Crystal structure and thermoelastic properties
of (Mg0.91Fe0.09)SiO3 postperovskite up
to 135 GPa and 2,700 K
Sang-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 bottom
400 km of Earth’s mantle (the D! region) over the past few decades,
yet the origin of these seismic structures has not been well
understood. Recent theoretical calculations have predicted many
unusual changes in physical properties across the postperovskite
transition, perovskite (Pv) 3 postperovskite (PPv), that may provide explanations for the seismic observations. Here, we report
measurements of the crystal structure of (Mg0.91Fe0.09)SiO3-PPv
under quasi-hydrostatic conditions up to the pressure (P)–temperature (T) conditions expected for the core-mantle boundary (CMB).
The measured crystal structure is in excellent agreement with the
first-principles calculations. We found that bulk sound speed (V!)
decreases by 2.4 " 1.4% across the PPv transition. Combined with
the predicted shear-wave velocity (VS) increase, our measurements
indicate that lateral variations in mineralogy between Pv and PPv
may result in the anticorrelation between the V! and VS anomalies
at the D! region. Also, density increases by 1.6 " 0.4% and
Grüneisen parameter decreases by 21 " 15% across the PPv
transition, which will dynamically stabilize the PPv lenses observed
in recent seismic studies.
equation of state ! mantle ! phase transition ! bulk sound speed !
Grüneisen parameter
T
he D! region is believed to play an important role for the
dynamics of the mantle and the core. The recent discovery
of the postperovskite (PPv) transition (1–3) at the P–T conditions relevant to the D! region has provided new opportunities
to understand the seismic observations and dynamic processes in
the region. First-principles calculations (1, 4, 5) have predicted
drastic changes in some geophysically important properties
across the PPv transition (6, 7). The unusual changes have been
attributed to the fundamental differences in crystal structure
between perovskite (Pv), a 3D network structure with cornersharing SiO6 octahedra, and PPv, a 2D layered structure with
both corner and edge sharing SiO6 octahedra (1, 4, 8, 9).
Therefore, measurements of the crystal structure provide a
fundamental test for the predicted properties of PPv. However,
synthesis of an appropriate single crystal for PPv in its stability
field is extremely challenging for current techniques, making
Rietveld refinement the only plausible method for studying the
crystal 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 sound
speed (V") decreases across the PPv transition whereas shearwave velocity (VS) increases. Shieh et al. (11) measured Pv # PPv
mixtures in (Mg0.91Fe0.09)SiO3 and suggested decreases in volume and bulk modulus, and therefore a decrease in V", across
the PPv transition, but the Fe contents of the individual phases
were not known and a limited number of diffraction lines were
used for constraining volume. Mao et al. (12) have achieved
denser data coverage for (Mg0.6Fe0.4)SiO3-PPv at a wider pres7382–7386 ! PNAS ! May 27, 2008 ! vol. 105 ! no. 21
sure range. Their data indicate that the bulk modulus of PPv
should be very high at CMB pressures (Table 2), suggesting a
large increase in V" across the PPv transition. However, no
pressure medium was used in this study. The larger amount of Fe
in Mao et al. (12) may cause the difference, yet a first-principles
calculation showed that Fe has little effect on the bulk modulus
of PPv (13).
We have measured x-ray diffraction patterns of
(Mg0.91Fe0.09)SiO3-PPv under quasi-hydrostatic stress conditions
with a chemically inert, insulating, compressible Ar pressure
medium at in situ high P–T conditions (37–126 GPa at 300 K and
135 GPa at 2,300–2,700 K) in the laser-heated diamond-anvil cell
[supporting information (SI) Fig. S1]. We measured at least 25
full-diffraction rings of PPv to d-spacing !1.1 Å, which is a
significant improvement over previous studies. Our dataset
enables us to constrain the changes in density, bulk modulus, and
Grüneisen parameter across the PPv transition and to measure
the crystal structure of PPv through the Rietveld refinements.
Results and Discussion
To synthesize PPv, we increased pressure directly to 120–130
GPa 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 observed
the synthesis of a Pv # PPv mixture from the amorphized starting
material. However, after 1 h of heating at slightly higher
pressure, the sample transforms completely to PPv. The P–T
conditions of the PPv transition we observed are consistent with
those expected for the D! discontinuity within experimental
uncertainties. 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 the
sample. The sufficient amount of Ar medium reduces the
thermal gradients and differential stresses in the sample.
After the synthesis of PPv, in situ diffraction measurements
were 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 did
not heat the sample during decompression. Down to 85 GPa, the
diffraction 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., and
M.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: [email protected].
