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Equations of state and phase boundary for stishovite and CaCl2-type SiO2

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Silica is thought to be present in the Earth's lower mantle in subducting plates, in addition to being a prototypical solid whose physical properties are of broad interest. It is known to undergo a phase transition from stishovite to the CaCl 2-type structure at ∼50-80 GPa, but the exact location and slope of the phase boundary in pressure-temperature space is unresolved. There have been many previous studies on the equation of state of stishovite, but they span a limited range of pressures and temperatures , and there has been no thermal equation of state of CaCl 2-type SiO 2 measured under static conditions. We have investigated the phase diagram and equations of state of silica at 21-89 GPa and up to ∼3300 K using synchrotron X-ray diffraction in a laser-heated diamond-anvil cell. The phase boundary between stishovite and CaCl 2-type SiO 2 can be approximately described as T = 64.6(49)·P-2830(350), with temperature T in Kelvin and pressure P in GPa. The stishovite data imply K 0 ʹ = 5.24(9) and a quasi-anharmonic T 2 dependence of-6.0(4) × 10-6 GPa·cm 3 /mol/K 2 for a fixed q = 1, g 0 = 1.71, and K 0 = 302 GPa, while for the CaCl 2-type phase K 0 = 341(4) GPa, K 0 ʹ = 3.20(16), and g 0 = 2.14(4) with other parameters equal to their values for stishovite. The behaviors of the a and c axes of stishovite with pressure and temperature were also fit, indicating a much more compressible c axis with a lower thermal expansion as compared to the a axis. The phase transition between stishovite and CaCl 2-type silica should occur at pressures of 68-78 GPa in the Earth, depending on the temperature in subducting slabs. Silica is denser than surrounding mantle material up to pressures of 58-68 GPa, with uncertainty due to temperature effects; at higher pressures than this, SiO 2 becomes gravitationally buoyant in the lower mantle.
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Equations of state and phase boundary for stishovite and CaCl2-type SiO2
Rebecca a. FischeR1,2,3,4,*, andRew J. campbell1, bethany a. chidesteR1,,
daniel m. Reaman1, elizabeth c. thompson1, JeFFRey s. pigott5,, Vitali b. pRakapenka6,
and Jesse s. smith7
1Department of the Geophysical Sciences, University of Chicago, 5734 S. Ellis Avenue, Chicago, Illinois 60637, U.S.A.
2Department of Mineral Sciences, National Museum of Natural History, Smithsonian Institution, P.O. Box 37012, MRC 119,
Washington, D.C. 20013-7012, U.S.A.
3University of California Santa Cruz, Department of Earth and Planetary Sciences, 1156 High Street, Santa Cruz, California 95064, U.S.A.
4Department of Earth and Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, U.S.A.
5School of Earth Sciences, Ohio State University, 125 S. Oval Mall, Columbus, Ohio 43210, U.S.A.
6Center for Advanced Radiation Sources, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, U.S.A.
7High Pressure Collaborative Access Team (HPCAT), Geophysical Laboratory, Carnegie Institution of Washington, 9700 S. Cass Avenue,
Argonne, Illinois 60439, U.S.A.
abstRact
Silica is thought to be present in the Earth’s lower mantle in subducting plates, in addition to being
a prototypical solid whose physical properties are of broad interest. It is known to undergo a phase
transition from stishovite to the CaCl2-type structure at 50–80 GPa, but the exact location and slope
of the phase boundary in pressure-temperature space is unresolved. There have been many previous
studies on the equation of state of stishovite, but they span a limited range of pressures and tem-
peratures, and there has been no thermal equation of state of CaCl2-type SiO2 measured under static
conditions. We have investigated the phase diagram and equations of state of silica at 21–89 GPa and
up to 3300 K using synchrotron X-ray diffraction in a laser-heated diamond-anvil cell. The phase
boundary between stishovite and CaCl2-type SiO2 can be approximately described as T = 64.6(49)·P
– 2830(350), with temperature T in Kelvin and pressure P in GPa. The stishovite data imply K0
ʹ =
5.24(9) and a quasi-anharmonic T2 dependence of –6.0(4) × 10–6 GPa·cm3/mol/K2 for a xed q = 1,
g0 = 1.71, and K0 = 302 GPa, while for the CaCl2-type phase K0 = 341(4) GPa, K0
ʹ = 3.20(16), and g0
= 2.14(4) with other parameters equal to their values for stishovite. The behaviors of the a and c axes
of stishovite with pressure and temperature were also t, indicating a much more compressible c axis
with a lower thermal expansion as compared to the a axis. The phase transition between stishovite and
CaCl2-type silica should occur at pressures of 68–78 GPa in the Earth, depending on the temperature
in subducting slabs. Silica is denser than surrounding mantle material up to pressures of 58–68 GPa,
with uncertainty due to temperature effects; at higher pressures than this, SiO2 becomes gravitationally
buoyant in the lower mantle.
Keywords: Silica, SiO2, stishovite, phase diagram, equation of state, phase transition, X-ray diffraction
intRoduction
Silica (SiO2) is expected to be present in subducted mid-
ocean ridge basalt in the Earth’s lower mantle (e.g., Hirose
et al. 2005). It may also occur in the Dʺ layer as a result of Si
and O becoming less soluble in liquid iron as the core cools
(Hirose et al. 2017), since the metal–silicate partitioning of
O and especially Si are strongly temperature dependent (e.g.,
Fischer et al. 2015; Tsuno et al. 2013). Despite its importance
in geophysics, as well as physics and materials science, there
remains disagreement surrounding the phase diagram of silica
at high pressures (P) and temperatures (T). Additionally, only
limited research has been done on the thermal equation of state
for the CaCl2-type phase of silica, stable under lower mantle
conditions. In this study, we focus on elucidating the location
and slope of the stishovite/CaCl2-type phase boundary, as well
as providing better constraints on the thermal equations of state
of these important phases.
Coesite (monoclinic SiO2 with space group C2/c) transforms
to stishovite (rutile-type SiO2 with space group P42/mnm) at
7–13 GPa and high temperatures (e.g., Zhang et al. 1996),
marking a transition in Si coordination from tetrahedral to
octahedral. At lower mantle pressures, stishovite undergoes a
second-order, reversible phase transition to the CaCl2-type struc-
ture (space group Pnnm) of SiO2, in which the tetragonal unit cell
of stishovite distorts into an orthorhombic unit cell (Tsuchida
and Yagi 1989). Reports of the location and slope of this phase
American Mineralogist, Volume 103, pages 792–802, 2018
0003-004X/18/0005–792$05.00/DOI: http://doi.org/10.2138/am-2018-6267 792
* E-mail: rebeccafischer@g.harvard.edu
† Present address: Department of Earth and Planetary Sciences, University of California
Davis, 1 Shields Avenue, Davis, CA 95616, U.S.A.
‡ Present address: Department of Earth, Environmental, and Planetary Sciences, Case
Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, U.S.A.
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2793
CaCl2-type SiO2 to higher pressures (89 GPa) and temperatures
(3300 K) than in previous work and with broader P-T coverage.
expeRimental methods
Symmetric-type diamond-anvil cells were used to generate high pressures,
with either 300 µm culet anvils or beveled anvils with 150 µm flats. Starting
materials were powdered natural quartz and amorphous Pt (Alfa Aesar, 99.9%)
in a ratio of 2:1 by volume in two of our samples, while the third sample con-
tained powdered natural quartz and spherical Pt (Alfa Aesar, 99.95%) in a ratio
of 3:1 by volume. Platinum was used to absorb the heating laser during the
experiment; it was chosen because it is a strong laser absorber, is inert, and has
a well-characterized equation of state (e.g., Dorogokupets and Oganov 2007).
The quartz was measured with a scanning electron microscope and determined
to contain no detectable Al. Samples composed of silica glass instead of natural
quartz (but otherwise identical) did not sufficiently crystallize at high tempera-
tures during the experiment. In each case, starting materials were mechanically
ball-milled to grind and mix the powders. The powder mixture was then pressed
into a flake 5 µm thick and loaded into a rhenium gasket (preindented to 27–33
GPa) between two layers of KBr, each 10–15 µm thick, which served as the
pressure medium and thermal insulator. KBr was used due to its extremely
efficient thermal insulating properties, hydrostaticity at high temperatures,
strong X-ray fluorescence that allows for precise alignment of the X-ray and
laser optics on the sample, and well-characterized equation of state while used
as a thermal insulator (Fischer et al. 2012). Prior to loading, the KBr was oven
dried and stored in a desiccator. The entire sample assembly was oven dried at
80–85 °C for 30–60 min after loading but before closing the cell to remove any
residual moisture.
boundary vary, with room-temperature measurements under
quasi-hydrostatic conditions on pure silica typically reporting a
transition pressure of 45–55 GPa (Andrault et al. 1998; Hemley
et al. 2000; Kingma et al. 1995; Nomura et al. 2010; Ono et al.
2002), in agreement with some theoretical calculations (Karki
et al. 1997; Togo et al. 2008; Tsuchiya et al. 2004); the location
of the phase boundary is affected by impurities such as Al and H
(e.g., Lakshtanov et al. 2007). High-temperature measurements
indicate a positive Clapeyron slope (Akins and Ahrens 2002;
Nomura et al. 2010; Ono et al. 2002) (Fig. 1). The CaCl2-type
structure converts to seifertite (α-PbO2-type silica) at pressures
of 120–140 GPa (Dubrovinsky et al. 1997; Grocholski et al.
2013), though there remains ambiguity over the precise location
and slope of this phase boundary as well (Murakami et al. 2003;
Shieh et al. 2005). The phase diagram of silica is known to be
subject to kinetic barriers, especially at room temperature, with
observations of a large number of metastable and/or amorphous
phases. These kinetic inhibitions are dependent on the degree
of hydrostaticity and the nature of the starting materials as well
as temperature-pressure pathways (e.g., Asahara et al. 2013;
Dubrovinsky et al. 2003; Haines et al. 2001; Hazen et al. 1989;
Hemley 1987; Kingma et al. 1993; Prakapenka et al. 2004;
Tsuchida and Yagi 1990).
