Critical penetration depth

In many practical situations, it is important to ensure that the sample presented for analysis is sufficiently thick (i. e. thicker than the highest critical penetration depth among the various fluorescent signals being used), so that the observed analytical signals no longer depend on sample thickness but only on analyte concentration. 

Next to the critical penetration depth it is also useful to define a critical thickness below which absorption and enhancement effects can be neglected. For analysis of such thin-fihn samples, the calibration relations of Eq. (8) and (9) are valid and matrix effect corrections need not be applied. By convention, dthi corresponds to the situation where the total attenuation in the sample is equal to 1 %. Table 11.7 lists typical dthm values for various fluorescent line energies in two matrices. 

Table 11.7 Critical penetration depth and thin film thickness of various fluorescent lines in two matrices. (Adapted from [17]).

Energy/Wavelength of K line Element E/keV A/nm Excitation Spectrum Tube anode Critical Penetration Depth dMdJpm Silicate Steel Thin Film Thickness d n/pm Silicate Steel ... 

Table 3 Critical penetration depth and thin film criteria for selected lines in silicate and steel matrices...

Element X-ray fluorescence K-L2 3 (Ka) line X-ray tube Critical penetration depth (pm) Limiting thin film thickness (pm) ... 

Fig. 4.4. Penetration depth z ofX-rays striking silicon at a variable glancing angle d>i. The curves were calculated for three different photon energies. The dashed vertical line signifies the respective critical angle [4.21],...

Fig. 33—Typical scratch curve of Sample 4, Fn is the normal load. Ft is the measured tangential force, Pd is the penetration depth, Rd is the residual depth. The critical load is 86.63 mN.

Figure 33 shows a typical scratch test curve of Sample 4. Both the penetration depth and the residual depth as well as the tangential force can be obtained from this curve. The critical load can be found from the transition stages plotted in the three curves. The critical load (L ) of Sample 4 is 86.63 mN. 

Figure 34 shows the critical load of all the samples. For the monolayer samples, Sample 1 has a higher critical load than Sample 2. The multilayers Samples 4, 5, and 6 have higher critical loads than monolayer Samples 1 and 2. Samples 5 and 6 have excellent scratch resistant properties. Only extremely small cracks are found in the scratch tracks of Samples 5 and 6. Therefore, there is no sudden change found in the force and penetration depth curves. Sample 7 has the lowest critical load, similar to the monolayer Sample 2. 

The terms in Eq. (6) include the gravitational constant, g, the tube radius, R, the fluid viscosity, p, the solute concentration in the donor phase, C0, and the penetration depth, The density difference between the solution and solvent (ps - p0) is critical to the calculation of a. Thus, this method is dependent upon accurate measurement of density values and close temperature control, particularly when C0 represents a dilute solution. This method has been shown to be sensitive to different diffusion coefficients for various ionic species of citrate and phosphate [5], The variability of this method in terms of the coefficient of variation ranged from 19% for glycine to 2.9% for ortho-aminobenzoic acid. 

The tuneable nature of the evanescent field penetration depth is critical to the effective operation of this sensor as it facilitates surface-specific excitation of fluorescence. This means that only those fluorophores attached to the surface via the antibody-antigen-labelled antibody recognition event... 

The cylindrical reactor-applicator has steel wall with thickness dose to 30 mm. This thickness permits to reach internal pressures above 30 Mpa. These operating pressure conditions are above the critical point of water. The internal diameter of the reactor is 50 mm and its length is 500 mm. The system is powered simultaneously with two 6-kW generators placed at the both ends of the reactor. This simultaneous supply is necessary to overcome the penetration depth within water. 

The penetration depth of waves is defined as the distance from the surface of the material at which the power drops to 1 /e from its value at the surface. The penetration depth of microwaves is equal to 15 mm for water at 20 °C. The electromagnetic energy transfer is ensured by matched alumina windows. The propagated mode within the reactor is theoretically the TEn mode. The interest of this system is to make very specific chemical reaction such as oxidation in aqueous medium under critical conditions. 

In the case of nonrelativistic laser intensity, linear theory does not allow propagation in overdense plasmas, namely when to 1 < iop(. = e(An/rn,.) 2n,J 2. In the extreme case of ultra-relativistic laser intensity (ao 2> 1), the cutoff frequency for propagation drops from u pe down to wpe/(l Tag)1/4 [11], where ao = eA/mec is the dimensionless amplitude of the laser field. Then, in order for the propagation to occur at plasma density appreciably higher than the ordinary critical density, ao 2> 1 is needed. This is also the case of overdense thin plasma layers (as proved by simulation [12]) whose thickness exceeds the skin penetration depth of the e.m. wave. Theoretical background and basic... 

On the other hand, it must be kept in mind that a number of critical issues are linked with the application of microwave in chemical scale-up (Ondruschka et al. 2004). Firstly, penetration depth of microwaves in... 

Image analysis for bimodal distributions is more complicated. With the classical method, the determination of the penetration depth, t, is critical, as one does not know whether to take the value of the larger or the smaller pores, or an intermediate one. 

Quantitative simulation of spectra as outlined above is complicated for particle films. The material within the volume probed by the evanescent field is heterogeneous, composed of solvent entrapped in the void space, support material, and active catalyst, for example a metal. If the particles involved are considerably smaller than the penetration depth of the IR radiation, the radiation probes an effective medium. Still, in such a situation the formalism outlined above can be applied. The challenge is associated with the determination of the effective optical constants of the composite layer. Effective medium theories have been developed, such as Maxwell-Garnett 61, Bruggeman 62, and other effective medium theories 63, which predict the optical constants of a composite layer. Such theories were applied to metal-particle thin films on IREs to predict enhanced IR absorption within such films. The results were in qualitative agreement with experiment 30. However, quantitative results of these theories depend not only on the bulk optical constants of the materials (which in most cases are known precisely), but also critically on the size and shape (aspect ratio) of the metal particles and the distance between them. Accurate information of this kind is seldom available for powder catalysts. 

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