PHYSICSOFTHE EARTH

AND PLAN ETA RYINTERIORS

ELSEVIER Physicsof the EarthandPlanetaryInteriors 87(1994)111121

Synthesisand re-investigationof the elasticpropertiesof single-crystalmagnesiumsilicateperovskite

Amir Yeganeh-Haeri1Centerfor High PressureResearchand DepartmentofEarth and SpaceSciences,State Universityof NewYork at StonyBrook,

StonyBrook,NY11794, USA

Received4 January1994; revisionaccepted18 April 1994

Abstract

Single crystals of MgSiO3 in the perovskitestructure havebeen grown at a peak pressureof 26 GPa andtemperatureof 1600 K using a 2000 ton uniaxial split-spherehigh-pressureapparatus(USSA-2000). Thespecimensweresubsequentlyutilized to re-investigatethesingle-crystalelasticpropertiesof this phaseat ambientconditionsusinglaserBrillouin spectroscopy.The nineadiabaticsingle-crystalelasticstiffnesscoefficients,in unitsofGPa, are: C11 = 482, C22 = 537, C33 = 485, C44 = 204, C55 = 186, C66 = 147, C12 = 144, C13 = 147, C23 = 146. TheresultingestimatedVoigtReussHill (VRH) aggregateisotropic elasticmoduli are: K = 264.0 and~ = 177.3 GPa,respectively.The single-crystalelasticmoduli of MgSiO3 perovskitedisplay apatternthat is elasticallysomewhatanisotropic.Themaximumshearandcompressionalvelocitiesare18% and7%greaterthan theminimum.The[010]crystallographicdirectioncontainsboth the fastestandthe slowest shearwave velocities. If, under lower mantleconditions,magnesiumsilicateperovskitegrainswere to becomepreferentiallyoriented,ashearwavepropagatinginthe Earths lower mantle could becomepolarizedwith two distinct velocities. The observeddensity and seismicparameterof the lower mantleover thedepthrangeof 10002700km arecomparedwith thecalculatedprofiles fora model mantleconsistingof pureperovskite(Mg089,Fe011)Si03andfor a mixturecomposedof silicate perovskiteand magnesiowstiteusing our new elasticity results.At present,literaturevaluesof thermoelasticpropertiesforsilicate perovskite, in particular, the coefficient of thermal expansionand the temperaturederivative of theisothermal bulk modulus,vary widely. Becauseof this disparity, we find that mantle models rangingfrom pureperovskiteto pyrolitic-type compositionsprovide acceptablefits to the seismicallyobserveddensityandvelocityprofilesof theEarths lower mantle.

1. Introduction damentalimportancein elucidatingthe composi-tion and mineralogyof the earths lower mantle.

Clearly an accurate characterization of the Over the pastdecadetherehavebeena numberelasticpropertiesof silicate perovskiteis of fun- of experimentalinvestigationsaimedatcharacter-

izing the elasticpropertiesand equation-of-state

1 Presentaddress:SeismologicalLaboratory, 252-21 Call- parametersof (Mg,Fe)Si03 perovskite (Yagi etfornia Institute of Technology, Pasadena,CA 91125, USA. al., 1982;Knittle andJeanloz,1987;Kudoh et al.,Fax: (818) 564 0715 1989; Yeganeh-Haeriet al., 1989a,b; Ross and

0031-9201/94/$07.00~ 1994 Elsevier ScienceB.V. All rights reservedSSDI0031-9201(94)02954-A

112 A. Yeganeh-Haeri/Physicsof theEarth and PlanetaryInteriors 87 (1994) 111121

Hazen,1990;Mao et al., 1991; for a summarysee The cell assemblyused in our experimentis iden-also Hemley and Cohen, 1992). The largestdif- tical to that developedby Ito andWeidner(1986).ference in the reported value of bulk modulus The singlecrystalsweregrownat a peakpressureamongall of the above-mentionedexperimental of 26 GPaandtemperatureof 1600K during astudieshasbeenonly about7%. The recentsyn- 45 mm run. The recoveredrun productconsistedthesisof good-qualitysingle crystalsof MgSiO3 of transparent,colorless,euhedralsingle crystalsperovskiteallowed us to more accurately con- with dimensionsrangingfrom 20 x 20 x 30 to 40strain the single-crystalelastic propertiesof this x 40 x 30 jim, although some crystals had di-importantphase. mensions in excess of 100 ~m. Initial petro-

The main purposeof this paper is to present graphicexaminationof the samplesrevealedthat,thenewlydeterminedsingle-crystalelasticmoduli within the resolution of the optical microscope,of MgSiO3 in the perovskitestructure.We also most of the smaller specimenshad uniform ex-use our elasticity data in conjunctionwith the tinction anda lack of twin lamellae,whereasthelatestmeasurementson thethermoelasticproper- largersampleswere always twinned. The natureties of silicate perovskite and magnesiowstite of these twins is similar to that previously de-conducted at elevated pressuresand tempera- scribedby White et al. (1985), Yeganeh-Haeriettures(Mao et al., 1991;Fei et al. 1992;Funamori al. (1989b)andWanget al. (1990).Electronprobeand Yagi, 1993; Wang et al. 1993) to construct microanalysis(EPMA) of the run productyieldeddensity and velocity profiles for two composi- a compositionof (Mg0988Si0998O3012).tional modelsover the depthrangeof 10002700 The crystalswere examinedusing X-ray pre-km. We then comparethesecalculatedprofiles cession photography and were proven to bewith thoseof the PREM model (Dziewonskiand MgSiO3 perovskite.The smaller specimensalsoAnderson,1981) and briefly discussthe implica- exhibited well-developed(110) and (001) typetions of these data on geophysically plausible growth faces, a habit that is ubiquitous in per-modelsfor the chemical constitutionof Earths ovskiteswith orthorhombicsymmetry.X-ray pho-lower mantle. tography methodswere initially used to select

only untwinnedcrystalsfor Brillouin spectroscopymeasurements.The selectedcrystalswere further