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
www.pnas.org"cgi"doi"10.1073"pnas.0711174105
Table 1. Selected Rietveld refinement results for PPv at high P–T
(Mg0.91Fe0.09)SiO3
Parameters
MgSiO3
This study
This study
Experiment (10)
Theory (2)
135 (2)
2,535 (150)
2.467 (2)
8.080 (7)
6.119 (4)
126 (2)
300
2.460 (1)
8.059 (3)
6.102 (2)
116
300
2.469
8.117
6.151
120
0
2.474
8.121
6.138
Atomic position parameters
yMg
0.247 (5, 6)
yO1
0.909 (13, 3)
yO2
0.644 (12, 3)
zO2
0.450 (10, 3)
0.248 (3)
0.919 (5)
0.637 (5)
0.432 (3)
0.257
0.943
0.640
0.442
0.253
0.928
0.636
0.441
Interatomic distances and angles
Si–O1 (%2), Å
1.70 (4, 1)
Si–O2 (%4), Å
1.73 (8, 2)
Mg–O1 (%2), Å
1.80 (8, 3)
Mg–O2 (%4), Å
1.92 (6, 2)
Mg–O2 (%2), Å
2.04 (6, 4)
!SiO1Si, °
129 (6, 1)
!SiO2Si, °
91 (5, 1)
1.66 (1)
1.71 (2)
1.85 (3)
1.88 (2)
2.15 (3)
134 (2)
92 (2)
Pressure, GPa
Temperature, K
a, Å
b, Å
c, Å
1.61
1.72
1.95
1.95
2.07
146
92
1.64
1.70
1.88
1.96
2.10
138
94
For the atomic parameters at high temperature, two different estimated uncertainties are presented: the first
number in the parentheses is 2" of Rietveld refinements and the second number is the standard deviation of the
four different data points measured at 2,400 –2,600 K and 135 GPa. We also include a Rietveld refinement (10) and
a first-principles prediction (2) for PPv. Crystal structure parameters from other first-principles studies are in
agreement with Oganov and Ono (2) within 1%.
Table 2. Volumes (V) and bulk moduli (K) of PPv and Pv
at high P
References
V,
Å3
K, GPa
a
b
c
XFe, mol%
Experiment: Postperovskite at 125 GPa and 300 K
This work
121.3(1)
657(16)
Mao et al. (12)
124.7
908
Shieh et al. (11)
120.8
653
9
40
9?
Experiment: Perovskite at 125 GPa and 300 K
This work
123.3(5)
679(10)
Fiquet et al. (18)
122.0
665
9
0
Theory: Postperovskite at 120 GPa and 0 K
Oganov and Ono (2)
122.7
Caracas and Cohen (34)
125.2
647
701
0
100
Theory: Perovskite at 120 GPa and 0 K
Oganov and Ono (2)
124.6
Caracas and Cohen (34)
126.8
648
715
0
100
For theory, the values are obtained from the LDA results (2, 34). The values
for ferromagnetic are chosen for FeSiO3 (see also Table S4 for details).
Shim et al.
tably suffer from various problems including texturing of the
sample and a smaller number of grains in an extremely small
x-ray sampling area, 5 % 5 #m2. Nevertheless, the dense distribution of our data points over a wide P–T range allows us to
GEOPHYSICS
sample indicate that PPv is not quenchable to ambient conditions
as reported (11).
Based on the degree of continuity in the diffraction rings and
preferred orientation, we selected a total of 4 high-temperature
patterns and a total of 22 room-temperature patterns for Rietveld refinements (14) (Fig. S2). Selected results are shown in
Table 1 with corresponding diffraction patterns in Fig. 1 a and
b (entire Rietveld results are presented in Tables S1, S2, and S3).
To assess the uncertainty, we also calculate the standard deviations of the fitted parameters from 4 diffraction patterns
measured at 2,400–2,600 K and 135 GPa assuming that the
change in atomic parameters for the 200 K temperature range
would be small. The magnitude of the latter estimation is similar
to the 1" from the Rietveld refinements (Table 1).
Rietveld refinements of the diffraction patterns obtained in
the diamond-anvil cell at these extreme P–T conditions inevi-
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 calculated intensities; black bars, calculated diffraction peak positions). Because of
peak 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 diffraction lines that overlap with those of PPv are labeled with ‘‘#.’’ (d) A Le Bail
fitting result for a diffraction pattern measured at low pressure. The backgrounds of the diffraction patterns were subtracted.
PNAS ! May 27, 2008 ! vol. 105 ! no. 21 ! 7383
O2
O1
b
c
a
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) and
Si–O2 (edge shared) bond distances, respectively. The error bars represent 2"
uncertainties. The shaded area highlights the pressure range where structural
changes are detected. The horizontal dark-gray lines represent the values
from a first-principles calculation (1) at 120 GPa and 0 K. (Inset) Shown are the
edge-shared SiO6 octahedra in PPv. The blue and white spheres represent Si
and O atoms, respectively. The red arrow indicates repulsion between the Si
atoms in adjacent octahedra and the blue arrows show the displacement of O2
atoms observed in our study.
examine the reliability of our results. Over the pressure range
where structural changes are expected to be small we observe
consistency among the refined parameters; for example, the
Si–O bond distances and !SiO2Si bond angle at 110–135 GPa
(Fig. 2). More importantly, within 2" our results are in good
agreement with first-principles predictions for most atomic
parameters at 110–135 GPa, supporting the first-principles
prediction of the crystal structure (Table 1, Fig. 2, and Fig. S3).
However, yO1 of a Rietveld refinement on MgSiO3-PPv at 116
GPa and 300 K reported by Ono et al. (10) is significantly larger
than those of our result and first-principles calculations, resulting
in larger differences between the Si–O1 and Si–O2 bond distances and a larger !SiO1Si angle.
The volume of PPv was measured between 37 and 126 GPa at
300 K to constrain the bulk modulus (K) (Fig. 3). The volumes
measured at the stable pressures of PPv (P ! 110 GPa) at 300
K show little data scatter. However, below 110 GPa, the volume
deviates from the trend observed at higher pressures. At 110
GPa, we found a discrete increase in the peak width (Fig. S4),
suggesting that PPv may undergo a previously unidentified
metastable change outside of its stability field. Another distinct
behavior was identified at 80 GPa where the volume rapidly
increases with decompression. The latter change is consistent
with the metastable behavior of Fe-rich PPv observed at P $90
GPa reported by Mao et al. (12). At the same pressure range, we
also observed a steep increase in the peak widths (Fig. S4). As
highlighted by a box in Fig. 1d, Le Bail fitting shows systematic
misfits for the data at P $75 GPa. This may indicate that the
crystal structure of the PPv phase is no longer that of the CaIrO3
type at this pressure range, which is well below the stable
pressure conditions of PPv.
