Dielectric polarization mechanism dipolar

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

Dielectric relaxation study is a powerful technique for obtaining molecular dipolar relaxation as a function of temperature and frequency. By studying the relaxation spectra, the intermolecular cooperative motion and hindered dipolar rotation can be deduced. Due to the presence of an electric field, the composites undergo ionic, interfacial, and dipole polarization, and this polarization mechanism largely depends on the time scales and length scales. As a result, this technique allowed us to shed light on the dynamics of the macromolecular chains of the rubber matrix. The temperature as well as the frequency window can also be varied over a wide... 

Microwave radiation, as all radiation of an electromagnetic nature, consists of two components, i.e. magnetic and electric field components (Fig. 1.3). The electric field component is responsible for dielectric heating mechanism since it can cause molecular motion either by migration of ionic species (conduction mechanism) or rotation of dipolar species (dipolar polarization mechanism). In a microwave field, the electric field component oscillates very quickly (at 2.45 GHz the field oscillates 4.9 x 109 times per second), and the strong agitation, provided by cyclic reorientation of molecules, can result in an... 

Typical concentrations of dopants (0.05-5 at.%) must result in the formation of dipolar pairs between an appreciable fraction of the dopant ions and the vacancies, e.g. 2La A-VA or 2Fel i+ -V( ). Donor-cation vacancy combinations can be assumed to have a stable orientation so that their initially random state is unaffected by spontaneous polarization or applied fields. Acceptor-oxygen vacancy combinations are likely to be less stable and thermally activated reorientation may take place in the presence of local or applied fields. The dipoles, once oriented in a common direction, will provide a field stabilizing the domain structure. A reduction in permittivity, dielectric and mechanical loss and an increase in the coercive field will result from the inhibition of wall movement. Since the compliance is affected by the elastic movement of 90° walls under stress, it will also be reduced by domain stabilization. 

Let us assume now, for example, that a step-like constant electric field of magnitude E0 is applied within a dielectric at any time t0, and remains constant for t>t0 (see Figure 1.27). Then, Pao = Pe + P, is almost instantaneously established. Thereafter, the acting relaxation processes (i.e., dipolar and/or charge-hopping and/or space charge polarization mechanisms) provoke that the polarization is not instantaneously established. 

The application of an electric field E across a linear dielectric material results in polarization P or the separation of positive and negative charges. The relative dielectric constant k is a measure of the capacity of a solid to store charge relative to vacuum and is related to the extent to which the charges in a solid polarize. Atomically there are four main polarization mechanisms electronic, ionic, dipolar, and space charge. 

MW-enhanced chemistry is based on the efficiency of interactions of molecules with waves by microwave dielectric heating effects. This phenomenon depends on the ability of materials to absorb MW radiation and convert it into heat. The electric component of the electromagnetic field has been shown to be the most important [22-24]. It results in two main mechanisms - dipolar polarization and ionic conduction. Irradiation of polar molecules at MW frequencies results in orientation of the dipoles or ions in the applied electric field (Scheme 4.1) [25]. 

Insulator and capacitor applications depend on the dielectric properties of ceramics, that is, on their polarization response to an applied electric field. The four polarization mechanisms which describe the displacement of charged species in ceramics are (1) electronic polarization—the shift of the valence electron cloud with respect to the nucleus (2) ionic or atomic polarization— movement of cation and anion species (3) dipolar polarization—perturbation of the thermal motion of ionic or molecular dipoles and (4) interfacial polarization—inhibition of charge migration by a physical barrier. Further discussion of polarization phenomena may be found in Reference 1. 

Strong covalent binding potentials determine the distance and direction of atomic binding. Changes in conformation of molecular groups are possible if barriers of rotational potentials can be overcome. The latter determine the intrinsic stiffness of molecular chains or segments. Weak interchain forces arise mainly from dipole interactions. Quantum-mechanical dipolar exchange forces are the main contributors even for nonpolar polymers. For polar polymers, permanent or induced dipoles are also involved they are responsible for dielectric orientational polarization (4). Mechanical loads in polymers are transmitted by covalent and by dipole forces. Electrical loads act directly on dipolar moments. 

Figures 12a and 12b show the dielectric constant (c ) as a function of frequency of LNMO and LCMO ceramics at different temperatures. It can be observed that the dielectric constant of both ceramics decreases as frequency increases. The decrease in the dielectric constant with increase in frequency can be explained by the behavior on the basis of electron happing from Fe to Fe ions or on basis of decrease in polarization with the increase in frequency. Polarization of a dielectric material is the quantity of the contributions of ionic, electronic, dipolar, and interfacial polarizations [63]. At low frequencies, polarization mechanism is keenly observed at low frequencies to the time var)ing electric fields. As the frequency of the electric field increases, different polarization contributions are filter out under leads to the decrement in net polarization under dielectric constant. Similar behavior has also been reported by different investigators earlier in the literature [60, 64]. The physical, magnetic, and dielectric properties of LMNO and LCMO are summarized in Table 1.

Displacements that occur between several equilibrium sites for which the probability of occupancy of each site depends on the strength of the external field. This mechanism is also known as dipolar or ion jump polarization and is depicted schematically in Fig. 14.10. Another definition of ion jump polarization is the preferential occupation of equivalent or near-equivalent lattice sites as a result of the applied field biasing one site with respect to the other. If the alignment occurs spontaneously and cooperatively, nonlinear polarization results and the material is termed ferroelectric. Because of the relatively large displacements, relative dielectric constants on the order of 5000 can be attained in these materials. Nonlinear dielectrics are dealt with separately in Chap. 15. But if the polarization is simply due to the motion of ions from one adjacent site to another, the polarization behavior is linear with voltage. These solids are discussed below. 

Almost all the formalism and the approximation schemes of Sections II and III have a natural extension to systems of polarizable dipolar particles, but the precise details of the extension depend on the way polarizability is introduced into the Hamiltonian. We refer to the two quite distinct Hamiltonian models that have been most thoroughly developed in this context as the constant-polarizability model and the fluctuating-polarizability model. The dielectric behavior of the former was first systematically investigated from a statistical mechanical viewpoint by Kirkwood and by Yvon, who considered the model almost exclusively in the absence of permanent dipole moments. (Kirkwood S subsequently pioneered an exact formulation of the statistical mechanics of polar molecules, but largely as a separate enterprise that did not attempt to treat the polarizability exactly.) The general case of polar-polarizable particles remained only very partially developed ... 

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