Calculation Of Diffraction Intensities Research Articles

Structural variety and stability of carbon honeycomb cellular structures

A new synthesized carbon honeycomb allotrope reported previously, built from graphene nanoribbons connected by sp3-bonded carbon junction lines, forms a family of cellular structures with high porosity and sorption capacity. In this work we first propose a complete set of possible honeycomb structures of different wall chiralities both the armchair and zigzag types, including considered earlier only theoretically, for the structural analysis of such structures by means of the high-energy electron diffraction method. The “completeness” of the model set made it possible to obtain nearly perfect coincidence of the experimental and calculated diffraction intensities. The contribution of graphite fragments and random structures, also involved in the analysis, turned out to be zero. Only a limited number of honeycomb structures of different types almost ideally describes the experiment. Thus we conclude that polydomain structures corresponding to a set of basic models formed in this investigation rather than formations dominated by random structures. The samples under study have demonstrated the unique cellular stability since were stored in vacuum ∼4.5 months before the reported measurements. Along with the original results the history of the carbon honeycomb cellular structures is briefly presented.

Structural and electrical properties of Cu-doped Ni–Zn nanocrystalline ferrites for MLCI applications

Polycrystalline Cu substituted Ni–Zn ferrites with chemical composition Ni[Formula: see text]Zn[Formula: see text]-Cu[Formula: see text]Fe2O4 (x = 0.00 to 0.25 in steps of 0.05) have been prepared by citrate gel autocombustion method. The samples for electrical properties have been sintered at 900[Formula: see text]C for 4 h. The X-ray diffraction patterns of all samples indicate the formation of single phase spinel cubic structure. The value of lattice parameter is decreases with increasing Cu concentration. The estimated cation distribution can be derived from X-ray diffraction intensity calculations and IR spectra. The tetrahedral and octahedral bond lengths, bond angles, cation–cation and cation–anion distances were calculated by using experimental lattice parameter and oxygen positional parameters. It is observed that Cu ions are distributed in octahedral site and subsequently Ni and Fe ions in tetrahedral site. The grain size of all samples has been calculated by Scanning Electron Microscopy (SEM) images. The variations in DC electrical resistivity and dielectric constant have been explained on the basis of proposed cation distribution.

Structural and dielectric studies of Mg2+ substituted Ni–Zn ferrite

AbstractPolycrystalline ferrites having the chemical formula Ni0.65−xZn0.35MgxFe2O4 (0 ⩽ x ⩽ 0.2) were prepared by solid state reaction route in steps of x = 0.04. The effect of incorporation of diamagnetic divalent magnesium at expense of nickel on the structural properties of these ferrites has been studied. The proposed cation distribution was derived from theoretical X-ray diffraction intensity calculations. These intensity calculations were done by varying the concentration of magnesium ions over two sites in the lattice. For a certain amount of magnesium concentration, the calculated and observed X-ray diffraction intensities were found to be in good agreement. Site occupancy of divalent diamagnetic magnesium was established from this cation distribution. The octahedral environment facilitates magnesium to enter the B-site at about 95 % and the remaining 5 % occupy tetrahedral sites (A-sites). The movements of cations between tetrahedral and octahedral sites as a result of magnesium substitution were discussed in the view of structural parameters, such as tetrahedral and octahedral bond lengths, cation-cation and cation-anion distances, bond angles and hopping lengths, which were calculated using experimental lattice constants and oxygen parameters. All structural parameters showed slight deviations from ideal values. Among all magnesium substituted samples, the ones with x = 0.12 exhibited insignificant variation in view of structural properties. Dielectric measurements were conducted at a standard frequency of 1 kHz. Large values of the recorded dielectric constants displayed typical characteristics of bulk ferrites. Both dielectric constant and loss values showed mixed variations, attributed to the loss of zinc ions during the sintering process.

Efficient calculation of diffracted intensities in the case of nonstationary scattering by biological macromolecules under XFEL pulses.

