The penetration depth

A value for the distance moved during diffusion by a sequence of random jumps can be calculated. It is found that (Section S3.1.1)  

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The standard NF T 65-001 gives a classification for bitumen as a function of their hardness. This is measured using a needle penetrability test, which measures the penetration depth of a weighted needle into the bitumen. Five grades have been defined. 

The detection of residual austenite in fact requires average frequency, however for comparison reasons (reference) with a different recognized method, it is recommended to use high frequency, as with high frequency of eddy currents the penetration depth is comparable in the diffraction method and eddy current method. 

In this case the probe diameter and the slot length are of similar size. The material chosen has penetration depth of 0.7 ram at the given frequency of 16.9 kHz. The slot depth is 7 times larger than the penetration depth. 

Dependence of the penetration depth on materials properties and excitation coil geometry... 

In contrast to the planar wave solution, the penetration depth in case of a coil can be described —besides the dependence on co and a— as a function of the depth z and the coil diameter R ... 

First, the eddy current density is damped while penetrating into the conductor (penetration effect). Here the frequency dependence of the penetration depth implies that for deep lying cracks low frequencies must be used for obtaining a sufficient current density in the vicinity of the crack. Secondly, due to the induction law the induced current density at the surface jco is diminished when using lower frequencies. Therefore, in total, there is a certain excitation frequency which results in a maximum response field from the crack. 

The simulation of the actual distortion of the eddy current flow caused by a crack turns out to be too time consuming with present means. We therefore have developed a simple model for calculating the optimum excitation frequencies for cracks in different depths of arbitrary test sarriples Using Equ. (2.5), we are able to calculate the decrease in eddy current density with increasing depth in the conductor for a given excitation method, taking into account the dependence of the penetration depth c on coil geometry and excitation frequency. 

Illuminating the sample at grazing angles. The penetration depth of photons depends on the cosine of the incidence angle and, therefore, can be reduced by this procedure. Although such an approach has limited use, it has been successfully employed in a few instances, such as for x-ray diffraction experiments. 

In each of these approaches, imaging is confined to the top of a single polymeric film by adjusting optical absorption. The penetration depth of the silylation agent and the attendant swelling of the polymer film must also be controlled to avoid distortion of the silylated image. Resists of this type are capable of very high resolution (Fig. 37). 

The penetration depth of this evanescent field, (defined to be the depth at which the evanescent field decays to 1/ of its original value,) is given... 

The shallow penetration of ion implantation would in itself make it appear useless as a technique for engineering appHcations however, there are several situations involving both physical and chemical properties in which the effect of the implanted ion persists to depths fat greater than the initial implantation range. The thickness of the modified zone can also be extended by combining ion implantation with a deposition technique or if deposition occurs spontaneously during the ion implantation process. In addition, ion implantation at elevated temperatures, but below temperatures at which degradation of mechanical properties could occur, has been shown to increase the penetration depths substantially (5). 

Erequencies from 1 kHz to 50 MHz are used for various appHcations (3). Ferromagnetic materials have a skin-effect response to eddy currents which restricts the penetration depth. Nonferromagnetic materials on the other hand can be inspected to greater depth. In 6061-T6 aluminum, for example, a cod having a 1-kHz frequency effectively penetrates the surface to a depth of 3.2 mm (1). The same probe in steel penetrates to a depth of 0.5... 

Thickness of the laminar layer is deterrnined both by the need to reproduce fine detail in the object and by the penetration depth of the actinic laser light into the monomer bath (21,76). There is thus a trade-off between precision of detail in the model and time required for stereohthography, ie, the number of layers that have to be written, and an optimum Light-absorbing initiator concentration in the monomer bath corresponding to the chosen layer thickness. Titanocene-based initiators, eg, bis-perfluorophenyltitanocene has been recommended for this apphcation (77). Mechanistic aspects of the photochemistry of titanocenes and mechanisms of photoinitiation have been reviewed (76). 

The effectiveness of a porous electrode over a plane surface electrode is given by the product of the active surface area S in cm /mL and the penetration depth Tp of the reaction process into the porous electrode. 

