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Cuboctahedron Model of Atomic Mass Based on a Dual Tetrahedral Coordinate System
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
James Garnett Sawyer, Marla Jeanne Wagner
The interatomic distances and electron shell structures follow the geometries of tetrahedron, octahedron, cuboctahedron, truncated octahedron, icosahedron, and rhombic dodecahedron. Fritsche and Benfield developed a coordination quantum of atoms which could be applied to quantum atomic electrons in the PTE (Fritsche, 1993) (Figure 8.11).
Tetrahedral Dual Coordinate System of Electron Orbital and Quantum Loop Theories in Three and Six Dimensions
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
James Garnett Sawyer, Marla Jeanne Wagner
All of the complex polyhedrons of crystallography, such as the tetrahedron, octahedron, cuboctahedron, truncated octahedron, rhombic dodecahedron, trapezohedron, pyritohedron, pentagonal dodecahedron, and icosahedron, are modeled on the 3D cube (except the hexagonal MI system).
Heteroepitaxy of diamond semiconductor on iridium: a review
Published in Functional Diamond, 2022
Weihua Wang, Benjian Liu, Leining Zhang, Jiecai Han, Kang Liu, Bing Dai, Jiaqi Zhu
Figure 8 shows the grain shape when α, β, and γ parameters are in different regimes, where Figure 8(a,b) shows the facets coexistence domains are surrounded by topological boundaries that depend on α/β parameters, α/γ parameters, respectively. When β or γ parameter is very small, the grain shape mainly depends on α parameter. When α is smaller than 1, the grain is a cube; when α is larger than 3, the grain is an octahedron; when α is at the range from 1 to 3, the shape is cuboctahedron. To obtain the (001)-preferred diamond grains, Chavanne et al. [159] proposed that α close to 3 promoted a faster growth rate of <001> directions and that lower than 1.5 led to a preferential growth in <111> direction. For the former, pyramid or octahedral grains are attained while other non-epitaxial grains are also overgrown. For the latter, those epitaxial grains grow and smooth (001) surfaces are observed. CVD parameters such as methane fraction and substrate temperature can be adjusted to get both α cases. What should be noted is that the model above never takes the effect of the substrate on the grain growth into account [160].
Dissimilarity measure of local structure in inorganic crystals using Wasserstein distance to search for novel phosphors
Published in Science and Technology of Advanced Materials, 2021
Shota Takemura, Takashi Takeda, Takayuki Nakanishi, Yukinori Koyama, Hidekazu Ikeno, Naoto Hirosaki
In this approach, W can be calculated as the local structures with different coordination numbers because the local structures are expressed as the distance distribution. To calculate W of the local structures with the different coordination numbers, seven kinds of ideal structures were selected: tetrahedron, trigonal bipyramid, octahedron, pentagonal bipyramid, cubic, square antiprism, and cuboctahedron. The center-ligand distances are the same in each ideal structure. Table 1 shows W of the seven kinds of ideal structures. The W between pentagonal bipyramid and square antiprism is the smallest at 0.067, but pentagonal bipyramid and square antiprism are dissimilar because the value is larger than 0.047 in Figure 2. Local structures with different coordination numbers indicate dissimilarity. Therefore, this quantitative dissimilarity can be calculated for any local structure, and a local structure with a different coordination number is dissimilar spontaneously.
Optimal orientations of discrete global grids and the Poles of Inaccessibility
Published in International Journal of Digital Earth, 2020
The methods described below will exhaustively generate all the possible orientations for each of several polyhedra. This is done at a coarse resolution using elliptical calculations. Duplicate orientations will be searched for and removed. Each remaining member of this sparsely-sampled orientation space will then used as a starting point for a hillclimbing algorithm which finds optimal orientations given some criteria of interest. Several polyhedra are considered here (Figure 1): the cuboctahedron, the regular dodecahedron, the regular icosahedron, the regular octahedron, and the regular tetrahedron. Since textual descriptions may be insufficient to recreate the algorithm, I provide source code on Github at https://github.com/r-barnes/Barnes2017-DggBestOrientations. Various software packages were used in the analysis (Barnes 2017; Becker et al. 2018; McIlroy et al. 2018; Wickham 2016; Wickham et al. 2018).