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41.
I. Lobato D. Van Dyck 《Acta Crystallographica. Section A, Foundations and Advances》2014,70(6):636-649
An efficient procedure and computer program are outlined for fitting numerical X‐ray and electron scattering factors with the correct inclusion of all physical constraints. The numerical electron scattering factors have been parameterized using five analytic non‐relativistic hydrogen electron scattering factors as basis functions for 103 neutral atoms of the periodic table. The inclusion of the correct physical constraints in the electron scattering factor and its derived quantities allows the use of the new parameterization in different fields. In terms of quality of the fit, the proposed parameterization of the electron scattering factor is one order of magnitude better than the previous analytic fittings. 相似文献
42.
Steen Hansen 《Journal of Applied Crystallography》2011,44(2):265-271
The effect of deviation from spherical symmetry is studied for the structure factor. This is done by combining the analytical expression for the excluded volume of an ellipsoid of revolution with the expression for the excluded volume correlation function for a sphere. This approach makes it possible to estimate the effect of small deviations from spherical symmetry as a function of axial ratio and volume fraction for relatively low volume fractions. The calculations are relevant for the case of short‐range potentials where the Percus–Yevick formula is frequently applied, and indicate that even minor deviations from spherical symmetry may lead to significant effects on the structure factor at low scattering angles. 相似文献
43.
Jianglin Feng 《Journal of Applied Crystallography》2011,44(3):625-627
A method is proposed for the initial identification of non‐hydrogen atomic species in a crystal from X‐ray diffraction intensities when the chemical composition is not available. When atom positions are determined, a portion of the scattering factor curve for each atom can be obtained by Fourier synthesis with reflections from concentric shells. From these curves, the atomic number and the isotropic displacement parameter for all non‐H atoms, and the scaling constant of the structure factors, can be approximately determined. 相似文献
44.
X. H. Sang A. Kulovits J. M. K. Wiezorek 《Acta Crystallographica. Section A, Foundations and Advances》2010,66(6):694-702
Accurate Debye–Waller (DW) factors and several low‐index structure factors of chemically ordered β‐NiAl at different temperatures have been measured using an off‐zone‐axis multi‐beam convergent‐beam electron diffraction method. The temperature dependences of DW factors of Ni and Al atoms are compared with previous experimental measurements and theoretical calculations. The temperature below which the DW factor of Ni becomes smaller than that of Al was found to be lower than previously reported. Structure factors are determined with an accuracy of 0.05% and compared with prior reports. 相似文献
45.
X. H. Sang A. Kulovits J. M. K. Wiezorek 《Acta Crystallographica. Section A, Foundations and Advances》2010,66(6):685-693
Debye–Waller (DW) factors and structure factors have been measured for Si using convergent‐beam electron diffraction (CBED) experiments with a transmission electron microscope equipped with a field‐emission gun and a post‐column energy‐filtering device. Si has been used here to evaluate the accuracy of multi‐beam near‐zone‐axis orientations for the simultaneous refinement of DW factors and multiple structure factors. Strong dynamic interactions among different beams are obtained by tilting the crystal to specific four‐ or six‐beam orientations near major zone axes, which provide sufficient sensitivity to determine accurate DW factors and structure factors. The DW factors of Si were measured using four‐beam conditions near the [001] zone axis for temperatures ranging from 96 to 300 K. A comparison of the multi‐beam near‐zone‐axis orientations with other CBED methods for DW and structure factor Fg refinement is presented. 相似文献
46.
Herein, a general method to calculate the scattering functions of polyhedra, including both regular and semi‐regular polyhedra, is presented. These calculations may be achieved by breaking a polyhedron into sets of congruent pieces, thereby reducing computation time by taking advantage of Fourier transforms and inversion symmetry. Each piece belonging to a set or subunit can be generated by either rotation or translation. Further, general strategies to compute truncated, concave and stellated polyhedra are provided. Using this method, the asymptotic behaviors of the polyhedral scattering functions are compared with that of a sphere. It is shown that, for a regular polyhedron, the form factor oscillation at high q is correlated with the face‐to‐face distance. In addition, polydispersity affects the Porod constant. The ideas presented herein will be important for the characterization of nanomaterials using small‐angle scattering. 相似文献
47.
Crystallographic least squares are a fundamental tool for crystal structure analysis. In this paper their properties are derived from functions estimating the degree of similarity between two electron‐density maps. The new approach leads also to modifications of the standard least‐squares procedures, potentially able to improve their efficiency. The role of the scaling factor between observed and model amplitudes is analysed: the concept of unlocated model is discussed and its scattering contribution is combined with that arising from the located model. Also, the possible use of an ancillary parameter, to be associated with the classical weight related to the variance of the observed amplitudes, is studied. The crystallographic discrepancy factors, basic tools often combined with least‐squares procedures in phasing approaches, are analysed. The mathematical approach here described includes, as a special case, the so‐called vector refinement, used when accurate estimates of the target phases are available. 相似文献
48.
Kenneth A. Rubinson Christopher Stanley Susan Krueger 《Journal of Applied Crystallography》2008,41(2):456-465
Small‐angle neutron scattering (SANS) provides a unique method to probe soft matter in the 10–100 nm length scale in solutions. In order to determine the shape and size of biological macromolecular structures correctly with SANS, a background‐subtracted, undistorted scattering curve must be measured, and the required accuracy and precision is especially needed at the short‐length‐scale limit. A true scattering curve is also needed to discern whether intermolecular interactions are present, which also are probed in the SANS experiment. This article shows how to detect intermolecular interactions so that subsequent structure modeling can be performed using only data that do not contain such contributions. It is also shown how control of many factors can lead to an accurate baseline, or background, correction for scattering from proteins, especially to account for proton incoherent scattering. Failure to make this background correction properly from proteins, polymers, nucleic acids and lipids can result in incorrect values for the calculated shapes and sizes of the molecules as well as the derived magnitudes of the intermolecular interactions. 相似文献
49.
Kyuyoung Heo Jinhwan Yoon Sangwoo Jin Jehan Kim Kwang‐Woo Kim Tae Joo Shin Bonghoon Chung Taihyun Chang Moonhor Ree 《Journal of Applied Crystallography》2008,41(2):281-291
Grazing‐incidence X‐ray scattering (GIXS) formulas for hexagonally perforated layer (HPL) structures with ABC and AB stacking sequences were derived, and used in the quantitative analysis of the two‐dimensional GIXS patterns of polystyrene‐b‐polyisoprene (PS‐b‐PI) diblock copolymer thin films supported on silicon substrates. This quantitative analysis provided detailed information (shape, size and size distribution, packing order, layer packing sequence, and orientation) about the HPL structure of the diblock copolymer films that cannot be easily obtained with conventional X‐ray and neutron scattering techniques or with conventional microscopic methods. 相似文献
50.
Kyungseon Joo 《中国物理 C》2009,33(12):1254-1256
We report the analysis status of single π0electroproduction in the resonance region to study the electromagnetic excitation of the nucleon resonances. The study is aimed at understanding of the internal structure and dynamics of the nucleon. The experiment was performed using an unpolarized cryogenic hydrogen target and 2.0 and 5.8 GeV polarized electron beam during the ele and e1-6 run periods with CLAS at Jefferson Lab. The new measurements will produce a data base with high statistics and large kinematic coverage for the hadronic invariant mass （W） up to 2.0 CeV in the momentum transfer （Q2） range of 0.3--6.0 GeV2. Preliminary results will be presented and compared with the various model calculations. 相似文献