P-V-T equation of state of MgSiO3 perovskite

PHYSICS O F T H E EARTH AND PLAN ETARY INTERIORS

ELSEVIER

Physics of the Earth and Planetary Interiors 105 (1998) 21-31

P - V - T equation of state of MgSiO 3 perovskite Guillaume Fiquet

Denis Andrault b,1, Agn~s Dewaele a, Thomas Charpin h, Martin Kunz c,2, Daniel Haiisermann c

a,*,

a Laboratoire de Sciences de la Terre, UMR CNRS 5570, Ecole Normale Sup~rieure de Lyon, 46 All~e d'Italie, 69364 Lyon cedex 07, France D~partement des G~omat~riaux, URA CNRS 734, lnstitut de Physique du Globe, 4 Place Jussieu, 75252 Paris cedex 05, France c European Synchrotron Radiation Facili~.', BP 220, 38043 Grenoble cedex, France

Received 17 March 1997; revised 22 June 1997; accepted 22 June 1997

Abstract A pressure-volume-temperature data set has been obtained for MgSiO 3 perovskite, using synchrotron X-ray diffraction with a laser-heated diamond-anvil cell. The unit cell parameters of the silicate perovskite were measured by angle dispersive X-ray diffraction using imaging plates up to pressures of 57 GPa and temperature in excess of 2500 K. These measurements are in good agreement with the previously reported data of Funamori et al. [Funamori, N., Yagi, T., Utsumi, W., Kondo, T., Uchida, T., Funamori, M., 1996. J. Geophys. Res. 101 (B4), 8257-8269] at lower pressure and yield (OK/OT)p = -0.027 GPa K - ~ for a fixed value K~ of 4 and a zero-pressure thermal expansion parameter a = 1.55 × 10 -5 K- ~ at 300 K. Assuming that the thermoelastic parameters of MgSiO 3 perovskite are applicable to perovskites with moderate iron content, the comparison of the density and K r profiles calculated for a mixture of perovskite and magnesiowiistite and for PREM model indicates that a pure perovskite lower mantle is very unlikely. On the other hand, we obtain a very good match with PREM density and K r profiles for a mixture of 83 vol % (Mg0.93Fe0.07)SiO3 perovskite and 17 vol % (Mgo.79Fe0.21)O magnesiowiistite, compatible with a pyrolytic lower mantle. © 1998 Elsevier Science B.V.

1. Introduction (Mg,Fe)SiO 3 with perovskite structure is generally accepted to be the dominant phase of the Earth's lower mantle (Liu, 1975, 1976; Mao et al., 1977; Ito and Matsui, 1978). A precise knowledge of its density and bulk modulus under various conditions of pressure ( P ) and temperature (T) is thus of prime importance in constraining composition and properties of the lower mantle. Recent progresses have

* Corresponding author. E-mail: [email protected] E-mail: andrault @ipgp.jussieu.fr 2 E-mail: [email protected]

been made by advances in high-pressure techniques, such as diamond-anvil cell and multi-anvil press techniques in combination with synchrotron radiation. The first high-pressure and high-temperature in situ diffraction study carried out by Mao et al. (1991) using a diamond-anvil cell with an external resistance heater was followed by numerous experimental studies conducted in various types of large volume presses (Wang et al., 1991; Funamori and Yagi, 1993; Wang et al., 1994; Morishima et al., 1994; Utsumi et al., 1995; Funamori et al., 1996). However, except for experiments using a modified Drickamer-type apparatus that reached 36 GPa (Funamori and Yagi, 1993) and a MA8-type high-pressure ap-

0031-9201/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S003 ! - 9 2 0 1 ( 9 7 ) 0 0 0 7 7 - 0

22

G. Fiquet et aL / Physics of the Earth and Planetao' Interiors 105 (1998) 21-31

paratus with sintered diamond anvils (Funamori et al., 1996), no experiments have been conducted under the lower mantle pressure and temperature conditions. Although the overall quality and quantity of data are improved (Wang et al., 1994; Funamori et al., 1996), there is still a large uncertainty in the equation of state of silicate perovskite when extrapolated to pressure and temperature conditions relevant to the Earth's lower mantle (i.e., 23-130 GPa). In this paper, we report new measurements of the equation of state of MgSiO 3 perovskite at pressures ranging from 28 to 57 GPa and temperatures in excess of 2500 K, using a laser-heated diamond-anvil cell technique at the dedicated high-pressure beamline ID30 of the ESRF (Grenoble). The major implications of these new measurements on MgSiO 3 perovskite for the composition of the lower mantle of the earth will be discussed.

2. Experimental techniques Angle-dispersive X-ray diffraction experiments were carried out in situ at high pressure and temperature in a laser-heated diamond-anvil cell at the ID30 beamline of the ESRF (Grenoble, France). A watercooled channel-cut Si (111) monochromator was used to produce a bright monochromatic X-ray beam at 29 keV from two phased undulators. A monochromatic X-ray focal spot of 10 /zm X 20 /xm (FWHM) was obtained at the sample location with two single-electrode bimorph mirrors at a wavelength of 0.4255 A and used in association with imaging plates located at 400 mm from the sample to collect data over a 2 0 interval from 4 to 25 °. However, the distance between focusing mirrors and sample tentatively set for the first experiment of this type to the shortest might have slightly lowered the resolution of the X-ray diffraction pattern. A diamond anvil cell with a large optical aperture (Chervin et al., 1995) equipped with type IIa diamond anvils with 0 300 /xm culets has been used, allowing for in situ pressure and temperature measurements and full 40 angle dispersive data collection. Rhenium gaskets preindented to a thickness of 60 /xm and drilled to a diameter of 100 ~m served as pressure chamber. Laser heating was achieved with a power stabilised 120 W cw sealed-

