Theoretical study of the properties of X-ray diffraction moiré fringes. I. Corrigenda and addenda

A detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. Firstly, prior to discussing the main subject of the paper, a previous article [Yoshimura (1997).Acta Cryst.A53, 810–812] on the two-dimensionality of diffraction moiré patterns is restated on a thorough calculation of the moiré interference phase. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect ofPendellösungintensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.

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Theoretical study of the properties of X-ray diffraction moiré fringes. II. Illustration of angularly integrated moiré images

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273319004601 ◽

2019 ◽

Vol 75 (4) ◽

pp. 610-623

Author(s):

Jun-ichi Yoshimura

Keyword(s):

Incident Wave ◽

Angular Width ◽

X Ray Diffraction ◽

Experimental Conditions ◽

Acta Cryst ◽

Low Contrast ◽

X Ray ◽

Moiré Fringes ◽

Wide Range ◽

Fringe Patterns

Using a theory of X-ray diffraction moiré fringes developed in a previous paper, labelled Part I [Yoshimura (2015). Acta Cryst. A71, 368–381], the X-ray moiré images of a silicon bicrystal having a weak curvature strain and an interspacing gap, assumed to be integrated for an incident-wave angular width, are simulation-computed over a wide range of crystal thicknesses and incident-wave angular width, likely under practical experimental conditions. Along with the simulated moiré images, the graphs of characteristic quantities on the moiré images are presented for a full understanding of them. The treated moiré images are all of rotation moiré. Mo Kα1 radiation and the 220 reflection were assumed in the simulation. The results of this simulation show that fringe patterns, which are significantly modified from simple straight fringes of rotation moiré, appear in some ranges of crystal thicknesses and incident-wave angular width, due to a combined effect of Pendellösung oscillation and an added phase difference from the interspacing gap, under the presence of a curvature strain. The moiré fringes which slope to the perpendicular direction to the diffraction vector in spite of the assumed condition of rotation moiré, and fringe patterns where low-contrast bands are produced with a sharp bend of fringes arising along the bands are examples of the modified fringe pattern. This simulation study provides a wide theoretical survey of the type of bicrystal moiré image produced under a particular condition.

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Differences and similarities among hypoxanthinium nitrate hydrate structures

Acta Crystallographica Section C Structural Chemistry ◽

10.1107/s2053229619008702 ◽

2019 ◽

Vol 75 (8) ◽

pp. 1036-1044 ◽

Cited By ~ 1

Author(s):

Małgorzata Katarzyna Cabaj ◽

Roman Gajda ◽

Anna Hoser ◽

Anna Makal ◽

Paulina Maria Dominiak

Keyword(s):

Room Temperature ◽

Temperature Phase ◽

X Ray Diffraction ◽

Acta Cryst ◽

X Ray ◽

Nitrate Hydrate ◽

Different Temperatures ◽

Lower Temperature ◽

Low Temperature Phase ◽

Nitrate Anions

Crystals of hypoxanthinium (6-oxo-1H,7H-purin-9-ium) nitrate hydrates were investigated by means of X-ray diffraction at different temperatures. The data for hypoxanthinium nitrate monohydrate (C5H5N4O+·NO3 −·H2O, Hx1) were collected at 20, 105 and 285 K. The room-temperature phase was reported previously [Schmalle et al. (1990). Acta Cryst. C46, 340–342] and the low-temperature phase has not been investigated yet. The structure underwent a phase transition, which resulted in a change of space group from Pmnb to P21/n at lower temperature and subsequently in nonmerohedral twinning. The structure of hypoxanthinium dinitrate trihydrate (H3O+·C5H5N4O+·2NO3 −·2H2O, Hx2) was determined at 20 and 100 K, and also has not been reported previously. The Hx2 structure consists of two types of layers: the `hypoxanthinium nitrate monohydrate' layers (HX) observed in Hx1 and layers of Zundel complex H3O+·H2O interacting with nitrate anions (OX). The crystal can be considered as a solid solution of two salts, i.e. hypoxanthinium nitrate monohydrate, C5H5N4O+·NO3 −·H2O, and oxonium nitrate monohydrate, H3O+(H2O)·NO3 −.

