Homogeneous electric field distributions

A switching electrode having nanometer dimensions leads to profound difference in poling of fe thin films and fe bulk crystals. In the case of fe thin films with a thickness of about 100 nm, a voltage application between the bottom electrode and an afm tip of 50-100 nm radius forms a quasi-homogeneous electric field. Such a distribution implies a conventional polarization reversal setup as in the case of uniform switching electrodes applied to polar faces of a fe sample. 

Figure 8.5 Example of electric field distribution. Assuming homogeneous conductivity (which is indeed an unlikely event), the field distribution between two arrays of opposing electrodes is shown. It is obvious that when...

The first and foremost requirement is the need to establish a homogeneous electric field at the working electrode surface and consequently an even current distribution. In this respect the relative positions of the working-, auxiliary- and reference-electrodes are of paramount importance. 

Fig. 12.7. Sadlej relation. The electric field mainly causes a shift of the electronic charge distribution toward the anode (a). A GTO represents the eigenfunction of a harmonic oscillator. Suppose that an electron oscillates in a parabolic potential energy well (with the force constant I ). In this situation, a homogeneous electric field corresponds to the perturbation x, that conserres the hannonicity with unchanged force constant k (b).

It can be assumed that a homogeneous electric field and, consequently, a uniform current density distribution are present over the entire electrode surface up to the very edge of the electrode, where the current density increases abruptly. This problem has been studied in detail in Refs. [2, 3, 5-7], and a relatively rough approximation will be used here. This approximation is based on the following assumptions ... 

In this expression the particle is considered to be exposed to a homogeneous electric field of strength . The shape of the particle is of no importance just as the electro-osmosis equation (11) is valid for an arbitrary shape of the porous plug. Restrictions on the applicability of expression (26) are similar to the case of electro-osmosis y. the double-layer must be thin compared with the dimensions of the particle, p. the particle must be insulating and the surface conductance at the interface must be so small that the distribution of the external field is practically uninfluenced by it. 

In contrast to a direct injection of dc or ac currents in the sample to be tested, the induction of eddy currents by an external excitation coil generates a locally limited current distribution. Since no electrical connection to the sample is required, eddy current NDE is easier to use from a practical point of view, however, the choice of the optimum measurement parameters, like e.g. the excitation frequency, is more critical. Furthermore, the calculation of the current flow in the sample from the measured field distribution tends to be more difficult than in case of a direct current injection. A homogenous field distribution produced by e.g. direct current injection or a sheet inducer [1] allows one to estimate more easily the defect geometry. However, for the detection of technically relevant cracks, these methods do not seem to be easily applicable and sensitive enough, especially in the case of deep lying and small cracks. 

Hong and Noolandi [72], Berg [278], and Pedersen and Sibani [359] have also noted the connection between the survival probability and homogeneous density distribution. Finally, the escape probability of an ion pair formed with a separation, r0, with an arbitrary monotonically decreasing potential energy of interaction and with electric field-dependent mobility and diffusion coefficient ions was found by Baird et al. [350] to be (see also Tachiya [357])... 

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