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Abstract

Among the various spectroscopic methods which today are applied in geochemistry and mineralogy, Mössbauer spectroscopy plays an important role for mainly two reasons: First, the high resolution and accuracy of the method enables quantitative measurements by the detection of very small energy differences. Second, although the applicability of Mössbauer spectroscopy is limited to a relatively small number of isotopes, the most suitable and common Mössbauer active element, iron, belongs to the five most abundant elements of the earth, and is by far the most abundant transition element. Accordingly, many of the important rock-forming or ore minerals contain iron as a main or substitutional ion and much important petrological and geochemical information may be obtained by the study of iron, using the Mössbauer effect. For instance, the oxygen fugacity fO2 is a very important parameter in rocks and ore forming processes. Changing Fe2+/Fe3+ ratios in Fe-bearing minerals document varying oxygen fugacities during their formation and their subsequent geological history. The Mössbauer effect is particularly well suited to study special properties of transition metals (such as Fe), e.g. changing oxidation and spin states, site-dependent electrical fields, magnetic hyperfine interactions etc. Therefore, most of the Mössbauer studies in geochemistry and mineralogy are made on 57Fe. Similarly, this paper deals mainly with Mössbauer spectroscopy on 57Fe, which is the Mössbauer active Fe isotope with 2.17% natural abundance. However, there are a number of other Mössbauer isotopes, such as 119Sn, 121Sb, 197Au etc., which have been investigated successfully with regard to geochemical as well as crystal chemical applications.

Introduction

Among the various spectroscopic methods which today are applied in geochemistry and mineralogy, Mössbauer spectroscopy plays an important role for mainly two reasons: First, the high resolution and accuracy of the method enables quantitative measurements by the detection of very small energy differences. Second, although the applicability of Mössbauer spectroscopy is limited to a relatively small number of isotopes, the most suitable and common Mössbauer active element, iron, belongs to the five most abundant elements of the earth, and is by far the most abundant transition element. Accordingly, many of the important rock-forming or ore minerals contain iron as a main or substitutional ion and much important petrological and geochemical information may be obtained by the study of iron, using the Mössbauer effect. For instance, the oxygen fugacity fO2 is a very important parameter in rocks and ore forming processes. Changing Fe2+/Fe3+ ratios in Fe-bearing minerals document varying oxygen fugacities during their formation and their subsequent geological history. The Mössbauer effect is particularly well suited to study special properties of transition metals (such as Fe), e.g. changing oxidation and spin states, site-dependent electrical fields, magnetic hyperfine interactions etc. Therefore, most of the Mössbauer studies in geochemistry and mineralogy are made on 57Fe. Similarly, this paper deals mainly with Mössbauer spectroscopy on 57Fe, which is the Mössbauer active Fe isotope with 2.17% natural abundance. However, there are a number of other Mössbauer isotopes, such as 119Sn, 121Sb, 197Au etc., which have been investigated successfully with regard to geochemical as well as crystal chemical applications.

It is impossible to report in a relatively short paper such as this one all the different aspects of Mössbauer spectroscopy. For this purpose, the reader is referred to the more detailed textbooks of Wertheim (1964), Greenwood & Gibb (1971), Bancroft (1973), Gonser (1975), Gütlich et al. (1978), Shenoy & Wagner (1978), Marfunin (1979), Long (1989), Long & Grandjean (1996), etc. More information on current research can be obtained from the Mössbauer Effect Data Center (MEDC), headed by J.G. Stevens in Asheville, N.C., USA. He has collected all publications on Mössbauer spectroscopy and edits the monthly Mössbauer Effect Reference and Data Journal as well as many data sets including one on minerals and related compounds. The main conference on Mössbauer spectroscopy is the International Conference on the Applications of the Mössbauer Effect (ICAME) which is organised every two years and which always has a session on Earth and Planetary Sciences, Mineralogy and Archaeology. For more information on the application of Mössbauer spectroscopy to mineralogy the reader is referred to the following chapter (McCammon, 2004) in this book.

The Mössbauer effect

The recoilless emission and resonant absorption of γ radiation by atomic nuclei in solids is called Mössbauer effect (Mössbauer, 1958). During the emission of a γ quantum by an atomic nucleus with the mass M in a gas or a fluid the γ quantum looses the recoil energy ER which is transmitted to the emitting nucleus:  

formula

where M is the mass of the emitting nucleus, c is the velocity of light, and Eγ is the recoil-free energy of the γ ray. This equation shows that ER increases with the square of Eγ and decreases with the mass M of the emitting atom. During the emission process, the energy of the γ quantum is decreased by ER In order to achieve absorption of the γ quantum by another atomic nuclei in a gas or a liquid, the energy of the γ quantum has to be increased by ER As a consequence, emission and absorption lines are separated by 2ER and recoilless emission as well as resonant absorption of γ radiation by atoms in a gas or in a liquid are not possible, taking the nearly vanishing half width/intensity ratio of 10–15into account (Fig. 1).

Fig. 1.

Separation of the emission and absorption lines by 2ER due to the recoil effect occurring during the emission and absorption of a γ ray by nuclei in gases or liquids. Resonant absorption is not possible (modified from Gütlich et al., 1978).

Fig. 1.

Separation of the emission and absorption lines by 2ER due to the recoil effect occurring during the emission and absorption of a γ ray by nuclei in gases or liquids. Resonant absorption is not possible (modified from Gütlich et al., 1978).

If, however, the emitting nucleus is incorporated into a solid crystal, the recoil energy may be annihilated because M → ∞ implies ER → 0, so that recoil-free emission and resonant absorption now become possible. At a given temperature, there is a certain portion f of the emitting nuclei where γ rays are emitted without loss of energy of the γ quantum (for instance by the excitation of lattice vibrations). This portion f is called the recoil-free fraction (Debye-Waller factor, Lamb-Mössbauer factor) and is given by:  

formula
 
formula

In these equations forumla is the component of the mean square vibrational amplitude of the emitting nucleus in the direction of the γ ray, λ is the wavelength of the γ quantum, ħ is Planck's constant divided by 2π, and Eγ= (2πħc)/λ is the recoil-free energy of the γ quantum. The recoil-free fraction depends on both a nuclear property, i.e. Ev, and a crystal property, i.e.forumlaThe recoil-free fraction f becomes larger with decreasing Eγ. For instance, f = 0.91 for the 14.413 keV transition of 57Fe and f = 0.06 for the 129 keV transition of 191Ir (Gütlich et al., 1978). With decreasing forumlaf distinctly increases. Because forumla usually decreases at low temperature, f increases with falling temperature; this is one reason why low-temperature measurements with the application of cryostats are very important in Mössbauer spectroscopy.

