Crystal structure and thermoelastic propertiesof (Mg0.91Fe0.09)SiO3 postperovskite upto 135 GPa and 2,700 KSang-Heon Shim*†, Krystle Catalli*, Justin Hustoft*, Atsushi Kubo‡, Vitali B. Prakapenka‡, Wendel A. Caldwell§,and Martin Kunz§

*Department of Earth, Atmospheric, and Planetary Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139;‡Center for Advanced Radiation Sources, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637; and §Lawrence Berkeley National Laboratory,1 Cyclotron Road, Berkeley, CA 94720

Edited by Russell J. Hemley, Carnegie Institution of Washington, Washington, DC, and approved March 13, 2008 (received for review November 27, 2007)

Intriguing seismic observations have been made for the bottom400 km of Earth’s mantle (the D� region) over the past few decades,yet the origin of these seismic structures has not been wellunderstood. Recent theoretical calculations have predicted manyunusual changes in physical properties across the postperovskitetransition, perovskite (Pv) 3 postperovskite (PPv), that may pro-vide explanations for the seismic observations. Here, we reportmeasurements of the crystal structure of (Mg0.91Fe0.09)SiO3-PPvunder quasi-hydrostatic conditions up to the pressure (P)–tempera-ture (T) conditions expected for the core-mantle boundary (CMB).The measured crystal structure is in excellent agreement with thefirst-principles calculations. We found that bulk sound speed (V�)decreases by 2.4 � 1.4% across the PPv transition. Combined withthe predicted shear-wave velocity (VS) increase, our measurementsindicate that lateral variations in mineralogy between Pv and PPvmay result in the anticorrelation between the V� and VS anomaliesat the D� region. Also, density increases by 1.6 � 0.4% andGruneisen parameter decreases by 21 � 15% across the PPvtransition, which will dynamically stabilize the PPv lenses observedin recent seismic studies.

equation of state � mantle � phase transition � bulk sound speed �Gruneisen parameter

The D� region is believed to play an important role for thedynamics of the mantle and the core. The recent discovery

of the postperovskite (PPv) transition (1–3) at the P–T condi-tions relevant to the D� region has provided new opportunitiesto understand the seismic observations and dynamic processes inthe region. First-principles calculations (1, 4, 5) have predicteddrastic changes in some geophysically important propertiesacross the PPv transition (6, 7). The unusual changes have beenattributed to the fundamental differences in crystal structurebetween perovskite (Pv), a 3D network structure with corner-sharing SiO6 octahedra, and PPv, a 2D layered structure withboth corner and edge sharing SiO6 octahedra (1, 4, 8, 9).Therefore, measurements of the crystal structure provide afundamental test for the predicted properties of PPv. However,synthesis of an appropriate single crystal for PPv in its stabilityfield is extremely challenging for current techniques, makingRietveld refinement the only plausible method for studying thecrystal structure. Currently only a single Rietveld refinement(10) exists for MgSiO3-PPv at 116 GPa and 300 K (Table 1).

Some theoretical studies (1, 4) have predicted that bulk soundspeed (V�) decreases across the PPv transition whereas shear-wave velocity (VS) increases. Shieh et al. (11) measured Pv � PPvmixtures in (Mg0.91Fe0.09)SiO3 and suggested decreases in vol-ume and bulk modulus, and therefore a decrease in V�, acrossthe PPv transition, but the Fe contents of the individual phaseswere not known and a limited number of diffraction lines wereused for constraining volume. Mao et al. (12) have achieveddenser data coverage for (Mg0.6Fe0.4)SiO3-PPv at a wider pres-

sure range. Their data indicate that the bulk modulus of PPvshould be very high at CMB pressures (Table 2), suggesting alarge increase in V� across the PPv transition. However, nopressure medium was used in this study. The larger amount of Fein Mao et al. (12) may cause the difference, yet a first-principlescalculation showed that Fe has little effect on the bulk modulusof PPv (13).

