Symmetry operation measures

2007 ◽  
Vol 29 (2) ◽  
pp. 190-197 ◽  
Author(s):  
Mark Pinsky ◽  
David Casanova ◽  
Pere Alemany ◽  
Santiago Alvarez ◽  
David Avnir ◽  
...  
Keyword(s):  
Symmetry Operation

Dimensional scaling as a symmetry operation

1989 ◽  
Vol 91 (12) ◽  
pp. 7791-7796 ◽  
Author(s):  
S. Kais ◽  
D. R. Herschbach ◽  
R. D. Levine
Keyword(s):  
Symmetry Operation ◽  
Dimensional Scaling

A New Method for Orientation Distribution Function Analysis

1985 ◽  
Vol 29 ◽  
pp. 443-449
Author(s):  
Munetsugu Matsuo ◽  
Koichi Kawasaki ◽  
Tetsuya Sugai
Keyword(s):  
Distribution Function ◽  
Spherical Harmonics ◽  
Orientation Distribution Function ◽  
Function Analysis ◽  
Orientation Distribution ◽  
Symmetry Operation ◽  
Composite Function ◽  
Odd Order ◽  
Pole Figures ◽  
Generalized Spherical Harmonics

AbstractAs a means for quantitative texture analysis, the crystallite orientation distribution function analysis has an important drawback: to bring ghosts as a consequence of the presence of a non-trivial kernel which consists of the spherical harmonics of odd order terms. In the spherical hamonic analysis, ghosts occur in the particular orientations by symmetry operation from the real orientation in accordance with the symmetry of the harmonics of even orders. For recovery of the odd order harmonics, the 9th-order generalized spherical harmonics are linearly combined and added to the orientation distribution function reconstructed from pole figures to a composite function. The coefficients of the linear combination are optimized to minimize the sum of negative values in the composite function. Reproducibility was simulated by using artificial pole figures of single or multiple component textures. Elimination of the ghosts is accompanied by increase in the height of real peak in the composite function of a single preferred orientation. Relative fractions of both major and minor textural components are reproduced with satisfactory fidelity In the simulation for analysis of multi-component textures.

scholarly journals Generating a High Valency Biotin Binder by Selecting Uniform Protein Assemblies via Crystallization

Crystals ◽  
2019 ◽  
Vol 9 (7) ◽  
pp. 353
Author(s):  
Orly Avraham ◽  
Yael Levi-Kalisman ◽  
Oded Livnah
Keyword(s):  
Quaternary Structure ◽  
Disulfide Bridge ◽  
Symmetry Operation ◽  
Added Value ◽  
Purification Process ◽  
Protein Assemblies ◽  
High Affinity ◽  
Covalent Crosslinking ◽  
Crystallographic Symmetry ◽  
Biotin Binding

Crystallization is a common practice in the purification process in small molecule synthesis while selecting the wanted product. For proteins it is rarely applied due to the methodological predicaments in obtaining crystals. Our observation of the stabilized octamers in the crystal structure of hoefavidin, a novel dimeric member of the avidin family, led to the notion of developing a novel biotechnological tool via covalent crosslinking. The avidin–biotin system has been exploited for decades utilizing the ultra-high affinity between avidin and biotin as a basis for numerous applications. Optimizing the system led to the discovery of a novel group of dimeric avidins including hoefavidin. Hoefavidin has a dynamic quaternary structure, where a dimer is the basis for generating the octamer via crystallographic symmetry operation. Upon biotin binding in solution hoefavidin dissociates solely into dimers. In order to stabilize the octamer, we designed the P61C mutant to form a disulfide bridge stabilizing the octamer and preventing dissociation upon biotin binding. The process of selecting P61C hoefavidin uniform octamers includes crystallization followed by dissolving the crystals. The P61C modified hoefavidin octamer can have a substantial added value to the various biotechnological applications and advances of the biotin based high affinity systems.

scholarly journals A symmetry-derived mechanism for atomic resolution imaging

2020 ◽  
Vol 117 (45) ◽  
pp. 27805-27810
Author(s):  
Matus Krajnak ◽  
Joanne Etheridge
Keyword(s):  
Electron Probe ◽  
Local Symmetry ◽  
Symmetry Operation ◽  
Specimen Thickness ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Contrast Mechanism ◽  
Electron Intensity ◽  
Resolution Imaging ◽  
Degree Of Similarity

