Polarization lattice

Electrooptic materials. The dependence of refractive index on the electric field or the lattice polarization is referred to as the electrooptic effect ... 

For the case of typical ionic crystals aP 1-10, and the weak coupling limit is applicable. The most important conclusion from this treatment is that the weak coupling limit leads to a perturbed Bloch type wave function characterized by equal probability for finding the electron at any point of the medium. Thus, in the case of the ionic crystals, the current description of the polaron is that of a mobile electron followed by lattice polarization. 

P is the macroscopic polarization. It consists of a lattice polarization b21 w originating from the electric dipole moment arising from the mutual displacement of the two sublattices, and of a second term b22 P originating from the pure electron polarization. According to definition, P and E are connected by... 

In conclusion, we present herein a rather compelling model for the short-time dynamics of the excited states in DNA chains that incorporates both charge-transfer and excitonic transfer. It is certainly not a complete model and parametric refinements are warranted before quantitative predictions can be established. For certain, there are various potentially important contributions we have left out disorder in the system, the fluctuations and vibrations of the lattice, polarization of the media, dissipation, quantum decoherence. We hope that this work serves as a starting point for including these physical interactions into a more comprehensive description of this system. 

Eq. (2.87) also suggests the possibility of spontaneous polarization , i.e. lattice polarization in the absence of an applied field. Considering Eq. (2.87), xe 00 as No. y -> 1, implying that under certain conditions lattice polarization produces a local field which tends to further enhance the polarization - a feedback mechanism. Such spontaneously polarized materials do exist and, as mentioned in Section 2.3, ferroelectrics constitute an important class among them. 

Thermal conductivity is the most difficult quantity to understand in terms of the electronic structure. Thermal energy can be stored in vibrational normal modes of the crystal, and one can transport thermal energy through the lattice of ions. These concepts seem to be macroscopic. Therefore, one can set up suitable wave packets to treat thermal conductivity as quantized matter. In particular, electron plus induced lattice polarization can be defined as polarons. For conduction electrons, the electrical conductivity and the thermal conductivity were first observed by Wiedemann and Franz as indicated in the following equation ... 

As has been pointed out previously, ionic compounds are characterized by a Fermi level EF that is located within an s-p-state energy gap Ef. It is for this reason that ionic compounds are usually insulators. However, if the ionic compound contains transition element cations, electrical conductivity can take place via the d electrons. Two situations have been distinguished the case where Ru > Rc(n,d) and that where Rlt < Rc(n,d). Compounds corresponding to the first alternative have been discussed in Chapter III, Section I, where it was pointed out that the presence of similar atoms on similar lattice sites, but in different valence states, leads to low or intermediate mobility semiconduction via a hopping of d electrons over a lattice-polarization barrier from cations of lower valence to cations of higher valence. In this section it is shown how compounds that illustrate the second alternative, Rtt < 72c(n,d), may lead to intermediate mobility, metallic conduction and to martensitic semiconductor metallic phase transitions. 

Gordon R, Hughes M, Leathern B, Kavanagh KL, Brolo AG (2005) Basis and lattice polarization mechanisms for light transmission through nanohole arrays in a metal film. Nano Lett 5 1243-1246... 

While experimental evidence for polaronic relaxation is extensive, other experiments render the polaron models problematic (i) the use of the Arrhenius relation to describe the temperature dependence of the mobility (see above) leads to pre-factor mobilities well in excess of unity, and (ii) the polaron models cannot account for the dispersive transport observed at low temperatures. In high fields the electrons moving along the fully conjugated segments of PPV may reach drift velocities well above the sound velocity in PPV.124 In this case, the lattice relaxation cannot follow the carriers, and they move as bare particles, not carrying a lattice polarization cloud with them. In the other limit, creation of an orderly system free of structural defects, like that proposed by recently developed self-assembly techniques, may lead to polaron destabilization and inorganic semiconductor-type transport of the h+,s and e s in the HOMO and LUMO bands, respectively. 

Similarly to electronic polarization, other polarization mechanisms can be invoked molecular polarization, which concerns the displacement of the nuclei of the molecule where the charge resides, and lattice polarization, which involves movements of the entire lattice. The energies and times corresponding to these processes are estimated from the intramolecular and lattice vibration frequencies. The energy and time of the various polarization processes are summarized in Table 2.2.1. 

Note The reference energy is bandwidth for residence time, energy gap for electronic polarization, molecular vibration ( 1,000 cm ) for molecular polarization, and lattice vibration (<100 cm- ) for lattice polarization. 

The DOS for CuO is in fact less well characterized than for the HTSC s theoretically, but generally the hybridization shift P is smaller because of the larger 0-0 distances, and we shall see below that A=Cp-Cd has increased to 1 eV. This increase can be attributed to an increase in cp, or Up , and reflects a smaller lattice polarization response due to the more ionic character in CuO. 

Fig. 28.13 Lattice polarization (net charge per CH unit) for (a) positive soliton, (b) negative soliton, (c) positive po-laron, (d) negative polaron in C40H42 from MNDO calculations. (From Ref. 114.)...

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