Octahedral tilting in the tungsten bronzes

2015 ◽  
Vol 71 (3) ◽  
pp. 342-348 ◽  
Author(s):  
Thomas A. Whittle ◽  
Siegbert Schmid ◽  
Christopher J. Howard
Keyword(s):  
Group Theory ◽  
Computer Program ◽  
Unit Cell ◽  
Group Symmetry ◽  
Space Group Symmetry ◽  
Space Group ◽  
X Ray ◽  
Unit Cells ◽  
Octahedral Tilting ◽  
Special Points

Possibilities for `simple' octahedral tilting in the hexagonal and tetragonal tungsten bronzes (HTB and TTB) have been examined, making use of group theory as implemented in the computer programISOTROPY. For HTB, there is one obvious tilting pattern, leading to a structure in space groupP63/mmc. This differs from the space groupP63/mcmfrequently quoted from X-ray studies – these studies have in effect detected only displacements of the W cations from the centres of the WO6octahedra. The correct space group, taking account of both W ion displacement and the octahedral tilting, isP6322 – structures in this space group and matching this description have been reported. A second acceptable tilting pattern has been found, leading to a structure inP6/mmmbut on a larger `2 × 2 × 2' unit cell – however, no observations of this structure have been reported. For TTB, a search at the special points of the Brillouin zones revealed only one comparable tilting pattern, in a structure with space-group symmetryI4/mon a `21/2 × 21/2by 2' unit cell. Given several literature reports of larger unit cells for TTB, we conducted a limited search along the lines of symmetry and found structures with acceptable tilt patterns inBbmmon a `21/22 × 21/2 × 2' unit cell. A non-centrosymmetric version has been reported in niobates, inBbm2 on the same unit cell.

Berechnung der Frequenzverschiebungen von isotopen CO-Molekülkristallen

1966 ◽  
Vol 21 (6) ◽  
pp. 836-842 ◽  
Author(s):  
Hartwig Johansen
Keyword(s):  
Carbon Monoxide ◽  
Unit Cell ◽  
Harmonic Oscillators ◽  
Group Symmetry ◽  
Temperature Phase ◽  
Lattice Vibrations ◽  
Space Group Symmetry ◽  
Space Group ◽  
Unit Cells ◽  
G Matrices

The frequencies of the optically active lattice vibrations of carbon monoxide in the low temperature phase are calculated. The crystal structure is reported to be cubic with space group symmetry Pa3 and with four molecules per unit cell. The infrared spectrum of solid carbon monoxide at 20 °K (2000—3000 cm-1) given by Ewing and Pimentel is used. The molecular crystal is considered as an ensemble of harmonic oscillators, and the FG-matrix method of Wilson is applied. With the help of the F- and G-Matrices of a single unit cell, representing the interactions with 18 neighbouring unit cells too, 21 frequencies of the normal crystal and the isotopic crystals 13CO, 14CO, C17O, C18O are calculated. The frequencies of the translational and rotational lattice vibrations contribute to a combination band in the observed region in accord with the expected halfwidth. The calculated F- and G-matrix elements may be used for all diatomic molecular crystals with space group symmetry Pa3.

Vacancies and electron localization in the incommensurate intergrowth compound (La0.95Se)1.21VSe2

1996 ◽  
Vol 52 (3) ◽  
pp. 398-405 ◽  
Author(s):  
Y. Ren ◽  
J. Baas ◽  
A. Meetsma ◽  
J. L. de Boer ◽  
G. A. Wiegers
Keyword(s):  
Reciprocal Lattice ◽  
Basic Structure ◽  
Unit Cell ◽  
Group Symmetry ◽  
Charge Balance ◽  
Layer Compound ◽  
Space Group Symmetry ◽  
Space Group ◽  
Structure Unit ◽  
Salt Structure

The structure of the inorganic misfit layer compound (La0.95Se)1.21VSe2 has been determined on the basis of a four-dimensional superspace group. The crystal is composed of an alternate stacking of VSe2 sandwiches and two-atom-thick LaSe layers. The first subsystem VSe2 has a distorted CdI2-type structure with V atoms in trigonal antiprisms of Se atoms. It has space-group symmetry C{\bar 1} and its basic structure unit-cell dimensions are a 11 = 3.576 (3), a 12 = 6.100 (2), a13 = 11.690 (2) Å, α 1 = 95.12 (2), β 1 = 85.96 (2) and γ = 89.91 (2)°. The second subsystem LaSe has a distorted rock-salt structure with space-group symmetry C{\bar 1} and a basic structure unit cell given by a 21 = 5.911 (2), a 22 = 6.101 (2), a 23 = 11.684 (2) Å, α 2 = 95.07 (2), β 2 = 85.76 (2), γ 2 = 90.02 (2)°. The two subsystems have the common (a* ν2, a* ν3) plane and have a displacive modulation according to the two mutually incommensurate periodicities along the v1 axes. The symmetry of the complete system is described by the superspace group Gs = C{\bar 1} [0.6050 (7), 0.0020 (7), −0.007 (1)] with C-centring (½,½, 0, ½). Reciprocal lattice parameters for this superstructure embedding are (a * 1, a * 2, a * 3, a * 4) = (a * 11, a * 12, a * 13, a * 21). For 2125 unique reflections with I> 2.5σ(I), measured using Mo Kα1 radiation, refinement smoothly converged to wR = 0.055 (R = 0.045) on a modulated structure model with 77 parameters including La vacancies. The presence of ~ 5% of La vacancies in the LaSe subsystem leads to an exact charge balance between La3+, V3+ and Se2−. The largest modulation occurs on the V atoms, which results in strong variation in the V—V distances. Thus, the semiconducting behaviour of this compound is interpreted in terms of La vacancies in LaSe and modulation-induced Mott localization in VSe2.

