Dielectric constant behavior near

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. 

Note 4. The Number of Dipoles per Unit Volume (Sec. 98). Between 25 and 100°C the value of 1 /t for water rises from TV to , while the increment in the value of l/(t — 1) is nearly the same, namely, from rs to TfV- Similarly in any solvent whose dielectric constant is large compared with unity the temperature coefficients of l/(e — 1) and of 1/e are nearly equal. In comparing the behavior of different solvents, let us consider now how the loss of entropy in an applied field will depend upon n, the number of dipoles per unit volume. Let us ask what will be the behavior if (e — 1) is nearly proportional to n/T as it is in the case of a polar gas. In this case we have l/(e — 1) nearly proportional to T/n and since in a liquid n is almost independent of T, wc have... 

We have seen that crystals can be safely transferred to mixed solvents and that the percentage of organic solvent may often be increased to any desired level provided that its gradual addition is coupled with a gradual reduction in temperature so as to keep the dielectric constant of the medium as near as possible to the value for the normal mother liquor. Such a result deserves explanation and comment about the behavior of the dielectric constant in mixed solvents as a function of temperature. 

It might be useful in some cases to raise the dielectric constant of mixed solvents by addition of suitable substances and it is known that dipolar molecules such as amino acids do so in pure water. These amino acids are virtually insoluble in nonpolar solvents but they dissolve readily in aqueous salt solutions and in most mixed solvents according to their highly polar structure. Most of what is known about their dielectric behavior concerns aqueous solutions, in which they were studied up to concentrations near saturation. 

Equation (24) renders intelligible the behavior of the dielectric constant of dipolar ions in polar solutions. It explains the linear increase of D with concentration, since changes in partial molar volumes, only slightly dependent on concentration, can only affect the DyVi term. It also explains the nearly identical values of D of the amino acids of the same moment, and the fact that D of a given amino acid is insensitive to changes in the dielectric constant of the solvent, for the change of solvent can directly affect 8 only through the term D V2. 

Pratt and co-workers have proposed a quasichemical theory [118-122] in which the solvent is partitioned into inner-shell and outer-shell domains with the outer shell treated by a continuum electrostatic method. The cluster-continuum model, mixed discrete-continuum models, and the quasichemical theory are essentially three different names for the same approach to the problem [123], The quasichemical theory, the cluster-continuum model, other mixed discrete-continuum approaches, and the use of geometry-dependent atomic surface tensions provide different ways to account for the fact that the solvent does not retain its bulk properties right up to the solute-solvent boundary. Experience has shown that deviations from bulk behavior are mainly localized in the first solvation shell. Although these first-solvation-shell effects are sometimes classified into cavitation energy, dispersion, hydrophobic effects, hydrogen bonding, repulsion, and so forth, they clearly must also include the fact that the local dielectric constant (to the extent that such a quantity may even be defined) of the solvent is different near the solute than in the bulk (or near a different kind of solute or near a different part of the same solute). Furthermore... 

Could this be behavior in terms of the Maxwell-Wagner dispersion, which would arise through conductivity in the double layer near the polyanion. In support of this, the dielectric constant falls as the frequency increases (Fig. 2.79). 

Likewise the different behavior of HCIO4 and (CeH5)3C0H in water and sulfuric acid cannot be explained by simple electrostatic models (25) as both solvents have nearly the same dielectric constant. Perchloric acid, which has pronounced EPA properties, is completely ionized in the EPD solvent, water, but it remains essentially unionized in the strong EPA solvent, sulfuric acid. Triphenylcarbinol, on the other hand, reacts quantitatively with the strong EPA solvent, H2SO4, but no interaction occurs with the strong EPD solvent, water. 

One may however look at the data in Table 1 from a different point of view (see also ref 22). It is seen that a transition from Ising to mean-field behavior is observed, if the dielectric constant decreases, the transition regime occuring somewhere near D = 4.5. Could the dielectric constant be the major parameter controlling criticality In the latter case specific interactions play an indirect role They shift and thus enabling phase separations to occur... 

Simulations of solvation dynamics following charge transfer at the water liquid/vapor interface[53,80] have shown that the solvent relaxation rate is quite close to that in bulk water, even though one might expect (based on the reduced interfacial dielectric constant and simple continuum model arguments) to have a significantly slower relaxation rate. The reason for this behavior is that the interface is deformed and the ion is able to keep its first solvation shell nearly intact. Since a major part of the solvation dynamics is due to the reorientation of first shell solvent dipoles, the rate relative to the bulk is not altered by much. 

As a consequence, the joins for (Pbi. (Bajc)Ti03 at low temperature and for Pb(Zri cTy03 at room temperature are interrupted by a morphotropic phase boundary (MPB), which separates tetragonal and rhombohedral phases (Fig. 14). The structural state of the oxides in the vicinity of the MPB is a subject of active inquiry, because many of the physical properties of PBZT ferroelectrics are maximized at the MPB. These include the dielectric constant, the piezoelectric constant, and the electromechanical coupling coefficients (Jaffe 1971, Thomann and Wersing 1982, Heywang and Thomann 1984). For industrial purposes, this behavior is exploited by annealing PBZT ferroelectrics with compositions near the MPB close to the Curie temperature in an... 

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. 

In order to analyze carefully the frequency-dependent ellipsometric measurements described in the previous section, a precise determination of the frequency dependence of the dielectric constant e is needed. While, the dielectric constant of nonpolar polymers is nearly constant over a wide range of frequencies, that of polar materials decreases with increasing frequency (50), In the optical range, e generally increases with the frequency and this behavior is known as normal dispersion. At these high frequencies, the origin of the polarizability is mainly electronic. However, at moderate and low frequencies the dielectric constant is enhanced compared with its optical frequency value due to the motion of the molecular dipoles. This regime is called anomalous dispersion. The orientational and electronic contributions are found in the well-known Clausius-Mossotti formula for instance. In the simplest model, the frequency dependence of the dielectric constant can be described by the Debye formula (50) ... 

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