Another important property of the Mössbauer effect is the extremely small line width Γ of the γ ray compared to its total energy Eγ. This line width is related to the lifetime of the nuclear excited state via the Heisenberg uncertainty principle with respect to energy and time. The uncertainty in energy δE corresponds to the lifetime & of the nuclear state and appears also as the line width γ of the γ ray. The two are related by the equation of Weisskopf & Wigner (1930):  

formula

Hence, the mean lifetime ι of the excited nuclear state is directly related to the width Γ of the relevant transition line. As an example, the first excited state of 57Fe has a mean lifetime ι = 1.43 × 10–7 s, yielding a line width Γ = 4.55 × 10–9 eV, which is exceedingly small compared to the energy of the corresponding γ radiation Eγ = 14.413 keV. This small line width enables the detection of small changes of the γ radiation energy on the order of 10–12 to 10–14 eV, which is in the range of nuclear hyperfine interactions, i.e. interactions between the nuclear moments and the surrounding electric or magnetic fields.

Weisskopf & Wigner (1930) also derived that the spectral line has Lorentzian or Breit-Wigner form and follows the formula  

formula

Nuclear transitions from an excited state (e) to the ground state (g), or vice versa, involve all possible energies within the range of AE. The transition probability or intensity as a function of energy, I(E), therefore yields a spectral line centred around the most probable transition energy Eγ (Fig. 2).

Suitable Mössbauer isotopes are those with a relatively low energy of the γ radiation Eγ and therefore a high recoil free fraction f, as well as a comparatively long mean lifetime ι of the first excited nuclear level and therefore a small half width Γ The most advantageous combination is found in 57Fe which has been used in more experiments than all the other isotopes shown in Table 1. However, other Mössbauer isotopes, successfully used in geochemistry and mineralogy, are e.g. 119Sn, 121Sb, 197Au etc. (Table 1).

Fig 2

Intensity I(E) as a function of transition energy E. δE = Γ = ħ/ι is the energy width of the excited state (e) with a mean life time ι corresponding to the full width of the transition spectral line Γ at half peak height I0/2 (modified from Gütlich et al., 1978).

Fig 2

Intensity I(E) as a function of transition energy E. δE = Γ = ħ/ι is the energy width of the excited state (e) with a mean life time ι corresponding to the full width of the transition spectral line Γ at half peak height I0/2 (modified from Gütlich et al., 1978).

It should also be mentioned that during the last years much progress has been made by using synchrotron radiation for the excitation of low-energy nuclear resonances, according to the original proposal by Ruby (1974). The so-called nuclear resonant forward scattering (NFS) of synchrotron radiation is a time-differential technique. Advantages of synchrotron radiation are time structure, coherence, highly collimated intensity (small beam size), polarisation, tuneability of energy etc. The new technique is far more sensitive for hyperfine parameters (isomer shift, quadrupole splitting, magnetic hyperfine interaction) compared to conventional Mössbauer spectroscopy and complements the conventional Mössbauer spectroscopy in the energy domain, but will certainly not replace it. Nuclear scattering of synchrotron radiation also includes nuclear inelastic scattering, which enables to determine phonon spectra by the simultaneous nuclear resonance absorption of a photon and creation or annihilation of one (or more) phonon(s). NFS will open a new field of applications in mineralogy and geochemistry. More details on NFS can be obtained from Gerdau & de Waard (1999).

Experimental

The principal set-up of a Mössbauer experiment with 57Fe is shown in Figure 3. A radioactive single line source (57Co/Rh) provides a γ radiation with energy of 14.413 keV by the decay of 57Co to 57Fe and via the transition from the first excited state of the Fe nucleus with spin 3/2 to the ground state of the Fe nucleus with spin 1/2. This γ radiation has in principle exactly the energy needed to excite the 57Fe nuclei in the absorber, to go from the ground state to the first excited state. If resonant absorption takes place, a detector (usually a proportional counter) behind the absorber observes a decrease of the count rate. In general, resonance absorption is not observed because the nuclear levels of the Fe nuclei in the absorber are shifted or even split by the so-called hyperfine interactions. To restore resonance absorption, the source is moved by an electromechanical drive system relative to the absorber. This causes a Doppler shift of the energy of the emitted γ radiation, which has the same order of magnitude as the shifts and splitting of the nuclear levels due to the hyperfine interactions in the absorber. The drive is operated at constant acceleration with a symmetric velocity shape in conjunction with a multi-channel analyser (usually 1024 channels) operated at “time mode” so that each channel corresponds to a distinct velocity range. The count rate registered as a function of the source velocity (mm/s) in a multi-channel analyser represents a Mössbauer spectrum. The velocity scale is often calibrated with the spectrum of a foil of metallic iron at room temperature. The whole measurement is repeated electromechanically so often that the counts in the channels in the off-resonant region (background) are about 1 million per channel. Experiments are usually performed with stationary absorber whereas the moving source is kept at ambient conditions. The absorber can be cooled, heated, kept under high pressure or brought into an external magnetic field.

Table 1.

Periodic table of the elements with all the Mössbauer isotopes marked appropriately (modified from the original table of the Mössbauer Effect Data Center).

graphic
graphic
Fig. 3.

Principal set-up of a Mössbauer experiment (for a description see text).

Fig. 3.

Principal set-up of a Mössbauer experiment (for a description see text).

Evaluation

The set-up described above produces two mirror-symmetric spectra (512 channels each), which usually are folded and then evaluated with computer fitting programs based on least-squares minimisation methods, generally assuming Lorentzian line shape (Eqn. 5). The fit gives the intensities (areas), positions, and half widths of the resonant absorption lines as exactly as possible. In most of these computer programs, the weighted mean square deviation χ2 between the experimental data points forumla and the corresponding theoretical values forumla has to be minimised:  

formula

A more sophisticated method evaluates the spectra by diagonalisation of the Hamiltonian for mixed magnetic and electrostatic interaction and fits directly the hyperfine parameters isomer shift δ, quadrupole splitting δEQand magnetic field H of a subspectrum, as well as the corresponding relative intensities (areas) and half widths (e.g. software MOESALZ by Lottermoser et al., 1993). Another method to analyse spectra is the fitting of quadrupole splitting distributions (QSDs) or hyperfine field distributions (HFDs) using the Voigt-based method of Rancourt & Ping (1991) and the software RECOIL by Lagarec and Rancourt which is distributed by Intelligent Scientific Applications Inc., Canada.

Hyperfine interactions

Hyperfine interactions between the nuclear moments and surrounding electric and/or magnetic fields perturb the nuclear energy levels and are of great importance in Mössbauer spectroscopy, because they provide the main chemical, physical, and crystallographic information. These perturbations can shift the nuclear energy levels as in the case of electric monopole interaction or can split degenerate nuclear levels into sublevels as in the case of electric quadrupole or magnetic dipole interaction. In practice, only these 3 kinds of hyperfine interactions are considered in Mössbauer spectroscopy.

Electric monopole interaction (isomer shift δ)

The electric monopole interaction is an electrostatic interaction between the positively charged nucleus of finite size and the negative electronic charge and causes a shift of the nuclear levels; this is called isomer shift δ0 (or IS0), because the effect depends on the difference in the averaged nuclear radii of the ground (g) and isomeric excited (e) states. The term “chemical shift” has also been used.

The energy difference δ E between the electrostatic potential of a point nucleus and a finite one in the electric field of the surrounding electrons is  

formula

with Ze being the nuclear charge, –e|ψ(0)|2 is the electronic charge density at the nucleus, and Ri the radius of the nucleus.

