Phys Chem Minerals (1998) 25:142±151
Springer-Verlag 1998
ORIGINAL PAPER
B.A. Kolesov ´ C.A. Geiger
Raman spectra of silicate garnets
Received: 3 December 1996 / Revised, accepted: 13 April 1997
Abstract The single-crystal polarized Raman spectra of four natural silicate garnets with compositions close to end-members almandine, grossular, andradite, and uvarovite, and two synthetic end-members spessartine and pyrope, were measured, along with the powder spectra of synthetic pyrope-grossular and almandine-spessartine solid solutions. Mode assignments were made based on a comparison of the different end-member garnet spectra and, in the case of pyrope, based on measurements made on additional crystals synthesized with 26 Mg. A general order of mode frequencies, i.e. R(SiO4)>T(metal cation)>T(SiO4), is observed, which should also hold for most orthosilicates. The main factors controlling the changes in mode frequencies as a function of composition are intracrystalline pressure (i.e. oxygen-oxygen repulsion) for the internal SiO4-vibrational modes and kinematic coupling of vibrations for the external modes. Low frequency vibrations of the X-site cations reflect their weak bonding and dynamic disorder in the large dodecahedral site, especially in the case of pyrope. Two mode behavior is observed for X-site cation vibrations along the pyrope-grossular binary, but not along the almandine-spessartine join.
Introduction The garnet group offers an excellent system to study the vibrational spectroscopic properties of silicate structures. Its structure is relatively complex compared to many inorganic substances, but because of its high symmetry (space group Ia3Åd), it affords a moderately simple spectrum and analysis. In addition, the large number of B.A. Kolesov Institute of Inorganic Chemistry, Lavrentiev prosp. 3, Novosibirsk 630090, Russia
)
C.A. Geiger ( ) Mineralogisch-Petrographisches Institut, Universität Kiel, Olshausenstr. 40, D-24098 Kiel, Germany Fax: +49 04 31 8 80-44 57; e-mail:
[email protected]
compositionally different end-members makes it possible to investigate changes in the spectra with changing chemistry. Compared to another common orthosilicate, olivine, relatively little work has been done on investigating its polarized single-crystal Raman spectrum. An understanding of the vibrational spectrum of garnet will enable more complex silicate structure groups (e.g. chain, sheet and framework silicates), whose structures and vibrational spectra are more complicated, to be investigated in more detail. In addition, from an applications point of view, the phonon spectrum of garnet can be used to infer thermodynamic properties (Hofmeister and Chopelas 1991b), which are of use in petrological and geophysical calculations. The first detailed Raman studies of garnet began in the 1960s with investigations on non-silicate garnets having important technological applications (e.g. Koningstein and Sonnich Mortensen 1968; McDevitt 1969). Later the geologically important silicate garnets (X3Y2Si3O12) were investigated (Moore et al. 1971; Hofmeister and Chopelas 1991a; Pinet and Smith 1993, 1994). Recent work has concentrated on the temperature (Gillet et al. 1992) and pressure dependence (Mernagh and Liu 1990; Schneider et al. 1990) of the Raman active modes. All these studies have provided a better understanding of the vibrational spectra of garnet, but work still needs to be undertaken in making mode assignments. It is not clear, for example, why translational frequencies of the SiO4-tetrahedra should be greater than those associated with the X-site cations (e.g. Hofmeister and Chopelas 1991a), when the mass of the latter are 2±4 times less than that of the SiO4 tetrahedron, and the force constant interactions between the X-site cations and SiO4 groups should be similar. In addition, the changes in Raman mode frequencies for compositionally well defined binary solid solutions need to be investigated with regard to the question of one mode or two mode behavior (see Hofmeister and Chopelas 1991a). In the present work, the single-crystal polarized Raman spectra of the six common silicate garnets pyrope (Mg3Al2Si3O12), almandine (Fe3Al2Si3O12), spessartine
143
(Mn3Al2Si3O12), grossular (Ca3Al2Si3O12), uvarovite (Ca3Cr2Si3O12) and andradite (Ca3Fe2Si3O12) have been measured and analyzed. The spectra, when combined with information from previous studies, enable the Raman active modes to be assigned and their frequencies as a function of composition to be described. In addition, the spectrum of pyrope is analyzed by measuring the mode shifts resulting from the replacement of 24Mg by 26Mg, because the isotope substitution method has proved successful in interpreting the vibrational spectra of inorganic solids and silicates (Tarte and Preudhomme 1970). This should aid in the assignment of a low frequency Raman mode located around 135 cm1 in pyrope (Hofmeister and Chopelas 1991a, Olijnyk et al. 1991), which is important for understanding the general lattice dynamic properties and the relatively large heat capacity of pyrope at low temperatures (Geiger et al. 1992). Lastly, the synthetic solid solution binaries pyrope-grossular and almandine-spessartine were measured using polycrystalline materials to investigate mode behavior with changing garnet composition.
