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Abstract

Garnet is an important phase in various technological applications and in nature as a major rock-forming mineral. The geological occurrence of silicate garnets is widespread and they are stable over an enormous range of rock compositions and pressure and temperature conditions. They are found in low-pressure metamorphic contact aureoles and they occur as complex solid solutions in the Earth's transition zone. Therefore, over the years a large amount of mineralogical, geochemical and mineral physics research has been directed toward garnet. It is, for example, a key mineral in many geochemical trace-element studies concerned with melting in the deep Earth, and in geophysical investigations of the upper mantle and transition zone its physical properties are of importance. In petrologic studies the thermodynamic mixing properties of garnet solid solutions play a central role in many geothermometers and geobarometers. The end-member aluminosilicate garnets [X3Al2Si3O12 with X = Fe2+ (almandine – Al), Mn2+ (spessartine – Sp), Mg (pyrope – Py), and Ca (grossular – Gr)] and their solid solutions (Fig. 1) have received much study regarding their structural, physical, chemical and thermodynamic properties (for a review of the latter see Geiger, 1999). However, there is no comprehensive review article related to their structural, crystal chemical and lattice dynamic properties, and there have been no attempts made to bring together and analyse the rich and diverse literature on spectroscopic investigations. This is the goal of this article.

Various spectroscopic measurements on aluminosilicate garnets covering the full range of the electromagnetic spectrum will be reviewed and an attempt will be made to reach a broad synthesis.

Introduction and philosophical approach

Garnet is an important phase in various technological applications and in nature as a major rock-forming mineral. The geological occurrence of silicate garnets is widespread and they are stable over an enormous range of rock compositions and pressure and temperature conditions. They are found in low-pressure metamorphic contact aureoles and they occur as complex solid solutions in the Earth's transition zone. Therefore, over the years a large amount of mineralogical, geochemical and mineral physics research has been directed toward garnet. It is, for example, a key mineral in many geochemical trace-element studies concerned with melting in the deep Earth, and in geophysical investigations of the upper mantle and transition zone its physical properties are of importance. In petrologic studies the thermodynamic mixing properties of garnet solid solutions play a central role in many geothermometers and geobarometers. The end-member aluminosilicate garnets [X3Al2Si3O12 with X = Fe2+ (almandine – Al), Mn2+ (spessartine – Sp), Mg (pyrope – Py), and Ca (grossular – Gr)] and their solid solutions (Fig. 1) have received much study regarding their structural, physical, chemical and thermodynamic properties (for a review of the latter see Geiger, 1999). However, there is no comprehensive review article related to their structural, crystal chemical and lattice dynamic properties, and there have been no attempts made to bring together and analyse the rich and diverse literature on spectroscopic investigations. This is the goal of this article.

Fig. 1.

The aluminosilicate garnet system almandine-pyrope-grossular-spessartine (X3Al2Si3O12, with X = Fe2+, Mg, Ca and Mn2+). It consists of four end members and six binary, four ternary and one quaternary solid solution system(s).

Fig. 1.

The aluminosilicate garnet system almandine-pyrope-grossular-spessartine (X3Al2Si3O12, with X = Fe2+, Mg, Ca and Mn2+). It consists of four end members and six binary, four ternary and one quaternary solid solution system(s).

Various spectroscopic measurements on aluminosilicate garnets covering the full range of the electromagnetic spectrum will be reviewed and an attempt will be made to reach a broad synthesis. They cover the regions between radio frequencies and γ radiation corresponding to energies between –11 < log10E (eV) < 7 and frequencies between 3 < log10v (Hz) < 21 (see Fig. 1 in Geiger, 2004, in this volume). The aluminosilicate garnets provide an optimal system for spectroscopic study, because the structure is cubic and the three crystallographically independent cations are located on special positions. The high symmetry allows for a rigorous analysis of spectroscopic results in comparison, for example, to most lower symmetry silicates. In addition, a number of different cations can occupy the X site and thus create a variety of end-members and solid solutions having large differences in their crystal chemical and physical properties. Thus, the nature of their compositional systematics can be used in an empirical way to help interpret complicated spectroscopic features that cannot otherwise be calculated a priori. The stage has now been reached where the level of spectroscopic research is quite mature and many important experimental results have been obtained.

What is to be done? Spectroscopy can be used as an analytical tool for use in “finger-printing type measurements” and in the geological sciences it is often in this role that it is employed. In the case of garnet, IR spectroscopy is used to determine the presence and concentration of OH groups, 57Fe Mössbauer spectroscopy is used to measure Fe2+/Fe3+ ratios, and micro-Raman spectroscopy is employed for the identification of small inclusions. These types of measurements and their interpretation are generally straightforward and a number of such studies describing the necessary experimental set-ups and results can be found in the literature. Purely standard analytical-type investigations of this sort will not be considered in this report. The approach adopted herein is different, as the various issues and results to be discussed are more academic in nature, at least in this stage of research. On the other hand, detailed discussion or analysis of purely solid-state physical phenomena (e.g. quantitative electronic bonding theory or properties etc.) will be limited. The aim is to find a “middle road” between routine analytical results, which say little about wide-ranging structural and crystal chemical properties, and more specialised theoretical considerations, which may not be of direct mineralogical or geochemical interest. This review attempts to analyse different published spectroscopic results in order to obtain a broad chemically-and physically-based description of garnet over different experimental length and time scales. The goal is “to put it all together”. There are a large number of important mineralogical and geochemical issues that can be addressed through spectroscopic measurements (see other chapters of this volume). In the case of garnet all of them cannot be discussed herein, but the following questions or areas of investigation are considered to be important and on the cutting edge of research; they will be emphasised in this article. They are:

  1. What is the nature of X-cation order/disorder in aluminosilicate garnet solid solutions? Diffraction experiments show that the X-cations in both synthetic and natural garnets are long-range disordered in space group forumla. However, little is known as to whether short-range order (SRO) is present and to what degree. All existing thermodynamic mixing models for aluminosilicate garnet solid solutions assume a statistically random X-cation distribution for a description of the configurational entropy (i.e., forumla where R is the gas constant and Xi are the mole fractions of the different components i), but this assumption has not been tested until recently. Physical properties, such as magnetic behaviour, can be greatly affected by atomic clustering, as can the nature of trace element substitution, for example. Spectroscopic methods can best address the issue of short-range order and clustering.

  2. What are the atomistic-level dynamic properties of garnet, how can they be described and how do they relate to or affect the macroscopic thermodynamic properties? The static crystal chemical properties of end-member garnets are known to great detail from diffraction measurements, but a quantitative description of the dynamic properties of the atoms is less certain. Vibrational spectroscopy (e.g. Raman and IR spectroscopy) provides a basis for investigating the lattice dynamic properties of a material at the atomistic level. Lattice dynamic study can help explain or be used to understand macroscopic mineral behaviour at different pressure and temperature conditions. Valuable information on thermodynamic properties such as heat capacity (Cp) and on bulk physical properties such as thermal expansion and elastic constants can be obtained. The lattice dynamic properties of solid solutions are understood even less, both in terms of experiment and theory, and here, once again, spectroscopic measurements play a fundamental role in providing understanding in this area.

  3. What are the microscopic energetic and bonding properties of end-member garnets and more importantly of garnet solid solutions? How can they be measured and described? The total energy of mixing of a system can be broken down into two parts, namely the elastic or strain energy and a chemical energy contribution (e.g.Ferreira et al., 1988). It is thought that local elastic strain energies are important in controlling the enthalpies of mixing, ΔHmix, for most silicate solid solutions, but other effects cannot be ignored (see Geiger, 2001). Local structural distortions arising from the exchange of different-sized cations give rise to elastic strain energies. Microscopic strain is a function of local structural relaxation in the vicinity where atomic exchange takes place and it can be described by local site properties such as bond lengths, polyhedral geometries and distortions. Vibrational spectroscopy (i.e., Raman and IR) can be used to characterise local structural heterogeneities and X-ray absorption spectroscopy can be used to obtain bond lengths and polyhedral geometries, for example, in solid solutions. In addition, electronic bonding properties such as crystal field stabilisation energies that can be considered a type of “chemical energy” are best determined spectroscopically via optical absorption methods.

  4. Where and how are trace elements incorporated in the garnet structure? Knowledge of trace element partitioning behaviour between coexisting phases plays a central role in many geochemical investigations. However, the atomistic-level crystal chemical aspects of trace element substitution in minerals are not understood quantitatively. Simple considerations, based on ionic radii and electronic charge, are often employed, for example, to determine at which structural site a trace element could be located. However, such an approach is conjectural. Spectroscopic measurements can be made to help determine on which crystallographic site or where structurally (e.g. in defect sites or dislocations or on a surface) a trace element is located. From this information, the behaviour and role of trace elements in geochemical and petrological processes can be better understood.

These four subjects will constitute the major themes in this article. However, before the spectroscopic results are discussed, the crystal chemistry and lattice-dynamic properties of garnet as revealed by diffraction experiments will be briefly reviewed. X-ray diffraction studies provide a basis from which most spectroscopic results can be interpreted. In fact, one can state that the diffraction experiment remains the most important and powerful method for elucidating the structural and crystal-chemical properties of crystalline materials. An inherent weakness of most spectroscopic methods lies in the fact that it is neither easy, nor possible in many cases, to calculate a priori a spectrum, whether it is a MAS NMR or Raman spectrum, for example. Thus, spectra often have to be interpreted empirically or by using crystal-chemical considerations that are based on diffraction results. The reason for the difficulty in calculating many spectra lies in the quantum mechanical aspects associated with the different spectroscopies and the nature of the energy transitions that are associated with them. The situation is changing rapidly, however, and spectra for some of the simpler and common silicates are being calculated using quantum mechanical methods and with reasonable results. Further computational developments should lead to major advances in spectroscopic investigations, and it is clear that combined computer simulation-spectroscopic studies are growing quickly and they will provide increased understanding for many mineral systems in the years to come. But returning to the field of experimentation, used together, diffraction and spectroscopic measurements enable broad and deep insight into the static and dynamic properties of a crystal over different length scales. We begin with a review of diffraction results on aluminosilicate garnets.

The structure, crystal chemistry and lattice dynamic properties of garnet as determined from diffraction experiments

Garnet end members – almandine, spessartine, pyrope and grossular

The structural and crystal chemical properties of the aluminosilicate garnets have been investigated intensively by X-ray and neutron scattering experiments at ambient conditions since Menzer solved the structure in 1926 (Menzer, 1926; 1928). Since this time, a large number of structural refinements on both synthetic and natural crystals have been undertaken. Furthermore, diffraction studies have investigated the effect of pressure and temperature on the garnet structure (see below). One can conclude that the static crystal chemical properties of the silicate garnets, as derived from the diffraction experiment, are now well understood.

The aluminosilicate garnet structure has the space group forumla, with Z = 8. The cations are located at crystallographic special positions, fixed by symmetry, and the oxygen atoms are at general positions. The divalent X cations occupy the 24c position of 222 (D2) point symmetry, the trivalent Al cation the 16a position of forumla (C3i) symmetry, and the Si cation the 24d position of forumla (S4) point symmetry (Table 1). The structure contains SiO4 tetrahedra and AlO6 octahedra that are connected over corners, thus building a three dimensional quasi-framework (Fig. 2a). There exist small cavities in which the divalent X cations are located, and it is here that cation exchange takes place allowing for extensive solid solution formation (extensive cation exchange can also occur at the octahedral Y site in silicate garnet, but such solid solutions are not considered in this report). The divalent cations are coordinated by 8 oxygen atoms that form a triangular dodecahedral site. The X cations are weakly bonded and there are two crystallographically independent bonds, the four shorter X–O(2) and the four longer X–O(4) bonds. The different cation-oxygen bond lengths for the four end-member aluminosilicate garnets are given in Table 2. There are a large number of shared polyhedral edges in garnet (Table 3) and this gives rise to its high density. The structural relationship between a SiO4 tetrahedron and surrounding dodecahedra is shown in Figure 2b, the relationship between neighbouring dodecahedra in Figure 2c and the relationship between an AlO6 octahedron and surrounding dodecahedra in Figure 2d.

Table 1.

Summary of crystallographic properties for garnet X3Y2Z3O12 of space group forumla.

SitePoint symmetryAtomic coordinatesSite coordinationWyckoff position

X2221/801/4824c
Yforumla000616a
Zforumla3/80¼424d
O1xyz496h
SitePoint symmetryAtomic coordinatesSite coordinationWyckoff position

X2221/801/4824c
Yforumla000616a
Zforumla3/80¼424d
O1xyz496h
Table 2.

Cation-oxygen bond distances for synthetic end-member aluminosilicate garnets at different temperatures (from Geiger et al., 1992b; Armbruster et al., 1992; Armbruster & Geiger, 1993; Geiger & Armbruster, 1997).

GarnetT (K)Si–O (Å)Al–O (Å)X–O(2) (Å)X–O(4) (Å)

Pyrope1001.634 (1)1.885 (1)2.195 (1)2.334 (1)
 2931.634 (1)1.886 (1)2.197 (1)2.340 (1)
 5001.635 (1)1.890 (1)2.202 (1)2.349 (1)
Almandine1001.636 (1)1.888 (1)2.220 (1)2.363 (1)
 2931.635 (1)1.890 (1)2.221 (1)2.371 (1)
 5001.637 (1)1.893 (1)2.225 (1)2.379 (1)
Spessartine1001.639 (1)1.899 (1)2.245 (1)2.399 (1)
 2931.640 (1)1.901 (1)2.246 (1)2.404 (1)
 5001.641 (1)1.902 (1)2.251 (1)2.414 (1)
Grossular1001.646 (1)1.923 (1)2.321 (1)2.483 (1)
 2931.646 (1)1.926 (1)2.322 (1)2.487 (1)
 5501.646 (1)1.929 (1)2.322 (1)2.498 (1)
GarnetT (K)Si–O (Å)Al–O (Å)X–O(2) (Å)X–O(4) (Å)

Pyrope1001.634 (1)1.885 (1)2.195 (1)2.334 (1)
 2931.634 (1)1.886 (1)2.197 (1)2.340 (1)
 5001.635 (1)1.890 (1)2.202 (1)2.349 (1)
Almandine1001.636 (1)1.888 (1)2.220 (1)2.363 (1)
 2931.635 (1)1.890 (1)2.221 (1)2.371 (1)
 5001.637 (1)1.893 (1)2.225 (1)2.379 (1)
Spessartine1001.639 (1)1.899 (1)2.245 (1)2.399 (1)
 2931.640 (1)1.901 (1)2.246 (1)2.404 (1)
 5001.641 (1)1.902 (1)2.251 (1)2.414 (1)
Grossular1001.646 (1)1.923 (1)2.321 (1)2.483 (1)
 2931.646 (1)1.926 (1)2.322 (1)2.487 (1)
 5501.646 (1)1.929 (1)2.322 (1)2.498 (1)
Table 3.

Linkages of the polyhedra in the garnet structure.

PolyhedronLinkage

tetrahedron4 corners with octahedra
 4 corners with dodecahedra
 2 edges with dodecahedra
octahedron6 corners with tetrahedra
 6 edges with dodecahedra
dodecahedron4 corners with tetrahedra
 2 edges with tetrahedra
 4 edges with octahedra
 4 edges with dodecahedra
PolyhedronLinkage

tetrahedron4 corners with octahedra
 4 corners with dodecahedra
 2 edges with dodecahedra
octahedron6 corners with tetrahedra
 6 edges with dodecahedra
dodecahedron4 corners with tetrahedra
 2 edges with tetrahedra
 4 edges with octahedra
 4 edges with dodecahedra
Fig. 2.

(a) Polyhedral structure model of aluminosilicate garnet. The SiO4 tetrahedra (red) and AlO6 octahedra (blue) are connected over corners and build a three-dimensional quasi-framework. The divalent X-site cations (yellow spheres) are located in the large dodecahedral site. (b) Structural relationship between a single SiO4 tetrahedron and surrounding dodecahedra. There are two edge-shared dodecahedra and four corner-shared dodecahedra. (c) Edge-sharing relationship between neighbouring dodecahedra in the garnet structure. Every dodecahedron shares four edges with other dodecahedra. (d) Structural relationship between an AlO6 octahedron and six surrounding edge-shared dodecahedra.

Fig. 2.

(a) Polyhedral structure model of aluminosilicate garnet. The SiO4 tetrahedra (red) and AlO6 octahedra (blue) are connected over corners and build a three-dimensional quasi-framework. The divalent X-site cations (yellow spheres) are located in the large dodecahedral site. (b) Structural relationship between a single SiO4 tetrahedron and surrounding dodecahedra. There are two edge-shared dodecahedra and four corner-shared dodecahedra. (c) Edge-sharing relationship between neighbouring dodecahedra in the garnet structure. Every dodecahedron shares four edges with other dodecahedra. (d) Structural relationship between an AlO6 octahedron and six surrounding edge-shared dodecahedra.

There are very few high quality high-pressure X-ray single-crystal refinements on aluminosilicate garnets. Hazen & Finger (1989) investigated the compressibility of a natural pyrope-rich crystal, and Zhang et al. (1998) extended considerably the pressures obtainable in high-pressure diffraction measurements (i.e., 33 GPa) in a study of synthetic pyrope. Their results showed that the two Mg–O bond lengths behave quite differently with increasing pressure with relative compressions for Mg–O(4) of 8.03(7)% and for Mg–O(2) of 3.71(7)% at 33 GPa, whereas the Al–O bonds compressed by 3.86(9)% and the Si–O bonds by 1.8(1)%. The AlO6 polyhedron becomes more distorted but the MgO8 and SiO4 polyhedra more regular with increasing pressure. The bulk moduli for the MgO8, AlO6 and SiO4 polyhedra are 107(1), 211(11) and 580(24) GPa, respectively, with K' fixed to a value of 4 (Zhang et al., 1998).

