Stability of the MgSiO3 analog NaMgF3 and its implication
for mantle structure in super-Earths
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Grocholski, B., S.-H. Shim, and V. B. Prakapenka (2010),
Stability of the MgSiO3 analog NaMgF3 and its implication for
mantle structure in super-Earths, Geophys. Res. Lett., 37,
L14204, doi:10.1029/2010GL043645. ©2010. American
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GEOPHYSICAL RESEARCH LETTERS, VOL. 37, L14204, doi:10.1029/2010GL043645, 2010
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Article
Stability of the MgSiO3 analog NaMgF3 and its implication
for mantle structure in super‐Earths
B. Grocholski,1 S.‐H. Shim,1 and V. B. Prakapenka2
Received 16 April 2010; revised 31 May 2010; accepted 7 June 2010; published 28 July 2010.
[1] First‐principles calculations on MgSiO3 suggested a
breakdown into MgO + SiO2 at pressure above 1000 GPa
with an extremely large negative Clapeyron slope,
isolating the lowermost mantles of larger super‐Earths
(∼10M!) from convection. Similar calculations predicted
the same type of breakdown in NaMgF3 to NaF + MgF2
at 40 GPa, allowing for experimental examination. We
found that NaMgF3 is stable to at least 70 GPa and 2500 K.
In our measurements on MgF2 (an SiO2 analog), we found
a previously unidentified phase (“phase X”) between the
stability fields of pyrite‐type and cotunnite‐type (49–53 GPa
and 1500–2500 K). A very small density increase (1%) at
the pyrite‐type → phase X transition would extend the
stability of NaMgF3 relative to the breakdown products.
Furthermore, because phase X appears to have a cation
coordination number intermediate between pyrite‐type (6)
and cotunnite‐type (9), entropy change (DS) would be
smaller at the breakdown boundary, making the Clapeyron
slope (dP/dT = DS/DV) much smaller than the prediction.
If similar trend occurs in MgSiO3 and SiO2, the breakdown
of MgSiO3 may occur at higher pressure and have much
smaller negative Clapeyron slope than the prediction,
allowing for large‐scale convection in the mantles of
super‐Earth exoplanets. Citation: Grocholski, B., S.‐H. Shim,
and V. B. Prakapenka (2010), Stability of the MgSiO3 analog
NaMgF3 and its implication for mantle structure in super‐Earths,
Geophys. Res. Lett., 37, L14204, doi:10.1029/2010GL043645.
1. Introduction
[2] Among recently discovered exoplanets, some may
have compositions similar to that of the Earth, i.e., super‐
Earths [Rivera et al., 2005]. Most of these planets have
much larger sizes (5 ∼ 10M!), with their internal pressures
(P) far in excess of Earth [Seager et al., 2007; Valencia et
al., 2007]. Therefore, in order to understand the heat
transport, thermal evolution, and internal structure of super‐
Earths, we need to study the phase relations of silicates to
extremely high pressures.
[3] Recent first‐principles calculations by Umemoto et
al. [2006a] proposed that the post‐perovskite form of
MgSiO3 breaks down to an oxide mixture (MgO + SiO2)
at ∼1000 GPa, corresponding to the core‐mantle boundary
pressure in 10M! super‐Earths. They predicted a strongly
negative Clapeyron slope (dP/dT = −30 MPa/K) of the
1
Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
2
GeoSoilEnviroCARS, University of Chicago, Chicago, Illinois,
USA.
Copyright 2010 by the American Geophysical Union.
0094‐8276/10/2010GL043645
breakdown — at least an order of magnitude larger than the
post‐spinel transition. Such a large negative Clapeyron slope
would make the breakdown boundary impermeable for
mantle convection, resulting in drastically different internal
structure and thermochemical evolution of larger super‐
Earths [Tackley, 1995; van den Berg et al., 2010].
[4] While our current static compression techniques, such
as the diamond‐anvil cell, are not capable of reaching the
predicted breakdown pressure, the prediction can be examined by studying analog materials which undergo the same
sequence of phase transitions as MgSiO3 but at much lower
pressures. Umemoto et al. [2006b] have also predicted a
breakdown of NaMgF3 to NaF + MgF2 at 40–48 GPa.
NaMgF3 is both isoelectronic and isostructural with MgSiO3
and undergoes a perovskite (Pv) → post‐perovskite (PPv)
transition at ∼30 GPa [Martin et al., 2006], compared to
∼120 GPa in MgSiO3. Furthermore, the unit‐cell axis ratios
of the Pv and PPv phases in NaMgF3 are close to those in
MgSiO3, making it an excellent analog material [Kubo et
al., 2008].