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Centrosymmetric or Noncentrosymmetric? Case Study, Generalization and Structural Redetermination of Sr5Nb5O17

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768197019642 ◽

1998 ◽

Vol 54 (4) ◽

pp. 399-416 ◽

Cited By ~ 28

Author(s):

S. C. Abrahams ◽

H. W. Schmalle ◽

T. Williams ◽

A. Reller ◽

F. Lichtenberg ◽

...

Keyword(s):

Niobium Oxide ◽

The Novel ◽

Physical Measurement ◽

X Ray Diffraction ◽

Acta Cryst ◽

Data Set ◽

Space Group ◽

X Ray ◽

Atomic Coordinates

The possibility that the structure of the novel semiconducting perovskite-related material strontium niobium oxide, Sr5Nb5O17, refined by Schmalle et al. [Acta Cryst. (1995), C51, 1243–1246] in space group Pnn2, might instead belong to space group Pnnm has been investigated following an analysis of the atomic coordinates that indicated the latter space group to be more likely. All I obs were carefully remeasured, first those within a hemisphere containing c *, then all that lay within the full sphere of reflection. Refinement was undertaken, with each of two different sets of weights, in each space group. Each data set was used under three limiting intensity conditions: I obs > 4σ(I obs), I obs > 2σ(I obs) and finally with all reflections, but setting magnitudes with I obs ≤ 0 equal to 0. Fourteen separate tests based only upon the X-ray diffraction data may be used to distinguish between Pnn2 and Pnnm. Nine tests favored the latter choice, four were indeterminate and one was not used. Seven further tests may be made on the basis of physical measurement; of these, three strongly indicated Pnnm, one was indeterminate and three could not be used. The evidence clearly suggests the space group is Pnnm. The use of all reflections, including those with negative magnitude set equal to zero, is essential to avoid ambiguity in the X-ray diffraction tests and achieve the highest reliability. Refinement with weights based on variances of Type A and Type B [Schwarzenbach et al. (1995). Acta Cryst. A51, 565–569] resulted in improved reliability compared with that obtained from a popular empirical weighting scheme. The revised structure differs in several respects from that published previously.

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A variable-temperature X-ray diffraction and theoretical study of conformational polymorphism in a complex organic molecule (DTC)

RSC Advances ◽

10.1039/c8ra08063a ◽

2018 ◽

Vol 8 (67) ◽

pp. 38445-38454 ◽

Cited By ~ 5

Author(s):

Andrea Gionda ◽

Giovanni Macetti ◽

Laura Loconte ◽

Silvia Rizzato ◽

Ahmed M. Orlando ◽

...

Keyword(s):

Theoretical Study ◽

Crystal Packing ◽

Variable Temperature ◽

Asymmetric Unit ◽

X Ray Diffraction ◽

X Ray ◽

Complex Organic Molecule ◽

Non Covalent Interactions ◽

Complex Organic ◽

Covalent Interactions

A small conformational change in the asymmetric unit has a significant effect on how non-covalent interactions determine (i) the crystal packing and (ii) the effect of T on the relative balance of electrostatics and dispersion–repulsions.

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The location of p-dichlorobenzene in a single crystal of zeolite H-ZSM-5 at high sorbate loading

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768195008524 ◽

1996 ◽

Vol 52 (1) ◽

pp. 140-144 ◽

Cited By ~ 37

Author(s):

H. van Koningsveld ◽

J. C. Jansen ◽

H. van Bekkum

Keyword(s):

