Earth and Planetary Science Letters 193 (2001) 501^508 www.elsevier.com/locate/epsl

Equation of state of lower mantle (Al,Fe)-MgSiO3 perovskite Denis Andrault a;b; *, Nathalie Bolfan-Casanova a;b , Nicolas Guignot a a

Laboratoire des Ge¨omate¨riaux, ESA7046, Institut de Physique du Globe, Paris, France De¨partement des Sciences de la Terre, Universite¨ Denis Diderot, Paris VII, France

b

Received 5 June 2001; received in revised form 10 August 2001; accepted 7 September 2001

Abstract The compression behavior of various (Al,Fe)-bearing MgSiO3 perovskites was investigated by powder X-ray diffraction up to 70 GPa on the ID30 beamline of ESRF (Grenoble, France). Using diamond anvil cell coupled with CO2 laser-heating, we obtained a reliable equation of state up to typical lower mantle pressures. In contrast to Fe which essentially increases the room pressure unit cell volume (V0 ), the effect of Al is to increase the bulk modulus of silicate perovskite. This result contrasts with previous determinations performed at pressures below 10 GPa on samples synthesized in the multi-anvil press. Such a difference can be explained by a change in the substitution mechanism of Al in MgSiO3 with increasing pressure and temperature, in agreement with recent ab-initio calculations. Our results confirm that the Earth's lower mantle (Mg+Fe)/Si ratio is greater than unity, because of the high stiffness of silicate perovskite. ß 2001 Elsevier Science B.V. All rights reserved. Keywords: perovskite; lower mantle; equations of state; substitution

1. Introduction The (Al,Fe)-MgSiO3 perovskite is thought to represent about 80% by volume of the Earth's lower mantle, which implies it is the most abundant silicate on Earth. Its chemical composition is not perfectly known because it is only stable below the 670-km depth discontinuity, at pressures above 24 GPa. If it eventually rises above this depth, it transforms back to majorite, or akimotoite, or can also react with magnesiowu«stite to produce ringwoodite. In the laboratory, it can be recovered at ambient conditions after decompres-

* Corresponding author. Tel.: +33 1 4427 4889; Fax: +33 14427 2487. E-mail address: [email protected] (D. Andrault).

sion, and this has enabled extensive studies of its crystal chemistry. The results have shown that (1) ferrous iron enters the structure to form (Mg13x Fex )SiO3 perovskite, still for a limited range of x values (x = 0.2) [1,2]. (2) Ca is a too big cation to enter the orthorhombic lattice of MgSiO3 , and instead is incorporated into a separate cubic CaSiO3 perovskite. (3) Al enters the MgSiO3 perovskite structure in amounts well above the mantle aluminum content, making the presence of other aluminous phases unlikely [3]. X-ray absorption measurements have suggested that 2Al enters the silicate perovskite by coupled substitution to MgSi [4], but theoretical calculations also point out the possibility of forming oxygen vacancies upon Al substitution in the Si site [5]. (4) The presence of Al in (Al,Fe)-MgSiO3 perovskite favors the incorporation of ferric iron

