JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. Bll, PAGES 25,955-25,968,NOVEMBER 10, 2000
The stability and P-V-T
perovskite in the Earth's
equation of state of CaSiO3
lower mantle
Sang-HeonShim and Thomas S. Duffy
Department of Geosciences,Princeton University, Princeton, New Jersey
Guoyin Shen
GeoSoilEnviro Consortium for Advanced Radiation Sources, University of Chicago
Chicago, Illinois
Abstract.
Energy dispersiveX-ray diffraction measurementsfor polycrystalline
CaSiO3 perovskite were carried out at in situ transition zone and lower mantle
P-T conditions(P=18-96 GPa, T=1238-2419 K) usingthe diamondanvil cell
and double-sidedlaser heating at the GeoSoilEnviro Consortium for Advanced
RadiationSources(GSECARS) sectorof the AdvancedPhoton Source.An analysis
of the temperature error sourcesin laser heating revealsthat the axial and radial
thermal gradients are the greatest error source. We have used measurementswhere
the combinedtemperatureerror (lcy) from all sourcesis •150 K. By obtaining
X-ray diffraction patterns at 8-22 GPa and 300-2200 K range, the high-temperature
phaseboundary between CaSi2Os+Ca2SiO4 and CaSiO3 perovskite was determined
to be 14-16 GPa, in contrastto the resultsof previouslarge-volumepress(LVP)
measurements
(9-11 GPa). The stability of cubicCaSiO3perovskitewasconfirmed
to 2300 km depth in the Earth's interior. No evidence of phase transformation
or break down to oxides was observed. The proposedtetragonal distortion, and
hence the phase transformation from distorted phase to cubic, was not observed.
The combined data set of this study and earlier LVP measurementswas fit to a
Birch-Murnaghan-Debye
equation.By fixingV0- 27.45cm3/mol,KTO-- 236GPa,
and K•0 = 3.9 from recentstaticcompression
data and 00 = 1000K, we obtain
70 = 1.92 4- 0.5 and q = 0.6 + 0.3. Although data to 69 GPa and 2380 K were used
in the fitting, this result is also consistentwith measurementsto 96 GPa. This
result yields not only density and bulk modulus but also higher-order thermoelastic
parameters, such as thermal expansivity and temperature dependence of bulk
modulus, at lower mantle P-T condition in an internally consistentway. This direct
measurement of the equation of state at lower mantle condition verifies that the
density and bulk modulus of CaSiO3 perovskite at lower mantle P-T condition• are
very closeto seismicvalues(within 1.5 and 3.0%, respectively).Thesedifferences
are sufficientlysmall that the abundanceof CaSiO3 perovskite will have negligible
effectson density and bulk modulus profiles for the mantle.
1.
Introduction
al., 1977; Tamaiand ¾agi,1989; Oguriet al., 1997;
Hiroseet al., 1999].
The physical properties and the phase transformaThere have been few detailed studies about the phase
tions of calcium-bearingphasesare important for un- relationshipsin the CaO-SiO2systemat transitionzone
derstanding
the dynamicsandthe evolutionof the man- conditions
[e.g.,Gasparik
et al., 1994;WangandWeid-
tle [Ringwood,
1975;DuffyandAnderson,
1989].In the net,1994].Thestabilityandthephysical
properties
of
transitionzone,calciumis largelyincorporatedinto the CaSiO3perovskite
havenot previously
beenexamined
garnetphaseand transformsbetween580 and 720 km directlyat lowermantleP-T conditions.The stabildepthinto CaSiO3in the perovskitestructure[Mao et ity at lowermantlepressures
wereconfirmedonly at
300K [Tamaiand Yagi,1989;Yagiet al., 1989;TarCopyright 2000 by the American GeophysicalUnion.
Paper number 2000JB900183.
0148-0227/00/2000JB900183509.00
rida and Richer,1989;Mao et al., 1989]. The P-V-T
equationof state (EOS) wasmeasuredusinga largevolumepress(LVP) [WangandWeldnet1994;Wanget
al., 1996].However,
thismeasurement
wasperformed
25,955
25,956
SHIM ET AL.' STABILITY
?
AND P-V-T
I
.½ '
I
'
/4--'Shen
ß
,,'
'
(1995)
I
'
I
'
[] Wang et al. (1996)
ß Shim et al. (2000) _
ß This study
Zerretal.
•
2000
I
and Lazor
•
3OOO
EOS OF CaSiOa PEROVSKITE
(1997)
:•:½ii½i½½
itiii:½½•iaq"':'"'"'""•
unß ß ß
'
Geotherm
-
1 ooo
0
20
40
60
80
100
120
140
Pressure (GPa)
Figure 1. P-T conditionsof this studyfor CaSiO3perovskite.Thoseof other studies[Mao et
al., 1989; Wang et al., 1996; Shim et al., 2000] are alsoplotted for comparison.Mantle P-T
conditionsare from the PreliminaryReferenceEarth Model (PREM) [Dziewonskiand Anderson,
1981]andBrownandShankland
[1981].Meltingcurvesof CaSiO3perovskite
(dash-dotted
lines)
are from $hen andLazor[1995]and Zerr et al. [1997].
at low P-T conditions(P < 12 GPa and T = 300- measurementson CaSiO3 perovskiteat 18-96 GPa and
1600K) and requireslong extrapolationto derivephys- 1238-2419 K, correspondingto the Earth's transition
ical properties, such as density and bulk modulus, at zoneand mostof the lowermantle (Figure 1).
lower mantle
conditions.
Recent new developmentsin the laser heating tech-
niqueswith the diamondanvil cell (DAC) enableus to
2. Experimental
explore the stability and the physical property of ma2.1.
terials directly at the Earth's deep interior conditions
Techniques
Sample Preparation
A naturalwollastonitefromNewburg,New York, was
used as the starting material. X-ray diffraction and
2000]. The improvementin temperaturehomogeneity
in scanningelectron microscopeanalysisof the starting
the heated area opens new opportunity to measurethe material confirmedthat is a pure phasewith only negP-V-T relationshipat extremeP-T conditions[Shim ligibleamounts(<0.1 tool %) of Fe and Mn impurities.
et al., 1998; Fiquet et al., 1998, 2000; Dewaele et al., The wollastonitepowderwas mixed with 10 wt % plat2000;$henet al., 2000]. Shim andDuffy [2000]showed inum powder, which was used as a laser beam absorber
that P-V-T measurementsusing the laser-heated di- and pressurestandard using the EOS of Holmes et al.
amondanvil cell (LHDAC) have the potentialto pro- [1989].
vide not only direct measurementsof density and bulk
A thin (10/•m) foil of the wollastonite-platinum
mixmodulus at lower mantle conditions but also to resolve
ture was loaded in a preindentedstainlesssteel gashigher-order thermoelastic parameters, such as the vol- ket with a 150-/•m-diameterhole and compressed
using
ume dependenceof Grfineisen parameter, temperature 300-/•m diamond anvils for experiments covering 10derivative of bulk modulus. However, they also demon- 70 GPa. For higher pressureswe loaded the foil in a 50strated that temperature inhomogeneitycould result in tim hole in a rhenium gasket. Beveled diamond anvils
systematic error in fitted parameters. This indicates with 100-/•m central fiats were used in this case. A
that the identification
of the error sources in laser heatpressuremedium and insulation layer of either NaC1 or
ing and their effectson EOS fitting is crucial to pursue argonwas loadedtogether with the samplefoil in sucha
[Boehleret al., 1990; $hen et al., 1996; Boehler,1996;
Shen et al., 1998; Fiquet et al., 2000; Dewaele et al.,
P-V-T measurementsand for making further technical
improvement in laser heating. Here we report P-V-T
way that the sample foil was not in direct contact with
the diamond
anvils.