tube wave guide CO 2 laser (TEM 00, Synrad model 57-1-28), pointed on the sample along an optical path determined by three silver-coated mirrors. A ZnSe lens (focal length 75 ram) was used to focus the laser beam onto the sample through the front diamond at an angle of 16° from the X-ray beam axis to produce hot spots typically 50-75 /zm in diameter. Silicate perovskite MgSiO 3 samples were synthesised in situ from synthetic MgSiO 3 glass mixed with platinum powder (grain size = 1 /zm) by laserheating, to form a disc-shaped polycrystatline aggregate, 70-80 /xm in diameter and 10-15 /zm thick. This starting material was loaded cryogenically in high-purity dry argon, used as pressure transmitting medium. Nominal pressures were measured by the ruby fluorescence technique, on a ruby grain 2-3 /zm in size located at the edge of the pressure chamber. At high temperature, pressure conditions were determined from the P - V - T equation of state of platinum used as pressure calibrant (Jamieson et al., 1982). Temperatures were inferred from the analysis of the thermal emission of the sample recorded during the X-ray diffraction pattern acquisition. For that purpose, we used the same optical design developed by Fiquet et al. (1996), where measurements are achieved with optical fibers guiding signals to a spectrometer coupled with a CDD (Charge Coupled Device) detector placed outside the hutch. Two different holographic gratings are used for ruby fluorescence (1800 g / m m ) and for thermal emission analysis (150 g/mm). This system allows also for a precise alignment of the sample and the laser focus spot after the X-ray beam location. The spectral response of the optical system is initially calibrated using several grey-body sources, including spectra of synthetic Mg2SiO 4 forsterite and CazSiO 4 larnite at their reported melting points (2163 K and 2400 K, respectively). After correction for spectral response, thermal spectra are fitted by a least-squares method to Wien's approximation of Planck's radiation function with an intrinsic precision within 50-60 K (see Shen and Lazor, 1995). Since the 10.6 /zm CO 2 laser wavelength is of the same order of the sample thickness and the hot spot created on the sample (50-75 /xm in diameter) is much larger than the X-ray beam size at sample location (10 k~m vertical by 20 p~m horizontal), significant temperature, gradi-

23

G. Fiquet et al. / Physics of the Earth and Planetary Interiors 105 (1998) 2 I-31

diffraction pattern and refinement is shown in Fig. 1. Lattice parameters and unit-cell volumes are listed in Table 1 for the various P - T conditions achieved in this study. For these calculations, 40 reflections were used on average in the unit cell determination, which allows for an accurate determination of the relative axis compressibilities. This is represented in Fig. 2, where lattice parameters are reported as a function of pressure at ambient temperature and T = 2000 + 150 K. The present results clearly show that the compression of the orthorhombic perovskite MgSiO 3 is anisotropic. The b-axis is 25% less compressible than the a- or c-axis at room temperature, with a-axis slightly more compressible than c. Linear regressions in the pressure range 2 5 - 6 0 GPa yield room temperature mean axial compressibilities of 9 . 8 X 10 -4 GPa - I , 6 . 2 X 10 -4 GPa -~ and 8.6X 10 -4 GPa ~ for a, b and c respectively. At high temperature, the three axis show higher linear compressibilities than at room temperature (10.3 x 10 -.4 GPa -~, 7 . 1 X 10 -4 GPa -~ and 9 . 3 X 1 0 4 GPa for a, b and c respectively), accompanied by a slight reduction of the orthorhombic distortion.

ents in the X-ray spot can be avoided, as already shown in a similar laser-heated diamond-anvil cell X-ray diffraction study (Fiquet et al., 1996). LeBail profile refinements (LeBail, 1992), using program package GSAS from Larson and Von Dreele (1994), were applied to the diffraction patterns, in order to obtain reliable high-pressure high-temperature cell parameters for MgSiO 3 perovskite as well as for the pressure calibrant, up to the maximum pressures of 57 GPa and temperatures of 2700 K.

3. Results and discussion All of the diffraction data were obtained inside the stability field of perovskite and no phase change was o b s e r v e d o v e r the studied pressure and temperature range. N o e v i d e n c e of d e c o m p o s i t i o n or reaction with the platinum used as pressure standard was o b s e r v e d during the experiments. The full profile LeBail refinements were applied using space group P b n m , which was o b s e r v e d from 26 G P a to the m a x i m u m pressure of 57 GPa. An e x a m p l e of the

MgSi03 + Pt in a r g o n / h s 1 3 3 _ 0 1 7 Lambda .4258 A, L-S c y c l e 405 I ,q~ o

I

I

Hist 1 Profiles

Obsd. and Diff.

I

I

I

I

I

I

P= 3 7 5 GPa - T= 2402 K ['AqSiO 3 Pbnm P :,(j0r

o H

ILl n

II

~ll I ~ I

II

lu II

IIHII

1

IIF'II IIn~qln Ilnl ~1 Ill

Ililli~l

nnun

r!

o~o I

I

.6 2-Theta,

I

.8 dog

1.0

I

I

1.2

1.4

I

1.6

I

1.8

I

2.0

I

2.2 XIOE

1

Fig. 1. Example of X-ray diffraction pattern of MgSiO3 perovskite obtained at 2400 K and 37.5 GPa, after correction and integration from an imaging plate exposed for 15 mn using a 10 X 20 tzm2 focused undulator beam at 29 keV monochromatic radiation. Crosses represent observed data and continuous line represents a LeBail profile refinement. The difference between the observations and the fit is shown below the spectrum. Perovskite pattern (lower ticks) is associated with reflections from the argon pressure-transmitting medium (upper ticks) and Pt pressure standard (intermediate ticks).