0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 0 1 ) 0 0 5 0 6 - 4

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[6,7]. Because of the relative ionic sizes of Fe3‡ and Al3‡ , it is likely that they enter preferentially into the dodecahedral and octahedral sites of the perovskite structure, respectively, but this point is not fully resolved yet. In more general terms, the mechanisms of Al substitution, the amount of FeII and FeIII and other structural defects in MgSiO3 perovskite are likely to depend on pressure, temperature, and oxygen fugacity, which makes it di¤cult to have a unique and de¢nitive vision of lower mantle perovskite. Several studies have addressed the equation of state of pure MgSiO3 perovskite, and a general agreement has been achieved. The bulk modulus, K0 , is close to 250 GPa when its ¢rst pressure derivative, KP0 , is ¢xed to 4, and using a higher order equation of state, the recent compression curves are well ¢tted by K0 = 260 GPa and KP0 = 3.7 [8,9]. As observed for many silicates, that show complete or partial (Mg,Fe) solid solution, the compression behavior is not very sensitive to the Fe content. In a previous study, Mao et al. [10] observed no substantial change of K0 for various (Mg,Fe)SiO3 perovskites up to 30 GPa. The main e¡ect of Fe is to slightly increase the room pressure perovskite unit cell volume, for î 3 for MgSiO3 and example from 162.6 to 163.8 A (Mg0:8 Fe0:2 )SiO3 compositions, respectively [11]. A recent X-ray di¡raction study reports a bulk modulus of about 235 GPa for a silicate perovskite with 5 mol% Al2 O3 , a value 10% lower than that of pure MgSiO3 perovskite [12]. The perovskite samples, prepared in a multi-anvil press at 26 GPa and 1500³C, were recovered at room pressure before being reloaded in a large volume press to study their compression. Similar results were recently reproduced (K0 = 225.5 þ 1.2 GPa) using a similar procedure for the perovskite synthesis, but a diamond anvil cell (DAC) for the compression measurements [13]. In both studies, bulk moduli were extracted from compression curves obtained in very limited pressure ranges below 10 GPa. However, because silicate perovskite occurs between 24 and 130 GPa in the lower mantle, an extrapolation of these results to the whole lower mantle is questionable. For example, a very particular compression behavior was evidenced at low pressures for SrZrO3 perovskite [14]. It

may be particularly critical in the case of AlMgSiO3 perovskite, for which the crystal chemistry is complicated by the presence of trivalent cations in the lattice. Recently, Brodholt [15] proposed that the substitution mechanism of Al in MgSiO3 perovskite could evolve with pressure, and that the sti¡ness of this phase could increase with pressure. Here, we present new bulk modulus measurements for various (Al,Fe)-MgSiO3 perovskites at lower mantle pressures. 2. Materials and methods Starting materials were synthetic MgSiO3 enstatite and synthetic Fe0:05 Mg0:95 SiO3 , Al0:05 MgSi0:95 O3 , (AlFe)0:05 (MgSi)0:95 O3 , and Al0:22 (MgSi)0:89 O3 glasses, where the subscript indicates the amount in mol% of cations. Composition of the three ¢rst glasses were checked by inductively coupled plasma atomic emission spectroscopy at the Bayerishes Geoinstitut (Table 1). Silicate perovskite samples were synthesized in the DAC using CO2 laser-heating. Starting materials were loaded cryogenically with argon in a 60^80 Wm hole of preindented Re-gaskets. Small ruby chips were used to measure pressure at less than 20 Wm distance from the probed sample. Samples were ¢rst compressed to 26^28 GPa before laser-heating at around 2300 K for several minutes (stabilized TEM00 CO2 laser). Pressure was also recorded after laser-heating, before the X-ray di¡raction experiments. Then, pressure was increased step by step to maximum pressures of 60^70 GPa. After each pressure increase, we repeated the CO2 laser-heating of the sample to relax the stresses that are eventually built on compression. We carefully avoided laser-heating the ruby chip, and considered stresses optimally reTable 1 Composition of starting glasses (wt%), analyzed by ICP^AES MgO Fe0:05 Mg0:95 SiO3 38.25 40.64 Al0:05 MgSi0:95 O3 (AlFe)0:05 (MgSi)0:95 O3 37.63

SiO2

FeO Al2 O3 Total

58.29 56.87 56.26

3.45 ^ 3.60

A fourth starting glass is Al0:22 (MgSi)0:89 O3 .

