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ties of pyrope and grossular to 60 kbar. Am Mineral 63:297±303. Hazen RM, Finger LW (1979) Crystal structure and Compressibility of zircon at high pressure.
Phys Chem Minerals (1998) 25:301±307

 Springer-Verlag 1998

ORIGINAL PAPER

L. Zhang ´ H. Ahsbahs ´ A. Kutoglu

Hydrostatic compression and crystal structure of pyrope to 33 GPa

Received: 24 March 1997 / Revised, accepted: 29 July 1997

Abstract The equation of state and crystal structure of pyrope were determined by single crystal X-ray diffraction under hydrostatic conditions to 33 GPa, a pressure that corresponds to a depth of about 900 km in the lower mantle. The bulk modulus KT0 and its pressure derivative 0 KT0 were determined simultaneously from an unweighted fit of the volume data at different pressures to a third order Birch-Murnaghan equation of state. They are 171(2) GPa and 4.4(2), respectively. Over the whole pressure range, MgO8 polyhedra showed the largest compression of 18.10(8)%, followed by AlO6 and SiO4 polyhedra, with compression of 11.7(1)% and 4.6(1)%, respectively. The polyhedral bulk moduli for MgO8, AlO6 and SiO4 are 107(1), 211(11) and 580(24) GPa, respec0 tively, with KT0 fixed to 4. Significant compression of up to 1.8(1)% in the very rigid SiŸO bonding in pyrope could be detected to 33 GPa. Changes in the degree of polyhedral distortion for all three types of polyhedra could also be observed. These changes could be found for the first time for AlO6 and SiO4 in pyrope. It seems that the compression of pyrope crystal structure is governed by the kinking of the AlŸOŸSi angle between the octahedra and tetrahedra. No phase transition could be detected to 33 GPa.

Introduction The elasticity and crystal structure of pyrope Mg3Al2 (SiO4)3 have been of wide interest (Levien et al. 1979; Leitner et al. 1980; ONeill et al. 1989; Webb 1989) because pyrope rich garnet is considered to be a major mineral in the Earths upper mantle and transition zone. In addition, it also appears as a major mineral in eclogites. We have studied pure synthetic pyrope up to 33 GPa because: (1) a more accurate determination of equation of

)

Li Zhang ( ) ´ H. Ahsbahs ´ A. Kutoglu Institute of Mineralogy, University of Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany Fax: +49-6421-285612

state using single crystal diffraction at pressures that cover the transition zone and down into the lower mantle would be helpful in tightly constraining the mineralogical compositions in these regions; (2) knowledge of the crystal structure of mantle minerals at pressures in stable and metastable states as well as the compression mechanisms is of fundamental interest for understanding phenomena like cation order-disorder, element partitioning and phase transition; (3) knowledge about SiŸO bonding at extended pressures is essential to understand the transition between four and six fold coordinated silicon which is characteristic of transition zone and lower mantle mineralogy. Single crystal X-ray diffraction potentially provides the most accurate unit-cell parameters and atomic coordinates of a crystal structure at high pressures. Experiments that cover the pressure range to the lower mantle (>24 GPa) are difficult and the previous pressure range was limited to about 20 GPa (Hazen and Finger 1989). Two major problems that dictate the pressure limit in the intensity measurement by single crystal X-ray diffraction are the reduced signal/noise ratio from intrinsic background of pressure cells and pressure transmitting media. In addition, higher target pressures reduce further the signal/noise ratio because in such an experiment the crystal volume is drastically limited. For example, the crystal volume for an experiment above 20 GPa is more than 5 times smaller than for an experiment at pressures lower than 10 GPa. This results in a very low signal/noise ratio that hampers an intensity measurement of reasonable quality. Secondly, most pressure transmitting media, including mixtures of alcohols, alcohols and water, and rare gases such as Ar and Ne become solid or stiff below 15 GPa (Bell and Mao 1980; Zhang and Ahsbahs 1998). This induces devitoric stresses and deteriorates the diffraction quality of a crystal. In this paper we demonstrate new advances in performing single crystal intensity measurement to 33 GPa. We present results of equation of state and atomic positional parameters of pyrope to a pressure of 33 GPa.

