Mossbauer effect isomer shift

Shenoy GK (1984) Mossbauer-effect isomer shift. In Long GJ (ed) Mossbauer Spectroscopy Applied to Inorganic Chemistry, Vol 1, pp 57-78. New York Plenum Press. 

Mossbauer spectroscopy The Mossbauer effect is resonance absorption of 7 radiation of a precisely defined energy, by specific nuclei. It is the basis of a form of spectroscopy used for studying coordinated metal ions. The principal application in bioinorganic chemistry is Fe. The source for the 7 rays is Co, and the frequency is shifted by the Doppler effect, moving it at defined velocities (in mm/s) relative to the sample. The parameters derived from the Mossbauer spectrum (isomer shift, quadrupole splitting, and the hyperfine coupling) provide information about the oxidation, spin and coordination state of the iron. 

Iron-supported-on-MgO catalysts behave in some ways differently from the above catalyst systems. That is, while the catalytic activity of these metallic-iron particles for the atmospheric-pressure ammonia synthesis depends markedly on particle size in the range 1.5-10 nm (206), the Mossbauer parameters (isomer shift, quadrupole splitting, and magnetic hyperfine splitting) are independent of iron particle size in this range (97). This thus rules out an electronic effect in the interpretation of the effect of particle... 

The equiatomic compounds EuLiBi and YbLiBi, containing divalent rare earths, are known. EuLiBi, which is extremely moisture-sensitive, was prepared from reaction of Eu, Li, and Bi in a 1 2 1 atomic ratio within Mo crucibles placed in steel ampoules jacketed by silica tubes at 1000 °C for 5-7 d (Prill et al., 2002). Powder X-ray diffraction indicates an orthorhombic TiNiSi-type structure (Pearson symbol oPl2, space group Pntm (No. 62), Z = 4), but atomic positions were not refined (section 5.4, fig. 9a). The presence of divalent europium is supported by Eu Mossbauer spectroscopy (isomer shift of -11 mm/s) and magnetic susceptibility measurements (effective magnetic moment of 8.3 mb, close to that of the free-ion value of 7.94 MB for Eu +). EuLiBi orders antiferromagnetically below 7.5 K. 

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

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...

The electron density i/ (0)p at the nucleus primarily originates from the ability of s-electrons to penetrate the nucleus. The core-shell Is and 2s electrons make by far the major contributions. Valence orbitals of p-, d-, or/-character, in contrast, have nodes at r = 0 and cannot contribute to iA(0)p except for minor relativistic contributions of p-electrons. Nevertheless, the isomer shift is found to depend on various chemical parameters, of which the oxidation state as given by the number of valence electrons in p-, or d-, or /-orbitals of the Mossbauer atom is most important. In general, the effect is explained by the contraction of inner 5-orbitals due to shielding of the nuclear potential by the electron charge in the valence shell. In addition to this indirect effect, a direct contribution to the isomer shift arises from valence 5-orbitals due to their participation in the formation of molecular orbitals (MOs). It will be shown in Chap. 5 that the latter issue plays a decisive role. In the following section, an overview of experimental observations will be presented. 

In a conventional Fe Mossbauer experiment with a powder sample, one would observe a so-called quadrupole doublet with two resonance lines of equal intensities. The separation of the lines, as given by (4.36), represents the quadrupole splitting The parameter Afg is of immense importance for chemical applications of the Mossbauer effect. It provides information about bond properties and local symmetry of the iron site. Since the quadrupole interaction does not alter the mean energy of the nuclear ground and excited states, the isomer shift S can also be derived from the spectrum it is given by the shift of the center of the quadrupole spectrum from zero velocity. 

Fig. 4.9 Magnetic dipole splitting (nuclear Zeeman effect) in pe and resultant Mossbauer spectrum (schematic). The mean energy of the nuclear states is shifted by the electric monopole interaction which gives rise to the isomer shift 5. Afi. g = Sg/tN and A M,e = refer to the...

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). 

The traditional interpretation of the isomer shift in Fe Mossbauer spectra is based on the following assumptions (a) the influence of the 3d electron configuration on the IS occurs via the shielding effect of the 3d electrons on the 3s and 4s electrons, (b) the variations in the 3s shell are dominant, and (c) the influence of the 4s shell occurs via the 4s population. 

Two other publications on Ir (73 keV) Mossbauer spectroscopy of complex compounds of iridium have been reported by Williams et al. [291,292]. In their first article [291], they have shown that the additive model suggested by Bancroft [293] does not account satisfactorily for the partial isomer shift and partial quadrupole splitting in Ir(lll) complexes. Their second article [292] deals with four-coordinate formally lr(l) complexes. They observed, like other authors on similar low-valent iridium compounds [284], only small differences in the isomer shifts, which they attributed to the interaction between the metal-ligand bonds leading to compensation effects. Their interpretation is supported by changes in the NMR data of the phosphine ligands and in the frequency of the carbonyl stretching vibration. 

It is much more difficult to observe the Mossbauer effect with the 130 keV transition than with the 99 keV transition because of the relatively high transition energy and the low transition probability of 130 keV transition, and thus the small cross section for resonance absorption. Therefore, most of the Mossbauer work with Pt, published so far, has been performed using the 99 keV transition. Unfortunately, its line width is about five times larger than that of the 130 keV transition, and hyperfine interactions in most cases are poorly resolved. However, isomer shifts in the order of one-tenth of the line width and magnetic dipole interaction, which manifests itself only in line broadening, may be extracted reliably from Pt (99 keV) spectra. 

Alloys of Pd-Au-Fe (2 at%) Mossbauer effect in Fe and Au, study of band filling, hyperfine fields, isomer shifts... 

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. 

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