Determination of point group harmonics for arbitrary j by a projection method. II. Icosahedral group, quantization along an axis of order 5

1984 ◽  
Vol 25 (5) ◽  
pp. 1187-1194 ◽  
Author(s):  
Jacques Raynal
Keyword(s):  
Projection Method ◽  
Point Group ◽  
Icosahedral Group ◽  
Group Quantization

Symmetry breaking in convergent-beam diffraction

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

scholarly journals The determination of point groups from imprecise molecular geometries

2021 ◽  
Author(s):  
Peter J. Knowles
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
Simple Function ◽  
Coordinate Frame ◽  
New Approach ◽  
Measure Of Symmetry ◽  
Point Groups

AbstractWe present a new approach for the assignment of a point group to a molecule when the structure conforms only approximately to the symmetry. It proceeds by choosing a coordinate frame that minimises a measure of symmetry breaking that is computed efficiently as a simple function of the molecular coordinates and point group specification.

scholarly journals Identification of an Al–Ni–O precipitate in combustion-synthesized NiAl

2000 ◽  
Vol 33 (5) ◽  
pp. 1217-1222
Author(s):  
A. Biswas ◽  
Madangopal K. ◽  
J. B. Singh ◽  
S. K. Roy ◽  
S. Banerjee
Keyword(s):  
Room Temperature ◽  
Point Group ◽  
Composition Analysis ◽  
Second Phase ◽  
X Ray ◽  
Selected Area Electron Diffraction ◽  
Phase Precipitate ◽  
Transmission Electron ◽  
Chemical Composition Analysis

The complete identity of a second-phase precipitate detected by transmission electron microscopy in combustion-synthesized NiAl was established. The crystal structure, including the point group, the space group and the lattice parameters, was determined by convergent and selected-area electron diffraction techniques. Energy dispersive X-ray spectroscopy was used for the determination of the chemical composition. Analysis established the phase to be the solid solution of NiO in Al2O3and presented evidence of the hitherto unreported room-temperature solubility.

scholarly journals Limitations of LEED-Structure Determination of Reconstructed Crystal Surfaces

1982 ◽  
Vol 37 (10) ◽  
pp. 1103-1118 ◽  
Author(s):  
H. Jagodzinski
Keyword(s):  
Structure Determination ◽  
Crystal Surface ◽  
Dimensional Space ◽  
Point Group ◽  
Two Dimensional ◽  
Crystal Surfaces ◽  
Difficult Situation ◽  
3 Dimensional ◽  
Lattice Constants

Although a strictly ordered reconstructed crystal surface may have the two-dimensional symmetry prescribed by the bulk (two-dimensional subsymmetry of the 3-dimensional space group), it belongs more frequently to a subgroup. In the LEED-pattern a lower symmetry of the translation group can easily be detected on account of the superstructure reflections observed. In this case anti-phase domains can hardly be avoided. An even more difficult situation arises if the symmetry of the point group is violated, although the symmetry of the diffraction pattern is not altered at the end of the reconstruction. Twin domains without changes of lattice constants have to be taken into account.Dynamical scattering of anti-phase domains is calculated by applying the "Cluster embedded chain"-method for various distributions of domains. It is shown that the incoherent superposition of scattering amplitudes, normally applied in LEED-calculations may lead to serious errors in structure determination. This effect is even more pronounced for twin domains. As an example we discuss the reconstruction of the (001)-surface of Si and Ge, and show that the wellknown (2 X 1)-structure is an averaged structure only, consisting of anti-phase domains with the (4 x 2)-structure. It may be concluded therefrom that none of the present model structures of this reconstruction agrees with this experimental observation.