302

Experimental details Samples Transparent, colorless single crystals of pyrope, Mg3Al2(SiO4)3 were synthesized and donated by Dr. C. A. Geiger, University of Kiel. For the measurement of the unit-cell parameters polished pyrope crystals with dimensions of about 100”60”40 m and about 80”80”25 m were used. High pressure X-ray diffraction technique In this experiment we have used modified Merill-Bassett diamond anvil cells. The diameter of the diamond culet was 600 m. Gaskets of the material Thyrodur 2709 (Ahsbahs 1996; Zhang et al. 1997b), preindented to about 60±85 m were used. By using this material the sample hole volume at 10 GPa is more than doubled compared to the Inconel gasket materials. This allowed significantly larger crystals to be accommodated in the sample hole and thus improved the signal/noise ratio. The starting diameters of sample holes range from about 300 to 400 mm. For a part of the experiments for measuring unit-cell parameters, a pyrope crystal was loaded together with four other garnet crystals. Rare gas neon or helium was used as pressure transmitting medium in the experiments for determining unit-cell parameters. For intensity measurements only helium was used as a pressure transmitting medium. Several ruby grains, which served as a pressure calibrant, were added to the pressure cell. The radial pressure gradient was checked in each experimental run. In the experiments with neon as a pressure transmitting medium this gradient was measured to be as high as 1 GPa at pressures of about 15 GPa; in the experiments with helium as a pressure medium it was measured to be 0.3±0.5 GPa across the sample hole at the highest pressure. The relatively large pressure gradient in neon induces severe broadening of reflections. For example, at about 15 GPa the halfwidth of the reflection (420), typically about 0.2 in w at ambient conditions, became doubled. In the helium medium no such broadening on the same reflection could be observed to 33 GPa, indicating a highly hydrostatic pressure environment around the crystal. Pressure was determined by using the pressure-induced shift of the R1 fluorescence line of ruby. The error of the pressure measurement was estimated and listed in Table 1. The measurements were completed with several consecutive pressure cell mounts. The unit-cell parameters of pyrope were measured at 38 different pressures in raising as well as in releasing pressure runs. Diffraction measurements were performed with a Stoe automated four circle diffractometer using MoKa radiation (0.71073 Š). The diffractometer was operated at up to 55 kV, 35 mA. The unitcell parameters were determined from up to 21 reflections with 2 q ranging from 13 to 39. Each reflection was centered in eight positions (King and Finger 1979) to reduce zero and crystal-centering errors. The unit-cell parameters were calculated using the procedure of Ralph and Finger (1982). There was no significant deviation between the unit-cell parameters constrained or not constrained to cubic symmetry in all the refinements. Intensity collection at high pressure A hemisphere of integrated intensities in reciprocal space at 7 different pressures up to 33 GPa were collected to a sin q/l=0.7035 ŠŸ1. The w-scan width was 1.2 with a step size of 0.01. A specially designed collimator, placed on the diffracted beam side of the diamond cell, was used to reduce the background produced mainly by the beryllium backing plates of the diamond cell. A reduction of the background to a factor of four has been achieved in this way (Zhang and Ahsbahs, in press). Data collections were carried out on one pyrope crystal in the diamond cell in the sequence of releasing pressure. The constant-precision mode was used with a maximum counting time per step of 6 s for reaching I/sI>20. Intensities of standard reflections were monitored every 2 hours, without any significant deviations observed. Profiles of several reflections were scanned at each pressure for monitoring hydrostatic pressure and crystal quality.

