Chiralities of nodal points along high-symmetry lines with screw rotation symmetry

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. We show that the edge remains protected from localization in the topological phase, and the local disorder caused by the amorphous structure results in critical scaling of the transport in the system. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.

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The usefulness of high index low symmetry zone axes for holz line analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126718 ◽

1987 ◽

Vol 45 ◽

pp. 384-385

Author(s):

C. M. Sung ◽

D. B. Williams

Keyword(s):

Lattice Parameter ◽

High Order ◽

Zone Axis ◽

High Index ◽

High Symmetry ◽

Second Phases ◽

Line Patterns ◽

Low Symmetry ◽

Line Analysis

Researchers have tended to use high symmetry zone axes (e.g. <111> <114>) for High Order Laue Zone (HOLZ) line analysis since Jones et al reported the origin of HOLZ lines and described some of their applications. But it is not always easy to find HOLZ lines from a specific high symmetry zone axis during microscope operation, especially from second phases on a scale of tens of nanometers. Therefore it would be very convenient if we can use HOLZ lines from low symmetry zone axes and simulate these patterns in order to measure lattice parameter changes through HOLZ line shifts. HOLZ patterns of high index low symmetry zone axes are shown in Fig. 1, which were obtained from pure Al at -186°C using a double tilt cooling holder. Their corresponding simulated HOLZ line patterns are shown along with ten other low symmetry orientations in Fig. 2. The simulations were based upon kinematical diffraction conditions.

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Systematic zone-Axis orientation of NM-scale particles for microdiffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100174448 ◽

1990 ◽

Vol 48 (4) ◽

pp. 262-263

Author(s):

E D Boyes ◽

L Hanna

Keyword(s):

Real Space ◽

Dark Field ◽

Zone Axis ◽

High Symmetry ◽

Lattice Imaging ◽

Cell Level ◽

Bright Field ◽

Axis Orientation ◽

Annular Dark Field ◽

Target Designation

A VG HB501 FEG STEM has been modified to provide track whilst tilt [TWIT] facilities for controllably tilting selected and initially randomly aligned nanometer-sized particles into the high symmetry zone-axis orientations required for microdiffraction, lattice imaging and chemical microanalysis at the unit cell level. New electronics display in alternate TV fields and effectively in parallel on split [+VTR] or adjacent externally synchronized screens, the micro-diffraction pattern from a selected area down to <1nm2 in size, together with the bright field and high angle annular dark field [HADF] STEM images of a much wider [˜1μm] area centered on the same spot. The new system makes it possible to tilt each selected and initially randomly aligned small particle into a zone axis orientation for microdiffraction, or away from it to minimize orientation effects in chemical microanalysis. Tracking of the inevitable specimen movement with tilt is controlled by the operator, with realtime [60Hz] update of the target designation in real space and the diffraction data in reciprocal space. The spot mode micro-DP and images of the surrounding area are displayed continuously. The regular motorized goniometer stage for the HB501STEM is a top entry design but the new control facilities are almost equivalent to having a stage which is eucentric with nanometric precision about both tilt axes.

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Using crystallographic symmetry in diffraction and contrast analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154494 ◽

1989 ◽

Vol 47 ◽

pp. 504-505

Author(s):

U. Dahmen ◽

K.H. Westmacott

Keyword(s):

Electron Microscopy ◽

High Symmetry ◽

Two Phase ◽

Tem Analysis ◽

Crystallographic Symmetry ◽

The Matrix ◽

Contrast Analysis ◽

Practical Tool ◽

Convergent Beam ◽

Beam Diffraction

Despite the increased use of convergent beam diffraction, symmetry concepts in their more general form are not commonly applied as a practical tool in electron microscopy. Crystal symmetry provides an abundance of information that can be used to facilitate and improve the TEM analysis of crystalline solids. This paper draws attention to some aspects of symmetry that can be put to practical use in the analysis of structures and morphologies of two-phase materials.It has been shown that the symmetry of the matrix that relates different variants of a precipitate can be used to determine the axis of needle- or lath-shaped precipitates or the habit plane of plate-shaped precipitates. By tilting to a special high symmetry orientation of the matrix and by measuring angles between symmetry-related variants of the precipitate it is possible to find their habit from a single micrograph.

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Arrangement Of Monomeric Units In Fibrin

10.1055/s-0038-1665755 ◽

1979 ◽

Author(s):

Jan Hermans

Keyword(s):

Fiber Axis ◽

High Symmetry ◽

Linear Polymers ◽

Fiber Volume ◽

High Fiber ◽

Rotation Axes ◽

Small Set ◽

Helical Turn ◽

The One ◽

Kinetics Of

Measurements of light scattering have given much information about formation and properties of fibrin. These studies have determined mass-length ratio of linear polymers (protofibrils) and of fibers, kinetics of polymerization and of lateral association and volume-mass ratio of thick fibers. This ratio is 5 to 1. On the one hand, this high value suggests that the fiber contains channels that allow the diffusion of enzymes such as Factor XHIa and plasmin; on the other hand, the high value appears paradoxical for a stiff fiber made up of elongated units (fibrin monomers) arranged in parallel. Such a high fiber volume is a property of only a small set out of many high-symmetry models of fibrin, which may be constructed from overlapping three-domain monomers which are arranged into strands, are aligned nearly parallel to the fiber axis and make adequate longitudinal and lateral contacts. These models contain helical protofibrils related to each other by rotation axes parallel to the fiber axis. The protofibrils may contain 2, 3 or 4 monomers per helical turn and there are four possible symmetries. A large specific volume is achieved if the ends of each monomer are slightly displaced from the protofibril axis, either by a shift or by a tilt of the monomer. The fiber containing tilted monomers is more highly interconnected; the two ends of a tilted monomer form lateral contacts with different adjacent protofibrils, whereas the two ends of a non-tilted monomer contact the same adjacent protofibril(s).

