Investigation of the Cs x Rb1−x TiOAsO4 Series. II. The Problems of Interpretation of Residual Electron Densities in a Polar Space Group

1998 ◽  
Vol 54 (5) ◽  
pp. 645-651 ◽  
Author(s):  
P. A. Thomas ◽  
M. N. Womersley
Keyword(s):  
Electron Density ◽  
Polar Space ◽  
Worst Case ◽  
Polar Structure ◽  
Space Group ◽  
Disordered Structure ◽  
Strong Inversion ◽  
Residual Electron Density ◽  
Optical Crystal ◽  
True Structure

The problems of refinements of structures in a polar space group, such as Pna21, are illustrated by the example of crystals in the Cs2x Rb2−2x Ti2O2As2O8, caesium rubidium titanyl arsenate, series, which are isostructural with the well known non-linear optical crystal KTiOPO4. It is shown in particular that errors in the data collection and/or refinement tend to contribute positive residual electron density in sites which are related by an inversion operation to the real Cs/Rb sites. This phenomenon is a consequence of the presence of two minima in least-squares space, representing here the possible coordinate sets x,y,z and x,y,−z, for a polar structure and is exacerbated in these structures by the presence of strong inversion psuedo-symmetry. It is shown that in the worst case, the positive residual electron density can be eliminated and an improved agreement to the observed data obtained by refinement of a partially micro-twinned disordered structure in which the Cs/Rb occupancy is split between the main sites and the inversion-related sites. It is argued that the true structure is micro-twinned, including partial occupancy of the additional sites.

A plastically bendable and polar organic crystal

CrystEngComm ◽  
2021 ◽  
Author(s):  
Sotaro Kusumoto ◽  
Akira Sugimoto ◽  
Daisuke Kosumi ◽  
Yang Kim ◽  
Yoshihiro Sekine ◽  
...  
Keyword(s):  
Mechanical Stress ◽  
Polar Space ◽  
Organic Crystal ◽  
Space Group ◽  
High Dielectric

In this communication, an organic crystal of the polar space group Pc that is capable of plastically bending in response to external mechanical stress is reported, and its high dielectric...

Struktur und X-X-Elektronendichteverteilung in Diaminoboranen des Typs (RCH3N)2BCH3 mit R = H, CH3

1991 ◽  
Vol 46 (1) ◽  
pp. 84-96 ◽  
Author(s):  
Norbert Niederprüm ◽  
Roland Boese ◽  
Günter Schmid
Keyword(s):  
Crystal Structure ◽  
Electron Density ◽  
Zone Melting ◽  
Infrared Light ◽  
Monoclinic Space Group ◽  
Difference Electron Density ◽  
Orthorhombic Space Group ◽  
Torsion Angles ◽  
Space Group ◽  
The Mean

Using a miniature zone melting device with focused infrared light it was possible to grow crystals of bis(dimethylamino)methylborane (1) and bis(monomethylamino)methylborane (2) at temperatures o f 182 K and 177 K, respectively. The crystal structure and the X - X difference electron density have been determined at temperatures o f 120 K (1) and 115 K (2).1 crystallizes in the orthorhombic space group Pbca with a = 758.87(7), b = 1559.74(12) and c = 1296.73(12) pm. The mean B - N distance is 143.1(3) pm.2 crystallizes in the monoclinic space group P21/c with a = 775.06(6), b = 1533.94(17), c = 1011.06(10) pm and β = 102.669(7)° with intermolecular N ··· H hydrogen bridges. The mean B - N distance is 141.5(2) pm.It is shown that the variation of torsion angles at small angles has more influence on bond lengths than the same or a greater variation at large angles and that it is necessary to pay more attention to the torsion angles ( C - B - N - C ) rather than to the interplanar angles (plane N ,B,N - plane N ,C,C ).

The crystal structure of Bis[2-(pyridin-2-ylamino)-4-(pyridin-2-yl)thiazole]iron(II) Bis(tetrafluoroborate) trihydrate

1984 ◽  
Vol 37 (2) ◽  
pp. 443 ◽  
Author(s):  
AT Baker ◽  
HA Goodwin ◽  
AD Rae
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Complex Cation ◽  
Monoclinic Space Group ◽  
Octahedral Structure ◽  
Space Group ◽  
X Ray ◽  
Disordered Structure ◽  
Distorted Octahedral ◽  
A Cell

The crystal structure of an iron(II) complex of 2-(pyridin-2-ylamino)-4-(pyridin-2-yl)tliazoe (paptH) has been determined by single-crystal X-ray diffractometry. [Fe(paptH)2] [BF4]2.3H2O is monoclinic, space group P21/c, with Z = 4 in a cell of dimensions a 8.968(6), b 9.038(4), c 41.15(2)�, β 94.81(2)�. The disordered structure was refined to a residual R 0.0826 for 2549 observed reflections. The ligands and anions are orientationally disordered, and the waters of crystallization are positionally disordered. Comprehensive constrained refinement, with 220 parameters for 139 atom positions, produced reliable geometry. The complex cation has a distorted octahedral structure of meridional configuration with both paptH ligands functioning as tridentates.

