electronic reprint
Journal of
Synchrotron
Radiation
ISSN 0909-0495
Editors: Å. Kvick, D. M. Mills and T. Ohta
Single-crystal synchrotron X-ray diffraction study of wüstite and
magnesiowüstite at lower-mantle pressures
Steven D. Jacobsen, Jung-Fu Lin, Ross J. Angel, Guoyin Shen, Vitali B. Prakapenka,
Przemyslaw Dera, Ho-kwang Mao and Russell J. Hemley
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J. Synchrotron Rad. (2005). 12, 577–583
Steven D. Jacobsen et al.
¯
Wüstite and magnesiowüstite
SXD at Mbar pressures
Journal of
Synchrotron
Radiation
ISSN 0909-0495
Received 10 May 2005
Accepted 12 July 2005
Single-crystal synchrotron X-ray diffraction study
of wüstite and magnesiowüstite at lower-mantle
pressures
Steven D. Jacobsen,a* Jung-Fu Lin,a,b Ross J. Angel,c Guoyin Shen,d Vitali B.
Prakapenka,d Przemyslaw Dera,a Ho-kwang Maoa and Russell J. Hemleya
a
Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road NW,
Washington, DC 20015, USA, bLawrence Livermore National Laboratory, 7000 East Avenue,
Livermore, CA 94550, USA, cDepartment of Geosciences, Virginia Polytechnic and State
University, Blacksburg, VA 24061, USA, and dConsortium for Advanced Radiation Sources,
University of Chicago, Chicago, IL 60637, USA. E-mail: s.jacobsen@gl.ciw.edu
This study demonstrates the use of monochromatic synchrotron X-ray radiation
of 40 keV for high-precision equation-of-state studies on sets of single crystals
analysed individually in the same diamond-anvil pressure cell. Angle-dispersive
zone-axis diffraction patterns were obtained from crystals of wustite-Fe0.93O and
magnesiowüstite-(Mg0.73Fe0.27)O to 51 GPa in a hydrostatic helium pressure
medium. The rhombohedral phase of Fe0.93O was observed above 23 GPa, and
its isothermal bulk modulus (K0) was determined to be 134 (4) GPa, assuming
K0 = 4. The rhombohedral phase of Fe0.93O is more compressible than B1structured Fe0.93O, with K0 = 146 (2) GPa. Magnesiowüstite-(Mg0.73Fe0.27)O
remains cubic over the experimental pressure range, and has a bulk modulus of
154 (3) GPa with K0 = 4.0 (0.1).
# 2005 International Union of Crystallography
Printed in Great Britain – all rights reserved
Keywords: single-crystal X-ray diffraction; megabar; zone-axis diffraction; diamond-anvil
cell; wüstite; magnesiowüstite; helium pressure medium; equation of state.
1. Introduction
Thermodynamic equations of state have long played a central
role in efforts to understand the nature of Earth’s deep
layered structure in terms of mineralogical (phase) and
compositional variation (e.g. Duffy & Anderson, 1989; Ita &
Stixrude, 1992; Jackson, 1998). Constraining the effects of
pressure, temperature and composition on the structure and
density of candidate high-pressure mineral assemblages is
therefore one of the primary goals of mineral physics. Singlecrystal compressibility studies have several distinct advantages
over powder diffraction studies because the data are threedimensional in nature, more data are available for leastsquares fitting because symmetry-equivalent reflections are
observed, and the diffraction peaks from a high-quality single
crystal are nominally sharper than from a powder subject to
intergranular stresses. Subtle phase transitions, such as lattice
distortions, are readily observed in single-crystal diffraction
data. Despite the advantages of using single-crystal samples
for compressibility and structural studies, relatively few
experiments on minerals have been carried out to pressures
above 20 GPa, mainly because working with fragile singlecrystal plates at higher pressures requires careful attention to
stress conditions of the sample, which can be minimized by the
use of gas-loaded pressure media such as helium. Although
J. Synchrotron Rad. (2005). 12, 577–583
helium crystallizes at 11 GPa (Besson & Pinceaux, 1979;
Loubeyre et al., 1993), solid helium remains sufficiently soft to
be considered hydrostatic to pressures of at least 50 GPa
(Takemura, 2001). Shu et al. (1998) reported the structure of
single-crystal Fe0.95O to 30 GPa in helium, Zha et al. (2000)
