PHYSICS
OFTHE
EARTH
A~DP
LAN
ETA RY
INTERIORS
_________
ELSEVIER
Physics of the Earth and Planetary Interiors 83 (1994) 13—40
P—V—T equation of state of (Mg,Fe)Si03 perovskite:
constraints on composition of the lower mantle
Yanbin Wang
‘~,
Donald J. Weidner, Robert C. Liebermann, Yusheng Zhao
Centerfor High Pressure Research
and Department of Earth and Space Sciences, State University of New York at Stony Brook,
Stony Brook, NY 11794, USA
(Received 21 September 1993; revision accepted 23 December 1993)
Abstract
Unit-cell volumes (V) of Mg11Fe~SiO3 perovskite (x = 0.0 and 0.1) have been measured along several isobaric
paths up to P = 11 GPa and T= 1300 K using a DIA-type, cubic anvil high-pressure apparatus (SAM-85). With a
combination of X-ray diffraction during heating cycles and Raman spectroscopy on recovered samples, pressure and
temperature conditions were determined under which the P—V—T behavior of the perovskite remains reversible. At
1 bar, perovskites of both compositions begin to transform to amorphous phases at T 400 K, accompanied by an
irreversible cell volume contraction. Electron microprobe and analytical electron microscopy studies revealed that
the iron-rich perovskite decomposed into at least two phases, which were Fe and Si enriched, respectively. At
pressures above 4 GPa, the P—V—T behavior of MgSiO3 perovskite remained reversible up to about 1200 K,
whereas the Mg09Fe015i03 exhibited an irreversible behavior on heating. Such irreversible behavior makes
equation-of-state data on Fe-rich samples dubious. Thermal expansivities (ay) of MgSiO3 perovskite were measured
directly as a function of pressure. Overall, our results indicate a weak pressure dependence in a~,for MgSiO3.
Analyses on the P—V—T data using various thermal equations of state yielded consistent results on1thermoelastic
for MgSiO
properties. The temperature derivative of the bulk modulus, (oK~/~T)~,
is —0.023(±0.011)GPa K
3
perovskite. Using these new results, we examine the constraints imposed by av and (8K/OT)~on the Fe/(Mg + Fe)
and (Mg + Fe)/Si ratios for the lower mantle. For a temperature of 1800 K at the foot of an adiabat (zero depth),
these results indicate an overall iron content of Fe/(Mg + Fe) = 0.12(1) for a lower mantle composed of perovskite
and magnesiowüstite. Although the (Mg + Fe)/Si ratio is very sensitive to the thermoelastic parameters of the
perovskite and it is tentatively constrained between 1.4 and 2.0, these results indicate that it is unlikely for the Jower
mantle to have a perovskite stoichiometry.
1. Introduction
An ~impo1~tantgoal of mineral physics and seismological research is to determine the chemical
composition of the Earth’s lower mantle by comparing the in situ determination of bulk (K) and
shear (i~) moduli, and density (p) with those
predicted from the properties of candidate mineral assemblages. It is generally accepted that
*
Corresponding author.
‘A National Science Foundation Science and Technology
Center.
(Mg,Fe)SiO3 perovskite may be the dominant
phase of the Earth’s lower mantle (Liu, 1975,
1976; Ito and Matsui, 1978; Ito and Yamada,
0031-9201/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved
SSDI 0031-9201(94)02925-2
14
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
1981; Knittle and Jeanloz, 1987; Ito and Takahashi, 1989). Thus, a precise knowledge of the
density and bulk modulus under various pressure
(F) and temperature (T) conditions for the perovskite is crucial in placing mineral physics constraints on composition of the lower mantle.
The dependence of K and p on composition
in the FeO—MgO—Si02 system at mantle conditions is illustrated in Fig. 1. Although the exact
values of K and p are sensitive to the properties
of perovskite and magnesiowüstite, the topology
of the diagram is general (see, e.g. Jackson, 1983;
Stixrude et al., 1992). The lines of constant density represent compositions that yield the same
density. As seen in this figure, density varies
mostly with changing iron content and is relatively insensitive to the silica content. The bulk
modulus, by contrast, is virtually independent of
iron content but is very sensitive to the Si/(Mg +
Fe) ratio. Thus, accurate laboratory determinations of both K and p are needed to place tight
constraints on a model mantle whose properties
are dominated by this composition range.
The reliability of any composition deduced
from comparison with seismic models rests critically on the accuracy of the experimental data.
Bulk modulus and density of perovskite under
deep mantle conditions depend on the ambient
properties, K0 and p~,as well as their pressure
and temperature derivatives. To date, K0, Po’
and their pressure derivatives are reasonably well
known, but measurements of temperature derivatives are still the subject of considerable debate.
Among these temperature derivatives, thermal
expansion [Lit, = —(8 ln p/0T)~] and (BKT/8T)T
(= K~(8ciV/8P)T)are of primary importance, because the former mainly affects the density and
therefore influences the Fe content, whereas the
Si02
En/QA
//
/
/
~
///////
/ / // /
MgO
Const.K
F/
Fig. 1. Portion of the MgO—FeO—Si02 ternary diagram showing the dependence of bulk modulus and density on composition at
lower-mantle conditions. The inset triangular diagram outlines the compositional region of interest which includes the magnesiumrich portion from forsterite (Fo) to enstatite (En). Lines labeled const. p (nearly vertical) illustrate compositions that have the same
density; const. K (horizontal) contours demonstrate compositions which have the same bulk modulus. Parameters used in the
calculation are from Table 7. based on the present study. Density increases with an increase in Fe content and is nearly
independent of the Si content; bulk modulus increases with an increase in the Si content and is independent of the Fe content.
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
latter is responsible for the bulk modulus and
thus constrains the Si content of the lower mantle.
Previous work on the equation of state of
silicate perovskite has been primarily on Febearing specimens (e.g. Knittle et al., 1986; Parise
et al., 1990; Mao et al., 1991). However, the
effects of iron content (x) on the stability of
perovskite are still poorly understood. Recently,
Fei and Wang (1992) observed that the stability
limit of iron in perovskite depends critically on
temperature. At 26 GPa, the critical temperature
for x = 0.1 is about 1873 K, below which magnesiowüstite and stishovite will exsolve, leaving an
iron-depleted perovskite. Thus, all previous attempts to measure the P—V—T properties were
performed outside the perovskite stability field,
so that the samples were likely to undergo irreversible changes in state at high temperature. If
iron diffuses out of perovskite during a heating
experiment, the volume data do not simply reflect
equation-of-state information but are contaminated by changes in chemical state as well.
In this paper, we report new results from a
systematic study on the P—V—T equations of state
of Mg1 _~Fe~SiO3
perovskite with x = 0.0 and 0.1
in a pressure range from 0 to 11 GPa and at
temperatures up to 1300 K. We measure Lit,
along virtually isobaric paths and thus directly
determine the pressure dependence of at,. The
entire dataset is then analyzed using several thermal equations of state, yielding consistent results
with (0KT/8T)p =
0.023(11) GPa K~ for
MgSiO3. This value contrasts sharply with that
for the x = 0.1 perovskite, for which the data are
generally consistent with those of Mao et al.
(1991), with a (8KT/8T)p value a factor of 2—4
more negative than that for MgSiO3. However,
for our iron-enriched samples, distinctive irreversible changes in state were observed to result
from heating. Thus, we do not believe that the
thermal expansion for this sample is reliable
whereas the Mg-rich end-member exhibited no
such change in state. These new data allow us to
examine the high-pressure and high-temperature
behavior of the silicate perovskite and to discuss
several important implications for the lower mantIe.
—
15
2. Experimental techniques
2.1. The specimens
Mg1~Fe~SiO3
perovskite specimens with x =
0.0 and 0.1 were synthesized in a 2000 ton uniaxial split-sphere apparatus (USSA-2000), previously described by Liebermann and Wang (1992).
Polycrystalline specimens, about 1.0 mm in diameter and 1.5 mm in length, were synthesized from
enstatite starting materials with the corresponding iron contents at P = 26 GPa and T = 1873—
2073 K, for run durations of 1—2 h; details of the
synthesis experiments have been described by
Wang et al. (1992). Electron microprobe and analytical electron microscopy analyses indicate that
these perovskite specimens are homogeneous in
composition, and that all of the Fe-enriched specimens have a measured x = 0.10(1). No other
elements are present at the detectability level of
the microprobe. These specimens have been studied by a variety of techniques including X-ray
diffraction (Parise et al., 1990), transmission electron microscopy (TEM) (Wang et al., 1992), Raman scattering (Durben and Wolf, 1992) and IR
spectroscopy (Lu et al., 1993).
2.2. Monochromatic X-ray experiments at 1 bar
The 1 bar V—T measurements were carried
out at the X7A beamline of the Brookhaven
National Synchrotron Light Source (NSLS) using
monochromatic X-rays at a wavelength of approximätely 0.7 A with a water-cooled channel-cut
Si(111) monochromator and a position-sensitive
detector (PSD). The intrinsic spatial resolution of
the PSD is about 30 ~m. With the current setup,
the diffraction peaks have full-width-at-half-maximum about 0.025—0.035° over the 26 interval
from 10°to 60°.Details of the experimental techniques have discussed by Cox et al. (1988) and
Zhao et al. (1993).
To avoid amorphization induced by grinding,
perovskite specimens were crushed into chunks
with linear dimensions of less than 300 i~mand
packed into a quartz capillary of 0.7 mm diameter. MgO powder was used as an internal standard. The capillary was mounted in a furnace
16
Y Wang et aL /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
consisting of a wire-wound BN tube of 1.25 in
(31.75 mm) diameter and an outer water-cooled
aluminum tube. Temperature was controlled by
an Eurotherm controller and measured by two
chromel—alumel thermocouples mounted just
above and below the sample. Temperature readings were generally stable within 1 K. During
data collection, the capillary was rocked by 10°at
a constant rate of 1°s_i, to eliminate any preferred orientation in the polycrystalline chunks.
Diffraction spectra were collected between 10°
and 60°in 20 for temperatures below 400 K, with
a step interval of 2°and a rate of 2°mm_i. At
higher temperatures, because of degradation of
the crystals, a much smaller range of 20, 15—25°,
was used to obtain diffraction patterns before
LAMBDA 0.7001
A,
L—S CYCLE
I
completely losing the signal. Because of the short
wavelength used, this smaller 20 interval covers
15 perovskite peaks, sufficient to determine the
unit-cell parameters.
Rietveld full-pattern refinements (Rietveld,
1969) were carried out to obtain the cell parameters at each temperature, using the programs of
the Generalized Structure Analysis System
(GSAS) of Larson and Von Dreele (1988). Both
perovskite and MgO were refined simultaneously.
The MgO data were then used to cross-check the
temperature measurements based on the measurements on MgO by Suzuki (1975). In general,
the inferred temperatures from the MgO lattice
parameters agree with the thermocouple measurement in 10 K. All of the perovskite unit-cell
249
OBSD. AND DIFF. PROFILES
I
I
+
-
0
+
0
+
N
I
I
I
1.0
2—THETA,
I
I I
III
I
2.0
DEC
Fig. 2. Examples ofX-ray diffraction spectra for MgSiO
I I
Ii
II
11111 I ~I
I III
III
II
11111 I
II
I 111111 I
liii!
