Hexagonal lattice ordering

Figure B3.6.4. Illustration of tliree structured phases in a mixture of amphiphile and water, (a) Lamellar phase the hydrophilic heads shield the hydrophobic tails from the water by fonning a bilayer. The amphiphilic heads of different bilayers face each other and are separated by a thin water layer, (b) Hexagonal phase tlie amphiphiles assemble into a rod-like structure where the tails are shielded in the interior from the water and the heads are on the outside. The rods arrange on a hexagonal lattice, (c) Cubic phase amphiphilic micelles with a hydrophobic centre order on a BCC lattice.

These observations consummated in a growth model that confers on the millions of aligned zone 1 nanotubes the role of field emitters, a role they play so effectively that they are the dominant source of electron injection into the plasma. In response, the plasma structure, in which current flow becomes concentrated above zone 1, enhances and sustains the growth of the field emission source —that is, zone 1 nanotubes. A convection cell is set up in order to allow the inert helium gas, which is swept down by collisions with carbon ions toward zone 1, to return to the plasma. The helium flow carries unreacted carbon feedstock out of zone 1, where it can add to the growing zone 2 nanotubes. In the model, it is the size and spacing of these convection cells in the plasma that determine the spacing of the zone 1 columns in a hexagonal lattice. 

It may be that this type of defect is a major cause of the line or edge type of defects that appear in most homogeneous solids. In contrast, the other defects produce only a disruption in the localized packing order of the hexagonal lattice, i.e.- the defect does not extend throughout the lattice, but only close to the specific defect. 

Fig. 5. Temperature variation of the hexagonal lattice parameters and of the volume of pure gadolinium measured by x-ray powder diffraction (this work). The values have been normalized to 300 K in order to show the relative changes. (The values at 300 K are a = 3.632 0.002 A, c = 5.782 0.002 A.) The lines represent the extrapolation of the lattice contribution from temperatures above Tq assuming a Debye temperature of 184 K (Bodnakov et al. 1998). The lowest part of the figure shows the magnetovolume effect, obtained by subtracting the lattice contribution from the volume expansion.

In order to discuss the hexatic phase it is necessary to introduce the idea of a disclination. Imagine a two-dimensional close packed hexagonal lattice drawn on a deformable sheet. If one chooses a particular lattice site as the centre of coordinates, the lattice will consist of six 60° sectors centred on this point. One now has two alternatives. 

The columnar order in 52a,b was explained by molecular folding the molecules are assumed to be in their U- (or wedge-) shaped conformation and six molecules self-assemble to a supramolecular disc. These discs are stacked in columns and arranged within a columnar hexagonal lattice (Fig. 8). Folding of similar mesogens was also seen by Heiney [65]. 

Recombinant [oil (VIII) ] 3 and [a2(VIII)]s molecules form highly ordered supramolecular assemblies. These assemblies may be formed by four triple-helical collagen VIII molecules that come together to form a tetrahedron via the hydrophobic patches on their G-termini. It has also been suggested that these tetrahedral structures may further associate to form hexagonal lattices, with the N-terminals of individual molecules interacting with either the N-terminals or with the triple-helical portion of molecules in other tetrahedrons (Stephan et al., 2004). 

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