Dynamical Diffraction Effects Research Articles

Effects of dynamic diffraction in coherent X-ray radiation from a beam of relativistic electrons in a periodic layered medium with three layers in a period

The possibilities of manifestation of dynamic diffraction effects in coherent X-ray radiation (CXR) of relativistic electrons in a periodic layered medium (PLM) with three different layers in a period are being investigated. A dynamic theory of CXR of relativistic electrons has been developed for the case of such a target. The corresponding formulas for the spectral-angular characteristics of parametric X-ray radiation (PXR) and diffracted transition radiation (DTR) are obtained and studied. The influence of asymmetric diffraction on the spectral-angular densities of PXR and DTR is shown. A striking effect of anomalous photoabsorption in PXR in a layered target, similar to the Bormann effect in a single crystal, is predicted.

Analysing the frame scaling in the presence of appreciable dynamical diffraction effects of 3D-ED data

Analysing the frame scaling in the presence of appreciable dynamical diffraction effects of 3D-ED data

Measuring Spatially-Resolved Potential Drops at Semiconductor Hetero-Interfaces Using 4D-STEM.

Characterizing long-range electric fields and built-in potentials in functional materials at nano to micrometer scales is of supreme importance for optimizing devices, e.g., the functionality of semiconductor hetero-structures or battery materials is determined by the electric fields established at interfaces which can also vary spatially. In this study, momentum-resolved four-dimensional scanning transmission electron microscopy (4D-STEM) is proposed for the quantification of these potentials and the optimization steps required to reach quantitative agreement with simulations for the GaAs/AlAs hetero-junction model system are shown. Using STEM the differences in the mean inner potentials (∆MIP) of two materials forming an interface and resulting dynamic diffraction effects have to be considered. This study shows that the measurement quality is significantly improved by precession, energy filtering and a off-zone-axis alignment of the specimen. Complementary simulations yielding a ∆MIP of 1.3V confirm that the potential drop due to charge transfer at the intrinsic interface is ≈0.1V, in agreement with experimental and theoretical values found in literture. These results show the feasibility of accurately measuring built-in potentials across hetero-interfaces of real device structures and its promising application for more complex interfaces of other polycrystalline materials on the nanometer scale.

Accurate structure models and absolute configuration determination using dynamical effects in continuous-rotation 3D electron diffraction data

Continuous-rotation 3D electron diffraction methods are increasingly popular for the structure analysis of very small organic molecular crystals and crystalline inorganic materials. Dynamical diffraction effects cause non-linear deviations from kinematical intensities that present issues in structure analysis. Here, a method for structure analysis of continuous-rotation 3D electron diffraction data is presented that takes multiple scattering effects into account. Dynamical and kinematical refinements of 12 compounds—ranging from small organic compounds to metal–organic frameworks to inorganic materials—are compared, for which the new approach yields significantly improved models in terms of accuracy and reliability with up to fourfold reduction of the noise level in difference Fourier maps. The intrinsic sensitivity of dynamical diffraction to the absolute structure is also used to assign the handedness of 58 crystals of 9 different chiral compounds, showing that 3D electron diffraction is a reliable tool for the routine determination of absolute structures.

Computer Simulation of the Effect of Coherent Dynamical Diffraction of Synchrotron Radiation in Crystals of Arbitrary Shape and Structure

Computer Simulation of the Effect of Coherent Dynamical Diffraction of Synchrotron Radiation in Crystals of Arbitrary Shape and Structure

Modeling and experimental validation of dynamical effects in Bragg coherent x-ray diffractive imaging of finite crystals

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the shape and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. Its strain imaging capability relies on Fourier transform--based iterative phase retrieval algorithms, which are mostly developed under the kinematical approximation. Such approximation prohibits the application of BCDI on larger crystals, which are commonly seen in most emerging functional materials. Understanding the dynamical effect in BCDI, as well as developing a validated method for modeling BCDI at the dynamical diffraction limit, is crucial for applying BCDI to hierarchical systems that contain micron-sized crystals and grains. Here we report a comparative study on the impact of dynamical diffraction effects by comparing the reconstruction results from two measurements of the same crystal. Forward simulation is implemented to show subtle changes of interference fringes in the diffraction pattern due to the dynamical diffraction, and is compared directly with the experimental data.

