F17_Mössbauer Spectroscopy

Mössbauer Spectroscopy of ⁵⁷Fe, Fe₂O₃, and Fe₃O₄

Aaron Durgin & Chase McCabe

Introduction

Mössbauer spectroscopy was performed to observe nuclear characteristics of 57Fe, Fe2O3, and Fe3O4. Mössbauer spectroscopy is a highly precise energy measurement technique that is able to detect energy changes of 1 part in 3 x1012. This technique takes advantage of recoil-free resonant absorption and emission in solids, otherwise known as the Mössbauer effect. The resulting spectrums were analyzed to observe the hyperfine interactions of the nucleus and its environment. These interactions consist of the isomer shift, quadrupole splitting, and the Zeeman effect. The Doppler effect was used to modulate the energy of the radiation source to create the spectrum. A quadrature Michelson interferometer was added to the apparatus to allow absolute velocity measurements.

Theory

Spectroscopy is used to quantitatively or qualitatively study the absorption, emission, or scattering of electromagnetic radiation in matter such as atoms or molecules. When electromagnetic radiation is absorbed, the incident energy excites a quantized structure to a higher energy level, known as an excited state. When the atom decays to a lower energy level, electromagnetic radiation is emitted. When the emission and absorption of electromagnetic radiation occur at the same energy, resonant absorption occurs. In 1958, Rudolf Mössbauer discovered resonant absorption of gamma rays interacting with solids.

Mössbauer Effect

There is a recoil energy E_r during absorption and emission that is quantified by E_r = Eγ²/(2mc²), where Eγ is the gamma ray energy and m is the mass of the nucleus. The conservation of energy dictates that the photon will lose some of its energy to recoil. Since gamma energy is relatively high (14.4 keV for ⁵⁷Co), this decreases the photon energy to a level where resonance would not be possible. Mössbauer discovered that nuclei within solids are contained within a lattice structure, and the mass in the recoil energy equation in altered to be the mass of the lattice. This causes the recoil to be effectively zero in solids, allowing for resonance and therefore spectroscopy.

Hyperfine Interactions

Small perturbations in the transition energy occur due to interactions between the nucleus and its environment. These interactions only cause a change of energy of ~10-9 to 10-7 eV, but they give insight into characteristics of the sample. There are three interactions that characterize Mössbauer spectroscopy: isomer shift, Zeeman effect, and quadrupole splitting.

These three effects are shown in the diagram to the right. Here, the isomer shift (𝜀) is shown as the difference between the dotted and solid figures. The Zeeman effect is shown by the arrows between the J = 1/2 and 3/2 states, with its relative energy values Δ0 and Δ1. Quadrupole splitting (𝛿) is shown as a shift in the J = 3/2 energy levels.

Doppler Effect

In order to view the spectrum and the corresponding hyperfine interactions of the nucleus, the radiation source energy needs to be modulated. This is done using the Doppler effect. Although this is generally used to measure a change in frequency, the equation can be rewritten to describe a change in energy: ∆E=Eγ(v/c) where Eγ is the gamma ray energy, v is the velocity of our source, and c is the speed of light. The hyperfine interactions cause shifts in energy from 10^-9 to 10^-7 eV; taking the upper bound the radiation source only needs to have a velocity of a few cm/sec to observe the interactions.

Quadrature Michelson Interferometer

Generally, the velocity differences between peaks are determined by looking up values from secondary sources and applying them to the recorded data. The quadrature Michelson interferometer allows for a direct measurement of the velocity changes. This setup measures changes in optical path length accurate to fractions of a wavelength, all while retaining the direction of change. In our experiment, one arm is attached to the back of the linear motor creating the Doppler shift. A more detailed explanation of the theory and setup can be found here.

Apparatus

The signal from the silicon detector is amplified and passed through a single channel analyzer; this is used to pass only the counts that fall within the 14.4 keV peak by sending a TTL pulse to the data acquisition card. The other single being read is the amplified voltage from the linear motor. The LabView program creates a histogram, plotting the relative energy of the incident gamma rays expressed as a bin number on the x-axis and the number of counts on the y-axis.

Quadrupole splitting is an effect resulting from the electric field gradient interacting with the nuclear quadrupole moment. This quadrupole moment is due to the spherical asymmetry of the nucleus; when the nucleus is perfectly symmetrical, there is no quadrupole splitting.

The Zeeman effect occurs when the internal magnetic field interacts with the magnetic dipole moment of the nucleus. The angular momentum of the dipole moment is expressed as a spin state, J. In 57Fe, the ground state has J = 1/2 and its excited state has J = 3/2. Each state is split into 2J+1 component levels, which are termed mj. Therefore there are eight possible transitions between the ground and the excited state. Selection rules state that Δmj = 0, ±1, so two transitions are forbidden leaving six allowed transitions.

The isomer shift results from different configurations of the nucleus and the electron cloud density between the source and absorber. The s-electron density has a finite

probability to overlap with the nucleus, and when it absorbs the γ-ray, the nuclear radius increases slightly. It follows that for different compounds (and therefore different nuclear configurations), the isomer shift will have different values.

The flow charts above show the BNC connections for the experiment. Pictures of some of the equipment are shown below.

A linear motor with the radioactive ⁵⁷Co source attached facing the detector with an iron sample in between.

The Mössbauer Drive. Motor switch set to Computing Amp., Velocity range set to 0.2 cm/sec, Velocity Multiplier set to 6.00, and Fidelity set approximately to the left.

The PX2T/CR amplifies the signal from the detector. RTD switch set up. Gain set to 3.0. The SR560 amplifies the velocity signal from the Linear Motor.

A single channel analyzer (left) and Ortec counter (right). The window or upper level was set to 1.42. The lower level was set to 3.55. The switch set down to Window.

Results

The data analysis software, Origin, was used to fit the data from the LabView program as Lorentzians. The raw data from the LabView Program contained a quadratic effect. This was removed by fitting the data to a quadratic and then subtracting off the effect from the original data. In the graphs below, the quadratic effect has been subtracted. A Lorentzian fit was performed for ⁵⁷Fe, Fe₂O₃, and Fe₃O₄. By using the data from the Quadrature Michelson Interferometer, a conversion factor was obtained to convert the x-axis from units of bins to units of energy. We obtained a factor of -227.01 ± 0.03 bins/Volt.

Experimental and theoretical values for ⁵⁷Fe, Fe₂O₃, and Fe₃O₄. The hyperfine interactions are: isomer shift (𝜀), quadrupole splitting (𝛿), Zeeman effect ground and excited state (Δ0 and Δ1 ).

All figures and pictures are original.

References

Bancroft, G. (1973). Mössbauer spectroscopy : An introduction for inorganic chemists and geochemists. New York: Wiley.
Brent Fultz, “Mössbauer Spectrometry”, in Characterization of Materials. Elton Kaufmann, Editor (John Wiley, New York, 2011).
Rueckner, Wolfgang. “B-2 Mossbauer Spectroscopy.” ipl.physics.harvard.edu/wp-uploads/2013/03/191b2.pdf.
Elsworth, Y., & James, J. F. (1973). An optical screw with a pitch of one wavelength. Journal of Physics E: Scientific Instruments, 6(11), 1134-1136.

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