Topologically well-defined crystals

As we all know, there are two aspects that make zeolites unique. First of all, being crystals, their intracrystalline surface is an inherent part of the crystal structure and hence they are topologically well defined. This is in sharp distinction to the ill-defined amorphous solids we are familiar with. The availability of solids with such a large and well defined surface area is certainly exciting and welcoming news to us. 

Within the framework of Bader s topological theory [7], atoms are well-defined subsystems with respect to the total system. Their contribution to the properties of the total system can be deduced from the electron density of the total system (ED, p). Consequently, an atom in an isolated molecule is different from that in a crystal. The emergence of atom in the latter case does not necessarily mean the emergence of the molecule. Thus, the dilemma of what a molecule in the crystal is, remains unresolved even within the topological theory of structure. 

All of the techniques discussed so far indicate that the solid surface is ordered on an atomic scale. Most of the surface atoms occupy equilibrium atomic positions that are located in well-defined rows separated by equal interatomic positions. This atomic order is predominant despite the fact that there are large numbers of atomic positions on the surface where atoms have different numbers of neighbors. A pictorial representation of the topology of a monatomic crystal on an atomic scale is shown in... 

The ferrierite has been further synthesized in fluoride medium in the presence of pyrrolidine molecules in the ciystalhzation processes [10P3]. Pyrrolidine molecules were accommodated in two sites, one within ferrierite cavity and another in the widest section of the 10-ring channel with the plane of the molecule perpendicular to the first. Both molecules show well-defined positions with little freedom to move from their most stable location, indicating the good fit of pyrrohdine to the ferrierite topology. This implies a strong templating role played by pyrrolidine in the crystallization of ferrierite. 

Most studies of nematics in fields are performed on thin films where the initial director field is dictated by surface anchoring. The thin film permits easy observation, and a well-defined initial state simplifies analysis. It should be noted, however, that a typical bulk liquid crystal transformed from the isotropic state contains many topological defects. These defects are likely to play a central role in the response of liquid crystalline materials to external fields,... 

As mentioned earlier, most studies of field interactions with liquid crystals are done using thin films with a well-defined initial state, usually a monodomain or a thin film with a simple distortion induced by incommensurate surface anchoring. These conditions simplify observation and theoretical analysis. However, most liquid crystal materials that are not specially prepared contain topological defects that are very important to their response to external fields. One class of defect commonly observed in nematics is the disclinalion line. At a disclination line the director field is ill defined. The director field turns around the disclination line a multiple of half-integer times. Several disclination lines are shown in Fig. 8. 

These two simple experimental systems show the presence in liquid crystals of two types of defect lines and point singularities. Liquid crystals contain a large variety of lines with well-defined geometries or topologies. There are also lines that have a continuous core (for example, in the capillary tube) the axial zone corresponds to a maximum of splay and is generally considered to be a defect line, although no discontinuities apart from the singular points are present. This situation is also encountered in the third type of defect - walls. 

Many systems are being studied to manipulate quantum information. Some make use of individual atoms cold trapped ions, neutral atoms in optical lattices, atoms in crystals. Other involve particle spins or photons in cavity QED or nonlinear optical setups as well as more exotic ones where geometric combinations of elementary excitations are defined as qubits, such as in topological quantum computing [8]. However, none of these systems has yet emerged as a definitive way to build a quantum information processor. A reason for this is that there is an essential dichotomy we need... 

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