[5] The breakdown product of NaMgF3 (NaF and MgF2)
are also analogs of MgO and SiO2. According to Umemoto et
al. [2006a] a large decrease in enthalpy at the pyrite‐type →
cotunnite‐type transition in SiO2 stabilizes the breakdown
products with respect to MgSiO3, due mainly to the
higher density of the cotunnite‐type SiO2 + B2‐MgO than
MgSiO3‐PPv. NaMgF3 is a good analog material for
MgSiO3 because its breakdown occurs from the same
thermodynamic driving force [Umemoto et al., 2006b]. The
predicted large negative Clapeyron slope (dP/dT = DS/DV)
can be explained by a large increase in the coordination
number of cation at the breakdown (6 → 9 for Si), which
would induce a large increase in entropy (DS). This highlights in particular the importance of the polymorphic
transitions of SiO2.
[6] The high‐P transition sequence for SiO2 has been
experimentally determined to be: quartz → coesite →
rutile‐type → CaCl2‐type → a‐PbO2‐type → pyrite‐type,
with the pyrite type appearing at 270 GPa [Kuwayama et al.,
2005]. MgF2 has the same sequence except the sequence
starts from the rutile type, the transition to the pyrite type
occurs at 14 GPa, the a‐PbO2‐type phase only appears
upon decompression [Haines et al., 2001]. Previous studies
reported that MgF2 undergoes a phase transition to the
cotunnite type at 35 GPa [Haines et al., 2001; Kanchana et
al., 2003; Umemoto et al., 2006a]. The cotunnite type has
been seen in many SiO2 analogs at high P and is predicted
be the stable phase of SiO2 above 750 GPa at 0 K [Oganov
et al., 2005]. Although Umemoto et al. [2006a] predicted
that the pyrite‐type SiO2 transforms directly to the cotunnite
type, similar compounds have structures with seven‐fold
coordination that appear before the cotunnite type, such as
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Photon Source using x‐rays with an energy of 40 keV,
MAR‐345 ccd detector and CeO2 to calibrate the detector.
[9] The sample was brought to pressure at room temperature and laser heated at 1500–2500 K for at least 30 minutes
while simultaneously collecting X‐ray diffraction patterns
every 2–3 minutes during the heating cycle, with temperature determinations made using spectral radiometry. Lattice
parameters were calculated using the UnitCell program
[Holland and Redfern, 1997]. We found all samples loaded
with platinum react with the diamond culets at P > 53 GPa
when heated at T > 2000 K, consistent with Ono et al.
[2005]. The PtC diffraction intensities approach those of
platinum after several minutes of laser heating, allowing for
ready identification of the contaminating phase in this
experiment. Care must be taken not to mistake these for
sample peaks, although the strong diffraction intensities
could be useful as a secondary pressure calibrant.
3. Results
Figure 1. Diffraction patterns of the (a) pyrite‐type, (b) phase
X, (c) cotunnite‐type MgF2, and (d) NaMgF3 collected with
40 keV x‐ray energy. The broad peaks Figure 1a are the result
of no laser annealing post‐conversion. The baddeleyite crystal structure is consistent with most of the diffraction intensities of phase X as shown in Figure 1b. Example of the product
of a heating run far in excess of the expected breakdown pressure of NaMgF3 shown in Figure 1d. The diffraction pattern
can be indexed as a combination of post‐perovskite and platinum carbide. The grey box shows the range where we expect
the most intense line expected for MgF2. The absence of
major line at the angular range shows the stability of PPv.
the baddeleyite type and SrI2 type [Shieh et al., 2006; Leger
et al., 1993].
[7] Here, we report a new high‐P phase transition in
MgF2 and find the stability of NaMgF3 to pressures well
above the predicted breakdown pressure.
2. Experimental Method
[8] Synthetic NaMgF3 was used in this study. Detailed
information on the sample is given by Hustoft et al. [2008].
MgF2 was obtained at 99.99% purity (Alfa‐Aesar). Thin
foils (10 mm) of NaMgF3 or MgF2 mixed with 10 wt%
platinum or gold used as a pressure calibrant and laser
absorber were loaded into the diamond‐anvil cells with
200 mm culets using argon as a pressure medium, with the
exception of one NaMgF3 sample loaded with MgO plates.
