CAMPO LIBRE Y CAMPO DIFUSO

Mossbauer spectroscopy is a technique where electric, magnetic, bonding and structural properties are detected. Time dependant properties can also be studied. The spectroscopy arises fi'om the Mossbauer effect which was discovered in 1957 by Rudolph Mossbauer*^. The Mossbauer effect is the capacity o f emission and absorption o f monochromatic gamma rays by the nucleus without recoil o f the nucleus. The detection o f the type o f bonding, electronic occupancy and structural environment is via the Mossbauer-active element nucleus. This occurs because there is an interaction between the nucleus and its environment. This leads to the splitting and shifting o f the nuclear subenergy levels. Information about transitions o f nuclear sublevels is then obtained in a spectrum. This is done by directing a gamma ray at the nucleus o f the atom being studied and detecting which energies have been absorbed. The spectrum usually plots y-ray counting rate against velocity*^’*^.

The Mossbauer effect is observed in many nuclei (including Sn, Eu, Gd, Dy, Fe). In this thesis, only ^^Fe Mossbauer, the most common type, is performed. Two types o f experiment can be conducted; transmission and emission. This thesis deals exclusively with transmission.

Mossbauer effect experiments use a very small amount o f sample material, commonly 10 mg cm'^ o f natural Fe for ^^Fe Mossbauer experiments. Mossbauer spectroscopy derives fi*om resonant emission and absorption o f y-rays fi'om the

nucleus. This only occurs if the absorption or emission is recoil-less. The energy o f recoil must be much smaller than the lowest quantised lattice vibrational energy

(Kb0d). Otherwise not all the energy will be passed on to the y-ray and some will

be lost as a phonon. In order for a recoil-less emission to be used in practice, the solid radioactive source material must be imbedded in a matrix. Since the line width ( F ) is very small, it is possible to detect very small energy interactions between nucleus and its environment. The small energy interactions are also known as hyperfine interactions.*^’*^’*^’**

In order for a range o f energies to be used (since the emitted y-ray has a discrete value) a source o f y-rays is moved back and forward to induce a Doppler shift. This gives a range o f values to the y-rays. For ^^Fe 1 mms ' is equal to 4.8x10 * eV. The source for ^^Fe Mossbauer is ^^Co. This is because ^^Co decays through a series o f steps to an excited ^^Fe. This excited ^^Fe then decays to ^^Fe ground state with the emission o f a 14.4 keV y-ray*^ ** (Figure 1.4).

Figure 1.4 Decay*^ scheme for ^ Co. 270 days 136 keV 7 = 5 /2 91% 14 4 keV 3/2 14 X lO'^s 0 stable 1/2

The energy that separates the ground state (I = 1/2) and the excited state (I = 3/2) is 14.4 keV. However hyperfine interactions can split these energy levels o f the absorber nucleus.

There are three main types o f interactions in Mossbauer spectroscopy; electric monopole, electric quadrupole and magnetic dipole.

1.8.1 Electric monopole

The electric monopole results from the interaction between the electronic charge density and the nuclear charge distribution. This interaction gives rise to the isomer shift ô. It is caused by the difference in the nuclear volume o f ground and excited state, and its interaction with the electron density. It is the change in electrostatic energy o f the nucleus with the electron cloud as the nucleus goes from the ground state to the excited state. Hence the isomer shift has two main contributions; nuclear and electronic. The electronic contributions are in the form o f the electron densities which are affected by oxidation states and electronic

structure®^’*^.

The isomer shift is essentially the observed difference o f the electric monopole interactions o f the absorber nucleus and the source nucleus (Figure 1.5). It also shows the shift in the centre o f gravity for other hyperfine interactions such as quadrupole splitting or magnetic splitting (doublet or a sextet).

This type o f interaction is usually observed in paramagnetic materials. There is also another contribution to the isomer shift and that is thermal vibration. This is a second order Doppler shift effect. This contribution*^ is usually about 0.07 mm/s for every 100 K.

Figure 1.5 Diagram showing the isomer shift^^

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nr

For comparisons, isomer shifts are usually relative to a standard absorber. This standard tends to be the elemental form o f the Mossbauer-active element being studied; in our case a-iron. Therefore a-Fe in our experiments will have an isomer shift o f zero86

1.8.2 Electric quadrupole.

This results fi’om the fact that in certain instances, the nucleus has a non-spherical charge distribution, that is I > 1/2. In this case there will be an interaction between the nucleus and any electric field gradient. This electric field gradient is due to asymmetric electron densities which can arise due to an asymmetric ligand arrangement or an asymmetric electron arrangement. In ^^Fe this splits the excited state (I = 3/2) into two substates. These are m\ = ±1/2 and nii = ±3/2. Under these circumstances the quadrupole splitting will be observed in the form o f a doublet (Figure 1.6). This type o f interaction leads to quadrupole splitting (A) and it is usually observed in paramagnetic materials*^’*^.

Figure 1.6 Diagram showing quadrupole splitting^^

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I_ _ _ I

The ground state o f Fe has no quadruple moment and hence does not split into sub-levels^^. The electric field gradient depends on its environment and has three different contributions; valence electrons o f the Mossbauer atom, crystal lattice and molecular orbitals. The quadrupole splitting gives information about bonding, structure, and electronic populations.

1.8.3 Magnetic dipole.

This hyperfine interaction (or Zeeman effect)*^ arises when the nuclear magnetic moment interacts with a magnetic field. This can either originate in the atom itself or be applied externally. If it is generated by the atom itself it is due to unpaired electrons. Its strength is also dependent on the spin state o f the material (high spin or low spin) and on the oxidation state o f the Mossbauer atom. In ^^Fe it leads to a magnetic hyperfine field Bhf. This type o f interaction raises the degeneracy and splits the ground level (I = 1/2) into two sublevels and the excited state (I = 3/2) into four sublevels. Because o f the selection rules that state that the difference in nuclear angular momentum quantum numbers can only have a value o f 0, +1 and - 1, only six transitions are allowed. In this case a six line spectrum (Figure 1.7) is observed (sextet)88

Figure 1.7 Diagram showing magnetic splitting^^. ) r p n n velocity I I L

nr

- 1

The splitting o f the lines is proportional to the magnetic field experienced by the nucleus. Thus it is an effective way o f determining the strength o f external magnetic field at the nucleus. Magnetic materials such as ferromagnetic or ferrimagnetic show magnetic hyperfine fields in their spectra. This type of interaction is also observed in paramagnetic materials under certain circumstances, for example, when the spin relaxation times are long*^’*^.

The magnetic hyperfine field gives information on the type o f magnetic interaction, the magnetic moment and the electronic structure*^.

1.8.4 Combined interactions.

The isomer shift can combine with the magnetic splitting or with the quadrupole splitting. In both cases a shift o f all the lines is observed. However a more complex interaction can occur and that is when both the quadropole and the magnetic interactions are present. The resultant is called the quadrupole shift (2e). This is observed as a shift o f the middle four lines o f the sextet in respect to the outer two*^’^^.