measured the cell parameters of MgO to 55 GPa, also in
helium and, most recently, Occelli et al. (2003) measured the
equation of state of single-crystal diamond in helium to
140 GPa.
This study highlights the use of monochromatic synchrotron
X-ray radiation at 40 keV for high-precision equation-of-state
studies on sets of single-crystal samples loaded together in the
same diamond cell in the 0.5 Mbar pressure range. X-ray
beams of diameter 5–20 mm allow angle-dispersive X-ray
diffraction patterns from different micro crystals to be
recorded separately for ease of indexing. The use of very thin
oriented plates (10 mm thickness) and relatively high X-ray
energies (40 keV) results in zone-axis-type diffraction
patterns from which high-precision cell parameters are
obtained for equation-of-state fitting. Since the degree of
oscillation necessary to obtain multiple classes of reflections is
relatively small (typically 5 !), the standard centering
procedures are adequate to keep the X-ray beam on a sample
of similar dimensions as the beam. In this study, we present
new data from two (of five) samples loaded simultaneously in
electronic reprint
doi:10.1107/S0909049505022326
577
SXD at Mbar pressures
the same cell; wustite-Fe0.93O and magnesiowüstite(Mg0.73Fe0.27)O. Whereas Fe1–xO is more relevant to
condensed matter physics as an archetypical transition metal
oxide with strongly correlated electrons (e.g. Struzhkin et al.,
2001; Kantor et al., 2004), (Mg,Fe)O is one of the most
important minerals in Earth science because it is likely the
most abundant non-silicate oxide in the planet, constituting
roughly 10–20% by volume of the Earth’s lower mantle. Our
main objective here is to outline the single-crystal diffraction
procedures and to report the high-pressure behaviour and
equation-of-state parameters for wüstite and a magnesiowüstite crystal of relevant composition to the Earth’s lower
mantle.
2. Experiment
High-pressure single-crystal X-ray diffraction experiments
were carried out on the BM-D beamline of GSECARS (sector
13) at the Advanced Photon Source. Monochromatic
synchrotron X-rays were focused to a spot size 6 mm wide by
20 mm in height (FWHM) at 40 keV. The wavelength
(0.30996 Å) was calibrated periodically using a CeO2 standard. Diffraction images were recorded in transmission mode
through the diamond cell on a MAR345 image plate positioned 38.58 cm from the sample.
Single-crystal Fe0.93O was synthesized by oxidizing a
centimetre-sized single crystal of metallic iron at 1473 K and
1011 atmospheres fO2 in a CO/CO2 gas-mixing furnace. The
sample was drop-quenched into a container of the same CO/
CO2 mixture below the furnace to prevent the formation of
magnetite upon cooling below 773 K. The recovered sample
consisted of a coarse-grained aggregate of Fe1–xO crystals,
ranging in size from about 50 to 500 mm. The cell parameters
of several Fe1–xO crystals were measured to be in the range
4.298–4.300 Å, corresponding to approximately Fe0.93O
(McCammon & Liu, 1984). A single crystal of magnesiowüstite-(Mg,Fe)O containing 27 mol% FeO (sample Fe27)
was synthesized by interdiffusing Fe and Mg between prereacted (Mg,Fe)O powders and single-crystal MgO. Details of
the magnesiowüstite crystal synthesis are given elsewhere
(Jacobsen et al., 2002).
A crystal of Fe0.93O and (Mg0.73Fe0.27)O, along with three
other magnesiowüstite compositions and an annealed rubysphere pressure marker, were loaded together in a symmetrictype diamond-anvil cell (Fig. 1). Samples were pre-oriented on
h110i in order to maximize the number of observable reflection classes, and polished into thin parallel plates using
impregnated-diamond film to approximately 10–12 mm thickness. The pressure cell was fitted with 50 full-cone WC seats
and diamond anvils with 300 mm flat culets. A rhenium gasket
was pre-indented to 25 GPa ( 35 mm thickness) and the
initial hole was drilled to 200 mm diameter. The cell was
loaded with compressed helium at 30000 psi, and initially
compressed to 7 GPa. At this initial pressure, the gasket
hole had reduced to 125 mm diameter. At the highest pressure (51 GPa), the gasket hole had further reduced to
100 mm diameter, and none of the 10–12 mm-thick crystals
578
Steven D. Jacobsen et al.