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^ 2.49 2.51

99.99 100 100

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leased when the ruby £uorescence doublet was found very well de¢ned [16]. Angle-dispersive X-ray di¡raction experiments were carried out at the ID30 beamline of the ESRF (Grenoble, France). A doubly focused monochromatic X-ray beam was used at a waveî , in association with imaging length of 0.3738 A plates and the fast scan technique available on ID30 to collect data over a 2a interval from 4 to 25³ (see [17,18] for details). X-rays were focused on a spot of about 15U20 Wm full width half maximum on the sample. Wavelength and sample detector distance were calibrated against the iodine absorption edge and the di¡raction pattern of a Si standard, respectively. Two-dimensional images were integrated after usual corrections of distortion and tilting [19], and treated using the GSAS package [20]. Unit cell parameters were determined from re¢nement in Rietveld mode at all experimental pressures. Errors in volume determination are dominated by the intrinsic experimental error on ID30 of about 0.1%. Errors

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in pressure are limited to less than 2% due to the very small pressure chamber and to the annealing of stresses. 3. Results and discussion We present a typical X-ray di¡raction pattern and related Rietveld re¢nement (Fig. 1). Argon and perovskite are the two major phases observed under pressure. In some rare cases we detected traces of stishovite, probably due to silica excess in the starting material. Rietveld re¢nements were performed on the X-ray di¡raction patterns of the quenched phases. In the simplest model, Fe2‡ and Fe3‡ sit in the dodecahedral site, while Al enters both perovskite sites when it is the only trivalent cation (for Al0:05 MgSi0:95 O3 and Al0:22 (MgSi)0:89 O3 compositions), or only in the octahedral site when Al and Fe are both present (for (AlFe)0:05 (MgSi)0:95 O3 ). Using this model for the crystal chemistry of perovskite, we

Fig. 1. Rietveld re¢nement of (AlFe)0:05 (MgSi)0:95 O3 perovskite recovered at room pressure, in the DAC, after compression to 60 GPa. In this re¢nement Al and Fe are considered located in octahedral and dodecahedral sites of the perovskite lattice, respectively. All di¡raction lines are well explained by the orthorhombic perovskite structure (space group Pbnm). The only di¡erence for di¡raction patterns recorded at higher pressures is additional lines due to the presence of the Ar pressure medium. As for all patterns recorded in the DAC, there is a signi¢cant background due to Compton di¡usion in diamond, which was subtracted for clarity.

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Table 2 Unit cell parameters and volumes re¢ned for the perovskite compounds analyzed in this study P (GPa) MgSiO3 [18] Atm 28.9 32.1 44.8 46.0 48.0 48.5 52.2 Fe0:05 Mg0:95 SiO3 Atm 26.5 30.0 34.6 39.3 45.0 49.6 53.2 57.4 Al0:05 MgSi0:95 O3 Atm 28.9 33.4 38.4 42.8 43.7 48.0 2nd run 32.8 36.5 41.2 46.5 50.3 54.1 57.2 (AlFe)0:05 (MgSi)0:95 O3 Atm 28.2 30.9 35.4 38.9 43.9 47.9 50.7 54.7 57.6 59.7 Al0:22 (MgSi)0:89 O3 26.4 32.4 36.8 40.6

a î) (A

b î) (A

c î) (A

V î 3) (A

4.7767(26) 4.6268(12) 4.6039(7) 4.5477(12) 4.5520(20) 4.5305(6) 4.5358(15) 4.5144(18)

4.9276(26) 4.7948(15) 4.7838(5) 4.7295(14) 4.7363(23) 4.7225(6) 4.7280(16) 4.7075(18)

6.8951(20) 6.6771(13) 6.6564(3) 6.5777(14) 6.5864(11) 6.5579(4) 6.5641(11) 6.5302(15)

162.306(52) 148.128(45) 146.602(21) 141.474(41) 142.001(45) 140.309(15) 140.771(40) 138.777(39)

4.7830(3) 4.6330(4) 4.6066(6) 4.5936(8) 4.5786(4) 4.5555(6) 4.5297(10) 4.5191(6) 4.5050(7)

4.9304(2) 4.8088(7) 4.7960(7) 4.7749(7) 4.7604(4) 4.7441(3) 4.7287(6) 4.7207(4) 4.7067(3)