2. Experimental techniques orientedand examinedwith an automatedfour-circle X-ray diffractometerand confirmed to be

2.1. Samplesynthesisand description twin free. The resulting lattice parameters,ob-tained from the centeredpositions of 24 high

The starting materialused for syntheseswas angle reflections, are a = 4.776(1)A, b =preparedby mixing appropriateproportions of 4.928(1)A and c = 6.894(2)A. These unit celltetra-ethyl-orthosilicateSi(0C2H5)4 of 99.99% edgesare in good agreementwith the previouspurity and an aqueoussolution of magnesium determinationof Ito and Matsui (1978). All to-nitrateMg(N03) . 6H~Oof 99.99%purity with an gether, four single crystals, two mounted alongSi/Mg ratio of 1. The precipitatedgelswerethen the c-axisandtwo along the[110]crystallographicgently heatedover a period of 24 h, they were direction, were prepared for acoustic velocityfurther heattreatedat 1220 K for approximately measurements.Themaximumdimensionsof these2 h. After removalfrom the furnacethe starting crystalsdid not exceed40 j.tm.materialwas cooled to ambient temperatureand In our previous elasticity study we encoun-pulverizedin an agatemortar. tereda greatdeal of difficulty in obtaininghigh-

High-pressuresynthesisruns were performed quality Brillouin signalson the perovskitespeci-usingthe 2000 ton uniaxial split-sphereapparatus menssynthesizedby Ito andWeidner(1986) us-(USSA-2000) installed at Stony Brooks High- ing either the 488.0or 514.5 nm wavelengthsofPressureLaboratory.This equipmenthas previ- the argon ion laserexcitation source(Yeganeh-ouslybeendescribedin detailby Gasparik(1989). Haeriet al., 1989a,b).Thesesinglecrystalsexhib-

A. Yeganeh-Haeri/Physicsof theEarth andPlanetaryInteriors 87(1994)111121 113

source. The radiation damage was not severe1600 underthis configuration.However,this modifica-

tion to the experimentalconfigurationinevitably

1200 resultedin a dramaticdecreasein the intensityofthe Brillouin signalbecausethe intensityof Bril-

800 bum scatteredlight is proportionalto the inverseof the incident wavelengthto the fourth power,that is, B ~ 1/A4. Therefore,datawere collectedover a limited region in crystallographicspace.

0 I I Subsequently,we were able to excite only nine495 545 595 845 695 longitudinalwaves.Wavelength(nm) The severelaser-inducedfluorescenceencoun-

Fig. 1. Emissionspectraof a single crystal of MgSiO3 per- teredin the crystals grown by Ito and Weidner

ovskitesynthesizedby Ito andWeidner(1986).The excitationsourcewas provided by the 488.0 nm line of an Ar ion laser (1986)canprobablybe attributedto the presenceoperating at 10 mW output power. Laserspot size was en- of transition metal impurities, such as V203,largedto about25 ~sm. Cr203 andFeOin thesesamples.Forinstance,it

is well known that radiation produceselectron-hole pairs in alkali halides.The hole becomes

ited an intense fluorescenceand would subse- self-trappedand recombinationwith an electronquently disintegrate into polycrystalline aggre- producesthe so-calledself-trappedexciton (STE)gates.Fig. 1 shows is the photoemissionspectra luminescence.Work is currently underprogressobtainedfrom oneof thesinglecrystalsgrown by to elucidate better the nature of this lumines-Ito andWeidner(1986).Note the presenceof the cencein silicate perovskite.large fluorescencepeakin the blue-greenregion When the new crystalswere mounted on theof the visible spectrum.Obtaining a robust Bril- Brillouin spectrometerandexcitedwith the 514.5bum signal under such efficient laser-induced nm line of an Ar + laser no fluorescencewasfluorescingconditionsis indeeda difficult task. detected and robust Brilbouin peaks appeared.As themirrors installedin the FabryPerotinter- Unlike the previous perovskitespecimens,theseferometerare particularly coated for maximum singlecrystalswere found to be stableunderthetransmittancein the 488.0514.5 nm region, such focused laserbeam. The quality of the spectraintenseand broadfluorescencecannotbe readily was also quite superior to that obtainedin ourfiltered. This fluorescencesignal easily entered earlier investigation.into the photodetectiondevice and overwhelmedthe Brilbouin peak. More importantly, after only 2.2. Acousticvelocitiesseveralhoursof exposureto the laserbeam,withlaserpowers as low as 5 mW, oncetransparent Brilbouin spectrawere gatheredin 53 uniquesinglecrystalswould becomefrosty looking. X-ray crystallographic orientations on silicate per-examinationof thesesamplesrevealedthe onset ovskite. More than 110 separatespectra wereof local twinning. Additional illumination by the collected, each having either different polariza-laserbeaminvariably resultedin the migrationof tion or different combinationsof growth surfacestwin domainsthroughoutthe crystals, transform- servingas incident andscatteredfaces.For manying single crystalsinto polycrystallineaggregates. crystallographicdirections several spectrawereIt is alsoclear from Fig. 1 that thesecrystalswere collected; theseredundantdata were averagednot as fluorescentin the red regionof the visible together.All datawere explicitly corrected forspectrum(e.g.650.0700.0nm). Therefore,in our the effect of mismatchbetweenthe samples re-previousstudy the spectrometerwasmodified to fractive index and that of the fluid (~5i45nm =operatein this region of the visible spectrumand 1.631)as outlined by Vaughan and Bass(1983).a krypton ion laser was used as the excitation The robustnessand precision of the Brillouin

