American Mineralogist, Volume 93, pages 1823–1828, 2008
Compression of single-crystal magnesium oxide to 118 GPa and a ruby pressure gauge for
helium pressure media
STEVEN D. JACOBSEN,1,* CHRISTOPHER M. HOLL,1 KIMBERLY A. ADAMS,1 REBECCA A. FISCHER,1
EMILY S. MARTIN,1 CRAIG R. BINA,1 JUNG-FU LIN,2 VITALI B. PRAKAPENKA,3 ATSUSHI KUBO,3 AND
PRZEMYSLAW DERA3
Department of Earth and Planetary Sciences, Northwestern University, Evanston, Illinois 60208, U.S.A.
Department of Geological Sciences, Jackson School of Geosciences, University of Texas, Austin, Texas 78712, U.S.A.
3
Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois 60637, U.S.A.
1
2
ABSTRACT
The pressure-volume equation of state (EoS) of single-crystal MgO has been studied in diamondanvil cells loaded with helium to 118 GPa and in a non-hydrostatic KCl pressure medium to 87 GPa
using monochromatic synchrotron X-ray diffraction. A third-order Birch-Murnaghan fit to the nonhydrostatic P-V data (KCl medium) yields typical results for the initial volume, V0 = 74.698(7) Å3,
bulk modulus, KT0 = 164(1) GPa, and pressure derivative, K′ = 4.05(4), using the non-hydrostatic ruby
pressure gauge of Mao et al. (1978). However, compression of MgO in helium yields V0 = 74.697(6)
Å3, KT0 = 159.6(6) GPa, and K′ = 3.74(3) using the quasi-hydrostatic ruby gauge of Mao et al. (1986).
In helium, the fitted equation of state of MgO underdetermines the pressure by 8% at 100 GPa when
compared with the primary MgO pressure scale of Zha et al. (2000), with KT0 = 160.2 GPa and K′ =
4.03. The results suggest that either the compression mechanism of MgO changes above 40 GPa (in
helium), or the ruby pressure gauge requires adjustment for the softer helium pressure medium. We
propose a ruby pressure gauge for helium based on shift of the ruby-R1 fluorescence line (Δλ/λ0) and
the primary MgO pressure scale, with P (GPa) = A/B{[1 + (Δλ/λ0)]B – 1}, where A is fixed to 1904
GPa and B = 10.32(7).
Keywords: MgO, helium pressure medium, static compression, equation of state, ruby fluorescence
INTRODUCTION
Magnesium oxide (MgO, periclase) is among the most widely
studied standard materials for testing experimental and theoretical methods of determining elastic properties (Spetzler 1970;
Jackson and Niesler 1982; Chang and Cohen 1984; Isaak et al.
1989; Chen et al. 1998; Duffy and Ahrens 1995; Karki et al. 1999;
Sinogeikin and Bass 2000; Zha et al. 2000; Speziale et al. 2001;
Jacobsen et al. 2002). MgO maintains the B1 (halite) structure to
multi-megabar pressures (Duffy et al. 1995) and is geophysically
important as end-member ferropericlase, (Mg,Fe)O, thought to
be the major non-silicate oxide of the lower mantle. Because of
its simple structure and geophysical relevance, knowledge of
accurate elastic properties of MgO pertains to problems ranging from experimental pressure scales to interpreting Earth’s
seismic structure.
Recent discoveries in mineral physics of the lower mantle,
especially electronic spin transitions of iron (Badro et al. 2003;
Lin et al. 2007) and the post-perovskite phase of MgSiO3 (Murakami et al. 2004; Oganov and Ono 2004), present the need for
reliable pressure scales in the 25–140 GPa range. In the deep
mantle, conditions of stress are essentially hydrostatic. Such
conditions of uniform stress are difficult to achieve in diamond
cells because no known element or compound remains fluid
above 10–15 GPa at 300 K (Angel et al. 2007). Although argon
* E-mail: steven@earth.northwestern.edu
0003-004X/08/1112–1823$05.00/DOI: 10.2138/am.2008.2988
and neon are commonly used as “quasi-hydrostatic” pressuretransmitting media in diamond cells, helium is preferred because
it applies near-hydrostatic stress to at least 50 GPa (Takemura
2001; Dewaele and Loubeyre 2007), preserving the quality
of delicate single-crystal plates ≤10 μm in thickness for highpressure crystallographic studies at lower-mantle pressures.
