Computer calculated diffraction patterns.
Diffraction patterns calculated by computing two dimensional Fourier transform of aperture electric field
Andrews, H. C.↗
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Fast calculation of diffraction patterns from an ensemble of aligned molecules
We report an algorithm to calculate electron diffraction patterns for molecules with anisotropic angular distribution, which is significantly faster than existing methods. The algorithm uses a transform to convert the molecular orientation distribution, which is a function of three Euler angles, to the atom-pair distribution functions which depend on the polar and azimuthal angles. The diffraction signal can then be calculated from the atom-pair distributions. We demonstrate the computation method numerically by calculating electron diffraction patterns for a symmetric top molecule (trifluoroiodomethane) and an asymmetric top molecule (formaldehyde) and show that it reduces the calculation time by approximately two orders of magnitude compared to the standard brute-force method. Here, the method can also be applied to the calculation of x-ray diffraction patterns.
74 ATOMIC AND MOLECULAR PHYSICS↗
Disorder and diffuse scattering in single-chirality (TaSe 4 ) 2 I crystals
The quasi-one-dimensional chiral compound (TaSe 4 ) 2 I has been extensively studied as a prime example of a topological Weyl semimetal. Upon crossing its phase transition temperature $T$ CDW ≈263K, (TaSe 4 ) 2 I exhibits incommensurate charge density wave (CDW) modulations described by the well-defined propagation vector ∼(0.05,0.05,0.11), oblique to the TaSe 4 chains. Although optical and transport properties greatly depend on chirality, there is no systematic report about chiral domain size for (TaSe 4 ) 2 I. In this study, our single-crystal scattering refinements reveal a bulk iodine deficiency, and Flack parameter measurements on multiple crystals demonstrate that separate (TaSe 4 ) 2 I crystals have uniform handedness, supported by direct imaging and helicity-dependent terahertz emission spectroscopy. Our single-crystal x-ray scattering and calculated diffraction patterns identify multiple diffuse features and create a real-space picture of the temperature-dependent (TaSe 4 ) 2 I crystal structure. Further, the short-range diffuse features are present at room temperature and decrease in intensity as the CDW modulation develops. These transverse displacements, along with electron pinning from the iodine deficiency, help explain why (TaSe 4 ) 2 I behaves as an electronic semiconductor at temperatures above and below $T$ CDW , despite a metallic band structure calculated from density functional theory of the ideal structure.
36 MATERIALS SCIENCE↗
The diffraction of satellite signals by isolated ionospheric irregularities
Isolated ionospheric irregularities, describing refraction and diffraction pattern calculations for satellite signals
Titheridge, J. E.↗
Effect of the Chemical State of the Surface on the Relaxation of the Surface Shell Atoms in SiC and GaN Nanocrystals
The effect of the chemical state of the surface of nanoparticles on the relaxation in the near-surface layer was examined using the concept of the apparent lattice parameter (alp) determined for different diffraction vectors Q. The apparent lattice parameter is a lattice parameter determined either from an individual Bragg reflection, or from a selected region of the diffraction pattern. At low diffraction vectors the Bragg peak positions are affected mainly by the structure of the near-surface layer, while at high Q-values only the interior of the nano-grain contributes to the diffraction pattern. Following the measurements on raw (as prepared) powders we investigated powders cleaned by annealing at 400C under vacuum, and the same powders wetted with water. Theoretical alp-Q plots showed that the structure of the surface layer depends on the sample treatment. Semi-quantitative analysis based on the comparison of the experimental and theoretical alp-Q plots was performed. Theoretical alp-Q relations were obtained from the diffraction patterns calculated for models of nanocrystals with a strained surface layer using the Debye functions.
Palosz, B.↗
Structure and Synthesizability of Iron–Sulfur Metal–Organic Frameworks
Sulfur-based metal–organic frameworks (MOFs) and coordination polymers (CPs) are an emerging class of hybrid materials that have received growing attention due to their magnetic, conductive, and catalytic properties with potential applications in electrocatalysis and energy storage. In this work, we report a high-throughput virtual screening protocol to predict the synthesizability of candidate metal–sulfur MOFs/CPs by computing the thermodynamically stable structures resulting from a particular combination of metal cluster, linker, cation, and synthetic conditions. Free energies are computed by using all-atom classical mechanical thermodynamic integration. Low-free-energy structures are refined using ab initio density functional theory, and pair distribution functions and powder X-ray diffraction patterns are calculated to complement and guide experimental structure determination. We validate the computational approach by retrospective predictions of the stable structure produced by experimental syntheses, and a subsequent screen predicts Fe 4 S 4 -BDT–TPP as a new thermodynamically stable one-dimensional (1D) CP comprising a redox-active Fe 4 S 4 cluster, a 1,4-benzenedithiolate (BDT) linker, and a tetraphenylphosphonium (TPP) countercation. Furthermore, this material is experimentally synthesized, and the 1D chain structure of the crystal is confirmed using microcrystal electron diffraction. The computational screening pipeline is generically transferable to neutral and ionic MOFs/CPs comprising arbitrary metal clusters, linkers, cations, and synthetic conditions, and we make it freely available as an open source tool to guide and accelerate the discovery and engineering of novel porous materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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).
