Absorber thickness

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... 

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... 

Particularly for thin Mossbauer absorbers with a low concentration of the resonance nuclide and high mass absorption, it may be problematic to apply the recommendation for sample preparation (f 0.2), because the resulting electronic absorption may be prohibitively high. In such a case, it may pay well to optimize the absorber thickness, i.e., the area density f. To this end, following the approach of Long et al. [33], we adopt the general expression ... 

The derivation of the expressions (3.3)-(3.6) is found in Appendix A (cf. CD-ROM). Since for most Fe-spectra the level of nonresonant background counts, Ab, may be in the range of 10-30% of the total counts, the absorber thickness is usually best adjusted to a value between the limits given above. The maximum of SNR( ) is naturally rather broad, such that deviations from / opt of even dz50% are fairly immaterial. 

Potzel et al. [60] used a Ga/ZnO single crystal source in combination with a single crystal absorber of natural ZnO and observed a resonance line width of 0.36 0.04 pm s for the 93.3 keV transition in Zn (at 4.2 K). This, after correction for finite absorber thickness, equals, within the limit of error, the minimum observable line width as deduced from the lifetime of 13.4 ps for the 93.3 keV state. The spectra observed by these authors are shown in Fig. 7.23. 

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.

Mossbauer spectroscopy with started only in 1965, when Harris et al. [322] measured the Mossbauer absorption spectra of the 99 keV transition of Pt in platinum metal as a function of temperature (between 20 and 100 K) and of absorber thickness and derived the temperature dependence of the Debye-Waller factor. 

Data from extrapolation to zero absorber thickness... 

Since natural Au consists solely of Au, the interface-selective enrichment technique cannot be applied in Au studies. The absorber thickness for Au is required to be large and therefore multilayered samples of Au layers/3r/ metal layers have to be prepared. The spectra for Au/Fe with varying Au-layer thickness are shown in Fig. 7.83 [437]. The results were interpreted as follows large magnetic hyperfine fields at Au sites exist only within two monolayers at the interface region, which are supposed to be induced by direct coupling with anti-ferromagnetically oriented Fe 3d atoms. 

Dilute alloys of Au with Fe, Co, Ni Au nuclear data, line width as function of absorber thickness... 

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 ... 

Let us now discuss some recent work by Sano and myself on completely characterizing barium stannate, a material first proposed by Plotnikova, Mitrofanov, and Shpinel (21), as a source for tin Mossbauer spectroscopy. It is easily prepared, is a stoichiometric compound and has all the properties one desires in a Mossbauer matrix. The recoil-free fraction at room temperature is about 0.55 with about a 10% error. The line width extrapolated to zero absorber thickness is about 6% larger than natural—i.e., the line width observed is ca. 0.318 mm./sec. at zero ab-... 

Figure 4. Electric quadrupole spectrum of Te in pure Te at 4.8°K. Source, in Cu at 82°K. Total absorber thickness, 30.0 mg./sq. cm. of tellurium enriched in Te—i.e., Te/Te = 40.4%. Individual lines (A this doublet have a full width at half maximum of 0./3 cm./sec. Our experimental line widths for absorbers vary from 0.67-101 cm./sec.

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 formula for the self-absorption factor is exact for gamma rays (see Experiment 3) but approximate for beta particles. That it is applicable at all is due to the near-linear decrease of the logarithm of the count rate with absorber thickness of a beta-particle group (see Figure 2.6 in the Radioanalytical Chemistry textbook). The obvious deviation is that this relation ends at the range of the maximum-energy beta particle, whereas it continues indefinitely for gamma rays. 

The efficiency for backside illumination (bi-facial cells) is limited because the carriers are generated outside the field zone in proximity to the poorly passivated contact (poor blue response). Further optimization of absorber thickness, diffusion length, and contact passivation appears to be feasible. 

The standard molybdenum contact is characterized by low optical reflection, which becomes relevant in efforts to reduce the absorber thickness (light trapping). A study of other metals has not identified clearly promising alternatives [78], Hence, an ohmic contact between TCO and chalcopyrite with good electrical and optical properties could also be useful in developing a cell with a high reflectivity metal/TCO back contact. 

The c.w. dye laser can also be passively mode-locked and two different arrangements have been used. The first employed two free flowing dye streams, one for the laser dye and the other for the absorber (see Fig. 4) [18, 19]. In the alternative arrangement, the saturable absorber dye flows in a narrow channel of variable thickness (0.2—0.5mm) and in contact with a 100% broadband reflectivity mirror. With an absorber thickness of 0.5 mm, output pulses of 1 ps duration have been obtained [20]. Pulses as short as 0.3ps were produced when the DODCI cell length was shortened to 0.2 mm. The subpicosecond pulses produced in this arrangement were transform-limited in bandwidth. 

Polyimide surface modification by a wet chemical process is described. Poly(pyromellitic dianhydride-oxydianiline) (PMDA-ODA) and poly(bisphenyl dianhydride-para-phenylenediamine) (BPDA-PDA) polyimide film surfaces are initially modified with KOH aqueous solution. These modified surfaces are further treated with aqueous HC1 solution to protonate the ionic molecules. Modified surfaces are identified with X-ray photoelectron spectroscopy (XPS), external reflectance infrared (ER IR) spectroscopy, gravimetric analysis, contact angle and thickness measurement. Initial reaction with KOH transforms the polyimide surface to a potassium polyamate surface. The reaction of the polyamate surface with HC1 yields a polyamic acid surface. Upon curing the modified surface, the starting polyimide surface is produced. The depth of modification, which is measured by a method using an absorbance-thickness relationship established with ellipsometry and ER IR, is controlled by the KOH reaction temperature and the reaction time. Surface topography and film thickness can be maintained while a strong polyimide-polyimide adhesion is achieved. Relationship between surface structure and adhesion is discussed. 

Polyimide surface modification with KOH or NaOH aqueous solution is well defined. The reaction initially gives potassium or sodium polyamate which is then protonated with acid to yield polyamic acid. The outermost layer (5 A) of PMDA-ODA can be completely modified within a minute of reaction in KOH solution. The depth of modification can be measured by a method using an absorbance-thickness relationship established with ellipsometry and external reflectance IR. The modification depth of PMDA-ODA treated with 1 M KOH aqueous solution at 22 °C for 10 min is approximately 230 A. Surface topography and film thickness can be maintained while a strong... 

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