IIfl
II
3.0
4.0
X1OE
1
3 perovskite obtained in this study. (A) A spectrum obtained at 400 K and 1
bar with monochromatic X-rays. Crosses represent observed data and continuous line is the fit using Rietveld full pattern
refinement technique. The difference between the observations and the fit is shown below the spectrum. Upper ticks below the
spectrum are peak positions of MgO, and lower ticks are those of perovskite. (B) A portion of a pattern obtained at 8.6 GPa and
1073 K using energy-dispersive technique with SAM-85. (Note that splitting of the triplet 020/112/200 is well resolved.) Peaks
used in unit-cell refinement are labeled; other peaks are either multiples that cannot be used in the refinement or are from parts in
the assembly.
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
parameters were refined with fixed atomic positions determined by Horiuchi et al. (1987) for
MgSiO3 and Parise et al. (1990) for Mg09
Fe
0 1SiO3.
Fig. 2A is a portion of the spectrum obtained
at
373 K, anpatterns
example of
of the
high-temperature
diffraction
MgSiO
Diffraction data are represented 3by perovskite.
the crosses
and refinement by the continuous line (for both
perovskite and MgO). The difference between
observations and the fit is shown below the pattern. The refinement could be further improved
by varying the atomic positions, but the cell parameters would not change.
17
2.3. High-pressure measurements
The second-stage anvils were composed of either
tungsten carbide or sintered diamond, with 6 x 6
2 square truncations, depending on
or 4 X 4 mm
the pressure range. The cubic pressure medium
was amorphous boron mixed with 20 wt % epoxy,2
with an edge length of 8 mm for the 6 x 6 mm2
anvils
6 mm for the
4 x 4 were
mm
anvils (8/6
(6/4 system)
system).andPyrophyllite
gaskets
used to provide lateral support for the anvils.
Fig. 3 illustrates the cell assembly for the 6/4
system. Well-sintered, polycrystalline perovskite
specimens were cut into disks of about 0.3—0.4
mm thickness and 1 mm in diameter and were
embedded in a NaC1—BN powder mixture which
provided a quasi-hydrostatic sample environment
at high temperatures. The equation of state of
NaCl was used to determine the cell pressure at
various temperatures (Decker, 1971). Graphite or
amorphous carbon was used as heating element.
A d.c. power supply provided a constant power
High-pressure P—V—T experiments were carned out with a DIA-type, cubic anvil apparatus
(SAM-85), described by Weidner et al. (1992).
-J
-
7
-
J
-~
•
300
~-
U
460
(I
~
~i U
620
Fig. 2 (continued).
780
940
1100
18
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
input so that temperatures were stable within 5 K
up to about 1400 K. Temperatures were measured by W095Re005—W074Re026 thermocouples.
bar perovskite and NaCI data collected in the
press, also provided a direct calibration between
Energy-dispersive X-ray diffraction data were
collected at a fixed scattering angle of about 7.5°
at the superconducting wiggler beamline (X17B1)
at NSLS. The X-ray beam was highly collimated,
typically 100 1LLm in the vertical dimension and
200 ~tm in the horizontal. In each run at a fixed
ram load, perovskite spectra were collected at the
same position in the sample at various temperatures, in an energy range up to 100 keV, with a
collection time of 300 s. Estimated temperature
variation in the diffracting volume is less than S
K.
The multichannel analyzer used in data collection was frequently calibrated with the character57Co,
129
istic
energies
of radioactive
standards
I, decay
and i09
Cd. Before
and after
each run, a
mixture of Si, Al
203, and MgO was placed in the
diffraction volume and the positions of the
diffraction peaks were used to calibrate the 20
angle. This standard mixture, together with the 1
the channel numbers and d-spacings. Generally,
standard errors for the calibrations were in the
range of 0.0005—0.0008 A in a single run. Fig.
2(B) is an example of the energy-dispersive spectra of perovskite obtained under high pressure
and temperature. The triplet (020, 112, and 200)
is well resolved; thus the experimental technique
provides sufficient resolution to determine the
unit-cell parameters of the orthorhombic perovskite. However, it is not sufficient to use only
the triplet to obtain cell parameters because of
poor statistics. In our unit-cell parameter determinations, about 15—25 diffraction lines are used,
which are subsets of the following: 111, 020, 112,
200, 220,
120, 023,
210, 221,
121, 130,
103, 222,
211, 022,
113, 204,
122,
004,
131, 202,
132, 024,
312, 133, 040, 224, and 400. An example of such
refinements is given in Table 1.
Six successful experiments were carried out at
pressures between 4 and 11 GPa. Table 2 summarizes the experimental conditions. Also listed in
zirconia end tugs
pyrophyllite
N~ 111111 r~I —
stainless steeltubing ~
4 ~UIhIIII
thermocouple
leads
-~-~
~
alumina /
TO tubing
F I ~ °~luminasleeve
IIIIUilI~I~-~~\\
\\
\
ppllP”’~
/
N
boron
samplenitride
chamber
sample
carbon heater
Pt heater lead Mo current disk
Fig. 3. Cell assembly for the 6/4 system with sintered diamond anvils for SAM-85. The electrical leads are Pt wires whose
cross-section area was chosen to minimize heat loss related to thermal conduction. This configuration minimizes temperature
gradient in the sample. A mixture of NaCI and BN is used to surround the specimen. Pressures are measured using NaCI
immediately next to the sample.
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
Table 1
A representative refinement of cell parameters of MgSiO
3
perovskite (8.60 GPa, 1073 K)
h k1
dObS
dca1
dObS
1 11
0 20
11 2
20 0
20 2
11 3
122
21 2
004
220
023
221
130
2 22
1 3 1
3 12
040
224
40 0
3.0520
2.4539
2.4209
2.3769
1.9555
1.8999
1.8404
1.8167
1.7181
1.7081
1.6736
1.6581
1.5464
1.5302
1.5083
1.3816
1.2264
1.2111
1.1887
3.0580
2.4531
2.4218
2.3782
1.9553
1.9020
1.8407
1.8164
1.7175
1.7075
1.6739
1.6571
1.5465
1.5290
1.5088
1.3813
1.2265
1.2109
1.1891
0.0020
—0.0003
—0.0004
—0.0005
+ 0.0001
—0.0011
—0.0002
0.0002
+ 0.0003
+ 0.0006
—0.0002
+ 0.0006
—0.0001
+ 0.0008
0.0003
+ 0.0004
—0.0001
+0.0002
—0.0003
a = 4.7564(11)
A,
b
4.9061(11) A, c
=
=
/°~cai
—1
6.8700(24)
Table 2 is Run 1 reported by Wang et al. (1991).
About 150 points were obtained in the P, T
space; run-to-run reproducibility of the perovskite unit cell volume is generally about ±0.15
A~ (about ±0.1%).
3. Results
3.1. Thermodynamic validity of the data on
(Mg,Fe)Si03 perovskite
As all of the measurements were taken outside
the stability field of these perovskite-structured
materials, we examine the reversibility of the
P—V—T behavior with a combination of X-ray
diffraction for temperature cycles and Raman
A;
v
=
160.31(6) A~.
spectroscopy on recovered samples, to verify that
our measurements are thermodynamically valid
and therefore can be used to predict the behavior
under lower-mantle conditions of pressure and
temperature. At 1 bar, unit-cell volume increases
Table 2
A summary of experiments for Mg1~Fe~SiO3perovskite
P (GPa)
19
Run no.
x
T range (K)
Comments
1a
0.0
7.1— 7.4
300—1200
A discontinuity observed near
630 K; sample amorphized at 1273 K
and then recrystallized to
enstatite
3A b
3B b
0.0
0.0
6.5— 7.4
4.0— 4.7
306— 880
300—1076
Reversed by heating and cooling
same sample as in 3A; heating only;
recovered sample examined by
Raman; reversible
5A b
SB b
0.0
0.0
8.5— 9.4
7.7— 8.5
625—1074
307—1373
Heating; same sample as in 5B
reversed by cooling and heating
to 1074 K; heated to 1373 K where
sample transformed to enstatite
8
0.0
10.6—10.9
675—1373
Heating only; transformed to
enstatite at 1373 K
6
0.1
9.1— 9.8
621—1273
Heating only; transformed to
enstatite at 1273 K
7
0.1
8.2— 9.3
305— 869
Reversed by heating and cooling;
recovered sample shows enstatite in
Raman
a Results reported earlier (Wang et al., 1991).
b For these runs, several heating cycles were carried out on two different pressure ranges denoted by A and B.
20
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
almost linearly with temperature from 300 to 400
K for MgSiO3 (and to 430 K for Mg0 9Fe0 1SiO3),
quenched from temperatures higher than 400 K
(Fig. 5(A)), similar to the observations reported
by Durben and Wolf (1992), who showed that the
direction of the peak shift is consistent with decrease in the unit-cell volume. Associated with
the residual shifts is a broad Raman band appearing near 650 cm’ wavenumber, characteristic of
tetrahedrally coordinated silicate glass (Durben
and Wolf, 1992).
The Mg09Fe01SiO3 sample recovered from
433 K shows a 0.26% irreversible volume decrease at 300 K (Fig. 4(B)), about 4 times greater
above which temperature irreversible V—T behavior is observed for both compositions (Figs. 4(A)
and (B)). Associated with this irreversibility is a
significant decrease in diffraction intensity (by
about one order of magnitude).
For MgSiO3, when the temperature was decreased to 300 K, the unit-cell volume exhibited a
0.06% decrease compared with that of the virgin
sample. Raman spectroscopy reveals an irreversible shift in Raman peaks for samples
I
I
I
I
I
A
1.002•
~—.
•
a
a
1.0000.998
0.996
.
-
I
I
I
I
B
1.002
•
•
C
•
a
N.
1
1.000
-I
0.998
Ii
I
I
I
0.996
I
100
I
I
200
300
Temperature,
I
I
400
500
K
Fig. 4. Unit-cell volume of perovskite as function of temperature at 1 bar normalized to the volume at 300 K. (A) MgSiO3. Solid
symbols represent data in the reversible temperature range: circles, data from this study, triangles, from Ross and Hazen (1989).
Open symbols show irreversible data on subsequent heating cycles in our study. The estimated 381 K data point of Ross and Hazen
(1989) is represented by the open triangle. (B) Mg09Fe01SiO3. Again, solid symbols show data in the reversible range: circles, from
this study; squares, from Parise et al. (1990). Open circles show irreversible data obtained at higher temperatures or in subsequent
heating cycle.
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
than that for MgSiO3. The remaining crystals
exhibited a larger thermal expansion as they were
heated again, with diffraction intensities continuing to decrease. Similar to the pure Mg samples,
residual shifts in the Raman peaks are observed
on the recovered samples (Fig. 5(B)).
A
I
I
21
Microprobe analyses on the Fe-bearing perovskite quenched from 600 K show a significant
heterogeneity in composition. Fig. 6(A) is a
back-scattered electron image of the sample in
which both Si- and Fe-enriched areas are seen by
the brighter appearance. These areas are gener-
MgSiO3 I perovskite
78K
‘(~1
before thermal
~
cycling
200
300
I
I
400
500
600
700
Raman shift (cm-’)
—
1~
(Mg,Fe)Si03 Perovskite, 300 K
200
300
400
Rarnan
500
Shift (cm-l)
600
700
Fig. 5. Raman spectra of perovskite after heating cycles at 1 bar. (A) MgSiO3 perovskite before (bottom) and after heating to 573 K
(top). An irreversible shift in the Raman peaks is observed. (B) Mg0 9Fe0 1SiO3 perovskite before (bottom) and after heating to 573
K (top). Similar irreversible shifts can be seen. Asterisks indicate Ar~plasma lines.
