Distribution fields

In field ion microscopy, one would also like to know how the field distributes itself above an emitter surface. This information is important in the quantitative interpretation of many field ion emission phenomena and experiments. It is also important in calculating the ion trajectory to enable a proper aiming in an atom-probe analysis. Unfortunately, not only does each tip have its own particular shape, but the presence of lattice steps also complicates the situation immensely. There are so far no reliable calculations for the field distribution above an emitter surface, nor for predictng the ion trajectory, nor yet for where the probe-hole 

While a proper aiming of the atom-probe can be experimentally determined, information on field lines and on equipotential lines is difficult to derive with an experimental method because of the small size of the tip. Yet this information is needed for interpreting quantitatively many experiments in field emission and in field ion emission. We describe here a highly idealized tip-counter electrode configuration which may be useful for describing field lines at a short distance away from the tip surface but far enough removed from the lattice steps of the surface. The electrode is assumed to consist of a hyperboloidal tip and a planar counter-electrode.30 In the prolate spheroidal coordinates, the boundary surfaces correspond to coordinate surfaces and Laplace s equation is separable, so that the boundary conditions can be easily satisfied. 

The prolate spherical coordinates (a, / , j ) are related to the rectangular coordinates by 

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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. 

Fia 5 Real Part of Calculated Field Distribution around Exciter Coil... 

The field distribution itself gives information about the location where the detector coil or coils should be placed. It can however be used as a basis for the calculation of defect signals... 

The magnetic field distribution near the surface of z = 0 separation is considered. The pattern has Ll = 0 magnetic permeability, over the pattern medium is 4 = 1. The equations for (p... 

Switching-Field Distribution. Both and have a strong relation with the recording process. determines the maximum output signal of a recording medium and hence the signal-to-noise ratio. ascertains how easily data can be recorded and erased or changed, but it also determines the maximum head field. On the other hand it also controls the ease with which data can be destroyed, eg, by stray fields. The lower the the more sensitive the medium is to all kinds of fields. In this way, influences the noise level as well. The squareness ratio S (= /Af ) can also be derived from the... 

The general engineering task in most apphcations of microwave power to materials or chemicals is to deduce from the geometry of samples and the electromagnetic (EM) environment (appUcator), the internal field distribution, E (r), and hence the distribution, P(r), of absorbed power. From this, the... 

FIG. 19-46 Magnetic-field distribution charts, a) Concurrent and counter-current wet drum magnetic separator, 1.2-m diameter, (h) Counterrotation wet drum magnetic separator, 1.2-m diameter. (Coutiesy of Sala International, Inc.)... 

The linear piezoeleetrie model can be used to demonstrate that the magnitude of the electric field encountered for a given polarization function is a sensitive function of the thickness of the sample. This behavior can be demonstrated by noting that the electric displacement at a given time is inversely proportional to the thickness. Thus, the thickness of the sample is an important variable for investigating effects such as conductivity that depend upon the magnitude of the electric field. Conversely, various input stress wave shapes can be used to cause various field distributions at fixed thicknesses. 

In bilayer LEDs the field distribution within the device can be modified and the transport of the carriers can be controlled so that, in principle, higher efficiencies can be achieved. On considering the influence of the field modification, one has to bear in mind that the overall field drop over the whole device is given by the effective voltage divided by the device thickness. If therefore a hole-blocking layer (electron transporting layer) is introduced to a hole-dominated device, then the electron injection and hence the efficiency of the device can be improved due to the electric field enhancement at the interface to the electron-injection contact, but only at expense of the field drop at the interface to the hole injection contact This disadvantage can be partly overcome, if three layer- instead of two layer devices are used, so that ohmic contacts are formed at the interfaces [112]. 

Increasing the electron mobility in the layer near to the electron contact proportionally increases the net injected electron current. The current may not change by exactly the same amount that the mobility is increased by if the density of injected electrons is large enough to change the electric field distribution. 

One of the attractive features of single mode waveguides is their ability to filter the spatial field distribution. All the wavefront aberrations only result in a photometric fluctuation easy to monitor. It results in a very good calibration of the interferometric data as firstly demonstrated by FLUOR, as seen in Fig. 8 (Coude du Foresto et al., 1998). Nevertheless, care has to be taken to keep in mind that turbulence may have a spectral selectivity in the launching pro-... 

Figure 1.3 Field distributions along the Ag-tip surface and corresponding Ag-tip geometry. z = 0 corresponds to the Au-substrate. r/R is the normalized radius from the pointdirectly beneath the tip (R is the Rayleigh length R = /2n). Reprinted with permission from S. Klein, Electrochemistry, 71, 114 (2003). Copyright 2003, The Electrochemical Society of Japan.

Enhanced electric-field distribution is illustrated schematically in Figure 3.8, based on reported electromagnetic simulations, for a dimer of a noble metal spherical nanoparticle. The optical field enhancement at the gap site occurs only when the incident polarization is parallel to the interparticle axis of the dimer. 

Figure 3.8 Schematic view of enhanced field distribution in the vicinity of a dimerof noble metal nanospheres. (Reproduced with permission from The Japan Society of Applied Physics [12]).

To summarize, we have shown here that enhanced electric-field distribution in metal nanoparticle assemblies can be visualized on the nanoscale by a near-field two-photon excitation imaging method. By combining this method and near-field Raman imaging, we have clearly demonstrated that hot spots in noble metal nanoparticle assemblies make a major contribution to surface enhanced Raman scattering. 

Dependence of the electric field distribution in the double layer on particle size [Zhdanov and Kasemo, 2002 Chen and Kucemak, 2004a, b], which, according to Zhdanov and Kasemo, should result in an increase in the rates of electrochemical reactions on nanometer-sized metal particles. 

Once the specific geometry of the medium is known, the Torrey equation can be solved [45-47]. To date, solutions for simple porous structures such as packed cylinders and spheres are not yet available. However, a one-dimensional model of both the magnetic field distribution and the diffusion is particularly useful for being intuitive and for developing the interpretation. 

Yasui et al. [29] have used solution of wave equation based on finite element method for characterization of the acoustic field distribution. A unique feature of the work is that it also considers contribution of the vibrations occurring due to the reactor wall and have evaluated the effect of different types of the reactor walls or in other words the effect of material of construction of the sonochemical reactor. The work has also contributed to the understanding of the dependence of the attenuation coefficient due to the liquid medium on the contribution of the vibrations from the wall. It has been shown that as the attenuation coefficient increases, the influence of the acoustic emission from the vibrating wall becomes smaller and for very low values of the attenuation coefficient, the acoustic field in the reactor is very complex due to the strong acoustic emission from the wall. 

To compute electrostatic potential and field distributions in very complex geometries, this equation, or one of its subsidiaries, can be solved numerically subject to a set of boundary conditions (McAllister et al.,... 

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