Dynamical Diffraction Theory Research Articles

Optical elements containing semitransparent wavelike films.

Novel optical elements containing semitransparent wavelike films embedded into the bulk of transparent material, which form a reflection image without transmitted light distortion, are studied. The dynamic theory of light diffraction by a locally periodic multilayer semitransparent wavelike film is developed. A simple analytical formula for near Bragg diffraction order intensity is obtained for the case when only one diffraction order lies within the hologram angular selectivity. The phase modulation of light transmitted through the optical element containing wavelike films is estimated for single-layer and multilayer wavelike films with an arbitrary shape of surface. The restrictions on the structure parameters for which transmitted light distortions would be negligible are obtained. A new type of high-quality color hologram is proposed and shown to be feasible by calculation of hologram diffraction efficiency and spectral selectivity for three colors. Other possible applications, such as monochrome and color head-up and head-mounted displays, and imaging on spectacle lenses, are discussed.

Edge localized modes of cold neutrons in periodic condensed media

It is found that for certain energies of discreet cold neutrons, quasi-stationary eigen solutions of the corresponding Schrodinger equation, which are localized in the layer of a periodic medium, exist. The localization time of these solutions is strongly dependent on the layer thickness, being finite for a finite layer thickness and increasing indefinitely upon a infinite growth of the layer thickness as the third power of the layer thickness. The problem has been solved in the two-wave approximation of the dynamic diffraction theory for the neutron propagation direction coinciding with the periodicity axes (normal incidence of the neutron beam on the layer). The expressions for neutron eigenwave functions in a periodic medium, the reflection and transmission coefficients, and the neutron wavefunction in the layer as a function of the neutron energy incident on the layer have been determined. It turns out that for the certain discrete neutron energies, the amplitudes of the neutron wavefunction in the layer reach sharp maxima. The corresponding energies are just outside of the neutron stop band (energies forbidden for neutron propagation in the layer) and determine the energies of neutron edge modes (NEMs) localized in the layer, which are direct analogs of the optical edge modes for photonic crystals. The dispersion equation for the localized neutron edge modes has been obtained and analytically solved for the case of thick layers. A rough estimate for the localization length L is L ~(db N)–1, where b is the neutron scattering length, d is the crystal period, and N is the density of nuclei in the crystal. The estimates of the localized thermal neutron lifetime show that acheaving of a lifetime close to the free neutron lifetime seems nonrealistic due to absorption of thermal neutrons and requires a perfect large size crystal. Nevertheless, acheaving the localized neutron lifetime exceeding by ~104 times the neutron time of flight through the layer appears as experimentally attainable. The perspectives of the NEM observation are briefly discussed. It is proposed to use NEM for ultrahigh thermal neutron monochromatization by means of NEM excitation in perfect single crystals.

Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices.

Diffraction in multilayers in the presence of interfacial roughness is studied theoretically, the roughness being considered as a transition layer. Exact (within the framework of the two-beam dynamical diffraction theory) differential equations for field amplitudes in a crystalline structure with varying properties along its surface normal are obtained. An iterative scheme for approximate solution of the equations is developed. The presented approach to interfacial roughness is incorporated into the recursion matrix formalism in a way that obviates possible numerical problems. Fitting of the experimental rocking curve is performed in order to test the possibility of reconstructing the roughness value from a diffraction scan. The developed algorithm works substantially faster than the traditional approach to dealing with a transition layer (dividing it into a finite number of thin lamellae). Calculations by the proposed approach are only two to three times longer than calculations for corresponding structures with ideally sharp interfaces.

Dynamic diffraction effects and coherent breathing oscillations in ultrafast electron diffraction in layered 1T-TaSeTe.

Anisotropic lattice movements due to the difference between intralayer and interlayer bonding are observed in the layered transition-metal dichalcogenide 1T-TaSeTe following femtosecond laser pulse excitation. Our ultrafast electron diffraction investigations using 4D-transmission electron microscopy (4D-TEM) clearly reveal that the intensity of Bragg reflection spots often changes remarkably due to the dynamic diffraction effects and anisotropic lattice movement. Importantly, the temporal diffracted intensity from a specific crystallographic plane depends on the deviation parameter s, which is commonly used in the theoretical study of diffraction intensity. Herein, we report on lattice thermalization and structural oscillations in layered 1T-TaSeTe, analyzed by dynamic diffraction theory. Ultrafast alterations of satellite spots arising from the charge density wave in the present system are also briefly discussed.