293 (5) 2402 (70) 1618 (103) 293 (5) 2070 (112) 2668 (171) 293 (5) 293 (5) 1916 (83) 293 (5) 2007 (103) 2269 (169) 293 (5) 293 (5) 1972 (94) 293 (5) 2171 (144) 293 (5) 293 (5) 293 (5) 1759 (72) 1976 (77) 293 (5) 2103 (160) 293 (5) 293 (5) 293 (5)

T (K)

6.6896 (26) 6.7023 (9) 6.6986 (8) 6.6713 (10) 6.7053 (13) 6.6992 (17) 6.6642 (15) 6.5740 (22) 6.5881 (18) 6.5715 (15) 6.5958 (20) 6.5804 (27) 6.5626 (10) 6.5501 (23) 6.5700 (26) 6.5532 (14) 6.5649 (42) 6.5508 (26) 6.5311 (14) 6.5935 (6) 6.6160 (16) 6.6219 (12) 6.5860 (9) 6.6256 (13) 6.5794 (25) 6.5552 (14) 6.8956 (14)

c (~k) 149.329 149.732 149.446 147.569 150.134 150.256 147.766 141.851 142.888 141.755 143.159 142.167 140.807 140.670 141.487 140.507 141.381 140.783 138.968 142.447 143.967 144.474 142.225 143.929 141.198 140.847 162.300

V (,~3) (59) (41) (29) (37) (65) (44) (33) (58) (37) (36) (51) (97) (45) (60) (57) (32) (82) (47) (41) (27) (118) (44) (32) (67) (87) (58) (110)

3.8204 (1) 3.8297 (1) 3.8289 (1) 3.8142 (1) 3.8310 (1) 3.8263 (1) 3.8067 (1) 3.7678 (1) 3.7752 (1) 3.7658 (1) 3.7804 (1) 3.7738 (2) 3.7597 (2) 3.7568 (2) 3.7677 (2) 3.7566 (2) 3.7675 (2) 3.7566 (2) 3.7453 (2) 3.7728 (1) 3.7916 (1) 3.7913 (l) 3.7720 (1) 3.7898 (1) 3.7709 (1) 3.7618 (1) 3.9256 (2)

a (.~)

b (,~) 4.8010 (5) 4.8051 (5) 4.8007 (6) 4.7860 (5) 4.8103 (16) 4.8014 (11) 4.7817 (7) 4.7368 (11) 4.7443 (10) 4.7336 (9) 4.7417 (15) 4.7346 (26) 4.7351 (I0) 4.7309 (15) 4.7407 (15) 4.7260 (10) 4.7349 (20) 4.7251 (17) 4.7132 (13) 4.7402 (9) 4.7657 (49) 4.7599 (10) 4.7383 (10) 4.7548 (18) 4.7439 (23) 4.7238 (11) 4.9278 (12)

a (,~)

4.6496 (10) 4.6493 (12) 4.6472 (6) 4.6218 (11) 4.6547 (23) 4.6714 (13) 4.6371 (10) 4.5553 (14) 4.5716 (12) 4.5571 (9) 4.5774 (12) 4.5632 (23) 4.5313 (19) 4.5395 (27) 4.5427 (17) 4.5368 (14) 4.5484 (23) 4,5483 (16) 4.5145 (17) 4.5576 (11) 4.5661 (19) 4.5835 (13) 4.5576 (l 1) 4.5688 (15) 4.5238 (16) 4.5485 (23) 4.7765 (11)

Platinum

Perovskite MgSiO 3

Table 1 Unit-cell parameters of platinum and MgSiO 3 perovskite used in the determination of EOS

V (,~3) 55.762 56.168 56.133 55.488 56.226 56.020 55.163 53.489 53.806 53.404 54.026 53.745 53.145 53.023 53.485 53.011 53.474 53.012 52.534 53.704 54.507 54.496 53.668 54.433 53.622 53.233 60.497

(5) (2) (3) (3) (3) (3) (3) (4) (2) (3) (3) (7) (8) (7) (7) (8) (8) (9) (7) (6) (5) (3) (4) (4) (6) (6) (11)

26.53 (20) 37.46 (46) 32.55 (68) 28.52 (20) 34.88 (73) 40.26 (113) 31.00 (20) 45.11 (20) 52.88 (55) 45.90 (30) 5t.52 (68) 55.73 (111) 48.33 (30) 49.51 (30) 56.14 (62) 49.59 (30) 57.53 (95) 49.59 (30) 54.33 (35) 43.t7 (30) 45.81 (47) 47.34 (50) 43.48 (30) 48.72 (106) 43.90 (30) 47.49 (30) 10 -4

EOS Pt

Pressure (in GPa)

28.00 (20) 29.20 (20) 30.10 (25) 30.10 (25) 30.10 (25) 31.00 (25) 31.00 (25) 43.00 (30) 43.30 (30) 43.00 (30) 45.50 (30) 46.00 (30) 46.10 (30) 45.90 (30) 45.85 (30) 45.70 (30) 45.70 (30) 45.70 (30) 51.00 (35) 39.50 (30) 41.40 (30) 41.30 (30) 41.30 (30) 42.00 (30) 43.90 (30) 46.20 (30) 10 -4

Ruby scale

7"

t~

t.m

25

G. Fiquet et al. / Physics of the Earth and Planeta~ Interiors 105 (1998) 21-31 6.80 •

i -~-3ooK

.'-~

676

......

i--U-

.

L~Z~Lmo,

~..~ 3..4~.2070

6.70 6.65

]~ /J eta,. (19~) - 2ooo Kj

2000K

lit2-).

~

"-'--.

