Infinite thickness

It may be seen from equation 7 that even if the wall of an initially stiess-fiee cylindei is infinitely thick, k = oo, the yield pressure cannot exceed T. ... 

Brown and Marco, Schack, and Stoever (see Tnlroducdion General References ). For a solid of infinite thickness (Fig. 5-5) and with m = 0,... 

FIG. 5-5 Heating and cooling of a solid of infinite thickness, neglecting edge effects. (This may he used as an approximation in the zone near the surface of a body of finite thickness.)... 

The evaluation of the various XRF measurements will be discussed for different effects in EDXRS the spectra evaluation is perfonned by different programs with varying assumptions, partially different mass attenuation coefficients are used, the calibration procedures are principally different (e.g., thin foils with given thickness, or, infinitely thick samples), measurement under atmospheric pressure or in vacuum, secondary excitation (enhancement) mainly of Al by Si radiation. 

When electrons strike an infinitely thick target, they are quickly slowed as they interact with the atoms of the target. Consequently, they do not penetrate at all deeply.12 Furthermore, different electrons... 

The region of greater practical importance, the region of 4 infinite thickness, is characterized by a horizontal line in Figure 6-4. This line is the upper limit of a curve the form of which is determined in part by the mass absorption coefficients of the element for the incident, and for the emergent x-ray beam. If the sample contains elements other than E, the mass absorption coefficients of these other elements will similarly help determine the intensity I s of the analytical line at infinite thickness of sample. 

The transition of the previous paragraph can be extended to include infinitely thick samples, the most common situation in x-ray emission spectrography. To determine composition, it is well to work with such... 

The discussion preceding Equation 7-5 points to the weight-fraction as the logical unit for the x-ray emission spectrography of infinitely thick samples. Were all complications absent, one might expect proportionality between analytical-line intensity and weight-fraction such that... 

At a temperature such that the solid phase is stable AF is necessarily positive and the stable crystal has infinite thickness. However, any crystal which has AG < 0 will be stable compared with the liquid, so that a crystal of finite thickness may be metastable if there is a free energy barrier to the formation of an infinite crystal. AG < 0 if ... 

The multilayer grows to infinite thickness at saturation pressure (P = Pq). 

This simple relationship between incident and transmitted light is well known as the Boguert-Lambert-Beer law. This expression renders positive values for Ij < Iq. In case of scattering material like TLC plates, a part of the scattered light is emitted as reflectance J from the plate surface to the top. For the hrst approximation of a parallel incident light beam with the intensity /g, some radiation may be scattered inside the layer and some radiation may be absorbed either by the sample or by the layer itself. According to the Schuster equations and with the abbreviation R (the diffuse reflectance of an infinitely thick layer). 

If the X-rays reflected from a large sample are detected and the sample is thicker than 3/jU, the assumption of infinite thickness is justified. Then the equation for the intensity It transmitted into the detector enjoys peculiar simplicity, because it is only a function of the effective irradiated volume... 

The Kubelka-Munk theory treats the diffuse reflectance of infinitely thick opaque layers [4], a situation achieved in practice for UV/VIS spectroscopy through the use of powder path lengths of at least several millimeters. In this instance, the Kubelka-Munk equation has the form... 

Figure 1. Flow net representing groundwater circulation near a river which intercepts homogeneous and isotropic aquifer of infinite thickness.

Derived from an analytical model for flat, infinitely thick liquid layer Effects of gas compressibility included Effects of gas/liquid ratio, liquid viscosity, and nozzle geometry not included X and Xm can be determined from the universal curves for metals in P29] for subsonic gas flow and in [330] for sonic/supersonic gas flow ... 

In the limit of a semi-infinite (thick) porous electrode with no gas-phase diffusion limitations, the chemical term Zhem reduces to an impedance reflecting co-limitation by oxygen absorption and transport. ... 

Spectra of solid samples are usually recorded in the units of reflectance (R) or percent reflectance (%/ ), which is analogous to percent transmittance in that reflectance equals the ratio of the reflected radiation to the incident radiation. With diffuse reflectance, the reflected signal is attenuated by two phenomena absorption (coefficient k) and scattering (coefficient s). Lollowing the Kubelka-Munk theory, these two coefficients are related to the reflectance of an infinitely thick sample, by... 

The simplest analytical solution assumes that the contact time is very short and the following assumptions are reasonable (a) the film moves with a flat velocity profile v0 (see Fig. 4a) (b) the film may be taken to be infinitely thick with respect to the penetration of the absorbed material and (c) the concentration at the interface x = 0 is cA0. The analytical... 

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