Experimental methods Natural and synthetic garnets were used for the polarized singlecrystal Raman spectroscopic measurements. The localities and compositions of the natural garnets used are listed in Table 1. Pyrope single crystals of normal isotopic composition up to 1 mm in diameter were synthesized from oxides following the methods described by Geiger et al. (1991). In addition, pyrope crystals were synthesized using MgO (from the Puma Group Company) enriched with 97.100.20% of the isotope 26Mg, with 1.82% 24Mg and 1.08% 25Mg. Single crystals of spessartine were grown hydrothermally following the procedures described in Geiger and Armbruster (1997). Synthetic polycrystalline almandine-spessartine and pyrope-grossular garnets were also measured. The synthesis conditions and characterization of the two solid solutions are discussed by Bosenick et al. (1995) and Geiger and Feenstra (1997). Polarized Raman spectra were recorded with a Triplemate, SPEX spectrometer equipped with a O-SMA, Si-diode array. The polarization plane of the transmitted radiation is rotated by the garnet structure. Hence, all spectra were recorded in back-scattering geometry. The 488 nm, 100 mW line of an Ar-laser was used for the spectral excitation. The laser beam was focused to a diameter of 2 m using a LD-EPILAN, 40/0.60 Pol., Zeiss objective with a focal distance of 2 mm and a numerical aperture of 0.6. The spectral slit was 5 cm1 or less. Measurements were made perpendicular to {100} and {110} of the garnet single crystals in order to obtain the desired symmetry active modes. Table 1 Localities and compositions of the investigated natural garnets Sample Mol% Almandine Uvarovite Andradite Grossular Mongolia Sweden Chukota, Ural, Russia Russia Pyrope Almandine Spessartine Grossular Uvarovite Andradite Ti-Andradite
3.92 80.36 13.72 ± ± 2.00 ±
2.09 ± 0.77 27.87 67.25 1.61 0.40
0.82 ± 1.12 ± ± 98.06 ±
0.37 0.64 0.13 97.8 0.06 1.01 ±
Structure and factor-group analysis of garnet The general formula of the silicate garnets is X3Y2Si3O12 or X3Y2(SiO4)3. The structure has space group Ia3Åd, with Z=8. The cations are located in special positions fixed by symmetry and the oxygens are in general positions (Menzer 1928). The divalent X-site cations occupy the 24c position of 222 (D2) point symmetry, the trivalent Y-site cations the 16a position of 3Å (C3i) symmetry, and the Si-cation the 24d position of 4Å (S4) point symmetry. Theoretical factor group analysis on garnet permits the total number of vibrations and the number of Raman and infrared active modes to be calculated (Koningstein and Sonnich Mortensen 1968; Moore et al. 1971). The total irreducible representation at the G-point is given as follows: G=3A1g+5A2g+8Eg+14F1g+14F2g+5A1u+5A2u +10Eu+17F1u+16F2u The A1g-, Eg-, and F2g-modes are Raman active, for a total of 25, and 17 F1umodes are active in the infrared. Table 2 gives a description of the zone-center Raman active vibrational modes for the X-site cations and SiO4-tetrahedra in the garnet structure (the Y-site does not produce Raman active vibrations). This analysis assumes that mode mixing is not present or weak, which is not strictly the case as considered in the Discussion.