114 A. Yeganeh-Haeri/PhysicsoftheEarth andPlanetaryInteriors87(1994)111121

Table 1Acoustic velocitiesfor MgSiO

3 perovskite

Propagationdirection Polarizationdirection Velocity (kms)

n2 n3 u1 u2 u3 Obs. Cal.

1.00 0.04 0.01 0.01 0.00 1.00 6.73 6.730.04 1.00 0.04 0.03 1.00 0.04 11.45 11.43

0.00 0.04 1.00 7.09 7.040.56 0.83 0.03 0.49 0.87 0.03 11.11 10.94

0.00 0.04 1.00 7.08 6.950.27 0.96 0.01 0.21 0.98 0.01 11.39 11.30

0.00 0.01 1.00 7.10 7.020.98 0.04 0.22 0.97 0.03 0.24 10.82 10.87

0.24 0.01 0.97 6.62 6.670.90 0.04 0.44 0.47 0.04 0.88 6.46 6.520.04 0.97 0.25 0.03 0.97 0.26 11.58 11.45

0.01 0.26 0.97 6.98 6.950.04 0.85 0.53 0.03 0.85 0.52 11.51 11.47

0.03 0.52 0.85 6.76 6.731.00 0.04 0.01 1.00 0.03 0.01 10.79 10.830.04 1.00 0.02 0.03 1.00 0.02 11.39 11.43

0.00 0.02 1.00 7.02 7.050.04 1.00 0.03 0.00 0.03 1.00 6.95 7.04

0.95 0.04 0.30 0.32 0.01 0.95 6.52 6.620.79 0.03 0.61 0.33 0.83 0.45 6.38 6.400.04 0.94 0.33 0.01 0.34 0.94 6.89 6.900.04 0.94 0.33 0.03 0.94 0.33 11.48 11.46

0.01 0.64 0.77 0.05 0.74 0.67 6.66 6.650.01 1.00 0.00 0.01 1.00 0.00 11.27 11.43

0.00 0.00 1.00 7.02 7.050.33 0.95 0.01 0.00 0.01 1.00 6.96 7.010.60 0.80 0.03 0.00 0.04 1.00 6.88 6.931.00 0.02 0.02 1.00 0.02 0.02 10.87 10.83

0.02 0.00 1.00 6.74 6.730.94 0.34 0.01 0.01 0.00 1.00 6.75 6.770.78 0.63 0.00 0.00 0.00 1.00 6.84 6.86

1.00 0.01 0.01 0.01 0.00 1.00 6.75 6.730.95 0.01 0.30 0.32 0.00 0.95 6.52 6.620.81 0.00 0.58 0.60 0.01 0.80 6.44 6.43

0.01 0.94 0.33 0.00 0.34 0.94 6.82 6.890.00 0.79 0.61 0.00 0.80 0.59 11.51 11.45

0.00 0.59 0.80 6.56 6.670.00 0.79 0.61 0.00 0.59 0.80 6.59 6.67

0.01 1.00 0.02 0.01 1.00 0.02 11.35 11.430.86 0.00 0.51 0.54 0.00 0.84 6.44 6.47

1.00 0.03 0.01 1.00 0.03 0.01 10.90 10.830.01 0.00 1.00 6.82 6.73

0.97 0.04 0.26 0.96 0.04 0.28 11.02 10.880.28 0.01 0.96 6.67 6.65

0.88 0.05 0.48 0.50 0.06 0.86 6.46 6.490.75 0.05 0.66 0.63 0.30 0.72 6.36 6.400.13 0.10 0.99 0.14 0.13 0.98 11.07 10.90

0.09 0.99 0.11 6.99 7.010.03 0.00 1.00 0.03 0.00 1.00 10.86 10.87

0.00 1.00 0.00 7.10 7.050.71 0.70 0.06 0.74 0.67 0.03 6.60 6.660.51 0.86 0.02 0.90 0.43 0.01 6.42 6.47

A. Yeganeh-Haeri/Physicsof theEarth and PlanetaryInteriors 87 (1994)111121 115

Table 1 (continued)

Propagationdirection Polarizationdirection Velocity (kms I)

n2 n3 u1 u2 u3 Obs. Cal.