22
1 • I I cuzg It (11. Pltv~is
(If lift’
Lci,ih 1111(1 Planetary Intcrjors ~.? I I994) 13- .J()
all~’very small in size (less than 1 hum). ~vhich
makes precise delcrniination of their con1po~ilion
difficult. Much snialler regions with such compositioflS are observed on the TEM scaIe~severd
analyses indicate small regions of (Mg.Fe)() arid
Si(), (Fig. 6(B)).
For the high-pressure data. as pressure variaLions arc generally sniall and rather reproducible
~‘tit1•i
tcnipcrature after non-hydrostatic stress has
been relaxed. ~ compare the observed unit-cell
volumes on 1X)tll cooling and reheating cycles. We
also examine the room—temperature ~olume un—
der pressure after quenching and compare the
After cycles to temperatures as high a~1270 K.
~ find that the cell ~olumes for both pews ~kites
at rooni temperature and under pressure arc
reproducible within our experimental error (about
I). I A).
The re~’ersihiIityof MgSiO, is indcpendeiitlv
confirmed h\ Ranian spectroscopy on specimens
recovered from the high-pressure measurements.
Crystals that have been treated at 7.2 GPa up to
$73 K and then at 4 GPa LI~tO 1073 K give a
Ranian spectrum identical to that of the virgin
specimens indicating that partial vitrification has
not occurrcd ( I ig. 7(A)). For Mg11 11Fe111Si()~.
nieasurement with the room-temperature cquation of slatc of pcrovskite (e.g. Mao et al.. ~99 1 ).
howe~cr.a specimen recovered from ~).SGPa and
873 K exhibits an additional Raman peak charac-
..
(A)
I ig.
(i. Eleciron nhicrogrdph~ol i’slg,
Fe11 15iO~ peros~kiIcafter cscled to bOO K at I bar. (A) Back-~.c~
tiered electron image
SI1()~%jOg ~..trong (.ontrust as ti resuil ol phase separation. The hrightcr spOt’. arc either more Fe or Si cunched than the matri\.
~vliose collipoSition renlains the saine as ~s1g1~Fe11SiO.. IloriLonlul scale. 13(1 pm. (B) Iranslllcsion dcctron microgr,iph sho~sing
~iiiialldIc ~, of Fc— 10(1 ‘,i—eiiriched plIases in the giass matrix. I Lorizontai sc,iie. 3 ~zrn.
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
teristic of the low-pressure phase enstatite (Fig.
7(B)). Thus, although our measurements are carned out at P, T conditions outside the stability
field of MgSiO3 perovskite, data obtained within
the metastable P, T range are thermodynamically
valid. As Mg09Fe01SiO3 exhibits irreversible behavior on temperature cycling, we conclude that
the equation-of-state information cannot be derived from these data. This is discussed further in
a later section.
3.2. P—V—T equations of state
Thermal expansion at constant pressures
Data at 1 bar. Rietveld refinement results for
both MgSiO
3 and Mg0 9Fe0 1SiO3 perovskite are
given in Table 3, in the temperature range where
the samples behaved reversibly. Our data are
combined with low-temperature measurements of
23
Ross and Hazen (1989) for MgSiO3 and with
those of Parise et al. (1990) for Mg0 9Fe0 1SiO3,
respectively, in Figs. 4(A) and 4(B). Because of
zero-point errors, the unit-cell volumes are normalized with respect to the 300 K volume in each
study, and both data sets are fitted by the Suzuki
formalism (Suzuki, 1975), and also by the following empirical expression:
2
(1)
at,= (8 ln V/8T)~=a +bT—cT
where T is in Kelvin and a, b, and c (greater
than zero) are constants.
There are several parameters in the Suzukitype fit (Suzuki, 1975; Hill and Jackson, 1989),
including Debye temperature (SD), the Grüneisen parameter (y), isothermal bulk modulus (K0)
and its pressure derivative (Ks), and the unit-cell
volume at a reference temperature, which is taken
to be 300 K. Previous studies have determined
(B)
Fig. t~(continued).
24
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
K0 = 261 GPa (Yeganeh-Haeri, 1993), ®D = 1030
K (Akaogi and Ito, 1993), and K~= 4 (Mao et al.,
1991). Using these parameters we obtained
av(300 K) = 1.7 x iO~ K’ for the Mg-rich
MgSiO3 perovskite
(A)
200
end-member and 1.6 X iO~ K~ for the Fe-rich
sample. The fit for Mg09Fe01SiO3 is also shown
in Figs. 8(A) and 8(B) (curve A).
Analyses using Eq. (1) indicate that for both
300
400
500
600
700
Raman shift (cm-’)
(B)
(Mg09’ Fe0~1)Si03 perovskite
1111
~IiI
200
300
400
500
1)
600
700
Raritan shift
(cnr
Fig. 7. Raman spectra of perovskite recovered from high-pressure,
high-temperature
runs. (A) MgSiO
3 perovskite before (bottom),
after (top) Runs 3A and 3B, and after another run to 5.2 GPa and about 900 K (middle). No irreversible changes can be seen. (B)
Mg09Fe015i03 perovskite before (bottom) and after (top) Run 7. (Note additional peak near 340 cm~ wavenumber, characteristic of the lower-pressure phase enstatite.)
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
compositions the constant c is of the order of
0.01 or less and contributes insignificantly to volumetric thermal expansion at temperatures above
100 K. This is mostly due to the incorporation of
the lower-temperature data of Ross and Hazen
(1989) and Parise et al. (1990): Eq. (1) must
converge at very low temperatures. Also, for
MgSiO
3, only the constant a can be reliably
obtained because the Ross and Hazen (1989)
data show a faster decrease in volume below 160
K, a behavior not expected as temperature approaches 0 K. A linear
a mean
thermal
5 fit
K_igives
between
77 and
400
expansion
of 1.6 x i0
K.
For Mg
09Fe01SiO3, Eq. (1) yields a =
0.970(±0.255)x i0~ and b300
= 1.734(±0.911)
x
K) = 1.5 x i0~
108, This
withfitcis= shown
0; thusin Fig.
av( 8 as curve B.
K
The mean a.,,. for MgSiO
3 perovskite between
77 and 400 K, 1.6 x i0~ K’, is in agreement
with the measurement of Ross and Hazen (1989)
between 77 and 298 K (1.5 x i0~ K~based on
a linear fit). These workers also measured the
volume of MgSiO, perovskite at 381 K. However,
at 381 K the single crystal became twinned (or
partially vitrified) so that only two peaks (220 and
004) were observed. The unit-cell volume at this
temperature was estimated based on the behavior
of the 220/004 doublet at 298 K under several
assumptions. From a two-point average, Ross and
Hazen (1989) 1obtained
thermal
of
betweena 298
and expansion
381 K. This
2.2
x
iO~
K
value, however, is not robust because of the inclusion of the point where the sample was behaving
irreversibly. As can be seen in Fig. 4(A), this
estimated volume (open triangle) is significantly
greater than all other measurements at similar
~.
temperatures.
As the T—V behavior of the two compositions
is very similar, we therefore combine all of the
data within the reversible temperature range and
fit the data with (1). We thus obtain a = 1.09(22)
x i0~, b = 1.90(81) x 10—8, and c = 1.44(58)><
10-2 for the temperature range up to 430 K. This
curve is not shown in Fig. 8; it lies between curves
A and B, and the resultant av(lbar, 300 K) =
a1Al, 300) is about 1.64 x i0~ K~.
Mao et al. (1991) analyzed the data of Knittle
et al. (1986) using Eq. (1) and obtained a = 3.01
25
X iO~, b = 1.500 x 10_8, and c = 1.139. This is
represented by curve C in Figs. 8(A) and 8(B).
They also obtained, from a least-squares fit of
their P—V—T data, a similar result for av(1, T),
with a = 2.87 X iO~, b = 2.505 x 108, and c =
1.276. This is shown as curve D in Figs. 8(A) and
8(B). Both fits are under the constraint of a~(3O0
K) = 2.2 X iO~K~from Ross and Hazen (1989)
and, clearly, systematically overestimate volume
of perovskite at temperatures above 300 K (IFig.
8(A)).
Fig. at
8(B)
illustrates
the temperature
dependence
1 bar
of thermal
expansion for
the
various models. Our fits A and B are in excellent
agreement
withonthephase
model equilibrium
analysis of Navrotsky
(1989), based
data and
Kieffer’s vibrational models (solid symbols). Our
least-squares fit to all of the P—V—T data on
MgSiO, yields a 1 bar thermal expansion shown
as curve E (see next section), which also agrees
extremely well with that of Navrotsky. Curves C
and D, on the other hand, do not fit experimental
data between 350 and 700 K (Fig. 8(A)), and give
too large a temperature dependence. A similar fit
to the data of Mao et al. (1991) by Stixrude et al.
(1992) falls between curves C and E and predicts
an even greater temperature dependence above
1000 K, a behavior not expected for most of the
materials.
Weare
demonstrate
here upthat
data
reversible only
to the
430 1K.bar
Allvolume
of the
data above 430 K are highly questionable and,
therefore, any extrapolation based on the highertemperature data cannot be regarded as reliable.
Knittle et a!. (1986) carried out thermal expansion measurements on a Mg
088Fe012SiO3 perovskite sample up to 840 K at 1 bar. However, the
cited uncertainties in their measurements are
about 0.3%, which is about the size of the irreversible volume change we have observed in our
sample (0.26%). Hill and Jackson (1989) care:fully
analyzed the Knittle et al. data using the Suzuki
formalism and found that the data above 600 K
could not be fitted with the same set of parameters as those below 600 K. Thus, it is highly
questionable whether the high-temperature behavior is reversible in the data of Knittle et al.
(1986).