The metastable behavior at P $110 GPa can also be identified
in the measured crystallographic parameters. Our Rietveld refinements show that the !SiO2Si bond angle increases discontinuously
and the Si–O2 bond distance becomes smaller than the Si–O1 bond
distance at 110 GPa. Both of these indicate that O2 is displaced
7384 ! www.pnas.org"cgi"doi"10.1073"pnas.0711174105
Fig. 3. Pressure–volume relations of PPv at 300 K (black solid circles) and
2,300 –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 points
P &110 and &80 GPa, respectively, to the Birch–Murnaghan equation. The
dotted curve is the fit for the Pv data points. The shaded areas highlight the
pressure ranges where changes in the compressional behavior of PPv were
identified. (Inset a) Residues of equation-of-state fits when all of the data at
P &110 GPa are included (filled circles) and when all of the data at P &80 GPa
are included (open squares). (Inset b) The Grüneisen parameter (%) of PPv
obtained from our high-temperature data points. The horizontal shaded area
in Inset b represents the range of % of Pv in the literature (18, 24, 25).
toward a line connecting adjacent Si4# ions as shown in Fig. 2 Inset.
We note that O2 is shared by two adjacent octahedra through their
edges, whereas O1 is shared by corners. Although the edge sharing
improves packing efficiency, it is less effective in shielding the
repulsion between two adjacent Si4# ions with strong positive
charges compared with corner sharing. The inward displacement of
O2 may enhance the shielding and help to reduce the repulsion
between adjacent Si4# ions. However, this may not be necessary in
the stability field perhaps because of the balance with external
stress. This also suggests that the properties of PPv measured at
conditions outside its stability field (P $ 110 GPa) can be
contaminated by metastability.
Because of the metastable behavior of PPv at low pressure, it is
not appropriate to set the reference state at ambient conditions for
the equation of state. We use the second-order Birch–Murnaghan
equation (15) by setting the reference state at 125 GPa and 300 K,
which are the stable conditions for PPv. When all of the data points
at P &80 GPa are included in the fit, we obtain a very high bulk
modulus at 125 GPa, K125GPa ' 833 ( 16 GPa, which is comparable
to Mao et al. (12) (Table 2). However, we found systematic residues
after the fit as shown in Fig. 3a, indicating that the compressional
behavior also changes at 110 GPa, consistent with our Rietveld
results. 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 GPa
deviate systematically from the trend observed at P &110 GPa. For
this fit, we obtained K125GPa ' 657 ( 16 GPa, which is consistent
with previous measurements on Pv # PPv mixtures (11) and the
first-principles predictions (1, 4, 16) (Table 2). We also conducted
volume measurements on perovskite (Pv) synthesized from the
same starting material by using the same pressure scale (Fig. 3). This
allows us to obtain robust constraints on density and bulk modulus
changes across the PPv transition without being seriously affected
by the inconsistencies among different pressure scales (17). Our
fitted bulk modulus (K0) of Pv to the third-order Birch–Murnaghan
equation is in agreement with previous reports (18) within the
estimated uncertainty (Table 2).
Shim et al.
1. Oganov AR, Ono S (2004) Theoretical and experimental evidence for a post-perovskite
phase of MgSiO3 in Earth’s D! layer. Nature 430:445– 448.
2. Murakami M, Hirose K, Kawamura K, Sata N, Ohishi Y (2004) Post-perovskite phase
transition in MgSiO3. Science 304:855– 858.
3. Shim SH, Duffy TS, Jeanloz R, Shen G (2004) Stability and crystal structure of MgSiO3
perovskite to the core-mantle boundary. Geophys Res Lett 31:L10603.
4. Iitaka T, Hirose K, Kawamura K, Murakami M (2004) The elasticity of the
MgSiO3 post-perovskite phase in the earth’s lowermost mantle. Nature 430:442–
445.
Shim et al.
complex interactions among temperature, composition, and
mineralogy.
Experimental Methods
A powder form of natural enstatite with 9 mol% Fe was mixed with 8 wt%
gold powder, which serves as an internal standard for pressure measurements
and a laser coupler for heating. The powder was compressed to foils with
thicknesses $5 #m. Rhenium gaskets were indented to thicknesses $25 #m
and 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 for
measurements for Pv and PPv, respectively. We used symmetric-type diamondanvil cells (DACs). Argon was cryogenically loaded in the DACs together with
the sample foil as a pressure-transmitting and insulation medium (Fig. S1). To
prevent direct contact between diamond anvils and the sample foil, two to
four particles (2–3 #m in diameter) of the starting material were placed
between the sample and diamond anvils as spacers.