Polarization anisotropy in light propagation inside opal-based photonic crystals

<p class="Abstract">Photonic crystals is expected to be the backbone of future optical integrated circuits. To realize this goal, light propagation and interaction with matters must be understood and controlled. In this work, we investigate the propagation of light inside opal-based photonic crystals along certain paths at the edge of its Brillouin Zone. Opal films made of polystyrene particles were prepared using self-assembly approach, the capillary deposition method. The structures and the optical properties of the resulting opals were characterized using scanning electron microscopy and polarization-resolved spectroscopy, respectively. The opal films have a face-centered cubic structure consisting of two domains showing preferential orientations. Domains in the form of ABC and ACB-type fcc crystals are oriented along the growth direction of the opal films. Light with frequencies near optical band gap shows a strong anisotropy. Light propagation inside opals depends on the polarization of the incident light. The intensity and the width of the extinction peaks for p-polarized incident light differ significantly from those of s-polarized light. The anisotropy disappears at frequencies above the optical band gap. The anisotropic light propagation is related to the strong anisotropy in equifrequency surface of band structure around the band gap. The shift of the extinction peaks and the variation of intensity of the extinction peaks will be discussed using the combination of kinematic and simplified dynamical diffraction theory.</p>

Selective sulfur dioxide adsorption on crystal defect sites on an isoreticular metal organic framework series

The widespread emissions of toxic gases from fossil fuel combustion represent major welfare risks. Here we report the improvement of the selective sulfur dioxide capture from flue gas emissions of isoreticular nickel pyrazolate metal organic frameworks through the sequential introduction of missing-linker defects and extra-framework barium cations. The results and feasibility of the defect pore engineering carried out are quantified through a combination of dynamic adsorption experiments, X-ray diffraction, electron microscopy and density functional theory calculations. The increased sulfur dioxide adsorption capacities and energies as well as the sulfur dioxide/carbon dioxide partition coefficients values of defective materials compared to original non-defective ones are related to the missing linkers enhanced pore accessibility and to the specificity of sulfur dioxide interactions with crystal defect sites. The selective sulfur dioxide adsorption on defects indicates the potential of fine-tuning the functional properties of metal organic frameworks through the deliberate creation of defects.

Polarization anisotropy in light propagation inside opal-based photonic crystals

<p class="Abstract">Photonic crystals is expected to be the backbone of future optical integrated circuits. To realize this goal, light propagation and interaction with matters must be understood and controlled. In this work, we investigate the propagation of light inside opal-based photonic crystals along certain paths at the edge of its Brillouin Zone. Opal films made of polystyrene particles were prepared using self-assembly approach, the capillary deposition method. The structures and the optical properties of the resulting opals were characterized using scanning electron microscopy and polarization-resolved spectroscopy, respectively. The opal films have a face-centered cubic structure consisting of two domains showing preferential orientations. Domains in the form of ABC and ACB-type fcc crystals are oriented along the growth direction of the opal films. Light with frequencies near optical band gap shows a strong anisotropy. Light propagation inside opals depends on the polarization of the incident light. The intensity and the width of the extinction peaks for p-polarized incident light differ significantly from those of s-polarized light. The anisotropy disappears at frequencies above the optical band gap. The anisotropic light propagation is related to the strong anisotropy in equifrequency surface of band structure around the band gap. The shift of the extinction peaks and the variation of intensity of the extinction peaks will be discussed using the combination of kinematic and simplified dynamical diffraction theory.</p>

Homogeneous self-standing curved monocrystals, obtained using sandblasting, to be used as manipulators of hard X-rays and charged particle beams