The calculation of diffracted intensities from an atomic model is a routine step in the course of structure solution, and its efficiency may be crucial for the feasibility of the study. An intense X-ray free-electron laser (XFEL) pulse can change the electron configurations of atoms during its action. This results in time-dependence of the diffracted intensities and complicates their calculation. An algorithm is suggested that enables this calculation with a computational cost comparable to that for the time-independent case. The intensity is calculated as a sum of the `effective' intensity and a finite series of `correcting' intensities. These intensities are calculated in the conventional way but with modified atomic scattering factors that are specially derived for a particular XFEL experiment. The total number of members of the series does not exceed the number of chemically different elements present in the object under study. This number is small for biological molecules; in addition, the correcting terms are negligible within the parameter range and accuracy acceptable in biological crystallography. The time-dependent atomic scattering factors were estimated for different pulse fluence levels by solving the system of rate equations. The simulation showed that the changes in a diffraction pattern caused by the time-dependence of scattering factors are negligible if the pulse fluence does not exceed the limit that is currently achieved in experiments with biological macromolecular crystals (10(4) photons Å(-2) per pulse) but become significant with an increase in the fluence to 10(6) or 10(8) photons Å(-2) per pulse.

Structure refinement from precession electron diffraction data

Electron diffraction is a unique tool for analysing the crystal structures of very small crystals. In particular, precession electron diffraction has been shown to be a useful method for ab initio structure solution. In this work it is demonstrated that precession electron diffraction data can also be successfully used for structure refinement, if the dynamical theory of diffraction is used for the calculation of diffracted intensities. The method is demonstrated on data from three materials - silicon, orthopyroxene (Mg,Fe)(2)Si(2)O(6) and gallium-indium tin oxide (Ga,In)(4)Sn(2)O(10). In particular, it is shown that atomic occupancies of mixed crystallographic sites can be refined to an accuracy approaching X-ray or neutron diffraction methods. In comparison with conventional electron diffraction data, the refinement against precession diffraction data yields significantly lower figures of merit, higher accuracy of refined parameters, much broader radii of convergence, especially for the thickness and orientation of the sample, and significantly reduced correlations between the structure parameters. The full dynamical refinement is compared with refinement using kinematical and two-beam approximations, and is shown to be superior to the latter two.

Response to Comment on “The Local Structure of Amorphous Silicon”

The averaged diffraction data alone cannot distinguish between models with different heterogeneous structures at length scales of about 2 nanometers, even when using high-resolution data. Although our approach to calculating diffraction intensities from the model differs from that of Roorda and Lewis, paracrystallinity in amorphous silicon is undeniably evident in the raw experimental fluctuation electron microscopy data.

In-Plane and Out-of-Plane Diffraction of H2 from Ru(001)

H(2) diffraction from the Ru(001) surface has been measured for incident energies E(i) = 78-150 meV and incident angles Θ(i) = 22.1-64.1°. In-plane and out-of-plane angular distributions were measured for incidence along [110] and [100] directions. Out-of-plane diffraction channels were found to be predominant for the explored experimental conditions regardless of the incidence direction. An analysis of diffraction intensities reveals that diffraction out of the scattering plane is enhanced for high incidence angles. Diffractive transitions with wavevector change in the surface plane and transversal to the incidence direction ΔK(⊥) were observed to be favored among the out-of-plane diffractive transitions. These features could be reproduced by model calculations of diffraction intensities performed using a three-dimensional soft potential. This suggests that a kinematic effect is responsible for the large out-of-plane intensities observed in experiment, more than any other features of the six-dimensional H(2)-surface interaction potential.

PCED2.0—A computer program for the simulation of polycrystalline electron diffraction pattern

A computer program for the simulation of polycrystalline electron diffraction patterns is described. PCED2.0, an upgraded version of the previous JECP/PCED, can be used as a teaching aid and research tool for phase identification, microstructure texture analysis, and phase fraction determination. In addition to kinematical theory for diffraction intensity calculation of polycrystalline samples, Blackman two-beam dynamical correction is included. March model is used for out-of-plane and in-plane texture simulation. A pseudo-Voigt function is used for the peak profile fitting of diffraction rings. User-friendly interface is improved in the handling of experimental diffraction data and the flexibility of indexing. Application of the program for the analysis of FePt thin films is given as an example.