This equation relates the electrostatic energy of the nucleus to its radius, which will in general be different for each nuclear state. Observations, however, are not made on the location of individual nuclear levels but on the γ ray resulting from transitions between two such levels. The energy of the γ ray represents the difference in electrostatic energy of the nucleus in two different states of excitation, which differ in nuclear radius. The expression for the change in energy of the γ ray due to the nuclear electrostatic interaction is therefore the difference of two terms evaluated from Equation 7 for the nucleus in the excited state δE e and the nucleus in the ground state δEg:

 

formula

The energy shift of Equation 8 is very small when considered in terms of the absolute value of energy of the γ quantum. However, in Mössbauer spectroscopy the nuclear transition energy in a source is compared with that in an absorber, which are different because of different electronic and crystallographic environment in the source and the absorber (Fig. 1). By this method and using a convenient compound as a standard, small differences in the energy of the γ rays can be detected without knowledge of the absolute value of the standard. For example, the energy of the γ ray of 57Fe is 14.413 keV (± 10 eV), but one can measure energy differences as small as 10–10 eV.

Fig. 4.

(a) Coulomb interaction between the nuclear charge and the electrons shifts the nuclear levels differently in the source and the absorber. (b) In the corresponding Mössbauer spectrum a single line is observed (no quadrupole and no magnetic hyperfine interaction). The difference between the position (centroid) of the line and the zero point of the velocity corresponds to the isomer shift δ0 (modified from Gütlich et al., 1978).

Fig. 4.

(a) Coulomb interaction between the nuclear charge and the electrons shifts the nuclear levels differently in the source and the absorber. (b) In the corresponding Mössbauer spectrum a single line is observed (no quadrupole and no magnetic hyperfine interaction). The difference between the position (centroid) of the line and the zero point of the velocity corresponds to the isomer shift δ0 (modified from Gütlich et al., 1978).

The isomer shift δ0 relative to a standard source can be calculated by taking the difference of Equation 8 written both for the source (ES) and the absorber (EA):

 

formula

In Equation 9 Ze is the nuclear charge, δR = Re– Rg, 2R = Re + Rg (Re and Rg differ only slightly from each other), forumla is the s-electron density at the absorber nuclei, and forumla is the s-electron density at the source nuclei (non-relativistic case). That means, δ0 depends on two factors. The first factor contains only nuclear parameters, namely the difference between the radius of the nucleus in the excited (isomeric) state and that of the ground state and is constant for a particular Mössbauer isotope. Thus Equation 9 can also be written:

 

formula

where the isomer shift calibration constant α = –0.25 ± 0.03 forumla mm/s for 57Fe (Grodzicki et al., 2003). The second factor in Equation 10 depends on the difference in the electronic charge density at the absorber nuclei and the source nuclei, depending on the chemical bonding, valence and spin state of the Mössbauer atom. Using always the same source, the isomer shift depends directly on the electron density at the absorber nuclei. In this case, Equation 10 can also be written as:

 

formula

Well-separated values for the isomer shift of Fe2+ as well as Fe3+ are found in ionic compounds. At first sight, this seems strange because Fe2+ with the electronic configuration [Ar]3d6 differs from Fe3+ with the electronic configuration [Ar]3d5 just by a single d electron. According to Equations 10 and 11 only the s electrons contribute to the isomer shift, because they have a finite probability at the nucleus. However, since the probability density of a 3d orbital extends into the core region, a 3d electron may be with a certain probability closer to the nucleus than a 3s electron. Accordingly, adding a d electron in going from Fe3+ to Fe2+ will reduce the attractive Coulomb potential for the 3s electron. This leads to an expansion of the 3s orbital and thus a reduced electron density at the nucleus. Because the isomer shift calibration constant α is negative for 57Fe, the isomer shift δ0 of Fe2+ is distinctly larger (about 0.7–0.8 mm/s in oxides) than δ0 of Fe3+, provided that the first coordination sphere including the coordination polyhedron remains unchanged. Typical Mössbauer spectra of Fe2+ and Fe3+ in garnets and babingtonite are displayed in Figures 6 and 7, respectively. The distances between the centroids of the doublets and the zero point of the velocity scale in mm/s correspond to the isomer shift δ = (δ0 + δSOD) of Fe2+ and Fe3+. The distinct difference between δ(Fe2+) and δ(Fe3+) can easily be recognised.

In summary, with increasing electron density at the 57Fe nucleus due to increasing valence or increasing covalent bonding character the isomer shift δ0 decreases. For instance, in both Fe2+ and Fe3+ compounds, δ0 decreases with decreasing coordination number of iron. This can be referred to increasing s-electron density at the Fe-nucleus due to stronger orbital overlap caused by smaller average cation-anion distances in a smaller coordination polyhedron with lower coordination number. However, this is true only for Mössbauer nuclei such as 57Fe, which have a smaller radius in the excited state than in the ground state and consequently δR/R and therefore α are negative. For Mössbauer nuclei with δR/R positive, such as 119Sn, increasing electron density at the nucleus is shown by an increase of the isomer shift.

Isomer shifts of Fe2+ and Fe3+ in babingtonite, Ca2Fe2+Fe3+Si5014OH, distinctly decrease with increasing temperature (Fig. 8). This temperature dependence of the isomer shift is mainly caused by the so-called second-order Doppler shift δSOD, which adds to the isomer shift δ0 caused by the electric monopole interaction (Eqn. 10), to give the total isomer shift δ:  

formula

Therefore, the name centre shift is used for δ by some authors. The isomer shift δ is evaluated from the Mössbauer spectra and referred to the isomer shift δ of α-iron at room temperature as a standard (δα-Fe). Considering the emitting or absorbing Mössbauer nucleus with mass M vibrating on its lattice site in the crystal, the second-order Doppler shift δSOD depends on the force constant K and the mean square displacement forumla of the nucleus according to the formula  

formula

Because the mean square displacement forumla increases with temperature, |δSOD| increases and therefore the isomer shift δ decreases (Eqns. 12 and 13).

The electric quadrupole interaction (quadrupole splitting ΔEQ)

Electric quadrupole interaction takes place between a nuclear quadrupole moment Q and an electric field gradient (EFG) q arising from the surrounding charges. If the nuclear charge distribution deviates from spherical symmetry (nuclear spin I > 1/2), the nucleus has a quadrupole moment. Q is positive for an elongated nucleus (cigar) and negative for a flattened nucleus (disc). The first excited state of the Fe nucleus with spin 3/2 has a positive quadrupole moment (0.16 barn) whereas the ground state with spin 1/2 has no quadrupole moment. Q is constant for a certain Mössbauer isotope and differences in the quadrupole splitting of different compounds under constant experimental conditions can only arise from changes of the EFG.

