Displacement dielectric

Fig. 1. Hysteresis loop of dielectric displacement, DI, versus appHed electric field where F is coercive field and PI j, PI, and P/ are the saturated,...

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... 

During the reaction the dielectric displacement changes from Dox to Dred (or vice versa), and the equilibrium value from Dox/2aeo to Drec[/2a eo. From Eq. (6.5) the contribution of the volume element AV to the energy of reorganization of the outer sphere is ... 

The dielectric displacement must be calculated from electrostatics for a reactant in front of a metal surface the image force has to be considered. For the simple case of a spherical ion in front of a metal electrode experiencing the full image interaction, a straightforward calculation gives ... 

Assuming that x CE, show that the electric field E contains a contribution that oscillates at a frequency 2w. Note J ext = D/eo, where D is the dielectric displacement. 

Note that Gp 0p of eq. (9) can be written in several equivalent but different looking forms, as is typical of electrostatic quantities in general. For example, it is often convenient to express the results in terms of the electrostatic scalar potential ( )(r) instead of the electric vector field E(r). In the formulation above, the dielectric displacement vector field associated with the solute charge distribution induces an electric vector field, with which it interacts. In the electrostatic... 

The dielectric constant of a medium is the constant of proportionality in the relation between the dielectric displacement and the strength of the electric field. The polarization of the medium is given by... 

In order to assess the orientational stability of the poled state, the temperature dependence of the dipole mobility of the side groups was examined through dielectric relaxation measurements. (13) No low temperature relaxation below Tg was observed in the frequency range studied (100 Hz-100 kHz). In addition, the dielectric constant was approximately equal to the square of the refractive index, indicating that below T only electronic and no significant orientational contributions to the dielectric displacement are present. Thus, it was expected that a given orientational state of the ensemble would be stable at temperatures significantly below Tg. 

In accordance to the Poisson equation, the source of the dielectric displacement D is given by the density of free (conducting) charges p ... 

It is also important to realize that piezoelectricity implies a linear coupling between dielectric displacement and strain, for example. However, in many ferroelectric materials, this response is linear only over a relatively limited field range (See for example, Figure 2.2). Non-linearity is especially important in ferroelectric materials which show a strong extrinsic contribution to the piezoelectric response [5], In addition, it is quite common for the response to be hysteretic. The amount of hysteresis that is observed depends strongly on the measurement conditions. Larger amplitude excitations often result in larger extrinsic contributions to the coefficients, and more non-linearity and hysteresis in the response. 

Figure 13.5 Amplitude and phase angle of the third harmonic of the field induced strain and dielectric displacement of a 60/40 PZT thin film.

Here >2 is the dielectric displacement along the ferroelectric axis, a the thickness, l the length and b the width of the sample. The electric field strength ENL at the crystal along the ferroelectric b-axis is a nonlinear function of the dielectric displacement. 

The occurrence of strong permanent fields may disturb the linear response regime in the dielectric response we have so far employed. The standard treatment of nonlinear dielectric response is based on the expansion of the dielectric displacement function D in powers of the electric field E, generally interrupted at the first correction ... 

The medium effects are introduced in terms of s (the dielectric permittivity) or (the susceptibility). At space point f conventional electrostatic expressions relate the electric field strength E(r), the dielectric displacement D(r) and the polarization field P(r) as... 

Fig. 28. (a) Sketch of current lines of the dielectric displacement current between a contact needle and a counter-electrode indicating the influence of the stray capacitance, (b) Equivalent circuit (including the stray capacitance) representing microelectrode measurements on single crystals and the two simplified subcases for ohmic and non-ohmic microelectrodes. 

The dielectric displacement vector varies with free charge density as div D = p, div D = 4tt,o. 

Even if one assumes that the water near a surface has the same structure as it does in bulk, the oscillations of the short-range interactions between surfaces could be explained by a nonlocal dielectric constant for water.24 This model assumes that the dielectric displacement field (D = epE 4- P) at a position r not only depends on the local electric field [D(r) = r(r)E(r), but also depends on the electric field in the whole space D(r) = jr(r,r )E(r )dr. In this model, the oscillations of the interactions are due to charge overscreening25 and are analogous to the charge density waves in plasmas.24... 

Width of the dead zone of the interface height step Converse piezoelectric constant Dielectric displacement... 

As mentioned above, domain switching in ferroelectrics is accompanied by domain nucleation, moving domain walls and restructuring of dipoles and charges. A characteristic feature of this irreversible process is the appearance of a hysteresis loop in the dependence of dielectric displacement... 

Figure 28. a) Ion redistribution process at the contact MX/MX concentration effects.117 b) Variation of the potentials, charge densities, and dielectric displacements at the contact of two Frenkel defect ionic conductors.94 (Reprinted from J. Maier, Ionic Conduction in Space Charge Regions. Prog. Solid St. Chem. 171-263, 23, Copyright 1995 with permission from Elsevier.)... 

This is the fundamental electric field equation that applies at any point in an isotropic medium. In this context the quantity e0e is the absolute permittivity of the material, and the ratio e, which we have called the dielectric constant of the material, is more properly termed the relative permittivity (with respect to the absolute permittivity of free space e0) and we shall use this term. The flux of dielectric displacement begins and ends on free charge and otherwise is continuous, even at an interface between two media. Electric field, on the other hand, is discontinuous at an interface between two different materials as a result of the different degrees of polarisation. 

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