Clausius -Mossotti relation

For static electric properties, the bulk property of interest is the dielectric polarization P. The magnitude of P can be estimated from (for example) the Clausius-Mossotti relation... 

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

Fortunately, they are several species of low-loss dielectric ceramics with tailored temperature coefficient of dielectric constant, which can be made lower than 1 ppm/K for a certain temperature window around room temperature. Physically, this can be accomplished either by intrinsic compensation of the temperature dependence of thermal volume expansion V(T) and lattice polarizability a(T) via the Clausius-Mossotti relation ... 

Using the cgs system the Clausius-Mossotti relation becomes... 

Molecular distortion polarizability is a measure of the ease with which atomic nuclei within molecules tend to be displaced from their zero-field positions by the applied electric field. (3) Orientation polarizability is a measure of the ease with which dipolar molecules tend to align against the applied electric field. The electron polarizability of an individual molecule is related to the -> permittivity (relative) of a dielectric medium by the -> Clausius-Mossotti relation. 

To describe local field effects associated with a crystalline environment, e.g. Cso arranged in a lattice of cubic symmetry, we use the Clausius-Mossotti relation [93] in the form... 

The dielectric response of materials is governed by the Clausius-Mossotti relation which is... 

This expression is known as the Clausius Mossotti relation. To simplify, the polarizability of the crystal can be taken as the sum of the electronic and atomic contributions. The electronic polarizability, aeiec, corresponds to the coupling of the electronic cloud of the otherwise immobile atoms with the electromagnetic wave, and it is a high-frequency process, whose contribution can be considered more or less frequency-independent below Es. The atomic... 

We now call attention to three closely related approximations. All three use the mean field result for and outside the core, given by (2.66b). The first also uses (2.70). With the use of (2.27) both A and Ay, can be determined for all r. Both approximations violate the core condition (2.65b). The resulting e is easy to compute via (2.15) and yields the Clausius-Mossotti relation. The resulting approximation for A(12) could be called the two-particle Clausius-Mossotti approximation. ... 

Using Equations (11.3)-(11.5) it is possible to derive the most widely used relationship between relative permittivity and polarisability, the Clausius-Mossotti relation. Equation (11.6), usually written ... 

Accounting for the CMLL local field Clausius-Mossotti relation [9-13, 22, 43]... 

Semiconductor cluster polarizabilities have been the subject of some very important experimental studies via beam-deflection techniques (Backer 1997 Schlecht et al. 1995 Schnell et al. 2003 Schafer et al. 1996 Kim et al. 2005) while they have been extensively studied using quantum chemical and density functional theory. In this research realm, one of the areas intensively discussed is the evolution of the cluster s polarizabilities per atom (PPA) with the cluster size. The PPA is obtained by dividing the mean polarizability of a given system by the number of its atoms. Such property offers a straightforward tool to compare the microscopic polarizability of a given cluster with the polarizability of the bulk (see O Fig. 20-16) as the latter is obtained by the hard sphere model with the bulk dielectric constant via the Clausius-Mossotti relation ... 

A (r, t)l8Q represents local fluctuations of the relative permittivity (dielectric constant) in the target. The task of classical light-scattering theory has been reduced to solving Equation [34]. The only role of quantum theory, therefore is to calculate the atomic polarizability a - m other words, the microscopic properties of the scattering medium. Once this is achieved, the polarizability can then be related to the dielectric constant through the well-known Clausius-Mossotti relation. 

Randomly arranged inclusions result in an isotropic effect of inclusions. For this case, the generalization of the Clausius-Mossotti relation can be applied. 

The generalization of the Clausius-Mossotti relation (Berryman, 1995 Mavko et ah, 1998) for randomly oriented ellipsoids instead of spheres gives in case of a porous material... 

Each dipole is uniquely described by its grid location r,- and polarizability O . The polarizabihties are calculated from the complex dielectric function e, of the material, using the Clausius Mossotti relation ... 

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