scholarly journals Synthesis, Crystal Structures and Thermal Properties of Ammine Barium Borohydrides

Inorganics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 57 ◽  
Author(s):  
Jakob B. Grinderslev ◽  
Mads B. Amdisen ◽  
Torben R. Jensen
Keyword(s):  
Synthesis Method ◽  
Earth Metal ◽  
Structure Type ◽  
Unit Cell ◽  
Group Symmetry ◽  
Orthorhombic Unit Cell ◽  
Space Group Symmetry ◽  
Space Group ◽  
Dihydrogen Bonds ◽  
Photographic Analysis

Ammine metal borohydrides show large compositional and structural diversity, and have been proposed as candidates for solid-state ammonia and hydrogen storage as well as fast cationic conductors. Here, we report the synthesis method of ammine barium borohydrides, Ba(BH4)2·xNH3 (x = 1, 2). The two new compounds were investigated with time-resolved temperature-varied in situ synchrotron radiation powder X-ray diffraction, thermal analysis, infrared spectroscopy and photographic analysis. The compound Ba(BH4)2·2NH3 crystallizes in an orthorhombic unit cell with space group symmetry Pnc2, and is isostructural to Sr(BH4)2·2NH3, forming octahedral [Ba(NH3)2(BH4)4] complexes, which are connected into a two-dimensional layered structure, where the layers are interconnected by dihydrogen bonds, N–Hδ+⋯−δH–B. A new structure type is observed for Ba(BH4)2·NH3, which crystallizes in an orthorhombic unit cell with space group symmetry P212121, forming a three-dimensional framework structure of [Ba(NH3)(BH4)6] complexes. The structure is built from distorted hexagonal chains, where NH3 groups form dihydrogen bonds to the nearby BH4−-groups within the chain. Ba(BH4)2·2NH3 is unstable at room temperature and releases NH3 in two subsequent endothermic reactions with maxima at 49 and 117 °C, eventually reforming Ba(BH4)2. We demonstrate that the thermal stability and composition of the gas release for the ammine alkaline earth metal borohydrides can be correlated to the charge density of the metal cation, but are also influenced by other effects.

Computer derivation of the symmetry elements implied in a structure description

1987 ◽  
Vol 20 (3) ◽  
pp. 264-269 ◽  
Author(s):  
Y. Le Page
Keyword(s):  
Computer Program ◽  
Experimental Evidence ◽  
Group Symmetry ◽  
Structural Symmetry ◽  
Space Group Symmetry ◽  
Space Group ◽  
Structure Description ◽  
Cell Data ◽  
Atomic Coordinates

The space-group symmetry implied in the atomic coordinates of a structure can be reconstructed by deriving the metric symmetry elements of the lattice from the cell data, and finding the location and the glide for corresponding space-group symmetry elements with the same orientation using the list of atomic coordinates. The MISSYM computer program designed along these principles treated correctly the known examples of overlooked symmetry or quasi-symmetry that were submitted to it. As no computer program operating on refined atomic coordinates can prove the presence of extra symmetry in the crystal, the user should scrutinize the experimental evidence and report either a different space group or the existence of pseudo-symmetry whenever extra structural symmetry elements are disclosed by the program. The MISSYM program is part of the NRCVAX system of programs.

