Answer to Question #343568 in General Chemistry for Bob

Question

Application limitations and strength of Mossbauer spectroscopy

Answer 1

The technique of Mössbauer spectroscopy is widely used in mineralogy to examine the valence state of iron, which is found in nature as Fe⁰ (metal), Fe²⁺, and Fe³⁺, as well as the type of coordination polyhedron occupied by iron atoms (trigonal, tetrahedral, octahedral, etc.). It is sometimes used to determine redox ratios in glasses and (less successfully) in rocks. Mössbauer spectroscopy is also used to assist in the identification of Fe oxide phases on the basis of their magnetic properties.Fundamental Principles of Mössbauer Spectroscopy

Figure 1. Details

The Mössbauer effect as generally applied to the study of minerals relies on the fact that ⁵⁷Fe, which is a decay product of ⁵⁷Co, is unstable. ⁵⁷Fe decays by giving off a gamma ray (γ-ray), along with other types of energy. Figure 1 shows the nuclear decay scheme for ⁵⁷Co → ⁵⁷Fe and various backscattering processes for ⁵⁷Fe that can follow resonant absorption of an incident gamma photon, modified from DeGrave et al. (2005) and Dyar et al. (2006). If a nucleus gives off radiation or any other form of energy (in this case, in the form of a γ-ray), the nucleus must recoil (or move) with an equal and opposite momentum to preserve its energy (E), in the same way that a gun (by analogy, the nucleus) recoils when a bullet (the γ-ray) is fired out of it. We describe this general case in terms of energy by saying that:

E_{γ-ray emission} = E_transition - E_R,

where

E_{γ-ray emission} = the energy of the emitted γ-ray

E_transition = the energy of the nuclear transition

E_R = the energy of the recoil.

Figure 2. Details

Figure 2 shows a schematic of the vibrational energy levels in a solid. On the left, the recoil energy E_R of an emitted gamma photon is less than what is needed to reach the next higher energy level, so that excitation of a vibrational mode has low probability. The probability that no excitation will occur is given the symbol f, which represents the fraction of recoil-free events. A gamma ray would be emitted without losing energy to the solid, in what is called a zero-phonon transition. In other words, sometimes the nucleus absorbs the energy of the γ-ray and it doesn't recoil (instead, the entire structure, rather than just the nucleus, absorbs the energy). The variable f indicates the probability of this happening. This process of recoil-less emission forms the basis for Mössbauer spectroscopy. On the right, E_R is significantly greater in energy than the lowest excitation energy of the solid, which is E_n+1- E_n. Absorption of the recoil energy, E_R, by the solid thus becomes probable, and the photon emerges with energy reduced by E_R and with Doppler broadening. In the figure, ω represents frequency, and ℏ is Planck's constant divided by 2π, and This figure is adapted from May (1971) and Dyar et al. (2006).

The Mössbauer effect occurs because in solids, the value of f is high enough that recoil-free absorption is possible. Thus an atom of ⁵⁷Co can decay to ⁵⁷Fe, which gives off a γ-ray, and may be absorbed without recoil by a nearby ⁵⁷Fe, which happens to have just the right splitting between the energy levels in its nucleus to absorb it. This scenario will only happen if the decaying Co atom is surrounded by the same atoms as the absorbing Fe. If the receiving Fe atoms are in a different matrix (say, in a mineral) than in the emitter, then no absorption can occur.

Figure 3. Details

When source and absorber atoms are in different local environments, their nuclear energy levels are different (Figure 3). At its simplest (blue), this appears in the transmission spectrum as a shift of the minimum away from zero velocity; this shift is generally called isomer shift (IS). The 1/2 and 3/2 labels represent the nuclear spin, or intrinsic angular moment, quantum numbers, I. Interaction of the nuclear quadrupole moment with the electric field gradient leads to splitting of the nuclear energy levels (red). For ⁵⁷Fe, this causes individual peaks in the transmission spectrum to split into doublets (red) having a quadrupole splitting of QS. When a magnetic field is present at the nucleus, Zeeman splitting takes place, yielding a sextet pattern (green); in the simplest case, the areas of the lines vary in the ratio of 3:2:1:1:2:3. For the spectrum shown, the outer lines have reduced intensity because of saturation effects. Two additional possible transitions shown in gray at lower right (m_I = -1/2 to +3/2 and m_I = +1/2 to -3/2) do not occur due to the selection rule, |Δm_I| ≤ 1. Note that the lengths of the transition arrows have been greatly shortened to allow the splittings to be seen clearly. This figure is adapted from Dyar et al. (2006).

So Mössbauer spectra are described using three parameters: isomer shift (δ), which arises from the difference in s electron density between the source and the absorber, quadrupole splitting (Δ which is a shift in nuclear energy levels that is induced by an electric field gradient caused by nearby electrons, and hyperfine splitting (for magnetic materials only). Graphically, quadrupole splitting is the separation between the two component peaks of a doublet, and isomer shift is the difference between the midpoint of the doublet and zero on the velocity scale (Figure 3). Mössbauer parameters are temperature-sensitive, and this characteristic is sometimes exploited by using lower temperatures to improve peak resolution and induce interesting magnetic phenomena.

