Susceptibility and Dielectric Constant

The macroscopic polarization vector, P, and the electric field, E, which generally are oriented in the same direction, are interrelated by the following expression  

And the capacity of a capacitor filled with a dielectric slab is 

FIGURE 1.26 Time-varying electric field applied across aparallel plate capacitor. Consequently, it is easy to show that 

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The electric susceptibility and dielectric constant of ferroelectric substances obey a Curie law dependence on temperature (Equation (9.13) ... 

In the spatially modulated case, (8.5) and (8.6) have to be modified using the polarization vector P = Px, Py) which is perpendicular to the tilt vector The constants C and Q. describe the strength of the bilinear and biquadratic coupling the P and P terms are necessary to stabilize the system, e has the physical meaning of an electric susceptibility, it can be written as = /o o with o being the vacuum permittivity and Xo (electric susceptibilities and dielectric constants are used in this chapter as dimensionless or relative quantities) corresponds to the electric susceptibility of the uncoupled system (C = = 0). Writing the Landau free energy g as g = ge + gpt results in a... 

Ax = X ( X Ae = E - Ej are the magnetic susceptibility and dielectric constants of the monomenc unit in directions parallel and peipendicular to the longitudinal axis of the molecule, respectively. 

An example of the type of behaviour encountered for exponential surface-state distributions is provided by n-Fe203 in 1M NaOH [69]. The equivalent conductance and susceptance of the circuit comprising Zss in parallel with C8c clearly show a power law dependence on values obtained from this model again obeyed the Mott-Schottky relationship, although the donor density of 8 x 1018 cm 3 and dielectric constant of 25 suggest that the true flat-band potential may lie rather positive of the value given. 

In contrast to Eqns. (9) and (10), Eqns. (11), and (12) can be used with dielectric models where P is determined using the susceptibility or dielectric constant (Eqn. 2). 

A phase transition at 80 °K was investigated by magnetic susceptibility, low field ESR, dc and microwave conductivity and dielectric constant measurements. The magnetic properties are discussed in terms of a singlet-triplet model above, in terms of ID Heisenberg model below the phase transition. 

This differs qualitatively from a conductivity increasing with decreasing temperature for uninterrupted strands. Similarly, it was shown (120, 342) that the specific heat and magnetic susceptibility for the interrupted strands can differ greatly both in magnitude and temperature dependence from that expected for continuous strands. The predicted optical conductivity and dielectric constant for the interrupted strand model (120,173,344) is more complicated than that for the continuous strands. 

Landolt-Bomstein Tables, Neue Serie Vol. lll/30b. Springer Verlag. Gurzadyan GG, Charra F (2000) High Fiequeney Properties of Dielectrie Crystals. Nonlinear Dieleetric Susceptibilities. Lee S-H, Roh Y (2007) Characterization of all the elastic, piezoelectric, and dielectric constants of tetragonal PMN-PT single crystals, Jpn J Appl Phys 46, 7B 4462 465 Levinson LM (1988) Electronic ceramics - Properties, Devices and Applications. Marcel Dekker, New York, NY... 

Figure 8.9. Simultaneous measurement of electric susceptibility (relative dielectric constants of the chiral enantiomer and racemate, top) and tilt susceptibility xe (labeled as 6/E, middle) and ratio k = x Xo) /x (bottom) in the smectic- phase of the chiral compound A7 (from [61]).

Interestingly, the contributions from the gradient of the electromagnetic field across the interface, Tfg xx and Tfg zzz, which scale with the mismatch in the optical dielectric constants of the media forming the interface [37], only appear in the susceptibility tensor components nd xl zzz- Therefore, these contributions may be rejected with a... 

Changes to the physical properties of a compound or material can have a dramatic influence on the susceptibility to microwave radiation. For example, ice has dielectric properties (e, 3.2 tan 8, 0.0009 e", 0.0029) that differ significantly from those of liquid water at 25 °C (s, 78 tan <5, 0.16 e", 12.48) [31], rendering it essentially microwave-transparent. Although liquid water absorbs microwave energy efficiently, the dielectric constant decreases with increasing temperature and supercritical water (Tc 374 °C) is also microwave-transparent. 

The third order nonlinear susceptibility is an important optical property of materials because of its contributions to numerous nonlinear optical processes. (1)(2) With the growing interest in all-op ical signal processing it has been proposed (3) recently that x ( 1, 2 3) and especially the degenerate third order nonlinear susceptibility x 3 (-w, to, 00) [defined as x (< >)], be utilized through its contributions to the changes in dielectric constant e with optical field strength E ... 

Grayish-white cubic crystals lustrous and brittle density 5.323 g/cm hardness 6.0 Mohs melts at 938.2°C vaporizes at 2,833°C a poor conductor of electricity electrical resistivity 47 microhm-cm dielectric constant 15.7 specific magnetic susceptibility (at 20°C) 0.122x10 insoluble in water, dilute acids and dilute alkalies attacked by concentrated nitric and sulfuric acids, aqua regia and fused alkalies. 

Thus, we see the initial connection between optical properties and the electrical and magnetic properties from the two previous sections. Substimtion of Eqs. (6.78) and (6.79) into (6.77) shows that the refractive index can be expressed in terms of the relative electric permittivity (dielectric constant), (cf. Table 6.5), and relative magnetic permeability of the medium, (1 - - x) [cf. Eq. (6.63)], where x is the magnetic susceptibility ... 

Since most ceramic substances (and most nonmetallic substances, for that matter) possess small magnetic susceptibilities, the quantity (1 - - x) is approximately unity, and the refractive index can be approximated as the square root of the dielectric constant ... 

The physical properties of solvents greatly influence the choice of solvent for a particular application. The solvent should be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapor pressure, temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity, also need to be considered. Electrical, optical, and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant, too. Furthermore, molecular... 

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