2103 (160)

1976 (rT~l,m.2oo r (lO3) 6.60

~

"1"11.1916 (83)-~

6.55

6.6o *~

c (A)

6.45

.... 25

~ .... 30

~-" 35

4.8 L ~ - ~ - g : k _ ~

4.6 i

'-~ ~ 40

--- •

-~"~

' ~ .... 45

• 50

55

_ _

60

!

the stress field. These measurements reported Fig. 3 clearly show that the non-hydrostatic stresses are significantly reduced on the sample at high temperature, with (o- E- c r 3) never exceeding 0.2 GPa for pressure ranging from 30 to 60 GPa. At room temperature, the magnitude of the non-hydrostatic stress can amount to as much as 0.6 GPa when measured before any laser-heating cycle. Among the 27 data points reported here, 12 have been recorded at simultaneous high pressure and high temperature, and 6 of them can be considered to be on a 2000 K isotherm within the uncertainty of the temperature measurement. The corresponding measured unit-cell volumes were fitted along isothermal curves with an Eulerian finite strain BirchMurnaghan equation of state:

[t0t i t ]I

-"

P=2KT.o .................................. 20

25

30

35

40

45

al 50

55

- -

,

60

" -

I-~-(4-K~,o)

P (GPa)

Fig. 2. Compression of the MgSiO~ perovskite a, b and c lattice parameters. Open and solid symbols are data recorded at room temperature and T= 2000+ 150 K, respectively. Curves are fits showing linear compression between 25 and 60 GPa at room temperature (solid curve) and 2000 K (dashed curve). The unit-cell volume of platinum, intimately mixed with perovskite sample, was obtained using the same fitting procedure. The P - V - T equation of state proposed by Jamieson et al. (1982) was then used for each temperature and volume measurement to determine the actual pressure of the sample during the experiments. In addition, the diffraction pattern can be used to estimate quantitatively the differential stresses developed inside the sample during the laser-heating. Non-hydrostaticity in the diamondanvil cell is indeed a crucial parameter because it affects both the determination of pressure and unitcell volume measurement of the sample (Meng et al., 1993). Following Weidner et al. (1992), we apply a method for determining deviatoric stresses, with modifications for the diamond-anvil cell geometry. It relates the elastic strain Adhkt/dhkl observed for the different platinum diffraction lines to the stress field via elastic moduli (MacFarlane et al., 1965; Simmons and Wang, 1971), which have been properly rotated to reflect the orientation of the crystal within

×

(1)

where Kr, o, K'r, o and Vr, o are the bulk modulus, its pressure derivative and the unit-cell volume at ambient pressure and temperature T (in K). The limited number of data points for this isotherm leads us adopt the assumption that K'r, o is a constant equal to 4. The Kr, o and Vr,0 parameters were thus determined at ambient temperature and at 2000 K for pressures ranging from 26 GPa to 57 GPa.

0.6 0.5

!l

o

!"

Room-temperature High-temperature (T > 1500 K)

0"4i =

0.3

•

I

[]

0.2 k

•

; ~ 0.1 ! v :

"

U []

~

0! 0

10

20 30 40 Pressure (GPa)

50

60

Fig. 3. Deviatoric stress (0"1- 0"3) as a function of pressure at room temperature (solid dots) and at high temperature (open squares).

G. Fiquet et al. / Physics of the Earth and Planetary Interiors 105 (1998) 21-31

26

• This work - ambient temperature] "'-~---This work - 2000 K ] v Funamofl et al. (1096) - 2000 K J

\,,,

60

'C

50

~" n

(dK/dT)= - 0 . 0 3 5 G P a W 1

',.

40

Ko= 194+ 13 GPa

~ '',..

Vo= 171.9 + 1.5 A3

\ "...... 0.

10

3

V.=162.6 + 0.5 A3

o

130

Y ............ 140

\

"".

-..

,",. -

~

'~..

150 160 170 Volume (A3)

......

~:;¢

:',"L-=;

i;i O~i'~K '

,t

180

Fig. 4. P-V diagram showing unit-cell along two isotherms. Lines represents best fit to the data, using a third-order BirchMurnaghan equation of state with K~ fixed to 4, at room temperature (solid line) and 2000 K (dashed line).

This is shown in Fig. 4, where molar volume measurements are reported as a function of pressure along with three data points at 2000 K taken from Funamori et al. (1996). At room temperature, a least-squares fit with Eq. (1) yields a bulk modulus K298, 0 of 256 + 7 GPa, associated with a reference 03 molar volume V298 = 162.6 _+ 0.5 A . On the other hand, we obtain at 2000 K a bulk modulus K20o0,o = 194-I- 13 GPa and a reference volume extrapolated at room-pressure V200o.0 = 171.9-t- 1 ,~3. This leads with a simple description of the temperature dependence of KT.o to ( d K r , 0 / d T ) = - 0.035 GPa K-1 It is also possible to obtain an average thermal expansion coefficient between 300 K and 2000 K which is ( O ~ ) 2 9 8 - 2 0 0 0 K - - 3 X 10 -5 K - j . Although the parameter (d KT.o/dT) is strictly speaking different from the usual (OK/aT)p, this result is in relatively good agreement with the data of Wang et al. (1994) for which (OK/ST)p is reported to be on average - 0 . 0 2 3 (11) GPa K -1 . This result compares very well with the experimental data of Funamori et al. (1996), which yield (OK/ST)p = - 0 . 0 2 8 (17). On the other hand, there is some discrepancy between our observations and the results of Mao et al. (1991), who reported for (OK/OT)p values from - 0 . 0 6 3 to - 0 . 0 8 0 GPa K -~, which cannot be only explained by the fact that Fe-bearing samples were investigated in their study. An explanation was proposed by Wang et al. (1994) who found that distinctive and irreversible changes occurred when Fe-rich

perovskites were heated, resulting in unreliable P V - T data. In the same manner, it is difficult to explain the difference with the study of Morishima et al. (1994), where an extremely low thermal expansion coefficient of 0.8 × 10 -5 K -~ is proposed at 20.5 GPa. An alternate possibility is to perform an inversion of the whole set of experimental data, based on the third-order Birch-Murnaghan equation of state at high temperature, proposed by Saxena and Zhang (1990) and Martinez et al. (1996). This equation is obtained by a modification of Eq. (1) as follows. Neglecting the second-order derivative of the bulk modulus, we obtain:

