Nonlinear dielectric constant

The isotropic coefficient and the anisotropic coefficients b(m> and c(m) can have both bulk and surface contributions and depend on crystal symmetry. The linear and nonlinear dielectric constants of the material, as well as the appropriate Fresnel factors at co and 2co, are incorporated into the constants a, b m) and c(m). Table 3.1 shows the susceptibilities contained in each of these constants. The models of Tom... 

With this background, we have proposed and developed a new purely electrical method for imaging the state of the polarizations in ferroelectric and piezoelectric material and their crystal anisotropy. It involves the measurement of point-to-point variations of the nonlinear dielectric constant of a specimen and is termed scanning nonlinear dielectric microscopy (sndm) [1-7]. This is the first successful purely electrical method for observing the ferroelectric polarization distribution without the influence of the screening effect from free charges. To date, the resolution of this microscope has been improved down to the subnanometer order. 

Here, 33, 333, 3333, and 33333 correspond to linear and nonlinear dielectric constants and are tensors of rank 2nd, 3rd, 4th and 5th, respectively. Even-ranked tensors including linear dielectric constant 33 do not change with polarization inversion, whereas the sign of the odd-ranked tensors reverses. Therefore, information regarding polarization can be elucidated by measuring odd-ranked nonlinear dielectric constants such as 333 and 33333. 

This equation shows that the alternating capacitance of different frequencies corresponds to each order of the nonlinear dielectric constant. Signals corresponding to 333, 3333 and 33333 were obtained by setting the reference signal of the lock-in amplifier in Figure 16.1 to frequency cop, 2 ujp and 3 uip of the applied electric field, respectively. 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

Perovskites have the chemical formula ABO, where A is an 8- to 12-coordinated cation such as an alkaU or alkaline earth, and B is a small, octahedraHy coordinated high valence metal such as Ti, Zr, Nb, or Ta. Glass-ceramics based on perovskite crystals ate characteri2ed by their unusual dielectric and electrooptic properties. Examples include highly crystalline niobate glass-ceramics which exhibit nonlinear optical properties (12), as well as titanate and niobate glass-ceramics with very high dielectric constants (11,14). 

PPQs possess a stepladder stmcture that combines good thermal stabiUty, electrical insulation, and chemical resistance with good processing characteristics (81). These properties allow unique appHcations in the aerospace and electronics industries (82,83). PPQ can be made conductive by the use of an electrochemical oxidation method (84). The conductivities of these films vary from 10 to 10 S/cm depending on the dopant anions, thus finding appHcations in electronics industry. Similarly, some thermally stable PQs with low dielectric constants have been produced for microelectronic appHcations (85). Thin films of PQs have been used in nonlinear optical appHcations (86,87). 

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

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 ... 

Figure 2. Nonlinear dielectric effect constant ( 10 scm7SC 2moF ) of Br(CH2)n, Br at 25 °C. Points represent the experimental results of Chelkowski (19, 20). The solid and dashed lines are calculated with 4>s, = 120 ° and +80 °, respectively, for thefirst and last C-C bonds. (Reproduced with permission from Ref 6. Copyright 1981, American...

Absolute measurements of nonlinear coefficients in GaAs in the millimeter region 10 —10 Hz have been determined 31 ) by mixing adjacent vibrational-rotational lines of a CO2 laser in a GaAs-filled waveguide which was matched to the difference frequencies. The experiments yielded the astonishing result that the nonlinear coefficient and the dielectric constant show opposite dispersions. 

Inagaki K, Terasaki I, Mori H, Mori T (2004) Large dielectric constant and giant nonlinear conduction in the organic conductor 0-(BEDT-TTF)2CsZn(SCN)4. J Phys Soc Jpn 73 3364-3369... 

Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

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