The equation of state of stishovite has been measured numer-
ous times since its discovery by Chao et al. (1962) (Supplemental1
Table S1 and references therein): at high pressures using
diamond-anvil cell (e.g., Andrault et al. 2003; Jiang et al. 2009;
Panero et al. 2003; Pigott et al. 2015; Ross et al. 1990; Yamanaka
et al. 2002), shock wave (e.g., Luo et al. 2002a; Lyzenga et al.
1983), large volume press (e.g., Liu et al. 1999; Nishihara et al.
2005; Wang et al. 2012), piston-cylinder apparatus (e.g., Li et
al. 1996), and computational (e.g., Cohen 1991; Driver et al.
2010; Karki et al. 1997a; Luo et al. 2002b; Tsuchiya et al. 2004)
methods, as well as on synthetic samples at ambient pressure
(e.g., Brazhkin et al. 2005; Weidner et al. 1982; Yoneda et al.
2012). Despite the number of prior studies on the stishovite equa-
tion of state, it has previously only been measured to 54 GPa and
1700 K (Wang et al. 2012) or 50 GPa and 2400 K (Pigott et al.
2015), requiring extrapolation to apply these equations of state
over the conditions of stishovite stability in the Earth.
The isothermal equation of state of CaCl2-type SiO2 has
been previously studied in a diamond-anvil cell (Andrault et al.
1998, 2003; Grocholski et al. 2013) and using computational
methods (Karki et al. 1997b; Oganov et al. 2005; Yang and Wu
2014). However, the only published thermal equation of state
of CaCl2-type SiO2 is based on a meta-analysis of shock wave
literature data (Akins and Ahrens 2002). Some previous studies
have instead fit a single equation of state to data on both the
stishovite and CaCl2-type structures (e.g., Yamazaki et al. 2014),
assuming that the two phases have the same compressibility and
thermal properties.
In this study, we use synchrotron X-ray diffraction in a laser-
heated diamond-anvil cell to determine the crystal structure
and density of SiO2 as a function of pressure and temperature
at lower mantle conditions. This information is used to map the
phase boundary between stishovite and CaCl2-type SiO2. By
combining these data with previous results at room temperature,
we construct thermal equations of state for both stishovite and
FiguRe 1. Previous results on the phase transition from stishovite
to CaCl2-type SiO2, compared to the phase boundary found in this
study. (top) Phase boundary at high temperatures. Filled gray hexagons
= observations of stishovite. Open gray pentagons = observations
of the CaCl2-type structure. Phase boundary from this study is from
Figure 3. (bottom) Transition pressures measured or calculated at room
temperature. Result from Wang et al. (2012) is a lower bound. Results
from Hemley et al. (2000) were obtained on either compression (higher
pressure) or decompression (lower pressure). (Color online.)
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2
794
Angle-dispersive synchrotron X-ray diffraction (XRD) was performed dur-
ing laser heating experiments at the Advanced Photon Source, Argonne National
Laboratory. Experiments were performed at Sector 13-ID-D, GeoSoilEnviro Center
for Advanced Radiation Sources (GSECARS) (Shen et al. 2005; Prakapenka et al.
2008), and Sector 16-ID-B, High Pressure Collaborative Access Team (HPCAT)
(Meng et al. 2015). At GSECARS, the X-ray beam was 3 × 4 µm with a wave-
length of 0.3344 Å, and the sample-to-detector distance was calibrated with 1 bar
diffraction of LaB6. At HPCAT, the X-ray beam was 5 × 7 µm with a wavelength
of 0.4066 Å, and the sample-to-detector distance was calibrated with 1 bar diffrac-
tion of CeO2. X-ray exposure times were 5–30 s.
Double-sided laser heating was performed with 1064 nm fiber lasers, focused
onto each side of the sample. Before each experiment, the X-ray beam was
coaligned with the temperature measurement system and heating lasers using X-ray
induced fluorescence of the KBr pressure medium in the sample (after heating,
it was confirmed that this alignment had been maintained). At each pressure, the
temperature was slowly stepped up by increasing the laser power until a target
temperature was reached, then the laser power was gradually decreased to zero,
with diffraction patterns collected on heating and cooling. The sample was held
fixed during heating. At each spot, a localized region of the sample was heated,
and the conversion from silica (which had become amorphous upon compression)
to stishovite was rapid (less than 1 min). The temperature was stable during our
X-ray data collection due to the subsolidus conditions. Power to the two lasers was
adjusted independently to minimize axial temperature gradients. At HPCAT, the
lasers had Gaussian intensity profiles and produced spots with diameters of 40 µm
(FWHM) on the samples, and at GSECARS, the lasers had “flat-top” intensity
profiles created with Pi-shapers and diameters of 25 µm on the samples. The
laser-heated spots were much larger than the X-ray beam to minimize the effects
of radial temperature gradients, and temperatures were measured from an area on
the sample a few micrometers across, comparable to the size of the X-ray beam.
Temperatures were determined by spectroradiometry using the graybody
approximation. The reported sample temperatures are an average of upstream and
downstream temperature measurements, corrected downward by 3% to account for
a small axial gradient through the sample (Campbell et al. 2007, 2009). Reported
temperature uncertainties include an analytical uncertainty of 100 K (e.g., Shen et
al. 2001), the difference between the upstream and downstream temperatures, and
uncertainty from the thickness correction (Campbell et al. 2007, 2009). At each
beamtime, temperature measurements in the diamond-anvil cell were benchmarked
by first analyzing a sample of iron at high pressures (Fischer et al. 2011, 2012, 2014)
to verify the location of the hcp–fcc transition (Komabayashi and Fei 2010). In each
case the temperature of the transition was confirmed within uncertainty, ensuring
compatibility between measurements made at different beamlines.
X-ray diffraction patterns were integrated to produce 2θ plots using Fit2D
(Hammersley et al. 1996) or Dioptas (Prescher and Prakapenka 2015), and peak
fitting was performed using PeakFit (Systat Software). Lattice parameters of each
phase were calculated from the measured d-spacings. Pressures were primarily
determined from the volume of B2-KBr using its thermal equation of state, which
was calibrated at room temperature and while used as a pressure medium during
laser heating experiments against the equations of state of numerous materials to
pressures of >100 GPa (Fischer et al. 2012); at high temperatures, KBr was mainly
calibrated against the Pt equation of state of Dorogokupets and Oganov (2007).
The platinum absorber also served as a secondary pressure standard in these ex-
periments using the equation of state of Dorogokupets and Oganov (2007), but in
some cases it was not usable. To measure the pressure, lattice parameters and their
uncertainties were determined as the average and standard deviation of 8 to 13 d-
spacings for KBr or 2 to 6 d-spacings for Pt. The temperature of the KBr insulator/
calibrant was corrected downward from the measured temperature to account for
axial thermal gradients through the insulating layer (Campbell et al. 2009), while
the temperature of the Pt was assumed to equal the sample temperature. Lattice
parameters of the sample were determined from 5 to 17 d-spacings for stishovite
or 7 to 20 d-spacings for the CaCl2-type structure.
Results
The silica samples became amorphous (Hemley et al. 1988)
or highly disordered (Prakapenka et al. 2004) upon compression,
and then crystallized in the stishovite or CaCl2-type structure
upon laser-heating. SiO2 phase identification was primarily based
on the splitting of the stishovite 210, 211, and 301 peaks upon
transformation to the CaCl2-type structure. An X-ray diffrac-
tion pattern collected at 74(2) GPa and 2160(120) K is shown
in Figure 2a, exhibiting the stishovite structure. All of the peaks
can be indexed as B2-KBr, stishovite-SiO2, fcc-Pt, or hcp-Re
(from the gasket). Figure 2b shows the evolution of the stishovite
301 peak during cooling at 74 GPa. At higher temperatures, a
single peak is seen; between 2160(120) and 1870(110) K, the
peak splits into the CaCl2-type 301 and 031 peaks, and at lower
temperatures a doublet is seen. In the 2D diffraction images, SiO2
peaks often appear as spots (Fig. 2b) due to Ostwald ripening
of the sample at high temperatures. These spots (including the
FiguRe 2. X-ray diffraction patterns of SiO2. (a) Representative
pattern from 74(2) GPa and 2160(120) K. All peaks correspond to
B2-KBr, stishovite, or platinum, with one reection from the rhenium
gasket. Black rectangle indicates region enlarged in b. Inset: 2D
diffraction image before integration. Yellow arrow indicates region
enlarged in part b. (b) Splitting of the stishovite 301 peak into the
CaCl2-type 301 and 031 peaks across the phase transition as a function
of temperature. Patterns were collected on cooling at 74 GPa. Yellow
pattern is from a. Patterns are offset vertically for clarity. The stishovite
301 peak splits between 2160(120) and 1870(110) K, bracketing the
phase transition. Insets: Fixed location in the lower left quadrant of the
2D diffraction images from 2160 K (upper) and 1870 K (lower), showing
the splitting of a single 301/031 reection. Image encompasses a 2θ
range of 0.5°. Temperature uncertainties are 110–180 K. (Color online.)
a
b
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2795
CaCl2-type 301 and 031 peaks) typically appear at random azi-
muthal angles; alternatively, in some instances, a single stishovite
301 reflection is observed to split across the phase boundary at
a fixed azimuthal angle (Fig. 2b insets).
X-ray diffraction data were collected from 21–89 GPa and up
to 3300 K (Fig. 3). Pressures determined from the KBr insulator
and Pt absorber agree within mutual 2σ uncertainties in every
instance, with no systematic offset between them (Supplemental1
Table S2). The phase transition from stishovite to the CaCl2-type
structure was observed at pressures of 60–80 GPa and high tem-
peratures with a positive Clapeyron slope (Fig. 3). The transition
between these phases was rapid and easily reversible. The pres-
sures, temperatures, phase identification, and lattice parameters
of all phases in this work are listed in Supplemental1 Table S2.
