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Abstract

The Mössbauer effect is the recoilless absorption and emission of γ rays by specific nuclei in a solid, and provides a means of studying the local atomic environment around the nuclei. It is a short-range probe, and is sensitive to (at most) the first two coordination shells, but has an extremely high energy resolution that enables the detection of small changes in the atomic environment. Mössbauer spectroscopy therefore provides information at the atomic level.

There are numerous textbooks and review chapters written about Mössbauer spectroscopy. A starting point is the previous chapter in this volume (Amthauer et al., 2004), and other reference sources directed at mineralogists include Bancroft (1973), Hawthorne (1988) and McCammon (2000).

The main objective of this chapter is to provide a brief introduction to Mössbauer spectroscopy applications in mineralogy. The approach is intended to be instructional rather than encyclopaedic in nature, so emphasis is placed on worked examples that are chosen to complement the theory presented in the previous chapter. Studies of the 14.4 keV transition in 57Fe comprise more than 95% of mineralogical Mössbauer investigations; hence this chapter is focused exclusively on 57Fe.

Methodology

The fundamentals of Mössbauer methodology can be found in the previous chapter as well as any textbook devoted to Mössbauer spectroscopy (e.g. Bancroft, 1973; Gütlich et al., 1978), so only those aspects relevant to the present chapter are outlined briefly below.

Introduction

The Mössbauer effect is the recoilless absorption and emission of γ rays by specific nuclei in a solid, and provides a means of studying the local atomic environment around the nuclei. It is a short-range probe, and is sensitive to (at most) the first two coordination shells, but has an extremely high energy resolution that enables the detection of small changes in the atomic environment. Mössbauer spectroscopy therefore provides information at the atomic level.

There are numerous textbooks and review chapters written about Mössbauer spectroscopy. A starting point is the previous chapter in this volume (Amthauer et al., 2004), and other reference sources directed at mineralogists include Bancroft (1973), Hawthorne (1988) and McCammon (2000).

The main objective of this chapter is to provide a brief introduction to Mössbauer spectroscopy applications in mineralogy. The approach is intended to be instructional rather than encyclopaedic in nature, so emphasis is placed on worked examples that are chosen to complement the theory presented in the previous chapter. Studies of the 14.4 keV transition in 57Fe comprise more than 95% of mineralogical Mössbauer investigations; hence this chapter is focused exclusively on 57Fe.

Methodology

The fundamentals of Mössbauer methodology can be found in the previous chapter as well as any textbook devoted to Mössbauer spectroscopy (e.g. Bancroft, 1973; Gütlich et al., 1978), so only those aspects relevant to the present chapter are outlined briefly below.

Experimental aspects

A Mössbauer apparatus is relatively simple and can be divided into three parts – the source, the absorber and the detector (Fig. 1). Since most source radiation is monochromatic, energy is generally varied using the Doppler effect by moving the source relative to the absorber (or vice versa); hence the source is commonly mounted on a drive system. Gamma rays that do not interact with the absorber pass through and are recorded by the detector, while those that are absorbed are then re-emitted in a different direction and are not recorded by the detector; hence the resulting Mössbauer spectrum shows dips instead of peaks. The energy scale of the resulting spectrum is typically expressed in mm/s for source velocities used to probe hyperfine interactions in 57Fe.

Fig. 1.

Schematic view of a Mössbauer spectrometer. The source is moved relative to the absorber with different velocities that shift the energy of the emitted gamma rays according to the Doppler effect. Gamma rays either pass through the absorber unaffected and then reach the detector, or they are absorbed and then re-emitted in a direction different to the detector (based on a drawing from Gütlich et al., 1978).

Fig. 1.

Schematic view of a Mössbauer spectrometer. The source is moved relative to the absorber with different velocities that shift the energy of the emitted gamma rays according to the Doppler effect. Gamma rays either pass through the absorber unaffected and then reach the detector, or they are absorbed and then re-emitted in a direction different to the detector (based on a drawing from Gütlich et al., 1978).

The source is generally a radioactive parent of the Mössbauer isotope, and γ rays are produced through nuclear decay. Over one hundred different Mössbauer transitions have been observed, although unfavourable nuclear properties limit the number of commonly used nuclei. Iron is a popular Mössbauer isotope because the half-life of its common parent, 57Co, is reasonably long (270 days), the natural linewidth is relatively small (0.097 mm/s), recoil-free fractions are generally high at room temperature and the absorption cross section is sufficiently high that reasonable spectra can be obtained even for absorbers with low iron concentrations. For radioactive parents that are magnetically ordered, such as 57Co, a non-magnetic matrix is used (e.g. Rh) to dilute the atoms sufficiently such that the emitted radiation is a single energy with no detectable broadening by magnetic interactions and a low probability of self-absorption (i.e., absorption by another nucleus in the source). The latter ensures that the source thickness (which affects the linewidth and recoil-free fraction) does not increase significantly with time. The source diameter is then determined by the number of parent nuclei required to achieve a sufficient count rate, and for conventional 57Co sources is on the order of 1 cm. The source diameter can be significantly reduced if the density of parent nuclei is increased to the level where broadening due to magnetic interactions just starts to occur. For 57Co nuclei, this enables the source to be reduced to a diameter of ca. 500 μm without significant loss in count rate, a so-called “point source”. Details of such sources are discussed further below.

Source radiation can also be generated by a particle accelerator, such as a synchrotron facility. There are many advantages to such an experiment, including the possibility for a small beam size with high signal/noise ratio that does not suffer from the limitations described above. Details of such experiments are beyond the scope of this chapter, but can be found along with many excellent reviews in the book by Gerdau & de Waard (1999).

The absorber (i.e. the sample) for Mössbauer spectroscopy can take many forms, including powder, glass, single crystal, and in favourable cases, even melt or liquid. Mössbauer spectra can be recorded under a large range of conditions, including temperatures from near absolute zero to at least 1200 °C, and pressures to at least 100 GPa. Spectra can also be collected under different strengths of external magnetic field, currently to at least 15 T. The conventional absorber diameter is ca. 1 cm, but this can be reduced using a point source by roughly two orders of magnitude. Such studies are discussed in more detail below.

Mössbauer isotopes with a high absorption cross section can be studied at extremely low concentrations. For example, 57Fe has a natural abundance of only 2.14%, yet adequate signal/noise ratios can be obtained for absorbers containing as little as 1.0 wt% FeO. This enables enriched 57Fe to be used for preparation of synthetic absorbers with barely detectable amounts of Fe; hence 57Fe Mössbauer measurements can be made in nearly iron-free systems. Use of enriched 57Fe also allows the study of extremely thin absorbers, such as those in the diamond anvil cell. 57Fe can be added homogeneously to study bulk properties, or it can be added inhomogeneously (e.g. deposited in a thin layer) to study surface properties. The same enrichment possibilities exist for 57Co as a source (in this case a single-line absorber would be used), although experimentally it is more difficult due to the need to work with radioactive materials.

The geometry of the Mössbauer spectrometer can be varied depending on the type of experiment. Transmission studies require a linear arrangement where the detector sits behind the source and absorber, and they provide information on all 57Fe nuclei in the absorber. The detector can also be placed in a backscattering geometry between the source and absorber, enabling the study of only the surface nuclei in the absorber. Recent reviews of the latter technique, called Conversion Electron Mössbauer Spectroscopy (CEMS) are given by Gancedo et al. (1997) and Nomura (1999).

Analytical aspects

A Mössbauer spectrum records the number of counts as a function of source velocity, where data scatter decreases with increasing collection time. Each site occupied by iron in the absorber contributes additively to the overall spectrum, which shows an increasing complexity depending on the number of overlapping contributions (Fig. 2). Data analysis can be divided into two parts: (1) removal of instrumental artefacts by folding and baseline correction; and (2) deconvolution to extract hyperfine parameters of individual contributions. The first part is generally straightforward, while the second part can be more challenging.

An important input to the task of spectral deconvolution is the constraints imposed by quantum mechanics. In the case of an ideal thin polycrystalline absorber with random crystallite orientation, quadrupole doublet components should have equal linewidths and areas, and magnetic sextet components (in the absence of quadrupole interaction) should have equal linewidths with areas in the ratio 3:2:1:1:2:3. These constraints must be relaxed in the case of preferred orientation, aniostropic recoil-free fraction (Goldanskii-Karyagan effect) and dynamic effects such as relaxation. Additionally, next-nearest neighbour effects or other variations in site geometry can lead to hyperfine parameter distributions, such that Lorentzian lineshapes are no longer appropriate fitting profiles.

Fig. 2.

Room temperature Mössbauer spectra of (a) cordierite, and (b) tourmaline. The spectrum of cordierite contains a single quadrupole doublet corresponding to octahedral Fe2+, while the spectrum of tourmaline has been deconvoluted into four quadrupole doublets, two corresponding to Fe2+ (horizontal shading), one corresponding to Fe3+ (black shading) and one corresponding to Fe2+–Fe3+ charge transfer (vertical shading).

Fig. 2.

Room temperature Mössbauer spectra of (a) cordierite, and (b) tourmaline. The spectrum of cordierite contains a single quadrupole doublet corresponding to octahedral Fe2+, while the spectrum of tourmaline has been deconvoluted into four quadrupole doublets, two corresponding to Fe2+ (horizontal shading), one corresponding to Fe3+ (black shading) and one corresponding to Fe2+–Fe3+ charge transfer (vertical shading).

The approach to deconvolution is part of a more general topic in spectroscopy (e.g. Hawthorne & Waychunas, 1988) and has been addressed in particular for Mössbauer analysis (e.g. Rancourt, 1996). Complex Mössbauer spectra may not yield unique solutions, even if a statistical minimum is found during the least-squares fitting process. Quite often complementary data such as from X-ray diffraction must be used, and it is often useful to vary parameters such as absorber temperature, pressure or composition for additional constraints.

Analytical fitting of Mössbauer data is performed almost exclusively using computer-based methods, and a number of software packages are available to expedite the process. The examples in this chapter were processed using either NORMOS (written by R.A. Brand and distributed by Wissenschaftliche Elektronik GmbH, Germany) or RECOIL (written by K. Lagarec & D. Rancourt and distributed by Intelligent Scientific Applications Inc, Canada).

Rock-forming minerals

A landmark discovery was reported by Bancroft et al. (1966) that hyperfine parameters deduced from Mössbauer spectroscopy could be used to elucidate structural details of minerals such as cation distribution. A pair of subsequent papers identified the empirical correlation between hyperfine parameters and the coordination and geometry of crystallographic sites (Bancroft et al., 1967; 1968), and thus one of the most common applications of Mössbauer spectroscopy in mineralogy was born.

The hyperfine parameters that are most often the focus of studies involving rock-forming minerals are the isomer shift and the quadrupole splitting. In the case of a single iron site, both parameters can be measured relatively easily from the Mössbauer spectrum. It is important to note, however, that the shift from zero velocity arises from the sum of the isomer shift plus the second-order Doppler shift, which collectively is generally referred to as the centre shift. The second-order Doppler shift is similar for most standard materials; hence the isomer shift is often taken to be equal to the centre shift. In this chapter the term centre shift will be used to refer to the experimentally measured shift from zero velocity.

Centre shifts were observed by Bancroft et al. (1967) to fall into specific ranges depending on the coordination, valence state and spin state of the iron atoms. This is related to influence of s electron density, which is in turn affected by p and d electrons through shielding effects. Figure 3 is compiled from numerous Mössbauer studies of iron compounds, and provides a guide for peak assignments. Although there is some overlap, the distinctive ranges generally serve to identify the spin state, valence state and (usually) coordination number pertaining to a particular iron site.

Fig. 3.

Approximate ranges for room temperature centre shifts (relative to α-Fe) observed in iron compounds according to (a) iron valence and spin state, and (b) coordination of high-spin Fe2+ and Fe3+ minerals. Data in (a) are compiled from Greenwood & Gibb (1971), Maddock (1985) and Hawthorne (1988), while data in (b) are taken from Seifert (1990), with additional data from Burns & Solberg (1990) for pentacoordinated Fe3+.

Fig. 3.

Approximate ranges for room temperature centre shifts (relative to α-Fe) observed in iron compounds according to (a) iron valence and spin state, and (b) coordination of high-spin Fe2+ and Fe3+ minerals. Data in (a) are compiled from Greenwood & Gibb (1971), Maddock (1985) and Hawthorne (1988), while data in (b) are taken from Seifert (1990), with additional data from Burns & Solberg (1990) for pentacoordinated Fe3+.

Quadrupole splitting is often regarded as a measure of site distortion. The underlying picture is more complex, however, since it can be described in terms of two contributions (Ingalls, 1964). The valence term reflects the asymmetry of the charge distribution arising from the valence electrons, while the lattice term measures the deviation from cubic symmetry of the neighbouring atoms in the crystalline lattice. The valence and lattice contributions for 57Fe are always of opposite sign, and together they determine the magnitude of the quadrupole splitting (Fig. 4). The quadrupole splitting therefore depends not only on the degree of distortion of the crystallographic site (which is reflected primarily by the lattice term), but also the valence, spin state and coordination of the absorber atoms (which influences more the valence term).

Fig. 4.

Schematic variation of the valence and lattice term contributions to the quadrupole splitting with increasing distortion of the octahedral site. The quadrupole splitting, ΔEq, is the sum of the valence and lattice terms (adapted from Ingalls, 1964).

Fig. 4.

Schematic variation of the valence and lattice term contributions to the quadrupole splitting with increasing distortion of the octahedral site. The quadrupole splitting, ΔEq, is the sum of the valence and lattice terms (adapted from Ingalls, 1964).

Hyperfine magnetic splitting is present when there is an internal magnetic field (or alternatively an externally applied magnetic field) experienced by the iron atoms. This commonly occurs in the case of magnetic ordering, and the magnitude of the hyperfine magnetic field (the hyperfine parameter that is measured experimentally) is related to the strength of magnetic exchange interactions between atoms. These vary depending on the valence and spin state of the iron atoms, as well as their coordination geometry.

The linewidth of absorption lines can provide additional information about the crystallographic sites occupied by iron. In a Mössbauer experiment with an infinitely thin source and absorber, a Lorentzian lineshape would be obtained with a minimum linewidth of twice the natural linewidth, i.e. 0.194 mm/s. In practice, allowing for instrumental broadening and finite thickness effects, a linewidth of approximately 0.24–0.28 mm/s would be obtained for iron occupying a single well-defined crystallographic site. In the case where iron sites differ slightly (geometry, bonding, next-nearest neighbour site occupancy, defects etc.), each configuration will contribute to the overall absorption with slightly different centre shift, quadrupole splitting and/or hyperfine magnetic field, resulting in a distribution of Lorentzian lineshapes. The resulting lineshape is no longer Lorentzian, but may be indistinguishable from a Lorentzian lineshape within the data scatter depending on the width of the distribution. The overall linewidth will be greater, however, since it reflects not only the individual site, but also its variations. Other effects within the absorber can also cause line broadening, including time-dependent fluctuations such as relaxation and diffusion.

The relative area of each subspectrum is related to the relative abundance of that particular site within the absorber, although the exact relationship is modified by effects including thickness and differing recoil-free fractions of individual sites.

As a final note, it is important to understand that hyperfine interactions between nuclei and their surrounding electrons are dynamic by nature, so that what is observed in the Mössbauer spectrum is not only an average over space (i.e. over all 57Fe atoms in the absorber), but also over time. The crucial parameter is the characteristic measurement time of the Mössbauer transition, which for 57Fe is roughly 10−8 s. Fluctuations in the local environment that are significantly faster than this measurement time give a well-defined average environment that is seen by the nucleus; hence hyperfine parameters can be treated as essentially static. Other conditions under which static behaviour can be observed are given by Rancourt & Ping (1991). In most Mössbauer studies of minerals, static hyperfine parameters can be assumed, but there are notable exceptions, e.g. absorbers with small grain size, and glasses with low iron concentration. The latter case is discussed in more detail below.