Palosz, B.↗
Unsupervised anomaly detection in MeV ultrafast electron diffraction
MeV ultrafast electron diffraction (MUED) is a pump-probe technique used to study the dynamic structural evolution of materials. An ultrashort laser pulse triggers structural changes, which are then probed by an ultrashort relativistic electron beam. To overcome low signal-to-noise ratios, diffraction patterns are averaged over thousands of shots. However, shot-to-shot instabilities in the electron beam can distort individual patterns, introducing uncertainty. Improving MUED accuracy requires detecting and removing these anomalous patterns from large datasets. In this work, we developed a fully unsupervised methodology for the detection of anomalous diffraction patterns. Using a convolutional autoencoder, we calculate the reconstruction mean squared error of the diffraction patterns. Based on the statistical analysis of this error, we provide the user an estimation of the probability that the pattern is normal, which also allows a posterior visual inspection of the images that are difficult to classify. This method has been trained with only 100 diffraction patterns and tested on 1521 patterns, resulting in a false positive rate between 0.2% and 0.4%, with a training time of 10 s per image and a test time of about 1 s per image. Here, the proposed methodology can also be applied to other diffraction techniques in which large datasets are collected that include faulty images due to instrumental instabilities.
43 PARTICLE ACCELERATORS↗
Analysis of near-field Cassegrain reflector - Plane wave versus element-by-element approach
A near-field Cassegrain reflector (NFCR) is an effective way to magnify a small phased array into a much larger-aperture antenna for limited scan applications. Traditionally the pattern analysis of NFCR is based on a plane wave approach, which simplifies the computation tremendously, but fails to provide design information about the most critical component of the whole antenna system, the feed array. Currently available computers make it possible to calculate the pattern of an NFCR by a more exact element-by-element approach. Each element in the feed array is considered individually, and the diffraction pattern from the subreflector is calculated by the geometrical theory of diffraction (including uniform theories at the shadow boundaries). The field contributions from all elements are superimposed at the curved main reflector surface, and a physical-optics integration is performed to obtain the secondary pattern.
Houshmand, Bijan↗
Exact and fast calculation of the X-ray pair distribution function
A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.
36 MATERIALS SCIENCE↗
Pattern distortion due to edge diffractions
Microwave aperture antenna in finite size ground plane, calculating radiation pattern distortion by superposition of boundary value and wedge diffraction solutions
Balanis, C. A.↗
Coexistence of vitreous and crystalline phases of H 2 O at ambient temperature
Formation of vitreous ice during rapid compression of water at room temperature is important for biology and the study of biological systems. Here, we show that Raman spectra of rapidly compressed water at greater than 1 GPa at room temperature exhibits the signature of high-density amorphous ice, whereas the X-ray diffraction (XRD) pattern is dominated by crystalline ice VI. To resolve this apparent contradiction, we used molecular dynamics simulations to calculate full vibrational spectra and diffraction patterns of mixtures of vitreous ice and ice VI, including embedded interfaces between the two phases. We show quantitatively that Raman spectra, which probe the local polarizability with respect to atomic displacements, are dominated by the vitreous phase, whereas a small amount of the crystalline component is readily apparent by XRD. The results of our combined experimental and theoretical studies have implications for detecting vitreous phases of water, survival of biological systems under extreme conditions, and biological imaging. The results provide additional insight into the stable and metastable phases of H 2 O as a function of pressure and temperature, as well as of other materials undergoing pressure-induced amorphization and other metastable transitions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Programs for calculating cell parameters in electron and X-ray diffraction
Ten programs for calculating cell parameters from single crystal electron diffraction patterns are presented. Most of the programs, written for use with a programmable desk calculator, are also applicable to X-ray diffraction work. The programs can be used to calculate d-spacings from electron diffraction plate measurements, and to determine cell data (including interplanar angles and zone angles) for all crystal systems. A program for rhombohedral-hexagonal conversions and one for matching crystal data from standards with apparent crystal parameters found in diffraction patterns are included. Because they allow rapid determination of data not present in X-ray listings or elsewhere in the literature, the programs facilitate identification of unknowns.