SHIMET AL.. STABILITYANDP-V-T EOSOF CaSiO3
PEROVSKITE
2.2.
X-Ray
Diffraction
0.03
'
I
'
'
'
I
'
'
'
I
'
25,957
'
EnergydispersiveX-ray diffraction(XRD) measurementswere carried out using a tapered undulator source
at the GeoSoilEnviro
Consortium
for Advanced
Radia-
tion Sources(GSECARS) sectorof the AdvancedPhoton Source[Riverset al., 1998].A 10/•mx 10/•m X-ray
beam was used. This small beam size is important to
collect the XRD spectra from an area with a homogeneoustemperature distribution, sincethe flat top of the
temperature profile is typically 20/•m in diameter.
For CaSiO3 perovskite, at least three diffraction lines
werereadily observedto 96 GPa and 2419 K (Figure 2)
and used for unit cell calculation. In most cases, two
diffraction lines were observedfor platinum. However,
at 85-96 GPa the 111 and 200 platinum peaks are overlapped by argon lines. Except in this region, at least
two lines of platinum were usedto calculate its unit cell
parameters.
0.02
0.01
0.00
-0.01
-0.02
,
0
O
300 K
ß
high temperature
, , I , , , I , , , I , , , I , , , I , , I
20
40
60
80
100
120
Pressure(GPa)
Figure 3. Productof elasticanisotropy
and uniaxial
stresscomponent
St for CaSiO3perovskiteat bothhigh
temperatureand 300 K [Shimet al., 2000]. The esti-
matederroris l cr. The hightemperaturedata points
showncorrespondto the pointsin Table 1.
92GPa
I
According
to latticestraintheory[Singh,
1993;Duffy
Ar+Re+Pt
2328K I
I
LAr
o
et al., 1999;Shimet al., 2000],relativeshiftsof individ.
In*
ualdiffraction
linesfora sample
undernonhydrostatic
stress
canbe described
by the differential
stress
t, elastic anisotropyS, andthe angle%0,
betweenthe diamond
cellstress
axisandthenormalto thediffracting
planes:
Pt
a(hkl) -a(hkl*)
NaCI-B2
43GPa[
(go
= -st(-3 os*'
o
1785K]
(1)
•
wherea(hkl) is the calculated
unit-cellparameterfrom
a singlediffractionline, and the asteriskdenotesa refer-
encediffractionline (in thisstudythe 200lineis usedas
.
a reference
for bothCaSiO3perovskite
andplatinum)
and the subscriptzero denotesambient conditions.The
differentialstressor uniaxialstresscomponent
t is the
difference
betweenthe principalstresses
in the axial and
radialdirections
of thediamond
anvilcell. F(hkl)is
22GPa
I
given by
1555K I
'-
Pt
h2k2 + k212+ 12h2
•'''
25
I''
30
''
I '''
35
' I '''
'1
40
45
' '''
Energy (keV)
I ' ' ' ' I ' ' ''
50
55
I
60
+ +
,
(2)
wherehkl are the Miller indicesof an individualdiffraction line. The slopeof a linearfit of the diffractiondata
to Equation(1) yieldsa parameter
that is theproduct
of the elasticanisotropyS andthe uniaxialstresscomFigure 2. X-ray diffractionpatternsof CaSiO3and
ponent
t. The detailsof the methodology
aredescribed
platinumat lowermantleP-T conditions.
The CaSiO3
elsewhere
[Shim
et
al.,
2000].
diffraction
linesare indexed.NaC1or argonwasused
The product St obtained from this fit can be used
as a pressure transmitting and insulation medium. B2
refersto the high-pressure
phaseof NaC1. The fluores- as an indicator
of the stresscondition
of the sample.
cence
linesof indiumandtungsten
(indicated
by aster- At a givenpressure
andtemperature
a largerSt value
isk)arisefromlaserandX-rayoptics.
indicates
a largeruniaxialstresscomponent
t sinceS
25,958
SHIM ET AL.. STABILITY
AND P-V-T
EOS OF CaSiO3 PEROVSKITE
is constant. Heterogeneousstress conditions induce a
range of St values at a given pressureas has been found
a
P = 22 GPa
T = 1633 K
by Shim et aI. [2000]for temperature-quenched
CaSiO3
perovskite samples. In this interpretation, the scatter
of previous static compressiondata points from different experiments at 300 K was explained by variations in
deviatoric
stress conditions.
In order to obtain
an accu-
rate P-V EOS, Shim et al. [2000]selecteddata points
with low St values(IStl _<0.005).
500
The St value of CaSiO3 perovskite at high tempera-
ture is alwayswithin the rangeof-0.005 •-, 0.005 (Fig- E
ure 3). In contrastto the 300 K casewherethe average
St value is +0.012 over the measuredpressurerange, the
St at high temperature has an averagevalue of 0. In ad-
dition, duringheating, a 20-30% decreaseof peak width
is readily observedfor both CaSiO3 perovskite and platinum. These indicate that while significant deviatoric
stressesin CaSiO3 perovskite may exist at room temperature, the stress state at high temperature is more
hydrostatic.
2.3.
Two
1000
-20
0
20
Radial Distance (pm)
Laser Heating
Nd:YLF
laser
beams
were
used to simultane-
ously heat the sampleon both sides. This techniquehas
beendescribedin detail elsewhere[Shenet al., 2000].
2000
The temperature is also measured on both sides inde-
pendently(Figure 4). This designreducesthe thermal
gradient alongthe loading axis of the DAC significantly.
To decreasethe thermal gradient along the radial di-
rection, a TEM0• (TEM: transverseelectromagnetic,
TEM0•: donutshapedmode) lasermodeis usedto provide a large (20-30 /•m) fiat-toppedtemperaturepro-
•E1500
file. The temperature profile acrossthe heated area is
measuredusing a charge-coupledevice with a spatial
resolutionof 1.7/•m (Figure 5).
Before each heating run we carefully alignedthe laser
beamsto the centerof the X-ray position(whichis visi-
1000
-20
X-ray
0
20
Radial Distance (pm)
Figure 5. Temperature profiles for the heated area at
(a) 22 GPa and (b) 92 GPa. To simplifythe diagram,
Insulation•
,':::• •:: /
:•
::.i
i;•iii,
;;i•
Sample
we present binned data for every third point. The two
sidesof the sample are denoted with different symbols.
The X-ray probed area is denoted by dotted lines.
ble dueto X-ray fluorescence)
usinga videomonitoring
Diamond
anvil/
•:;
':½•
I '•:z•:•
•::•:
%
::::•
• •;•:.
