The polar phase of Li2Ge4O9at 298, 150 and 90 K

2013 ◽  
Vol 69 (10) ◽  
pp. 1091-1095 ◽  
Author(s):  
Günther J. Redhammer ◽  
Gerold Tippelt
Keyword(s):  
Three Dimensional ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Polar Phase ◽  
Orthorhombic Space Group ◽  
Ferroelectric State ◽  
Space Group Symmetry ◽  
Space Group ◽  
Coordination Spheres

Dilithium tetragermanate is orthorhombic, space groupP21ca, at 298 K, and is thus in a polar and probably a ferroelectric state. The structure contains two independent Li, four Ge and nine O atoms, all on general positions with site symmetry 1. Three tetrahedrally coordinated Ge positions form crumpled crankshaft-like chains, forming sheets within theacplane, and these are interconnected by the fourth, octahedrally coordinated, Ge sites along thebdirection. The GeO4tetrahedra and GeO6octahedra form a three-dimensional framework containing two different cavities, hosting the two 4+1-coordinated Li sites. Cooling to 90 K does not alter the space-group symmetry; the tetrahedral chains behave as a rigid unit and changes occur mainly within the Li coordination spheres.

scholarly journals Dimanganese(II) hydroxide vanadate, Mn2(OH)[VO4]

2014 ◽  
Vol 70 (7) ◽  
pp. i33-i33 ◽  
Author(s):  
Kewen Sun ◽  
Angela Möller
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Point Group Symmetry ◽  
Distorted Octahedral Coordination ◽  
Trigonal Bipyramidal ◽  
Distorted Octahedral ◽  
Coordination Spheres ◽  
Distorted Trigonal Bipyramidal

Dimanganese(II) hydroxide vanadate was obtained from hydrothermal reactions. The crystal structure of the title compound is isotypic with that of Zn2(OH)[VO4]. Three crystallographically independent Mn2+ions are present, one (site symmetry .m.) with a distorted trigonal-bipyramidal and two (site symmetries .m. and 1) with distorted octahedral coordination spheres. These polyhedra are linked through common edges, forming a corrugated layer-type of structure extending parallel to (100). A three-dimensional framework resultsviaadditional Mn—O—V—O—Mn connectivities involving the two different tetrahedral [VO4] units (each with point-group symmetry .m.). O—H...O hydrogen bonds (one bifurcated) between the OH functions (both with point-group symmetry .m.) and the [VO4] units complete this arrangement.

Crystal structures of the relaxor oxide Pb2(ScTa)O6in the paraelectric and ferroelectric states

2002 ◽  
Vol 35 (2) ◽  
pp. 233-242 ◽  
Author(s):  
P. M. Woodward ◽  
K. Z. Baba-Kishi
Keyword(s):  
Powder Diffraction ◽  
Lone Pair ◽  
Domain Size ◽  
Group Symmetry ◽  
Coordination Polyhedra ◽  
Ferroelectric State ◽  
Space Group Symmetry ◽  
Space Group ◽  
Paraelectric State ◽  
Cooperative Ordering

The crystal structure of the relaxor ferroelectric Pb2ScTaO6has been refined from high-resolution neutron time-of-flight powder diffraction data recorded at various temperatures from 4 to 400 K. Upon warming, Pb2ScTaO6undergoes a first-order transition at 295 K from the rhombohedral ferroelectric state into the cubic paraelectric state. At 4.2 K, in the ferroelectric state, this compound adoptsR3 space-group symmetry, witha= 8.15231 (7) Å and α = 89.8488 (3)°. At 400 K, in the paraelectric state, this compound adoptsFm\bar{3}mspace-group symmetry, witha= 8.15345 (3) Å. In the ferroelectric state, the Pb2+coordination polyhedra are quite asymmetric, clearly indicating the presence of a stereoactive electron lone pair. The Sc3+and Ta5+ions are also shifted away from the centers of their respective octahedra, each toward an octahedral face. The large displacement parameters associated with both the Pb and the O ions, in the 400 K structure reveal significant local shifts of these ions from their ideal sites in the paraelectric state. Thus, the paraelectric to ferroelectric transition is driven by long-range cooperative ordering of the cation displacements. Synchrotron X-ray powder diffraction measurements are used to estimate the domain size of the Sc3+/Ta5+ordering and the ferroelectric cation displacements as 88 nm and 10 nm, respectively.

scholarly journals Temperature-resolved study of three [M(M′O4)4(TBPO)4] complexes (MM′ = URe, ThRe, ThTc)

2006 ◽  
Vol 62 (1) ◽  
pp. 68-85 ◽  
Author(s):  
Madeleine Helliwell ◽  
David Collison ◽  
Gordon H. John ◽  
Iain May ◽  
Mark J. Sarsfield ◽  
...  
Keyword(s):  
Crystal Structures ◽  
Room Temperature ◽  
Atomic Displacement ◽  
The Body ◽  
Group Symmetry ◽  
Orthorhombic Space Group ◽  
Space Group Symmetry ◽  
Space Group ◽  
Group I ◽  
Atomic Displacement Parameters