0.00 1.00 0.01 0.00 1.00 0.02 11.39 11.431.00 0.00 0.00 6.03 5.99

0.02 1.00 0.02 0.01 1.00 0.02 11.47 11.431.00 0.01 0.00 5.99 5.99

0.71 0.70 0.01 0.74 0.68 0.00 6.61 6.660.49 0.49 0.72 0.46 0.52 0.72 10.85 11.13

0.61 0.78 0.17 6.75 6.800.52 0.49 0.70 0.49 0.51 0.71 10.97 11.12

0.61 0.78 0.14 6.80 6.790.22 0.25 0.94 0.23 0.29 0.93 11.00 10.99

0.33 0.92 0.21 6.97 6.930.03 0.05 1.00 0.04 0.07 1.00 10.94 10.87

0.01 1.00 0.07 7.03 7.040.02 0.00 1.00 0.02 0.00 1.00 10.97 10.87

0.00 1.00 0.00 7.12 7.050.50 0.53 0.69 0.62 0.76 0.19 6.78 6.78

1.00 0.01 0.03 0.01 1.00 0.00 5.95 5.990.51 0.52 0.69 0.61 0.77 0.17 6.85 6.780.52 0.52 0.68 0.62 0.77 0.16 6.73 6.78

0.71 0.70 0.01 0.74 0.68 0.01 6.56 6.660.90 0.44 0.02 0.42 0.91 0.01 6.49 6.411.00 0.03 0.01 0.03 1.00 0.00 6.08 5.99

Polarizationsof the shearwavesare known; numberof data 73; rms error0.085 km s~.Refractiveindex: n~= 1.760, n~= 1.770, n7 = 1.785.

spectrawere deducedfrom the internal consis- bocities is 0.085 km s~(see also Table 1). It istencyandreproducibility of theresultsfrom spec- importantto point out that our newlydeterminedimen to specimenwith different crystallographic single-crystalelasticcoefficientsfor MgSiO3 per-orientations,and by the redundantdetermina- ovskite are,far superiorto our previousmeasure-tions of acousticvelocities.The final set of acous- ments,and as such,the earlier resultsshould notic velocities consistingof 73 independentcorn- longerbe used.pressional and shear modes is presentedinTable 1.

3. Discussionand conclusions2.3. Singlecrystalelastic moduli

3.1. Comparisonwith previousstudiesThe inversion method developedby Weidner

andCarleton(1977)wasusedto calculatesingle- Pressurevolumedata for silicate perovskitecrystal elastic moduli from the measuredveboci- havebeenreportedby severaldifferent investiga-ties. In the inversion,a densityof 4.108 g cm

3 tors, each employing either a different type ofwas adoptedfor the silicate perovskite.The nine sampleor experimentaltechnique.A comparisonadiabatic single-crystal elastic coefficients of of all the literaturevalues for the bulk modulusMgSiO

3 perovskite along with the estimated and linear compressibilitiesof (Mg,Fe)Si03 per-isotropic aggregatepropertiesaregiven in Table ovskite is given in Table 3. Mao et al. (1991)2. The velocity surfaceof MgSiO3 perovskiteis discuss in some detail the differencesin bulkillustrated in Fig.2. The root meansquaredevia- modulusand linear compressibibitiesamongthetion of the best-fit model from the observedye- various static compressionexperiments.For ex-

116 A. Yeganeh-Haeri/Physicsof theEarth and PlanetaryInteriors 87 (1994)111121

Table2 14Single-crystalelasticcoefficientsfor MgSiO

3 perovskitedeter-minedat iO~GPaand 22CC

~ 12 -

11 482(4) 0.00240 I~-u ~22 537(3) 0.00213 10 -33 485(5) 0.0023944 204(2) 0.00490 855 186(2) 0.0053866 147(3) 0.0067812 144(6) 0.00048 613 147(6) 0.0005823 146(7) 0.00049__________________________________________ 4 I ___________ I

Isotropic aggregateproperties a b c aCrystal OrientationVoigt Reuss Hill . .

Fig. 2. The velocity surfaceof MgSiO3 perovskiteprojectedK 264.2 263.7 264.0(5.0) on to ab, bc, and ac planes. The solid points areis 178.5 176.2 177.3(3.5) experimentallydeterminedvelocities.Thesolidline is thebest

11.06 11.02 11.04 fit model. The rms deviationof the model from themeasuredV~ 6.59 6.55 6.57 velocities is 0.085 km s~.V,1. 8.03 8.01 8.02

C.~(GPa);S~,(GPa 1); velocities(km s i)~Linear compressibilities: j3~= 1.33, p6 = 1.14, ~ = 1.31 well as to the lower pressuresattained in the(TPa~)~density= 4.108 g cm

3~Ap = 0.07 As = 0.18, A = a static compressionstudiesof Ross and Hazenmeasureof elastic anisotropyexpressedin termsof acousticvelocities:Ap =(~max 1,min)/ V, aggregate;A~=(~cm,,,, (1990)andKudoh et al. (1989). Wealso note that~min)/ v, aggregate. the primary purposeof conductinga static com-

pressionexperimentis to measurethe pressurederivativeof the bulk modulus,yet in almost all

ample, the disparity may be attributed to the cases a value of 4 has been assumedfor Koccurrenceof non-hydrostaticpressurein the (Table 3). Takenat facevalue andnotwithstand-measurementsof Yagi et al. (1982) and Knittle ing the differencesnoted above,and neglectingand Jeanboz(1987), and to uncertaintiesin vol- the differencebetweenadiabaticand isothermalume measurement,pressure determination, as conditions, there is now a fair amountof agree-

Table3Bulk modulusandlinear compressibilitydata for silicateperovskite

K j3~ P6 p~ K Method Sample Pre.media Max.press.

