Enumeration of four-connected three-dimensional nets. I. Conversion of all edges of simple three-connected two-dimensional nets into crankshaft chains

1999 ◽  
Vol 55 (2) ◽  
pp. 332-341 ◽  
Author(s):  
Shaoxu Han ◽  
Joseph V. Smith
Keyword(s):  
Least Squares ◽  
Mathematical Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Theoretical Frameworks ◽  
Space Group ◽  
Association Structure ◽  
Atomic Coordinates

Various topological approaches to mathematical analysis, classification and enumeration of four-connected three-dimensional (3D) nets are listed. Four-connected 3D nets are being generated systematically by conversion of edges of a vertical stack of congruent three-connected two-dimensional (2D) nets into chains. This paper describes 57 3D nets obtained by converting into crankshaft chains all edges of the simpler 2D nets in the catalog of the Consortium of Theoretical Frameworks. Atomic coordinates are given for distance-least-squares modeling in the highest space group. Nine nets occur in known structures: tridymite, Zn2P2O8 \cdot organic, aluminophosphates AlPO-5 (International Zeolite Association Structure Commission code AFI), AlPO-8 (AEI), AlPO-11 (AEL), AlPO-25 (ATV), AlPO-41 (AFO), AlPO-54 (VFI) and AlPO-H2 (AHT).

Enumeration of four-connected three-dimensional nets. III. Conversion of edges of three-connected two-dimensional nets into saw chains

1999 ◽  
Vol 55 (2) ◽  
pp. 360-382 ◽  
Author(s):  
Shaoxu Han ◽  
Joseph V. Smith
Keyword(s):  
Three Dimensional ◽  
Mirror Plane ◽  
Two Dimensional ◽  
Acta Cryst ◽  
Systematic Enumeration ◽  
Association Structure ◽  
Tetrahedral Bonding ◽  
Cell Data ◽  
Unit Cell Data ◽  
Atomic Coordinates

A three-repeat saw (s) chain has each vertical edge separated by a tooth composed of two tilted edges zig and zag. Some horizontal (h) edges from a parallel stack of three-connected two-dimensional (2D) nets can be converted into an s chain. Each resulting four-connected vertex in the three-dimensional (3D) net may be part of either one, two or three s chains. The first type of (h,s)* 3D net is related by a sigma-type mirror plane to a (h,z)* net listed in paper II [Han & Smith (1998). Acta Cryst. A55, 342–359]. The second type does not have an (h,z)* relative. Using the same three-connected 2D nets as in paper II, 174 four-connected 3D nets were selected from the first two types, including six in known structures: `nepheline hydrate' (International Zeolite Association Structure Commission code JBW), AlPO4-12-TAMU (ATT), offretite (OFF), Linde Type L (LTL), SUZ-4 (SZF) and ZSM-10 (ZST). The third type with three back-to-back s chains is represented by edingtonite (EDI), and systematic enumeration is in progress. The geometrical and topological properties of the 3D nets are given. Idealized unit-cell data and atomic coordinates for tetrahedral bonding were obtained for 40 selected 3D nets by distance-least-squares (DLS) refinement.

Die Röntgenstrukturanalyse von (CO)9Co3CΟΒΒr2Ν(C5)3. X-ray Structure Analysis of (CO)9Co3COBBr2N(C2H5)3

1976 ◽  
Vol 31 (3) ◽  
pp. 342-344 ◽  
Author(s):  
Volker Bätzel
Keyword(s):  
Least Squares ◽  
Structure Analysis ◽  
Reliability Index ◽  
Three Dimensional ◽  
Diagonal Matrix ◽  
Crystal Data ◽  
Block Diagonal Matrix ◽  
Fourier Methods ◽  
Space Group ◽  
X Ray

Using three dimensional X-ray data collected on a four circle diffractometer, the structure of (CO)9Co3COBBr2N(C2H5)3 was solved by Patterson and Fourier methods. Least squares refinement with a block-diagonal matrix leads to a reliability index of R = 10.7%. Crystal data: α = 13.277(6) Å, b = 10.17(1) Å, c = 9.22(2) Å; α = 91.12(6)°, β = 87.61(4)°, γ = 98.79(2)°; space group P1̅; Z = 2; V = 1229,7 Å3; Dx = 1.97 gcm-3.

