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Isothermal compression curve of MgSiO3 tetragonal garnet
1
Physics of the Earth and Planetaty Interiors, 74(1992)1—7 Elsevier Science Publishers B.V., Amsterdam
Isothermal compression curve of MgSiO3 tetragonal garnet T. Yagi
a,
Y. Uchiyama
a
M. Akaogi
13
and E. Ito
a Institute for Solid State Physics. University of Tokyo, Tokyo 106, Japan b Department of Chemistry, Gakushuin University, Tokyo 171, Japan Institute for Study of Earth’s Interior, Okayama University, Misasa, Tottori 682-02, Japan
(Received 30 December 1991: revision accepted 19 May 1992)
ABSTRACT Yagi, T., Uchiyama, Y., Akaogi, M. and Ito, E., 1992. Isothermal compression curve of MgSiO3 tetragonal garnet, Phys. Earth Planet. Inter., 74: 1—7. The bulk modulus of MgSiO3 tetragonal garnet was measured using a diamond anvil-type high-pressure apparatus combined with synchrotron radiation. An imaging plate X-ray detector was used to get high resolution diffraction data and the whole—powder—pattern decomposition method was employed to analyze the tetragonal unit cell which was only slightly distorted from cubic symmetry. The isothermal bulk modulus (K0) of the garnet-structured MgSiO3 was determined to be 161 GPa when (dK/dP)0 was assumed to be 4. Combining this result with previous results, the compositional dependence of the bulk modulus of majorite in a pyrope-enstatite join is expressed as K0(GPa)
=
(171.8 ±3.5) — (0.11 ±O.S)XEfl
where XEfl is the mole fraction of the enstatite composition in majorite.
1. Introduction Majorite (garnet-structured pyroxene—garnet solid solution) plays an important role in many petrological models of the Earth (e.g. Ringwood, 1975; Bass and Anderson, 1984). Both pyroxene and garnet are important constituents of the upper mantle. The solubility of pyroxene in garnet increases drastically with pressure and majorite is formed in a wide compositional range above 15 GPa (e.g. Akaogi and Akimoto, 1977; Kanzaki, 1987; Gasparik, 1989). Therefore an accurate knowledge of the elastic properties of majorite is essential for a better understanding of the mineralogy from upper mantle to transition zone.
Correspondence to: T. Yagi, Institute for Solid State Physics, University of Tokyo, Tokyo 106, Japan. 0031-9201/92/$05.00 © 1992
—
In spite of its importance, however, little experimental work has been carried out so far because of the difficulties of synthesizing the correct amount of majorite to enable elastic property measurements to be made. Jeanloz (1981) studied the bulk modulus of majorite found in natural meteorite, which has a composition of approximately (Mg079Fe021)Si03, by means of a highpressure X-ray diffraction study using a diamond anvil apparatus combined with a conventional X-ray source and film technique. Although majorite of this composition was slightly distorted from cubic to tetragonal symmetry, the lack of resolution of the X-ray system made it impossible to analyze it as tetragonal, Jeanloz had analyzed it as having quasi cubic symmetry. He obtained a bulk modulus of 221 GPa, which was much larger than the value estimated from the systematics in other garnet-structured solid solutions.
Elsevier Science Publishers B.V. All rights reserved
2
T. YAGI ET AL.
Yagi et al. (1987) studied the isothermal compression of synthetic garnets and majorites of four different compositions; pure pyrope(Py), almandine(Alm), and two majorites with compositions En58—Py42 and Fs18—A1m82. A high-pressure X-ray diffraction study was performed using a cubic anvil-type high-pressure apparatus combined with a synchrotron radiation and energy dispersive X-ray system. The majorites and garnets studied had cubic symmetry. All the diffraction lines were well resolved in spite of the relatively low resolution of the energy dispersive X-ray diffraction technique. The volume compression data thus obtained had small scatter among the data and the isothermal compression curves were determined very accurately. It was found that in both enstatite—pyrope and ferrosilite—almandine joins, the bulk modulus decreased slightly with increasing pyroxene compositions. Bass and Kanzaki (1990) performed Brillouin spectroscopy using a synthetic polycrystalline sample with composition En41—Py59. The adiabatic bulk modulus obtained was 164 ±15 GPa, which was intermediate between the KT values of Py~00 and En58—Py42 reported previously by Yagi et al. (1987). Ignoring the small difference between KT and K~,they proposed the following equation for the compositional dependence of the bulk modulus of majorite in the Py—En join 22XEfl
K(GPa) = 172.9 O. where XEfl is the mole fraction of enstatite composition in majorite. Extrapolation of this systematics to MgSiO 3 endmember results in a serious disagreement with the very large bulk modulus of the pyroxene-composite majorite as reported by Jeanloz (1981). The purpose of this present study is to measure the bulk modulus of MgSiO3 majorite accurately and clarify the composition-bulk modulus systematics in the whole compositional range of pyrope—enstatite. —
2. Experimental details A majorite specimen of pure MgSiO3 composition was synthesized at 20 GPa and 2200°Cusing a double-stage cubic-octahedral press at the Insti-