Case study: Accurate site populations of Fe2+ and Fe3+ in majorite garnet

One of the more common mineralogical applications of Mössbauer spectroscopy is the determination of iron site distributions in rock-forming minerals. To illustrate this application, the determination of accurate site distributions in (Mg,Fe)SiO3 majorite garnet is described. Further details can be found in McCammon & Ross (2003).

The structure of majorite garnet has tetragonal symmetry with two distinct dodecahedral sites (D1 and D2), two distinct octahedral sites (O1 and O2) and three distinct tetrahedral sites (T1, T2 and T3) (Fig. 5). In the end-member MgSiO3 majorite, the dodecahedra are occupied exclusively by Mg, the tetrahedra exclusively by Si, Mg is ordered preferentially on the larger O1 site, and Si is ordered preferentially on the smaller O2 site (Angel et al., 1989). Each dodecahedral site shares edges with two octahedral sites and two tetrahedral sites.

Fig. 5.

Polyhedral model of the MgSiO3 majorite garnet structure viewed down (a) [001] and (b) [010] based on the structure refinement of Angel et al. (1989). Inequivalent positions are labelled and shaded as follows: tetrahedra (light grey), octahedra (dark grey) and dodecahedra (black).

Fig. 5.

Polyhedral model of the MgSiO3 majorite garnet structure viewed down (a) [001] and (b) [010] based on the structure refinement of Angel et al. (1989). Inequivalent positions are labelled and shaded as follows: tetrahedra (light grey), octahedra (dark grey) and dodecahedra (black).

A room temperature Mössbauer spectrum of Mg0.9Fe0.1SiO3 majorite garnet is illustrated in Figure 6. Based on the starting assumption that quadrupole doublets have equal component widths and areas, visual inspection of the spectrum suggests that there are a minimum of three quadrupole doublets. The first attempt at fitting is three Lorentzian doublets with all component areas and widths constrained to be equal (Fig. 6a). The centre shifts, quadrupole splittings and linewidths of the Fe2+ doublets are relatively well constrained, since the high-velocity components of two of the peaks do not overlap with any other peaks – this allows the positions of their low-velocity components to be determined relatively unambiguously based on the constraint of equal component areas and widths. The hyperfine parameters of the Fe3+ doublet are less well constrained than those for the Fe2+ doublets, but nevertheless are restricted by the spectrum morphology to a relatively narrow range. This exercise allows the assignment of peaks based on centre shift values (given in parentheses relative to α-Fe) to dodecahedral Fe2+ (1.25 mm/s), octahedral Fe2+ (1.15 mm/s) and Fe3+ (0.33 mm/s) (see Fig. 3).

Fig. 6.

Room temperature Mössbauer spectra of Fe0.1Mg0.9SiO3 majorite fitted using (a) Lorentzian lineshapes, (b) extended Voigt-based fitting (xVBF) analysis and (c) full transmission integral with xVBF analysis. (d) Mössbauer spectrum of the same sample at 77 K fitted using the full transmission integral and xVBF analysis. Doublets in all spectra are shaded as follows: dodecahedral Fe2+ (unshaded), octahedral Fe2+ (black), octahedral Fe3+ (grey). The subspectra are offset from the total spectrum for clarity, and the residuals (i.e. the difference between calculated and experimental data) are shown above each spectrum.

Fig. 6.

Room temperature Mössbauer spectra of Fe0.1Mg0.9SiO3 majorite fitted using (a) Lorentzian lineshapes, (b) extended Voigt-based fitting (xVBF) analysis and (c) full transmission integral with xVBF analysis. (d) Mössbauer spectrum of the same sample at 77 K fitted using the full transmission integral and xVBF analysis. Doublets in all spectra are shaded as follows: dodecahedral Fe2+ (unshaded), octahedral Fe2+ (black), octahedral Fe3+ (grey). The subspectra are offset from the total spectrum for clarity, and the residuals (i.e. the difference between calculated and experimental data) are shown above each spectrum.

The centre shift of the Fe3+ doublet is most consistent with octahedral coordination, and shows values similar to those for Fe3+ in “skiagite” garnet forumla (0.36 mm/s) where Fe3+ is known to be in octahedral coordination (Woodland & Ross, 1994). Additional evidence that Fe3+ occupies octahedral sites comes from chemical composition data combined with the accurate site distributions calculated below that allow a stoichiometric site occupancy model only if all Fe3+ is assumed to be octahedral (McCammon & Ross, 2003). Finally, tetrahedral Fe3+ has been reported to occur in natural garnet only in rare circumstances, such as when cations such as Sn, Zr or Ti are present that preferentially fill the octahedral sites (Amthauer et al., 1976). It is worthwhile to note, however, that tetrahedral Fe3+ is well known in synthetic garnets such as YIG (Y3Fe5O12) and other rare earth iron garnets.

The two structurally distinct dodecahedral sites have different geometry, and metrics such as the quadratic elongation (Robinson et al., 1971) show their different distortions. The linewidth of the dodecahedral Fe2+ peak in the Mössbauer spectrum is not significantly broadened (0.37 mm/s), which suggests that Fe2+ is concentrated on only one of the sites, otherwise the linewidth would be larger due to the significantly different values of quadrupole splitting expected from the two sites. In a similar way the narrow linewidth of the octahedral Fe2+ peak (0.28 mm/s) suggests that Fe2+ occupies primarily only one of the two octahedral sites, since the sites differ in both distortion and mean M–O distance. In contrast, the broader linewidth of the Fe3+ doublet (0.50 mm/s) suggests that Fe3+ occupies both of the octahedral sites in the structure.

While the positions of all peaks in the majorite garnet spectra are well constrained, their relative areas are more ambiguous due to the overlap of the Fe3+ doublet with the low-velocity components of both Fe2+ doublets. The model dependence of the relative areas can be illustrated by exploring other fitting models. A more realistic fitting approach for a solid solution such as majorite garnet is a distribution of Lorentzian lines, such as a quadrupole splitting distribution (QSD) (Rancourt & Ping, 1991; Rancourt, 1994a), which has evolved to include correlations between hyperfine parameters, the so-called extended Voigt-based fitting (xVBF) analysis (Lagarec & Rancourt, 1997) (Fig. 6b). The centre shifts and quadrupole splittings of the doublets remain essentially unchanged in the xVBF approach compared to the Lorentzian model, but the relative areas are 10–19% different (Table 1). This arises from the overlap of doublets corresponding to octahedral Fe2+ and Fe3+, which leads to a lineshape dependence of their relative areas. The model dependence of hyperfine parameters in majorite is relatively minor since all of the subspectral contributions are relatively well resolved, but the situation becomes more critical when subspectra overlap more strongly. When the separation between subspectra becomes smaller than the linewidth, it is no longer possible to resolve individual contributions (Dollase, 1975; see also Rancourt, 1994b).

Table 1.

Relative areas calculated from majorite garnet Mössbauer spectra.

T [K]Fitting model[viii]Fe2+[VI]Fe2+Fe3+

293Lorentzian0.774(5)0.078(5)0.149(4)
293xVBF10.773(5)0.093(5)0.134(4)
293xVBF with FTI10.794(11)0.082(19)0.123(17)
293xVBF with FTI1 corrected for recoil-free fractions0.804(13)0.083(20)0.113(18)
77xVBF with FTI10.800(10)0.081(15)0.120(12)
77xVBF with FTI1 corrected for recoil-free fractions0.802(12)0.081(17)0.117(14)
T [K]Fitting model[viii]Fe2+[VI]Fe2+Fe3+

293Lorentzian0.774(5)0.078(5)0.149(4)
293xVBF10.773(5)0.093(5)0.134(4)
293xVBF with FTI10.794(11)0.082(19)0.123(17)
293xVBF with FTI1 corrected for recoil-free fractions0.804(13)0.083(20)0.113(18)
77xVBF with FTI10.800(10)0.081(15)0.120(12)
77xVBF with FTI1 corrected for recoil-free fractions0.802(12)0.081(17)0.117(14)

1 xVBF: extended Voigt-based fitting; FTI: full transmission integral Standard deviations are based on statistical analysis of the fitting model only, and do not represent the cumulative error of the measurement.

The site occupancy of each type of Fe cation in the crystal structure is related to the relative area fraction of the corresponding subspectrum. These quantities are often taken to be equal, but in reality there are many factors that can influence the relative areas (e.g. Rancourt, 1989). In the present example there are two factors which are potentially important: finite absorber thickness effects and unequal site recoil-free fractions.

The effective dimensionless absorber thickness is given by  

formula
where σ0 is the cross-section at resonance for the Mössbauer transition (= 2.56 • 10−18 cm2 for 57Fe), fa is the recoil-free fraction of the absorber, and na is the number of 57Fe atoms per cm2. The sample of Mg0.9Fe0.1SiO3 majorite was synthesised using 64% enriched 57Fe to compensate for the small amount of material available from the high-pressure run. The resulting 1.5 mg was spread over a diameter of 0.6 cm. Using an averaged value for the room temperature recoil-free fraction of 0.7 (Amthauer et al., 1976; DeGrave & Van Alboom, 1991), the dimensionless effective thickness is calculated from Equation 1 to be 3.5, which corresponds to 8.6 mg Fe/cm2 of non-enriched iron.

The effect of finite absorber thickness causes spectral distortion and leads to overestimation of the less abundant components. The effect can be investigated experimentally, where area ratios determined for absorbers with different effective thicknesses are extrapolated to zero thickness (e.g. Skogby et al., 1992). A more rigorous approach is to (1) deconvolute the spectral data to obtain the spectrum in the thin-absorber limit (Rancourt, 1989, 1996) or (2) fit the spectral data directly with the full transmission integral (integration of the product of the emission and absorption profile over the entire energy range). The Mössbauer spectrum was fitted with the full transmission integral using an xVBF analysis (Fig. 6c), which leads to a 9–13% reduction in relative area compared to the original xVBF analysis for the doublets corresponding to octahedral Fe2+ and Fe3+ (Table 1). An identical result was obtained by extracting the spectrum in the thin-absorber limit (Rancourt, 1989, 1996). The degree of relative area reduction increases with decreasing linewidth (Ping & Rancourt, 1992) and decreasing relative area (Rancourt, 1989). For example, for an absorber with a thickness of 5 mg Fe/cm2 (a typical thickness used in Mössbauer experiments), the observed area overestimates the “true” relative area by approximately 50% for narrow doublets with low intensity (ca. 5% relative area) (Rancourt, 1989).

A difference in recoil-free fraction for Fe2+ and Fe3+ will change the relative areas of the subspectra by an amount that increases with increasing temperature (e.g.De Grave & Van Alboom, 1991). The relative site populations are given by  

formula
where ni is the number of Fe atoms in site i, ntotal is the number of Fe atoms in all sites, Ai is the area of spectrum i, Atotal is the total spectrum area, fi is the recoil-free fraction of site i and favg, the average recoil-free fraction, is given by  
formula
(e.g.Rancourt et al., 1994). The recoil-free fractions can be calculated from the Mössbauer Debye temperature (ΘM) based on the Debye model (e.g.McCammon, 2000), where ΘM values are most commonly determined from the temperature dependence of the centre shift (e.g.De Grave & Van Alboom, 1991).The Mössbauer Debye temperatures for Fe2+ and Fe3+ in garnet can be estimated from data of Amthauer et al. (1976) and DeGrave & Van Alboom (1991) to be 340 K and 400 K, respectively (here the difference between Fe2+ occupying the dodecahedral site versus the octahedral site is considered to be relatively small). The corresponding room temperature recoil-free fractions calculated from the Debye model are 0.70 and 0.77 for Fe2+ and Fe3+, respectively. Correction of the relative areas from room temperature spectra using Equations 2 and 3 reduces the relative area for Fe3+ (Table 1). If the same approach is used to correct the relative areas of the 77 K spectrum (where recoil-free fractions of Fe2+ and Fe3+ are estimated to be 0.88 and 0.90, respectively), results are identical to values for room temperature-corrected spectra within experimental error (Table 1).A different approach to correct relative areas for recoil-free fraction effects in garnets was used by Woodland & Ross (1994). They calculated an empirical factor to be used in a form of Equation 2 from andradite-“skiagite” and almandine-“skiagite” garnet data, based on the comparison of measured area ratios and Fe3+/ΣFe determined from chemical composition data. Excellent agreement with the data in Table 1 is obtained if their empirical correction is applied to the Lorentzian fit of the majorite garnet Mössbauer data (calculated Fe3+/ΣFe = 0.112), while agreement is slightly worse if the correction is applied to the thickness-corrected xVBF fit of the majorite garnet data (calculated Fe3+/ΣFe = 0.092). This likely reflects the nature of their approach, which was to use Lorentzian-fit Mössbauer data that were uncorrected for thickness effects. Such an approach should be used with caution since it carries the implicit assumption that thickness effects will be similar, but probably results in a closer approximation to true Fe3+/ΣFe values for garnet than to ignore recoil-free fraction effects altogether.Corrections for recoil-free fraction effects are hence recommended for garnet based on the above analysis, which is likely related to the different geometry and bonding of sites occupied by Fe2+ and Fe3+ in the garnet structure. A similar conclusion was reached for (Mg,Fe)(Si,Al)O3 perovskite (Lauterbach et al., 2000). In contrast, Rancourt et al. (1994) found no difference in recoil-free fractions for Fe2+ and Fe3+ based on a comprehensive data analysis of annite, where Fe2+ and Fe3+ occupy similar sites in the structure.The example of majorite garnet has illustrated site assignments based on centre shift values, and the influence of lineshape, thickness effects and differing recoil-free fractions on relative areas. It demonstrates one approach to fitting and data interpretation, but should not be taken to imply that it is the only approach, nor that it is a general approach that can be used for any mineral. It is also worth emphasising that it is quite often necessary to apply constraints to the fitting model from complementary methods such as X-ray diffraction or chemical analysis.

Glasses and other amorphous materials

Glasses and amorphous materials differ from rock-forming minerals in that they are non-crystalline and lack a long-range structure. Diffraction techniques are of limited use, therefore, and short-range methods such as Mössbauer spectroscopy are valuable in determining the local atomic arrangement. Figure 7 shows a comparison of local iron environments in crystalline CaFeSi2O6 (i.e. hedenbergite) and calculated arrangements in amorphous CaFeSi2O6 glass (Rossano et al., 2000). While the local iron environments are generally similar throughout the lattice in a crystalline material, there are local site-to-site distortions in the geometry of the polyhedra surrounding the iron atoms in a glass that give rise to broadened spectra (Fig. 8). Mössbauer spectroscopy probes interactions between the nucleus and atoms up to the second coordination shell; hence the hyperfine parameters measured for glasses and other amorphous materials are interpreted in a similar manner to those for crystals.

Fig. 7.

Ball and stick model of (a) crystalline CaFe2+Si2O6 hedenbergite looking down [100], and (b) amorphous CaFe2+Si2O6 glass. For clarity only the iron (black) and oxygen (grey) atoms are shown. In hedenbergite the iron sites are regular and show long-range ordering, while in the glass there are site-to-site distortions and no long-range order. Iron occupies a single octahedral site in hedenbergite, while it has been suggested on the basis of EXAFS and molecular dynamics simulations to occupy a continuous spectrum of four- and five-coordinated sites in the glass (Rossano et al., 2000).

