2. Symmetry

2016 ◽  
pp. 24-38
Author(s):  
A. M. Glazer
Keyword(s):  
Crystal Structure ◽  
Reflection Point ◽  
Notation System ◽  
Space Group ◽  
Space Groups ◽  
Different Types ◽  
Point Groups

In order to explain what crystals are and how their structures are described, we need to understand the role of symmetry, for this lies at the heart of crystallography. ‘Symmetry’ explains the different types of symmetry: rotational, mirror or reflection, point, chiral, and translation. There are thirty-two point groups and seven crystal systems, according to which symmetries are present. These are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Miller indices, lattices, crystal structure, and space groups are described in more detail. Any normal crystal belongs to one of the 230 space group types. Crystallographers generally use the International Notation system to denote these space groups.

Frequency distribution of space groups in soluble and membrane proteins and their complexes

2021 ◽  
Vol 77 (6) ◽  
pp. 187-191
Author(s):  
Rajneesh K. Gaur
Keyword(s):  
Membrane Proteins ◽  
Frequency Distribution ◽  
Data Bank ◽  
Frequency Distributions ◽  
Space Group ◽  
Space Groups ◽  
Group Frequency ◽  
Different Types ◽  
Analytical Assessment ◽  
Three Space

The space-group frequency distributions for two types of proteins and their complexes are explored. Based on the incremental availability of data in the Protein Data Bank, an analytical assessment shows a preferential distribution of three space groups, i.e. P212121 > P1211 > C121, in soluble and membrane proteins as well as in their complexes. In membrane proteins, the order of the three space groups is P212121 > C121 > P1211. The distribution of these space groups also shows the same pattern whether a protein crystallizes with a monomer or an oligomer in the asymmetric unit. The results also indicate that the sizes of the two entities in the structures of soluble proteins crystallized as complexes do not influence the frequency distribution of space groups. In general, it can be concluded that the space-group frequency distribution is homogenous across different types of proteins and their complexes.

scholarly journals From space to superspace and back: Superspace Group Finder

2008 ◽  
Vol 41 (6) ◽  
pp. 1182-1186 ◽  
Author(s):  
Ivan Orlov ◽  
Lukas Palatinus ◽  
Gervais Chapuis
Keyword(s):  
Crystal Structure ◽  
Dimensional Space ◽  
Flexible Structures ◽  
Three Dimensional ◽  
Real Space ◽  
Space Group ◽  
Space Groups ◽  
Group A ◽  
Modular Composition ◽  
Three Dimensional Space

The symmetry of a commensurately modulated crystal structure can be described in two different ways: in terms of a conventional three-dimensional space group or using the superspace concept in (3 +d) dimensions. The three-dimensional space group is obtained as a real-space section of the (3 +d) superspace group. A complete network was constructed linking (3 + 1) superspace groups and the corresponding three-dimensional space groups derived from rational sections. A database has been established and is available at http://superspace.epfl.ch/finder/. It is particularly useful for finding common superspace groups for various series of modular (`composition-flexible') structures and phase transitions. The use of the database is illustrated with examples from various fields of crystal chemistry.

scholarly journals Different Roles of Ce3+ Optical Centers in Oxyorthosilicate Nanocrystals at X-ray and UV Excitation

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 114 ◽  
Author(s):  
Vladyslav Seminko ◽  
Pavel Maksimchuk ◽  
Iryna Bespalova ◽  
Yuri Malyukin
Keyword(s):  
Crystal Structure ◽  
Dominant Role ◽  
Luminescence Spectra ◽  
Photoluminescence Intensity ◽  
Bulk Crystals ◽  
Space Group ◽  
X Ray ◽  
Oxygen Coordination ◽  
Cation Sites

Luminescence properties of Lu2SiO5:Ce3+ and Y2SiO5:Ce3+ nanocrystals were studied using photo- and X-ray luminescence techniques. The crystal structure of Re2SiO5 nanocrystals (P21/c space group) differs from the crystal structure of Re2SiO5 bulk crystals (C2/c space group) with 9- and 7-oxygen-coordinated cation positions instead of 6- and 7-coordinated ones observed for Re2SiO5 bulk crystals. Two optical centers (Ce1 and Ce2) were observed for Re2SiO5:Ce3+ nanocrystals originating from cerium ions substituting 9- and 7-oxygen-coordinated cation sites. Preferential substitution of larger cation sites by cerium ions leads to higher photoluminescence intensity of Ce1 centers, however, Ce2 centers are the main centers for electron-hole recombination, so only Ce2 band is observed in X-ray luminescence spectra. The features of oxygen coordination of Ce1 and Ce2 centers and high content of oxygen vacancies in Re2SiO5:Ce3+ nanocrystals can provide preferential trapping of electrons near Ce2 centers, and therefore, the dominant role of Ce2 band in X-ray luminescence spectra.