Rhenium gaskets were used for all experiments with a
sample chamber of 120 mm. Pressures were determined in‐
situ from the equations of state for platinum [Holmes et al.,
1989] or gold [Tsuchiya, 2003]. We loaded a total of four
samples of NaMgF3 and two samples of MgF2. Experiments
were performed at the GSECARS sector at the Advanced
[10] We heated four different samples of NaMgF3 a total
of 15 times at T ≥ 2000 K for between 20–70 minutes to
74 GPa. The best diagnostic for determining if NaMgF3
breakdown occurs is the most intense lines of the high‐P
polymorphs of MgF2. This line is between 1.80–1.85 Å for
both “phase X” (see below) and cotunnite type. Calculations
based on Hustoft et al. [2008] show that no diffraction lines
of the Pv or PPv phases exist in this region. As shown in
Figure 1d, we found the appearance of PPv, but no evidence
of MgF2 up to 74 GPa. We do not find evidence for the
“N‐phase” reported by Martin et al. [2006].
[11] Previous measurements of MgF2 found the pyrite‐
type phase (Pa!3) stable to 35 GPa and the cotunnite‐type
phase (Pnma) stable above this pressure after laser heating at
T < 1500 K [Haines et al., 2001]. We find a new phase
(“phase X”) at pressures between the stability fields of the
pyrite‐ and cotunnite‐type phases (Figures 1a–1c). Phase X
is stable between 49 and 55 GPa upon compression at T ≥
1500 K, and stable upon decompression at 300 K to 26 GPa.
Once formed, phase X is metastable to at least 71 GPa and
temperatures 2000 K, near the maximum pressure of this
experiment. When cold compressed to 64 GPa and then
heated to 1700 K, MgF2 converts directly to the cotunnite
type as reported by Haines et al. [2001] (Figures 1a–1c).
Above 55 GPa, heating the previously synthesized phase X
results in the growth of the most intense line of the cotunnite‐type phase. We were able to convert the cotunnite‐
type phase back to phase X at ∼50 GPa and 2000 K upon
decompression. The back transformation is sluggish, taking
a full 30 min of laser heating at 2000 K before sudden
recrystallization of the sample to phase X with an accompanying drop in pressure by 4 GPa. This demonstrates that
phase X is a thermodynamically stable high‐P polymorph in
MgF2 whose stability field exists between those of the
pyrite‐ and cotunnite‐type phases.
[12] We investigated the crystal structure of phase X
using the powder diffraction patterns combined with the
CRYSFIRE and DICVOL programs [Shirley, 1999; Boultif
and Louer, 2004]. Among many high‐P polymorphs found
in SiO2 analogs, the two most likely crystal structures found
between the stability fields of pyrite type and cotunnite type
are the baddeleyite type (P21/c) and SrI2 type (Pbca). These
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Figure 2. Room temperature volume compression of
MgF2 with pressure. Closed and open symbols are compression and decompression, respectively. Lines are fits to the
data using second order Birch‐Murnaghan equation for reference volume at 17.5 GPa for pyrite type (Vr = 105.88 Å3,
Kr = 233 ± 20 GPa), 43.4 GPa for phase X (Vr = 95.75 Å3,
Kr = 319 ± 20 GPa), and 42.1 GPa for cotunnite type (Vr =
89.90 Å3, Kr = 262 ± 20 GPa).
are both distorted versions of the fluorite structure with
well‐constrained axial ratios. Equation of state parameters
for phase X and other MgF2 phases are given in Figure 2,
but fail to help determine if phase X is monoclinic or
orthorhombic.
[13] According to the reported sequence of phase transitions in SiO2 analogs, the SrI2 type is most likely structure
for phase X [Moriwaki et al., 2006; Vajeeston et al., 2006;
Lowther et al., 1999]. However, no orthorhombic solutions
satisfied the expected axial ratios for the SrI2‐type: a:b:c ’
1:2:2. We found the fit to the monoclinic baddeleyite
structure provides reasonable lattice constants (Table 1).
However, this solution cannot fit two diffraction lines at
2.529 Å and 1.900 Å, which appear in the diffraction patterns using both types of pressure calibrants and are therefore unlikely to be contamination (Figure 1b).
[14] The baddeleyite‐type phase is normally found instead
of pyrite type, with both of these phases transforming to the
SrI2‐type phase before transforming to cotunnite at higher P
[Ohtaka et al., 2005]. However, systematic high resolution
investigation of SiO2 analogs at high temperature and quasi‐
hydrostatic conditions is lacking. Further, phase X could be
an unidentified low‐symmetry crystal structure not yet seen
in any SiO2 analogs or a mixture of two (or even more)
polymorphs. Mixed phases may be experimentally inevitable
if the phase stability fields are narrow in pressure. In addition,
computer simulations of SiO2 analogs usually find numerous
phases within small energy differences of each other at 0 K
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[Lowther et al., 1999; Oganov et al., 2005; Moriwaki et al.,
2006].