Fig. 7.

Ball and stick model of (a) crystalline CaFe2+Si2O6 hedenbergite looking down [100], and (b) amorphous CaFe2+Si2O6 glass. For clarity only the iron (black) and oxygen (grey) atoms are shown. In hedenbergite the iron sites are regular and show long-range ordering, while in the glass there are site-to-site distortions and no long-range order. Iron occupies a single octahedral site in hedenbergite, while it has been suggested on the basis of EXAFS and molecular dynamics simulations to occupy a continuous spectrum of four- and five-coordinated sites in the glass (Rossano et al., 2000).

Fig. 8.

Room temperature Mössbauer spectra of (a) crystalline CaFe2+Si2O6 hedenbergite, and (b) amorphous Ca–Fe2+–Si–O glass. The single quadrupole doublet in hedenbergite is narrow according to the single octahedral site occupied by iron, while the glass spectrum shows a strongly asymmetric and broadened quadrupole doublet due to the range of different iron environments. The glass spectrum is based on data from Alberto et al. (1996).

Fig. 8.

Room temperature Mössbauer spectra of (a) crystalline CaFe2+Si2O6 hedenbergite, and (b) amorphous Ca–Fe2+–Si–O glass. The single quadrupole doublet in hedenbergite is narrow according to the single octahedral site occupied by iron, while the glass spectrum shows a strongly asymmetric and broadened quadrupole doublet due to the range of different iron environments. The glass spectrum is based on data from Alberto et al. (1996).

Centre shifts observed for glasses fall into similar ranges as those for crystalline materials based on valence and coordination number (Table 2); hence they are valuable in assessing likely coordination numbers. This is particularly useful for glasses, since crystallographic information is not available to the same degree as for crystalline materials. Centre shifts have been used, for example, to infer a change in coordination of Fe3+ from octahedral to tetrahedral with increasing Fe3+ concentration in the system CaO–MgO–Al2O3–SiO2–Fe–O (Mysen et al., 1985a) (Fig. 9).

Fig. 9.

Variation of centre shift with Fe3+/ΣFe measured from room temperature Mössbauer spectra of glasses in the systems MgO–Al2O3–SiO2–Fe–O and CaO–Al2O3–SiO2–Fe–O (after Mysen et al., 1985a). The decrease in centre shift from 0.61 to 0.29 mm/s with increasing Fe3+ concentration was interpreted to indicate a change from octahedral to tetrahedral coordination. Typical error bars are shown for low, moderate and high Fe3+ concentrations.

Fig. 9.

Variation of centre shift with Fe3+/ΣFe measured from room temperature Mössbauer spectra of glasses in the systems MgO–Al2O3–SiO2–Fe–O and CaO–Al2O3–SiO2–Fe–O (after Mysen et al., 1985a). The decrease in centre shift from 0.61 to 0.29 mm/s with increasing Fe3+ concentration was interpreted to indicate a change from octahedral to tetrahedral coordination. Typical error bars are shown for low, moderate and high Fe3+ concentrations.

Quadrupole splitting is related to site distortion in the same manner as for crystalline materials, which leads to a range of values within glasses due to significant variations in site-to-site distortion. Quadrupole splitting may provide a diagnostic for glass properties, as shown by a correlation between quadrupole splitting and the glass transition temperature (as measured by DTA) for oxide glasses where Fe3+ is substituted in small quantities for network forming cations (Nishida et al., 1991) (Fig. 10).

Fig. 10.

Correlation between quadrupole splitting and glass transition temperature (as measured by DTA) for aluminate, borate, gallate, tellurite, titanate and vanadate glasses (solid circles), phosphate and fluoride glasses (open circles) and sulphate glasses (open squares), where Fe3+ substitutes for network formers (solid symbols) or for network modifiers (open symbols) (after Nishida et al., 1991).

Fig. 10.

Correlation between quadrupole splitting and glass transition temperature (as measured by DTA) for aluminate, borate, gallate, tellurite, titanate and vanadate glasses (solid circles), phosphate and fluoride glasses (open circles) and sulphate glasses (open squares), where Fe3+ substitutes for network formers (solid symbols) or for network modifiers (open symbols) (after Nishida et al., 1991).

Hyperfine magnetic splitting can be observed in amorphous materials such as metallic glasses (also referred to as glassy metals or amorphous alloys). There is a vast literature describing the application of Mössbauer spectroscopy to metallic glasses, and interested readers are referred to a review by Longworth (1987) as a starting point for further information. A topic more relevant to silicate glasses is that of dynamic broadening due to magnetic relaxation (e.g. Hoy, 1984). The atomic relaxation time can be thought of as a measure of the time interval over which the hyperfine magnetic field (resulting from the electrons) does not change. If the relaxation time is very short, the nucleus sees only an average of all fields, which in the paramagnetic case is zero. Hence the observed hyperfine magnetic splitting is zero. This is expected to be nearly always true for paramagnetic Fe2+, where the dominant spin-lattice relaxation term ensures a short relaxation time. In paramagnetic Fe3+, however, spin-spin interactions usually dominate, which means that relaxation times can be slowed down when exchange coupling becomes negligible. This can occur in dilute amorphous systems such as Fe3+-doped silicate glasses, where Fe3+ atoms are simply too far apart to interact appreciably. In this case the atomic relaxation time can lengthen to the point where an essentially static magnetic field is experienced by the nucleus, hence giving rise to hyperfine magnetic splitting, even though the bulk material is paramagnetic. Recall that the characteristic measurement time of the Mössbauer transition in 57Fe is roughly 10−8 s. If atomic relaxation times are significantly shorter, the time-averaged magnetic field will be zero, but if relaxation times are significantly longer, the time-averaged hyperfine field will be non-zero and magnetic hyperfine splitting will be observed. If relaxation times are comparable to 10−8 s, however, the resulting spectra will show broadened lines with shapes determined by the relevant relaxation parameters. This is the case, for example, when concentrations of Fe3+ in Na-Fe-Si-O-Cl glass are low (Fig. 11). At 5.1 wt% Fe3+, the atomic relaxation time is sufficiently short at room temperature that a typical glass quadrupole doublet is observed (Fig. 11a), but at lower Fe3+ concentrations the atomic relaxation time becomes longer to the point where broadening can be observed in room temperature spectra (Fig. 11b). Atomic relaxation times can be lengthened further by reducing the temperature, in some cases to the point where well resolved magnetic sextets can be observed (e.g. Williams et al., 1998).

Table 2.

Range of glass centre shifts.

Iron environmentcentre shift1 [mm/s]

[VIII]Fe2+1.20–1.30
[VIII]Fe2+1.05–1.10
[VIII]Fe2+0.90–0.95
[VIII]Fe3+0.35–0.55
[VIII]Fe3+0.20–0.32
Iron environmentcentre shift1 [mm/s]

[VIII]Fe2+1.20–1.30
[VIII]Fe2+1.05–1.10
[VIII]Fe2+0.90–0.95
[VIII]Fe3+0.35–0.55
[VIII]Fe3+0.20–0.32

1 relative to α-Fe

From Dyar (1985) for phosphate, borate and silicate glasses.

Fig. 11.

Room temperature Mössbauer spectra of glass in the system Na–Fe–Si–O–Cl containing (a) 5.1 wt% Fe and (b) 2.3 wt% Fe. Broadening due to spin relaxation can be seen in spectrum (b) as a greater deviation from the baseline (dotted line).

Fig. 11.

Room temperature Mössbauer spectra of glass in the system Na–Fe–Si–O–Cl containing (a) 5.1 wt% Fe and (b) 2.3 wt% Fe. Broadening due to spin relaxation can be seen in spectrum (b) as a greater deviation from the baseline (dotted line).

Broadened linewidths are one of the most marked characteristics of Mössbauer spectra of glasses. As in the case of crystalline materials, the minimum possible linewidth in glasses is determined by the Heisenberg uncertainty principle, hence line broadening results primarily from site-to-site variations in geometry. If fluctuations in the environment are completely random and uncorrelated, individual Lorentzian contributions will be symmetrically broadened in a Gaussian distribution. More likely, however, are correlations between hyperfine parameters, such as between isomer shift and quadrupole splitting, which lead to asymmetrical broadening. There is a vast literature devoted to the analytical treatment of hyperfine parameter distributions, and a good starting point is the review by Campbell & Aubertin (1989).

Relative areas of subspectra are related to site abundance as in the case for crystalline materials. Although thickness effects may be less significant than for crystals due to (1) intrinsically broadened lines (Ping & Rancourt, 1992) or (2) the use of small absorber thicknesses due to high electronic absorption in glasses with high silica content (e.g. Long et al., 1983), their influence should nevertheless be at least considered for each spectrum. Equally important to the determination of accurate relative areas is the use of appropriate analytical lineshapes and fitting models to deconvolute the spectrum. Finally, differences in recoil-free fractions for Fe2+ and Fe3+ must be considered. On the one hand, Mössbauer and wet chemical analysis determinations of Fe3+/ΣFe in silicate glasses show no systematic deviations from one another (Mysen et al., 1985b; Dingwell, 1991), while on the other hand, differences in recoil-free fractions in sodium iron silicate glasses have been reported by Holland et al. (1999). Nishida (1995) noted a correlation between the Mössbauer Debye temperature (which is related to the recoil-free fraction in the Debye model) and the structural role of Fe3+ in various inorganic glasses, which could account for compositional influences on recoil-free fractions.

Case study: Determination of Fe3+Fe in a basaltic glass

A common application of Mössbauer spectroscopy in the study of glasses is the determination of iron environment and oxidation state. These can have profound effects on the physical properties of melts (e.g. Dingwell & Virgo, 1987), which has motivated numerous studies of glass compositions relevant to natural magmatic systems. To illustrate this application, the determination of accurate site distributions in synthetic glass with basaltic composition is described. Further details can be found in Partzsch et al. (in print).

The room temperature Mössbauer spectrum of a ferrobasaltic glass synthesised at 1187 °C and an oxygen fugacity of 1.4 log-bar units above the fayalite-magnetite-quartz (FMQ) buffer is shown in Figure 12. Visual inspection of the spectrum suggests two dominant components, one due to Fe2+ and one due to Fe3+, but the latter component is not well resolved due to the broadened absorption lines. It is clear that the line positions of the Fe3+ component as well as its relative area will be highly dependent on the analytical lineshape used to fit the Mössbauer data.

Fig. 12.

Room temperature Mössbauer data, subspectra and residuals for basaltic glass fitted using (a) Lorentzian lineshapes, (b) histogram distributions of quadrupole splitting, (c) extended Voigt-based fitting (xVBF) analysis. Fe3+ absorption is shaded grey in each spectrum. The one-dimensional quadrupole splitting (ΔEq) probability distributions for Fe2+ (unshaded) and Fe3+ (grey) are shown to the right of spectra (a) and (b), and the two-dimensional correlated centre shift (δ) and ΔEq distributions are shown to the right of spectrum (c). For the latter, contour lines indicate equal probabilities, where δ and ΔEq are highly correlated in the Fe2+ distribution, while in the Fe3+ distribution nearly all sites have the same value of 5. All spectra were extracted in the thin-absorber limit (Rancourt, 1989, 1996).

Fig. 12.

Room temperature Mössbauer data, subspectra and residuals for basaltic glass fitted using (a) Lorentzian lineshapes, (b) histogram distributions of quadrupole splitting, (c) extended Voigt-based fitting (xVBF) analysis. Fe3+ absorption is shaded grey in each spectrum. The one-dimensional quadrupole splitting (ΔEq) probability distributions for Fe2+ (unshaded) and Fe3+ (grey) are shown to the right of spectra (a) and (b), and the two-dimensional correlated centre shift (δ) and ΔEq distributions are shown to the right of spectrum (c). For the latter, contour lines indicate equal probabilities, where δ and ΔEq are highly correlated in the Fe2+ distribution, while in the Fe3+ distribution nearly all sites have the same value of 5. All spectra were extracted in the thin-absorber limit (Rancourt, 1989, 1996).

There are numerous papers in the literature that debate the suitability of different fitting models for hyperfine parameter distributions, and the reader is referred to a selection of these for further information (e.g. Campbell & Aubertin, 1989; Vandenberghe et al., 1994; Rancourt, 1996). In the present example the results of various fitting models will be examined, where thickness effects are first corrected for by deconvoluting the spectral data to obtain the spectrum in the thin-absorber limit (Rancourt, 1989; 1996). This was performed to remove sources of line broadening other than those due to site-to-site variations in hyperfine parameters.

Early attempts to fit Mössbauer data of glasses and amorphous materials employed multiple Lorentzian lines as an approximation to the distribution of hyperfine parameters. Figure 12a illustrates such an approach, where quadrupole doublets are successively added until an adequate fit is obtained (the statistical significance of adding another doublet can be tested using an F test, e.g. Bevington, 1969). The quadrupole splitting probability distribution shows three discrete lines for Fe2+ and one for Fe3+ corresponding to each of the doublets (Fig. 12a), but this does not imply that each doublet corresponds to a unique environment. The only robust parameters that can be determined are the weighted average centre shift and quadrupole splitting values for Fe2+ and Fe3+ absorption. Their relative areas are only approximately constrained by the intensity of the shoulder at ca. 1.0 mm/s, however, due to the limited spectral constraints on the lineshape of Fe3+ absorption.

A different approach to fitting Mössbauer data of glasses and amorphous materials is to assume distributions of hyperfine parameters. A simple approach that does not require knowledge of the shape of the distribution is to divide the parameter range into discrete steps and then solve for the probability of each step (see Vandenberghe et al., 1994 for a review of these so-called histogram methods). This is illustrated in Figure 12b, where the spectrum was fit using two histogram distributions of quadrupole doublets with Lorentzian lineshape. A smoothing function was used to dampen oscillations in the probability distributions, and the starting and ending values were forced to zero (Wivel & Mørup, 1981). The centre shifts and quadrupole splittings for the Fe2+ and Fe3+ distributions are similar to those obtained for the Lorentzian model, while the relative area of Fe3+ absorption is slightly less (Table 3). This is due in part to the higher intensity at the tails of the Lorentzian lineshape, which tends to overestimate relative areas compared to a more Gaussian form. The probability distributions resulting from the histogram fit indeed resemble Gaussian lineshapes, which leads to a third approach in Mössbauer data fitting of glasses.

Based on the resemblance of hyperfine parameter probability distributions to Gaussians in a wide variety of different amorphous systems, an approach has been developed to fit Mössbauer spectra of glasses and amorphous materials using sums of Gaussians (e.g. Rancourt & Ping, 1991). The method has been refined to include multidimensional correlations between hyperfine parameter distributions, the so-called extended Voigt-based fitting (xVBF) analysis (Lagarec & Rancourt, 1997). The approach has been applied to Mössbauer spectra of silicate glasses, e.g. Alberto et al. (1996); Rossano et al. (1999). Figure 12c illustrates such a fit to the basaltic glass spectrum. The hyperfine parameters derived from the fit are similar to those for the histogram distribution, but they additionally reveal the correlation between centre shift and quadrupole splitting for the Fe2+ and Fe3+ distributions (Fig. 12c).

Table 3.

Hyperfine parameters for different fits to basaltic glass spectrum.