%
Thermal
system. The intensity of this diamond fluorescenceis
103-104 times weaker than the thermal radiation.
The temperature is determinedby fitting the meaRadiation
sured spectrum of thermal radiation, which is corrected
for systemresponse,to the Planckequation.Assuming
gray body radiation, we fit emissivityand temperature.
By measuring temperature acrossthe heated area on
both sidesof the sample we obtain information on the
Figure 4. Schematicdiagram of double-sided
laser- three-dimensionaltemperature distribution within the
heated diamond cell geometry.
X-rayed volume. To obtain the temperature of the sam-
SHiM ET AL.: STABILITY AND P-V-T EOS OF CaSiO3PEROVSKITE
pied volume, we assumethat the temperature profile is
axially symmetric, based on the observation of a heated
area with an axially symmetric intensity distribution.
We obtain an averagetemperature of the X-rayed area
by integrating along the radial temperature distribution. The temperature near the edge of the probed area
will contribute more to the average temperature of the
sample due to its larger area. To account for this effect,
we calculatethe averagetemperatureTavg:
Tavg
=
7rR2
,
(3)
where r is the distance from the center of heated area,
T(r) is the temperatureat r, and R is the radiusof Xray probed area. The subscript i denotes each temperature datum along the radial direction. This is identical
to taking a weighted average, and thus the estimated
temperature error can be calculated using the standard
deviation. The estimated error from the Planck equation fitting is also included in the calculation of error.
25,959
sured thermal radiation spectrum also contains some
noise due to the dielectric coating of the laser optics.
The error produced by this noise was determined by
taking upper and lower bounds on slopeswhich define
the noise envelope. This also contributes <20 K to the
temperature uncertainty.
The radial thermal gradient has long been a significant problem in laser heating. Our approach is to improve temperature homogeneityby both decreasingthe
X-ray beam size and increasingthe heated area. The
former can be readily achievedwith a third generation
synchrotronsource, and the latter is achievedby us-
ing a higher-modelaserbeam,e.g.,TEM01 [$henet aI.,
000].
The radial gradient is still a major problem if there is
misalignmentbetween the heated area and X-ray probe
area. For example, a 20-/•m misalignment could result
in 200 K uncertainty(seeFigure $). Furthermore,inho-
mogeneousdistribution of absorption material could result in a situation where only part of the sample couples
to the laser. In this case, the XRD pattern is obtained
More detailed informationcan be found elsewhere(A. from material at a range of temperatures. By using
Kavner et al., manuscriptin preparation,2000).
submicron-sizedplatinum we can make a very homogeSince we measure the temperature profile on both neous mixture and so minimize this problem.
sides, we directly calculate the thermal gradient along
The axial thermal gradient is another important erthe stress axis of the DAC. To obtain the temper- ror source. While decreasingthe sample thicknessmay
ature for the probed volume, the temperatures from help to reduce this problem, this results in a poorer Xboth sides are averaged. We typically heat the sample ray diffraction pattern. When single-sidedheating is
for 3 min or more while collecting a single XRD spec- used and temperature is measured from both sides of
trum. During this time, at least three pairs of ther- the sample, the maximum axial thermal gradient was
mal radiation spectra are collected. These were used to 200 K or more [,..qhen
et aI., 2000]. If an insulationmadetect time-dependent temperature fluctuations during terial is not used and the sample directly touches the
the XRD
measurement.
Including all sources of uncertainty, the estimated
diamond anvils, the axial temperature problem may be
even more severe due to high thermal conductivity of
random
errorinsample
temperature,
cr(Tsample),
was diamond. Systematicerror due to the axial gradient
calculated
from
in single-sidedheating can lead to overestimation of
higher-order thermoelastic terms in the P-V-T EOS
2
fit [ShimandDuffy,2000].
cr
(Tsample)2
- 22
1• (T[Ti]
-2q-if[T1,
r2]
2
In order to obtain a high-quality XRD pattern the
sample must be heated for a sufficient period of time
i=1
1
+7
2
(typicallya few minutes).The temperatureshouldnot
i=1
(4) changevery much during this interval. For most of our
where a is the estimated error, T is temperature, and
runs, the temperature fluctuation over the data collection time was <50
K.
T(t) is the time variationof temperature. The subscript
As a furthertest, we performedtwo differenttemperi denotesthe two sidesof the sample. In (4), the first ature profile calculationsand comparedthese for each
term includes the error from radial thermal gradient temperature measurement. The first is calculated by
for each side of the sample, the secondterm is the error fitting the data to Planck equation as describedabove.
from the axial thermal gradient, and the third term is In thesecond
case,weusethe following
relationship
bethe error from time variation of temperature on each tween radiation intensity I and temperature for blackside. This treatment is expected to give more reliable body radiation:
averagetemperature than simply taking the peak temI -- 5rrT4,
(5)
perature, which has o•en been usedin previous studies.
We used thermal radiation measuredover the range where s is the total emissivity and cr is the Stefan670-830 nm to fit the Planck equation. If we fit a differ- Boltzmann constant. Using the peak temperature ob-
ent wavelengthrange (for example,dividing the range tained from the Planck fit and the measuredintensity
into halvesor quartersand perform separatefits), the at the central peak temperature,we calculatethe protemperature difference does not exceed 20 K. The mea- portionality factor. Assuming that this factor is con-
25,960
SHIM
ET AL.: STABILITY
AND
P-V-T
EOS OF CaSiOa PEROVSKITE
stant, we then usethe measuredintensityto calculate
temperatureawayfromthe hot spot(A. Kavneret al.,
manuscriptin preparation,2000). For data analysiswe
selectedonly thosedata points for which there is no
I
25OO
significantdifferencebetweenthe temperatureprofile
calculatedby this methodand the temperatureprofile
obtainedby fitting to the Planck equation.
The importanceof the thermalpressure
effectin LHDAC has been extensivelydiscussed[Heinz, 1990; Fi-
2OOO
'
'
'
'
I
'
'
I-owithout
CaPv II
I-e- withCaPv
'
'
I
'
'
o
'
'
I
'
quetet al., 1996;Dewaeleet al., 1998;Andraultet al.,
1998].We account
for changes
in pressure
duringheatingby measuring
the diffractionlineof an internalstan- Idard,platinum,at hightemperature
andusetheP-V-T
EOS of Pt [Holmeset al., 1989]for pressure
determination. The pressuregenerallychangesby 5-10 GPa
duringheating,whichshowsthe importanceof in situ
pressure
measurement.
While the total changein pressureduringheatingis typically10-20%,we observed
that the pressuremay either increaseor decrease
dur-
'
'
I
.•..,,•This
study
-
_Ca2SiO4+
I(9
CaPv+løwPphasel
/ /I/.•/ /'Pe
/
Perovskite
CaSi2Os
__•,
•
'
-
1500
TamaiandYagi---•/[: •
(1989)
1000
500
Wangand
l:
I
--;./-I
I
/ I
I
Weidner
(19941
/•' I ! Ir
Gaskparik•,//!l
/I
? /
/ I/
/
/ / I/
etal'(19947//
t /
,,,,
5
, , , , ,
10
15
20
25
Pressure (GPa)
ing heating.
