Computing Maximal Subgroups and Wyckoff Positions of Space Groups

A new family of high temperature superconductors based on Pb2Sr2YCu3O9−δ has recently been reported. One method of improving Tc has been to replace Y partially with Ca. Although the basic structure of this type of superconductors is known, the detailed structure is still unclear, and various space groups has been proposed. In our work, crystals of Pb2Sr2YCu3O9−δ with dimensions up to 1 × 1 × 0.25.mm and with Tc of 84 K have been grown and their superconducting properties described. The defects and crystal symmetry have been investigated using electron microscopy performed on crushed crystals supported on a holey carbon film.Electron diffraction confirmed x-ray diffraction results which showed that the crystals are primitive orthorhombic with a=0.5383, b=0.5423 and c=1.5765 nm. Convergent Beam Electron Diffraction (CBED) patterns for the and axes are shown in Figs. 1 and 2 respectively.

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Symmetry breaking in convergent-beam diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154378 ◽

1989 ◽

Vol 47 ◽

pp. 480-481

Author(s):

D.J. Eaglesham

Keyword(s):

Symmetry Breaking ◽

Point Group ◽

X Ray Diffraction ◽

Multiple Diffraction ◽

Space Groups ◽

Atomic Displacements ◽

Small Probe ◽

Phase Sensitive ◽

Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

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Transmission Electron Microscopy study of Bi-based superconducting phases

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173388 ◽

1990 ◽

Vol 48 (4) ◽

pp. 50-51

Author(s):

J.G. Wen ◽

K.K. Fung

Keyword(s):

Electron Microscopy ◽

Transmission Electron Microscopy ◽

Single Crystals ◽

Microscopy Study ◽

Electron Microscopy Study ◽

Space Groups ◽

Superconducting Phases ◽

Ceramic Samples ◽

Transmission Electron ◽

Modulated Structures

Bi-based superconducting phases have been found to be members of a structural series represented by Bi2Sr2Can−1Cun−1On+4, n=1,2,3, and are referred to as 2201, 2212, 2223 phases. All these phases are incommensurate modulated structures. The super space groups are P2/b, NBbmb 2201, 2212 phases respectively. Pb-doped ceramic samples and single crystals and Y-doped single crystals have been studied by transmission electron microscopy.Modulated structures of all Bi-based superconducting phases are in b-c plane, therefore, it is the best way to determine modulated structure and c parameter in diffraction pattern. FIG. 1,2,3 show diffraction patterns of three kinds of modulations in Pb-doped ceramic samples. Energy dispersive X-ray analysis (EDAX) confirms the presence of Pb in the three modulated structures. Parameters c are 3 0.06, 38.29, 30.24Å, ie 2212, 2223, 2212 phases for FIG. 1,2,3 respectively. Their average space groups are all Bbmb.

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The Maximal Subgroups of the Low-Dimensional Finite Classical Groups

10.1017/cbo9781139192576 ◽

2009 ◽

Cited By ~ 80

Author(s):

John N. Bray ◽

Derek F. Holt ◽

Colva M. Roney-Dougal

Keyword(s):

Maximal Subgroups ◽

Classical Groups ◽

Finite Classical Groups ◽

Low Dimensional

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Minimal supergroups and magnetic space groups (III)

Annales de Physique ◽

10.1051/anphys/197702020169 ◽

1977 ◽

Vol 2 ◽

pp. 169-177

Author(s):

E. F. Bertaut

Keyword(s):

Space Groups

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Equivalency relations in magnetic space groups (II)

Annales de Physique ◽

10.1051/anphys/197514090109 ◽

1975 ◽

Vol 14 (9) ◽

pp. 109-124 ◽

Cited By ~ 1

Author(s):

E. F. Bertaut

Keyword(s):

Space Groups

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Solid State Analysis and Theoretical Explorations on Polymorphic and Hydrate Forms of p-Hydroxybenzaldehyde Isonicotinichydrazone: Effect of Additives on Polymorphic Crystallization

10.26434/chemrxiv.6489425.v1 ◽

2018 ◽

Author(s):

Lincy Tom ◽

Victoria A. Smolenski ◽

Jerry P. Jasinski ◽

M.R. Prathapachandra Kurup

Keyword(s):

Hirshfeld Surface ◽

Framework Analysis ◽

Reaction Conditions ◽

Space Groups ◽

Effect Of Additives ◽

Ft Ir ◽

Packing Arrangement ◽

The Stability ◽

Ir And Raman ◽

Isonicotinic Hydrazide

The reaction of p-hydroxybenzaldehyde with an equimolar amount of isonicotinic hydrazide afforded two polymorphic and hydrate forms of p-hydroxybenzaldehyde isonicotinichydrazone (HBIH) by varying the experimental reaction conditions. The compounds are fully characterized by means of single crystal and powder diffraction methods, vibrational spectroscopy (FT-IR and Raman), thermal and elemental analysis. The compound crystallizes in three different forms in two different space groups, P21/c (form PA and PB) and Pbca (PC). The Hirshfeld surface analysis shows the differences in the relative contributions of intermolecular interactions to the total Hirshfeld surface area for the HBIH molecules. The calculated pairwise interaction energies (104-116 kJ/mol) can be related to the stability of the crystals. Energy framework analysis identifies the interaction hierarchy and their topology. The geometry and conformation of the three forms are essentially similar which differ only by packing arrangement.

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