Magnetic splitting

As previously stated, the energy of a nuclear dipole moment in an external magnetic field, B, is given by 

The Physical Chemistry of Materials Energy and Environmental Applications 

FIGURE 4.61 Effect of the magnetic interaction in the energy levels of57Te. 

FIGURE 4.62 57Fe Mossbauer absorption spectrum resulting from magnetic splitting. 

A nucleus with a spin greater than zero has a magnetic moment p. and therefore interacts with a magnetic field. The requirements for the observation of magnetic splitting of Mossbauer lines is that at least one of the 

In the case of an additional electric quadrupole interaction (when 0), as is shown in (d), the substates of the excited state with m/ = 3/2 and 1/2 shown in (c) are pairwise shifted up and downwards in energy in opposite directions by the so-called first-order quadrupole shift This leads to an asymmetry of the resulting splitting pattern in the Mossbauer spectrum, as shown in the lower part of (d). 

Energy-level scheme and resultant spectra for the combined hyperfine interactions with a strong magnetic field. Part (a) represents the nuclear ground and excited states without hyperfine interactions, (b) with isomer shift, (c) the pure magnetic dipole splitting of ground and excited states, and (d) with additional line shifts due to first-order electric 

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Tables 1 and 2 indicate that the results obtained for the 72- and 36-atom models are essentially the same. This is indicative of the aromatic rings in the ligands having no significant effect on the calculated energy differences, charges, or magnetic splittings. We do not expect there to be a marked difference in the...

Most valuable chemical information can be extracted from Mbssbauer parameters such as the isomer shift (5), the quadrupole splitting (AEq), the magnetic splitting (AEm), and the asymmetry parameter (n). 

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. 

The perturbation of the four substates of the excited 7 = 3/2 manifold by induces a typical asymmetry of the resulting magnetically split Mossbauer spectrum as pictured at the bottom of Fig. 4.10 for positive the inner four lines, 2-5, are shifted to lower velocities, whereas the outer two lines, 1 and 6, are shifted to higher velocities by equal amounts. In first order, the line intensities are not affected. For negative the line asymmetry is just inverted, as the quadmpole shift of the nuclear 1/2 and 3/2 states is opposite. Thus, the sign and the size of the EFG component along the field can be easily derived from a magnetic Mossbauer spectrum with first-order quadrupole perturbation. 

Distinct quadrupole shifts do occur as well in magnetically split spectra of single-crystals, poly crystalline powder or frozen solution samples. In all three cases, the line shifts obey the simple first-order expression at high-field condition. 

The spin-Hamiltonian concept, as proposed by Van Vleck [79], was introduced to EPR spectroscopy by Pryce [50, 74] and others [75, 80, 81]. H. H. Wickmann was the first to simulate paramagnetic Mossbauer spectra [82, 83], and E. Miinck and P. Debmnner published the first computer routine for magnetically split Mossbauer spectra [84] which then became the basis of other simulation packages [85]. Concise introductions to the related modem EPR techniques can be found in the book by Schweiger and Jeschke [86]. Magnetic susceptibility is covered in textbooks on molecular magnetism [87-89]. An introduction to MCD spectroscopy is provided by [90-92]. Various aspects of the analysis of applied-field Mossbauer spectra of paramagnetic systems have been covered by a number of articles and reviews in the past [93-100]. 

For the evaluation of magnetically split Mossbauer spectra within the spin-Hamiltonian formalism, the purely -dependent Hamiltonian must be extended by an appropriate... 

Figure 6.13 shows the Mossbauer spectra of ferritin [51], which is an iron-storage protein consisting of an iron-rich core with a diameter around 8 nm with a structure similar to that of ferrihydrite and which is surrounded by a shell of organic material. At 4.2 K essentially all particles contribute to a magnetically split component, but at higher temperatures the spectra show the typical superposition of a doublet and a sextet with a temperature dependent area ratio. At 70 K the sextet has disappeared since all particles have fast superparamagnetic relaxation at this temperature. 

The fluctuations of the magnetization direction around an easy axis, known as collective magnetic excitations, can be considered fast compared to the time scale of Mossbauer spectroscopy because there are no energy barriers between magnetization directions close to an easy direction, and the magnetic splitting in the... 

The value is derived from a zero-field spectrum recorded at 150 K. A q could not be determined at 4.2 K because the compound is in the limit of slow paramagnetic relaxation and the strong unquenched orbital moment forces the internal field into the direction of an easy axis of magnetization. As a consequence, the quadrupole shift observed in the magnetically split spectra results only from the component of the EFG along the internal field and the orientation of the EFG is not readily known dbabh is a bulky N-coordinating amide... 

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