Sincethe pressureat elevatedtemperatureis describedby the sumof a static pressureat 300 K and
thermalpressure,
oneneedsto propagateboththe temperatureerrorandvolumeerrorinto the pressure
term.
The estimated pressureerror is
+ 57
Figure 6. Phasediagramof CaSiO3. The four separate heatingruns are denotedwith numbers.Open
andsolidsymbols
represent
samples
withoutandwith
CaSiO3perovskite(CaPv), respectively.The starting
assemblages
of CaSiO3 perovskiteand lower-pressure
phases
(thiscoexistence
is dueto incomplete
transformationby shorttestheating)isshownbytheopencircle
with a plus. The proposedphaseboundariesbetween
Ca2SiO•+CaSi205and CaSiO3perovskiteare plotted.
whererr[V(Pt)] is the estimatedvolumeerror for platinumanda(T) is the estimatedtemperatureerror (equation (4)).
Ca2SiO4 diffraction lines were observed not only at
the heated spot but also 20/•m away from the heated
3.
Results
3.1.
and
Low-Pressure
of CaSiO3
Discussion
Phase Boundary
Perovskite
The phase diagram of the CaSiO3 system has been
spot. Consideringthe thermal gradient(10-50 K//•m),
it seemsthat •-Ca2SiO4 can form at fairly low tempera-
ture (about 1000K). The X-ray exposuretime required
to detect the •-Ca2SiO4 peaks was 30 min. So the absenceof the peak at high temperature may be caused
studied by the LVP technique[Wang and Weidner, by insufficientexposuretime (i.e., 3 min).
The second heating run was performed starting at
1994; Gaspariket al., 1994]. Thesemeasurements
reported that the •-Ca2SiO4+CaSi205 assemblage,
which
is disproportionated from walstromite-type CaSiO3,
transforms to CaSiO3 perovskite at 9-11 GPa at high
temperature. In order to verify the proposed phase
boundary, four heating runs covering 8-22 GPa and
300-2200 K were performed(Figure 6).
The sample was compressedwithout heating to 10.4
GPa, and wollastonite persistsmetastably to this pressure. Upon heating to 1670-1820 K, no diffraction except platinum lines was observedat high P-T. According to previous studies the P-T conditions are closeto
the walstromite-/•-Ca2SiO4 + CaSi205 phase bound-
12.1 GPa. At high temperature, relatively strongdiffraction lines were observed which can be identified
as those
of a Ca2SiO4 phase. Five polymorphs have been reported for this stoichiometry at ambient pressureand
!
hightemperature,i.e., "/, •, •L, •7, and • in orderof
increasingtemperature. Although the detailed structure of some of these phases is still controversial due
to their nonquenchable nature, the powder XRD patterns are well known. Using the proposedcrystal structures, we calculated XRD patterns for these phases,"/
[Mummeet al., 1995],• [Jostet al., 1977],c•[ [II'inets
and Bikbau,1990],c•/ [Mummeet al., 1995],and c•
in the XRD
ary. Walstromite[Trojer, 1969], /•-Ca2SiO4[Jost et [Eyseland Hahn, 1970]. The differences
al., 1977], and CaSi205 [Angel et al., 1996] have low patterns are very small due to the subtledifferencesbesymmetry (triclinic, monoclinic, and triclinic, respec- tween the structures. However, one diffraction line at
tively). The weak expected diffraction intensity due 2.0• isstrong
forthehigh-temperature
phases
(c• and
to low symmetry may be responsible for the lack of
observeddiffraction peaks. However, after quench, •-
c•/) compared
to lower-temperature
phases(-/and •).
Indeed, in our experiment this peak is observedonly
SHIM ET AL.: STABILITY AND P-V-T
EOS OF CaSiO3 PEROVSKITE
25,961
at high temperature. Furthermore, Wang and Weidner would like to stress that our observation is based on in
[1994]reporteda phasetransformation
from/• to c• at
situ XRD
measurements.
Kanzaki et al. [1991] reported the P-T conditions
9 GPa and 1350 K. Thus, this phase can be identified
as the c•• phase. However, the subtle differencebetween of the synthesisof various calcium silicate phasesus-
c• and c• preventsus from differentiatingbetween ing the LVP. A glasswas observedafter quenchfrom
those structures. As shown in Figure 6, this run covers 15 GPa and 1800 K, which they identified as a quench
P-T conditions which were reported as in the stability product of CaSiO3 perovskite. Using the LHDAC,
field of CaSiO3 perovskite instead of Ca2SiO4 by LVP Tamai and Yagi [1989]synthesized
CaSiO3perovskite
measurements.
at _P> 13.8 GPa, suggestinga boundary that is inter-
After quench,the 2-• line disappears
but other
mediate
between this and other studies.
Although we do not have a P-T path that directly
phaselines were observed. At 20 /•m away from the
crosses
the phase boundary, the high P-T data points
heated area, we could find the peaks which can be idenconstrain
the phase boundary to within :k2 GPa. In
tified as those of titanite-type CaSi•.O5[Angel et al.,
contrast
to
the previousLVP study, our result is based
1996]as well as thoseof/•-Ca2SiO4.
on
observation
during pressureincrease. Thus, the kiA previously unheated spot containing walstromitenetics
of
the
transformation
from CaSiO3 perovskite to
type CaSiO3 was found after further compressionto
Ca2SiO4+CaSi205
cannot
affect
our observation. The
17.9 GPa. Before the heating run we exposedthe samnature
of
the
transformation
from
Ca2SiO4+CaSi205
ple to the laser for 30 s to test laser coupling and
to
CaSiO3
perovskite
is
not
well
known.
However, in
X-ray-laser alignment. Immediately after this operruns
3
and
4
where
we
start
from
the
low-pressure
ation, strong CaSiO3 perovskite lines appeared. We
rapid transformationfrom Ca2SiO4qperformeda third heating run at this spot. At high phaseassemblage,
CaSi205
to
CaSiO3
perovskite was observed. So it is
temperature the CaSiO3 perovskitediffraction lines are
likely
that
this
transformation
may be lessaffectedby
clearly observed.All obtained peaks are assignedto either CaSiO3 perovskiteor platinum. One more heating kinetic effects. Strictly speaking, however, the phase
run at 19.2 GPa was performed at an area that had not boundarydeterminedby this study is an upper bound.
been directly heated previouslyand which contained
Ca2SiO4 peaks. Only CaSiO3 perovskite and platinum
3.2. Stability of CaSiO3 Perovskite
peaks were observedfor this run.
at Lower
Mantle
Conditions
The P-T conditions of these observations are plot-
ted in Figure 6. The Ca2SiO4+CaSi205 assemblageis
stable to 15 GPa, and the phase boundary to CaSiO3
perovskite lies between 15 and 17 GPa. In contrast,
previousLVP studies reported the phase boundary at
much lower pressure, 9-12 GPa. Wang and Weid-
net [1994] observedthe phase boundary in situ by
XRD at high P-T usingLVP. They initially synthesized
CaSiO3 perovskite at high P-T and then decreased
the pressureat a fixed temperature. The growth of
the Ca2SiO4+CaSi205 assemblageat the expense of
CaSiO3 perovskite was used as a criterion to determine the boundary. They observedthat the perovskite
phasediminishesafter 20 rain of heating at (10 GPa
and 1300 K, which means that this reaction is sluggish. Indeed,CaSiO3perovskitepersistsdownto I GPa
at 300 K. Although the metastable persistencewill
be weaker at high temperature, Wang and Weidner's
The stability of CaSiO• perovskite has been con-
firmedto lowermantle pressuresat 300 K [Tamai and
¾agi, 1989; ¾agi et al., 1989; Tarrida and Richet, 1989;
Mao et al., 1989;Shim et al., 2000]. However,the stability has never been studied directly at lower mantle
P-T conditions. We measured the XRD patterns at
in situ lower mantle conditions(18 ( P ( 96 GPa,
1238 • T ( 2419 K, Figure 1). CaSiO3 perovskite
diffraction lines were readily observed in all of our
runs (Figure 2). No peak splittingor new peakswere
found. This indicates that CaSiO• perovskite is stable
to 2300 km depth in the Earth's interior.