Thin-limit1Thick2

LorentzianHistogramxVBF3xVBF3

Fe2+
Mean centre shift (rel to α-Fe) [mm/s]1.02(2)1.03(4)1.03(1)1.03(1)
Mean quadrupole splitting [mm/s]1.93(7)1.90(1)1.91(1)1.91(3)
Relative area0.72(3)0.74(3)0.74(2)0.72(2)
Fe3+
Mean centre shift (rel to α-Fe) [mm/s]0.39(6)0.34(2)0.36(3)0.38(4)
Mean quadrupole splitting [mm/s]1.04(10)1.17(2)1.16(4)1.16(6)
Relative area0.28(3)0.26(3)0.26(2)0.28(2)
Thin-limit1Thick2

LorentzianHistogramxVBF3xVBF3

Fe2+
Mean centre shift (rel to α-Fe) [mm/s]1.02(2)1.03(4)1.03(1)1.03(1)
Mean quadrupole splitting [mm/s]1.93(7)1.90(1)1.91(1)1.91(3)
Relative area0.72(3)0.74(3)0.74(2)0.72(2)
Fe3+
Mean centre shift (rel to α-Fe) [mm/s]0.39(6)0.34(2)0.36(3)0.38(4)
Mean quadrupole splitting [mm/s]1.04(10)1.17(2)1.16(4)1.16(6)
Relative area0.28(3)0.26(3)0.26(2)0.28(2)

1 spectra were corrected for thickness effects by extracting the thin-absorber limit spectrum (Rancourt, 1989, 1996)

2 not corrected for thickness effects

3 xVBF: extended Voigt-based fitting

Standard deviations are based on statistical analysis of the fitting model only, and do not represent the cumulative error of the measurement.

The centre shifts of Fe2+ and Fe3+ absorption are relatively well determined (Table 3), and comparison with empirical data suggests predominantly octahedral coordination for both cations (Table 2). As a final step to determining an accurate value for Fe3+/ΣFe in the basaltic glass, possible corrections to the relative areas must be considered. Thickness effects were already accounted for in using the spectrum extracted in the thin-absorber limit; however it is nevertheless instructive to examine their effect on the results. The xVBF model was applied to the uncorrected spectrum, and essentially identical hyperfine parameters were obtained, but with a larger relative area for Fe3+ (Table 3). This is consistent with the overestimation of Fe3+ expected for thicker absorbers, since the dimensionless effective thickness for the basaltic glass was 2 (ca. 5 mg Fe/cm2). There was no correction for recoil-free fractions since compositions are close to those used by Mysen et al. (1985b) and Dingwell (1991), where no systematic differences in Fe3+/ΣFe were noted between Mössbauer and wet chemistry results. In addition, the coordination based on the centre shift data for Fe2+ and Fe3+ is similar; hence the review by Nishida (1995) would suggest similar recoil-free fractions. A more accurate approach, however, would be to collect spectra at lower temperature, e.g. 77 K.

Microscopic absorbers

The typical diameter of absorbers (i.e. samples) studied using conventional transmission Mössbauer spectroscopy is on the order of one cm, which complements the similar diameter of conventional 57Co sources (the parent isotope for 57Fe) (see discussion above regarding source specifications). The source to absorber distance must be chosen to maximise count rate, while minimising geometric effects. The solid angle of radiation subtended by the absorber is given by 2π (1 – cos α), where α is defined as shown in Figure 13 (the maximum possible solid angle is 4π, which corresponds to radiation emitted in all directions). The count rate increases with increasing solid angle, which depends on both absorber diameter and source to absorber distance. The source to absorber distance cannot be reduced indiscriminately, however, because of geometric effects that cause energy shifts and spectral distortion.

Fig. 13.

Schematic diagram of source radiation geometry showing flat and curved absorbers (after Bara & Bogacz, 1980). Symbols: D – source to absorber distance; d – absorber diameter; a – half angle subtended by the absorber; θ – angle of the γ ray relative to the direction of source velocity.

Fig. 13.

Schematic diagram of source radiation geometry showing flat and curved absorbers (after Bara & Bogacz, 1980). Symbols: D – source to absorber distance; d – absorber diameter; a – half angle subtended by the absorber; θ – angle of the γ ray relative to the direction of source velocity.

Geometric effects arise because a photon travelling at angle θ to the direction of source velocity experiences a Doppler energy shift of ΔE = (v/c) E0 cos θ, where E0 is the unperturbed photon energy, v is the source velocity and c is the speed of light. The cos θ term changes the energy distribution of emitted gamma rays, which ultimately affects the shapes, widths and positions of the resulting Mössbauer absorption lines. The effect is more pronounced in thick, flat absorbers, where the gamma ray passes through differing absorber path lengths (i.e. thicknesses) depending on the angle θ (note that this additional effect is negligible for curved absorbers, since absorber thickness is independent of θ – see Fig. 13). These effects have been calculated in detail by Bara & Bogacz (1980), which enable values of α to be selected based on experimental parameters and the desired resolution. For example, a value of α < 10° produces line shifts of less than 0.04 mm/s with negligible line broadening and lineshape distortion at source velocities of 5 mm/s (the geometric effect increases with increasing source velocity). This calculation assumes a point source, but since conventional sources are sheet emitters, this translates to roughly α < 5°. For comparison, a value of α = 12° for a flat source at source velocities of 5 mm/s would produce a line shift of ∼ 0.2 mm/s, line broadening of ∼ 0.4 mm/s and marked spectral distortion (Bara & Bogacz, 1980).

The minimum source to absorber distance can be calculated as a function of absorber diameter for the constraint that α < 5° (Table 4). For absorber diameters of one cm, the source to absorber distance should be no less than 6 cm, which is typically the case anyway for cryostats and furnaces. However the absorber diameter can be reduced from one cm to a certain degree without a significant compromise in signal quality by decreasing the source to absorber distance. To avoid geometrical effects, it is crucial to use a masking shield so that all gamma rays not passing through the absorber are absorbed by the shield and never reach the detector. The main limitation in using smaller diameter absorbers arises from the smaller number of gamma rays that pass through the absorber, so the tolerable limit for such an exercise depends on the activity of the source, the nature of the absorber and the efficiency of the counting chain. One further consideration is that the source vibration changes the solid angle, resulting in a count rate that is roughly a parabolic function of the source velocity. The magnitude of this effect increases with increasing source vibration amplitude and decreasing source to absorber distance. The effect can be profound for the smaller source to absorber distances listed in Table 4, particularly for absorbers with low Mössbauer absorption. The parabolic baseline can be reduced by increasing the frequency of source vibration (hence decreasing the amplitude for a given source velocity), but the most effective method to reduce the effect (although not eliminate it completely) is to collect Mössbauer spectra on both sweeps of the source movement (i.e. to collect data in triangular mode, not flyback mode), and simply fold the two resulting mirror-image spectra to obtain the final spectrum.

Table 4.

Minimum source-absorber distances for conventional sources.

absorber diameter [mm]source-absorber distance13 [mm]

1269
1057
846
634
423
211
16
0.53
0.10.6
absorber diameter [mm]source-absorber distance13 [mm]

1269
1057
846
634
423
211
16
0.53
0.10.6

1 α < 5° (Bara & Bogacz, 1980)

A more effective method to record Mössbauer spectra of absorbers with small diameter is to replace the conventional Mössbauer source (typically 3.7 GBq spread over an area of roughly 1 cm2, giving a specific activity of 3.7 GBq/cm2) with a point source. Typical point sources that are commercially produced have activities of ca. 370 MBq spread over an area of 0.25 mm2, giving a specific activity of ca. 592 GBq/cm2. The source to absorber distance can be reduced appropriately to achieve a similar count rate, and gamma rays are collimated to the selected absorber diameter using a shield with high atomic number (e.g. Ta). Since the signal quality depends on absorber density (measured in mg Fe/cm2) and not the total amount of iron in the absorber, the reduction in size has little effect on the effective thickness of the absorber. When electronic absorption due to heavier elements (e.g. heavier than K) is low and the point source is relatively new (< 1 year old), high quality Mössbauer spectra (comparable to conventional measurements) can be recorded on absorbers with diameters as small as 100 μm (McCammon, 1994).

The point source is produced by significantly increasing the density of 57Co in the source matrix. The penalty, however, is a rapid increase in source thickness, which limits the useable lifetime of the source. The dimensionless effective source thickness can be calculated from  

formula
where σ0 is the resonance cross section of the transition (= 2.56 • 10−18 cm2 for the 14.4 keV 57Fe transition), fs is the recoil-free fraction of the source, and n is the number of 57Fe atoms per cm2. Figure 14 illustrates a comparison of the effective source thickness evolution with time for a conventional source and a point source. A higher source thickness translates to a greater source linewidth and smaller recoil-free fraction, where most would consider these effects to render the source unusable after it reached an effective thickness of ca. 2. A point source should therefore be renewed roughly every year, compared to a conventional source whose usable lifetime is limited only by its declining count rate.

Fig. 14.

Variation of dimensionless effective source thickness with age for a conventional 1.85 GBq source with 4 GBq/cm2 and a 0.74 GBq point source with 74 GBq/cm2 (after McCammon, 1994).

Fig. 14.

Variation of dimensionless effective source thickness with age for a conventional 1.85 GBq source with 4 GBq/cm2 and a 0.74 GBq point source with 74 GBq/cm2 (after McCammon, 1994).

There are other possibilities to achieve high spatial resolution with Mössbauer spectroscopy. An imaging technique has been described in which a velocity gradient is imposed on the absorber by rotating it relative to the source, and then a spatial map of Mössbauer absorption is constructed for the absorber (Norton, 1987; Atzmony et al., 1987). A different approach incorporates a position sensitive proportional counter, which enables the collection of 256 simultaneous Mössbauer spectra along an absorber of up to 50 mm length (Cashion et al., 1990; Smith et al., 1992). Further improvement of spatial resolution may be anticipated with developments in synchrotron studies of nuclear forward scattering (Gerdau & DeWaard, 1999), while other possibilities include development of a Mössbauer electron microscope which would focus conversion electrons using conventional electron optics (Rancourt & Klingelhöfer, 1994).

Mössbauer spectra collected with point sources are analysed in the same manner as spectra collected with conventional sources, but there are additional considerations that must be taken into account. As shown in Figure 14, the effective thickness of the source increases rapidly with time, so that the thin source approximation used by most Mössbauer fitting programs is no longer valid for old point sources (older than ca. one year old). This becomes important for the determination of accurate site distributions, so the best approach in this case (short of acquiring a newer point source) is to fit the spectra using the full transmission integral. Another consideration in analysing spectra collected with point sources is that absorbers with small diameter are likely to be single crystals. Deconvolution of overlapped single crystal spectra can be challenging, since the constraint of equal areas can no longer be used if the Mössbauer atom sites have non-cubic point group symmetry. A rigorous approach requires knowledge of the single crystal orientation and the direction of the electric field gradient (EFG) relative to the crystallographic axes, from which the theoretical area ratios can be determined (e.g. Pfannes & Gonser, 1973). The EFG orientation is known for only a small number of crystals, however. Spectral measurements at different orientations of the crystal with respect to the gamma rays can provide additional constraints, but these depend on the shape of the spectrum and the point group symmetry of the Mössbauer atom sites. Assumptions to increase the number of fitting constraints such as equal component area ratios for M1 and M2 Fe2+ doublets in clinopyroxene have been made based on single crystal measurements of hedenbergite, but have not been rigorously tested at the relevant compositions (McCammon et al., 2000).

Applications

The method to collect Mössbauer spectra on samples at ambient pressure using a point source has been termed the Mössbauer “milliprobe” (Hawthorne, 1992). Since the absorber can take a variety of forms (Fig. 15), a number of applications have been discovered for the technique since it was first described by McCammon et al. (1991). The following provides an overview of these applications involving a point source, with specific examples of their use.

Fig. 15.

Possible absorber configurations for Mössbauer spectroscopy. (a) Polycrystalline absorber for conventional transmission Mössbauer spectroscopy with ∼ 1 cm diameter beam size. (b) “Thick section” absorber with thickness determined by desired effective absorber thickness. The area outside the region to be studied is masked with a heavy metal foil (e.g. Ta). (c) Single crystal absorber where the crystal is mounted behind a hole drilled in a heavy metal foil. (d) Polycrystalline absorber prepared by placing grains inside a hole drilled in a heavy metal foil. In (b), (c) and (d) the beam size is determined by the diameter of the holes drilled in the heavy metal foil, and can be as small as ∼ 100 μm in diameter.

Fig. 15.

Possible absorber configurations for Mössbauer spectroscopy. (a) Polycrystalline absorber for conventional transmission Mössbauer spectroscopy with ∼ 1 cm diameter beam size. (b) “Thick section” absorber with thickness determined by desired effective absorber thickness. The area outside the region to be studied is masked with a heavy metal foil (e.g. Ta). (c) Single crystal absorber where the crystal is mounted behind a hole drilled in a heavy metal foil. (d) Polycrystalline absorber prepared by placing grains inside a hole drilled in a heavy metal foil. In (b), (c) and (d) the beam size is determined by the diameter of the holes drilled in the heavy metal foil, and can be as small as ∼ 100 μm in diameter.

Zoning profiles in minerals can provide information regarding chemical processes that occurred during formation of a mineral assemblage. Mössbauer spectroscopy provides an estimate of Fe2+ and Fe3+ relative abundance in individual phases, which can be used in conjunction with oxygen barometers to determine oxygen fugacity during mineral formation. McCammon et al. (2001) studied garnet peridotites from the Wesselton kimberlite (South Africa) that were zoned in both major and trace elements. Mössbauer spectra were collected of thick sections (Fig. 15b) where masking foil covered different parts of garnet single crystals: core, rim, secondary rim. The resulting Fe3+/ΣFe values were combined with major element compositions of garnet, olivine and orthopyroxene as well as activity-composition models to determine oxygen fugacities for the different regions based on the olivine-orthopyroxene-garnet oxybarometer. Results showed a progressive increase in oxygen fugacity during the course of metasomatism, where the final metasomatic event (perhaps related to the kimberlite eruption itself) was sufficiently oxidising to destabilise diamond.

Samples from high-pressure experiments allow a controlled study of materials at conditions relevant to the Earth's interior. While it is often possible to synthesise samples with enriched 57Fe and hence obtain sufficient material for conventional Mössbauer measurements, particular sample forms such as single crystals require measurements using a point source. For example Bolfan-Casanova et al. (2002) studied the solubility of hydrogen in ferropericlase as a function of pressure. It was necessary to use single crystals for the infrared measurements that were used to determine H concentration, and Mössbauer spectroscopy was used to determine Fe3+/ΣFe (absorber configuration shown in Fig. 15c). The OH solubility trends combined with Fe3+ concentrations measured in both hydrous and anhydrous experiments suggest the incorporation of H as isolated hydroxyl groups via reduction of Fe3+, and allowed an estimate of the bulk hydrogen content of the lower mantle.

Mineral inclusions in diamond can be measured using Mössbauer spectroscopy, depending on their size and iron concentration. When diamonds crystallise in the Earth's mantle, they can enclose minerals from their surroundings and protect the minerals from alteration during their rapid ascent to the surface. McCammon et al. (1998) studied garnet and clinopyroxene inclusions in diamonds from George Creek (USA) (absorber configuration shown in Fig. 15c). These diamonds comprised two growth generations, one free of CO2 (believed to be the oldest) and one CO2-bearing. Mössbauer spectra showed that both garnet and clinopyroxene contained only small concentrations of Fe3+ in the CO2-free generation, which is consistent with the reducing conditions expected during diamond formation. Another study by McCammon et al. (1997) examined the redox state of iron in ferropericlase and former silicate perovskite inclusions from diamonds believed to have originated in the lower mantle (absorber configuration shown in Fig. 15c). The low Fe3+ concentration in ferropericlase and high Fe3+ concentration in former silicate perovskite are consistent with high-pressure experiments, and contribute to the growing evidence that the relative concentration of Fe3+ is high in the lower mantle, even though conditions might be quite reducing.