The temperature-dependent structural and atomistic-level dynamic properties of the aluminosilicate garnets were investigated in a series of single-crystal X-ray studies on synthetic almandine, pyrope, spessartine and grossular crystals (Geiger et al., 1992b; Armbruster et al., 1992; Armbruster & Geiger, 1993; Geiger & Armbruster, 1997; see also Pavese et al., 1995 and Rodehorst et al., 2002). Much of the analysis focussed on the temperature-dependent behaviour of the atomic displacement parameters (i.e., Uij), because in the case of ordered end-member garnet, they can be used to describe the dynamic properties of the atoms and polyhedra. The results show that the SiO4 tetrahedron and the AlO6 octahedron can be considered, at least in terms of their diffraction-determined vibrational properties, as rigid bodies between 0 and 500 K. The behaviour of the XO8 dodecahedron is different, because it does not vibrate as a rigid polyhedral body. Unlike the situation for the SiO4 and AlO6 polyhedra, the difference atomic displacement parameters along the bonding vectors between the central X cation and the surrounding oxygen atoms are a function of temperature. It was shown, thereby, that the X cations vibrate in an anisotropic manner with their greatest vibrational displacement in the plane of the longer X–O(4) bonds (Fig. 3). The vibrational amplitudes of the X cations in the different end members are a function of both their mass and size. Mg (amu 24; 0.92 Å – Shannon, 1976) in pyrope has the largest vibrational amplitudes followed by Fe2+ (amu 56; 0.92 Å) in almandine, Mn2+ (amu 55; 0.96 Å) in spessartine and lastly by Ca (amu 40; 1.12 Å) in grossular. The vibrational amplitudes, especially along X–O(4), increase with increasing temperature. Armbruster & Geiger (1993) also calculated the mean-square translational and librational amplitudes of the rigid SiO4 tetrahedra in pyrope and almandine. The three SiO4 translations [T(SiO4)11 = T(SiO4)22 and T(SiO4)33, with T(SiO4)33 parallel to forumla ] have mean-square amplitudes between 0.001 and 0.002 Å2 at 100 K increasing to about 0.003 and 0.004 Å2 at 500 K. The librational amplitudes are greater; those perpendicular to the forumla axis [i.e., L(SiO4)11 = L(SiO4)22] have values of about 3.0–3.5 Å2 at 100 K and 6.5–7.5 Å2 at 500 K. Librations around forumla were not measurable.

Fig. 3.

Atomic vibrational amplitudes for a given XO8 site for different end member garnets as calculated from their difference atomic mean-square displacements between 500/550 and 100 K – from top to bottom, the MgO8 dodecahedron in pyrope, the FeO8 dodecahedron in almandine, the MnO8 dodecahedron in spessartine, and the CaO8 dodecahedron in grossular. The projections are approximately along two-fold axes and the projections in the right-hand column are rotated approximately 90° about the horizontal line of the projections in the left-hand column. The central X cation shows measurable anisotropic vibration (i.e., a “rattling” motion) with the largest amplitudes in the plane of the longer X–O(4) bonds. The eight surrounding oxygen anions have smaller vibrational amplitudes and they are primarily related to rigid SiO4 librations (from Geiger et al., 1992b; Armbruster et al., 1992; Armbruster & Geiger, 1993; Geiger & Armbruster, 1997).

Fig. 3.

Atomic vibrational amplitudes for a given XO8 site for different end member garnets as calculated from their difference atomic mean-square displacements between 500/550 and 100 K – from top to bottom, the MgO8 dodecahedron in pyrope, the FeO8 dodecahedron in almandine, the MnO8 dodecahedron in spessartine, and the CaO8 dodecahedron in grossular. The projections are approximately along two-fold axes and the projections in the right-hand column are rotated approximately 90° about the horizontal line of the projections in the left-hand column. The central X cation shows measurable anisotropic vibration (i.e., a “rattling” motion) with the largest amplitudes in the plane of the longer X–O(4) bonds. The eight surrounding oxygen anions have smaller vibrational amplitudes and they are primarily related to rigid SiO4 librations (from Geiger et al., 1992b; Armbruster et al., 1992; Armbruster & Geiger, 1993; Geiger & Armbruster, 1997).

Garnet solid solutions

There have been several diffraction studies directed towards various synthetic and natural garnet solid solutions (Armbruster et al., 1992; Ganguly et al., 1993; Ungaretti et al., 1995) and they document diffraction-average structural variations, such as bond lengths and angles, polyhedral distortions etc., as a function of composition. Because of the large number of shared polyhedral edges in the garnet structure (Table 3), the substitution of different X cations at the dodecahedral site produces distortion in all polyhedra. This is confirmed by computational studies of rigid unit modes (RUMs), which can be considered as low-energy vibrations that propagate through a structure without causing any distortion of the tetrahedra, for example. They show that a framework-like description (i.e., Fig. 2a) of garnet is not quantitatively correct (Hammonds et al., 1998). In garnet, there are no RUMs and cation substitution on the dodecahedral X site results in distortion of the SiO4 tetrahedra. Local information on both the static crystal chemical and dynamic atomistic properties of solid solutions can only be obtained with difficultly using diffraction methods. Results must be analysed and interpreted with care, because the standard X-ray diffraction experiment involving “Bragg” reflections delivers structural information averaged over thousands of unit cells (Oberti, 2001), and it cannot provide local unit cell or smaller scale structural information. Clearly, local structural information of element-specific properties (e.g. bonds lengths and angles) cannot be obtained (see, however, Geiger & Armbruster, 1999, for an X-ray refinement in which Mg–O and Ca–O bond lengths were determined in a Gr90Py10 crystal). Diffuse scattering studies do offer the potential to provide local information such as short-range order, but such measurements and the associated data analysis are difficult, and little work in this area has been done on silicate or garnet solid solutions.

Along these lines, it is often assumed in mineralogical investigations that a bond length for a given polyhedral site, as determined by diffraction methods, changes monotonically and continuously as a function of composition – across a binary solid solution, for example. This behaviour has been described as the “virtual crystal approximation” (VCA – Martins & Zunger, 1984; Urusov, 2001), and it assumes that there is no local structural relaxation in the solid solution. The VCA represents a mean field model and it is questionable if such a treatment can be used to understand the physical properties of garnet solid solutions (Bosenick et al., 2000; 2001). On the other hand, it is generally accepted that atomic radii remain approximately constant for a given coordination state from structure to structure or over a range of composition (Pauling, 1967; Shannon, 1976). Thus, element-specific bonds should have nearly the same lengths and character in a solid solution as they have in the respective end-member phases. In the case of alloys and semiconductors, this situation has been described as the “state of alternating bonds” (Martins & Zunger, 1984; see also Urusov, 2001) and the bond length can be described as following the “Pauling limit”. The two alternatives are obviously contradictory and relatively little has been done, at least in the field of silicates, in the way of trying to determine which model provides the proper description for solid solutions and to what extent. The situation for the case of the XO8 dodecahedron for a binary aluminosilicate garnet solid solution is shown in Figure 4. Needless to say, a proper bond description is necessary if strain mechanisms and elastic energies in solid solutions are to be described, and macroscopic thermodynamic properties and trace element substitution mechanisms are to be understood (see Geiger, 1999; Bosenick et al., 2001; van Westrenen et al., 2003).

Fig. 4.

The two crystallographically independent (Mg,Ca)–O bond lengths for binary Py-Gr solid solutions. The different dashed lines represent hypothetical Mg–O and Ca–O bond lengths as a function of composition, as they could occur with the “state of alternating bonds” (or in the “Pauling limit”). The solid straight lines represent the case for average (Mg/Ca)–O bonds without local relaxation and define the “virtual crystal approximation”. The data points are from the diffraction study of Ganguly et al. (1993).

Fig. 4.

The two crystallographically independent (Mg,Ca)–O bond lengths for binary Py-Gr solid solutions. The different dashed lines represent hypothetical Mg–O and Ca–O bond lengths as a function of composition, as they could occur with the “state of alternating bonds” (or in the “Pauling limit”). The solid straight lines represent the case for average (Mg/Ca)–O bonds without local relaxation and define the “virtual crystal approximation”. The data points are from the diffraction study of Ganguly et al. (1993).

A final point should be stressed before beginning the review on spectroscopic results. Most garnet crystals in nature are complex solid solutions that contain a number of components and, in addition, they typically have experienced complicated P–T histories. Therefore, subtle structural and crystal-chemical properties or their variations as a function of composition are sometimes not observable in their spectra and, therefore, a quantitative interpretation is not always possible. Thus, much of our understanding of the structural, crystal-chemical and lattice-dynamic properties of garnet is based on results obtained on well-characterised synthetic materials and this point, while elementary, should not be forgotten.

The structure, crystal chemistry and lattice-dynamic properties of garnet as determined from spectroscopic experiments

Spectroscopic results on aluminosilicate garnets will be reviewed and analysed based on the following methods: Raman and IR spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, optical absorption spectroscopy, Mössbauer spectroscopy, electron spin resonance (ESR) spectroscopy, and X-ray absorption (fine structure) spectroscopy (XAS or XAFS). The various methods are characterised by different experimental length scales and compared to the diffraction experiment they are short. Most of the element-specific spectroscopies (e.g. NMR, Mössbauer, ESR, XAFS) deliver chemical and structural information over short length scales, which for the most part are less than about 10 Å around the atom being studied. Those methods involving nuclear transitions (NMR, Mössbauer) have generally the shortest length scales, because they measure variations in the electric field gradient in the vicinity of the nucleus being probed. Those spectroscopies involving electronic transitions or excitations (optical absorption, XAFS) could be expected to have slightly longer characteristic length scales, and XAFS can sometimes be used to obtain information beyond the first or second nearest neighbours. Vibrational spectroscopy has, in contrast to all of the element specific methods, experimental length scales somewhere between those of the nuclear spectroscopies and the long-range diffraction experiment. In addition to local structural and crystal chemical information, some of the spectroscopies can be used to obtain dynamic information of atoms or structural units such as coordination polyhedra. Here, of course, Raman and IR spectroscopy play a central role, but Mössbauer and X-ray absorption spectroscopy can also be used to study the vibrational behaviour of atoms and several results on garnet will be presented. Detailed discussions behind the physics of the different spectroscopic methods themselves will not be made; they can be found in the other chapters of this book.

Vibrational (Raman and IR) spectroscopy

Raman and IR spectroscopy can be used to study the lattice dynamic and crystal chemical properties of garnet. Lattice dynamic information can be linked to bulk thermodynamic properties (e.g. Cp and S) and can be used to understand the response of the garnet structure to variations in temperature and pressure. Vibrational spectra can also give information on local structural properties of solid solutions, for example, which can be related to thermodynamic mixing properties (i.e., ΔHmix and ΔVmix). There have been a number of Raman and IR studies on both natural and synthetic aluminosilicate garnets and the quality of the spectra has improved over the years (see Kolesov & Geiger, 1998, and Geiger, 1998, for a list of references). Some of the more recent results will be discussed here.

Garnet affords a moderately simple vibrational spectrum and mode analysis because of its high symmetry and the different bonding properties associated with the tetrahedral, octahedral and dodecahedral cations. The structure has 20 atoms in the formula unit and the 4 formula units in the primitive unit cell will give rise to 240 total vibrations, three of which will be acoustic modes (i.e., 3n – 3 vibrations, where n is the number of atoms). Group theory analysis is used to determine the number, type and symmetry of the different vibrations (see Fateley et al., 1971, and Sherwood, 1972, for a detailed discussion). It gives the irreducible representation at the Γ point as:  

formula
The gerade A1g, Eg and F2g modes are Raman active for a total of 25 and the 17 ungerade F1u modes are active in the infrared. A lattice dynamic analysis for most silicates, including garnet, generally assumes that SiO4 groups can be treated as rigid quasi-“molecular units” (cf. Hammonds et al., 1998) with internal vibrations occurring at the highest energies. The other “types” of vibrations, often called lattice vibrations, which include translations and librations of the SiO4 tetrahedra and the Al and X cations, occur at relatively low energies and are strongly a function of the local crystal chemical environment.

Raman spectra of garnet end members at ambient conditions and at low temperatures

Polarised single-crystal Raman spectra of end-member or nearly end-member pyrope, almandine, spessartine and grossular are shown in Figure 5. The assignments for the high-energy internal SiO4 modes are known, while those for the modes at the lower energies are a matter of some discussion and herein we present the most recent results (Kolesov & Geiger, 1998, 2000 – see Table 4). Difficulties arise because of kinematic mode coupling and mixing in the low-wavenumber region as is typical for many structures including silicates (Sherwood, 1972; Geiger & Kolesov, 2002). In addition, all 25 predicted Raman-active modes are not observed in the different spectra. The lower wavenumber region contains external SiO4 rotational/librational, R(SiO4), and translational, T(SiO4), vibrations and translations (T) of the X cations. Vibrations associated with the Al cation are not Raman active. The A1g spectra for all end members show three intense, totally symmetric modes around 350 cm–1, 550 cm–1 and 900 cm–1 that are assigned to librational, internal bending and stretching vibrations of the SiO4 tetrahedron, respectively. The wavenumbers of the T(SiO4) vibrations are about 1.5 to 2 times lower than R(SiO4) modes, because they involve all the atoms in the tetrahedral unit, whereas for R(SiO4) vibrations only the oxygen atoms are involved (i.e., the reduced mass is greater for a translation). For most garnets only one intense mode is observed in the Eg spectra at less than 250 cm–1 and it is assigned to a T(SiO4) vibration. Two strong F2g modes are observed at low wavenumbers between 170 cm–1 and 280 cm–1 for all garnets except pyrope. They are assigned to X cation (x,y)-translations. In the case of grossular, for example, the bands at 280 and 247 cm–1 are assigned to Ca(x,y)-translations. The wavenumber difference between these two modes is a result of variations in the force constants acting between Ca and the oxygen atoms in the x–y plane of the dodecahedral site. Weak modes are observed in the Eg spectra at 256 cm–1 in almandine, 269 cm–1 in spessartine, and 320 cm–1 in grossular. They are thought to be X-cation (z)-translations based on their wavenumbers as a function of composition and their placement relative to the R(SiO4) mode of the same Eg symmetry. They occur at higher wavenumbers than the F2gX-cation vibrations because their associated force constants are stronger. Thus, the Raman modes can be described in a general, but not strictly absolute, scheme from high to low energies as: v3 > v1 > v4 > v2 > R(SiO4) > T(X2+ cation) > T(SiO4).

Table 4.

Raman mode assignments for end-member aluminosilicate garnets (from Kolesov & Geiger, 1998).

 PyropeAlmandineSpessartineGrossular
 A1gEgF2gA1gEgF2gA1gEgF2gA1gEgF2g

(Si–O)stretch928 1066916 1038905 1029880 1007
 945902871930897863913*879849904*848827
(si-O)bend563626*650556596630552592*630550592630
  525598 521*581 522573* 529582
  375512 370500 372500 420512
492475475483
R(SiO4)364344383342323350321376373389
353355*350*319*351
322314302333
T(SiO4) 211222 167170 162175 181186
T(X)284#  256216 269221 320280
135171196247
 PyropeAlmandineSpessartineGrossular
 A1gEgF2gA1gEgF2gA1gEgF2gA1gEgF2g

(Si–O)stretch928 1066916 1038905 1029880 1007
 945902871930897863913*879849904*848827
(si-O)bend563626*650556596630552592*630550592630
  525598 521*581 522573* 529582
  375512 370500 372500 420512
492475475483
R(SiO4)364344383342323350321376373389
353355*350*319*351
322314302333
T(SiO4) 211222 167170 162175 181186
T(X)284#  256216 269221 320280
135171196247

# broad and possibly an overtone of the F2g band at 135 cm–1 – see Kolesov & Geiger (2000)

Table 5.

29Si NMR peak assignments for pyrope-grossular garnets (from Bosenick et al., 1995).

Fig. 5.

Polarised single-crystal Raman spectra of the four end-member aluminosilicate garnets (from Kolesov & Geiger, 1998). Note that some spectra have an expanded abscissa.

Fig. 5.

Polarised single-crystal Raman spectra of the four end-member aluminosilicate garnets (from Kolesov & Geiger, 1998). Note that some spectra have an expanded abscissa.

The spectrum of pyrope shows some exceptions to this scheme and it has some unusual features, such as the placement of a broad low-energy F2g mode at about 133 cm–1 at 298 K that has a large T(Mg) character (Fig. 6). Thus, in spite of the lighter mass of Mg compared to that of Ca, Fe2+ or Mn2+ in the other garnets, its F2g vibration occurs at a lower energy than the F2g modes associated with the other three cations. Its assignment is based on its wavenumber shift behaviour following isotopic substitution of 26Mg for 24Mg (Kolesov & Geiger, 1998). This mode softens slightly to 127 cm–1 at 5 K, possibly indicating some dynamic instability (Kolesov & Geiger, 2000) and its line width at 298 K (FWHH = 10 cm–1) is much greater than at 5 K (FWHH = 3.5 cm–1). The interpretation is that the decrease in line width is associated with a damping of high-amplitude Mg vibrations in the plane of the longer Mg–O(4) bonds (Fig. 3). The observed mode softening indicates anharmonic behaviour compared to the other modes that show an increase in wavenumber with decreasing temperature as expected for “normal” mode Grüneisen behaviour (see below – Gillet et al., 1992).

Fig. 6.

Raman A1g + Eg (left) and F2g spectra (right) of pyrope at 5 K and 295 K in the low wavenumber region (from Kolesov & Geiger, 2000). Note the change in line width of the mode around 130 cm–1 at the two different temperatures.

Fig. 6.

Raman A1g + Eg (left) and F2g spectra (right) of pyrope at 5 K and 295 K in the low wavenumber region (from Kolesov & Geiger, 2000). Note the change in line width of the mode around 130 cm–1 at the two different temperatures.

Raman spectra of pyrope and grossular at high pressure and high temperature

Mernagh & Liu (1990) studied the effect of pressure (to a maximum of 14 GPa), using a diamond-anvil cell, on the Raman spectra of pyrope, grossular and almandine, and Olijnyk et al. (1991) studied pyrope and almandine up to about 22 GPa. In the most detailed study to date, Gillet et al. (1992) recorded the Raman spectra of pyrope and grossular as a function of temperature from 300 to 1300 K at 1 atm and as a function of pressure from 1 atm up to 22 GPa at room temperature (Fig. 7). The spectra give no evidence for any phase transitions and all observed modes increase or decrease monotonically in energy with increasing pressure and temperature, respectively, including the lowest wavenumber mode in pyrope. The results show that the modes associated with the internal SiO4 stretching vibrations generally have larger pressure shifts (3 to 4 cm–1/GPa) than the lower energy modes below 650 cm–1 (1 to 3 cm–1/GPa) and an analogous behaviour is also the case for the temperature related shifts (2 to 4·10–2 cm–1/K) versus (1 to 3·10–2 cm–1/K). From these data, the isobaric and isothermal mode Grüneisen parameters at 298 K and 1 bar, respectively, for Py and Gr were calculated using:  

formula
where αo is the coefficient of thermal expansion and KT is the isothermal bulk modulus at ambient P and T. There appears to be a more pronounced difference in the mode wavenumber behaviour between the internal and external modes in pyrope than in grossular (Fig. 8). Gillet et al. (1992) also analysed the mean wavenumber shift versus crystal bulk modulus relationship for a number of different orthosilicates, including garnet, and concluded that their main compression mechanism is through bond shortening with only minor polyhedral tilting. In contrast, framework silicate structures such as quartz, and high-pressure structures such as coesite having corner-linked SiO6 groups, show polyhedral tilting as a result of compression. In the case of garnet, the large number of shared polyhedral edges appears to buttress and stiffen the structure against polyhedral tilting and this is consistent with the absence of rigid unit modes in the structure (Hammonds et al., 1998).