Stixrudeet al. [1996]proposeda tetragonaldistortion
of CaSiO• perovskite over the entire mantle pressure
range at the ground state basedon first principles calculations. The fact that the expected peak splitting from
the distortion has never been reported at lower mantle
[1994]observation
mayindicatethat theirtemperature pressuresat 300 K was attributed to the low resolu-
wastoo low (T ( 1600K) to overcome
the energybar- tion of the energydispersiveX-ray diffraction(EDXD)
rier from CaSiO3perovskiteto the Ca2SiO4+CaSi205
assemblage,
sothat CaSiO3perovskite
may be ableto
survivemetastablyin the Ca2SiO4+CaSi205stability
fieldin their experiment.Thustheir boundaryshould
be considered as a lower bound.
technique. On the basis of the assumptionthat CaSiO•
perovskite is tetragonally distorted at 300 K, the phase
transformation to cubic is predicted to be 2200 K at
80 GPa [Stixrudeet al., 1996].
No evidence of distortion and hence the phase trans-
A quenchexperiment
usingthe LVP wasperformed formation to cubic was detected at 300 K in a related
by Gasparik
et al. [1994].As shownin Figure6, their study [Shim et al., 2000] and at high temperatureby
phaseboundary
issimilarto thatof WangandWeidner this study. However, calculated XRD patterns show
[1994]but4-5 GPalowerthanthisstudy.The reason that the peaksplittingby the proposeddistortion(0.7%
for the discrepancy
with this studyis not clear,but we changeof c/a ratio at 300 K) may be very closeto or
25,962
SHIM ET AL.: STABILITY
AND P-V-T
below the resolution limit of EDXD. Increasing temper-
EOS OF CaSiO3 PEROVSKITE
The Griineisenparameter is assumedto be a function
ature is expectedto decreasethis distortion[$tizrude of volume only:
et al., 1996].Thus,althoughwe observed
a 20-30%decreasein peak width at high temperature, the splitting
'= 3'0
,
(11)
may still not be detectable if the distortion is significantly lower than at 300 K. However,the magnitude
whereq is assumedto be constant. The Debyetemperof the proposeddistortion (0.7% changeof ½/a ratio) ature can also be described as a function of volume:
is smaller than the estimated
volume error.
Thus it is
expected that, even if exists, this distortion does not
affect the P-V-T EOS fitting result. Higher-resolution
q
techniques,such as angle-dispersiveX-ray diffraction,
are need to further investigate the proposeddistortion. In this approach,the fitted parameters are V0, K•0,
•=•0exp/'ø'(V)
)
ß
3.3. P-V-T
Equation
of CaSiO3 Perovskite
of State
(12)
K•0, '0, q, and 00.
This EOS has the advantage that it yields higherorder thermoelastic terms in an internally consistent
1990;JacksonandRigP-V-T measurements for CaSiO3 perovskite have way [StixrudeandBulkowinski,
onlybeencarriedout below12 GPa [Wanget al., 1996] den, 1996]. The first three terms (Vo,KTo,K•o)are
where the material is metastable. A long extrapolation
is thus required to apply the results to the lower mantle. Furthermore, the limited P-T coverageprecludes
constraints on higher-order thermoelastic parameters.
obtained from 300 K data. It has been shown that q
In this study,we usedP,V,T data pointsat 20-69 GPa
be better constrained. The EOS is not sensitive to the
and 1272-2380
choice of 00.
K.
Accordingto Mie-Griineisen theory the total pressure
cannotbe well-constrained
with LVP data alone[Jacksonand Rigden,1996]. Shim and Duffy [2000]found
that the increasedP-T range of DAC data allowsq to
Sincethe thermal gradientsare the major sourceof
Ptot(V,T) at a givenvolumeand temperaturecan be error, we useonly data points which have averagetemexpressedas a sum of static compressionat a reference peraturesfromequation(4) with an estimatedstandard
temperature
Pst(V,T0) andthe thermalpressure
•Pth deviationof <150 K. These data points are listed in Table 1. Including data points with greater temperature
variation does not systematically affect the result, but
Ptot(V,T) =Pst (V,T0)+ APth(V,T).
(7) it increasesthe residual of the fit. Although the PFor the static pressureterm the Birch-Murnaghanequa- V-T measurementswere performed to 96 GPa at high
tion is used.
temperature, sincethe platinum peakswere overlapped
The Debye model can be used to describethermal by argon diffraction lines near megabar pressures,the
pressure
term in (7). Indeed,it hasbeensuggested
that calculatedpressureshave large uncertainties. Although
the Debye model is a good approximationfor MgSiOa we do not usethese points in the fit, they are consistent
perovskiteand MgO [Anderson,1998].We expectthat with lower P-T data points.
Since CaSiO3 perovskite is unstable at ambient Pthe Debyeassumptionshouldbe reasonablefor CaSiO3
perovskiteas it has high symmetry and a close-packed T conditions, there is no direct measurement of V0
and no elasticity measurementsat ambient conditions.
structure.With this model,the termsin (7) are
DAC measurementshave been performed to 130 GPa at
to the temperature T at a given volume V:
300K [Tamaiand Yagi,1989; Yagiet al., 1989;Tarrida
and Richer,1989;Mao et al., 1989].Fitting thesedata
to (8) yieldsKT0 = 280 GPa, assuming
K•,0 = 4. However, LVP measurements
[Wang et al., 1996],systematicsin the CaTiO3-CaSiO3system[Sinelnikovet al.,
1998],andfirst principlecalculations
[Karki and Crain,
1998]all suggestthat the bulk modulusmay be smaller
(230-245GPa). Indeed,Shim et al. [2000]foundthat
.{1-•(4-K•0)
•(•)2/3-1]}
(8)
APth
_ 7(V)
[&h(V,
T)- Eth(V,
T0)]
(9)
V
'
whereKz0 is the isothermalbulk modulus,K½0is its
the previous DAC measurementsare significantly contaminated by nonhydrostatic stress,so that they yield
higher /fT0. By monitoring the St value, Shim et al.
pressurederivative, and • is the Grfineisenparameter.
