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Electromagnetic diffraction by plane reflection diffraction gratings
A plane wave theory was developed to study electromagnetic diffraction by plane reflection diffraction gratings of infinite extent. A computer program was written to calculate the energy distribution in the various orders of diffraction for the cases when the electric or magnetic field vectors are parallel to the grating grooves. Within the region of validity of this theory, results were in excellent agreement with those in the literature. Energy conservation checks were also made to determine the region of validity of the plane wave theory. The computer program was flexible enough to analyze any grating profile that could be described by a single value function f(x). Within the region of validity the program could be used with confidence. The computer program was used to investigate the polarization and blaze properties of the diffraction grating.
Electromagnetic diffraction efficiencies for plane reflection diffraction gratings
Results are presented of research activities on holographic grating research. A large portion of this work was performed using rigorous vector diffraction theory, therefore, the necessary theory has been included in this report. The diffraction efficiency studies were continued using programs based on a rigorous theory. The simultaneous occurrence of high diffraction efficiencies and the phenomenon of double Wood's anomalies is demonstrated along with a graphic method for determining the necessary grating parameters. Also, an analytical solution for a grating profile that is perfectly blazed is obtained. The performance of the perfectly blazed grating profile is shown to be significantly better than grating profiles previously studied. Finally, a proposed method is described for the analysis of coarse echelle gratings using rigorous vector diffraction that is currently being developed.
Analytical inversions in remote sensing of particle size distributions. I - Multispectral extinctions in the anomalous diffraction approximation. II Angular and spectral scattering in diffraction approximations
Consideration is given to analytical inversions in the remote sensing of particle size distributions, noting multispectral extinctions in anomalous diffraction approximation and angular and spectral scattering in diffraction approximation. A closed-form analytical inverse solution is derived in order to reconstruct the size distribution of atmospheric aerosols. The anomalous diffraction approximation to Mie's solution is used to describe the particles. Experimental data yield the geometrical area of aerosol polydispersion. Size distribution is thus found from a set of multispectral extinction measurements. In terms of the angular and spectral scattering of light in a narrow forward cone, it is shown that an analytical inverse solution may also be found for the Fraunhofer approximation to the Kirchhoff diffraction, and for an improved expression of this approximation due to Penndorf (1962) and Shifrin-Punina (1968).
Streaking images that appear only in the plane of diffraction in undoped GaAs single crystals: Diffraction imaging (topography) by monochromatic synchrotron radiation
Streaking images restricted to the direction of the diffraction (scattering) vector have been observed on transmission through undoped GaAs. These disruption images (caused by the reduction of diffraction in the direction of observation) appear both in the forward and in Bragg diffracted directions in monochromatic synchrontron radiation diffraction imaging. This previously unobserved phenomenon can be explained in terms of planar defects (interfaces) or platelets which affects the absorption coefficient in anomalous transmission. Such regions of the crystal look perfect despite the presence of imperfections when the scattering vector is not perpendicular to the normal of the platelets. The observed crystallographic orientation of these interfaces strongly indicates that they are antiphase boundaries.
Time resolved X-ray diffraction using the FIDDLE diagnostic at NIF: Preliminary assessment of diffraction precision
The Flexible Imaging Diffraction Diagnostic for Laser Experiments (FIDDLE) is a new diagnostic at the National Ignition Facility (NIF) designed to observe in situ solid-solid phase changes at high pressures using time resolved X-ray diffraction. FIDDLE currently incorporates five Icarus Ultrafast X-ray Imager sensors that take 2 ns snapshots and can be tuned to collect X-rays for tens of ns. The platform utilizes the laser power at NIF for both the laser drive and the generation of 10 keV X-rays for ~10 ns using a Ge backlighter foil. We aim to use FIDDLE to observe diffraction at different times during compression to probe the kinetics of phase changes. Pb undergoes two solid-solid phase transitions during ramp compression: from FCC to HCP and HCP to BCC. Results will be reported on some of the first shots using the FIDDLE diagnostic at NIF on ramp compressed Pb to a peak pressure of ~110 GPa and a single undriven CeO2 calibration shot. A discussion of the uncertainties in the observed diffraction is included.
