scholarly journals Partial rotational lattice order–disorder in stefin B crystals

2014 ◽  
Vol 70 (4) ◽  
pp. 1015-1025 ◽  
Author(s):  
Miha Renko ◽  
Ajda Taler-Verčič ◽  
Marko Mihelič ◽  
Eva Žerovnik ◽  
Dušan Turk
Keyword(s):  
Crystal Lattice ◽  
Crystal Structures ◽  
Electron Density ◽  
Rejection Rate ◽  
Lattice Order ◽  
Space Group ◽  
Space Groups ◽  
Additional Layer ◽  
Diffraction Patterns ◽  
Ordered Layers

At present, the determination of crystal structures from data that have been acquired from twinned crystals is routine; however, with the increasing number of crystal structures additional crystal lattice disorders are being discovered. Here, a previously undescribed partial rotational order–disorder that has been observed in crystals of stefin B is described. The diffraction images revealed normal diffraction patterns that result from a regular crystal lattice. The data could be processed in space groupsI4 andI422, yet one crystal exhibited a notable rejection rate in the higher symmetry space group. An explanation for this behaviour was found once the crystal structures had been solved and refined and the electron-density maps had been inspected. The lattice of stefin B crystals is composed of five tetramer layers: four well ordered layers which are followed by an additional layer of alternatively placed tetramers. The presence of alternative positions was revealed by the inspection of electron-density score maps. The well ordered layers correspond to the crystal symmetry of space groupI422. In addition, the positions of the molecules in the additional layer are related by twofold rotational axes which correspond to space groupI422; however, these molecules lie on the twofold axis and can only be related in a statistical manner. When the occupancies of alternate positions and overlapping are equal, the crystal lattice indeed fulfills the criteria of space groupI422; when these occupancies are not equal, the lattice only fulfills the criteria of space groupI4.

On the treatment of settings of space-groups and crystal structures by spezialized short Hermann-Mauguin space-group symbols

2002 ◽  
Vol 217 (4) ◽  
Author(s):  
H. Burzlaff ◽  
H. Zimmermann
Keyword(s):  
Crystal Structures ◽  
Shift Vector ◽  
Space Group ◽  
Space Groups ◽  
Matrix Description ◽  
Simple Rules ◽  
The Matrix ◽  
Free Parameters ◽  
Generating Operators

AbstractFrom the short Hermann-Mauguin space-group symbol a set of generating operators can be derived. The matrix description of the operators depends on three free parameters related to the origin of the setting. Simple rules allow the specification of an origin, the origin of the symbol. The use of any other origin is notated by appending a shift vector from the symbol origin to the new one selected.

scholarly journals Identification of crystal symmetry from noisy diffraction patterns by a shape analysis and deep learning

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Leslie Ching Ow Tiong ◽  
Jeongrae Kim ◽  
Sang Soo Han ◽  
Donghun Kim
Keyword(s):  
Deep Learning ◽  
Target Material ◽  
Group Classification ◽  
Crystal Symmetry ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Classes ◽  
Diffraction Patterns ◽  
Well Differentiated

AbstractThe robust and automated determination of crystal symmetry is of utmost importance in material characterization and analysis. Recent studies have shown that deep learning (DL) methods can effectively reveal the correlations between X-ray or electron-beam diffraction patterns and crystal symmetry. Despite their promise, most of these studies have been limited to identifying relatively few classes into which a target material may be grouped. On the other hand, the DL-based identification of crystal symmetry suffers from a drastic drop in accuracy for problems involving classification into tens or hundreds of symmetry classes (e.g., up to 230 space groups), severely limiting its practical usage. Here, we demonstrate that a combined approach of shaping diffraction patterns and implementing them in a multistream DenseNet (MSDN) substantially improves the accuracy of classification. Even with an imbalanced dataset of 108,658 individual crystals sampled from 72 space groups, our model achieves 80.12 ± 0.09% space group classification accuracy, outperforming conventional benchmark models by 17–27 percentage points (%p). The enhancement can be largely attributed to the pattern shaping strategy, through which the subtle changes in patterns between symmetrically close crystal systems (e.g., monoclinic vs. orthorhombic or trigonal vs. hexagonal) are well differentiated. We additionally find that the MSDN architecture is advantageous for capturing patterns in a richer but less redundant manner relative to conventional convolutional neural networks. The proposed protocols in regard to both input descriptor processing and DL architecture enable accurate space group classification and thus improve the practical usage of the DL approach in crystal symmetry identification.