Synthesis and Structure of the Methylated Tren Derivative N,N,N-Tris(2-aminoethyl)-N-methylammonium Chloride Trihydrochloride

2002 ◽  
Vol 55 (4) ◽  
pp. 263 ◽  
Author(s):  
A. G. Blackman
Keyword(s):  
Crystal Structure ◽  
Coordination Number ◽  
Dimethyl Sulfate ◽  
Space Group ◽  
One Dimensional ◽  
X Ray ◽  
Counter Ions ◽  
Different Types ◽  
Methylammonium Chloride ◽  
Ethyl Amine

The synthesis and X-ray crystal structure of the new tren derivative N,N,N-tris(2-aminoethyl)-N-methylammonium chloride trihydrochloride are detailed. The compound was synthesized by methylation of tris(2-phthalimido-ethyl)amine using dimethyl sulfate followed by acid deprotection. N,N,N-Tris(2-aminoethyl)-N-methylammonium chloride trihydrochloride crystallizes in the hexagonal space group P63 and the X-ray crystal structure reveals one-dimensional chains of cations extensively hydrogen-bonded to two different types of chloride counter ions, one of which exhibits a coordination number of nine. The cation is a poor ligand towards both CoIII and NiII.

Lack of a threefold rotation axis in α-Fe2O3and α-Cr2O3crystals

2015 ◽  
Vol 71 (2) ◽  
pp. 203-208 ◽  
Author(s):  
Michał Stękiel ◽  
Radosław Przeniosło ◽  
Izabela Sosnowska ◽  
Andrew Fitch ◽  
Jacek B. Jasiński ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Rotation Axis ◽  
Magnetic Ordering ◽  
Evidence Based ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Transmission Electron

The crystal structure of α-Fe2O3and α-Cr2O3is usually described with the corundum-type trigonal crystal structure based on the space group R\bar 3c. There are, however, some observations of the magnetic ordering of both α-Fe2O3and α-Cr2O3that are incompatible with the trigonal symmetry. We show experimental evidence based on X-ray powder diffraction and supported by transmission electron microscopy that the symmetry of the crystal structure of both α-Fe2O3and α-Cr2O3is monoclinic and it is described with the space groupC2/c(derived from R\bar 3c by removing the threefold rotation axis). The magnetic orderings of α-Fe2O3and α-Cr2O3are compatible with the magnetic space groupsC2/candC2/c′, respectively. These findings are in agreement with the idea from Curie [(1894),J. Phys.3, 393–415] that the dissymmetry of the magnetic ordering should be associated with a dissymmetry of the crystal structure.

3D Braided Geometry Structures Based on Space Group

2010 ◽  
Vol 152-153 ◽  
pp. 1156-1161 ◽  
Author(s):  
Wen Suo Ma ◽  
Bin Qian Yang ◽  
Xiao Zhong Ren
Keyword(s):  
Group Theory ◽  
Symmetry Groups ◽  
The Novel ◽  
Geometrical Structures ◽  
Braided Group ◽  
Space Group ◽  
Space Groups ◽  
Geometry Structure ◽  
Point Groups ◽  
Space Point

3D braided group theory is dissertated. The analysis procedure is described from the existing braided geometry structure to the braided space group; 3D braided geometrical structures are finally described by means of group theory. Some of novel 3D braided structures are deduced from the braided space groups. By describing the 3D braided materials with braided space point and braided space groups, the braided space groups are not always the same as symmetry groups of crystallographic because novel lattices can be produced and the reflection operation cannot exist in braided space point groups. Braided point and space groups are theoretical basis for deriving the novel braided geometry structure.

Systematic prediction of new ferroelectrics in space groups P31 and P32

2003 ◽  
Vol 59 (5) ◽  
pp. 541-556 ◽  
Author(s):  
S. C. Abrahams
Keyword(s):  
Crystal Structure ◽  
Confidence Level ◽  
Inorganic Crystal Structure Database ◽  
Space Group ◽  
Space Groups ◽  
Structure Database ◽  
Inorganic Crystal ◽  
Atomic Coordinates ◽  
Crystal Structure Database