Fig. 7.

Raman-active modes in synthetic pyrope and grossular as a function of temperature (left). Raman-active modes in synthetic pyrope and grossular as a function of pressure (right) (from Gillet et al., 1992).

Fig. 7.

Raman-active modes in synthetic pyrope and grossular as a function of temperature (left). Raman-active modes in synthetic pyrope and grossular as a function of pressure (right) (from Gillet et al., 1992).

Fig. 8.

Variation in the wavenumber behaviour for different modes in synthetic pyrope and grossular as a function of pressure (left) and temperature (right). The wavenumber regions for the internal SiO4 modes and lattice modes are marked (from Gillet et al., 1992).

Fig. 8.

Variation in the wavenumber behaviour for different modes in synthetic pyrope and grossular as a function of pressure (left) and temperature (right). The wavenumber regions for the internal SiO4 modes and lattice modes are marked (from Gillet et al., 1992).

Raman spectra of binary almandine-spessartine and pyrope-grossular solid solutions

Kolesov & Geiger (1998) measured the unpolarised Raman spectra of synthetic almandine-spessartine and pyrope-grossular garnets. The spectra are consistent with symmetry and give no indication of any symmetry lowering due to, for example, long-range cation ordering (cf. Hofmeister & Chopelas, 1991). The first binary is characterised by the mixing of X cations (i.e., Fe2+ and Mn2+) of similar size and mass, while in the second there are marked differences between Mg and Ca. The various modes for Al-Sp garnets shift monotonically as a function of composition across the binary with no major breaks or discontinuities (Fig. 9). This is termed one-mode behaviour (Sherwood, 1972), as first discussed in the case of garnet by Hofmeister & Chopelas (1991). The situation is different for Py-Gr garnets, because here two-mode behaviour for the T(Ca) and T(Mg) vibrations appears to be well developed. Here, the individual F2g T(X) modes, for example, cannot be followed completely across the binary (Fig. 10), reflecting differences in mass between Mg and Ca and also in their bonding properties. A rigorous interpretation of the vibrational spectra of solid solutions is not always a simple matter. The solid solution process leads to a breaking of long-range translational symmetry and standard group theory analysis may not apply in many cases.

Fig. 9.

Wavenumber behaviour of selected Raman-active modes for synthetic almandine-spessartine solid solutions (from Kolesov & Geiger, 1998).

Fig. 9.

Wavenumber behaviour of selected Raman-active modes for synthetic almandine-spessartine solid solutions (from Kolesov & Geiger, 1998).

Fig. 10.

Wavenumber behaviour of selected Raman-active modes for synthetic pyrope-grossular solid solutions (from Kolesov & Geiger, 1998).

Fig. 10.

Wavenumber behaviour of selected Raman-active modes for synthetic pyrope-grossular solid solutions (from Kolesov & Geiger, 1998).

Infrared spectra of garnet end members at ambient conditions

Single-crystal IR reflectance measurements have been made on natural nearly end-member pyrope, almandine, spessartine and grossular (Hofmeister & Chopelas, 1991; McAloon & Hofmesiter, 1995; Hofmeister et al., 1996), and powder transmission IR spectra of natural and synthetic end-member garnets have been recorded a number of times (see Geiger, 1998, for a list of references). The IR bands in powder spectra are a combination of transverse (TO) and longitudinal (LO) optic modes and this can result in a shifting of the TO component towards the LO component; this is most pronounced for intense bands in the MIR region. Thus, phonon energies derived from single-crystal reflectance measurements are more exact and the spectra of pyrope, almandine and grossular are shown, together with the calculated absorption spectra, in Figure 11 (Hofmeister, pers. commun.). 17 bands are observed in the spectra of almandine and grossular and 16 for pyrope. The energy placement of the various types of F1u modes is similar to analogous modes observed in the Raman spectra. The internal v1 and v3 stretching vibrations of the SiO4 tetrahedra are located between 800 and 1100 cm–1 and are separated from the v2 and v4 bending vibrations located between 400 and 650 cm–1. The external vibrations of the SiO4 tetrahedra [(T(SiO4) and R(SiO4)] and the translations of the X cations are located at lower wavenumbers. In contrast to Raman activity in garnet, IR active modes include Al vibrations, which lie between 240 and 500 cm–1 (Hofmeister & Chopelas, 1991; Hofmeister et al., 1996). Because all IR modes have the same symmetry, mode coupling is present (Cahay et al., 1981; Geiger, 1998), whereas coupling should, in general, be less pronounced between Raman-active modes of different symmetry.

Fig. 11.

Single-crystal IR reflectance spectra of natural nearly end-member garnets: (a) pyrope, (b) almandine and (c) grossular as shown at the top of each figure. The dielectric functions are shown in the middle and the resulting normalised absorption spectra are observed at the bottom of each figure (from Hofmeister, pers. commun.).

Fig. 11.

Single-crystal IR reflectance spectra of natural nearly end-member garnets: (a) pyrope, (b) almandine and (c) grossular as shown at the top of each figure. The dielectric functions are shown in the middle and the resulting normalised absorption spectra are observed at the bottom of each figure (from Hofmeister, pers. commun.).

Infrared spectra at elevated pressures and temperatures

Dietrich & Arndt (1982) made some of the earliest MIR powder transmission measurements on garnet at non-ambient conditions in an externally heated diamond anvil cell. Since this time, little further work has been done. They studied a natural garnet of composition Py41Al45Gr13 up to pressures of 5 GPa and at 25, 100 and 250 °C. As with the Raman-active modes, the IR modes increase linearly in wavenumber with increasing pressure and decrease with increasing temperature. Dietrich & Arndt (1982) undertook, in addition, first-order model lattice dynamic calculations in order to interpret the bulk compressibility behaviour of the garnet structure. From an analysis of their microscopic mode Grüneisen parameters, they concluded that vibrations of the rigid SiO4 groups make only a small contribution to the macroscopic Grüneisen parameter. Their relative contribution to garnet's elastic properties should be small in comparison to the lower wavenumber R(SiO4), T(SiO4), T(Al) and T(X) vibrations.

Infrared spectra of binary solid solutions

The powder transmission IR spectra of both natural and synthetic garnet solid solutions have been recorded many times (see Geiger, 1998, and Boffa Ballaran et al., 1999, for references). There have also been single-crystal IR reflectance measurements made on a series of natural Al-Py-rich garnets (Hofmeister et al., 1996). Only some of the more recent powder measurements will be reviewed, with an emphasis on the phonon systematics (i.e., wavenumber behaviour and band broadening) as a function of composition for synthetic garnets along a given binary join and their relation to macroscopic thermodynamic mixing properties.

Geiger et al. (1989) measured the powder MIR spectra of synthetic Al-Py and Al-Gr garnets and analysed the relationship between MIR phonon energies and macroscopic volume of mixing, ΔVmix, behaviour for both joins. The spectra show that the wavenumber shifts for all modes across the Al-Py join are linear, whereas for the Al-Gr join a mode near 400 cm–1 showed small, but measurable positive asymmetric deviations from linear behaviour (Fig. 12). The Al-Py binary is characterised by ideal volumes of mixing, ΔVmix = 0, while the Al-Gr join shows positive, ΔVmix > 0, asymmetric deviations with greater non-ideality at grossular-rich compositions (Geiger, 1999). Thus, the volume of mixing behaviour is reflected in the wavenumber systematics of certain vibrational modes and this study established a direct link between microscopic and macroscopic properties in garnet.

Fig. 12.

Variation in the wavenumber for an IR mode located between 375 cm–1 and 400 cm–1 for different composition Al-Gr solid solutions shown as short vertical lines, with the straight dash-dot line connecting the two end members (above). The excess molar volume of mixing for this binary is shown as a dotted line (below). Note the similarities in the positive asymmetric deviations from linear behaviour for both (from Geiger et al., 1989).

Fig. 12.

Variation in the wavenumber for an IR mode located between 375 cm–1 and 400 cm–1 for different composition Al-Gr solid solutions shown as short vertical lines, with the straight dash-dot line connecting the two end members (above). The excess molar volume of mixing for this binary is shown as a dotted line (below). Note the similarities in the positive asymmetric deviations from linear behaviour for both (from Geiger et al., 1989).

Geiger (1998) undertook a systematic powder transmission IR study of all six binaries in the four-component aluminosilicate garnet system (Fig. 1) in an attempt to assign the different modes, following upon the work of Hofmeister & Chopelas (1991) and Hofmeister et al. (1996), to further investigate “microscopic-macroscopic” relationships. No additional modes or splitting of bands, which would indicate a reduction of the symmetry from forumla; resulting from long-range X-cation ordering, were observed. The task of assigning modes for solid solution compositions is complicated because mode coupling is present, marked two-mode behaviour occurs in a number of the joins (Py-Gr, Al-Gr, Py-Sp) and not all 17 bands are observed for all compositions. Two-mode behaviour is restricted to the lower energy modes and especially those with strong X-cation vibrational character. The spectra of Al-Sp garnets show, in contrast, one-mode behaviour as in their Raman spectra. Non-linear behaviour in the factor group splitting (defined by the wavenumber value of the term [B – (C + D)/2] that is based on three internal SiO4 modes – see Geiger, 1998, for a labelling of the bands), which is a function of vibrational coupling between isolated SiO4 groups (Moore et al., 1971; Omori, 1971), was observed for the Al-Gr and Py-Gr binaries. For the other binaries, linear behaviour for the factor group splitting was observed. Finally, in the case of Py-Gr, and possibly Al-Gr garnets, it was noted that the lowest energy modes with measurable T(X) character in intermediate compositions decreased in wavenumber (or “softened”) relative to their energies in the end-member compositions. The interpretation is that the vibration behaviour of Mg/Fe and Ca varies as a function of composition across these joins such that the vibrational amplitudes of Mg and Fe increase with increasing Ca content in the garnet. Such behaviour could provide an explanation for the low-temperature excess heat capacities of mixing in Py-Gr garnet solid solutions (Geiger, 1998).

Boffa Ballaran et al. (1999) undertook a detailed IR powder study on three binaries of synthetic Al-Py, Al-Gr and Py-Gr garnets in order to investigate local structural heterogeneities over different length scales and their relationship to the macroscopic thermodynamic mixing properties. The idea is, basically, that phonons of different energies are associated with different length scales and, thus, IR spectra can be used to characterise the range of local structural heterogeneities occurring in a substitutional solid solution. Boffa Ballaran et al. (1999) propose length scales of ∼ 2–5 Å at 1500 cm–1, ∼ 6–25 Å at 500 cm–1 and ∼ 60–150 Å at 50 cm–1. The spectra show non-linear variations in the wavenumber behaviour for some modes of Al-Gr and Py-Gr garnets, while those for Al-Py garnets showed linear behaviour. The magnitude of the deviations from linear behaviour for certain internal SiO4 modes could be correlated with the magnitude of the excess volumes of mixing for the respective binaries. Boffa Ballaran et al. (1999) also undertook for the first time a quantitative analysis of the line widths of the absorption bands occurring in three different wavenumber regions (i.e., 1200–780 cm–1, 680–280 cm–1 and 275–50 cm–1). Line broadening in vibrational spectra results from local structural and chemical heterogeneities arising from the solid solution process and it has been observed in a variety of structure types (e.g. Chang et al., 1966). The challenge is to measure it quantitatively and to interpret the underlying physical cause. Using the autocorrelation function, Boffa Ballaran et al. (1999) measured the line broadening and showed that the greatest range of distortion or structural heterogeneity occurs in Py-Gr garnets followed by Al-Gr and then Al-Py (Fig. 13). In other words, Py-Gr garnets are the most heterogeneous on a local scale and Al-Py the least. Furthermore, a correlation between the enthalpy of mixing behaviour, ΔHmix, measured previously by calorimetry, and the line broadening behaviour was noted, at least for Py-Gr garnets (Fig. 14). This supports the proposal that local elastic strain energies resulting from structural heterogeneity generate macroscopic positive enthalpies of mixing. Thus, the mode systematics observed in powder IR spectra (i.e., phonon energies and line broadening) can provide information on macroscopic thermodynamic behaviour and, perhaps in some cases, can serve as a quantitative measure for it.

Fig. 13.

Variation in Δcorr values (which are a measure of band width) in cm–1 for the wavenumber region between 280 and 680 cm–1 (above) and the wavenumber region between 780 and 1200 cm-1 (below) as a function of composition for synthetic Py-Al (open triangles), Al-Gr (open squares) and Py-Gr solid solutions (open circles). The garnet end member with the largest X cation for the respective binary is plotted on the right hand side (from Boffa Ballaran et al., 1999).

Fig. 13.

Variation in Δcorr values (which are a measure of band width) in cm–1 for the wavenumber region between 280 and 680 cm–1 (above) and the wavenumber region between 780 and 1200 cm-1 (below) as a function of composition for synthetic Py-Al (open triangles), Al-Gr (open squares) and Py-Gr solid solutions (open circles). The garnet end member with the largest X cation for the respective binary is plotted on the right hand side (from Boffa Ballaran et al., 1999).

Fig. 14.

Comparison plots of the calorimetrically determined enthalpies of mixing (ΔHmix) for synthetic Py-Gr garnets, where end-member Py is on the left and Gr on the right side of the composition axis (above; data shown as solid diamonds – Newton et al., 1977), and Al-Gr solid solution garnets, where end-member Al is on the left and Gr on the right of the composition axis (below; data shown as solid inverted triangles – Geiger et al., 1987) and those calculated (solid curves) from a determination of the band broadening (i.e., Δcorr) measured in the IR powder spectra from both solid solutions (from Boffa Ballaran et al., 1999).

Fig. 14.

Comparison plots of the calorimetrically determined enthalpies of mixing (ΔHmix) for synthetic Py-Gr garnets, where end-member Py is on the left and Gr on the right side of the composition axis (above; data shown as solid diamonds – Newton et al., 1977), and Al-Gr solid solution garnets, where end-member Al is on the left and Gr on the right of the composition axis (below; data shown as solid inverted triangles – Geiger et al., 1987) and those calculated (solid curves) from a determination of the band broadening (i.e., Δcorr) measured in the IR powder spectra from both solid solutions (from Boffa Ballaran et al., 1999).

Finally, Boffa Ballaran et al. (1999) undertook low-temperature far-infrared (FIR) measurements on the end members Al, Py and Gr, and FIR and mid-infrared measurements on the solid solution Py60Gr40. In the case of the end members, the lowest energy mode for Py softened slightly with decreasing temperature, while those for Gr and Al either did not change or increased in energy slightly. In the case of Py60Gr40, there was marked softening of the lowest energy mode with decreasing temperature and this was interpreted as possibly indicating an incipient phase transition.

MAS NMR spectroscopy

There have been few MAS NMR measurements on aluminosilicate garnets, because investigations have to be largely restricted to synthetic samples that do not contain paramagnetic ions. The electric field gradient around the Si nucleus is sensitive to small changes in local environment and thus 29Si NMR measurements can be used to obtain information on the nature of local structural and electronic properties such as, for example, the possible occurrence of short-range order in garnet solid solutions. The latter will be discussed for a series of pyrope-grossular garnets.

29Si NMR spectra of pyrope and grossular

Synthetic pyrope and grossular do not contain paramagnetic ions and they can be studied by 29Si MAS NMR spectroscopy. Their spectra are shown in Figure 15 (Geiger et al., 1990; 1992). Both are characterised by a single narrow resonance line that is located at –72.1 ppm for pyrope and –83.9 ppm for grossular. The spectra are simple to interpret. The structural relationship between an SiO4 tetrahedron and surrounding dodecahedra and octahedra is given in Table 3. In the case of pyrope, each SiO4 tetrahedron is surrounded by two edge- and four corner-sharing dodecahedra that are occupied by Mg and in the case of grossular by Ca. In both garnets Al occupies the octahedra. Thus, the structural and electronic environment around every 29Si atom, for which in space group there is only one crystallographic site, in each end member is identical: only a single NMR resonance results. The Si chemical shift is more negative in grossular because Ca has 20 electrons, while Mg has 12. Thus, the shielding is greater in grossular.

Fig. 15.

29Si MAS NMR spectrum of synthetic pyrope (above) and grossular (below). (from Geiger et al., 1990, 1992a.)

Fig. 15.

29Si MAS NMR spectrum of synthetic pyrope (above) and grossular (below). (from Geiger et al., 1990, 1992a.)

29Si NMR spectra of pyrope-grossular solid solutions

A series of synthetic intermediate Py-Gr solid solutions were synthesised at high temperatures and pressures in a piston-cylinder device, quenched to ambient conditions and studied by 29Si MAS NMR spectroscopy. Their spectra at 298 K are shown in Figure 16 (Bosenick et al., 1995). All the crystals were cubic in symmetry as determined by optical and X-ray measurements. The spectra are considerably different in appearance than those of the two end members because of the various possible local environments around the 29Si nuclei in the solid-solution crystals. The different resonances reflect the different local Ca and Mg cation configurations around each Si atom and can be explained as follows: In the case where the electric field gradient around Si would only be sensitive to first-shell dodecahedral cation interactions in opposite edge-sharing dodecahedra (Fig. 2b), the spectra of the various solid solutions would show no more than three resonances. That is, one resonance corresponding to the cation configuration Mg-Si-Mg at –72.1 ppm as observed in pyrope, one resonance at –83.9 ppm corresponding to Ca–Si–Ca as in grossular and one resonance between –72.1 and –83.9 ppm corresponding to the mixed configuration Mg–Si–Ca. However, many more resonances, up to 13 different ones, are observed and thus the four corner-sharing dodecahedra must come into play. A statistical analysis shows that there are 3 · 5 = 15 unique and possible local first- and second-shell dodecahedral cation configurations around a tetrahedral site. The statistical probability for any given configuration is a function of the garnet bulk composition so that, for example, the configuration CaCa–CaCaCaCa (the first two cations describe the first-shell configuration and the second set of four cations describes the second shell) becomes more likely with increasing grossular content in the garnet and vice versa for the MgMg–MgMgMgMg configuration. Bosenick et al. (1995) give general formulae for calculating the theoretical probabilities for the 15 configurations assuming a random distribution of Ca and Mg cations. The important point is that 29Si NMR spectroscopy is quantitative in the sense that the intensities of the experimental resonances are proportional to the number or concentrations of each of the different local cation configurations in the crystal. Thus, the calculated probabilities, which describe a statistical random cation arrangement, can be compared to the experimentally measured intensities of the different resonances after each of them has been assigned to a given configuration (Table 5 – see Bosenick et al., 1995, for a discussion of the resonance assignments). Thereby, the type and degree of short-range cation ordering can be determined. The measured spectra (Fig. 16) indicate a small degree of local cation order for solid solutions with compositions between 0.15 < XCa < 0.75. Pyrope-rich compositions show, for example, a greater preference for the MgMg–MgMgMgMg configuration compared to that given by a random distribution of Mg and Ca cations, and analogously there is a greater preference for the CaCa–CaCaCaCa configuration in grossular-rich compositions.

