Login 
It is more than 50 years since Rudolf Mössbauer discovered the resonant emission/absorption of a nuclear γ-ray photon. Since its discovery in 1957, this famous effect, known as the Mössbauer Effect, has found specific spectroscopic applications in physics, chemistry, metallurgy, materials engineering, corrosion, biology, bio-medicine, astronomy, archaeology, numismatics and forged art.
Accordingly, for this important discovery, Mössbauer received the 1961 Nobel Prize in Physics. Today, Mössbauer Spectroscopy continues to support fundamental and applied scientific research by providing a unique tool for extracting local information via nuclear hyperfine interactions in materials.
In this article, we briefly introduce key aspects of the physics of Mössbauer Spectroscopy in terms of measurements and materials’ applicability, in order to promote this powerful technique to potential end users.
Physical principles
A nuclear resonant spectroscopy based on the Mössbauer Effect can be elaborated similarly to any kind of atomic spectroscopy – Infrared (IR), Visible (VIS) or Ultraviolet (UV). There are both conceptual and practical differences between atomic and nuclear spectroscopy, however. Whereas in case of atomic spectroscopy the energies of the emitted photons are relatively small – typically a few eV or fractions of eV – in the case of nuclear absorption / emission, more energetic photons with typical energies of 104-105 eV are involved.
Therefore, in the case of atomic spectroscopy the recoil of the atom can be simply neglected during the emission/absorption process, while the nuclear recoil is no longer negligible due to the involved energetic γ-ray photons.
Recoilless γ-ray events are still possible by binding the nuclei in a solid state lattice (either crystalline or amorphous), but the recoilless emission/absorption of a γ-ray photon has a profound quantum origin. It can be explained by considering the fact that nuclear events take place probabilistically with/without exciting the phonon system, in such a way that the averaged energy transferred toward the phonons can equate the overall recoil energy.
Accordingly, in solid materials there is always a fraction of recoilless nuclear absorption/emission events (called the Debye-Waller factor, f), which allow the design of a nuclear resonant spectroscopy, also known as Mössbauer Spectroscopy. In other words, the larger the Debye-Waller factor, f, the more sensitive the spectroscopic detection is.
According to Debye’s model, the f factor can be increased by either minimising the energy of the involved γ photons or maximising the bounding of the Mössbauer nuclide in the crystal lattice. The Debye-Waller f factor is also inverse proportional to the temperature of the crystal lattice, so that at lower temperatures the f factor is larger. This is explained by the fact that, at lower temperatures, mainly the phonon ground state is populated. Hence, the excitation of the phonons on the first excited state (the most distanced in the Debye model) becomes less probable supporting so more recoilless γ-ray events.
Such increase of the resonance effect at lower temperatures is another peculiarity of the nuclear γ resonance, as compared to the case of the atomic resonances, where the superposition of the emission and absorption lines increases at higher temperatures due to the thermal broadening.
Finally, it is well known that the resolution of any resonance measurement technique depends strongly on the line width of the absorption/emission lines, which in the case of nuclear γ-ray resonance depends on the lifetime of the nuclide on the excited state. The above energy related conditions require γ photons of as low and as monochromatic energy as possible, respectively, which reduces drastically the number of nuclides that would be effective in a nuclear resonant technique.
Typical energies involved in the Mössbauer Effect of the most usual nuclides are: 104 – 105 eV for the γ photons, 10-8 – 10-9 eV for the natural line-width of the excited state, 1-10 eV for chemical bindings and 10-2 – 10-3 eV for both phonon and free-atom recoils. At these energies, the resulting resolving power (ν/Δν) in Mössbauer Spectroscopy is of the order of 1011 -1014, which is significantly greater than a maximum value of 108 in case of the most powerful atomic spectroscopy techniques. Hence, a nuclear resonance spectroscopy represents an unrivalled powerful tool for measuring extremely fine perturbation of the nuclear levels, induced either by external factors or just by the interaction of the nuclide with the surrounding environment.
