Relative absorption depth

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. 

Another useful parameter in discussing the propagation of radiation into the surface region of a highly absorbing material is the optical skin depth. This is defined as the distance z into a material at which the ratio of transmitted intensity to incident intensity eqnals a value of He. Thus the optical skin depth can be defined as the reciprocal of the absorption coefficient and is useful in discussing relative penetration depths in different materials. For example, the optical skin depth of silver at an... 

Fig. 4 A Schematic cross section of metal film growth and corresponding scanning electron micrographs (below) of the gold nanocavities fabricated with a = 350 nm latex spheres of thickness t for (a) ajl, (b) a, and (c) 2.1a [91]. B Measured energy dispersion of the reflectivity for TM polarized light as a function of the in-plane wave vector for increasing relative void depth, i=t/(2a) (a-c). Log color scale white dotted lines show a zone-folded plasmon dispersion, sample orientations of 4> = 30° in all cases, (i-iv) k space cuts through dispersion relation at (i) (i,E) = (0.25,2.2 eV) (ii) (i,E) = (0.4,2.2 eV) (in) (i,E) = (0.4,1.7 eV) (iv) (f, ) = (0.6,2.2 eV), symmetry shown above (i). Light shade corresponds to absorption features [93]...

Comparing curves 1 -6 in Fig. 2.34a, one can see that at the medium-substrate interface, the reflectances Ros and Rop decrease relative to those at the air-substrate interface and reach a minimum for the interface systems with the least difference between n and ns. At the same time, the absorption depths AR and AR (SNR) increase (Fig. 2.347>), and their maximum value for p-polarized radiation is reached at when the difference between ny and ns is at a min-... 

Measurement of the reflectivity AR/R from experimental spectra of thin dielectric layers on metals is complicated by the fact that if the absorption depth AR is taken as the band intensity then the experimental values of reflectivity, (AR// )exp will differ from the calculated values of AR/R. The reasons are the following. First, the band wings are distorted by the presence of the layer, effectively causing a shift of the spectral baseline relative to the reflectance of the bare... 

Figure 4. Theoretical curves (lines) fitted to experimental Bi 876 nm data (points) for (a) absorption, (b) Faraday rotation at 0.18 G, and (c) PNC rotation at relative optical depths of 1, 1, and 10, respectively. The theoretical curves for Faraday and PNC take into account dilution by off-mode laser light.

One of the main parameters of a resonance curve is its position on the velocity axis. In Figure 8.5a, a resonance curve is presented schematically when the emitter and absorber are one and the same motionless substance the maximum of absorption falls on the zero value of relative velocity. Intensity of absorption (depth of curve minimum) is proportional to the probability of the resonance absorption, / So, such measurements enable the measurement of a change in the atomic mobility in a sample under different treatments... 

ESR characterization was performed in situ in order to avoid any contact of the pretreated solids with air. Spectra, recorded as the first derivative of the absorption, were obtained at room temperature or 77K using a Varian E9 spectrometer working in the X band. The g values were measured relative to a DPPH reference (g = 2.0036). The sample tubes were filled with the solid to a height greater than the depth of the resonant cavity and the number of paramagnetic species was calculated by double integration of the recorded spectra normalized to that of Varian Strong Pitch sample (g = 2.0028, 3. lO spins, cm" ). 

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... 

From this equation it can be seen that the depth of penetration depends on the angle of incidence of the infrared radiation, the refractive indices of the ATR element and the sample, and the wavelength of the radiation. As a consequence of lower penetration at higher wavenumber (shorter wavelength), bands are relatively weaker compared to a transmission spectrum, but surface specificity is higher. It has to be kept in mind that the refractive index of a medium may change in the vicinity of an absorption band. This is especially the case for strong bands for which this variation (anomalous dispersion) can distort the band shape and shift the peak maxima, but mathematical models can be applied that correct for this effect, and these are made available as software commands by some instrument manufacturers. 

The depth-profile of photon absorption is analogous to that for UV-visible light, i.e. I = Io exp(-Ad), where the mass energy absorption coefficient, u/g is used instead of the extinction coefficient. Particulate energy absorption can be described by relative stopping powers. 

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