We have measured x-ray diffraction patterns of(Mg0.91Fe0.09)SiO3-PPv under quasi-hydrostatic stress conditionswith a chemically inert, insulating, compressible Ar pressuremedium at in situ high P–T conditions (37–126 GPa at 300 K and135 GPa at 2,300–2,700 K) in the laser-heated diamond-anvil cell[supporting information (SI) Fig. S1]. We measured at least 25full-diffraction rings of PPv to d-spacing �1.1 Å, which is asignificant improvement over previous studies. Our datasetenables us to constrain the changes in density, bulk modulus, andGruneisen parameter across the PPv transition and to measurethe crystal structure of PPv through the Rietveld refinements.

Results and DiscussionTo synthesize PPv, we increased pressure directly to 120–130GPa without heating and then heated for 1.5 h at 1,500–2,700 K.During the first heating of the sample at 125 GPa, we observedthe synthesis of a Pv � PPv mixture from the amorphized startingmaterial. However, after 1 h of heating at slightly higherpressure, the sample transforms completely to PPv. The P–Tconditions of the PPv transition we observed are consistent withthose expected for the D� discontinuity within experimentaluncertainties. Even at the maximum P–T in our experiments,strong diffraction intensities were detected for Ar (Fig. 1),indicating that a significant amount of Ar still surrounds thesample. The sufficient amount of Ar medium reduces thethermal gradients and differential stresses in the sample.

After the synthesis of PPv, in situ diffraction measurementswere conducted between 2,300 and 2,700 K at 135 GPa (Fig. 1a)and then the sample was temperature quenched to 126 GPa (Fig.1b). Diffraction patterns were measured during decompression(Fig. 1 c and d). To prevent reverse transformation to Pv, we didnot heat the sample during decompression. Down to 85 GPa, thediffraction peaks remained sharp, but broadened rapidly at P�80 GPa (Fig. 1d). Also the diffraction patterns of the recovered

Author contributions: S.-H.S. designed research; S.-H.S., K.C., J.H., A.K., V.B.P., W.A.C., andM.K. performed research; S.-H.S. analyzed data; and S.-H.S. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

†To whom correspondence should be addressed. E-mail: sangshim@mit.edu.

This article contains supporting information online at www.pnas.org/cgi/content/full/0711174105/DCSupplemental.

© 2008 by The National Academy of Sciences of the USA

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sample indicate that PPv is not quenchable to ambient conditionsas reported (11).

Based on the degree of continuity in the diffraction rings andpreferred orientation, we selected a total of 4 high-temperaturepatterns and a total of 22 room-temperature patterns for Ri-etveld refinements (14) (Fig. S2). Selected results are shown inTable 1 with corresponding diffraction patterns in Fig. 1 a andb (entire Rietveld results are presented in Tables S1, S2, and S3).To assess the uncertainty, we also calculate the standard devi-ations of the fitted parameters from 4 diffraction patternsmeasured at 2,400–2,600 K and 135 GPa assuming that thechange in atomic parameters for the 200 K temperature rangewould be small. The magnitude of the latter estimation is similarto the 1� from the Rietveld refinements (Table 1).

Rietveld refinements of the diffraction patterns obtained inthe diamond-anvil cell at these extreme P–T conditions inevi-

tably suffer from various problems including texturing of thesample and a smaller number of grains in an extremely smallx-ray sampling area, 5 � 5 �m2. Nevertheless, the dense distri-bution of our data points over a wide P–T range allows us to

Table 1. Selected Rietveld refinement results for PPv at high P–T

Parameters

(Mg0.91Fe0.09)SiO3 MgSiO3

This study This study Experiment (10) Theory (2)

Pressure, GPa 135 (2) 126 (2) 116 120Temperature, K 2,535 (150) 300 300 0a, Å 2.467 (2) 2.460 (1) 2.469 2.474b, Å 8.080 (7) 8.059 (3) 8.117 8.121c, Å 6.119 (4) 6.102 (2) 6.151 6.138

Atomic position parametersyMg 0.247 (5, 6) 0.248 (3) 0.257 0.253yO1 0.909 (13, 3) 0.919 (5) 0.943 0.928yO2 0.644 (12, 3) 0.637 (5) 0.640 0.636zO2 0.450 (10, 3) 0.432 (3) 0.442 0.441

