Introduction to Mössbauer Spectroscopy: Part 2
So far we have seen one Mössbauer spectrum: a single line corresponding to the emitting and absorbing nuclei being in identical environments. As the environment of the nuclei in a system we want to study will almost certainly be different to our source the hyperfine interactions between the nucleus and the its environment will change the energy of the nuclear transition. To detect this we need to change the energy of our probing gamma-rays. This section will show how this is achieved and the three main ways in which the energy levels are changed and their effect on the spectrum.
As shown previously the energy changes caused by the hyperfine interactions we will want to look at are very small, of the order of billionths of an electron volt. Such miniscule variations of the original gamma-ray are quite easy to achieve by the use of the doppler effect. In the same way that when an ambulance's siren is raised in pitch when it's moving towards you and lowered when moving away from you, our gamma-ray source can be moved towards and away from our absorber. This is most often achieved by oscillating a radioactive source with a velocity of a few mm/s and recording the spectrum in discrete velocity steps. Fractions of mm/s compared to the speed of light (3x1011mm/s) gives the minute energy shifts necessary to observe the hyperfine interactions. For convenience the energy scale of a Mössbauer spectrum is thus quoted in terms of the source velocity, as shown in Fig1.
Fig1: Simple spectrum showing the velocity scale and motion of source relative to the absorber
With an oscillating source we can now modulate the energy of the gamma-ray in very small increments. Where the modulated gamma-ray energy matches precisely the energy of a nuclear transition in the absorber the gamma-rays are resonantly absorbed and we see a peak. As we're seeing this in the transmitted gamma-rays the sample must be sufficiently thin to allow the gamma-rays to pass through, the relatively low energy gamma-rays are easily attenuated.
In Fig1 the absorption peak occurs at 0mm/s, where source and absorber are identical. The energy levels in the absorbing nuclei can be modified by their environment in three main ways: by the Isomer Shift, Quadrupole Splitting and Magnetic Splitting.
The isomer shift arises due to the non-zero volume of the nucleus and the electron charge density due to s-electrons within it. This leads to a monopole (Coulomb) interaction, altering the nuclear energy levels. Any difference in the s-electron environment between the source and absorber thus produces a shift in the resonance energy of the transition. This shifts the whole spectrum positively or negatively depending upon the s-electron density, and sets the centroid of the spectrum.
As the shift cannot be measured directly it is quoted relative to a known absorber. For example 57Fe Mössbauer spectra will often be quoted relative to alpha-iron at room temperature.
The isomer shift is useful for determining valency states, ligand bonding states, electron shielding and the electron-drawing power of electronegative groups. For example, the electron configurations for Fe2+ and Fe3+ are (3d)6 and (3d)5 respectively. The ferrous ions have less s-electrons at the nucleus due to the greater screening of the d-electrons. Thus ferrous ions have larger positive isomer shifts than ferric ions.
Nuclei in states with an angular momentum quantum number I>1/2 have a non-spherical charge distribution. This produces a nuclear quadrupole moment. In the presence of an asymmetrical electric field (produced by an asymmetric electronic charge distribution or ligand arrangement) this splits the nuclear energy levels. The charge distribution is characterised by a single quantity called the Electric Field Gradient (EFG).
In the case of an isotope with a I=3/2 excited state, such as 57Fe or 119Sn, the excited state is split into two substates mI=±1/2 and mI=±3/2. This is shown in Fig2, giving a two line spectrum or 'doublet'.
Fig2: Quadrupole splitting for a 3/2 to 1/2 transition. The magnitude of quadrupole splitting, Delta, is shown
The magnitude of splitting, Delta, is related to the nuclear quadrupole moment, Q, and the principle component of the EFG, Vzz, by the relation Delta=eQVzz/2.
In the presence of a magnetic field the nuclear spin moment experiences a dipolar interaction with the magnetic field ie Zeeman splitting. There are many sources of magnetic fields that can be experienced by the nucleus. The total effective magnetic field at the nucleus, Beff is given by:
|Beff = (Bcontact + Borbital + Bdipolar) + Bapplied|
the first three terms being due to the atom's own partially filled electron shells. Bcontact is due to the spin on those electrons polarising the spin density at the nucleus, Borbital is due to the orbital moment on those electrons, and Bdipolar is the dipolar field due to the spin of those electrons.
This magnetic field splits nuclear levels with a spin of I into (2I+1) substates. This is shown in Fig3 for 57Fe. Transitions between the excited state and ground state can only occur where mI changes by 0 or 1. This gives six possible transitions for a 3/2 to 1/2 transition, giving a sextet as illustrated in Fig3, with the line spacing being proportional to Beff.
Fig3: Magnetic splitting of the nuclear energy levels
The line positions are related to the splitting of the energy levels, but the line intensities are related to the angle between the Mössbauer gamma-ray and the nuclear spin moment. The outer, middle and inner line intensities are related by:
|3 : (4sin2theta)/(1+cos2theta) : 1|
meaning the outer and inner lines are always in the same proportion but the middle lines can vary in relative intensity between 0 and 4 depending upon the angle the nuclear spin moments make to the gamma-ray. In polycrystalline samples with no applied field this value averages to 2 (as in Fig3) but in single crystals or under applied fields the relative line intensities can give information about moment orientation and magnetic ordering.
These interactions, Isomer Shift, Quadrupole Splitting and Magnetic Splitting, alone or in combination are the primary characteristics of many Mössbauer spectra. The next section will show some recorded spectra which illustrate how measuring these hyperfine interactions can provide valuable information about a system.
Mössbauer spectroscopy is a versatile technique that can be used to provide information in many areas of science.
Hyperfine interactions at work