258(20) 1.58 1.19 1.10 4(assuming) DAC PolyX me 7 1266 (6) 3.9(0.4) DAC PolyX None 111 2247(14) 1.41 1.07 1.57 4(assuming) DAC SingX mew 10 3247 (5) 1.31 1.20 1.56 B.S. SingX 4254 (5) 1.31 1.05 1.24 4(assuming) DAC SingX me 12 5273 (4) 1.29 1.03 1.31 4(assuming) DAC PolyX Ne 30 6261 (4) 1.34 1.08 1.43 4(assuming) DAC PolyX Ne 30 7264 (5) 1.33 1.14 1.31 B.S. SingX 8

K (GPa); linear compressibilities(TPa i); DAC, diamond anvil cell; B.S., Brillouin scattering;PolyX, polycrystalline sample;SingX, single-crystalsample;Pre.media,pressuremedium; mew, methanolethanolwater;me, methanolethanol;Ne, neon;max.press.,max.pressureattainedin theexperiment(GPa).(1) Yagi et al. (1982);(2) Knittle andJeanloz(1987);(3) Kudohetal. (1989);(4) Yeganeh-Haeriet al. (1989a,b);(5) RossandHazen(1990);(6) and(7) Maoet al. (1989,1991) data reportedherewasobtainedfrom a least-squaresfit of threedifferentsamplesof(Fe~,Mg1_~)SiO3wherex = 0.0, 0.1 and0.2; (8) this study.

A. Yeganeh-Haeri/Physicsof theEarthand PlanetaryInteriors 87 (1994)111121 117

ment concerning the bulk modulus of silicate 16.00perovskite.

3.2. Crystalstructureand elasticity of MgSiO3 14.00

On the basisof single-crystalstructuralrefine-ments, Horiuchi et al. (1987) suggestedthat the ~ 12.00 __._._..._._._._._._._.structure of MgSiO3 perovskite is essentially ~composedof chainsof rigid andrelatively regular ~Si06 octahedrathat extendin threedimensions. .~ 10.00 1 20 25 30Such a topology inevitably leadsto an elastically ~ ~ (GPa)stiff structurebecauseit is hardto deformchains ~

load-bearingframework.The large td ofthe elastic stiffnesscoefficientsof MgSiO3,espe- 13.480cially moduli C11, C22 and C33, indeeddemon-stratethe strengthof this material (Table 2). 12.570

The single-crystalelastic moduli of MgSiO3perovskitealsodisplay apatternthat is elastically 11.680 ___________________________________somewhatanisotropic.The maximum shearandcompressionalvelocities are 18% and7% greater 10.750290 389 488 587 686 785 864 983 1082than the minimum (Table 2). On a comparative

Temperature(K)basis,the differencesbetweenthe maximum and Fig. 3. (a) Variation of octahedralrotation angles ~ (solidminimum shear and compressionalvelocities in line) and w (dashed-dottedline) asa functionof pressure.(b)olivine, which is considered to be extremely Variation of the sameangles(open circles= ~ closedcirclesanisotropic, are about 25% and 24%, respec- w) with increasingtemperature.Data arefrom Wangetal.tively. The [010] crystallographicdirection in per- (1993).ovskitecontainsboth the fastestand the slowestshearwavevelocity (Table 2). The fastestwave ispolarizedparallel to the [001] direction (i.e. C~) ent conditionsthe and w octahedralrotationandthe slowest is polarizedalong the [100] crys- anglesfor MgSiO3 are 14.35 and 11.67,whereastalbographicdirection (i.e. C66). If under lower at 30 GPa they are 15.6 and 11.89, respectively.mantle conditionsmagnesiumsilicate perovskite Interestingly, analysis of the high-temperaturegrainswereto becomepreferentiallyoriented,as unit cell dataof Wanget al. (1993) indicatesthatopposedto being randomlyoriented,ashearwave both ~ and w decreaseslightly with increasingpropagatingin the Earths lower mantle could temperature(Fig. 3b). It appearsthat the netbecomepolarizedwith two distinct velocities, effect of these two offsetting and competing

It is useful to look at the effects of pressure mechanismsis suchthat the overall distortion ofand temperatureon the degreeof structuraldis- the perovskitestructure,at leastup to 3036 GPatortion by examiningthe rotationangles~ and w. and 12001500 K, is comparablein magnitudeThe linear compressibilitydata(Table 2) allow us with thatobservedat 1 barand300 K.to calculate directly the pressuredependenceof~ and w, assumingthat the Si06 octahedrabe- 3.3. Elasticityand compositionof the lowermantlehave as rigid and rather regular units. As seenfrom Fig. 3(a). increasesslightly, while w does Compositionalmodelsdeemedappropriatefornot changesignificantly with increasingpressure. the Earths deep mantle range from pyroliteThis is consistentwith earlier observationsof (silica-poor) to pyroxene(silica-rich) stoichiome-Knittle andJeanboz(1987).For instance,at ambi- tries.Underlowermantleconditions,this compo-