26
Y Wang et at. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
Table 3
Reversible unit-cell parameters of (Mg,Fe)Si0
3 perovskite under various P, T conditions
b(A)
c(A)
V(A~)
Angle-dispersive data on MgSiO3 perovskite
295
4.77650(9)
337
4.77758(9)
i0~
356
4.77802(11)
iO~
379
4.77888(11)
397
4.77976(27)
404
4.77992(26)
4.92699(10)
4.92827(10)
4.92906(12)
4.92938(11)
4.92964(28)
4.92996(27)
6.89563(12)
6.89784(12)
6.89884(14)
6.89949(14)
6.90015(27)
6.90052(27)
162.280(4)
162.411(4)
162.476(5)
162.531(4)
162.585(10)
162.610(9)
Angle-dispersive data on Mg09Fe01SiO, perovskite
300
4.7896(2)
335
4.7910(3)
371
4.7924(3)
i0~
405
4.7940(4)
435
4.7947(5)
4.9315(3)
4.9323(4)
4.9329(4)
4.9334(5)
4.9341(6)
6.9054(3)
6.9072(3)
6.9085(3)
6.9096(4)
6.9106(5)
163.10(1)
163.22(1)
163.32(1)
163.42(1)
163.49(2)
Energy-dispersive data on MgSiO3 perovskite
Run 3A
295
4.7724(19)
7.06(2)
623
4.7395(23)
7.07(3)
647
4.7395(25)
7.08(3)
674
4.7410(24)
7.17(3)
729
4.7418(26)
7.25(3)
778
4.7447(27)
7.36(3)
829
4.7447(26)
7.44(5)
880
4.7456(26)
7.24(3)
751
4.7424(26)
7.06(3)
635
4.7396(26)
6.98(3)
580
4.7391(26)
6.87(3)
497
4.7372(25)
6.69(3)
396
4.7373(26)
6.53(3)
306
4.7349(26)
4.9244(23)
4.8921(25)
4.8929(25)
4.8947(26)
4.8964(27)
4.8975(27)
4.8989(26)
4.9004(27)
4.8971(26)
4.8944(26)
4.8934(26)
4.8913(26)
4.8899(26)
4.8882(26)
6.9027(60)
6.8516(64)
6.8548(57)
6.8526(66)
6.8597(60)
6.8634(61)
6.8640(60)
6.8632(60)
6.8578(60)
6.8548(59)
6.8525(59)
6.8509(58)
6.8463(59)
6.8438(59)
162.22(13)
158.86(15)
158.96(14)
159.02(15)
159.26(15)
159.48(15)
159.54(15)
159.61(15)
159.26(14)
159.02(14)
158.91(14)
158.7404)
158.59(14)
158.40(14)
Run 3B
3.95(3)
4.02(4)
4.05(4)
4.11(3)
4.18(3)
4.25(2)
4.33(2)
4.39(2)
4.53(2)
4.68(2)
4.74(2)
P(GPa)
T(K)
a(A)
300
323
374
428
483
537
594
648
774
898
1076
4.7502(23)
4.7499(26)
4.7512(21)
4.7531(21)
4.7565(21)
4.7569(22)
4.7590(22)
4.7601(23)
4.7617(25)
4.7667(26)
4.7712(29)
4.9035(23)
4.9058(26)
4.9054(25)
4.9038(31)
4.9047(21)
4.9073(22)
4.9074(23)
4.9114(23)
4.9147(25)
4.9165(26)
4.9200(29)
6.8597(23)
6.8588(59)
6.8606(56)
6.8624(51)
6.8624(47)
6.8643(49)
6.8682(51)
6.8683(53)
6.8727(56)
6.8774(59)
6.8855(66)
159.78(12)
159.82(14)
159.89(14)
159.95(12)
160.09(11)
160.24(12)
160.40(12)
160.5703)
160.8404)
161.17(14)
161.63(16)
301
625
649
673
699
723
749
774
799
872
973
1074
4.7749(8)
4.7325(12)
4.7339(15)
4.7342(15)
4.7362(15)
4.7385(14)
4.7399(14)
4.740704)
4.741706)
4.746105)
4.7521(15)
4.756306)
4.9283(8)
4.888703)
4.8897(14)
4.8904(15)
4.8907(14)
4.8924(13)
4.894003)
4.894603)
4.8952(15)
4.8977(15)
4.903104)
4.9066(15)
6.9018(19)
6.8289(34)
6.8301(37)
6.8336(39)
6.8341(38)
6.8365(35)
6.8390(35)
6.8408(35)
6.8427(40)
6.846708)
6.8540(37)
6.8614(40)
162.42(5)
157.99(8)
158.10(8)
158.21(9)
158.30(9)
158.49(8)
158.64(8)
158.73(8)
158.83(9)
159.15(9)
159.70(8)
160.13(9)
Run 5A
io~
9.43(3)
9.37(3)
9.31(3)
9.29(3)
9.28(3)
9.26(4)
9.24(6)
9.14(7)
8.85(8)
8.77(7)
8.6000)
Y Wang et at. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
27
Table 3 (continued)
P(GPa)
T(K)
a(A)
b(A)
c(A)
V(A~)
Run 5B
8.51(7)
8.20(11)
8.20(11)
8.10(11)
8.09(11)
8.0701)
8.03(11)
7.98(10)
7.9500)
7.9100)
7.8700)
7.8300)
7.7600)
7.71(10)
7.6400)
7.7900)
7.97(10)
8.0700)
8.1700)
8.24(8)
8.31(8)
8.42(8)
8.53(8)
8.6000)
8.60(10)
7.60(20)
823
723
723
673
647
623
597
573
548
523
497
473
422
373
307
373
474
523
573
625
675
723
825
923
1073
1276
4.7462(11)
4.7442(11)
4.743802)
4.743102)
4.7400(12)
4.740403)
4.7388(12)
4.738402)
4.737302)
4.736503)
4.735502)
4.735602)
4.733603)
4.732400)
4.729400)
4.731301)
4.7344(10)
4.735902)
4.738102)
4.738102)
4.740102)
4.742600)
4.745601)
4.749602)
4.756401)
4.7666(21)
4.899801)
4.8970(11)
4.897702)
4.896001)
4.8958(11)
4.895303)
4.8955(12)
4.894102)
4.894002)
4.893802)
4.892701)
4.893002)
4.8900(17)
4.8886(13)
4.887002)
4.889400)
4.8911(9)
4.891302)
4.8920(9)
4.8940(12)
4.895902)
4.896800)
4.899801)
4.900802)
4.906101)
4.9180(21)
6.853801)
6.847301)
6.849003)
6.8470(32)
6.8468(32)
6.8456(35)
6.8444(34)
6.8431(34)
6.8408(34)
6.8399(34)
6.840102)
6.8378(33)
6.8377(38)
6.8346(27)
6.8327(27)
6.8325(29)
6.8378(26)
6.8429(26)
6.843800)
6.8480(26)
6.8500(26)
6.8495(22)
6.8567(23)
6.8608(26)
6.8700(24)
6.8895(58)
159.39(7)
159.08(7)
159.13(7)
159.01(7)
158.89(7)
158.86(8)
158.78(7)
158.69(7)
158.60(7)
158.54(7)
158.48(7)
158.44(7)
158.28(8)
158.12(6)
157.92(6)
158.06(6)
158.34(6)
158.51(6)
158.63(5)
158.79(6)
158.97(6)
159.07(5)
159.43(6)
159.70(6)
160.31(6)
161.5003)
298
677
727
778
829
876
879
929
983
1024
4.7778(34)
4.7262(14)
4.7301(22)
4.7313(17)
4.7342(14)
4.7365(17)
4.735406)
4.7371(21)
4.7374(24)
4.7409(17)
4.9253(31)
4.881106)
4.8775(15)
4.8814(11)
4.8819(15)
4.8835(12)
4.885603)
4.8844(16)
4.8859(21)
4.8915(11)
6.8975(59)
6.8113(47)
6.8172(45)
6.8157(29)
6.8153(35)
6.8163(30)
6.8190(33)
6.8226(43)
6.8162(46)
6.8209(36)
162.3106)
157.1300)
157.28(9)
157.41(6)
157.51(8)
157.66(6)
157.76(7)
157.86(9)
157.77(10)
158.18(7)
Run 8
10.61(9)
10.59(8)
10.58(9)
10.58(8)
10.84(8)
10.84(8)
10.84(5)
10.88(6)
10.68(10)
Data at high pressures. Raw unit-cell volume data
for MgSiO, perovskite are listed in Table 3.
These data are also presented in Fig. 11, in the
form of [V(P, T) V(P, 300)]/V(P, 300), where
V(P, 300) is from a third-order Birch—Murnaghan
equation of state (Mao et al., 1991). During an
increasing temperature path at a constant ram
load, the sample pressure varied by a fraction of
1 GPa (Table 3). Pressure corrections were therefore applied to obtain av at constant mean pressures. The magnitude of the corrections is gener—
ally within the size of the error bar in volume
determination.
Fig. 9 shows the unit-cell volume of MgSiO,
perovskite after pressure correction for mean
pressures from 4.35 to 10.73 GPa. Previously, we
reported a volume discontinuity in MgSiO, perovskite at 625 K for data at P = 7.2 GPa and
interpreted it as a phase transition (Run 1 in
Table 1; see Wang et al., 1991). In subsequent
runs, a change in slope is also observed at similar
temperatures, but the magnitude of the disconti-
28
Y Wang eta!. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
D
I
1.020
I
I
I
I
I
I
I
-
1.015-
~
1.010-
..
p
~
I
,‘
-
A
-
..,....
-
/
1.005
I
-
.---~~
-
00
1.000-0
0
•.
0
ioo
o
8
-
I
I
I
I
I
I
I
I
200
300
400
500
600
700
800
900
I
I
400
600
I
800
I
I
I
I
I
1000
1200
1400
1600
1800
1000
2000
Temperature, K
Fig. 8. Thermal expansion of (Mg,Fe)Si0
3 perovskite at 1 bar. (A) A compilation of the existing data for Fe-rich perovskite at 1 bar.
Large solid symbols are data in the reversible temperature range: circles, from this study; squares, from Parise et al. (1990). Open
circles show data on cooling and second heating cycle (this study). Small solid circles with large error bars show data from Knittle et
al. (1986); the errors cited by these workers are about the same size of the irreversible volume decrease measured in the present
study. Curve A: Suzuki fit; curve B: Eq. (1) for the (Mg,Fe)Si03 perovskite data in the reversible temperature range (e.g.
represented by the large solid symbols). Curve C is Mao et al. (1991) fit to Knittle et al. (1986) data at 1 bar (a = 3.01 x i0~,
b = 1.500 x 108, and c = 1.139). Curve D is by using Eq. (1) with a = 2.87 X iO~, b = 2.505 X io~, and c = 1.276 from the
least-squares 1,
fit to
andtheir
missP—V—T
the datadata
above
(Mao
350 et
K.al.,
Curve
1991).
E isBoth
the resultant
fits C and1 bar
D were
a~(1,T)
obtained
from under
least-squares
the constraint
fit to theofwhole
av(1,data
300 set
K)
2.2>< 1iO~
from
bar K
to 11 GPa and from 300 to 1300 K. (B) A comparison of the 1 bar thermal expansion from various fits. Curves shown in
(A) are labeled correspondingly. Solid symbols represent calculations of Navrotsky (1989) based on phase equilibrium and
vibrational data.
Y Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
nuity is not reproducible. As 625 K is close to the
temperature where non-hydrostatic stress in the
NaCl pressure markers becomes vanishingly small
as indicated by analyses using NaCl (Weidner et
al., 1992), we now believe that the apparent discontinuity is more likely to have been caused by
relaxation of non-hydrostatic stress. Therefore,
we have discarded all of the data below 620 K
obtained during the first heating cycle. In Figs. 9
162
161
160
159
___________________________________
I
-~
I
I
I
161
160
I
~
159
158
I
I
I
I
I
161
160
159
158
161
_______________________________________
160
•
8.93;~
~
159
and 11, the data below 620 K are those obtained
on cooling or second heating cycles after the
deviatoric stress has been relaxed. A total of 81
data points was used in thermal expansivity measurements for MgSiO,.
Similar to the analysis on the 1 bar data, we fit
each data set by two schemes: (a) Eq. (1) (solid
lines), and (b) a Suzuki-fit extended to high pressures with an assumed Debye temperature of
1030 K (dashed lines). The last term in Eq. (1) is
found again to be unnecessary because uncertainties in the parameter c are larger than the absolute value. Within the temperature range of each
data set, the two fits give virtually identical average thermal expansion. The Suzuki fits give
GrUneisen parameters ranging from 1.17 to 1.49,
with an average about 1.3(2) over the pressure
range (Table 4).
