Mössbauer Spectroscopy

• Resonant Absorption
  
• Isomer Shift
  
• Quadrupole Splitting
  
• Magnetic Splitting
  
• Experimental Setup
  
• Example Spectra
  

Resonant Absorption

Mössbauer Spectroscopy is a very sensitive and accurate way of gathering information about chemical systems. It can be used to determine bonding, structural, magnetic, time-dependant and dynamical properties of systems.

The Mössbauer effect involves resonant absorption of gamma rays by atoms of the same isotope. The source of the gamma rays is a radioactive isotope of an element which decays into an excited state of the isotope under study, which returns to its ground state by the emission of a gamma ray or electron. For most experiments the main source used is ⁵⁷Co in Rh, which undergoes a nuclear decay (electron capture) to ⁵⁷Fe in its I=5/2 excited state. This can decay in two ways as shown by figure 1, the main one gives a 14.4 keV excited state. The decay of this state via gamma rays or conversion electrons is used in Mössbauer spectroscopy of iron systems.

Figure 1. Nuclear Decay of ⁵⁷Co to ⁵⁷Fe leading to 14.4 keV Mössbauer gamma ray.

Normally, when a gamma ray is absorbed or emitted some of the kinetic energy of the photon is lost as recoil energy. This means that under normal conditions resonant absorption is prevented. If, however, the atom is bonded to other atoms (say, in a crystal) then its effective mass is increased by a large factor, reducing the energy it absorbs from the gamma ray, ie the "atom" is now so massive it doesn't recoil. In these conditions it is possible to achieve resonant absorption by modulating the energy of the gamma ray beam, by oscillating the the gamma ray source with the resulting Doppler shift changing the energy of the photons. When the modulated beam matches the difference in energy between the ground and first excited state of the absorber (ie at resonance) then the gamma rays are resonantly absorbed. This gives a reduction in the number of counts at the detector giving an output like that in figure 2, which shows a very simple spectrum for an emitter and absorber in the same surroundings.

Figure 2. Simplest Mössbauer spectrum obtained from emitter and absorber in identical conditions.

This output can be affected by temperature and three other factors:

i) Isomer shift
ii) Quadrupole splitting
iii) Magnetic splitting.

Isomer Shift

The isomer shift results from the difference in the electron densities at the nuclear sites in the emitting and absorbing atoms. This difference in density changes the Mössbauer transition energy and so the Mössbauer spectrum is shifted. See figure 3(a). In a non-relativistic case the isomer shift is given by the following formula:

Where Z is the atomic number, e is the electronic charge, R is the effective nuclear radius, c is the velocity of light, E_g is the energy of the Mössbauer gamma ray, the r(0) terms are the total electron densities at the nucleus for absorber and source respectively and DR = R_excited - R_ground .

This isomer shift is something that can be calculated in fits and gives a way of distinguishing between, for example, different ion charge states as they give different isomer shifts. This is due to the different electronic structures of different types of ion.

The s orbitals have the largest density at the nucleus and it is these that cause the isomer shifts. The 3d orbital partially shields the nucleus from the influence of the 3s, and so the ion with the most electrons in the 3d orbital will do the most shielding, ie the Fe²⁺. This smaller density gives a greater magnitude of difference between the emitter and absorber, hence a larger isomer shift.

Quadrupole Splitting

If the nuclei under investigation do not have a charge distribution that is spherically symmetric then the nucleus will possess an electric nuclear quadrupole moment. This moment interacts with an asymmetric electronic charge distribution to give a splitting, D, of nuclear energy levels. For example ⁵⁷Fe has I=3/2 and leads to two states m₁=1/2 and m₂=3/2. See figure 3(b). As the quadrupole moment is fixed for each state/isotope this can be used to probe the electronic configuration.

This interaction can also be used as a guiding point for the fitting of the spectra. The largest component of the electric field gradient, V_zz, is given by the formula:

and is associated with the quadrupole splitting of energy levels by the following formula:

The angular dependance of the quadrupole splitting can be used to determine the orientation of spins in the structures being observed.

Figure 3. Effects of Isomer shift and Quadrupole splitting on Mössbauer spectra.