KT, o = K298, 0 -F ---~-T~]p(T- 298)

(2)

where K298,o is the value at ambient conditions and where the derivative (aKr,o/OT) P is assumed to be constant over the whole temperature range. The unit-cell volume VT,o is given by the following expression:

V~- o = V298,oexp fz~sar,odT

(3)

where V298,0 and aT, 0 are the unit-cell volume at ambient conditions and the thermal expansion at T and ambient pressure respectively, with the following expression for O~T,O:

aT, o = a o + a l T

(4)

We have proceeded to a generalised non-linear inversion, in which six parameters, namely V298.o, K298,0, K~98,0, (OK/OT)p, a o and a l, can be refined. However, and considering our limited data set, some of these parameters were fixed during inversion, in order to increase the resolution on the temperature derivative of the bulk modulus (OK/OT) e and the expression of the thermal expansivity. The bulk modulus has been for instance extensively studied by high-pressure single-crystal (Kudoh et al., 1987; Ross and Hazen, 1989) and polycrystalline X-ray diffraction experiments (Yagi et al., 1982; Knittle and Jeanloz, 1987; Mao et al., 1991), Brillouin scattering (Yeganeh-Haeri et al., 1989) and has been therefore fixed to values for that a general agreement can be found, i.e., K298, 0 = 261 GPa and its pressure derivative K~98,0 = 4. In the same man-

G. Fiquet et al. / Physics of the Earth and Planetao" Interiors 105 (1998) 21-31

ner, the unit-cell volume at ambient conditions V298.0 o3 has been fixed to 162.3 A . The other parameters were refined taking large a priori uncertainties, as follows (~K/OT)p = - 0 . 0 2 + 0.06 GPa K i, c% = 2X10-s+_4X10 5 K-~ and o q = l _ + l x 1 0 -8 K-2. Results obtained after convergence are summarised in Table 2, for three different inversions realised (1) with our data set only, (2) the combination of data sets of Funamori et al. (1996), Utsumi et al. (1995) and Wang et al. (1994), which are the only ones to report measurements on pure MgSiO 3 perovskite, and (3) all data sets. A posteriori errors on these parameters calculated from the resolution matrix under the assumption of normally distributed errors are also reported in Table 2. One notices that results obtained from (1) our data set only show quite large uncertainties (5 X 10 3 GPa K ~) in the determination of (OK/OT)p, compared to that obtained with (3) the whole available data (1 X 10 -s GPa K -~). The constraints on the three inverted parameters obtained with (1) are however very strong, compared to those discussed by Funamori et al. (1996). This might be partly explained by the fact that only uncertainties on the measurements of pressure and volume were directly taken into account in these calculations. Temperature uncertainties were, however, considered through the pressure uncertainties calculation. Temperature fluctuations ranging from 6 K to 121 K were indeed observed during the X-ray diffraction acquisition, and added to the previously mentioned intrinsic error of 50-60 K. The resulting temperature uncertainties were then taken into account in the pressure calculation, according to the P-V-T equation of state of platinum. As an alternative, one could possibly use the nominal pressures given by the ruby fluorescence technique. In this case, the uncertainty is reduced but the results obtained clearly show that such a pressure measurement does not give the actual pressure measurement under the laser-heating conditions inside the sample volume sampled by the X-ray spot, as previously described by Fiquet et al. (1996) and Andrault et al. (1997). Therefore, only pressures determined from platinum were used for calculations of the equation of state of perovskite. As shown in Table 2, the different inversions worked out give very similar results and provide good constraints on the different parameters. These

27

results are illustrated in Fig. 5, where the isothermal compression curves calculated from parameters optimised with (1) and (3) are reported along with experimental data plotted for comparison. This figure also includes experimental measurements obtained for isotherms 1000, 1500 and 2000 K by Funamori et al. (1996), and a compression curve at 2000 K as calculated with the values reported by Mao et al. (1991), i.e., (~K/~T)p= - 0 . 0 6 3 GPa K - I , and c~ = 3.01 x 10 -s + 1.5 X 10 -s T - 1.139 T - 2 at zero-pressure. One notices the very good agreement between the calculated curves with (1) and the reported data points from Funamori et al. (1996). There is a small discrepancy between the results obtained with (1) and the curves calculated with (2) or (3). This arises from the weight represented in the inversion by more than 200 data points (Wang et al., 1994; Utsumi et al., 1995; Funamori et al., 1996) compared to 27 (this work), though both inversions give a similar (OK/~T) e = - 0 . 0 2 6 (1) GPa K L and only a very slight change in the expression of the thermal expansion. Likewise, these results are in relatively good agreement with other attempts to constrain the thermoelastic parameters of the silicate perovskite (Anderson et al., 1997), which yield (OK/OT)p = - 0 . 0 3 0 GPa K - l and a zero-pressure thermal expansion parameters of the order of 1.6 X 10 s K t at 300 K. On the other hand, our measurements are incompatible with the 2000 K isothermal compression curve as calculated from the optimised parameters proposed by Mao et al. (1991). Considering the only slight differences observed between the thermoelastic parameters inversed from (1) and from (2)-(3), we choose, therefore, to use in the following discussion the set of thermoelastic parameters identified with (1), obtained from measurements at the highest pressure and temperature conditions achieved so far. Assuming that thermoelastic parameters of MgSiO 3 perovskite are applicable to perovskites with moderate iron content and that V29s.0 and P298,0 are the only parameters affected by change in iron content (Anderson et al., 1995), we calculate the density and K r profiles from the thermoelastic parameters obtained with (1). We use the temperature profile of Brown and Shankland (1981) fixed at 670 km depth at 1873 K and two temperature profiles extrapolated at larger depth with different linear temperature gradients ~'T of 0.45 and

