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 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.

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.

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.

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.

scholarly journals Symmetry Relations Between Space Groups in Layered Germanate Structures: Modeling Crystal Structures

2014 ◽  
Vol 70 (a1) ◽  
pp. C1763-C1763
Author(s):  
Nelly Flores-Sanchez ◽  
Ivonne Rosales ◽  
Lauro Bucio
Keyword(s):  
Crystal Structures ◽  
Rietveld Refinement ◽  
Structural Model ◽  
Structural Data ◽  
X Rays ◽  
Monoclinic System ◽  
Space Group ◽  
Space Groups ◽  
Group Type ◽  
Symmetry Relations

Structural models for the new layered germanates ScInGe2O7 and ScFeGe2O7 were analyzed within the framework of symmetry relations between space groups. These compounds were supposed to be hettotypes of the thortveitite mineral, (Sc,Y)2Si2O7, which was considered as the aristotype. Thortveitite crystallizes in the monoclinic system, and the symmetry is described by the space group type C2/m. Other monoclinic hettotypes for the thortveitite are FeInGe2O7 (PDF 01-070-8447, ICSD - 94487), space group C2/m (No. 12); TbInGe2O7 (PDF 01-072-6515, ICSD - 96360), space group C2/c (No. 15); and FeYGe2O7 (PDF 01-072-6099, ICSD - 95935), space group P21/m (No. 11). All these space groups are related by symmetry. By the use of these relations, we proposed starting models for the crystal structures of ScInGe2O7 and ScFeGe2O7. For ScInGe2O7 this was found to be isostructural to FeInGe2O7 reported by our laboratory [1]. The structural data for this compound were obtained by conventional Rietveld refinement of the powder diffraction data of X-rays, using the GSAS program and EXPGUI [2, 3] interface. For ScFeGe2O7 the symmetry related structural model was found in the triclinic system by symmetry reduction from the space group C2/m (unique axis b) to the triclinic space group P1 (figure 1). Rietveld refinement was performed reaching to the following results: lattice parameters a = 5.3434 (8), b = 5.3145 (8), c = 4.8732 (7 ) Å, α = 99 468 (2), β = 97 257 (2), γ = 104 609 (2)0, V = 130.03 (5) A3, Z = 1; WRp = 0.047, Rp = 0.04 and reduced χ2 of 2.176 for 64 variables. This study was sponsored by CONACyT project CB-2011/167624.

Die Kristallstrukturen von Verbindungen des Typs A2TeX6 (A = K, NH4, Rb, Cs; X = Cl, Br, I) / The Crystal Structures of Compounds A2TeX6 (A = K, NH4, Rb, Cs; X = Cl, Br, I)

1989 ◽  
Vol 44 (10) ◽  
pp. 1187-1194 ◽  
Author(s):  
Walter Abriel ◽  
André du Bois
Keyword(s):  
Crystal Structure ◽  
Low Temperature ◽  
Crystal Structures ◽  
Soft Mode ◽  
Type Structure ◽  
Ionic Radii ◽  
Space Group ◽  
Space Groups ◽  
Structure Space

With the determination of the crystal structure of (NH4)2TeI6 the list of the descriptions of A2TeX6 structures is further completed. At 293 K three structure types are observed with an antifluorite packing of cations and anions: The cubic K2PtCl6 type structure (space group Fm 3̄ m, Z = 4), the tetragonal Rb2TeI6 type structure (space group P4/mnc, Z = 2), and the monoclinic K2TeBr6 type structure (space group P21/n, Z = 2). The latter type was found for (NH4)2TeI6 with a = 8.0694(7), b = 8.0926(9), c = 11.7498(8) Å and β = 89.605(8)° and refined to a final Rw of 0.065. From ionic radii ratios the symmetry of the A2MX6 type structures can be predicted including a prediction of low temperature instability (soft mode condensation). Group-subgroup relationships connect the corresponding space groups and the space groups of the high/low temperature polymorphs.

scholarly journals One molecule, three crystal structures: conformational trimorphism of N-[(1S)-1-phenylethyl]benzamide

2020 ◽  
Vol 76 (8) ◽  
pp. 1229-1233
Author(s):  
Fermin Flores Manuel ◽  
Martha Sosa Rivadeneyra ◽  
Sylvain Bernès
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Solvent Mixtures ◽  
Screw Axis ◽  
Intermolecular Hydrogen Bonds ◽  
Space Group ◽  
Space Groups ◽  
Compound C ◽  
Chain Axis ◽  
Phenyl Rings

The title compound, C15H15NO, is an enantiopure small molecule, which has been synthesized many times, although its crystal structure was never determined. By recrystallization from a variety of solvent mixtures (pure acetonitrile, ethanol–water, toluene–ethanol, THF–methanol), we obtained three unsolvated polymorphs, in space groups P21 and P212121. Form I is obtained from acetonitrile, without admixture of other forms, whereas forms II and III are obtained simultaneously by concomitant crystallizations from alcohol-based solvent mixtures. All forms share the same supramolecular structure, based on infinite C 1 1(4) chain motifs formed by N—H...O intermolecular hydrogen bonds, as usual for non-sterically hindered amides. However, a conformational modification of the molecular structure, related to the rotation of the phenyl rings, alters the packing of the chains in the crystal structures. The orientation of the chain axis is perpendicular and parallel to the crystallographic twofold screw axis of space group P21 in forms I and II, respectively. As for form III, the asymmetric unit contains two independent molecules forming parallel chains in space group P212121, and the crystal structure combines features of monoclinic forms I and II.

A Priori Prediction of Crystal Structures

1996 ◽  
Vol 453 ◽  
Author(s):  
I. D. Brown
Keyword(s):  
Crystal Structures ◽  
Short Range ◽  
A Priori ◽  
Range Order ◽  
Space Group ◽  
Space Groups ◽  
Unit Space ◽  
Two Factors ◽  
Symmetry Operations ◽  
Principle Of Maximum

AbstractThe arrangement of atoms in a crystal is determined by two factors, the bonding preferences of individual atoms (giving rise to short range order), and the translational symmetry operations of the space group (giving rise to long range order). Chemical rules can be used to determine which atoms are bonded, and hence the maximum possible symmetry of the formula unit. Space group theory is then used to find the space groups that are compatible with this symmetry. In favourable cases, using the principle of maximum symmetry, the structure can be completely determined, but in all cases the analysis yields insights into the restrictions that determine what crystal structures might be possible.

On the choice of origins in the description of space groups

1980 ◽  
Vol 153 (3-4) ◽  
Author(s):  
H. Burzlaff ◽  
H. Zimmermann
Keyword(s):  
Monoclinic Symmetry ◽  
International Space ◽  
Space Group ◽  
Space Groups ◽  
Simple Rules

AbstractThe set of origins available in the description of space groups is investigated with respect to equivalence. Privileged origins may be derived employing two different criteria: (i) A unique origin can be found for each short international space-group symbol by the application of simple rules (origin related to the symbol). (ii) The first standard settings of the International Tables (1952) are chosen such that the set of equivalent origins is a subset of the origins of their affine or Euclidean normalizers respectively. A list of the affine normalizers for space groups with higher than monoclinic symmetry is presented.

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