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Tolerance is theoretical and practical principles

Ukrainian Religious Studies ◽

10.32420/1996.4.69 ◽

1996 ◽

pp. 13-23

Author(s):

Mykhailo Babiy

Keyword(s):

Religious Diversity ◽

The Other ◽

Nodal Points ◽

Characteristic Features ◽

The One ◽

Ukrainian Society

Political ideological pluralism, religious diversity are characteristic features of modern Ukrainian society. On the one hand, multiculturalism, socio-political, religious differentiation of the latter appear as important characteristics of its democracy, as a practical expression of freedom, on the other - as a factor that led to the deconsocialization of society, gave rise to "nodal points" of tension, confrontational processes, in particular, in political and religious spheres.

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Self-Assembly of a Chiral Cubic Three-Connected Net from the High Symmetry Molecules C60 and SnI4

10.26434/chemrxiv.12196788 ◽

2020 ◽

Author(s):

Daniel B. Straus ◽

Robert J. Cava

Keyword(s):

Organic Synthesis ◽

Self Assembly ◽

Van Der Waals ◽

Van Der Waals Forces ◽

High Symmetry ◽

Molecular Chirality ◽

Chiral Materials ◽

Self Assembled ◽

Chiral Centers

The design of new chiral materials usually requires stereoselective organic synthesis to create molecules with chiral centers. Less commonly, achiral molecules can self-assemble into chiral materials, despite the absence of intrinsic molecular chirality. Here, we demonstrate the assembly of high-symmetry molecules into a chiral van der Waals structure by synthesizing crystals of C60(SnI4)2 from icosahedral buckminsterfullerene (C60) and tetrahedral SnI4 molecules through spontaneous self-assembly. The SnI4 tetrahedra template the Sn atoms into a chiral cubic three-connected net of the SrSi2 type that is held together by van der Waals forces. Our results represent the remarkable emergence of a self-assembled chiral material from two of the most highly symmetric molecules, demonstrating that almost any molecular, nanocrystalline, or engineered precursor can be considered when designing chiral assemblies.

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The Interplay of Open-Shell Spin-Coupling and Jahn-Teller Distortion in Benzene Radical Cation Probed by X-ray Spectroscopy

10.26434/chemrxiv.12799922.v2 ◽

2020 ◽

Author(s):

Marta L. Vidal ◽

Michael Epshtein ◽

Valeriu Scutelnic ◽

Zheyue Yang ◽

Tian Xue ◽

...

Keyword(s):

High Harmonic ◽

Open Shell ◽

Spin Coupling ◽

High Symmetry ◽

Teller Distortion ◽

Spectral Window ◽

X Ray ◽

Jahn Teller ◽

X Ray Absorption ◽

Jahn Teller Distortion

We report a theoretical investigation and elucidation of the x-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization as well as the measurement of the carbon K-edge spectra of both species using a table-top high-harmonic generation (HHG) source are described in the companion experimental paper [M. Epshtein et al., J. Phys. Chem. A., submitted. Available on ChemRxiv]. We show that the 1sC -> pi transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence of the unpaired (spectator) electron in the pi-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1sC ->pi* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation. The prominent split structure of the 1sC -> pi* band of the cation is attributed to the interplay between the coupling of the core -> pi* excitation with the unpaired electron in the pi-subshell and the Jahn-Teller distortion. The calculations attribute most of the splitting (~1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and estimate the additional splitting due to structural relaxation to be around ~0.1-0.2 eV. These results suggest that x-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller effect in benzene cation.

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Pseudopotential Band Calculations along a High-Symmetry Axis. Part 2. Spin-Orbit Interaction and the (111) Direction

10.21236/ada252397 ◽

1991 ◽

Author(s):

D. Y. Agassi ◽

J. B. Restorff

Keyword(s):

Symmetry Axis ◽

Orbit Interaction ◽

High Symmetry ◽

Spin Orbit ◽

Spin Orbit Interaction

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GIS Technologies in Course of Mathematical Cartography

Geodesy and Cartography ◽

10.22389/0016-7126-2017-921-3-30-35 ◽

2017 ◽

Vol 921 (3) ◽

pp. 30-35

Author(s):

N.G. Ivlieva ◽

V.F. Manukhov

Keyword(s):

Software Tools ◽

Digital Models ◽

Map Projection ◽

Gis Technologies ◽

Surface Distortion ◽

Nodal Points ◽

Projection Properties ◽

Special Software

GIS are closely related to mathematical cartography, as they work with spatially coordinated data. Practical course in mathematical cartography should meet the requirements of time and include tasks involving the use of modern GIS technologies. The functionality of GIS packages allow you to easily create maps in a given map projection, draw graticules and measured grids, perform dimensions on maps. This article is devoted to the research of map projection properties on the basis of GIS technologies in a practical course of mathematical cartography. The focus is on visual way to display local and regional distortions on maps. To create lines of equal distortion should use special software tools that allow to build digital models of surface distortion distribution directly on formulas or be interpolated both discretely located nodal points and isolines.

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