Recoil-free fraction using

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. 

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... 

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. 

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... 

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 quadrupole splitting (as shown in Section I, C, 3) and the relaxation of the magnetic hyperfine interaction (as will be seen presently) are also related closely to the symmetry, and thus the structure of the surface. Determination of the surface structure using these parameters then follows the pattern outlined above for the recoil-free fraction. For clarification, this pattern will be illustrated in the following section for the magnetic relaxation. 

Mossbauer spectroscopy may be used for semi-quantitative or qualitative determination of Fe2 /Fe3 ratios Table II shows that a rather good correlation exists between Mossbauer and chemical analysis for Fe2 /Fe3 ratios in clay mineral samples, but these measurements must be obtained at lower temperatures (< 150 K) in order to maximize the recoil-free fractions of both valence states in the sample ... 

The dependence of the isomer shift (41) and recoil-free fraction (9, 42-48) on particle size has also been suggested, but such relationships may be somewhat tenuous. It is clear that caution must be exercised in the use of methods hitherto described in the interpretation and correlation of microcrystallite size. Recent work has suggested (12) that ferric oxide may react with the support when calcined at high temperatures, e.g. for 2 hr at 500°C. The presence and contribution... 

Mossbauer spectroscopy is the study of recoilless resonant fluorescence " Sn Mossbauer spectroscopy has been found to be a most usefifl method for studying the bonding and stereochemistry of tin compounds in the solid state. The two most important parameters are the isomer shift (5, mm s ) and the quadrupole sphtting (A q, nuns ), although the recoil-free fractions and temperature coefficients can also supply useful structural indications. 

Another consideration for calculating relative abundances from the relative areas is the difference in recoil-free fractions corresponding to the specific sites. The Debye model allows recoil-free fractions to be estimated using Equation (15) (this Chapter), and combined with the results listed in Table A2, gives recoil-free fractions of the two components at 4.2 K of 0.91 and 0.96. This results in, at most, a 2% correction to the relative areas in order to obtain the relative abundances. The situation is different at room temperature, however, where recoil-free fractions of the two components are calculated to be 0.70 and 0.92, which results in a correction of more than 10%. 

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 ... 

The total cross-section in any direction is independent of polarisation, but the individual line cross-sections are not. A typical oriented crystal Mossbauer spectrum of FeCOa is shown in Fig. 6.15. One of the consequences of the modified theory is that the theoretical area ratio is comparatively insensitive to the recoil-free fraction and that it is unrealistic to determine it by an area ratio method. The presence of impurities and imperfections in the mineral specimens was held to explain some of the experimental deviations from prediction. No direct evidence for anisotropy of the recoil-free fraction was obtained, a conclusion since verified by Goldanskii [50], who made new polarisation measurements using single crystals of FeCOa as polariser and analyser. 

Both a-tin [15] and jS-tin [16] have been used as sources, the latter giving a broader line because of a small unresolved quadrupole interaction, but both suffer from a very low recoil-free fraction at room temperature (f = 0-039 for /3-tin). 

A source matrix which shows no line broadening due to unresolved quadrupole splitting and which gives a large recoil-free fraction at room temperature is barium stannate, BaSnOa [18], and this is rapidly becoming the most popular source for tin MQssbauer spectroscopy. The /-fraction is 0-6 at 293 K and 0-46 at 690 K. The source linewidth is close to the natural width [19]. A method of preparation has been detailed [19], and the material can also be used with high eflSciency in a resonant counter [18]. 

Another useful source can be made using a 3% Sn-97% Pd alloy [20]. The latter has a face-centred cubic structure which places the tin atoms in a cubic environment. The linewidth is consequently close to natural, and the recoil-free fraction is 0-42 at 297 K. 

No quadrupole or magnetic hyperhne interactions have been detected, and the only general application would appear to be the use of the recoil-free fraction in lattice-dynamical studies. 

Detailed measurement of the recoil-free fraction in germanium metal [8] has since been reinterpreted [11] using a different lattice-dynamical model. 

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