Magnetic Splitting

When placed in a magnetic field a nucleus with a magnetic moment has a dipole interaction with the field. The interaction raises the degeneracy of nuclear states with angular momentum quantum number I>0 to 2I+1. For example the ⁵⁷Fe ground state I=1/2 splits into two, and excited state I=3/2 splits into four. The selection rule of Dm_I=0, ±1 gives six possible transitions. See figure 4.

Figure 4. Effect on Mössbauer spectra produced by magnetic splitting.

The splitting is directly proportional to the magnetic field applied and so Mössbauer provides a way of measuring it. The field experienced by the system is a combination of applied and hyperfine: hyperfine field is only due to the unpaired spin of the atoms own electrons. If all electrons are paired then applied field produces a magnetic splitting of its own.

Although the lines 1,3,4 & 6 are fixed in their relative intensity, of 3:1:1:3, the 2^nd and 5^th can vary. The relative size of the 2^nd and 5^th lines are given by the following formula:

The angle theta being the angle between the gamma ray beam and the axis of quantization of the nuclear spins. In a powder sample all of the orientations are random and the relative intensity of lines 2 and 5 becomes 2 (this is also true in a single crystal where theta is 54.74°). When theta is zero the relative intensity becomes a minimum of zero, and becomes a maximum of 4 when theta equals 90° .

The effective hyperfine field, B_e, generated by the applied field can be calculated from the different contributions to it. They are related by the following formula: [1]

B_c and B_d are the contact and dipolar components of the hyperfine field, B_a is the applied field and B_dm is the demagnetising field. The angular term is the same as for the quadrupole splitting. Hence we expect the dipolar terms to vary in a similar way to the quadrupole ones. The contact term stays constant with field. The applied field is what we are actually supplying by external magnets. The demagnetization field is generated by all the spins in the sample being aligned parallel to the applied field and so creating their field to oppose that applied.

Experimental Setup

Although there are some differences in apparatus used for room temperature and cryostat experiments the method of data acquisition is basically the same. It can be summarised by the block diagram in figure 5.

Figure 5. Block Diagram of typical Mössbauer spectrometer. [5]

The 4.2K spectrometers are kept at this temperature by liquid helium, which inevitably boils off and so needs to be constantly monitored to ensure that it doesn't boil dry. This is especially important in the case of superconducting magnets used for high field experiments. If the magnets are allowed to warm up they become normal conducting again and the large currentd flowing in them can cause them to become very hot and possibly damage them.

For example the 10T magnet here at liverpool consists of a split-pair of coils wound from Nb₃Sn and NbTi wire in series. The outer part of the coil is made from NbTi as this is cheaper than Nb₃Sn but has a lower critical field. Nb₃Sn is so much more expensive as it is very brittle as well as having a high critical field, meaning it cannot be drawn into wires and has to be moulded into shape in situ. The coils take a maximum current of 57.7A, producing a field of 10T. This apparatus is shown in figure 6.

Figure 6. Diagram of the 10T magnet assembly.

The inner liquid helium store is surrounded by a liquid nitrogen jacket to reduce the boil off of liquid helium, the outer surface of the liquid helium container being enclosed within the liquid nitrogen temperature of 77K as opposed to room temperature of 300K. The liquid nitrogen jacket is filled automatically from an autopressurising liquid nitrogen dewar whenever its level drops below a certain mark. The level of the liquid helium is monitored by a superconducting probe and when the levels are low they must be replenished by refilling manually from a liquid helium dewar. The probe is removed and a U-shaped arm is used to transfer the liquid, with the dewar pressurised by hand. All recording is stopped during this process as helium boil off can affect the vibrator.

All spectrometers need to be calibrated, usually by using a film of metal containg the Mössbauer isotope eg. a foil of metallic ⁵⁷Fe at room temperature, to determine things like alinearity in the oscillators and all isomer shifts are quoted relative to the calibration.

Example Spectra

A Single Crystal of Magnetite under in increasing applied magnetic fields.

A sample of Sb₂O₃ showing both 3+ and 5+ charge states.

A sample of Haematite (Fe₂O₃) which can be compared with the following spectrum...

...of Magnetite (Fe₃O₄).