Absorber thickness, effective

Fig. 2.7 Dependence of the experimental line width Cexp on the effective absorber thickness t for Lorentzian lines and inhomogenously broadened lines with quasi-Gaussian shape (from [9])...

Fig. 2.8 (a) Fractional absorption of a Mossbauer absorption line as function of the effective absorber thickness t. (b) The depth of the spectrum is determined by fs. The width for thin absorbers, t 1, is twice the natural line width F of the separate emission and absorption lines (see (2.30)). AE is the shift of the absorption line relative to the emission line due to chemical influence... 

Nuclear resonance absorption for the 136 keV transition has been established by Steiner et al. [174]. The authors used a metal source and an absorber of metallic tantalum to determine the mean lifetime of the 136 keV level from the experimental line width ( 52.5 mm s for zero effective absorber thickness) and found a value of 55 ps. This has been the only report so far on the use of the 136 keV excited state of Ta for Mossbauer experiments. 

Table 7.8 Summary of results obtained for the four Os Mossbauer transitions studied. The absorber thickness d refers to the amount of the resonant isotope per unit area. The estimates of the effective absorber thickness t are based on Debye-Waller factors / for an assumed Debye temperature of 0 = 400 K. For comparison with the full experimental line widths at half maximum, Texp, we give the minimum observable width = 2 S/t as calculated from lifetime data.

Long GL, Cranshaw TE, Longworth G (1983) The ideal Mossbauer effect absorber thickness. Moss Effect RefData 16 42-49... 

G.J. Long, T.E. Cranshaw, G. Longwoith, The ideal Mossbauer effect absorber thicknesses. Mdssbauer Eff. Ref. Data J. 6, 42-49 (1983)... 

K effective absorber thickness Ap(0) difference of p(0) between source and... 

It was stated in the preceding section that 2 is a suitable choice of effective absorber thickness. Table 4 presents the needed area density of the lanthanide (in natural isotopic abundance) or the actinide for different measuring temperatures and various Debye temperatures. For intermetallic compounds 0 200 K is a good guess. A typical Mossbauer absorber covers an area of 2-4 cm. For most cases about 0.5 g of material suffices. As said before, powder samples are fine, single crystals are not necessary. 

Transmission, by collimator in x-ray optical system, 113 of x-rays by windows, 45 Transmittance of x-rays, as function of absorber thickness, 11 Transmitted beam, components, 18 Tubes, x-ray, see X-ray tubes Tungstate solutions, absorption effects in, 168-170... 

Au (metal) Resonance effect as function of absorber thickness, isomer shift, Debye temperature of source and absorber... 

If we express the effective thickness t for the resonant absorption in terms of the total absorber thickness t in g cm, a nuclear absorption coefficient can be defined in cm g such that = t. The signal amplitude is then given by ... 

Figure 17.6 Intensity distribution or attenuation curve is shown as a function of absorber thickness for a typical energetic heavy ion penetrating into a metal. The effect of range straggling is indicated by the Gaussian distribution of ranges. (From Leo, 1987.)...

The effective film thickness parameters, dely and dellx are proportional to n2, while deIIz is proportional to l/n23 (2). Therefore, measured absorbances in submonolayer coverage may not be expected to vary linearly with the surface coverage. The reader is referred to reference 1 for more detailed discussion. 

Effect of Thickness of Adsorbing Film. Earlier studies of effect of film thickness (3) indicated that the trend between graphite film thickness and amount of benzalkonium adsorbed was small, from about 2 to 4 fig. benzalkonium per cm.2 for variation from 200 to 1000 fig. graphite per cm.2. The analyses by chemical methods for heparin adsorbed were not precise enough to show any trend. Chemical analysis did show that from 1.5 to 7.5 fig. of heparin was absorbed on from 400 to 1000 fig. of PVPyr per cm.2, but the range of heparin was so great at each PVPyr level that no clear trend could be seen. More recent autoradiographic studies with each kind of film indicate that for brief exposures to heparin solution in distilled water there is indeed a trend for more heparin to be adsorbed on thicker films of either kind. 

As mentioned above, gases frequently absorb only in narrow wavelength bands, as indicated for water vapor in Fig. 8-33. These curves also indicate the effect of thickness of the gas layer on monochromatic absorptivity. 

How important is this effect for micas It is apparent from calculations presented by Rancourt (1989) and data in Hargraves et al. (1990) that small spectral contributions are always overestimated when thickness effects are considered. This conclusion has considerable implications for Mossbauer spectra of micas because the Fe peaks are often small relative to those of Fe, and therefore vulnerable to exaggeration by thickness effects. For example, consider a sample with an average value (for micas, cf Rancourt et al. 1994a) off= 0.5, and an ideal absorber thickness of 3.3 x 10 Fe/cm. If a doublet in this sample has an area of 10% of the total area, then its true area when corrected for thickness is 7% (see Fig. 5 in Rancourt 1989). An apparent area of 30% would have a true area of 26%, and so on. These error estimates are only approximations, as they apply to fits using Lorentzian lines that are well-separated the problems are aggravated in situations where peak overlap occurs (as is frequently the case with micas ). 

Fig. 3.7 Curves illustrating the changes in the relative intensity of two hyperfine lines caused by saturation effects (a) with change in recoilless fraction, (b) with change in absorber thickness.

The latter gave only a weak effect, although it could be enhanced by conversion to a gold amalgam. All subsequent work has used the platinum matrix. The appropriate decay schemes are shown in Fig. 16.27. Estimates of the excited-state half-life made by extrapolating the linewidth of a Pt/Pt source and a gold-foil absorber to zero absorber thickness, are = 1-93(10) ns [89] and 1-892(14) ns [19]. 

If effective absorbance and photothermal conversion efficiency are independent on the fluence, absorbed energy should be proportional to the latter and the slopes can be discussed simply in terms of thermal expansion coefficient of polymer Aims. The coefficient of linear expansion of rubber and glass states, ttg and Of, below and above glass-rubber transition temperature (Tg) of PMMA is (2.5-2.7) X 10- K and (5.6-5.S) X W K , respectively 3S). We consider that the one-dimensional expansion is induced along the perpendicular direction to the film, since polymer film outside the area irradiated by the excimer laser is of course hard. Then, the volume expansion could be replaced by the linear one along the thickness, so that corresponds to the change in the slope below... 

The shift in activation spectrum with thickness of an aromatic polymer exposed to solar radiation demonstrates the importance of testing these materials in the form in which they will be used in practice. The type of ultraviolet absorber required to screen the harmful wavelengths and its effectiveness will differ with the thickness of the aromatic-type polymeric tested. Due to differences among different types of polymeric materials in the effect of thickness on their wavelength sensitivities, the form in which they are tested can change their stability ranking. 

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