# Introduction

Mössbauer spectroscopy is a spectroscopic technique discovered by Rudolf Mössbauer in 1957. It is based on the phenomenon called Mössbauer effect where a gamma ray photon is absorbed or emitted without loss of energy due to recoil of the nucleus. The most studied Mössbauer isotope is 57Fe.

In Mössbauer spectroscopy, the energy levels depend slightly on the environment of the atomic nucleus. There are three types of nuclear interactions:  chemical (isomer shift), electric (quadrupole interaction) and magnetic (magnetic ordering). It is possible to investigate nucleus specifically, but it is possible only when the transitions are between the ground state and the lowest excited state.

# Principle

Gamma rays are the shortest wavelength part of electromagnetic radiation. The energy of the photon is the highest and it’s in the order of transitions in atomic nucleus (Figure 1).

Energy in the atomic nucleus can be in different levels: lowest energy is in the ground state (Eg) and the higher energies in the excited states (Ee). The gamma rays are emitted as the energy difference when the nucleus returns from the excited state to the ground state:

E0=Ee-Eg

E0 depends on the environment of the Mössbauer nucleus and it is possible to control through Doppler effect, so when emitting nucleus, the source is moved and when absorbing nucleus, the sample is moved.

The nucleus gets recoil impulse (pr) of the opposite direction when gamma rays are emitted:

Pr=mvr=-E0/c

When the photon is emitted from the nucleus, its total energy at the nucleus above the ground state is E+1/2mv2, where m is the mass and vr the speed of emitting species. After the emission, the energy of emitted gamma ray photon is Eg and the velocity vr+v so the total energy of the system is Eg+1/2m(vr+v). So, the energy loss between E and Eg is:

ΔE0=E-Eg=1/2mv2+mvvr=Er-ED

So ΔE0 reflects the difference between two environments. When the ΔE0=0, it is possible to observe the resonance absorption experimentally.

Resonance absorption is not possible due to the recoil energy (Er), since gamma rays lose their capability to be absorbed by similar nuclei. However, in Mössbauer phenomenon, the recoil-free emission is possible. When the emitting nucleus is part of the crystal lattice, recoil can be avoided, since the entire crystal lattice gains the recoil energy and it becomes meaningless. The probability of recoil emission increases with the decreasing of Eor temperature. So, to eliminate the recoil of the nucleus, samples must be solid. Figure 1. Electromagnetic spectrum. Figure from Wikipedia. (License: CC BY-SA 3.0)

# Mössbauer spectrometer

Mössbauer spectrometer consist of radioactive source, collimator and the detector. The source of gamma rays contains some radioactive compound, e.g in case of iron, 57Co. Since resonance absorption is required, the source needs to be vibrated to generate the Doppler effect. The collimator works as a non-parallel gamma ray filter and detector measures the intensity of the transmitted gamma ray beam. Parts are shown in Figure 2.

Mössbauer spectroscopy has been used to study many elements, but the most studied is iron (57Fe). All of the Mössbauer active elements are shown in the Figure 3. Figure 2. Mössbauer spectrometer. Figure from Wikipedia. (License: Public Domain) Figure 3. Mössbauer active elements marked with *. Original periodic table template from Wikipedia. (License: Public Domain)

# Mössbauer spectrum

The source is moved from smaller to larger energies to the center of the emission spectrum (Doppler shift). This shift is relative to the center of the absorption spectrum. Level of transmission spectrum is determined at each value of velocity. It is determined by how much there is overlapping between the shifted emission spectrum and absorption spectrum. The greater the overlapping, the smaller the transmission.

So, in Mössbauer spectrum the intensity of gamma-rays is plotted as a function of source velocity. The absorbed gamma rays are seen as negative peaks in the spectrum. The information about the chemical environment of the absorbing nuclei can be obtained from the intensities, positions and amount of the peaks. In Figure 4, the spectrum of 57Fe is presented. Figure 4. Mössbauer spectrum of 57Fe. Figure from Wikipedia.(License: CC BY-SA 4.0)

# Hyperfine parameters

The interaction between nuclear moments and surrounding electric or magnetic field are described via hyperfine parameters. In Mössbauer spectroscopy, these parameters are isomer shift, quadrupole interaction and magnetic interaction. By using these parameters, it is possible to identify a specific compound by comparing it to standard spectra.

Isomer shift ΔE0 is the shift between two different nuclear levels in different environments. It depends on coordination, oxidation and spin states and electron densities of atoms. Electric quadrupole interaction ΔEdescribes nuclear quadrupole moment and its interaction with the electric field gradient present in the nucleus. It is created by surrounding ions and valence electrons of the Mössbauer nucleus. Isomer shift and quadrupole splitting for 57Fe are shown in Figure 5.

Magnetic splitting ΔEM describes the interactions between the nucleus and surrounding magnetic field. This can also be called as Zeeman effect. By using all of these three parameters, it is possible to compare the spectrum for standard spectra database and identify a particular compound. Figure 5. Isomer shift and quadrupole splitting and corresponding Mössbauer spectra for 57Fe. Figure from Wikipedia. (License: CC0 1.0)

# Applications

Via Mössbauer spectroscopy, it is possible to observe tiny changes in the chemical environment of the nucleus of the sample. This includes changes in oxidation states and magnetic environment.  Mössbauer spectroscopy can be used for identifying the composition of iron-containing compunds. For example, NASA uses Mössbauer spectrometer as one of the in situ-instruments for collecting data from iron containing rocks in Mars.

Mössbauer spectroscopy can be also used for studying iron containing proteins and enzymes in bio-organic chemistry.

• Possible to observe the resonance absorption
• All information with one measurement
• Perfectly specific for the investigated nucleus
• Small sample size (0.1-10 mg)

• Limited number of gamma ray sources
• Samples must be solid
• Need of recoil-free emission

# References

N.N Greenwood and T.C. Gibb (1971). Mössbauer Spectroscopy. ISBN 978-94-009-5697-1.

G.K. Wertheim (1964). Mössbauer effect: principles and applications. ISBN 1483251810.

R.L. Cohen (1980). Applications of Mössbauer spectroscopy. ISBN 0-12-178402-9.

M. D. Dyar, D. G. Agresti, M. W. Schaefer, C. A. Grant and E. C. Sklute (2006). Mössbauer spectroscopy of earth and planetary materials. Vol.34:83-125.

R.H.Herber (1967). The Mössbauer effect and its applications in chemistry. Advances in chemistry vol.68, pp(1-20). DOI: 10.1021/ba-1967-0068.ch001.

https://en.wikipedia.org/wiki/Mössbauer_spectroscopy

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