Thermal expansivities of MgSiO, perovskite at
800 K are plotted as a function of pressure in Fig.
10, where the overall errors are estimated to be
0.2 X iO~ K’ (for discussion of error analysis,
see Section 4.1). Because the 1 bar data correspond to a much lower temperature, they cannot
be compared directly with the high-pressure data.
We therefore extrapolate the 1 bar data to 800 K
(the solid square), based on the Suzuki fit. A
slight decrease in av is observed as pressure
increases, with the average a~being 2.1(2) x i0~
K—1 over the entire pressure range. A linear least
squares fit of the data gives a 8a~/0P of
—0.033(11) x i0~ GPa~ K~,corresponding to
a (8KT/8T)p = 0.022 GPa/K
For the data
reported previously (Wang et al., 1991), we applied a similar pressure correction (magnitude
about 0.2 GPa) and obtained a slightly higher av
of 1.7(2) x i0~ K’ between 630 and 1200 K
(open circle). However, these data were not used
in the equation-of-state analyses.
Similar analyses on Mg
0 9Fe0 15i03 show a significantly
higher
apparent
thermal expansion. An
‘ak’ of 3.19(10) x i0~ K~ is obtained from run
—
158
157
-______________________________________
159
158
157
156
155
10.73 GPa
_____________________________________
I
400
600
800
Temperature,K
1000
1200
Fig. 9. Unit-cell volume of MgSiO, perovskite as a function of
temperature at various constant pressures (from top to bottom):
4.35 GPa
Run GPa
3B), (from
7.06 GPa
8.14
GPa (from
Run(from
SB), 9.02
Run(from
5A), Run
and 3A),
(F) 10.73
GPa (from Run 8). Dashed curves represent Suzuki-type fit
with fixed Debye temperature 1094 K; solid curves show
linear fits using Eq. (1).
29
~.
6, averaged over a wider temperature interval
1 inaa much
ternbetween 620 and 1100 K. Run 7 gives
smaller value of 2.44(10) x i0~ K—
perature range from 350 to 873 K, and the recovered sample has partially transformed into enstatite according to our Raman data (Fig. 7(B)).
30
Y Wang et a!. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
The large variations in thermal expansion are
probably due to the back-transformation. Variation in the Fe/(Mg + Fe) ratio in the perovskite
may also occur as Fe may preferentially partition
Table 4
Average thermal expansion and Grüneisen parameters of
MgSiO, perovskites
(p~a
Trange
(CPa)
(K)
Grflneisen
1’
(OV)
(10’
y
into the second phase. Thus, the P—V—T behavior of this perovskite may not represent the equa-
K-1)
i0~
4.4(4) e
7.1(5)
7.2(2)
8.1(5)
8.9(5)
77— 400
300—1076
306— 880
625—1174
307—1276
625—1074
1.64(6)
1.91(4)
1.9100)
1.67(20)~
2.39(6)
2.36(9)
d
1.58(8)
1.18(5)
1.25(4)
1.0002)
1.49(3)
1.43(5)
tion of state.
P—V—T equations of state
Several (empirical) thermal equations of state
are used to fit the data for MgSiO
3 perovskite: an
extended high-temperature Murnaghan equation
of state and the Birch—Murnaghan equation of
10.7(2)
677—1024
1.9307)
1.1700)
a(
), Average value,
b Average thermal expansion, by fitting the data to ln(V) = a
state, as well as the Mie—Grüneisen equation of
state with the thermal pressure approach (Anderson, 1984).
The first of these is obtained through an expansion of the bulk modulus at a constant ternperature (T) to the first-order term in pressure,
KT(P, T) = KT(l, T) + [0KT(l,
T)/0P]TP;
where KT(1, T) = KT(l, 300) (0KT/0T)l,00 (T
+ bT, for the given temperature range (after pressure correction),
Grüneisen parameter (y) from fitting the data to the Suzuki
formalism with fixed Debye temperature 1030 K (Akaogi and
Ito, 1993).
d Data below 300 K from Ross and Hazen (1989).
Numbers in parentheses give pressure range from which
data are obtained, not pressure uncertainty.
Data from Wang et al. (1991), after pressure correction,
4
I
—
I
I
I
I
I
800 K
93-
‘H~~~—~+t
~-
-
0
>~ 10
0
I
I
I
I
I
I
2
4
6
8
10
12
Pressure, GPa
Fig. 10. Thermal expansivity of MgSiO3 perovskite at 800 K as a function of pressure. Solid symbols, from the present study; open
symbols, data from Wang et al. (1991) after a small pressure correction of 0.2 GPa over 1000 K. The 1 bar value (square) is an
extrapolation of data up to 430 K to 800 K. Solid line is a least-squares fit to the solid symbols; dashed curve is calculated thermal
expansion at 800 K using the average thermoelastic parameters for MgSiO, perovskite in Table 5. (Note that in the equation of
state analysis the 1 bar data included are those within the reversible temperature range (less than 400 K).)
Y Wang et a!. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
300)
+
1/2
(02K~/0T2)1300
(T 300)2, 300and
2KT/0P0T)l
(T
(8
300 indicates
values at 1
bar and 300 K. Integrating KT(P, T) =
—V(0P/0V)T at a constant (and arbitrary) T
yields
(8KT/0P)T
(8KT,/0P)l
— 300); the=subscript
1,
V(P, T)
=
V(1, T)[KT(P, T)/KT(l, T)]
where V(1, T)
be
noted that Murnaghan
(2) is the same
form asofthe
roomtemperature
equation
state
in
which the ambient parameters, V(1, 300),
KT(l, 300), K-(1, 300), are replaced by those at 1
bar and temperature T.
Similar extensions can be made for the Birch—
Murnaghan equation of state, yielding
P = 3/2KT{( VT/V)
(VT/V)~~~]
—
300+
—
1/K
(2)
—
x {i
V(1, 300) exp(fa(1, T) dT), K~
2KT/0P0T),
300 + (8
300 x (T 300)
and the integration is from 300 K to T. It should
=
31
=
3/4(4-K~)[vT/v2/3
—
—
(0KT/8P)i
}
(3)
with VT = V(1, T), KT = KT(l, T), and K~=
[8KT(1, T)/0P]T, whose expressions are the same
—
1500K
0.03
i]
M SiO
-
1276
0.02
-
1100K
::---:~iO74
~~76
~f537
483
428
0.00
~°°
0
3~2~3~
~
497I~)
396k
~ 427
3O6I~
~II
307
5
10
Pressure, GPa
Fig. 11. A summary of results from the three P—V—T equations of state (Eqs. (2)—(4)) on MgSiO,. Data are presented as volumetric
strain, lV(P, T) — V(P, 300 K)]/J/(P, 300 K), where V(P, 300 K) is from Birch—Murnaghan equation of state at the measured P.
Numbers next to the data points are temperatures (in K). Fitting results (lines) are presented as volumetric strain at various
temperatures from 500 to 1500 K. Three dashed lines are from the Murnaghan, the Birch—Murnaghan, and the Mie—Grüneisen
equations ofstate, using the parameters given in Table 5. The solid lines are fits using the Birch—Murnaghan equation of state with
the average parameters in Table 5.
32
V Wang et a!. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
as in the extended Murnaghan equation of state
presented above.
We choose the Mie—GrUneisen equation of
state with thermal pressure in the following form
(e.g. Anderson et al., 1989):
~th
=
f (dP/dT)~ dT=
Assuming that
ture, we obtain
~th
=
aKT
fa(v,
T)KT(V, T) dT
is independent of tempera-
j a(1, T)K~(1, T) dT
+
[0K~(1, 300)/0T}~ln(V,~/V)(T—300)
(4)
This equation has been used extensively in recent
studies on P—V—T equation of state of mantle
minerals (e.g. Mao et a!., 1991, Fei et al., 1992a,
1992b).
Common to these equations of state are
the fitting parameters av(1, T), KTO, K~
0=
(0KTO/0P)T, and (8KT/0T)p. In general,
(0K~/0T)~ is very sensitive to the choice of
a~(l,T). Because our 1 bar data are in a very
small temperature range, we treat cx~(l,T) as a
fitting parameter in the form of (1). For all three
equations of state, the parameter c is found again
very small with uncertainties greater than2 the
in
value;
we This
therefore
the term
crv(l, T).
can alsoignore
be justified
by thec/T
thermal
expansion behavior corrected to constant pressures: cxy(P~
0051,T) is almost linear with temperature throughout the P, T range. In fact, ignoring
this term does not affect the results for constants
a and b. Our limited pressure and temperature
range does not allow a determination
of the
see2KT/0T2 and
02KT/
ond-order
derivatives
0P/clT.
Thus,
we extract0three parameters, a, b,
and (0KT/0T)p from the data, assuming
KTO(l, 300) = 261 GPa and K’
1-0 = 4. The results
are shown in Fig. 11 and summarized in Table 5.
The error bars in Fig. 11 are based on estimates of uncertainties from three sources (see
next section for error analysis): (1) uncertainties
3), (2)
in
the volumein refinements
(about 0.1 using
A the
uncertainties
pressure determination
NaCI standard (up to 0.2 GPa); (3) systematic
Table 5
Parameters extracted from thermal equations of state for
MgSiO
3 perovskite
Equation of state
Parameters
2a
Murnaghan
(IKT/IT)p=
_2.61(1.06)x10_
(2)
a= l627W.197)x10_sb
Birch-Murnaghan
(3)
(3KT/8Tp=-2~9(1.O2)x102
a= 1.647(0.180)X10~
b = 0.821(0.337)x 10-8
Mie—Grilneisen
(BKT/aT)P = —2.250.07)x 10—2
(4)
a = 1.651(0.190)X i05
b = 0.823(0.333)x iO~
Average
(IKT/IT)p= —2.3(1.1)x 10-2
a = 1.64(0.19)>< io’
b=0.86(0.34)x108
a Average temperature derivative of isothermal bulk modulus
(in GPa K~).
The 1-bar thermal expansion cs
b
=
a + bT (where a is in K1
and b in K2).
uncertainties caused by change in diffraction geometry. The last two contributions are also propagated in volume using the room-temperature
equation of state of perovskite. For clarity, the
pressure uncertainties are not shown in Fig. 11.
Results from different thermal equations of state
agree well within the uncertainty and give almost
identical fits to the data, as can be seen in Fig.
11. From these fits, an average (0KT/0T)p =
—0.023(11) for
GPa/K’
is obtained,
with
the
parameters
av(1, T)
(Table 5).along
On the
other
hand, if we use the value of cn~(l,T) obtained
from the 1 bar data alone via Eq. (1) as a constraint in fitting the high-pressure data in Fig. 11,
we obtain (8KT/0T)p = 0.026(3) GPa/K 1~
The average temperature derivative of the
isothermal bulk modulus, —0.023(11) GPa/K’,
is inconstant-pressure
excellent agreement
with thatInobtained
the
approach.
Fig. 10,from
we
compare the 800 K thermal expansion, both from
the constant pressure data and from the equa—
tions of state. The pressure dependence, according to Fig. 10, predicts an ar,. value about 1.6 X
iO~K~ at 36 OPa, which agrees very well with
the data reported by Funamori and Yagi (1993),
in which
study
pressureThe
and
temperature were
not
directly
measured.
Anderson-Grilneisen
parameter, ~T = —(8KT/8T)p/(aKT), decreases
with both pressure and temperature, ranging from
V Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
4.0 at 1 bar and 800 K to 3.4 at 10 GPa and 1300
K. At 40 GPa and 2000 K, the predicted value is
about 2.5.