Single crystals can be studied using Mössbauer spectroscopy down to sizes of only a few hundred microns in diameter. Mössbauer measurements of oriented single crystals allow the direction of the electric field gradient relative to the crystallographic axes to be calculated, which can provide important constraints in deconvoluting overlapped single crystal Mössbauer spectra (see above). Tennant et al. (2000) studied single crystals of the clinopyroxene hedenbergite in order to determine the electric field gradient (EFG) and mean squared displacement (MSD) tensors (absorber configuration shown in Fig. 15c). They found that the principal values and directions of both the EFG and MSD are well defined, and as required by the site symmetry, one principal direction of each of the tensors lies along the 2-fold b axis of the crystal. In addition, Vzz (the principal axis of the EFG) lies essentially parallel to the c axis, which means that it can be easily located in needle-shaped crystals of hedenbergite with similar composition.

Thin sections of mineral assemblages are easily studied using techniques such as optical microscopy and electron microprobe analysis, where microstructures and spatial relationships between mineral grains provide constraints on processes which occurred during the history of the assemblage. Conventional transmission Mössbauer measurements on thin sections are not possible because (1) the glass absorbs close to 100% of the 14.4 keV gamma rays; and (2) typical thin section thicknesses do not provide sufficient 57Fe atoms for a reasonable signal. These problems can be overcome, however, using a microdrill to remove mineral grains as powder (hence avoiding the difficulty of analysing single crystals), mounting the powder within a small diameter hole in Ta foil, and using a point source to collect Mössbauer spectra (absorber configuration shown in Fig. 15d). Proyer et al. (2004) examined the effect of Fe3+ on garnet-clinopyroxene thermometry in a suite of eclogite samples from Dabie Shan (China). By measuring Fe3+ directly on the minerals grains from which the geothermometry determinations were made, errors due to compositional variation within the eclogite assemblage could be eliminated.

Crystal-melt assemblages can form at subliquidus conditions during magmatic processes. The oxygen fugacity exerts a major control on the redox state of iron (Fe3+/Fe2+) in the liquid, which in turn influences melt rheology and density, and determines in part the crystallisation sequence and composition of the precipitating minerals. Oxygen fugacity therefore plays a dominant role in magmatic crystallisation-differentiation processes and its knowledge is important to modelling and retrieving parameters such as liquid lines of descent. Calibration of Fe3+/Fe2+ in quenched melts equilibrated at different temperatures and oxygen fugacities has led to methods for estimating oxygen fugacity conditions in magmas (e.g. Kress & Carmichael, 1991); however, these methods are calibrated only for high temperatures at predominantly oxidising conditions. Calibration at temperatures more relevant to natural magmas, i.e. subliquidus conditions, requires the measurement of Fe3+/ΣFe in glass with high spatial resolution to avoid perturbation due to crystals. Partzsch et al. (in print) determined Fe3+/ΣFe values using point source Mössbauer spectroscopy in quenched ferrobasaltic and transitional alkali-basaltic compositions that were equilibrated at controlled oxygen fugacities and super- to subliquidus temperatures (absorber configuration shown in Fig. 15b). Results were compared with existing calibrations to quantify the effect of composition and temperature.

Rare minerals can be studied using Mössbauer spectroscopy even if only a few grains are available. For example gladiusite [(Fe2+,Mg)4forumla(PO4)(OH)11(H2O)], a recently discovered mineral from the Kola Peninsula (Russia), occurs as fine needles in a low-temperature hydrothermal assemblage. Since the needles are intergrown with other minerals and are easily oxidised by grinding, it was not possible to collect sufficient quantities of pure and unaltered gladiusite for conventional Mössbauer spectroscopy. Fortunately only a few of the roughly 10 μm thick needles were required for measurements using a point source, which allowed a robust determination of Fe3+/ΣFe (absorber configuration shown in Fig. 15d). Sokolova et al. (2001) used this data in conjunction with single crystal refinements performed on crystals from the same sample to constrain site distributions and the topology of the crystal structure.

Concluding remarks

This chapter has presented applications of Mössbauer spectroscopy in mineralogy, with two worked examples. They were chosen to illustrate one approach to common problems encountered in Mössbauer spectroscopy, but by no means do they represent the breadth of possible applications. McCammon (2003) recently reviewed state-of-the-art Mössbauer spectroscopy in the geosciences, and concluded that there are not only numerous existing applications, but there are also many anticipated innovations on the horizon that promise additional applications of Mössbauer spectroscopy in the future. However, while Mössbauer spectroscopy has taken a place in some laboratories alongside techniques such as the electron microprobe and X-ray diffraction in the routine analysis of iron-bearing samples, its use is by no means universal. This is partly due to the challenge of data analysis, despite the widespread availability of computer-based fitting methods. It is not trivial in many cases to relate the extracted hyperfine parameters to the underlying structure and properties of the material without a significant amount of experience, and many pitfalls have been documented, e.g. by Rancourt (1998). Short courses such as the one this chapter was prepared for help to address this problem, but new possibilities may be on the horizon. There are many relatively routine applications of Mössbauer spectroscopy that could benefit from an integrated approach to spectral analysis, and the current development of automated data analysis through the use of genetic algorithms, fuzzy logic and artificial neural networks (De Souza et al., 2002) may provide the breakthrough that is needed to broaden the use of Mössbauer spectroscopy in the geosciences.

References

Alberto
,
H.V.
Pinoto da Cunha
,
J.L.
Mysen
,
B.O.
Gil
,
J.M.
Ayres de Campos
,
N.
(
1996
):
Analysis of Mössbauer spectra of silicate glasses using a two-dimensional Gaussian distribution of hyperfine parameters
.
J. Non-Cryst. Solids
 ,
194
:
48
57
.
Amthauer
,
G.
Annersten
,
H.
Hafner
,
S.S.
(
1976
):
The Mössbauer spectrum of 57Fe in silicate garnets
.
Z. Kristallogr.
 ,
143
:
14
55
.
Amthauer
,
G.
Grodzicky
,
M.
Lottermoser
,
W.
Redhammer
,
G.
(
2004
):
Mössbauer spectroscopy: Basic principles
. In
Beran
,
A.
Libowitzky
,
E.
(eds.):
Spectroscopic methods in mineralogy /EMU Notes Mineral.
 ,
6/
.
Budapest
:
Eötvös Univ. Press
,
345
367
.
Angel
,
R.J.
Finger
,
L.W.
Hazen
,
R.M.
Kanzaki
,
M.
Weidner
,
D.J.
Liebermann
,
R.C.
Veblen
,
D.R.
(
1989
):
Structure and twinning of single-crystal MgSiO3 garnet synthesized at 17 GPa and 1800 °C
.
Am. Mineral.
 ,
74
:
509
512
.
Atzmony
,
U.
Norton
,
S.J.
Swartzendruber
,
L.J.
Bennett
,
L.H.
(
1987
):
Mössbauer imaging: experimental result
.
Nature
 ,
330
:
153
154
.
Bancroft
,
G.M.
(
1973
):
Mössbauer spectroscopy. An introduction for inorganic chemists and geochemists.
 
New York (N.Y.)
:
McGraw-Hill
.
Bancroft
,
G.M.
Maddock
,
A.G.
Burns
,
R.G.
Strens
,
R.G.J.
(
1966
):
Cation distribution in anthophyllite from Mössbauer and infra-red spectroscopy
.
Nature
 ,
212
:
913
915
.
Bancroft
,
G.M.
Maddock
,
A.G.
Burns
,
R.G.
(
1967
):
Applications of the Mössbauer effect to silicate mineralogy - I. Iron silicates of known crystal structure
.
Geochim. Cosmochim. Acta
 ,
31
:
2219
2246
.
Bancroft
,
G.M.
Burns
,
R.G.
Stone
,
A.J.
(
1968
):
Applications of the Mössbauer effect to silicate mineralogy - II. Iron silicates of unknown and complex crystal structures
.
Geochim. Cosmochim. Acta
 ,
32
:
547
559
.
Bara
,
J.J.
Bogacz
,
B.F.
(
1980
):
Geometric effects in Mössbauer transmission experiments
.
Mössbauer Eff. Ref. Data J.
 ,
3
:
154
163
.
Bevington
,
P.R.
(
1969
):
Data reduction and error analysis for the physical sciences
 .
New York (N.Y.)
:
McGraw-Hill
.
Bolfan-Casanova
,
N.
Mackwell
,
S.J.
Keppler
,
H.
McCammon
,
C.
Rubie
,
D.C.
(
2002
):
Pressure dependence of H solubility in magnesiowüstite up to 25 GPa: Implications for the storage of water in the Earth's lower mantle
.
Geophys. Res. Lett.
 ,
29
:
Art. No. 1449 (doi:10.1029/2001GL014457)
.
Burns
,
R.G.
Solberg
,
T.C.
(
1990
):
57Fe-bearing oxide, silicate, and aluminosilicate minerals
. In
Coyne
,
L.M.
McKeever
,
S.W.S.
Blake
,
D.F.
(eds.):
Spectroscopic characterization of minerals and their surfaces /ACS Symp. Ser.
 ,
415
/.
Washington (D.C.)
:
Am. Chem. Soc.
,
262
283
.
Campbell
,
S.J.
Aubertin
,
F.
(
1989
):
Evaluation of distributed hyperfine parameters
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to inorganic chemistry. Vol. 3.
 
New York (N.Y.)
:
Plenum Press
,
183
242
.
Cashion
,
J.D.
Weiser
,
P.S.
McGrath
,
A.C.
Pollard
,
R.J.
Smith
,
T.F.
(
1990
):
Imaging Mössbauer spectroscopy - A new technique for materials analysis
.
Hyperfine Interact.
 ,
58
:
2507
2512
.
De Grave
,
E.
Van Alboom
A.
(
1991
):
Evaluation of ferrous and ferric Mössbauer fractions
.
Phys. Chem. Miner.
 ,
18
:
337
342
.
De Souza
,
P.
Garg
,
V.
Klingelhöfer
,
G.
Gellert
,
R.
Gütlich
,
P.
(
2002
):
Portable and automatic Mössbauer analysis
.
Hyperfine Interact.
 ,
139
:
705
714
.
Dingwell
,
D.B.
(
1991
):
Redox viscometry of some Fe-bearing melts
.
Am. Mineral.
 ,
76
:
1560
1562
.
Dingwell
,
D.B.
Virgo
,
D.
(
1987
):
The effect of oxidation state on the viscosity of melts in the system Na2O-FeO-Fe2O3-SiO2
.
Geochim. Cosmochim. Acta
 ,
51
:
195
205
.
Dollase
,
W.A.
(
1975
):
Statistical limitations of Mössbauer spectral fitting
.
Am. Mineral.
 ,
60
:
257
264
.
Dyar
,
M.D.
(
1985
):
A review of Mössbauer data on inorganic glasses: the effects of composition on iron valency and coordination
.
Am. Mineral.
 ,
70
:
304
316
.
Gancedo
,
J.R.
Davalos
,
J.Z.
Gracia
,
M.
Marco-Sanz
,
J.F.
(
1997
):
The use of Mössbauer spectroscopy in surface studies. A methodological survey
.
Hyperfine Interact.
 ,
110
:
41
50
.
Gerdau
,
E.
DeWaard
,
H.
(eds.) (
1999
):
Nuclear resonant scattering of synchrotron radiation /Hyperfine Interact.
 ,
123–124/
.
Dordrecht
:
Kluwer Academic Publishers
.
Greenwood
,
N.N.
Gibb
,
T.D.
(
1971
):
Mössbauer spectroscopy.
 
London
:
Chapman & Hall
.
Gütlich
,
P.
Link
,
R.
Trautwein
,
A.
(
1978
):
Mössbauer spectroscopy and transition metal chemistry.
 
Berlin
:
Springer-Verlag
.
Hawthorne
,
F.C.
(
1988
):
Mössbauer spectroscopy
. In
Hawthorne
,
F.C.
(ed.):
Spectroscopic methods in mineralogy and geology /Rev. Mineral.
 ,
18/
.
Washington (D.C.)
:
Mineral. Soc. Am.
,
255
340
.
Hawthorne
,
F.C.
(
1992
):
Mineralogy. Geotimes
 ,
37
(
2
):
39
.
Hawthorne
,
F.C.
Waychunas
,
G.A.
(
1988
):
Spectrum-fitting methods
. In
Hawthorne
,
F.C.
(ed.):
Spectroscopic methods in mineralogy and geology /Rev. Mineral.
 ,
18
/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
63
98
.
Holland
,
D.
Mekki
,
A.
Gee
,
I.A.
McConville
,
C.F.
Johnson
,
J.A.
Johnson
,
C.E.
Appleyard
,
P.
Thomas
,
M.
(
1999
):
The structure of sodium iron silicate glass - a multi-technique approach
.
J. Non-Cryst. Solids
 ,
253
:
192
202
.
Hoy
,
G.R.
(
1984
):
Relaxation phenomena for chemists
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to inorganic chemistry. Vol. 1.
 
New York (N.Y.)
:
Plenum Press
,
195
226
.
Ingalls
,
R.
(
1964
):
Electric-field gradient tensor in ferrous compounds
.
Phys. Rev.
 ,
133
:
A787
A795
.
Kress
,
V.C.
Carmichael
,
I.S.E.
(
1991
):
The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states
.
Contrib. Mineral. Petrol.
 ,
108
:
82
92
.
Lagarec
,
K.
Rancourt
,
D.G.
(
1997
):
Extended Voigt-based analytic lineshape method for determining N-dimensional correlated hyperfine parameter distributions in Mössbauer spectroscopy
.
Nucl. Instrum. Methods Phys. Res. B
 ,
129
:
266
280
.
Lauterbach
,
S.
McCammon
,
C.A.
van Aken
,
P.
Langenhorst
,
F.
Seifert
,
F.
(
2000
):
Mössbauer and ELNES spectroscopy of (Mg,Fe)(Si,Al)O3 perovskite: A highly oxidised component of the lower mantle
.
Contrib. Mineral. Petrol.
 ,
138
:
17
26
.
Long
,
G.L.
Cranshaw
,
T.E.
Longworth
,
G.
(
1983
):
The ideal Mössbauer effect absorber thickness
.
Möss. Effect Ref. Data J.
 ,
6
:
42
49
.
Longworth
,
G.
(
1987
):
Mössbauer effect studies of metallic glasses
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to inorganic chemistry. Vol. 2.
 
New York (N.Y.)
:
Plenum Press
,
289
342
.
Maddock
,
A.G.
(
1985
):
Mössbauer spectroscopy in mineral chemistry
. In
Berry
,
F.J.
Vaughan
,
D.J.
(eds.):
Chemical bonding and spectroscopy in mineral chemistry.
 