scholarly journals VI. Tabulated data for the examination of the 230 space-groups by homogeneous X-rays

1924 ◽  
Vol 224 (616-625) ◽  
pp. 221-257 ◽  
Keyword(s):  
Crystal Structures ◽  
Chemical Society ◽  
Unit Cell ◽  
X Rays ◽  
Screw Axis ◽  
Monoclinic System ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Relative Arrangement

The object of the present paper is to express the conclusions of mathematical crystallography in a form which shall be immediately useful to workers using homogeneous X-rays for the analysis of crystal structures. The results are directly applicable to such methods as the Bragg ionisation method, the powder method, the rotating crystal method, etc., and summarise in as compact a form as possible what inferences may be made from the experimental observations, whichever one of the 230 possible space-groups may happen to be under examination. It is only in certain cases that the spacings of crystal planes as determined by the aid of homogeneous X-rays agree with the values of those spacings which would be expected from ordinary crystallographic calculations. In the majority of cases the relative arrangement of the molecules in the unit cell leads to apparent anomalies in the experimental results, the observed spacings of certain planes or sets of planes being sub-multiples of the calculated spacings. The simplest case (fig. 8) of such an apparent anomaly is found in the space-group C 2 2 of the monoclinic system, where the presence of a two-fold screw-axis, because it interleaves halfway the (010) planes by molecules which are exactly like those lying in the (010) planes, except that they have been rotated through 180°, leads to an observed periodicity which is half the periodicity to be inferred from the dimensions of the unit cell, that is, leads to an observed spacing for (010) which is half the calculated. All screw-axes produce similar results, and, in general, a p -fold screw-axis leads to an observed spacing for the plane perpendicular to it which is 1/ p th that to be inferred from the dimensions of the cell. Besides those produced by the screw-axes, other abnormalities arise out of the presence of glide-planes. The simplest case of this is shown by the space-group C s 2 (fig. 4) of the monoclinic system, in which the second molecule is obtained from the first by a reflection in a plane parallel to (010) and half a primitive translation parallel to that plane. If we look along a direction perpendicular to this glide-plane, the projections of the two molecules on the (010) plane are indistinguishable except in position, which is equivalent to saying that, for the purposes of X-ray interference, certain planes perpendicular to this plane of projection are interleaved by an identical molecular distribution. Furthermore, since the translation associated with the glide-plane must always be half a primitive translation parallel to the glide-plane, we know that the interleaving is always a submultiple of the full spacing and the periodicity is again reduced in a corresponding manner. The use of this method for discriminating between the various space-groups of the monoclinic system was described by Sir Wm. Bragg in a lecture to the Chemical Society. In the present paper the method has been extended to the whole of the 230 space-groups possible to crystalline structures. In general, it may be said that if a crystal possesses a certain glide-plane, a certain set of planes lying in the zone whose axis is perpendicular to that glide-plane will have their periodicity reduced by one-half.

An Improved Synthesis, Molecular-Structure, and Properties of 1,4-Dihydro-Dicyclopropa[b,g]naphthalene

1991 ◽  
Vol 44 (2) ◽  
pp. 265 ◽  
Author(s):  
B Halton ◽  
R Boese ◽  
D Blaser ◽  
Q Lu
Keyword(s):  
Molecular Structure ◽  
Crystal Lattice ◽  
Electron Density ◽  
Marked Improvement ◽  
Structure And Properties ◽  
Difference Electron Density ◽  
Space Group ◽  
Density Maps ◽  
Bent Bonds

A marked improvement in the preparation of 1,4-dihydrodicyclopropa[ b,g ]naphthalene (4) from isotetralin (7) has been achieved by selecting conditions which avoid the unwanted olefin (12). The easily available dicycloproparene (4) has C2h symmetry in the crystal lattice with the space group P21/n. The geometry is readily rationalized by the concept of 'bent bonds' that are also suggested by X-X difference electron density maps. Cheletropic biaddition of dichlorocarbene to (4) provides the dicyclobutanaphthalenes (15) and (16). Attempted Petersen olefination to mono- and di-alkylidene derivatives, e.g. (21) and (22), is foiled by a reluctance of (4) to provide an easily interceptible anion.