The subscript zero denotes ambient conditions. The
vibrational energy can be calculated from the Debye [2000]was able to characterizethe stressconditionof
sampleat high pressure. Their static compressionresult
model,
9nRT
Eth- (O/T)
3fo/r
•o e••'
is usedin this study (Table 2).
The Debye temperature 00 is normally constrained
by calorimetric measurements. However, owing to the
The Debyetemperatureis givenby 0, n is the numberof instability of CaSiO3 perovskite at ambient conditions,
atoms in a formula unit, and the R is the gas constant. this quantity has not been measured. For MgSiO3 per-
SHIM ET AL.: STABILITY AND P-V-T EOS OF CaSiOsPEROVSKITE
25,963
Table 1. CaSiO3Data Usedin P-V-T EOS Fittinga
Experiment 1, NaC1
Experiments 2-4, Ar
P, GPa
V, A •
T, K
P, GPa
V, A •
T, K
35.5(7)
35.2(7)
35.5(8)
35.9(7)
34.8(7)
34.8(7)
36.1(8)
35.4(9)
35.8(7)
42.8(10)
43.4(9)
42.3(10)
46.6(11)
46.3(21)
47.2(11)
47.4(11)
47.2(12)
41.599(62)
41.648(29)
41.658(36)
41.785(17)
41.855(22)
41.919(21)
41.813(40)
41.789(43)
41.843(8)
40.965(43)
41.010(34)
41.096(97)
40.438(39)
40.338(60)
40.309(71)
40.396(94)
40.431(58)
1416(54)
1410(54)
1450(60)
1592(44)
1733(49)
1687(51)
1648(41)
1640(41)
1625(55)
1669(31)
1785(66)
1993(73)
1485(46)
1589(35)
1493(51)
1520(45)
1585(50)
24.3(12)
25.0(10)
24.6(9)
23.6(6)
21.9(16)
22.4(7)
21.6(8)
67.4(24)
68.4(23)
68.5(24)
67.2(23)
22.0(4)
21.7(7)
20.6(5)
21.0(7)
56.2(16)
64.3(20)
43.311(13)
43.287(29)
43.447(30)
43.408(25)
43.418(74)
43.434(48)
43.467(37)
38.261(57)
38.203(25)
38.168(25)
38.058(60)
43.658(64)
43.662(14)
43.543(9)
43.569(33)
39.992(67)
38.515(83)
1808(141)
1756(144)
1788(89)
1686(59)
1555(117)
1633(78)
1539(80)
1652(24)
1533(40)
1410(17)
1272(28)
1488(45)
1668(62)
1511(62)
1365(54)
2380(67)
1752(116)
•The numberin parentheses
is theestimated
uncertainty
(let).
ovskiteit hasbeenmeasured
to be 1000K [Akaogiand '0 = 1.92 + 0.05 and q = 0.6 + 0.3. This result is proIto, 1993].We assumeherethat •o of CaSiO3perovskite jected on to the P-T plane is in Figure 7. The residual
is the same as for MgSiO3 perovskite.
of fit is also shownin Figure 8. Sincethe residual is ran-
By fixing Vo, KTO, K•o, and •o, only two param- domly distributed around zero, it is likely that terms of
eters, '0 and q, are fit using the Birch-Murnaghan- higher order than q, such as volume dependenceof q
Debye(BMD) equation(equation(7)-(12)) and data itself, are not resolvableby this study.
Table 2 comparesthe EOS parametersfrom the study
shownin Table 1. No weightingwas used. As shownin
previoussimulationsof P-V-T data [Shimand Duffy, with thoseof Wanget al. [1996]andresultsfor MgSiOs
2000], 'o is mainly constrainedby low-pressureand perovskite[Jacksonand Rigden,1996; Fiquet et al.,
high-temperaturedata points and q by high-pressure 2000]. The fits to the BMD equationwere alsoperand high-temperaturedata points. For this reason, formed for the individual data sets. The LVP data
we combinedour data with the LVP data [Wang et [Wanget al., 1996]aloneyields70 = 1.74:[:0.17 and
al., 1996]. The fit for the combineddata set yields q - -3.5 + 4.9. Here '•0 is marginally consistentwith
Table 2. Thermoelastic
Parametersfor CaSiO3Perovskite
a
CaSiOsPerovskite
Parameter
ThisStudy
Wang
MgSiOsPerovskite
Jackson Fiquet
Vo,cm3 mo1-1
27.45(2)
27.45(2)
24.43
24.43
K•-o, GPa
236(4)
232(8)
262
259.5(9)
K•,o
3.9(2)
4.8(3)
4.0b
3.69(4)
'o
1.92(5)
1.7c
1.33
1.4c
q
0.6(3)
1.0
b
1.0
b
1.4(5)
0o,K
1000
b
1100
b
1000
b
1100
b
ao, 10-5 K-x
(dKT/dT)p,GPaK-x
2.2(3)
3.0(5)
-0.028(11) -0.033(8)
1.57
-0.021
2.18(12)
-0.017(2)
6•,
5.2(21)
5.2
5.6d
4.8c
•The numberin parentheses
is the estimateduncertainty(let). The thermoelasticparameters
for CaSiOsperovskite
are from Wanget al. [1996]and the
thermoelastic
parametersfor MgSiOsperovskiteare from Jacksonand Rigden
[1996]and Fiquetet al. [2000].
bAssumed value.
CInferred
value.
aDerived
fromtheparameters
givenby Fiquetet al. [2000].
25,964
SHIM ET AL.' STABILITY
AND P-V-T
EOS OF CaSiOa PEROVSKITE
25OO
+ o Thi•;st.u'dy
:
[]
:
.'
.
Wcng
.etalv.'(1996
) ..
0
,
,
,
,
0
,
.
.
,
,
,
,
2000
,
" " 43;'51'•L43•45
,' ,'141
01,' '
,. ',.,4366?.•0,•...
•,.•.•
'T ' ,':
"
I, I Iik3,.41 ,T 41,a•__.'
.'
,'
',
.'
' [] ,'
.' III .'
41.78•' ' .'40431140
34
"
'
:
: '-"'•-4;40
., 43.•,4
• •3'66
,' 36.31
'
"40'31.1•0
•'4
ø
..........,."
.•..•
."
'•.";,!i•¾•F•,.•;•
-rr..'
'
IOO0
5OO
.' 43',42"4=J•3.47
.' T
,'
,'
1500
."36.38
_46
r•41-•44 .'43 :"42 :"41 :'40
;,
,'
, '
0
•
20
',
, '
[
I'
40
,
,'
.'39
,
I
.'38
'
.,
,
,'1
60
I
lOO
Pressure (GPa)
Figure 7. P-V-T data for CaSiO3 perovskite projected on the P-T plane. Isochronsfrom the
best fitting BMD equation are plotted for comparison. The measured volume of each point is
listed next to the point. The error bars denotethe estimateduncertainty(let). High-pressure
data points(opencircles)werenot usedin the fit.
the above result within the uncertainty,and q is not
constrainedin this case, consistentwith expectations
basedon the simulationsof Shim and Duffy [2000].A
fit to our P,T data points aloneyields7o - 2.00 + 0.08
and q - 0.9 + 0.4, which agreeswith the above result
within the uncertainty. Interestingly,the BMD fit for
the LVP data set for CaSiO3 perovskite doesnot constrain % as well as for MgSiO3 perovskite data set. This
is causedby the fact that the high-temperaturerun for
a-
(,r - ,..