Interatomic distances and anglesSi–O1 (�2), Å 1.70 (4, 1) 1.66 (1) 1.61 1.64Si–O2 (�4), Å 1.73 (8, 2) 1.71 (2) 1.72 1.70Mg–O1 (�2), Å 1.80 (8, 3) 1.85 (3) 1.95 1.88Mg–O2 (�4), Å 1.92 (6, 2) 1.88 (2) 1.95 1.96Mg–O2 (�2), Å 2.04 (6, 4) 2.15 (3) 2.07 2.10�SiO1Si, ° 129 (6, 1) 134 (2) 146 138�SiO2Si, ° 91 (5, 1) 92 (2) 92 94

For the atomic parameters at high temperature, two different estimated uncertainties are presented: the firstnumber in the parentheses is 2� of Rietveld refinements and the second number is the standard deviation of thefour different data points measured at 2,400–2,600 K and 135 GPa. We also include a Rietveld refinement (10) anda first-principles prediction (2) for PPv. Crystal structure parameters from other first-principles studies are inagreement with Oganov and Ono (2) within 1%.

Table 2. Volumes (V) and bulk moduli (K) of PPv and Pvat high P

References V, Å3 K, GPa XFe, mol%

Experiment: Postperovskite at 125 GPa and 300 KThis work 121.3(1) 657(16) 9Mao et al. (12) 124.7 908 40Shieh et al. (11) 120.8 653 9?

Experiment: Perovskite at 125 GPa and 300 KThis work 123.3(5) 679(10) 9Fiquet et al. (18) 122.0 665 0

Theory: Postperovskite at 120 GPa and 0 KOganov and Ono (2) 122.7 647 0Caracas and Cohen (34) 125.2 701 100

Theory: Perovskite at 120 GPa and 0 KOganov and Ono (2) 124.6 648 0Caracas and Cohen (34) 126.8 715 100

For theory, the values are obtained from the LDA results (2, 34). The valuesfor ferromagnetic are chosen for FeSiO3 (see also Table S4 for details).

a

b

c

d

Fig. 1. Rietveld refinements of the x-ray diffraction patterns of(Mg0.91Fe0.09)SiO3-PPv at high P–T (a–c) (crosses, observed intensities; red lines,calculated intensities; black lines, difference between observed and calcu-lated intensities; black bars, calculated diffraction peak positions). Because ofpeak overlaps with the diffraction lines from the internal pressure standard(Au), the pressure medium (Ar), and the gasket (Re), some angle ranges(shown in blue lines) are excluded from the Rietveld refinements. The diffrac-tion lines that overlap with those of PPv are labeled with ‘‘�.’’ (d) A Le Bailfitting result for a diffraction pattern measured at low pressure. The back-grounds of the diffraction patterns were subtracted.

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examine the reliability of our results. Over the pressure rangewhere structural changes are expected to be small we observeconsistency among the refined parameters; for example, theSi–O bond distances and �SiO2Si bond angle at 110–135 GPa(Fig. 2). More importantly, within 2� our results are in goodagreement with first-principles predictions for most atomicparameters at 110–135 GPa, supporting the first-principlesprediction of the crystal structure (Table 1, Fig. 2, and Fig. S3).However, yO1 of a Rietveld refinement on MgSiO3-PPv at 116GPa and 300 K reported by Ono et al. (10) is significantly largerthan those of our result and first-principles calculations, resultingin larger differences between the Si–O1 and Si–O2 bond dis-tances and a larger �SiO1Si angle.

The volume of PPv was measured between 37 and 126 GPa at300 K to constrain the bulk modulus (K) (Fig. 3). The volumesmeasured at the stable pressures of PPv (P � 110 GPa) at 300K show little data scatter. However, below 110 GPa, the volumedeviates from the trend observed at higher pressures. At 110GPa, we found a discrete increase in the peak width (Fig. S4),suggesting that PPv may undergo a previously unidentifiedmetastable change outside of its stability field. Another distinctbehavior was identified at 80 GPa where the volume rapidlyincreases with decompression. The latter change is consistentwith the metastable behavior of Fe-rich PPv observed at P �90GPa reported by Mao et al. (12). At the same pressure range, wealso observed a steep increase in the peak widths (Fig. S4). Ashighlighted by a box in Fig. 1d, Le Bail fitting shows systematicmisfits for the data at P �75 GPa. This may indicate that thecrystal structure of the PPv phase is no longer that of the CaIrO3type at this pressure range, which is well below the stablepressure conditions of PPv.

