Lattice periodicity, liquid structure

The best geometrical parameters of periodic Si structures were theoretically estimated before the structure preparation [4]. Using the procedure described elsewhere [5], the grooved Si samples were created with lattice constant A=16, 8, and 4 pm, each sample with number of Si walls m=50 and the samples with A=24, 12, and 10 pm, m = 3 and 4. The lattice constant A may be written as A=Dsi + Dap. The Si structures were infiltrated by commercial nematic liquid crystal E7. 

Different spectroscopic, microscopic and diffraction methods like IR and Raman spectroscopy, TEM or XRD were applied to characterize educts, intermediates or products of the sol-gel process. For a detailed insight into the mechanism of the fluorolytic sol-gel process, however, the application of NMR spectroscopy is the method of choice. The NMR experiments, both in liquid and in solid state, allow direct observations of local structures and their changes even if the matrices suffer from a loss of lattice periodicity. For the fluorolytic so-gel process both liquid state NMR experiments were realized for the alkoxide solutions, sols and thin gels as well as solid state MAS NMR experiments for the alkoxide, dried alkoxide fluoride gels and high-surface fluorides including H,... 

Let us now turn our attention to liquid water. Just as in ice I, molecular motions may be divided into rapid vibrations and slower diffusional motions. In the liquid, however, vibrations are not centred on essentially fixed lattice sites, but around temporary equilibrium positions that are themselves subject to movement. Water at any instant may thus be considered to have an I-structure. An instant later, this I-structure will be modified as a result of vibrations, but not by any additional displacements of the molecules. This, together with the first I-structure, is one of the structures that may be averaged to allow for vibration, thereby contributing to the V-structure. Lastly, if we consider the structure around an individual water molecule over a long time-period, and realize that there is always some order in the arrangement of adjacent molecules in a liquid even over a reasonable duration, then we have the diffusionally averaged D-structure. 

Micellar solutions are isotropic microstructured fluids which form under certain conditions. At other conditions, liquid crystals periodic in at least one dimension can form. The lamellar liquid crystal phase consists of periodically stacked bilayers (a pair of opposed monolayers). The sheetlike surfactant structures can curl into long rods (closing on either the head or tail side) with parallel axes arrayed in a periodic hexagonal or rectangular spacing to form a hexagonal or a rectangular liquid crystal. Spherical micelles or inverted micelles whose centers are periodically distributed on a lattice of cubic symmetry form a cubic liquid crystal. 

Figure 3. Schematic representation of a phospholipid-water phase diagram. The temperature scale is arbitrary and varies from lipid to lipid. For the sake of clarity phase separations and other complexities in the 20-99% water region are not indicated. Structures proposed for the phospholipid bilayers at different temperatures are shown on the right-hand side. At low temperature, the lipids are arranged in tilted one-dimensional lattices. At the pre-transition temperature, two-dimensional arrangements are formed with periodic undulations. Above the main phase, transitions lipids revert to one-dimensional lattice arrangements, separated somewhat from each other, and assume mobile liquid-like conformations.

Without tlie periodic array, there arc no longer lattice wave numbers but a distributed structure factor S(q), The phase will vary in a complicated way, but an average measurable S (q)S(q) exists and is spherically symmetric. This is just what is needed for a calculation of the resistivity of the liquid metals. The first such calculation using pseudopotentials (Harrison, 1963b) followed an earlier and conceptually similar calculation by Ziman (1961). It involved the direct substitution of S (q)S(q), obtained by X-ray diffraction experiments on the liquid, into... 

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