Low-Dose Electron Crystallography: Structure Solution and Refinement

There is a wealth of materials that are beam sensitive and only exist in nanometric crystals, because the growth of bigger crystals is either impossible or so complicated that it is not reasonable to spend enough time and resources to grow big crystals before knowing their potential for research or applications. This difficulty is encountered in minerals, zeolites, metal-organic frameworks or molecular crystals, including pharmaceuticals and biological crystals. In order to study these crystals a structure determination method for beam sensitive crystals of nanometric size is needed. The nanometric size makes them destined for electron diffraction, since electrons interact much more strongly with matter than X-rays or neutrons. In addition, for the same amount of beam damage, electron diffraction yields more information than X-rays. The recently developed low-dose electron diffraction tomography (LD-EDT) not only combines the advantages inherent in electron diffraction, but is also optimized for minimizing the electron dose used for the data collection. The data quality is high, allowing not only the solution of complex unknown structures, but also their refinement taking into account the dynamical diffraction effects. Here we present several examples of crystals solved and refined by this method. The range of the crystals presented includes two synthetic oxides, Sr5CuGe9O24 and (Na2/3Mn1/3)3Ge5O12, a natural mineral (bulachite), and a metal organic framework (Mn-formiate). The dynamical refinement can be successfully performed on data sets that needed less than 0.1 e−/Å2 for the entire data set.

Imaging Ultrafast Dynamical Diffraction Wave Fronts in Strained Si with Coherent X Rays.

Dynamical diffraction effects in thin single crystals produce highly monochromatic parallel x-ray beams with a mutual separation of a few microns and a time delay of a few femtoseconds-the so-called echoes. This ultrafast diffraction effect is used at X-Ray Free Electron Lasers in self-seeding schemes to improve beam monochromaticity. Here, we present a coherent x-ray imaging measurement of echoes from Si crystals and demonstrate that a small surface strain can be used to tune their temporal delay. These results represent a first step toward the ambitious goal of strain tailoring new x-ray optics and, conversely, open up the possibility of using ultrafast dynamical diffraction effects to study strain in materials.

Dynamical diffraction effects in STEM orbital angular momentum resolved electron energy-loss magnetic chiral dichroism

In this work we derive sum rules for orbital angular momentum(OAM) resolved electron magnetic chiral dichroism (EMCD) which enable the evaluation of the strength of spin and orbital components of the atomic magnetic moments in a crystalline sample. We also demonstrate through numerical simulations that these rules appear to be only slightly dependent from the dynamical diffraction of the electron beam in the sample, making possible their application without the need of additional dynamical diffraction calculations.

Vacancy Clustering in Dislocation-Free High-Purity Germanium

A germanium crystal of high purity was grown in H2 with a maximum dislocation density of 3000 cm−2, which was estimated by white beam x-ray topography. Due to a dynamical diffraction effect, the topographs revealed the existence of vacancy clusters in the form of voids in dislocation-free parts of the crystal. Etch pit density analysis, the standard technique employed for crystalline wafers to determine dislocation density, failed to reliably represent dislocations in dislocation-free parts of the crystal. On the other hand, we were able to identify a different type of etching pattern for a dislocation-free crystal. Microwave photoconductance decay was utilized to determine the charge carrier lifetime, which was found to be up to 500 μs for regions with dislocations, while being only 100 μs for dislocation-free parts of the crystal.