While the phase transition could be observed on both heating
and cooling, data collected on cooling were favored for use in
equation of state fitting due to their lower deviatoric stresses.
The stress state in the experiments was quasi-hydrostatic due to
the high temperatures at which the data were collected. This can
be seen, for example, by comparing the Pt peak widths in these
experiments to those measured at room temperature in He or Ne
(e.g., Dorfman et al. 2012), with the latter being much broader.
discussion
Phase transition in silica
The location and slope of the phase boundary between
stishovite and CaCl2-type SiO2 has been constrained (Fig. 3); it
can be approximately described as T = 64.6(49)·P – 2830(350),
with temperature in Kelvin and pressure in gigpascals. The
covariance between the two fitted parameters is –1690. The co-
variance between two parameters a and b can be translated into
a correlation coefficient, defined as r = covariance(a,b)/(σa·σb).
The correlation coefficient varies between –1 (perfect negative
correlation) and +1 (perfect positive correlation), with a value
of zero indicating no correlation. The correlation coefficient
between the slope and intercept of our phase boundary is r =
–0.99, indicating a near-perfect anticorrelation between them.
Figure 1 compares the phase boundary from this work to those
reported in the literature. It lies in the same region of P-T space
as those of previous studies, agreeing best with the boundary
of Ono et al. (2002) at pressures of 65–85 GPa and with the
boundaries of Nomura et al. (2010) and Yamazaki et al. (2014)
at pressures below 60 GPa. These data are consistent with
observations of the CaCl2-type phase from Shieh et al. (2005) at
73–75 GPa, and with most of the observations of the stishovite
phase from Wang et al. (2012).
The boundary presented here has a slightly shallower slope
than those of previous studies, with reported values of approxi-
mately 83 K/GPa (Ono et al. 2002), 89 K/GPa (Nomura et al.
2010), 129 K/GPa (Yamazaki et al. 2014), and 180 K/GPa (Akins
and Ahrens 2002). An extrapolation of this phase boundary to
300 K yields a predicted transition pressure of 49 GPa. This
value agrees with some reported transition pressures at 300 K
within uncertainty (Grocholski et al. 2013; Hemley et al. 2000;
Kingma et al. 1995; Nomura et al. 2010; Yamazaki et al. 2014)
(Fig. 1), while other experimental studies report higher transi-
tion pressures (Andrault et al. 1998; Ono et al. 2002; Wang et al.
2012), which could be due to slow kinetics at room temperature,
since kinetics are known to play a role in the SiO2 phase diagram
(e.g., Prakapenka et al. 2004). Some previous high temperature
studies anchored their phase boundary to a measured transition
pressure at 300 K (e.g., Akins and Ahrens 2002; Ono et al. 2002).
These kinetic inhibitions may result in an overestimate of the
transition pressure at 300 K, which may explain the slightly
shallower slope reported here. The difference in slope may also
be related to the very strong anticorrelation between the slope
and intercept of the phase boundary; a higher transition pressure
at 300 K would produce a steeper slope. The data in this study
cross the stishovite–CaCl2-type SiO2 phase boundary at three
different pressures, more high-temperature crossings than in pre-
vious studies (e.g., Akins and Ahrens 2002; Nomura et al. 2010;
Ono et al. 2002; Yamazaki et al. 2014). They also span a much
wider range of pressures and temperatures, to better constrain
this phase boundary while maintaining broad consistency with
previous measurements.
The slope of our observed phase boundary is also significantly
less steep than that calculated by Yang and Wu (2014), who
reported a slope of 200(52) K/GPa (from Gibbs free energies)
or 185(48) K/GPa (from shear instability), and that calculated
by Tsuchiya et al. (2004), who found a slope of 167 K/GPa.
Extrapolating this phase boundary to 0 K gives a transition pres-
sure of 44 GPa, lower than that of most theoretical studies of
SiO2, which yield transition pressures of, for example, 46 GPa
(Yang and Wu 2014), 47 GPa (Karki et al. 1997a), 53 GPa (Togo
et al. 2008), 56 GPa (Tsuchiya et al. 2004), and 64 GPa (Lee and
Gonze 1995). This may be due in part to possible curvature of
the phase boundary at lower temperatures than those investigated
here (Tsuchiya et al. 2004; Yang and Wu 2014).
Thermal equation of state of stishovite
These data were used to construct an equation of state for
stishovite, relating its pressure, molar volume, and temperature.
To ensure that the fitted equation of state would be compatible
with the observed behavior of stishovite at ambient temperature,
these data were first combined with those from several previous
studies obtained at 300 K (Andrault et al. 2003; Grocholski et al.
FiguRe 3. Phase diagram results on silica. Filled orange circles =
observations of the stishovite structure. Open green circles = CaCl2-
type structure. (Color online.)
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2
796
2013; Hemley et al. 2000; Ross et al. 1990; Yamanaka et al. 2002)
(Fig. 4a). The primary criteria for choosing these studies from the
many that exist in the literature is that they were all performed
in a quasi-hydrostatic pressure medium: an alcohol mixture
(Andrault et al. 2003; Ross et al. 1990; Yamanaka et al. 2002),
neon (Grocholski et al. 2013), hydrogen (Hemley et al. 2000),
or argon (Yamanaka et al. 2002), without any laser annealing.
When combining data sets, it is important to give care-
ful consideration to compatibility of the pressure standards.
Hemley et al. (2000), Ross et al. (1990), and Yamanaka et al.
(2002) all used ruby fluorescence to monitor the pressure in
their experiments (Mao et al. 1986). Here their pressures have
been converted to the ruby scale of Dorogokupets and Oganov
(2007), since the KBr pressure scale used in the present experi-
ments was calibrated against the Pt scale of Dorogokupets and
Oganov (2007). Grocholski et al. (2013) used gold as a pressure
standard, and their pressures were recalculated using the gold
equation of state of Dorogokupets and Oganov (2007). Andrault
et al. (2003) used quartz as a pressure standard; their data were
not corrected, but they were all obtained from pressures below
10 GPa, where most pressure scales are compatible.
A Mie-Grüneisen equation of state was fit to the combined
data set, in which the total pressure is described as the sum of
an isothermal pressure, a harmonic thermal pressure (PTH) term,
and a quasi-anharmonic pressure (PAN) term:
P(V,T) = P(V, 300 K) + [PTH(V,T) – PTH(V, 300 K)] +
[PAN(V,T) – PAN(V, 300 K)]. (1)
The isothermal pressure term P(V, 300 K) is given by the
third-order Birch-Murnaghan equation of state (Birch 1952):
P
V,300 K
( )
=3K0f1+2f
( )
5
21+3
2K0
'4
( )
f
(2)
where K0 is the isothermal bulk modulus, K0
ʹ is its pressure
derivative at constant temperature, f = 0.5·[(V/V0)–2/3 – 1] is the
Eulerian strain, and the subscript 0 indicates values at 1 bar. The
harmonic thermal pressure term in Equation 1 can be derived
from a Debye-type thermal energy (e.g., Dewaele et al. 2006):
P
TH V,T
( )
=9nRγ
V
θD
8+TT
θD
3
0
θD/T
z3dz
ez1
(3)
where n is the number of atoms per formula unit, R is the ideal
gas constant, g = g0(V/V0)q is the Grüneisen parameter, q is a
constant describing the volume dependence of g, and θD = θ0
exp{[1 – (V/V0)q]g0/q} is the Debye temperature. The quasi-
anharmonic pressure term is fit as:
P
AN V,T
( )
=γ
VcT2(4)
where c is a fitted constant. The T2 dependence is derived from
the lowest-order term of the high-temperature expansion of the
anharmonic free energy (Oganov and Dorogokupets 2004).
Since stishovite can be recovered as a metastable phase to
ambient conditions, its properties at 1 bar are well characterized.
Here a measured volume of 14.02 cm3/mol was used (Wang et al.
2012); this value is in agreement with those of most recent experi-
mental studies (e.g., Table 1). Recent Brillouin spectroscopy and
ultrasonic interferometry measurements of stishovite constrain its
adiabatic bulk modulus at 1 bar to be 301–316 GPa (Brazhkin et al.
2005; Jiang et al. 2009; Li et al. 1996; Yoneda et al. 2012) (Table
1). Here the value of 305 GPa was used for the adiabatic K0 from
Li et al. (1996). The adiabatic (KS) to isothermal (KT) conversion
is given by KS = KT(1 + αgT), where α is the thermal expansion
coefficient. Using T = 300 K, α = 1.647 × 10–5/K from Nishihara
et al. (2005), and the calculated g0 (see below), an isothermal K0
of 302 GPa was calculated. The heat capacity (CP) of stishovite at
1 bar was measured by Akaogi et al. (2011), and the correspond-
ing Debye temperature (θ0) was calculated to be 1109 K (Akaogi
et al. 2011). Using these values for CP, V0, KS, and α at 1 bar, the
Grüneisen parameter can be calculated as:
FiguRe 4. Pressure-volume-temperature data and equation of state
ts (Tables 1–2) for stishovite and CaCl2-type SiO2 (a), and residuals to
these ts (b). Curves in a are isotherms calculated for the midpoint of the
indicated temperature ranges. Solid curves and lled symbols: stishovite.
Dashed curves and open symbols = CaCl2-type SiO2. Curves in a are
truncated at the edge of the stability elds of the phases (Grocholski et
al. 2013; Shen and Lazor 1995; Zhang et al. 1996) (Fig. 3), but some
metastable data are shown. Circles = this study. Diamonds = Hemley et
al. (2000). Squares = Grocholski et al. (2013). Upward-pointing triangles
= Ross et al. (1990). Right-pointing triangles = Andrault et al. (2003).