Release 2002/2 of the Inorganic Crystal Structure Database (FIZ Karlsruhe, Germany, and Institute Laue–Langevin, Grenoble, France) contains 62 entries in space group P31 and ten entries in space group P32 for 49 different materials including eight families with two or more isostructural members. The structural criteria for ferroelectricity are satisfied for 16 new structure types at a confidence level that depends on the reliability of each determination. LaBGeO5, a mineral with stillwellite structure, was previously reported as ferroelectric and forms an additional family with seven other members or related structures that satisfy the criteria. Ten structures reported in space group P31 or P32 are dubious or incorrect, with atomic coordinates that satisfy supergroup symmetry. One material is probably pyroelectric but is unlikely to become ferroelectric, and three others are either incompletely solved or incompletely refined. Among the predicted new ferroelectrics are Cu2BaGeS4, Fe3(Fe,Si)O4(OH)5, Se4S5, K2HCr2AsO10, IV-RbNO3, Rb2Sc(NO3)5, Na3ReO5, Nd14(GeO4)2(BO3)6O8, CsHgCl3, Ba2Cu2AlF11, KYF4, SrS2O6·4H2O, Cu3PbTeO6(OH)2, ReH(CO)4, Ni2(NH3)9Mo(CN)8·2H2O and the 6T polytype of Ca1.89Ta1.80Sm0.16Ti0.10O7, in addition to β-LaBSiO5, PbBAsO5 and BaBAsO5 in the stillwellite family.

scholarly journals Структурные особенности твердых растворов Nd-=SUB=-x-=/SUB=-Gd-=SUB=-1-x-=/SUB=-Cr-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

2021 ◽  
Vol 129 (1) ◽  
pp. 41
Author(s):  
К.Н. Болдырев ◽  
Н.Н. Кузьмин ◽  
Е.А. Добрецова
Keyword(s):  
Crystal Structure ◽  
Transition Region ◽  
Absorption Spectra ◽  
Solid Solutions ◽  
Concentration Effect ◽  
Optical Studies ◽  
Space Group ◽  
Space Groups ◽  
Significant Concentration

Optical studies of NdxGd1-xCr3(BO3)4 0.01≤x≤1 crystals have been carried out. A significant concentration effect of the Nd3+ ion on the crystal structure of these solid solutions was identified. It was found from the absorption spectra of neodymium ions in the 4I9/2→11F3/2 transition region that at a concentration x>0.6 two nonequivalent Nd3+ centers appear, which is explained by the formation of two polytype modifications with space groups R32 and C2/c. At a concentration x<0.6, only one modification with the space group R32 is observed.

Zur Kenntnis des Kupfer-Oxid-Arsenats Cu4O(A sO4)2 / On the Copper Oxide Arsenate Cu4O(AsO4)2

1996 ◽  
Vol 51 (9) ◽  
pp. 1279-1282 ◽  
Author(s):  
M. Staack ◽  
Hk. Müller-Buschbaum
Keyword(s):  
Crystal Structure ◽  
Copper Oxide ◽  
Single Crystal ◽  
Copper Ions ◽  
Space Group ◽  
X Ray ◽  
Different Types ◽  
Symmetry Space ◽  
Symmetry Space Group ◽  
Anionic Part

The copper oxide arsenate Cu4O(AsO4)2 has been prepared and investigated by single crystal X-ray techniques. The compound crystallizes with triclinic symmetry, space group C1i-P1̄, a = 6.4148(7), b = 7.6549(5), c = 8.2241(7) Å, α = 98.52(1), β = 112.39(1), 7 = 98.38(1)°, Z = 2. Cu4O(AsO4)2 is isotypic to Cu4(PO4)2O . Copper ions on one of the four specified sites show nearly planar coordination by O2- and may be assigned to the anionic part of the crystal structure. One of the nine different types of oxygen atoms is coordinated by copper exclusively. The compound is therefore classified as an oxide arsenate.

Systematic prediction of new inorganic ferroelectrics in point group 4

1999 ◽  
Vol 55 (4) ◽  
pp. 494-506 ◽  
Author(s):  
S. C. Abrahams
Keyword(s):  
Crystal Structure ◽  
Point Group ◽  
Inorganic Crystal Structure Database ◽  
Space Group ◽  
Space Groups ◽  
Group 4 ◽  
Structure Database ◽  
Inorganic Crystal ◽  
Crystal Structure Database

The latest release of the Inorganic Crystal Structure Database contains a total of 87 entries corresponding to 70 different materials in point group 4. The structures reported for 11 materials in space group P4 satisfy the criteria for ferroelectricity, as do four in P41, one each in P42 and P43, 12 in I4, including seven that form three families, and another three in I41. Three previously known ferroelectrics were also listed in I4 and one in I41. In addition, the listing for point group 4 contains 22 entries for nonferroelectric materials and three with misassigned space groups. Among the newly predicted ferroelectrics in point group 4, assuming the validity of the underlying structural reports, are Ce5B2C6, modulated NbTe4, Na3Nb12O31F, Ca2FeO3Cl, K4CuV5O15Cl, TlBO2, CrOF3, PbTeO3, VO(HPO3)(H2O).3H2O, MgB2O(OH)6, β-tetragonal boron, CuBi2O4, WOBr4, Na8PtO6, SbF2Cl3, Ba1.2Ti8O16, Ni[SC(NH2)2]4Cl2, Ca2SiO3Cl2, the mineral caratiite, NbAs, β-NbO2 and Ag3BiO3.

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