the prepared Ag-NPs were predominantly spherical, with an average diameter of 13.9 nm. DLS and zeta potential studies showed stable small-size Ag-NPs of an average size of 6.8 nm. Ag-NPs elucidate outstanding reduction efficiency against 4-NP, 2-NP, 2-NA, and 2,4,6-TNP with rate constants of 1.71 × 10−3 s−1, 2.32 × 10−3 s−1, 2.88 × 10−3 s−1, and 1.54 × 10−3 s−1, respectively. Additionally, stability and reusability of Ag-NPs revealed stability for up to 15 days and excellent recyclability with small activity loss. This study constittutes an environmentally friendly approach for the synthesis of Ag-NP nanoparticles and their applications in improved organic chemical reduction rates and transformations.

Coupling x-ray photon correlation spectroscopy and dynamic coherent x-ray diffraction imaging: Particle motion analysis from nano-to-micrometer scale

Coupling x-ray photon correlation spectroscopy and dynamic coherent x-ray diffraction imaging: Particle motion analysis from nano-to-micrometer scale

Dynamic diffraction of planar X-rays in a crystal lattice with a weak deformation field

In this paper, we consider the problem of the formation of a wave field during dynamic X-ray diffraction under conditions of weak deformation of the crystal lattice induced by a temperature gradient directed along the diffraction vector. Within the framework of the Takagi equations, which describe the propagation of the amplitudes of transmitted and reflected waves in the grating, analytical solutions dependence on the deformation parameters of these amplitudes are given. The angular width of the reflected X-ray radiation, as well as its dependence on the thickness of the single crystal, has been studied. It is shown that with increasing deformation, the rocking curves of the crystal slowly broaden, and their maximum intensity increases, reaching unity (the case of complete transfer). With a further increase in the deformation of the reflecting planes, the rocking curves continues to widen, and their maximum slowly decreases. It is also shown that the angular width of the complete transfer x-rays is directly proportional to the thickness of the sample under study. All observed phenomena are given a theoretical interpretation based on the general theory of dynamic scattering based on the Takagi equations and the eikonal approximation for weakly deformed crystal lattice fields.