Measuring Shock Stage of ltokawa Regolith Grains by Electron Back-Scattered Diffraction and Synchrotron X-Ray Diffraction
We have been analyzing Itokawa samples in order to definitively establish the degree of shock experienced by the regolith of asteroid Itokawa, and to devise a bridge between shock determinations by standard light optical petrography, crystal structures as determined by electron and X-ray diffraction techniques. We are making measurements of olivine crystal structures and using these to elucidate critical regolith impact processes. We use electron back-scattered diffraction (EBSD) and synchrotron X-ray diffraction (SXRD). We are comparing the Itokawa samples to L and LL chondrite meteorites chosen to span the shock scale experienced by Itokawa, specifically Chainpur (LL3.4, Shock Stage 1), Semarkona (LL3.00, S2), Kilabo (LL6, S3), NWA100 (L6, S4) and Chelyabinsk (LL5, S4). In SXRD we measure the line broadening of olivine reflections as a measure of shock stage. In this presentation we concentrate on the EBSD work. We employed JSC's Supra 55 variable pressure FEG-SEM and Bruker EBSD system. We are not seeking actual strain values, but rather indirect strain-related measurements such as extent of intra-grain lattice rotation, and determining whether shock state "standards" (meteorite samples of accepted shock state, and appropriate small grain size) show strain measurements that may be statistically differentiated, using a sampling of particles (number and size range) typical of asteroid regoliths. Using our system we determined that a column pressure of 9 Pa and no C-coating on the sample was optimal. We varied camera exposure time and gain to optimize mapping performance, concluding that 320x240 pattern pixilation, frame averaging of 3, 15 kV, and low extractor voltage yielded an acceptable balance of hit rate (>90%), speed (11 fps) and map quality using an exposure time of 30 ms (gain 650). We found that there was no strong effect of step size on Grain Orientation Spread (GOS) and Grain Reference Orientation Deviation angle (GROD-a) distribution; there was some effect on grain average Kernel Average Misorientation (KAM) (reduced with smaller step size for the same grain), as expected. We monitored GOS, Maximum Orientation Spread (MOS) and GROD-a differences between whole olivine grains and sub-sampled areas, and found that there were significant differences between the whole grain dataset and subsets, as well as between subsets, likely due to sampling-related "noise". Also, in general (and logically) whole grains exhibit greater degrees of cumulative lattice rotation. Sampling size affects the apparent strain character of the grain, at least as measured by GOS, MOS and GROD-a. There were differences in the distribution frequencies of GOS and MOS between shock stages, and in plots of MOS and GOS vs. grain diameter. These results are generally consistent with those reported this year. However, it is unknown whether the differences between samples of different shock states exceeds the clustering of these values to the extent that shock stage determinations can still be made with confidence. We are investigating this by examination of meteorites with higher shock stage 4 to 5. Our research will improve our understanding of how small, primitive solar system bodies formed and evolved, and improve understanding of the processes that determine the history and future of habitability of environments on other solar system bodies. The results will directly enrich the ongoing asteroid and comet exploration missions by NASA and JAXA, and broaden our understanding of the origin and evolution of small bodies in the early solar system, and elucidate the nature of asteroid and comet regolith.
Synchrotron-based diffraction-enhanced imaging and diffraction-enhanced imaging combined with CT X-ray imaging systems to image seeds at 30 keV
Utilized the upgraded Synchrotron-based non-destructive Diffraction-enhanced imaging and Diffraction-enhanced imaging coupled with CT X-ray imaging systems to image the chickpea seeds, to enhance the contrast in plant root architecture, visibility of fine structures of root architecture growth and some aspects of physiology at acceptable level. DEI-CT images were acquired with 30 keV synchrotron X-rays. A series of DEI-CT slices were assembled together, to form a 3D data set. DEI-CT images explored more structural information and morphology. Noticed detailed anatomical, physiological observations, and contrast mechanisms. Furthermore, with these systems, some of the complex plant traits, root morphology, growth of laterals and subsequent laterals can be visualized directly.
Operando X-Ray Diffraction During High Temperature Electrolysis
This work presents the design, development, and deployment of an operando X-ray diffraction (XRD) system for high-temperature electrolysis (HTE), enabling real-time characterization of solid oxide electrolysis cells (SOECs) under true operational conditions. The integration of an HTE test stand within a synchrotron radiation environment, mimicking the conditions of a laboratory setup, aims to enhance our understanding of the degradation processes affecting the performance and longevity of SOECs. Utilizing a custom furnace and a high precision motor stack assembly at the Stanford Synchrotron Radiation Lightsource (SSRL), the system revealed unparalleled insights into the structural evolution of SOEC components through various operational stages, including initial heat ramp, cell reduction, fuel ramp, and wet electrolysis. Initial results demonstrate the significant impact of the initial heating and cooling on secondary phase formation within the SOEC, highlighting the utility of operando XRD for developing more efficient and durable hydrogen production technologies.