X-Ray Dynamical Diffraction in Powder Samples with Time-Dependent Particle Size Distributions

ABSTRACTIn situ X-ray diffraction is one of the most useful tools for studying a variety of processes, among which crystallization of nanoparticles where phase purity and size control are desired. Growth kinetics of a single phase can be completely resolved by proper analysis of the diffraction peaks as a function of time. The peak width provides a parameter for monitoring the time evolution of the particle size distribution (PSD), while the peak area (integrated intensity) is directly related to the whole diffracting volume of crystallized material in the sample. However, to precisely describe the growth kinetics in terms of nucleation and coarsening, the correlation between PSD parameters and diffraction peak widths has to be established in each particular study. Corrections in integrated intensity values for physical phenomena such as variation in atomic thermal vibrations and dynamical diffraction effects have also to be considered in certain cases. In this work, a general correlation between PSD median value and diffraction peak width is deduced, and a systematic procedure to resolve time-dependent lognormal PSDs from in situ XRD experiments is described in details. A procedure to correct the integrated intensities for dynamical diffraction effects is proposed. As a practical demonstration, this analytical procedure has been applied to the single-phase crystallization process of bismuth ferrite nanoparticles.

Improved measurement of electric fields by nanobeam precession electron diffraction

The electric field in a silicon p–n junction has been measured using pixelated scanning transmission electron microscopy. By using a convergence angle of 3.2 mrad, a spatial resolution better than 1 nm can be achieved leading to a rigid shift of the transmitted beam as it passes through an electric field. By precessing the beam around the optical axis at an angle of 0.1°, the effects of dynamical diffraction can be reduced. This leads to an improved measurement of the electric field from the shift of the transmitted beam. Different algorithms have been used to measure this shift, and template matching leads to a more accurate measurement of the electric field than the often-used center of mass method.

Coherent X-ray radiation excited by a beam of relativistic electrons in a layered periodic structure

The dynamic theory of coherent X-ray radiation, excited in a periodic layered medium by a divergent beam of relativistic electrons in the Bragg scattering geometry, is developed. In framework of the two-wave approximation of the dynamic theory of diffraction, expressions describing the spectral-angular and angular distributions of parametric X-ray radiation (PXR) and diffracted transition radiation (DTR) are obtained taking into account the multiple scattering of the relativistic electrons by the atoms of the target. Based on the expressions obtained, the possibilities of the manifestation of the effects of dynamical diffraction in coherent X-rays were investigated. The influence of the asymmetry of the electron Coulomb field reflection with respect to the target surface (the reflecting layers situate nonparallel to target surface) on the spectral-angular characteristics of the PXR and the DTR under conditions of the electron multiple scattering is estimated. It is shown that at a fixed Bragg angle the width of the PXR spectrum increases when the angle of incidence of the electron on the target decreases, which leads to an increase in the PXR angular density. In the same conditions the width of the frequency domain of total external reflection and the amplitude of the DTR spectrum also increase, which leads to a significant increase in the angular density of the DTR. The obtained analytical expressions can be used to determine the optimal parameters of the experiment on confirmation of the predicted dynamic effects.

Direct measurement of electrostatic potentials at the atomic scale: A conceptual comparison between electron holography and scanning transmission electron microscopy

Off-axis electron holography and first moment STEM are sensitive to electromagnetic potentials or fields, respectively. In this work, we investigate in what sense the results obtained from both techniques are equivalent and work out the major differences. The analysis is focused on electrostatic (Coulomb) potentials at atomic spatial resolution. It is shown that the probe-forming/objective aperture strongly affects the reconstructed electrostatic potentials and that, as a result of the different illumination setups, dynamical diffraction effects show a specific response with increasing specimen thickness. It is shown that thermal diffuse scattering is negligible for a wide range of specimen thicknesses, when evaluating the first moment of diffraction patterns.

