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Mössbauer Spectroscopy
by Emily Edwards and Zi Wang
Abstract
In this experiment, our goal was to observe a Mössbauer spectrum of iron compounds in order to explore the Mössbauer effect and other phenomena including isomer shifting, quadrupole splitting, and the Zeeman effect. This allowed us to learn more about atomic structures. To achieve this aim, we used 57Fe compounds to absorb emitted photons from a source of 57Co, which was oscillating in order to create a Doppler shift. We then used LabVIEW, Origin, and MATLAB software to analyze the data to find peaks in the counts vs. energy plot which indicated the possible nuclear transition energies of 57Fe compounds and allowed us to find energy values of above phenomena. Our results for the magnetic hyperfine splitting, isomer shifts, and quadrupole splitting all fell within 3 standard deviations of the accepted values, except for some values for Fe3O4.
Introduction
In quantum mechanics, electron can be excited to quantized energy levels while atoms or nuclei can also have quantized energy level. Transitions between different energy level happen when nuclei absorb or emit photon with the required energy. After the nuclei absorb the photons and goes to an excited state, a decay will happen eventually and re-emit the photons in a random direction. If we collect the photon and make a spectrum, there will be peaks formed by fewer photons at transition energies. Transitions usually occur with recoil. Emitting or absorbing photons requires the nuclei to take away some of the transition energy by conservation of momentum. So, the re-emitted photons have less energy and can’t excite another same transition process. But fortunately, Mössbauer method involves the recoilless resonant absorption. This happens because the recoil of a nucleus is almost zero if the nucleus is embedded in a lattice.
Rudolf Mössbauer discovered the recoil-free emission and absorption of gamma rays in 1957. Later on, Mössbauer spectroscopy was developed by using the Mössbauer effect to take very precise measurements of atoms. Mössbauer spectroscopy lets us measure atomic properties such as magnetic hyperfine splitting (Zeeman effect), isomer shift, and quadrupole splitting. With it, we are able to detect very small changes on the order of 1 part in 100 billion. With Mössbauer spectroscopy we have three main components: a radioactive source, a sample material, and a detector.
Theory
Mössbauer spectroscopy involves two main effects: The Mössbauer effect and the Doppler shift. The Mössbauer effect involves a nearly recoilless emission and absorption of photons. This is because the source and sample are both in a crystal lattice. Without the crystal lattice, the recoil energy from photon emission and absorption is far too large to allow us to measure the effects we want. This can be calculated with the following equation for recoil energy:
where Eγ is the initial photon energy (14.4 keV for our case), m is the mass of the atom, and c is the speed of light. For 57Fe, the recoil energy is 1.96 x 10-3 eV, which is much larger than the effects we want to measure, which are on the order of 10-7.
The reason for the moving radiation source is to create a Doppler effect. This allows for small changes in energy of the radiation source, which allows us to scan through the atomic hyperfine structure.
The Doppler shift for energy is represented by the following equation:
where E0 is the initial energy (14.4 keV again), v is the velocity of the source, and c is the speed of light.
There are three main effects that we can see: magnetic hyperfine splitting (Zeeman effect), isomer shifting, and quadrupole splitting.
Magnetic Hyperfine Splitting
When atoms are exposed to a magnetic field, their spectral lines undergo splitting. In the case of 57Fe, six spectral lines are formed from the ground state and excited state. The ground state splits into a -1/2 and 1/2 part, while the excited state splits into a -3/2, -1/2, 1/2, and 3/2 part. There are six transitions due to quantum selection rules.
Quadrupole Splitting
There can be an electric field gradient inside the nucleus. So if the atoms in the lattice have a non-perfect symmetry, the charge of the nucleus can slightly change depending on its orientation. As a result, we get a pair of peaks to show in the spectrum.
Isomer Shift
The isomer shift is caused by a difference in the nuclear isomers in the sample and source. When an atom enters an excited state, the nuclear radius changes. If the source and sample isomers are different, the energy level shifts between them will be different. This causes all the peaks to shift off from the center by a factor of delta.
Natural Line Width
The natural line width of Mössbauer line is related to Heisenberg uncertainty and the half-life of the excited nuclear state. They are related by:
∆E ∆t ≥ Γ/τ = h / 2π.
Where Γ is the natural line width and τ is the half life time. We can measure the full width at half maximum of the absorption peak and the half life of the excited state decay can then be calculated.
Experimental Setup and Methods
The following diagram shows our experimental setup.
Photons are detected at the silicon detector which are then amplified by an internal amplifier. This signal is then sent to another amplifer and then to the SCA, which outputs a TTL signal to mark that an event has occurred. This signal is then sent to the NI DAQ (Data acquisition device) which outputs to a LabVIEW program.