Testing the triple network structure of the cubic Im3̄m (I) phase by isomorphous replacement and model refinement

This study provides further tests of the validity of the triple network structure of the body-centred Imm (I) cubic phase in polycatenar (phasmidic) liquid crystals, proposed by Zeng et al., Nat. Mater., 2005, 4, 562. New hemiphasmid compounds were synthesised, two of which (6 and 7) display the above phase, while 8 shows the hexagonal columnar phase. Comparison of 3-d electron density maps based on small-angle X-ray diffraction of two compounds with different proportions of high and low electron density regions (aliphatic and aromatic) helped with phasing the X-ray reflections of the cubic structure. This variant of the isomorphous replacement technique gave further support to the triple network structure proposed earlier. Furthermore, fitting calculated diffraction intensities of geometrical models to the observed ones confirmed that the oscillating segment cross-section of two of the three networks (the “octahedral networks”) are genuine structural features rather than artefacts. A rational explanation is proposed for the variable thickness of the aromatic network segments. The study has highlighted complexities of molecular packing in bicontinuous phases of thermotropic liquid crystals that are not encountered in related phases in lyotropics or block copolymers.

Wave packet calculations for helium scattering by a xenon monolayer

The interaction of low energy helium atomic beams with a rigid monolayer of xenon atoms was studied with a pseudo spectral wave packet method. The calculated diffraction intensities were compared to experimental scan curve data, finding similar trends in the relative values of the peaks. The calculated elastic diffraction patterns were strongly asymmetric for beams incident along directions other than ΓK and ΓM, supporting the argument that the inelastic scattering will also be very sensitive for experimental angles of incidence which deviate slightly from the high-symmetry directions.

Small-angle X-ray scattering analysis of the periodic tricontinuous network structure of symmetricABCtriblock copolymers

The periodic tricontinuous network structure (TNS) of symmetric isoprene (I)–styrene (S)–2-vinylpyridine (P) triblock copolymers has been studied by small-angle X-ray scattering (SAXS). The observed SAXS profiles were compared with the calculated diffraction intensities based on the model electron density distributions constructed for a pair of surfaces parallel to the infinite periodic minimal surface. In the model, an imaginary minimal surface exists at the centre of the styrene labyrinth and both I/S and S/P interfaces are on the parallel surfaces, powder orientation of the model structure being assumed. The experimental SAXS patterns for the samples with different styrene volume fractions,i.e.0.48 and 0.66, which are the lower and higher extremes for tricontinuous network structure, are well explained by the model calculation for surfaces parallel to the Gyroid minimal surface.

Quantitative intensity measurement of equal thickness fringes in Si and MgO crystal images with an energy-filtering transmission electron microscope using an imaging plate.

Quantitative measurement of intensity profiles of equal thickness fringes has been carried out in Si and MgO crystal images with an energy-filtering transmission electron microscope using an imaging plate. The crystals have a 90 degrees wedge-shape with [110] surfaces for Si and with [100] surfaces for MgO, and are observed under the exact axial incidence of a 200 keV electron beam along the [100] axis for Si and along the [110] axis for MgO. The intensities are measured in bright field and 022 and 040 dark field images for Si, and in bright field and 111, 002, 220, 113, 222, and 004 dark field images for MgO, with and without an energy slit having +/- 5 eV energy width for incident electrons. The intensity profiles obtained from the images are presented as standard experimental data for calculation of electron diffraction intensities. A few simulation programs for high-resolution transmission electron microscopy are checked by comparing the calculated diffraction intensities with the experimental data. The complex potential suitable for matching the data is discussed.

Photoelectron diffraction intensity calculation by using tensor low-energy electron diffraction theory

We applied the tensor low-energy electron diffraction (LEED) approximation to photoelectron diffraction (PED) for efficient structural searches of complex surfaces including multiple parameters to be optimized. It turned out that the tensor LEED scheme can be included into the multiple-scattering cluster model usually utilized for PED intensity calculation with slight modification concerning the treatment of the atomic displacements of photoelectron emitters. The results of numerical calculation for a simple system show that the approximation is applicable to PED over almost the same range of displacements as in tensor LEED.