Left-pointing triangles = Yamanaka et al. (2002). Horizontal and vertical
error bars in b are both uncertainties in measured pressure. Data have
been corrected to a common pressure scale. (Color online.)
b
a
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2797
γ0=α*KS*V
CP
=1.7
1
. (5)
Using this value for g0 along with the measured V0 and K0T, an
unweighted nonlinear least-squares minimization was used to fit
Equations 1–4 to the combined stishovite data set. Since fitting q
always resulted in a value of 1, a common approximation, q was
fixed at 1 to determine K0
ʹ and c.
The resulting parameters are shown in Table 1, and isotherms
calculated from this fit are compared to the data in Figure 4a.
Figure 4b shows the residuals to this fit, which range from –4.2
to +4.9 GPa. The root mean squared (rms) misfit in pressure is
1.8 GPa when considering only the data from this study, compa-
rable to the 2σ uncertainty on the pressure measurements; the rms
misfit is 1.6 GPa when considering all of the data in the fit. The
covariance between K0
ʹ and c is –0.0027 × 10–8, corresponding to
a correlation coefficient of r = –0.74, which reflects a significant
anti-correlation between these two parameters in this fit. This equa-
tion of state is fit to data spanning up to 75 GPa and 300–3300 K, a
significant advance over previous equations of state of stishovite,
which reached a maximum pressure of 54 GPa (Wang et al. 2012)
and maximum temperature of 2400 K (Pigott et al. 2015).
Table 1 compares our equation of state parameters to those of
various previous studies on stishovite. Supplemental1 Table S1
includes equation of state parameters from a more exhaustive list of
prior studies, reaching back as far as the 1960s. The fitted value of
K0
ʹ = 5.24(9) agrees with various previous studies within mutual 2σ
uncertainties, including those based on ultrasonic interferometry
at high pressures (Li et al. 1996), X-ray diffraction under static
compression (Panero et al. 2003), dynamic compression (Luo et
al. 2002a; Lyzenga et al. 1983), and theoretical calculations (Luo
et al. 2002b). This result for K0
ʹ is broadly consistent with other
recent studies (e.g., Table 1) reporting that stishovite has a K0
ʹ
greater than the canonical value of 4 (Birch 1952). It falls above
the values obtained in some recent studies (e.g., Table 1), which
may be understood as a tradeoff between K0 and K0
ʹ (Supplemental1
Fig. S1a). K0 and K0
ʹ are inversely correlated in literature studies
of stishovite, and this fit agrees with the trend defined by previous
studies (Supplemental1 Fig. S1a). Prior studies have not resolved
an anharmonic pressure term for stishovite, so comparisons to
previous fits cannot be made.
Thermal equation of state of CaCl2-type silica
Equations 1–4 have been similarly fit to the P-V-T data on
CaCl2-type silica to construct a thermal equation of state for this
phase. As for stishovite, the data on the CaCl2-type phase were
combined with data obtained in previous studies at 300 K to ensure
that the fit correctly captures the properties of this phase at ambient
temperature. The data of Hemley et al. (2000) and Grocholski et
al. (2013) were used and corrected to a common pressure scale.
The CaCl2-type phase of SiO2 cannot be recovered to 1 bar,
which makes fitting its thermal equation of state more challenging.
To reduce the number of fitting parameters, which was necessary
given the resolution of the data, the same V0, θ0, q, and c as for
stishovite were used. The volumes predicted by the CaCl2-type
equation of state were also forced to match those of the stishovite
equation of state at the phase boundary, since this transition is sec-
ond-order with no accompanying volume change (e.g., Andrault
et al. 2003). Again, a nonlinear least-squares minimization routine
was used to determine K0, K0
ʹ, and g0. The resulting parameters are
listed in Table 2, and isotherms calculated from the fit are com-
pared to the data in Figure 4a. The residuals to this fit are shown
in Figure 4b, which span from –2.6 to +3.1 GPa. The rms misfit
in pressure is 1.5 GPa, or 1.4 GPa for the data in this study alone,
comparable to the 2σ uncertainty on the pressure measurements.
Table 1. Equation of state parameters for stishovite, from this study and a selection of previous studies
Study V0 (cm3/mol) K0 (GPa) K0
g0 q θT c (GPa·cm3/mol/K2) Method
This study 14.017 302 5.24(9) 1.71 1 1109 –6.0(4) × 10–6 XRD
Andrault et al. (2003) 14.0053(18)a 309.9(11) 4.59(23) XRD
Liu et al. (1999) 14.0135(6)a 294(2) 5.3 XRD
Nishihara et al. (2005) 14.020(3)a 296(5) 4.2(2) 1.33(6) 6.1(8) 1160(120) XRD
Pigott et al. (2015) 13.97 312.9 4.8 1.55 2.9 1109 XRD
Wang et al. (2012) 14.017 294(2) 4.85(12) 1.66(7) 2.9(4) 1130(100) XRD
Yamanaka et al. (2002) 14.03a 292(13) 6 XRD
Panero et al. (2003) 13.97a 312.9(34) 4.8(2) 1.35 1 shock/XRDb,c
Luo et al. (2002a) 13.94 306(5) 5.0(2) 1.35 2.6(2) shockc
Lyzenga et al. (1983) 14.01 306 5.4d 1.38 3.2 shockc
Li et al. (1996) 14.06a 305(5)e 5.3(1)f ultrasonics
Yoneda et al. (2012) 298–317e,g ultrasonics
Brazhkin et al. (2005) 316(4)e Brillouin
Jiang et al. (2009) 301(1)–315(1)e,g 3.73(10)–4.34(16)f,g Brillouin
Weidner et al. (1982) 14.01a 308–324e,g Brillouin
Cohen (1991) 13.90 324 4.04 calculatedh
Driver et al. (2010) 14.19(4) 305(20) 3.7(6) 1.22(1) 2.22(1) calculated
Karki et al. (1997a) 13.83 313 4.24 calculatedh
Luo et al. (2002b) 14.03 296.4(37) 4.9(1) calculated
Tsuchiya et al. (2004) 289–321 4.1–4.2 calculatedh
Notes: Equation of state parameters are as defined in the text for 1 bar and 300 K, and all bulk moduli are isothermal, unless otherwise noted. Entries in italics were
held fixed in the fits. Stated uncertainties for this study do not incorporate covariance between terms. For more stishovite equations of state from the literature,
see Supplemental1 Table S1.
a Measured volume.
b High-temperature data are from literature.
c Shock wave data may span multiple phases.
d (∂KT/∂P)0S.
e K0S.
f (∂KS/∂P)0T.
g Reuss-Voigt bounds.
g Results are from 0 K.
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2
798
This is the first thermal equation of state of this phase determined
in a diamond-anvil cell; previously, its only thermal equation of
state was based on a meta-analysis of shock wave data (Akins and
Ahrens 2002). Here the quantity of equation of state data for this
phase were markedly increased, improving our understanding of
its physical properties and its role in the Earth’s interior.
Table 2 lists equation of state parameters for the CaCl2-type
phase from several previous studies. In comparison to other experi-
mental studies (Andrault et al. 1998, 2003; Grocholski et al. 2013),
a higher K0 [341(4) GPa] and lower K0
ʹ [3.20(16)] are reported
here, though this is the first study to report an experimentally de-
termined K0
ʹ for this phase. This variability in measured parameters
can be understood in terms of the strong tradeoff between K0 and
K0
ʹ (Supplemental1 Fig. S1b). If K0
ʹ is fixed at 4 as in Andrault et
al. (2003) and Grocholski et al. (2013), then K0 = 321.8(11) GPa,
in much better agreement with these studies. This fit (Table 2)
indicates a correlation coefficient between K0 and K0
ʹ of r = –0.97
(Supplemental1 Table S3), indicating that these parameters are
almost perfectly inversely correlated. The Grüneisen parameter
also exhibits moderate tradeoffs with the other fitted parameters,
with an r = 0.45 with K0 and r = –0.63 with K0
ʹ. The fitted value of
g0 = 2.14(4) is higher than that of Akins and Ahrens (2002) (1.4),
who do not report an uncertainty on their fit but cover less of P-T
space. In comparison to theoretical studies, this value for K0 is
significantly higher than that of Oganov et al. (2005) at 1 bar; at
50 GPa, the new equation of state yields KT = 490 GPa, not far
from the calculated values of Karki et al. (1997b) (509 GPa) and
Yang and Wu (2014) (501–504 GPa) at this pressure.
Stishovite and the CaCl2-type phase of silica have similar
behavior under high pressures and temperatures, but with several
differences in their properties that are resolved here. The CaCl2-
type structure has a higher K0 than stishovite does (Tables 1–2),
with a much lower value of K0
ʹ. This results in the CaCl2-type being
more compressible at the phase boundary, and is reflected in the
different curvatures of their isotherms (Fig. 4a). At 49 GPa and
300 K, the isothermal bulk modulus of CaCl2-type SiO2 (487 GPa)
is lower than that of stishovite (541 GPa). The g0 found for the
CaCl2-type phase is higher than that of stishovite for the same value
of q, indicating that the CaCl2-type has greater thermal expansivity.
Stishovite lattice parameter fits
The compressibility and thermal expansion of each axis of a
tetragonal phase can be described independently using a pseudo-
equation of state, replacing V with a3 or c3. Here a high-temperature
third-order Birch-Murnaghan equation of state was used, to bet-
ter facilitate comparisons with results of previous studies (e.g.,
Nishihara et al. 2005; Pigott et al. 2015). The high-temperature
Birch-Murnaghan equation of state is identical to the regular
Birch-Murnaghan equation of state (Eq. 2), except that the bulk
modulus is replaced by:
K0T
( )
=K0300 K
( )
+T300 K
( )
K
T
(6)
and the 1 bar volume is replaced by
V0T
()
=V0300K
()
*exp
300K
T
αdT
(7)
where α is the thermal expansion coefficient, approximated here
as a constant (e.g., Angel 2000).