Wüstite and magnesiowüstite
had bridged the gap between the diamonds based on visual
observation and the diffraction patterns.
Zone-axis-type diffraction patterns were obtained from the
pre-oriented thin-crystal platelets because the excitation error
from Bragg diffraction is sufficiently low at 40 keV. At each
crystal position the cell was oscillated about the vertical axis
(!) between 9 for 60 s exposure times, resulting in the
observation of two to three classes (six to 12 total reflections)
for indexing and least-squares refinement (on d-spacings)
using the Unit Cell refinement software package with regression diagnostics (Holland & Redfern, 1997). Unit-cell parameters were obtained at various pressures up to 51 GPa
using the ruby fluorescence pressure scale (Mao et al., 1986).
Hydrostatic conditions were maintained in the helium pressure medium to the maximum pressure, which was monitored
by the separation of the R1 and R2 ruby fluorescence peaks,
illustrated in Fig. 2. For the purpose of equation-of-state
fitting, ambient-pressure cell parameters were determined
outside the cell at 300 K.
3. Results and discussion
3.1. Wüstite-Fe0.93O
In Fe0.93O, six to ten reflections of the h00 and hk0 classes
were available for indexing. A phase transition from the cubic
(B1) structure to the rhombohedral (distorted-B1) phase was
observed above 22 GPa upon splitting of the cubic 220
reflection into two sets of the rhombohedral 110 and 104
reflections, representing two (of the four) twin domains in the
rhombohedral distortion (Shu et al., 1998). Evolution of the
220 reflection with pressure is illustrated in Fig. 3, along with
details (inset) from the image plate. We note that this is the
highest pressure that the cubic phase of Fe1–xO has been
reported. Systematic errors in the pressure determination
were ruled out as a cause for the discrepancy in the transition
pressure compared with previous studies by checking zeropressure ruby spectra outside the cell. The transition pressure
of the rhombohedral distortion is known to depend on the
stress conditions on and within the sample, and thus possibly
Figure 1
Five single-crystal samples of (Mg,Fe)O loaded into the same diamond
cell for equation-of-state studies in the 0.5 Mbar range. Numbers indicate
the percent of Fe in each sample. Here we report the behaviour of Fe0.93O
and Fe27. The X-ray spot size on the samples was approximately 6 mm
20 mm (FWHM), allowing each crystal to be analysed individually. The
gasket material is rhenium, and the culet size is 300 mm.
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J. Synchrotron Rad. (2005). 12, 577–583
SXD at Mbar pressures
also on the degree of non-stoichiometry (x) of Fe1–xO. In
previous powder diffraction studies, the transition pressure
typically ranges from about 8–10 GPa under non-hydrostatic
conditions (Zou et al., 1980; Dubrovinsky et al., 2000; Fei &
Mao, 1994) to roughly 16 GPa for both Fe0.92O and Fe0.98O
under quasi-hydrostatic conditions (Yagi et al., 1985; Fei &
Mao, 1994). The transition pressure of Fe0.95O from the singlecrystal study of Shu et al. (1998) in helium was 18 GPa.
Figure 2
Ruby fluorescence spectra from outside the diamond cell at 1 atm
(shorter wavelengths) and from 51 GPa (longer wavelengths). Hydrostatic pressure conditions were achieved in this experiment using a helium
pressure medium. This figure illustrates minimal separation between the
R1 and R2 fluorescence lines (R1 R2 in nm), a proxy for differential
stress in the cell. For comparison, the 1 atm spectrum is also shown shifted
(dashed line) under the 51 GPa spectrum (solid line). The R1 R2
separation at 50 GPa in a 4:1 methanol:ethanol pressure medium was
reported to be 2.0 nm (Takemura, 2001).
Although we could not observe the 111 reflection, previous
studies indicate that splitting of the 220 and 111 reflections
occurs simultaneously, so we conclude that the transition
pressure in this study is elevated by 4–5 GPa compared with
the previous single-crystal study (Shu et al., 1998), further
illustrating the enigmatic behaviour of Fe1–xO at high pressure
(Mao et al., 1996).
