Dielectric polarizability

The molar dielectric polarizability of a mixture of two solvents is expressed as Pi2 and is given by Eq. (18), in which f and denote mole... 

When there are small differences in dielectric polarizability and also in the limits of very small and very large separation, the general Lifshitz formula reduces to simpler, power-law forms. 

Dielectric polarizabilities are useful for prediction of dielectric constants of new materials and compounds whose dielectric constants have not been measured, and in calculations of energies of the formation and migration of defects. In addition, deviations from the polarizability additivity rule are useful in understanding certain physical properties such as thermodynamic functions and ionic and electronic conductivity." ... 

Dielectric polarizabilities, ao, defined by Roberts, include both ionic and electronic components, and are related to the measured dielectric constant, k, by the Clausius-Mosotti (C-M) equation ... 

This rule can be applied to both electronic and dielectric polarizabilities, but here we discuss the rule only insofar as it applies to dielectric polarizabihties. The molecular or oxide additivity rule has been applied to hydrates, to the compounds MTiOs where M = Mg, Ca, Sr, and Ba, to dolomite (CaMg(C03)2), zircon (ZrSi04), and spinel (MgAl204), to several titanates andzirconates andKMgFs, and to a variety of minerals. " ... 

Table 2 shows that agreements between observed dielectric polarizabilities and those calculated from the sum of the oxide polarizabilities according to equation (3) are typically 1%. This excellent agreement indicates that oxide polarizabilities can be used in conjunction with the C-M relationship to predict dielectric constants of many compounds. 

According to equation (4), total molar dielectric polarizability of a compound can be calculated ( caic) as a simple linear combination of individual ion polarizabihties, o (ion) ... 

The set of dielectric polarizabilities found in Table 3 appears to be significantly different from the sets of Roberts and Lasaga and Cygan. However, the differences arise primarily because of the large difference in q d(03 ) 2.01 A3 (Table 3) vs. 2.387 A3 or 237 A Roberts and Lasaga and Cygan chose these latter values because they had no... 

Figure 1 Table of ion dielectric polarizabilities given in A. Shannon. )...

The physical properties of fluorides are determined mainly by the high ionicity of the metal-fluorine bond and the low polarizability of the fluoride ion (see Dielectric Polarizabilities of Oxides Fluorides). Therefore, magnetism based on superexchange interactions and high optical transparency in a wide spectral range are the most interesting properties. They define, together with the anionic conductivity in flnorite-like compounds, the main area of possible applications of flnorides in material science or industry. 

Defects in Solids Dielectric Polarizabilities of Oxides Fluorides Diffraction Methods in Inorganic Chemistry Electronic Stmcture of Solids Fluorides Solid-state Chemistry Halides Solid-state Chemistry Intercalation Chemistry Non-crystalUne Solids Oxides Solid-state Chemistry Phosphates Solid-state Chemistry Polyphosphazenes Sol-Gel Synthesis of Solids Solids Computer Modeling Stmcture Property Maps for Inorganic Solids Zeolites. 

It has been reported that the dielectric constant of thin BST films decreases with decreasing film thickness when metal electrodes are adopted even without any interfacial non-perovskite material. This is due to the intrinsic interfacial low dielectric layer that originates from the termination of the chemical bonding of the perovskite structure at the interfaced. The large dielectric, polarizability of the perovskite can not penetrate into the metal layer due to the extremely high carrier concentration of the metal. 

Shannon R. D. (1993) Dielectric polarizabilities of ions in oxides and fluorides. J. Appl. Phys. 73, 348-366. 

As frequency increases, all dispersion curves decrease to virtually zero. This indicates that EB is produced by the dipolar-orientational mechanism whereas the anisotropy of the dielectric polarizability of the macromolecules is virtually imper-ceptile in the Kerr effect. The displacement of curves towards higher frequencies with... 

It has been shown that the main medianism responsible for EB in solutions of rigid-chain polymers is the rotation of their polar molecules as a whole whereas the anisotropy of the dielectric polarizability of the macromolecules only provides a small contribution to the Kerr effect. Hence, the general theory of the Kerr effect for rigid dipole particles with axial symmetry of the optical polarizability can be... 