tute for Study of the Earth’s Interior (ISEI), Okayama University (Ito and Takahashi, 1989). The starting material used was single crystals of enstatite synthesized by Ozima (Takei et al., 1984). The crystals were crushed into a fine powder, loaded in a tube-shaped furnace, and kept in the above condition for 10 mm. As the majorite phase is only formed above 2000°C,a specimen in the high temperature part of the sample chamber was extracted and checked, by means of micro focus X-ray diffractometer, to be a single phase of garnet-structured MgSiO3. High pressure X-ray diffraction studies were performed using a lever and spring-type diamond anvil apparatus (Yagi and Akimoto, 1982). The pressure was measured using the ruby fluorescence technique (Piermarini et al., 1975). Hydrostaticity of the pressure is very important to get reliable compression curves. A mixture of methanol and ethanol (4: 1 by volume) was used as a pressure-transmitting medium. Three to five small ruby chips, spread in the sample chamber, were used to measure the pressure as well as to check the hydrostaticity and uniformity of pressure. High resolution angle dispersive X-ray diffraction experiments were carried out using synchrotron radiation at the Photon Factory in the National Laboratory for High Energy Physics (KEK), Tsukuba. A monochromatized X-ray of wavelength 0.6888 A (corresponds to the absorption edge of zirconium) was collimated to a thin beam (diameter 120 /.Lm) and the diffracted X-ray was detected by an imaging plate (IP) which has a higher sensitivity and a wider dynamic range of intensity compared with the conventional film method (Miyahara et al., 1986). In order to obtain higher resolution and greater accuracy, an IP detector was placed 185 mm from the sample which was more than three times larger than the usual Debye camera. The IP was divided into small pixels and the X-ray intensities recorded in each pixel were measured by a laser-scanning reader and converted into two-dimensional digital intensity data. The size of each pixel was 100 ~.tm X 100 ~zm. The area of the IP used for the analysis was 220 mm x 25 mm. This data was then integrated along
ISOTHERMAL COMPRESSION CURVE OF MgSiO
3 TETRAGONAL GARNET
a polar axis which coincided with the Debye rings observed on the IP, and the powder diffraction intensity was obtained as a function of 20 angle. Since the intensity along the Debye rings are averaged, a very reliable intensity profile could be obtained. MgSiO3 has a low-scattering power and, in spite of the high intensity of the synchrotron radiation source, an exposure time as long as 5 h is required to obtain high quality data which can be used for profile analysis. An example of the diffraction patterns obtained at 6.6 GPa is shown in Fig. 1. The splitting of the lines, caused by the slight distortion from cubic to tetragonal (e.g. (400) and (004)), can be seen, which clearly indicates the high resolution of the present system. The whole-powder pattern decomposition (WPPD) method was applied to obtain lattice parameters of tetragonal unit cell from the digitized X-ray intensity data. This is a kind of profile fitting method. Lattice parameters, which constrain the positions of the diffraction peaks, and the intensities of each diffraction peak are the primary parameters to be fitted. This method provides a strong means of determining unit cell parameters of low-symmetry crystals when observed diffraction lines overlap each other and are difficult to separate. The details of the WPPD method are explained by Toraya (1986). An example of this analysis is shown in Fig. 2, in which a small portion of the observed and calculated
3
intensities of the data in Fig. 1 are plotted as a function of the 20 angle. The small vertical bars at the bottom of the figure represent the positions of the diffraction peaks and the difference between the observed and calculated profile intensities are plotted under that. In total, 46—54 reflections in the 20 angle from 12.5°to 28.5° were used for the analyses.
3. Results and discussions All the experimental results are summarized in Table 1. In the WPPD method, the precision of the obtained lattice parameters is expressed by the residual factors, and not by the error bars as in the conventional least-squares analysis. In the present analysis, residual factors are of the order of 1%, which indicates the high accuracy of the present experiment. The isothermal compression curve of MgSiO3 majorite obtained using the P—V data (listed in Table 1) is shown in Fig. 3. The Birch—Murnaghan equation of state was fitted to this compression curve. In spite of the high accuracy of the present experiments, the relatively small pressure range of the measurement compared with the high bulk modulus of the sample made it difficult to determine the two parameters, bulk modulus K0 and its 1 bar pressure derivative (dK/dP)0, simultaneously. When
2B(2~=O.6888A) Fig. 1. An example of the integrated diffraction profile of MgSiO3 tetragonal garnet obtained at P = 6.6 GPa using an Imaging Plate. Exposure time was 5 h at room temperature.
4
T. YAGI ET AL
1520
4
1500 >~ Cl)
ci) £
4-
**
+
.‘“<
~L1L I
25.00
1480
*1)
I
E I
25.5° 26.0° 20(X=0.6888A)
II
1460 I
26.5°
1440
Fig. 2. An example of the WPPD analysis. Observed (cross) and calculated (dotted line) intensities in the selected area are plotted as a function of 2 0 angle. The vertical bars represent the positions of diffraction peaks, and the lower curve indicates differences between the observed and the calculated intensities.
(dK/dP)0 is assumed to be 4, K0 is calculated to be 161.2 GPa. The bulk moduli obtained by changing (dK/dP)0 from 2 to 6 are shown in Fig. 4. Any combination of K0 and (dK/dP)0 on this line satisfies the experimental data equally well. It is clear from this figure that even considering (dK/dP)0 as small as 2, the bulk modulus of MgSiO3 majorite cannot be larger than that of pyrope. The pressure dependence of the axial ratio of the tetragonal unit cell (c/a) is shown in Fig. 5.
1420
0
2
4
6
8
Fig. 3. Isothermal compression curve of MgSiO3 tetragonal garnet at room temperature. The error bars of pressure at each measurement are within the size of the squares. The error bars of unit-cell volume cannot be expressed explicitly because of the nature of the WPPD method (see text). Solid line is the Birch—Murnaghan equation with K0 = 161.2 GPa and (dK/dP)0 = 4.