The 200 reflections of the cubic phase are surrounded by a
motif of satellite reflections at (2 , 0, 0), (2, , 0) and
(2 , , 0), connected along h00 by streaks of diffuse
scattering (Fig. 4). The diffraction features around 200 are
attributed to long-range order of defect clusters in the structure (Koch & Cohen, 1969; Gavarri & Carel, 1989; Welberry &
Christy, 1997). In agreement with previous X-ray studies at
room pressure, we note that superlattice reflections are more
intense on the low-angle side of the Bragg diffraction.
Although the superlattice reflections decrease in intensity with
increasing pressure as the rhombohedral phase is approached,
they do not entirely disappear for the rhombohedral phase,
and the (2 , 0, 0) satellite on the low-angle side of 200 is
especially apparent in the diffraction pattern of the rhombohedral phase at 28 GPa (Fig. 4c). The 200 Bragg reflection of
the rhombohedral phase, i.e. R(102), becomes broad along 020
(i.e. ), but remains as sharp in 2 as the cubic 200 at lower
pressures.
Variation of the unit-cell parameters with pressure for the
cubic and rhombohedrally distorted phases of Fe0.93O are
given in Table 1. Volume–pressure curves are plotted in Fig. 5.
We fitted the P–V data of cubic Fe0.93O to a third-order BirchMurnaghan equation of state using the EOS-FIT (V5.2) least-
Figure 3
Evolution of the cubic 220 reflection in Fe0.93O to 51 GPa. The structure is
still cubic at 22.8 GPa, as shown by the detail of the unsplit 220 peak with
satellite reflections shown inset (origin is to the right). Splitting of the
R(110) and R(104) reflections is completely resolved in the 27–50 GPa
pressure range, and d/hdi increases from 0.038 at 27 GPa to 0.054 at
51 GPa. There is no indication of additional splitting over this pressure
range.
J. Synchrotron Rad. (2005). 12, 577–583
Figure 4
Evolution of the 200 reflection and surrounding superlattice reflections in
Fe0.93O with pressure (the origin is vertical). The strongest satellite
reflection at (2 , 0, 0) is still observed in the rhombohedral phase, but is
absent at pressures above 40 GPa, indicating the disappearance of
long-range order of defect clusters.
Steven D. Jacobsen et al.
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Wüstite and magnesiowüstite
579
SXD at Mbar pressures
squares package (Angel, 2001). Since there are relatively few
data points below 20 GPa, we fixed K0 = 4.0 and varied V0 and
K0, resulting in V0 = 79.41 (0.04) Å and K0 = 146 (2) GPa,
in good agreement with the bulk modulus for Fe0.95O of
149 (3) GPa (Shu et al., 1998) and for Fe0.92O of
147 (2) GPa (Fei, 1996).
The measured molar volume data for the rhombohedral
phase fall below the cubic-phase molar volumes calculated by
extrapolating the equation of state of the cubic phase to
pressures above the phase transition, as required by the
thermodynamics of a phase transition that does not include a
significant contribution from the entropy change accompanying the transition. We also note that the excess volume
(Vrhomb Vcubic) arising from the transition does not extraTable 1
Unit-cell parameters for magnesiowüstite and wüstite at high pressure.
(Mg0.73Fe0.27)O
Cubic Fe0.93O
Rhombohedral Fe0.93O
P (GPa)†
a (Å)
a (Å)
a (Å)
c (Å)
0.00
7.70
10.6
12.0
13.7
15.0
22.8
27.7
31.6
35.3
38.5
41.5
43.6
46.0
48.7
51.1
4.2599 (3)
4.1953 (19)
4.1745 (7)
4.1660 (8)
4.1526 (28)
4.1440 (8)
4.0944 (15)
4.0707 (18)
4.0514 (7)
4.0332 (10)
4.0172 (18)
4.0037 (19)
3.9941 (19)
3.9865 (14)
3.9747 (21)
3.9641 (19)
4.2980 (6)
4.2299 (13)
4.2085 (8)
4.1979 (22)
4.1842 (11)
4.1751 (23)
4.1255 (26)
2.8359 (7)
2.8149 (8)
2.7986 (14)
2.7826 (10)
2.7694 (9)
2.7599 (20)
2.7522 (11)
2.7463 (30)
2.7309 (18)
7.361
7.352
7.332
7.342
7.331
7.302
7.299
7.282
7.277
† Precision in the pressure determination is considered to be 0.05–0.1 GPa.