Previous static-compression studies of MgO using helium as
the pressure medium reached 55 GPa (Zha et al. 2000) and 52
GPa (Speziale et al. 2001), both employing energy dispersive
synchrotron X-ray diffraction from polycrystalline samples.
Here we extend P-V measurements of MgO to 118 GPa on
single crystals in helium using angle-dispersive, monochromatic
synchrotron X-ray diffraction. The extended pressure range improves analysis of the pressure derivative of the bulk modulus
(K′) from Birch-Murnaghan equations of state. Using pressures
from the quasi-hydrostatic ruby scale of Mao et al. (1986), the
fitted EoS for MgO compressed in helium exhibits unusually
low values of K′ = 3.7. Deviation of K′ from typical ultrasonic
and Brillouin scattering values of 4.0–4.1 (Jackson and Niesler
1982; Sinogeikin and Bass 2000) and the primary MgO pressure scale with K′ = 4.03 (Zha et al. 2000) accounts for about
8–10 GPa pressure difference (ΔP) in the 100–120 GPa pressure
range. Because an upwards adjustment in pressure was required
in going from the non-hydrostatic ruby-pressure gauge (Mao et
al. 1978) to the so-called quasi-hydrostatic pressure gauge (Mao
et al. 1986) calibrated in an argon medium, a similar adjustment
for the softer helium medium can account for the anomalously
1823
1824
JACOBSEN ET AL.: EQUATION OF STATE OF MgO AND A RUBY GAUGE FOR HELIUM MEDIA
low K′ reported here for MgO, as well as the anomalously low
K′ = 3.0(1) reported for single-crystal diamond compressed in
helium to 140 GPa (Occelli et al. 2003). Several recent studies
have proposed such adjustment in ruby-fluorescence pressures
for helium media using various equations of state of metals
(Dewaele et al. 2004; Chijioke et al. 2005; Silvera et al. 2007).
Here we calibrate the ruby-pressure gauge for helium against
the primary MgO pressure scale of Zha et al. (2000). The new
pressure gauge will be useful for future high-pressure crystallographic studies of minerals compressed with helium in the
25–140 GPa range of the lower mantle.
EXPERIMENTAL METHODS
Magnesium oxide [100]-substrates with >99.95% purity were obtained commercially from MTI Corporation. Diamond lapping film was used to polish the
MgO to 5–8 μm thickness. Cleavage fragments measuring approximately 10 × 10
μm were prepared for loading into diamond-anvil cells. We used symmetric-piston
diamond cells, fitted with beveled diamond anvils having 100 μm inner culets and
300 μm outer culets. Rhenium gaskets were pre-indented to 26–28 GPa, resulting
in about 25 μm initial gasket thickness. An electrostatic discharge machine was
used to erode symmetric holes approximately 80 μm diameter in the Re gaskets,
just smaller than the 100 μm inner culet. The diamond cells were also fitted with
cubic boron nitride (cBN) seats, placed downstream of the synchrotron source to
allow wide angular access to diffracted X-rays, while tungsten carbide seats were
used on the upstream side. The cBN seats allowed oscillation of cells about the
vertical axis by ±10°, without producing diffraction from the parts of the diamond
cell (Fig. 1).
Diamond cells were loaded using the COMPRES/GSECARS gas-loading
system at sector 13 of the Advanced Photon Source (Rivers et al. 2008). Helium
was compressed at ~160 MPa into the diamond cells, which were closed with a
piston to about 4–6 GPa under in situ video monitoring and ruby fluorescence. At
this initial loading pressure, gasket-hole diameters had reduced by 40% to about 50
μm diameter. Annealed ruby spheres were used as pressure markers. Three separate
helium runs were carried out on the 13-BMD beamline of GSECARS, labeled runs
1, 2, and 3 in the tables and figures. In the present analysis, data from all three helium
runs have been merged into a single data set (Table 1). In a separate diamond cell
with 200 μm flat culets, an MgO crystal and ruby pressure markers were loaded
with a KCl pressure medium (Table 2). In all runs, X-ray diffraction patterns were
recorded on a MAR-345 image plate using monochromatic synchrotron radiation
at 45 keV (λ = 0.27552 Å). Representative diffraction patterns from the helium
and KCl runs are shown in Figure 1.