Angle-dispersive diffraction measurements on PPv were conducted at the
13IDD beamline of the Advanced Photon Source (APS) using the MarCCD
detector. We measured diffraction patterns of Pv at the 13IDD beamline of
APS and the 12.2.2 beamline of the Advanced Light Source (ALS) by using the
Mar345 imaging plate. We used a monochromatic beam with an energy of 30
keV. The size of the x-ray beam was 5 % 5 #m2 and 10 % 10 #m2 at GeoSoilEnviro 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 detector
were 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, GSECARS, and 12.2.2. We used Nd:YLF laser beams with a TEM01 mode. For in situ
double-sided laser heating at GSECARS, we colinearly aligned the sample, incident x-ray beam, and laser beams, to measure x-ray diffraction from the center of
the heated spot, which has a smaller thermal gradient. Temperature of the
samples was estimated by fitting the measured thermal radiation spectra to the
Planck equation. The wavelength dependence of the emissivity of the sample is
unknown and assumed to be constant. The uncertainty in temperature measurements is ) (150 K at the studied pressure range (30). Pressure is calculated from
the volume of gold, which is constrained by three to four diffraction lines, and the
equation of state is according to Tsuchiya (31).
To measure the equation of state of Pv, separate samples were prepared for
low-pressure measurements by using the same starting material and the same
pressure scale (gold). Ar and NaCl are used as pressure media for data at below
and above 54 GPa, respectively. The Pv phase was synthesized at 50 GPa and
2,000 K for 30 min. Before each diffraction measurement, we annealed the
samples to reduce differential stresses by using laser heating.
One-dimensional diffraction patterns were obtained by integrating diffraction rings using the Fit2D software (32). The absorption from the cBN backing
plate and the diamond anvils was corrected. Based on the degree of continuity of
the diffraction rings and preferred orientation, we selected a total of 4 among 11
high-temperature diffraction patterns and a total of 22 among 38 roomtemperature diffraction patterns for Rietveld refinements (14).
In the Rietveld analysis, we refined all of the atomic position parameters as
well as unit-cell parameters, preferred orientation function, peak profile
shape function, scale factors, and thermal parameters. During the refinement,
the temperature factors of the atoms are constrained to be the same, to
prevent ‘‘overfitting’’ of the data (33).
ACKNOWLEDGMENTS. We thank T. L. Grove for providing the starting
materials and T. S. Duffy, T. L. Grove, R. van der Hilst, and two anonymous
reviewers for discussions that improved the manuscript. Portions of this
work were performed at GeoSoilEnviro Consortium for Advanced Radiation Sources (GSECARS) at Advanced Photon Source (APS) and beamline
12.2.2 at Advanced Light Source (ALS). This work was supported in part by
National Science Foundation (NSF) Award EAR0337005 (to S.-H.S.). GSECARS is supported by the NSF and Department of Energy. The 12.2.2
beamline is supported by the Consortium for Materials Properties Research
in Earth Sciences under NSF. Use of APS and ALS is supported by the DOE.
5. Tsuchiya T, Tsuchiya J, Umemoto K, Wentzcovitch RM (2004) Phase transition in MgSiO3
perovskite in the earth’s lower mantle. Earth Planet Sci Lett 224:241–248.
6. Wookey J, Stackhouse S, Kendall JM, Brodholt J, Price GD (2005) Efficacy of the postperovskite phase as an explanation for lowermost-mantle seismic properties. Nature
438:1004 –1007.
7. Wentzcovitch RM, Tsuchiya T, Tsuchiya J (2006) MgSiO3 postperovskite at D! conditions. Proc Natl Acad Sci USA 103:543–546.
8. Shim SH, Kubo A, Duffy TS (2007) Raman spectroscopy of perovskite and postperovskite phases of MgGeO3 to 123 GPa. Earth Planet Sci Lett 260:166 –178.
PNAS ! May 27, 2008 ! vol. 105 ! no. 21 ! 7385
GEOPHYSICS
By combining our measurements on Pv and PPv, we find that
density increases by 1.6 ( 0.4% and bulk modulus decreases by
3.3 ( 2.7%, resulting in a 2.4 ( 1.4% decrease in bulk sound speed
(V") across the PPv transition. This agrees with the previous
first-principles predictions (1, 4). Combined with a shear-wave
velocity (VS) increase proposed by Brillouin spectroscopy (19) and
first-principles (1, 4) studies, our result indicates that lateral variations in mineralogy between Pv and PPv can result in the anticorrelation between the V" and VS anomalies at the lowermost
mantle, consistent with previous first-principles predictions (6, 7):
VS would be higher but V" would be lower at a PPv-rich region than
those at a Pv-rich region. Seismic studies have documented the
anticorrelation at the mid- to lowermost-mantle (20–22). Therefore, lateral variations in the mineralogy may provide a viable
explanation for some of the anomalies existing below the PPv
transition depth in the mantle (2), which is perhaps 2,500–2,700 km.
However, according to Mao et al. (23) the transition depth may be
significantly elevated (by 300–400 km per 10% Fe) with an Fe
enrichment.
A total of 11 volume data points of PPv were measured at the P–T
conditions directly relevant to the D! layer. All of the data points
exhibit 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 is
the isothermal bulk modulus). Because temperature is sufficiently
higher than the expected Debye temperature of PPv, a Grüneisen
parameter (%) can be obtained for each data point from: % '
&KTV/CV ' (dP/dT)V V/3R (CV is the specific heat and R is the gas
constant, 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–T
conditions (18, 24, 25), suggesting a 21 ( 15% decrease in % across
the PPv transition (Fig. 3b). Care must be taken with this comparison, because the estimations for PPv and Pv are based on different
pressure scales, the consistency of which is unknown. Furthermore,
calculation of the % of Pv at 135 GPa from the existing data requires
a long extrapolation. Nevertheless, recent Raman measurements on
Pv and PPv in MgGeO3 found a large decrease in the rate of
pressure-induced phonon shift, which is consistent with a 25 ( 6%
reduction in % across the PPv transition (8). The lower % indicates
that the density jump across the PPv transition at mantle temperature can be higher than 1.6% which is observed at 300 K.
