Absolute permittivity

Heuristic Fxplanation As we can see from Fig. 22-31, the DEP response of real (as opposed to perfect insulator) particles with frequency can be rather complicated. We use a simple illustration to account for such a response. The force is proportional to the difference between the dielectric permittivities of the particle and the surrounding medium. Since a part of the polarization in real systems is thermally activated, there is a delayed response which shows as a phase lag between D, the dielectric displacement, and E, the electric-field intensity. To take this into account we may replace the simple (absolute) dielectric constant by the complex (absolute) dielectric... 

In this expression, e is the fundamental charge (the absolute value of the charge of an electron), Z and z2 are the charge numbers of the two ions, r12 is the distance between the centers of the ions, and E0 is the vacuum permittivity (see inside the back cover for the value of this fundamental constant). 

The mio / o is more convenient io use then the value oT the permittivity in absolute Units. 

Equations (10.23) and (10.24) hold for the /3-phase as well and could be inserted into Eqn. (10.22). The additivity of pt with respect to the elastic and electric potential is based on 1) the assumption of linear elastic theory (which is an approximation) and 2) the low energy density of the electric field (resulting from the low value of the absolute permittivity e0 = 8.8x10 12 C/Vm). In equilibrium, V/i, = 0 and A V, = df-pf = 0. Therefore, in an ionic system with uniform hydrostatic pressure, the explicit equilibrium condition reads Aa/fi=A)... 

Figure 1.3 Dielectric spectra for range of alcohols in the frequency range of 107-10n Hz. The absolute permittivities at low frequencies fall as the size of the alcohol increases and they began to respond to the microwave fields at lower frequencies because their relaxation times become longer. The loss factors that control the efficiency of conversion of microwave into thermal energies also reach their maxima at lower frequencies. The loss tangent is the ratio of the loss factor and permittivity at that frequency. (Idealised from the raw data illustrated in Ref. 10.)...

From the value of the resonant frequency and its change with temperature or other external parameters the permittivity of a dielectric sample and its temperature or field dependence can be determined. In case of superconductors, the temperature dependence of the magnetic field penetration depth can be determined [8], Since the mode spectrum of a resonator is controlled both its physical dimensions and by the material properties, the physical dimensions of all resonator components have to be known with tight tolerances. Relative changes of permittivity or penetration depth can be determine with much higher accuracy than absolute values. 

The high frequency limit of for this second process is therefore n. The result of the fit is shown in Table III where the mean values of the various parameters and their associated 95% confidence intervals are given. Considering the small amplitude of the second dispersion both in absolute t rms and in relation to the main dispersion the parameters 6m, n and Y are quite well defined, and therefore it may be concluded that the double Debye representation is an acceptable description of the dielectric behaviour of water up to around 2THz. Other alternative interpretations are clearly possible but no attempt has been made here to follow these up at this stage. What is clear is that a small subsidiary dispersion region in the far infrared is necessary to account for all the presently available permittivity data, and that such a dispersion is centred around 650GHz and has an amplitude of about 2.4 in comparison with that of the principal dispersion which is approximately 75. 

Once the complex reflectivity amplitude is known, the relation (2.121) determines e(a>). Nevertheless, the absolute reflectivity, unimportant as regards 0(cu) [see (2.120)] becomes essential for the permittivity. Earlier work on a number of crystal samples showed us that the maximum reflectivity at 4 K was greater than 90%. However, due to free sample mounting, the front face of the crystal is not perfectly planar, and accurate direct measurements of the absolute reflectivity are impossible. Fortunately, surface structures II and III allow probing the bulk reflectivity around 3982 A High-resolution spectra (0.3 cm 1) of structure II (cf. Section III) show the absence of any constructive intereference. This, together with numerical simulations,121 indicates that the bulk reflectivity should be very close to 100% (within 2%) at the maximum. 

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