The 1 bar lattice parameters a0 = 4.178 Å and c0 = 2.668 Å
were used for stishovite, as measured by Nishihara et al. (2005).
Again the present data were pooled with those of several 300 K
compression studies (Andrault et al. 2003; Grocholski et al. 2013;
Hemley et al. 2000; Ross et al. 1990; Yamanaka et al. 2002), cor-
rected to a common pressure scale. For the a axis of stishovite,
K0a, Kʹ
0a, αa, and K0a/T were fit (Table 3). A linear temperature
dependence of α was found to be statistically insignificant. The a
axis of stishovite is much more compressible than the bulk crystal
[K0a = 269(4) GPa compared to K0 = 302 GPa], with a lower K0
ʹ
[Kʹ
0a = 4.55(19) compared to K0
ʹ = 5.24(9)]. Figure 5 (upper panel)
shows the raw data from this study and the previous studies used
in the fit (Andrault et al. 2003; Grocholski et al. 2013; Hemley
et al. 2000; Ross et al. 1990; Yamanaka et al. 2002), compared to
calculated isotherms. The pressure residuals span a range of –3.6
to +2.9 GPa (Supplemental1 Fig. S2), with an rms misfit of 1.0
GPa. All of the parameters covary strongly with each other (|r|
> 0.6), with the strongest correlations between K0a and Kʹ
0a and
between αa and K0a/T (both r = –0.95) (Supplemental1 Table S4).
Table 3 also compares the lattice parameter fit for the stishovite
a axis to results from previous studies, obtained using X-ray
diffraction, Brillouin spectroscopy, and theoretical calculations.
There is a remarkable degree of consensus on the compressibility
of the a axis, with K0a in the studies listed in Table 3 spanning the
range 240(5)–284(5) GPa; the value found in this study, 269(4)
GPa, falls in the middle of this range. The value of K0a/T =
–0.020(2) GPa/K agrees well with that reported by Nishihara et
al. (2005) [–0.023(4) GPa/K], and the value of αa = 2.11(12) ×
10–5 K–1 matches those of Nishihara et al. (2005) [2.06(14) × 10–5
K–1] and Wang et al. (2012) [2.46(19) × 10–5 K–1] within mutual
2σ uncertainties, and is compatible with the thermal expansion
expression of Pigott et al. (2015) at high temperatures.
Table 2. Equation of state parameters for the CaCl2-type phase of silica, from this study and previous studies
Study V0 (cm3/mol) K0 (GPa) K0
g0 q θT c (GPa·cm3/mol/K2) Method
This study 14.017 341(4)a 3.20(16)a 2.14(4)a 1 1109 –6.0 × 10–6 XRD
Andrault et al. (1998) 14.112(2) 282(1) 4.29 XRD
Andrault et al. (2003) 13.94(5) 334(7) 4 XRD
Grocholski et al. (2013) 14.044(9) 317(3) 4 XRD
Akins and Ahrens (2002) 14.00 291 4.3 1.4 1 shockb
Karki et al. (1997b) 509 calculatedc
Oganov et al. (2005) 13.72 258.354 4.6135 calculatedd
Yang and Wu (2014) 501–504 calculatede
Notes: Equation of state parameters are as defined in the text for 1 bar and 300 K, and all bulk moduli are isothermal. Entries in italics were held fixed in the fits.
Stated uncertainties for this study do not incorporate covariance between terms; the variance-covariance matrix for this fit is shown in Supplemental1 Table S3.
a Variance-covariance matrix for this fit is shown in Supplemental1 Table S3.
b Meta-analysis of literature data. c At 50 GPa and 0 K. d At 0 K. e At 50 GPa, Voigt-Reuss bounds.
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2799
The data from this study and literature data (Grocholski et
al. 2013; Hemley et al. 2000) on the c axis of stishovite exhibit
a much higher degree of scatter than those on the a axis (Fig. 5,
lower panel), as observed in previous studies (e.g., Nishihara et
al. 2005). Therefore, in the lattice parameter fit for the stishovite
c axis, Kʹ
0c and K0c/T were held fixed to the values found for
the a axis (Table 3), and K0c and αc were fit (Table 3). Isotherms
calculated from the fit are compared to the data in Figure 5 (lower
panel). The pressure residuals range from –10.1 to +13.6 GPa
(Supplemental1 Fig. S3), and the fit has an rms misfit in pressure
of 4.5 GPa. K0c and αc have a correlation coefficient r = –0.93.
Previous experimental studies on the c axis of stishovite have
reported K0c values spanning 411–556 GPa. The value of 435(9)
GPa reported here falls within this range, agreeing within mutual
2σ uncertainties with values reported previously using X-ray
diffraction (Liu et al. 1999; Nishihara et al. 2005; Pigott et al.
2015), which tend to be lower than values reported using Bril-
louin spectroscopy (Jiang et al. 2009; Weidner et al. 1982) and
computational results (Cohen 1991). The value of αc = 1.70(11)
× 10–5 K–1 falls intermediate between those reported previously by
Nishihara et al. (2005) and Wang et al. (2012), agreeing with both
of these values within mutual 2σ uncertainties, and also agrees
well with the expression of Pigott et al. (2015) for thermal expan-
sion at high temperatures. The c axis of stishovite exhibits a lower
thermal expansion than the a axis by 19%, as reported previously
(Table 3). It is more incompressible than the bulk crystal [K0c =
435(9) GPa], and significantly (62%) more incompressible than
the a axis, an effect that has also been reported previously (Table
3). The higher compressibility of the a axis has been attributed to a
greater degree of flexibility in the corner-sharing linkages of SiO6
octahedra along the a axis, as opposed to the stiffer edge-sharing
linkages along the c axis (Nishihara et al. 2005).
The axial c/a ratio of stishovite can be calculated from our lat-
tice parameter fits (Supplemental1 Fig. S4). The c/a ratio of stisho-
vite increases approximately linearly with decreasing volume, by
0.0057 per cm3/mol. The temperature effect on the c/a ratio is
not apparent from the data given the measurement uncertainties,
which are large relative to the observed variations in c/a (variation
of only 1.5% over the range of conditions in this study).
To evaluate internal consistency, volumes calculated from the
equation of state of stishovite were compared to volumes calcu-
lated as V = a2c from the lattice parameter fits for the a and c axes.
Supplemental1 Figure S5 shows the misfit between these volumes
as a function of volume for temperatures of 300–3500 K over the
entire pressure range of stishovite stability (Shen and Lazor 1995;
Zhang et al. 1996) (Fig. 3). It reaches a maximum of 0.5% misfit
in volume at 2500 K and low pressures, but is less than 0.1% over
most of the range of conditions investigated (less than uncertainties
on most measured volumes). The fits of the a and c axes slightly
overestimate the volume at lower volumes (up to 13.5 cm3/mol)
and underestimate the volume at higher volumes.
Just beyond the transition pressure, the a axis of the CaCl2-type
phase expands and the b axis shrinks (Supplemental1 Fig. S6) (e.g.,
Andrault et al. 2003; Hemley et al. 2000); this behavior precludes
a simple fit for the CaCl2-type lattice parameters as was done here
for stishovite. A much smaller splitting between the a and b axes
was observed here than in previous studies at 300 K (Grocholski
et al. 2013; Hemley et al. 2000). This difference does not appear
to be a thermal effect, since both axes expand with increasing tem-
perature, such that the difference between them is approximately
independent of temperature. It may be due to the more hydrostatic
conditions of this study caused by the high temperatures at which
the data were collected. The data from this study on the c axis of
the CaCl2-type phase are compatible with those of previous studies
at 300 K (Grocholski et al. 2013; Hemley et al. 2000), and shows a
FiguRe 5. Pressure-lattice parameter-temperature data and ts
(Table 3) for the a axis (upper panel) and c axis (lower panel) of stishovite.
Curves are isotherms calculated for the midpoint of the indicated
temperature ranges, and are truncated at the edge of the stability eld of
stishovite (Shen and Lazor 1995; Zhang et al. 1996) (Fig. 3), but some
metastable data are shown. Symbols are as in Figure 4. Data have been
corrected to a common pressure scale. Residuals to these ts are shown
in Supplemental1 Figures S2–S3. (Color online.)
Table 3. Lattice parameter fits for the a and c axes of stishovite, from this study and a selection of previous studies
Study K0a (GPa) K
0aK0a/∂T (GPa/K) αa (K–1) K0c (GPa) K
0cK0c/∂T (GPa/K) αc (K–1) Method
This study 269(4) 4.55(19) –0.020(2) 2.11(12) × 10–5 435(9) 4.55 –0.020 1.70(11) × 10–5 XRD
Andrault et al. (2003) 250.9(16) 5.48(32) XRD
Liu et al. (1999) 269(9) 513(32) XRD
Nishihara et al. (2005) 240(5) 6.2(5) –0.023(4) 2.06(14) × 10–5 411(9) 4 –0.036(21) 1.22(24) × 10–5 XRD
Pigott et al. (2015) 284(5) 4 –0.050(3) 450(20) 4 –0.091(7) XRD
Wang et al. (2012) 2.46(19) × 10–5 1.87(20) × 10–5 XRD
Jiang et al. (2009) 256 521 Brillouin
Weidner et al. (1982) 253 556 Brillouin
Cohen (1991) 262 615 calculated
Notes: Entries in italics were held fixed in the fits. Stated uncertainties for this study do not incorporate covariance between terms; the variance-covariance matrix
for the a axis fit is shown in Supplemental1 Table S4.
FISCHER ET AL.: EQUATIONS OF STATE AND PHASE BOUNDARY FOR SIO2
800
higher compressibility than the c axis of stishovite at these condi-
tions (Supplemental1 Fig. S6).