Results Raman spectra Figures 1a±f show the polarized Raman spectra of the six different end-member silicate garnets. The A1g spectra of the silicate garnets contain three intense modes around 350, 550 and 900 cm1, which can be assigned to rotational (R) (i.e. librational), internal bending and stretching vibrations of the SiO4-tetrahedra, respectively (Table 2). The approximate frequencies for these three different types of vibrations in garnet are therefore easily defined. These vibrations are also observed in Eg- and F2g-symmetries. Figures 2a±c show the low frequency region between 450 and 100 cm1 for synthetic 26Mg3Al2Si3O12 and Table 2 Symmetry analysis of the silicate garnets and the Raman active modes Internal (SiO)bend
External X2+
(Si-O)str
T(SiO4)
R(SiO4)
n2(E) n4(F2) n1(A1) n3(F2) A1g 1 Eg 2 F2g 1
± 1 3
1 1 ±
± 1 3
± ± 1 (z) 1 (z) 1 (z) 1 (z) 2(x, y) 3(x, y, z) 2(x, y)
144
Fig. 1a±f Polarized single-crystal spectra of the six end-member silicate garnets. The E(g) and F(2g) spectra are normalized in intensity to the A(1g) spectrum, which contains the most intense peaks 24
Mg3Al2Si3O12 pyrope. Table 3 lists the frequencies of the A1g-, Eg-, and F2g-symmetry related modes observed for both samples. A total of 17 modes can be observed. In the case of pure Mg-translations the isotopic substitution should result in frequency shifts described by: r m26 Mg n24 Mg 1:033 n26 Mg m24 Mg The nonpolarized spectra of the synthetic pyrope-grossular and almandine-spessartine garnets between 400 and 100 cm1 are shown in Fig. 3.
Discussion Spectrum of pyrope It remains to be clarified where the frequencies of the external translations of the SiO4-groups and the X-site cations in garnet are located. As a starting point, the polarized spectra of pyrope enriched in the isotope 26Mg and of normal isotopic compositions (i.e. 24Mg) are considered. The following analysis is in order. The F2g-mode located at about 135 cm1 in pyrope (Fig. 2c) is assigned to a largely Mg(x, y)-translation [T(Mg(x, y))], because its frequency shift (»3.7%) associated with isotopic substitution (Table 3) is great compared to the other modes and, more importantly, is in excellent agreement with that calculated. Temperature dependent
145 Table 3 Mode frequencies of normal and isotopically enriched pyrope
Fig. 2a±c Polarized single-crystal Raman spectra of synthetic 26 Mg3Al2Si3O12 (top) and 24Mg3Al2Si3O12 (bottom) pyrope
single-crystal X-ray refinements have shown that the Mgcation in pyrope shows substantial anisotropic dynamic disorder within the large dodecahedral X-site of D2 point symmetry (Armbruster et al. 1992). The largest amplitude of vibration of Mg is in the plane of the four longer MgO(4) bonds (2.340 (2) at 298 K), which is defined by 2C2© symmetry axes. We believe that this broad lowenergy mode at 135 cm1 is associated with Mg-motions within the plane of these longer bonds. This vibration gives rise to the so-called ªrattlingº motion of Mg in pyrope (Armbruster et al. 1992). Hofmeister and Chopelas (1991a) did not consider this mode a fundamental in their analysis of their Raman spectra. The very weak and broad mode in pyrope located around 284 cm1 (Fig. 2a) is associated with the largest isotopic shifts (i.e. about 10 cm1 and a 3.52% frequency shift) and is, therefore, assigned to a Mg(z)-translation of Eg-symmetry. This mode has a significantly higher energy than the T(Mg(x, y)) mode at 135 cm1, and is therefore interpreted to be associated with vibrations in the plane of the four shorter MgO(2) bonds (2.197 (2) at 298 K) of the X-site.
Symmetry
24
Mg3Al2Si3O12 (cm1)
26
Mg3Al2Si3O12 (cm1)
Shift (cm1)
Shift (%)
F2g A1g F2g F2g A1g Eg F2g F2g F2g A1g F2g Eg F2g Eg F2g Eg F2g
1066.0 928.0 878.8 650.6 562.8 525.0 512.1 492.4 383.2 364.1 353.2 344.5 322.0 284.0 212.5 210.9 136.5
1065.8 928.0 870.8 650.0 562.8 525.0 511.8 492.0 383.2 364.0 353.2 339.5 321.7 274.0 210.7 208.1 131.5
0.2 0.0 0.0 0.6 0.0 0.0 0.3 0.4 0.0 0.1 0.0 5.0 0.3 10.0 1.8 2.8 5.0
0.02 0.00 0.00 0.09 0.00 0.00 0.06 0.08 0.00 0.03 0.00 1.45 0.09 3.52 0.85 1.33 3.68