Table 1 Unit-cell parameters of pyrope at pressure P (GPa)

V (Š3)

a (Š)

0.0 11.4545(8) Measured in helium pressure medium 3.48(5) 11.3846(8) 8.57(5) 11.2893(7) 11.53(5) 11.2353(7) 15.28(10) 11.1717(8) 16.10(20) 11.1576(9) 17.95(22) 11.1258(8) 20.65(20) 11.0894(9) 22.23(23) 11.0672(8) 22.41(20) 11.0594(8) 23.02(30) 11.0540(14) 23.78(30) 11.0455(9) 24.07(20) 11.0335(8) 25.52(30) 11.0208(9) 26.82(20) 11.0062(7) 28.76(30) 10.9821(10) 29.88(40) 10.9665(9) 30.91(30) 10.9549(8) 32.47(30) 10.9339(9) 33.38(30) 10.9259(8) Measured in neon pressure medium 2.30(5) 11.3991(8) 2.49(5) 11.3954(7) 3.28(5) 11.3794(7) 4.85(5) 11.3499(8) 6.00(5) 11.3230(7) 6.88(5) 11.3106(6) 8.03(5) 11.2898(7) 9.36(5) 11.2669(7) 10.75(5) 11.2434(9) 11.44(10) 11.2302(10) 12.03(30) 11.2208(8) 13.36(30) 11.1997(11) 13.89(10) 11.1888(11) 14.60(50) 11.1770(10) 11.163(2) 15.61(50) a 16.74(50) a 11.144(3) 11.133(4) 17.51(50) a a 11.107(3) 19.24(50) 11.087(4) 21.58(80) a a

1502.9(3) 1475.5(3) 1438.8(3) 1418.3(3) 1394.3(3) 1389.0(3) 1377.2(3) 1363.7(3) 1355.5(3) 1352.7(3) 1350.7(5) 1347.6(3) 1343.2(3) 1338.6(3) 1333.3(3) 1324.5(4) 1318.9(3) 1314.7(3) 1307.1(3) 1304.3(3) 1481.2(3) 1479.7(3) 1473.5(3) 1462.1(3) 1451.7(3) 1446.9(3) 1439.0(3) 1430.3(3) 1421.3(3) 1416.3(4) 1412.8(3) 1404.8(4) 1400.7(4) 1396.3(4) 1390.9(9) 1384 (1.0) 1380 (1.1) 1370 (1.2) 1363 (1.3)

Not used in fitting EOS

Table 2 Intensity refinement parameters for pyrope at pressure (GOF goodness of fit) P (GPa) Rmerge Weight 1/sI2

0.0 3.48 8.57 11.53 15.28 24.07 32.47

3.33 5.18 5.43 6.70 6.76 6.35 5.50

Rw

R

GOF

1.30 1.87 2.03 1.90 1.90 2.43 2.53

2.02 3.28 3.59 4.38 4.48 5.42 5.51

1.50 1.84 1.94 1.71 1.76 2.22 2.28

Used for refinement

I > 3s

132 136 130 121 132 125 117

62 63 60 58 63 60 62

The program package CRYMIS was used for data reductions and structure refinements (Kutoglu 1995). The observed integrated intensities were calculated according to Lehmann and Larsen (1974). They were corrected for absorption by the diamonds and beryllium backing plates. The intensities of the symmetrically equivalent reflections were averaged in Laue group m3m, yielding among

303 Table 3 Positional, thermal parameters, selected bond angles and lengths of pyrope at pressure. B is the isotropic temperature displacement parameter. Standard deviations are given in parentheses P (GPa) O

x y z B

4”Mg(1)ŸO(4) 4”Mg(2)ŸO(4) 6”AlŸO 4”SiŸO

3.48

8.57

11.53

15.28

24.07

32.47

0.0332(2) 0.0497(2) 0.6537(2) 0.54(5)

0.0331(2) 0.0518(3) 0.6541(3) 0.54(5) a

0.0330(3) 0.0527(3) 0.6535(4) 0.54(5) a

0.0333(3) 0.0539(3) 0.6536(3) 0.54(5) a

0.0327(3) 0.0545(3) 0.6535(3) 0.54(5) a

0.0325(3) 0.0566(3) 0.6536(4) 0.54(5) a

0.0321(4) 0.0571(3) 0.6527(4) 0.54(5) a

2.197(2) 2.348(2) 1.889(2) 1.627(2)

