Symmetry-Based Transformable and Foldable Plate Structures

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Valentina Beatini
Keyword(s):  
The Other ◽  
Rigid Plate ◽  
Plate Structures ◽  
Symmetry Operations

This paper presents a novel family of modular flat-foldable rigid plate structures composed by assemblies of 4R-linkages. First, in the field of foldable plates, the proposed system is characterized by being not only foldable but also transformable: the slope of one module over the other is capable of changing not only magnitude but also sign. This transformable behavior extends the range of application of foldable plates from simply larger–smaller configurations to substantially different configurations and usages. The transformable curve is obtained by means of symmetry operations on the spherical length of links. For each module, three configurations can be designed. Various examples are illustrated.

scholarly journals Absolute Structure Determination using Electron Microscopy

1976 ◽  
Vol 34 ◽  
pp. 484-485
Author(s):  
O. Van der Biest
Keyword(s):  
Dark Field ◽  
Dynamical Theory ◽  
Zone Axis ◽  
Background Intensity ◽  
Lithium Ferrite ◽  
Screw Axis ◽  
Left Handed ◽  
Beam Orientation ◽  
Absolute Structure ◽  
Symmetry Operations

When the symmetry operations, which constitute the space group of a structure, do not include an inversion or a reflection operation, then the structure can exist in two forms, a right-handed and a left-handed one, called enantiomorphs. The presence of the two enantiomorphs coexisting within a sample can be verified in the electron microscope by imaging in dark field in a multi-beam orientation, with the electron beam parallel with a zone axis, along which the crystal does not show a center of symmetry in projection (1). One takes advantage here of violations in Friedel's Law (2), which may cause a difference in background intensity between the two structures. An example is shown in Fig. 1, where an inversion boundary runs through a thick wedge-shaped crystal of lithium ferrite. Ordered lithium ferrite may occur in two enantiomorphic forms P43 32 (right-handed screw axis), and P41 32 (left-handed screw axis). In this paper it will be shown that it is possible to determine uniquely the configuration of the structure using the results of the dynamical theory.

scholarly journals Properties of Projection Lines in the Space of the Orientation Distribution Function

1989 ◽  
Vol 10 (3) ◽  
pp. 243-264 ◽  
Author(s):  
A. Morawiec ◽  
J. Pospiech
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Analytical Description ◽  
Orientation Distribution ◽  
Orientation Space ◽  
The Relationship ◽  
Symmetry Operations

The relationship between the orientation distribution function (ODF) and the pole figure is based on the geometry of projection lines in the orientation space.The paper presents an analytical description of the projection lines and their transformations by symmetry operations. Using simple algebraical rules some properties of the projection lines as well as some properties of the associated projection lines (coupled due to the centrosymmetry of the pole figure) have been derived.

scholarly journals Double crystallographic groups and their representations on the Bilbao Crystallographic Server

2017 ◽  
Vol 50 (5) ◽  
pp. 1457-1477 ◽  
Author(s):  
Luis Elcoro ◽  
Barry Bradlyn ◽  
Zhijun Wang ◽  
Maia G. Vergniory ◽  
Jennifer Cano ◽  
...  
Keyword(s):  
Irreducible Representations ◽  
Site Symmetry ◽  
Crystallographic Groups ◽  
Space Groups ◽  
Symmetry Approach ◽  
Wyckoff Position ◽  
Double Space ◽  
Elementary Band ◽  
Symmetry Relations ◽  
Symmetry Operations

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPGandREPRESENTATIONS DSG). The toolDCOMPRELprovides compatibility relations between the irreducible representations of double space groups at differentkvectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The programDSITESYMimplements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the programBANDREPcalculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results ofBANDREPhave been extensively applied in the description of and the search for topological insulators.

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