This ratio decreases very slightly but meaningfully, with pressure. This means that the tetragonal unit cell distorts more under pressure. When the result of Fig. 5 is expressed by a linear equation, the variation of the c/a ratio is expressed by the following c/a = 0.9925 0.00014P (GPa) —
TABLE 1 Experimental results 3) Run No.
P(GPa)
a(A)
MJ404 1.43 11.478 MJ305 2.35 11.451 MJ3O1 2.63 11.454 MJ402 4.34 11.416 MJ1O1 4.86 11.402 MJ1O6 5.37 11.386 MJ403 6.58 11.371 MJ302 7.08 11.349 MJ1O2 8.60 11.332 MJ1O3 11.315 3. 9.72 b R-factor in the WPPD method. a Weighted V0=1513.1A
10
Pressure (GPa)
c(A)
v(A
11.389 11.361 11.361 11.320 11.309 11.293 11.274 11.252 11.234 11.214
1500.4 1489.7 1490.5 1475.3 1470.2 1464.0 1457.6 1449.3 1442.6 1435.7
VI V 0 0.9916 0.9845 0.9851 0.9751 0.9717 0.9676 0.9633 0.9578 0.9534 0.9488
a
Rwp(%) b 1.2 0.6 1.1 1.3 1.0 0.6 1.1 1.1 1.1 0.8
ISOTHERMAL COMPRESSION CURVE OF MgSIO
5
3 TETRAGONAL GARNET
TABLE 2 Unit cell parameters of MgSiO3 tetragonal garnets at 1 bar 3) c a0(A) c0(A) V0(A 0/a0 Reference 11.491 11.501 11.516 11.509
Cu 0.
11.406 11.480 11.428 11.423
1506.1 1518.5 1515.6 1513.1
0.9926 0.9982 0.9924 0.9925
Kato and Kumazawa (1985) Angel et al. (1989) Matsubara et al. (1990) This study
(Il
~0 0
1
2
3
4 dK0/dP
5
6
7
Fig. 4. Variation of bulk modulus K0 when different (dK/dP)0 values were assumed for MgSiO3 tetragonal garnet. Any combination of K0 and (dK/dP)0 on this line satisfies the present experimental results.
1.000 0.998 0.996 ~ 0.994 0 0
UDO
~ 0.992
DO
0
0.990 0.988 0.986 0.984 0
2
4 6 Pressure (GPa)
8
10
Fig. 5. Pressure variation of an axial ratio c / a for MgSiO3 tetragonal garnet. The ratio in this pressure range can be expressed as follows: c/a = 0.9925 — 0.00014P (GPa).
Recently it has been reported that when MgSiO3 majorite is subjected to hydrostatic pressure at room temperature, a discontinuous change of the Raman spectrum is observed at 25 GPa (Chopelas, private communication, 1991). Although it is suggested that this change may be caused by the transformation from tetragonal to cubic symmetry, the present result suggests that the transformation to cubic symmetry under high pressure is unlikely to occur. There are several reports on the unit cell dimensions of MgSiO3 majorite which are summarized in Table 2. Compared with many other high-pressure minerals, the unit cell dimensions of MgSiO3 majorite synthesized in different laboratories are relatively scattered. It is said that the distortion from cubic to tetragonal symmetry is caused by the ordering of the cations in the structure. If that is the case, it is quite reasonable that the degree of ordering depends on the condition of synthesis and the resulting unit cell dimensions are scattered. The present values of the unit cell volume and the c/a ratio are located in the middle of the reported values. It is not known how this ordering affects the elastic properties although the bulk modulus is usually insensitive to this kind of effect. The bulk modulus obtained in this present experiment is plotted in Fig. 6, together with the results obtained by previous studies. The reason for the large disagreement between the results obtained by Jeanloz (1981) and this present study is not clear. The difference in the chemical composition could be partially responsible. However, the bulk modulus on the Fs—Alm join is only a few percent greater than that on the En—Py join (Yagi et a!., 1987). An addition of a certain amount of iron cannot cause such a great difference. Another possibility is that the analysis, as-
6
T. YAGI ET AL.
230
r
220
(1987) and by the present study, the following equation can be obtained for the chemical composition dependence of the bulk modulus of majorite in the entire compositional range between pyrope and enstatite
-
210 CU 0. C,
200
K0(GPa) -
=
(171.8 ±3.5)
—
(0.11 ±O.S)XEfl
Ci)
~0 0
190 180
Mg
3AI2Si,O,2
40 60 Pyroxene mol%
80
100 Mg4SI4O,2
Fig. 6. Bulk modulus of majorite vs. composition in the enstatite—pyrope join determined by various experimental techniques. Solid squares represent the present result. Open squares (Yagi et al., 1987) and solid circle (Jeanloz, 1981) were obtained by means of high pressure X-ray diffraction measurements. Open triangle is the result of Bass and Kanzaki (1990) by means of Brillouin spectroscopy. Solid line is the compositional dependence of the isothermal bulk modulus and is expressed by the following equation; K0 (GPa) = (171.8 ±3.S)—(0.11±O.S)XE~, where XE,, is the mole fraction of enstatite component in majorite.
suming a quasi-cubic structure, may cause a serious difference. In order to check this possibility, we have analyzed our X-ray data assuming a quasi-cubic structure by fitting a simple Gaussian curve to each broad diffraction profile. However, this analysis increases the calculated volume systematically by about 0.04% and affects the bulk modulus only by 0.6%. Even though the reason for the disagreement is not clear, the bulk modulus is mainly determined by the packing of oxygen ions and is not very sensitive to slight changes in chemical composition or small distortions in symmetry. Considering all these factors, it is unlikely that the bulk modulus of majorite in the pyrope— enstatite join increases drastically near the enstatite endmember. Using the isothermal bulk moduli of the three different compositions reported by Yagi et al.