RESULTS AND DISCUSSION
Up to eight reflections of the hk0 class were indexed (Fig.
1) and used in least-squares cell refinement with “UnitCell,” a
non-linear regression routine by Holland and Redfern (1997).
For initial analysis of EoS parameters, unit-cell volumes from
helium runs 1–3 are listed in Table 1, along with pressures determined from the quasi-hydrostatic pressure scale of Mao et al.
(1986). The ruby fluorescence signal was lost in the six highest
pressures of run 3, where we relied on the diamond-Raman shift
using Equation 4a of Sun et al. (2005), calibrated against the ruby
scale of Mao et al. (1986). The diamond-Raman pressures were
weighted less in the EoS fitting by assuming a relatively large
F IGURE 1. [100]-zone
diffraction patterns of singlecrystal MgO compressed in
a helium pressure medium
at 40 and 110 GPa (upper
panels) and in a KCl pressure
medium at 7.4 and 80 GPa
(lower panels) taken with
monochromatic synchrotron
radiation at 45 keV. Diffraction
patterns are rotated to place the
(2,0,0) diffraction spots on the
horizontal axis.
JACOBSEN ET AL.: EQUATION OF STATE OF MgO AND A RUBY GAUGE FOR HELIUM MEDIA
Run
X-ray diffraction data for single-crystal MgO compressed
in helium
Ruby R1 shift
(Δλ/λ0)
Ruby-scale P
Volume (Å3)
MgO-scale P
(GPa)*
(GPa)†
0.0001
74.698(3)‡
1
0.00439
8.5(1)
71.184(37)
8.5
1
0.00626
12.2(2)
69.812(36)
12.4
1
0.00781
15.3(2)
68.759(33)
15.7
1
0.00929
18.2(1)
67.911(32)
18.5
1
0.01182
23.4(1)
66.483(31)
23.6
1
0.01407
28.1(1)
65.279(33)
28.3
1
0.01495
29.9(1)
64.813(32)
30.3
1
0.01712
34.5(1)
63.631(37)
35.5
1
0.01858
37.6(1)
62.882(37)
39.1
1
0.01983
40.4(1)
62.287(36)
42.0
1
0.02100
42.9(1)
61.744(30)
44.8
1
0.02281
46.9(1)
61.029(30)
48.7
1
0.02409
49.7(1)
60.426(29)
52.1
1
0.02556
53.0(1)
59.931(29)
55.1
1
0.02694
56.1(1)
59.430(29)
58.1
1
0.02841
59.5(1)
58.867(28)
61.7
1
0.02984
62.8(1)
58.335(28)
65.3
1
0.03103
65.6(2)
57.918(28)
68.2
1
0.03220
68.3(2)
57.480(27)
71.3
2
0.00340
6.5(1)
71.896(7)
6.6
2
0.00436
8.4(1)
71.169(7)
8.6
2
0.00591
11.5(1)
70.070(6)
11.7
2
0.00683
13.3(1)
69.472(6)
13.5
2
0.00948
18.6(2)
67.798(6)
18.9
2
0.01144
22.6(2)
66.655(7)
23.0
2
0.01374
27.4(1)
65.404(6)
27.8
3
0.00228
4.3(1)
72.788(7)
4.4
3
0.00413
7.9(1)
71.229(7)
8.4
3
0.00598
11.6(1)
69.907(6)
12.1
3
0.00907
17.8(1)
67.977(7)
18.3
3
0.01207
23.9(1)
66.270(6)
24.4
3
0.01529
30.6(1)
64.535(6)
31.5
3
0.01804
36.5(1)
63.176(6)
37.6
3
0.01974
40.1(1)
62.412(5)
41.4
3
0.02140
43.7(1)
61.548(5)
45.9
3
0.02277
46.8(1)
61.031(5)
48.7
3
0.02469
51.0(1)
60.252(5)
53.2
3
0.02660
55.3(3)
59.593(5)
57.1
3
0.02795
58.4(3)
59.084(5)
60.3
3
0.02990
62.9(1)
58.339(7)
65.3
3
0.03146
66.5(1)
57.744(5)
69.4
3
0.03275
69.6(2)
57.271(5)
72.8
3
0.03487
74.6(4)
56.471(5)
78.9
3
0.03712
80.0(13)
55.834(5)
84.0
3
0.03955
85.0(1)
55.110(5)
90.1
3
89.0(20)§
54.628(5)
94.4
3
96.2(20)§
53.719(4)
102.9
3
99.6(20)§
53.361(4)
106.4
3
102.4(20)§
53.067(4)
109.4
3
106.3(20)§
52.639(4)
113.8
3
111.0(20)§
52.239(4)
118.1
Note: Standard deviations in the last digits are shown in parentheses.