26l 261 261 261 261 261

262.4 261 263

Direct measurements Wang et al. (1994) Utsumi et al. (1995) Funamori et al. (1996) (1) this work (2) other sets (3) all sets

Indirect measurements Jackson and Rigden (1996) Gillet et al. (1996) Anderson et al. (1997) 4 4 4

4 4 4 4 4 4

- 0.030

- 0.021

-0.023 -0.02 0.028 -0.027 -0.026 -0.026

1.57 1.75 1.6

1.98 1.19 1.11 1.17

(17) (5) (1) (1)

(7) (17) b (7) (1) b

1.64 (19)

% (10 -5 K - t ) a

(11)

K ~ o , r ( a K / O T ) e (GPa K -L)

aot(T)=ot0+oq T + o ~ 2 / T 2. bLinear extrapolation to 0 K of the expression a ( T ) = % + ceI T. CRoss and Hazen (1989), Wang et al. (1994), Utsumi et al. (1995) and Funamori et al. (1996).

Ko, T (GPa)

Ref.

Table 2 Equation of state parameters of MgSiO 3 perovskite

4.90

0.82 1.20 1.61 1.51

(80) (10) (4) (2)

0.86 (34)

a l (10 s K - 2 )

- 0 . 4 7 (20)

otz (K)

consistent with PVT from four reports c

multi-anvil multi-anvil multi-anvil laser-heated DAC multi-anvil

Comments

t~

t

t.n

2.

g~

G. Fiquet et al. / Physics of the Earth and Planetary Interiors 105 (1998) 21-31

1650 i 175.0 ~,<, ~.E 165 0 ~ K '

24ooK "" ~-_'"~-~.~p.

1000 K

145 0

135"%?0

,o~o K

26GOK

.!o.o,~, ""2222- - .

20.0

40.0

60.0

Pressure (GPa) Fig. 5. P - V - T diagram for MgSiO3 perovskite. The curves were calculated with the thermoelasticparameters obtainedin the inversion of (1) our data set only (solid lines), and (3) the combination of (Wang et al., 1994; Utsumi et al., 1995; Funamoriet al., 1996 and this work) data sets (dashed lines) at 300, 1000, 1500, 2000. 2400 and 2600 K respectively.The isothermalcompressioncurves calculated from the optimised parameters are reported along with experimental data plotted for comparison. Open dots stand for experimental measurementsfrom Funamori et al. (1996) at 300. 1000, 1500 and 2000 K. Open squares represent our measurements. For comparison purpose, the grey solid line represents a compression curve at 2000 K as calculated with the values reported by Mao et al. (1991), i.e., (aK/~T)p =-0.063 GPa K i, and c~= 3,01 × 10-5 + 1.5× l0 -s T - 1.139 T - 2 at zeropressure.

0.6 K / k m for comparing our results with the lower mantle density distribution according to the PREM seismic model (Dziewonski and Anderson, 1981). The profile obtained from the inversion for MgSiO 3 composition appears to be by 4 - 5 % lower than that of PREM whereas the profile obtained for a (Mgo.gFe0. ])SiO 3 composition matches well the density distribution of the lower mantle within less than 0.5% deviation on average (Fig. 6a), taking for a (Mg09Fe0.1)SiO 3 composition the room temperature measurement V298.0 of Parise et al. (1990). The density profiles calculated with other temperature profiles ( V T of 0.45 and 0.6 K / k m ) appear indistinguishable from PREM. On the other hand, the K T profile of pure perovskite is 5% larger than that of PREM, as obtained from the relationship K s = KT(I + a3"T) with the c~ and 3' values tabulated by Brown and Shankland (1981) as a function of depth (see Fig. 6b). Likewise, the K v profiles calculated along other temperature profiles (~7T of 0.45 and 0.6 K / k m ) show a signifi-

29

cant deviation from PREM except in the vicinity of the core-mantle boundary. A significant amount of (Mg,Fe)O is thus required to match the PREM K T profile. Using the thermoelastic parameters of Fei et al. (1992) for (Mg0.6Feo4)O magnesiowListite and assuming a lower mantle with only two phases, 15-20% (by volume) magnesiowtistite is needed to reproduce the PREM K r profile. The best fit (less than 0.5% on average) is obtained by combining 83 vol % perovskite and 17 vol % magnesiowiistite. Fixing the iron partitioning coefficient between magnesiowtistite and perovskite to 3 (e.g., Martinez et al., 1997) and assuming that the magnesiowiistite bulk modulus KT. o is weakly dependent on the Fe

5.8

-

-

--PREM this work

5.6

g.-

-- -- -with VT=0,45 K/km 7 ......... with VT=0.60 K/km _ - - . MgSiOa c o m p

E 5.4 5.2

r

~

.

T~¢~, . d r ' - = - ' - s~

~

"~ 5.0 E

a 4.8 4.6 ~ ....

40

i ....

50

i ....

60

i ....

i ....

i ....

70 80 90 P (GPa)

i ....

i ....