London
:
Chapman & Hall
,
141
208
.
McCammon
,
C.A.
(
1994
):
A Mössbauer milliprobe: Practical considerations
.
Hyperfine Interact.
 ,
92
:
1235
1239
.
McCammon
,
C.A.
(
2000
):
Insights into phase transformations from Mössbauer spectroscopy
. In
Redfern
,
S.
Carpenter
,
M.
(eds.):
Transformation processes in minerals /Rev. Mineral. Geochem.
 ,
39/
.
Washington, DC
:
Mineralogical Society of America
,
241
264
.
McCammon
,
C.A.
(
2003
):
Mössbauer spectroscopy in the geosciences: Highlights and perspectives
.
Hyperfine Interact.
 ,
144/145
:
289
296
.
McCammon
,
C.A.
Ross
,
N.L.
(
2003
):
Crystal chemistry of ferric iron in (Mg,Fe)(Si,Al)O3 majorite with implications for the transition zone
.
Phys. Chem. Miner.
 ,
30
:
206
216
.
McCammon
,
C.A.
Chaskar
,
V.
Richards
,
G.G.
(
1991
):
A technique for spatially resolved Mössbauer spectroscopy applied to quenched metallurgical slags
.
Meas. Sci. Technol.
 ,
2
:
657
662
.
McCammon
,
C.A.
Hutchison
,
M.
Harris
,
J.
(
1997
):
Ferric iron content of mineral inclusions in diamonds from São Luiz: A view into the lower mantle
.
Science
 ,
278
:
434
436
.
McCammon
,
C.
Chinn
,
I.
Gurney
,
J.
McCallum
,
M.
(
1998
):
Ferric iron content of mineral inclusions in diamonds from George Creek, Colorado determined using Mössbauer spectroscopy
.
Contrib. Mineral. Petrol.
 ,
133
:
30
37
.
McCammon
,
C.A.
Tennant
,
W.C.
Miletich
,
R.M.
(
2000
):
A new method for single crystal measurements: Application to studies of mineral inclusions in diamonds
.
Hyperfine Interact.
 ,
126
:
241
245
.
McCammon
,
C.A.
Griffin
,
W.L.
Shee
,
S.H.
O'Neill
,
H.S.C.
(
2001
):
Oxidation during metasomatism in ultramafic xenoliths from the Wesselton kimberlite, South Africa: Implications for the survival of diamond
.
Contrib. Mineral. Petrol.
 ,
141
:
287
296
.
Mysen
,
B.O.
Virgo
,
D.
Neumann
,
E.-R.
Seifert
,
F.A.
(
1985a
):
Redox equilibria and the structural states of ferric and ferrous iron in melts in the system CaO-MgO-Al2O3-SiO2-FeO: relationships between redox equilibria, melt structure and liquidus phase equilibria
.
Am. Mineral.
 ,
70
:
317
331
.
Mysen
,
B.O.
Carmichael
,
I.S.E.
Virgo
,
D.
(
1985b
):
Acomparison of iron redox ratios in silicate glasses determined by wet-chemical and 57Fe Mössbauer resonant absorption methods
.
Contrib. Mineral. Petrol.
 ,
90
:
101
106
.
Nishida
,
T.
(
1995
):
Mössbauer effect in inorganic glasses
.
Hyperfine Interact.
 ,
95
:
23
39
.
Nishida
,
T.
Shindo
,
H.
Takashima
,
Y.
(
1991
):
Discovery of a linear relationship between the glass transition temperature of oxide glasses and the quadrupole splitting of the Fe3+ substituted for the individual network-forming cations (NWF)
.
Hyperfine Interact.
 ,
69
:
603
606
.
Nomura
,
K.
(
1999
):
Conversion electron Mössbauer spectrometry
. In
Miglierini
,
M.
Petredis
,
D.
(eds.):
Mössbauer spectroscopy in materials science
 .
Dordrecht
:
Kluwer
,
63
78
.
Norton
,
S.J.
(
1987
):
Mössbauer imaging
.
Nature
 ,
330
:
151
153
.
Partzsch
,
G.M.
Lattard
,
D.
McCammon
,
C.A.
:
Mössbauer spectroscopic determination of Fe3+/Fe2+ in synthetic basaltic glass: A test of empirical fO2 equations under superliquidus and subliquidus conditions
.
Contrib. Mineral. Petrol.
 ,
in print
.
Pfannes
,
H.D.
Gonser
,
U.
(
1973
):
Goldanskii-Karyagin effect versus preferred orientations (texture)
.
Appl. Phys.
 ,
1
:
93
102
.
Ping
,
J.Y.
Rancourt
,
D.G.
(
1992
):
Thickness effects with intrinsically broad absorption lines
.
Hyperfine Interact.
 ,
71
:
1433
1436
.
Proyer
,
A.
Dachs
,
E.
McCammon
,
C.A.
:
Pitfalls in geothermometry of eclogites: Fe3+ and changes in the mineral chemistry of omphacite at ultrahigh pressures
.
Contrib. Mineral. Petrol.
 ,
in print
.
Rancourt
,
D.G.
(
1989
):
Accurate site populations from Mössbauer spectroscopy
.
Nucl. Instrum. Methods Phys. Res.
 ,
B44
:
199
210
.
Rancourt
,
D.G.
(
1994a
):
Mössbauer spectroscopy of minerals I. Inadequacy of Lorentzian-line doublets in fitting spectra arising from quadrupole splitting distributions
.
Phys. Chem. Miner.
 ,
21
:
244
249
.
Rancourt
,
D.G.
(
1994b
):
Mössbauer spectroscopy of minerals II. Problem of resolving cis and trans octahedral Fe2+ sites
.
Phys. Chem. Miner.
 ,
21
:
250
257
.
Rancourt
,
D.G.
(
1996
):
Analytical methods for Mössbauer spectral analysis of complex materials
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to magnetism and materials science, Vol. 2.
 
New York & London
:
Plenum Press
,
105
124
.
Rancourt
,
D.G.
(
1998
):
Mössbauer spectroscopy in clay science
.
Hyperfine Interact.
 ,
117
:
3
38
.
Rancourt
,
D.G.
Klingelhöfer
,
G.
(
1994
):
Possibility of a Mössbauer resonant-electron microscope
. In
Fourth Seeheim Workshop on Mössbauer Spectroscopy (Seeheim, Germany), Abstr.
, P
129
.
Rancourt
,
D.G.
Ping
,
J.Y.
(
1991
):
Voigt-based methods for arbitrary-shape static hyperfine parameter distributions in Mössbauer spectroscopy
.
Nucl. Instrum. Methods Phys. Res.
 ,
B58
:
85
97
.
Rancourt
,
D.G.
Christie
,
I.A.D.
Royer
,
M.
Kodama
,
H.
Robert
,
J.-L.
Lalonde
,
A.E.
Murad
,
E.
(
1994
):
Determination of accurate [4]Fe3+, [6]Fe3+, and [6]Fe2+ site populations in synthetic annite by Mössbauer spectroscopy
.
Am. Mineral.
 ,
79
:
51
62
.
Robinson
,
K.
Gibbs
,
G.V.
Ribbe
,
P.H.
(
1971
):
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
.
Science
 ,
172
:
567
570
.
Rossano
,
S.
Balan
,
E.
Morin
,
G.
Bauer
,
J.-P.
Calas
,
G.
Brouder
,
C.
(
1999
):
57Fe Mössbauer spectroscopy of tektites
.
Phys. Chem. Miner.
 ,
26
:
530
538
.
Rossano
,
S.
Ramos
,
A.Y.
Delaye
,
J.-M.
(
2000
):
Environment of ferrous iron in CaFeSi2O6 glass; contributions of EXAFS and molecular dynamics
.
J. Non-Cryst. Solids
 ,
273
:
48
52
.
Seifert
,
F.
(
1990
):
Phase transformation in minerals studied by 57Fe Mössbauer spectroscopy
. In
Mottana
,
A.
Burragato
,
F.
(eds.):
Absorption spectroscopy in mineralogy.
 
Amsterdam
:
Elsevier
,
145
170
.
Skogby
,
H.
Annersten
,
H.
Domeneghetti
,
M.C.
Molin
,
G.M.
Tazzoli
,
V.
(
1992
):
Iron distribution in orthopyroxene: A comparison of Mössbauer spectroscopy and X-ray refinement results
.
Eur. J. Mineral.
 ,
4
:
441
452
Smith
,
P.R.
Cashion
,
J.D.
Brown
,
L.J.
(
1992
):
Imaging Mössbauer spectroscopic measurements of an inhomogeneous sample
.
Hyperfine Interact.
 ,
71
:
1503
1506
.
Sokolova
,
E.
Hawthorne
,
F.C.
McCammon
,
C.A.
Liferovich
,
R.P.
(
2001
):
The crystal structure of gladiusite
, (Fe2+,Mg)4forumla(PO4)(OH)u(H2O).
Can. Mineral.
 ,
39
:
1121
1130
.
Tennant
,
W.C.
McCammon
,
C.A.
Miletich
,
R.
(
2000
):
Electric-field gradient and mean-squared-displacement tensors in hedenbergite from single crystal Mössbauer milliprobe measurements
.
Phys. Chem. Miner.
 ,
27
:
156
163
.
Vandenberghe
,
R.E.
De Grave
,
E.
de Bakker
,
P.M.A.
(
1994
):
On the methodology of the analysis of Mössbauer spectra
.
Hyperfine Interact.
 ,
83
:
29
49
.
Williams
,
K.F.E.
Johnson
,
C.E.
Thomas
,
M.F.
(
1998
):
Mössbauer spectroscopy measurement of iron oxidation states in float composition silica glasses
.
J. Non-Cryst. Solids
 ,
226
:
19
23
.
Wivel
,
C.
Mørup
,
S.
(
1981
):
Improved computational procedure for evaluation of overlapping hyperfine parameter distributions in Mossbauer spectra
.
J. Phys. E: Sci. Instrum.
 ,
14
:
605
610
.
Woodland
,
A.B.
Ross II
,
C.R.
(
1994
):
A crystallographic and Mössbauer spectroscopy study of
forumla, (almandine-“skiagite”) and forumla (andradite-“skiagite”) garnet solid solutions.
Phys. Chem. Miner.
 ,
21
:
117
132
.

The manuscript was significantly improved through constructive reviews by A. Woodland and E. Libowitzky.

Figures & Tables

Fig. 1.

Schematic view of a Mössbauer spectrometer. The source is moved relative to the absorber with different velocities that shift the energy of the emitted gamma rays according to the Doppler effect. Gamma rays either pass through the absorber unaffected and then reach the detector, or they are absorbed and then re-emitted in a direction different to the detector (based on a drawing from Gütlich et al., 1978).

Fig. 1.

Schematic view of a Mössbauer spectrometer. The source is moved relative to the absorber with different velocities that shift the energy of the emitted gamma rays according to the Doppler effect. Gamma rays either pass through the absorber unaffected and then reach the detector, or they are absorbed and then re-emitted in a direction different to the detector (based on a drawing from Gütlich et al., 1978).

Fig. 2.

Room temperature Mössbauer spectra of (a) cordierite, and (b) tourmaline. The spectrum of cordierite contains a single quadrupole doublet corresponding to octahedral Fe2+, while the spectrum of tourmaline has been deconvoluted into four quadrupole doublets, two corresponding to Fe2+ (horizontal shading), one corresponding to Fe3+ (black shading) and one corresponding to Fe2+–Fe3+ charge transfer (vertical shading).

Fig. 2.

Room temperature Mössbauer spectra of (a) cordierite, and (b) tourmaline. The spectrum of cordierite contains a single quadrupole doublet corresponding to octahedral Fe2+, while the spectrum of tourmaline has been deconvoluted into four quadrupole doublets, two corresponding to Fe2+ (horizontal shading), one corresponding to Fe3+ (black shading) and one corresponding to Fe2+–Fe3+ charge transfer (vertical shading).

Fig. 3.

Approximate ranges for room temperature centre shifts (relative to α-Fe) observed in iron compounds according to (a) iron valence and spin state, and (b) coordination of high-spin Fe2+ and Fe3+ minerals. Data in (a) are compiled from Greenwood & Gibb (1971), Maddock (1985) and Hawthorne (1988), while data in (b) are taken from Seifert (1990), with additional data from Burns & Solberg (1990) for pentacoordinated Fe3+.

Fig. 3.

Approximate ranges for room temperature centre shifts (relative to α-Fe) observed in iron compounds according to (a) iron valence and spin state, and (b) coordination of high-spin Fe2+ and Fe3+ minerals. Data in (a) are compiled from Greenwood & Gibb (1971), Maddock (1985) and Hawthorne (1988), while data in (b) are taken from Seifert (1990), with additional data from Burns & Solberg (1990) for pentacoordinated Fe3+.

Fig. 4.

Schematic variation of the valence and lattice term contributions to the quadrupole splitting with increasing distortion of the octahedral site. The quadrupole splitting, ΔEq, is the sum of the valence and lattice terms (adapted from Ingalls, 1964).

Fig. 4.

Schematic variation of the valence and lattice term contributions to the quadrupole splitting with increasing distortion of the octahedral site. The quadrupole splitting, ΔEq, is the sum of the valence and lattice terms (adapted from Ingalls, 1964).

Fig. 5.

Polyhedral model of the MgSiO3 majorite garnet structure viewed down (a) [001] and (b) [010] based on the structure refinement of Angel et al. (1989). Inequivalent positions are labelled and shaded as follows: tetrahedra (light grey), octahedra (dark grey) and dodecahedra (black).

Fig. 5.

Polyhedral model of the MgSiO3 majorite garnet structure viewed down (a) [001] and (b) [010] based on the structure refinement of Angel et al. (1989). Inequivalent positions are labelled and shaded as follows: tetrahedra (light grey), octahedra (dark grey) and dodecahedra (black).

Fig. 6.

Room temperature Mössbauer spectra of Fe0.1Mg0.9SiO3 majorite fitted using (a) Lorentzian lineshapes, (b) extended Voigt-based fitting (xVBF) analysis and (c) full transmission integral with xVBF analysis. (d) Mössbauer spectrum of the same sample at 77 K fitted using the full transmission integral and xVBF analysis. Doublets in all spectra are shaded as follows: dodecahedral Fe2+ (unshaded), octahedral Fe2+ (black), octahedral Fe3+ (grey). The subspectra are offset from the total spectrum for clarity, and the residuals (i.e. the difference between calculated and experimental data) are shown above each spectrum.

Fig. 6.

Room temperature Mössbauer spectra of Fe0.1Mg0.9SiO3 majorite fitted using (a) Lorentzian lineshapes, (b) extended Voigt-based fitting (xVBF) analysis and (c) full transmission integral with xVBF analysis. (d) Mössbauer spectrum of the same sample at 77 K fitted using the full transmission integral and xVBF analysis. Doublets in all spectra are shaded as follows: dodecahedral Fe2+ (unshaded), octahedral Fe2+ (black), octahedral Fe3+ (grey). The subspectra are offset from the total spectrum for clarity, and the residuals (i.e. the difference between calculated and experimental data) are shown above each spectrum.

Fig. 7.

Ball and stick model of (a) crystalline CaFe2+Si2O6 hedenbergite looking down [100], and (b) amorphous CaFe2+Si2O6 glass. For clarity only the iron (black) and oxygen (grey) atoms are shown. In hedenbergite the iron sites are regular and show long-range ordering, while in the glass there are site-to-site distortions and no long-range order. Iron occupies a single octahedral site in hedenbergite, while it has been suggested on the basis of EXAFS and molecular dynamics simulations to occupy a continuous spectrum of four- and five-coordinated sites in the glass (Rossano et al., 2000).

Fig. 7.

Ball and stick model of (a) crystalline CaFe2+Si2O6 hedenbergite looking down [100], and (b) amorphous CaFe2+Si2O6 glass. For clarity only the iron (black) and oxygen (grey) atoms are shown. In hedenbergite the iron sites are regular and show long-range ordering, while in the glass there are site-to-site distortions and no long-range order. Iron occupies a single octahedral site in hedenbergite, while it has been suggested on the basis of EXAFS and molecular dynamics simulations to occupy a continuous spectrum of four- and five-coordinated sites in the glass (Rossano et al., 2000).