[15] The measured volumes for pyrite‐type MgF2 are consistent with Haines et al. [2001] (Figure 2). If baddeleyite‐
type is assigned to phase X, at the pyrite‐type → phase X
transition, we found a small volume decrease (1%), which
appears to be reasonable given that the coordination number
of cation increases by 1 (6 → 7). In addition, examples
of direct transformation from the pyrite structure to the
cotunnite structure are rare and intermediate phases are not
surprising.
[16] Our measurements on cotunnite‐type MgF2 are consistent with the axial ratios of other cotunnite‐type SiO2
analogs: a/b ’ 0.86 and (a + b)/c ’ 3.76 [Dewhurst and
Lowther, 2001; Morris et al., 2001]. Our a lattice parameter for cotunnite‐type MgF2 is 3% higher than the previous
result [Haines et al., 2001]. We attribute this difference to
overlapped diffraction intensities of phase X and cotunnite
type of Haines et al. [2001], resulting in misidentified peak
positions. In particular, we do not observe peaks at 1.88 and
1.78 Å in our diffraction patterns on cotunnite‐type – both of
these could be from phase X. The mixed phase in the earlier
study [Haines et al., 2001] could be due to pressure gradients, insufficient laser heating, and a relatively large X‐ray
beam size. We note, however, that the volume difference
between the pyrite‐ and cotunnite‐type, which is 7%, is
consistent with computations on MgF2 [Kanchana et al.,
2003] and experimental results on cotunnite types in other
SiO2 analogs [Morris et al., 2001]. If the baddelyite‐type is
assigned to phase X, our data indicate a large volume
decrease for the phase X → cotunnite‐type transition, 6%,
Table 1. Observed and Calculated d‐Spacing for the Baddeleyite
and Orthorhombic Solutions for Phase Xa
Baddeleyite‐Type
Obs dsp (Å)
Calc dsp (Å)
2.529
2.490
2.071
2.023
1.985
1.947
1.900
1.830
1.802
1.773
1.631
1.561
1.552
1.468
1.445
1.438
1.318
1.265
1.245
‐
2.495
2.071
2.009
1.982
1.941
‐
1.845
1.803
1.764
1.637
1.565
1.552
1.466
1.441
1.440
1.317
1.264
1.248
Orthorhombic
h
k
l
1
0
2
1
2
1
1
1
1
1
1
2
0
−2
−1
1
1
1
2
2
1
1
0
2
3
1
2
2
1
2
1
2
2
1
3
1
1
2
2
−1
2
1
−2
0
−2
−3
0
2
1
−3
2
Calc dsp (Å)
h
k
l
2.523
‐
‐
2.020
1.983
1.947
1.897
‐
1.804
1.775
1.633
‐
‐
1.468
1.446
1.438
1.319
1.265
1.245
2
1
1
2
3
0
2
2
1
3
0
1
1
0
2
2
0
3
1
2
0
2
2
2
0
4
1
4
4
2
3
2
3
3
3
2
2
1
2
0
1
3
a
Both are not able to fit all the diffraction lines, which could be due to
other phases (including cotunnite‐type MgF 2 ). The baddeleyite‐type
MgF2 (Z = 4) has lattice parameters of a = 4.587(3) Å, b = 4.324(3) Å,
c = 4.769(3) Å, b = 98.38(5)°. The orthorhombic solution (Z = 8) has
a = 7.172(6) Å, b = 5.840(4) Å, c = 4.471(3) Å. Texturing in the
sample and the potential for mixed phases make determining the crystal
structure difficult. Attempts were made to fit the diffraction intensities
to the orthorhombic SrI2 structure with a:b:c ’ 1:1:2, but was found to
not fit the diffraction peak positions very well. This phase or mixture
of phases may be a quenchable high temperature phase as it is
synthesized above ∼1500 K in these experiments.
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which appears to be consistent with a larger increase in the
coordination number of cation (7 → 9) (Figure 2).
4. Discussion and Planetary Implications
[17] The stability of NaMgF3 (a MgSiO3 analog) to the P–T
conditions well above those of the breakdown predicted by
the simulation of Umemoto et al. [2006b] can be explained
by insufficient understanding on phase transitions in MgF2
(an SiO2 analog) at high P–T. The breakdown reaction is
predicted to be driven by the significant enthalpy reduction
at the pyrite‐type → cotunnite‐type phase transition that
stabilizes the breakdown products relative to NaMgF3‐PPv
[Umemoto et al., 2006b].