Structure cristalline et moléculaire du cyclopentadiényle dicarbonyle triphénylphosphine manganèse, MnC5H5(CO)2P(C6H5)3

1973 ◽  
Vol 51 (18) ◽  
pp. 3027-3031 ◽  
Author(s):  
Claude Barbeau ◽  
Klaus Sorrento Dichmann ◽  
Louis Ricard
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Triphenyl Phosphine ◽  
Triclinic Space Group ◽  
Space Group ◽  
Bond Lengths ◽  
Atomic Parameter

The crystalano molecular structure of cyclopentadienyl manganese dicarbonyl-triphenyl phosphine has been determined by means of three dimensional data obtained by a Buerger precession camera. 2931 independent intensities were utilized in the refinement of the structure using the least-squares method. The final disagreement factor is 0.11. MnC5H5(CO)2P(C6H5)3 crystallizes in the triclinic space group.[Formula: see text]The molecule shows atomic parameter almost identical to those of MnC5H5(CO)3 except for the Mn—C bond lengths which change from 1.80 to 1.73 Å. The Mn—P distance (2.236 Å) and the unchanged parameters for the Mn—C5H5 group confirm the strong donating power of the cyclopentadienyl group. [Journal translation]

The crystal structure of ferrinatrite, Na3(H2O)3[Fe(SO4)3] and its relationship to Maus's salt, (H3O)2K2{K0.5(H2O)0.5}6[Fe3O(H2O)3(SO46](OH)2

1977 ◽  
Vol 41 (319) ◽  
pp. 375-383 ◽  
Author(s):  
F. Scordari
Keyword(s):  
Crystal Structure ◽  
Hydrogen Bonds ◽  
Least Squares ◽  
Three Dimensional ◽  
Iron Ions ◽  
Space Group ◽  
R Value ◽  
Oxygen Atoms

SummaryFerrinatrite crystallizes in space group P, with a = 15·566(5), c = 8·69(1) Å, and Z = 6. The crystal structure was solved by three-dimensional Patterson and Fourier syntheses, and refined by least squares employing 2378 independent reflexions to a final R value of 0·068. The iron ions occupy special positions and are surrounded octahedrally by oxygen atoms. Fe3+O6 octahedra and SO4, tetrahedra are linked together to form infinite chains of Fe-O-S linkages in the [0001] direction. These chains are linked to each other by [NaO5(H2O)2] polyhedra and probably by hydrogen bonds. The topology of the arrangement is the same as that of the hypothetical P312 structure proposed by Moore and Araki (1974).

A crystallographic and spectroscopic study of mercury(II) dithiocarbamate

1981 ◽  
Vol 59 (18) ◽  
pp. 2746-2749 ◽  
Author(s):  
Chung Chieh ◽  
Sing Kwen Cheung
Keyword(s):  
Mass Spectrum ◽  
Spectroscopic Study ◽  
Least Squares ◽  
Least Squares Method ◽  
Two Dimensional ◽  
Polymeric Compound ◽  
Full Matrix ◽  
Space Group ◽  
Polymeric Networks ◽  
Ir Bands

Ammonium dithiocarbamate, H2NCS2NH4, decomposes easily but the anion forms a stable mercury(II) complex, the crystals of which are orthorhombic with a = 7.851(3), b = 17.565(7), c = 12.051(3) Å, and space group Pbca. The structure was solved by the Patterson method and refined by the full-matrix least-squares method to an R of 0.038 for 781 reflections. The structure consists of layers of two-dimensional polymeric networks. The dimeric subunits in the layer containing two each of mutually connected Hg atoms and dithiocarbamates are further linked by other bridging dithiocarbamates forming a sheet-like structure. Each Hg atom bonds to four S atoms from four separate dithiocarbamates with Hg—S distances of 2.499(4), 2.508(4), 2.533(4), and 2.629(4) Å. The ir bands observed were: ν(NH2), 3320, 3220, 3125; δ(NH2), 1600; ν(C—N), 1395; ρr(NH2), 1172; and v(C—S), 840 cm−1. The mass spectrum of this polymeric compound gave peaks corresponding to Hg, S2, CNH2, HNCS, S, CS2, S5, S4, S3, and S8 in the order of their intensities.

Enumeration of four-connected three-dimensional nets. II. Conversion of edges of three-connected 2D nets into zigzag chains

1999 ◽  
Vol 55 (2) ◽  
pp. 342-359 ◽  
Author(s):  
Shaoxu Han ◽  
Joseph V. Smith
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Association Structure

Four-connected three-dimensional (3D) nets were systematically enumerated by converting some horizontal edges of a vertical stack of three-connected two-dimensional (2D) nets into vertical zigzag chains. 77 out of 131 2D nets were selected for enumeration, and different arrangements of zigzag edges and horizontal edges were investigated. This yielded 138 3D nets of which 19 are represented by known structures: cristobalite; tridymite; MAPO-39 (International Zeolite Association Structure Commission code ATN); svyatoslavite; Li-A(BW) (ABW); cancrinite (CAN); AlPO-31 (ATO); MAPO-36 (ATS); BaFe2O4; `nepheline hydrate' (JBW); bikitaite (BIK); KBGe2O6; CsAlSi5O12 (CAS); UiO-6 (OSI); Theta-1 (TON); ZSM-12 (MTW); ZSM-23 (MTT); AlPO-53C; and CIT-5 (CFI).