* Ruby-scale pressures from Mao et al. (1986) with standard deviation of 0.1
GPa, unless the pressure difference before and after volume measurement is
greater, as reported.
† Calculated pressure from the primary MgO scale of Zha et al. (2000).
‡ Experimental V0 from single-crystal X-ray diffraction data of Jacobsen et al.
(2002).
§ Pressures from diamond-Raman shift, Sun et al. (2005), assumed uncertainty
is ±2.0 GPa.
uncertainty of ±2 GPa. Volumes from the non-hydrostatic run in
KCl are provided in Table 2, with ruby pressures calculated from
the non-hydrostatic ruby gauge of Mao et al. (1978).
Volume-compression data from the three helium runs and one
non-hydrostatic run (KCl medium) are plotted together in Figure
2. Using the experimental initial volume V0 = 74.698(3) Å3 of
Jacobsen et al. (2002) and fitting a third-order Birch-Murnaghan
equation of state to the non-hydrostatic data (KCl medium) yields
V0 = 74.698(7) Å3, KT0 = 164.1(9) GPa, and K′ = 4.05(4). When
TABLE 2.
X-ray diffraction data for single-crystal MgO compressed
in a KCl pressure medium
Ruby-scale P (GPa)*
Volume (Å3)
3.6(1)
73.100(7)
7.4(1)
71.791(7)
10.6(1)
70.606(6)
13.5(1)
69.620(6)
16.2(1)
68.695(7)
18.9(1)
67.858(7)
22.8(1)
66.847(7)
26.9(1)
65.785(6)
31.1(1)
64.735(6)
36.6(6)
63.546(6)
41.4(4)
62.573(7)
49.1(1)
61.258(7)
52.2(2)
60.709(6)
53.5(4)
60.493(6)
55.9(8)
60.062(6)
58.1(1)
59.617(7)
61.1(1)
59.257(7)
63.5(2)
58.830(7)
65.9(1)
58.485(7)
68.7(2)
58.247(6)
71.2(2)
57.737(6)
73.9(3)
57.335(6)
76.2(3)
57.116(6)
80.1(1)
56.609(6)
83.5(3)
56.107(6)
86.6(1)
55.792(6)
* Non-hydrostatic ruby-scale pressures from Mao et al. (1978).
Volume (Å3)
TABLE 1.
1825
Pressure (GPa)
FIGURE 2. Volume-compression data of single-crystal MgO in a
non-hydrostatic KCl pressure medium (open circles) and in helium
(filled circles). The dashed curve is the fitted EoS using the ruby gauge
of Mao et al. (1986). The solid curve shows the primary MgO equation
of state from Zha et al. (2000).
the V0 point is excluded from the fitting, we obtain V0 = 74.73(8)
Å3, KT0 = 163(2) GPa, and K′ = 4.08(7). If K′ is fixed to 4.03 after
Zha et al. (2000), we obtain V0 = 74.69(4) Å3 and KT0 = 164.6(7)
GPa. Because exclusion of experimental V0 or fixing K′ does not
1826
JACOBSEN ET AL.: EQUATION OF STATE OF MgO AND A RUBY GAUGE FOR HELIUM MEDIA
influence the fitted parameters beyond one standard deviation,
the preferred three-parameter fit to the non-hydrostatic data are
shown in Figure 2 by the dotted curve.
