Of dielectric susceptibility

Note, that Vogel-Fulcher law in the form of Eq. (1.26) was established firstly empirically (see e.g. Ref. [26]) while general theoretical description of its physical nature is still absent. The consideration of hierarchy of relaxational processes allowed to obtain the law in the form (1.26) for T = Tm only, where is the temperature of dielectric susceptibility maximum. The influence of random electric fields on relaxation barriers and hence on relaxation processes also permits to describe the disordered system by Vogel-Fulcher law in supposition of independent (parallel) relaxation processes [34]. 

We note that the dielectric properties of relaxor ferroelectric films have been investigated numerically in Ref. [81] by Monte-Carlo method. The authors obtained the increase of the temperature of dielectric susceptibility maximum and the decrease of the maximum height under the film thickness decrease. Below we investigate the relaxor films properties theoretically on the base of approach suggested in Ref. [82]. 

The dependence of dielectric susceptibility and ME tunability on the magnetic field is shown in Fig. 4.34. It is seen that the effect of FME coupling between the polarization and magnetization on the tunability and dielectric susceptibility is very high. Namely in the absence of flexomagnetic effects the tunability due to the quadratic ME coupling could not exceed one percent (see Fig. 4.34b), while the FME coupling leads to the tunability of about 10-30 % (see Fig. 4.34d). 

In general, however, tensor Qij is biaxial but the biaxiaUty is small, on the order of yPo where is the length corresponding to nematic correlations. This correlation length may be found, for example, from the light scattering in the isotropic phase close to the transition to the nematic phase. Then, at each point, that is locally, the anisotropic part of dielectric susceptibility tensor is biaxial and traceless 8ei + 5e2 + 8e3 = 0 with 8e2 8E3. 

Fig. 13.8 Qualitative temperature dependence of dielectric susceptibility in the SmC phase with the Goldstone mode plateau and the soft mode cusp...

Grigalaitis, Banys, Lapinskas, et al. Incorporates temperature dependence of dielectric susceptibility as a function of PbTiOs nanocrystal size Limited to isolated particles or particle distributions without interactions. 10... 

Can liquids in which the constituents are dipoles be ferroelectric For instance, if we could make a colloidal solution of small particles of the ferroelectric BaTi03, would this liquid be ferroelectric The answer is no, it would not. It is true that such a liquid would have a very high value of dielectric susceptibility and we might call it superparaelec-tric in analogy with the designation often used for a colloidal solution of ferromagnetic particles, which likewise does not show any collective behavior. An isotropic liquid cannot have polarization in any direction, because every possible rotation is a symmetry operation and this of course is independent of whether the liquid lacks a center of inversion, is chiral, or not. Hence we have at least to diminish the symmetry and go to anisotropic liquids, that is, to liquid crystals, in order to examine an eventual appearance of pyroelectricity or ferroelectricity. To... 

Single-step perturbation methods have also been applied to electrostatic processes. One study probed the dielectric properties of several proteins at a microscopic level [41,42], Test charges were inserted at many different positions within or around each protein, and a dielectric relaxation free energy was computed, which is related to a microscopic dielectric susceptibility (see Sect. 12.3). 

Figure 12. Temperature dependence of the inverse dielectric susceptibility (xr ) of DNP along the principal axis for polymerization. (Reproduced with permission from Ref. 16. Copyright 1980, Ferroelectric. ...

Schmidt number 3 phys chem A dimensionless number used In electrochemistry, equal to the product of the dielectric susceptibility and the dynamic viscosity of a fluid divided by the product of the fluid density, electrical conductivity, and the square of a characteristic length. Symbolized SC3. shmit. nam bar thre ) Schoeikopf s acid orgchem A dye of the following types l-naphthol-4,8-dlsulfonlc acid, l-naphthylamine-4,8-disulfonicadd,and l-naphthylamine-8-sulfonicadd may be toxic. shol.kopfs, as-3d ... 

It is noteworthy that the neutron work in the merging region, which demonstrated the statistical independence of a- and j8-relaxations, also opened a new approach for a better understanding of results from dielectric spectroscopy on polymers. For the dielectric response such an approach was in fact proposed by G. Wilhams a long time ago [200] and only recently has been quantitatively tested [133,201-203]. As for the density fluctuations that are seen by the neutrons, it is assumed that the polarization is partially relaxed via local motions, which conform to the jS-relaxation. While the dipoles are participating in these motions, they are surrounded by temporary local environments. The decaying from these local environments is what we call the a-process. This causes the subsequent total relaxation of the polarization. Note that as the atoms in the density fluctuations, all dipoles participate at the same time in both relaxation processes. An important success of this attempt was its application to PB dielectric results [133] allowing the isolation of the a-relaxation contribution from that of the j0-processes in the dielectric response. Only in this way could the universality of the a-process be proven for dielectric results - the deduced temperature dependence of the timescale for the a-relaxation follows that observed for the structural relaxation (dynamic structure factor at Q ax) and also for the timescale associated with the viscosity (see Fig. 4.8). This feature remains masked if one identifies the main peak of the dielectric susceptibility with the a-relaxation. 