Samples and Mössbauer isotopes
As already explained, due to fundamental restrictions, there are just a few practical Mössbauer nuclides, most notable 57Fe, 119Sn and 151Eu. In addition, these isotopes also have the advantage of being generated in the excited state by parent nuclides (57Co, 119mSn, 151Sm) with long life time (∼ years). Other Mössbauer isotopes (e.g. 197Au, 121Sb) might be effective, but, due to the very short life time (days) of the parent nuclides, they can be only used in conjunction with nuclear activation facilities (a detailed review on the applications of less common Mössbauer Spectroscopy isotopes is given in reference3).
In terms of suitable materials for Mössbauer studies, practically any material containing Mössbauer isotopes can be studied via Mössbauer spectroscopy. These include organic, inorganic, solid state as well as polymers or colloids containing Mössbauer isotopes. By far the most common Mössbauer isotope for practical and fundamental studies is 57Fe. This is because 57Fe presents the lowest energy of the γ photons (e.g. a transition of 14.4 keV) and the longest lifetime on the first excited state (∼ 97 ns), giving rise to the shortest natural line-width (about 4.66 × 10-9 eV) and consequently to the highest relative resolving power of about 3 × 1014.
Having also the largest effective resonant absorption cross section of about 2.57 × 10-22 m2, combined with the fact that Fe is present in a huge range of industrially important materials, 57Fe is by far the most efficient and convenient isotope for Mössbauer Spectroscopy. In fact, more than 95% reported Mössbauer studies concern materials and compounds containing Fe. For this reason, we will focus this article on the technical aspects of 57Fe Mössbauer Spectroscopy.
Measurement technique
“…The most common measurement technique of a Mössbauer spectrum is based on transmission geometry, as shown diagrammatically in Figure 1.
Parent radioactive nuclides in a Mössbauer radioactive source transform, by a nuclear reactions, in the Mössbauer isotopes in an excited state, which emit via recoil-free events exactly the monochromatic radiation of interest. For example, 57Co nuclides in a Rh matrix, transform by electron capture in 57Fe nuclides on the second excited state, which via a second des-excitation emit the 14.4 keV radiation with an energy bandwidth of only 5 × 10-9 eV (figure 2). The embedding matrix of the parent/Mössbauer nuclides in the source is carefully selected, in order to avoid any kind of quadrupole or magnetic splitting interactions.
Hence, a very monochromatic (but not coherent) beam radiates the sample/absorber containing stable 57Fe nuclides, prepared for the resonant absorption of the incoming radiation. The tuning of the incoming radiation over the specific energy spectrum of the absorbing nuclides is realised via the Doppler effect. An electro-mechanical transducer oscillates mechanically the source with a periodic and symmetric variation of the velocity around zero, giving rise to a corresponding variation of the energy of the incoming radiation in the interval E0 ± δE, with δE/E0 of order of v/c (v = source velocity, c = light velocity).
Typical velocities of a few mm/s are enough to cover the energy interval containing most of the hyperfine interactions taking place at the 57Fe nuclide in the absorber. A γ-ray detector measures the transmitted radiation. The synchronisation of the gamma ray counting and the source velocity is achieved in a multi channel analyser (data acquisition block), in which channels are consecutively open by the same waveform generator commanding the velocity transducer.
Accordingly, bunches of counts are accumulated in channels corresponding to well defined velocities of the source relative to the absorber. The experimental spectrum shows the dependence of the intensity of the absorbed radiation versus the relative velocity between the source and the absorber (energy channel).
Depending on the hyperfine interactions in the sample (subsequently described), a typical spectrum may consist of either a singlet, a doublet, a sextet or any combination of these (considering non-polarized radiation).