Structure Analysis of C60 Low-Temperature Phase by Electron Crystallography with Cryo-TEM

The crystal structure of C60 at liquid helium temperature was examined by the electron diffraction method using an imaging plate and cryo-TEM (transmission electron microscopy). The crystal of C60 was so thin that the electron scattering from this sample was able to be treated kinematically. However, the least-squares fitting among observed and kinematically calculated diffraction intensities resulted in an R-factor of 0.23 for a structure model with only one major orientation. Similar large R-factors are usually reported in the electron crystallography of thin crystals, in which a single perfect structure was assumed as a model structure. By considering structural disorders in the C60 crystal, however, the R-factor could be reduced to 0.12, when a minor crystal in a different orientation and also the f.c.c. (face-centered cubic) component were introduced to the model in addition to the major orientation crystal. Disorder in the crystal might be as important a factor as the dynamical scattering effect to be considered in electron crystallography for analyzing structures of thin crystals.

XRDA: a program for energy-dispersive X-ray diffraction analysis on a PC

XRDA, an analysis software for energy-dispersive X-ray diffraction data obtained from samples compressed in a diamond-anvil cell using synchrotron radiation, is described. The code takes advantage of the recent availability of inexpensive fast PC's and the widespread Windows graphical environment. The program offers an efficient way to analyze the numerous diffraction patterns usually recorded as a function of pressure. In addition to X-ray data file management, peak profile fitting and diffraction intensity calculations, crystalline structure determinations can easily be performed.

Projection description of cubic quasiperiodic crystals with phason strains

A new projection description for a cubic quasiperiodic crystal (CQC), including a projection matrix, diffraction-intensity calculation and a linear phason matrix, has been proposed. The simulated electron diffraction patterns with appropriate phason parameters agree well with the experimental ones obtained for a rapidly solidified V6Ni16Si7 alloy. The transition from the CQC to its crystalline approximants is treated using the linear-phason-strain concept.

Replication of very small periodic gratings with proximity x-ray lithography

Abstract This paper describes our recent results in high resolution synchrotron radiation lithography. Theoretically we show an image analysis based on the absorbed dose distribution in the x-ray resist rather than on the diffraction intensity calculations. Experimental results are presented, demonstrating a successful replication of very small periodic gratings using high resolution SiC/W masks and a high performance commercial x-ray stepper.

Dirac-fock calculations of scattering factors and mean inner potentials for neutral and ionised atoms

Tables of X-ray and electron scattering factors are essential for programs that calculate diffraction intensities or simulate images. These tables are calculated from atomic charge densities derived from Hartree Fock programs for atoms. The most frequently used results are those due to Doyle and Turner who used Coulthard's relativistic Hartree Fock program. They did not calculate scattering factors for all elements and other results using different programs were used to complete the tables given in the International Tables for Crystallography. As microscopy and diffraction become more quantitative it has become important to reexamine the calculation of atomic scattering factors using more recent Hartree Fock codes to quantify more precisely differences due to solid state effects. We also feel it is desirable to calculate all naturally occuring elements, and their common ionised states, using the same program.The charge densities were calculated using the Multi-Configuration Dirac-Fock code of Grant et al.

The complex coordinate scattering theroy and its application to the study of the surface asymmetry effect in helium diffraction from copper

AbstractThe Complex Coordinate Scattering Theory is reformulated for the general case of a time‐independent Hamiltonian. It is applied to scattering of He atoms from a Cu(115) crystal surface by constracting the Green operator for the T‐matrix from the eigenvectors of both the complex scaled Hamiltonian and its transposed (“right” and “left” eigenvectors), which are different in this case. The weakly asymmetric corrugation function describing the (115) face of Cu is shown to cause a strong dependence of the calculated diffraction intensities upon the direction of the incident atomic beam. The calculated transition probabilities are in excellent agreement with the experimentally measured ones, previously obtained by Perreau and Lapujoulade. We show that additional information about the gas atom/surface physisorption interaction potential can be obtained if the incident angle of the atomic beam (the angles between the beam and the surface normal) is changed from γ to −γ. © 1993 John Wiley & Sons, Inc.

Alkali-metal-plated graphite surfaces: He interaction and diffraction

Theoretical calculations and experimental data are reported for He scattering from a graphite surface covered with an alkali-metal overlayer. The computed interaction potential has a very shallow well depth (⩽, 1 meV) in the case of a (2 × 2) layer. The predicted corrugation is also very small, corresponding to rather weak elastic diffraction beams. The calculated diffraction intensity is less than 2 percent of the specular intensity for a 17.4 meV He beam. No He diffraction was observed in the experiment on K, Rb, and Cs overlayers, indicating that these surfaces are even less corrugated than the calculation predicts.