scholarly journals (E)-3-(4-Cyclohexyl-3-fluorobenzylidene)chroman-4-one

2012 ◽  
Vol 68 (6) ◽  
pp. o1972-o1972 ◽  
Author(s):  
Kaalin Gopaul ◽  
Mahidansha M. Shaikh ◽  
Neil A. Koorbanally ◽  
Deresh Ramjugernath ◽  
Bernard Omondi
Keyword(s):  
Electron Density ◽  
Benzene Ring ◽  
Dihedral Angle ◽  
Title Compound ◽  
Asymmetric Unit ◽  
Compound C ◽  
Density Peaks ◽  
Residual Electron Density

The title compound, C22H21FO2, exhibits substitutional disorder of the F atom and a H atom in the asymmetric unit with different occupancies, the refined F:H ratio being 0.80 (2):0.20 (2). The dihedral angle between the fluorinated benzene ring and the benzene ring of the chromanone system is 37.30°. There are two relatively high residual electron-density peaks associated with the disorder.

scholarly journals The crystal structure of meta-dinitrobenzene

1946 ◽  
Vol 188 (1012) ◽  
pp. 51-62 ◽  
Keyword(s):  
Crystal Structure ◽  
Fourier Series ◽  
Electron Density ◽  
Benzene Ring ◽  
Double Fourier Series ◽  
Unit Cell ◽  
Regular Hexagon ◽  
Space Group

The crystal of meta-dinitrobenzene, C 6 H 4 (N O 2 ) 2 , is orthorhombic pyramidal. The dimensions of the unit cell, which contains 4 molecules, are a = 13.3A, b = 14.1 A, c = 3.80A and the space group is Pbn . The method of double Fourier series has been applied, and a projection of the electron density on the ab plane has been made. The plane of the benzene ring of the molecule is inclined at an angle of 20° to the b -axis, and is parallel to the a -axis. Within the limits of experiment, the benzene ring is a regular hexagon of side 1.41 A. The C—N links do not lie in the plane of the ring, but make an angle of 15° with it. The C-N distance is 1.54 A, the N -O distances have been assumed the same, 1.20 A, and the O-O distance is 2.17 A. The closest approach of O to CH in adjacent molecules is about 3.0 A, that between O and O about 3.2 A, and that between CH and CH is 3.8 A. A discussion of the packing of the molecules in the structure is given.

scholarly journals Phase transition and structures of the twinned low-temperature phases of (Et4N)[ReS4]

2020 ◽  
Vol 76 (3) ◽  
pp. 231-235
Author(s):  
Eduard Bernhardt ◽  
Regine Herbst-Irmer
Keyword(s):  
Phase Transition ◽  
Low Temperature ◽  
Title Compound ◽  
Room Temperature ◽  
Monoclinic Space Group ◽  
Rapid Cooling ◽  
Space Group ◽  
Disordered Structure ◽  
Β Phase ◽  
Α Phase

The title compound, tetraethylammonium tetrathiorhenate, [(C2H5)4N][ReS4], has, at room temperature, a disordered structure in the space group P63 mc (Z = 2, α-phase). A phase transition to the monoclinic space group P21 (Z = 2, γ-phase) at 285 K leads to a pseudo-merohedral twin. The high deviation from the hexagonal metric causes split reflections. However, the different orientations could not be separated, but were integrated using a large integration box. Rapid cooling to 110–170 K produces a metastable β-phase (P63, Z = 18) in addition to the γ-phase. All crystals of the β-phase are contaminated with the γ-phase. Additionally, the crystals of the β-phase are merohedrally twinned. In contrast to the α-phase, the β- and γ-phases do not show disorder.

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.

Two alkali calcium borates exhibiting second harmonic generation and deep-UV cutoff edges

2019 ◽  
Vol 43 (24) ◽  
pp. 9354-9363
Author(s):  
Peng Ren ◽  
Yun Yang ◽  
Hao Li ◽  
Zhihua Yang ◽  
Shilie Pan
Keyword(s):  
Second Harmonic Generation ◽  
Harmonic Generation ◽  
Second Harmonic ◽  
Polar Space ◽  
Structure Property ◽  
Space Group ◽  
Structure Property Relationships ◽  
Deep Uv

KCa4B3O9 and K0.59Rb0.41Ca4B3O9 crystallize in the polar space group with moderate SHG responses. Calculations were performed to elucidate the structure–property relationships.

Die Kristallstruktur von [Na(12-Krone-4)2+]2Se82- · (Se6, Se7) / The Crystal Structure of [Na(12-Crown-4)2+]2Se82- · (Se6, Se7)

1991 ◽  
Vol 46 (10) ◽  
pp. 1287-1292 ◽  
Author(s):  
Rüdiger Staffel ◽  
Ulrich Müller ◽  
Andreas Ahle ◽  
Kurt Dehnicke
Keyword(s):  
Crystal Structure ◽  
Structure Determination ◽  
Title Compound ◽  
Crystal Structure Determination ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Disordered Structure

The title compound was prepared from sodium polyselenide and 12-crown-4 in DMF solution in the presence of cerium(III)chloride in the form of black needles. The crystal structure determination by X-ray diffraction shows a partially disordered structure, in which the anionic units Se82- · Se7 and Se82- · Se6 are present in the ratio 0.72/0.28. These units are associated to layers parallel to (100); the layers alternate with pseudohexagonal layers of [Na(12-crown-4)2]+ ions. Space group P1̅, Z = 2, 3903 observed unique reflections, R = 0.114, wR= 0.084. Lattice dimensions at -65°C: a = 1247.9(3), b = 1367.8(8), c = 1660(1) pm, α = 94.65(5), β = 98.94(3), γ = 91.10(3)°.

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