A second Mössbauer Spectroscopy measurement technique is based on the detection of conversion electrons, which are generated via desexcitations of 57Fe nuclides after Mössbauer absorptions take place inside the sample. Such conversion electrons can leave the surface of the sample only from a relative small depth, typically of up to 200 nm for most of the conversion electrons involved in the 57Fe Mössbauer Spectroscopy. This measurement technique is therefore suitable for surface analysis, and it is called Conversion Electron Mössbauer Spectroscopy (CEMS).
Finally, a third Mössbauer measurement technique involves synchrotron facilities. An X-ray radiation pulse (100 ps length, 200 ns timing/rest) is sent over the sample via a high resolution monochromator (107 resolving power for a radiation of 14.4 keV). The pulse excites at once all the 57Fe Mössbauer nuclides in the sample, up on the first excited state where the lifetime is about 100 ns.
The simultaneous des-excitation of all nuclides takes place during this time, giving rise to a characteristic quantum beat modulation in the successive decay. This is related to the interference of all the possible close frequency waves generated by des-excitations between the involved nuclear levels which are perturbed by the hyperfine interactions. The specific time beat spectra can be analysed via special fitting procedures providing information about all the occurring hyperfine interactions in the sample.
57Fe Mössbauer Spectroscopy
57Fe is a stable isotope characterised by a positive quadrupole moment (Q > 0) and a lower average nuclear radius in the first excited state as compared to the nuclear radius in the ground state (δR/R < 0). The nuclear spin, I, takes a value of 3/2 on the first excited level and 1/2 on the ground state, leading to a magnetic Zeeman degeneracy of 4 (mΙ = -3/2, -1/2, 1/2 and 3/2) and 2 (mΙ = 1/2, -1/2 ) nuclear wave-functions on the first excited level and the ground state, respectively.
Energetically, the first excited state is located at 14.4 keV from the ground state (Figure 2). A second excited state at 136 keV is far less involved in Mössbauer studies and will be neglected in this discussion.
Excluding the main nuclear interactions giving rise to the specific nuclear levels (and corresponding wave-functions), there are three types of non-negligible perturbations due to the interaction of the 57Fe nucleus with the surrounding electron distributions (known as hyperfine interactions), producing small shifts or splitting of the nuclear levels.
Two of the hyperfine interactions have an electrostatic origin and are due to the interaction of the nuclear electric monopole with the electric potential raised up by the electrons at the nucleus and of the nuclear electric quadrupole moment with the second derivative of the potential (electric field gradient) at the nucleus, respectively.
The first hyperfine interaction leads to a shift of the nuclear levels and is proportional to the electronic charge density at the nucleus coming from s type electrons. While the density of the most external s electrons in case of Fe atoms/ions in a solid matrix is sensitive to the distribution of their own 3d electrons, it is clear that the involved shift (known as isomer shift), might provide useful information about both the oxidation state and the spin state of the Fe atoms/ions in the compound.
The second hyperfine interaction, depending on mΙ2, leads to a splitting of the excited nuclear level in two sub-levels (mΙ2 being either 1/4 or 9/4). This splitting (known as a quadrupole splitting) carries information on either nuclear parameters (e.g. the nuclear quadrupole moment) or local electronic parameters (the main component Vzz of the electric field gradient, in case of axial symmetry and in addition the asymmetry parameter η, in case of non-axial symmetry).
The electric field gradient, seen as a negative second derivative of the potential due to the all-surrounding electric charge, carries useful information from the charge distribution of both the valence electrons of the involved atom and from surrounding ions. For example, in the simplest case of Fe3+ ion (3d5 electrons of spherical symmetry), the only contribution to the quadrupole splitting comes from the crystal field created by surrounding ions.
Finally, the third hyperfine interaction has a magnetic origin (Zeeman type) and is due to the interaction of the nuclear magnetic moment with a magnetic field at the nucleus. The magnetic field at the nucleus could have different origins (external, demagnetising, Fermi-contact, dipolar, or exchange). Such an interaction, proportional to both mΙ and the magnetic field at the nucleus, removes completely the degeneracy of both the excited and the ground nuclear levels, giving rise to a fourfold splitting of the excited level and a twofold splitting of the ground level.
