Bulk symmetry

Instead, we believe the electronic structure changes are a collective effect of several distinct processes. For example, at surfaces the loss of the bulk symmetry will induce electronic states with different DOS compared to bulk. As the particle sizes are decreased, the contribution of these surface related states becomes more prominent. On the other hand, the decrease of the coordination number is expected to diminish the d-d and s-d hybridization and the crystal field splitting, therefore leading to narrowing of the valence d-band. At the same time, bond length contraction (i.e. a kind of reconstruction ), which was observed in small particles [89-92], should increase the overlap of the d-orbitals of the neighboring atoms, partially restoring the width of the d-band. 

In Fig. 10 the micro-diffraction patterns of I5 and D5 particles are shown. These patterns are identical to the ones calculated by Yang et al. (1 1) based on the non-Fcc model. This type of particles is a very important example of departures from the Fee bulk symmetry. In addition is also an example of pol i hedral particles formed by several units. 

Electronic excitation energy in a crystal is in many cases highly mobile It may diffuse very rapidly through many thousands of molecules and eventually be trapped at some appropriate defect site. If, then, photoreaction occurs at this site, the stereochemistry of the reaction pathway will be determined by the symmetry of this site, and not by the symmetry of the bulk crystal. Nevertheless, the bulk symmetry is found empirically to be the determining factor in most cases studied (topochemical control). 

The largest component of the Y-tensor is in the conjugation direction. Therefore,.even though no particular bulk symmetry is required for nonzero x > a medium in which all conjugated polymeric chains align in the same direction should have a larger x value along the chain direction relative to that in an amorphous or disordered form of the same polymer. Studies of x in ordered or stretch-oriented polymers as discussed below confirm this prediction. Finally, the polymeric chains should pack as closely as possible in order to maximize the hyperpolarizability density and hence x ... 

Other nonlinear optical spectroscopies have gained much prominence in recent years. Two techniques in particular have become quite popular among surface scientists, namely, second harmonic (SHG) [55] and sum-frequency (SFG) [56] generation. The reason why both SHG and SFG can probe interfaces selectively without being overwhelmed by the signal from the bulk is that they rely on second-order processes that are electric-dipole forbidden in centrosymmetric media by breaking the bulk symmetry, the surface places the molecular species in an environment where their second-order nonlinear susceptibility, the term responsible for the absorption of SHG and SFG signals, becomes non-zero. 

The atomic structure of a surface is usually not a simple termination of the bulk structure. A classification exists based on the relation of surface to bulk structure. A bulk truncated surface has a structure identical to that of the bulk. A relaxed surface has the symmetry of the bulk structure but different interatomic spacings. With respect to the first and second layers, lateral relaxation refers to shifts in layer registry and vertical relaxation refers to shifts in layer spacings. A reconstructed surface has a symmetry different from that of the bulk symmetry. The methods of structural analysis will be delineated below. 

---