Our data on Mg0 9Fe0 1SiO3 perovskite, which
are irreversible in the P—V—T measurement, are
in general agreement with the data of Mao et al.
(1991). When we combined our data with those of
Mao et al. above,
and analyzed
them in theansame
way as
outlined
we obtained
apparent
‘(OKT/OT)p’ of
0.06(1) GPa/K 1, without any
constraint on av(l, 300). However, this value is
suspect because of the irreversible behavior revealed by Raman spectroscopy. We shall further
discuss the problems of these data in the next
—
4. Discussion
4.1. Error analysis
equations
of by
state
are based
on Experimentally,
small volume changes
caused
pressure
and
temperature. Bulk modulus, thermal expansion,
and their P, T derivatives are first- and secondorder derivatives of the volume and are extremely
sensitive to uncertainties in P—V—T measurements. Therefore, it is important to examine the
effects of uncertainties on the results. We first
discuss effects of systematic errors such as pressure uncertainties introduced by using a particular pressure standard,
As the measured pressure (em) using the
equation of state of any standard material can
only be an approximation to the true pressure
(P), so we express ~m by the following function
of P and T:
P = (1 +a~P+b(T— 30O~+
1~5\
\
the perovskite sample, J”(P, T), may be approximated by that obtained at ~m in the following
way
ln V(P T)
=ln ~‘c(Pm’
T) + (8 ln !~/0P)(P~Pm)
= In taP+b’T—
J’(Pm’ T) 300~1
(8 ln J”1/0P)
16
>< L
.11
Thus the true sample volume is approximately
V(P T) = V(P T) exp{/3 [aP+b(T—300)]}
—
S
S
and the true thermal expansion a
5(P, T) =
0 ln ~“1(p,T)/0T can be expressed as
a/P, T) =am—Oas/OP[aP+b(T—300)]
section.
m
33
I
•~.
I
“ ‘
where parameters a and b represent effects of
pressure and temperature, respectively, on differences in pressure determination using various
equations of state for various standards. More
terms may be included if enough information is
available in comparing various pressure standards.
In our case, ~m is measured using Decker’s
equation of state for NaC1. The true volume of
+ f35b
(8)
and its pressure derivative is
0cn5/OP
2a
2)[aP+b(T— 300)]
= Oam/OP— {(0
+ (Oct /OP)a} + 5/0P
(0/3 /OP)b
(9)
S
where /3~is compressibility of the sample and we
have used the identity 0/3/OT =
Oct/OP. One
may carry out further derivatives for a
5. In our
experiments, however, the second-order pressure
derivatives on thermal expansion is not resolvable
and therefore will be neglected in the analysis.
From Eqs. (7)—(9), systematic errors increase linearly with pressure and temperature.
Decker (1971) estimated that at room temperature the pressure uncertainties in his equation
of state increase with pressure; at 10 GPa, the
uncertainty is about 0.17 GPa. We expect this to
be representative of the order of magnitude
among various pressure standards. Thus we assume a in Eq. (5) to be of the order of 0.02. We
have carried out some measurements to examine
the difference in pressure using NaC1 and gold.
We find that at about 6 GPa and 973 K, where
the non-hydrostatic stress has presumably relaxed, the equation of state for gold (Jamiesen et
al., 1982) predicts a pressure about 0.4 GPa higher
than that calculated from NaCI. This, with a =
0.02, corresponds to b = 0.0004 GPa/K
With
these rough estimates, at maximum conditions of
—
~.
34
Y Wang et a!. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
P = 11 GPa, and T = 1300 K, maximum systematic uncertainties in volume of perovskite is about
0.2%, or about 0.4 A3, according to Eq. (7).
Similar uncertainties for both thermal expansivity
and Octv/OP are about 10—15%. These errors are
comparable with those listed in Table 5 and thus
will not affect final results significantly.
On the other hand, Meng et al. (1994) have
shown that for NaC1, equations of state of Decker
(1971) and Birch (1986) predict rather consistent
pressures with 0.1 GPa at pressures of 10—20
GPa and temperatures up to 1500 K. Thus, effects on pressure uncertainties using different
equations of state for NaCI are much smaller
than those we have discussed for NaCI and Au
above.
Experimentally, the following sources of errors
may be identified during a high-P, high-T measurement:
(1) pressure uncertainty as a result of errors in
measuring unit-cell volume of NaCI. In this study,
maximum error in pressure determination using
the NaC1 volume is about 0.2 GPa, corresponding
to about 0.1 A3 in volume in perovskite.
our case, we have demonstrated that for NaCI
(our pressure standard and pressure medium)
deviatoric stress vanishes on heating to above 600
K and, consequently, we have discarded all of the
data that might have been ‘contaminated’ by the
deviatoric stress. The diamond-anvil cell experiments of Mao et al. (1991) used gold as the
pressure standard and neon as the pressure
medium. A recent study (Meng et al., 1993) has
demonstrated that in this case deviatoric stress
may contribute significantly to pressure determination and thus influence the P—V—T relations.
Gold has a very high K/pc ratio (about six), which
magnifies the effects of deviatoric stress in pressure measurements (Meng et al., 1993b). Therefore, at least part of the discrepancies in the two
compositions may be attributable to deviatoric
stress in the diamond-anvil cell experiments.
Given all these uncertainties, we estimate that
the errors in thermal expansion should be about
(0.2—0.3)>< i0~ K—1. These are the errors plotted in Fig. 10.
4.2. Comparison
of Results for MgSiO
3 and
(2) Uncertainties introduced by the perovskite
equation of state in pressure corrections on the
unit-cell volume. These corrections are about the
same magnitude as (1).
(3) Systematic errors in the diffraction setup.
An important error may be due to change in
diffraction
geometry
high-pressure
measurements relative
to for
the the
1 bar
standard calibration. With the current experimental setup, maximum errors caused by diffraction geometry are
estimated to be about i0~ in ~d/d, which are
probably the most significant errors in pressure
and volume determination.
Suchinerrors
may cor3 error
the NaCI
volrespond
to
about
0.4
A
ume, and about 0.5 GPa in pressure. All of these
errors are less significant in measuring constantpressure thermal expansion as long as each measurement is carried out at the same sample position. Thus, the constant-pressure approach may
be better constrained as far as these systematic
errors are concerned.
(4) The presence of deviatoric stress in either
large-volume apparatus or diamond-anvil cells will
give rise to erroneous pressure determination. In
Mg09Fe01SiO3 perovskite
In Table 6, we compare our (OK~/0T)~
data
with laboratory measurements on other silicates
and oxides. The values of (0KT/0T)p for MgSiO3
perovskite
Table
5 (from
0.021oftothe 0.026
1) from
fall well
within
the range
availGPa
K—
able laboratory data for silicates and oxides. From
these data, it appears that iron content generally
does not have a significant effect on (0KT/0T)p.
For instance, MgO and Mg
0 5Fe04O have identical values of (OKT/OT)P; the same is true for
olivine
and the
with ironhowever,
content xhas
up an
to
10%. The
x = /30.1phase
perovskite,
apparent (OKT/OT)p a factor of 3—4 more negative than that of the end-member.
The back-transformation to enstatite observed
in the x = 0.1 perovskite below 870 K makes the
low (0KT/OT)p suspicious. Such an irreversible
process may cause abnormal behavior in thermal
expansion. Our 1 bar data on Mg
09Fe01SiO3
revealed that, during decomposition, the unit-cell
volume of the remaining perovskite crystals first
decreases and then increases sharply with in—
—
Y Wang Ct al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
Table 6
(1IKT/IT)p (in CPa K—’) for selected oxides and orthosilicates
(8K
1-/IT)~
(300 K)
(1KT/IT)p
(1200 K)
MgO
0.027
0.031
Mg0 6Fe,40
~
0030
CaO
Mg2SiO4 (a)
Mg,54Fe016SiO4(a)
Mg, 8Fe02SiO4 (a)
Mg2SiO4(fl)
Mg165Fe032SiO4(/3)
Mg2SiO4 (y)
Grossular
Gr97An,Py,”
Gr76An22 d
Pyrope
Py AIm
MgSiO3 (pv)
Mg09Fe01SiO3(pv) ~
a
b
d
—01021
—01021
—0.021
—0.020
0.022
(—0.026)
(—0.027)
—0.016
—0.021
—0.020
0.016
—0.026
—0.026
—0.023
—0.020
0.022
partition into magnesiowüstite, resulting in an
iron-depleted perovskite. Thus, we have two types
of metastability issues for the Fe-bearing perovskite. The first is the stability of the structure.
All of our experiments are outside the stability
region for the perovskite. However, reversibility
indicates that we are measuring the state properties for MgSiO3. The second metastability is the
Fe/Mg ratio. None of the experiments to date,
including those of Mao et a!. (1991), have measured volume in a P, T region where the Fe/Mg
ratio is stable in the perovskite structure. Once
.
—0.025
—0.021
0.025
K— o.o~3
(—0.063) to
(—0.080)
Fei et al. (1992a).
Meng et at. (1993a).
Fei et at. (1992b).
Isaak et at. (1992); An, andradite; Gr, grossular; Py, pyrope.
Suzuki and Anderson (1983); AIm, almandine.
This study.
Mao et al. (1991).
Other data from Anderson et al. (1992); (... ), average,
creasing temperature (Fig. 4(B)). We compare
this observation with those of Ming et al. (1990)
on Fe2SiO4 spinel. These workers showed that
when spinel back-transforms to fayalite in air, its
unit-cell volume first drops with increasing ternperature and then rises at a far greater rate.
Decomposition to iron oxide was observed by
X-rays, and was found to be similar to the behavior observed for (Mg,Fe) perovskite.
An additional concern is the recent results on
maximum Fe solubility in perovskite in a
Mössbauer spectroscopy study on samples
quenched at 26 GPa (Fei and Wang, 1992). These
workers show that Mg0 9Fe01SiO3 perovskite requires T> 1873 K to be stable, below which temperature the equilibrium phase assemblage contains magnesiowüstite and stishovite in addition
to perovskite. When such a decomposition occurs, iron leaves the perovskite and tends to
35
.
temperature is high enough for diffusion to occur, it is possible that the material can break
down via defect reactions, or an iron-rich phase
may form which may drastically affect the state of
the perovskite and invalidate the measurement of
equation of state variables. This is our preferred
explanation, in view of the above experimental
evidence to question the behavior of Mg09Fe01
SiO3 perovskite.
4.3. Implications for the lower mantle
.
We examine the constraints imposed by our
new data on the composition of the lower mantle
with the assumption that thermoelastic parameters of MgSiO3 perovskite are applicable to perovskites with moderate Fe content (x up to about
0.1); this assumption is supported by the data for
other structures given in Table 7. One way to
make such an analysis is to compute a complete
profile for density and adiabatic bulk modulus
K1, or the seismic parameter 1 (Ks/p), throughout the lower-mantle pressure and temperature
range. However, given the limited pressure and
temperature range for the available experimental
volume data, extrapolations of the first- and second-order derivatives of the volumes to the deep
lower mantle have progressively larger uncertainties. Therefore, we will take an alternative approach, to examine K1 and density at a shallow
depth in the lower mantle and compare the corresponding seismic observations.
We choose a depth of 1071 km (P = 41.86
GPa) because this is well below the 670 km
discontinuity and in a region where the seismic
profiles are well constrained. In the Preliminary
36
V Wang et a!. /Physics of theEarth and Planetary Interiors 83 (1994) 13—40
Reference Earth Model (PREM), p and K1 at
3 and 363.8 GPa,
this depth are
4.621 g cm
respectively
(Dziewonski
and Anderson, 1981).