The source is attached to a linear motor which is powered by the Mössbauer driver S3, which in turn is powered by a function generator set to generate a triangle wave. The linear motor outputs its velocity data to a pre-amplifer which then sends it to the NI DAQ. When the TTL trigger signal reaches the DAQ, the DAQ sends the velocity data at the time to the LabVIEW program. This gives us the energies at which events occur, although the energy values are in the form of channels at the time and must be converted to actual energy units later.
Analysis
After we set up the experiment, data was collected from the LabVIEW program. And the program wrote data to an Excel spreadsheet periodically. And all the data collected during a run was wrote to a spreadsheet at the end of the run. We then used Origin to create a histogram by plotting the count of photon events at particular energy against the channel number which is proportional to the voltage in the detector. The data was fitted in origin using Lorentzian function. Because Lorentzian line shape can be used to demonstrate spectral lines of broadened resonance. And it is also good at approximating line shapes in spectra of paramagnetic materials where the electronic environment for all the Fe nuclei is identical [2].
Because the distance between the source and detector is only a few inches, photons are not all detected in a parallel direction, and the triangle wave of velocity was distorted. So, we need to subtract a quadratic polynomial from each plotting [3]. But we decided not to involve background noise in data analysis for the sake of simplicity. Further reason will be explained in the results section. And following are the histograms including background noise.
Figure 1 [1]: Diagram of the apparatus
Figure 2: Absorption spectrum of 57Fe in pure iron.
In the spectrum of pure iron sample, six peaks are clear seen. The center of six peaks is at energy equal to zero since there is only Zeeman effect as we stated before.
Figure 3: Absorption spectrum of 57Fe in Fe3O4.
It can be seen that instead of the ordinary 6 peaks, there are 9 peaks in the histogram. The left six peaks are from three doublet peaks. The left division of these three doublet peaks are the A peaks, while the right division are the B peaks. This is due to the fact that Fe3O4 crystal geometry contains tetrahedral and octahedral sites which contains Fe2+ and Fe3+ ions [4].
As a result, we calculated the parameters of the A and B peaks separately.
Figure 4: Absorption spectrum of 57Fe in Fe2O3.
The peaks in Fe2O3 are less observable. It’s hard to tell if there are six peaks without fitting with Lorentzian function. The count of photon events at particular energy is smaller than that of Fe3O4. This is not because we spend less time taking data from Fe2O3 sample, actually a longer period of time was involved. One of the reasons could be the amount of 57Fe isotope in Fe2O3 is much less than that of pure iron or Fe3O4. So, there is less possibility for photons to excite the nuclei in Fe2O3. As a result, the peaks would not be as clear as in the other iron samples.
Results
From the pure iron results, we can tell all measured values are within 3 standard deviation of the expected value. But the p value is very high which could be due to small number of data points. The results for Fe3O4 are mostly within 5 standard deviation from the expected value except the
isomer shift. I compared our results with other student’s results from before, I found that one of the reasons is our uncertainty is too small since we didn’t involve background noise and velocity calibration. Another reason could be the error in calibration of pure iron data while we were converting channel number to energy. The results of Fe2O3 once again indicated the possibility that errors are mainly come from calibration since only the isomer shift is off. And a high p value is also because of few data points for Fe2O3. To recap, we didn’t consider background noise because only isomer shift results are off. Also, subtraction of the background would not contribute to the isomer shift being off.
Conclusion
We measured the spectrum of 57Fe in pure iron, Fe3O4, and Fe2O3 using Mössbauer spectroscopy. We got a better understanding of the nuclear properties of 57Fe nucleus through the calculation of the Zeeman effect, isomer shift, and quadrupole splitting. More error propagation including removing background noise and calibrating the velocity of the radiation source with quadrature interferometer, could be done in the future experiment to make sure there is less standard deviation between the measured values and expected values. Also, more data points can be taken for pure iron and Fe2O3 to make the results statistically significant.
References
[1] MXP Wiki, “Mossbauer Apparatus”. University of Minnesota https://sites.google.com/a/umn.edu/mxp/advanced-experiments/mossbauer-effect-lab/mossbauerapparatus
[2] Dyar, D. M. (2021, April 29). Mössbauer spectroscopy. Retrieved May 06, 2021, from http://serc.carleton.edu/research_education/geochemsheets/techniques/mossbauer.html
[3] Preston, R.S.,et al. “Mossbauer effect in metallic iron.” Physical Review, vol. 128, no. 5, 1962, pp. 22072218., doi:10.1103/physrev.128.2207
[4] Wolfgang Rueckner. ”B-2 Mossbauer Spectroscopy”, Physics 191r, Harvard University. http://ipl.physics.harvard.edu/wp-uploads/2013/03/191b2.pdf
Special thanks to Kurt Wick and Professor Daniel Cronin-Hennessy.
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