118 A. Yeganeh-Haeri/Physicsof theEarth and PlanetaryInteriors 87 (1994) 111121

sitional variation correspondsto petrobogicalas-semblagesof ~ 7080% (by volume) perovskitewith 3020% magnesiowustiteor to pure per 5280ovskite Testsof thesecompositionalmodelscan (A)be madeby comparingthe elastic propertiesim .~ 5020plied by a given assemblagewith those inferredfrom seismology 4760

The currentdatabasefor thermoelasticprop-ertiesof silicate perovskiteand magnesiowstiteis presentedin Table 4. The following analysis 4.500 I I I I Irestson the variationof densityand seismic pa- 120.0rameterover a depth range of 10002700 km ~ - -This depth rangewas selectedbecauseboth at ~ 1090 - - -shallowerdepths in the vicinity of the 670 km ,~ ~ o - - - - ~ (B)discontinuity and in the deeperregions of the - - -Earths mantle near the D layer, the density ~ ~ 0 /andvelocity structuresare quite complex Corn 76 0puted densityandvelocity trajectoriesfor a pureperovskite, (Mg089,Fe011)Si03,modeled as a ~ 13~ 16 1900 2200 2500function of depthareshownin Figs. 4(a)and(b). Depth(kin)All calculationswereperformedalong a 2000 K Fig. 4. Comparisonof the observeddensity(a) and seismicadiabat initiated at zero pressure (Anderson, parameter(b) vs. the calculatedprofiles for a pure (Mg089,1989). It is clear from thesefiguresthat a pure Feoii)Si03perovskitemodel. The filled circles are from theperovskitemodel canprovide a satisfactoryfit to PREMmodel. All necessaryelasticity data aregiven in Table

4. The shadedarearepresentsthe uncertaintyin the miner-the density and velocities observed seismically alogicalmodel. Dashed-dottedline asexplainedin text.throughoutthe entirelower mantleprovidedthatthe coefficientof thermalexpansionandtemper-aturederivativeof the isothermalbulk modulus,of silicate perovskiteare 3.61 x iO~ K and morerecentanalysisof Stixrudeet al. (1992),and

5.8 x 10~ GPa K1, respectively.This is implies that the Earthsmantleis compositionally

consistent with earlier suggestionsof Jackson stratified (e.g.the lower mantle is silica-enriched(1983), BukowinskiandWolf (1990),andwith the relativeto the uppermantle). It is useful to note

that density perturbationsdrive mantle convec-tion. And becausedensityperturbationsare es-

Table 4 .. . sentially susceptibleto changesin Mg/Fe ratioThermoelasticpropertiesof silicate perovskite and magne- .siowstiteusedin this study ratherthan to changesin silicon content,a lower3Property (Mg, Fe)Si0

3 (Mg, Fe)O mantle composedof ferromagnesiumperovskite

K 264 162 with anFe/(Mg + Fe) ratio of 0.11 would, there-(iKT / ~P) 3.9 4.0 fore, not impose a completeblockadeon whole(aK/aT)~x 10-2 (2.3, 8.0) 2.7 mantleconvection.(aK/aFe) O.OXFe ~

9.OXFe It is important to realize that to date thereis 177.3 132 haveonly been threeseparatemeasurementsof(~is/~) x10-2 24 thermoelasticproperties of silicate perovskite

(a,s/aFe) - ~79.0XF conducted at simultaneoushigh pressuresanda x i0~ (1.65,4.0) 3.8 temperatures(Mao et al., 1991; Funamori and

Yagi 1993 Wang et al., 1993). The experimentsNumbersin parenthesesindicatetherangeof a given parame-ter as reportedby severaldifferent investigators.K and ~ of Mao et al. (1991)yielded a ratherlargecoeffi-(GPa); temperaturederivatives(GPaK 1); a (K 1) cient of thermalexpansion,that is, a ~ 3.5(0.5)X

A. Yeganeh-Haeri/Physicsof theEarth andPlanetaryInteriors 87 (1994) 111121 119

10 ~ K1 and a very largenegativetemperaturederivative of the isothermal bulk modulus, 5280(aK/8T)p ~ 63(05)x 102 GPa K1 On theother hand, the measurementsof Wang et al(1993) yielded significantly lower values of a = 50201 65(0 19) x iO~K1 and(8K/aT)p= 23(11)x 102 GPa K More recently Funamoriand 4780Yagi (1993) measuredthermal expansivityof sili-cateperovskitefrom 300 to 1900 K at a constant 4500 I I I I Ipressureof 36 GPa.These authorsdeterminedthe thermalexpansivity of MgSiO