SiO2 in the deep Earth
It has been demonstrated experimentally that free silica is one
of the phases that forms when mid-ocean ridge basalt (MORB)
compositions are subjected to the pressures and temperatures of
Earth’s lower mantle, which may occur in subducting slabs. For
example, at 40–60 GPa and 2100 K, a MORB composition has
been shown to contain 15–19 wt% stishovite (Hirose et al. 2005;
Perrillat et al. 2006; Ricolleau et al. 2010). Subducted continental
crust likely contains an even higher proportion of free silica (e.g.,
Irifune et al. 1994; Ishii et al. 2012). Due to its abundance in these
geological settings, it is important to consider the density of SiO2
at lower mantle conditions.
Figure 6 shows the density of SiO2 at the P-T conditions of the
Earth’s transition zone and lower mantle. Along a mantle geotherm
(Brown and Shankland 1981), the phase transition from stishovite
to CaCl2-type SiO2 occurs at a pressure of 78 GPa, or a depth of
1840 km. Two possible slab temperature profiles were also con-
sidered, a “hot slab” that is 200 K cooler than the mantle geotherm
and a “cold slab” that is 600 K cooler (e.g., Syracuse et al. 2010).
These lower temperatures increase the density of SiO2, and push
the phase transition to lower pressures (75 GPa in a hot slab and
68 GPa in a cold slab). The minimum temperature inside the slab
can be 100–500 K cooler than the slab surface (e.g., Syracuse et
al. 2010); any silica present in the interior of a slab could there-
fore have a slightly higher density and lower transition pressure
than considered here. Figure 6 also shows the density profile of
the Earth from the Preliminary Reference Earth Model (PREM,
Dziewonski and Anderson 1981). Along a mantle geotherm, silica
is denser than the surrounding mantle to a pressure of 58 GPa, or
a depth of 1420 km, and is less dense than the mantle at greater
depths. In a cold slab, silica is denser than the mantle up to 68
GPa or 1640 km. At greater depths in the Earth (124–128 GPa or
2690–2770 km, depending on temperature), the CaCl2-type silica
will transform to seifertite (Grocholski et al. 2013).
implications
A thermal equation of state has been constructed for stishovite
that extends to significantly higher pressures and temperatures than
previous studies (e.g., Pigott et al. 2015; Wang et al. 2012), and
the first thermal equation of state of CaCl2-type silica measured
in a laser-heated diamond-anvil cell is reported (Fig. 4), greatly
improving the pressure and temperature coverage for this phase.
This P-T coverage makes these equations of state more accurate
and less prone to errors in extrapolation when applying them to
understanding the deep Earth.
Free silica is unlikely to be present in a pyrolitic lower mantle,
but may occur in a subducting slab (e.g., Hirose et al. 2005). Based
on measurements of the phase boundary between stishovite and
CaCl2-type SiO2 (Fig. 3), this phase transition should occur at pres-
sures of 68–78 GPa in the Earth’s lower mantle, with uncertainty
due to temperature. Because this transition is second order with no
discontinuity in density, it is unlikely that it would be observable
as a seismological reflection, though it may be detectable based
on seismic velocities and anisotropy (e.g., Yang and Wu 2014).
However, it is important to know the depth of this transition in
modeling the density of silica in the Earth, because these two
phases have different compressibilities and thermal properties
(Tables 1–2). Silica is denser than the surrounding mantle up to
pressures of 58–68 GPa, or depths of 1420–1640 km, depending
on temperature. At shallower depths, silica can contribute to the
gravitational force pulling on a sinking slab. At greater depths,
silica is less dense than the mantle, providing a source of buoy-
ancy to resist the downward motion of the slab. Recently it has
been suggested that SiO2 may exsolve from the core as it cools
(Hirose et al. 2017). Silica entering the lower mantle this way
will tend to ascend buoyantly until it is consumed by the SiO2-
undersaturated mantle.
acknowledgments
We are grateful to the editor for handling our manuscript and to two anonymous
reviewers for their constructive feedback. We thank Dion Heinz, Jacob Britz, and
beamline scientist Clemens Prescher for assistance with running experiments. This work
was supported by a National Science Foundation (NSF) Graduate Research Fellowship,
Illinois Space Grant Consortium Graduate Research Fellowship, International Centre
for Diffraction Data Ludo Frevel Crystallography Scholarship, University of Chicago
Plotnick Fellowship, and NSF Postdoctoral Fellowship (EAR-1452626) to R.A.F.
and NSF grant EAR-1427123 to A.J.C. J.S.P. was supported by the OSU Presidential
Fellowship and NSF grant EAR-0955647 awarded to Wendy R. Panero and thanks
CDAC for the HPCAT beamtime award. J.S.S. acknowledges the support of DOE-BES/
DMSE under Award DE-FG02-99ER45775. Portions of this work were performed at
GeoSoilEnviroCARS (Sector 13), Advanced Photon Source (APS), Argonne National
Laboratory (ANL). GeoSoilEnviroCARS is supported by the NSF–Earth Sciences (EAR-
1634415) and the Department of Energy (DOE), Geosciences (DE-FG02-94ER14466).
Portions of this work were performed at HPCAT (Sector 16), APS, ANL. HPCAT
operation is supported by DOE-NNSA under Award No. DE-NA0001974, with partial
instrumentation funding by NSF. This research used resources of the APS, a U.S. DOE
Office of Science User Facility operated for the DOE Office of Science by ANL under
Contract No. DE-AC02-06CH11357.
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Manuscript received august 3, 2017
Manuscript accepted February 8, 2018
Manuscript handled by haozhe liu
Endnote:
1Deposit item AM-18-56267, Supplemental Tables and Figures. Deposit items are
free to all readers and found on the MSA web site, via the specific issue’s Table of
Contents (go to http://www.minsocam.org/MSA/AmMin/TOC/2018/May2018_data/
May2018_data.html).
... Unit cell parameters of SiO 2 phases are summarized in Supplementary Table 2. We compared measured cell volumes in the system SiO 2 -H 2 O to the calculated cell volumes of anhydrous silica phases at each pressure and temperature using appropriate thermal equations of state (EoS) (Andrault et al., 2003;Fischer et al., 2018;Grocholski et al., 2013;Sun et al., 2019) to calculate the percent relative change in unit cell volume: ...
... Having established that the starting mixture with 15.2 wt.% H 2 O has far more H 2 O than required to saturate SiO 2 , we now (Fischer et al., 2018;Grocholski et al., 2013;Murakami et al., 2003;Nomura et al., 2010). We observe little difference in the stishovite to β-stishovite transition between the hydrous and anhydrous systems, whereas the β-stishovite to seifertite phase boundary is found to be ∼20 GPa higher in pressure in the hydrous system. ...
... The stishovite to β-stishovite transition results in a small but abrupt decrease in c/a axial ratio as tetragonal stishovite distorts to orthorhombic β-stishovite, whereas the transition to the seifertite structure results in a large increase (Fig. 3b). The transition boundary between stishovite and β-stishovite in our experiments is not significantly shifted from the dry silica system (e.g., ∼74 GPa and ∼1900 K) (Fischer et al., 2018), consistent with our observation that stishovite and β-stishovite have approximately the same H 2 O content at the transition. We estimate the transition to seifertite at a pressure of ∼145 GPa, about 20 GPa higher than in the dry system (Sun et al., 2019), suggesting a larger H 2 O capacity in β-stishovite than in seifertite, although we do not have a tight constraint on the phase boundary. ...
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Subduction of oceanic lithosphere transports surface H2O into the mantle. Recent studies show that dense SiO2 in the form of stishovite, an abundant mineral in subducted oceanic crust at depths greater than ∼270 km, has the potential to host and transport a considerable amount of H2O into the lower mantle, but the H2O storage capacity of SiO2 phases at high pressure and temperature remains uncertain. We investigate the hydration of stishovite and its higher-pressure polymorphs, β-stishovite and seifertite, with in situ X-ray diffraction experiments at high pressures and temperatures. The H2O contents in SiO2 phases are quantified based on observed increases in unit cell volume relative to the anhydrous SiO2 system. Density functional theory (DFT) computations permit calibration of water content as a function of volume change based on interstitial substitution of H2O. Regression of our experimental data indicates an H2O storage capacity in stishovite of ∼3.5 wt% in the transition zone and shallow lower mantle, decreasing to about 0.8 wt% at the base of the mantle. We find that SiO2-bearing subducted oceanic crust can accommodate all the H2O in slab lithosphere that survives sub-arc dehydration. Hydration of silica phases in subducted oceanic crust and their unparalleled capacity to host significant amounts of H2O even at high mantle temperatures provides a unique mechanism for transport and storage of water in the deepest mantle.
... However, their occurrence could contribute to seismic observations of enhanced densities in some regions (Hirose et al., 2005;Niu, 2014;Niu et al., 2003;Sun et al., 2016). On the other hand, the rutile-type stishovite displays much higher sound velocities than typical mantle minerals (Yang & Wu, 2014;Zhang et al., 2021), although its density is similar to that of mineral aggregates in a pyrolite composition (Fischer et al., 2018;Irifune et al., 2010). Stishovite undergoes a pseudoproper ferroelastic transition to a CaCl 2 -type post-stishovite phase with a spontaneous strain Hemley et al., 2000). ...
... It has been theoretically shown that subducted MORB with 20 vol% stishovite undergoing the post-stishovite transition could produce a V S reduction of up to ∼6.5% and a V P reduction of up to ∼1.5% at the mid-lower-mantle depth that can help explain seismic wave velocities (Wang et al., 2020). However, the post-stishovite transition has a positive Clapeyron slope of 65 K/GPa and would occur at ∼1,800 km depth at relevant P-T conditions of a cold subducting slab (77 GPa and 1706 K; Fischer et al., 2018). The transition depth is thus too deep to be consistent with these aforementioned regional seismic V S anomalies at shallower lower mantle depths. ...