Therefore, the higher density of PPv would dynamically stabilize the
PPv lenses documented in recent seismic studies (26, 27) and
influence the flow at the base of the mantle (28).
Our study shows that the dominant mantle silicate undergoes
significant 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 Grüneisen parameter
found in this study. From the observed strong lateral heterogeneities, seismic studies (29) have inferred large variations in temperature and composition at the lowermost mantle. Yet the large
Clapeyron slope of the PPv transition and the proximity of the
transition to the CMB (2, 5, 8) will make the mineralogy at the
lowermost mantle very sensitive to both temperature and composition. Our study shows that some of the lateral heterogeneities can
be explained by changes in mineralogy at the D! region. Therefore,
the strong heterogeneity at the D! region may be a consequence of
9. Shim SH (2008) The postperovskite transition. Annu Rev Earth Planet Sci 36:569 –599.
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GPa. Am Mineral 91:475– 478.
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a natural (Mg,Fe)SiO3 orthopyroxene. Proc Natl Acad Sci USA 103:3039 –3043.
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structure and volume of ferromagnesian post-perovskite. Geophys Res Lett 33:L12S02.
13. Stackhouse S, Brodholt JP, Price GD (2006) Elastic anisotropy of FeSiO3 end-members of
the perovskite and post-perovskite phases. Geophys Res Lett 33:L01304.
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refinement. Acta Crystallogr 22:151–152.
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Shim et al.
Supporting Information
Shim et al. 10.1073/pnas.0711174105
SI Text
Data Processing and Rietveld Analysis. Diffraction rings obtained
from samples at high temperature or samples quenched from
high temperature in the laser-heated diamond anvil cell (Fig. S1)
tend to be spotty because of recrystallization and crystal growth.
We found that the diffraction rings of postperovskite Fig. S2) are
much more continuous than those of perovskite [for example,
figure 1 of Shim et al. (1)] after heating to similar temperatures
for similar durations. Yoshino and Yamazaki (2) reported that
the grain size of the postperovskite phase is significantly smaller
than that of the perovskite phase in CaIrO3 for the same heating
duration at similar temperatures. Therefore, the smoother rings
in postperovskite may result from its smaller grain size. Most of
our diffraction patterns are well explained by pure postperovskite with an internal pressure standard, pressure medium, and
gasket material. Some previous measurements have shown that
it is difficult to achieve a complete transformation to the
postperovskite phase when the perovskite phase is present in the
starting material (3–5). In the previous studies, either no pressure medium was used or diffraction lines from the medium were
not clearly resolved at high P. Therefore, the difficulty of
achieving a complete transformation from perovskite starting
materials reported earlier may be because of insufficient thermal
insulation as well as kinetic effect. It appears less difficult to
obtain pure postperovskite from metastable amorphous or gel
starting materials (6).
However, in some diffraction patterns, we found a few weakintensity dots that are not explained by postperovskite, internal
pressure standard, pressure medium, or gasket material (Fig. S2).
Some of these dots are located near the expected peak positions of
perovskite. However, these dots are isolated with each other in
location and do not form rings. Furthermore, after integration, the
intensity at the location of the dots is still in background level.
Therefore, these dots could be from a highly oriented remnant
phase, which should not exceed 1% of the sample volume based on
their diffraction intensities. One likely source is the spacer particles
that are in direct contact with diamond (a good thermal conductor)
and therefore are heated to only low temperatures (Fig. S1).
High-temperature heating is important to overcome the kinetic
effect for the postperovskite transition.
The effect from preferred orientation was fit to a spherical
harmonics correction function (7) with a harmonic order of 4.
Within its stability field, postperovskite develops relatively small
preferred orientation in our study. We obtained a preferred
orientation index, J, of 1.0–1.5 at the stable P–T conditions of
postperovskite (J ! 1 for no preferred orientation and J ! " for
a single crystal). The degree of preferred orientation is similar
to that found in a recent Rietveld study on MgGeO3 postperovskite (8). We believe that this low degree of preferred orientation is caused by the use of an argon pressure medium. Within
the estimated uncertainty from Rietveld refinements, we do not
resolve any significant changes in preferred orientation within
the stability field of postperovskite.
Some fit residues still remain after Rietveld refinements as
shown in Fig. 1. The relatively small sampling volume of XRD
measurements in the laser-heated diamond-anvil cell may lead to
spottiness of diffraction rings (Fig. S2) that can influence the
refinement results. Yet the dense data distribution in the stability
field of postperovskite allows us to examine the reliability of our
refinements through comparisons of the refined parameters over
the pressure–temperature range where structural changes are
expected to be small. For example, a line at 9.6° shows some
Shim et al. www.pnas.org/cgi/content/short/0711174105
mismatch in Fig. 1a. However, in Fig. 1b, this line shows very
little mismatch. Nevertheless, the structural parameters obtained from these two patterns are still in good agreement as
shown in Fig. 2, indicating that the spottiness in our measurements do not have a large impact on our refinement results. Also,
a large d-spacing coverage (i.e., more diffraction lines) helps to
improve the accuracy of the refined parameters in Rietveld
analysis through reducing the effect of intensity-sampling errors
in individual diffraction lines. We expand the measured dspacing range by using x-ray semitransparent cBN seats.