Fig. 8.

Room temperature Mössbauer spectra of (a) crystalline CaFe2+Si2O6 hedenbergite, and (b) amorphous Ca–Fe2+–Si–O glass. The single quadrupole doublet in hedenbergite is narrow according to the single octahedral site occupied by iron, while the glass spectrum shows a strongly asymmetric and broadened quadrupole doublet due to the range of different iron environments. The glass spectrum is based on data from Alberto et al. (1996).

Fig. 8.

Room temperature Mössbauer spectra of (a) crystalline CaFe2+Si2O6 hedenbergite, and (b) amorphous Ca–Fe2+–Si–O glass. The single quadrupole doublet in hedenbergite is narrow according to the single octahedral site occupied by iron, while the glass spectrum shows a strongly asymmetric and broadened quadrupole doublet due to the range of different iron environments. The glass spectrum is based on data from Alberto et al. (1996).

Fig. 9.

Variation of centre shift with Fe3+/ΣFe measured from room temperature Mössbauer spectra of glasses in the systems MgO–Al2O3–SiO2–Fe–O and CaO–Al2O3–SiO2–Fe–O (after Mysen et al., 1985a). The decrease in centre shift from 0.61 to 0.29 mm/s with increasing Fe3+ concentration was interpreted to indicate a change from octahedral to tetrahedral coordination. Typical error bars are shown for low, moderate and high Fe3+ concentrations.

Fig. 9.

Variation of centre shift with Fe3+/ΣFe measured from room temperature Mössbauer spectra of glasses in the systems MgO–Al2O3–SiO2–Fe–O and CaO–Al2O3–SiO2–Fe–O (after Mysen et al., 1985a). The decrease in centre shift from 0.61 to 0.29 mm/s with increasing Fe3+ concentration was interpreted to indicate a change from octahedral to tetrahedral coordination. Typical error bars are shown for low, moderate and high Fe3+ concentrations.

Fig. 10.

Correlation between quadrupole splitting and glass transition temperature (as measured by DTA) for aluminate, borate, gallate, tellurite, titanate and vanadate glasses (solid circles), phosphate and fluoride glasses (open circles) and sulphate glasses (open squares), where Fe3+ substitutes for network formers (solid symbols) or for network modifiers (open symbols) (after Nishida et al., 1991).

Fig. 10.

Correlation between quadrupole splitting and glass transition temperature (as measured by DTA) for aluminate, borate, gallate, tellurite, titanate and vanadate glasses (solid circles), phosphate and fluoride glasses (open circles) and sulphate glasses (open squares), where Fe3+ substitutes for network formers (solid symbols) or for network modifiers (open symbols) (after Nishida et al., 1991).

Fig. 11.

Room temperature Mössbauer spectra of glass in the system Na–Fe–Si–O–Cl containing (a) 5.1 wt% Fe and (b) 2.3 wt% Fe. Broadening due to spin relaxation can be seen in spectrum (b) as a greater deviation from the baseline (dotted line).

Fig. 11.

Room temperature Mössbauer spectra of glass in the system Na–Fe–Si–O–Cl containing (a) 5.1 wt% Fe and (b) 2.3 wt% Fe. Broadening due to spin relaxation can be seen in spectrum (b) as a greater deviation from the baseline (dotted line).

Fig. 12.

Room temperature Mössbauer data, subspectra and residuals for basaltic glass fitted using (a) Lorentzian lineshapes, (b) histogram distributions of quadrupole splitting, (c) extended Voigt-based fitting (xVBF) analysis. Fe3+ absorption is shaded grey in each spectrum. The one-dimensional quadrupole splitting (ΔEq) probability distributions for Fe2+ (unshaded) and Fe3+ (grey) are shown to the right of spectra (a) and (b), and the two-dimensional correlated centre shift (δ) and ΔEq distributions are shown to the right of spectrum (c). For the latter, contour lines indicate equal probabilities, where δ and ΔEq are highly correlated in the Fe2+ distribution, while in the Fe3+ distribution nearly all sites have the same value of 5. All spectra were extracted in the thin-absorber limit (Rancourt, 1989, 1996).

Fig. 12.

Room temperature Mössbauer data, subspectra and residuals for basaltic glass fitted using (a) Lorentzian lineshapes, (b) histogram distributions of quadrupole splitting, (c) extended Voigt-based fitting (xVBF) analysis. Fe3+ absorption is shaded grey in each spectrum. The one-dimensional quadrupole splitting (ΔEq) probability distributions for Fe2+ (unshaded) and Fe3+ (grey) are shown to the right of spectra (a) and (b), and the two-dimensional correlated centre shift (δ) and ΔEq distributions are shown to the right of spectrum (c). For the latter, contour lines indicate equal probabilities, where δ and ΔEq are highly correlated in the Fe2+ distribution, while in the Fe3+ distribution nearly all sites have the same value of 5. All spectra were extracted in the thin-absorber limit (Rancourt, 1989, 1996).

Fig. 13.

Schematic diagram of source radiation geometry showing flat and curved absorbers (after Bara & Bogacz, 1980). Symbols: D – source to absorber distance; d – absorber diameter; a – half angle subtended by the absorber; θ – angle of the γ ray relative to the direction of source velocity.

Fig. 13.

Schematic diagram of source radiation geometry showing flat and curved absorbers (after Bara & Bogacz, 1980). Symbols: D – source to absorber distance; d – absorber diameter; a – half angle subtended by the absorber; θ – angle of the γ ray relative to the direction of source velocity.

Fig. 14.

Variation of dimensionless effective source thickness with age for a conventional 1.85 GBq source with 4 GBq/cm2 and a 0.74 GBq point source with 74 GBq/cm2 (after McCammon, 1994).

Fig. 14.

Variation of dimensionless effective source thickness with age for a conventional 1.85 GBq source with 4 GBq/cm2 and a 0.74 GBq point source with 74 GBq/cm2 (after McCammon, 1994).

Fig. 15.

Possible absorber configurations for Mössbauer spectroscopy. (a) Polycrystalline absorber for conventional transmission Mössbauer spectroscopy with ∼ 1 cm diameter beam size. (b) “Thick section” absorber with thickness determined by desired effective absorber thickness. The area outside the region to be studied is masked with a heavy metal foil (e.g. Ta). (c) Single crystal absorber where the crystal is mounted behind a hole drilled in a heavy metal foil. (d) Polycrystalline absorber prepared by placing grains inside a hole drilled in a heavy metal foil. In (b), (c) and (d) the beam size is determined by the diameter of the holes drilled in the heavy metal foil, and can be as small as ∼ 100 μm in diameter.

Fig. 15.

Possible absorber configurations for Mössbauer spectroscopy. (a) Polycrystalline absorber for conventional transmission Mössbauer spectroscopy with ∼ 1 cm diameter beam size. (b) “Thick section” absorber with thickness determined by desired effective absorber thickness. The area outside the region to be studied is masked with a heavy metal foil (e.g. Ta). (c) Single crystal absorber where the crystal is mounted behind a hole drilled in a heavy metal foil. (d) Polycrystalline absorber prepared by placing grains inside a hole drilled in a heavy metal foil. In (b), (c) and (d) the beam size is determined by the diameter of the holes drilled in the heavy metal foil, and can be as small as ∼ 100 μm in diameter.

Table 1.

Relative areas calculated from majorite garnet Mössbauer spectra.

T [K]Fitting model[viii]Fe2+[VI]Fe2+Fe3+

293Lorentzian0.774(5)0.078(5)0.149(4)
293xVBF10.773(5)0.093(5)0.134(4)
293xVBF with FTI10.794(11)0.082(19)0.123(17)
293xVBF with FTI1 corrected for recoil-free fractions0.804(13)0.083(20)0.113(18)
77xVBF with FTI10.800(10)0.081(15)0.120(12)
77xVBF with FTI1 corrected for recoil-free fractions0.802(12)0.081(17)0.117(14)
T [K]Fitting model[viii]Fe2+[VI]Fe2+Fe3+

293Lorentzian0.774(5)0.078(5)0.149(4)
293xVBF10.773(5)0.093(5)0.134(4)
293xVBF with FTI10.794(11)0.082(19)0.123(17)
293xVBF with FTI1 corrected for recoil-free fractions0.804(13)0.083(20)0.113(18)
77xVBF with FTI10.800(10)0.081(15)0.120(12)
77xVBF with FTI1 corrected for recoil-free fractions0.802(12)0.081(17)0.117(14)

1 xVBF: extended Voigt-based fitting; FTI: full transmission integral Standard deviations are based on statistical analysis of the fitting model only, and do not represent the cumulative error of the measurement.

Table 2.

Range of glass centre shifts.

Iron environmentcentre shift1 [mm/s]

[VIII]Fe2+1.20–1.30
[VIII]Fe2+1.05–1.10
[VIII]Fe2+0.90–0.95
[VIII]Fe3+0.35–0.55
[VIII]Fe3+0.20–0.32
Iron environmentcentre shift1 [mm/s]

[VIII]Fe2+1.20–1.30
[VIII]Fe2+1.05–1.10
[VIII]Fe2+0.90–0.95
[VIII]Fe3+0.35–0.55
[VIII]Fe3+0.20–0.32

1 relative to α-Fe

From Dyar (1985) for phosphate, borate and silicate glasses.

Table 3.

Hyperfine parameters for different fits to basaltic glass spectrum.

Thin-limit1Thick2

LorentzianHistogramxVBF3xVBF3

Fe2+
Mean centre shift (rel to α-Fe) [mm/s]1.02(2)1.03(4)1.03(1)1.03(1)
Mean quadrupole splitting [mm/s]1.93(7)1.90(1)1.91(1)1.91(3)
Relative area0.72(3)0.74(3)0.74(2)0.72(2)
Fe3+
Mean centre shift (rel to α-Fe) [mm/s]0.39(6)0.34(2)0.36(3)0.38(4)
Mean quadrupole splitting [mm/s]1.04(10)1.17(2)1.16(4)1.16(6)
Relative area0.28(3)0.26(3)0.26(2)0.28(2)
Thin-limit1Thick2

LorentzianHistogramxVBF3xVBF3

Fe2+
Mean centre shift (rel to α-Fe) [mm/s]1.02(2)1.03(4)1.03(1)1.03(1)
Mean quadrupole splitting [mm/s]1.93(7)1.90(1)1.91(1)1.91(3)
Relative area0.72(3)0.74(3)0.74(2)0.72(2)
Fe3+
Mean centre shift (rel to α-Fe) [mm/s]0.39(6)0.34(2)0.36(3)0.38(4)
Mean quadrupole splitting [mm/s]1.04(10)1.17(2)1.16(4)1.16(6)
Relative area0.28(3)0.26(3)0.26(2)0.28(2)

1 spectra were corrected for thickness effects by extracting the thin-absorber limit spectrum (Rancourt, 1989, 1996)

2 not corrected for thickness effects

3 xVBF: extended Voigt-based fitting

Standard deviations are based on statistical analysis of the fitting model only, and do not represent the cumulative error of the measurement.

Table 4.

Minimum source-absorber distances for conventional sources.

absorber diameter [mm]source-absorber distance13 [mm]

1269
1057
846
634
423
211
16
0.53
0.10.6
absorber diameter [mm]source-absorber distance13 [mm]

1269
1057
846
634
423
211
16
0.53
0.10.6

1 α < 5° (Bara & Bogacz, 1980)

Contents

GeoRef

References

References

Alberto
,
H.V.
Pinoto da Cunha
,
J.L.
Mysen
,
B.O.
Gil
,
J.M.
Ayres de Campos
,
N.
(
1996
):
Analysis of Mössbauer spectra of silicate glasses using a two-dimensional Gaussian distribution of hyperfine parameters
.
J. Non-Cryst. Solids
 ,
194
:
48
57
.
Amthauer
,
G.
Annersten
,
H.
Hafner
,
S.S.
(
1976
):
The Mössbauer spectrum of 57Fe in silicate garnets
.
Z. Kristallogr.
 ,
143
:
14
55
.
Amthauer
,
G.
Grodzicky
,
M.
Lottermoser
,
W.
Redhammer
,
G.
(
2004
):
Mössbauer spectroscopy: Basic principles
. In
Beran
,
A.
Libowitzky
,
E.
(eds.):
Spectroscopic methods in mineralogy /EMU Notes Mineral.
 ,
6/
.
Budapest
:
Eötvös Univ. Press
,
345
367
.
Angel
,
R.J.
Finger
,
L.W.
Hazen
,
R.M.
Kanzaki
,
M.
Weidner
,
D.J.
Liebermann
,
R.C.
Veblen
,
D.R.
(
1989
):
Structure and twinning of single-crystal MgSiO3 garnet synthesized at 17 GPa and 1800 °C
.
Am. Mineral.
 ,
74
:
509
512
.
Atzmony
,
U.
Norton
,
S.J.
Swartzendruber
,
L.J.
Bennett
,
L.H.
(
1987
):
Mössbauer imaging: experimental result
.
Nature
 ,
330
:
153
154
.
Bancroft
,
G.M.
(
1973
):
Mössbauer spectroscopy. An introduction for inorganic chemists and geochemists.
 
New York (N.Y.)
:
McGraw-Hill
.
Bancroft
,
G.M.
Maddock
,
A.G.
Burns
,
R.G.
Strens
,
R.G.J.
(
1966
):
Cation distribution in anthophyllite from Mössbauer and infra-red spectroscopy
.
Nature
 ,
212
:
913
915
.
Bancroft
,
G.M.
Maddock
,
A.G.
Burns
,
R.G.
(
1967
):
Applications of the Mössbauer effect to silicate mineralogy - I. Iron silicates of known crystal structure
.
Geochim. Cosmochim. Acta
 ,
31
:
2219
2246
.
Bancroft
,
G.M.
Burns
,
R.G.
Stone
,
A.J.
(
1968
):
Applications of the Mössbauer effect to silicate mineralogy - II. Iron silicates of unknown and complex crystal structures
.
Geochim. Cosmochim. Acta
 ,
32
:
547
559
.
Bara
,
J.J.
Bogacz
,
B.F.
(
1980
):
Geometric effects in Mössbauer transmission experiments
.
Mössbauer Eff. Ref. Data J.
 ,
3
:
154
163
.
Bevington
,
P.R.
(
1969
):
Data reduction and error analysis for the physical sciences
 .
New York (N.Y.)
:
McGraw-Hill
.
Bolfan-Casanova
,
N.
Mackwell
,
S.J.
Keppler
,
H.
McCammon
,
C.
Rubie
,
D.C.
(
2002
):
Pressure dependence of H solubility in magnesiowüstite up to 25 GPa: Implications for the storage of water in the Earth's lower mantle
.
Geophys. Res. Lett.
 ,
29
:
Art. No. 1449 (doi:10.1029/2001GL014457)
.
Burns
,
R.G.
Solberg
,
T.C.
(
1990
):
57Fe-bearing oxide, silicate, and aluminosilicate minerals
. In
Coyne
,
L.M.
McKeever
,
S.W.S.
Blake
,
D.F.
(eds.):
Spectroscopic characterization of minerals and their surfaces /ACS Symp. Ser.
 ,
415
/.
Washington (D.C.)
:
Am. Chem. Soc.
,
262
283
.
Campbell
,
S.J.
Aubertin
,
F.
(
1989
):
Evaluation of distributed hyperfine parameters
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to inorganic chemistry. Vol. 3.
 