Each splitting remains proportional to the magnetic field at the nucleus and hence, provides useful information about its local origin. In case of zero applied field, the Fermi-contact field is by far the dominant contribution in most situations. This field is due to a net spin density of the s electrons at the nucleus, which is proportional to the overall net spin density and hence to the atomic magnetic moment.
This internal field called magnetic hyperfine field, is most often proportional to the atomic magnetic moment and allows specific studies on the magnetic state of the material containing embedded Mössbauer nuclides. Usually, the magnetic hyperfine interaction is much stronger than the quadrupole one and the magnetically split levels become just slightly perturbed by a quadrupole shift correction.
Depending on the sample, a typical Mössbauer spectrum is accumulated in a period of a few hours up to a few days. Once a spectrum is acquired, it remains just a data processing problem to obtain experimentally all the hyperfine parameters (isomer shift, IS, quadrupole shift/splitting, ε/QS, magnetic hyperfine field, Hhyp), from which unique and valuable information can be extracted about the sample’s structure, chemical surroundings, electron delocalisation and valence states, magnetic configurations and Fe phase composition.
It is worth mentioning that the natural abundance of the 57Fe isotope is about 2%. Therefore, any material containing Fe might be optimally analysed via 57Fe Mössbauer Spectroscopy, if ∼ 10 mg/cm2 of natural Fe, or equivalently, 0.15 mg/cm2 of 57Fe is present in the sample.
While a sample may contain Fe atoms/ions in different local configurations or belonging to different metallurgical phases, the overall spectrum consists of a superposition of the above mentioned components specific to the involved configurations. In turn, each spectral component is composed by one, two or six lines of Lorentzian shape, centred on the resonance velocity, which may be often expressed as a linear combination of the involved hyperfine parameters.
Therefore, one of the major advantages of Mössbauer Spectroscopy, as a local microscopic technique, is related to the fact that it can provide complex information about the electronic configurations and magnetic state at each Fe site or on each Fe phase in the sample. From the magnetic point of view, for example, it appears as a very powerful complementary method to the usual magnetic measurement techniques.
When the hyperfine magnetic field is only due to the spin contribution, the hyperfine field is proportional and anti-parallel to the Fe net magnetic moment. Because the averaged hyperfine magnetic field shows similar temperature dependence as the net magnetisation, magnetic relaxation phenomena on each Fe phase can be studied by following either the broadening of the sextet lines or the transition from the sextet (which characterises a magnetically ordered state) to a doublet/singlet (which characterises a paramagnetic/superparamagnetic state).
Moreover, the orientation of the local magnetic moment (Fe spin) with respect to the direction of the incident γ-rays (laboratory axis) of each Fe phase can be extracted from the intensity ratio between the second (or fifth line) and the third (or the fourth) line of the sextet spectrum, R23=I2/I3.
Finally, high depth selectivity Mössbauer measurements can be performed using a 57Fe tracer layer technique. This involves the deposition of a 57Fe layer with the same phase composition as the main sample, but enriched in 57Fe at the desired depth or interface. The Mössbauer signal is therefore provided mainly from the enriched layer, resulting in depth selective information with an unprecedented spatial resolution of about 1 nm. This confers Mössbauer Spectroscopy excellent effectiveness in revealing complex information about the surface and interface properties.
Concluding remarks
Mössbauer Spectroscopy offers unique information about hyperfine interactions and local parameters at atomic and nuclear level in compounds containing a Mössbauer isotope. The most common Mössbauer isotope is 57Fe and due to the abundance of Fe in various organic and inorganic compounds of industrial interest, this technique continues to serve the academic and industrial communities as a powerful experimental tool in materials science, chemistry, biophysics, magnetism and nano-magnetism and corrosion, to name a few.
Published: 31st May 2013 in AWE International