(4)
(4)
(7)
(5)
(4)
(10)
(5)
(15)
(9)
polate to zero in the neighbourhood of the phase-transition
pressure and, therefore, in contrast to previous studies (e.g.
Shu et al., 1998; Mao et al., 1996), we propose that the transition is possibly weakly first-order in character.
Owing to the relatively low precision of previous powder
diffraction studies [wherein the separation of R(110) and
R(104) is not resolved] and limited pressure range of the
previous single-crystal X-ray diffraction study (Shu et al.,
1998), the equation of state of the high-pressure rhombohedral phase of Fe1–xO has not been previously determined.
The distorted Fe1–xO structure was predicted to be less
compressible (higher bulk modulus) than cubic Fe1–xO (Fei,
1996) based upon the variation of measured 200 d-spacings
with pressure. We obtained unit-cell volumes of the rhombohedral phase (set in the equivalent hexagonal cell,
Table 1) to within a few parts in 104, allowing us to
estimate for the first time the compressibility of
the high-pressure phase. We obtained an internally
consistent equation of state by solving first for the
V (Å3)
parameters at a reference pressure of 28 GPa and
then back-calculating zero-pressure parameters
from the fit. Setting P28 GPa as the reference pressure and fitting our experimental data between 28
and 51 GPa, we obtain equation-of-state parameters V28 GPa = 51.28 (0.03) Å3 and K28 GPa =
238 (4) GPa, with K280 GPa = 3.5 (fixed). The fitted
51.27 (2)
volume at 28 GPa is in excellent agreement with
50.45 (3)
the experimental value of 51.27 (0.02) Å3 at
49.74 (4)
49.23 (3)
27.7 GPa. The rhombohedral phase equation-of48.69 (3)
state parameters obtained by directly fitting the
48.16 (6)
high-pressure data with a reference pressure of
47.88 (3)
47.56 (9)
28 GPa correspond to V0 = 59.85, K0 = 132 GPa
47.00 (5)
and K0 = 4.2. The P–V data were then fitted using
an ambient reference pressure of 1 atm (but
Figure 5
Left: normalized volume–pressure data for cubic and rhombohedral phases of Fe0.93O (filled symbols) with fitted equations of state (solid lines).
Variation of the c/a ratio with pressure (filled circles) is shown on the right. The equation of state of the rhombohedral phase was determined first by
fitting the high-pressure data to a 28 GPa reference pressure, and then back-calculating V0, K0 and K0 . Direct fitting of the P–V data (without a P0 data
point) yields consistent equation-of-state parameters (see text for details). Error bars are within the size of the symbols.
580
Steven D. Jacobsen et al.
Wüstite and magnesiowüstite
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J. Synchrotron Rad. (2005). 12, 577–583
SXD at Mbar pressures
without the calculated V0) using fixed K0 = 4.0, resulting in
V0 = 59.72 (0.22) Å3 and K0 = 134 (4) GPa, which are well
within one standard deviation of the values obtained by
extrapolating the P28 GPa parameters back to P0. This crosscheck demonstrates the internal consistency of the fitting
method, and thus we conclude that a best estimate for the bulk
modulus of rhombohedral Fe0.93O is 134 (4) GPa, assuming
K0 = 4. The higher compressibility (lower K0) of the rhombohedral phase compared with the cubic phase is not thermodynamically inconsistent with a weakly first-order phase
transition, nor is the fact that the calculated molar volumes at
1 atm are similar. We use the fitted V0 of the rhombohedral
phase (Table 1) to calculate MV0 = 11.99 (0.04) cm3, corresponding to 0 = 5.667 (0.018) g cm3, which is within 2 of
the initial density of the cubic Fe0.93O, with MV0 =
11.95 (0.001) cm3 and 0 = 5.683 (0.003) g cm3.
