Mössbauer Spectroscopy

Cong Chen and Andrew Vold

University of Minnesota

Methods of Experimental Physics Spring 2013

Abstract

In this experiment, we attempted to utilize the Mössbauer Effect to measure the isomer shift, δ, the quadrupole splitting energy, µ, and the Zeeman Splitting energies, Δ0 and Δ1, of Fe foil, Fe2O3, and Fe3O4. We accomplished this by observing the resonant absorption of Fe2O3 and Fe3O4 absorbers. The Doppler Shift was used to probe the hyperfine splitting of the nuclear transition energies.

Introduction

The precision of Mössbauer Spectroscopy has made it a widely used experimental method to study the nuclear properties of various materials. The precision of Mössbauer Spectroscopy is fine enough to actually observe the gravitational red shift of photons on earth, confirming General Relativity. Mössbauer Spectroscopy combines two phenomena known as recoilless emission/absorption and Doppler shifting to allow for the detailed study of the nuclear properties of various materials.

The Mössbauer Effect is the basis for Mössbauer Spectroscopy. The Mössbauer Effect is the result of placing a source and absorber within crystal lattices. By doing this a phenomenon known as recoilless emission/absorption occurs. Recoilless emission/absorption allows for a phenomenon known as resonant absorption to occur. Resonant absorption is the absorption of an emitted gamma ray, which has energy identical to that of a nuclear transition [7].

Recoilless emission/absorption requires the placement of the source and absorber in a crystal lattice, to obtain a high effective mass. This must be done because the gamma rays have energy of 14.4 keV, giving them enough momentum to induce significant recoil of the source and absorber. As a result of conservation of energy, the induced recoil energy will reduce the energy of the gamma ray [8]. In this experiment, a 57Co source will be immersed in a metallic foil, and the Fe2O3 and Fe3O4 absorbers will be placed in Aluminum holders.

The Mössbauer Effect also requires Doppler shifting. This must be used because the source and absorbers are not in identical electromagnetic environments. As a result of this, the nuclear transition energies of the absorber will be slightly perturbed from that of the source [8]. In order to observe the altered nuclear transition energies, the energy of the gamma ray must be slightly shifted. In this experiment, low velocity Doppler shifting was used to provide the fine energy shifting of the gamma rays. By observing the resonant absorption of the Doppler shifted gamma rays, we were able obtain values for the isomer shift, quadrupole splitting, and Zeeman splitting for each of the absorbers.

Theory

All radioactive isotopes undergo nuclear transitions. In this experiment, 57Co experienced electron capture decay, resulting in excited 57Fe. This isotope has a mean lifetime of 9.77x10^-8 s [8]. The 57Co spectrum has several energy peaks, in this experiment, we were interested in the 14.4 keV peak. The uncertainty of the gamma ray energy was found by inserting the mean lifetime of excited 57Fe into the Heisenberg Uncertainty Principle, yielding a pulse width of 4.67x10^-9 eV [8]. It was important for this peak to have such a low uncertainty because of a phenomenon known as convolution. When a gamma ray energy peak is scanned across an energy space of an absorber, it is averaged in a window formed by the absorber energy peaks. Since the uncertainty of the gamma ray energy is very small, averaging has a minimal effect, making convolution negligible [8].

In this experiment, resonant absorption was needed for the observation of the Mössbauer spectrum of the absorber materials. The Mössbauer spectrum is the spectrum of gamma rays which interact with the detector. Gamma rays without sufficient energy for resonant absorption passed through the absorber and were detected. The gamma rays which did have sufficient energy for resonant absorption were absorbed and reemitted in a radial direction by the absorber, creating dips in the spectrum. Resonant absorption occurs when a gamma ray from a nuclear transition is identical to the excitation energy of an absorber material. Resonant absorption must occur in solids because of the bound nature of the atoms in the solid. Since the emitted gamma rays have energy, they also have momentum given by E/c. Using the conservation of momentum and some simple algebra, the recoil energy, ER, is given by:

ER = Eγ^2/2Mc^2

In this equation, Eγ is the energy of the nuclear transition, M is the mass of the source or absorber, and c is the speed of light [7]. By using this equation, one can find that a free Fe nucleus would have recoil energy of approximately 0.004 eV. This loss of energy is far too large to induce any resonant absorption. Putting the emitter in a crystal structure with mass 10^-12 kg would result in energy loss of approximately 1.85x10^-19 eV [7].

In order to observe the hyperfine splitting of the energy levels in the materials, Doppler shifting was used. Doppler shifting was used because the hyperfine energy splittings were many orders of magnitude smaller than that of the energy of nuclear transition. By moving the source of the radiation, we caused a shift in frequency, and thus, the energy of the gamma rays. The Doppler shifted energy equation can be found by multiplying the binomially expanded Doppler frequency by the initial gamma ray energy:

Eγ = 14400(1+v/c)

According to this equation, adjusting the velocity of the source or the absorber causes a very fine change in the energy of the gamma ray. In this experiment, the source was moving with a velocity on the order of a few mm per second. Inserting this into equation (2), the energy of the gamma ray was shifted on the order of 10-11. Energy shifting of this magnitude was fine enough to observe the hyperfine energy splitting. With the tools of Mössbauer Spectroscopy, we were able to observe the isomer shift, the quadrupole splitting energies, and the Zeeman Splitting energies.