We introduce an image-contrast mechanism for scanning transmission electron microscopy (STEM) that derives from the local symmetry within the specimen. For a given position of the electron probe on the specimen, the image intensity is determined by the degree of similarity between the exit electron-intensity distribution and a chosen symmetry operation applied to that distribution. The contrast mechanism detects both light and heavy atomic columns and is robust with respect to specimen thickness, electron-probe energy, and defocus. Atomic columns appear as sharp peaks that can be significantly narrower than for STEM images using conventional disk and annular detectors. This fundamentally different contrast mechanism complements conventional imaging modes and can be acquired simultaneously with them, expanding the power of STEM for materials characterization.

Symmetry Operation

2016 ◽  
Author(s):  
Vladimir I. Minkin
Keyword(s):  
Symmetry Operation

LATTICE DYNAMICS OF CALCIUM FLUORIDE: PART I. LYDDANE, SACHS, TELLER FORMULA, DIFFUSE X-RAY SCATTERING, AND SPECIFIC HEAT

1962 ◽  
Vol 40 (1) ◽  
pp. 74-90 ◽  
Author(s):  
S. Ganesan ◽  
R. Srinivasan
Keyword(s):  
Specific Heat ◽  
Calcium Fluoride ◽  
Inelastic Neutron Scattering ◽  
Interaction Force ◽  
Inelastic Neutron ◽  
Symmetry Operation ◽  
Absorption Frequency ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

The reported violation of the Lyddane, Sachs, Teller formula in calcium fluoride has been shown to arise from an error due to the non-application of a symmetry operation in the second neighbor fluorine–fluorine interaction in Cribier's work. By correct deduction of the force constants, the diffuse X-ray scattering measurements are shown to be in accord with the Lyddane, Sachs, Teller formula, but the specific heat calculation on this model is in disagreement with the experimental data.Reflection measurements in the infrared and dispersion of refractive index are shown to be consistent with the principal infrared absorption frequency near 40 μ and not near 51 μ as assumed in the previous model. The calculation of the specific heat using this new infrared frequency agreed with the measurements only at very low and very high temperatures.The two curves are brought into agreement by assuming that the non-Coulomb cross interaction force constant β1 between first neighbor calcium and fluorine decrease with the wave vector. The diffuse X-ray scattering was recalculated on the model, which explained the specific heat data, and was again found to be in agreement with the Lyddane, Sachs, Teller formula. It is suggested that detailed infrared and inelastic neutron scattering studies be made on this crystal.

Revision of Ferroelastic Structures of n-Heptyl- and n-Octylammonium Dihydrogen Phosphate Crystals

1997 ◽  
Vol 53 (2) ◽  
pp. 272-279 ◽  
Author(s):  
J. Fábry ◽  
V. Petrícek ◽  
I. Císarová ◽  
J. Kroupa
Keyword(s):  
Hydrogen Bond ◽  
Hydrogen Bonds ◽  
Structure Determination ◽  
Symmetry Operation ◽  
Double Layers ◽  
Dihydrogen Phosphate ◽  
Hydrogen Bond Acceptor ◽  
Space Group ◽  
Unit Cells ◽  
Pass Through

This study deals with the structure determination of C7H15NH3 +.H2PO4 − (C7ADP) and C8H17NH3 +.H2PO4 − (C8ADP). The samples used in this study were not subjected to a phase transition after they had been crystallized. Unlike a previous structure determination, weak reflections, now with indices h = 2n + 1, were included. This means that both structures are described in unit cells with the lattice parameters a twice as long as given previously. Both structures are quite similar; two double layers of dihydrogen phosphates, which are interconnected by hydrogen bonds (2.52–2.62 Å), pass through each unit cell. Alkylammonium groups interact with these dihydrogen phosphates via longer hydrogen bonds (>2.75 Å), while the rest of the aliphatic chains interact via van der Waals contacts. All H atoms were localized and no disorder of the H atoms was detected. Both structures described in the space group P121/n1 exhibit a reproducible ferroelastic switching. The hypothetical prototypic phase is orthorhombic with the space group number 60 P2/b21/n21/a. All atoms except two hydrogen species exist in pairs linked by the lost symmetry operations derived from the prototypic space group and are brought close to each other – up to 0.25 Å – under the action of them. Each of these two different H atoms is involved in an asymmetric hydrogen bond between an oxygen pair. Under the action of a lost symmetry operation each of these H atoms is displaced from one oxygen towards the other. Therefore, it is assumed that during the ferroelastic switching the jumps of these two hydrogen species take place between the pertinent hydrogen-bond acceptor and donor O atoms. Hence, these O atoms reverse their role as hydrogen-bond donors and acceptors during the ferroelastic switching.

