Long range ordering

The smectic A phase is a liquid in two dimensions, i.e. in tire layer planes, but behaves elastically as a solid in the remaining direction. However, tme long-range order in tliis one-dimensional solid is suppressed by logaritlimic growth of tliennal layer fluctuations, an effect known as tire Landau-Peierls instability [H, 12 and 13]... 

Figure C2.2.4. Types of smectic phase. Here tire layer stacking (left) and in-plane ordering (right) are shown for each phase. Bond orientational order is indicated for tire hexB, SmI and SmF phases, i.e. long-range order of lattice vectors. However, tliere is no long-range translational order in tliese phases.

STM measurements suggested for the bilayer fonned by Cu and coadsorbed Cl either a (5 x 5) long range order similar to that of the (111) plane of CuCl or a (4 x 4)-based stmcture [46, 77, 78], while the bilayer fonned with Cu... 

Amphiphiles often have a complex phase behaviour with several liquid crystalline phases These liquid crystalline phases are often characterised by long-range order in one directior together with the formation of a layer structure. The molecules may nevertheless be able tc move laterally within the layer and perpendicular to the surface of the layer. Structura information can be obtained using spectroscopic techniques including X-ray and neutror diffraction and NMR. The quadrupolar splitting in the deuterium NMR spectrum can be... 

In the simplest emulsions just described, the final separation is into two Hquid phases upon destabilization. The majority of emulsions are of this kind, but in some cases the emulsion is divided into more than two phases. One obvious reason for such a behavior is the presence of a material that does not dissolve in the oil or the water. One such case is the presence of soHd particles, which is common in emulsions for food, pharmaceuticals, and cosmetics. Another less trivial reason is that the surfactant associates with the water and/or the oil to form a colloidal stmcture that spontaneously separates from the two hquid phases. This colloidal stmcture may be an isotropic Hquid or may be a semisoHd phase, a Hquid crystal, with long-range order. 

The techniques can be broadly classified into two groups those which directly identify the atomic species present and then provide structural information about the identified species from diffraction or scattering effects (EXAFS, SEXAFS, and XPD) and those which are purely diffraction-based and do not direcdy identify the atoms involved, but give long-range order information on atomic positions from... 

All real surfaces will contain defects of some kind. A crystalline surface must at the very least contain vacancies. In addition, atomic steps, facets, strain, and crystalline subgrain boundaries all can be present, and each will limit the long-range order on the surface. In practice, it is quite difficult to prepare an atomically flat surface. 

Like X-ray and electron diffraction, neutron diffraction is a technique used primarily to characterize crystalline materials (defined here as materials possessing long-range order). The basic equation describing a diffraction experiment is the Bra equation ... 

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