Mossbauer effect calculations

It will be evident from the above discussion of the nature and origin of the Mossbauer effect that it should be possible to calculate Mossbauer parameters accurately using quantum-mechanical methods. This has not proved to be a straightforward matter, and the subject of the calculation... 

In Fig. 10 are presented some computer generated Mossbauer spectra with different degrees of rhombic asymmetry (A < 1/3 and fi =0) so that the effect of the variation of A can be seen. Both Mossbauer effect and ESR show easily measurable differences between spectra calculated from models with z = <100> and z = <111 >. The Mossbauer spectra are really quite different for the two models as seen in Fig. 11 and the ESR spectra give an isotropic g =3.3 for the trigonal case (if /a=—9) and isotropic g =4.3 for the rhombic case [if u = 0.75 (1—3 A)]. Thus we have an experimental method to distinguish between these two possibilities. It is striking that the Mossbauer data in the cases ferrichrome A, enterobactin and benzohydroxamic acid are best fit with 2 in <100>... 

A question of recent interest is whether the two iron sites in each molecule are equivalent (58), Mossbauer effect studies (28) and ESR studies (59) of human serum transferrin could detect no difference in the spectra of the two iron sites, but recently a very careful study by Aasa (27) has shown small differences in the ESR spectrum due to a small change in the ESR parameter A. The Mossbauer data were shown to be in good agreement with a calculation by Spartalian and Oosterhuis (28) and more recently by Tsang, Boyle and Morgan (60). The spin Hamiltonian parameters for each experimental study are presented in Table 4. 

The ESR experiment by Aasa (27) yields two sets of spin Hamiltonian parameters — one for each iron site. A Mossbauer spectrum calculated from each set of Aasa s parameters has been found to be no different from the calculation assuming identical sites. This indicates that the ESR experiment is much more sensitive to small effects than the Mossbauer technique. 

Experimental values of Fe moments in Y2Fe14B as obtained by means of polarized neutron studies (Givord et al. 1985d) and 57Fe Mossbauer effect measurements (R. Fruchart et al. 1987) are given in the first and second line of table 13. In the bottom part of the table results of three different types of band structure calculations are given. 

The samples were characterized by X-ray fluorescence spectroscopy (XRFS), X-ray powder dififiaction (XRD), scanning electron microscopy(SEM) and Mossbauer effect spectroscopy(MES). For MES measurements the Co in chromium matrix was served as the source. Isomeric shift values were given in relation to metallic iron. Spectra were computer-fitted and Mossbauer parameters were calculated. 

Figure 55 shows Mossbauer spectra of a powdered specimen of stoichiometric LuFc204 in the paramagnetic state (Tanaka et al. 1980). Three absorption peaks at around 300 K amalgamate into one peak at 400 K. This is an example of motional narrowing of resonance absorption and is well accounted for by a stochastic theory developed by Kubo and Anderson and applied to the Mossbauer effect by Blume (Tjon and Blume 1968, Blume 1968). Solid lines in the figure are profiles calculated by... 

In the stochastic theory of lineshape developed by Blume [31], the spectral lines are calculated under the influence of a time-dependent Hamiltonian. The method has been successfully applied to a variety of dynamic effects in Mossbauer spectra. We consider here an adaptation due to Blume and Tjon [32, 33] for a Hamiltonian fluctuating between two states with axially symmetric electric field gradients (efg s), the orientation of which is parallel or perpendicular to each other. The present formulation is applicable for states with the same... 

Relativistic quantum mechanics yields the same type of expressions for the isomer shift as the classical approach described earlier. Relativistic effects have to be considered for the calculation of the electron density. The corresponding contributions to i/ (0)p may amount to about 30% for iron, but much more for heavier atoms. In Appendix D, a few examples of correction factors for nonrelativistically calculated charge densities are collected. Even the nonrelativistically calculated p(0) values accurately follow the chemical variations and provide a reliable tool for the prediction of Mossbauer properties [16]. 

Fig. 4.2 Temperature dependence of the isomer shift due to the second-order Doppler shift, sod- The curves are calculated for different Mossbauer temperatures 0m by using the Debye model whereby the isomer shift was set to (5 = 0.4 mm s and the effective mass to Meff =100 Da, except for the dashed curve with Meff = 57 Da...

In molecular DFT calculations, it is natural to include all electrons in the calculations and hence no further subtleties than the ones described arise in the calculation of the isomer shift. However, there are situations where other approaches are advantageous. The most prominent situation is met in the case of solids. Here, it is difficult to capture the effects of an infinite system with a finite size cluster model and one should resort to dedicated solid state techniques. It appears that very efficient solid state DFT implementations are possible on the basis of plane wave basis sets. However, it is difficult to describe the core region with plane wave basis sets. Hence, the core electrons need to be replaced by pseudopotentials, which precludes a direct calculation of the electron density at the Mossbauer absorber atom. However, there are workarounds and the subtleties involved in this subject are discussed in a complementary chapter by Blaha (see CD-ROM, Part HI). 

Table 7.8 Summary of results obtained for the four Os Mossbauer transitions studied. The absorber thickness d refers to the amount of the resonant isotope per unit area. The estimates of the effective absorber thickness t are based on Debye-Waller factors / for an assumed Debye temperature of 0 = 400 K. For comparison with the full experimental line widths at half maximum, Texp, we give the minimum observable width = 2 S/t as calculated from lifetime data.

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