Fig. 16.

29Si MAS NMR spectra of synthetic Py-Gr solid solutions: (a) pyrope-rich garnets, (b) grossular-rich garnets and (c) intermediate pyrope-grossular garnets (from Bosenick et al., 1995).

Fig. 16.

29Si MAS NMR spectra of synthetic Py-Gr solid solutions: (a) pyrope-rich garnets, (b) grossular-rich garnets and (c) intermediate pyrope-grossular garnets (from Bosenick et al., 1995).

It is well known that cation order/disorder is normally temperature dependent; this aspect was studied by further NMR measurements on Py-Gr garnets by Bosenick et al. (1999). Here, pyrope-rich garnets of composition Py85Gr15 and Py75Gr25 were synthesised at three different temperatures (1000, 1200 and 1400 °C) and 3 GPa and quenched to ambient conditions, and their 29Si MAS NMR spectra recorded. An analysis of the spectra showed no change in the cation ordering state for Py85Gr15, but small spectral variations between the different Py75Gr25 samples were observed, such that the higher the synthesis temperature, the greater the Ca-Mg disorder. From the experimentally determined ordering states, the configurational entropy of mixing, Sconf, was calculated. The maximum reduction compared to the completely disordered state was calculated to be 2 J/mol·K or less. Bosenick et al. (2000) undertook static lattice energy calculations and Monte Carlo simulations on the pyrope-grossular system in order to investigate the energetics of the ordering process and to test the experimentally determined NMR-based cluster occupancies. The calculations show that short-range Ca-Mg ordering in garnet is, indeed, energetically favourable and that it should increase with decreasing temperature, and it is most pronounced for garnets near the 50:50 composition.

Optical absorption spectroscopy

There have been many optical absorption measurements made on natural and synthetic aluminosilicate garnets and their solid solutions at ambient conditions and also at different pressures and temperatures (White & Moore, 1972; Frentrup & Langer, 1982; Smith & Langer, 1983; Burns, 1993; Geiger & Rossman, 1994; Geiger et al., 2000; Taran et al., 2002; Khomenko et al., 2002 and references therein). Absorption can occur in the NIR/VIS/UV regions and arises from electronic excitations of various transition metal cations and through charge transfer processes. Spectra give information on the site location of the various cations (both major and minor elements), the nature of the electronic bonding, colour and also on crystal field stabilisation energies (Wildner et al., 2004, in this volume). High pressure and temperature measurements can give information on local site behaviour under different physical conditions. Some of the more important studies will be summarised below.

Optical absorption spectra of almandine, almandine-rich garnet and spessartine

The spectrum of synthetic end-member almandine is characterised by three broad partially overlapping bands located in the NIR at about 4200, 5700 and 7600 cm–1 (Smith & Langer, 1983; Geiger & Rossman, 1994). The optical absorption spectra of natural almandine-rich garnet solid solutions are similar in appearance. Spectra of a natural crystal of composition Al77Py18Gr5, for example, as a function of temperature from 78 to 489 K, are shown in Figure 17 (White & Moore, 1972). Three broad bands, corresponding to the wavenumbers 4300, 5900 and 7700 cm–1, can be observed and they vary only slightly over this temperature range. They correspond to transitions to three upper t2g electronic levels from the ground state of Fe2+ (Fig. 18). The assignments for the transitions can be obtained using semi-empirical point-charge models or from quantum mechanical simulations (Newman et al., 1978; Geiger et al., 2003). They can also be rationalised using basic crystal chemical considerations. In the case of the garnet structure, the triangular dodecahedron can be considered as being derived by “twisting the upper and lower faces of a cube in opposite directions from above and below”. Consider that the z axis is perpendicular to these two opposite cube faces and that it bisects their centre and, further, the x and y axes intersect the edges at the sides of the cube. In this situation, of the five Fe2+ d orbitals (see Wildner et al., 2004, in this volume), the dxy orbital and the dz2 orbital will suffer the least repulsion from the oxygen ligands, because they point to faces of the “distorted cube”, and since the cube is compressed along the pseudo-four-fold z axis, the dxy orbital will be destabilised relative to the dz2 orbital. There is also a rhombohedral distortion that gives rise to compression along the x axis and an elongation along the y axis. Thus, the dyz orbital is stabilised and the dxz orbital is destabilised relative to the dx2–y2 orbitals that point to the edges of the cube. The relative orbital splittings shown in Figure 18 are obtained. A lower energy band related to the eg level transition is not observed in experimental spectra, because it occurs in the wavenumber region where the more intense lattice vibrations (see above) of garnet are present and is hidden by them.

Fig. 17.

Single-crystal optical absorption spectrum of a natural garnet of composition Al77Py18Gr5 between 490 and 78 K (from White & Moore, 1972) showing the three t2g transitions in the NIR region.

Fig. 17.

Single-crystal optical absorption spectrum of a natural garnet of composition Al77Py18Gr5 between 490 and 78 K (from White & Moore, 1972) showing the three t2g transitions in the NIR region.

Fig. 18.

Schematic representation of the 3d electronic energy levels in the case of: (a) a free spherical field, (b) a field of a perfect cube and (c) for Fe2+ in the dodecahedral site in garnet. Δc (i.e. 10Dq) is the crystal field splitting. The approximate separations of the d energy levels with respect to the ground state for Fe2+ in the dodecahedral site of symmetry D2 in almandine are shown at the far right (from Geiger & Rossman, 1994).

Fig. 18.

Schematic representation of the 3d electronic energy levels in the case of: (a) a free spherical field, (b) a field of a perfect cube and (c) for Fe2+ in the dodecahedral site in garnet. Δc (i.e. 10Dq) is the crystal field splitting. The approximate separations of the d energy levels with respect to the ground state for Fe2+ in the dodecahedral site of symmetry D2 in almandine are shown at the far right (from Geiger & Rossman, 1994).

Khomenko et al. (2002) investigated charge transfer phenomena occurring in the UV region in both natural and synthetic almandine crystals. The placement of an intense ligand-metal charge transfer band located in the UV region, whose low-energy wing extends into the visible region (Fig. 19), is known to play a role in determining the colour of garnet. They argued that in the case of almandine-rich garnets small concentrations of Fe3+ and/or Ti4+ located on the octahedral site allowed intervalence charge transfer with Fe2+ at the dodecahedral site, which in turn intensifies and shifts the low-energy wing of the ligand-metal charge transfer band into the VIS region. Variations in the colour of natural almandine crystals, which can be red, orange-red, pinkish or violet, are thought to be a function of these electronic interactions.

Fig. 19.

Single-crystal optical absorption spectrum of synthetic almandine in the NIR/VIS/UV regions at different pressures showing two spin-allowed Fe2+ d-d bands (the lowest wavenumber d-d band in the NIR and was not recorded), a number of weak spin-forbidden bands and the low-energy wing of an intense Fe2+–O charge transfer band in the UV region (from Smith & Langer, 1983).

Fig. 19.

Single-crystal optical absorption spectrum of synthetic almandine in the NIR/VIS/UV regions at different pressures showing two spin-allowed Fe2+ d-d bands (the lowest wavenumber d-d band in the NIR and was not recorded), a number of weak spin-forbidden bands and the low-energy wing of an intense Fe2+–O charge transfer band in the UV region (from Smith & Langer, 1983).

Mn2+ in spessartine has five d electrons with one occurring in each of the five different d orbitals. The spin-multiplicity selection rule of optical absorption spectroscopy states that the total number of unpaired electrons in an atom must remain the same before and after an electronic transition occurs and, thus, spin-allowed electronic transitions in spessartine should not be possible. It turns out, however, that such electronic transitions do in fact occur, but with very low probability and they are termed spin-forbidden transitions. They are observed as weak absorption bands in the visible energy region (Fig. 20). Their assignment to specific d-level transitions is not a simple matter, but it has been attempted several times. A summary and analysis of results is given in Smith & Langer (1983). The occurrence and the energy of Mn2+ spin-forbidden bands is of interest, because they can give information on the degree of covalency of the Mn–O bonding through a determination of the semi-empirical Racah B parameter (see Burns, 1993; Wildner et al., 2004). Spin-forbidden bands also occur, of course, in other transition metal containing garnets. Theoretical-based work discussing the assignments of the spin-forbidden bands relating to Fe2+ in almandine (see Fig. 19) is given in Kang-Wei & Sang-Bo (1984).

Fig. 20.

Single-crystal optical absorption spectrum of synthetic spessartine in the NIR/VIS/UV regions at different pressures showing spin-forbidden bands (from Smith & Langer, 1983).

Fig. 20.

Single-crystal optical absorption spectrum of synthetic spessartine in the NIR/VIS/UV regions at different pressures showing spin-forbidden bands (from Smith & Langer, 1983).

High-pressure optical absorption spectra of almandine and spessartine

High-pressure optical absorption measurements on synthetic almandine (Fig. 19Smith & Langer, 1983) up to about 10 GPa at 300 K show that the spin-allowed electronic absorption bands shift systematically to higher energies (Table 6) with increasing pressure and give no indication of any phase change. The crystal field splitting (Δ or 10Dq) and CFSE values for Fe2+ increase with increasing pressure and their values are given in Table 7. One can derive from crystal field theory the relationship:  

formula
where R1–atm is the mean Fe–O bond length at 1 atmosphere and RP the corresponding length at a given pressure. The 1 – atm value can be obtained from crystal structure refinements, and using Equation 3 one obtains the RP values shown in Table 7. They show that the mean

Fe2+–O distance in almandine decreases by 3.3% from 1 atm to 10 GPa (Smith & Langer, 1983). These workers also calculated from their spectra the mean linear compressibility:  

formula
and the bulk modulus for the dodecahedral site as KT(dodec) = 1235 ± 250 kbar.

Smith & Langer (1983) also measured the spectrum of synthetic spessartine to 11.2 GPa in order to investigate the nature of Mn2+–O bonding (Fig. 20). This can be done by determining the pressure variations of the spin-forbidden bands and by calculating the Racah B parameter. The bands decrease in energy with increasing pressure (Table 8) and the value of B decreases from 817 cm–1 at (1 – atm) to 813 cm–1 at 5.6 GPa and finally to 810 cm–1 at 11.2 GPa. This indicates a small increase in Mn–O bond covalency with increasing pressure (Smith & Langer, 1983).

Table 6.

Wavenumbers of spin-forbidden and spin-allowed bands (*) for synthetic almandine as a function of pressure (from Smith & Langer, 1983; Frentrup & Langer, 1982, for values in parentheses).

Band1 atm5.1 GPa10.1 GPaPressure shift (cm−1/kbar)

127,20027,20027,100−1.0
2(24,900)
323,20023,70024,100+9.0
422,80023,000
521,800?21,80021,600−2.0?
6(20,900)21,000??
719,90019,80019,700−2.0
819,10019,00019,000−1.0?
917,60017,30017,000−6.0
1016,20015,80015,600−6.0
1114,40014,10013,900−5.0
12*7,6007,8008,200+6.0
13*5,8006,1006,700+9.0
Band1 atm5.1 GPa10.1 GPaPressure shift (cm−1/kbar)

127,20027,20027,100−1.0
2(24,900)
323,20023,70024,100+9.0
422,80023,000
521,800?21,80021,600−2.0?
6(20,900)21,000??
719,90019,80019,700−2.0
819,10019,00019,000−1.0?
917,60017,30017,000−6.0
1016,20015,80015,600−6.0
1114,40014,10013,900−5.0
12*7,6007,8008,200+6.0
13*5,8006,1006,700+9.0
Table 7.

Selected properties for synthetic almandine garnet determined by optical absorption spectroscopy as a function of pressure (from Smith & Langer, 1983).

Property1 atm5.4 GPa10.1 GPa

10Dq (cm−1)5,3805,7066,352
CFSE-Fe2+ (cm−1)3,7803,9444,270
Fe−O (Å)2.3002.2732.225
Property1 atm5.4 GPa10.1 GPa

10Dq (cm−1)5,3805,7066,352
CFSE-Fe2+ (cm−1)3,7803,9444,270
Fe−O (Å)2.3002.2732.225

Optical absorption spectra of almandine-pyrope/spessartine solid solutions

The NIR spectra of a series of natural almandine-pyrope and almandine-spessartine garnets were recorded by Geiger & Rossman (1994) in order to investigate average dodecahedral FeO8 site properties and the CFSE's for Fe2+ in both binaries. Spectra from both solid solutions show three broad spin-allowed bands located between 4,000 and 10,000 cm–1. Their energies vary as function of the garnet bulk composition because of small variations in the average Fe2+–O bond lengths and the geometry of the FeO8 site. White & Moore (1972) proposed earlier that variations in the energies of the t2g orbitals give information on how the FeO8 dodecahedron is distorted. The dxz and dyz orbitals provide the best measure of this, because they are the orbitals most directed towards the oxygen ligands located at the corners of the dodecahedron. Differences in their energies, as a function of composition along the Al-Py and Al-Sp binaries, are shown in Figure 21 and suggest that the greater the difference in energy, the greater is the distortion of a FeO8 dodecahedron. Thus, FeO8 distortion should decrease slightly with increasing Py content and increase with increasing Sp content in garnet. A quantitative measure of this distortion in terms of bond lengths or angles, for example, does not exist.

Fig. 21.

Difference in energy between the highest energy electronic transition 5B2 level and the lower 5B3 level for Fe2+ in Py-Al and Sp-Al solid solutions (from Geiger & Rossman, 1994).

Fig. 21.

Difference in energy between the highest energy electronic transition 5B2 level and the lower 5B3 level for Fe2+ in Py-Al and Sp-Al solid solutions (from Geiger & Rossman, 1994).

The spectra also allow a calculation of the CFSE for Fe2+ in the two solid solutions. CFSE's contribute to the total energetics of a system and in the case of an isostructural solid solution they could play an important role in affecting the macroscopic enthalpy of mixing, ΔHmix, behaviour (Geiger & Rossman, 1994). Burns (1993) discussed how CFSE's enter into the ΔHmix, and showed that the latter cannot be ideal, i.e. ΔHmix = 0, in the case where the CFSE changes as a function of composition across, for example, a solid solution binary. This is the case for both Al-Py and Al-Sp garnets (Fig. 22). The excess ΔCFSE's are negative for both binaries and less so for Al-Sp garnets than for Al-Py solid solutions. Because they are negative, they should act to stabilise both solid solutions against positive ΔHmix arising from elastic strain effects, which are typically positive in nature (see Fig. 14).

Fig. 22.

Excess CFSEs of Fe2+ for the two binary solid solutions Py-Al and Sp-Al. The lines represent a least-squares best-fit symmetric mixing model to the two different data sets (from Geiger & Rossman, 1994).

Fig. 22.

Excess CFSEs of Fe2+ for the two binary solid solutions Py-Al and Sp-Al. The lines represent a least-squares best-fit symmetric mixing model to the two different data sets (from Geiger & Rossman, 1994).

Optical absorption spectra of pyrope containing minor concentrations of transition metals

Geiger et al. (2000) measured the optical absorption spectra of different synthetic pyrope crystals containing small concentrations of Ni, Co, Cr, Ti and V. Taran et al. (2002) investigated the effects of pressure and temperature on a number of the same garnets. A goal of the first study was to determine the site occupation for the different cations based on the crystal field spectra and also their oxidation states. This is something that is not easy to do with analytical results as obtained from the electron microprobe, for example. The spectra show that Ni2+ and Co2+ are located on the X site and Cr3+ on the octahedral Y site, as expected based on results from previous studies on natural crystals (Burns, 1993), whose spectra are very similar in appearance. The spectrum of Ti-containing pyrope was featureless thereby indicating that most of the Ti was in the oxidation state +4. Ti4+ has no d electrons and will not have any spin-allowed electronic transitions (this sample is discussed further below in the section on ESR spectroscopy with regard to the question of Ti3+). The spectrum of a V-containing pyrope was complicated and indicated that octahedral V3+ was present, as well as tetrahedral and/or octahedral V4+. Taran et al. (2002) proposed that V4+ was tetrahedrally coordinated. Their spectra recorded up to 600 K at 1 atm and to 8 GPa at room temperature permit a determination of the element specific polyhedral expansions and compressions, as well as the nature of spin-orbit coupling for the case of Co2+.

Mössbauer spectroscopy

There have been many Mössbauer studies undertaken on aluminosilicate garnets, both synthetic and natural, most of which are analytical in nature, whereby the Fe2+/Fe3+ ratio for dodecahedral/octahedral iron was recorded. Here, we will focus on those few studies that are directed towards the crystal chemical (e.g. electronic and magnetic) and lattice dynamic properties of almandine and almandine-bearing solid solutions.

All studies to date have been powder measurements and spectra have been recorded at different pressure and temperature conditions. Theoretical calculations have also been done to help interpret the spectroscopic results. Discussions on the theory behind and terms associated with Mössbauer spectroscopy can be found in Amthauer et al. (2004) in this volume.

