www.sciencemag.org/cgi/content/full/334/6057/792/DC1
Supporting Online Material for
Phase Transition of FeO and Stratification in Earth’s Outer Core
Haruka Ozawa,* Futoshi Takahashi,* Kei Hirose, Yasuo Ohishi, Naohisa Hirao
*To whom correspondence should be addressed. E-mail: [email protected] (H.O.);
[email protected] (F.T.)
Published 11 November 2011, Science 334, 792 (2011)
DOI: 10.1126/science.1208265
This PDF file includes:
Materials and Methods
Figs. S1 to S10
Tables S1 and S2
References (28–35)
Materials and Methods
High-pressure and -temperature experiments
The high-pressure and -temperature (P-T) conditions were generated in a laserheated diamond-anvil cell (DAC) using double-beveled anvils with 40 µm culet (28). We
prepared the starting material by mixing the powders of Fe0.96O and metallic iron
(Kojundo Chemical Lab., 99.999% purity). The same Fe0.96O powder was used in our
previous study (5). No diffraction peak from iron was observed in the second run (Figs.
2C-E), indicating that the sample pellet used in this experiment included minimal amount
of Fe metal. The sample mixture was loaded into a hole in a pre-indented rhenium gasket,
together with thermal insulation layers of SiO2 glass. After loading, they were dried in a
vacuum oven at 393 K, and subsequently the sample chamber was flushed with dry argon
and squeezed in argon atmosphere. The samples were heated by a couple of 100 W
single-mode Yb fiber lasers using the double-side heating technique. We used beamshaping optics, which converts a Gaussian beam to one with a flatter energy distribution,
in an attempt to reduce radial temperature gradient in the sample. The laser-heated spot
was ~15 µm in diameter. Temperature was measured by the spectroradiometric method
(29).
All the high P-T experiments were conducted at BL10XU of SPring-8. Angledispersive x-ray diffraction (XRD) spectra were collected on a charge coupled device
(CCD) or an imaging plate (IP) detector with typical exposure times of 10 sec and 3 min,
respectively. A monochromatic incident x-ray beam with a wavelength of 0.413880.42387 Å was collimated to about 6-µm area (full-width of half maximum) on the
sample. Only for one XRD image shown in Fig. S2, we changed the wavelength to
0.31106 Å to observe peaks with smaller d-spacings. Two-dimensional XRD images
were integrated in order to give a conventional one-dimensional diffraction profile using
the IPAnalyzer software (30). The Rietveld crystal structure refinements of the diffraction
patterns were performed by using the GSAS program (31) (Fig. S1). Sample temperature
was obtained by averaging the variations in 6 µm area across the hot spot, which
corresponds to the x-ray beam size, yielding the uncertainties of less than ±12% (28).
Pressure was determined from the measured unit-cell volume of hcp-Fe using its thermal
equation of state (EOS) proposed by Dewaele et al. (32) in run #1. For run #2, we
calculated the pressure based on the room-T EOS of B8 FeO (18) and thermal parameters
same as those for B1 FeO (33). The pressure errors arising from uncertainties in unit-cell
volume and temperature were ±3-6 GPa (run #1) and ±3-12 GPa (run #2).
Numerical simulations of core convection
Navier-Stokes and energy equations for incompressible Boussinesq fluid are solved
in a rotating spherical shell (34), in which convection is driven only thermally by secular
cooling of the core. We implement the liquid structural change into numerical modeling
using a method of phase function like studies of mantle convection (19). Simulations
were performed repeatedly with varying the Clapeyron slope, density jump, and width of
the structural change, and the Rayleigh number (Table S2).
Temperature is defined as the deviation with respect to the adiabatic temperature.
The velocity field is represented as a sum of the poloidal and toroidal fields, with which
the equation of continuity is satisfied automatically. Input nondimensional parameters
2
focused in this study are; (i) the scaled Clapeyron slope, χ = dP/dT / (ρgo/β), where ρ, go,
and β are fluid density, gravitational acceleration at the core-mantle boundary (CMB),
and superadiabatic temperature gradient at the CMB, (ii) the Rayleigh number, Ra =
αgoβD4/(νκ), where α, D, ν, and κ are thermal expansivity, outer core thickness, kinematic
viscosity, and thermal diffusivity, respectively, and (iii) the phase boundary Rayleigh
number, Rb = ΔρgoD3/(ρνκ), where Δρ is the density change due to structural change in
liquid (Table S2). The phase buoyancy parameter PB, often used in the mantle convection
studies (19, 20), is defined as PB = χ Rb/Ra = (Δρ/αρ2goD)(dP/dT). The Rb/Ra ratio
indicates the effect of structural change over that of thermal buoyancy.