An increase in deviatoric stress with compression was reported
for argon by radial diffraction measurements (9). However, no
thermal annealing was conducted in the measurements, whereas
the samples were heated to temperatures of 2,300–2,700 K for
#1 h in the stable P–T conditions of postperovskite in our study.
The unit-cell parameters calculated from the 111 and 200
diffraction lines of gold agree well, which indicates low deviatoric
stress in our measurements.
In Rietveld refinements, we excluded some angle ranges where
intense gold and argon diffraction lines overlap with the lines of
postperovskite, to prevent artifacts introduced from misfits of
those lines to the relatively weak postperovskite lines adjacent to
them. A total of 26–31 diffraction lines are used for the Rietveld
refinement of postperovskite. For in situ high-temperature measurements, although azimuthal angular coverage was the same,
because of the absorption from laser mirrors for some portions
of the rings, we use an azimuthal angle of 270° of the rings. Le
Bail fitting (10) was conducted for all of the diffraction patterns
by using the GSAS package (11) to constrain unit-cell parameters and peak-shape parameters. At the final stage of refinements all of the parameters are refined simultaneously to obtain
reasonable estimation of uncertainty. The unit-cell parameters
from both the Le Bail and Rietveld methods agree within 2!
uncertainties. The reliability factors, Rwp, of our refinements
range between 3 and 14%.
Pressure Scale. Pressure was calculated from the equation of state
of gold by Tsuchiya (12) by using the measured volume and
temperature. From our measurements on the equation of state
of perovskite, we found that the gold scale by Tsuchiya (12) yields
the closest match with the results obtained by using the platinum
scales. There exist differences of 10–20 GPa over 100 GPa of
pressure among the existing gold scales (13). Although less
difference can be found in the existing platinum scales, the
platinum scales (14, 15) are constrained from shock-wave data
only. However, the gold scale has been studied extensively with
many different techniques (13, 14, 16–23).
Most of the equation-of-state data of perovskite have been
measured by using the platinum scale (24). However, recent
studies (13, 25) have shown that some platinum and gold scales
could yield as much as a 10–20 GPa difference at 100 GPa, which
makes comparison of data sets tied to different scales unreliable.
Therefore, it was important for us to measure the equations of
state of perovskite and postperovskite by using the same pressure
scale.
The volume of gold was calculated from three to four diffraction lines. The standard deviation of pressure from different
lines is 1 GPa on average. Previous studies used this for the error
bar of pressure. However, including the uncertainties in the
equation-of-state parameters, the uncertainty of pressure should
be higher. Therefore, we use a factor of 2 larger values of the
standard deviation (2!) for the error bar of pressure.
1 of 10
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2 of 10
Fig. S1. Schematic diagram of the sample setup used in our measurements. To prevent direct contact between the sample foil and diamond anvils, we placed
spacer particles of the starting material below and above the foil.
Shim et al. www.pnas.org/cgi/content/short/0711174105
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Fig. S2. An unrolled projection of a 2D raw diffraction image for the pattern presented in Fig. 1b. The major diffraction lines from postperovskite, gold (internal
pressure standard), argon (pressure medium), and rhenium (gasket material) are indicated by red, black, blue, and open arrows, respectively.
Shim et al. www.pnas.org/cgi/content/short/0711174105
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Fig. S3. Crystal structure of postperovskite. The red, blue, and white spheres represent Mg, Si, and O atoms, respectively. The orange, red, and yellow sticks
represent shorter, intermediate, and longer Mg–O bond distances, respectively.
Shim et al. www.pnas.org/cgi/content/short/0711174105
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Fig. S4. The full width at half-maximum of the 022 diffraction line of (Mg0.91Fe0.09)SiO3 postperovskite at 300 K (black circles) and 2,300 –2,700 K (red circles).
The error bars represent estimated 2! uncertainties. An expanded view of the data points above 80 GPa is shown in the inset. The increase in width at 110 GPa
is subtle and may not be detectable in measurements without a pressure medium (26). The width between 110 and 125 GPa at 300 K is similar in magnitude to
that at high temperature and 135 GPa, supporting the stability of postperovskite during decompression measurements to 110 GPa. The changes we observed
cannot be found in the data by Shieh et al. (5), because no data points exist between 35 and 80 GPa in their data. Although their data below 35 GPa and above
80 GPa appear to align in a single compressional curve as is also the case for our data if the points between 75 and 115 GPa are ignored (Fig. 3), the observation
of a steep change at 80 GPa does not support the inclusion of the lower-pressure data points for equation-of-state fit, as also argued by Mao et al. (26).