The metastable behavior at P �110 GPa can also be identifiedin the measured crystallographic parameters. Our Rietveld refine-ments show that the �SiO2Si bond angle increases discontinuouslyand the Si–O2 bond distance becomes smaller than the Si–O1 bonddistance at 110 GPa. Both of these indicate that O2 is displaced

toward a line connecting adjacent Si4� ions as shown in Fig. 2 Inset.We note that O2 is shared by two adjacent octahedra through theiredges, whereas O1 is shared by corners. Although the edge sharingimproves packing efficiency, it is less effective in shielding therepulsion between two adjacent Si4� ions with strong positivecharges compared with corner sharing. The inward displacement ofO2 may enhance the shielding and help to reduce the repulsionbetween adjacent Si4� ions. However, this may not be necessary inthe stability field perhaps because of the balance with externalstress. This also suggests that the properties of PPv measured atconditions outside its stability field (P � 110 GPa) can becontaminated by metastability.

Because of the metastable behavior of PPv at low pressure, it isnot appropriate to set the reference state at ambient conditions forthe equation of state. We use the second-order Birch–Murnaghanequation (15) by setting the reference state at 125 GPa and 300 K,which are the stable conditions for PPv. When all of the data pointsat P �80 GPa are included in the fit, we obtain a very high bulkmodulus at 125 GPa, K125GPa � 833 � 16 GPa, which is comparableto Mao et al. (12) (Table 2). However, we found systematic residuesafter the fit as shown in Fig. 3a, indicating that the compressionalbehavior also changes at 110 GPa, consistent with our Rietveldresults. Therefore, we conduct a separate fit only for the data at P�110 GPa. The fit residues show that the data points at P �110 GPadeviate systematically from the trend observed at P �110 GPa. Forthis fit, we obtained K125GPa � 657 � 16 GPa, which is consistentwith previous measurements on Pv � PPv mixtures (11) and thefirst-principles predictions (1, 4, 16) (Table 2). We also conductedvolume measurements on perovskite (Pv) synthesized from thesame starting material by using the same pressure scale (Fig. 3). Thisallows us to obtain robust constraints on density and bulk moduluschanges across the PPv transition without being seriously affectedby the inconsistencies among different pressure scales (17). Ourfitted bulk modulus (K0) of Pv to the third-order Birch–Murnaghanequation is in agreement with previous reports (18) within theestimated uncertainty (Table 2).

a

b

c

O2

O1

Fig. 2. The Si–O bond distances (Lower) and �SiO2Si angle (Upper) in(Mg0.91Fe0.09)SiO3-PPv at 300 K (black circles) and 2,400–2,600 K (red circles).(Lower) The filled and open circles represent the Si–O1 (corner shared) andSi–O2 (edge shared) bond distances, respectively. The error bars represent 2�

uncertainties. The shaded area highlights the pressure range where structuralchanges are detected. The horizontal dark-gray lines represent the valuesfrom a first-principles calculation (1) at 120 GPa and 0 K. (Inset) Shown are theedge-shared SiO6 octahedra in PPv. The blue and white spheres represent Siand O atoms, respectively. The red arrow indicates repulsion between the Siatoms in adjacent octahedra and the blue arrows show the displacement of O2atoms observed in our study.