Extended flexibility of neutron Larmor diffraction for increased diffraction range in mosaicity measurements
Larmor diffraction (LD) is a neutron scattering technique that offers enhanced resolution by harnessing the Larmor precession of neutron spins in a magnetic field. By encoding subtle changes in neutron momentum transfer into significant alterations in the Larmor phase of neutron spins, LD can be employed to measure lattice expansion, lattice distortion, and mosaicity with exceptional resolution. As originally proposed by Rekveldt et al., LD necessitates the magnetic field boundaries to be tilted to be parallel to the crystal plane of interest. Here, this report explores the fundamental principles shared between LD and spin-echo small-angle neutron scattering (SESANS). Drawing inspiration from the flexibility of SESANS to adjust magnetic field boundaries to optimize the resolution in the measurement of the neutron momentum transfers q, we will demonstrate that the strict requirement of parallel alignment between the magnetic field boundaries and the crystal plane can be relaxed for the measurements of mosaicity. Such relaxation will expand the accessible diffraction angles for these situations that are highly constrained.
Symmetrization of Strong Hydrogen Bond under High Pressure in Bihydroxide-Ion-Containing NaCu 2 (SO 4 ) 2 ·H 3 O 2 Revealed by Experimental Charge Density, Single-Crystal Electron Diffraction, and Neutron Diffraction Studies
In minerals and inorganic compounds, strong hydrogen bonding can lead to the formation of complex ionic species such as the H 3 O 2 – bihydroxide anion and Zundel cation H 5 O 2 + . We studied [NaCu 2 (SO 4 ) 2 ·H 3 O 2 ] natrochalcite, which contains bihydroxide anions and undergoes hydrogen bond symmetrization at the lowest pressure reported so far among inorganic compounds. Hydrogen bond symmetrization leads to changes in the bulk modulus, seismic wave velocities, and proton mobility and plays a primary role in high-temperature superconductivity, but its characteristics are not well understood due to a lack of systematic studies and limitations of experimental methods sensitive to this subtle change. In this work, we applied experimental charge density analysis based on in situ single-crystal X-ray diffraction data, along with the single-crystal neutron and electron diffraction experiments, to probe the behavior of hydrogen atoms during the hydrogen bond symmetrization process under high-pressure conditions. On the way to the symmetrical H-bonding, natrochalcite undergoes a series of complex redistributions of electron density, which we trace with multipole refinement and detailed analysis of changes in the Laplacian of electron density values. Additionally, we deconvoluted the equation of state (volume of the unit cell vs pressure relation) into the atomic equation of states describing dependencies of atomic charges or volumes vs pressure.
Exploring 2D X-ray diffraction phase fraction analysis with convolutional neural networks: Insights from kinematic-diffraction simulations
Abstract Deep-learning models are effective for analyzing the complex information in 2D X-ray diffraction (XRD) patterns. Accurately collecting parameters of the material sample is crucial during model training, significantly impacting model performance. In this study, we employ a kinematic-diffraction simulator to generate simulated 2D XRD patterns for Ti–6Al–4V alloy, allowing precise control of sample parameters. These simulated patterns are used to train convolutional neural networks, predicting $$\upbeta$$ β -phase volume fractions. The training data set consists exclusively of 2D XRD patterns with pure $$\upalpha$$ α - or pure $$\upbeta$$ β -phase, while the testing set incorporates patterns with intermediate phase volume fraction. In particular, we investigate how the architectures of the model influence prediction reliability and computational performance. Experimental results reveal that, with appropriate training, the convolutional neural network accurately detects intermediate phase volume fractions even trained with only pure-phase patterns, achieving a mean square error accuracy of $$9.4 \times 10^{-4}$$ 9.4 × 10 - 4 . Graphical abstract
Electromagnetic diffraction efficiencies for plane reflection diffraction gratings
The theory and computer programs, based on electromagnetic theory, for the analysis and design of echelle gratings were developed. The gratings are designed for instruments that operate in the ultraviolet portion of the spectrum. The theory was developed so that the resulting computer programs will be able to analyze deep (up to 30 wavelengths) gratings by including as many as 100 real or homogeneous diffraction orders. The program calculates the complex amplitude coefficient for each of the diffracted orders. A check on the numerical method used to solve the integral equations is provided by a conservation of energy calculation.
