Dielectric response anisotropic materials

We usually think of van der Waals forces in terms of attraction or repulsion based on differences in polarizability. What if materials are anisotropic, for example, bire-fringent with different polarizabilities in different directions Imagine that substance A has a principal optical axis pointing parallel to the interface between A and m, that is, there is a dielectric response coefficient e parallel to the interface but a permittivity in directions perpendicular to the principal axis (see Fig. LI.20). 

For valence band excitations, however, a different method has to be used to study the anisotropic dielectric properties due to the smaller q ( rv- 0.02 A 1 for 20 eV energy loss with 100 kV incoming beam energy), which means that the momentum transfer in the low loss region is mostly due to q. This requires the sample to be oriented in a certain direction relative to the direction of the electron beam to study the dielectric response in a particular orientation. Because of the small beam size available in cFEG TEM, a specific orientation of a thin section with millimeter size area can be easily obtained by ion beam thinning techniques to directly measure the anisotropic properties of the material. 

An applied electric field can be the electric held component of an electromagnetic wave, in which case electronic excitations or other optical responses may ensue. These are the topic of the next chapter. Here, the concern is with electrostatics, specihcally, the dielectric, or insulative, properties of materials. In an electrical conductor, an applied electric held, E, produces an electric current - ions, in the case of an ionic conductor, or electrons, in the case of an electronic conductor. Electrical conductivity has already been examined in earlier chapters. In insulating solids, the topic of the current discussion, the response to an applied electric held is a static spatial displacement of the bound ions or electrons, resulting in an electrical polarization, P, or net dipole moment (charge separahon) per unit volume, which is a vector quantity. In a homogeneous linear and isotropic medium, the polarization and electric held are aligned. In an anisotropic medium, this need not be so. The fth component of the polarization is related to the jth component of the electric held by ... 

An important aspect of the enhanced intrinsic response of ferroelectrics is anisotropy, the direction dependence of properties. By symmetry, ferroelectric crystals are anisotropic with respect to dielectric, mechanical, and electromechanical properties, and this issue is essential when designing devices that exploit the highest material responses by correctly orienting single crystals [8, 33-35]. The crystal axes, along which the highest material response occurs, may not coincide with the polar directions of spontaneous polarization for a given ferroelectric phase. This is the case... 

The relation between P and E defines the dielectric properties of the material. As the optical response of metals is in general non-local in space and in time and anisotropic, we have ... 

The combination of molecular order and fluidity in a single phase results in several remarkable properties unique to liquid crystals. By now, it is quite evident that the constituent molecules of liquid crystal mesophases are structurally very anisotropic. Because of this shape anisotropy, all the molecular response functions, such as the electronic polarizability, are anisotropic. The long range order in the liquid-crystal phases prevents this molecular anisotropy from being completely averaged to zero, so that all the macroscopic response functions of the bulk material, such as the dielectric constant, are anisotropic as well. We have, therefore, a flexible fluid medium whose response to external perturbations is anisotropic. 

Contemporary applications of liquid crystals [1,2] exploit the unique properties of these materials arising from their anisotropic response to external fields and forces. For example, the anisotropy in the dielectric properties makes it possible to construct electro-optical displays, and the characteristic response time of such devices is determined by the anisotropic viscoelastic properties of the liquid crystal [3]. In turn, these viscoelastic properties are related to various kinds of flows and deformations of the material in question. The exact number and nature of viscoelastic constants required to characterise fully the properties of the phase are determined by careful consideration of both static and dynamic behaviour [4]. The specific focus of this Datareview is the description of experimental techniques for measuring the various types of viscosity coefficients allowed in nmiatic phases. 

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