THE STRUCTURE OF AGGREGATES—A CLASS OF 20-FACED SPACE-FILLING POLYHEDRA

1965 ◽  
Vol 43 (11) ◽  
pp. 2052-2055 ◽  
Author(s):  
F. W. Smith
Keyword(s):  
Diamond Lattice ◽  
Space Filling ◽  
Delaunay Simplices ◽  
Voronoi Polyhedra ◽  
Polyhedral Cells ◽  
Structure Of Aggregates

An example is given of a class of partitions of space into polyhedral cells having an average of 20 faces each. The structure is derived from the Voronoi polyhedra of slightly distorted versions of the diamond lattice, which in turn are duals of the Delaunay simplices of the diamond lattice. A particular member of this class is described: it is a 20-faced stereohedron that packs to fill space by isometries including a rotation.

Simulation of 3-Dimensional Cell Population Growth Processes in Polyhedral Cellular Systems

2007 ◽  
Vol 537-538 ◽  
pp. 579-590
Author(s):  
Tamás Réti ◽  
Ibolya Zsoldos
Keyword(s):  
Population Growth ◽  
Cell Population ◽  
Cell Decomposition ◽  
Cellular Systems ◽  
Space Filling ◽  
Growth Processes ◽  
Cell Nucleation ◽  
Cell Population Growth ◽  
Polyhedral Cells ◽  
New Perspective

In order to simulate the polyhedral grain nucleation in alloys, 3-D cell population growth processes are studied in space-filling periodic cellular systems. We discussed two different methods by which space-filling polyhedral cellular systems can be constructed by topological transformations performed on “stable” 3-D cellular systems. It has been demonstrated that an infinite sequence of stable periodic space-filling polyhedral systems can be generated by means of a simple recursion procedure based on a vertex based tetrahedron insertion. On the basis of computed results it is conjectured that in a 3-D periodic, topologically stable cellular system the minimum value of the average face number 〈f〉 of polyhedral cells is larger than eight (i.e. 〈f〉 > 8). The outlined algorithms (which are based on cell decomposition and/or cell nucleation) provide a new perspective to simulate grain population growth processes in materials with polyhedral microstructure.

New types of space-filling polyhedra with fourteen faces

1986 ◽  
Vol 42 (4) ◽  
pp. 282-286 ◽  
Author(s):  
M. E. Rosa ◽  
M. A. Fortes
Keyword(s):  
General Solution ◽  
Lattice Point ◽  
Periodic Structures ◽  
Space Filling ◽  
Truncated Octahedron ◽  
Pure Rotation ◽  
Topological Solution ◽  
Polyhedral Cells ◽  
Four Square

A study of the staggered packing of identical hexagonal prisms leading to four-connected periodic structures with polyhedral cells of fourteen faces has been undertaken. Special attention was given to those packings that lead to periodic structures with two polyhedra per lattice point, and such that the two polyhedra are related by a pure rotation and/or enantiomorphism. The general solution for packings of this type was obtained and the topology of the intervening polyhedra was determined. It is shown that polyhedra with eight hexagonal faces and six square faces, topologically isomorphic to the truncated octahedron, can be packed with or without a rotation. The polyhedra which can be packed with the respective enantiomorphs (with or without rotation) have four square faces, four pentagonal faces and six hexagonal faces. Each type of packing is compatible with Bravais lattices of any category and each topological solution is compatible with a range of convex shapes.

The dislocation structure of a 10° [110] tilt boundary in silicon

1983 ◽  
Vol 41 ◽  
pp. 114-115
Author(s):  
B. Cunningham ◽  
D.G. Ast
Keyword(s):  
Dislocation Structure ◽  
Tilt Angle ◽  
Imaging Technique ◽  
Diamond Lattice ◽  
Tilt Boundary ◽  
Formation Mechanisms ◽  
Diffraction Contrast ◽  
Lattice Fringe ◽  
Tilt Boundaries ◽  
Chemically Vapor Deposited

There have Been a number of studies of low-angle, θ < 4°, [10] tilt boundaries in the diamond lattice. Dislocations with Burgers vectors a/2<110>, a/2<112>, a<111> and a<001> have been reported in melt-grown bicrystals of germanium, and dislocations with Burgers vectors a<001> and a/2<112> have been reported in hot-pressed bicrystals of silicon. Most of the dislocations were found to be dissociated, the dissociation widths being dependent on the tilt angle. Possible dissociation schemes and formation mechanisms for the a<001> and a<111> dislocations from the interaction of lattice dislocations have recently been given.The present study reports on the dislocation structure of a 10° [10] tilt boundary in chemically vapor deposited silicon. The dislocations in the boundary were spaced about 1-3nm apart, making them difficult to resolve by conventional diffraction contrast techniques. The dislocation structure was therefore studied by the lattice-fringe imaging technique.

Convolutional Neural Network of Atomic Surface Structures to Predict Binding Energies for High-Throughput Screening of Catalysts

2019 ◽  
Author(s):  
Seoin Back ◽  
Junwoong Yoon ◽  
Nianhan Tian ◽  
Wen Zhong ◽  
Kevin Tran ◽  
...  
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Convolutional Neural Network ◽  
High Throughput ◽  
High Throughput Screening ◽  
Binding Energies ◽  
Surface Structures ◽  
Voronoi Polyhedra ◽  
Atomic Surface

We present an application of deep-learning convolutional neural network of atomic surface structures using atomic and Voronoi polyhedra-based neighbor information to predict adsorbate binding energies for the application in catalysis.

Enhanced Magnetic Frustration in a New High Entropy Diamond Lattice Spinel Oxide

2020 ◽  
Author(s):  
Sourav Marik ◽  
Deepak Singh ◽  
Bruno Gonano ◽  
Fabien Veillon ◽  
Denis Pelloquin ◽  
...  
Keyword(s):  
Diamond Lattice ◽  
Magnetic Frustration ◽  
Spinel Oxide ◽  
High Entropy

Region of Interest Based MRI Brain Image Compression Using Peano Space Filling Curve

2016 ◽  
Vol 11 (2) ◽  
pp. 114-120 ◽  
Author(s):  
C. Peter Devadoss ◽  
Balasubramanian Sankaragomathi ◽  
Thirugnanasambantham Monica
Keyword(s):  
Image Compression ◽  
Region Of Interest ◽  
Space Filling ◽  
Brain Image ◽  
Space Filling Curve ◽  
Mri Brain ◽  
Filling Curve ◽  
Mri Brain Image
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