The soft mode concept can be extended to all distortive phase transitions (transitions with relatively small atomic displacements), even if they are only close to second order. In the case of a ferro-distortive transition, as for example in BaTiOs or KDP, the order parameter is proportional to the spontaneous electric polarization Fj. d F/ dp is not only proportional to co, but also to the dielectric susceptibility. This does not, however, mean that all components of the order parameter eigenvector must contribute to Ps. 

Figure 6.34 Electrical conductivity and dielectric susceptibility of phosphorus-doped silicon at T 10" K. The dielectric susceptibility shows a divergence as the transition is approached from the insulator side. Notice the sharp, but continuous threshold in a(n) on the metallic side. (After Hess et ai,...

One of the important characteristics of ferroelectrics is that the dielectric constant obeys the Curie- Weiss law (equation 6.48), similar to the equation relating magnetic susceptibility with temperature in ferromagnetic materials. In Fig. 6.55 the temperature variation of dielectric constant of a single crystal of BaTiOj is shown to illustrate the behaviour. Above 393 K, BaTiOj becomes paraelectric (dipoles are randomized). Polycrystalline samples show less-marked changes at the transition temperature. 

There are many sources of this paradoxical situation, in which a theoretical understanding lags far behind experiment in such a practically relevant area as electro-diffusion. There was a period of intense qualitative development in this area in the 1920s until the early 1950s when the modern classics of chemical physics developed the theory of electrolytic conductance and related phenomena [11]—[13]. These works were mainly concerned with the mean field approach to microscopic mechanisms determining such properties of electrolyte solutions as ion diffusivity, dielectric susceptibility, etc. in particular, they were concerned with the effects of an externally applied stationary and alternating electric field upon the above properties... 

Equations (6) and (7) express these relationships. are the elastic compliance constants OC are the linear thermal expansion coefficients 4 and d jj,are the direct and converse piezoelectric strain coefficients, respectively Pk are the pyroelectric coefficients and X are the dielectric susceptibility constants. The superscript a on Pk, Pk, and %ki indicates that these quantities are defined under the conditions of constant stress. If is taken to be the independent variable, then O and are the dependent quantities ... 

Observation of magnetic susceptibility relaxation after perturbation of a spin equilibrium would be the most direct way to measure the dynamics of the equilibrium. This does not appear to have been reported as measured in solution. In principle susceptibility relaxation as a function of frequency could be measured much as dielectric relaxation is examined. The requirement is for a sufficiently strong magnetic field with very sensitive detection. A nonequilibrium magnetic susceptibility has been generated by light at low temperatures in the solid state (39). 

Thus the spectral function L(z) of an isotropic medium is represented as a linear combination of two spectral functions determined for an anisotropic medium pertinent to longitudinal ( ) ) and transverse (K ) orientations of the symmetry axis with respect to the a.c. field vector E. It is shown in GT, Section V, that these spectral functions are proportional to the main components of the dielectric-susceptibility tensor. 

The dielectric susceptibility x is related to the relative dielectric constant er by x = er — 1 Equations (1.4) are only valid for small fields. Large amplitudes of the ac field lead to strong non-linearities in dielectrics, and to sub-loops of the hysteresis in ferroelectrics. Furthermore, the dielectric response depends on the bias fields as shown in Figure 1.4. From the device point of view this effect achieves the potential of a tunable dielectric behavior, e. g. for varactors. 

Figure 1.9 Reciprocal dielectric susceptibility at the phase transition of lithium tantalate (second order phase transition) and of barium titanate (first order phase transition).

Figure 15.3 Temperature dependences of the linear thermal expansion, Al/l [2], refractive index, n [3] and reciprocal dielectric permittivity, 1 /x (Samara, unpublished) for pmn showing deviations from linear response at a temperature (I d) much higher than the peak (Tm) in the dielectric susceptibility (from [14]).

Complex dielectric susceptibility data such as those in Figure 15.6 provide a detailed view of the dynamics of polar nanodomains in rls. They define relaxation frequencies, /, corresponding to the e (T) peak temperatures Tm, characteristic relaxation times, r = 1/tu (where uj = 2nf is the angular frequency), and a measure of the interaction among nanodomains as represented by the deviation of the relaxation process from a Debye relaxation. Analysis of data on pmn and other rls clearly shows that their dipolar relaxations cannot be described by a single relaxation time represented by the Debye expression... 

Domains in fe crystals are well-known to have a considerable influence on the value of their complex dielectric susceptibility, x = x — , X" and related quantities [51], Owing to its mesoscopic character the domain wall susceptibility strongly reflects the structural properties of the crystal lattice. This is most spectacular in crystals with inherent disorder, where the... 

The dielectric theory may be expressed in a nonlocal form based on the definition of the susceptibility and permittivity in a form that makes these physical quantities the kernel of appropriate integral equations. 

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