A technique to obtain self-standing curved crystals has been developed. The method is based on a sandblasting process capable of producing an amorphized layer on the substrate. It is demonstrated that the amorphized layer behaves as a thin compressive film, causing the curvature of the substrate. This procedure permits the fabrication of homogeneously curved crystals in a fast and economical way. It is shown that a sandblasted crystal can be used as an X-ray optical element for astrophysical or medical applications. A sandblasted bent crystal can also be used as an optical element for steering charged particles in accelerator beamlines. Several samples were manufactured and bent using the sandblasting method at the Sensor and Semiconductor Laboratory of Ferrara, Italy. Their curvature was verified using interferometric profilometry, showing a deformation in agreement with the Stoney formalism. The curvature of the machined samples was also tested using γ-ray diffraction at the Institut Laue–Langevin (ILL), Grenoble, France. A good agreement with the dynamical theory of diffraction was observed. In particular, the experiment showed that the crystalline quality of the bulk was preserved. Moreover, the method allowed curved samples to be obtained free of any additional material. Finally, a crystalline undulator was produced using sandblasting and tested using γ-ray diffraction at the ILL. The crystal showed a precise undulating pattern, so it will be suitable for hard X-ray production.

Revisiting La0.5Sr1.5MnO4 lattice distortion and charge ordering with multi-beam resonant diffraction.

Sinusoidal wave type distortions of La0.5Sr1.5MnO4 in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction (MRXD) with (7/4 7/4 0) fractional primary diffraction. Two four-beam diffractions with opposite asymmetry were measured at 6.5545 keV and compared with the curves simulated by the dynamical X-ray diffraction theory. This approach provides the possibility of resolving the distortion modes which are perpendicular to the momentum transfer by a single azimuthal scan. The paper also demonstrates the sensitivity of MRXD profiles versus incident X-ray energy in the vicinity of the Mn K edge to the charge disproportion between the two manganese sites, reconfirming the small charge disproportion feature.

Quantum-information approach to dynamical diffraction theory

We present a simplified model for dynamical diffraction of particles through a periodic thick perfect crystal based on repeated application of a coherent beam splitting unitary at coarse-grained lattice sites. By demanding translational invariance and a computationally tractable number of sites in the coarse-graining we show how this approach reproduces many results typical of dynamical diffraction theory and experiments. This approach has the benefit of being applicable in the thick, thin, and intermediate crystal regimes. The method is applied to a three-blade neutron interferometer to predict the output beam profiles, interference patterns, and contrast variation.

Electron channelling contrast imaging of dislocations in a conventional SEM

Dislocations in shock loaded tantalum single crystals were imaged using both transmission electron microscope (TEM) and electron channelling contrast image (ECCI) in a scanning electron microscope with a conventional backscattered electron detector. The results were compared with backscattered electron intensity profiles across dislocations calculated via the dynamic theory of electron diffraction. A one-to-one correspondence between ECCI and TEM is established. High voltage and low index reflections should be used to obtain the highest dislocation contrast and greatest imaging depth.

Channeling‐enhanced EDX for polarity resolved crystal orientation determination

Using channeling‐enhanced energy‐dispersive X‐ray spectroscopy (EDX), we demonstrate polarity sensitive orientation determination of a non‐centrosymmetric crystal in the scanning electron microscope. The authors observe a characteristic asymmetry in the channeling‐enhanced, angle‐dependent EDX data of a GaAs sample, which is in good agreement to simulations using the dynamical theory of diffraction for the incident electron beam. This allows us to assign the orientation of the GaAs crystal according to the non‐centrosymmetric point group. The method shown here overcomes the limitation of a reduced point‐group sensitivity of electron backscatter diffraction patterns and electron channeling patterns for crystalline phases that contain atoms of approximately equal electron scattering cross sections.

Asymmetric structure of germanene on an Al(111) surface studied by total-reflection high-energy positron diffraction

The structure of germanene on an Al(111) surface has been experimentally investigated using the total-reflection high-energy positron diffraction (TRHEPD) method. The observed spot intensities are asymmetric, revealing no mirror symmetry in the atomic coordinates of germenene with respect to the 〈110〉 direction. Quantitative TRHEPD rocking curve analysis, based on dynamical diffraction theory, has revealed that the germanene layer has a 3 × 3 structure with asymmetrical buckling due to the protrusion of one of the Ge atoms in the unit cell, which is unlike the structural model proposed in previous studies. The magnitude of the buckling was found to be 0.94 Å, and the spacing between the germanene and the Al(111) substrate to be 2.51 Å. The new structure proposed in the present investigations, though different from that reported in studies before, does not contradict the other characteristics which were found experimentally in the previous studies.