The EFG is determined by the extranuclear charges (electrons and lattice ions) and is non-zero if the charge distribution around the nucleus deviates from cubic symmetry. The electric field gradient is the second derivative of the potential V at the nucleus of all surrounding electric charges. It is a 3 × 3 second-rank tensor and is given by  

formula
 
formula
are the components of the EFG tensor. Because Vij = Vji, the tensor is symmetric and according to Laplace's equation it is also traceless, i.e.:  
formula

In principal-axis systems, the off-diagonal elements of the EFG tensor become zero. If the principal axes are chosen in such a way that  

formula
the EFG can be described by two independent parameters: (i) the electric field gradient  
formula
and (ii) the asymmetry parameter  
formula
where 0 ≤ η ≤ 1 due to Equations 16 and 17.

If the Mössbauer isotope is located at a structural position with the site symmetry of a 3- or 4-fold symmetry axis, then Vxx = Vyy and η becomes zero so that the EFG is axially symmetric. For cubic point symmetry, the EFG is zero.

For a nuclear 1/2 → 3/2 transition, as in 57Fe, the quadrupole splitting δEQ (or δ, QS) is:  

formula
and in the case of axial symmetry (η = 0)  
formula

The quadrupole interaction splits the first excited level (I = 3/2) of the Fe nucleus in two sublevels. Hence, two transitions from the ground state to the split excited state are possible and the corresponding Mössbauer spectrum (Fig. 5) exhibits two resonant absorption lines separated by the quadrupole splitting δEQ. The distance between the centroid of both lines and the zero point of the velocity scale corresponds to the isomer shift 8. Both lines should have equal intensities except for the occurrence of an anisotropic recoil-free fraction f in a polycrystalline sample (Goldanskii-Karyagin effect) or in the presence of texture or relaxation.

The quadrupole splitting δEQ is another important parameter for the application of the Mössbauer effect in chemistry, solid state physics and crystallography, because δEQ provides a wealth of information on the electronic and crystallographic structure.

Within the frame of crystal-field theory (CFT), deviations of the EFG from cubic symmetry may be thought to arise from two contributions:

  • the so-called lattice contribution, qlat or forumla resulting from charges of the surrounding ions,

  • the so-called valence electron contribution,qval or forumla resulting from an anisotropic electron distribution in the valence shell of the Mössbauer atom.

Fig. 5.

Quadrupole splitting in the case of a 1/2 → 3/2 nuclear transition, such as in 57Fe. The first excited state of the nucleus with spin 3/2 is split into two sublevels whereas the ground state with spin 1/2 is not split. Now two transitions from the ground state to both excited sublevels are possible and in the corresponding Mössbauer spectrum two lines (quadrupole doublet) are observed. (b) The distance between the positions of both lines in mm/s corresponds to the quadrupole splitting δEQ. The distance in mm/s between zero velocity and the centroid of both lines corresponds to the isomer shift δ (modified from Gütlich et al., 1978).

Fig. 5.

Quadrupole splitting in the case of a 1/2 → 3/2 nuclear transition, such as in 57Fe. The first excited state of the nucleus with spin 3/2 is split into two sublevels whereas the ground state with spin 1/2 is not split. Now two transitions from the ground state to both excited sublevels are possible and in the corresponding Mössbauer spectrum two lines (quadrupole doublet) are observed. (b) The distance between the positions of both lines in mm/s corresponds to the quadrupole splitting δEQ. The distance in mm/s between zero velocity and the centroid of both lines corresponds to the isomer shift δ (modified from Gütlich et al., 1978).

Therefore, Vzz can be expressed by the following formula:  

formula
γ and R0 are the so-called Sternheimer antishielding and shielding factors, respectively, which account for the induced charge polarisation of the electrons in closed shells by forumla and forumla respectively. On the one hand, the electron shell of a Mössbauer atom is distorted by electrostatic interaction with the non-cubic charge distribution in its surroundings, which increases forumla This antishielding effect is accounted for by the correction factor (1 – γ) with γ &≈–9. On the other hand, an anisotropic charge distribution in the valence shell causes a deformation of the inner closed shells, yielding a reduction of forumla. Therefore, forumlahas to be corrected by the shielding factor (1 – R0) with R0&≈ 0.10–0.15.

Equation 22 is useful for the qualitative interpretation of the quadrupole splitting in Mössbauer spectra. In the case of “high-spin” Fe3+ with the formal electron configuration [Ar]forumla the five 3d orbitals are occupied each by one electron with the same spin direction. This spin arrangement is almost spherically symmetric and therefore forumla is expected to be very small. However, recent non-empirical electronic structure calculations (Grodzicki et al., 1997; Keutel et al., 1999; Grodzicki & Amthauer, 2000; Grodzicki et al., 2001) have shown that even in cases where forumla should vanish according to CFT the anisotropy of the valence shell yields the dominating contribution to Vzz. The most striking example is Fe3+ in epidote, Ca2Al2Fe3+Si3O12OH. The reason is that the formally empty spin-down forumla orbitals undergo strong covalent interactions with the ligand orbitals and become partially occupied. In the case of high-spin Fe2+ with the electron configuration [Ar]forumla the single spin-down d electron occupies the d orbital with the lowest energy with its spin antiparallel to the five other d electrons. This causes a strong asymmetry of the Fe2+ electron distribution around the nucleus and therefore forumla always makes the dominant contribution to the quadrupole splitting, which usually is about an order of magnitude larger than the lattice contribution forumla. This is the main reason why in general a quadrupole doublet assigned to high-spin Fe2+exhibits a large quadrupole splitting δEQ (~ 3 mm/s), whereas a quadrupole doublet assigned to high-spin Fe3+ often exhibits a smaller quadrupole splitting δEQ (~ 0.5 mm/s). Typical Mössbauer spectra of a Fe2+-bearing pyrope garnet and a Fe3+-bearing andradite garnet are shown in Figure 6. The spectrum of babingtonite, Ca2Fe2+Fe3+Si5O14OH, containing both Fe2+as well as Fe3+, is displayed in Figure 7. From the area ratios of Fe2+ and Fe3+ doublets, the Fe2+/Fe3+ ratio can be determined with very high precision (±1%) if possible different recoil-free fraction fi (i = Fe2+ or Fe3+) and saturation effects are considered.

In compounds with octahedrally coordinated low-spin Fe2+ with the electron configuration [Ar]forumla as in pyrite, the negative charge distribution around the nucleus is more symmetric and the quadrupole splitting is small; whereas in compounds with low-spin Fe3+ with the electron configuration [Ar]forumla the negative charge distribution around the nucleus is more asymmetric and therefore the quadrupole splitting is larger than in high-spin Fe3+ compounds. In general, forumla does not exceed values of &≈ 0.50 mm/s so that only for small quadrupole splittings the valence and the lattice contribution may be of similar size. Especially, in high-spin Fe2+ compounds, forumla is about an order of magnitude smaller than forumla and has opposite sign.

The quadrupole splitting of Fe2+ at the octahedral positions of the babingtonite structure exhibits a strong decrease with increasing temperature whereas the quadrupole splitting of Fe3+ is almost independent of temperature (Fig. 8). This difference in the temperature dependence of ΔEQ for Fe2+ (high-spin) and Fe3+ (high-spin) is very characteristic. As mentioned above, the high-spin Fe3+ cation has a forumla(6A1g) electronic ground state and is spherically symmetric. Low-spin Fe2+ behaves similarly as a result of its forumla(1A1g) configuration in the ground state. Therefore, it is unlikely that there will be any low-lying excited levels in either of these configurations that can be thermally occupied, and it is predicted and observed that the EFG in both Fe3+ (high-spin) and Fe2+(low-spin) compounds will be essentially independent of temperature.