The crystal structures of the title complexes were measured at several temperatures between room temperature and 100 K. Each sample shows reversible crystal-to-crystal phase transitions as the temperature is varied. The behaviour of [U(ReO4)4(TBPO)4] (I) and [Th(ReO4)4(TBPO)4] (II) (TBPO = tri-n-butylphosphine oxide) is very similar; at room temperature, crystals of (I) and (II) are isostructural, with space group I\bar 42m, and reducing the temperature to 100 K causes a lowering of the space-group symmetry to C-centred cells, space groups Cc for (I) and Cmc21 for (II). The variation of lattice symmetry of [Th(TcO4)4(TBPO)4] (III) was found to be somewhat different, with the body-centred cubic space group, I\bar 43m, occurring at 293 K, a reduction of symmetry at 230 K to the C-centred orthorhombic space group, Cmc21, and a further transition to the primitive orthorhombic space group, Pbc21, below 215 K. Elucidation of the correct space-group symmetry and the subsequent refinement was complicated in some cases by the twinning by pseudo-merohedry that arises from the lowering of the space-group symmetry, occurring as the temperature is reduced. All three of the crystal structures determined at room temperature have high atomic displacement parameters, particularly of the n Bu groups, and (III) shows disorder of some of the O atoms. The structures in the space group Cmc21, show some disorder of n Bu groups, but are otherwise reasonably well ordered; the structures of (I) in Cc and (III) in Pbc21 are ordered, even to the ends of the alkyl chains. Inter-comparison of the structures measured below 293 K, using the program OFIT from the SHELXTL package, showed that generally, they are remarkably alike, with weighted r.m.s. deviations of the M, M′ and P atoms of less than 0.1 Å, as are the 293 K structures of (I) and (II) with their low-temperature counterparts. However, the structure of (III) measured in the space group Cmc21 is significantly different from both the structure of (III) at 293 K and that found below 215 K, with weighted r.m.s. deviations of the Th, Tc and P atoms of 0.40 and 0.37 Å, respectively. An extensive network of weak intra- and intermolecular C—H...O hydrogen bonds found between the atoms of the n Bu and [M′O4] groups probably influences the packing and the overall geometry of the molecules.

Symmetrieverwandtschaften bei Varianten des Perowskit-Typs

2002 ◽  
Vol 58 (4) ◽  
pp. 594-606 ◽  
Author(s):  
Oliver Bock ◽  
Ulrich Müller
Keyword(s):  
Phase Transitions ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Temperature Dependent ◽  
Space Group Symmetry ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Reductions ◽  
Jahn Teller ◽  
Perovskite Type

The relationships among the huge number of derivative structures of the perovskite type are rationalized in a concise manner using group–subgroup relations between space groups. One family tree of such relations is given for perovskites having tilted coordination octahedra. Further group–subgroup relations are concerned with distortions of the octahedra, such as Jahn–Teller distortions or with atoms shifted from the octahedron centres. In these cases, the space-group symmetry reductions must allow site symmetry reductions of the occupied sites in the perovskite structure. On the other hand, subgroups in which the perovskite sites split into different independent sites are necessary for derivative structures with atom substitutions, such as in the elpasolites A 2 EMX 6. In addition, substitutions and distortions can be combined in adequate subgroups. Substitutions may also involve the occupation of atom sites of perovskite by molecular groups such as N(CH3)4 + or other organic cations, or by molecules like acetonitrile. If they are ordered, their molecular symmetry requires further space-group symmetry reductions. The anions can be replaced by cyanide ions or by NO2 − ions; space-group symmetry then depends on the temperature-dependent degree of order. The relationships can be used to predict if and what kind of twinning may occur in phase transitions and whether second-order phase transitions are possible.

scholarly journals Multiplicity-weighted Euler's formula for symmetrically arranged space-filling polyhedra

2020 ◽  
Vol 76 (5) ◽  
pp. 580-583
Author(s):  
Zbigniew Dauter ◽  
Mariusz Jaskolski
Keyword(s):  
Three Dimensional ◽  
Group Symmetry ◽  
General Character ◽  
Two Dimensional ◽  
Asymmetric Unit ◽  
Space Filling ◽  
Space Group Symmetry ◽  
Space Group ◽  
Space Groups ◽  
Modified Formula

The famous Euler's rule for three-dimensional polyhedra, F − E + V = 2 (F, E and V are the numbers of faces, edges and vertices, respectively), when extended to many tested cases of space-filling polyhedra such as the asymmetric unit (ASU), takes the form Fn − En + Vn = 1, where Fn, En and Vn enumerate the corresponding elements, normalized by their multiplicity, i.e. by the number of times they are repeated by the space-group symmetry. This modified formula holds for the ASUs of all 230 space groups and 17 two-dimensional planar groups as specified in the International Tables for Crystallography, and for a number of tested Dirichlet domains, suggesting that it may have a general character. The modification of the formula stems from the fact that in a symmetrical space-filling arrangement the polyhedra (such as the ASU) have incomplete bounding elements (faces, edges, vertices), since they are shared (in various degrees) with the space-filling neighbors.

