The intrinsic group–subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells

2022 ◽  
Vol 78 (1) ◽  
Author(s):  
Martin Cramer Pedersen ◽  
Vanessa Robins ◽  
Stephen T. Hyde
Keyword(s):  
Minimal Surfaces ◽  
Subgroup Lattice ◽  
Unit Cells ◽  
Lattice Graphs ◽  
Conventional Unit

The intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group–subgroup lattice graphs.

scholarly journals MODELING OF PACKING DENSITY OF THE SIMPLEST HEXAGONAL LATTICE. I

2021 ◽  
pp. 39-52
Author(s):  
D.V. Fomin ◽  
Keyword(s):  
Packing Density ◽  
Hexagonal Lattice ◽  
Hexagonal Crystal ◽  
Crystal Lattices ◽  
Unit Cells ◽  
Overlapping Spheres ◽  
Conventional Unit

The article deals with the primitive and conventional unit cells of the cubic and densely packed hexagonal crystal lattices. The author analyzes the methods used for determining the spatial packing density and the distance between particles in a crystal. The spherical and cubic models of packing of equal-sized non-overlapping spheres are also considered. A comparative assess-ment of their effectiveness based on practical calculations is presented.

OPTIMIZATION OF BROADBAND MICROWAVE ABSORBER USING GENETIC ALGORITHM

2020 ◽  
Vol 65 (6) ◽  
pp. 90-97
Author(s):  
Hai Pham Van ◽  
Tu Vu Minh ◽  
Van Mai Ngoc ◽  
Dien Pham Van ◽  
Cuong Tran Manh
Keyword(s):  
Genetic Algorithm ◽  
Absorption Spectrum ◽  
Digital Technology ◽  
Optical Loss ◽  
Wide Frequency Range ◽  
Simple Random Sample ◽  
Work Demands ◽  
Unit Cells ◽  
Enormous Number ◽  
Conventional Unit

In recent years, scientists have been focusing on coding metamaterials absorbers to take full advantage of digital technology. This technology is mostly based on the fact that the absorption spectrum of a full-sized metamaterial varies with the different number and position of the defect elements in conventional unit cells (UCs) in it. However, both of their traditional methods namely simple random sample and combination of fundamental meta-block struggle with the enormous number of possible configurations especially when the number of UCs increases. In this article, we represent 5 configurations with different numbers of UCs, 2x2, 3x3, 4x4, 5x5, and 6x6 UCs, all of which maintain average absorption higher than 90% over a 10 GHz wide frequency range of interest between 17 GHz and 27 GHz. These results are obtained by using a genetic algorithm to generate configurations with higher optical loss through the process. Comparing to the conventional methods' result, our approach has achieved a significant improvement in the absorption spectrum. Furthermore, our methods could be applied to more structures with different sizes and numbers of UCs, thus provided a reliable tool to design practical metamaterials that serve the real work demands.

The Mirror: Mother of All Symmetries in Crystals

2020 ◽  
Vol 12 (3) ◽  
pp. 289-313
Author(s):  
Mohammad Abdul Wahab
Keyword(s):  
Mirror Symmetry ◽  
Point Group ◽  
Prima Facie ◽  
Fundamental Symmetry ◽  
Combination Scheme ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Group Symmetries ◽  
The Given ◽  
Conventional Unit

Mirror symmetry is found to be the only fundamental symmetry in crystalline solids because all other symmetries, such as rotation, inversion, rotoreflection, rotoinversion and translational periodicity can be easily derived from suitable combinations of mirrors. Similarly, the point group symmetries can also be derived from the same. The mirror combination scheme is found to work in accordance with the principle of Wigner-Seitz cells and Brillouin Zones (and not with the conventional unit cells as proposed by Bravais), where the zone boundaries of a Brillouin zone represent different sets of Bragg planes obtained from diffraction pattern of the given crystal, while the diffraction of given crystal takes place in terms of decreasing interplanar spacing in reciprocal space. Because the Wigner Seitz cells, the Brillouin zones and the diffraction patterns possess defined origin and exhibit spherical symmetry, they cannot have translational symmetry of any kind (microscopic or macroscopic). Results obtained on the basis of this concept help us to remove the existing ambiguities in crystallography and make the crystal structure determination simple. Further, prima facie the diffraction patterns are found to take care of the proposed 'systematic absences' arising due to the so called lattice centering, glide planes and screw axes without actually taking them into consideration. This newly and first discovered concept is expected to explain all other complicated or less understood issues related to crystallography.

