Long-range hybrid structure

Structural and textural characterisation of pure SBA-15 and hybrid GFP/SBA-15 Pure SBA-15 and GFP/SBA-15 hybrid were characterised by X-ray powder diffraction, HRTEM and volumetric analysis. Calcined SBA-15 (Fig. 1, curve A) show the typical XRD pattern of an ordered hexagonal network of mesopores with (10), (11) and (20) reflections. The presence of well resolved (11) and (20) peaks indicate that the calcined material used for the preparation of the hybrid materials have a long-range order. The hexagonal XRD pattern was still clearly observed in the hybrid material (GFP/SBA-15), as all the three main reflections were found (Fig. 1, curve B), indicating that the sonication and the GFP physical adsorption does not affect the framework integrity of the material. 

It is possible in principle to calculate all of these modes from the theory of the electronic structure, which is equivalent to the calculation of all the force constants. Indeed we will see that this is possible in practice for the simple metals by using pseudopotential theory. In covalent solids, even within the Bond Orbital Approximation, this proves extremely difficult because of the need to rotate and to optimize the hybrids, and it has not been attempted. The other alternative is to make a model of the interactions, which reduces the number of parameters. The most direct approach of this kind is to reduce the force constants to as few as possible by symmetry, and then to include only interactions with as many sets of neighbors as one has data to fit- for example, interactions with nearest and next-nearest neighbors. This is the Born-von Karman expansion, and it has somewhat surprisingly proved to be very poorly convergent. This simply means that in all systems there arc rather long-ranged forces. 

Figure 14 An xy projection of an initial-guess structure generated by the hybrid scheme of Equation [70], incorporating long-range interactions. From Ref. 85.)...

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