Mixed Alkali Systems: Structure and 29Si MASNMR of Li2Si2O5 and K2Si2O5

1998 ◽  
Vol 54 (5) ◽  
pp. 568-577 ◽  
Author(s):  
B. H. W. S. de Jong ◽  
H. T. J. Supèr ◽  
A. L. Spek ◽  
N. Veldman ◽  
G. Nachtegaal ◽  
...  
Keyword(s):  
Relaxation Times ◽  
Three Dimensional ◽  
Lattice Relaxation ◽  
Chair Conformation ◽  
Spin Lattice Relaxation ◽  
Group Symmetry ◽  
Orthorhombic Space Group ◽  
Acta Cryst ◽  
Space Group ◽  
Spin Lattice

Li2Si2O5, M r = 150.05, λ(Mo Kα) = 0.71073 Å, 293 K, orthorhombic, Ccc2, a = 5.807 (2), b = 14.582 (7), c = 4.773 (3) Å, V = 404.2 (3) Å3, μ(Mo Kα) = 0.78 mm−1, Z = 4, D x = 2.466 Mg m−3, R 1 = 0.045 for 249 reflections with I > 2.0σ(I), wR 2 = 0.1138 for all 261 reflections. K2Si2O5, M r = 214.36, λ(Mo Kα) = 0.71073 Å, 150 K, monoclinic, Cc, a = 16.322 (2), b = 11.243 (2), c = 9.919 (1) Å, β = 115.97 (1)°, V = 1636.4 (4) Å3, μ(Mo Kα) = 2.11 mm−1, Z = 12, D x = 2.610 Mg m−3, R 1 = 0.0385 for 2370 reflections with I > 2.0σ(I), wR 2 = 0.0785 for all 2711 reflections. The crystal structures of Li2Si2O5 and K2Si2O5 have been determined and refined. The lithium phyllosilicate sheet topology and structure based on three-dimensional data and refined in the orthorhombic space group Ccc2 confirm the previous determination by Liebau [Acta Cryst. (1961), 14, 389–395] from two-dimensional data, but described in the lower monoclinic Cc space-group symmetry. Potassium disilicate, on the other hand, is not a phyllosilicate but forms a three-dimensional defect cristobalite structure built from Q 3 silica units. In this structure, one Si—O—Si bridge, common to four six-membered T-rings, i.e. rings consisting of six silica tetrahedra in the chair conformation, is missing, resulting in 14-membered T-rings. Continuous sheets built up from these rings form a layer connected to layers above and below by six-membered T-rings in the chair conformation. 29Si MASNMR shows a good correlation between Si—O—Si angle and 29Si chemical shift for K2Si2O5, Li2Si2O5 and KLiSi2O5. The 29Si spin lattice relaxation times, T 1, are 335, 689 and 〈1256〉 s for Li2Si2O5, KLiSi2O5 and K2Si2O5, respectively. The pronounced non-linearity in hygroscopicity in glassy potassium–lithium disilicates is not observed in the osmolality of 0.8M potassium–lithium chloride aqueous solutions.

The atomic anisotropic displacement tensor – completing the picture

2015 ◽  
Vol 71 (4) ◽  
pp. 467-470 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Helge B. Larsen
Keyword(s):  
Point Group ◽  
Transformation Property ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Tensor Representation ◽  
Space Group Symmetry ◽  
Space Group ◽  
Simplified Approach ◽  
Displacement Parameter ◽  
Isotropic Displacement Parameter

A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representationUto point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011),International Tables for Crystallography, Vol. A,Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd].

TABLES, a program to display space-group symmetry information in three dimensions

1987 ◽  
Vol 20 (6) ◽  
pp. 532-535 ◽  
Author(s):  
C. Abad-Zapatero ◽  
T. J. O'Donnell
Keyword(s):  
Computer Graphics ◽  
Computer Program ◽  
Three Dimensional ◽  
Spatial Location ◽  
Three Dimensions ◽  
Group Symmetry ◽  
Space Group ◽  
Interactive Display ◽  
Symmetry Operators ◽  
Group Information

TABLES is a computer program developed to display the crystal symmetry and the spatial location of the different symmetry operators for a given space group using interactive computer graphics. It allows the three-dimensional interactive display of the space-group information contained in International Tables for Crystallography [(1983), Vol. A. Dordrecht: Reidel]. Such a program is useful as a teaching aid in crystallography and is valuable for exploring molecular packing arrangements.

Sign in / Sign up

Export Citation Format

Share Document