Periodic average structures of colloidal quasicrystals

The non-crystallographic symmetry of d-dimensional (dD) quasiperiodic structures is incompatible with lattice periodicity in dD physical space. However, dD quasiperiodic structures can be described as irrational sections of nD (n > d) periodic hypercrystal structures. By appropriate oblique projection of particular hypercrystal structures onto physical space, discrete periodic average structures can be obtained. The boundaries of the projected atomic surfaces give the maximum distance of each atom in a quasiperiodic structure from the vertices of the reference lattice of its average structure. These maximum distances turn out to be smaller than even the shortest atomic bond lengths. The metrics of the average structure of a 3D Ammann tiling, for instance, with edge lengths of the unit tiles equal to the bond lengths in elemental aluminium, correspond almost exactly to the metrics of face-centred-cubic aluminium. This is remarkable since most stable quasicrystals contain aluminium as the main constitutent. The study of the average structure of quasicrystals can be a valuable aid to the elucidation of the geometry of quasicrystal-to-crystal transformations. It can also contribute to the derivation of the physically most relevant Brillouin (Jones) zone.

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X-RAY DIFFRACTION STUDY OF THE MODULATED STRUCTURE IN SUPERCONDUCTING SINGLE-CRYSTAL Bi2Sr2CaCu2Oy

Modern Physics Letters B ◽

10.1142/s0217984988000795 ◽

1988 ◽

Vol 02 (08) ◽

pp. 985-991 ◽

Cited By ~ 3

Author(s):

X. CHU ◽

Z.H. MAI ◽

Y.F. YAN ◽

J.H. WANG ◽

D.N. ZHENG ◽

...

Keyword(s):

Experimental Data ◽

Single Crystal ◽

Diffraction Study ◽

Basic Structure ◽

X Ray Diffraction ◽

Modulated Structure ◽

Space Group ◽

One Dimensional ◽

X Ray ◽

Average Structure

X-ray precession technique1 has been utilized to study the reciprocal space of the superconducting single crystal Bi 2 Sr 2 CaCu 2 O y. An average structure with space group of Pnnn and a real structure with the superspace group of [Formula: see text] or [Formula: see text] have been found for this one dimensional modulated incommensurate material. As well, a basic structure with the space group of Fmmm is derived from the experimental data.

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Direct determination of defect structures

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1524/zkri.1996.211.10.669 ◽

1996 ◽

Vol 211 (10) ◽

Author(s):

R. B. Neder ◽

A. Halbhuber ◽

F. Frey

Keyword(s):

Fourier Transforms ◽

Direct Determination ◽

Extended Defects ◽

Defect Structures ◽

Resolution Function ◽

One Dimensional ◽

Average Structure ◽

Experimental Resolution

AbstractA procedure for the direct determination of defect structures is presented. The procedure uses the average structure to calculate starting phases. An iterative cycle of inverse Fourier transforms and interpretations of the scattering density is applied. Within each cycle the scattering density is interpreted to yield a structure deviating from the average structure by missing, replaced or shifted atoms. The procedure usually converges after a few cycles and allows a direct determination of substitutional and displacement disorder. By analyzing the correlations between different atoms, extended defects can be recognized. The current results are preliminary and have been limited to an idealized one dimensional situation, under the assumption of a negligible experimental resolution function.

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Aravaite, Ba2Ca18(SiO4)6(PO4)3(CO3)F3O: modular structure and disorder of a new mineral with single and triple antiperovskite layers

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520618012271 ◽

2018 ◽

Vol 74 (6) ◽

pp. 492-501 ◽

Cited By ~ 1

Author(s):

Biljana Krüger ◽

Hannes Krüger ◽

Evgeny V. Galuskin ◽

Irina O. Galuskina ◽

Yevgeny Vapnik ◽

...

Keyword(s):

Diffuse Scattering ◽

Structure Refinement ◽

New Mineral ◽

Stacking Sequence ◽

Single Crystal Diffraction ◽

Qualitative Modelling ◽

One Dimensional ◽

Average Structure ◽

Layer Sequence ◽

Swiss Light Source

The crystal structure of the new mineral aravaite Ba2Ca18(SiO4)6(PO4)3(CO3)F3O [R{\bar 3}m, a = 7.12550 (11), c = 66.2902 (13) Å, V = 2914.81 (8) Å3, Z = 3] was solved from single-crystal diffraction data, collected using synchrotron radiation at the X06DA beamline of the Swiss Light Source. The unit cell of this modular mineral contains six layers of {Ba(PO4)1.5(CO3)0.5}3.5− (T-layer), three triple antiperovskite layers (tAP) {(F2OCa12)(SiO4)4}4+, and three single antiperovskite layers (sAP) {(FCa6)(SiO4)2}3+. The structure refinement confirms a model with a layer sequence of T–sAP–T–tAP as an average structure of this mineral. However, one-dimensional diffuse scattering observed parallel to c* implies imperfections in the stacking sequence of the average structure. Qualitative modelling of disorder confirms that the alternating sequence of T–sAP and T–tAP blocks is disturbed. The blocks occurring in this new mineral are known from other so-called hexagonal intercalated antiperovskite structures: T–sAP (stracherite and zadovite group), T–tAP (ariegilatite and nabimusaite group).