The low energy Eg- and F2g-modes around 210 cm1 in pyrope having the relatively moderate frequency shifts (Table 3), caused by the isotopic substitution, suggest that these modes are related to translational motions of the SiO4-tetrahedra [T(SiO4)4] and not Mg-cations. This assignment is also consistent with their mode intensities and frequency shifts as a function of composition across the pyrope-grossular join (Fig. 3 and see discussion in section ªMode compositional dependence in the solid solution garnet spectreº.). It is clear from the observed isotopic shifts that kinematic coupling does occur between T(SiO4)4 and T(Mg) modes. This phenomenon is more strongly developed in the external F1u infrared active modes of garnet (Cahay et al. 1981; Geiger, work submitted for publication). Therefore, it is difficult to describe the external vibrations as originating solely from certain atoms or polyhedral units. In the garnet structure each SiO4-tetrahedron shares opposite edges with X-site dodecahedra and the SiO4-groups and the X-sites cations must vibrate against each other. The assumption that the SiO44 tetrahedra can be treated as purely independent structural units is not strictly fulfilled. Spectra of the other silicate garnets The frequencies of T(SiO4)4 modes should be 1.5±2 times lower than those of R(SiO4)4 modes, because their vibrations consist of the entire tetrahedral unit, whereas for the latter only the oxygen anions are involved. For the other silicate garnets, only one intense mode is observed in the Eg-spectra in the frequency region less than 250 cm1. Therefore, this peak is assigned to a T(SiO4)4 mode (Table 4). All three predicted T(SiO4)4 F2g-modes cannot be observed because of probable band overlap. Two F2g-modes are observed at low frequencies between 170 and 280 cm1 in all silicate garnets except pyrope
146
Fig. 3 Low frequency Raman spectra of synthetic pyrope-grossular and almandine-spessartine solid solutions
(Fig. 1 and Table 4). They are assigned to X2+(x, y)-translations, as the mode at 135 cm1 in pyrope. In the case of grossular, for example, the two modes at 280 and 247 cm1 decrease strongly in intensity with decreasing grossular content along the pyrope-grossular binary (Fig. 3) and, therefore, are assigned to Ca(x, y)-translations. The splitting of these two modes is a result of the two different force constants acting between Ca and the oxygen atoms in the XY bonding plane of the X-site. It is unclear why only one Mg(x, y)-translation mode is observed in the F2g-spectrum of pyrope, whereas two are observed for the other garnets. In the case of the former, the broad F2g-band at 135 cm1 may consist of two components. A weak mode is observed in the Eg spectra at 256 cm1 in almandine, 269 cm1 in spessartine, 320 cm1 in grossular, and 298 cm1 in andradite (Table 4). An analogous mode could not be observed in the case of uvarovite. These modes are assigned to a X2+(z)-translation based on their frequency dependence as a function of composition and their placement relative to a R(SiO4) mode of Eg symmetry (see next section). We have no satisfactory explanation why they are so weak in intensity. Table 4 lists all the observed Raman active modes and their symmetry assignments for the six silicate garnets
studied herein (compare to Hofmeister and Chopelas 1991a). As can be observed in Fig. 1, only two Eg-modes, instead of three, as predicted factor group analysis (Table 2), are observed in the frequency range expected for the SiO4 bending vibrations (450±650 cm1), whereas two Eg-modes, instead of one, are observed in the frequency range assigned to external SiO4 rotations. It is possible that the Eg rotational mode with the higher energy (at 400 cm1) can be assigned to an internal SiO4 bending motion. In this case, the vibration can be described by a displacement of oxygen atoms around the S4-axis and hence, an internal bending frequency will differ little from an external rotational frequency if interactions between the oxygen atoms in the tetrahedron are weak. This situation is possible for a SiO4-tetrahedron having 4Å point symmetry. Mode compositional dependence for the end-member garnet spectra Figures 4a±d show plots of the different mode frequencies of the various garnets as a function of their unit-cell dimension (cf. Hofmeister and Chopelas 1991a). Mode behavior can be related to both composition and structure. The following conclusions are permitted by the data. The frequency of the symmetric (SiO) stretching mode in the silicate garnets correlates with their cell dimensions (Moore et al. 1971; Hofmeister and Chopelas 1991a). There is no appreciable change in the XSiO4
147 Table 4 Mode assignments and symmetries of the Raman active modes of the silicate garnets Pyrope
Almandine
Eg
F2g
A1g
945
1066 902 871
916
626 a 525 375
650 598 512 492
556
344
383 353 322
342
T(SiO4)4
211
222
2+
284
A1g (SiO)str. (SiO)bend
R(SiO4)4
T(X ) a
928 563
364
135
Spessartine
Eg
F2g
A1g
930
1038 897 863
905
630 581 500 475
552
596 521 a 370 323
355 a 314
350
Grossular
Eg
F2g
A1g
913 a
1029 879 849
880
592 a 522 372 321
630 550 573 a 500 475 350 a 302
Uvarovite
Andradite
Eg
F2g
A1g
Eg
904 a
1007 848 827
876
1002 894 864 838
630 582 512 483
526
590 526
618
389 351 333
370
366
388
176
178
174
174
272 242
298
264 236
592 529 420
376 373 319 a
167
170
162
175
181
186
256
216 171
269