Grain boundary strain localization in a CdTe solar cell revealed by scanning 3D X-ray diffraction microscopy
Scanning 3DXRD was used to visualize strain localization at grain boundaries with a high spatial resolution of 100 nm.
The multiple diffraction origin of extra reflections in electron diffraction from an epitaxial system
Thin film sandwich Ag/Ni/Cu, demonstrating multiple electron diffraction
Diffraction-Based Optical Switch
Method and system for controllably redirecting a light beam, having a central wavelength lambda, from a first light-receiving site to a second light-receiving site. A diffraction grating is attached to or part of a piezoelectric substrate, which is connected to one or two controllable voltage difference sources. When a substrate voltage difference is changed and the diffraction grating length in each of one or two directions is thereby changed, at least one of the diffraction angle, the diffraction order and the central wavelength is controllably changed. A diffracted light beam component, having a given wavelength, diffraction angle and diffraction order, that is initially received at a first light receiving site (e.g., a detector or optical fiber) is thereby controllably shifted or altered and can be received at a second light receiving site. A polynomially stepped, chirped grating is used in one embodiment. In another embodiment, an incident light beam, having at least one of first and second wavelengths, lambda1 and lambda2, is received and diffracted at a first diffraction grating to provide a first diffracted beam. The first diffracted beam is received and diffracted at a second diffraction grating to produce a second diffracted beam. The second diffracted beam is received at a light-sensitive transducer, having at least first and second spaced apart light detector elements that are positioned so that, when the incident light beam has wavelength lambda1 or lambda2 (lambda1 not equal to lambda2), the second diffracted beam is received at the first element or at the second element, respectively; change in a selected physical parameter at the second grating can also be sensed or measured. A sequence of spaced apart light detector elements can be positioned along a linear or curvilinear segment with equal or unequal spacing.
Application of Powder Diffraction Methods to the Analysis of the Atomic Structure of Nanocrystals: The Concept of the Apparent Lattice Parameter (ALP)
The applicability of standard methods of elaboration of powder diffraction data for determination of the structure of nano-size crystallites is analysed. Based on our theoretical calculations of powder diffraction data we show, that the assumption of the infinite crystal lattice for nanocrystals smaller than 20 nm in size is not justified. Application of conventional tools developed for elaboration of powder diffraction data, like the Rietveld method, may lead to erroneous interpretation of the experimental results. An alternate evaluation of diffraction data of nanoparticles, based on the so-called 'apparent lattice parameter' (alp) is introduced. We assume a model of nanocrystal having a grain core with well-defined crystal structure, surrounded by a surface shell with the atomic structure similar to that of the core but being under a strain (compressive or tensile). The two structural components, the core and the shell, form essentially a composite crystal with interfering, inseparable diffraction properties. Because the structure of such a nanocrystal is not uniform, it defies the basic definitions of an unambiguous crystallographic phase. Consequently, a set of lattice parameters used for characterization of simple crystal phases is insufficient for a proper description of the complex structure of nanocrystals. We developed a method of evaluation of powder diffraction data of nanocrystals, which refers to a core-shell model and is based on the 'apparent lattice parameter' methodology. For a given diffraction pattem, the alp values are calculated for every individual Bragg reflection. For nanocrystals the alp values depend on the diffraction vector Q. By modeling different a0tomic structures of nanocrystals and calculating theoretically corresponding diffraction patterns using the Debye functions we showed, that alp-Q plots show characteristic shapes which can be used for evaluation of the atomic structure of the core-shell system. We show, that using a simple model of a nanocrystal with spherical shape and centro-symmetric strain at the surface shell we obtain theoretical alp-Q values which match very well the alp-Q plots determined experimentally for Sic, GaN, and diamond nanopowders. The theoretical models are defined by the lattice parameter of the grain core, thickness of the surface shell, and the magnitude and distribution of the strain field in the surface shell. According to our calculations, the part of the diffraction pattern measured at relatively low diffraction vectors Q (below 10/angstrom) provides information on the surface strain, whle determination of the lattice parameters in the grain core requires measurements at large Q-values (above 15 - 20/angstrom).