Fig. 6.

Mössbauer spectra of 57Fe in an Fe2+ bearing pyrope (Mg,Fe2+)3Al2Si3O12 (upper spectrum) and an andradite forumla (lower spectrum) taken at liquid nitrogen temperature of the absorber. The net resonant absorption is plotted as the function of the source velocity (mm/s). The squares represent the measured spectrum and the solid line represents the calculated spectrum. The doublet with the large quadrupole splitting ΔEQ and the high isomer shift δ in the upper spectrum is assigned to Fe2+ in the dodecahedral position of the garnet structure, the doublet with the smaller quadrupole splitting ΔEQ and the lower isomer shift δ is assigned to octahedral Fe3+ in the garnet structure (Amthauer et al., 1976).

Fig. 6.

Mössbauer spectra of 57Fe in an Fe2+ bearing pyrope (Mg,Fe2+)3Al2Si3O12 (upper spectrum) and an andradite forumla (lower spectrum) taken at liquid nitrogen temperature of the absorber. The net resonant absorption is plotted as the function of the source velocity (mm/s). The squares represent the measured spectrum and the solid line represents the calculated spectrum. The doublet with the large quadrupole splitting ΔEQ and the high isomer shift δ in the upper spectrum is assigned to Fe2+ in the dodecahedral position of the garnet structure, the doublet with the smaller quadrupole splitting ΔEQ and the lower isomer shift δ is assigned to octahedral Fe3+ in the garnet structure (Amthauer et al., 1976).

The situation is somewhat more complex for octahedrally coordinated high-spin Fe2+ and low-spin Fe3+. For an ideal octahedron, the electronic configurations are [Ar]forumla(5T2g) and [Ar]forumla(2T1g), respectively. In general, however, the coordination polyhedra will be somewhat distorted so that the degeneracy of the t2g levels is partially

Fig. 7.

Mössbauer spectrum of 57Fe in babingtonite, Ca2Fe2+Fe3+Si5O14, taken at 525 K (lower spectrum) and 30 K (upper spectrum) absorber temperature. The deviation of the solid line from the data divided by the square root of the background (= residual) is plotted below the spectrum. Two doublets are well resolved at both absorber temperatures, which are assigned to Fe2+ and to Fe3+ in two crystallographically different octahedral positions of the babingtonite structure. From the area ratio, the Fe2+/Fe3+ ratio can be determined with high precision (±1%). The Fe2+/Fe3+ area ratio evaluated from both spectra is not 1:1 as indicated from to the formula of pure babingtonite. A portion (&≈ 20%) of Fe2+ is substituted by Mn2+ in agreement with the chemical analysis of this sample (Amthauer, 1980).

Fig. 7.

Mössbauer spectrum of 57Fe in babingtonite, Ca2Fe2+Fe3+Si5O14, taken at 525 K (lower spectrum) and 30 K (upper spectrum) absorber temperature. The deviation of the solid line from the data divided by the square root of the background (= residual) is plotted below the spectrum. Two doublets are well resolved at both absorber temperatures, which are assigned to Fe2+ and to Fe3+ in two crystallographically different octahedral positions of the babingtonite structure. From the area ratio, the Fe2+/Fe3+ ratio can be determined with high precision (±1%). The Fe2+/Fe3+ area ratio evaluated from both spectra is not 1:1 as indicated from to the formula of pure babingtonite. A portion (&≈ 20%) of Fe2+ is substituted by Mn2+ in agreement with the chemical analysis of this sample (Amthauer, 1980).

Fig. 8.

(a) Quadrupole splitting QS (ΔEQ) and (b) isomer shift IS (δ) of Fe2+ and Fe3+ in babingtonite, Ca2Fe2+Fe3+Si5O14OH, plotted as function of the temperature (Amthauer, 1980).

Fig. 8.

(a) Quadrupole splitting QS (ΔEQ) and (b) isomer shift IS (δ) of Fe2+ and Fe3+ in babingtonite, Ca2Fe2+Fe3+Si5O14OH, plotted as function of the temperature (Amthauer, 1980).

or completely removed. Very often the splitting of the t2g levels is of the order of 10–100 meV so that thermal occupation of low-lying excited states is possible. This leads to a more or less pronounced temperature dependence of the quadrupole splitting decreasing with increasing temperature. As an example, the quadrupole splitting of Fe2+ at the dodecahedral site of pyrope decreases by 0.54 mm/s with increasing temperature from 80 K to 681 K (Amthauer et al., 1976). This temperature dependence of ΔEQ may in turn be used to estimate the splitting between the ground and excited electronic state although such inferences occasionally may be misleading as recent calculations on chlorite have shown (Lougear et al., 2000).

At this point of the discussion, a short comparison with another Mössbauer isotope, i.e. 119Sn, should be made. The energy of the γ radiation Ey = 23.87 keV for 119Sn and Ey = 14.413 keV for 57Fe. Therefore, the recoil-free fraction at a given temperature f(T) is distinctly smaller for 119Sn than for 57Fe. This is not such a serious problem because the lower recoil-free fraction of the source and the absorber can be compensated by longer measuring times in order to obtain a 119Sn Mössbauer spectrum with a sufficiently good signal/noise ratio. More difficulties arise from the differences of the mean lifetimes ι of the excited states of both isotopes, which are ι= 17.25 ns for 119Sn and ι= 97.81 ns for 57Fe. The calculated line width of 57Fe (2Γ = 0.194 mm/s) is about three times smaller than the calculated line width of 119Sn (2Γ = 0.6456 mm/s). That is the reason why smaller energy shifts and splittings due to hyperfine interactions can be much better resolved by 57Fe than by 119Sn Mössbauer spectroscopy. This statement can be verified by a comparison of the 57Fe Mössbauer spectrum of an andradite, Ca3Fe3+2Si3O12, in Figure 6 and the 119Sn Mössbauer spectrum of a tin-bearing andradite Ca3(Fe3+,Sn4+)Si3O12 in Figure 9. Both ions, Fe3+ as well as Sn4+, occupy the distorted octahedra of the garnet structure, which have the point symmetry forumla. However, the expected quadrupole splitting appears only in the quadrupole doublet of octahedral Fe3+in Figure 6 but not in the single line of octahedral Sn4+ in Figure 9, which is somewhat broadened due to an unresolved quadrupole splitting.

Fig. 9.

Mössbauer spectrum of 119Sn in a tin-bearing andradite Ca3(Fe3+,Sn4+)Si3O12 taken at room temperature of the absorber. The single line is assigned to octahedral Sn4+ (Amthauer et al., 1979).

Fig. 9.

Mössbauer spectrum of 119Sn in a tin-bearing andradite Ca3(Fe3+,Sn4+)Si3O12 taken at room temperature of the absorber. The single line is assigned to octahedral Sn4+ (Amthauer et al., 1979).