6.9025(1) 6.6933(8) 6.6719(4) 6.6457(3) 6.6208(5) 6.5885(5) 6.5661(6) 6.5465(4) 6.5247(4)

162.775(8) 149.120(26) 147.404(22) 145.768(19) 144.306(18) 142.389(17) 140.640(27) 139.658(18) 138.346(16)

4.7811(5) 4.6270(5) 4.6067(11) 4.5953(45) 4.5828(9) 4.5606(7) 4.5511(9)

4.9384(3) 4.8070(6) 4.7897(10) 4.7755(42) 4.7499(9) 4.7567(6) 4.7491(7)

6.9186(3) 6.6958(8) 6.6715(9) 6.6288(64) 6.6287(8) 6.6134(6) 6.6003(8)

163.355(16) 148.929(22) 147.203(32) 145.470(150) 144.294(30) 143.468(17) 142.658(22)

4.6122(5) 4.5972(7) 4.5777(4) 4.5571(3) 4.5391(4) 4.5268(13) 4.5081(5)

4.7926(5) 4.7811(6) 4.7679(4) 4.7506(3) 4.7390(3) 4.7282(10) 4.7145(4)

6.6793(5) 6.6586(7) 6.6362(4) 6.6103(2) 6.5878(3) 6.5617(8) 6.5450(3)

147.642(21) 146.355(27) 144.843(16) 143.107(10) 141.708(12) 140.443(29) 139.103(13)

4.7803(7) 4.6311(5) 4.6171(4) 4.6024(8) 4.5887(6) 4.5624(17) 4.5622(9) 4.5374(9) 4.5339(9) 4.5056(17) 4.5038(17)

4.9370(6) 4.8123(7) 4.7993(6) 4.7776(10) 4.7733(7) 4.7691(13) 4.7495(10) 4.7371(7) 4.7314(7) 4.7237(12) 4.7189(15)

6.9153(7) 6.7003(7) 6.6799(7) 6.6473(9) 6.6272(7) 6.6116(16) 6.5766(14) 6.5663(10) 6.5496(10) 6.5328(8) 6.5239(7)

163.203(30) 149.326(22) 148.017(21) 146.165(38) 145.160(28) 143.859(49) 142.502(33) 141.135(31) 140.498(31) 139.039(45) 138.653(42)

4.6353(11) 4.6052(5) 4.5808(8) 4.5681(7)

4.8259(9) 4.8040(4) 4.7860(6) 4.7847(5)

6.7436(19) 6.7184(4) 6.6825(8) 6.6723(5)

150.849(48) 148.634(19) 146.503(31) 145.835(24)

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505

Table 2 (Continued) P (GPa)

a î) (A

b î) (A

c î) (A

V î 3) (A

37.5 52.0 57.9 64.6 68.9

4.5744(5) 4.5225(8) 4.4941(11) 4.4817(9) 4.4611(5)

4.7877(6) 4.7659(10) 4.7382(12) 4.7108(11) 4.7085(9)

6.6876(5) 6.6167(6) 6.5839(6) 6.5509(6) 6.5336(6)

146.464(20) 142.614(30) 140.198(34) 138.305(25) 137.241(24)