It has also been proposed that Fe1–xO adopts a lowersymmetry structure at higher pressures and 300 K, as
evidenced by possible further splitting of the R(104) peak
above 40 GPa (e.g. Yagi et al., 1985; Fei, 1996). Additional
splitting of R(104) was not observed to 51 GPa in the current
hydrostatic study, and there is no evidence for an additional
transition in the evolution of the c/a ratio with pressure
(Fig. 5). Since the cubic-to-rhombohedral distortion was not
evident in our single-crystal experiment until P > 23 GPa
(compared with 16 GPa in quasi-hydrostatic powder
studies), it may also be expected that any subsequent
(monoclinic) distortions would not occur until well above
40 GPa. The presence of an additional pressure-induced
distortion is also suggested by the presence of a monoclinic
(C2/m) phase of nearly stoichiometric Fe0.99O at 10 K,
observed during a low-temperature neutron diffraction study
(Fjellvåg et al., 2002). Although we did not observe any further
distortion of the rhombohedral phase to 51 GPa, the possibility that such a distortion was missed owing to the limited
three-dimensional access to reciprocal space in the singlecrystal diffraction experiment cannot be ruled out.
wave data for (Mg0.6Fe0.4)O (Vassiliou & Ahrens, 1982) and
from static compression of (Mg0.6Fe0.4)O to 26 GPa (Rosenhauer et al., 1976). On the other hand, compositions containing
greater than about 75 mol% Fe1–xO do become rhombohedral
above 20 GPa (Mao et al., 2002; Kondo et al., 2004; Lin et al.,
2002), indicating that the addition of Mg to Fe1–xO acts to
stabilize the B1 structure at high pressure, consistent with
recent single-crystal elasticity studies (Jacobsen et al., 2004).
Volume–pressure data for (Mg0.73Fe0.27)O are listed in
Table 1, and plotted in Fig. 6. The fitted equation-of-state
parameters for this composition are V0 = 77.30 (0.09) Å3,
K0 = 154 (3) GPa and K0 = 4.0 (0.1). The bulk modulus
obtained on a similar crystal (from the same bulk sample) with
lower-pressure single-crystal data to 9 GPa (Jacobsen et al.,
2002) is 158.4 (0.4) GPa with K0 = 5.5 (1), somewhat higher
than the current study. The difference in equation-of-state
parameters between this study and those of Jacobsen et al.
(2002) may be due to the limited pressure range of the
previous study or from the use of different pressure scales
(quartz volume versus ruby fluorescence). Our value of K0 =
154 (3) GPa is also about 1 below K0 = 157 (K0 = 4)
reported for (Mg,Fe)O containing 40 mol% FeO (Rosenhauer et al., 1976), but it is in excellent agreement with the
values of K0 = 154 (3) and K0 = 4.0 (0.4) recently reported
for (Mg0.64Fe0.36)O (van Westrenen et al., 2005). Equation-ofstate parameters for (Mg,Fe)O are summarized in Table 2. The
compression data for (Mg,Fe)O are plotted as the Birchnormalized pressure (F) against Eulerian strain ( f) in Fig. 7,
providing a more visual representation of how K0 = dK/dP ’
4.0. Despite these rather small differences in K for the ironbearing magnesiowüstites, we conclude that the bulk modulus
of lower-mantle (Mg,Fe)O is not expected to vary from pure
MgO by more than 10 GPa.
3.2. Magnesiowüstite-(Mg0.73Fe0.27)O
We also report the volume compression of a magnesiowüstite crystal loaded in the same cell as the Fe0.93O. Previous
static-compression equation-of-state studies on magnesiowüstite at 300 K and above 10 GPa have focused on either the
MgO end member (e.g. Duffy et al., 1995; Speziale et al., 2001;
Zha et al., 2000; Fei, 1999) or on Fe-rich compositions
containing 40 mol% FeO (Rosenhauer et al., 1976), 60–
80 mol% FeO (Richet et al., 1989; Lin et al., 2002) or between
80 and 95 mol% FeO (Mao et al., 2002; Kondo et al., 2004).
Since lower-mantle compositions are expected to be somewhat
lower (10–30 mol% FeO) (e.g. Andrault, 2001), we have
undertaken a compressibility study of (Mg0.73Fe0.27)O because
it is more applicable to the study of the Earth’s interior.