57Fe Mössbauer spectrum of almandine at 1 atm and as a function of temperature

57Fe Mössbauer spectra of synthetic end-member almandine and natural almandine-rich garnet solid solutions have been recorded a number of times (Lyubutin & Dodokin, 1971; Prandl & Wagner, 1971; Murad & Wagner, 1987; Evans & Sergent, 1975; Amthauer et al., 1976; Geiger et al., 1992b; Geiger et al., 2003). The spectrum of synthetic end-member almandine from 10.0 to 9.2 K is shown in Figure 23. The paramagnetic spectrum at T > 10 K is characterised by a single quadrupole split doublet originating from Fe2+ in the dodecahedral site. The large isomer shift value of δ ≈ 1.30 mm/s at 298 K has been interpreted as indicating a high degree of ionic bonding (Evans & Sergent, 1975; Amthauer et al., 1976). The quadrupole splitting, ΔEQ, of about 3.5–3.6 mm/s is very large and one of the highest reported for ferrous iron in crystalline oxides or silicates. The spectrum of almandine at elevated temperatures was measured by Lyubutin & Dodokin (1971) and it shows a decrease in both δ and ΔEQ with increasing temperature. The temperature behaviour of δ is due entirely to the relativistic part, δrel (see Amthauer et al., 2004). The Debye temperature for Fe2+ on the dodecahedral site was calculated as forumla = 340 K versus values of 400 K and 550 K for Fe3+ on the octahedral and tetrahedral sites, respectively. This is partly a function of a decrease in bonding strength with increasing coordination. Prandl & Wagner (1971) determined the sign of the electric quadrupole coupling tensor and proposed that VZZ is negative with η = 0.13. Thus, the low-energy line of almandine's spectrum corresponds to the m = ±1/2 → m = ±3/2 transition and the high-energy line to m = ±1/2 → m = ±1/2, as also shown by Amthauer et al. (1976). Murad & Wagner (1987) measured the spectrum of synthetic almandine at low temperatures with an emphasis on investigating the magnetic transition. They showed that magnetic order begins gradually between 10.4 and 9.6 K with about 50% of the crystal being magnetically ordered at 9.6 K (Fig. 23). At 4.2 K, the spectrum is complex and can be fitted by two eight-line magnetic hyperfine patterns that have equal intensities. Murad & Wagner (1987) proposed that the two pattern spectra was probably a result of the existence of two different polar angles (73 and 90°) between the z axis of the electric field gradient tensor and the direction of the magnetic hyperfine field, and that it was not a result of static subsite disorder of Fe2+ (i.e., Fe2+ residing in slightly different structural sites).

Fig. 23.

57Fe Mössbauer spectra of synthetic almandine from 10.0 to 9.2 K showing the onset of magnetic ordering (from Murad & Wagner, 1987).

Fig. 23.

57Fe Mössbauer spectra of synthetic almandine from 10.0 to 9.2 K showing the onset of magnetic ordering (from Murad & Wagner, 1987).

One noticeable feature of the paramagnetic spectrum of almandine is the slightly asymmetric quadrupole split doublet. The physical reason behind this has been a matter of some discussion (see Amthauer et al., 1976; Murad & Wagner, 1987; Geiger et al., 1992b). Normally for most crystalline phases the two lines of a Fe2+ doublet have the same area, but in the case of almandine the high-velocity line is slightly more intense and has a slightly narrower half width compared to the low-velocity line. Doublet asymmetry can arise through a preferred orientation of the particles in a powder measurement, through magnetic relaxation and also through an effect known as anisotropic recoil-free fraction or the Gol'danskii-Karyagin effect (Murad & Wagner, 1987; Geiger et al., 1992b). For almandine the texture effect can be ruled out, because it has poor cleavage and, moreover, its spectrum recorded where the absorber is fixed at an angle of 54° 44' with respect to the incident gamma ray shows no difference compared to that measured perpendicular to the incident radiation. Magnetic relaxation (Amthauer et al., 1976) is also unlikely to play an important role, because the doublet asymmetry does not increase with decreasing temperature, and it is not a function of garnet composition (see below). This leaves the possibility of anisotropic recoil-free fraction as investigated by Geiger et al. (1992). Here, the physical nature of atomic vibrations of Fe2+ must be considered. It can be shown using quantum mechanics that the probability of recoilless emission or absorption, f, is a function of the Debye-Waller factor:  

formula
where k is the wave vector of the radiation and forumla is the mean square vibrational amplitude of the atom (in diffraction studies normally given as forumla. As temperature increases, so does the vibrational amplitude of an atom, here 57Fe2+, and this leads to a decrease in the recoil-free fraction. When there is vibrational anisotropy of the Mössbauer nucleus, there can be directional anisotropy in the recoil-free fraction that can be expressed as:  
formula
where forumla and forumla are the mean square vibrational amplitudes perpendicular and parallel to the symmetry axis, and θ is the angle between the symmetry axis and the direction of propagation of the γ radiation, and this affects the nuclear transition probabilities. In the case where f(θ), the intensity ratio, Rq, of the two Fe2+ lines is given by the transition probabilities:  
formula
where θq is the angle between the K vector of the incident gamma rays and the principal axis of the electric field gradient. The ratio of the transitions can be expressed as the difference between the mean square of the vibrational amplitudes of Fe2+:  
formula
In almandine, the temperature-dependent single-crystal X-ray measurements show that Fe2+ vibrates in a distinctly anisotropic manner (Fig. 3) and thus Rq is not unity. From X-ray measurements at 293 K (Geiger et al., 1992b), the values of forumla and forumla are 0.0074 Å and 0.0026 Å, respectively, and one calculates a value of = 1.035. If one fits the areas of the two resonance lines of the spectra, one obtains a value of = 1.037, which is in good agreement with the X-ray value. The vibrational amplitudes of Fe2+ are, of course, temperature dependent and the same calculation can be made at any temperature where experimental data are available. This was done and it was shown that Rq decreases with decreasing temperature, as expected.

High-pressure 57Fe Mössbauer spectrum of almandine

Huggins (1976) studied the effect of pressure on Fe–O bonding in a natural almandine-rich garnet by undertaking a Mössbauer study using a diamond anvil cell. The results show that the δ values decrease slightly with increasing pressure from 1.31 mm/s at 1 atm, to 1.25 mm/s at 5.5 GPa, to 1.24 mm/s at 10.0 GPa and 15.0 GPa. This general behaviour is observed in other Fe2+-containing silicates and oxides and can be interpreted as indicating an increase in 3s-electron density at the nucleus with increasing pressure resulting from increased delocalisation of the 3d electrons towards the neighbouring oxygen atoms (Huggins, 1976). This is equivalent to an increase in the covalency of the Fe2+–O bonds resulting from increased overlap of the 3d and oxygen electron orbitals upon compression. Increased sharing of the 3d electrons results in less shielding of the 3s electrons at the Fe2+ nucleus and a decrease in the isomer shift value.

57Fe Mössbauer spectra of binary almandine-pyrope/spessartine/grossular solid solutions

Geiger et al. (2003) measured the Mössbauer spectra of three binary synthetic aluminosilicate garnet solid solutions, almandine-pyrope, almandine-spessartine and almandine-grossular at 77 and 298 K. Spectra at 77 K are shown in Figure 24. Systematic measurements over a range of garnet compositions, together with accompanying electronic structure calculations, were made to address three main issues: (i) average Fe–O bonding properties and X-site distortion and (ii) average Fe2+ vibrational behaviour as a function of garnet composition, and also (iii) the question of short-range cation ordering. They are considered in order.

Fig. 24.

57Fe Mössbauer spectra recorded at 77 K for selected intermediate garnet compositions for the three binary synthetic solid solutions Al-Py, Al-Sp and Al-Gr (from Geiger et al., 2003).

Fig. 24.

57Fe Mössbauer spectra recorded at 77 K for selected intermediate garnet compositions for the three binary synthetic solid solutions Al-Py, Al-Sp and Al-Gr (from Geiger et al., 2003).

With regards to Fe–O bonding, the δ values recorded for all solid solution compositions are remarkably constant with δ= 1.27 (± 0.01) mm/s and 1.41 (± 0.01) mm/s at 298 K and 77 K, respectively. This result indicates that the bonding of Fe2+ with its surrounding oxygen ligands does not measurably change as a function of garnet bulk composition. This supports the view that the local FeO8 dodecahedral sites do not increase or decrease significantly in size as a function of the molar volume of garnet and that Fe–O bond lengths should remain approximately constant. The electronic structure calculations show that the covalent part of the Fe–O bond is almost exclusively determined by the 4sp orbitals, and that its contribution is almost an order of magnitude greater than that associated with the 3d electrons. This important result puts into the question the use of crystal field theory for describing quantitatively the electronic properties of Fe2+ in garnet. CFT is a model that only describes d-orbital interactions with ligands that are treated as simple point charges. The quantum mechanical calculations also show that although the covalent bonding component contributes a relatively small fraction to the total Fe–O bond its effect on the EFG around Fe2+ is marked.

The spectra of the different compositions show measurable variations in their Fe2+ doublet asymmetry. For example, the spectra of Al-Gr solid solutions show a relatively symmetric doublet, while the doublet measured for Al-Sp garnets shows an increase in asymmetry with increasing spessartine content (Fig. 24). As in the case of end-member almandine, the high-velocity line is slightly narrower and more intense than the low-velocity line. The nature of doublet asymmetry could be related to variations in Fe2+ vibrational behaviour (i.e., recoil-free fraction) as a function of garnet bulk composition. However an analysis shows that no significant variations in the vibrational behaviour of Fe2+ is expected, because the observed doublet asymmetries can not be reconciled with the known crystal chemical properties of garnet. For example, the molar volume of almandine-bearing solid solutions increases measurably with the incorporation of a grossular component, and this expansion could possibly lead to an increase in the volume of the local FeO8 dodecahedra (VCA-like behaviour). This should lead to an increase in the vibrational amplitude of Fe2+ along Fe–O(4) and thus greater anisotropic recoil-free fraction. However, the experimental data are not consistent with these predictions, because doublet asymmetry does not vary greatly along the Al–Gr binary. The spectroscopic data indicate, once again, that local FeO8 dodecahedra retain approximately the same size and geometry in the different solid solutions. Variations in doublet asymmetry should have another physical cause.

Mössbauer spectroscopy can, in principle, because it is a local and element specific spectroscopy analogous to 29Si NMR spectroscopy, be used to investigate the issue of short-range cation order in almandine-containing solid solutions. The question is whether the EFG around Fe2+ is sufficiently sensitive to local structural modifications caused by variations in surrounding next nearest neighbour X-site configurations (Fig. 2c). Five different local dodecahedral configurations around a Fe2+ cation are possible. For example, in Al-Gr garnets they are Ca-Ca-Ca-Ca, Fe-Ca-Ca-Ca, Fe-Fe-Ca-Ca, Fe-Fe-Fe-Ca, and Fe-Fe-Fe-Fe. In theory, each configuration should be characterised by its own quadrupole doublet, if each central 57Fe atom would be affected in an analogous manner as the 29Si atoms in NMR measurements of Py-Gr garnets. The Mössbauer spectra show that this clearly is not the case (Fig. 24). Moreover, the line widths of the single doublets for the three different garnet solid solutions are, in general, not significantly broadened (0.24–0.30 mm/s for the most part) compared to the values observed in end-member almandine (0.24–0.27 mm/s). The EFG around Fe2+ is simply not sensitive to variations in surrounding local cation configurations and the related structural distortions. Mössbauer spectroscopy is unsuitable for characterising short-range order in garnet. The physical reason is given by the nature of the dodecahedral site and revealed by the electronic structure calculations (Geiger et al., 2003). Fe–O bonds are long (Table 2) and this leads to negligible covalence and ligand contributions to the electric field gradient and, therefore, 3d shell anisotropy is only weakly affected by structural modifications from or beyond the first nearest neighbour oxygen atoms.

Electron spin resonance spectroscopy

There have been very few ESR measurements made on garnet and even less single crystal studies. One reason for this lies in the high concentration of paramagnetic ions occurring in most natural crystals. We review here a single crystal ESR study on a synthetic Ti-containing pyrope crystal previously studied by optical absorption spectroscopy (Geiger et al., 2000). Discussions on the principles of ESR spectroscopy can be found in Calas (1988).

Electron spin resonance spectrum of Ti3+ in pyrope

The common oxidation state of Ti in natural silicates is as Ti4+, but there are reports where Ti3+ has been found (see Burns, 1993). There have been several mineralogical investigations made on natural Ca-rich titanium-containing garnets in which Ti3+ has been inferred. In synthetic garnets Ti3+ was proposed to have been found in Ti-andradite and Ti-pyrope (see Rager et al., 2003, for a list of references). In most of these studies, the presence of Ti3+ was based on indirect arguments, because the oxidation state of Ti was inferred indirectly from chemical analysis and stoichiometric considerations for the garnet in question. Thus, the conclusions are problematic, because in natural Ca-rich garnets other transition metal cations such as Fe and Mn can be present and, moreover, they can occur in different oxidation states. Furthermore, the presence of OH groups, Fe3+ substituting for Si, and cations with the oxidation state +4 on the Y site makes the assumption of strict garnet stoichiometry problematic (i.e., 8 cations and 12 oxygens in the formula unit).

Rager et al. (2003) addressed the question of Ti3+ in a well-characterised synthetic pyrope of approximate composition Mg3.01(2)Al1.93(2)Ti0.04(1)Si3.00(2)O12 using single crystal ESR spectroscopy. Previous optical absorption measurements showed that most of the Ti is present as Ti4+, because no d-d absorption bands were observed in the NIR/VIS/UV spectrum. Microprobe analysis indicated that most Ti should be on the octahedral site. The 16a sites in the unit cell of garnet are magnetically equivalent in twos because of the inversion centre (Table 1). Therefore, in the case of Ti3+ with one d electron, eight ESR transitions are to be expected with an arbitrary orientation of B0 with respect to the crystal axes. The eight signals will degenerate further, if the crystal is oriented in a magnetic field. With the forumla axis perpendicular to B0 a maximum of four signals will appear (Fig. 25), where each represents four crystallographically equivalent octahedral sites. They are magnetically equivalent and not discernible in ESR, because there exists at least one symmetry operation in forumla that transforms B0 in all four sites without changing its orientation. Of the four magnetically independent sites, one resonance must be angular independent, whereas the other three should exhibit an angular dependence that is repeated every 60° as shown in Figure 26. The ESR angular dependence is described by the spin Hamiltonian, B = βεB0gS, with S = 1/2. The calculated values are shown in Figure 26, and they match the experimental data well. Thus, Rager et al. (2003) concluded that Ti3+ is present in the synthetic pyrope and it is located only on the octahedral site. Its concentration cannot be quantified in the absence of standards, but it must be very low considering that the single-crystal optical spectroscopic measurements did not reveal any absorption bands (Geiger et al., 2000). This observation illustrates well the sensitivity differences between the two spectroscopic methods.

Fig. 25.

Single-crystal ESR spectrum of Ti3+ in synthetic pyrope recorded with forumla perpendicular to B (from Rager et al., 2003).

Fig. 25.

Single-crystal ESR spectrum of Ti3+ in synthetic pyrope recorded with forumla perpendicular to B (from Rager et al., 2003).

Fig. 26.

Experimental (open squares) and fitted (crosses) magnetic resonance fields for the four observed Ti3+ EPR signals upon rotation around the forumla axis (from Rager et al., 2003).

Fig. 26.

Experimental (open squares) and fitted (crosses) magnetic resonance fields for the four observed Ti3+ EPR signals upon rotation around the forumla axis (from Rager et al., 2003).

X-ray absorption spectroscopy

Most XAFS measurements on garnet, which are few, are relatively recent (i.e., since 1990). Some of the earlier interpretations are thus rather exploratory in nature, as compared to the other spectroscopic methods. There are several reports on natural and synthetic aluminosilicate garnet end members and solid solutions on both major and minor elements. Local structural as well as dynamic information has been obtained. Discussions on “X-ray Absorption Near Edge Structure” (XANES) and “Extended X-ray Absorption Fine Structure” (EXAFS) measurements can be found in Mottana (2004) and in Galoisy (2004) in this volume.

X-ray absorption spectra of almandine, pyrope, spessartine and grossular and their solid solutions: The major elements Fe, Mn, Ca and Al

Quartieri et al. (1993) undertook XAFS measurements at the Fe K edge on four natural Py-Al-Gr solid solutions (Fig. 27) and performed XANES and EXAFS analyses. This study was followed by measurements on synthetic end-member almandine at a series of temperatures between 20 and 473 K (Quartieri et al., 1997). The most recent investigation of Quartieri and co-workers considered a series of synthetic almandine-spessartine garnets, which were studied at the Fe and Mn K edges between 77 and 473 K (Sani et al., in press). In the first study, the oxidation state of Fe2+ in garnet was confirmed along with its polyhedral coordination. The average Fe–O bond lengths were also measured. In the second study on end-member almandine, the Debye-Waller factors (given as σ) and Fe–O bond lengths as a function of temperature were determined (Table 9). Fe–O(4) bond lengths and the associated Debye-Waller factors increase measurably with increasing temperature, while the Fe–O(2) bonds and associated Debye-Waller factors have a smaller temperature dependence. Thus, once again, the anisotropic vibrational behaviour for Fe2+ in almandine is confirmed. (It should be noted that the Debye-Waller factor derived from XAFS measurements is different from that obtained from X-ray diffraction. In XAFS measurements, the Debye-Waller factor describes the mean square relative displacement between absorbing and backscattering atoms. In the diffraction experiment, the absolute mean square displacement of an atom along a bond direction is obtained – see Sani et al., in press, for further discussion.) The vibrational energies for the two Fe–O(2) and Fe–O(4) bonds, calculated using a simple Einstein model, are 437 cm–1 and 207 cm–1, respectively, and they agree roughly with those determined by Raman spectroscopy.

Table 8.

Wavenumbers of spin-forbidden bands of Mn2+ in synthetic spessartine as a function of pressure (from Smith & Langer, 1983).

Band1 atm5.6 GPa11.2 GPaPressure shift (cm−1/kbar)

124,50024,40018,900-1.8
224,30024,20024,300−4.5
323,75023,50023,800-5.8
423,20023,00023,100-7.1
521,60021,60022,400−0.9
620,80020,80021,5000
719,00020,80019,600-
Band1 atm5.6 GPa11.2 GPaPressure shift (cm−1/kbar)

124,50024,40018,900-1.8
224,30024,20024,300−4.5
323,75023,50023,800-5.8
423,20023,00023,100-7.1
521,60021,60022,400−0.9
620,80020,80021,5000
719,00020,80019,600-
Table 9.

Debye-Waller factors and Fe−O bond lengths determined from XAFS measurements on synthetic almandine (Quartieri et al., 1997).

T(K)σ2Fe-O(2)2)σ2Fe-O(4)2)RFe-O(2) (Å)RFe-O(4) (Å)

200.008(1)0.011(2)2.211(7)2.340(12)
770.008(1)0.011(2)2.213(7)2.347(10)
1000.008(1)0.011(2)2.210(8)2.350(12)
2000.008(1)0.015(2)2.216(7)2.354(13)
3000.008(1)0.017(3)2.216(7)2.352(15)
3730.009(1)0.023(4)2.219(8)2.348(21)
4730.011(2)0.026(4)2.216(8)2.366(26)
T(K)σ2Fe-O(2)2)σ2Fe-O(4)2)RFe-O(2) (Å)RFe-O(4) (Å)

200.008(1)0.011(2)2.211(7)2.340(12)
770.008(1)0.011(2)2.213(7)2.347(10)
1000.008(1)0.011(2)2.210(8)2.350(12)
2000.008(1)0.015(2)2.216(7)2.354(13)
3000.008(1)0.017(3)2.216(7)2.352(15)
3730.009(1)0.023(4)2.219(8)2.348(21)
4730.011(2)0.026(4)2.216(8)2.366(26)
Fig. 27.