Single Crystal ◽

Cross Sections ◽

Unit Cell ◽

Molecular Axis ◽

X Ray Diffraction ◽

Orthorhombic Space Group ◽

Acta Cryst ◽

Elliptical Cross ◽

X Ray ◽

Structural Aspects

The crystal structure of a high-loaded complex of H-ZSM-5 with eight molecules of p-dichlorobenzene per unit cell has been solved by single-crystal X-ray diffraction. The orthorhombic space group P212121 with a = 20.102 (6), b = 19.797 (9), c = 13.436 (3) Å and V = 5347 (3) Å3 has four Si23.92Al0.08O48.2C6H4Cl2 units per unit cell. Dx = 2.164 Mg m−3, λ(MoKα) = 0.71073 Å and μ(Mo Kα) = 0.876 mm−1. The final R(wR) = 0.046 (0.039), w = 1/σ 2(F), for 6090 observed reflections with I > 1.0σ(I) measured at 293 K. The straight channel parallel to [010] is slightly corrugated. The elliptical cross sections have limiting apertures of 6.0 × 4.9 Å (r oxygen = 1.35 Å). The sinusoidal channel parallel to [100] is elliptical with major and minor axes of 6.1 × 4.8 Å, respectively. One of the two independent p-dichlorobenzene molecule lies at the intersection of the straight and sinusoidal channels with its long molecular axis almost parallel to (100) and deviating ~8° from [010]. The second p-dichlorobenzene molecule is in the sinusoidal channel. Its long molecular axis deviates almost 7° from [100] and is practically parallel to (010). The structural aspects are in all details comparable to those in the high-loaded H-ZSM-5/p-xylene complex [van Koningsveld, Tuinstra, van Bekkum & Jansen (1989). Acta Cryst. B45, 423–431] , except for the main interaction forces between the p-dichlorobenzene molecules at the channel intersection.

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Estimating the structure factors in X-ray diffraction

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273318007593 ◽

2018 ◽

Vol 74 (5) ◽

pp. 481-498 ◽

Cited By ~ 2

Author(s):

Paul F. Fewster

Keyword(s):

Diffraction Theory ◽

Bragg Angle ◽

Enhancement Effect ◽

Diffraction Effect ◽

X Ray Diffraction ◽

Acta Cryst ◽

X Ray ◽

Background Removal ◽

Structure Factors ◽

Path Lengths

This article takes the concepts of the `new diffraction theory' [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher-order peaks are due to path lengths of nλ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated.

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Multipole electron densities and atomic displacement parameters in urea from accurate powder X-ray diffraction

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s205327331900799x ◽

2019 ◽

Vol 75 (4) ◽

pp. 600-609 ◽

Cited By ~ 2

Author(s):

Bjarke Svane ◽

Kasper Tolborg ◽

Lasse Rabøl Jørgensen ◽

Martin Roelsgaard ◽

Mads Ry Vogel Jørgensen ◽

...

Keyword(s):

Electron Density ◽

Molecular System ◽

Atomic Displacement ◽

High Symmetry ◽

X Ray Diffraction ◽

High Quality ◽

Acta Cryst ◽

X Ray ◽

Density Determination ◽

Structure Factors

Electron density determination based on structure factors obtained through powder X-ray diffraction has so far been limited to high-symmetry inorganic solids. This limit is challenged by determining high-quality structure factors for crystalline urea using a bespoke vacuum diffractometer with imaging plates. This allows the collection of data of sufficient quality to model the electron density of a molecular system using the multipole method. The structure factors, refined parameters as well as chemical bonding features are compared with results from the high-quality synchrotron single-crystal study by Birkedalet al.[Acta Cryst.(2004), A60, 371–381] demonstrating that powder X-ray diffraction potentially provides a viable alternative for electron density determination in simple molecular crystals where high-quality single crystals are not available.

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Kα2 elimination algorithm for Cu, Co and Cr radiations

Journal of Applied Crystallography ◽

10.1107/s0021889883009905 ◽

1983 ◽

Vol 16 (1) ◽

pp. 24-27 ◽

Cited By ~ 17

Author(s):

G. Platbrood

Keyword(s):

Calculation Method ◽

Target Material ◽

X Ray Diffraction ◽

Acta Cryst ◽

X Ray ◽

Signal Noise ◽

Elimination Algorithm ◽

Suitable Target ◽

Noise Ratio

It is well known that the extraneous Kα 2 line complicates the interpretation of X-ray diffraction spectra. Experience has shown that the arms and weights calculated by Ladell's method [Laddell, Parrish & Taylor (1959). Acta Cryst. 12, 561–567] have to be determined for each user's X-ray diffractometer, rather than using the published coefficients, for an accurate Kα 2 elimination. When different materials are analyzed, the signal/noise ratio can be optimized by choosing a suitable target material. Kα 2 correction coefficients have been calculated for Cu, Co and Cr radiations using a fast Fourier calculation method.

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