100 110 120

750

700

--PREM this work

650

-- -- -with VT=0.45 K/km

600

........ with VT=0.60 K/km

~.~,~.

rr 550 ~- 500 450 40O 35O 4o

50

Fig. 6. Comparison profiles

with

PREM

60

70

of the density lower

80

P (GPa)

mantle

p(P)

90

100

110

and bulk modulus

model

along

120

KT(P)

the temperature

profile of Brown and Shankland (1981) (solid grey line). Error bars represent I% deviation. (a) p(P) versus p (PREM): lines represent density profiles calculated with a (Mg0.qFe0])SiO3 composition with parameters inverted from (1) (solid line), and along linear temperature gradient tTT = 0.45 K/km (dashed line) and 7T = 0.6 K/kin (dotted line). MgSiO3 density profile is shown for comparison (dashed grey line). (b) KT(P) versus KT (PREM): similar plot for K T. Bulk modulus of MgSiO3 perovskite is significantlyhigher than that of PREM.

30

G. Fiquet et aL / Physics of the Earth and Planetary Interiors 105 (1998) 21-31 2.0

References ...... density1

"O 1.5 ~

1.0

rr a.

0.5

(,)

~

%

1

°.'="

0,0

I:l -0.5 20

40

60 80 P (GPa)

100

120

Fig. 7. Misfit between density and K T profiles for PREM and for a two-phase lower mantle model with 83 vol% (Mg0.93Fe0.o7)SiO 3 perovskite and 17 vol% (Mgo.79Fe0.21)O magnesiowiistite, as calculated with thermoelastic parameters obtained from this study and from Fei et al. (1992) for magnesowiistite.

fraction (Jackson et al., 1978; Richet et al., 1989), the compositions have to be close to (Mg0.93Fe0.07)SiO 3 and (Mg0.79Fe0.21)O for perovskite and magnesiowiistite respectively, in order to reproduce the PREM density profile with such an assemblage (Fig. 7). These results are consistent with the previous studies of Wang et al. (1994) and Yagi and Funamori (1996) and mean that within the uncertainty of these measurements, a pure pervoskite lower mantle is very unlikely. On the other hand, a pyrolitic composition for the lower mantle appears consistent with the new data.

Acknowledgements We wish to thank I. Daniel for her help provided on ID30 during the first commissioning period and set-up adjustment. We also thank J. Matas for his important contribution in the inversion procedure, P. Richet for MgSiO 3 glass starting material, S. Bauchau, F. Blaznik and L. Andr6 for their assistance during the experiments on ID30. Comments made by F. Guyot, Ph. Gillet and two anonymous reviewers have significantly improved the manuscript. This work is CNRS-INSU-DBT 'Th~me Terre Profonde' contribution n ° 85.

Anderson, O.L., Masuda, K., Guo, D., 1995. Pure silicate perovskite and the PREM lower mantle model: a thermodynamic analysis. Phys. Earth Planet. Int. 89, 35-49. Anderson, O.L., Masuda, K., Isaak, D.G., 1997. Limits on the value of 6 r and y for MgSiO 3 perovskite. Phys. Earth Planet. Int., in press. Andrault, D., Fiquet, G., Itir, J.P., Richet, P., Gillet, Ph., Haiisermann, D., Hanfland, M., 1997. Pressure in the laser-heated diamond-anvil cell: implications for the study of the Earth's interior. Submitted to Eur. J. Mineral. Brown, J.M., Shankland, T.J., 198l. Thermodynamic parameters in the earth as determined from seismic profiles. Geophys. J. R. Astron. Soc. 66, 579-596. Chervin, J.C., Canny, B., Besson, J.M., Pruzan, Ph., 1995. A diamond anvil cell for IR microspectroscopy. Rev. Sci. Instrum. 66 (3), 2595-2598. Dziewonski, A.M., Anderson, D.L, 1981. Preliminary reference Earth model. Phys. Earth Planet. Int. 25, 297-356. Fei, Y., Mao, H.K., Shu, J., Hu, J., 1992. P - V - T equation of state of magnesiowiistite. Phys. Chem. Mineral. 18, 416-422. Fiquet, G., Andrault, D., Iti~, J.P., Gillet, Ph., Richet, P., 1996. High-pressure and high-temperature X-ray diffraction study of periclase in a laser-heated diamond anvil cell. Phys. Earth Planet. Int. 95, 1- 17. Funamori, N., Yagi, T., 1993. High pressure and high temperature in situ X-ray observation of MgSiO 3 perovskite under lower mantle conditions. Geophys. Res. Lett. 20 (5), 387-390. Funamori, N., Yagi. T., Utsumi, W., Kondo, T., Uchida, T., Funamori, M., 1996. Thermoelastic properties of M g S i Q perovskite determined by in situ X-ray observations up to 30 GPa and 2000 K. J. Geophys. Res. 101 (B4), 8257-8269. Gillet, Ph., Guyot, F., Wang, Y., 1996. Microscopic anharmonicity and equation of state of MgSiO 3 perovskite. Geophys. Res. Lett. 23 (21), 3043-3046. ho, E., Matsui, Y., 1978. Synthesis and crystal-chemical characterization of MgSiO 3 perovskite. Earth Planet. Sci. Lett. 38, 443-450. Jackson, I., Rigden, S., 1996. Analysis of P - V - T data: constraints on the thermoelastic properties of high-pressure minerals. Phys. Earth Planet. Int. 96, 85-112. Jackson, I., Liebermann, R.C., Ringwood, A.E., 1978. The elastic properties of (Mg xF e l - x)O solid solutions. Phys. Chem. Mineral. 3, 11-31. Jamieson, J.C., Fritz, J.N., Manghnani, M.H., 1982. Pressure measurement at high temperature in X-ray diffraction studies: gold as a primary standard. In: Akimoto, S., Manghnani, M.H. (Eds.), High Pressure Research in Geophysics, Reidel, Boston, pp. 27-48. Knittle, E., Jeanloz, R., 1987. Synthesis and equation of state of (Mg, Fe)SiO 3 perovskite to over 100 gigapascals. Science 235, 668-670. Kudoh, Y., Ito, E., Takeda, H., 1987. Effect of pressure on the crystal structure of perovskite-type MgSiO 3. Phys. Chem. Mineral. 14, 350-354. Larson, A.C., Von Dreele, R.B., 1994. GSAS, General Structure