As discussed in the previous section, the dielectric properties of materials at microwave frequencies are strongly dependent on the ionic polarization. Theoretical dielectric constants of materials can be obtained from the dielectric polarizabilities of composing ions through the understanding of crystal structure. Let us consider the basic relationships between the dielectric polarizabilities and dielectric constants and how the control of dielectric properties and the search for new materials can be achieved by the additive rule. 

From the Clausius-Mosotti equation (Equation 22.16), the relationship between the dielectric polarizabilities and the measured dielectric constant can be expressed by Equation 22.17. 

Shannon and Subramanian applied this relationship to calculate the dielectric polarizabilities of materials practically. Real polarizabilities of materials can be obtained from the additivity rule of the polarizabilities, which are a simi of the polarizabilities of composing ions as given in Equation 22.18 ... 

According to this additivity rule of polarizabilities, the dielectric polarizabilities of the complex compositions can be obtained from the polarizabilities of the composing molecules, and the dielectric polarizabilities of molecules can be obtained from the sum of polarizabilities of composing ions. Heydweiier applied the additivity rule of the polarizabilities first to calculate the polarizabilities of anhydrous salts and water molecules, in which the dielectric polarizability of water molecules aD(H20) was 3.2 3.5A similar to the value of 3.25 obtained for ice by Wilson et al. ° Also, Jonker and Van Santen" analyzed the polarizabilities of MTi03 (M = Mg, Ca, Sr, Ba) and Lasaga and Cygan derived the polarizabilities of 24 silicate minerals by this additivity rule. 

For the specimens sintered at 1200°C, the observed dielectric polarizability calculated from Equation 22.17 showed 14.090 A, while the theoretical dielectric polarizability calculated from Equation 22.18 showed 14.41 A, and the relative deviation ((0 5. - 0Cti,j.o)/(0Vj.j x 100)) was -2.91%. However, the theoretical dielectric polarizabihties modified by Equation 22.20 and Equation 22.24 are 14.187 A (deviation -1.57%) and 14.189 A (deviation -1.56%), respectively, as shown in Eigure 22.3. These results agree with the reports of Shannon, within 0.5 to 1.5%... 

With the change in composition, the atomic interactions of materials should be changed, which result in changes in the bond valence of the material. According to Equation 22.2 and Equation 22.3, the bond valence of PCCN was calculated and is shown in Table 22.4. As the calcium content, whose atomic size (1.34 A, C.N. = 12) is smaller than lead (1.34 A, C.N. = 12), increased, the bond valence of the A-site decreased. For PCMT, the similar tendency of the dielectric polarizabilities and A-site bond valence with calcium content was confirmed. The bond... 

FIGURE 22.6 Dielectric polarizability deviation of PCCN, PCMT specimens with A-site bond valence. 

Assuming the mixture of dielectrics and spherical pores with 3-0 connectivity, the dielectric constant (K) and loss quality (Qf) of ceramics with different porosity can be evaluated by the dielectric mixing rule. For the specimens with porosity, the dielectric polarizabilities modified by Maxwell s Equation were closer to the theoretical values rather than those modified by Wiener s Equation. The predicted loss quality obtained from intrinsic ones and Maxwell s Equation was agreed with the observed values. 

In addition, most semicrystalline polymers, particularly those produced commercially, are partially oriented i.e. their chains have an overall alignment that may impart to the bulk polymer certain advantageous properties, e.g. increased mechanical strength or dielectric polarizability. Molecular orientation, whether arising from crystallization under stress or deformation of a solidified polymer, or in naturally occurring oriented crystalline polymers such as cellulose or keratin, is always associated with an orientational morphology. 

Polarizability (i.e., static dielectric polarizability), a, is a measnre of the linear response of the electronic clond of a chemical species to a weak external electric field of strength E. For isotropic molecnles, the dipole moment, fi, is... 

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