Other parameters such as the Ekman number, E = ν/(2ΩD2) with rotation rate Ω; the
Prandtl number, Pr = ν/κ; and the core radius ratio, η = ri/ro, where ri and ro are the radii
of the inner and outer cores, are fixed at E = 2 × 10−4, Pr = 1, and η = 0.35, respectively.
Present simulations were performed with Ra = 1.0 to 2.5 × 106, while the realistic value
in the core may be in the order of 1029 using the following values; α ~ 10-5 K-1, go ~ 10 m
s-2, D ~ 2 × 106 m, κ ~ 10-5 m2 s-1, ν ~ 10-6 m2 s-1, and β ~ 10-3 K m-1. It is similar to the
value used in King et al. (35).
We use no-slip and fixed temperature boundary conditions for the velocity field and
temperature field, respectively. The model uses 60 radial grid meshes for combined
compact difference scheme (34). Spherical harmonic expansion is performed up to 63 in
degree and order. The time integration method is the Crank-Nicolson scheme for the
diffusion terms and the third-order Adams-Bashforth, Adams-Moulton scheme for the
other terms. Each run is time-stepped at least for 0.25 nondimensional time units. Timeaverage is taken after time-stepping the initial 0.1 time units in order to avoid the effects
of initial condition. Nondimensional temperature is made dimensional in Fig. 3F and Figs.
S7 to S10 using the scale of βD = 2350 K.
3
Fig. S1.
Observed (red crosses) and Rietveld-fitted pattern (green line) at 284 GPa and 300 K.
Vertical bars indicate the calculated peak positions. The difference profile (pink line) is
on the same scale. A caked two-dimensional diffraction image is also shown.
4
Fig. S2
A caked-two-dimensional diffraction image collected at 293 GPa and 300 K in run #2
with λ = 0.31106 Å. Dark spots indicated by arrows represent the diffraction peaks from
B2 FeO.
5
6000
(A)
Liquid
5000
4000
B2
B1
Temperature (K)
3000
B8
(B)
Liquid
5000
4000
3000
2000
200
B2
B1
B8
250
300
Pressure (GPa)
350
Fig. S3
P-T path of the experiments in (A) run #1 and (B) run #2. Same symbols as Fig. 1. The
load pressure was changed between the symbols connected by a broken line.
6
Fig. S4
Volumes per formula unit of B2 (solid symbols) and B8 structures (open symbols) of
FeO at room temperature observed in the second run. Compression curve for B8 Fe0.95O
is from Sata et al. (18).
7
Fig. S5
XRD patterns obtained in run #1 shown in chronological order (from bottom to top).
Corresponding P-T conditions are listed in Table S1. Red, blue, and black dots indicate
the peaks from B2 FeO, B8 FeO, and hcp-Fe, respectively. Asterisks show the peaks
from rhenium (gasket).
8
Fig. S6
XRD patterns obtained in run #2 shown in chronological order (from bottom to top). See
Table S1 for corresponding P-T conditions. Green dots indicate the peaks from B1 FeO.
Other symbols are same as Fig. S5.
9
Fig. S7
Simulation results with varying the Clapeyron slope (χ) and density jump (Δρ) of the
liquid structural change for Ra = 2.5 × 106 (fixed) (Table S2). (A) Meridional crosssection of the core flow (arrows) and temperature (color) averaged over longitude and
time for models C and D1–D3 (Table S2). Hot (cold) regions are denoted by red (blue).
The corresponding time-averaged radial profiles of the rms radial velocity and the
horizontally averaged temperature for models A1, C, and D1–D3 (Table S2) are shown in
(B) and (C), respectively. The temperature is plotted with respect to the CMB
temperature. The gray layer in (A) and the vertical dashed lines in (B, C) represent the
nominal range of the liquid structural boundary.
10
Fig. S8
Simulation results with changing the Clapeyron slope and density jump for Ra = 1.75 ×
106 (fixed) (Table S2). Same as Fig. S7 but for models A2, B5, and D4–D6 (Table S2).
11
Fig. S9
Simulation results with changing the Clapeyron slope and density jump for Ra = 1.0 ×
106 (fixed) (Table S2). Same as Fig. S7 but for models A3, B6, D7 and D8 (Table S2).
