Local superstructures

Figure 21 [001] HREM image of a local superstructure corresponding to a new periodicity a = 3a.

Fig. 6. YBa2Cu30T.s [001] HREM images of crystallites exhibiting local superstructures corresponding to a new periodicity (a) a = 3a and (b) 3 and 4 rfuo-...

Asymmetric simhaiity measures allow fuzzy super- and substructure searching. A substructure search is defined as looking for structures containing the given query and a superstructure search is defined as looking for structures embedded in the given query. In both cases asymmetric local similarity is estimated. 

It was observed, under conditions when the nickel-aluminide mixtures of the same ratio were fully reacted, that the titanium aluminides were essentially unreacted reactions were only localized. Because the products were of such small size, it was difficult to identify them, but they were thought to be TiAlj or ordered superstructures TiQAl23 or TigAl24. No further studies have been carried out on these samples. 

We have assumed so far, implicitly, that the interactions are strictly local between neighboring atoms and that long-ranged forces are unimportant. Of course the atom-atom interaction is based on quantum mechanics and is mediated by the electron as a Fermi particle. Therefore the assumption of short-range interaction is in principle a simplification. For many relevant questions on crystal growth it turns out to be a good and reasonable approximation but nevertheless it is not always permissible. For example, the surface of a crystal shows a superstructure which cannot be explained with our simple lattice models. 

To include all of these complexities requires a different approach from the one described so far. The design approach based on the optimization of a superstructure can be used to solve such problems14. Figure 26.36 shows the superstructure for a problem involving two operations and a single source of fresh water14. The superstructure allows for reuse from Operation 1 into Operation 2, reuse from Operation 2 to Operation 1, local recycles around both operations, fresh water supply to both operations and... 

Mesophase with a helicoidal superstructure of the director, formed by chiral, calamitic or discotic molecules or by doping a uniaxial nematic host with chiral guest molecules in which the local director n precesses around a single axis. 

The STM images of large superstructures on metal surfaces exhibit a very simple form. As shown first time by Tersoff and Hamann (1983, 1985), at the low-bias limit, the STM images of large superstructures on metal surfaces are independent of tip electronic states, and an STM image is simply a contour of an important quantity of the sample surface only the Fermi-level local density of states (LDOS), taken at the center of curvature of the tip. An attempt was also made to interpret the observed atom-resolved images of semiconductors... 

A cholesteric, or chiral nematic (N ) phase. This is a positionally disordered fluid in which the constituent molecules align on average their axes along a common direction called the nematic director. Being the DNA helices chiral, the orientational order develops an additional macro-helical superstructure with the twist axis perpendicular to the local director. The phase thus consists of local nematic layers continuously twisted with respect to each other, with periodicity p/2 (where p is the cholesteric pitch see Fig. 8a) [27,28]. For 150-bp helices, the N phase appears at a concentration around 150 mg/mL in 100 mM monovalent salt conditions. This LC phase is easily observed in polarized optical microscopy. Since the N pitch extends to tens of micrometers (that is, across... 

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