Doppler velocity

In an actual Mdssbauer transmission experiment, the radioactive source is periodically moved with controlled velocities, +u toward and —d away from the absorber (cf. Fig. 2.6). The motion modulates the energy of the y-photons arriving at the absorber because of the Doppler effect Ey = Eq + d/c). Alternatively, the sample may be moved with the source remaining fixed. The transmitted y-rays are detected with a y-counter and recorded as a function of the Doppler velocity, which yields the Mdssbauer spectrum, r(u). The amount of resonant nuclear y-absorption is determined by the overlap of the shifted emission line and the absorption line, such that greater overlap yields less transmission maximum resonance occurs at complete overlap of emission and absorption lines. 

We are interested in the transmission of y-quanta through the absorber as a function of the Doppler velocity. The radiation is attenuated by resonant absorption, in as much as emission and absorption lines are overlapping, but also by mass absorption due to photo effect and Compton scattering. Therefore, the number Tt E2)AE of recoilless y-quanta with energies EXo E + AE traversing the absorber is given by... 

The calibration procedure is sufficiently accurate for Doppler velocities in the regime 0 to 10 mm s beyond this range, laser calibration is more suitable. Calibration with ot-iron, as described, can also be used for Mossbauer measurements with other isotopes, e.g., Ni, Au, and Ir, for which suitable standard absorbers are not available (provided that the Doppler velocity range of interest is not significantly greater than 10 mm s ). This, of course, requires that the spectrometer is temporarily equipped with a Co source and an a-iron absorber. 

Fig. 3.19 Schematic illustration of the measurement geometry for Mossbauer spectrometers. In transmission geometry, the absorber (sample) is between the nuclear source of 14.4 keV y-rays (normally Co/Rh) and the detector. The peaks are negative features and the absorber should be thin with respect to absorption of the y-rays to minimize nonlinear effects. In emission (backscatter) Mossbauer spectroscopy, the radiation source and detector are on the same side of the sample. The peaks are positive features, corresponding to recoilless emission of 14.4 keV y-rays and conversion X-rays and electrons. For both measurement geometries Mossbauer spectra are counts per channel as a function of the Doppler velocity (normally in units of mm s relative to the mid-point of the spectrum of a-Fe in the case of Fe Mossbauer spectroscopy). MIMOS II operates in backscattering geometry circle), but the internal reference channel works in transmission mode...

The isomer shift of a resonance line (or the centroid of a line multiplet) in an experimental Mossbauer spectrum in terms of the Doppler velocity (mm s ) necessary to achieve resonance absorption is given by... 

In 1971, Walcher [326] succeeded in observing a resonance effect of about 0.6% in as a function of the Doppler velocity using a TI2O3 source and an enriched (81% ° Hg) HgO absorber at 4.2 K. The half-width turned out to be Fexp = 76 (10) mm s corresponding to a lower limit of the half-life of fi/2 > 0.1 ns. It is clear that the properties of the ° Hg Mossbauer isotope do not render it an interesting isotope from a chemical point of view. 

According to (4.22)-(4.24), the isomer shift is given in terms of Doppler velocity... 

Conversion of Doppler velocity into y-energy increments ... 

Fig. 1. Model Spectra re-binned to CRIRES Resolution To demonstrate the potential for precise isotopic abundance determination two representative sample absorption spectra, normalized to unity, are shown. They result from a radiative transfer calculation using a hydrostatic MARCS model atmosphere for 3400 K. MARCS stands for Model Atmosphere in a Radiative Convective Scheme the methodology is described in detail e.g. in [1] and references therein. The models are calculated with a spectral bin size corresponding to a Doppler velocity of 1 They are re-binned to the nominal CRIRES resolution (3 p), which even for the slowest rotators is sufficient to resolve absorption lines. The spectral range covers ss of the CRIRES detector-array and has been centered at the band-head of a 29 Si16 O overtone transition at 4029 nm. In both spectra the band-head is clearly visible between the forest of well-separated low- and high-j transitions of the common isotope. The lower spectrum is based on the telluric ratio of the isotopes 28Si/29Si/30Si (92.23 4.67 3.10) whereas the upper spectrum, offset by 0.4 in y-direction, has been calculated for a ratio of 96.00 2.00 2.00.

In order to detect shifts and splitting in the nuclear levels due to hyperfine interactions in iron, one needs an energy range of at most 5 10-8 eV around E0, which is achieved with Doppler velocities in the range of-10 to +10 mm/s. 

To extend the integration time further, it is necessary to introduce acceleration into the target s motion model. The range to the target should now be expressed as r = ra + vat + a0t2/2. The matched filter concept now leads to the three-dimensional range-Doppler-velocity... 

Liu et aU622] used a laser Doppler velocity and size (LDVS) measurement technique to determine the local size, velocity, and number flow density of droplets in the spray cone during spray deposition of a liquid steel. The experimental setup is schematically depicted in Fig. 6.7.1615] The measured results showed that smaller... 

Figure 12, in which the calibration constant, k, in mm./sec. channel, is shown as a function of the analyzer address. In this manner the linearity of the velocity scale can be readily determined over the range of Doppler velocities of interest in most iron and tin Mossbauer experiments.]... 

DOVAP Doppler Velocity and Position DST daylight saving time... 

Figure 27-12 Mossbauer spectrum of cyclooctatetraene iron tricarbonyl in octane at 78°K. Notice that a spread of Doppler velocities of about 3 mm sec-1 is enough to give the full spectrum. (Courtesy of Professor R. C. D. Breslow and the Journal of the American Chemical Society.)...

A Mossbauer spectrum that has helped to corroborate the structure of cyclooctatetraene iron tricarbonyl is shown in Figure 27-12. The separation of the two absorption peaks in Figure 27-12 corresponds to a sample Doppler velocity of 1.23 mm sec-1. This Doppler effect means that there is the very small energy difference of 1.4 X 10 6 kcal mole 1 in the two transitions shown. 

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