12
Fig. S10
Simulation results with changing the Clapeyron slope and density jump for Ra = 2.5 x
106 (fixed) (Table S2). Similar to Fig. S7 but for models with more gradual structural
change. The liquid structure changes in a gray region in (A) and between two vertical
dashed lines in (B, C), which is much broader than in other models. Other parameters in
respective models are same as those in models C, B3, and B4 (Table S2).
13
Table S1.
Summary of high-pressure experimental results.
Run
cycle
VFe (Å3)*
VB8 (Å3)†
PFe (GPa)
1
1
3
4
14.046
13.821
13.730
13.722
13.661
13.941
22.60(34)
22.12(24)
21.94(14)
21.94(20)
21.98(20)
22.00(30)
270(3)
291(3)
305(5)
304(3)
324(5)
299(6)
5
2
5
7
12
17
18
22
22.12(6)
21.82(12)
22.14(4)
22.16(8)
23.60(12)
23.62(12)
23.70(6)
23.72(4)
23.74(2)
23.28(8)
22.62(22)
22.64(18)
22.66(22)
PB8 (GPa)
287(4)
311(7)
288(3)
288(5)
230(5)
230(5)
234(5)
231(4)
227(3)
240(4)
268(11)
271(9)
274(12)
T (K)
Stable structure
2430(240)
2660(300)
3170(390)
2990(270)
4180(410)
4160(440)
B8
B8
B2
B2
B2
B2
2400(200)
4100(330)
2730(300)
3090(210)
3400(200)
3690(280)
4880(570)
4410(420)
3770(330)
3750(270)
3110(210)
4020(300)
4740(410)
B8
B2
B8
B2
B8
B1
B1
B1
B8
B1
B8
B2
B2
Listed
in chronological
order
for eachuncertainties
run.
Number
in parenthesis
indicates
in the last digits.
Number
in parenthesis indicates uncertainty in the last digits.
*
* The unit-cell volume of hcp Fe was calculated from 100 and 101 lines.
†The unit-cell volume of hcp Fe was calculated from 100 and 101 lines.
† The unit-cell volume of Fe0.96O was calculated from four lines of 002, 100, 101, and 102, and three
The unit-cell volume of Fe0.96O was calculated from three lines of 002, 100, and 102, and four lines of 002,
lines101,
of 002,
the
first and
second
runs, respectively.
100,
and 100,
102 inand
the 102
first in
and
second
runs,
respectively.
14
Table S2.
Nondimensional parameter values used in each model. Choice of the model parameters, c
and Rb/Ra, is guided by the typical Earth values of D ~ 2 × 106 m, go ~ 10 m s−2, ρ ~ 104
kg m−3, α ~ 10−5 K−1, and β ~ 10−3 K m−1. With these values, we obtain χ ~ -0.1, Rb/Ra ~
0.5, and PB ~ -0.05 from the present experimental results on FeO.
Model
A1
A2
A3
B1
B2
B3
B4
B5
B6
C
D1
D2
D3
D4
D5
D6
D7
D8
χ
0.0
0.0
0.0
-0.2
-0.2
-0.2
-0.2
-0.2
-0.2
-0.1
-0.05
-0.05
-0.05
-0.05
-0.05
-0.05
-0.05
-0.05
Ra
2.5 × 106
1.75 × 106
1.0 × 106
2.5 × 106
2.5 × 106
2.5 × 106
2.5 × 106
1.75 × 106
1.0 × 106
2.5 × 106
2.5 × 106
2.5 × 106
2.5 × 106
1.75 × 106
1.75 × 106
1.75 × 106
1.0 × 106
1.0 × 106
Rb
0.0
0.0
0.0
5.0 × 105
1.25 × 106
2.5 × 106
5.0 × 106
3.5 × 106
2.0 × 106
2.5 × 106
1.25 × 106
5.0 × 106
1.0 × 107
8.75 × 105
3.5 × 106
7.0 × 106
2.0 × 106
4.0 × 106
Rb/Ra
0.0
0.0
0.0
0.2
0.5
1.0
2.0
2.0
2.0
1.0
0.5
2.0
4.0
0.5
2.0
4.0
2.0
4.0
PB
0.0
0.0
0.0
-0.04
-0.1
-0.2
-0.4
-0.4
-0.4
-0.1
-0.025
-0.1
-0.2
-0.025
-0.1
-0.2
-0.1
-0.2
15
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Acknowledgments: We thank S. Tateno for technical support and T. Komabayashi, S. Urakawa,
T. Hattori, and R. M. Wentzcovitch for discussion. XRD measurements were conducted
at SPring-8 (proposal 2010B0087). All XRD patterns are provided in the supporting
online material.
3