adjusted the atomic parameters to the experimental pro¢les. Compared with MgSiO3 , atomic positions and polyhedral bond lengths are found to vary less than 5 and 2%, respectively, for all perovskite compounds recovered at room pressure. These results are in agreement with a previous study performed on iron-bearing perovskite with well-characterized FeIII /gFe ratio [21]. For the ¢ve di¡erent (Al,Fe)-MgSiO3 compositions analyzed, the unit cell volume increases with increasing Fe and Al contents at all experimental pressures (Table 2). In order to better compare the results, we report the unit cell volume, normalized to that of pure MgSiO3 perovskite, as a function of pressure and composition (Fig. 2). It appears that the e¡ect of the Al content on the unit cell volume is larger than that of Fe at all pressures, as shown by comparison between Al0:05 MgSi0:95 O3 and Fe0:05 Mg0:95 SiO3 samples. In addition, the solution of Al in the structure leads to a higher slope in this V^P diagram, which means that Al perovskite is less compressible than pure or Fe-bearing perovskite. After decompression, we could record the room pressure volume (V0 ) of the magnesium silicate perovskites, except for the Al0:22 (MgSi)0:89 O3 composition because of amorphization during decompression. Thus, for this compound the calculation of the bulk modulus is less accurate, because the strong constraint of the V0 cannot be used. Di¡erent Birch^Murnaghan equations of state were used to estimate (V0 , K0 , KP0 ) for these perovskite compounds. With increasing (Al,Fe) contents, we calculate signi¢î 3 for cant increases of V0 from 162.4 to 163.5 A MgSiO3 and Al0:22 (MgSi)0:89 O3 respectively ; of K0 from 259(3) to 289(6) GPa, when KP is ¢xed to 3.7 (see [8]); and of K0 from 249(3) to 275(6) GPa when KP is ¢xed to 4 (see Table 3). While the a unit cell parameter remains very

similar for all compositions, the b and c axes appear to be more sensitive to the Al and Fe contents. We used the (a,b,c) cell parameters of the orthorhombic lattice to estimate the angles of ro-

Fig. 2. Comparison of the compression behavior of various perovskite compounds. (Al,Fe)-MgSiO3 perovskite unit cell volumes are normalized to that of pure MgSiO3 perovskite [18] ‰…V Pv 3V MgSiO3 †=V MgSiO3 Š. Also shown are previous data obtained on perovskite samples synthesized in multi-anvil press apparatus [12,13]. Note that our low-pressure volumes are similar to previous studies. Discrepancy between slopes can be explained by di¡erent perovskite crystal chemistries, due to di¡erences in synthesis conditions. In our experiments, samples were annealed with a CO2 laser after each compression step, which allowed the defect concentration to reequilibrate at each pressure. The annealing technique makes our experimental conditions much closer to those present in the Earth's lower mantle.

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Fig. 3. Tilt angles of the rigid SiO6 octahedra in perovskite as a function of composition and pressure (cosx = ac /bc and p cos3 = 2ac /cc ). Fe0:05 Mg0:95 SiO3 and (AlFe)0:05 (MgSi)0:95 O3 perovskite samples are omitted for clarity. Higher distortion angles are found for higher Al contents. The orthorhombic distortion is also found to increase with pressure for all compounds. Theoretically calculated distortion angles for MgSiO3 and Mg3 Al2 Si3 O12 are reported for comparison (solid lines [15]). Trends are found compatible, if theoretical distortion angles are all shifted to slightly higher values. Experimental points reported in parentheses are considered not reliable.

tation of the SiO6 octahedra relative to the pseudo-cubic axes (Fig. 3). It appears that the distortion increases signi¢cantly with pressure up to 70 GPa. Especially, the x angle (cosx = ac /bc ) is more sensitive to pressure than the 3 angle p (cos3 = 2ac /cc ). As the distortion was reported to decrease slightly with increasing temperature at high pressure [8], it is probable that lower mantle perovskite remains with similar orthorhombic distortion at all mantle depths. Note that the Al0:22 (MgSi)0:89 O3 perovskite appears to be much more distorted than the other samples (see Fig. 3). This would explain why this compound

