Hollow hexagon

PYROMORPHITE. The mineral pvroinorphite is lead chlorophosphate with a formula corresponding to Pb PO Cl. The phosphorus is sometimes replaced by arsenic and the lead by calcium. It occurs in prismatic, sometimes hollow, hexagonal crystals or may appear m massive forms. It is brittle hardness, 3.5-4 specific gravity, 7.04 luster, resinous color, green, yellow-green, yellow, brown, and less often gray or white translucent to opaque. 

An algebraic solution has been found for the numbers of hollow hexagons , a class of primitive coronoids [40, 45, 65], The solution was adapted to a class of special [2/>]annulenes [66]. It may also be adapted, even more directly, to the... 

Here = 0, 1, 2, 3, 4, 5, and each of these values is associated with a characteristic shape of the circular coronoid. These shapes were already known at least to Balaban (1971), who investigated their important role in the studies of annulenes cf. also a later work in this area (Cyvin SJ, Brunvoll and Gutman 1990). The same shapes are also encountered under the studies of certain primitive single coronoids called hollow hexagons (Cyvin SJ, Brunvoll and Cyvin 1989d Cyvin SJ, Brunvoll, Cyvin, Bergan and Brendsdal 1991), where the extremal property = hOj ax( ) corona hole is of interest. A detailed treatment of this topic is offered in Vol. 

The minerals exist as plates, laths, blocks, tubes, and hollow hexagonal prisms. Those with the most perfectly formed crystal structures— triclinic kaolinite, dickite and nacrite— occur as plates usually with many hexagonal angles [Figure l(above)]. Those with imperfect structures—halloysite and monoclinic disordered kaolinite—occur as laths, tubes, and hollow prisms [Figure 1 (below)]. 

Figure 7. Electron micrograph of cross section of Drosophi/a leg hexagonal lattice arrangement of thick (myosin) and tl " filaments appear hollow in this inse —...

At a pressure of 1 x 10 5 Torr 1,4-cyclohexadiene, the surface shows ordered domains of hexagonal rings approximately 18 A in diameter made up of six adsorbed molecules with an intermolecular distance of approximately 10 A (Figure 7.22a). A ( 43 x y/43)i 7.6° structure was proposed as schematically shown in Figure 7.22b. 1,4-Cyclohexadiene adsorbs in a boat configuration on bridge or hollow sites on the Pt (1 1 1) surface with comparable adsorption energies of 145.6 and 141.6kj mol-1, respectively [39]. 

Fig. 9 Schematic representation of three approaches to generate nanoporous and meso-porous materials with block copolymers, a Block copolymer micelle templating for mesoporous inorganic materials. Block copolymer micelles form a hexagonal array. Silicate species then occupy the spaces between the cylinders. The final removal of micelle template leaves hollow cylinders, b Block copolymer matrix for nanoporous materials. Block copolymers form hexagonal cylinder phase in bulk or thin film state. Subsequent crosslinking fixes the matrix hollow channels are generated by removing the minor phase, c Rod-coil block copolymer for microporous materials. Solution-cast micellar films consisted of multilayers of hexagonally ordered arrays of spherical holes. (Adapted from [33])...

Zhang L, Bartels C, Yu Y, Shen H, Eisenberg A. Mesosized crystal-like structure of hexagon-ally packed hollow hoops by solution self-assembly of diblock copolymers. Phys Rev Lett 1997 79 5034-5037. 

Fig. 9 Molecular structures of TPC (Du) and MDABCO (Di ) [154], Crystal structure packing in (MDABCO ) TPC (C6o ) (a) TPC molecules form a hexagonal hollow and the MDABCO cation fits into the hollow the Ceo" molecules are docked into the hollow in TPC layer in a key-keyhole relationship [top view (h) and side view (c)] to form Di DnC6o" Colors C, dark yellow. H, pale blue and N, dark blue. Calculated Fermi surface at 160 K in (d) layer A and (e) layer B. (f) Projection of the (MDABCO )-TPC layer on the Cgo layer A (red color MDABCO )...

The dominant features in the structure are the hexagonal rings of six Si-0 tetra-hedra, these rings forming hollow columns parallel to the z-axis. Within the... 

Second, the third layer could be positioned over those hollows marked with a dot. This third layer, which we could label C, would not be directly over either A or B, and the stacking sequence when repeated would be ABC ABC AB...and so on. This is known as cubic close-packing (cep) (Figure 1.4). (The names hexagonal and cubic for these structures arise from the resulting symmetry of the structure—this will be discussed more fully later on.)... 

Fig. 77. Schematic drawing of the liquid-crystal templating mechanism. Hexagonal arrays of cylindrical micelles form (possibly mediated by the presence of silicate ions), with the polar groups of the surfactants (light grey) to the outside. Silicate species (dark grey) then occupy the spaces between the cylinders. The final calcination step burns off the original organic material, leaving hollow cylinders of inorganic material [473]...

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