Recoil-free fraction effects

However, in contrast, the resonance effect increased by cooling both the source and the absorber. Mdssbauer not only observed this striking experimental effect that was not consistent with the prediction, but also presented an explanation that is based on zero-phonon processes associated with emission and absorption of y-rays in solids. Such events occur with a certain probability/, the recoil-free fraction of the nuclear transition (Sect. 2.4). Thus, the factor/is a measure of the recoilless nuclear absorption of y-radiation - the Mdssbauer effect. 

Using the value t = 0.2 for the effective thickness, the amount of resonance nuclei ( Fe) for a good thin absorber can be easily estimated according to the relation = tl(fA-(to)- For a quadrupole doublet with two equal absorption peaks of natural width and a recoil-free fraction of the sample/a = 0.7 one obtains... 

Kaltseis et al. [234] have investigated the recoil-free fraction of the 46.5 keV transition of W in anhydrous lithium tungstate. Their results can be expressed by an effective Debye temperature of 172 9 K which is in good agreement with a value of 205 40 K derived from X-ray diffraction measurements of Li2W04 powder. 

As is well known, the recoil-free fraction of very small crystals differs markedly from that of bulk material. Roth and Horl [236] observed a decrease of the/-factor from 0.61 to 0.57 in going from 1 p,m crystals to microcrystals with a diameter of about 60 A. Two effects will contribute to this decrease (1) the low frequency cutoff, because the longest wavelength must not exceed the dimensions of the crystal, and (2) high frequency cut-off caused by the weaker bonds between surface atoms. 

Wender and Hershkowitz [237] used the sensitivity of the recoil-free fraction in tungsten Mossbauer spectroscopy to deduce the effect of irradiation of tungsten compounds by Coulomb excitation of the resonance levels (2 states of I82,i84,i8 y with 6 MeV a-particles. While no effect of irradiation on the/-factors could be observed for tungsten metal in agreement with [233], a decrease of/was measured for WC, W2B, W2B5, and WO3 after irradiation. 

Au microcrystals Effect of crystal size on recoil-free fraction... 

The intensity of the Mossbauer effect is determined by the recoil-free fraction, or /factor, which can be considered as a kind of efficiency. It is determined by the lattice vibrations of the solid to which the nucleus belongs, the mass of the nucleus and the photon energy, Ea and is given by ... 

The intensity of a Mossbauer spectrum depends not only on the recoil-free fractions of the source and the absorber and on the number of absorbing nuclei, but also on the linewidth of the absorption lines and on whether or not saturation effects occur. The following approximate expression is valid for relatively thin absorbers [17] ... 

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. 

Dr. Stockier What, if any, is the effect of the difference in the recoil-free fraction of the two compounds of tin ... 

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

Consider first a Mossbauer isotope with a large associated resonant irradiation energy. The large recoil energy thus results in a small recoil-free fraction, and in the transmission mode the Mossbauer effect is only observed by measuring a small change in the primary beam intensity. The radiation reemitted as a result of these recoil-free events may, however, be superimposed on a weak background if observed for a direction different from the primary beam (SO). Thus, measurement of this radiation intensity versus... 

This internal pressure effect may actually be quite general in Mbssbauer effect studies of small particles, as discussed by Schroeer et al. for the recoil-free fraction (156) and the isomer shift (157). In addition, Schroeer (152) has summarized a number of origins for Mossbauer parameters being particle size dependent. Thus, from the above discussion, it seems apparent that a priori particle size determination using the recoil-free fraction, quadrupole splitting, or isomer shift is not possible for an arbitrary catalytic system. However, the "experimental calibration of these parameters, which not only facilitates particle size measurement, may also provide valuable information about the chemical state (e.g., electronic, defect, stress) of the small particles. This point will be illustrated later. 

The area of the peaks in each Mossbauer doublet roughly corresponds to the amount of Fe actually present in that site (in fact, this is often assumed), but with some caveats. The first of these is the effect of differential recoil by Fe atoms in different sites. It is well-known that the area of a Mossbauer doublet (pair of peaks) is a function of peak width r, sample saturation G(x), and the Mossbauer recoil-free fraction/ Bancroft (1969 1973) uses the following formulations for area ratios in a mineral where there is only a single site for Fe, and it may be occupied by either Fe or Fe ... 

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 effective Debye temperature of the source matrix should be high so that the recoil-free fraction is substantial. High-melting metals and refractory materials such as oxides are the obvious choices. 

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