Measurement and Reduction of Radiation Damage in Frozen Hydrated Crystalline Specimens

1978 ◽  
Vol 36 (3) ◽  
pp. 70-77 ◽  
Author(s):  
R.M. Glaeser ◽  
S.B. Hayward
Keyword(s):  
Diffraction Pattern ◽  
Structural Information ◽  
Structural Disorder ◽  
Structural Features ◽  
Biological Macromolecules ◽  
Diffraction Intensity ◽  
Object Structure ◽  
Specimen Material ◽  
Unit Cells ◽  
Identical Unit

Highly ordered or crystalline biological macromolecules become severely damaged and structurally disordered after a brief electron exposure. Evidence that damage and structural disorder are occurring is clearly given by the fading and eventual disappearance of the specimen's electron diffraction pattern. The fading and disappearance of sharp diffraction spots implies a corresponding disappearance of periodic structural features in the specimen. By the same token, there is a oneto- one correspondence between the disappearance of the crystalline diffraction pattern and the disappearance of reproducible structural information that can be observed in the images of identical unit cells of the object structure. The electron exposures that result in a significant decrease in the diffraction intensity will depend somewhat upon the resolution (Bragg spacing) involved, and can vary considerably with the chemical makeup and composition of the specimen material.

Electron microscopy of niobium and tantalum hydrides

1978 ◽  
Vol 36 (1) ◽  
pp. 644-645
Author(s):  
T. Schober
Keyword(s):  
Electron Microscopy ◽  
Heat Storage ◽  
Measurement Techniques ◽  
Metal Hydrides ◽  
Detailed Understanding ◽  
Storage Devices ◽  
Unit Cells ◽  
Endothermic Reactions ◽  
Hydrogen Reactions ◽  
New Phase

Nb, Ta and V are prototype substances for the study of the endothermic reactions of H with metals. Such metal-hydrogen reactions have gained increased importance due to the application of metal-hydrides in hydrogen- und heat storage devices. Electron microscopy and diffraction were demonstrated to be excellent methods in the study of hydride morphologies and structures (1). - Figures 1 and 2 show the NbH and TaH phase diagrams (2,3,4). EM techniques have contributed substantially to the elucidation of the structures and domain configurations of phases β, ζ and ε (1,4). Precision length measurement techniques of distances in reciprocal space (5) recently led to a detailed understanding of the distortions of the unit cells of phases ζ and ε (4). In the same work (4) the existence of the new phase η was shown. It is stable near -68 °C. The sequence of transitions is thus below 70 %.

Crystal Structure Analysis of Cu-Zr Alloys by Convergent Beam Diffraction

1981 ◽  
Vol 39 ◽  
pp. 354-355
Author(s):  
A. F. Marshall ◽  
J. W. Steeds ◽  
D. Bouchet ◽  
S. L. Shinde ◽  
R. G. Walmsley
Keyword(s):  
Crystal Structure ◽  
Point Group ◽  
Intermetallic Phase ◽  
Three Dimensional ◽  
Crystal Structure Analysis ◽  
Ion Milling ◽  
Composition And Structure ◽  
Unit Cells ◽  
Sputter Deposited ◽  
Convergent Beam

Convergent beam electron diffraction is a powerful technique for determining the crystal structure of a material in TEM. In this paper we have applied it to the study of the intermetallic phases in the Cu-rich end of the Cu-Zr system. These phases are highly ordered. Their composition and structure has been previously studied by microprobe and x-ray diffraction with sometimes conflicting results.The crystalline phases were obtained by annealing amorphous sputter-deposited Cu-Zr. Specimens were thinned for TEM by ion milling and observed in a Philips EM 400. Due to the large unit cells involved, a small convergence angle of diffraction was used; however, the three-dimensional lattice and symmetry information of convergent beam microdiffraction patterns is still present. The results are as follows:1) 21 at% Zr in Cu: annealed at 500°C for 5 hours. An intermetallic phase, Cu3.6Zr (21.7% Zr), space group P6/m has been proposed near this composition (2). The major phase of our annealed material was hexagonal with a point group determined as 6/m.

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

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