Magnetic dipole splitting, Mossbauer

Figure 2A. Schematic diagram of Mossbauer parameters isomer shift (6), quadrupole splitting (AEq) and magnetic dipole splitting of the nuclear energy states of 57pe leading to various hyperfine splitting in Mossbauer spectra.

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...

We have learned from the preceding chapters that the chemical and physical state of a Mossbauer atom in any kind of solid material can be characterized by way of the hyperfine interactions which manifest themselves in the Mossbauer spectrum by the isomer shift and, where relevant, electric quadrupole and/or magnetic dipole splitting of the resonance lines. On the basis of all the parameters obtainable from a Mossbauer spectrum, it is, in most cases, possible to identify unambiguously one or more chemical species of a given Mossbauer atom occurring in the same material. This - usually called phase analysis by Mossbauer spectroscopy - is nondestructive and widely used in various kinds of physicochemical smdies, for example, the studies of... 

In the course of Mossbauer measurement, the energy of gamma quanta is ordinarily modulated by a mechanical movement of the source relative to the absorber. The spectrum is essentially a plot of Mossbauer transition count rates as a function of velocity of the source relative to the absorber. If no resonance occurs, the spectrum would be a horizontal line with no variations while resonance occurs, there would be a decrease in the intensity at certain velocity values as shown in Figure 5.4. In interpreting the spectrum the Mossbauer parameters can be obtained, i.e. the isomer shift, the electric quadruple splitting, and the magnetic dipole splitting. 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

Fig. 7.4 Top Nuclear energy levels of Fe as shifted by electrical monopole (left), or as split by electrical quadrupole (center) or by magnetic dipole interaction (right), schematized for hematite at room temperature (5 > 0 vs. a-Fe, EQ < 0, Bhf 0). Bottom Schematic Mossbauer spectra corresponding to the energy levels schematized on top (J. FriedI, unpubl.).

Mossbauer spectroscopy senses the hyperfine interactions, which are present at the nucleus of the Mossbauer isotope. The electrical monopole interaction causes the isomer shift and the electric quadrupole interaction leads to the quadrupole splitting, which in the case of Fe causes a two-line Mossbauer pattern. The magnetic dipole interaction leads to a magnetically split six-line pattern (Figure 4). In the following text, these interactions and their deduction from Mossbauer spectra will be discussed. 

Figure 1. Hyperfine interactions for Fe nuclei, showing the nuclear energy level diagram for (a) an unperturbed nucleus (b) electric monopole interaction (isomer shift) (c) electric quadrupole interaction (quadrupole splitting) and (d) magnetic dipole interaction (hyperfine magnetic splitting). Each interaction is shown individually, accompanied by the resulting Mossbauer spectrum.

The magnetic hyperfine splitting (MHS) depends on the nuclear spin quantum numbers and /g of the excited and ground state of the Mossbauer nucleus and on the effective magnetic field at the Mossbauer nucleus, which includes contributions from the local electronic spin, from the orbital momentum, from dipole terms, and from external fields. 

Since the Mossbauer transition in Fe is of the magnetic dipole type (M ). there are only transitions between nuclear sublevels with A/nj = 0, 1 and A/= +1. This selection rule yields only six transitions between the two ground state sublevels (/= 1/2) and the four excited state sublevels (7=3/2). Figure 9 illustrates the splitting of the nuclear levels, the allowed transitions, and the resulting Fe Mossbauer spectrum, a sextet due to the magnetic hyperfine interaction. 

Since the di,scovery more than 40 years ago, Mossbauer spectroscopy has become an extremely powerful analytical tool for the investigation of various types of materials. In most cases, only two parameters are needed, viz. the isomer shift and the quadrupole splitting, to identify a specific sample. In case of magnetically ordered materials, the magnetic dipole interaction is a further helpful parameter for characterization. In the following... 

Magnetic dipole interaction between the nuclear magnetic dipole moment and a magnetic field at the nucleus. The observable Mossbauer parameter is the magnetic splitting AEm . This quantity gives information on the magnetic properties of the material under study. 

Fig. 2.6 Typical Fe Mossbauer spectrum resulting from magnetic dipole interaction. The energies of the ground and excited state splitting can be determined as depicted in the figure and described in the text...

Figure 5.2 The influence of magnetic interaction with respect to the excited nuclear state of Fe. (From Schiinemann and Winkler. ) The influence of magnetic interaction with respect to the excited nuclear state of Fe. The latter splits into four sublevels. The selection rule for magnetic dipole (Ml) transitions (AI = 1 and AMi = 0, 1) yields the observed six-line pattern, (a) The Mossbauer spectrum of a metaUic iron foil, (b) The Mossbauer spectrum of the iron carrier protein ferritin. 2000 lOP Publishing Ltd.

In addition to the isomer shift and the quadrupole splitting, it is possible to obtain the hyperfine coupling tensor from a Mossbauer experiment if a magnetic field is applied. This additional parameter describes the interactions between impaired electrons and the nuclear magnetic moment. Three terms contribute to the hyperfine coupling (i) the isotropic Fermi contact, (ii) the spin—dipole... 

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