Experimental XANES spectra at the Fe K edge for three natural almandine-containing garnets (MP 18, MP 17, MP 12) and a Fe3+-containing garnet (bric) and hematite (Fe2O3). The individual spectra were normalised with respect to the high-energy side of the curve (from Quartieri et al., 1993).

Fig. 27.

Experimental XANES spectra at the Fe K edge for three natural almandine-containing garnets (MP 18, MP 17, MP 12) and a Fe3+-containing garnet (bric) and hematite (Fe2O3). The individual spectra were normalised with respect to the high-energy side of the curve (from Quartieri et al., 1993).

In terms of solid solutions and local dodecahedral bonding behaviour, Quartieri et al. (1993) proposed that the average local FeO8 site geometry does not vary greatly as a function of the Ca content in garnet, although this was not quantified. Sani et al. (in press) did quantify this aspect in their study of Al-Sp garnets in which they determined Fe/Mn–O(2) and Fe/Mn–O(4) bond lengths, which are approximately independent, i.e. remained constant in length, of garnet composition (Fig. 28). Moreover, the Debye-Waller factors associated with both Fe and Mn, corresponding to the two crystallographic X–O bonds, also do not vary as a function of garnet composition. These results are consistent with the proposal that the “state of alternating bonds” (or the Pauling limit) provides a better description for X–O bond lengths in garnet solid solutions than the “virtual crystal approximation”.

Fig. 28.

The two crystallographically independent Fe–O and Mn–O bond lengths, shown as different dashed lines, for synthetic Al-Sp garnet compositions determined from XAS measurements made at 77 K (Sani et al., in press). The data, where the squares are average Fe–O and the circles average Mn–O bond lengths, were fitted by a linear least-squares procedure and the resulting bond lengths were extrapolated to the end-member compositions. The solid lines represent VCA behaviour.

Fig. 28.

The two crystallographically independent Fe–O and Mn–O bond lengths, shown as different dashed lines, for synthetic Al-Sp garnet compositions determined from XAS measurements made at 77 K (Sani et al., in press). The data, where the squares are average Fe–O and the circles average Mn–O bond lengths, were fitted by a linear least-squares procedure and the resulting bond lengths were extrapolated to the end-member compositions. The solid lines represent VCA behaviour.

Quartieri et al. (1995) undertook XANES measurements on a series of natural garnet solid solutions in the system Py-Al-Gr at the Ca K-edge, along with model simulations, in order to investigate the local structural environment around the Ca dodecahedra. The experimental spectra and simulations are shown in Figure 29. It was concluded that small spectral variations between different garnet compositions are largely related to differences in the ligand-shell geometries around Ca, and that they do not depend on the type of nearest neighbour X-site cation in edge-sharing dodecahedra (Fig. 2c). It was proposed further, however, that, unlike the situation with FeO8 dodecahedra, the structural properties of the CaO8 dodecahedra vary as a function of garnet bulk composition, but this was not quantified in terms of bond lengths etc. and thus the exact crystal chemical situation is difficult to evaluate.

Fig. 29.

Experimental XANES spectra at the Ca K edge for six natural grossular-containing garnets. The grossular contents decrease from top to bottom from 2.90 to 0.24 Ca cations in the formula unit. The individual spectra were normalised with respect to the high-energy side of the curve (left). Simulated XANES spectra for the different garnet samples (right – from Quartieri et al., 1995).

Fig. 29.

Experimental XANES spectra at the Ca K edge for six natural grossular-containing garnets. The grossular contents decrease from top to bottom from 2.90 to 0.24 Ca cations in the formula unit. The individual spectra were normalised with respect to the high-energy side of the curve (left). Simulated XANES spectra for the different garnet samples (right – from Quartieri et al., 1995).

Wu et al. (1996) measured XANES spectra of four aluminosilicate garnets at the Al K-edge (Fig. 30). The lowest energy peak A varies measurably as a function of garnet composition and Wu et al. (1996) considered that this is related to the electronic configuration of the X-site cations in surrounding edge-sharing dodecahedra (Fig. 2d).

Fig. 30.

Experimental XANES spectra at the Al K edge for grossular, spessartine, almandine and pyrope (left) and their simulated spectra (right) from Wu et al., (1996).

Fig. 30.

Experimental XANES spectra at the Al K edge for grossular, spessartine, almandine and pyrope (left) and their simulated spectra (right) from Wu et al., (1996).

This peak reflects transitions towards empty 3p electronic states of Al mixed with empty states of the X cation. Peak B was attributed to transitions from the 1s orbital to unoccupied p-like states. Peak C arises from intershell multiple scattering in the second coordination shell, namely from the Si and X cations. Peak D is related to single-scattering events from oxygen in the first-coordination shell. These assignments followed from simulations using multiple-scattering calculations using clusters containing a minimum of 40 atoms. Wu et al. (1996) concluded that it was necessary to include atoms located outside of the first coordination sphere around Al in order to correctly simulate the experimental spectra. For grossular, for example, a 49-atom cluster with 36 O + 6 Si + 6 Ca atoms is required to match the experimental spectra. Thus, they concluded that electronic core transitions in Al are not just affected by its immediate nearest neighbours, but also by so-called “long-range” structural and electronic effects.

X-ray absorption spectra of pyrope and grossular: The minor element Yb3+

XAFS is an excellent experimental method for investigating the incorporation of and the local structural environment around minor or trace elements in crystals. Quartieri et al. (1999) addressed this issue with respect to the rare earth element Yb3+ in synthetic garnets. The rare earth elements play an important role in many geochemical and petrological studies, but not much is known about their crystal chemical behaviour in silicates and garnet is no exception. For example, there has been debate on the nature of Henry's law behaviour for trace elements. Discussion has centred on the question of how or where trace elements are located, for example, in defects or in crystallographic sites. In order to address this issue, XANES spectra of synthetic pyrope and grossular containing about 1 wt% Yb3+ were recorded at the LI and LIII edges at temperatures between 77 and 343 K (Fig. 31). An analysis of the data showed that Yb3+ is incorporated in the dodecahedral site in both garnets. A determination of the Yb–O(2) and Yb–O(4) bond lengths showed that structural relaxation occurs around Yb3+ in both host structures, and that their lengths are different from the Ca–O bond lengths in the host grossular structure and the Mg–O bonds in the host pyrope structure. They are also different from the Yb–O bond lengths in the synthetic garnet Yb3Al5O12. The presence of a trivalent cation on the X site in aluminosilicate garnet must result in nonstoichiometry and there are several possible substitutional mechanisms that could allow the incorporation of rare earth elements. Quartieri et al. (1999) concluded that a mechanism involving one-third dodecahedral vacancies, i.e., VIII2[Yb3+] + VIII■ = VIII3[Ca2+/Mg2+], is most consistent with the experimental data.

Fig. 31.

Experimental XANES spectra recorded at 77 K of Yb-containing grossular, Yb-containing pyrope and Yb2O3 at the (a) LI edge and the (b) LIII edge (from Quartieri et al., 1999).

Fig. 31.

Experimental XANES spectra recorded at 77 K of Yb-containing grossular, Yb-containing pyrope and Yb2O3 at the (a) LI edge and the (b) LIII edge (from Quartieri et al., 1999).

Discussion and analysis

The different spectroscopic investigations give a very wide range of results relating to the structural, crystal chemical and lattice dynamic properties of aluminosilicate garnet and their behaviour under different pressure and temperature conditions. When viewed separately, the different types of experimental spectra and the information they provide may seem to have little in common with diffraction results or even with each other. However, the various spectroscopic results can be analysed and integrated to produce a synthesis, and thereby a more complete “picture” of the aluminosilicate garnets begins to emerge. One can state that the different spectroscopic investigations taken individually are often rather narrow in scope and give limited information on physical and chemical properties. However, on the other hand, the information they deliver is often detailed and quantitative. A goal of this work is to present a state-of-the-art review and a comprehensive “picture” of the aluminosilicate garnets and in this section the four main issues given in the introduction will be addressed with an attempt to integrate the various results discussed above.

X-site cation order/disorder in solid solutions

The traditional assumption that the X cations in garnet are randomly distributed over the dodecahedral sites needs to be rethought. The 29Si MAS NMR spectra of synthetic pyrope-grossular solid solutions synthesised at high temperatures (> 1000 °C) indicate small degrees of short-range Ca and Mg order in the more intermediate compositions. A slight preference for Ca-rich clusters, above that expected based upon a random statistical cation distribution, appears to be energetically favoured in more grossular-rich compositions and Mg-rich clusters in more pyrope-rich compositions, for example. NMR spectroscopy is a powerful tool for addressing the question of short-range order, because in the case of garnet the experimental spectra give a direct measure of the type and concentration of different local Ca and Mg configurations. It provides information that cannot be obtained by standard X-ray diffraction measurements or other spectroscopies and, in addition, no model-dependent calculations are required to fit and interpret the spectra. For garnet, 29Si MAS NMR spectroscopy appears to be unique and unrivalled among the different spectroscopies in this regard. Its limitation is that measurements are not possible on garnets containing paramagnetic cations (i.e., Fe2+ and Mn2+). Thus, the question of short-range X-site cation order/disorder in, for example, natural almandine-bearing garnets that crystallise at relatively low temperatures (500 to 900 °C) remains unanswered. Other spectroscopies must be used to address the question of short-range order (SRO) in almandine- and spessartine-containing solid solutions, but the experimental problem is very difficult to address. 57Fe Mössbauer spectroscopy appears unsuitable for this question, because of the nature of the garnet structure. The electric field gradient around Fe2+ in garnet is not measurably modified by structural or chemical variations beyond the oxygen ligands of the dodecahedron. Hard mode Raman and IR spectroscopy, with a focus on a precise determination of line widths, could, in theory, be able to discern relative variations in structural state resulting from SRO. However, it is not possible to extract quantitative information on the type of configurations or their concentrations directly from the spectra, only relative variations in structural heterogeneity resulting from clustering. It is unlikely that this situation will change with more careful experimental measurements, because a main problem lies in simulating quantitatively phonon spectra. Quantitative simulations of the lattice dynamic properties of garnet, and especially of solid solution compositions, appear years away from realisation. At this point in time, it seems that XAFS measurements may offer the best possibility to investigate further the question of SRO in garnet. Specifically, measurements on the Al K edge indicate that next nearest neighbour X-site cations influence the nature of the spectra and, here, further work could be done looking at different solid solution compositions. Once again, a major challenge will be in undertaking quantitative simulations to fit and interpret the experimental XAFS data. It also remains to be seen if the method has the necessary resolution for this problem.

An important issue related to SRO concerns the substitution behaviour of cations in silicate solid solutions. In an attempt to explain the asymmetric excess volume of mixing behaviour observed in a number of binary silicate solid solutions, Newton & Wood (1980) constructed a simple crystal chemical model to explain substitution mechanisms and microscopic strain behaviour. They proposed, in general, that when large cations at small concentrations replace smaller cations in their host structure that strong local structural distortion occurs in the vicinity of the substitutional site. This gives rise to “forbidden zones” close to the larger cations and thus the further incorporation of large cations is precluded (i.e., “anti-clustering” is predicted). In the case of Py-Gr garnets this would mean that the occurrence of neighbouring Ca cations in edge-sharing dodecahedra in a pyrope-rich host (i.e., formation of Ca-rich clusters) would be energetically unfavourable. This prediction appears to be partly at odds with experimental NMR data and also with static energy simulations on Py-Gr garnets (Bosenick et al., 2000), the later of which that show that there is no energetic barrier against certain types of clustering. An alternative crystal chemical model describing atomic substitution behaviour is that the incorporation of large Ca cations tends to “open up” or dilate the garnet structure locally in the vicinity of the substitution, so that the further substitution of large Ca cations in the vicinity would be energetically favourable. Such a mechanism would lead, of course, to cation clustering. Investigating the crystal chemical behaviour and the nature of SRO is not only of interest and important for thermodynamic reasons, but also for understanding, for example, the nature of trace element substitution in silicates. With the present level of knowledge, however, this issue is not fully understood. More experimental study, especially element-specific spectroscopic measurements (29Si NMR and XAFS, for example), is required to describe atomic level substitutional mechanisms and order-disorder behaviour in garnet solid solutions.

Lattice dynamic properties

A description and understanding of the lattice dynamic properties of the various end-member garnets have improved greatly over the last 15 years. The standard picture has evolved rapidly from a static structure, based on a “ball and stick” or polyhedral model, to one that considers the vibrations of atoms and polyhedral units. Important results have been obtained from both diffraction and spectroscopic studies, and they can be compared and contrasted. The X-ray diffraction results on the four aluminosilicate garnet end members as a function of temperature show that the SiO4 tetrahedra and AlO6 octahedra vibrate as rigid bodies below at least 500 K, whereas the XO8 dodecahedra do not. The X-site cations have marked anisotropic amplitudes of vibration that are a function of their mass and size (Fig. 3). The amplitude of vibration increases with increasing temperature mostly in the plane of the longer X–O(4) bonds. The translational and librational amplitudes of vibration of the rigid SiO4 tetrahedra were also determined by diffraction measurements.

Vibrational spectroscopy gives, in contrast, information on the energy of the different vibrations. Here, of course, the SiO4 groups cannot be described as strictly rigid because their internal bending and stretching energies can be measured, as well as external SiO4 librations and translations. Translations of the Al and X cations can also be determined. There are measurable differences between the force constants associated with the different X cations in the different garnet end members. 57Fe Mössbauer spectroscopy and XAFS measurements can give information on atomic vibrations through a determination of their respective Debye-Waller factors. The results show that Fe2+ and Mn2+ in almandine and spessartine, respectively, vibrate in an anisotropic manner and their amplitudes of vibration along X–O(4) increase with increasing temperature. Raman spectra of pyrope support a similar behaviour for the case of Mg, where the temperature dependence of the line width of a low-energy mode reflects the amplitude of vibration of Mg in the Mg–O(4) plane. A slight softening of this same mode indicates that there is dynamic instability associated with the Mg vibration. Considering all the various results, it should be stated once again (e.g. Geiger, 1999) that there is no direct experimental evidence to date, either diffraction- or spectroscopy-based, for static sub-site X-cation disorder within the dodecahedral site in end-member garnet despite repeated proposals for it in the literature. This issue is not strictly of purely crystal chemical interest alone, because the nature of the X-cation vibrations affects garnet's thermodynamic properties (Geiger, 1999; Geiger & Kolesov, 2002). The question of X-cation behaviour provides an excellent example of how diffraction and spectroscopic measurements can be used together to address a crystal-chemical problem. Various experimental results show that a problem can be “approached from different directions” and that a consistent physical description can be obtained.

Other lattice dynamic properties of garnet, as revealed by their Raman and IR spectra, are now understood relatively well. The mode assignments for spectra of the different end members are known, with some small uncertainties. The relative energy placement of atomic and internal and external polyhedral vibrations can be largely understood using simple crystal chemical considerations. The degree and extent of mode mixing and coupling must be determined more fully. Here, there is a need for further IR and Raman measurements on synthetic garnets that have been isotopically enriched in a given element. Raman spectra recorded at high pressure and temperatures are also fairly well understood. The aluminosilicate garnet structure appears stable to high pressures and temperatures and shows no phase transitions. The results show that the SiO4 tetrahedra are relatively insensitive against compression and expansion as a function of pressure and temperature, respectively, compared to the dodecahedral site. This finding is in good agreement with temperature- and pressure-dependent single-crystal X-ray studies. There is a need for different low temperature spectroscopic studies that can give additional lattice dynamic information. Here, the vibrational behaviour of the X cations is of special interest, as is a description of the magnetic behaviour (i.e., magnons) for the case of Fe2+ in almandine and for Mn2+ in spessartine.

A determination of the vibrational behaviour of various X-site cations in garnet solid solution compositions is a much more difficult problem to address, but recent work indicates that this question can be tackled experimentally. Such study is important, if a quantitative understanding of the lattice dynamic (i.e., thermodynamic) properties of solid solutions is to be obtained. Of the different spectroscopic methods, Mössbauer and Raman or IR spectroscopy do not appear to be suitable to address this issue. Mössbauer spectroscopy can give, in principle, a measure of the vibrational amplitudes of Fe2+, but in the case of garnet other factors (i.e., subtle nearest neighbour effects) also come into play and make such a determination difficult. Phonon spectra can show line broadening related to the vibrational behaviour of the X cations, but this is difficult to quantify on an absolute basis. Moreover, it is a complicated matter to strictly separate line broadening related to dynamic effects from that arising from structural heterogeneity in solid solutions. It is concluded that XAFS measurements provide the best opportunity to quantify element specific atomic vibrations in solid solutions. The XAS Debye-Waller factors for Fe2+ and Mn2+, for example, have been determined in a series of Al-Sp garnet solid solutions. They retain constant values in both the X–O(2) and X–O(4) planes as a function of garnet composition, which is consistent with one-mode phonon behaviour for low-energy vibrations with a strong Fe/Mn character, as is observed in IR and Raman spectra. XAFS measurements are needed on the Mg and Ca absorption edges for a series of Py-Gr garnets in order to quantify their vibrational behaviour. Phonons with a strong Mg or Ca character show two-mode behaviour for Py-Gr garnets, which is consistent with the strong difference in both size and mass between these two cations. A determination of the vibrational properties of Mg and Ca is of interest because Py-Gr garnets have large excess heat capacities at low temperature. Static lattice energy calculations on Py-Gr garnets (Bosenick et al., 2000), which can reveal local Mg–O and Ca–O bond lengths, support the proposal that the vibrational amplitude of Mg in the Mg–O(4) plane could increase with increasing Ca content in garnet. Such behaviour could explain the observed decrease in energy of T(Mg) vibrations in the phonon spectra of Py-Gr garnets, and could provide a physical explanation for the heat capacity observations.