Magnetic hyperfine interaction (magnetic hyperfine splitting ΔEM)

The magnetic hyperfine splitting ΔEM arises from the interaction of the nuclear magnetic dipole moment μ and a magnetic field H at the nucleus: the Zeeman effect. Each nucleus with spin I > 0 has a non-zero magnetic dipole moment μ. There are several effects contributing to the magnetic field at the nucleus. The most important are:

  • The dominant contribution to the local magnetic field H arises from the so-called Fermi contact interaction. If an ion contains a partially filled valence shell with a different number of spin-up and spin-down electrons, as e.g. the 3d shell in high-spin Fe2+ or Fe3+, the s electrons of the ion core will be polarised due to differences in the exchange interaction between electrons with parallel and antiparallel spins. Since electrons with parallel spins repel each other more effectively than those with antiparallel spins, the spin-up 3d electrons in the case of Fe2+ or Fe3+ polarise the core 3s shell in such a way that the probability density of the spin-up 3s electron is shifted closer to the nucleus, resulting in a spin density at the nucleus with the same sign as the spin of the valence shell. In turn, the increased density of the spin-up 3s electron at the nucleus displaces the spin-up 2s electron density near the nucleus resulting in a spin density with a sign opposite to the valence spin due to the spin-down 2s electron density. Since the probability density of the 2s electrons at the nucleus is much larger than that of the 3s electrons, the polarisation of the 2s shell dominates the spin density at the nucleus. The resulting Fermi contact interaction field Hs has, therefore, a sign opposite to the magnetic field arising from the 3d electrons of the valence shell. In metals the polarised conduction electrons also contribute to the contact interaction with the nucleus.

  • The orbital motion of valence electrons with the total orbital momentum quantum number L gives rise to a contribution HL to the magnetic field at the nucleus. In metallic iron this term is estimated to be 7 T. HL makes no contribution in the case of Fe3+ because L = 0.

  • A contribution from the so-called spin-dipolar field HD which arises from the electron spin of the parent atom.

  • Hext is the value of a magnetic field at the nucleus induced by an external magnetic field (up to 10 T). This contribution is effectively zero away from a large magnet.

  • The demagnetisation field DM and the Lorentz field (4/3 πM) are very small.

Therefore, a general expression for the magnetic field acting at the nucleus would be:  

formula
The magnetic dipole interaction can be described by the Hamiltonian  
formula
 
formula

where g is the gyromagnetic ratio, μn is the nuclear magneton and I is the nuclear spin. Diagonalisation of the first-order perturbation matrix yields the eigenvalues EM of HM as  

formula
 
formula
with  
formula

The magnetic dipole interaction splits the nuclear state with the spin quantum number I into 2I +1 equally spaced sublevels, which are characterised by the sign and the magnitude of the nuclear spin quantum number mI. Therefore, the magnetic dipole interaction in 57Fe splits the first excited state with the spin 3/2 into 4 and the ground state with the spin 1/2 into 2 sublevels, schematically displayed in Figure 10. Considering the selection rules for magnetic dipole transitions, i.e. ΔI = 1 and ΔmI = 0, ± 1, six transitions are allowed, which are shown in Figure 10. They are labelled from 1 to 6 with increasing energy. The corresponding Mössbauer spectrum exhibits 6 resonant absorption lines (sextet), also shifted from zero velocity by the electric monopole interaction (isomer shift). The relative intensities of these lines in a spectrum of a powder absorber without texture should be 3:2:1:1:2:3 (with increasing energy). The Mössbauer spectrum of metallic iron obtained at room temperature represents such a type of spectrum and is shown in Figure 11. This spectrum is often used to calibrate the velocity scale because the positions of the absorption lines and the local magnetic field H are known with high accuracy.

Fig. 10.

Magnetic dipole splitting (schematic) in 57Fe without quadrupole interaction (H ≠ 0, Vzz = 0) and with quadrupole interaction (H ≠ 0, Vzz > 0) The resulting Mössbauer spectra (sextets) are shown below. The centroid of the six lines is shifted by the isomer shift. ΔEM(g) refers to the splitting of the ground state, ΔEM(e) to the splitting of the excited state. EQ = 1/2ΔEQ (modified from Gütlich et al., 1978).

Fig. 10.

Magnetic dipole splitting (schematic) in 57Fe without quadrupole interaction (H ≠ 0, Vzz = 0) and with quadrupole interaction (H ≠ 0, Vzz > 0) The resulting Mössbauer spectra (sextets) are shown below. The centroid of the six lines is shifted by the isomer shift. ΔEM(g) refers to the splitting of the ground state, ΔEM(e) to the splitting of the excited state. EQ = 1/2ΔEQ (modified from Gütlich et al., 1978).

Fig. 11.

Mössbauer spectrum of α-Fe taken at room temperature, indicating magnetic hyperfine interaction. The spectrum exhibits no quadrupole interaction because the point symmetry of the iron positions is cubic. Such a spectrum of α-Fe is often used to calibrate the velocity scale of the electromechanical drive system. At room temperature, the splitting of the two outermost lines (1 and 6 in Fig. 10) is 10.6245 mm/s. The intensity ratio of the lines corresponds to the theoretical values of 3:2:1:1:2:3.

Fig. 11.

Mössbauer spectrum of α-Fe taken at room temperature, indicating magnetic hyperfine interaction. The spectrum exhibits no quadrupole interaction because the point symmetry of the iron positions is cubic. Such a spectrum of α-Fe is often used to calibrate the velocity scale of the electromechanical drive system. At room temperature, the splitting of the two outermost lines (1 and 6 in Fig. 10) is 10.6245 mm/s. The intensity ratio of the lines corresponds to the theoretical values of 3:2:1:1:2:3.

Combined electric and magnetic hyperfine interactions

The point symmetry of the Fe site in the structure of α-Fe at ambient P, T conditions is cubic and therefore there is no quadrupole splitting (Vzz = 0). The distances between the lines 1 and 2, 2 and 3, 4 and 5, 5 and 6 are equal. However, this situation is very rare. Quite often there is additional quadrupole splitting, because the symmetry of the lattice positions occupied by Fe is lower than cubic and quadrupole interaction is expected (Vzz ≠ 0) in addition to the electric monopole and the magnetic dipole interaction. Assuming EQEM, the quadrupole interaction causes a perturbation of the magnetic dipole interaction. This situation is often observed in the Mössbauer spectra of Fe3+compounds. Assuming also Vzz > 0, i.e. the sign of the EFG is positive, the sublevels of the excited state with mI = 3/2 and mI = –3/2, are shifted by the amount of 1/2AEQ to higher energies, whereas the sublevels of the excited state with mI = 1/2 and mI = –1/2 are shifted by the same amount to lower energies. As a consequence, the sublevels of the excited level are no longer equidistant and the lines 1, 2, 5, and 6 are typically shifted in the way shown in the right part of Figure 10. The direction of the energy shift is reversed if Vzz < 0. Therefore, it is possible to determine δEQ as well as the sign of Vzz from a magnetically split Mössbauer spectrum of a powdered sample. The Mössbauer spectrum of andradite garnet, forumla, taken at 5 K absorber temperature, shows such a type of spectrum (Fig. 12). If EQEM, the situation is more complex.

