Regular octahedron

Cation Electronic configuration Octahedron (regular) (pyroxene Ml) Tetragonally elongated octahedron (olivine Ml) Trigonally compressed octahedron (olivine M2) Monoclinic six-coordinated site (pyroxene M2)... 

The operation of some of the other improper rotation axes can be illustrated with respect to the five Platonic solids, the regular tetrahedron, regular octahedron, regular icosahedron, regular cube and regular dodecahedron. These polyhedra have regular faces and vertices, and each has... 

Octahedron (regular) A polyhedron with eight equal-sized, equilateral triangular faces and six apices (comers). 

Referring to Problem 3, what should the ratio 710/711 be if the equilibrium crystal is to be a regular octahedron, that is, to have (10) and (11) edges of equal length ... 

Figure Bl.8.4. Two of the crystal structures first solved by W L Bragg. On the left is the stnicture of zincblende, ZnS. Each sulphur atom (large grey spheres) is surrounded by four zinc atoms (small black spheres) at the vertices of a regular tetrahedron, and each zinc atom is surrounded by four sulphur atoms. On the right is tire stnicture of sodium chloride. Each chlorine atom (grey spheres) is sunounded by six sodium atoms (black spheres) at the vertices of a regular octahedron, and each sodium atom is sunounded by six chlorine atoms.

An extreme example of hybidization is the structure proposed for sulphur hexafluoride, SFe. The six S-F bonds are dhected to the apices of a regular octahedron. An aiTangement which would satisfy this number of covalent bonds is sp d hybridization. The ground state of the sulphur atom is s p° and... 

Ooso (structure I) has a regular octahedral cluster of 6 B atoms surrounded by a larger octahedron of 6 radially... 

Moreover, he made the inspired guess that the six secondary valences were directed toward the corners of a regular octahedron. 

Octahedral Having the symmetry of a regular octahedron. In an octahedral species, a central atom is surrounded by six other atoms, one above, one below, and four at the comers of a square, 176 complex in transitional metals, 418-420 geometric isomerism, 415 Octane number, 584... 

They contain octahedral MF (Table 1.3) [33] in XeF+RuF the attraction of XeF+ distorts the octahedron by pulling one fluorine towards it, so that there is one long Ru-F distance of 1.919 A compared with the others of 1.778-1.835 A (EXAFS measurements indicate KRuF6 has regular octahedral coordination (Ru-F 1.845 A)) [19]. 

The bond lengths make a more regular octahedron than in the d5 ruthenium analogue, possibly partly a consequence of the symmetrical electron distribution in the d6 Rh3+ ion (Table 2.4) [85],... 

We need six orbitals to accommodate six electron pairs around an atom in an octahedral arrangement, as in SF6 and XeF4, and so we need to use two d-orbitals in addition to the valence s- and p-orbitals to form six sp3d2 hybrid orbitals (Fig. 3.18). These identical orbitals point toward the six corners of a regular octahedron. 

The holes in the close-packed structure of a metal can be filled with smaller atoms to form alloys (alloys are described in more detail in Section 5.15). If a dip between three atoms is directly covered by another atom, we obtain a tetrahedral hole, because it is formed by four atoms at the corners of a regular tetrahedron (Fig. 5.30a). There are two tetrahedral holes per atom in a close-packed lattice. When a dip in a layer coincides with a dip in the next layer, we obtain an octahedral hole, because it is formed by six atoms at the corners of a regular octahedron (Fig. 5.30b). There is one octahedral hole for each atom in the lattice. Note that, because holes are formed by two adjacent layers and because neighboring close-packed layers have identical arrangements in hep and ccp, the numbers of holes are the same for both close-packed structures. 

The richness of coordination chemistry is enhanced by the variety of shapes that complexes can adopt. The most common complexes have coordination number 6. Almost all these species have their ligands at the vertices of a regular octahedron, with the metal ion at the center, and are called octahedral complexes (1). An example of an octahedral complex is the hexacyanoferrate(ll) ion, [Fe(CN)f, 4. ... 

For elements adjacent to the noble gases the principal orbitals used in bond formation are those formed by hybridisation of the s and p orbitals. For the transition elements there are nine stable orbitals to be taken into consideration, which in general are hybrids of five d orbitals, one s orbital, and three p orbitals. An especially important set of six bond orbitals, directed toward the comers of a regular octahedron, are the d2sps orbitals, which are involved in most of the Werner octahedral complexes formed by the transition elements. 

When tt o d eigenfunctions are available, as in trivalent cobalt, quadrivalent palladium and platinum, etc., six equivalent bond eigenfunctions of strength 2.923 and directed toward the comers of a regular octahedron can be formed. These form the bonds in a great many octahedral complexes. 

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