Hardness is determined by measuring the penetration (depth or area) when a harder material, such as diamond, is pushed into the surface of the material of interest under a specified load. Tme hardness is defined as the force divided by the projected area. Vickers hardness tests, which employ a pyramid-shaped indentor, are frequently used to characterize ceramics however, Vickers hardness calculations normally employ total surface area rather than projected area (43). Measurements are made on the diamond impression shown in Figure 6. Vickers hardness is calculated using... 

The lower the value of the more likely it is that S is positive indicating a thermodynamic tendency for the process to occur. Longitudinal wave theory has been appHed to the defoamer spreading process as in equation 5 where P is the penetration depth of a spreading droplet of initial radius R, viscosity Tj, and density p. 

The grounding or penetration depth of the electrical resistance in conductors is, according to Eq. (3-42), dependent on the specific resistance and the frequency. The penetration depth, t, is the distance at which the field strength has fallen by 1/e,- is the relative permeability [35] ... 

Referring to Fig. 23-6, through 3)3 are hereby the average distances of the conductor from the ground x, through X3 are the average distances of the conductor from the pylon axis a is the distance of the affected conductor from the pylon axis, and d is the penetration depth in the soil from ... 

Both XRF and EPMA are used for elemental analysis of thin films. XRF uses a nonfocusing X-ray source, while EPMA uses a focusing electron beam to generate fluorescent X rays. XRF gives information over a large area, up to cm in diameter, while EPMA samples small spots, (om in size. An important use of EPMA is in point-to-point analysis of elemental distribution. Microanalysis on a sub- lm scale can be done with electron microscopes. The penetration depth for an X-ray beam is normally in the 10-(om range, while it is around 1 (om for an electron beam. There is, therefore, also a difference in the depth of material analyzed by XRF and EPMA... 

X-Ray Fluorescence analysis (XRF) is a well-established instrumental technique for quantitative analysis of the composition of solids. It is basically a bulk evaluation method, its analytical depth being determined by the penetration depth of the impinging X-ray radiation and the escape depth of the characteristic fluorescence quanta. Sensitivities in the ppma range are obtained, and the analysis of the emitted radiation is mosdy performed using crystal spectrometers, i.e., by wavelength-dispersive spectroscopy. XRF is applied to a wide range of materials, among them metals, alloys, minerals, and ceramics. 

All three techniques probe 500 A to 1 pm or so in depth for opaque materials, depending on the penetration depth of the incident light. For transparent materials, essentially bulk properties are measured by PL and Modulation Spectroscopy. All three techniques can be performed in ambient atmosphere, since visible light is used both as incident probe and signal. 

At (j> the penetration depth approaches a minimum, particularly for reflective surfaces such as chemi-mechanically polished Si. Total reflection disappears on rough surfaces (Fig. 4.3). Below rj> the penetration depth is in the range of a few nanometers (Fig. 4.4). 

As previously discussed, the JKR theory predicts that the detachment force is independent of the Young s modulus. Yet despite that, when Gady et al. [117] measured the detachment force of polystyrene particles from two elastomeric substrates having Young s moduli of 3.8 and 320 MPa, respectively, they found that the detachment force from only the more compliant substrate agreed with the predicted value. The force needed to separate the particle from the more rigid substrate was about a factor of 20 lower. Estimates of the penetration depth revealed that the particles would penetrate into the more compliant substrate more deeply than the heights of the asperities. Thus, in that case, the spherical particle approximation would be reasonable. On the other hand, the penetration depth... 

As indicated above, the penetration depth is on the order of a micrometer. That means that in ATR, absorption of infrared radiation mostly occurs within a distance 8 of the surface and ATR is not as surface sensitive as some other surface analysis techniques. However, ATR, like all forms of infrared spectroscopy, is very sensitive to functional groups and is a powerful technique for characterizing the surface regions of polymers. 

Fillers (calcium carbonate, calcium sulfate, aluminum oxide, bentonites, wood flour) increase the solid content of the dispersion. They are added up to 50%, based on PVAc. The purpose of the addition is the reduction of the penetration depth, provision of thixotropic behavior of the adhesive, gap filling properties and the reduction of the costs. Disadvantage can be the increase of the white point and a possible higher tool wear. 

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