The uncertainties of the coefficients include the effect of the uncertainties of (dK/dP)0. Akaogi et al. (1987) made an argument, using the systematics of the bulk modulus in the pyrope—majorite join reported by Yagi et al. (1987), that the pyrolite model is in harmony with the sound velocity profile of the upper mantle and transition zone obtained by the seismic velocity observations. At that time, there still remained the uncertainty that the bulk modulus might change drastically near the pyroxene endmember. The present results clarify that such a situation cannot occur and that the bulk modulus decreases monotonously with increasing pyroxene composition, which strengthens the argument made by Akaogi et al. (1987).
Acknowledgments We wish to thank H. Toraya for providing the computer program of the WPPD method used for this study. H. Fujihisa, H. Yusa, and T. Kikegawa are gratefully acknowledged for their support throughout the experiments carried out at the Photon Factory. Thanks are also due to an anonymous reviewer and J.-P. Poirier for helpful comments on this manuscript. This work has been performed under the approval of the Photon Factory Program Advisory Committee (Proposal No. 91-089).
References Akaogi, M. and Akimoto, S., 1977. Pyroxene-garnet solidsolution in the systems Mg4Si4O12—Mg3A12Si3O12 and Fe4Si4O12—Fe3A12Si3O12 at high pressures and high temperatures. Phys. Earth Planet. Inter., 15: 90—106. Akaogi, M., Navrotsky, A., Yagi, T. and Akimoto, S., 1987. Pyroxene—garnet transformation: thermochemistry and
ISOTHERMAL COMPRESSION CURVE OF MgSiO
3 TETRAGONAL GARNET
elasticity of garnet solid solutions, and application to a pyrolite mantle. In: M.H. Manghnani and Y. Syono (Editors), High-Pressure Research in Mineral Physics. Terrapub, Tokyo, pp. 251—260. Angel, R.J., Finger, L.W., Hazen, R.M., Kanzaki, M. Weidncr, D.J., Liebermann, R.C. and Veblen, D.R., 1989. Structure and twinning of single-crystal MgSiO3 garnet synthesized at 17 GPa and 1800°C. Am. Mineral., 74: 509—512. Bass, J.D. and Anderson, D.L., 1984. Composition of the upper mantle: geophysical tests of two petrological models. Geophys. Res. Lett., 11: 229—232. Bass, J.D. and Kanzaki, M., 1990. Elasticity of a majorite—pyrope solid solution. Geophys. Res. LetL, 17: 1989—1992. Gasparik, T., 1989. Transformation of enstatite—diopside— jadeite pyroxenes to garnet. Contrib. Mineral. Petrol., 102: 389—405. Ito, E. and Takahashi, E., 1989. Postspinel transformations in the system Mg25i04—Fe2SiO4 and some geophysical implications. J. Geophys. Res., 94: 10637—10646. Jeanloz, R., 1981. Majorite: vibrational and compressional properties of a high-pressure phase. J. Geophys. Res., 86: 6171—6179. Kanzaki, M., 1987. Ultrahigh-pressure phase relations in the system Mg4Si4O12—Mg3Al2Si3O12. Phys. Earth Planet. Inter., 49: 168—175. Kato, T. and Kumazawa, M., 1985. Garnet phase of MgSiO3 filling the pyroxene—ilmenite gap at very high temperature. Nature, 316: 803—805. Matsubara, R., Toraya, H., Tanaka, S. and Sawamoto, H.,
7
1990. Precision lattice-parameter determination of (Mg,Fe)SiO3 tetragonal garnets. Science, 247: 697—699. Miyahara, I., Takahashi, K., Amemiya, Y., Kamiya, N. and Satow, Y., 1986. A new type of X-ray area detector utilizing laser stimulated luminescence. Nucl. Instr. Methods, A246: 572—578. Piermarini, G.J., Block, S., Barnett, J.D. and Forman, R.A., 1975. Calibration of the pressure dependence of the R1 ruby fluorescence line to 195 kbar. J. Appl. Phys., 46: 2774—2780. Ringwood, A.E., 1975. Composition and Petrology of the Earth’s Mantle. McGraw-Hill, New York, 618 pp. Takei, H., Hosoya, S. and Ozima, M., 1984. Synthesis of large single crystals of silicates and titanates. In: I. Sunagawa (Editor), Materials Science of the Earth’s Interior. Terrapub, Tokyo, pp. 107—130. Toraya, H., 1986. Whole-powder-pattern fitting without reference to a structural model: application to X-ray powder diffractometer data. 1. Appl. Crystallogr., 19: 440—447. Yagi, T., Akaogi, M., Shimomura, 0., Tamai, H. and Aidmoto, 5., 1987. High pressure and high temperature equations of state of majorite. In: M.H. Manghnani and Y. Syono (Editors), High-Pressure Research in Mineral Physics. Terrapub, Tokyo, pp. 141—147. Yagi, T. and Akimoto, S., 1982. Rapid X-ray measurements to 100 GPa range and static compression of a-Fe203. In: S. Akimoto and M.H. Manghnani (Editors), Advances in Earth and Planetary Sciences 12, High-Pressure Research in Geophysics, Center for Academic Publications Japan/ Reidel, Tokyo/Dordrecht, pp. 81—90.