G. Fiquet et al. / Physics of the Earth and Planetary Interiors 105 (1998) 21-31 Analysis System, Los Alamos National Laboratory, LAUR: 86-748. LeBail, A., 1992. Extracting structure factors from powder diffraction data by iterating full pattern profile fitting. In: Prince, E., Taliek, J.K. (Eds.), Accuracy in Powder Diffraction II, Special Publication 846, 213, National Institute of Standards and Technology, Gaithersburg, MD. Liu, L.G., 1975. Post-oxide phases of forsterite and enstatite. Geophys. Res. Lett. 2, 417-419. Liu, LG., 1976. Orthorhombic perovskite phases observed in olivine, pyroxene, and garnet at high pressures and temperatures. Phys. Earth Planet. Inter. 11,289-298. MacFarlane, R.E., Rayne, J.A., Jones, C.K., 1965. Anomalous temperature dependence of shear modulus C44 for platinum. Phys. Lett. 18, 91-92. Mao, H.K., Yagi, T., Bell, P.M., 1977. Mineralogy of the earth's deep mantle. Carnegie Inst. Washington Yearbook 76, 502504. Mao. H.K., Hemley, R.J., Fei, Y., Shu, J.F., Chert, L.C., Jephcoat, A.P., Wu, Y.. 1991. Effect of pressure, temperature, and composition on lattice parameters and density of (Fe, Mg)SiO 3 perovskites to 30 GPa. J. Geophys. Res. 96 (B5), 8069. Martinez, I., Zhang. J.. Reeder, R.J., 1996. In-situ X-ray diffraction at high pressure and high temperature of aragonite and dolomite. Evidence for dolomite breakdown to aragonite and magnesite. Am. Mineral. 81, 611-624. Martinez, 1., Wang, Y., Liebermann, R.C., Guyot, F., 1997. Microstructures and iron partitioning in perovskite-magnesiowiistite assemblages: an analytical transmission electron microscopy study. J. Geophys. Res., in press. Meng, Y., Weidner, D.J., Fei, Y., 1993. Deviatoric stress in a quasi-hydrostatic diamond-anvil cell: effect on the volumebased pressure calibration. Geophys. Res. Lett. 20 (12), 11471150. Morishima, H., Ohtani, E., Kato, T., Shimomura, O., Kikegawa, T., 1994. Thermal expansion of MgSiO 3 perovskite at 20.5 GPa. Geophys. Res. Lett. 21,899-902. Parise, J.B., Wang, Y., Yeganeh-Haeri, A., Cox, D.E., Fei, Y., 1990. Crystal structure and thermal expansion of (Mg, Fe)SiO 3 perovskite. Geophys. Res. Lett. 17 (12), 2089-2092. Richet, P., Mao, H.K., Bell, P.M., 1989. Bulk moduli of magne-

31

siowiistites from static compression measurements. J. Geophys. Res. 94, 3037-3045. Ross, N.L., Hazen, R.M., 1989. High-pressure crystal chemistry of MgSiO 3 perovskite. Phys. Chem. Mineral. 17, 228-237. Saxena, S.K., Zhang, J., 1990. Thermochemical and pressurevolume-temperature systematics of data on solids, example: tungsten and MgO. Phys. Chem. Mineral. 17, 45-51. Shen, G., Lazor, P., 1995. Measurement of melting temperatures of some minerals under lower mantle conditions. J. Geophys. Res. 100 (B9), 17699-17713. Simmons, G., Wang, H.. 1971. Single crystal elastic constants and calculated aggregate properties, M.I.T. Press, Cambridge. Utsumi. W.. Funamori, N., Yagi, T., Ito, E., Kikegawa, T., Shimomura, O., 1995. Thermal expansivity of MgSiO 3 perovskite under high pressures up to 20 GPa. Geophys. Res. Lett. 22 (9), 1005-1008. Wang, Y., Weidner, D.J., Liebermann, R.C., Liu, X., Ko, J., Vaughan, M.T., Zhao, Y., Yeganeh-Haeri, A., Pacalo, R.E., 1991. Phase transition and thermal expansion of MgSiO 3 perovskite. Science 251, 410-413. Wang, Y., Weidner, D.J., Liebermann, R.C., Zhao, Y., 1994. PVT equation of state of (Mg, Fe)SiO 3 perovskite: constraints on composition of the lower mantle. Phys. Earth Planet. Inter. 83, 13-40. Weidner, D.J., Vaughan, M.T., Ko, J., Wang, Y., Liu, X., Yeganeh-Haeri, A., Pacalo, R.E., Zhao, Y., 1992. Characterization of stress, pressure, and temperature in SAM85, a DIA type high pressure apparatus, In: Syono, Y., Manghnani, M.H. (Eds.), High-Pressure Research: Application to Earth and Planetary Sciences. Terra Scientific Publishing, Tokyo/AGU, Washington, DC. Yagi, T.. Funamori, N., 1996. Chemical composition of the lower mantle inferred from the equation of state of MgSiO 3 perovskite. Philos. Trans. R. Soc. Lond., Ser. A 354, 1371-1384. Yagi, T.. Mao, H.K., Bell, P.M., 1982. Hydrostatic compression of perovskite-type MgSiO 3. In: Saxena, S.K. (Ed.), Advances in Physical Chemistry. 2. Springer-Verlag, New York, pp. 317-325. Yeganeh-Haeri, A.. Weidner, D.J., Ito, E., 1989. Elasticity of MgSiO~ in the perovskite structure. Science 243, 787-789.