... Modeling the * as a function of Al contents using a polynomial function results in Al = 0.0014 * 2 − 0.154 * + 4.235 where Al is expressed in mol% and * is in GPa (Figure 5a). Using a Clapeyron slope of 65 K/GPa from a recent experimental study (Fischer et al., 2018), the post-stishovite transition can be extrapolated to high P-T conditions of the lower mantle: the transition pressure could be lowered by approximately 30 GPa in stishovite with 1 mol% Al and by 52 GPa with 3 mol% Al. Along a cold subducting slab which is taken as approximately 500 K colder than a typical normal mantle (Katsura et al., 2010;Tan et al., 2002), the post-stishovite transition is expected to occur at 740 km depth with 3 mol% Al and at 1,250 km depth with 1 mol% Al (Figure 5b). ...
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Seismic studies have found seismic scatterers with −2 to −12% shear velocity anomalies along some subducting slabs at 700–1900 km depth. The ferroelastic post‐stishovite transition in subducted mid‐ocean ridge basalt (MORB) has been linked to these seismic features, but compressional and shear wave velocities (VP and VS) and full elastic moduli (Cij) of Al,H‐bearing stishovite and post‐stishovite at high pressure remain uncertain. Here we have determined Raman shifts of optic modes and equation of state parameters of two hydrated Al‐bearing stishovite crystals, Al1.3‐SiO2 (1.34 mol% Al and 0.55 mol% H) and Al2.1‐SiO2 (2.10 mol% Al and 0.59 mol% H), up to ∼70 GPa in diamond anvil cells coupled with Raman spectroscopy and X‐ray diffraction. The experimental data are modeled using a pseudoproper Landau theory to derive full Cij and sound velocities across the post‐stishovite transition at high pressure. The Al and H dissolution in stishovite significantly reduces the transition pressure to 21.1 GPa in Al1.3‐SiO2 and to 16.1 GPa in Al2.1‐SiO2, where the transition is manifested by approximately 29% VS reduction. Considering that stishovite with approximately 1.3 mol% Al and 0.6 mol% H could account for 20 vol% in subducted MORB at the top‐lower mantle, the Al,H‐bearing post‐stishovite transition with a Clapeyron slope of 65 K/GPa would occur at about 1060 km depth with −7(4)% VS anomaly. The VS anomalies across the Al,H‐bearing post‐stishovite transition can help explain the seismically‐observed depth‐dependent VS anomalies along some subducting slabs in the top‐ to mid‐lower‐mantle depths including the Tonga subducting slab.
... If the effect of the AlOOH component on the transition pressure of stishovite is assumed to be linear, we can use the transition pressure of SiO 2 and our data (SI Appendix, Fig. S6) to determine a reduction of ∼8.5 GPa/mol % AlOOH at room temperature. At high temperature, the transition pressure of stishovite increases due to its positive Clapeyron slope, which was proposed to be 65 to 88 K/GPa in pure SiO 2 based on in situ X-ray diffraction measurements (49,50). Using an average value of 76 K/GPa, we would expect silica with 5, 6, and 7 mol % AlOOH component to undergo a transformation to poststishovite at about 25 GPa and 1,200, 1,800, and 2,400 K, respectively (SI Appendix, Fig. S9). ...
Article
Water transported by subducted oceanic plates changes mineral and rock properties at high pressures and temperatures, affecting the dynamics and evolution of the Earth’s interior. Although geochemical observations imply that water should be stored in the lower mantle, the limited amounts of water incorporation in pyrolitic lower-mantle minerals suggest that water in the lower mantle may be stored in the basaltic fragments of subducted slabs. Here, we performed multianvil experiments to investigate the stability and water solubility of aluminous stishovite and CaCl 2 -structured silica, referred to as poststishovite, in the SiO 2 -Al 2 O 3 -H 2 O systems at 24 to 28 GPa and 1,000 to 2,000 °C, representing the pressure–temperature conditions of cold subducting slabs to hot upwelling plumes in the top lower mantle. The results indicate that both alumina and water contents in these silica minerals increase with increasing temperature under hydrous conditions due to the strong Al ³⁺ -H ⁺ charge coupling substitution, resulting in the storage of water up to 1.1 wt %. The increase of water solubility in these hydrous aluminous silica phases at high temperatures is opposite of that of other nominally anhydrous minerals and of the stability of the hydrous minerals. This feature prevents the releasing of water from the subducting slabs and enhances the transport water into the deep lower mantle, allowing significant amounts of water storage in the high-temperature lower mantle and circulating water between the upper mantle and the lower mantle through subduction and plume upwelling. The shallower depths of midmantle seismic scatterers than expected from the pure SiO 2 stishovite–poststishovite transition pressure support this scenario.
... subducting slabs, stishovite SiO 2 undergoes reversible phase transition to the CaCl 2 -type structure (Pnnm space group) with an orthorhombic symmetry [73,74]. The CaCl 2 -type structure consists of octahedra connected by vertices and edges, with network being similar to the known post-spinel CF-type and CT-type structures. ...
Article
Synchrotron-based high-pressure single-crystal X-ray diffraction experiments were conducted on a new CaFe1.2Al0.8O4 phase at ambient temperature and up to a maximum pressure of 61 GPa. Crystals of CaFe1.2Al0.8O4 were synthesized at 24 GPa and 1500 °C. This phase has orthorhombic unit cell parameters (a = 8.9785(1) Å, b = 2.9158(1) Å, c = 10.4253(6) Å, V = 286(3) ų, Z = 8), crystallizes with a space group Pnma, and exhibits K0,T of 195(2) GPa. At pressures ∼50 GPa, unit cell volume of CaFe1.2Al0.8O4 drops by about 7% over a small pressure interval. By combining results from synchrotron-based high-pressure single-crystal X-ray diffraction and electronic structure calculations, it is shown that these changes in the compression behaviour are associated with changes of the electronic state of iron in the octahedral site. Thus, CaFe1.2Al0.8O4 is stable under the conditions of the transition zone and lower mantle and, therefore, may be considered as a likely Al carrier in the Earth's deep geospheres.
... An SiO 2 phase is reported to co-occur in fifteen diamonds hosting sublithospheric inclusions in our data sets. While coesite (monoclinic, C2/c) has been identified, the assumption is that the original inclusions were formed in the stishovite structure (tetragonal rutile-type, P4 2 /mnm), which is the stable SiO 2 phase from ~ 9 to 75 GPa Fischer et al. 2018). SiO 2 occurs with majoritic garnet in seven diamonds in our dataset and the co-occurring majoritic garnets yield pressures of ~ 10 to 22 GPa (Table 1-Available at: https:// doi.org/10.5683/SP3/LIVK1K). ...
... Regarding the first step, we performed GAP-MD simulations at 300 K which indeed showed a tetragonal-to-orthorhombic transition (Fig. 6c), consistent with the change from rutile-type stishovite to the distorted-rutile-like CaCl 2 -type. The analysis showed a transition region between 65 GPa and 70 GPa, somewhat higher than in experimental 65,66 and other theoretical results 54,64 . The observation of this transition is encouraging, since CaCl 2 -type silica had not been explicitly included in the training database. ...
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Silica (SiO2) is an abundant material with a wide range of applications. Despite much progress, the atomistic modelling of the different forms of silica has remained a challenge. Here we show that by combining density-functional theory at the SCAN functional level with machine-learning-based interatomic potential fitting, a range of condensed phases of silica can be accurately described. We present a Gaussian approximation potential model that achieves high accuracy for the thermodynamic properties of the crystalline phases, and we compare its performance (and performance–cost trade-off) with that of multiple empirically fitted interatomic potentials for silica. We also include amorphous phases, assessing the ability of the potentials to describe structures of melt-quenched glassy silica, their energetic stability, and the high-pressure structural transition to a mainly sixfold-coordinated phase. We suggest that rather than standing on their own, machine-learned potentials for silica may be used in conjunction with suitable empirical models, each having a distinct role and complementing the other, by combining the advantages of the long simulation times afforded by empirical potentials and the near-quantum-mechanical accuracy of machine-learned potentials. This way, our work is expected to advance atomistic simulations of this key material and to benefit further computational studies in the field.
... where the superscript "met" is the liquid Fe-O-Si metal and SiO 2 is the exsolved phase that may be stishovite, β-stishovite, seifertite, pyrite-type, or even melt in the T-P regime of this study (Andrault et al., 2020;Das et al., 2020;Fischer et al., 2018). As described in Text S2 in Supporting Information S1, we carried out several DFT simulations for free energies of SiO 2 phases at 55 and 135 GPa. ...
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Plain Language Summary According to planetary formation models, the Earth's core experienced two stages in its history: during the early stage of accretion, the iron‐rich core gained light elements from the silicate mantle at high temperatures; in the subsequent stage of evolution, the core gradually cooled down and this might have led to changes in core composition. During these two stages, solubility of light elements in liquid iron determines their gain and loss limits and thus is of fundamental importance. In this study, we obtained the free energies of Fe‐O‐Si liquids and predicted the exsolution boundaries of SiO2. The derived data show that Si and O would be precipitated out of the core as SiO2 crystals at the core‐mantle boundary with the secular cooling of the Earth's core, because the temperature effects are more significant than previous empirical extrapolations. With the predicted exsolution boundaries at various temperatures, we were able to provide new constraints on how the Earth's core evolved from the previous accretion stage to the present‐day status.
... The compositions of the mantle and core of Earth therefore provide a record of the accretional history of the planet. Any model of Earth's core formation should match the mantle composition of the major and trace elements (e.g., Fischer et al., 2018;Piet et al., 2017;Rubie et al., 2011;Rudge et al., 2010;Wade & Wood, 2001). Traditionally, the moderately siderophile elements (e.g., Ni, Co, V, and Cr), those that have somewhat similar preferences for both the metal and silicate, have been used as the principal constraint on the accretional history of Earth (e.g., Fischer et al., 2015;Siebert et al., 2012). ...
