Recoil temperature dependence

The recoil-free fraction depends on the oxidation state, the spin state, and the elastic bonds of the Mossbauer atom. Therefore, a temperature-dependent transition of the valence state, a spin transition, or a phase change of a particular compound or material may be easily detected as a change in the slope, a kink, or a step in the temperature dependence of In f T). However, in fits of experimental Mossbauer intensities, the values of 0 and Meff are often strongly covariant, as one may expect from a comparison of the traces shown in Fig. 2.5b. In this situation, valuable constraints can be obtained from corresponding fits of the temperature dependence of the second-order-Doppler shift of the Mossbauer spectra, which can be described by using a similar approach. The formalism is given in Sect. 4.2.3 on the temperature dependence of the isomer shift. 

The temperature dependence of sod is related to that of the recoil-free fraction /(T) = Qxp[— x )Ey / Hc) ], where (x ) is the mean square displacement (2.14). Both quantities, (x ) and can be derived from the Debye model for the energy distribution of phonons in a solid (see Sect. 2.4). The second-order Doppler shift is thereby given as [20]... 

Thus making samples not too thick helps in getting sharper spectra and facilitates the quantitative interpretation. Finally, particularly in the Mossbauer spectra of small catalyst particles, one should be aware of the temperature dependence of the absorption area through the recoil-free fraction. If the spectrum contains contributions from surface and bulk phases, the intensity of the former will be greatly underestimated if the spectrum is measured at room temperature. The only way to obtain reliable concentrations of surface and bulk phases is to determine their spectral contributions as a function of temperature and make an extrapolation to zero Kelvin [13]. 

The Mossbauer effect involves the resonance fluorescence of nuclear gamma radiation and can be observed during recoilless emission and absorption of radiation in solids. It can be exploited as a spectroscopic method by observing chemically dependent hyperfine interactions. The recent determination of the nuclear radius term in the isomer shift equation for shows that the isomer shift becomes more positive with increasing s electron density at the nucleus. Detailed studies of the temperature dependence of the recoil-free fraction in and labeled Sn/ show that the characteristic Mossbauer temperatures Om, are different for the two atoms. These results are typical of the kind of chemical information which can be obtained from Mossbauer spectra. 

Figure 14. Temperature dependence of recoil-free fractions for in Snl ...

Other Compounds. The molecular crystal I2 has been studied by Pasternak, Simopoulos, and Hazony (26). By measuring the temperature dependence of the recoilless fraction they obtained an effective Moss-bauer temperature, Om = 60°K., which is considerably less than the range found for the alkali iodides, Om = 100° to 120 °K. Because the covalent intramolecular bonding in I2 is much stronger than the intermolecular bonding, it is reasonable to assume for data interpretation that the recoil energy is taken up by the entire I2 molecule. 

The recoil-free fraction /, while strictly speaking not the result of a chemical interaction, can indirectly provide useful chemical, as well as structural, information. As shown earlier, / is related to , the mean square vibrational amplitude of the resonant atom in the direction of the y ray. The temperature dependence of is often approximated using the... 

It was proposed that the temperature dependence of polymer 5 arises from the temperature dependence of the kA step. Specifically, it was suggested that the polymer segments to which the radicals are attached are conformationally stressed. There are two possible modes for the newly formed radicals to relax and become separated They can rotate or recoil away from each other (Scheme 9). These secondary motions of the polymer arise from the relaxation of unfavorable bond conformations that are formed during the polymer casting process. The increased thermal energy facilitates the rotation and recoil relaxation processes, which effectively increases the rate constant for diffusion of the radicals out of the cage, kA. This leads to decreased radical-radical recombination and consequently an increase in photodegradation efficiency. 

Iron may also occur as an interlayer species. Mossbauer spectra show the presence of an Fe2+ aquo complex in the interlayer of montmorillonite (13). The labile nature of this Fe2+ is suggested by the large temperature dependence of its recoil-free-fraction. In contrast, Fe3+ aquo complexes are unlikely to occur as discrete species in a clay interlayer. Instead, Fe(0H)2(H20)4 complexes will condense to form ferric hydroxy polymers which, in a clay interlayer, might form two-dimensional sheets or three-dimensional pillars. Such pillars in nontronite have been characterized by Gangas et al. (14). 

Mossbauer and Wiedemann 1960) where is the recoil energy (= 3.13425 x 10 J for the 14.4 keV transition of Fe), ke is the Boltzmann constant, and 0m is the characteristic Mossbauer temperature, where m can be determined from temperature dependant measurements of the centre shift as described by Equation (2). The recoil-free fraction of the absorber can also be determined through temperature dependant measurements of the relative area according to Equation (13). In either case, a phase transformation can be recognised as either a discontinuity or a change in slope of the recoil-free fraction plotted as a function of temperature. 

Equation (1.10) indicates that the probability of zero-phonon emission decreases exponentially with the square of the y-ray energy. This places an upper limit on the usable values of Ey, and the highest transition energy for which a measurable Mdssbauer effect has been reported is 155 keV for Os. Equation 1.10 also shows that/increases exponentially with decrease in which in turn depends on the firmness of binding and on the temperature. The displacement of the nucleus must be small compared to the wavelength X of the y-ray. This is why the Mossbauer effect is not detectable in gases and non-viscous liquids. Clearly, however, a study of the temperature dependence of the recoil-free fraction affords a valuable means of studying the lattice dynamics of crystals. 

The recoil-free fraction is anisotropic, and the temperature dependence of /... 

As an example, we have recently been comparing the reactivity of the intermediates derived from recoiling silicon atoms with the reactivity of thermally generated silylene SiH2 toward silane and methylsilane. This pair of substrates was chosen because Paquin and Ring have studied the temperature dependence of the relative rate of insertion of thermally generated silylene into the Si—bonds of these molecules (33). 

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