3 perovskiteto 120.0be 1 7(02)x iO~K~ The measurementof Fu

Lu 1090namori and Yagi (1993) is in reasonableaccord ~Z (B)with thoseof Wanget al (1993), but somewhatat 980oddswith the results of Mao et al (1991) Thethermal expansivity reported by Funamori and ~ 870Yagi (1993) at 36 GPa is also in fair agreement 78.0with the zero-pressureresults of Parise et al.(1990) and Ross and Hazen (1989), indicating ~ is~o 1600 1900 2200 2500that thepressuredependenceof a is rathersmall. Depth (kin)More measurementsovera widerrangeof condi-tions areneededto confirm thisobservation. Fig. 5. Comparisonof the observeddensity(a) and seismic

parameter(b) vs. the calculatedprofiles for a pyrolite-typeA pivotal question, then is whether a pure . .. .model. The iron partition coefficientbetweenperovskiteandperovskitemodel can still be plausible giventhat magnesiowstitewas setat 3.3. Symbols are the same as in

the thermal expansivity and the temperature Fig. 4.derivativeof bulk modulushavebeenreducedbyfactors of about 2 and 3, respectively,from thevalues appropriateto Figs. 4(a) and (b). If the Bukowinski and Wolf (1990), but in sharp con-coefficientof thermalexpansionandthe temper- trast to that of Stixrudeet al. (1992).aturederivativeof bulk modulusof silicate per- Of course, it would be highly desirableto useovskite areas low as thosereportedby Wang et the variationof compressionaland shearvelocityal. (1993) and Funamoriand Yagi (1993)then a in addition to density and seismic parameterpure perovskitemodel mantlewould be too fast throughout the lower mantle, to place tighterby about several percent in t, to provide an constraintson the rangeof acceptablechemicalacceptablefit to the seismic data. This is shown models. However, the absenceof the pressure,by the dash-dottedline in Fig. 4(b). On the other temperatureand mixed derivativesof compres-hand, by increasingthe magnesiowstite,or in sional and,especially,shearvelocitiesfor magne-other words the olivine contentof the system, sium-, iron-, aluminum- andcalcium-bearingsili-and by performingthe calculationsalonga 1750 cate perovskitessignificantly hinders the robust-K adiabat, the quality of the fit improved sub- nessof such an approach.It is also worth re-em-stantially.A model mixture composedof 75% (by phasizingthat the value of the shearmodulusofvolume) silicate perovskiteand 25% magnesio- MgSiO3 perovskitemeasuredat ambientcondi-wiistite,consistentwith a pyrolitic-type composi- tions is comparablewith the shearmodulusof thetion, agreesreasonablywell with the densityand Earths lower mantle at a depthof 971 km (seeseismic parameterthroughoutthe lower mantle, table II of the PREM model).Normally, acousticThe resultsof this calculationare shownin Figs. velocities tend to increasewith increasingpres-5(a) and (b). This observation is also in accord sure and decreasewith increasingtemperature;with the earlier analysesof Jackson(1983) and sucha high ambientconditionshearvelocity can-

120 A. Yeganeh-Haeri/PhysicsoftheEarth andPlanetaryInteriors87(1994)111121

not be easily reconciledwith the velocity struc- sion spectraof MgSiO3 perovskitewerecollectedture of the lower mantle short of invoking some in the laboratory of D. Schiferl at Los Alamosanomalousbehaviorin a statevariable,eitherby NationalLaboratory,to whom I amthankful.Therequiringa largenegativetemperaturederivative crystal synthesisexperimentswere conductedator by requiring a large negativesecondpressure Stony Brooks High-PressureLaboratorywhich isderivative. The distinction betweenthesevarious supportedby the National Science Foundationscenariosmust await further study. Moreover, Centerfor High PressureResearch(CHiPR)andalthoughthe pressurederivativeof the bulk mod- the StateUniversityof NewYork at Stony Brookulus of silicate perovskitehas beenmeasuredto undergrantEAR89-20239.TheBrilbouin scatter-over100 GPa,the uncertaintyin this parameteris ing laboratoryis supportedby NSF grantEAR88-still rather large and in need of further refine- 04087.Mineral PhysicsInstituteContributionNo.ment. For example,perturbationsof K = 3.9 100.0.4within its stateduncertaintycanhaveasignifi-cant effect on the computedseismic parameterand henceon the inferredchemicalcomposition, Referencesas shown by the shadedregion in Fig. 4(b). In Anderson, DL., i989. Theory of the Earth. Blackwell Scien-addition, no measurementshave yet been con- tific, Boston.ducted on the acousticpropertiesof magnesio- Bukowinski, MS. and Wolf, G.H., 1990. Thermodynamicallywstite at sufficiently high statesof compression consistentdecompression:Implicationsfor thelower man-(e.g. P> 50130GPa) andat high temperatures tie composition.J. Geophys.Res., 95: 12 58312593.

Dziewonski,A. andAnderson,DL., 1981. PreliminaryRefer-characteristicof the Earthsdeepmantle. enceEarth Model.Phys.EarthPlanet. Inter., 15: 297356.

With all theseuncertaintiesin mind, we will Fei, Y., Mao, H.-K., Shu, J. and Hu, J., 1992. PVT equa-stopshortof a completeperturbationof composi- tion of state of magnesiowstite(Mg06,Fe04)O. Phys.tion (i.e. perovskite to magnesiowstiteratio), Chem. Mineral., 18: 416421.temperatureand thermoelasticpropertiesof per- Funamori, N. and Yagi, T., 1993. High pressureand hightemperaturein situ X-ray observation of MgSiO3 per-ovskite in the exhaustivesearchfor a unique ovskite under lower mantle conditions. Geophys. Res.lower mantlecomposition.In conclusion,the cur- Lett., 20: 387390.rent seismicand mineralphysicsdatacannotun- Gasparik, T., 1989. Transformationof enstatitediopsideequivocallyconstrainthe chemicalcompositionof jadeitepyroxenesto garnet.Contrib. Mineral. Petrol., 102:the Earths lower mantle. Not until thesevan- 389405.