William Barlow’s early publications in the ‘Zeitschrift für Krystallographie und Mineralogie’ and their influence on crystal structure research

2019 ◽  
Vol 234 (11-12) ◽  
pp. 769-785 ◽  
Author(s):  
Peter Paufler
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Crystal Morphology ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Starting Point ◽  
Diffraction Patterns ◽  
Structure Research

AbstractThe English crystallographer William Barlow is famous for two achievements, both published in German, in Zeitschrift für Krystallographie und Mineralogie between 1894 and 1901. They concern the derivation of all possible symmetrical arrangements of points in space and the idea to represent crystal structures by replacing points by spheres. His results had an impact upon crystal structure modelling and describing crystal morphology. Utilizing self-made models, he found the 230 space group types of symmetry obtained earlier by both E. S. Fedorow and A. Schoenflies in a different manner. The structures he proposed before the discovery of X-ray diffraction served in some cases as starting point for the interpretation of diffraction patterns thereafter.

scholarly journals Some more space-group corrections

2014 ◽  
Vol 70 (9) ◽  
pp. 834-836 ◽  
Author(s):  
Lawrence M. Henling ◽  
Richard E. Marsh
Keyword(s):  
Crystal Structures ◽  
Cambridge Structural Database ◽  
Space Group ◽  
Space Groups ◽  
Structural Database

A survey of approximately 100 000 entries in recent releases of the Cambridge Structural Database (CSD) has uncovered 156 crystal structures that were apparently described in inappropriate space groups. We have revised these space groups and prepared CIFs containing the new coordinates and brief comments describing the revisions.

X-ray powder diffraction data for three red azo pigments: sodium, barium, and ammonium lithol salts

2017 ◽  
Vol 32 (3) ◽  
pp. 187-192 ◽  
Author(s):  
Alicja Rafalska-Łasocha ◽  
Marta Grzesiak-Nowak ◽  
Piotr Goszczycki ◽  
Katarzyna Ostrowska ◽  
Wiesław Łasocha
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Monoclinic Space Group ◽  
Powder Diffraction Data ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Cell Parameters ◽  
Synthesis Procedure ◽  
Diffraction Patterns

Lithol reds belong to the group of azo pigments, which were popular artists’ colouring materials in the first half of the twentieth century. These pigments were also used in many branches of industry. Here, we report X-ray powder diffraction data, unit-cell parameters, and space groups for three compounds from this group: sodium (E)-2-((2-hydroxynaphthalen-1-yl)diazenyl)naphthalene-1-sulphonate monohydrate (Na lithol red), monoclinic, space group C2/c, with cell parameters a = 33.343(7), b = 6.667(2), c = 16.397(4) Å, β = 90.83°, V = 3644.51 Å3, Z = 8; barium (E)-2-[(2-hydroxynaphthalen-1-yl)diazenyl]naphthalene-1-sulphonate trihydrate (Ba lithol red), monoclinic, space group P21/m, with cell parameters a = 17.758(9), b = 6.209(4), c = 16.857(8) Å, β = 92.07°, V = 1857.39 Å3, Z = 2; and ammonium (E)-2-[(2-hydroxynaphthalen-1-yl)diazenyl]naphthalene-1-sulphonate monohydrate (NH4 lithol red), monoclinic, space group P2/c, with cell parameters a = 17.721(5), b = 6.428(3), c = 16.911(5) Å, β = 100.31(3)°, V = 1895.31 Å3, and Z = 4. In the first and third cases we synthesised the pigments in their monohydrate form, performed X-ray powder diffraction measurements, and indexed all of the obtained diffraction maxima. In the case of the barium compound, despite many efforts in the course of the synthesis procedure, the powder diffraction patterns of the obtained samples were not of the best quality. Nevertheless, we indexed the best one and found a reliable space group and cell parameters.