Physics of the Earth and Planetaty Interiors, 74(1992)1—7 Elsevier Science Publishers B.V., Amsterdam
Isothermal compression curve of MgSiO3 tetragonal garnet T. Yagi
a,
Y. Uchiyama
a
M. Akaogi
13
and E. Ito
a Institute for Solid State Physics. University of Tokyo, Tokyo 106, Japan b Department of Chemistry, Gakushuin University, Tokyo 171, Japan Institute for Study of Earth’s Interior, Okayama University, Misasa, Tottori 682-02, Japan
(Received 30 December 1991: revision accepted 19 May 1992)
ABSTRACT Yagi, T., Uchiyama, Y., Akaogi, M. and Ito, E., 1992. Isothermal compression curve of MgSiO3 tetragonal garnet, Phys. Earth Planet. Inter., 74: 1—7. The bulk modulus of MgSiO3 tetragonal garnet was measured using a diamond anvil-type high-pressure apparatus combined with synchrotron radiation. An imaging plate X-ray detector was used to get high resolution diffraction data and the whole—powder—pattern decomposition method was employed to analyze the tetragonal unit cell which was only slightly distorted from cubic symmetry. The isothermal bulk modulus (K0) of the garnet-structured MgSiO3 was determined to be 161 GPa when (dK/dP)0 was assumed to be 4. Combining this result with previous results, the compositional dependence of the bulk modulus of majorite in a pyrope-enstatite join is expressed as K0(GPa)
=
(171.8 ±3.5) — (0.11 ±O.S)XEfl
where XEfl is the mole fraction of the enstatite composition in majorite.
1. Introduction Majorite (garnet-structured pyroxene—garnet solid solution) plays an important role in many petrological models of the Earth (e.g. Ringwood, 1975; Bass and Anderson, 1984). Both pyroxene and garnet are important constituents of the upper mantle. The solubility of pyroxene in garnet increases drastically with pressure and majorite is formed in a wide compositional range above 15 GPa (e.g. Akaogi and Akimoto, 1977; Kanzaki, 1987; Gasparik, 1989). Therefore an accurate knowledge of the elastic properties of majorite is essential for a better understanding of the mineralogy from upper mantle to transition zone.
Correspondence to: T. Yagi, Institute for Solid State Physics, University of Tokyo, Tokyo 106, Japan. 0031-9201/92/$05.00 © 1992
—
In spite of its importance, however, little experimental work has been carried out so far because of the difficulties of synthesizing the correct amount of majorite to enable elastic property measurements to be made. Jeanloz (1981) studied the bulk modulus of majorite found in natural meteorite, which has a composition of approximately (Mg079Fe021)Si03, by means of a highpressure X-ray diffraction study using a diamond anvil apparatus combined with a conventional X-ray source and film technique. Although majorite of this composition was slightly distorted from cubic to tetragonal symmetry, the lack of resolution of the X-ray system made it impossible to analyze it as tetragonal, Jeanloz had analyzed it as having quasi cubic symmetry. He obtained a bulk modulus of 221 GPa, which was much larger than the value estimated from the systematics in other garnet-structured solid solutions.
Elsevier Science Publishers B.V. All rights reserved
2
T. YAGI ET AL.
Yagi et al. (1987) studied the isothermal compression of synthetic garnets and majorites of four different compositions; pure pyrope(Py), almandine(Alm), and two majorites with compositions En58—Py42 and Fs18—A1m82. A high-pressure X-ray diffraction study was performed using a cubic anvil-type high-pressure apparatus combined with a synchrotron radiation and energy dispersive X-ray system. The majorites and garnets studied had cubic symmetry. All the diffraction lines were well resolved in spite of the relatively low resolution of the energy dispersive X-ray diffraction technique. The volume compression data thus obtained had small scatter among the data and the isothermal compression curves were determined very accurately. It was found that in both enstatite—pyrope and ferrosilite—almandine joins, the bulk modulus decreased slightly with increasing pyroxene compositions. Bass and Kanzaki (1990) performed Brillouin spectroscopy using a synthetic polycrystalline sample with composition En41—Py59. The adiabatic bulk modulus obtained was 164 ±15 GPa, which was intermediate between the KT values of Py~00 and En58—Py42 reported previously by Yagi et al. (1987). Ignoring the small difference between KT and K~,they proposed the following equation for the compositional dependence of the bulk modulus of majorite in the Py—En join 22XEfl
K(GPa) = 172.9 O. where XEfl is the mole fraction of enstatite composition in majorite. Extrapolation of this systematics to MgSiO 3 endmember results in a serious disagreement with the very large bulk modulus of the pyroxene-composite majorite as reported by Jeanloz (1981). The purpose of this present study is to measure the bulk modulus of MgSiO3 majorite accurately and clarify the composition-bulk modulus systematics in the whole compositional range of pyrope—enstatite. —
2. Experimental details A majorite specimen of pure MgSiO3 composition was synthesized at 20 GPa and 2200°Cusing a double-stage cubic-octahedral press at the Insti-