Group-theoretical analysis of octahedral tilting in ferroelectric perovskites

2002 ◽  
Vol 58 (6) ◽  
pp. 934-938 ◽  
Author(s):  
Harold T. Stokes ◽  
Erich H. Kisi ◽  
Dorian M. Hatch ◽  
Christopher J. Howard
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Landau Theory ◽  
Group Symmetry ◽  
Theoretical Methods ◽  
Space Group Symmetry ◽  
Space Group ◽  
First Order ◽  
Octahedral Tilting ◽  
Group Theoretical Analysis

Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present. This results in a list of 40 different structures, each with a unique space-group symmetry. The list is compared with that of Aleksandrov & Bartolomé [Phase Transit. (2001), 74, 255–335] and a number of differences are found. The group–subgroup relationships between the structures are also determined, along with an indication of those phase transitions that must be first order by Landau theory.

scholarly journals The crystal structure of the alums

1935 ◽  
Vol 148 (865) ◽  
pp. 664-680 ◽  
Keyword(s):  
Crystal Structure ◽  
Group Theory ◽  
Unit Cell ◽  
High Symmetry ◽  
Space Group ◽  
X Ray

The literature on the structure of the alums is fairly extensive, for though the formula is complex, the problem is greatly simplified by the high symmetry of the crystal. Nevertheless, none of the proposed structures has been fully supported by X-ray measurements. The first published work was that of Vegard and Schjelderup, but, though they arrived at the correct unit cell, their structure involved an improbable arrangement of atoms, in which the identity of even the SO 4 group was lost. On this ground it was strongly criticized by Schaefer and Schubert, and Niggli showed that it was also incompatible with space-group theory. From Vegard and Schjelderup's measurements he assigned the alums to the space-group T h 2 (Pn3), but Wyckoff, by means of Laue and rotation photographs, showed that this was incorrect, and that the space-group was T h 2 (Pa3).

scholarly journals Crystallographic CourseWare

1999 ◽  
Vol 32 (2) ◽  
pp. 327-331
Author(s):  
M. E. Kastner
Keyword(s):  
Crystal Growth ◽  
Graduate Students ◽  
Reciprocal Space ◽  
Group Symmetry ◽  
Space Group Symmetry ◽  
Space Group ◽  
Computer Animations ◽  
Growth Plane ◽  
Unit Cells ◽  
Interactive Exercises

Crystallographic CourseWareis a set of computer animations and interactive exercises designed to assist undergraduate and introductory graduate students in their learning of crystallography. Topics discussed include crystal growth, plane- and space-group symmetry elements, unit cells and asymmetric units, reciprocal space, precession photographs, and an introduction to reading theInternational Tables for Crystallography.

Structure determination of A 2 M 3+TaO6 and A 2 M 3+NbO6 ordered perovskites: octahedral tilting and pseudosymmetry

2006 ◽  
Vol 62 (3) ◽  
pp. 384-396 ◽  
Author(s):  
Paris W. Barnes ◽  
Michael W. Lufaso ◽  
Patrick M. Woodward
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Structure Determination ◽  
Unit Cell ◽  
Powder Diffraction Data ◽  
Space Group ◽  
X Ray ◽  
Cell Dimensions ◽  
Octahedral Tilting ◽  
Unit Cell Dimensions

The room-temperature crystal structures of six A 2 M 3+ M 5+O6 ordered perovskites have been determined from neutron and X-ray powder diffraction data. Ba2YNbO6 adopts the aristotype high-symmetry cubic structure (space group Fm\overline 3m, Z = 4). The symmetries of the remaining five compounds were lowered by octahedral tilting distortions. Out-of-phase rotations of the octahedra about the c axis were observed in Sr2CrTaO6 and Sr2GaTaO6, which lowers the symmetry to tetragonal (space group = I4/m, Z = 2, Glazer tilt system = a 0 a 0 c −). Octahedral tilting analogous to that seen in GdFeO3 occurs in Sr2ScNbO6, Ca2AlNbO6 and Ca2CrTaO6, which lowers the symmetry to monoclinic (space group P21/n, Z = 2, Glazer tilt system = a − a − c +). The Sr2 MTaO6 (M = Cr, Ga, Sc) compounds have unit-cell dimensions that are highly pseudo-cubic. Ca2AlNbO6 and Ca2CrTaO6 have unit-cell dimensions that are strongly pseudo-orthorhombic. This high degree of pseudosymmetry complicates the space-group assignment and structure determination. The space-group symmetries, unit-cell dimensions and cation ordering characteristics of an additional 13 compositions, as determined from X-ray powder diffraction data, are also reported. An analysis of the crystal structures of 32 A 2 MTaO6 and A 2 MNbO6 perovskites shows that in general the octahedral tilt system strongly correlates with the tolerance factor.