Time-of-flight Fourier Spectrometry with UCN

The report presents the first experience of using a time-of-flight Fourier spectrometer of ultracold neutrons (UCN). The description of the spectrometer design and first results of its testing are presented. The results of the first experiments show that the spectrometer may be used for obtaining UCN energy spectra in the energy range of 60÷200 neV with a resolution of about 5 neV. The application of TOF Fourier spectrometry technique allowed us to obtain the energy spectra from the diffraction of monochromatic ultracold neutrons on a moving grating. Lines of 0, +1 and +2 diffraction orders were simultaneously recorded, which had previously been impossible to be done by other methods. These results have made it possible to make a comparison with the recent theoretical calculations based on the dynamical theory of neutron diffraction on a moving phase grating.

Structure refinement using precession electron diffraction tomography and dynamical diffraction theory

Structure refinement using precession electron diffraction tomography and dynamical diffraction theory

Importance of Determination of Crystal Quality in Protein Crystals when Performing High-Resolution Structural Analysis

We show that the extinction effect explained by the dynamical theory of diffraction must be considered even in the case of protein crystals. Equal-thickness fringes, which are attributed to the Pendellösung effect, were clearly observed in the region of a tapered glucose isomerase crystal with wedge-like edges using X-ray topography carried out with a beam of monochromatic synchrotron radiation. This indicates that the perfection of this glucose isomerase crystal is high enough to produce this dynamical theory-related effect: this surely leads to difficulty in the collection of accurate integrated intensities of diffraction spots for X-ray structural analysis. Therefore, it is important to determine whether the crystal quality of a protein crystal under analysis is adequate to obtain accurate three-dimensional structures of protein molecules for X-ray structural analyses. We show that X-ray diffraction rocking-curve measurements can provide clues for this determination.

Rotation of X-ray polarization in the glitches of a silicon crystal monochromator.

EXAFS studies on dilute samples are usually carried out by collecting the fluorescence yield using a large-area multi-element detector. This method is susceptible to the 'glitches' produced by all single-crystal monochromators. Glitches are sharp dips or spikes in the diffracted intensity at specific crystal orientations. If incorrectly compensated, they degrade the spectroscopic data. Normalization of the fluorescence signal by the incident flux alone is sometimes insufficient to compensate for the glitches. Measurements performed at the state-of-the-art wiggler beamline I20-scanning at Diamond Light Source have shown that the glitches alter the spatial distribution of the sample's quasi-elastic X-ray scattering. Because glitches result from additional Bragg reflections, multiple-beam dynamical diffraction theory is necessary to understand their effects. Here, the glitches of the Si(111) four-bounce monochromator of I20-scanning just above the Ni K edge are associated with their Bragg reflections. A fitting procedure that treats coherent and Compton scattering is developed and applied to a sample of an extremely dilute (100 micromolal) aqueous solution of Ni(NO3)2. The depolarization of the wiggler X-ray beam out of the electron orbit is modeled. The fits achieve good agreement with the sample's quasi-elastic scattering with just a few parameters. The X-ray polarization is rotated up to ±4.3° within the glitches, as predicted by dynamical diffraction. These results will help users normalize EXAFS data at glitches.

Coherent X-ray radiation by relativistic electron in a structure “amorphous layer-vacuum-periodic layered medium”

The dynamic theory of coherent X-ray radiation by relativistic electron crossing a three-layer structure consisting of an amorphous substance layer, a layer of vacuum and a layer with artificial periodic structure has been developed. The process of radiation and propagation of X-ray waves in an artificial periodic structure have been considered based on two-wave approximation of dynamic diffraction theory in Laue scattering geometry.