Article
Many nonmetals and metal dioxides MO2, including the dense form of SiO2 stishovite, crystalize in a rutile structure at low pressure and transform to a denser CaCl2 structure under high pressure. Structures and transformations in MO2 dioxides hence serve as an archetype for applications in materials science and inside the Earth and terrestrial planets. Despite its significance, however, the deformation behavior of MO2 compounds in the CaCl2 structure is very poorly constrained. Here we use radial x-ray diffraction in a diamond-anvil cell and study MnO2 as a representative system of the MO2 family. We identify the dominant slip systems and constrain texture evolution in CaCl2-structured phases. After phase transition to a CaCl2 structure above 3.5 GPa, the dominant (010)[100] and secondary {110}[001] and {011}[0-11] slip systems induce a 121 texture in compression. Further compression increases the activity of the {011}〈0−11〉 slip system, with an enhanced 001 texture at ∼50GPa. During pressure release, the 001 texture becomes dominant over the original 121 texture. This clearly demonstrates the effect of pressure on the deformation behavior and slip systems of CaCl2-structured dioxides. Finally, MnO2 transforms back to a rutile structure upon pressure release, with a significant orientation memory, highlighting the martensitic nature of the CaCl2 to rutile structural transformation. These findings provide key guidance regarding the plasticity of CaCl2-structured dioxides, with implications in materials and Earth and planetary science.
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We have fabricated novel controlled-geometry samples for the laser-heated diamond-anvil cell (LHDAC) in which a transparent oxide layer (SiO2) is sandwiched between two laser-absorbing layers (Ni) in a single, cohesive sample. The samples were mass manufactured (>10^4 samples) using a combination of physical vapor deposition, photolithography, and wet and plasma etching. The double hot-plate arrangement of the samples, coupled with the chemical and spatial homogeneity of the laser-absorbing layers, addresses problems of spatial temperature heterogeneities encountered in previous studies where simple mechanical mixtures of transparent and opaque materials were used. Here we report thermal equations of state (EOS) for nickel to 100 GPa and 3000 K and stishovite to 50 GPa and 2400 K obtained using the LHDAC and in situ synchrotron X-ray microdiffraction. We discuss the inner core composition and the stagnation of subducted slabs in the mantle based on our refined thermal EOS.
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The distributions of major and minor elements in Earth's core and mantle were primarily established by high pressure, high temperature metal-silicate partitioning during core segregation. The partitioning behaviors of moderately siderophile elements can be used to constrain the pressure-temperature conditions of core formation and the core's composition. We performed experiments to study the partitioning of Ni, Co, V, Cr, Si, and O between silicate melt and Fe-rich metallic melt in a multianvil press and diamond anvil cell, up to 100 GPa and 5700 K. Combining our new results with data from 18 previous studies, we parameterized the effects of pressure, temperature, and metallic melt composition on partitioning. Ni and Co partitioning are insensitive to composition. At low pressures, these elements become less siderophile with increasing temperature, with this trend reversing above ∼45 GPa. V and Cr partitioning are much more sensitive to metallic melt composition and less sensitive to pressure. Partitioning of Si and O are insensitive to pressure, but with strong and moderate temperature dependences, respectively. Our new parameterizations of Ni and Co partitioning suggest that the Earth's distributions of these elements can be matched by single-stage core-mantle equilibration at 54 ± 5 GPa and 3300-3400 K. These conditions would result in 8.5 ± 1.4 wt% Si and 1.6 ± 0.3 wt% O in the core, compatible with the core's measured density. However, this single-stage model matches the Earth's V and Cr distributions less well. We also incorporated our parameterizations into models of multi-stage core formation over evolving pressure-temperature-oxygen fugacity conditions, reproducing the Earth's Ni and Co distributions while simultaneously producing a core whose light element composition is consistent with its density.
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An overview of the in situ laser heating system at the High Pressure Collaborative Access Team, with emphasis on newly developed capabilities, is presented. Since its establishment at the beamline 16-ID-B a decade ago, laser-heated diamond anvil cell coupled with in situ synchrotron x-ray diffraction has been widely used for studying the structural properties of materials under simultaneous high pressure and high temperature conditions. Recent developments in both continuous-wave and modulated heating techniques have been focusing on resolving technical issues of the most challenging research areas. The new capabilities have demonstrated clear benefits and provide new opportunities in research areas including high-pressure melting, pressure-temperature-volume equations of state, chemical reaction, and time resolved studies.
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The Earth's core is about ten per cent less dense than pure iron (Fe), suggesting that it contains light elements as well as iron. Modelling of core formation at high pressure (around 40-60 gigapascals) and high temperature (about 3,500 kelvin) in a deep magma ocean predicts that both silicon (Si) and oxygen (O) are among the impurities in the liquid outer core. However, only the binary systems Fe-Si and Fe-O have been studied in detail at high pressures, and little is known about the compositional evolution of the Fe-Si-O ternary alloy under core conditions. Here we performed melting experiments on liquid Fe-Si-O alloy at core pressures in a laser-heated diamond-anvil cell. Our results demonstrate that the liquidus field of silicon dioxide (SiO2) is unexpectedly wide at the iron-rich portion of the Fe-Si-O ternary, such that an initial Fe-Si-O core crystallizes SiO2 as it cools. If crystallization proceeds on top of the core, the buoyancy released should have been more than sufficient to power core convection and a dynamo, in spite of high thermal conductivity, from as early on as the Hadean eon. SiO2 saturation also sets limits on silicon and oxygen concentrations in the present-day outer core.
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Following the discovery of stishovite (the highest-pressure polymorph of silica known from natural samples), many attempts have been made to investigate the possible existence of denser phases of silica at higher pressures. Based on the crystal structures observed in chemical analogues of silica, high-pressure experiments on silica and theoretical studies, several possible post-stishovite phases have been suggested. But the likely stable phase of silica at pressures and temperatures representative of Earth's lower mantle remains uncertain. Here we report the results of an X-ray diffraction study of silica that has been heated to temperatures above ~2,000 K and maintained at pressures between 68 and 85 GPa. We observe the occurrence of a new high-pressure phase which we identify with the aid of first-principles total-energy calculations. The structure of this phase (space group Pnc2) is intermediate between the α-PbO2 and ZrO2 structures, and is denser than other known silica phases.
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Lattice strain measurements under nonhydrostatic compression in a diamond anvil cell were used to examine dense SiO2. Experiments were performed using energy dispersive x-ray diffraction and solid-state Ge detector fixed at 2θ=12°. The collecting time was 5-30 min for each spectrum. Spectra were collected only after sufficient time elapsed after pressurization such that stress relaxation was observed to be negligible. The data were analyzed using lattice strain theory.
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We performed new diffraction experiments to clarify the equation of state (EoS) of stishovite after we suspected systematic errors in previous experimental reports. Using diamond anvil cells, we repeated both single-crystal X-ray diffraction measurements under hydrostatic conditions and powder diffraction measurements using the laser-annealing technique and NaCl pressure medium. The major improvement is the increase in precision of the pressure determination using the quartz and NaCl equations of state. Using both sets of data, the stishovite bulk moduli were refined to K0 = 309.9(1.1) GPa and K0′ = 4.59(0.23). We also reinvestigated the mechanism of the phase transformation to the CaCl2-structured polymorph of SiO2 at about 60 GPa. We confirm no volume discontinuity at the transition pressure, but the CaCl2 form appears slightly more compressible than the rutile-structured form of SiO2. This change in compression behavior is used for quantitative analyses of the spontaneous strains of the pressure-induced phase transition.
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The effect of electronic dispersion over a wide variety of SiO2 polymorphs (faujasite, ferrierite, α-cristobalite, α-quartz, coesite, and stishovite) is investigated using state-of-the-art density functional theory. Different functionals and dispersion correction schemes are compared, ranging from the local density approximation to fully nonlocal exchange-correlation functionals. It is shown that both empirical dispersion corrections and fully nonlocal functionals improve the energetics and give correct volumetric data. However, the correct volume results come from error cancellation between an overestimation of the Si-O distance and an underestimation of the Si-O-Si angle. Quantum Monte Carlo is used to compute the quartz-cristobalite energy difference within an accuracy of 0.2 kCal/mol per SiO2 unit. This demonstrates the feasability of achieving subchemical accuracy on extended systems, and confirms the validity of the Slater-Jastrow ansatz for describing SiO2 polymorphs.
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Diffraction experiments at high pressures provide measurement of the variation of the unit-cell parameters of the sample with pressure and thereby the variation of its volume (or equivalently its density) with pressure, and sometimes temperature. This last is known as the ‘Equation of State’ (EoS) of the material. It is the aim of this chapter to present a detailed guide to the methods by which the parameters of EoS can be obtained from experimental compression data, and the diagnostic tools by which the quality of the results can be assessed. The chapter concludes with a presentation of a method by which the uncertainties in EoS parameters can be predicted from the uncertainties in the measurements of pressure and temperature, thus allowing high-pressure diffraction experiments to be designed in advance to yield the required precision in results. The variation of the volume of a solid with pressure is characterised by the bulk modulus, defined as K = − V ∂ P /∂ V . Measured equations of state are usually parameterized in terms of the values of the bulk modulus and its pressure derivatives, K′ = −∂ K /∂ P and K″ = −∂2 K /∂ P 2, evaluated at zero pressure. These zero-pressure (or, almost equivalent, the room-pressure values) are normally denoted by a subscript “0,” thus: K = − V (∂ P /∂ V ) P =0, K ′ = −(∂ K /∂ P ) P =0, and K ″ = −(∂2 K /∂ P 2) P =0. However, throughout this chapter a number of notational conventions are followed for ease of presentation. Unless specifically stated, the symbols K′ and K ″ (without subscript) refer to the zero-pressure values at ambient temperature, all references to bulk modulus, K …