Anomalies in silicon carbide polytypes

1963 ◽  
Vol 272 (1351) ◽  
pp. 490-502 ◽  
Keyword(s):  
Silicon Carbide ◽  
Basic Structure ◽  
Microscopic Investigation ◽  
Unit Cell ◽  
Dislocation Theory ◽  
Dislocation Mechanism ◽  
Space Group ◽  
X Ray ◽  
Unit Cells ◽  
Surface Examination

Frank’s dislocation theory of the origin of polytypism received direct experimental support from the observation of a correlation between the step height of growth spirals on silicon carbide polytypes and the heights of their X-ray unit cells (Verma 1952, 1957). A detailed X-ray diffraction and microscopic investigation of silicon carbide structures has revealed anomalies that cannot be explained on the dislocation theory. Three new unusual polytypes 36 H a , 36 H b and 90 R are described in detail. The structures 36 H a and 36 H b were found in a single crystal piece and have identical lattices with a = b = 3.078 Å and c = 90.65 Å. Both structures belong to the space group P 3 m . The polytype 90 R belongs to the space group R 3 m with hexagonal unit cell dimensions a = b = 3.078 Å, c = 226.6 Å. The detailed atomic structure of type 90 R has been worked out and has a Zhdanov symbol [(23) 4 3322] 3 . It is shown that the polytypes 36 H a and 36 H b are based on the 6 H phase while type 90 R is based on the 15 R phase. The creation of such polytypes requires a screw dislocation with a Burgers vector which is an integral multiple of the c spacing of the basic structure, and is therefore not understood on Frank’s theory. A surface examination of the faces of these crystals does not reveal any growth spirals, showing that they have not grown by the dislocation mechanism. The growth of the different polytypes of silicon carbide is discussed and it appears that screw dislocations determine the surface structure but not the contents of the unit cell and therefore the cause of polytypism needs to be reconsidered.

Cadmium complexes of thiones. Part II.1 A synthetic, solution, and solid-state MAS 111/113Cd NMR study of cadmium complexes of 1,3-thiazolidine-2-thione, and the structures of [tetrakis(1,3-thiazolidine-2-thione)cadmium] trifluoromethanesulfonate ([Cd(C3H5NS2)4](CF3SO3)2) and [tetrakis(1,3-thiazolidine-2-thione)cadmium][tetrakis(nitrato-O,O')cadmate] ([Cd(C3H5NS2)4][Cd(O2NO)4])

2001 ◽  
Vol 79 (9) ◽  
pp. 1330-1337
Author(s):  
Umarani Rajalingam ◽  
Philip AW Dean ◽  
Hilary A Jenkins ◽  
Michael Jennings ◽  
James M Hook
Keyword(s):  
Point Group ◽  
Mas Nmr ◽  
Unit Cell ◽  
Group Symmetry ◽  
Cadmium Complexes ◽  
Space Group ◽  
X Ray ◽  
Nmr Data ◽  
Group I ◽  
Cp Mas Nmr

Treatment of Cd(O3SCF3)2 with the stoichiometric quantity of 1,3-thiazolidine-2-thione (tztH) allows isolation of [Cd(tztH)4](O3SCF3)2 (1). When tztH:Cd [Formula: see text] 2 the reaction of Cd(NO3)2·4H2O with tztH leads to [Cd(tztH)4][Cd(O2NO)4] (2). The structures of both 1 and 2 have been determined by single crystal X-ray analysis. Colourless crystals of 1 are orthorhombic, space group Fdd2, with eight molecules per unit cell (Z = 8) of dimensions a = 20.139(3), b = 23.332(5), c = 14.214(3) Å. Those of 2 are tetragonal, space group I [Formula: see text], with four molecules per unit cell (Z = 4) of dimensions a = 13.8853(11), c = 8.077(2) Å. The discrete homoleptic cation [Cd(tztH)4]2+ is characterized for the first time in 1 and 2. The cations are of point group symmetry C2 and S4 in 1 and 2, respectively. In both cases the ligands are S-bound, and the CdS4 kernel is a squashed tetrahedron. In 2, the eight-coordinate anion [Cd(O2NO)4]2- is characterized for the second time. 113Cd CP MAS NMR data are reported for solid 1 and 2, and also for solids produced by fusing Cd(NO3)2·4H2O with different molar ratios amounts of tztH, and by fusing Cd(O3SCF3)2 with six mol equivalents of tztH. In the Cd(NO3)2·4H2O:tztH mixtures, species identified include unreacted cadmium salt 2 ([Cd(tztH)4](NO3)2) and possibly Cd(tztH)3(NO3)2. [Cd(tztH)4](NO3)2 becomes the major species only when a significant excess of tztH is used. In the mixtures with tztH:Cd > 4, neither Cd(NO3)2·4H2O nor Cd(O3SCF3)2 form complexes containing more than four tztH ligands. Reduced-temperature 111Cd NMR data are reported for Cd(ClO4)2·6H2O:tztH mixtures in MeOH. Species identified are Cd(tztH)w2+(solv) (w = 0–3).Key words: 1,3-thiazolidine-2-thione, cadmium complexes, X-ray analysis, 113Cd CP MAS NMR, solution 111Cd NMR, tetrakis(1,3-thiazolidine-2-thione)cadmium(2+) cation, tetrakis(nitrato-O,O')cadmate(2–) anion.

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