RHEED intensities from two-dimensional heteroepitaxial nanoscale systems of GaN on a Si surface

This paper presents a computer program, which facilitates the calculation of changes to the intensity of RHEED oscillations from the heteroepitaxial structures of (0001)GaN films nucleated on a Si surface. The calculations are based on the use of a dynamical diffraction theory and different models of scattering crystal potential. New version program summaryTitle of program: RHEED_DIFF_WProgram Files doi:10.17632/hn3pt6ytky.1Licensing provisions: GNU General Public License 3Programming language used: C++Journal reference of previous version: Computer Physics Communications 185 (2014) 3001–3009Does the new version supersede the previous version?: No. It does supersede version AETW_v1_0.Reasons for the new version: Responding to the users’ feedback we presented a practical procedure of construction of simulation program, which facilitates the calculation of changes to the intensity of RHEED oscillations in the function of the glancing angle of incidence of the electron beam, employing various models of scattering crystal potential for heteroepitaxial structures of hexagonal (0001)GaN films nucleated on a Si surface. GaN has a wurtzite crystal structure with alternating planes of Ga and N atoms and lattice constants a=3.189Å and c=5.185Å [1]. Choosing the top surface to be z=0, the N atoms are located at z=nd where d=5.185/2Å and n is an integer, and Ga atoms are at z=nd−u, where u=3c/8 (as shown in Fig. 1).The nature of physical problem: Since the discovery of molecular beam epitaxy, which allows formation of layers (crystals) with a controlled composition of subsequent monolayers, the research attempts of many laboratories have been focused on studying the dynamics of formation of both monolayers and specific heterojunction structures, that is the structures with monocrystalline interfaces created by materials of various chemical compositions (different physical and chemical properties). The fundamental scientific problem in such research is to specify both interface type and growth mechanism for subsequent layers. Researchers and technologists manufacturing two-dimensional nanoscale systems frequently use RHEED rocking curves (the specular beam intensities versus the glancing angle) to control growth of films at the atomistic level of accuracy. The structural properties of the GaN/Si interface have been meticulously studied by many [3–5], and crucial problem of the direct growth of GaN on Si is the formation of amorphous silicon nitride (SiN) at the GaN/Si interface.Typical running time: The typical running time is machine and user-parameters dependent, i.e. the number of layers for both the substrate and the growing layers included in the calculations.The method of solution: RHEED intensities are calculated within the general framework described in Ref. [2] with the model of the scattering potential for heterostructures: (1)UCombined(z)=∑nUsubstrate(z)+∑n(Ulayer(z)+Uaddlayer(z)), where the Uaddlayer represents the diffuse scattering on the topmost layer.Summary of revisions: The presented version of computer program implements original algorithms of self-consistent calculations for scattering potentials GaN(0001)/Si(111) and solving a time-independent Schrödinger equation for high-energy electrons (Fig. 2). [Display omitted] [Display omitted] [Display omitted] [Display omitted] During the numerical calculations of the changes in the intensity of the specular beam in the function of the glancing angle, it was assumed that the electron energy equals 10 keV, the glancing angle was increased from 0.5° to 7°, and the value of α parameter =0.1 and β=0.5 for the MODEL3 of the scattering potential [2]. Figs. 3–4 present the situation where on the crystalline Si(111) substrate a single GaN layer was placed, where the GaN growth on Si is having a thin amorphous layer. It can be observed that for a very thin layer of GaN, a clear minimal amplitude of RHEED oscillation occurs with the coverage of the GaN layer equal to about 0.5.

Polarization angular-resolved transmission spectroscopy of opal films

In this paper, we investigated the angular behavior of light transmission through opal films over a broad range of wavelengths and angles. The opal films were prepared using the capillary deposition method (CDM). The observation of many well-defined diffraction peaks indicates that the CDM results in opal films with high quality. Peaks overlapping at normal incidence split when samples are rotated. The angular shift of these peaks was found to satisfy the kinematical diffraction theory very well. Furthermore, the variation of intensity with incident angle can be interpreted in terms of a simplified dynamical diffraction theory. Moreover, the presence of two differently oriented domains in CDM-made opal films is essential in discussing the measured spectra. These domains can be assigned to parallel microscopic stripes of ABC and ACB type fcc structures. Angular-resolved spectroscopy with polarized incident light shows interesting polarization dependence of light propagation inside opals.