[18] However, our study reveals that MgF2 may not
transform directly from pyrite type to cotunnite type. In fact,
the pyrite‐type → cotunnite‐type transition requires a
drastic increase in the coordination number of cation from 6
to 9. Intermediate phases (baddelyite type, SrI2 type, or
other structures) between the pyrite type and cotunnite type
may have a coordination of 7 or 8. Therefore, the stability of
the new phase in MgF2 would not make the breakdown
products energetically more favorable until higher P, which
can explain our observation of the stability of the PPv phase
to higher P.
[19] The discrepancy between our experiments and the
computation [Umemoto et al., 2006b] could be due in part to
the inability of the quasi‐harmonic approximation (QHA) to
properly account for thermal effects. The computational
results indicate the breakdown occurs at lower pressures at
higher temperatures based on a QHA of the change in
entropy with temperature [Umemoto et al., 2006b]. The
QHA used to estimate the slope only works well to temperatures at which the thermal expansivity starts to deviate
from linear behavior, in the case of NaF this limit is under
1000 K, possibly invalidating the results above these temperatures. The newly identified phase X synthesized at high
P–T should be a good test for the QHA in the MgF2 system
as it should be valid to ∼1500 K, while current computational results do not find another phase between pyrite‐ and
cotunnite‐types at 0 K [Kanchana et al., 2003; Umemoto et
al., 2006b].
[20] Failure to observe the breakdown could be due to
kinetic effects, as we cannot rule out insufficient heating
duration to overcome activation barriers. Higher temperature
heating is helpful [Catalli et al., 2009], but the low melting
temperature of NaMgF3 limits the temperature during experiments to T ≤ 2300 K. We note that we conducted
heating up to ∼1 hr, which should help reducing kinetic
effects.
[21] We observe the pyrite → phase X transition, and the
phase X → cotunnite‐type transition together with its
reverse transition, documenting the stability of phase X in
MgF2. Together with small volume difference between
pyrite type and phase X, the new phase may not be dense
enough to energetically stabilize the breakdown products
over the PPv phase.
[22] Assuming neighborite and MgF2 are good analogs for
the silicate and oxide systems, this is of particular importance for the phase relations in MgSiO3 and SiO2. Although
at zero K the cotunnite‐type is stable over pyrite at ∼750 GPa,
the enthalpy of the SrI2‐type SiO2 is close enough that it
may be the stable phase at high T [Oganov et al., 2005].
L14204
Further, other structures such as orthorhombic Pbc21 have
been found to be computationally stable between the stability fields of a‐PbO2 and cotunnite in MgH2 [Moriwaki et
al., 2006]. If SrI2, baddeleyite, or other structures with the
coordination number of cations smaller than nine are stable
before the stability field of cotunnite type, this will likely
stabilize MgSiO3−PPv over breakdown products at all
pressures inside super‐Earths, because the predicted breakdown pressure is already close to the core‐mantle boundary
pressure of larger super‐Earths (10M!). Therefore, no major
barrier for the mantle convection would exist in super‐
Earths. If even larger Earth‐like exoplanets would exist
(>10M!) and have sufficient internal mantle pressures for
the breakdown, the boundary may have a much smaller
negative Clapeyron slope, as entropy change would be
smaller due to a smaller increase in the coordination number
of Si (7 or 8 → 9, instead of 6 → 9). Therefore, our finding
implies that the mantles of super‐Earths would not be
strongly stratified, unlike the first‐principles predictions
[Umemoto et al., 2006b].
[23] Acknowledgments. The authors would like to thank K. Catalli
for experimental assistance and Justin Hustoft for helpful discussions.
We would like to thank the two anonymous reviewers for helpful comments that improved this manuscript. This work was performed in the
GeoSoilEnviroCARS sector of the Advanced Photon Source (APS),
Argonne National Laboratory. GeoSoilEnviroCARS is supported by the
NSF and the DOE. Use of the APS is supported by the DOE. This work
was supported by NSF to S.‐H. S. (EAR0738655).
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B. Grocholski and S.‐H. Shim, Department of Earth, Atmospheric,
and Planetary Sciences, Massachusetts Institute of Technology, 77
Massachusetts Ave., Cambridge, MA 02139, USA. ([email protected]
com)
V. B. Prakapenka, GeoSoilEnviroCARS, University of Chicago, 5640
South Ellis Ave., Chicago, IL 60637, USA.
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