Dynamical diffraction effects on the geometric phase of inhomogeneous strain fields

In specimens with an inhomogeneous displacement field in electron beam direction dynamical diffraction effects lead to complex non-linear properties of the diffracted electron wave. Consequently, the diffracted beam’s phase contains information about the inhomogeneous displacement field. These phases are experimentally and theoretically investigated under different excitation errors and specimen thicknesses as well as for different depths of the displacement field. An inclined InGaAs layer with a larger lattice constant than the surrounding GaAs matrix serves as controlled displacement field, which is inhomogeneous in electron beam direction with a continuously changing depth. The phase and amplitude of the diffracted beam are measured by dark-field electron holography. The measurements agree with calculations performed by numerical propagation of the electron wave using the Darwin-Howie-Whelan equations. A strong dependency on the excitation conditions is found showing that the interplay between dynamical effects and the strain field must be considered in the interpretation of the geometric phase.

Effects of Dynamical Electron Diffraction on Phase Shift Detected by Electron Holography

Effects of Dynamical Electron Diffraction on Phase Shift Detected by Electron Holography

Electron diffraction determines molecular absolute configuration in a pharmaceutical nanocrystal.

Determination of the absolute configuration of organic molecules is essential in drug development and the subsequent approval process. We show that this determination is possible through electron diffraction using nanocrystalline material. Ab initio structure determination by electron diffraction has so far been limited to compounds that maintain their crystallinity after a dose of one electron per square angstrom or more. We present a complete structure analysis of a pharmaceutical cocrystal of sofosbuvir and l-proline, which is about one order of magnitude less stable. Data collection on multiple positions of a crystal and an advanced-intensity extraction procedure enabled us to solve the structure ab initio. We further show that dynamical diffraction effects are strong enough to permit unambiguous determination of the absolute structure of material composed of light scatterers.

Intrinsic spatial resolution limit of the analyzer-based X-ray phase contrast imaging technique

Dynamical diffraction effects always play a role when working with perfect single crystals. The penetration of X-rays respect to the surface normal during diffraction (extinction depth - 1/σe) in perfect single crystals does not have a constant value. The value changes for different angular positions on the crystal diffraction condition. For higher X-ray energies this value can change from few micrometers to tens of millimeters for each different crystal angular position in the small angular range of the diffraction condition. This effect may spread a single point in the object (sample) as a line in the image detector, especially if the crystal is set (or if the sample angularly deviates the beam) at lower diffraction angle positions, where the surface component of X-ray penetration can achieve huge values. Then, for imaging experiments where the dynamical diffraction occurs, such intrinsic property can affect the image resolution. We have modeled and experimentally checked such a dynamical diffraction property using, as example, an Analyzer-based X-ray phase contrast imaging setup (ABI) at two different X-ray energies: 10.7 keV and 18 keV. The results show that our theoretical model is consistent with the measured results. For higher energies the blur effect is enhanced and intrinsically limits the image spatial resolution.

Influence of dynamic screening on the conductivity of hydrogen plasma including electron–electron collisions

We investigate the dynamical conductivity of dense hydrogen plasmas on the basis of the effective interaction potential (taking into account static or dynamic screening and diffraction effects). We apply a generalized Drude–Lorentz formula related to the dynamical conductivity with collision frequency. The influence of electron–ion collisions as well as the influence of both electron–ion and electron–electron collisions were taken into account via a renormalization factor. All calculations were performed on the basis of the effective potential with static or dynamic screening.

Simple method for optimization of classical electron magnetic circular dichroism measurements: The role of structure factor and extinction distances

Electron magnetic circular dichroism (EMCD), the electron wave analog of x-ray magnetic circular dichroism (XMCD), allows for the element specific measurement of the spin and orbital magnetic moments with up to nanometer resolution. However, due to dynamical diffraction effects, the signal-to-noise ratios of EMCD spectra are often very low. We describe a simple set of rules, how to set up a geometry for a classical EMCD experiment on an arbitrary crystal structure to get a maximum dichroic signal. The procedure is based on an evaluation of the structure factor and extinction distances. Proof-of-concept simulations and experiments on a FeGe crystal present a successful test of these guidelines.