Permittivity dependence

Another derivation of the reiative permittivity dependence of in k has been made by Amis [12, 21, 244] using a Coulomb energy approach for the ion-dipole interaction. Considering the mutual potential energy between an ion A of charge za e and a dipole B of dipole moment at a distance tab leads eventually to Eq. (5-95) ... 

The required analysis of the t.d.s. data in terms of permittivity depends upon the experimental method. For the direct reflection method (Figures 5 and 6) from equations (5) and (7) we obtain... 

This explanation of the properties of BaTiOa implies that the properties of ceramic ferroelectrics will be highly sensitive to the conditions under which the given material was prepared. This is illustrated by the diagram in Fig. 195, which shows that permittivity depends significantly on the purity of raw materials and on firing temperature. 

Ferroeleciric substances exhibit a hysteresis loop on the curves of the dependence of polarization on electric field intensity (Fig. 193). In the case of non-ferroelectric substances, this dependence is linear and its slope is related to the permittivity value. Figure 193 indicates that with ferroelectrics, the permittivity depends on the field intensity as well as on the direction of changes in the field intensity. When the electric field is cut oft, the dielectric shows remanent polarization (electrical analogy with ferromagnetic substances). 

Nevertheless the use of dielectric materials obtained by conductive filler dispersion (carbon black, graphite fibres, metallic powders) is limited. As a matter of a fact material performances are dependent on the filler content as well as particle aggregation phenomena. These composites require a high level of reproducibility and their behaviour is linked to the control of electronic inter-particular transfer. The measured parameter (complex permittivity) depends on the texture of the percolation aggregates and consequently on the processing conditions. The percolation threshold (the particle concentration, after which particles are in contact and the electrical current exists) depends on the particle shape (sphere, plates or fibres). 

In general, polarizability, a, is difficult to determine experimentally. However, the ratio of the capacity of a condenser in a vacuum to that in the medium under consideration, i.e., the relative permittivity (earlier, dielectric constant), of the medium, can be measured. At low frequencies, the relative permittivity of electrical nonconductors is almost independent of the frequency. At high frequencies, the relative permittivity depends on the frequency, since the permanent dipoles are no longer able to establish a preferred orientation, because of rapid alteration of the field. 

Za and Zi are the charges of the ion in the adsorbed state and in the bulk solution. A somewhat more general model of the compact layer as a nonuniform dielectric slab whose local dielectric permittivity depends on the normal coordinate, (z), results in the formula (88b) containing the ratio of the effective thickness for the overall compact layer, Lh = (43tCh) , and that of its inner part between the bulk metal and the adsorption plane, L (again, the charge of the adsorbed ion is considered here as the point charge localized at the distance a from the surface) [262] ... 

Figure 4 Dielectric shell model. The total permittivity s will be a function of the permittivity of the continuous phase, 8 g, the volume ftac-tion of particles, and the permittivity of the particles, 8 . The particle permittivity depends on the core and shell permittivities, 8 and 8 jjj, and the ratio between the particle radius R and the shell thickness d.

To analyze the solvent effect on the process [9.45], it is often convenient to represent the temperature and permittivity dependencies of InK in approximated form ... 

Fig. 3.28 Relative dielectric permittivity dependence on mean grain size calculated on the basis of Eqs. (3.83) and (3.93) for different values of dispersion parameter a (nm) 1 (1), 2 (2), 10 (3), 50 (4), 100 (5)...

Contrary to binary oxides the exchange integral depends on the particle radius and temperature via the size and temperature dependence of the dielectric permittivity e TJt). In particular, one has to substitute s T,R) for 82 in Eq. (4.6) for exchange integral, where r is average nanoparticle radius. The calculations of dielectric permittivity dependence on temperature and particles size have been performed analogously to those described in Sects. 3.2.2.2 and 3.2.2.3 and lead to Barrett-type formula, which could be found in Ref. [48]. In Fig. 4.18 two roots (rji fixed temperature and particle... 

W imply the presence of the stretches in the equation between D and E. In this case the dielectric is no longer ideal and the permittivity depends on fire strain. 

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