Ð SiŸOŸAl a

0.00

2.186(3) 2.312(3) 1.888(3) 1.623(3)

131.0(2)

129.8(2)

2.173(4) 2.281(4) 1.870(4) 1.619(4) 129.4(2)

2.169(3) 2.258(3) 1.867(3) 1.613(3) 128.8(2)

2.154(3) 2.237(3) 1.856(3) 1.611(3) 128.3(2)

2.131(4) 2.187 (4) 1.841(4) 1.601(4) 127.1(2)

2.115(4) 2.160(4) 1.816(4) 1.598(4) 126.9(2)

Fixed to the value at ambient pressure

117 and 136 unique intensities for the data sets at different pressures. The intensities were corrected for Lorenz and polarization effects. No correction of the absorption by the crystal was applied to the intensities. Neutral atomic scattering factors (International Table of Crystallography 1974) were used in the structure refinements. The refined parameters were a linear scaling factor and the positional parameters for the oxygen atom. Isotropic displacement parameters at high pressures were fixed to the value at ambient pressure. The reflections that obviously overlap with diamond reflections were rejected in the refinements. The refinement conditions and the refined parameters are included in Table 2 and 3.

Results and Discussion Equation of state (EOS) There have been extensive efforts to determine the equation of state of pyrope using various experimental techniques. The previous data are summarized in Table 4. Bonczar and Graham (1977), Webb (1989), Sato et al. (1978) and Levien at al. (1979) determined both bulk modulus and its pressure derivative simultaneously. Takahashi and Liu (1970) and Leger et al. (1990) determined EOS of pyrope up to 35 GPa on polycrystalline samples, but the bulk modulus and its pressure derivative could not be determined unambiguously. Our intention in this work is to measure more precise data in the pressure range that covers the whole upper mantle, transition zone and down to lower mantle so that both values can be determined simultaneously.

The measured unit-cell parameters of pyrope at 38 pressures are listed in Table 1. The strained crystal in neon medium at pressures above 15 GPa is revealed in the large standard deviations of unit-cell parameters. They are about 2 to 3 times as large as those at lower pressures. They are marked in Table 1 and were not used for determining EOS. In the data measured in hydrostatic helium medium no such behavior can be observed. The unit-cell parameters at 33 GPa can be determined to the same precision as at ambient pressure. The volume data from ambient pressure to 33 GPa were fitted to a third order BirchMurnaghan equation of state h i P ˆ 3=2KT0 …V0 =V †7=3 ÿ…V0 =V †5=3 n io  h 0 …1† 1 ‡ 3=4 4 ÿ KT0 …V0 =V †2=3 ÿ1 ; 0

where KT0 and KT0 is the isothermal bulk modulus and its first pressure derivative, V0 and V the unit-cell volume at ambient pressure and at high pressure, respectively. Due to measurable pressure gradient at pressures above the solidifying pressures of Ne and He the estimated errors in the pressure determination, which were derived by measuring several ruby grains around the crystal, were subject to relatively large uncertainties. To avoid a biased weighting scheme we used an unweighted fit for Eq. (1), instead of a weighted one like Zhang et al. (1997b). In the fittings the V0 was fixed to the value determined in this study. The

Table 4 Bulk modulus and its pressure derivative for pyrope Mg3Al2(SiO4)3 (SC single crystal, PC polycristalline) K (GPa)



K©©

P (GPa)

Sample

Method

References

168.2(4) 173.0(9) 173.6(4) 175(1) 172.8(3) 190(6) 171(3) 175(1) 172.8 a 174(3) 171(2)

4.74(16) ± 4.93(6) ± ± 5.45 a 1.8(7) 4.5(5) 3.8(1.0) 4a 4.4(2)

± ± Ÿ0.28(4) ± ± ± ± ± ± ± ±

1 0 3 0 0 35 10 5 25 4.7 32.5

SC SC SC SC SC PC PC SC PC SC SC

Ultrasonic Ultrasonic Ultrasonic Brillouin scattering Brillouin scattering X-ray diffraction X-ray diffraction X-ray diffraction X-ray diffraction X-ray diffraction X-ray diffraction

