Recoilless fraction

The Mossbauer effect can only be detected in the solid state because the absorption and emission events must occur without energy losses due to recoil effects. The fraction of the absorption and emission events without exchange of recoil energy is called the recoilless fraction, f. It depends on temperature and on the energy of the lattice vibrations /is high for a rigid lattice, but low for surface atoms. 

Nii ,Pd ,(x 0-0.995) Absorber recoilless fraction, energy shift, and as function of x 5 values from temperature dependence of SOD calculation of and comparison with measurements in applied fields... 

Conroy and Perlow [235] have measured the Debye-Waller factor for W in the sodium tungsten bronze Nao.gWOs. They derived a value of/= 0.18 0.01 which corresponds to a zero-point vibrational amplitude of R = 0.044 A. This amplitude is small as compared to that of beryllium atoms in metallic beryllium (0.098 A) or to that of carbon atoms in diamond (0.064 A). The authors conclude that atoms substituting tungsten in bronze may well be expected to have a high recoilless fraction. 

In a subsequent measurement at a potential of -0.9 V, the resonant absorption of the doublet underwent a marked drop, an effect that may be due to an increase in the solubility of the oxide, and thus in a loss of solid in the electrode, and/or to a modification in the recoilless fraction of the solid induced by the hydration of the lattice. 

Results obtained from the alkali iodides on the isomer shift, the NMR chemical shift and its pressure dependence, and dynamic quadrupole coupling are compared. These results are discussed in terms of shielding by the 5p electrons and of Lbwdins technique of symmetrical orthogonalization which takes into account the distortion of the free ion functions by overlap. The recoilless fractions for all the alkali iodides are approximately constant at 80°K. Recent results include hybridization effects inferred from the isomer shifts of the iodates and the periodates, magnetic and electric quadrupole hyperfine splittings, and results obtained from molecular iodine and other iodine compounds. The properties of the 57.6-k.e.v. transition of 1 and the 27.7-k.e.v. transition of 1 are compared. 

Alkali Iodides. Figure 8 shows the experimental data obtained for the recoilless fraction, /, at 80°K. The area (13), line width (13), and the temperature (26) methods have all been used to analyze these data. Uncertainties in the background corrections (13) are caused by rather large errors. However, the striking feature is that the recoilless fraction changes only little from Lil to Csl. 

The recoilless fraction, /, has been calculated (13) for monotomic lattices using the Debye approximation. When the specific heat Debye temperatures of the alkali iodides are inserted in the Debye-Waller factor, a large variation of f follows (from 0.79 in Lil to 0.15/xCsI). It is not... 

Figure 8. Theoretical and experimental values of recoilless fraction, f for alkali iodides at 80°K. DEL symbolizes Ref, (9),/—(19), HDD—(13), PSH—(26)...

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. 

In a basic Mossbauer experiment, the reduction in transmission (9) (Figure 2) or the increase in scattered intensity of radiation (2) (Figure 3) is observed as a function of the relative velocity between a source and an absorber. The full width at half maximum of the resonance curve r is related to the mean life of the radiating state by the uncertainty relation r 2h/r. The depth of the curve, c, is related to /, the magnitude of the recoilless fraction of gamma rays emitted, and hence to the crystalline properties of the solid. Finally, the displacement of the curve from zero relative velocity indicates the energy difference between emitted and absorbed radiation and is proportional to the s-electron... 

In most experiments reported, 195Au sources embedded in platinum matrices were used. For these sources, the recoilless fraction, even at liquid helium temperatures, is small, and the resonance effects are of the order of a few per cent at best. Buym and Grodzins (5) searched for... 

However, this freely recoiling state is not a stationary state of the Hamiltonian in relevant experimental situations, where the Fe nucleus is bound to other atoms in a condensed phase. In general, a series of discrete lines appear in the spectrum (Figure 1, bottom), corresponding to a range of possible final states. Conventional Mossbauer spectroscopy relies on the presence of a narrow line ( f = i) at Eo, with an area proportional to the recoilless fraction... 

Figure 5 presents an example of the excitation probability S (v) and the VDOS D (v) for the iron atom in the molecule Fe(TPP)(l-MeIm)(CO), as determined from measurements on a polycrystalline sample. Sharp features in both representations of the experimental data clearly identify vibrational frequencies above 100 cm, although low-frequency vibrational features are more apparent in the VDOS representation. The VDOS also provides the most convenient estimate of the mode composition factor ej, since the area of each feature directly yields the sum of values for all contributing vibrations. This avoids the need to remove the additional factors in equation (5) that contribute to the area of a feature in S (v), with the subtleties associated with determining an appropriate value for the recoilless fraction Z. However, calculation of D (v) from S (v) involves implicit assumptions that may not be valid in some situations, for example, when more than one molecular species contributes to the experimental signal or when vibrational anisotropy is significant. 

N is the tme amount of each species and C is the correction factor. So the degree of correspondence between peak areas and actual Fe occupancy depends on three assumptions, namely that (1) the linewidths of the Fe " and Fe peaks are the same (2) saturation corrections are unnecessary if samples are correctly prepared as thin absorbers (Rancourt et al. 1993 a), and (3) the amount of recoil-free fraction for both Fe and Fe in those sites is the same. The equal linewidth assumption is only reasonable in end members, but most fitting routines can allow linewidths to vary. Thickness corrections can also be dealt with (see below). Recoilless fractions depend greatly on local bond strengths and angles (Hawthorne 1988), and thus different values of/are likely in cases where two sites have radically different geometries. 

Fig. 3.7 Curves illustrating the changes in the relative intensity of two hyperfine lines caused by saturation effects (a) with change in recoilless fraction, (b) with change in absorber thickness.

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