tute for Study of the Earth’s Interior (ISEI), Okayama University (Ito and Takahashi, 1989). The starting material used was single crystals of enstatite synthesized by Ozima (Takei et al., 1984). The crystals were crushed into a fine powder, loaded in a tube-shaped furnace, and kept in the above condition for 10 mm. As the majorite phase is only formed above 2000°C,a specimen in the high temperature part of the sample chamber was extracted and checked, by means of micro focus X-ray diffractometer, to be a single phase of garnet-structured MgSiO3. High pressure X-ray diffraction studies were performed using a lever and spring-type diamond anvil apparatus (Yagi and Akimoto, 1982). The pressure was measured using the ruby fluorescence technique (Piermarini et al., 1975). Hydrostaticity of the pressure is very important to get reliable compression curves. A mixture of methanol and ethanol (4: 1 by volume) was used as a pressure-transmitting medium. Three to five small ruby chips, spread in the sample chamber, were used to measure the pressure as well as to check the hydrostaticity and uniformity of pressure. High resolution angle dispersive X-ray diffraction experiments were carried out using synchrotron radiation at the Photon Factory in the National Laboratory for High Energy Physics (KEK), Tsukuba. A monochromatized X-ray of wavelength 0.6888 A (corresponds to the absorption edge of zirconium) was collimated to a thin beam (diameter 120 /.Lm) and the diffracted X-ray was detected by an imaging plate (IP) which has a higher sensitivity and a wider dynamic range of intensity compared with the conventional film method (Miyahara et al., 1986). In order to obtain higher resolution and greater accuracy, an IP detector was placed 185 mm from the sample which was more than three times larger than the usual Debye camera. The IP was divided into small pixels and the X-ray intensities recorded in each pixel were measured by a laser-scanning reader and converted into two-dimensional digital intensity data. The size of each pixel was 100 ~.tm X 100 ~zm. The area of the IP used for the analysis was 220 mm x 25 mm. This data was then integrated along
ISOTHERMAL COMPRESSION CURVE OF MgSiO
3 TETRAGONAL GARNET
a polar axis which coincided with the Debye rings observed on the IP, and the powder diffraction intensity was obtained as a function of 20 angle. Since the intensity along the Debye rings are averaged, a very reliable intensity profile could be obtained. MgSiO3 has a low-scattering power and, in spite of the high intensity of the synchrotron radiation source, an exposure time as long as 5 h is required to obtain high quality data which can be used for profile analysis. An example of the diffraction patterns obtained at 6.6 GPa is shown in Fig. 1. The splitting of the lines, caused by the slight distortion from cubic to tetragonal (e.g. (400) and (004)), can be seen, which clearly indicates the high resolution of the present system. The whole-powder pattern decomposition (WPPD) method was applied to obtain lattice parameters of tetragonal unit cell from the digitized X-ray intensity data. This is a kind of profile fitting method. Lattice parameters, which constrain the positions of the diffraction peaks, and the intensities of each diffraction peak are the primary parameters to be fitted. This method provides a strong means of determining unit cell parameters of low-symmetry crystals when observed diffraction lines overlap each other and are difficult to separate. The details of the WPPD method are explained by Toraya (1986). An example of this analysis is shown in Fig. 2, in which a small portion of the observed and calculated
3
intensities of the data in Fig. 1 are plotted as a function of the 20 angle. The small vertical bars at the bottom of the figure represent the positions of the diffraction peaks and the difference between the observed and calculated profile intensities are plotted under that. In total, 46—54 reflections in the 20 angle from 12.5°to 28.5° were used for the analyses.
3. Results and discussions All the experimental results are summarized in Table 1. In the WPPD method, the precision of the obtained lattice parameters is expressed by the residual factors, and not by the error bars as in the conventional least-squares analysis. In the present analysis, residual factors are of the order of 1%, which indicates the high accuracy of the present experiment. The isothermal compression curve of MgSiO3 majorite obtained using the P—V data (listed in Table 1) is shown in Fig. 3. The Birch—Murnaghan equation of state was fitted to this compression curve. In spite of the high accuracy of the present experiments, the relatively small pressure range of the measurement compared with the high bulk modulus of the sample made it difficult to determine the two parameters, bulk modulus K0 and its 1 bar pressure derivative (dK/dP)0, simultaneously. When
2B(2~=O.6888A) Fig. 1. An example of the integrated diffraction profile of MgSiO3 tetragonal garnet obtained at P = 6.6 GPa using an Imaging Plate. Exposure time was 5 h at room temperature.
4
T. YAGI ET AL
1520
4
1500 >~ Cl)
ci) £
4-
**
+
.‘“<
~L1L I
25.00
1480
*1)
I
E I
25.5° 26.0° 20(X=0.6888A)
II
1460 I
26.5°
1440
Fig. 2. An example of the WPPD analysis. Observed (cross) and calculated (dotted line) intensities in the selected area are plotted as a function of 2 0 angle. The vertical bars represent the positions of diffraction peaks, and the lower curve indicates differences between the observed and the calculated intensities.
(dK/dP)0 is assumed to be 4, K0 is calculated to be 161.2 GPa. The bulk moduli obtained by changing (dK/dP)0 from 2 to 6 are shown in Fig. 4. Any combination of K0 and (dK/dP)0 on this line satisfies the experimental data equally well. It is clear from this figure that even considering (dK/dP)0 as small as 2, the bulk modulus of MgSiO3 majorite cannot be larger than that of pyrope. The pressure dependence of the axial ratio of the tetragonal unit cell (c/a) is shown in Fig. 5.
1420
0
2
4
6
8
Fig. 3. Isothermal compression curve of MgSiO3 tetragonal garnet at room temperature. The error bars of pressure at each measurement are within the size of the squares. The error bars of unit-cell volume cannot be expressed explicitly because of the nature of the WPPD method (see text). Solid line is the Birch—Murnaghan equation with K0 = 161.2 GPa and (dK/dP)0 = 4.