Crystallography of quasi-crystals

1986 ◽  
Vol 42 (4) ◽  
pp. 261-271 ◽  
Author(s):  
T. Janssen
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Crystal Phase ◽  
Two Dimensional ◽  
Space Group ◽  
Quasi Crystals ◽  
Special Case

The symmetry of quasi-crystals, a class of materials that has recently aroused interest, is discussed. It is shown that a quasi-crystal is a special case of an incommensurate crystal phase and that it can be described by a space group in more than three dimensions. A number of relevant three-dimensional quasi-crystals is discussed, in particular dihedral and icosahedral structures. The symmetry considerations are also applied to the two-dimensional Penrose patterns.

The Prediction of Three-Dimensional Stress Concentration Factors

1959 ◽  
Vol 63 (585) ◽  
pp. 549-551 ◽  
Author(s):  
I. M. Allison
Keyword(s):  
Stress Concentration ◽  
Mathematical Analysis ◽  
Three Dimensional ◽  
Stress Raiser ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Torsional Loading ◽  
Loading System ◽  
Concentration Factors ◽  
Stress Concentration Factors

Two-Dimensional Stress concentration factors may be obtained more quickly and simply than the corresponding three-dimensional factors, either by experiment or mathematical analysis. It would be convenient to obtain information, for varying geometry in the two-dimensional case of a particular type of stress raiser, e.g. a shoulder, groove or hole, and use this either to predict the three-dimensional stress concentration factors or to extend the range of existing three-dimensional results. Clearly a comparison is only possible if the three-dimensional stress raiser embodies a plane of symmetry (which gives the geometry of the similar two-dimensional stress raiser), and if the loading conditions can be reproduced in both the two- and three-dimensional cases. The latter requirement restricts the correlation to the stress concentration factors obtained in tension and in bending. The three-dimensional torsional loading system has no plane of symmetry which can be simulated in two dimensions.

Crystal and Molecular Structure of Difluorochlorine(III)-hexafluoroarsenate(V), ClF2AsF6

1971 ◽  
Vol 49 (15) ◽  
pp. 2539-2543 ◽  
Author(s):  
H. Lynton ◽  
J. Passmore
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Chlorine Atom ◽  
Crystal And Molecular Structure ◽  
Three Dimensional ◽  
Monoclinic Space Group ◽  
Arsenic Atom ◽  
Space Group

Crystals of difluorochlorine(III)hexafluoroarsenate(V), ClF2AsF6, are monoclinic, space group A2/a, a = 10.676(9), b = 7.673(7), c = 8.064(7) Å, β = 113.40(5)°. The structure was refined by three dimensional least squares methods to R = 0.045 for 185 independent observed reflections. The chlorine atom has two nearest fluorine neighbors at 1.541(14) Å, with a F—Cl—F angle of 103.17(0.70)°, and two longer fluorine bonds at 2.339(14) Å. All five atoms lie in a plane. The arsenic atom is octahedrally coordinated to six fluorine atoms and is connected to two ClF2+ groups via trans fluorine bridges.

Die Kristall- und Molekülstruktur von β -Bromo(2-diäthylaminoäthanolato)kupfer(ll) / The Crystal and Molecular Structure of β-Bromo(2-diethylaminoethanolato)copper(II)

1975 ◽  
Vol 30 (1-2) ◽  
pp. 14-18 ◽  
Author(s):  
R. Mergehenn ◽  
L. Merz ◽  
W. Haase
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Crystal And Molecular Structure ◽  
Three Dimensional ◽  
Unit Cell ◽  
Triclinic Space Group ◽  
Polymeric Structure ◽  
Space Group ◽  
X Ray

The crystal and molecular structure of β-bromo(diethylaminoethanolato)copper(II) has been determined from three dimensional X-ray diffractometer data. The compound crystallizes in the triclinic space group Pï with one dimer in a unit cell of dimensions α=10.180(II), b=7.999(9), c=6.227(7) Å and a=110.69(4), β=103.12(4), γ=73.82(4)[°]. The structure was refined by least-squares methods using 1944 independent reflexions to give a final R-index of 0,05. The molecule consists of dimeric Cu2O2-units with Cu—O distances of 1.900(4) Å and 1.914(4) A, respectively. The dimers are additional bridged by bromines, so that a “polymeric” structure results; Cu—Br distances are 2.357(2) and 3.660(2) A, respectively. The Cu—Cu distances are 3.003(2) (oxygen bridges) and 4.506(2) Å (bromine bridges).

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