New York (N.Y.)
:
Plenum Press
,
183
242
.
Cashion
,
J.D.
Weiser
,
P.S.
McGrath
,
A.C.
Pollard
,
R.J.
Smith
,
T.F.
(
1990
):
Imaging Mössbauer spectroscopy - A new technique for materials analysis
.
Hyperfine Interact.
 ,
58
:
2507
2512
.
De Grave
,
E.
Van Alboom
A.
(
1991
):
Evaluation of ferrous and ferric Mössbauer fractions
.
Phys. Chem. Miner.
 ,
18
:
337
342
.
De Souza
,
P.
Garg
,
V.
Klingelhöfer
,
G.
Gellert
,
R.
Gütlich
,
P.
(
2002
):
Portable and automatic Mössbauer analysis
.
Hyperfine Interact.
 ,
139
:
705
714
.
Dingwell
,
D.B.
(
1991
):
Redox viscometry of some Fe-bearing melts
.
Am. Mineral.
 ,
76
:
1560
1562
.
Dingwell
,
D.B.
Virgo
,
D.
(
1987
):
The effect of oxidation state on the viscosity of melts in the system Na2O-FeO-Fe2O3-SiO2
.
Geochim. Cosmochim. Acta
 ,
51
:
195
205
.
Dollase
,
W.A.
(
1975
):
Statistical limitations of Mössbauer spectral fitting
.
Am. Mineral.
 ,
60
:
257
264
.
Dyar
,
M.D.
(
1985
):
A review of Mössbauer data on inorganic glasses: the effects of composition on iron valency and coordination
.
Am. Mineral.
 ,
70
:
304
316
.
Gancedo
,
J.R.
Davalos
,
J.Z.
Gracia
,
M.
Marco-Sanz
,
J.F.
(
1997
):
The use of Mössbauer spectroscopy in surface studies. A methodological survey
.
Hyperfine Interact.
 ,
110
:
41
50
.
Gerdau
,
E.
DeWaard
,
H.
(eds.) (
1999
):
Nuclear resonant scattering of synchrotron radiation /Hyperfine Interact.
 ,
123–124/
.
Dordrecht
:
Kluwer Academic Publishers
.
Greenwood
,
N.N.
Gibb
,
T.D.
(
1971
):
Mössbauer spectroscopy.
 
London
:
Chapman & Hall
.
Gütlich
,
P.
Link
,
R.
Trautwein
,
A.
(
1978
):
Mössbauer spectroscopy and transition metal chemistry.
 
Berlin
:
Springer-Verlag
.
Hawthorne
,
F.C.
(
1988
):
Mössbauer spectroscopy
. In
Hawthorne
,
F.C.
(ed.):
Spectroscopic methods in mineralogy and geology /Rev. Mineral.
 ,
18/
.
Washington (D.C.)
:
Mineral. Soc. Am.
,
255
340
.
Hawthorne
,
F.C.
(
1992
):
Mineralogy. Geotimes
 ,
37
(
2
):
39
.
Hawthorne
,
F.C.
Waychunas
,
G.A.
(
1988
):
Spectrum-fitting methods
. In
Hawthorne
,
F.C.
(ed.):
Spectroscopic methods in mineralogy and geology /Rev. Mineral.
 ,
18
/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
63
98
.
Holland
,
D.
Mekki
,
A.
Gee
,
I.A.
McConville
,
C.F.
Johnson
,
J.A.
Johnson
,
C.E.
Appleyard
,
P.
Thomas
,
M.
(
1999
):
The structure of sodium iron silicate glass - a multi-technique approach
.
J. Non-Cryst. Solids
 ,
253
:
192
202
.
Hoy
,
G.R.
(
1984
):
Relaxation phenomena for chemists
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to inorganic chemistry. Vol. 1.
 
New York (N.Y.)
:
Plenum Press
,
195
226
.
Ingalls
,
R.
(
1964
):
Electric-field gradient tensor in ferrous compounds
.
Phys. Rev.
 ,
133
:
A787
A795
.
Kress
,
V.C.
Carmichael
,
I.S.E.
(
1991
):
The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states
.
Contrib. Mineral. Petrol.
 ,
108
:
82
92
.
Lagarec
,
K.
Rancourt
,
D.G.
(
1997
):
Extended Voigt-based analytic lineshape method for determining N-dimensional correlated hyperfine parameter distributions in Mössbauer spectroscopy
.
Nucl. Instrum. Methods Phys. Res. B
 ,
129
:
266
280
.
Lauterbach
,
S.
McCammon
,
C.A.
van Aken
,
P.
Langenhorst
,
F.
Seifert
,
F.
(
2000
):
Mössbauer and ELNES spectroscopy of (Mg,Fe)(Si,Al)O3 perovskite: A highly oxidised component of the lower mantle
.
Contrib. Mineral. Petrol.
 ,
138
:
17
26
.
Long
,
G.L.
Cranshaw
,
T.E.
Longworth
,
G.
(
1983
):
The ideal Mössbauer effect absorber thickness
.
Möss. Effect Ref. Data J.
 ,
6
:
42
49
.
Longworth
,
G.
(
1987
):
Mössbauer effect studies of metallic glasses
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to inorganic chemistry. Vol. 2.
 
New York (N.Y.)
:
Plenum Press
,
289
342
.
Maddock
,
A.G.
(
1985
):
Mössbauer spectroscopy in mineral chemistry
. In
Berry
,
F.J.
Vaughan
,
D.J.
(eds.):
Chemical bonding and spectroscopy in mineral chemistry.
 
London
:
Chapman & Hall
,
141
208
.
McCammon
,
C.A.
(
1994
):
A Mössbauer milliprobe: Practical considerations
.
Hyperfine Interact.
 ,
92
:
1235
1239
.
McCammon
,
C.A.
(
2000
):
Insights into phase transformations from Mössbauer spectroscopy
. In
Redfern
,
S.
Carpenter
,
M.
(eds.):
Transformation processes in minerals /Rev. Mineral. Geochem.
 ,
39/
.
Washington, DC
:
Mineralogical Society of America
,
241
264
.
McCammon
,
C.A.
(
2003
):
Mössbauer spectroscopy in the geosciences: Highlights and perspectives
.
Hyperfine Interact.
 ,
144/145
:
289
296
.
McCammon
,
C.A.
Ross
,
N.L.
(
2003
):
Crystal chemistry of ferric iron in (Mg,Fe)(Si,Al)O3 majorite with implications for the transition zone
.
Phys. Chem. Miner.
 ,
30
:
206
216
.
McCammon
,
C.A.
Chaskar
,
V.
Richards
,
G.G.
(
1991
):
A technique for spatially resolved Mössbauer spectroscopy applied to quenched metallurgical slags
.
Meas. Sci. Technol.
 ,
2
:
657
662
.
McCammon
,
C.A.
Hutchison
,
M.
Harris
,
J.
(
1997
):
Ferric iron content of mineral inclusions in diamonds from São Luiz: A view into the lower mantle
.
Science
 ,
278
:
434
436
.
McCammon
,
C.
Chinn
,
I.
Gurney
,
J.
McCallum
,
M.
(
1998
):
Ferric iron content of mineral inclusions in diamonds from George Creek, Colorado determined using Mössbauer spectroscopy
.
Contrib. Mineral. Petrol.
 ,
133
:
30
37
.
McCammon
,
C.A.
Tennant
,
W.C.
Miletich
,
R.M.
(
2000
):
A new method for single crystal measurements: Application to studies of mineral inclusions in diamonds
.
Hyperfine Interact.
 ,
126
:
241
245
.
McCammon
,
C.A.
Griffin
,
W.L.
Shee
,
S.H.
O'Neill
,
H.S.C.
(
2001
):
Oxidation during metasomatism in ultramafic xenoliths from the Wesselton kimberlite, South Africa: Implications for the survival of diamond
.
Contrib. Mineral. Petrol.
 ,
141
:
287
296
.
Mysen
,
B.O.
Virgo
,
D.
Neumann
,
E.-R.
Seifert
,
F.A.
(
1985a
):
Redox equilibria and the structural states of ferric and ferrous iron in melts in the system CaO-MgO-Al2O3-SiO2-FeO: relationships between redox equilibria, melt structure and liquidus phase equilibria
.
Am. Mineral.
 ,
70
:
317
331
.
Mysen
,
B.O.
Carmichael
,
I.S.E.
Virgo
,
D.
(
1985b
):
Acomparison of iron redox ratios in silicate glasses determined by wet-chemical and 57Fe Mössbauer resonant absorption methods
.
Contrib. Mineral. Petrol.
 ,
90
:
101
106
.
Nishida
,
T.
(
1995
):
Mössbauer effect in inorganic glasses
.
Hyperfine Interact.
 ,
95
:
23
39
.
Nishida
,
T.
Shindo
,
H.
Takashima
,
Y.
(
1991
):
Discovery of a linear relationship between the glass transition temperature of oxide glasses and the quadrupole splitting of the Fe3+ substituted for the individual network-forming cations (NWF)
.
Hyperfine Interact.
 ,
69
:
603
606
.
Nomura
,
K.
(
1999
):
Conversion electron Mössbauer spectrometry
. In
Miglierini
,
M.
Petredis
,
D.
(eds.):
Mössbauer spectroscopy in materials science
 .
Dordrecht
:
Kluwer
,
63
78
.
Norton
,
S.J.
(
1987
):
Mössbauer imaging
.
Nature
 ,
330
:
151
153
.
Partzsch
,
G.M.
Lattard
,
D.
McCammon
,
C.A.
:
Mössbauer spectroscopic determination of Fe3+/Fe2+ in synthetic basaltic glass: A test of empirical fO2 equations under superliquidus and subliquidus conditions
.
Contrib. Mineral. Petrol.
 ,
in print
.
Pfannes
,
H.D.
Gonser
,
U.
(
1973
):
Goldanskii-Karyagin effect versus preferred orientations (texture)
.
Appl. Phys.
 ,
1
:
93
102
.
Ping
,
J.Y.
Rancourt
,
D.G.
(
1992
):
Thickness effects with intrinsically broad absorption lines
.
Hyperfine Interact.
 ,
71
:
1433
1436
.
Proyer
,
A.
Dachs
,
E.
McCammon
,
C.A.
:
Pitfalls in geothermometry of eclogites: Fe3+ and changes in the mineral chemistry of omphacite at ultrahigh pressures
.
Contrib. Mineral. Petrol.
 ,
in print
.
Rancourt
,
D.G.
(
1989
):
Accurate site populations from Mössbauer spectroscopy
.
Nucl. Instrum. Methods Phys. Res.
 ,
B44
:
199
210
.
Rancourt
,
D.G.
(
1994a
):
Mössbauer spectroscopy of minerals I. Inadequacy of Lorentzian-line doublets in fitting spectra arising from quadrupole splitting distributions
.
Phys. Chem. Miner.
 ,
21
:
244
249
.
Rancourt
,
D.G.
(
1994b
):
Mössbauer spectroscopy of minerals II. Problem of resolving cis and trans octahedral Fe2+ sites
.
Phys. Chem. Miner.
 ,
21
:
250
257
.
Rancourt
,
D.G.
(
1996
):
Analytical methods for Mössbauer spectral analysis of complex materials
. In
Long
,
G.J.
Grandjean
,
F.
(eds.):
Mössbauer spectroscopy applied to magnetism and materials science, Vol. 2.
 
New York & London
:
Plenum Press
,
105
124
.
Rancourt
,
D.G.
(
1998
):
Mössbauer spectroscopy in clay science
.
Hyperfine Interact.
 ,
117
:
3
38
.
Rancourt
,
D.G.
Klingelhöfer
,
G.
(
1994
):
Possibility of a Mössbauer resonant-electron microscope
. In
Fourth Seeheim Workshop on Mössbauer Spectroscopy (Seeheim, Germany), Abstr.
, P
129
.
Rancourt
,
D.G.
Ping
,
J.Y.
(
1991
):
Voigt-based methods for arbitrary-shape static hyperfine parameter distributions in Mössbauer spectroscopy
.
Nucl. Instrum. Methods Phys. Res.
 ,
B58
:
85
97
.
Rancourt
,
D.G.
Christie
,
I.A.D.
Royer
,
M.
Kodama
,
H.
Robert
,
J.-L.
Lalonde
,
A.E.
Murad
,
E.
(
1994
):
Determination of accurate [4]Fe3+, [6]Fe3+, and [6]Fe2+ site populations in synthetic annite by Mössbauer spectroscopy
.
Am. Mineral.
 ,
79
:
51
62
.
Robinson
,
K.
Gibbs
,
G.V.
Ribbe
,
P.H.
(
1971
):
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
.
Science
 ,
172
:
567
570
.
Rossano
,
S.
Balan
,
E.
Morin
,
G.
Bauer
,
J.-P.
Calas
,
G.
Brouder
,
C.
(
1999
):
57Fe Mössbauer spectroscopy of tektites
.
Phys. Chem. Miner.
 ,
26
:
530
538
.
Rossano
,
S.
Ramos
,
A.Y.
Delaye
,
J.-M.
(
2000
):
Environment of ferrous iron in CaFeSi2O6 glass; contributions of EXAFS and molecular dynamics
.
J. Non-Cryst. Solids
 ,
273
:
48
52
.
Seifert
,
F.
(
1990
):
Phase transformation in minerals studied by 57Fe Mössbauer spectroscopy
. In
Mottana
,
A.
Burragato
,
F.
(eds.):
Absorption spectroscopy in mineralogy.
 
Amsterdam
:
Elsevier
,
145
170
.
Skogby
,
H.
Annersten
,
H.
Domeneghetti
,
M.C.
Molin
,
G.M.
Tazzoli
,
V.
(
1992
):
Iron distribution in orthopyroxene: A comparison of Mössbauer spectroscopy and X-ray refinement results
.
Eur. J. Mineral.
 ,
4
:
441
452
Smith
,
P.R.
Cashion
,
J.D.
Brown
,
L.J.
(
1992
):
Imaging Mössbauer spectroscopic measurements of an inhomogeneous sample
.
Hyperfine Interact.
 ,
71
:
1503
1506
.
Sokolova
,
E.
Hawthorne
,
F.C.
McCammon
,
C.A.
Liferovich
,
R.P.
(
2001
):
The crystal structure of gladiusite
, (Fe2+,Mg)4forumla(PO4)(OH)u(H2O).
Can. Mineral.
 ,
39
:
1121
1130
.
Tennant
,
W.C.
McCammon
,
C.A.
Miletich
,
R.
(
2000
):
Electric-field gradient and mean-squared-displacement tensors in hedenbergite from single crystal Mössbauer milliprobe measurements
.
Phys. Chem. Miner.
 ,
27
:
156
163
.
Vandenberghe
,
R.E.
De Grave
,
E.
de Bakker
,
P.M.A.
(
1994
):
On the methodology of the analysis of Mössbauer spectra
.
Hyperfine Interact.
 ,
83
:
29
49
.
Williams
,
K.F.E.
Johnson
,
C.E.
Thomas
,
M.F.
(
1998
):
Mössbauer spectroscopy measurement of iron oxidation states in float composition silica glasses
.
J. Non-Cryst. Solids
 ,
226
:
19
23
.
Wivel
,
C.
Mørup
,
S.
(
1981
):
Improved computational procedure for evaluation of overlapping hyperfine parameter distributions in Mossbauer spectra
.
J. Phys. E: Sci. Instrum.
 ,
14
:
605
610
.
Woodland
,
A.B.
Ross II
,
C.R.
(
1994
):
A crystallographic and Mössbauer spectroscopy study of
forumla, (almandine-“skiagite”) and forumla (andradite-“skiagite”) garnet solid solutions.
Phys. Chem. Miner.
 ,
21
:
117
132
.

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