221 196
320
280 247
F2g
A1g
Eg
F2g
874
995 842 816
516
574 492 382
593 a 553 494 452
370
352
509 459
325 312
Modes not observed herein but by Hofmeister and Chopelas (1991a)
Fig. 4a±d Dependencies of vibrational frequencies on the unit-cell constant of garnet. A1g-modes (circles), Eg-modes (squares), and F2g-modes (triangles)
148
Fig. 5 Change in the frequency of T(SiO4) vibrations plotted against the reciprocal square-root of the reduced mass of (X2+SiO4)
chemical interaction among the different garnets. This is also apparent based on the frequency changes of the Xsite cation translations (see below, this section). We propose, therefore, that the changing of the SiO stretching vibration frequencies is largely controlled by repulsive interactions between the oxygen atoms. The frequencies of external translations of the SiO4tetrahedron show, in the case of the aluminosilicate garnets, a linear dependence as a function of the reciprocal square-root of the reduced masses of the X-site cations and the SiO4-tetrahedron (Fig. 5). We interpret this as indicating that the electron orbitals, the ionic radii of the Xsite cations, as well as the cation-anion interaction potentials, do not greatly affect the T(SiO4)-mode frequencies. Instead, coupling of these modes with X-site cations translations appears to be the main factor in controlling their frequency. The frequency of the SiO4-bending and -rotational modes (Figs. 4b, c) is controlled in the same manner as the stretching and translational vibrations. It is observed that the Eg-modes associated with rotational vibrations in grossular are greater in frequency compared to those of the other garnets (Fig. 4c). We consider that this is a result of coupling of this mode with X2+-translations (Fig. 4d) of the same Eg-symmetry, because the same relationship is observed for isotopically enriched pyrope (Fig. 2b, Table 3). Mode compositional dependence in the solid solution garnet spectra Two binary garnet solid solutions were investigated, namely the pyrope-grossular and almandine-spessartine joins. In the case of the latter, only small changes in the spectra with changing composition are expected based on the similarities in the size and mass of Mn2+ and Fe2+ cations (0.96 vs. 0.92 and 54.94 vs. 55.85 a.m.u., respectively). The pyrope-grossular join should,
on the other hand, show considerable differences in the spectra as a function of composition across the binary. An important proposal regarding the mode behavior of garnet solid solutions was made by Hofmeister and Chopelas (1991a) and concerns the phenomena of twomode behavior (Sherwood 1972). Hofmeister and Chopelas (1991a) interpreted the occurrence of twomode behavior in certain garnet binaries on the basis of large size and mass differences between the mixing X-site cations. Two mode behavior is best illustrated by the pyrope-grossular binary. Figure 3 shows the low frequency spectra for this solid solution. Two types of mode behavior can be observed. The mode located at about 210 cm1 in pyrope and 186 cm1 in grossular, which is assigned to a T(SiO4)-vibration (Table 4), shows one mode behavior, because it is traceable across the binary. It remains relatively intense with changing X-site composition. The case is different for vibrations associated with X-site cations in the dodecahedral site. The modes at about 135 cm1 [Mg(x, y)-translation] and 250 and 280 cm1 [Ca(x, y)-translations) show two-mode behavior, because they decrease in intensity towards intermediate solid solution compositions until they are no longer observable (Fig. 3). In the solid solution compositions, the frequency of the ªMg translation modeº appears to decrease with increasing substitution of Ca in garnet. The ªCa-related modesº broaden and the frequencies remain nearly constant in the range 75±100 mol% grossular, but then decrease in peak widths of the frequency with increasing pyrope component between 75 and 50 mol% grossular. At grossular contents below about 50 mol%, their intensities are too weak to observe. These Ca-translational modes show two-mode behavior because their frequencies do not overlap with that of Mg in pyrope and vice versa. The frequencies of the Mgand Ca-translations are not a simple linear function between the two end-member garnets, but are instead associated with their corresponding dispersion curves. Phonons of a given optical branch of kÐ0 may become Raman active when a certain defect level concentration (i.e. solid solution) is reached. Therefore, the observed frequencies of the phonons associated with the X-site will be changed within the region defined by the dispersion branch, when substitution takes place. This assumes that the interactions between the substituting cations are weak. This should be valid for Mg-vibrations in pyrope-rich solid solutions and Ca-vibrations in grossular-rich compositions. Lattice dynamic calculations for structures as complicated as garnet have not been undertaken and thus a rigorous physical explanation is not at hand. In most instances where two mode behavior has been reported (Barker and Sievers 1975 and references therein), and the physics described, it occurs in structurally simpler two component alkali halides and type III-V semiconductors of the general formula A yB1-yC. In solid solution compounds of these