On the more theoretical side, much work needs to be done in developing quantitative lattice dynamic models and in simulating phonon spectra. It has been pointed out (Kolesov & Geiger, 2000) that published calculations cannot reproduce the Raman spectrum of pyrope, for example, at low energies. This may hinge on the simplified harmonic or quasi-harmonic assumptions adopted in the lattice dynamic calculations. A further challenge involves both simulating and obtaining a physical understanding of two-mode behaviour in solid solutions. Two-mode behaviour could be a general phenomenon for a number of different silicate solid solution structure types, but it has been best studied in garnet and, here, some understanding of its underlying physical nature may be possible to achieve. Accurate lattice dynamic calculations for solid solutions will be difficult to perform, and they will be tedious and expensive to undertake, but they are critically needed in order to obtain the thermodynamic properties of solid solution systems at different P–T conditions. It is this author's opinion that traditional phase-equilibrium investigations, which have been undertaken to great extent with great expense in the past, will not always provide the necessary thermodynamic data that are needed for a variety of geochemical and geophysical calculations. There has been a tremendous effort made to formulate and improve, for example, macroscopic-based thermodynamic mixing models for silicate solid solutions (see Geiger, 2001). They have, unfortunately, little predictive power outside of the P–T range in which they are fit, because they have little underlying physical basis. A next step that is required in the development of more quantitative and robust thermodynamic solution models is an understanding of the solid solution process at the microscopic level. Thus, there is great future potential in lattice dynamic studies of rock-forming silicates.

Microscopic energetic properties and microscopic-macroscopic relationships

Microscopic-scale distortions and structural modifications that arise from an exchange of atoms of different sizes produce microscopic strain and elastic energies, which in turn have an important control on many macroscopic physical and thermodynamic properties. Physical descriptions of static structural heterogeneities and strain fields in solid solutions are beginning to emerge using different spectroscopic measurements. Here, for example, so-called hard mode vibrational spectroscopy is used to describe these microscopic properties over different length scales and it has been applied to several binary aluminosilicate garnet solid solutions. Spectral systematics, including phonon wavenumber shifts and line broadening as a function of composition, can be linked to macroscopic thermodynamic mixing behaviour. Mode wavenumber variations can reflect “average” microscopic structural distortion and can be related to ΔVmix behaviour, such as ideal mixing, ΔVmix = 0, or positive deviations, ΔVmix > 0, from ideality. Variations in line widths reflect local structural heterogeneities over different length scales, which in turn give rise to strain gradients and elastic energies that are energetically destabilising. They, in turn, have a large effect on ΔHmix behaviour. A good experimental precision in variations of mode wavenumbers and line broadening can be obtained from powder IR and Raman spectra that are relatively simple to collect. A disadvantage of this type of study is that it is empirical in nature and the results are difficult to quantify on an absolute basis. Bond lengths and angles and measures of polyhedral distortion, for example, or values of elastic energies cannot be obtained directly from the spectra. Only relative information can be determined.

XAFS measurements can, in contrast, provide quantitative local structural information on solid solutions. A determination of Fe/Mn–O bond lengths for a series of Al-Sp garnets appears to show, for example, that the “state of alternating bonds” describes better, compared to the VCA model, the local bond length behaviour for the X site in solid solutions. Such behaviour is associated with structural relaxation. XAFS appears to be a good experimental method in investigating the nature of local site distortion/relaxation in garnet and more study in this area is needed. Further work on different binary solid solutions is needed to better understand polyhedral site and structural relaxation behaviour as a function of garnet composition. Studies as a function of P and T could also be useful. Once again, the question is more than of pure academic interest. The type and degree of structural relaxation affects microscopic strain energies and thus macroscopic properties. Static lattice energy simulations on garnet solid solutions show that thermodynamic mixing properties (i.e., ΔVmix and ΔHmix) vary considerably depending on how the local X–O bonds are simulated in model calculations (Bosenick et al., 2001). The VCA leads to a large overestimation of excess thermodynamic mixing properties, while calculations made assuming local relaxation give results in reasonable agreement with experimental data. In a related issue, it should be noted that simulations also show that trace element substitution behaviour in garnet is better explained, if one assumes a model invoking X-site relaxation (van Westrenen et al., 2003).

Other atomistic-level properties such as CFSE's of Fe2+, for example, play a role in determining the total energetics in garnet. The CFSE represents only a small fraction of the total energy of a silicate system. However, in the case of isostructural solid solutions it could influence thermodynamic mixing behaviour, which normally involves only small variations in energies between end-member phases. Mössbauer and optical absorption spectroscopy investigations show that Fe–O bonding in garnet is largely ionic. Both types of spectroscopic measurements have been made at high pressures and they show that the degree of covalency increases with increasing pressure, which results from Fe–O bond compression and electronic orbital overlap. The same behaviour is true for Mn–O in spessartine. There has been very little spectroscopic work, for example, on describing the electronic bonding type or behaviour for the other cations in garnet. Bonding properties have been investigated by electronic structure calculations of charge density distribution and they predict that the chemical bonding is similar in all of the aluminosilicate garnets (cf. Ungaretti et al., 1995).

Trace element substitution and behaviour

There are only a few spectroscopic studies that have been made to identify and characterise minor and trace elements and to determine their substitution mechanisms in garnet. These results provide, however, the only direct experimental evidence, in many cases, relating to the structural incorporation and site location(s) of elements at low concentration levels. This information cannot easily be determined by X-ray diffraction or by chemical analysis with electron microprobe, ion probe or ICP techniques. This area of research in mineralogy and geochemistry has barely been scratched, and there is much to be done before a good understanding of trace element substitution and partitioning behaviour for all silicates is at hand.

The structural incorporation of about 1 wt% of the rare earth element Yb3+ in synthetic pyrope and grossular was investigated using XAFS measurements. The results show that it substitutes at the X site and this must lead to deviations from ideal garnet stoichiometry. Local structural relaxation occurs around the Yb cations. The incorporation of trace amounts of Ti3+ in synthetic pyrope was investigated by single crystal ESR measurements. They show unequivocally that Ti in this low oxidation state can occur, and that the cation is located on the octahedral site.

Further spectroscopic work is needed to describe the incorporation and site partitioning behaviour of other rare earth and trace elements in garnet. Investigations are needed to clarify substitutional mechanism(s) as a function of concentration from the ppb level up to several wt% for a given element. It is not completely clear at this point, for example, if certain trace elements at ppb levels are incorporated on well-defined crystallographic sites or, possibly in some cases, as defects. Because of its sensitivity, ESR spectroscopy is an excellent method to investigate trace element substitution behaviour at very low concentration levels. Studies of trace elements using XAFS have also just begun and, here, many elements of the periodic table are open for study.

General outlook

This review article has attempted to present and analyse some of the more important spectroscopic results that have been obtained on aluminosilicate garnets. The different methods and types of measurements have developed rapidly and extensively over the past 30 years. Spectroscopic results have contributed greatly to an understanding of the structural, crystal chemical and lattice dynamic properties of garnet. Spectroscopic studies have come of age and the different methods are now a standard part of mineralogical and geochemical research programs. After reviewing “where we have been” in the past, it should be briefly discussed “where we should go” in the future. Clearly, measurements at different pressure and temperature conditions are necessary and, here, the low temperature regime must not be forgotten. It has largely been ignored in many mineralogical investigations, but a number of physical phenomena occur at low temperatures or are best investigated in this region (e.g. magnetic phase changes, structural distortions in solid solutions). Further work on the electronic bonding and magnetic properties in garnet are needed. Neither has received detailed attention in mineralogical studies in spite of their importance. The chemical and physical properties of minerals are ultimately a reflection of the electronic bonding between atoms and in the case of silicates much investigation remains to be done in this area. The role of minor defects such as OH groups and the incorporation of various trace elements and their relationship to nonstoichiometry are poorly understood. In spite of the number of IR studies looking at OH in natural garnets, little is known about the substitutional mechanisms by which it can be incorporated. The same is true for many trace elements. This is surprising when one considers the amount of analytical work that has been done in geochemistry in measuring trace elements in garnet. All discussion in this article has centred on bulk chemical and physical properties, and nothing was discussed on surface properties. Very little study has been done on the surface properties of garnet and here spectroscopic measurements will play a major role in the years to come.

Many important spectroscopic results on aluminosilicate garnets have been obtained from measurements on well-characterised synthetic materials. A number of structural and crystal chemical properties are reflected in small or subtle spectroscopic features (e.g. minor line broadening or small variations in line shapes or areas) that are only interpretable through studies on synthetic compositions. Natural garnet crystals are in most cases compositionally complex and they have experienced a complicated P–T history. Thus, their spectra are sometimes not completely interpretable in a rigorous way. Synthesis experiments can be designed to produce chemical and structural variations in order to address specific questions. Results from this review show that systematic measurements on synthetic solid solutions or specially designed measurements focusing on a given garnet composition can yield fundamental and important results. Because some garnets must be synthesised at high pressures, the amount of material available for study can be limited. Hence, some spectroscopic methodologies (e.g. NMR and Mössbauer spectroscopy) need to be modified in order to make measurements on small amounts of material. Or, alternatively, studies can be done on materials that are isotopically enriched with 29Si or 57Fe, for example.

Finally, it is clear that the combination of spectroscopic measurements with theoretical-type calculations or simulations is very powerful. Herein lies the future of many mineralogical and geochemical investigations. For some types of spectroscopic investigations, we have reached or are quickly reaching the limits of understanding using a purely empirical approach. Further “standard” experimental measurements will reveal little new information. For example, the powder IR and Raman spectra of most rock-forming silicates have been recorded a number of times. The general spectral features are largely understood and further powder measurements will not provide a better understanding of their lattice dynamic properties. This can only be obtained via calculations. Thus, what is critically needed in many spectroscopic studies is the ability to interpret or fit spectra with the help of physically based atomistic-level simulations. This work will be challenging, but is necessary, if the chemical and physical properties of minerals are to be understood in a fundamental way.

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Many of the results presented herein were obtained from collaborations with different mineralogists and spectroscopists. I thank G. Amthauer, T. Armbruster, B.A. Kolesov, K. Langer, S. Quartieri, H. Rager and G.R. Rossman for fruitful collaboration over the years. A. Hofmeister kindly provided the single-crystal IR reflectance spectra. Thanks also to H. Rager and S. Quartieri for reviewing parts of the text and M. Andrut, A. Beran and E. Libowitzky who made comments over the entire manuscript.

Figures & Tables

Fig. 1.

The aluminosilicate garnet system almandine-pyrope-grossular-spessartine (X3Al2Si3O12, with X = Fe2+, Mg, Ca and Mn2+). It consists of four end members and six binary, four ternary and one quaternary solid solution system(s).

Fig. 1.

The aluminosilicate garnet system almandine-pyrope-grossular-spessartine (X3Al2Si3O12, with X = Fe2+, Mg, Ca and Mn2+). It consists of four end members and six binary, four ternary and one quaternary solid solution system(s).

Fig. 2.

(a) Polyhedral structure model of aluminosilicate garnet. The SiO4 tetrahedra (red) and AlO6 octahedra (blue) are connected over corners and build a three-dimensional quasi-framework. The divalent X-site cations (yellow spheres) are located in the large dodecahedral site. (b) Structural relationship between a single SiO4 tetrahedron and surrounding dodecahedra. There are two edge-shared dodecahedra and four corner-shared dodecahedra. (c) Edge-sharing relationship between neighbouring dodecahedra in the garnet structure. Every dodecahedron shares four edges with other dodecahedra. (d) Structural relationship between an AlO6 octahedron and six surrounding edge-shared dodecahedra.

Fig. 2.

(a) Polyhedral structure model of aluminosilicate garnet. The SiO4 tetrahedra (red) and AlO6 octahedra (blue) are connected over corners and build a three-dimensional quasi-framework. The divalent X-site cations (yellow spheres) are located in the large dodecahedral site. (b) Structural relationship between a single SiO4 tetrahedron and surrounding dodecahedra. There are two edge-shared dodecahedra and four corner-shared dodecahedra. (c) Edge-sharing relationship between neighbouring dodecahedra in the garnet structure. Every dodecahedron shares four edges with other dodecahedra. (d) Structural relationship between an AlO6 octahedron and six surrounding edge-shared dodecahedra.

Fig. 3.

Atomic vibrational amplitudes for a given XO8 site for different end member garnets as calculated from their difference atomic mean-square displacements between 500/550 and 100 K – from top to bottom, the MgO8 dodecahedron in pyrope, the FeO8 dodecahedron in almandine, the MnO8 dodecahedron in spessartine, and the CaO8 dodecahedron in grossular. The projections are approximately along two-fold axes and the projections in the right-hand column are rotated approximately 90° about the horizontal line of the projections in the left-hand column. The central X cation shows measurable anisotropic vibration (i.e., a “rattling” motion) with the largest amplitudes in the plane of the longer X–O(4) bonds. The eight surrounding oxygen anions have smaller vibrational amplitudes and they are primarily related to rigid SiO4 librations (from Geiger et al., 1992b; Armbruster et al., 1992; Armbruster & Geiger, 1993; Geiger & Armbruster, 1997).

Fig. 3.

Atomic vibrational amplitudes for a given XO8 site for different end member garnets as calculated from their difference atomic mean-square displacements between 500/550 and 100 K – from top to bottom, the MgO8 dodecahedron in pyrope, the FeO8 dodecahedron in almandine, the MnO8 dodecahedron in spessartine, and the CaO8 dodecahedron in grossular. The projections are approximately along two-fold axes and the projections in the right-hand column are rotated approximately 90° about the horizontal line of the projections in the left-hand column. The central X cation shows measurable anisotropic vibration (i.e., a “rattling” motion) with the largest amplitudes in the plane of the longer X–O(4) bonds. The eight surrounding oxygen anions have smaller vibrational amplitudes and they are primarily related to rigid SiO4 librations (from Geiger et al., 1992b; Armbruster et al., 1992; Armbruster & Geiger, 1993; Geiger & Armbruster, 1997).

Fig. 4.

The two crystallographically independent (Mg,Ca)–O bond lengths for binary Py-Gr solid solutions. The different dashed lines represent hypothetical Mg–O and Ca–O bond lengths as a function of composition, as they could occur with the “state of alternating bonds” (or in the “Pauling limit”). The solid straight lines represent the case for average (Mg/Ca)–O bonds without local relaxation and define the “virtual crystal approximation”. The data points are from the diffraction study of Ganguly et al. (1993).

Fig. 4.

The two crystallographically independent (Mg,Ca)–O bond lengths for binary Py-Gr solid solutions. The different dashed lines represent hypothetical Mg–O and Ca–O bond lengths as a function of composition, as they could occur with the “state of alternating bonds” (or in the “Pauling limit”). The solid straight lines represent the case for average (Mg/Ca)–O bonds without local relaxation and define the “virtual crystal approximation”. The data points are from the diffraction study of Ganguly et al. (1993).

Fig. 5.

Polarised single-crystal Raman spectra of the four end-member aluminosilicate garnets (from Kolesov & Geiger, 1998). Note that some spectra have an expanded abscissa.

Fig. 5.

Polarised single-crystal Raman spectra of the four end-member aluminosilicate garnets (from Kolesov & Geiger, 1998). Note that some spectra have an expanded abscissa.

Fig. 6.

Raman A1g + Eg (left) and F2g spectra (right) of pyrope at 5 K and 295 K in the low wavenumber region (from Kolesov & Geiger, 2000). Note the change in line width of the mode around 130 cm–1 at the two different temperatures.

Fig. 6.

Raman A1g + Eg (left) and F2g spectra (right) of pyrope at 5 K and 295 K in the low wavenumber region (from Kolesov & Geiger, 2000). Note the change in line width of the mode around 130 cm–1 at the two different temperatures.

Fig. 7.

Raman-active modes in synthetic pyrope and grossular as a function of temperature (left). Raman-active modes in synthetic pyrope and grossular as a function of pressure (right) (from Gillet et al., 1992).

Fig. 7.

Raman-active modes in synthetic pyrope and grossular as a function of temperature (left). Raman-active modes in synthetic pyrope and grossular as a function of pressure (right) (from Gillet et al., 1992).

Fig. 8.

Variation in the wavenumber behaviour for different modes in synthetic pyrope and grossular as a function of pressure (left) and temperature (right). The wavenumber regions for the internal SiO4 modes and lattice modes are marked (from Gillet et al., 1992).

Fig. 8.

Variation in the wavenumber behaviour for different modes in synthetic pyrope and grossular as a function of pressure (left) and temperature (right). The wavenumber regions for the internal SiO4 modes and lattice modes are marked (from Gillet et al., 1992).

Fig. 9.

Wavenumber behaviour of selected Raman-active modes for synthetic almandine-spessartine solid solutions (from Kolesov & Geiger, 1998).

Fig. 9.

Wavenumber behaviour of selected Raman-active modes for synthetic almandine-spessartine solid solutions (from Kolesov & Geiger, 1998).

Fig. 10.

Wavenumber behaviour of selected Raman-active modes for synthetic pyrope-grossular solid solutions (from Kolesov & Geiger, 1998).

Fig. 10.

Wavenumber behaviour of selected Raman-active modes for synthetic pyrope-grossular solid solutions (from Kolesov & Geiger, 1998).

Fig. 11.

Single-crystal IR reflectance spectra of natural nearly end-member garnets: (a) pyrope, (b) almandine and (c) grossular as shown at the top of each figure. The dielectric functions are shown in the middle and the resulting normalised absorption spectra are observed at the bottom of each figure (from Hofmeister, pers. commun.).

Fig. 11.

Single-crystal IR reflectance spectra of natural nearly end-member garnets: (a) pyrope, (b) almandine and (c) grossular as shown at the top of each figure. The dielectric functions are shown in the middle and the resulting normalised absorption spectra are observed at the bottom of each figure (from Hofmeister, pers. commun.).

Fig. 12.

Variation in the wavenumber for an IR mode located between 375 cm–1 and 400 cm–1 for different composition Al-Gr solid solutions shown as short vertical lines, with the straight dash-dot line connecting the two end members (above). The excess molar volume of mixing for this binary is shown as a dotted line (below). Note the similarities in the positive asymmetric deviations from linear behaviour for both (from Geiger et al., 1989).

Fig. 12.

Variation in the wavenumber for an IR mode located between 375 cm–1 and 400 cm–1 for different composition Al-Gr solid solutions shown as short vertical lines, with the straight dash-dot line connecting the two end members (above). The excess molar volume of mixing for this binary is shown as a dotted line (below). Note the similarities in the positive asymmetric deviations from linear behaviour for both (from Geiger et al., 1989).

Fig. 13.

Variation in Δcorr values (which are a measure of band width) in cm–1 for the wavenumber region between 280 and 680 cm–1 (above) and the wavenumber region between 780 and 1200 cm-1 (below) as a function of composition for synthetic Py-Al (open triangles), Al-Gr (open squares) and Py-Gr solid solutions (open circles). The garnet end member with the largest X cation for the respective binary is plotted on the right hand side (from Boffa Ballaran et al., 1999).

Fig. 13.

