Long-period commensurate structure

Some special attention should be placed on the p (bulk) phase as well. Although this form is often reported as being non-crystalline, it gives rise to sharp Bragg reflections commensurate with lamellar order with a long period of 12.3 A [74] and fiber periodicity of 16.6 A (which corresponds to two monomer units) [67]. Thus, it differs from real crystals in the sense that it is mesomorphic. This phase also includes the presence of absorbed solvent and may be obtained by extended exposure to solvent vapor or solvent (cf., the solvent section). In particular, it has been found to appear as an intermediate step in the transformation from the solvent induced clathrate-like structure to the solvent-free well-ordered a phase [74], The a and fi (bulk) phases may coexist and are closed related to one another but are still structurally incompatible. 

On the basis of ab initio calculations of the electronic structure and electronic susceptibility, the relations between the nesting properties of the Fermi surface and the features of commensurate long-period nanostructures in alloys have been studied. 

To summarize, we may conclude that in alloys with commensurate long-period states, as well as in systems with incommensurate LPNS, the electronic structure features, in particular the local FS geometry, play a decisive role in the formation and stabilization of long-period states. 

Incommensurate structures have been known for a long time in minerals, whereas TTF-TCNQ is one of the very first organic material in which a incommensurate phase has been observed. There are two main types of incommensurate crystal structures. The first class is that of intergrowth or composite structures, where two (or more) mutually incommensurate substructures coexist, each with a different three-dimensional translational periodicity. As a result, the composite crystal consists of several modulated substructures, which penetrate each other and we cannot say which is the host substructure. The second class is that of a basic triperiodic structure which exhibits a periodic distortion either of the atomic positions (displa-cive modulation) and/or of the occupation probability of atoms (density modulation). When the distortion is commensurate with the translation period of the underlying lattice, the result is a superstructure otherwise, it is an incommensurately modulated structure (IMS) that has no three-dimensional lattice periodicity. 

Self-assembly of long-chain alkanethiols on the Au( 111) surface has been studied by a number of different techniques including AFM, and it has been consistently shown that the molecules form a commensurate (V3 x a/3)R30° structure. AFM studies can also provide additional information on the mechanical properties of the organic layers [136], which are interesting in that they serve as a model system for lubricants [137]. Above a critical applied load of 280 nN for the Cjg thiols, it has been found that the monolayers were dismpted, and that the subsequent image corresponded to that of the Au(l 11) substrate. However, on reducing the load to substantially below the critical value, the surface apparently healed, and the characteristic periodicity of the thiol overlayer returned. The exact way in which this phenomenon occurs is not completely understood [138]. Possibilities include displacement of the thiols by the tip, binding of the thiols to the tip, or desorption of the thiols into a liquid phase. 

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