This ratio decreases very slightly but meaningfully, with pressure. This means that the tetragonal unit cell distorts more under pressure. When the result of Fig. 5 is expressed by a linear equation, the variation of the c/a ratio is expressed by the following c/a = 0.9925 0.00014P (GPa) —
TABLE 1 Experimental results 3) Run No.
P(GPa)
a(A)
MJ404 1.43 11.478 MJ305 2.35 11.451 MJ3O1 2.63 11.454 MJ402 4.34 11.416 MJ1O1 4.86 11.402 MJ1O6 5.37 11.386 MJ403 6.58 11.371 MJ302 7.08 11.349 MJ1O2 8.60 11.332 MJ1O3 11.315 3. 9.72 b R-factor in the WPPD method. a Weighted V0=1513.1A
10
Pressure (GPa)
c(A)
v(A
11.389 11.361 11.361 11.320 11.309 11.293 11.274 11.252 11.234 11.214
1500.4 1489.7 1490.5 1475.3 1470.2 1464.0 1457.6 1449.3 1442.6 1435.7
VI V 0 0.9916 0.9845 0.9851 0.9751 0.9717 0.9676 0.9633 0.9578 0.9534 0.9488
a
Rwp(%) b 1.2 0.6 1.1 1.3 1.0 0.6 1.1 1.1 1.1 0.8
ISOTHERMAL COMPRESSION CURVE OF MgSIO
5
3 TETRAGONAL GARNET
TABLE 2 Unit cell parameters of MgSiO3 tetragonal garnets at 1 bar 3) c a0(A) c0(A) V0(A 0/a0 Reference 11.491 11.501 11.516 11.509
Cu 0.
11.406 11.480 11.428 11.423
1506.1 1518.5 1515.6 1513.1
0.9926 0.9982 0.9924 0.9925
Kato and Kumazawa (1985) Angel et al. (1989) Matsubara et al. (1990) This study
(Il
~0 0
1
2
3
4 dK0/dP
5
6
7
Fig. 4. Variation of bulk modulus K0 when different (dK/dP)0 values were assumed for MgSiO3 tetragonal garnet. Any combination of K0 and (dK/dP)0 on this line satisfies the present experimental results.
1.000 0.998 0.996 ~ 0.994 0 0
UDO
~ 0.992
DO
0
0.990 0.988 0.986 0.984 0
2
4 6 Pressure (GPa)
8
10
Fig. 5. Pressure variation of an axial ratio c / a for MgSiO3 tetragonal garnet. The ratio in this pressure range can be expressed as follows: c/a = 0.9925 — 0.00014P (GPa).
Recently it has been reported that when MgSiO3 majorite is subjected to hydrostatic pressure at room temperature, a discontinuous change of the Raman spectrum is observed at 25 GPa (Chopelas, private communication, 1991). Although it is suggested that this change may be caused by the transformation from tetragonal to cubic symmetry, the present result suggests that the transformation to cubic symmetry under high pressure is unlikely to occur. There are several reports on the unit cell dimensions of MgSiO3 majorite which are summarized in Table 2. Compared with many other high-pressure minerals, the unit cell dimensions of MgSiO3 majorite synthesized in different laboratories are relatively scattered. It is said that the distortion from cubic to tetragonal symmetry is caused by the ordering of the cations in the structure. If that is the case, it is quite reasonable that the degree of ordering depends on the condition of synthesis and the resulting unit cell dimensions are scattered. The present values of the unit cell volume and the c/a ratio are located in the middle of the reported values. It is not known how this ordering affects the elastic properties although the bulk modulus is usually insensitive to this kind of effect. The bulk modulus obtained in this present experiment is plotted in Fig. 6, together with the results obtained by previous studies. The reason for the large disagreement between the results obtained by Jeanloz (1981) and this present study is not clear. The difference in the chemical composition could be partially responsible. However, the bulk modulus on the Fs—Alm join is only a few percent greater than that on the En—Py join (Yagi et a!., 1987). An addition of a certain amount of iron cannot cause such a great difference. Another possibility is that the analysis, as-
6
T. YAGI ET AL.
230
r
220
(1987) and by the present study, the following equation can be obtained for the chemical composition dependence of the bulk modulus of majorite in the entire compositional range between pyrope and enstatite
-
210 CU 0. C,
200
K0(GPa) -
=
(171.8 ±3.5)
—
(0.11 ±O.S)XEfl
Ci)
~0 0
190 180
Mg
3AI2Si,O,2
40 60 Pyroxene mol%
80
100 Mg4SI4O,2
Fig. 6. Bulk modulus of majorite vs. composition in the enstatite—pyrope join determined by various experimental techniques. Solid squares represent the present result. Open squares (Yagi et al., 1987) and solid circle (Jeanloz, 1981) were obtained by means of high pressure X-ray diffraction measurements. Open triangle is the result of Bass and Kanzaki (1990) by means of Brillouin spectroscopy. Solid line is the compositional dependence of the isothermal bulk modulus and is expressed by the following equation; K0 (GPa) = (171.8 ±3.S)—(0.11±O.S)XE~, where XE,, is the mole fraction of enstatite component in majorite.
suming a quasi-cubic structure, may cause a serious difference. In order to check this possibility, we have analyzed our X-ray data assuming a quasi-cubic structure by fitting a simple Gaussian curve to each broad diffraction profile. However, this analysis increases the calculated volume systematically by about 0.04% and affects the bulk modulus only by 0.6%. Even though the reason for the disagreement is not clear, the bulk modulus is mainly determined by the packing of oxygen ions and is not very sensitive to slight changes in chemical composition or small distortions in symmetry. Considering all these factors, it is unlikely that the bulk modulus of majorite in the pyrope— enstatite join increases drastically near the enstatite endmember. Using the isothermal bulk moduli of the three different compositions reported by Yagi et al.