could not be recovered at room pressure. Our results on Al perovskite are compatible with recent ab-initio calculations [15]: the variations of the x and 3 angles are found to have similar slopes, even if the calculation underestimates the distortion angles at all pressures. Our results con£ict drastically from previous reports, which suggested a decrease of the silicate perovskite bulk modulus with increasing Al content [12,13]. We note, however, that in contrast with the clear di¡erence of the slope of compression curves, perovskite volumes of all studies are in relatively good agreement with each other at low pressures. In particular, all (Al,Fe)-MgSiO3 perovskite volumes reported up to date show higher volume than MgSiO3 perovskite. The explanation for the bulk modulus discrepancy possibly lies in variations of the Al perovskite crystal chemistry due to di¡erent synthesis conditions. In previous studies, perovskite samples were synthesized at a single pressure below 30 GPa in a multianvil press, whereas in this study the samples were annealed at each compression step from about 27 to 70 GPa. With this procedure, the perovskite crystal chemistry can evolve along the compression curve, because the defect concentration is reequilibrated at each pressure. Another possible explanation is the synthesis temperature that was signi¢cantly di¡erent in the various studies. Samples were for example prepared at 1773 K in the multi-anvil press [12], and at about 2300 K in our experiments. Such temperature variation can afTable 3 Results of bulk moduli calculations

KP ¢xed to 4 MgSiO3 Fe0:05 Mg0:95 SiO3 (AlFe)0:05 (MgSi)0:95 O3 Al0:05 MgSi0:95 O3 Al0:22 (MgSi)0:89 O3 KP ¢xed to 3.7 (see [8]) MgSiO3 Fe0:05 Mg0:95 SiO3 (AlFe)0:05 (MgSi)0:95 O3 Al0:05 MgSi0:95 O3 Al0:22 (MgSi)0:89 O3

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K0 (GPa)

dK

V0 î 3) (A

dV

248.8 255.4 265.0 266.7 275.5

2.5 2.0 3.7 2.8 6.0

162.4 162.7 163.2 163.3 163.5

0.2 0.1 0.2 0.2 0.4

259.0 261.9 271.9 270.6 289.1

2.7 2.4 3.8 2.7 6.3

162.3 162.7 163.1 163.3 163.1

0.2 0.1 0.2 0.2 0.3

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fect population of point defects. Finally, discrepancies could be due to the experimental procedure used in previous studies that consists in recovering metastable perovskite samples at ambient P^T conditions before loading again at high pressure. It is possible that the perovskite structure, and in particular the local structure around Al, FeIII , and EO defects is signi¢cantly a¡ected. Recent ab-initio calculations [15] report that higher pressures favor the coupled Al substitution mechanism (2AlIMgSi) at the expense of the defect mechanism 2AlSi +EO I2Si. This change of substitution mechanism with pressure can be explained by the di¡erent unit cell compacity that they involve: the defect mechanism yields a lower compacity compared to the coupled substitution mechanism. Thus, the possibility of the two types of Al substitution implies that the knowledge of unit cell volume alone is not enough to de¢ne density, because of the variable amount of oxygen vacancies between each model. Also, if di¡erent perovskite samples do not have the same crystal chemistry, di¡erences in unit cell compressibility can be expected. In any case, extrapolation of the low-pressure compression curve to lower mantle pressures does not appear to be appropriate for aluminous silicate perovskite, because mantle temperatures are su¤ciently high to reequilibrated defect concentrations, as in our experiments. Therefore, as ab-initio calculations suggest a decrease of oxygen vacancy concentration with increasing pressure, we argue that our unit cell volumes can be coupled to a simple atomic model without oxygen vacancies to calculate accurately molar densities for lower mantle (Al,Fe)-MgSiO3 perovskite. 4. Conclusions Due to its abundance, the knowledge of the PVT equation of state of (Al,Fe)-MgSiO3 perovskite is of ¢rst importance to model the mineralogy of the lower mantle. The general procedure is to adjust density and sound-of-speed pro¢les provided by seismology to experimentally measured densities and bulk moduli [8,9]. As the lower mantle Al content is estimated to about 4.4 wt% for a