(x3)
where a is the anharmonicity and a is the thermal ex-
pansivity. Assuming7o from the LVP data set represents%p and 7o from this data set represents70T,
the parameter a0 can be estimated to be 0.5 •,, 0.8 x
10-5 t(-1 Thisvalueis onlya roughestimate,because the volume variation
in the LVP
data is con-
trolled nearly equally by both pressureand temperCaSiO3 perovskitewas performed over a narrow pres- ature so a0 may be underestimated. The a0 value
surerange(1-12 GPa), as shownin Figure 7, and the has also been measured by vibrational spectroscopy
the
temperature range is smaller than that of the MgSiO3 [Cillet et al., 1998]. In vibrationalspectroscopy
value
can
be
measured
for
individual
modes,
but
our
perovskitedata set (T _<2000 K). Our LHDAC data
for CaSiO3 perovskiteby itself yields a good constrain value would be consideredas a weightedaverageof all
modes. Since the weighting schemeis not well known,
for % as well as for q.
As shown in Figure 7, the total volume variation of it is difficult to compareour value to vibrational specthe LVP data is controlled by pressureand tempera- troscopyresults directly. However, our value is slightly
ture by nearly equal amounts. However,it is the pres- smaller than those of spectroscopyresults for other
mantlesilicates:
0 -,• -5.9 x 10-5 K-1 for/•-Mg2SiO4
[Reynard
et
al.,
1996],-0.5 •,, -6.0 x 10-5 K-1 for
•12% of the volume changeis by pressureand 2%
forsterite
[Gillet
et
al., 1997],0.9 •,, -2.6 x 10-5 K-1
by temperature. Thus the temperature contribution
for
ilmenite-type
MgSiO3
[ReynardandRubie,1996],
is more dominant in the LVP data set than the LHsure that controls the volume variation
in our data set'
DAC data set and the pressurecontribution is dominant
for LHDAC. In the quasi-harmonicassumptionthe
and0 • -10 x 10-5 K-• forMgSiOa
perovskite
[Gillet
Grfineisen parameter and its volume variation should
be the same regardlessof whether measuredunder iso-
of pressureand temperature, direct measurementof the
anharmoniceffect has been performed for MgSiO3 per-
et al., 1996]. From Raman measurements
as a function
that
baric (denotedas '7P and qp) or isothermal(denoted ovskite[Gillet et al., 2000]. It was alsoobserved
as 7T and qT) conditions[Gillet et al., 1998].The dif- the anharmonicity is small at lower mantle conditions.
ference between these parameters can be attributed to
These observationssupport the useof a harmonic model
anharmonic
for lower mantle
effects'
constituents.
SHIM ET AL.' STABILITY AND P-V-T EOS OF CaSiO3 PEROVSKITE
25,965
4
0
20
40
60
80
100
Pressure (GPa)
Figure 8. Residual of P-V-T
EOS fit for CaSiO3 perovskite. The error bars denote estimated
uncertainty(la). Solidcirclesare presentdata usedin the fitting. Open circlesand squaresshow
highest pressuredata that were not used in the fitting.
We also performed a weighted fit on the combined measuredunder the same experimental conditions, and
data set usingweightscalculatedfrom the estimatedun- it was demonstrated that deviatoric stresses are minicertaintiesfor pressure,volume, and temperature. The mal. Thus the resultsobtained by fixing the static comresultin this caseis •/0 - 1.885:0.21 and q = 0.3 5: 2.2. pression
term to that of Shimet al. [2000]areinternally
As shownby Shim and Duffy [2000],the lower P-T
measurements control the fit due to their low estimated
errorsfor P,V,T. Thus the volumedependenceterm q
cannot
be constrained.
consistent.
Wang et al. [1996]useda high-temperatureBirchMurnaghan equation and polynomial expansion for the
thermal pressure to fit their LVP data. However, the
limited P-T range does not allow constraints to be
Above 90 GPa, we have two data points that are
not usedin the fitting due to the large uncertaintyin placedon higher-orderterms. For example,(OKT/OT)p
measured pressure. If those are included in the com-
was not resolved directly in their EOS fit.
bineddata set, the resultbecomes•/0 = 1.955:0.04 and
q = 0.9 5: 0.2, which yields a larger q but one that is
within mutual uncertainties.Includingthesepointsexpandsthe pressurerangeby 30% and hencethey have
a more significanteffect on q than data points at lower
Instead,
-0.028
(dKT/dT)
P
pressure.
Earlier DAC and LVP measurements
reportedmuch
-0.032
differentstatic compressioncurvesfor this material. As
discussed
by ShimandDuffy [2000],the reference
static
compressioncurve at 300 K has a strong effect on the
value of q. We performed a P-V-T EOS fit for the
combineddata set by fixing the static compression
term
to that of Wanget al. [1996](Table 2). As dscussd
above,the compression
curveof earlierstudies[Tamai
and Yagi, 1989; Yagi et al., 1989; Mao et al., 1989;
Tartida and Richer,1989]are essentiallythe sameas
that of Wang et al. [1996]at large compressions.A
-0.036
1•''''
0
I.....Wang
etal.(1996)
•'''
20
i ......
40
60
-0
-0.040
i,,,
80
I,
1O0
,-';"1'",...,
....
120
140
Pressure(GPa)
significantlydifferent result was obtained for the fitted
Figure 9. Thermal expansivity• and temperature deparametersin this case,especiallyfor q: '7 = 2.06 q-0.05 pendenceof bulk modulus,(OKT/OT)p, at lowermanand q = 2.6 + 0.3. This wouldindicatea significantvol- tle pressuresand 2500 K. For comparison,curvescalcu-
umedependence
of the thermal pressure.In this study, lated from the preferredparameterset by Wang et al.
the data set at 300 K and high temperature were both [1996]are alsopresented.
25,966
SHIM ET AL.. STABILITY
AND P-V-T
700
6.0
EOS OF CaSiO3 PEROVSKITE
discrepancies,3.6-4.0 and 1.3-2.7, respectively. Here
PREM
we presentthe result by Jacksonand Rigden[1996],
which assumesq - 1, and the LHDAC result by Fiquet
et al. [2000]. SignificantdifferencesbetweenCaSiOa
This study
Wang et al. (1996)
600 •
,._.
_•-.
5.5
KS
500
perovskiteand MgSiO3 perovskite can be found for the
bulk modulus and Grfineisen parameter.
Profiles of density p and adiabatic bulk modulus Ks
were calculated using the B MD equation at lower man-
•'
tle P-T conditions(Figure 10) and comparedwith the
seismic
modelPREM [Dziewonski
andAnderson,1981].
o
Lower mantle temperatures were taken from Brown and
Shankland[1981].The densityand adiabaticbulk mod400 •
5.0
ulus of CaSiOa perovskiteare very closeto that of the
lower mantle: 3% greater for the adiabatic bulk modulus but indistinguishablewithin estimated error and
1.5% greater for density. However, the bulk modulus
reportedby Wang et al. [1996]is significantlyhigher
than that of PREM (6.5-13.5%).