149
Fig. 6a±d Selected Raman mode frequencies as a function of composition along the pyrope-grossular binary
types the Raman active phonons must be associated with displacements of the atoms in both sublattices, which preserve the center of mass of the unit cell. Silicate structures, including garnet, are considerably more complicated structurally involving a number of different type of vibrations of a number of different atoms over different sublattices. Hence, vibrations on one sublattice will not necessarily be linked to those of another. It is not expected, therefore, that two mode behavior will occur for vibrations other than those of the X-site cations in garnet solid solutions, unless other modes couple strongly to them. External (SiO4)4 vibrational modes are expected to show one mode behavior as a function of composition. Figures 6 and 7 show the dependencies of certain mode frequencies versus composition for the pyrope-grossular and almandine-spessartine solid solutions. The mode frequency changes associated with the latter binary are linear as a function of composition across the join. The modes display one mode behavior, because the masses and chemical bonding properties of Fe2+ and Mn2+ are similar to one another. Mode behavior is very different for X-site vibrations across the pyrope-grossular join. Conversely, the change in mode frequencies across both series for
Table 5 Selected mode frequencies for almandine-spessartine garnets Mol% Spess.
T(SiO4) Eg
T(X2+) F2g
R(SiO4) A1g
(SiO)bend A1g
(SiO)str. A1g
0 13 25 50 75 100
167.9 167.5 166.2 165.0 165.0 166.0
215.8 214.2 215.8 215.4 218.7 221.2
340.4 341.8 343.0 344.6 347.4 349.4
554.0 552.5 552.9 552.6 552.0 551.5
916.0 914.2 913.0 908.0 906.7 904.7
SiO stretching and bending frequencies, which show one mode behavior, are similar. Selected mode frequencies are listed in Tables 5 and 6. The behavior of the low frequency Raman modes along the pyrope-grossular binary is similar to that displayed by the IR active modes (Bosenick et al. 1995). The frequencies of the modes of the solid solutions tend to decrease away from the two end-members pyrope and grossular. This shift to lower could be the frequencies cause for the excess heat capacities measured for pyrope-grossular garnets (Haselton and Westrum 1980), assuming that the zone-center vibrations are representative for the complete phonon density of states at low energies. The new mode assignments presented
150
Fig. 7a±d Selected Raman mode frequencies as a function of composition along the almandine-spessartine binary
Table 6 Selected mode frequencies for pyrope-grossular garnets
Mol% Gross.
T(Mg) F2g
T(SiO4) Eg
0 10 25 50 75 90 100
135.0 127.0
208.2 203.5 198.1 189.5 183.7 182.0 180.8
T(Ca) F2g
235.0 244.0 247.0 246.0
T(Ca) F2g
R(SiO4) A1g
(SiO)bend A1g
(SiO)str A1g
254.0 280.0 278.0 277.0
362.8 364.0 366.0 367.6 371.4 372.0 371.9
560.0 559.5 558.5 554.8 551.5 549.8 547.5
924.7 920.5 914.0 901.0 890.0 882.8 877.5
herein will enable better estimates of the heat capacity of garnets via lattice dynamic model density of state calculations (e.g. Hofmeister and Chopelas 1991b) and may give better agreement between experiment and calculation.
composition. We think that the general order of mode frequencies, i.e. R(SiO4)>T(metal cation)>T(SiO4), is true for most orthosilicates, excepting those where very heavy or light cations are present. This is a result of the similarity of the chemical interactions of the different vibrational units and their masses.
Conclusions
Acknowledgements Anne Bosenick synthesized the isotopically enriched pyrope and Anne Feenstra the almandine-spessartine garnets. Björn Winkler provided several beneficial discussions, as well a critical review of an early draft of the manuscript. We thank them all. This research has been supported in part by a grant from the Deutsche Forschungsgemeinschaft Ge 659/2-3.
A new assignment of the Raman active modes for the silicate garnets has been presented. It leads to a relatively simple explanation of the frequencies as a function of
151
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