If the electrons around the Fe atom create a magnetic field, as in the case of magnetite, then the energy levels in the Fe nucleus will split to allow six possible nuclear transitions, and a sextet (six-peak) spectrum results. The positions of the peaks in the sextet defines what is called the hyperfine splitting (Hint or BHf, depending on the units used) of the nuclear energy levels.

Iron atoms in different local environments and those having different oxidation states absorb at different, diagnostic energies. A typical Mössbauer spectrum thus consists of sets of peaks (usually doublets and sextets), with each set corresponding to an iron nucleus in a specific environment in the sample (an Fe nuclear site). Different sets of peaks appear depending on what the Fe nucleus "sees" in its environment. The nuclear environment depends on a number of factors including the number of electrons (Fe⁰, Fe²⁺, Fe³⁺), the number of coordinating anions, the symmetry of the site, and the presence/absence of magnetic ordering (which may be temperature-dependent). Thus the spectrum of a given mineral may consist of a superposition of doublets and sextets.

Figure 4. Details

The combination of isomer shift and quadrupole splitting parameters (along with the hyperfine field, in the case of magnetically ordered phases) is usually sufficient to identify the valence state and site occupancy of Fe in a given site and individual mineral (Figure 4). In minerals, these ranges have largely been determined empirically from Mössbauer spectra measured with use of spectrum-fitting routines commonly available to the geological community. Exact values of Mössbauer parameters are difficult to predict from theory because long-range interactions in complicated mineral structures are difficult to anticipate.

As seen in Figure 4, Fe atoms in minerals are predictably found in coordination polyhedra of appropriate size based on radius ratios. The top half of Figure 4 plots the isomer shift and quadrupole splitting of several minerals whose iron valence state and coordination number are independently known (usually from single crystal X-ray diffraction), and the bottom of the figure shows the resultant groupings. Fe³⁺ occurs primarily in 4- or 6-coordination with oxygen, while Fe²⁺ may be rarely 4- or 5- coordinated, commonly 6-coordinated, and occasionally 8-coordinated with oxygen. Fe in 4-fold coordination with sulfur has subtly different parameters due to the effects of covalent bonding. Variations in Mössbauer parameters that are characteristic of each type of coordination polyhedron can be related to polyhedral site distortion; a thoughtful discussion of this topic can be found in Burns & Solberg (1988).Mössbauer Spectroscopy Instrumentation - How Does It Work?

Figure 5. Details

The basic elements of a Mössbauer spectrometer are a source, sample, detector, and a drive to move the source or absorber. Most commonly, this is done by moving the source toward and away from the sample, while varying velocity linearly with time. For example, for ⁵⁷Fe, moving the source at a velocity of 1 mm/sec toward the sample increases the energy of the emitted photons by about ten natural linewidths. For simplicity, "mm/sec" is the conventional "energy" unit in Mössbauer spectroscopy. It is also possible to leave the source stationary and oscillate the sample, as is done with synchrotron Mössbauer. The location of the detector relative to the source and the sample defines the geometry of the experiment (Figure 5); most commonly, either transmission or backscatter modes are used.Applications

The combination of isomer shift and quadrupole splitting (along with the hyperfine field, in the case of magnetic phases) is used to identify the valence state and site occupancy of Fe in a given site and individual mineral (Figure 4). If the phase is magnetically ordered, additional information in the form of a value for the magnetic field (usually given in Teslas) can help with identification of some phases.

In some cases, Mössbauer spectrometers are also used to identify minerals. This application is limited, however, by the fact that many different minerals can have site geometries that are the same, such that their Mössbauer spectra and the resultant peak parameters will also be the same. For example, the spectra of amphibole and pyroxene group minerals are all very similar, so you could not tell these minerals apart by their Mössbauer spectra alone!Strengths and Limitations of Mössbauer Spectroscopy?StrengthsAlong with wet chemistry, Mössbauer spectroscopy remains the "gold standard" for quantitative determination of the valence state of iron in minerals and identification of various iron oxides. It is also well-suited for determination of the coordination number of Fe atoms.Limitations

The biggest limitation of the Mössbauer is that it is inherently a bulk technique; it uses powders spread thinly across an absorber to get optimal experimental conditions. In recent years, improvements in electronics and detectors have made it possible to run very small samples (1-5 mg). Another approach to this problem is the Mössbauer milliprobe developed by Catherine McCammon at Bayreuth (e.g. McCammon, 1994). This modification, which uses a lead plate to restrict gamma rays to a small diameter (~100 μm), can be used to study single grains in thin sections or single crystals.

The vast majority of rock-forming minerals on Earth contain Fe²⁺ in octahedral coordination, and thus have very similar Mössbauer parameters. For example, pyroxene, amphibole, and mica spectra are all nearly indistinguishable. Furthermore, most minerals exhibit a range of Mössbauer parameters as a function of cation substitution. Finally, the parameters vary as a function of temperature, and the magnitude of that variation is distinctive to each mineral composition. For these reasons, Mössbauer spectroscopy is not ideally suited to mineral identification (except for iron oxides, where magnetic properties can be extremely diagnostic) and is typically not used for this purpose (though it has been pressed into such service in extraterrestrial applications).