NMR Spectroscopy of Tetra(propyn- 1-yl)silane in the Solid State and in Solution

2003 ◽  
Vol 58 (8) ◽  
pp. 809-812 ◽  
Author(s):  
Bernd Wrackmeyer ◽  
Oleg L. Tok ◽  
Amin Badshah
Keyword(s):  
Solid State ◽  
Bulk Material ◽  
Point Group ◽  
Coupling Constants ◽  
Data Set ◽  
Tin Compounds ◽  
X Ray ◽  
Nmr Data ◽  
Solid State Structures

The crystal structure of tetra(propyn-1-yl)silane, Si(C≡CMe)4 1, has revealed a completely asymmetric molecule (point group C1). Since this finding concerns a single crystal, the bulk material of 1 was studied by solid-state 29Si and 13C MAS NMR. This confirmed the result of the X-ray analysis, and by comparison with previous NMR measurements of the tin analogue 1(Sn) it is concluded that 1 and 1(Sn) must have very similar solid-state structures which are in contrast to those known for other tetra(alkyn-1-yl)silicon and -tin compounds. The NMR data set of 1 in solution was completed by determination of the magnitude of coupling constants 1J(13C,13C).

Spectroscopic investigations of hydrogen bonding interactions in the gas phase. V.t The identification and determination of the geometry and electric dipole moment of the hydrogen bonded heterodimer formed between oxirane and hydrogen fluoride, (CH 2 ) 2 O • • • HF, by infrared and microwave spectroscopy

1981 ◽  
Vol 373 (1755) ◽  
pp. 511-526 ◽  
Keyword(s):  
Hydrogen Fluoride ◽  
Point Group ◽  
Centrifugal Distortion ◽  
Rotational Constants ◽  
Rotational Spectra ◽  
Hydrogen Bonding Interactions ◽  
Pyramidal Configuration ◽  
Centrifugal Distortion Constants ◽  
Hydrogen Bonded

The hydrogen bonded heterodimer formed between oxirane and hydrogen fluoride has been identified through its infrared and microwave spectra. Rotational constants/MHz and centrifugal distortion constants/kHz for the following isotopic varieties have been derived from an analysis of the rotational spectra in the vibrational ground state: A B A (CH 2 ) 2 160* • -HF 16099 3638.75 3462.31 15.3 25.8 (CH2)2160- • *DF 15984 3605.66 3434.85 14.1 20.9 For the species (CH2)2180 • • • HF only the rotational constants 7059.7 MHz and B — C = 135 MHz could be obtained. It is established from arguments based on Pband A that the dimer has a pyramidal configuration at the oxygen atom and that the molecular point group is (7g. If the justifiable assumption is made that the monomer geometries are unchanged on dimer formation, then the observed rotational constants for (CH 2 )2160* • -H F leadtor0(O* • *F) = 2.627 A ja n d ^ = 71.8°, where ^ is the angle between the plane of the three-membered ring and the H—F direction. Replacement of H by D in the hydrogen bond does not significantly change these values.

Determination of twinning relationships between diopside dendrites

2010 ◽  
Vol 43 (6) ◽  
pp. 1393-1399
Author(s):  
Shan-Rong Zhao ◽  
Hai-Jun Xu ◽  
Hong-Wei Liu ◽  
Roger Mason ◽  
Hui-Fang Liu
Keyword(s):  
Point Group ◽  
Symmetry Plane ◽  
Twin Plane ◽  
Twin Structure ◽  
Electron Backscattered Diffraction ◽  
Twofold Axis ◽  
Relationship Analysis ◽  
The Third ◽  
Good Lattice

Electron backscattered diffraction, used to determine the orientations of dendritic crystals of synthetic diopside, revealed novel twinning relationships between three dendrite crystals. The three crystals, considered pairwise, are related by two twinning laws: for two pairs, twin plane {\overline 251} and twin axis 〈\overline 142〉 perpendicular to the twin plane; and for the third pair, twin plane {\overline 221} and twin axis 〈\overline 356〉 perpendicular to the twin plane. The twin axes and twin planes between the latter pair of crystals closely match the twofold axis and symmetry plane inside the third crystal. The distribution of the three dendrite crystals in the twin structure shows overall 2/msymmetry, so the point group of diopside controls the whole combination of three crystals. The twin laws have been analysed using the theories of Mallard and Friedel, and twin indices and twin obliquity calculated. The complex twin laws yield a good lattice coincidence, and lattice relationship analysis based on the {201} plane confirms the twin laws.

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