Mossbauer isomer

Figure 8. Saturation magnetization (Gs) and the Mossbauer Isomer shift (6) vs S102/A1203 ratio. The arrows show the ratio =17, at which the acidity is highest.

Shenoy, G.K., Wagner, F.E. Mossbauer Isomer Shifts. North Holland, Amsterdam (1978)... 

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]. 

Fig. 4.1 The electric monopole interaction between the nuclear charge and the electron density at the nucleus shifts the energy of the nuclear states and gives the Mossbauer isomer shift...

For a comparison of experimental Mossbauer isomer shifts, the values have to be referenced to a common standard. According to (4.23), the results of a measurement depend on the type of source material, for example, Co diffused into rhodium, palladium, platinum, or other metals. For Fe Mossbauer spectroscopy, the spectrometer is usually calibrated by using the known absorption spectrum of metallic iron (a-phase). Therefore, Fe isomer shifts are commonly reported relative to the centroid of the magnetically split spectrum of a-iron (Sect. 3.1.3). Conversion factors for sodium nitroprusside dihydrate, Na2[Fe(CN)5N0]-2H20, or sodium ferrocyanide, Na4[Fe(CN)]6, which have also been used as reference materials, are found in Table 3.1. Reference materials for other isotopes are given in Table 1.3 of [18] in Chap. 1. 

Mossbauer isomer shifts of iron-containing compounds are traditionally explained... 

Based on these two comments, one might be tempted to conclude that the calculation of Mossbauer isomer shifts is a very involved subject where accuracy is difficult to achieve. The reason why this is not the case is revealed in Fig. 5.3, which analyzes the contributions of the iron Is, 2s, 3s, and 4s (valence shell) to the... 

If one pursues the calibration approach, one has to stick to a given combination of density functional and basis set, since the calibration will change for each such combination. Calibration curves have been reported for a number of widely used density functionals and basis sets. The results of a relatively comprehensive study are collected in Table 5.4. The standard deviation of the best fits is on the order of 0.08 mm s which appears to be the intrinsic reliability of DFT for predicting Mossbauer isomer shifts. 

Table 5.4 Linear fit data for Fe Mossbauer isomer shift predictions using the linear equation 5 = h (p - c) + a. A collection of 21 iron complexes with varying charge, oxidation- and spin-states have been studied (taken from [11])...

Core electrons are highly relativistic and DFT methods may show systematic errors in calculating the charge density at the nucleus because of the inherent approximations. Fortunately, this does not hamper practical calculations of isomer shifts of unknown compounds, because only differences of li//(o)P are involved. In practice, the reliability of the results depends more on the number of compounds used for calibration and how wide the spread of their isomer shift values was. The isomer shift scale for several Mossbauer isotopes has been calibrated by this approach, among which are Au [1], Sn [4], and Fe [5-9]. For details on practical calculation of Mossbauer isomer shifts, see Chap. 5. 

Appendix D Relativistic Corrections for the Mossbauer Isomer Shift... 

Electron spin resonance, nuclear magnetic resonance, and neutron diffraction methods allow a quantitative determination of the degree of covalence. The reasonance methods utilize the hyperfine interaction between the spin of the transferred electrons and the nuclear spin of the ligands (Stevens, 1953), whereas the neutron diffraction methods use the reduction of spin of the metallic ion as well as the expansion of the form factor [Hubbard and Marshall, 1965). The Mossbauer isomer shift which depends on the total electron density of the nucleus (Walker et al., 1961 Danon, 1966) can be used in the case of Fe. It will be particularly influenced by transfer to the empty 4 s orbitals, but transfer to 3 d orbitals will indirectly influence the 1 s, 2 s, and 3 s electron density at the nucleus. 

Fig. 14c. Rv vs. percent spin reduction in Ni2+ compounds Fig. 14 d. Ry vs. Mossbauer isomer shift in Fe2+ compounds...

High spin Fe2+ has the configuration 3 de (tig eg). Although we could examine the relationship between Rv and dS as for Mn2+, Co2+, and Ni2+, we prefer in this case to look at Ry as a function of the occupation of the combination of 3d and 4s orbital by ligand electrons which is measured by the Mossbauer isomer shift. In general, the coefficient f0, fn, and fs are not known for Fe2+. In addition, possible spin-orbit coupling makes it difficult to determine the spin reduction by magnetic structures. However, the isomer shift allows us to determine approximately the occupancy of the 4 s orbitals and there are many experimental results available. 

An approximately linear relationship also exists between Rv and the Fe2+ Mossbauer isomer shift, i.e., between shortening of Fe2+—X bonds and increased electron transfer to the 4s orbitals of Fe2+. 

Oxidation State Formal Valence EPR g Values (Temperature) Mossbauer Isomer Shift, 8 (mm/s) Cx (nm), (Extinction Coefficient, xl0 3, per Fe)... 

Mossbauer isomer shift and quadrupole splitting are commonly used to obtain information about the bonding environment around source nuclides. The isomer shift arises from the electric monopole interaction of the nucleus with the electrons and depends on the... 

Mossbauer isomer shifts are strongly related to the back-bonding ability of the ligand known from a comparative study of NO, CO, PR3, and SR2 ligands in six-coordinate iron complexes (104), which explains the change in the observed isomer shifts of the [Fe(NO)(cyclam-ac)F compound series ( = 0.02, 0.28, and... 

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