In general, there is an angle θ between the main component of the electric field gradient Vzz and the axis of the magnetic field H as shown in Figure 13. If EQEMand the EFG tensor is axially symmetric, then θ can also be determined from the Mössbauer spectra according to the following formula obtained by a first-order perturbation treatment:

 

formula

Fig. 12.

Mössbauer spectrum of an andradite garnet, forumla, taken at an absorber temperature of 5 K. The spectrum exhibits combined electric quadrupole and magnetic dipole interaction. The following parameters are derived: H = 51.7 T, ΔEQ = 0.60 mm/s, δα-Fe = 0.50 mm/s, θ = 55.3°.

Fig. 12.

Mössbauer spectrum of an andradite garnet, forumla, taken at an absorber temperature of 5 K. The spectrum exhibits combined electric quadrupole and magnetic dipole interaction. The following parameters are derived: H = 51.7 T, ΔEQ = 0.60 mm/s, δα-Fe = 0.50 mm/s, θ = 55.3°.

As shown in Figure 13, it is also possible to determine the angles between the crystallographic axes a, b, c and Vzz or H if oriented single crystals are measured and the wavevector k is parallel to a certain crystallographic direction (Lottermoser et al., 1996).

Fig. 13.

Schematic view of the angular connections between the EFG axes Vxx, Vyy, Vzz and the crystallographic axes a, b, c, the magnetic field H and the wave vector k of the γ ray.

Fig. 13.

Schematic view of the angular connections between the EFG axes Vxx, Vyy, Vzz and the crystallographic axes a, b, c, the magnetic field H and the wave vector k of the γ ray.

In andradite, forumla, Fe3+ occupies an octahedral position with site symmetry 3 so that the EFG is axially symmetric. Andradite orders antiferromagnetically below 10 K and therefore the Mössbauer spectrum taken at 5 K absorber temperature exhibits combined magnetic and quadrupole interactions (Fig. 12). The sign of the quadrupole interaction is positive. The angle θ between Vzz and H evaluated from the spectrum according to Equation 29 is 55°30', i.e., within the experimental error, in fairly good agreement with the angle of 54°44' between the directions <100> and <111> in a cubic crystal. Andradite is cubic (SG Ia3d) and the 3-fold axis and Vzz have to be parallel to <111>. Therefore, the direction of the magnetic field H at temperatures below the Néel point is most probably parallel to <100>.

The local magnetic field H at 5 K evaluated from the Mössbauer spectrum of andradite in Figure 12 is 51.7(4) T. This is a typical value for Fe3+ in silicates. In general, local magnetic fields of Fe3+ in oxidic environments are larger than those of Fe2+. For comparison, the size of the magnetic field of Fe2+ in fayalite, Fe2SiO4, at 5 K is 32.28(1) T at the M1 position and 11.7(3) T at the M2 position (Lottermoser et al., 1996).

Conclusions

Mössbauer spectroscopy is a powerful method not only to determine geochemically or petrologically interesting quantities such as the Fe2+/Fe3+ ratio in minerals, but also to provide many informations on nuclear physics, mineral physics, and crystal chemistry of minerals and cannot easily be replaced in the near future by other methods. However, for a sophisticated and quantitative interpretation of the spectra, electronic structure calculations based on the density functional theory are needed (Grodzicki, 1985; Grodzicki & Amthauer, 2000). Nuclear forward scattering using synchrotron radiation opens a new field of research in geochemistry and mineralogy.

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Figures & Tables

Fig. 1.

Separation of the emission and absorption lines by 2ER due to the recoil effect occurring during the emission and absorption of a γ ray by nuclei in gases or liquids. Resonant absorption is not possible (modified from Gütlich et al., 1978).

Fig. 1.

Separation of the emission and absorption lines by 2ER due to the recoil effect occurring during the emission and absorption of a γ ray by nuclei in gases or liquids. Resonant absorption is not possible (modified from Gütlich et al., 1978).

Fig 2

Intensity I(E) as a function of transition energy E. δE = Γ = ħ/ι is the energy width of the excited state (e) with a mean life time ι corresponding to the full width of the transition spectral line Γ at half peak height I0/2 (modified from Gütlich et al., 1978).

Fig 2

Intensity I(E) as a function of transition energy E. δE = Γ = ħ/ι is the energy width of the excited state (e) with a mean life time ι corresponding to the full width of the transition spectral line Γ at half peak height I0/2 (modified from Gütlich et al., 1978).

Fig. 3.

Principal set-up of a Mössbauer experiment (for a description see text).

Fig. 3.

Principal set-up of a Mössbauer experiment (for a description see text).

Fig. 4.

(a) Coulomb interaction between the nuclear charge and the electrons shifts the nuclear levels differently in the source and the absorber. (b) In the corresponding Mössbauer spectrum a single line is observed (no quadrupole and no magnetic hyperfine interaction). The difference between the position (centroid) of the line and the zero point of the velocity corresponds to the isomer shift δ0 (modified from Gütlich et al., 1978).

Fig. 4.

(a) Coulomb interaction between the nuclear charge and the electrons shifts the nuclear levels differently in the source and the absorber. (b) In the corresponding Mössbauer spectrum a single line is observed (no quadrupole and no magnetic hyperfine interaction). The difference between the position (centroid) of the line and the zero point of the velocity corresponds to the isomer shift δ0 (modified from Gütlich et al., 1978).

Fig. 5.

Quadrupole splitting in the case of a 1/2 → 3/2 nuclear transition, such as in 57Fe. The first excited state of the nucleus with spin 3/2 is split into two sublevels whereas the ground state with spin 1/2 is not split. Now two transitions from the ground state to both excited sublevels are possible and in the corresponding Mössbauer spectrum two lines (quadrupole doublet) are observed. (b) The distance between the positions of both lines in mm/s corresponds to the quadrupole splitting δEQ. The distance in mm/s between zero velocity and the centroid of both lines corresponds to the isomer shift δ (modified from Gütlich et al., 1978).

Fig. 5.

Quadrupole splitting in the case of a 1/2 → 3/2 nuclear transition, such as in 57Fe. The first excited state of the nucleus with spin 3/2 is split into two sublevels whereas the ground state with spin 1/2 is not split. Now two transitions from the ground state to both excited sublevels are possible and in the corresponding Mössbauer spectrum two lines (quadrupole doublet) are observed. (b) The distance between the positions of both lines in mm/s corresponds to the quadrupole splitting δEQ. The distance in mm/s between zero velocity and the centroid of both lines corresponds to the isomer shift δ (modified from Gütlich et al., 1978).

Fig. 6.