Temperature estimates have larger uncertainties.
Table
7
Thermoelastic
parameters used in modeling the lower mantle
Perovskite
Magnesiowüstite
Mg,_~Fe~SiO
3 12.25
Mg1_~Fe~O
3 moL’
24.46 + 1.03x
+ l.OOy
~70,
KTQ,cmCPa
261(5)
157
4.0(2)
4.0
(IKT/3T)p,
—0.023(11) a
—0.027
Hereestimated
we adoptbytheBrown
adiabatic
gradient
andtemperature
Shankland (1981)
and an adiabatic foot temperature at zero depth
T
0 = 1800 K (corresponding to about 2040 K at
670 km) in the trade-off analysis. We assume that
orthorhombic
(Pbnm)
perovskite
the discusstable
phase
throughout
the lower
mantleis (see
sions by Wang et al., 1992). For magnesiowustite,
we use the thermoelastic parameters determined
by Fei et al. (1992a). Other possible lower-mantle
phases are poorly known. Initially, we therefore
assume a lower mantle with only two phases,
perovskite and magnesiowüstite (Table 7).
GPa K-’
a, K’
2
b,
K
c~K
r
®D,
1.64(19)e—5 aa
0.86(34)e—8
3.8371e—5
0.9372e—8
0.7445
1.50
500
4.41
—
1.3(2)
1030(20)
3~73a
K
~T(1, ~D)
•
Data for magnesiowüstite are from Fei et al. (1991); a(1, T) =
a + bT — cT2. Iron partitioning coefficient K~~VW
= [y/(1 —
y)]/[x/(i—x)]=4. Debye temperature (®~)for the perovskite is from Akaogi and Ito (1993).
a Data are obtained from this study.
0.15
+
~i
I~I~i
0.10
0.05
~
.
2.0
-
1,5
-
•
•
-
-
1.0~
.
-•
-
0.5-
-•
•.
-
(~).01
1
I
I
I
I
I
2
3
4
3.9
4.2
a v
I
I
I
-
I
I
-0.04 -0.02 0.00 1600 1800 2000
K
0’
(dKT/dT)p
T0
Fig. 12. Dependence of model chemical variables (Fe/(Mg + Fe) and (Mg + Fe)/Si) on measured perovskite thermoelastic
parameters (1 bar average thermal expansion, a~,in i0~ K’, (3KT/IP)T, and (0KT/IT)p, in GPa K) as each parameter is varied
from the preferred value (as indicated by the dot). T0 is the lower-mantle adiabatic foot temperature (in K). Horizontal error bars
are estimated uncertainties in the parameters. Small variations (about 0.3%) in K1 can cause (Mg + Fe)/Si to change between 1.4
to 2.0; thus, this ratio cannot be as tightly constrained as Fe/(Mg + Fe).
Y Wang et a!. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
Stishovite may also be present if Fe/(Mg + Fe)
is high and/or (Mg + Fe)/Si is low (e.g., Ito et
al., 1984). Recent studies indicate that maximum
iron solubility in perovskite increases strongly with
temperature; at 26 GPa, x = 0.1 perovskite is
stable at T> 1873 K (Fei and Wang, 1992). The
iron partitioning coefficient between magnesiowüstitemuch
and less
perovskite,
the other and
hand,
appears
pressureondependent,
ranges
from three to four in the temperature interval of
1300—1900 K (Guyot et al., 1988; Kanamoto et
a!., 1992). Thus, for an overall (Mg + Fe)/Si> 1
and Fe/(Mg + Fe) < 0.15 (as is the case in the
following calculations), stishovite is less likely to
be present in the lower mantle.
Our goal is to seek an appropriate molar ratio
of perovskite to magnesiowüstite that satisfies the
seismically determined bulk modulus and density.
To do this, we calculate K, and density of perovskite and magnesiowüstite at pressure and temperature conditions at 1071 km depth using the
Birch—Murnaghan equation of state. The average
bulk modulus of the two-phase composite is then
estimated using the Hashin—Shtrikman bounds
(e.g. Watt et al., 1976). Because of the lack of
information on temperature and pressure dependence of the shear moduli of the two phases, we
use their ambient values, 177 GPa for perovskite
(Yeganeh-Haeni, 1993) and 129 GPa for magnesiowUstite (Anderson et al., 1992), respectively,
throughout the analysis. By matching the seismic
bulk modulus and density, both total iron content
(Fe/(Mg + Fe)) and molar ratio of the two phases
((Mg + Fe)/Si) can be uniquely determined. Following Hemley et al. (1992), we assume that thermoelastic properties of both phases are independent of the iron content, at least within the range
concerned in our problem. This assumption renders the results insensitive to the partitioning
coefficient of iron between perovskite and magnesiowüstite, which is taken to be four throughout the analysis. The best fit for the Fe/(Mg + Fe)
and (Mg + Fe)/Si ratios are shown in Fig. 12 as
the dots; uncertainties in these parameters are
represented by the sizes of the horizontal bars.
Throughout the analysis, thermoelastic parameters of magnesiowüstite are assumed to be exact.
To examine the resolution of this analysis, we
37
determine the dependence of the chemical vanables (Fe/(Mg + Fe) and (Mg + Fe)/Si) on the
thermoelastic parameters (ak, K~,,and (OKT/
0T)~)by perturbing one of the perovskite parameters while keeping others fixed at the values
represented by the dots, under the simultaneous
constraints of K1 = 363.8 GPa and p = 4.621 g
3 from PREM at 1071 km. In addition, the
cm
effects
of the lower-mantle temperature (represented by the adiabatic foot temperature at zero
depth) are also shown. In Fig. 12, each curve
shows the effects of the corresponding parameter
on determination of composition of the lower
mantle.
Our best match gives an Fe/(Mg + Fe) ratio
about 0.12. Varying the perovskite parameters
within their uncertainties introduces uncertainties of the order of 0.01; thus the Fe/(Mg ± Fe)
ratio is well constrained in this analysis. This iron
content is in agreement with the analyses of
Stixrude et al. (1992) and Hemley et al. (1992),
but T
0 is somewhat lower than that suggested by
those workers. This agreement is primarily due to
the coincidence that, although the data of Mao et
al. (1991) gave a very high estimate in thermal
expansion at 1 bar, the exceptionally large negative (0KT/OT)p implies a strong pressure dependence in thermal expansion, so that under lowermantle pressures, their thermal expansion data
are in general agreement with ours.
The iron content of Fe/(Mg + Fe) = 0.12(1) is
consistent with the typical upper-mantle iron contents. These results are in contrast to the earlier
conclusion that a lower mantle with upper mantle
iron content may be about 2.5% less dense than
the seismically determined lower-mantle densities
(Jeanloz and Knittle, 1989). As density is primarily determined by Fe/(Mg + Fe) but insensitive
to (Mg + Fe)/Si (Fig. 1), our inferred iron content implies that a lithosphere entering the lower
mantle by subduction would be neutrally buoyant,
with no gravitational resistance. Thus, chemical
stratifications, if they exist, will not inhibit
whole-mantle convection.
The (Mg + Fe)/Si ratio is primarily controlled
by K,, and the constraints are not as robust. This
ratio is extremely sensitive to (0KT/OT)P; the
relative large uncertainty for this parameter
Y
38
Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
(±0.011 GPa/K’) corresponds to a wide range
of (Mg + Fe)/Si from 1.3 to 2.2. The large uncertainty in (0KT/OT)p is primarily due to the jimited pressure range in the present study; more
experiments are needed to extend the pressure
range in studying the equation of state of perovskite. Other parameters provide relatively
tighter constraints; altogether, a wide range of
values from 1.5 to 2.0 are still acceptable for
(Mg + Fe)/Si. Although this range appears to be
large, we point out that such a range corresponds
to only ±10 GPa uncertainty in the adiabatic
bulk modulus (i.e. less than 3%). Given the uncertainties in K0 and the pressure and temperature derivatives for perovskite, the extrapolated
K~at 1071 km depth may have an uncertainty of
about ±30GPa (about 1%). Seismic data may
have similar uncertainties. Thus, Stixrude et al.
(1992) found that perovskite fractions as low as
45% are still acceptable at lo’ confidence level in
their analysis. Clearly, an unequivocal determination of the (Mg + Fe)/Si ratio awaits more precise experimental measurements and seismic observation. At this stage, however, it appears that
it is unlikely for the lower mantle to have a
perovskite stoichiometry (i.e. (Mg + Fe)/Si = 1L
By contrast, the pyrolite composition falls well
into this range of (Mg + Fe)/Si. Thus, a chemically uniform mantle appears consistent with the
new data.
5. Conclusions
A systematic study has been carried out on the
thermal equation of state of (Mg,Fe)SiO3 perovskite up to 11 GPa and 1300 K. Thermodynamic validity of the P—V—T behavior of MgSiO3
perovskite under these metastable conditions is
examined and verified. The iron-rich perovskite
exhibits an irreversible behavior and, therefore,
its P—V—T behavior cannot be regarded as representative of that under stable conditions. The
measured temperature derivative of the isothermal bulk modulus of MgSiO3 perovskite,
(OKT/OT)p =
0.023(1 1) GPa/K
falls well
within the range of the laboratory measurements
for silicates and oxides. Assuming that this value
—
~,
maybe applied for perovskite with moderate iron
content, the new data are used to constrain the
composition of the lower mantle. We found that
the Fe/(Mg + Fe) ratio is well constrained at
0.12(1), consistent with the conclusions of Hemley
et al. (1992) and Stixrude et al. (1992). The predicted (Mg ±Fe)/Si ratio based on our new data
is inconsistent with previous conclusions that the
lower mantle exhibits pure perovskite stoichiometry. Our data give a ‘normal’ (OKT/OT)p for the
perovskite compared with other silicates and oxides, and indicate that the inferred (Mg + Fe)/Si
ratio is consistent with the pyrolite composition.
6. Acknowledgments
We thank Y. Meng and Y. Fei for useful
discussions. During the course of the experiment
at NSLS, we have benefited a great deal from the
assistance of the SAM-85 team: M.T. Vaughan,
K. Kusaba, K. Leinenweber, B. Li, X. Li, X. Liu,
Y. Meng, R.E. Pacalo, and A. Yeganeh-Haeni.
We thank D. Durben, T. Clough, and G. Wolf for
helping carry out the Raman spectroscopy measurements, D. Presnall and Y. Fei for providing
starting materials for synthesizing the specimens,
D.E. Cox and J.B. Parise for help in conducting
the 1-bar experiments at the X7 beamline, D.
Chapman, N. Lazarz, and W. Tomlinson of the
X17B1 beamline for assistance in the high-pressure experiments, and two anonymous reviewers
for helpful comments and suggestions. The synthesis experiments were carried out at the Stony
Brook High Pressure Laboratory. The laboratory
and the SAM 85 experiments at NSLS are supported by the NSF Center for High Pressure
Research (EAR 892920239). This research was
supported by NSF grant EAR 9104775. This paper is Mineral Physics Institute Contribution 78.
7. References
Akaogi, M. and Ito, E., 1993. Heat capacity of MgSiO3
perovskite. Geophys. Res. Lett., 20, 105—108.
Anderson, O.L., 1984. A universal thermal equation of state.