3OO
4.
Conclusion
4.5
40
60
80
100
120
Pressure (GPa)
Figure 10. Density and adiabaticbulk modulusof
CaSiO3perovskiteat lowermantle P-T conditionscalculatedusingthe parametersof this study(solidlines)
and Wanget al. {1996](dottedlines)togetherwith the
BMD equation. Seismicdata (PREM) are shownas
Recent improvements in the laser heated diamond
anvil cell (LHDAC) techniqueopen up new opportunities to measure material properties at the conditions
of the deep interior of the Earth. The phase boundary betweenCa2SiO4+CaSi205and CaSiOaperovskite
was found by in situ measurementsto lie at 14-16 GPa
in contrastto earlier large-volumepress(LVP) results
solid circles. The error bars for this study denote the
which reported 9-11 GPa. This work demonstratesthat
estimateduncertainty(lcr) calculatedfrom Table2.
the LHDAC
can be used for in situ determination
of
phase boundaries.
The stability of cubic CaSiOa perovskitewas demonstratedto 2200 km depth (96 GPa). No evidenceof a
by interpolating data points to isochoricand isobaric phasetransformation such as tetragonal distortion or
conditionsthey obtained this parameter as well as
breakdownto oxideswas observed.However,a very
Other parameters were then derived from these. To smalltetragonaldistortion(c/a ratio change<0.7%)
comparewith our results, we list their preferred param- wouldnot be detectableby this work. Sincethe magnieters in Table
2.
Usingthe BMD results,cr and (d/•T/dT)? were determined at 1 bar and 300 K (Table 2) and for 0120 GPa and 2500 K (Figure 9) using the valuesin
Table 2 and the equationsgiven by Jacksonand Rigden
[1996].
At 1 bar and 300 K, (014T/OT)? is consistent
for both
tude of distortion is smaller than the estimated volume
error of this study, even if it exists, our EOS fit result
may not be affectedsignificantly.
In this study,energydispersiveX-ray diffractionmeasurementswere performed directly at lower mantle PT conditions. Data covering 20-69 GPa and 12722380 K as well as 16-105
GPa at 300 K were com-
studies, but the present a0 is significantly lower than binedwith data of Wanget al. [1996](P =0-12 GPa,
that of Wang et al. [1996]. SinceCaSiOa perovskite :r =300-1600K) andfit to the Birch-Murnaghan-Debye
is unstable at ambient conditions, direct measurement (BMD) equation. Only data showinghomogeneous
of ao is not possible. This value from both studies is temperatures,small thermal gradient, and hydrostatic
basicallya projection of high P-T data to ambient con- stressconditionswere used in the fitting. The comditions. The calculationsof a and (OKT/OT)p at high plete set of thermoelasticparameters are V0 = 27.45 +
pressureand 2500 K (Figure 9) showthat our 70 and
0.02mol/cm
2, KTO= 236+ 4 GPa,/•0 = 3.9+ 0.2,
yields smallertemperature sensitivityof bulk modulus % = 1.92 q- 0.05, q = 0.6 q- 0.3. Using this equaand larger temperature sensitivityof densitythan those tion, we calculate not only the density and bulk modof Wanget al. [1996]at lowermantleconditions.
ulus but also higher-orderthermoelastic
terms (e.g.,
The thermoelastic parameters of CaSiO3 perovskite (OKT/OT)p, c•) at lowermantleP-T conditions
(Figare also compared with those of MgSiO3 perovskite in ure 9).
Table 2. Unfortunately,K•o and q of MgSiO3 per-
In contrastto previousresults,both the densityand
ovskite from currently available data show significant bulk modulusof CaSiOa perovskiteare very closeto
SHIM ET AL.: STABILITY
those of lower mantle seismic models.
AND P-V-T
In an earlier man-
tle chemicalmodel[Ita andStixrude,1992]a chemically
distinct lower mantle was proposed. Bulk sound velocity profilesfor upper mantle mineral assemblageswere
unable to fit the lower mantle
seismic models.
A ma-
jor reasonfor this discrepancywas their choiceof high
bulk modulusof CaSiO3perovskite(KTo = 301.4GPa).
Our results indicate that the bulk modulus of CaSiO3
perovskiteis much smaller at lower mantle conditions.
EOS OF CaSiOa PEROVSKITE
25,967
Fiquet, G., D. Andrault, J.P. Itie, P. Gillet, and P. Richet,
X-ray diffraction of periclase in a laser-heated diamondanvil cell, Phys. Earth Planet. Inter., 95, 1-17, 1996.
Fiquet, G., D. Andrault, A. Dewaele, T. Charpin, M. Kunz,
and D. H/Susermann,P-V-T equation of state of MgSiO3
perovskite, Phys. Earth Planet. Inter., 105, 21-31, 1998.
Fiquet, G., A. Dewaele, D. Andrault, M. Kunz, and T. L.
Bihan, Thermoelastic properties and crystal structure of
MgSiO• perovskite at lower mantle pressureand temperature conditions, Geophys. Res. Lett., 27, 21-24, 2000.
Gasparik, T., K. Wolf, and C. M. Smith, Experimental determination of phase relations in the CaSiO• system from
8 to 15 GPa, Am. Mineral., 79, 1219-1222, 1994.
Gillet, P., F. Guyot, and Y. Wang, Microscopic anharmonicity and equation of state of MgSiO•-perovskite, Geophys.
Acknowledgments.
We thank S. Speziale and A.
Kavner for experimental assistanceand R. Boehler, G. Fiquet, and P. Gillet for valuable comments. This work was
supportedby the NSF. Portions of this work were performed
Res. Lett., 23, 3043-3046, 1996.
at GeoSoilEnviroCARS(GSECARS), Sector 13, Advanced Gillet, P., I. Daniel, and F. Guyot, Anharmonic properties
Photon Source at Argonne National Laboratory. GSEof Mg•.SiOa-forsterite measured from the volume depenCARS is supported by the National Science Foundationdence of the Raman spectrum, Eur. J. Mineral., 9, 255Earth Sciences,Department of Energy-Geosciences,W. M.
262, 1997.
Keck Foundation, and the U.S. Department of Agriculture. Gillet, P., R. J. Hemley, and P. F. McMillan, Vibrational
Use of the Advanced Photon Source was supported by the
U.S. Department of Energy, Basic Energy Sciences, Office
of Energy Research, under contract W-31-109-Eng-38.
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T. S. Duffy and S.-H. Shim Department of Geosciences,
Princeton University, Guyot Hall, Washington Road,
Princeton, NJ 08544. (e-maih sangshim•princeton.edu;
duffy•princeton.edu)
G. Shen, GSECARS, University of Chicago, Chicago, IL
60637 (e-mail: [email protected])
2000 K, Eos Trans. A CU, 79(•5), Fall Meet. $uppl., F861,
1998.
Shim, S.-H., T. S. Duffy, and G. Shen, The equation of state
(ReceivedDecember14, 1999; revisedMay 3, 2000;
acceptedMay 22, 2000.)