Hemley, R. andCohen,R.E., 1992. Silicate perovskite.Annu.ables have been accurately characterizedcan Rev. EarthPlanet. Sci., 20: 553600.questionsconcerningthe exactconstitutionof the Horiuchi, H., Ito, E. andWeidner,D.J.,1987. Perovskite-typeEarthslower mantleandwhetherit is chemically MgSiO3: single crystal x-ray diffraction study. Am. Mm-dissimilarfrom the uppermantle,be answered. eral., 72: 357360.

Ito, E. and Matsui, Y., 1978. Synthesisand crystal chemicalcharacterizationof MgSiO3 perovskite.Earth Planet. Sci.Lett., 38: 443450.

Acknowledgments Ito, E. and Weidner,D.J., 1986. Crystal growthof MgSiO3perovskite.Geophys.Res. Lett., ii: 464466.

I thank two anonymousrefereesfor their con- Jackson,I., 1983. Somegeophysicalconstraintson the chemi-structive and helpful reviews. I am indebted to cal compositionof the earthslower mantle.EarthPlanet.

Sci. Lett., 62: 91103.my advisor Don Weidnerfor many valuable dis- Knittle, E. and Jeanloz,R., 1987. Synthesisand equationofcussionsand comments,and for the use of the stateof (Mg, Fe)Si03 perovskiteto over 100 gigapascals.Brillouin scatteringfacility at Stony Brook, with- Science,235: 668670.out which this studywould not havebeenpossi- Kudoh,Y., Ito, E. andTakeda,H., 1989. Effect of pressureonble. I also thank Y. Wangfor experimentalassis- the crystal structure of perovskite-typeMgSiO3. Phys.

Chem. Mineral., 14: 350354.tance in synthesisruns. I am grateful to Thomas Mao, H-K., Hemley, R., Shu, J., Chen,L.-C., Jephcoat,A.,J. Ahrensfor financial support that madepossi- Wu, Y. and Bassett,W., 1989. The effect of pressure,ble the completion of the manuscript.The emis- temperatureand composition on the lattice parameters

A. Yeganeh-Haeri/Physicsof theEarth andPlanetaryInteriors 87 (1994) 111121 121

and density of (Mg,Fe)Si03 perovskites to 30 GPa. Wang, Y., Guyot, F., Yeganeh-Haeri,A. and Liebermann,

CarnegieInst. WashingtonYear Book, 19881989, pp. R.C., 1990. Twinning in MgSiO3 perovskite.Science,248:8289. 468471.

Mao, H.-K., Hemley, R., Shu, J., Chen,L.-C., Jephcoat,A., Wang,Y., Weidner,D.J. andLiebermann,R.C., 1993. PVTWu, Y. and Bassett,W., 1991. The effect of pressure, equationof stateof (Mg,Fe)Si03perovskite:Constraintstemperatureand composition on the lattice parameters on compositionof the lower mantle. Phys.Earth Planet.and density of (Mg,Fe)5i03 perovskites to 30 GPa. J. Inter., submitted.Geophys.Res., 96: 80968079. Weidner,D.J.andCarleton,H., 1977. Elasticity of Coesite.J.

Parise,J., Wang,Y., Yeganeh-Haeri,A., Fei, Y. andCox, D., Geophys.Res., 82: 13341346.1990. Crystal structure and thermal expansionof (Mg, White, T.J., Segal,R.L., Barry, J.C. and Hutchinson,L., 1985.Fe)Si03perovskite.Geophys.Res. Lett., 17: 20892092. Twin boundariesin perovskite.Ada. Cryst.,B41: 9398.

Ross,N. andHazen,R.M., 1989. Single crystalx-ray diffrac- Yagi, T., Mao,H-K. and Bell, P.M., i982. Hydrostatic corn-tion study of MgSiO3 perovskitefrom 77 to 400 K. Phys. pressionof perovskite-typeMgSiO3, In: S.K. Saxena(Edi-Chern.Mineral., 16: 415420. tor), Advancesin Physical Geochemistry,Vol. 2. Springer,

Ross,N. and Hazen,R.M., 1990. High pressurecrystal chern- New York, pp. 317325.istry of MgSiO3 perovskite. Phys. Chem. Mineral., 17: Yeganeh-Haeri,A., Weidner,D.J. and Ito, E., 1989a.Elastic-228237. ity of MgSiO3 in the perovskite structure.Science,243:

Stixrude, L., Hemley., R.J., Fei, Y. and Mao, H.-K., 1992. 787789.Thermoelasticityof silicateperovskiteandmagnesiowOstite Yeganeh-Haeri,A., Weidner,D.J. and Ito, E., i989b.Single-and the stratification of the earthsmantle.Science,257: crystal elastic moduli of magnesiummetasilicate per-10991101. ovskite In: A. Navrotsky andD.J. Weidner(Editors), Per-

Vaughan,M.T. andBass,J.D., 1983. Single-crystalproperties ovskite: A Structureof GreatInterestto Geophysicsandof protoenstatite:A comparisonwith orthoenstatite.Phys. Material Science.AGU Monogr. No. 45, Am. Geophys.Chem.Mineral., 10: 6268. Union, pp. 1326.