Shim et al. www.pnas.org/cgi/content/short/0711174105
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Table S1. Rietveld refinement results for (Mg0.91Fe0.09)SiO3 postperovskite at its stable P–T conditions
Pressure, GPa
Temperature, K
Rwp
a, Å
b, Å
c, Å
135 (1)
2604 (150)
0.073
2.462 (1)
8.081 (3)
6.121 (2)
135 (2)
2535 (150)
0.122
2.467 (2)
8.080 (7)
6.119 (4)
134 (1)
2457 (150)
0.118
2.466 (1)
8.079 (5)
6.118 (2)
134 (2)
2385 (150)
0.085
2.466 (1)
8.069 (4)
6.121 (3)
Atomic position parameters
yMg
yO1
yO2
zO2
0.251 (3)
0.911 (6)
0.639 (6)
0.442 (4)
0.247 (5)
0.909 (13)
0.644 (12)
0.450 (10)
0.246 (4)
0.905 (8)
0.639 (8)
0.446 (6)
0.237 (4)
0.908 (8)
0.637 (6)
0.445 (6)
1.69 (2)
1.70 (3)
1.79 (4)
1.93 (3)
2.09 (3)
130 (3)
93 (2)
1.70 (4)
1.73 (8)
1.80 (8)
1.92 (6)
2.04 (6)
129 (6)
91 (5)
1.71 (3)
1.70 (5)
1.78 (5)
1.93 (4)
2.08 (4)
127 (4)
93 (3)
1.70 (3)
1.69 (3)
1.85 (6)
1.89 (3)
2.13 (4)
128 (4)
94 (2)
Interatomic distances and angles
Si–O1 ('2), Å
Si–O2 ('4), Å
Mg–O1 ('2), Å
Mg–O2 ('4), Å
Mg–O2 ('2), Å
!SiO1Si, °
!SiO2Si, °
The numbers in the parentheses are 2! uncertainties. Rietveld refinement tends to underestimate the uncertainty of refined parameters (27). Therefore, we
use a factor of two larger error bars (2!) than the estimated uncertainty from Rietveld refinements.
Shim et al. www.pnas.org/cgi/content/short/0711174105
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Table S2. Rietveld refinement results for (Mg0.91Fe0.09)SiO3 postperovskite at its stable P conditions
Pressure, GPa
Rwp
a, Å
b, Å
c, Å
126 (2)
0.067
2.460 (1)
8.059 (3)
6.102 (2)
126 (3)
0.101
2.460 (1)
8.058 (3)
6.103 (2)
125 (1)
0.086
2.461 (1)
8.070 (2)
6.106 (1)
124 (2)
0.093
2.463 (1)
8.070 (2)
6.107 (1)
123 (1)
0.099
2.465 (1)
8.071 (2)
6.110 (1)
122 (2)
0.081
2.466 (1)
8.077 (2)
6.115 (1)
120 (2)
0.103
2.468 (1)
8.092 (3)
6.120 (1)
120 (1)
0.083
2.470 (1)
8.088 (2)
6.121 (1)
117 (1)
0.096
2.471 (1)
8.103 (3)
6.130 (1)
116 (2)
0.103
2.472 (1)
8.109 (4)
6.133 (2)
114 (3)
0.095
2.474 (1)
8.116 (4)
6.136 (2)
0.250 (3)
0.921 (5)
0.630 (5)
0.434 (3)
0.256 (3)
0.920 (5)
0.635 (5)
0.434 (3)
0.255 (3)
0.922 (4)
0.638 (5)
0.432 (3)
0.247 (3)
0.917 (4)
0.635 (5)
0.432 (3)
0.260 (3)
0.924 (4)
0.646 (4)
0.436 (3)
0.253 (2)
0.918 (4)
0.629 (4)
0.436 (3)
0.247 (3)
0.909 (5)
0.632 (5)
0.437 (3)
0.263 (2)
0.924 (4)
0.643 (4)
0.439 (3)
0.254 (2)
0.917 (3)
0.627 (3)
0.439 (3)
0.247 (3)
0.911 (4)
0.617 (5)
0.447 (3)
Interatomic distances and angles
Si–O1 ('2), Å
1.66 (1)
1.66 (1)
Si–O2 ('4), Å
1.71 (2)
1.67 (2)
Mg–O1 ('2), Å
1.85 (3)
1.85 (3)
Mg–O2 ('4), Å
1.88 (2)
1.92 (2)
Mg–O2 ('2), Å
2.15 (3)
2.16 (3)
!SiO1Si, °
134 (2)
134 (2)
!SiO2Si, °
92 (2)
95 (2)
1.66 (1)
1.69 (2)
1.80 (3)
1.93 (2)
2.12 (3)
134 (2)
93 (2)
1.65 (1)
1.71 (3)
1.83 (3)
1.91 (2)
2.13 (3)
135 (2)
92 (2)
1.67 (1)
1.70 (2)
1.85 (3)
1.89 (2)
2.16 (3)
133 (2)
93 (2)
1.65 (1)
1.75 (2)
1.81 (3)
1.91 (2)
2.07 (2)
136 (2)
90 (1)
1.67 (1)
1.66 (2)
1.81 (2)
1.96 (2)
2.14 (2)
133 (2)
96 (1)
1.70 (2)
1.68 (2)
1.80 (3)
1.92 (2)
2.15 (3)
129 (2)
95 (2)
1.65 (1)
1.73 (2)
1.79 (2)
1.95 (2)
2.06 (2)
136 (2)
91 (1)
1.68 (1)
1.65 (3)
1.81 (3)
1.98 (2)
2.14 (3)
133 (2)
97 (2)
1.70 (2)
1.60 (2)
1.82 (3)
2.03 (3)
2.16 (3)
130 (2)
102 (2)
Atomic position parameters
yMg
0.248 (3)
yO1
0.919 (5)
yO2
0.637 (5)
zO2
0.432 (3)
The numbers in the parentheses are 2! uncertainties.