Synthese und Kristallstrukturen von Diazadien-Komplexen der Erdalkalimetalle / Syntheses and Crystal Structures of Diazadiene Complexes of the Alkaline Earth Metals

1995 ◽  
Vol 50 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Volker Lorenz ◽  
Bernhard Neumüller ◽  
Karl-Heinz Thiele
Keyword(s):  
Crystal Lattice ◽  
Crystal Structures ◽  
Structure Determination ◽  
Alkaline Earth ◽  
Alkaline Earth Metals ◽  
The Other ◽  
Calcium Atom ◽  
Space Group ◽  
X Ray ◽  
Moisture Sensitive

(DME)2] 1 (R = C6H4-4-CH3; DME = dimethoxyethane) was prepared by reaction of calcium with NR=CPh-CPh=NR in DME solution. The compound forms orange, moisture sensitive crystals, which were characterized by an X-ray structure determination [space group orthorhombic, P212121, Z = 4, 4634 observed unique reflections, R = 0.046; lattice dimensions at –70 °C: a = 1340.2(3), b = 1528.1(3), c = 1609.1(3) pm]. The calcium atom is coordinated by the four oxygen atoms of two chelating DME molecules and two nitrogen atoms of the diazadiene ligand, bonded in its enediamide form.[Ba2(DME)3(NPh–CPh=CPh–NPh)2 · DME] 3 was obtained from barium metal and NPh=CPh-CPh=NPh in DME solution as red crystals [space group monoclinic, P2l/c, Z = 4, 4000 observed unique reflections, R = 0.166; lattice dimensions at -70 °C: a = 1704.5(3), b = 1786.1(4), c = 2177.4(4) pm, β = 105.98(3)°]. The two barium atoms are bridged by two differently bonded diazadiene ligands (μ2-Ν,Ν′;μ-Ν, σ-Ν′). Additionally, one of the barium atoms is coordinated to two DME molecules and the other one to only one of the ether molecules. A further DME molecule is a constituent of the crystal lattice.

scholarly journals Mathematical Crystallography in the 21st century

2014 ◽  
Vol 70 (a1) ◽  
pp. C18-C18
Author(s):  
Marjorie Senechal
Keyword(s):  
Crystal Structures ◽  
21St Century ◽  
New Materials ◽  
Space Group ◽  
Space Groups ◽  
Group Assignment ◽  
New Directions

The solution of simple crystal structures in 1914 sent crystallographers to the library stacks to dig out, dust off, and learn to use the lattices and space groups that mathematicians had discovered in the century before. In 2014 space group assignment is a job for computers, but mathematical crystallography is anything but routine. New materials stretch the boundaries of "pattern," simulations stretch the boundaries of "possible," and mathematicians study structures on all scales, from nano to n-dimensional. In this talk I will outline challenges and new directions posed by 21st century crystallography.

Solving crystal structures inP1: an automated procedure for finding an allowed origin in the correct space group

2000 ◽  
Vol 33 (2) ◽  
pp. 307-311 ◽  
Author(s):  
Maria Cristina Burla ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
Carmelo Giacovazzo ◽  
Giampiero Polidori
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Structural Model ◽  
Structure Refinement ◽  
Human Intervention ◽  
Space Group ◽  
Space Groups ◽  
Structure Solution ◽  
Actual Space ◽  
Complex Crystal

Crystal structure solution inP1 may be particularly suitable for complex crystal structures crystallizing in other space groups. However, additional efforts and human intervention are often necessary to locate correctly the structural model so obtained with respect to an allowed origin of the actual space group. An automatic procedure is described which is able to perform such a task, allowing the routine passage to the correct space group and the subsequent structure refinement. Some tests are presented proving the effectiveness of the procedure.

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