Introduction to Mössbauer Spectroscopy
Mössbauer spectroscopy is a versatile technique that can be used to provide information in many areas of science such as Physics, Chemistry, Biology and Metallurgy. It can give very precise information about the chemical, structural,
magnetic and time-dependent properties of a material. Key to the success of the technique is the discovery of recoilless gamma ray emission and absorption, now referred to as the 'Mössbauer Effect', after its discoverer Rudolph Mössbauer, who first observed the effect in 1957 and received the Nobel Prize in Physics in 1961 for his work.
This introduction to the theory and applications of Mössbauer spectroscopy is composed of four sections. First the theory behind the Mössbauer effect is explained. Next how the effect can be used to probe atoms within a system is shown. Then the principal factors of a Mössbauer spectrum are illustrated with spectra taken from research work. Finally a bibliography of books and web sites is given for further and more detailed information.
The Mössbauer Effect
Nuclei in atoms undergo a variety of energy level transitions, often associated with the emission or absorption of a
gamma ray. These energy levels are influenced by their surrounding environment, both electronic and magnetic, which can change or split these energy levels. These changes in the energy levels can provide information about the atom's local environment within a system and ought to be observed using resonance-fluorescence. There are, however, two major obstacles in obtaining this information: the 'hyperfine' interactions between the nucleus and its environment are extremely small, and the recoil of the nucleus as the gamma-ray is emitted or absorbed prevents resonance.
In a free nucleus during emission or absorption of a gamma ray it recoils due to conservation of momentum, just like a gun recoils when firing a bullet, with a recoil energy E R . This recoil is shown in Fig1. The emitted gamma ray has E R  less energy than the nuclear transition but to be resonantly absorbed it must be E R  greater  than the transition energy due to the recoil of the absorbing nucleus. To achieve resonance the loss of the recoil energy must be overcome in some way.
Fig1: Recoil of free nuclei in emission or absorption of a gamma-ray
As the atoms will be moving due to random thermal motion the gamma-ray energy has a spread of values E D  caused by
the Doppler effect. This produces a gamma-ray energy profile as shown in Fig2. To produce a resonant signal the two energies need to overlap and this is shown in the red-shaded area. This area is shown exaggerated as in reality it is extremely small, a millionth or less of the gamma-rays are in this region, and impractical as a technique.
Fig2: Resonant overlap in free atoms. The overlap shown shaded is greatly exaggerated
What Mössbauer discovered is that when the atoms are within a solid matrix the effective mass of the nucleus is very much greater. The recoiling mass is now effectively the mass of the whole system, making E R  and E D  very small. If the
gamma-ray energy is small enough the recoil of the nucleus is too low to be transmitted as a phonon (vibration in the crystal lattice) and so the whole system recoils, making the recoil energy practically zero: a recoil-free event. In this situation, as shown in Fig3, if the emitting and absorbing nuclei are in a solid matrix the emitted and absorbed gamma-ray is the same energy: resonance!
modulate
Fig3: Recoil-free emission or absorption of a gamma-ray when the nuclei are in a solid matrix such as a crystal
lattice
If emitting and absorbing nuclei are in identical, cubic environments then the transition energies are identical and this produces a spectrum as shown in Fig4: a single absorption line.
Fig4: Simple Mössbauer spectrum from identical source and absorber
Now that we can achieve resonant emission and absorption can we use it to probe the tiny hyperfine interactions between an atom's nucleus and its environment? The limiting resolution now that recoil and doppler broadening have been eliminated is the natural linewidth of the excited nuclear state. This is related to the average lifetime of the excited state before it decays by emitting the gamma-ray. For the most common Mössbauer isotope, 57Fe, this linewidth is 5x10-9ev. Compared to the Mössbauer gamma-ray energy of 14.4keV this gives a resolution of 1 in 1012, or the equivalent of a small speck of dust on the back of an elephant or one sheet of paper in the distance between the Su
n and the Earth. This exceptional resolution is of the order necessary to detect the hyperfine interactions in the nucleus.
As resonance only occurs when the transition energy of the emitting and absorbing nucleus match exactly the effect is isotope specific. The relative number of recoil-free events (and hence the strength of the signal) is strongly dependent upon the gamma-ray energy and so the Mössbauer effect is only detected in isotopes with very low lying excited states. Similarly the resolution is dependent upon the lifetime of the excited state. These two factors limit the number of isotopes that can be used successfully for Mössbauer spectroscopy. The most used is 57Fe, which has both a very low energy gamma-ray and long-lived excited state, matching both requirements well. Fig5 shows the isotopes in which the
Mössbauer effect has been detected.
Fig5: Elements of the periodic table which have known Mössbauer isotopes (shown in red font).
Those which are used the most are shaded with black
Armed with the Mössbauer effect and a suitable isotope how can we use these properties to investigate a system?
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.
Fundamentals of Mössbauer Spectroscopy
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.
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
Fig6: Simple spectrum showing the velocity scale and motion of source relative to the absorber
sufficiently thin to allow the gamma-rays to pass through, the relatively low energy gamma-rays are easily attenuated.
In Fig6 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.
Isomer Shift
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.
Quadrupole Splitting
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 m I =±1/2 and m I =±3/2. This is shown in Fig 7, giving a two line spectrum or 'doublet'.
Fig 7: 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, V zz , by the relation Delta=eQV zz /2.
Magnetic Splitting
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, B eff  is given by:
B eff  = (B contact  + B orbital  + B dipolar ) + B applied
the first three terms being due to the atom's own partially filled electron shells. B contact  is due to the spin on those electrons
polarising the spin density at the nucleus, B orbital  is due to the orbital moment on those electrons, and B dipolar  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 m I  changes by 0 or 1. This gives six possible
transitions for a 3/2 to 1/2 transition, giving a sextet as illustrated in Fig8, with the line spacing being proportional to B eff .

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