Fig. 3. Pressure–volume relations of PPv at 300 K (black solid circles) and2,300–2,700 K (red solid circles), and Pv at 300 K (black open circles) in(Mg0.91Fe0.09)SiO3. The solid and dashed curves are the fits for the data pointsP �110 and �80 GPa, respectively, to the Birch–Murnaghan equation. Thedotted curve is the fit for the Pv data points. The shaded areas highlight thepressure ranges where changes in the compressional behavior of PPv wereidentified. (Inset a) Residues of equation-of-state fits when all of the data atP �110 GPa are included (filled circles) and when all of the data at P �80 GPaare included (open squares). (Inset b) The Gruneisen parameter (�) of PPvobtained from our high-temperature data points. The horizontal shaded areain Inset b represents the range of � of Pv in the literature (18, 24, 25).

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By combining our measurements on Pv and PPv, we find thatdensity increases by 1.6 � 0.4% and bulk modulus decreases by3.3 � 2.7%, resulting in a 2.4 � 1.4% decrease in bulk sound speed(V�) across the PPv transition. This agrees with the previousfirst-principles predictions (1, 4). Combined with a shear-wavevelocity (VS) increase proposed by Brillouin spectroscopy (19) andfirst-principles (1, 4) studies, our result indicates that lateral vari-ations in mineralogy between Pv and PPv can result in the anti-correlation between the V� and VS anomalies at the lowermostmantle, consistent with previous first-principles predictions (6, 7):VS would be higher but V� would be lower at a PPv-rich region thanthose at a Pv-rich region. Seismic studies have documented theanticorrelation at the mid- to lowermost-mantle (20–22). There-fore, lateral variations in the mineralogy may provide a viableexplanation for some of the anomalies existing below the PPvtransition depth in the mantle (2), which is perhaps 2,500–2,700 km.However, according to Mao et al. (23) the transition depth may besignificantly elevated (by 300–400 km per 10% Fe) with an Feenrichment.

A total of 11 volume data points of PPv were measured at the P–Tconditions directly relevant to the D� layer. All of the data pointsexhibit nearly constant volume at different temperatures (V �121.85 � 0.08 Å3), which allows us to constrain thermal pressure,(dP/dT)V � �KT (� is the thermal expansion parameter and KT isthe isothermal bulk modulus). Because temperature is sufficientlyhigher than the expected Debye temperature of PPv, a Gruneisenparameter (�) can be obtained for each data point from: � ��KTV/CV � (dP/dT)V V/3R (CV is the specific heat and R is the gasconstant, Fig. 3b).

The measured � of PPv at 135 GPa and 2,300–2,700 K is 0.79 �0.12, which is smaller than that of Pv (0.94–1.07) at the same P–Tconditions (18, 24, 25), suggesting a 21 � 15% decrease in � acrossthe PPv transition (Fig. 3b). Care must be taken with this compar-ison, because the estimations for PPv and Pv are based on differentpressure scales, the consistency of which is unknown. Furthermore,calculation of the � of Pv at 135 GPa from the existing data requiresa long extrapolation. Nevertheless, recent Raman measurements onPv and PPv in MgGeO3 found a large decrease in the rate ofpressure-induced phonon shift, which is consistent with a 25 � 6%reduction in � across the PPv transition (8). The lower � indicatesthat the density jump across the PPv transition at mantle temper-ature can be higher than 1.6% which is observed at 300 K.Therefore, the higher density of PPv would dynamically stabilize thePPv lenses documented in recent seismic studies (26, 27) andinfluence the flow at the base of the mantle (28).

Our study shows that the dominant mantle silicate undergoessignificant changes in crystal structure across the PPv transition,which may lead to unexpected changes in some physical properties,such as decreases in bulk sound speed and Gruneisen parameterfound in this study. From the observed strong lateral heterogene-ities, seismic studies (29) have inferred large variations in temper-ature and composition at the lowermost mantle. Yet the largeClapeyron slope of the PPv transition and the proximity of thetransition to the CMB (2, 5, 8) will make the mineralogy at thelowermost mantle very sensitive to both temperature and compo-sition. Our study shows that some of the lateral heterogeneities canbe explained by changes in mineralogy at the D� region. Therefore,the strong heterogeneity at the D� region may be a consequence of

complex interactions among temperature, composition, andmineralogy.