507

pyrolitic Earth's model [22], e¡ects of Al on perovskite elasticity must be considered. In this paper, we treat these e¡ects as perturbations from previous calculations [18]. Our results point out an increase of the perovskite sti¡ness and room pressure volume with increasing Al content (Table 3), which implies relatively higher bulk modulus (K(P)) and lower density (b(P)) compared to (Mg,Fe)SiO3 perovskite at given depths in the lower mantle (we here assume that perovskite thermal properties are not much a¡ected by Al, due to lack of data). To reproduce the geophysical pro¢les, the lower mantle should contain relatively higher magnesiowu«stite and Fe contents, in order to counterbalance the e¡ects of Al on K(P) and b(P), respectively. We thus con¢rm that the lower mantle (Mg+Fe)/Si ratio is signi¢cantly higher than unity. Acknowledgements We thank M. Mezouar and T. Le Bihan for help in experiments, D.R. Neuville for providing Al0:22 (MgSi)0:89 glass, I. Daniel for helpful discussions, and S.A.T. Redfern, J. Brodholt and an anonymous reviewer for fruitful review. This is CNRS and IPGP contribution.[BW] References [1] F. Farges, F. Guyot, D. Andrault, Y. Wang, Local structure around Fe in Mg0:9 Fe0:1 SiO3 : An X-ray absorption spectroscopy study at Fe-K edge, Eur. J. Mineral. 6 (1995) 303^312. [2] Y. Fei, Y. Wang, L.W. Finger, Maximum solubility of FeO in (Mg,Fe)SiO3 perovskite as a function of temperature at 26 GPa: Implication for the FeO content in the lower mantle, J. Geophys. Res. 101 (1996) 11525^11530. [3] T. Irifune, Absence of an aluminous phase in the upper part of the Earth's lower mantle, Nature 370 (1994) 131^ 133. [4] D. Andrault, D. Neuville, A.M. Flank, Y. Wang, Cation coordination sites in Al-MgSiO3 perovskite, Am. Mineral. 83 (1998) 1045^1053. [5] N.C. Richmond, J.P. Brodholt, Calculated role of aluminum in incorporation of ferric iron into magnesium silicate perovskite, Am. Mineral. 83 (1998) 947^951. [6] C.A. McCammon, Perovskite as a possible sink for ferric iron in the lower mantle, Nature 387 (1997) 694^696.

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[7] B.J. Wood, D.C. Rubie, The e¡ect of alumina on phase transformations at the 660-kilometer discontinuity from Fe-Mg partitioning experiments, Science 273 (1996) 1522^1524. [8] G. Fiquet, A. Dewaele, D. Andrault, M. Kunz, T. Le Bihan, Thermoelastic properties and crystal structure of MgSiO3 perovskite at lower mantle pressure and temperature conditions, Geophys. Res. Lett. 27 (2000) 21^24. [9] N. Funamori, T. Yagi, W. Utsumi, T. Kondo, T. Uchida, M. Funamori, Thermoelastic properties of MgSiO3 perovskite determined by in situ X-ray observations up to 30 GPa and 2000 K, J. Geophys. Res. 101 (1996) B8257^ B8269. [10] H.K. Mao, R.J. Hemley, Y. Fei, J.F. Shu, L.C. Chen, A.P. Jephcoat, Y. Wu, W.A. Basset, E¡ect of pressure, temperature and composition on the lattice parameters and density of three (Fe,Mg)SiO3 perovskites up to 30 GPa, J. Geophys. Res. 96 (1991) B8069^B8079. [11] B. O'Neil, R. Jeanloz, MgSiO3 -FeSiO3 -Al2 O3 in the Earth's lower mantle: Perovskite and garnet at 1200 km depth, J. Geophys. Res. 99 (1994) 19901^19915. [12] J. Zhang, D.J. Weidner, Thermal equation of state of aluminum-enriched silicate perovskite, Science 284 (1999) 782^784. [13] A. Kubo, T. Yagi, S. Ono, M. Akaogi, Compressibility of Mg0:9 Al0:2 Si0:9 O3 perovskite, Proc. Jpn. Acad. 76 (2000) 103^107. [14] D. Andrault, J.P. Poirier, Evolution of the distortion of perovskites under pressure: an EXAFS study of BaZrO3 ,

[15] [16] [17]

[18]

[19] [20] [21]

[22]

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