The isomer shift is the shift in the spectral lines, resulting from a change in the interaction between the nucleus and the electron cloud. In this experiment, the isomer shift occurred because the radii of the ground and excited electron energy levels were shifted. Differences in the radius and the electron density of the emitter and absorber affect the Coulomb interaction between the nucleus and the electrons, leading to an energy shift.

Quadrupole splitting is the result of an interaction between the nuclear quadrupole moment and the surrounding electric field gradient. Quadrupole splitting will be seen as two symmetric dips. Superimposed with Zeeman Splitting and the Isomer Shift, Quadrupole splitting will result in a discrepancy between the distance between the two left most peaks and the distance between the two right most peaks, resulting in a loss of reflective symmetry.

Zeeman Splitting is the result of an interaction between the nuclear magnetic dipole moment and the internal magnetic field created by an unpaired electron in the 1s orbital [7]. The resulting spectra has only six transitions, instead of eight. This is the result of selection rules. As a result of this, two transitions are forbidden [8]. By use of recoilless emission and Doppler shifting, all of the Mössbauer parameters will be observed.

Apparatus & Experimental Procedure

A diagram of the apparatus, created by a previous year's group, is shown in Figure 1. The function generator provided a sync signal of 14Hz to the driver model, which powered the linear motor with a linearly changing velocity. The driver sent a triangular wave signal with peak to peak voltage corresponding to velocity. This signal was then amplified by the SR 560 with a gain of 3 and was sent into the DAQ. The detector outputted an analog signal with a peak to peak voltage corresponding to the energy of the gamma ray whenever it detected a gamma ray. This signal was sent to the PX2T/CR, which amplified the signal and sent it to the SCA. The SCA outputted a TTL pulse whenever a 14.4 keV photon signal entered. These pulses were then sent to the DAQ where they were binned according to the velocity of the motor at that instant.

Figure 1: Experimental Setup

The SCA had to be calibrated, in order to achieve this. The calibration began with comparing the peak locations of the spectra of 241Am and 133Ba. The spectra of these isotopes allowed us to find the location of the 14.4 keV peak in the 57Co spectrum. A plot of the 57Co spectrum is shown in Figure 2. Once we found the location of the 14.4 keV peak, we scanned it, using the SCA with a small window. The center of the peak determined the center of the SCA window, and the width of the peak determined the window size of the SCA for the remainder of the experiment. This caused the SCA to trigger only when a pulse corresponding to a 14.4 keV gamma ray was sent from the detector.

Figure 2: Spectrum of 57Co. The 14.4 keV peak is the third peak.

Data Analysis

The resulting histograms were entered into our analysis program, Origin. We first masked out all of the outlier points. Next, the histograms had a quadratic background, so they were fit to a second order polynomial, and the quadratic background was subtracted out. Then a smoothing algorithm was used to reveal the shape of the energy peaks. Finally, the six peaks were fitted to Lorentzian Distributions, using a least squared fitting algorithm. With the data fitted to Lorentzian Distributions, we were able to extract the Mössbauer parameters and their corresponding uncertainties.

This procedure was first used for 1 mm. thick Fe foil. The spectrum from Fe foil theoretically has no isomer shift or quadrupole splitting. As a result of this, it was used for calibration. We began by converting the x axis from bins to velocity in mm/s by comparing the width of the spectrum to the accepted standard of 10.6 mm/s. Once the x-axis was scaled to velocity, it was then scaled to Doppler shifted energy in eV.

The same histogram fitting procedure was then be used for Fe2O3 and Fe3O4. The resulting spectra for Fe2O3 and Fe3O4 are shown in Figures 3 and 4. From the spectra of these compounds, we were able to calculate the isomer shift, quadrupole splitting, and Zeeman splitting values. The peak locations and their uncertainties were what were used to obtain parameter values and their uncertainties.

Figure 3: Spectrum of Fe203.

Figure 4: Spectrum of Fe304.

In order to calculate these values, a Least Squares method was used to solve an overdetermined system of equations. The system of equations was composed of equations for the energy transitions [7].Solving the system of equations yielded equations for each of the parameters with peak locations being the variables. In order quantify the uncertainties of these parameters, propagation errors was applied to the equations of the parameters.

Conclusion

By utilizing recoilless emission/absorption and Doppler shifting, many nuclear properties can be observed. In this experiment we used radioactive 57Co to observe the isomer shift, quadrupole splitting, and Zeeman splitting for Fe2O3 and Fe3O4. The isomer shift values were off by 3.5σ for Fe2O3 and 4.12σ for Fe3O4. The quadrupole splitting energies were off by 0.3σ for Fe2O3. The Zeeman Splitting energies were off by 2.0σ and 2.4σ for Fe foil, 8.8σ and 3.2σ for Fe2O3, and 4.81σ and 1.6σ for Fe3O4 [7]. The data we had collected was quite accurate. Each of the parameter values were off by a few percent, compared to the accepted values. The reason for our large standard deviation difference was because of our rough systematic error analysis. To begin, the 10.6 mm/s value for the Fe foil calibration did not have any uncertainties. As a result of this, we had to assume that its uncertainty was ±0.1 mm/s. Next, we could not find any specifications of our Mössbauer drive. As a result of this, we underestimated the uncertainty on the peak locations of our histograms. Finally, we assumed that the pulse coming from the Mössbauer Drive into the DAQ was a perfect triangle wave. This, however, is impossible, so this assumption could have added to the underestimation of data uncertainties. If we had a thorough systematic error analysis, our results would be much closer to the accepted values.

References

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