Variation in Δcorr values (which are a measure of band width) in cm–1 for the wavenumber region between 280 and 680 cm–1 (above) and the wavenumber region between 780 and 1200 cm-1 (below) as a function of composition for synthetic Py-Al (open triangles), Al-Gr (open squares) and Py-Gr solid solutions (open circles). The garnet end member with the largest X cation for the respective binary is plotted on the right hand side (from Boffa Ballaran et al., 1999).

Fig. 14.

Comparison plots of the calorimetrically determined enthalpies of mixing (ΔHmix) for synthetic Py-Gr garnets, where end-member Py is on the left and Gr on the right side of the composition axis (above; data shown as solid diamonds – Newton et al., 1977), and Al-Gr solid solution garnets, where end-member Al is on the left and Gr on the right of the composition axis (below; data shown as solid inverted triangles – Geiger et al., 1987) and those calculated (solid curves) from a determination of the band broadening (i.e., Δcorr) measured in the IR powder spectra from both solid solutions (from Boffa Ballaran et al., 1999).

Fig. 14.

Comparison plots of the calorimetrically determined enthalpies of mixing (ΔHmix) for synthetic Py-Gr garnets, where end-member Py is on the left and Gr on the right side of the composition axis (above; data shown as solid diamonds – Newton et al., 1977), and Al-Gr solid solution garnets, where end-member Al is on the left and Gr on the right of the composition axis (below; data shown as solid inverted triangles – Geiger et al., 1987) and those calculated (solid curves) from a determination of the band broadening (i.e., Δcorr) measured in the IR powder spectra from both solid solutions (from Boffa Ballaran et al., 1999).

Fig. 15.

29Si MAS NMR spectrum of synthetic pyrope (above) and grossular (below). (from Geiger et al., 1990, 1992a.)

Fig. 15.

29Si MAS NMR spectrum of synthetic pyrope (above) and grossular (below). (from Geiger et al., 1990, 1992a.)

Fig. 16.

29Si MAS NMR spectra of synthetic Py-Gr solid solutions: (a) pyrope-rich garnets, (b) grossular-rich garnets and (c) intermediate pyrope-grossular garnets (from Bosenick et al., 1995).

Fig. 16.

29Si MAS NMR spectra of synthetic Py-Gr solid solutions: (a) pyrope-rich garnets, (b) grossular-rich garnets and (c) intermediate pyrope-grossular garnets (from Bosenick et al., 1995).

Fig. 17.

Single-crystal optical absorption spectrum of a natural garnet of composition Al77Py18Gr5 between 490 and 78 K (from White & Moore, 1972) showing the three t2g transitions in the NIR region.

Fig. 17.

Single-crystal optical absorption spectrum of a natural garnet of composition Al77Py18Gr5 between 490 and 78 K (from White & Moore, 1972) showing the three t2g transitions in the NIR region.

Fig. 18.

Schematic representation of the 3d electronic energy levels in the case of: (a) a free spherical field, (b) a field of a perfect cube and (c) for Fe2+ in the dodecahedral site in garnet. Δc (i.e. 10Dq) is the crystal field splitting. The approximate separations of the d energy levels with respect to the ground state for Fe2+ in the dodecahedral site of symmetry D2 in almandine are shown at the far right (from Geiger & Rossman, 1994).

Fig. 18.

Schematic representation of the 3d electronic energy levels in the case of: (a) a free spherical field, (b) a field of a perfect cube and (c) for Fe2+ in the dodecahedral site in garnet. Δc (i.e. 10Dq) is the crystal field splitting. The approximate separations of the d energy levels with respect to the ground state for Fe2+ in the dodecahedral site of symmetry D2 in almandine are shown at the far right (from Geiger & Rossman, 1994).

Fig. 19.

Single-crystal optical absorption spectrum of synthetic almandine in the NIR/VIS/UV regions at different pressures showing two spin-allowed Fe2+ d-d bands (the lowest wavenumber d-d band in the NIR and was not recorded), a number of weak spin-forbidden bands and the low-energy wing of an intense Fe2+–O charge transfer band in the UV region (from Smith & Langer, 1983).

Fig. 19.

Single-crystal optical absorption spectrum of synthetic almandine in the NIR/VIS/UV regions at different pressures showing two spin-allowed Fe2+ d-d bands (the lowest wavenumber d-d band in the NIR and was not recorded), a number of weak spin-forbidden bands and the low-energy wing of an intense Fe2+–O charge transfer band in the UV region (from Smith & Langer, 1983).

Fig. 20.

Single-crystal optical absorption spectrum of synthetic spessartine in the NIR/VIS/UV regions at different pressures showing spin-forbidden bands (from Smith & Langer, 1983).

Fig. 20.

Single-crystal optical absorption spectrum of synthetic spessartine in the NIR/VIS/UV regions at different pressures showing spin-forbidden bands (from Smith & Langer, 1983).

Fig. 21.

Difference in energy between the highest energy electronic transition 5B2 level and the lower 5B3 level for Fe2+ in Py-Al and Sp-Al solid solutions (from Geiger & Rossman, 1994).

Fig. 21.

Difference in energy between the highest energy electronic transition 5B2 level and the lower 5B3 level for Fe2+ in Py-Al and Sp-Al solid solutions (from Geiger & Rossman, 1994).

Fig. 22.

Excess CFSEs of Fe2+ for the two binary solid solutions Py-Al and Sp-Al. The lines represent a least-squares best-fit symmetric mixing model to the two different data sets (from Geiger & Rossman, 1994).

Fig. 22.

Excess CFSEs of Fe2+ for the two binary solid solutions Py-Al and Sp-Al. The lines represent a least-squares best-fit symmetric mixing model to the two different data sets (from Geiger & Rossman, 1994).

Fig. 23.

57Fe Mössbauer spectra of synthetic almandine from 10.0 to 9.2 K showing the onset of magnetic ordering (from Murad & Wagner, 1987).

Fig. 23.

57Fe Mössbauer spectra of synthetic almandine from 10.0 to 9.2 K showing the onset of magnetic ordering (from Murad & Wagner, 1987).

Fig. 24.

57Fe Mössbauer spectra recorded at 77 K for selected intermediate garnet compositions for the three binary synthetic solid solutions Al-Py, Al-Sp and Al-Gr (from Geiger et al., 2003).

Fig. 24.

57Fe Mössbauer spectra recorded at 77 K for selected intermediate garnet compositions for the three binary synthetic solid solutions Al-Py, Al-Sp and Al-Gr (from Geiger et al., 2003).

Fig. 25.

Single-crystal ESR spectrum of Ti3+ in synthetic pyrope recorded with forumla perpendicular to B (from Rager et al., 2003).

Fig. 25.

Single-crystal ESR spectrum of Ti3+ in synthetic pyrope recorded with forumla perpendicular to B (from Rager et al., 2003).

Fig. 26.

Experimental (open squares) and fitted (crosses) magnetic resonance fields for the four observed Ti3+ EPR signals upon rotation around the forumla axis (from Rager et al., 2003).

Fig. 26.

Experimental (open squares) and fitted (crosses) magnetic resonance fields for the four observed Ti3+ EPR signals upon rotation around the forumla axis (from Rager et al., 2003).

Fig. 27.

Experimental XANES spectra at the Fe K edge for three natural almandine-containing garnets (MP 18, MP 17, MP 12) and a Fe3+-containing garnet (bric) and hematite (Fe2O3). The individual spectra were normalised with respect to the high-energy side of the curve (from Quartieri et al., 1993).

Fig. 27.

Experimental XANES spectra at the Fe K edge for three natural almandine-containing garnets (MP 18, MP 17, MP 12) and a Fe3+-containing garnet (bric) and hematite (Fe2O3). The individual spectra were normalised with respect to the high-energy side of the curve (from Quartieri et al., 1993).

Fig. 28.

The two crystallographically independent Fe–O and Mn–O bond lengths, shown as different dashed lines, for synthetic Al-Sp garnet compositions determined from XAS measurements made at 77 K (Sani et al., in press). The data, where the squares are average Fe–O and the circles average Mn–O bond lengths, were fitted by a linear least-squares procedure and the resulting bond lengths were extrapolated to the end-member compositions. The solid lines represent VCA behaviour.

Fig. 28.

The two crystallographically independent Fe–O and Mn–O bond lengths, shown as different dashed lines, for synthetic Al-Sp garnet compositions determined from XAS measurements made at 77 K (Sani et al., in press). The data, where the squares are average Fe–O and the circles average Mn–O bond lengths, were fitted by a linear least-squares procedure and the resulting bond lengths were extrapolated to the end-member compositions. The solid lines represent VCA behaviour.

Fig. 29.

Experimental XANES spectra at the Ca K edge for six natural grossular-containing garnets. The grossular contents decrease from top to bottom from 2.90 to 0.24 Ca cations in the formula unit. The individual spectra were normalised with respect to the high-energy side of the curve (left). Simulated XANES spectra for the different garnet samples (right – from Quartieri et al., 1995).

Fig. 29.

Experimental XANES spectra at the Ca K edge for six natural grossular-containing garnets. The grossular contents decrease from top to bottom from 2.90 to 0.24 Ca cations in the formula unit. The individual spectra were normalised with respect to the high-energy side of the curve (left). Simulated XANES spectra for the different garnet samples (right – from Quartieri et al., 1995).

Fig. 30.

Experimental XANES spectra at the Al K edge for grossular, spessartine, almandine and pyrope (left) and their simulated spectra (right) from Wu et al., (1996).

Fig. 30.

Experimental XANES spectra at the Al K edge for grossular, spessartine, almandine and pyrope (left) and their simulated spectra (right) from Wu et al., (1996).

Fig. 31.

Experimental XANES spectra recorded at 77 K of Yb-containing grossular, Yb-containing pyrope and Yb2O3 at the (a) LI edge and the (b) LIII edge (from Quartieri et al., 1999).

Fig. 31.

Experimental XANES spectra recorded at 77 K of Yb-containing grossular, Yb-containing pyrope and Yb2O3 at the (a) LI edge and the (b) LIII edge (from Quartieri et al., 1999).

Table 1.

Summary of crystallographic properties for garnet X3Y2Z3O12 of space group forumla.

SitePoint symmetryAtomic coordinatesSite coordinationWyckoff position

X2221/801/4824c
Yforumla000616a
Zforumla3/80¼424d
O1xyz496h
SitePoint symmetryAtomic coordinatesSite coordinationWyckoff position

X2221/801/4824c
Yforumla000616a
Zforumla3/80¼424d
O1xyz496h
Table 2.

Cation-oxygen bond distances for synthetic end-member aluminosilicate garnets at different temperatures (from Geiger et al., 1992b; Armbruster et al., 1992; Armbruster & Geiger, 1993; Geiger & Armbruster, 1997).

GarnetT (K)Si–O (Å)Al–O (Å)X–O(2) (Å)X–O(4) (Å)

Pyrope1001.634 (1)1.885 (1)2.195 (1)2.334 (1)
 2931.634 (1)1.886 (1)2.197 (1)2.340 (1)
 5001.635 (1)1.890 (1)2.202 (1)2.349 (1)
Almandine1001.636 (1)1.888 (1)2.220 (1)2.363 (1)
 2931.635 (1)1.890 (1)2.221 (1)2.371 (1)
 5001.637 (1)1.893 (1)2.225 (1)2.379 (1)
Spessartine1001.639 (1)1.899 (1)2.245 (1)2.399 (1)
 2931.640 (1)1.901 (1)2.246 (1)2.404 (1)
 5001.641 (1)1.902 (1)2.251 (1)2.414 (1)
Grossular1001.646 (1)1.923 (1)2.321 (1)2.483 (1)
 2931.646 (1)1.926 (1)2.322 (1)2.487 (1)
 5501.646 (1)1.929 (1)2.322 (1)2.498 (1)
GarnetT (K)Si–O (Å)Al–O (Å)X–O(2) (Å)X–O(4) (Å)

Pyrope1001.634 (1)1.885 (1)2.195 (1)2.334 (1)
 2931.634 (1)1.886 (1)2.197 (1)2.340 (1)
 5001.635 (1)1.890 (1)2.202 (1)2.349 (1)
Almandine1001.636 (1)1.888 (1)2.220 (1)2.363 (1)
 2931.635 (1)1.890 (1)2.221 (1)2.371 (1)
 5001.637 (1)1.893 (1)2.225 (1)2.379 (1)
Spessartine1001.639 (1)1.899 (1)2.245 (1)2.399 (1)
 2931.640 (1)1.901 (1)2.246 (1)2.404 (1)
 5001.641 (1)1.902 (1)2.251 (1)2.414 (1)
Grossular1001.646 (1)1.923 (1)2.321 (1)2.483 (1)
 2931.646 (1)1.926 (1)2.322 (1)2.487 (1)
 5501.646 (1)1.929 (1)2.322 (1)2.498 (1)
Table 3.

Linkages of the polyhedra in the garnet structure.

PolyhedronLinkage

tetrahedron4 corners with octahedra
 4 corners with dodecahedra
 2 edges with dodecahedra
octahedron6 corners with tetrahedra
 6 edges with dodecahedra
dodecahedron4 corners with tetrahedra
 2 edges with tetrahedra
 4 edges with octahedra
 4 edges with dodecahedra
PolyhedronLinkage

tetrahedron4 corners with octahedra
 4 corners with dodecahedra
 2 edges with dodecahedra
octahedron6 corners with tetrahedra
 6 edges with dodecahedra
dodecahedron4 corners with tetrahedra
 2 edges with tetrahedra
 4 edges with octahedra
 4 edges with dodecahedra
Table 4.

Raman mode assignments for end-member aluminosilicate garnets (from Kolesov & Geiger, 1998).

 PyropeAlmandineSpessartineGrossular
 A1gEgF2gA1gEgF2gA1gEgF2gA1gEgF2g

(Si–O)stretch928 1066916 1038905 1029880 1007
 945902871930897863913*879849904*848827
(si-O)bend563626*650556596630552592*630550592630
  525598 521*581 522573* 529582
  375512 370500 372500 420512
492475475483
R(SiO4)364344383342323350321376373389
353355*350*319*351
322314302333
T(SiO4) 211222 167170 162175 181186
T(X)284#  256216 269221 320280
135171196247
 PyropeAlmandineSpessartineGrossular
 A1gEgF2gA1gEgF2gA1gEgF2gA1gEgF2g

(Si–O)stretch928 1066916 1038905 1029880 1007
 945902871930897863913*879849904*848827
(si-O)bend563626*650556596630552592*630550592630
  525598 521*581 522573* 529582
  375512 370500 372500 420512
492475475483
R(SiO4)364344383342323350321376373389
353355*350*319*351
322314302333
T(SiO4) 211222 167170 162175 181186
T(X)284#  256216 269221 320280
135171196247

# broad and possibly an overtone of the F2g band at 135 cm–1 – see Kolesov & Geiger (2000)

Table 5.

29Si NMR peak assignments for pyrope-grossular garnets (from Bosenick et al., 1995).

Table 6.

Wavenumbers of spin-forbidden and spin-allowed bands (*) for synthetic almandine as a function of pressure (from Smith & Langer, 1983; Frentrup & Langer, 1982, for values in parentheses).

Band1 atm5.1 GPa10.1 GPaPressure shift (cm−1/kbar)

127,20027,20027,100−1.0
2(24,900)
323,20023,70024,100+9.0
422,80023,000
521,800?21,80021,600−2.0?
6(20,900)21,000??
719,90019,80019,700−2.0
819,10019,00019,000−1.0?
917,60017,30017,000−6.0
1016,20015,80015,600−6.0
1114,40014,10013,900−5.0
12*7,6007,8008,200+6.0
13*5,8006,1006,700+9.0
Band1 atm5.1 GPa10.1 GPaPressure shift (cm−1/kbar)

127,20027,20027,100−1.0
2(24,900)
323,20023,70024,100+9.0
422,80023,000
521,800?21,80021,600−2.0?
6(20,900)21,000??
719,90019,80019,700−2.0
819,10019,00019,000−1.0?
917,60017,30017,000−6.0
1016,20015,80015,600−6.0
1114,40014,10013,900−5.0
12*7,6007,8008,200+6.0
13*5,8006,1006,700+9.0
Table 7.

Selected properties for synthetic almandine garnet determined by optical absorption spectroscopy as a function of pressure (from Smith & Langer, 1983).

Property1 atm5.4 GPa10.1 GPa

10Dq (cm−1)5,3805,7066,352
CFSE-Fe2+ (cm−1)3,7803,9444,270
Fe−O (Å)2.3002.2732.225
Property1 atm5.4 GPa10.1 GPa

10Dq (cm−1)5,3805,7066,352
CFSE-Fe2+ (cm−1)3,7803,9444,270
Fe−O (Å)2.3002.2732.225
Table 8.

Wavenumbers of spin-forbidden bands of Mn2+ in synthetic spessartine as a function of pressure (from Smith & Langer, 1983).

Band1 atm5.6 GPa11.2 GPaPressure shift (cm−1/kbar)

124,50024,40018,900-1.8
224,30024,20024,300−4.5
323,75023,50023,800-5.8
423,20023,00023,100-7.1
521,60021,60022,400−0.9
620,80020,80021,5000
719,00020,80019,600-
Band1 atm5.6 GPa11.2 GPaPressure shift (cm−1/kbar)

124,50024,40018,900-1.8
224,30024,20024,300−4.5
323,75023,50023,800-5.8
423,20023,00023,100-7.1
521,60021,60022,400−0.9
620,80020,80021,5000
719,00020,80019,600-
Table 9.

Debye-Waller factors and Fe−O bond lengths determined from XAFS measurements on synthetic almandine (Quartieri et al., 1997).

T(K)σ2Fe-O(2)2)σ2Fe-O(4)2)RFe-O(2) (Å)RFe-O(4) (Å)

200.008(1)0.011(2)2.211(7)2.340(12)
770.008(1)0.011(2)2.213(7)2.347(10)
1000.008(1)0.011(2)2.210(8)2.350(12)
2000.008(1)0.015(2)2.216(7)2.354(13)
3000.008(1)0.017(3)2.216(7)2.352(15)
3730.009(1)0.023(4)2.219(8)2.348(21)
4730.011(2)0.026(4)2.216(8)2.366(26)
T(K)σ2Fe-O(2)2)σ2Fe-O(4)2)RFe-O(2) (Å)RFe-O(4) (Å)

200.008(1)0.011(2)2.211(7)2.340(12)
770.008(1)0.011(2)2.213(7)2.347(10)
1000.008(1)0.011(2)2.210(8)2.350(12)
2000.008(1)0.015(2)2.216(7)2.354(13)
3000.008(1)0.017(3)2.216(7)2.352(15)
3730.009(1)0.023(4)2.219(8)2.348(21)
4730.011(2)0.026(4)2.216(8)2.366(26)

Contents

GeoRef

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