Bonczar and Graham 1977 Babuska et al. 1978 Webb 1989 Leitner et al. 1980 ONeill et al. 1989 Takahashi and Liu 1970 Sato et al. 1978 Levien at al. 1979 Leger et al. 1990 Hazen et al. 1994 This study

a

Fixed at this value

304

fit to the EOS with data measured in helium pressure me0 dium yielded KT0=171(2) GPa and KT0 =4.4(2), respectively. The fit with data 0in neon pressure medium yielded GPa and KT0 =6.4 (6). The KT0=168(1) GPa KT0=159(3) 0 and KT0 =4.7(1) were determined if volume data measured both in helium and in neon were used together in fitting the EOS. Considering the conversion of KS=KT(1+a gT) and taking a=2.69”10Ÿ5/K (Meagher 1975), g=1.5 and T=298 K, we obtained after the conversion KS=173 GPa which agrees excellently with the value KS=172.8(3) determined by ONeill et al. (1991) using Brillouin spectroscopy and with values determined by Babuska et al. (1978) and Webb (1989) who used ultrasonic techniques (Table 4). The different results obtained from0 the fit using danot simulta measured in neon show that KT0 and KT0 can 0 taneously be determined by this data set. If KT0 was fixed to 4.4 in the fit, KT0=168.6(7) GPa was obtained which agrees reasonably with KT0=171(2) determined above using data measured in helium. It is clear that the EOS determined using data measured in helium is more reliable.

Fig. 1 The changes of bond lengths for MgO8, AlO6 and SiO4 to 33 GPa. The standard deviations are smaller than the symbols

Polyhedral compression The atomic positional parameters of pyrope at 7 pressures are listed in Table 3. The interatomic distances (bond lengths) as well as polyhedral volumes are presented in Table 3 and Figs. 1, 2 respectively. Our data determined in diamond cell at ambient pressure agree well with data measured by Ambruster et al. (1992). The improved high pressure techniques used in this work made it possible that the precision in the positional parameters at 33 GPa is comparable with those at ambient pressure. On this basis, good accuracy in the interatomic distances can be obtained over the whole pressure range, from which the polyhedral volumes as well as some of their elastic properties can be calculated. MgO8 polyhedra The MgO8 polyhedra comprise about 32.3% of the unitcell volume at ambient pressure. The compression of the two individual bond lengths shows strong anisotropy. The longer bond Mg(2)ŸO(4) is twice as compressible as shorter Mg(1)ŸO(4) bond, 8.03(7)% versus 3.71(7)% at 33 GPa respectively (Fig. 3). The polyhedral volume showed a compression of 18.10(8)% which is larger than the unit-cell volume compression of 13.026(3)% in the same pressure range (Fig. 2). The bulk modulus is determined to be 107(1) GPa by a fit of the MgO8 polyhedral 0 volume data to a Birch-Murnaghan EOS with KT0 fixed to 4. An unconstrained fit of the above data yielded a 0 KT0=105(6) and KT0 =4.2(6). Hazen and Finger (1989) reported a polyhedral bulk modulus of 160 GPa for CaO8 in andradite. This value is much larger than that determined for MgO8 in this study. Since the bulk modulus of andradite Ca3Fe2(SiO4)3 determined up to 14 GPa is 162(5) GPa (Zhang et al. 1996) which is smaller than that of pyrope, 171(2) GPa, and the polyhedral volume of CaO8 is about 20% larger than MgO8, it is expected from bulk modulus-

Fig. 2 Relative change of polyhedral volumes, unit-cell volume and cavity volume (V/V0) to 33 GPa

volume relationship that CaO8 should have a lower bulk modulus. We suggest that the value determined for CaO8 (Hazen and Finger 1989) may be overestimated somewhat. AlO6 and SiO4 polyhedra The volume of AlO6 and SiO4 polyhedra together accounts for about 12% of the unit-cell volume; the AlO6 octahedra and SiO4 tetrahedra account for 9.6% and 2.3% respectively. To 33 GPa the AlŸO bond length exhibits a compression of 3.86(9)% and the AlO6 octahedral volume a compression of 11.7(1)% (Fig. 3). The relatively rigid SiŸO bond length has a compression of only 1.8(1)% and the SiO4 tetrahedra show a volume compres-