In contrast to wüstite, the (Mg0.73Fe0.27)O sample does not
exhibit a rhombohedral distortion over the experimental
pressure range to 51 GPa. The absence of any phase transitions in this composition is consistent with previous shockJ. Synchrotron Rad. (2005). 12, 577–583
Figure 6
Comparative compressibility of single-crystal (Mg,Fe)O, with data from
this study on (Mg0.73Fe0.27)O (solid line, filled circles, error within the
symbol), cubic Fe0.93O (dash-dotted line) and rhombohedral Fe0.93O
(dotted line). The equation of state of single-crystal MgO (Zha et al.,
2000) is shown by the dashed line.
Steven D. Jacobsen et al.
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Wüstite and magnesiowüstite
581
SXD at Mbar pressures
Table 2
Equation-of-state parameters of (Mg,Fe)O from hydrostatic single-crystal compression studies.
P range (GPa)
0 (g cm3)
V0 (Å3)
K0 (GPa)
K0
Reference
Cubic Fe0.95O
Cubic Fe0.93O
Rhomb Fe0.93O
(Mg0.73Fe0.27)O
MgO
0–18
5.729
79.88
149 (3)
4.0 (fixed)
Shu et al. (1998)
0–51
5.683 (0.003)
79.41 (0.04)
146 (2)
4.0 (fixed)
This study
23–51
5.667 (0.018)
59.72 (0.22)†
134 (4)†
4.0 (fixed)
This study
0–51
4.195 (0.005)
77.30 (0.09)
154 (3)
4.0 (0.1)
This study
0–55
3.585
74.68
160.2 (0.7)
4.03 (0.03)
Zha et al. (2000)
† Calculated by directly fitting the experimental P–V data with 1 atm reference pressure.
We thank J. Shu for assistance with the helium gas loading,
S. J. Mackwell for help with the (Mg,Fe)O sample synthesis,
and C. T. Prewitt for discussions. Support for this study was
provided by the National Science Foundation EAR-0440112
and a Carnegie Fellowship to SDJ, with additional support
from the Carnegie/DOE Alliance Center. GSECARS is
supported by the National Science Foundation – Earth
Sciences (EAR-0217473), Department of Energy – Geosciences (DE-FG02-94ER14466) and the State of Illinois. Use
of the APS was supported by the US Department of Energy,
Basic Energy Sciences, Office of Energy Research, under
Contract No. W-31-109-Eng-38.
References
Figure 7
Plot of the Birch-normalized pressure (F) against Eulerian strain ( f ) for
the Fe0.93O and (Mg0.73Fe0.27)O crystals. The plot visually confirms that K0
is close to 4 for both Fe0.93O phases. K0 was allowed to refine in the
(Mg,Fe)O data set, yielding 4.0 (0.1). The values of V0 used to calculate
the F–f plot were determined experimentally for (Mg0.73Fe0.27)O (V0 =
77.30 0.02 Å3) and cubic Fe0.93O (V0 = 79.40 0.04 Å3), and were
taken from the fitted equation of state for the rhombohedral phase of
Fe0.93O (V0 = 59.72 0.22 Å3).
4. Conclusions
Megabar equation-of-state studies on single-crystal mineral
samples will soon be routine (Occelli et al., 2003; Zha et al.,
2000; this study), and are expected to provide tighter
constraints on the behaviour of minerals at very high pressure
because cell parameters can be obtained to within a few parts
in 104 or better. The use of micro crystals measuring 20 mm
across and 10 mm thick allows multiple compositions (or
multiple orientations) to be loaded together in the same
megabar cell, and the use of focused synchrotron X-rays at
high energies ( 40 keV) can be used to study the crystals
individually at nominally identical pressures. In this study the
equations of state of Fe0.93O and (Mg0.73Fe0.27O) were determined simultaneously. The quality of single-crystal diffraction
patterns and the expanded pressure range over previous
studies facilitated the determination of the equation of state of
rhombohedrally distorted Fe0.93O. In contrast to prediction,
our results indicate that the rhombohedral phase of Fe0.93O is
more compressible than cubic Fe0.93O.
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