Polkowski, G.↗
Electromagnetic scattering by impedance structures
The scattering of electromagnetic waves from impedance structures is investigated, and current work on antenna pattern calculation is presented. A general algorithm for determining radiation patterns from antennas mounted near or on polygonal plates is presented. These plates are assumed to be of a material which satisfies the Leontovich (or surface impedance) boundary condition. Calculated patterns including reflection and diffraction terms are presented for numerious geometries, and refinements are included for antennas mounted directly on impedance surfaces. For the case of a monopole mounted on a surface impedance ground plane, computed patterns are compared with experimental measurements. This work in antenna pattern prediction forms the basis of understanding of the complex scattering mechanisms from impedance surfaces. It provides the foundation for the analysis of backscattering patterns which, in general, are more problematic than calculation of antenna patterns. Further proposed study of related topics, including surface waves, corner diffractions, and multiple diffractions, is outlined.
Balanis, Constantine A.↗
Note on use of slope diffraction coefficients for aperture antennas on finite ground planes
The use of slope diffraction coefficients along with regular diffraction coefficients for calculating the radiation patterns of aperture antennas in a finite ground plane is investigated. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The expressions for the incident magnetic field in terms of the magnetic current in the aperture are given. The slope of the incident magnetic field is calculated and closed form expressions are presented.
Cockrell, C. R.↗
Method to Determine the Distribution of Substituted or Intercalated Ions in Transition-Metal Dichalcogenides: Fe x VSe 2 and Fe 1– x V x Se 2
Multiple techniques are combined to determine the amount of intercalation and/or substitution in transition-metal dichalcogenides. Kiessig fringes in the X-ray reflectivity pattern are used to calculate thickness. Laue oscillations in the specular diffraction pattern of the crystallographically aligned samples determine the number of unit cells in the coherently diffracting domains. The amount of impurity phase(s) is estimated by the difference between the thickness of the films and the size of the domains. If the difference is small relative to the total film thickness, the composition of the crystalline phase can be determined from X-ray fluorescence measurements. The number of unit cells possible can be calculated from the amount of each element determined by X-ray fluorescence measurements using in-plane lattice parameters, and the amount of the anion should agree with the number of unit cells determined from the Laue oscillations. The total amount of the metal relative to that required for the number of unit cells from the Laue oscillations provides a direct determination of the relative amount of intercalation and/or substitution in the crystalline dichalcogenide. So the utility of this approach is illustrated in Fe x V 1–y Se 2 samples. The relative amount of intercalation versus substitution was determined independently using electron microscopy and Rietveld refinement of diffraction patterns and is consistent with this new approach.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Table of interplanar spacings for crystal-structure determinations by X-ray diffraction with molybdenum, copper, cobalt, iron, and chromium radiations
For a simple diffraction pattern, the time required to calculate interplanar distances from measurements of the pattern is not excessive. If more than a few lines are present, however, or if several patterns are to be studied, it is very advantageous to have available a table giving interplanar spacings directly in terms of the linear measurements made on the film of the lines appearing on the diffraction pattern. The preparation of the table given here was undertaken when the expansion of research activities involving X-ray diffraction techniques indicated that such a table would greatly decrease the time required to analyze diffraction patterns. The table was prepared for use with K alpha(sub 1) radiation from the following target materials: molybdenum, copper, cobalt, iron, and chromium.
METALS - STRUCTURES↗
Ultrahigh thermal conductivity in three-dimensional covalent organic frameworks
Covalent organic frameworks (COFs) are a new, growing class of crystalline polymers with exceptional characteristics such as low density, mechanical strength, and flexibility. Taking three-dimensional (3D) COF-300 derivatives as an example, we apply molecular dynamics simulations to show that ultrahigh thermal conductivity (>15 W/(mK)) is achieved at a pore size of d = 0.63 nm. This is the first observation of such an outstanding intrinsic thermal conductivity of a 3D polymer in all directions. Further temperature-dependent thermal conductivity calculations and X-ray diffraction (XRD) patterns highlight the importance of maintaining microscopic order for a large thermal conductivity. We also demonstrate that the tunability and anisotropy in COFs provide sufficient room to engineer and obtain desired thermal conductivity. These findings provide a fundamental understanding of structure-thermal conductivity relation in COFs and shine a light on high-thermal-conductivity COFs for thermal management applications.
36 MATERIALS SCIENCE↗