Mössbauer spectra of 57Fe in an Fe2+ bearing pyrope (Mg,Fe2+)3Al2Si3O12 (upper spectrum) and an andradite forumla (lower spectrum) taken at liquid nitrogen temperature of the absorber. The net resonant absorption is plotted as the function of the source velocity (mm/s). The squares represent the measured spectrum and the solid line represents the calculated spectrum. The doublet with the large quadrupole splitting ΔEQ and the high isomer shift δ in the upper spectrum is assigned to Fe2+ in the dodecahedral position of the garnet structure, the doublet with the smaller quadrupole splitting ΔEQ and the lower isomer shift δ is assigned to octahedral Fe3+ in the garnet structure (Amthauer et al., 1976).

Fig. 6.

Mössbauer spectra of 57Fe in an Fe2+ bearing pyrope (Mg,Fe2+)3Al2Si3O12 (upper spectrum) and an andradite forumla (lower spectrum) taken at liquid nitrogen temperature of the absorber. The net resonant absorption is plotted as the function of the source velocity (mm/s). The squares represent the measured spectrum and the solid line represents the calculated spectrum. The doublet with the large quadrupole splitting ΔEQ and the high isomer shift δ in the upper spectrum is assigned to Fe2+ in the dodecahedral position of the garnet structure, the doublet with the smaller quadrupole splitting ΔEQ and the lower isomer shift δ is assigned to octahedral Fe3+ in the garnet structure (Amthauer et al., 1976).

Fig. 7.

Mössbauer spectrum of 57Fe in babingtonite, Ca2Fe2+Fe3+Si5O14, taken at 525 K (lower spectrum) and 30 K (upper spectrum) absorber temperature. The deviation of the solid line from the data divided by the square root of the background (= residual) is plotted below the spectrum. Two doublets are well resolved at both absorber temperatures, which are assigned to Fe2+ and to Fe3+ in two crystallographically different octahedral positions of the babingtonite structure. From the area ratio, the Fe2+/Fe3+ ratio can be determined with high precision (±1%). The Fe2+/Fe3+ area ratio evaluated from both spectra is not 1:1 as indicated from to the formula of pure babingtonite. A portion (&≈ 20%) of Fe2+ is substituted by Mn2+ in agreement with the chemical analysis of this sample (Amthauer, 1980).

Fig. 7.

Mössbauer spectrum of 57Fe in babingtonite, Ca2Fe2+Fe3+Si5O14, taken at 525 K (lower spectrum) and 30 K (upper spectrum) absorber temperature. The deviation of the solid line from the data divided by the square root of the background (= residual) is plotted below the spectrum. Two doublets are well resolved at both absorber temperatures, which are assigned to Fe2+ and to Fe3+ in two crystallographically different octahedral positions of the babingtonite structure. From the area ratio, the Fe2+/Fe3+ ratio can be determined with high precision (±1%). The Fe2+/Fe3+ area ratio evaluated from both spectra is not 1:1 as indicated from to the formula of pure babingtonite. A portion (&≈ 20%) of Fe2+ is substituted by Mn2+ in agreement with the chemical analysis of this sample (Amthauer, 1980).

Fig. 8.

(a) Quadrupole splitting QS (ΔEQ) and (b) isomer shift IS (δ) of Fe2+ and Fe3+ in babingtonite, Ca2Fe2+Fe3+Si5O14OH, plotted as function of the temperature (Amthauer, 1980).

Fig. 8.

(a) Quadrupole splitting QS (ΔEQ) and (b) isomer shift IS (δ) of Fe2+ and Fe3+ in babingtonite, Ca2Fe2+Fe3+Si5O14OH, plotted as function of the temperature (Amthauer, 1980).

Fig. 9.

Mössbauer spectrum of 119Sn in a tin-bearing andradite Ca3(Fe3+,Sn4+)Si3O12 taken at room temperature of the absorber. The single line is assigned to octahedral Sn4+ (Amthauer et al., 1979).

Fig. 9.

Mössbauer spectrum of 119Sn in a tin-bearing andradite Ca3(Fe3+,Sn4+)Si3O12 taken at room temperature of the absorber. The single line is assigned to octahedral Sn4+ (Amthauer et al., 1979).

Fig. 10.

Magnetic dipole splitting (schematic) in 57Fe without quadrupole interaction (H ≠ 0, Vzz = 0) and with quadrupole interaction (H ≠ 0, Vzz > 0) The resulting Mössbauer spectra (sextets) are shown below. The centroid of the six lines is shifted by the isomer shift. ΔEM(g) refers to the splitting of the ground state, ΔEM(e) to the splitting of the excited state. EQ = 1/2ΔEQ (modified from Gütlich et al., 1978).

Fig. 10.

Magnetic dipole splitting (schematic) in 57Fe without quadrupole interaction (H ≠ 0, Vzz = 0) and with quadrupole interaction (H ≠ 0, Vzz > 0) The resulting Mössbauer spectra (sextets) are shown below. The centroid of the six lines is shifted by the isomer shift. ΔEM(g) refers to the splitting of the ground state, ΔEM(e) to the splitting of the excited state. EQ = 1/2ΔEQ (modified from Gütlich et al., 1978).

Fig. 11.

Mössbauer spectrum of α-Fe taken at room temperature, indicating magnetic hyperfine interaction. The spectrum exhibits no quadrupole interaction because the point symmetry of the iron positions is cubic. Such a spectrum of α-Fe is often used to calibrate the velocity scale of the electromechanical drive system. At room temperature, the splitting of the two outermost lines (1 and 6 in Fig. 10) is 10.6245 mm/s. The intensity ratio of the lines corresponds to the theoretical values of 3:2:1:1:2:3.

Fig. 11.

Mössbauer spectrum of α-Fe taken at room temperature, indicating magnetic hyperfine interaction. The spectrum exhibits no quadrupole interaction because the point symmetry of the iron positions is cubic. Such a spectrum of α-Fe is often used to calibrate the velocity scale of the electromechanical drive system. At room temperature, the splitting of the two outermost lines (1 and 6 in Fig. 10) is 10.6245 mm/s. The intensity ratio of the lines corresponds to the theoretical values of 3:2:1:1:2:3.

Fig. 12.

Mössbauer spectrum of an andradite garnet, forumla, taken at an absorber temperature of 5 K. The spectrum exhibits combined electric quadrupole and magnetic dipole interaction. The following parameters are derived: H = 51.7 T, ΔEQ = 0.60 mm/s, δα-Fe = 0.50 mm/s, θ = 55.3°.

Fig. 12.

Mössbauer spectrum of an andradite garnet, forumla, taken at an absorber temperature of 5 K. The spectrum exhibits combined electric quadrupole and magnetic dipole interaction. The following parameters are derived: H = 51.7 T, ΔEQ = 0.60 mm/s, δα-Fe = 0.50 mm/s, θ = 55.3°.

Fig. 13.

Schematic view of the angular connections between the EFG axes Vxx, Vyy, Vzz and the crystallographic axes a, b, c, the magnetic field H and the wave vector k of the γ ray.

Fig. 13.

Schematic view of the angular connections between the EFG axes Vxx, Vyy, Vzz and the crystallographic axes a, b, c, the magnetic field H and the wave vector k of the γ ray.

Table 1.

Periodic table of the elements with all the Mössbauer isotopes marked appropriately (modified from the original table of the Mössbauer Effect Data Center).

graphic
graphic

Contents

GeoRef

References

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