S15MossbauerSpectroscopy

Mossbauer Spectroscopy

Nathan Bosch and Jeffrey Zacher

University of Minnesota

School of Physics and Astronomy

Minneapolis, MN, 55455

Abstract

Mossbauer spectroscopy was utilized to observe the hyperfine splittings of the 14.4keV nuclear transition of !57Fe, !Fe2O3, and !Fe3O4. A !57Co source was placed on a moving platform to induce a Doppler-Effect energy shift, and absorption of these x-rays at specific velocity was determined by observing local minima in the x-ray counts on the opposite side of the samples. Isomer shift, Quadrupoles splitting, and the Zeeman effect were observed for the three samples,

Introduction

Mossbauer Spectroscopy is a type of gamma ray spectroscopy that takes advantage of recoilless absorption and emission of source and emitter nuclei embedded in a crystal lattice. It yields a high-resolution investigation of the energy levels of samples, and is used by many branches of science to provide precise information on magnetic, structural, and chemical properties. Mossbauer Spectroscopy was the basis for the Pound-Rebka experiment, the only terrestrial demonstration of the existence of gravitational redshift. In our experiment we analyzed the 14.4keV energy level transition of a various iron-based samples foil and observed three forms of transition-level splittings at the neV scale: namely, the Isomer shift, Quadrupole Splitting, and Zeeman Splitting. This resolution of 1neV in 14.4keV is analogous to a single star in all the stars of the Andromeda galaxy.

Theory (reduced)

Photon Energy

Fundamental to this technique is the Mossbauer effect, which refers to the recoilless absorption and emission of nuclei embedded in a crystal lattice. The means that when embedded in a crystal lattice, the effective mass of the nucleus is that of the entire lattice, resulting in a negligible portion of the transition energy going into recoil. This allows resonant absorption, which means that absorption and emission occur at precisely a transition energy.

In order to produce a continuous range of photon energies, the Doppler Effect is utilized. This is done by moving the source relative to the sample. In order to produce a continuous range of photon energies, the Doppler Effect is utilized. This is done by moving the source relative to the sample. When moving at millimeters per second, the fractional change in energy do to the Doppler Effect, v/c, is on the order of 10^-10.

Due to resonant absorption, and the continuous nature of the Doppler Effect, the maximal resolution of mossbauer spectroscopy is characterized by the linewidth of the radioactive source’s emission. This linewidth is related to the mean lifetime of the states via the Heisenberg Uncertainty Principle, τ Γ = h

For an excited Fe57 daughter of a prepared* 57Co source the mean lifetime of the 14.4keV peak is about 141ns [3], yielding a natural linewidth on the order of 10-14neV.

* When superheated, the 57Co 14.4keV emission demostrates no quadrupole, zeeman, or isomer splittings. There is a single photon energy. This prevents convolutions of these hyperfine effects amongst themselves.

Isomer Shift

The isomer shift occurs when the emitter and absorber have non-identical charge distributions. When this happens, the overlap between the probabilistic s-orbital and the nucleus will have different Coulombic interactions for the emitter and absorber. This effect manifests itself as a uniform energy increase in all of the absorption lines that we would otherwise expect to see

Zeeman Splitting

A nucleus has an inherent magnetic dipole moment. When the magnetic dipole moment interacts with magnetic fields surrounding the nucleus the states that can be occupied are split, allowing more possibilities for transitions.

Quadrupole Splitting

This non spherical charge distribution induces an electric field gradient outside of the nucleus. In turn, the the interaction between the electric field gradient and quadrupole moment split the atomic states that it can occupy. This splitting causes two absorption bands that we observe as being placed symmetric about the isomer shift.

Figure 1. The three effects superimposed. Note that 2 transitions(not shown) are disallowed by quantum mechanics.

Apparatus

The apparatus[4] shown below is a classic emitter-sample-detector spectroscopy setup with the inclusion of a linear motor, or ‘drive’ which oscillates the radiation source.

Figure 2. This is the most important parts of our Mossbauer apparatus.[4]

A function generator inputs a !14Hz triangle wave signal into the Mossbauer Driver which then controls the velocity of the Mossbauer Linear Motor. The motor oscillates the source, and, via the Doppler effect, alters its energy with respect to the stationary sample’s inertial frame. Beyond the source is the thin iron-compound sample, which can absorb transition-energy photons. The photons which were absorbed are re-emitted in a random direction when a sample nucleus de-excites, resulting in less photons of that (transition) energy travelling through to the detector.

In order to isolate the potential Fe-transition photons from other emissions of !57Co, the amplified signal is passed through a single channel analyzer. Whenever the SCA recieves a signal corresponding to a 14.4keV photon within the user-defined window, it triggers a data-acquisition device (DAQ) to read the linear-motor “velocity”.

A labview program converts this data into a histogram of counts vs velocity, which is equivalent to counts vs energy.

Data Analysis and Results

Due to inherent imperfection of the linear motor, velocity was not a perfect triangle wave. This resulted in very slight quadratic distortion of our data. This was corrected for by removing the central peak-data, fitting the remaining with a quadratic polynomial, and subtracting this background out.

Next we determined the exact relationship between the linear motor 'velocity' bin value, and true velocity. This was done by analyzing a 57Fe foil first, which has a well documented separation between the first and last absorption peaks of 10.657mm/s. The 57Fe foil also served as a reference for 0-velocity, since it has no isomer shift, and is thus symmetric about 0mm/s.

The data was smoothed with a Savitzky-Golay algorithm in !OriginLab and fit with Lorentzian peaks. Having determined the peak location, determination of splitting characteristics was obtainable via symmetry arguments.

Figures 3-5. Mossbauer Characteristics of various samples. Central line added to emphasize isomer shift. Note that !Fe3O4 demostrates a dual crystal nature - a mixture of α and β states. Original figure.

Table 1.The acquired values are within primarily within 3 standard deviations of accepted values.

Results

In summary, Mossbauer Spectroscopy is a powerful technique that allows us to observe hyperfine energy splittings on the neV scale. We were able to observe Quadrupole, Isomer, and Zeeman Splitting in various iron compounds. Our experiment veryifies the absence of quadrupole shift in 57Fe and largely agrees with accepted values. Due to the very long data acquisition times, we were unable to get enough data to fully resolve the alpha and beta states of !Fe2O3 (~1wk). Previous students have shown discrepancies in !Fe2O3 measurements, supporting the data's suggestion that the !Fe2O3 sample is slightly impure. Quantification of mossbauer drive uncertainties would improve error analysis.

Acknowledgements

The authors would like to thank Kurt Wick for all his advice and troubleshooting expertise throughout the semester, and Kai Zhang for helping us get started quickly.

References

1. Duarte, Javier; Campbell, Sara. “Mössbauer Spectroscopy” Thesis. Massachusetts Institute of Technology, 2009. Mit.edu. MIT, 6 Apr. 2009. Web.

2. Perepelitsa, Dennis V. "Mossbauer Spectroscopy of 57F E." Thesis. Massachusetts Institute of Technology, 2007. Mit.edu. MIT, 6 Apr. 2007. Web..

3. Pfeifer, Carrie. "Mössbauer Effect Using Co57." (n.d.): n. pag. UMNwiki. Web.

4. Brent Fultz, “Mössbauer Spectrometry”, in Characterization of Materials. Elton Kaufmann, Editor (John Wiley, New York, 2011).

5. van der Kraan, A. M. (1973), Mössbauer effect studies of surface ions of ultrafine α-Fe2O3 particles. phys. stat. sol. (a), 18: 215–226. doi: 10.1002/pssa.2210180120