305

Fig. 3 Relative changes of bond length di/d0 at high pressures in different polyhedra, where d0 is the bond length at ambient pressure. The anisotropic compression in bond lengths of MgŸO is shown by the solid symbols. Significant compression in SiŸO bond length is evident

sion of 4.6(1)% at the highest pressure (Fig. 2). The small but significant compression of SiŸO bonding in pyrope can be determined for the first time over a large pressure range. The bulk moduli of AlO6 and SiO4 are 211(11) and 580(24) GPa respectively, with their pressure derivatives fixed to 4. Since the average AlŸO bond length 1.889(2) Š in pyrope is 6.3% smaller than the value of Fe3+ŸO 2.016(2) Š in andradite at ambient pressure, it is surprising that the polyhedral bulk modulus of AlO6 is about 36% smaller than that of Fe3+O6 in andradite, with a value of 330 (33) GPa (Hazen and Finger 1989). Recent results observed in Fe2+O6 and MgO6 octahedra in different minerals of distinct crystal structures did show an anomalous bulk modulus-volume relationship (Hazen 1993; Zhang et al. 1996; Zhang et al. 1997b). It is not yet clear if AlO6 and Fe3+O6 would provide another example of this anomaly. More precise determination of polyhedral bulk modulus of Fe3+O6 is needed. The compressibility of SiŸO bonding has been of great interest, especially in the context of the transition between four and six fold coordinated silicon in the Earths transition zone and lower mantle. The high incompressibility of SiŸO bonding, however, made it difficult to determine, for example, the bulk modulus of SiO4 in the mantle minerals. Recent experiments at extended pressures (Kudoh and Takeuchi 1985; Hazen and Finger 1989; Hugh-Jones and Angel 1994; Zhang et al. 1997b; this study) revealed significant compression of SiŸO bond lengths (Fig. 4). It is noted that the compressibility of SiŸO bonding exhibits a very broad range. For example, from ambient pressure to 19 GPa the SiŸO bond in pyrope experienced compression of only 1.1%, whereas that of andradite was 3.1%. Their relevant SiO4 bulk moduli are 580(24) and 200(20) GPa, respectively.

Fig. 4 Compression of the SiŸO bond in different minerals. Significant compression of SiŸO bond length is only observable for measurements to relatively high pressures. SiŸO bond shows distinct compressibilities in minerals. n CaFeSi2O6 (Zhang et al. 1997b), l Mg3Al2(SiO4)3 (this study), n LiScSiO4 (Hazen et al. 1996), l Mg3Al2(SiO4)3 (Levien et al. 1979), s Ca3Fe2(SiO4)3 (Hazen and Finger 1989), s CaMgSi2O6 (Levien and Prewitt 1981), ] Al2SiO5 (Ralph et al. 1984), t SiO2 (Glinnemann 1987), +ZrSiO4 (Hazen and Finger 1979), u Ni2SiO4 (Finger et al. 1979), u Mg2SiO4 (Kudoh and Takeuchi 1985)

Polyhedral distortion and compression mechanism The degree of polyhedral distortion can be characterized with distortion indices. We have used the following parameters (Renner and Lehmann 1986) to characterize the change of polyhedral distortion at high pressure: Bond length distortions (BLD) n di ÿ d 100 X BLD …%† ˆ n iˆ1 d Edge length distortions (ELD) ELD …%† ˆ

n 100 X jxi ÿ xj n iˆ1 x

Angular distortions (AD) AD …%† ˆ aj ˆ

n 100 X aj n j

m X ai ÿ aideal iˆ1

aideal

where di, xi are the bond length and edge length, dÅ and xÅ the average bond and edge length in a polyhedron, a the polyhedral angle and aideal the polyhedral angle of a regular polyhedron.

