Permittivity solids

Figure 35. Frequency dependence in the submillimeter wavelength region of the real (a, b) and imaginary (c, d) parts of the complex permittivity. Solid lines Calculation for the composite HC-HO model. Dashed lines Experimental data [51]. Dashed-and-dotted lines show the contributions to the calculated quantities due to stretching vibrations of an effective non-rigid dipole. The vertical lines are pertinent to the estimated frequency v b of the second stochastic process. Parts (a) and (c) refer to ordinary water, and parts (b) and (d) refer to heavy water. Temperature 22.2°C.

Figure 50. Calculated contributions of the ionic permittivity for the imaginary (a, c) and real (b, d) parts of the total complex permittivity (solid lines) dashed lines refer to the calculation, neglecting the ionic dispersion, (a, b) For NaCl-water solution (c, d) for KCl-water solution. Cm = 0.5 mol/liter, Tion/r = 10.

Fig. 2.58 Dielectric permittivity (solid) and loss (open), (triangle) 104 Hz, (circle) 102 Hz, (square) 10° Hz. (a) P2MCBM, (b) P3MCBM, (c) P4MCBM, (d) P2,3 DCBM, (e) P2.4DCBM, (0 P2,5DCBM, (g) P2.6DCBM, (h) P3,4DCBM, and (i) P3.5DCBM. (From ref. [39])...

In lead zh conate, PbZrOs, the larger lead ions are displaced alternately from the cube corner sites to produce an antifeiToelectric. This can readily be converted to a feiToelectric by dre substitution of Ti" + ions for some of the Zr + ions, the maximum value of permittivity occumirg at about the 50 50 mixture of PbZrOs and PbTiOs. The resulting PZT ceramics are used in a number of capacitance and electro-optic applicahons. The major problem in dre preparation of these solid soluhons is the volatility of PbO. This is overcome by... 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

The pioneering work of Von Hippel [15] and his coworkers, who obtained dielectric data for organic and inorganic materials, still remains a solid basis. Study of dielectric permittivity as a function of temperature is, however, less well developed, particularly for solids. 

Another important group of oxide materials with a very low electrical conductivity is the oxide dielectrics. A number of these are based upon the perovskites, MXO3 or M0 X02. The archetype of these materials is BaTiC>3, which has a high dielectric constant, or relative permittivity to vacuum, the value at room temperature being 1600, and commercial use is made of the isostructural PbTi(>3 and ZrTi03 which form solid solutions, the PZT dielectrics. These materials lose their dielectric properties as the temperature... 

Water absorption can also cause significant changes in the permittivity and must be considered when describing dielectric behavior. Water, with a dielectric constant of 78 at 25°C, can easily impact the dielectric properties at relatively low absorptions owing to the dipolar polarizability contribution. However, the electronic polarizability is actually lower than solid state polymers. The index of refraction at 25°C for pure water is 1.33, which, applying Maxwell s relationship, yields a dielectric constant of 1.76. Therefore, water absorption may actually act to decrease the dielectric constant at optical frequencies. This is an area that will be explored with future experiments involving water absorption and index measurements. 

Table 13.1 does not explain, however, why the ionic solid silver chloride, which is well known to be poorly soluble in water, dissolves readily in liquid ammonia, despite a much less favorable relative permittivity. The reason is that the silver ion interacts strongly with specific ammonia molecules... 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

Fig. 2.12 Relationship between the ion association constants (log KA) and the reciprocal of solvent permittivity (1 /er) (solid line) and between the degree of ion association (a) and log (c/(A) (dotted curve), (open circles Bu4NPic in AN, NB, MeOH, Ac, Py, DCE, o-dichlorobenzene, acetic acid, chlorobenzene and benzene closed squares KCI in ethanolamine, MeOH, EtOH, acetic acid and H20-dioxane mix-tures). The solid line was obtained using a Eq. (2.19) for 0 = 0.6 nm.

ASTM D150, 1998 (2004). Test methods for AC loss characteristics and permittivity (dielectric constant) of solid electrical insulation. 

ASTM D2520, 2001. Standard test methods for complex permittivity (dielectric constant) of solid insulating materials at microwave frequencies to 1650°C. 

ASTM 1986. Standard Methods Qf Test for Complex Permittivity (Dielectric Constant) of Solid Electrical Insulating Materials at Microwave Frequencies and Temperatures 1q 1650°C. Document D 2520-86 (Reapproved 1990). Philadelphia, PA. American Society for Testing and Materials (ASTM). 

Nelson, S., Kraszewski, A. and You, T. 1991. Solid and particulate material permittivity relationships. Journal of Microwave Power. 26 (1) 45. 

Most solid surfaces in water are charged. Reason Due to the high dielectric permittivity of water, ions are easily dissolved. The resulting electric double layer consist of an inner Stern or Helmholtz layer, which is in close contact with the solid surface, and a diffuse layer, also called the Gouy-Chapman layer. 

How does the electric potential change with respect to distance from the interface On the solution side the potential decays as described before. We have a Stern and a diffuse layer. For a semiconductor the potential variation at the solid side is also of interest. It also decays and this decay can be described as the decay of the diffuse layer. We only have to replace the salt concentration by the concentration of electrons ce and holes ch and we have to use the appropriate dielectric permittivity. 

Table 6.2 Dielectric permittivity e, refractive index n, and main absorption frequency in the UV for various solids, liquids, and polymers at 20°C (Refs. [109,128,129], handbooks, and own measurements.).

In this section we have to calculate the complex permittivity s (v) and the absorption coefficient a(v) of ordinary (H2O) water over a wide range of frequencies. It is rather difficult to apply rigorous formulas because the fluctuations of the calculated characteristics occur at a small reduced collision frequency y typical for water (in this work we employ for calculations the standard MathCAD program). Such fluctuations are seen in Fig. 13b (solid curve). Therefore the calculations will be undertaken for two simplified variants of the hat model. Namely, we shall employ the planar libration-regular precession (PL-RP) approximation and the hybrid model.26... 

Figure 28. Experimental frequency dependences of dielectric parameters recorded for liquid water (a) Real (curve 1) and imaginary (curve 2) parts of the complex permittivity at 27°C. The data are from Refs. 42 (solid lines) and 17 (circles), (b) Absorption coefficient. Solid line and crosses 1 refer to 1°C filled circles 2 refer to 27°C dashed line and squares 3 refer to 50°C. For lines the data from Ref. 17 were employed, for circles the data are from Ref. 42, for crosses and squares the data are from Ref. 53.

Figure 30. Imaginary (a) and real (b) parts of the complex permittivity of liquid water H20 at 22.2°C. Ordinary water is represented by solid lines, heavy water is represented by dashed lines. To the left from vertical lines (for v < 20 cm 1). calculation is performed using approximation [17] modified as described in Appendix 3.2 in the rest region, it is performed using the data 51 given in Table XII.

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