J. Geodyn., 1: 185—214.
V Wang et a!. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
Anderson, O.L., Isaak, D.G. and Yamamoto, 5., 1989. Anharmonicity and the equation of state for gold. J. Appl. Phys.,
65: 1534—1543.
Anderson, DL., Isaak, D. and Oda, H., 1992. High-temperalure elastic constant data on minerals relevant to geophysics. Rev. Geophys., 30: 57—90.
Birch, F., 1986. Equation of state and thermodynamic parameters of NaC1 to 300 kbar in the high-temperature domain.
J. Geophys. Res., 91: 4949—4954.
Brown, J.M. and Shankland, TI., 1981. Thermodynamic parameters in the Earth as determined from seismic profiles.
Geophys. J.R. Astron. Soc., 66: 579—596.
Cox, D.E., Toby, B.H. and Eddy, MM., 1988. Acquisition of
powder diffraction data with synchrotron radiation. Aust.
J. Phys., 41: 117—131.
Decker, DL., 1971. High-pressure equation of state for NaC1,
KC1, and CsCl. J. Appl. Phys., 42: 3239—3244.
Durben, D.J. and Wolf, G.H., 1992. High-temperature behavior of metastable MgSiO3 perovskite: a Raman spectroscopic study. Am. Miner., 77: 890—893.
Dzjewonski, AM. and Anderson, DL., 1981. Preliminary
reference Earth model. Phys. Earth Planet. Inter., 25:
297—356.
Fei, Y. and Wang, Y., 1992. The maximum solubility of iron in
(Mg,Fe)Si03 perovskite as a function of temperature. Eos,
Trans. Am. Geophys. Union, 73: 596 (abstract).
Fei, Y., Mao, H.K., Shu, I. and Hu, I., 1992a. P—J/—T
equation of state of magnesiowustite (Mg0 6Fe04)O. Phys.
Chem. Minerals, 18: 416—422.
Fei, Y., Mao, H.K., Shu, J., Parthasarathy, G., Bassett, WA.
and Ko, J., 1992b. Simultaneous high-P, high-T X ray
diffraction study of /3-(Mg,Fe)2SiO4 to 26 GPa and 900 K.
J. Geophys. Res., 97: 4489—4495.
Funarnori, N. and Yagi, T., 1993. High pressure and high
temperature in situ X-ray observation of MgSiO3 perovskite under lower mantle conditions. Geophys. Res.
Lett., 20: 387—390.
Guyot, F., Madon, M., Peyronneau, J. and Poirier, J.P., 1988.
X-Ray microanalysis of high-pressure/high-temperature
phases synthesized from natural olivine in a diamond-anvil
cell. Earth Planet. Sci. Lett., 90: 52—64.
Hemley, R.J., Stixrude, L., Fei, Y. and Mao, H.K., 1992.
Constraints on lower mantle composition from P — v— T
measurements of (Fe,Mg)Si03-perovskite and (Fe,Mg)O.
In: Y. Syono and M.H. Manghnani (Editors), High Pressure Research in Mineral Physics. American Geophysical
Union, Washington, DC, pp. 183—189.
Hill, R.J. and Jackson, I., 1989. The thermal expansion of
ScA1O3 — A silicate perovskite analogue. Phys. Chem.
Minerals, 17: 89—96.
Horiuchi, H., Ito, E. and Weidner, D.J., 1987. Perovskite-type
MgSiO3: single crystal X-ray diffraction study. Am. Mmeral., 72: 357—360.
Isaak, D.G., Anderson, O.L. and Odaa, H., 1992. High-ternperature thermal expansion and elasticity of calcium-rich
garnets. Phys. Chem. Minerals, 19: 106—120.
Ito, E. and Matsui, Y., 1978. Synthesis and crystal chemical
characterization of MgSiO
39
3 perovskite. Earth Planet. Sci.
Lett., 38: 443—450.
Ito, E. and Yamada, H., 1981. Stability relations of silicate
spinels, ilmenites and perovskite. In: S. Akimoto and M.H.
Manghnani (Editors), High Pressure Research in Mineral
Physics. American Geophysical Union, Washington, DC,
pp. 405—419.
Ito, E. and Takahashi, E., 1989. Postspinel transformations in
the system Mg2SiO4—Fe2SiO4 and some geophysical implications. I. Geophys. Res., 94: 10637—10646.
Ito, E., Takahashi, E. and Matsui, Y., 1984. The mineralogy
and chemistry of the lower mantle: an implication of the
ultrahigh-pressure phase relations in the system Mg—
FeO—Si02. Earth Planet. Sci. Lett., 67: 238—248.
Jackson, I., 1983. Some geophysical constraints on the chemical composition of the earth’s lower mantle. Earth Planet.
Sci. Lett., 62: 91—103.
Jamiesen, IC., Fritz, J.N. and Manghnani, M.H., 1982. Pressure measurement at high temperature in X-ray diffraction studies: gold as a primary standard. In: S. Akirnoto
and M.H. Manghnani (Editors), High-Pressure Research
in Geophysics. Center for Academic Publications Japan,
Tokyo, pp. 27—48.
Jeanloz, R. and Knittle, E., 1989. Density and composition of
the lower mantle. Philos. Trans. R. Soc. London, Set. A,
328: 377—389.
Kanomoto, M., Irifune, T., Fujino, K., Yagi, T. and Yusa, H.,
1992. Determination of element partitioning among highpressure phases for (Mg,Fe)2SiO4 olivine with an analytical electron microscope (in Japanese). 33rd High Pressure
Conference of Japan, Kumamoto, 18—20 November :1992,
High Pressure Society of Japan, Tokyo, pp. 300—301.
Knittle, F. and Jeanloz, R., 1987. Synthesis and equation of
state of (Mg,Fe)Si03 perovskite to over 100 gigapascals.
Science, 255: 1238—1240.
Knittle, E., Jeanloz, R. and Smith, G.L., 1986. The thermal
expansion of silicate perovskite and stratification of the
Earth’s mantle. Nature, 319: 214—216.
Larson, AC. and von Dreele, R.B., 1988. GSAS Manual.
Rep. LAUR 86-748, Los Alamos National Laboratory, Los
Alamos, NM, 150 pp.
Liebermann, R.C. and Wang, Y., 1992. Characterization of
sample environment in a multianvil split-sphere apparatus.
In: Y. Syono and M.H. Manghnani (Editors), High Pressure Research in Mineral Physics. American Geophysical
Union, Washington, DC, pp. 19—31.
Liu, L.G., 1975. Post-oxide phases of forsterite and enstatite.
Geophys. Res. Lett., 2: 417—419.
Liu, L.G., 1976. Orthorhombic perovskite phases observed in
olivine, pyroxene, and garnet at high pressures and temperatures. Phys. Earth Planet. Inter., 11: 289—298.
Lu, R., Hoffmeinster, AM. and Wang, Y., 1991. Thermodynamic properties of orthorhombic magnesium silicate perovskites, EQS Trans., AGU, 72: 464 (abstract).
Mao, H.K., Hemley, R.J., Shu, J., Chen, L., Jephcoat, A.P.,
Wu, Y. and Bassett, WA., 1991. Effect of pressure, ternperature, and composition on the lattice parameters and
V
40
density of (Mg,Fe)Si0
Wang et al. /Physics of the Earth and Planetary Interiors 83 (1994) 13—40
3-perovskite to 30 GPa. J. Geophys.
Res., 91: 8069—8079.
Meng, Y., Weidner, D.J., Gwanmesia, GD., Liebermann,
R.C., Vaughan, MT., Wang, Y., Leinenweber, K., Pacalo,
RE., Yeganeh-Haeri, A. and Zhao, Y., 1993a. In-situ high
P—T X-ray diffraction studies on three polymorphs (a, /3,
y) of Mg2SiQ4. J. Geophys. Res., 98: 22199—22207.
Meng, Y., Weidner, D.J. and Fei, Y., 1993b. Deviatoric stress
in a quasi-hydrostatic diamond anvil cell: effect on the
volume-based pressure calibration. Geophys. Res. Lett.,
18: 1147—1150.
Ming, L.C., Kim, Y.H., Manghnani, M.H., Usha-Devi, S., Ito,
E. and Xie, H.S., 1991. Back transformation and oxidation
of (Mg,Fe)2SiO4 spinels at high temperatures. Phys. Chem.
Minerals, 18: 171—179.
Navrotsky, A., 1989. Thermochemistry of perovskite. In: A.
Navrotsky and D.J. Weidner (Editors), Perovskite: A
Structure of Great Interest to Geophysics and Materials
Science. American Geophysical Union, Washington, DC,
pp. 67—80.
Parise, J.B., Wang, Y., Yeganeh-Haeri, A., Cox, D.E. and Fei,
Y., 1990. Crystal structure and thennal expansion of
(Mg,Fe)Si03 perovskite. Geophys. Res. Lett., 17: 2089—
2092.
Rietveld, H.M., 1969. A profile refinement method for nuclear and magnetic structures. J. Appl. Crystallogr., 2:
65—71.
Ross, N.L. and Hazen, R.M., 1989. Single-crystal X-ray
diffraction study of MgSiO3 perovskite from 77 to 400 K.
Phys. Chem. Minerals, 16: 415—420.
Stixrude, L., Hemley, R.J., Fei, Y. and Mao, H.K., 1992.
Thermoelasticity of silicate perovskite and magnesiowhstite
and stratification of the Earth’s mantle. Science, 257:
1099—1101.
Suzuki, I., 1975. Thermal expansion of periclase and olivine,
and their anharmonic properties. I. Phys. Earth., 23: 145—
159.
Suzuki, I. and Anderson, O.L., 1983. Elasticity and thermal
expansion of a natural garnet up to 1000 K. J. Phys. Earth,
31: 125—138.
Wang, Y., Weidner, D.J., Liebermann, R.C., Liu, X., Ko, I.,
Vaughan, M.T., Zhao, Y., Yeganeh-Haeri, A. and Pacalo,
R.E.G., 1991. Phase transition and thermal expansion of
MgSiO3 perovskite. Science, 251: 410—413.
Wang, Y., Guyot, F. and Liebermann, R.C., 1992. Electron
microscopy of (Mg,Fe)Si03 perovskite: evidence for structural phase transitions and implications for the lower
mantle. J. Geophys. Res., 97: 12327-12347.
Watt, J.P., Davies, G.F. and O’Connel, R.J., 1976. The elastic
properties of composite materials. Rev. Geophys. Space
Phys., 14: 541—563.
Weidner, D.J., Vaughan, MT., Ko, J., Wang, Y., Liu, X.,
Yeganeh-Haeri, A., Pacalo, RE. and Zhao, Y., 1992.
Characterization of stress, pressure, and temperature in
SAM85, a DIA type high pressure apparatus. In: Y. Syono
and M.H. Manghnani (Editors), High Pressure Research
in Mineral Physics. American Geophysical Union, Washington, DC, pp. 13—17.
Yeganeh-Haeri, A., 1993. Elastic properties of several highpressure mantle phases and high temperature Brillouin
spectroscopy. PhD, State University of New York at Stony
Brook, Stony Brook, New York, pp. 160.
Zhao, Y., Weidner, D.J., Parise, J.B. and Cox, D.E., 1993.
Thermal expansion and structural distortion of perovskite
— data for NaMgF3 perovskite. Part I. Phys. Earth Planet.
Inter., 76: 1—16.