Experimental MethodsA powder form of natural enstatite with 9 mol% Fe was mixed with 8 wt%gold powder, which serves as an internal standard for pressure measurementsand a laser coupler for heating. The powder was compressed to foils withthicknesses �5 �m. Rhenium gaskets were indented to thicknesses �25 �mand a hole was drilled at the center of the indentation for the sample chamber.Diamond anvils with 200-�m flat and 100-�m beveled culets were used formeasurements for Pv and PPv, respectively. We used symmetric-type diamond-anvil cells (DACs). Argon was cryogenically loaded in the DACs together withthe sample foil as a pressure-transmitting and insulation medium (Fig. S1). Toprevent direct contact between diamond anvils and the sample foil, two tofour particles (2–3 �m in diameter) of the starting material were placedbetween the sample and diamond anvils as spacers.

Angle-dispersive diffraction measurements on PPv were conducted at the13IDD beamline of the Advanced Photon Source (APS) using the MarCCDdetector. We measured diffraction patterns of Pv at the 13IDD beamline ofAPS and the 12.2.2 beamline of the Advanced Light Source (ALS) by using theMar345 imaging plate. We used a monochromatic beam with an energy of 30keV. The size of the x-ray beam was 5 � 5 �m2 and 10 � 10 �m2 at GeoSoil-Enviro Consortium for Advanced Radiation Sources (GSECARS) and 12.2.2,respectively. This is smaller than the size of the laser-heated spot that is 20�m in diameter. The sample-to-detector distance and the tilt of the detectorwere calibrated by using the diffraction patterns of CeO2 or LaB6.

For the synthesis of high-pressure phases and annealing of deviatoric stresses,we used laser-heating systems at Massachusetts Institute of Technology, GSE-CARS, and 12.2.2. We used Nd:YLF laser beams with a TEM01 mode. For in situdouble-sided laser heating at GSECARS, we colinearly aligned the sample, inci-dent x-ray beam, and laser beams, to measure x-ray diffraction from the center ofthe heated spot, which has a smaller thermal gradient. Temperature of thesamples was estimated by fitting the measured thermal radiation spectra to thePlanck equation. The wavelength dependence of the emissivity of the sample isunknown and assumed to be constant. The uncertainty in temperature measure-ments is �150 K at the studied pressure range (30). Pressure is calculated fromthevolumeofgold,which is constrainedbythreetofourdiffraction lines,andtheequation of state is according to Tsuchiya (31).

To measure the equation of state of Pv, separate samples were prepared forlow-pressure measurements by using the same starting material and the samepressure scale (gold). Ar and NaCl are used as pressure media for data at belowand above 54 GPa, respectively. The Pv phase was synthesized at 50 GPa and2,000 K for 30 min. Before each diffraction measurement, we annealed thesamples to reduce differential stresses by using laser heating.

One-dimensional diffraction patterns were obtained by integrating diffrac-tion rings using the Fit2D software (32). The absorption from the cBN backingplate and the diamond anvils was corrected. Based on the degree of continuity ofthe diffraction rings and preferred orientation, we selected a total of 4 among 11high-temperature diffraction patterns and a total of 22 among 38 room-temperature diffraction patterns for Rietveld refinements (14).

In the Rietveld analysis, we refined all of the atomic position parameters aswell as unit-cell parameters, preferred orientation function, peak profileshape function, scale factors, and thermal parameters. During the refinement,the temperature factors of the atoms are constrained to be the same, toprevent ‘‘overfitting’’ of the data (33).

ACKNOWLEDGMENTS. We thank T. L. Grove for providing the startingmaterials and T. S. Duffy, T. L. Grove, R. van der Hilst, and two anonymousreviewers for discussions that improved the manuscript. Portions of thiswork were performed at GeoSoilEnviro Consortium for Advanced Radia-tion Sources (GSECARS) at Advanced Photon Source (APS) and beamline12.2.2 at Advanced Light Source (ALS). This work was supported in part byNational Science Foundation (NSF) Award EAR0337005 (to S.-H.S.). GSE-CARS is supported by the NSF and Department of Energy. The 12.2.2beamline is supported by the Consortium for Materials Properties Researchin Earth Sciences under NSF. Use of APS and ALS is supported by the DOE.

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