scholarly journals Gauge-Independent Theory of Symmetry. II.

1965 ◽  
Vol 18 (2) ◽  
pp. 109 ◽  
Author(s):  
HA Buchdahl ◽  
LJ Tassie
Keyword(s):  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Equation Of Motion ◽  
Symmetry Operation ◽  
Quantum Mechanical ◽  
Translation Invariant ◽  
Translation Operators ◽  
Physical Symmetry ◽  
Magnetic Translation ◽  
Quantum Mechanical Systems

This paper develops a gauge-independent symmetry theory of non-relativistic quantum mechanical systems, in line with that previously considered in the context of classical mechanics. We first discuss at length the motivation for adopting the view that the invariance of a system K under a physical symmetry operation .<I' should be taken to mean invariance of the equation of motion of K under a certain gauge-independent unitary transformation U c( .<1'). The formal development of the theory is then carried through, and some detailed examples are presented. In particular, corresponding to every direction along which a system K happens to be translation invariant there exists a gauge-independent generator of translations which leaves K invariant but which is not, in general, a component of either the canonical or the kinetic momentum. The connexion between such invariant generators of translations and the so-called magnetic translation operators is referred to.

scholarly journals DISCRETE SYMMETRIES OF LOW-DIMENSIONAL DIRAC MODELS: A SELECTIVE REVIEW WITH A FOCUS ON CONDENSED-MATTER REALIZATIONS

2015 ◽  
Vol 57 (1) ◽  
pp. 3-17 ◽  
Author(s):  
R. WINKLER ◽  
U. ZÜLICKE
Keyword(s):  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Discrete Symmetry ◽  
Symmetry Operation ◽  
Free Electrons ◽  
Quantum Theories ◽  
Dimensional Spacetime ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Low Dimensional

The most fundamental characteristic of a physical system can often be deduced from its behaviour under discrete symmetry transformations, such as time reversal, parity and chirality. Here, we review some of the basic symmetry properties of the relativistic quantum theories for free electrons in ($2+1$)- and ($1+1$)-dimensional spacetime. Additional flavour degrees of freedom are necessary to properly define symmetry operations in ($2+1$) dimensions, and are generally present in physical realizations of such systems, for example in single sheets of graphite. We find that there exist two possibilities for defining any flavour-coupling discrete symmetry operation of the two-flavour ($2+1$)-dimensional Dirac theory. Some physical implications of this previously unnoticed duplicity are discussed.

scholarly journals Bis{N-[(diethylamino)dimethylsilyl]anilinido-κ2N,N′}nickel(II)

2012 ◽  
Vol 68 (4) ◽  
pp. m357-m357
Author(s):  
Juan Chen ◽  
Jing Li
Keyword(s):  
Bond Length ◽  
Metal Atom ◽  
Symmetry Operation ◽  
Tetrahedral Geometry ◽  
Distorted Tetrahedral Geometry

The mononuclear NiIIamide, [Ni(C12H21N2Si)2], has the NiIIatomN,N′-chelated by theN-silylated anilinide ligands. The ligands are arrangedcisto each other and obey theC2-symmetry operation. The two ends of the N—Si—N chelating unit exhibit different affinities for the metal atom: the Ni—Nanilinidebond length is 1.913 (3) Å and Ni—Namineis 2.187 (3) Å. The four-coordinate NiIIion demonstrates a distorted tetrahedral geometry.

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