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Cluster configurations in modulated EuV x Mo8±y O14 crystals

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768199000452 ◽

1999 ◽

Vol 55 (4) ◽

pp. 467-483 ◽

Cited By ~ 1

Author(s):

H. Leligny ◽

D. Grebille ◽

P. Roussel ◽

Ph. Labbé ◽

M. Hervieu ◽

...

Keyword(s):

X Ray Diffraction ◽

Structural Result ◽

One Dimensional ◽

X Ray ◽

Metallic Clusters ◽

Main Cluster ◽

Unit Cells ◽

Density Modulation ◽

Average Structures ◽

The Eu

Three orthorhombic crystals of chemical formula Eu x V y Mo8±z O14 were investigated by X-ray diffraction (Mo Kα radiation, λ = 0.71073 Å). They have nearly the same lattice parameters (a ≃ 11.3, b ≃ 10.0, c ≃ 9.2 Å), display one-dimensional incommensurate modulations of wavevector q* = γc* and are characterized by the same superspace group Cmca(00γ)s00. The crystals differ both in their compositions (namely Eu0.976(6)V1.13(5)Mo7.10(5)O14, Eu0.986(4)V1.10(3)Mo7.30(1)O14 and EuMo7.96(1)O14) and in their γ components [0.195 (2), 0.245 (2) and 0.286 (3), respectively]. The average structures of these crystals appear closely related to the structures of LaMo7.7O14 (not modulated) and LaMo8O14 (modulated); however, two main differences are outlined: first, the modulation direction is c in the Eu-containing crystals but b in the modulated La-containing crystal [q* = (1/3)b*], second, the Eu-containing crystals have centrosymmetric structures while the La-containing crystals have polar structures (space group C2ca). The Mo (or Mo and V) atoms are stacked to form (001) layers of metallic clusters. The density modulation of these structures implies the existence of the new types of clusters Mo9, Mo10, Mo6V4, Mo7V3 and Mo8V2 besides the clusters M 8 (Mo8, Mo6V2 and Mo7V) and M 7 (Mo7 and Mo6V) which are already known. Mo8 units with cis and trans configurations and Mo6V2 units with a trans configuration appear as the main cluster types in these crystals. The nature of the metallic clusters changes along c, but inside one (001) layer it is likely that only one cluster type with a given configuration is present. The main structural result is the formation, in some unit cells, of strong intercluster Mo—Mo, Mo—V or V—V bonds with distances close to 2.6 Å within a layer as well as between two neighbouring layers.

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100069387 ◽

1970 ◽

Vol 28 ◽

pp. 478-479

Author(s):

Teruo Someya ◽

Jinzo Kobayashi

Keyword(s):

Surface Layer ◽

Electric Fields ◽

Quantitative Study ◽

Recent Progress ◽

Ferroelectric Domain ◽

Resolving Power ◽

Surface Pattern ◽

Crystal Surfaces ◽

One Dimensional ◽

Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

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Structure and function of neural networks in the retina

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100102213 ◽

1988 ◽

Vol 46 ◽

pp. 26-27

Author(s):

Peter Sterling

Keyword(s):

Ganglion Cells ◽

Three Dimensional ◽

Structure And Function ◽

Synaptic Connections ◽

Visual Axis ◽

One Dimensional ◽

Cat Retina ◽

Ultrathin Sections ◽

And Function ◽

Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

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Intergrowth of modulated structures in high Tc Bi-Sr-Ca-Cu-O superconductors

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173510 ◽

1990 ◽

Vol 48 (4) ◽

pp. 76-77

Author(s):

A.Q. He ◽

G.W. Qiao ◽

J. Zhu ◽

H.Q. Ye

Keyword(s):

Twin Structure ◽

Modulated Structure ◽

High Tc ◽

One Dimensional ◽

Lattice Constants ◽

Superconducting Phases ◽

Modulated Structures ◽

Layer Structures

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.

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Electronic structure studies of conducting polymers by electron energy-loss spectroscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100163265 ◽

1996 ◽

Vol 54 ◽

pp. 160-161

Author(s):

J. Fink

Keyword(s):

Electronic Structure ◽

Conducting Polymers ◽

Conjugated Polymers ◽

Electron Acceptors ◽

Electron Donors ◽

Light Emitting ◽

One Dimensional ◽

New Class ◽

Electrical Conductivities ◽

Electron Energy Loss

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.

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