Shim et al. www.pnas.org/cgi/content/short/0711174105
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Table S3. Rietveld refinement results for (Mg0.91Fe0.09)SiO3 postperovskite at its metastable P conditions
Pressure, GPa
Rwp
a, Å
b, Å
c, Å
106 (4)
0.075
2.480 (1)
8.135 (5)
6.151 (2)
106 (3)
0.094
2.480 (1)
8.133 (5)
6.151 (2)
104 (3)
0.099
2.482 (2)
8.132 (5)
6.152 (3)
104 (3)
0.061
2.487 (1)
8.133 (6)
6.156 (3)
98 (3)
0.052
2.491 (1)
8.144 (7)
6.167 (3)
95 (2)
0.048
2.493 (1)
8.169 (7)
6.174 (3)
89 (2)
0.054
2.504 (1)
8.189 (7)
6.195 (4)
89 (3)
0.059
2.502 (1)
8.226 (9)
6.189 (4)
88 (2)
0.066
2.502 (1)
8.224 (9)
6.186 (4)
81 (1)
0.088
2.522 (2)
8.283 (9)
6.242 (4)
78 (1)
0.068
2.533 (1)
8.338 (8)
6.270 (6)
0.246 (4)
0.920 (5)
0.617 (6)
0.456 (5)
0.255 (3)
0.916 (5)
0.637 (5)
0.448 (5)
0.238 (3)
0.921 (5)
0.614 (5)
0.461 (5)
0.241 (3)
0.928 (6)
0.612 (6)
0.452 (6)
0.256 (6)
0.922 (7)
0.626 (9)
0.457 (6)
0.237 (7)
0.916 (7)
0.622 (13)
0.441 (7)
0.241 (3)
0.924 (7)
0.619 (5)
0.450 (4)
0.236 (4)
0.931 (9)
0.615 (6)
0.446 (5)
0.251 (4)
0.923 (8)
0.620 (6)
0.465 (6)
0.244 (5)
0.908 (7)
0.607 (10)
0.449 (8)
Interatomic distances and angles
Si–O1 ('2), Å
1.67 (2)
1.67 (1)
Si–O2 ('4), Å
1.55 (3)
1.59 (3)
Mg–O1 ('2), Å
1.88 (4)
1.88 (4)
Mg–O2 ('4), Å
2.11 (3)
2.06 (3)
Mg–O2 ('2), Å
2.13 (3)
2.13 (3)
!SiO1Si, °
135 (3)
134 (2)
!SiO2Si, °
106 (3)
103 (3)
1.68 (2)
1.70 (4)
1.80 (3)
1.98 (3)
2.06 (3)
132 (3)
94 (3)
1.67 (2)
1.57 (3)
1.94 (5)
2.06 (4)
2.15 (3)
135 (3)
105 (3)
1.65 (2)
1.57 (5)
1.97 (8)
2.05 (4)
2.20 (5)
139 (4)
105 (4)
1.67 (2)
1.64 (7)
1.84 (8)
2.08 (5)
2.05 (5)
135 (3)
99 (6)
1.70 (2)
1.64 (3)
1.93 (5)
1.96 (3)
2.24 (3)
132 (3)
99 (2)
1.67 (3)
1.62 (3)
1.96 (7)
2.03 (4)
2.18 (4)
136 (4)
101 (3)
1.65 (2)
1.60 (3)
2.04 (6)
2.01 (4)
2.25 (4)
140 (4)
103 (3)
1.69 (2)
1.62 (6)
1.90 (5)
2.14 (6)
2.08 (4)
136 (3)
102 (5)
1.75 (3)
1.58 (5)
1.86 (7)
2.11 (5)
2.26 (5)
128 (4)
107 (4)
Atomic position parameters
yMg
0.247 (3)
yO1
0.921 (5)
yO2
0.610 (5)
zO2
0.459 (5)
The numbers in the parentheses are 2! uncertainties.
Shim et al. www.pnas.org/cgi/content/short/0711174105
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Table S4. The volumes and bulk moduli of postperovskite and perovskite at ambient and core-mantle boundary pressures
V, Å3
K, GPa
0 GPa
125 GPa
0 GPa
125 GPa
K(
0 GPa
Postperovskite
This work
Mao et al. (26)
Shieh et al. (5)
Ono et al. (28)
Guignot et al. (29)
164.7 (10)
157.2
164.9
162.9†
162.2*
121.3 (1)
124.7
120.8
121.5
120.4
221 (16)
272
215
237
231
657 (16)
908
653
677
671
4*
6*
4*
4*
4*
Perovskite
This work
163.2
123.3 (5)
264 (5)
679 (10)
Jackson and Rigden (30)‡
Fiquet et al. (24)
162.3
162.3
123.3
122.0
262
259
706
665
XFe, mol%
P scale
Medium
9
40
9?
0
0
Au-T
Pt-J
Pt-H
Au-A
MgO-S
Ar
None
Ar
NaCl
NaCl
3.8 (2)
9
Au-T
Ar ("0 GPa)
NaCl (#50 GPa)
4.0
3.7
0
0
Pt-H
Ar ("50 GPa)
None (#50 GPa)
We note that the smaller error bars from some measurements (28, 29) resulted mainly because they fixed V0, whereas we varied V0 and K0 during the fitting.
Au-T, gold EOS by Tsuchiya et al. (12); Au-A, gold EOS by Anderson et al. (20); MgO-S, periclase EOS by Speziale et al. (31); Pt-H, platinum EOS by Holmes et al.
(15); Pt-J, platinum EOS by Jamieson et al. (14).
*Fixed.
†Fixed the volume to a first-principles result (32).
‡Fit for a combined dataset. References therein.
Shim et al. www.pnas.org/cgi/content/short/0711174105
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