Thickness broadening

The relative absorption depth of the Mossbauer line is determined by the product of the recoU-free fraction/s of the Mossbauer source and the fractional absorption z t) of the sample, abs = fs-e f), where c(t) is a zeroth-order Bessel function ((2.32) and Fig. 2.8). Since c(t) increases Unearly for small values of t, the thin absorber approximation, c(t) t/2, holds up to t 1. On the other hand, values as small as t = 0.2 may cause already appreciable thickness broadening of the Mossbauer lines, according to (2.31), Fexp + 0.135t). In practice, therefore the sample... 

One can also infer in turn from these arguments that the relative absorption depth of a Mossbauer line should not exceed 10-15%, because of the increasing thickness broadening and the related line distortions. 

It is difficult to give an exact limit because the impact of thickness broadening depends on the intrinsic width of experimental lines [31], which often exceeds the natural width 2r at by 0.05—0.1 mm s for Fe as studied in inorganic chemistry. This inhomogeneous broadening, which is due to heterogeneity and strain in the sample, causes a reduction of the effective thickness. Rancourt et ai. have treated this feature in detail for iron minerals [32]. 

The comparison of the results of very different methods has to be judged very precisely, as, e.g., the given thickness of a layer is a function of the limit of detection (EOD) of a method. Additionally, the detected areas vary from about 0.01 up to about 400 mm-. Therefore, the methods with a low level of detection and with a high sensitivity (high slope of the calibration function) give a higher value for the layer thickness. Furthermore, the layers are broadened with time by diffusion. 

The phenomena of beam broadening as a function of specimen thickness are illustrated in Fig. 4.20 each figure represents 200 electron trajectories in silicon calculated by Monte Carlo simulations [4.91, 4.95-4.97] for 100-keV primary energy, where an infinitesimally small electron probe is assumed to enter the surface. In massive Si the electrons suffer a large number of elastic and inelastic interactions during their paths through the material, until they are finally completely stopped. The resulting penetration depth of the electrons is approximately 50 pm and in the... 

Fig. 4.20. Comparison of beam broadening in Si as a function of thickness for 100 keV primary electron energy (A) bulk specimen, (B) 200 nm, (C) 50 nm thickness.

The main factor in causing filiform corrosion is the relative humidity of the atmosphere, and if this is below 65% (the critical relative humidity for the atmospheric corrosion of most metals, see Section 2.2) it will not occur. As the relative humidity increases the thickness of the filaments increases at 65-80% relative humidity they are very thin, at 80-95% relative humidity they are much wider and at approximately 95% relative humidity they broaden sufficiehtly to form blisters. 

GC peak broadening Thick film column is used. Thick film should... 

A vertical CVD reactor (cf. Figure lb) consists of an axlsymmetrlc enclosure with the deposition surface perpendicular to the Incoming gas stream. The reactant gases are typically Introduced at the top and fiow down towards the heated susceptor. Thus, the least dense gas Is closest to the growth Interface which destabilizes the fiow. The result Is recirculation cells which Introduce not only film thickness and composition variations but also broaden Junctions between layers. This Is particularly of... 

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])...

Although Lorentzian line shapes should be strictly expected only for Mossbauer spectra of thin absorbers with effective thickness t small compared to unity, Margulies and Ehrman have shown [9] that the approximation holds reasonably well for moderately thick absorbers also, albeit the line widths are increased, depending on the value of t (Fig. 2.7). The line broadening is approximately... 

Conclusions. A Mossbauer sample with a low content of the resonance nuclide has ideal thickness when it attenuates the incident radiation by ca. 63-85% (/ie t = 1-2, C /Co e - e ). However, the optimization should be subordinated to the requirement of a thin absorber having an effective thickness / < 1 to avoid excessive line broadening. 

Fig. 9.3 Mossbauer spectra (A q = 2 mm s ) in the energy domain and in the time domain. High effective thickness t ff appears in the energy domain as line broadening and in the time domain as dynamical beats which are superimposed over the quantum beats. (Taken from [7])...

The phase-transition temperature, 7 , and the width of transition, A7j/2, were operationally defined based on EPR data, as shown in Figure 10.6a. As a rule, in the presence of polar carotenoids the phase transition broadens and shifts to lower temperatures (Subczynski et al. 1993, Wisniewska et al. 2006). The effects on Tm are the strongest for dipolar carotenoids, significantly weaker for monopolar carotenoids, and negligible for nonpolar carotenoids. The effects decrease with the increase of membrane thickness. Additionally, the difference between dipolar and monopolar carotenoids decreases for thicker membranes (Subczynski and Wisniewska 1998, Wisniewska et al. 2006). These effects for lutein, P-cryptoxanthin, and P-carotene are illustrated in Figure 10.6b... 

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