The uncertainties of the coefficients include the effect of the uncertainties of (dK/dP)0. Akaogi et al. (1987) made an argument, using the systematics of the bulk modulus in the pyrope—majorite join reported by Yagi et al. (1987), that the pyrolite model is in harmony with the sound velocity profile of the upper mantle and transition zone obtained by the seismic velocity observations. At that time, there still remained the uncertainty that the bulk modulus might change drastically near the pyroxene endmember. The present results clarify that such a situation cannot occur and that the bulk modulus decreases monotonously with increasing pyroxene composition, which strengthens the argument made by Akaogi et al. (1987).
Acknowledgments We wish to thank H. Toraya for providing the computer program of the WPPD method used for this study. H. Fujihisa, H. Yusa, and T. Kikegawa are gratefully acknowledged for their support throughout the experiments carried out at the Photon Factory. Thanks are also due to an anonymous reviewer and J.-P. Poirier for helpful comments on this manuscript. This work has been performed under the approval of the Photon Factory Program Advisory Committee (Proposal No. 91-089).
References Akaogi, M. and Akimoto, S., 1977. Pyroxene-garnet solidsolution in the systems Mg4Si4O12—Mg3A12Si3O12 and Fe4Si4O12—Fe3A12Si3O12 at high pressures and high temperatures. Phys. Earth Planet. Inter., 15: 90—106. Akaogi, M., Navrotsky, A., Yagi, T. and Akimoto, S., 1987. Pyroxene—garnet transformation: thermochemistry and
ISOTHERMAL COMPRESSION CURVE OF MgSiO
3 TETRAGONAL GARNET
elasticity of garnet solid solutions, and application to a pyrolite mantle. In: M.H. Manghnani and Y. Syono (Editors), High-Pressure Research in Mineral Physics. Terrapub, Tokyo, pp. 251—260. Angel, R.J., Finger, L.W., Hazen, R.M., Kanzaki, M. Weidncr, D.J., Liebermann, R.C. and Veblen, D.R., 1989. Structure and twinning of single-crystal MgSiO3 garnet synthesized at 17 GPa and 1800°C. Am. Mineral., 74: 509—512. Bass, J.D. and Anderson, D.L., 1984. Composition of the upper mantle: geophysical tests of two petrological models. Geophys. Res. Lett., 11: 229—232. Bass, J.D. and Kanzaki, M., 1990. Elasticity of a majorite—pyrope solid solution. Geophys. Res. LetL, 17: 1989—1992. Gasparik, T., 1989. Transformation of enstatite—diopside— jadeite pyroxenes to garnet. Contrib. Mineral. Petrol., 102: 389—405. Ito, E. and Takahashi, E., 1989. Postspinel transformations in the system Mg25i04—Fe2SiO4 and some geophysical implications. J. Geophys. Res., 94: 10637—10646. Jeanloz, R., 1981. Majorite: vibrational and compressional properties of a high-pressure phase. J. Geophys. Res., 86: 6171—6179. Kanzaki, M., 1987. Ultrahigh-pressure phase relations in the system Mg4Si4O12—Mg3Al2Si3O12. Phys. Earth Planet. Inter., 49: 168—175. Kato, T. and Kumazawa, M., 1985. Garnet phase of MgSiO3 filling the pyroxene—ilmenite gap at very high temperature. Nature, 316: 803—805. Matsubara, R., Toraya, H., Tanaka, S. and Sawamoto, H.,
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1990. Precision lattice-parameter determination of (Mg,Fe)SiO3 tetragonal garnets. Science, 247: 697—699. Miyahara, I., Takahashi, K., Amemiya, Y., Kamiya, N. and Satow, Y., 1986. A new type of X-ray area detector utilizing laser stimulated luminescence. Nucl. Instr. Methods, A246: 572—578. Piermarini, G.J., Block, S., Barnett, J.D. and Forman, R.A., 1975. Calibration of the pressure dependence of the R1 ruby fluorescence line to 195 kbar. J. Appl. Phys., 46: 2774—2780. Ringwood, A.E., 1975. Composition and Petrology of the Earth’s Mantle. McGraw-Hill, New York, 618 pp. Takei, H., Hosoya, S. and Ozima, M., 1984. Synthesis of large single crystals of silicates and titanates. In: I. Sunagawa (Editor), Materials Science of the Earth’s Interior. Terrapub, Tokyo, pp. 107—130. Toraya, H., 1986. Whole-powder-pattern fitting without reference to a structural model: application to X-ray powder diffractometer data. 1. Appl. Crystallogr., 19: 440—447. Yagi, T., Akaogi, M., Shimomura, 0., Tamai, H. and Aidmoto, 5., 1987. High pressure and high temperature equations of state of majorite. In: M.H. Manghnani and Y. Syono (Editors), High-Pressure Research in Mineral Physics. Terrapub, Tokyo, pp. 141—147. Yagi, T. and Akimoto, S., 1982. Rapid X-ray measurements to 100 GPa range and static compression of a-Fe203. In: S. Akimoto and M.H. Manghnani (Editors), Advances in Earth and Planetary Sciences 12, High-Pressure Research in Geophysics, Center for Academic Publications Japan/ Reidel, Tokyo/Dordrecht, pp. 81—90.