306

Fig. 6 The change of the kinking angle SiŸOŸAl to 33 GPa

Fig. 5 The changes of polyhedral distortions versus V/V0 of polyhedral volume changes to 33 GPa. MgO8 and SiO4 become more regular, AlO6 becomes more distorted with increasing compression

The results calculated as above are presented in Fig. 5. MgO8 polyhedra become much more regular with increasing pressure, as indicated by Hazen and Finger (1978) in their study to 6.1 GPa. Our current data in a much larger pressure range revealed also changes of polyhedral distortion for AlO6 and SiO4 that were not observed in previous work. The AlO6 octahedra become more distorted and, most strikingly, the SiO4 tetrahedra become more regular with increasing pressure. It is expected that compression of the garnet crystal structure is a result of the compression in the constituent polyhedra. In fact, the polyhedral volume MgO8, AlO6 and SiO4 together accounts for about 44.2% of the unitcell volume. The bulk modulus of pyrope, calculated with the polyhedral bulk moduli weighted by their volume fraction, is 165 GPa, which is comparable to the value 171(2) GPa determined from the unit-cell volume. The close agreement of these two values could imply that it is possible to obtain a bulk modulus from those of the constituent polyhedra in a very close packed structure like

garnet. In other words the compression of the pyrope crystal structure could be accounted for by polyhedral compression. Since the volume fractions of AlO6 and SiO4 and voids in pyrope increase by about 2% from ambient pressure to 33 GPa at the expense of that of MgO8, it is clear that MgO8 contributes primarily to the compression of the whole structure. There could be several mechanisms that result in polyhedra compression in the pyrope structure. Firstly, a change in the degree of polyhedra distortion induces a change in the polyhedral volume of MgO8 at high pressures, which accounts for a large portion of the MgO8 compression and thus the compression of the whole structure. Secondly, if we only consider AlO6 and SiO4 in the garnet crystal structure, the linkages between AlO6 and SiO4 parallel to the crystallographic axes are similar to chains which are again connected with each other and form a three dimensional framework. In this case it is reasonable to expect that a compression of the structure can be induced by kinking the SiŸOŸAl angle between the two polyhedra. In pyrope this kinking was manifested in the continuous decrease of the SiŸOŸAl angle from 131.0(2) to 126.9(2) degrees between ambient pressure and 33 GPa (Fig. 6). The fact that both competing mechanisms may be correlated with each other makes it difficult to fix which one plays a primary role. A linear relationship between normalized distortion parameters for MgO8 and AlO6 polyhedra and the normalized SiŸOŸAl kinking angle (Fig. 7), however, suggests strongly that the kinking (bending) between AlO6 and SiO4 is the governing factor in the compression of the pyrope structure. From the study of comparative compressibilities of garnet Hazen et al. (1994) suggested that the framework of octahedra and tetrahedra dictates the garnet compression, especially the valence state of octahedrally coordinated cations plays a primary role. A high valence state of cations in octahedra generally leads to an incompressible structure as a whole. From our results presented

307

Fig. 7 The linear correlation of the normalized polyhedral distortion parameters in MgO8 and AlO4 with relative kinking of SiŸOŸAl angle. D denotes distortion parameters at pressures and D0 the value at ambient pressure. For MgO8 the bond length distortion (BLD) and for AlO6 the edge length distortion (ELD) was used

above and the previous work it seems that kinking of the SiŸOŸM angle ± M denotes cations at octahedral positions ± is restrained if cations of high valence state occupy octahedral positions. This could be checked in a structural study of majorite by determining the magnitude of SiŸOŸSi and SiŸOŸMg bending at high pressures (R. M. Hazen, personal communication). Acknowledgements We thank C. A. Geiger for the kind donation of a pyrope crystal, S. S. Hafner for support, R. Angel for his critical reading and discussions that improved the manuscript. R. M. Hazen and another anonymous reviewer are thanked for constructive comments. Financial support was provided by Deutsche Forschungsgemeinschaft under Zh31/1±2.

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