Mössbauer Spectroscopy

Nuclear Spin Angular Momentum (I):

The nuclear spin (I) of an atom is defined as the total angular momentum of the nucleus. The ground state nuclear spin for a given atom is dependent on the number of protons and neutrons in the nucleus and can be a half integer value (1/2, 3/2, 5/2, etc.) or an integer value (1, 2, 3, etc.). Nuclear spin excited states, I + 1n, where n is an integer value, exist and can be accessed if enough energy is applied to the nucleus.

Instrument Setup:

The general instrument setup is shown in Figure 1. The source that generates gamma rays is connected to a driver, which continuously moves the source with respect to the sample (the necessity of this will be explained below). The gamma rays then hit the solid sample, which is frequently suspended in an oil. Upon passing through the sample, the resulting transmitted radiation hits the detector, which measures the intensity of the beam upon interaction with the sample.

Figure 1. General instrumentation setup.

Gamma Ray Generation:

The source used to generate the gamma rays for the experiment needs to be of the same isotope as the atoms in the sample that are absorbing the radiation. For example, for ⁵⁷Fe Mössbauer spectroscopy, a radioactive ⁵⁷Co source is utilized. ⁵⁷Co decays (half life = 272 days) to the excited state of ⁵⁷Fe, I = 5/2. The resulting excited state further decays to either the I = 3/2 excited state or to the I = 1/2 ground state. Relaxation from the I = 3/2 excited state of ⁵⁷Fe to the ground state produces a gamma ray of desired energy for the experiment. However, the energy of the generated gamma ray does not exactly match the energy required for a nuclear excitation of the atom in a molecule. Returning to the example of ⁵⁷Fe, the energy levels of the I = 1/2 and I = 3/2 states change upon putting Fe within a molecule, where the oxidation and spin state of the metal as well as the ligand environment influence the electron field gradient at Fe. Therefore, to tune the energy of the resulting gamma ray, the source is moved with respect to the sample during the experiment using a driver (Figure 1). The conventional "energy" unit in Mössbauer spectroscopy is mm/s.

What Does a Typical Mössbauer Spectrum Look Like?:

In a Mössbauer spectrum, the percent transmission (dips in % transmission or the location of a peak that indicate gamma rays were absorbed at that energy) is plotted against the energy of the transition (mm/s). A typical spectrum is shown in Figure 2. The two peaks together are considered a single quadruple doublet, which is the result of two types of observable nuclear interactions:

1. The isomer shift (or chemical shift, δ, mm/s) is a measure of nuclear resonance energy and is related to the oxidation state of the atom. In Figure 2, the isomer shift is the energy value half way between the peaks in the spectrum. Table 1 includes the typical ranges of isomer shifts for given oxidation states and spin states of Fe.

Table 1. Some typical ranges of isomer shifts for Fe-containing compounds.¹

Oxidation state	Spin state (S)	Isomer shift range (mm/s)
Fe(II)	0	–0.3 to 0.5
Fe(II)	2	0.75 to 1.5
Fe(III)	1/2	–0.2 to 0.4
Fe(III)	5/2	0.2 to 0.55

2. The quadrupole splitting (ΔE_Q, mm/s) is a measure of how the electric field gradient around the atom affects the nuclear energy levels of the atom. Like the isomer shift, ΔE_Q provides information about the oxidation state. The spin state and the symmetry of the electron density around the atom (placement of ligands around a metal) will also affect the observed ΔE_Q. In Figure 2, the quadrupole splitting is the energy difference in mm/s between the two peaks in the spectrum.

Figure 2. A typical Mössbauer spectrum is plotted with velocity (energy) along the x axis and % transmission along the y axis. Here we see a single quadrupole doublet, with isomer shift, δ, and quadrupole splitting, ΔE_Q.

Isomer Shift and Quadrupole Splitting - What Nuclear Transitions Do These Values Represent?:

Here we will consider the nuclear spin transitions for an Fe atom (I = 1/2 ground state). The isomer shift is directly related to the electron transition in the s orbital of the atom from the I = 1/2 to an excited state (Figure 3). If the surrounding electric field gradient is non-spherical, due to either a non-spherical electronic charge or asymmetric ligand arrangement, the nuclear energy level splits (Figure 3), i.e., the I = 3/2 excited state splits into two m_I states ± 1/2 and ± 3/2. As a result, both nuclear transitions are observed in the Mössbauer spectrum and the distance between the two resulting peaks is called the quadrupole splitting. The quadrupole splitting value is therefore a measure of the effect on the nuclear energy levels with the electric field gradient around the atom.

Figure 3. Observable nuclear interactions in a ⁵⁷Fe Mössbauer spectrum including isomer shift, quadrupole splitting, and hyperfine splitting in the presence of a magnetic field.

Hyperfine Splitting:

Hyperfine splitting (or Zeeman splitting) can also be observed in the presence of an internal or external magnetic field. In the presence of a magnetic field, each nuclear energy level, I, splits into 2I + 1 sub-states. For example, in an applied magnetic field the nuclear energy level I = 3/2 would split into 4 non-degenerate states including 3/2, 1/2, -1/2 and -3/2, with 6 allowed transitions (Figure 3).

Zero field ⁵⁷Fe Mössbauer of ferrocene at 5 K.

δ = 0.54 mm/s

ΔE_Q = 2.4 mm/s

Referring to Table 1, we see that the isomer shift at 0.54 mm/s falls into several possible oxidation state/spin state ranges (Table 1). In cases such as this, it is not possible to determine the oxidation state and spin state based on δ-values alone. Chemists must use other characterization methods to gather evidence to support oxidation state and spin state assignments. Based on the proton NMR of ferrocene, we know that ferrocene is diamagnetic, and therefore must have a spin state of S = 0. The structure of ferrocene allows us to determine that the Fe center is in the 2+ oxidation state. The isomer shift value of 0.54 mm/s is close to the typical range of Fe(II), S = 0 compounds and therefore the Mössbauer spectrum is consistent with other characterization data.

Here, we learned about the basic principles of Mössbauer spectroscopy, including details on the experimental setup, the gamma ray source, and the information that can be gathered from a Mössbauer spectrum. We collected the zero field ⁵⁷Fe Mössbauer spectrum of ferrocene.

Mössbauer spectroscopy is a powerful technique that provides information about the electronic field gradient around an atom. While there are numerous Mössbauer active atoms, only elements with a suitable gamma ray source (long-lived and low-lying excited nuclear energy state) can take advantage of this technique. The most commonly studied atom is ⁵⁷Fe, which is used to characterize inorganic/organometallic molecular species, bioinorganic molecules, and minerals. For example, Mössbauer spectroscopy has been used extensively to study iron-sulfur (Fe/S) clusters found in metalloproteins.² Fe/S clusters are involved in a variety of functions, ranging from electron transport to catalysis. ⁵⁷Fe Mössbauer spectroscopy has helped elucidate valuable information about Fe/S clusters in proteins, including, but not limited to, the number of unique iron centers present in a Fe/S cluster as well as the oxidation state and spin state of those ions.