A three-parameter fit to the helium-medium data from all
three runs (Table 1) yields V0 = 74.687(6) Å3, KT0 = 159.6(6), and
K′ = 3.74(3), plotted as the dashed curve in Figure 2. Excluding
the six highest pressures of run 3, which were determined from
the diamond-Raman shift (Sun et al. 2005), yields the same
EoS parameters within uncertainty: V0 = 74.697(7) Å3, KT0 =
159.5(6) GPa, and K′ = 3.74(3) (using ruby pressures only). For
comparison with Speziale et al. (2001), who fixed KT0 = 160.2
GPa, we obtain V0 = 74.695(6) GPa and K′ = 3.709(8) with fixed
KT0 = 160.2 GPa. The resulting K′ is significantly lower than the
reported Speziale et al. (2001) value of K′ = 3.99(1), however,
when the Speziale et al. (2001) data set is fitted with three parameters, they obtain V0 = 74.53(2) Å3, KT0 = 170(1) GPa, with K′ =
3.59. To further analyze the current results in comparison with
the helium-only data of Speziale et al. (2001) and the primary
MgO pressure scale (Zha et al. 2000), all the data are plotted in
Figure 3 as normalized pressure (F) against Eulerian strain (f),
where F = P/3f(1+2f)5/2 and f = [(V0/V)2/3 – 1]/2. The F-f plot is
a convenient way of viewing the compression data because the
third-order Birch-Murnaghan EoS can be drawn as a straight
line with slope 3K0(K′ – 4)/2 and intercept of K0.
Non-hydrostatic (KCl medium) compression data of MgO
are plotted as open circles in Figure 3 and fitted EoS shown as
a dotted line with K′ = 4.05(4). In contrast, helium-medium data
(filled circles in Fig. 3) exhibit K′ < 4, shown by the dashed line
with K′ = 3.74(3). To demonstrate the reproducibility of this
FIGURE 3. F-f plot for MgO compression data based on the thirdorder Birch-Murnaghan equation of state. The non-hydrostatic run in
KCl is shown by open circles. Current runs 1–3 using helium media
are shown by filled circles, and the helium-media data of Speziale et al.
(2001) are shown by filled triangles. All helium-media data sets using
ruby pressures of Mao et al. (1986) give K′ = 3.74, which underestimate
the pressure by 8–10% at 100–120 GPa compared with the primary MgO
scale (solid line, Zha et al. 2000).
observation, we shaded runs 1 and 3 differently in Figure 3, showing that both runs are consistent with K′ < 4. Furthermore, if the
helium-only data of Speziale et al. (2001) are re-analyzed with
a third-order Birch-Murnagahn EoS we obtain KT0 = 165(1) GPa
and K′ = 3.74(7), shown by the filled triangles and dash-dotted
line in Figure 3. Thus, three separate helium-medium datasets
produce K′ = 3.74, namely runs 1 and 3 of the current study, and
Speziale et al. (2001), helium subset.
Because the current measurements were conducted on singlecrystal samples using angle-dispersive diffraction compared
with polycrystalline samples and energy dispersive techniques
(Zha et al. 2000; Speziale et al. 2001), we consider the possible
magnitude of deviatoric stress on measured lattice parameters.
Dewaele and Loubeyre (2007) estimated differences in the stress
component along the diamond-cell loading axis compared with
stress in the plane normal to the loading axis for helium media
to be 0.3–0.5 GPa at 150 GPa. Because the estimated deviatoric
stress of 0.3 GPa at 100 GPa (Dewaele and Loubeyre 2007) is
on the order of the precision of the ruby-pressure determination, we did not make a correction to our lattice parameters for
deviatoric stress. We also note that 0.3 GPa is over 25× < ΔP of
~8 GPa calculated between the quasi-hydrostatic ruby pressures
and MgO pressures at 100 GPa. Finally, because we also carried
out identical single-crystal and angle-dispersive measurements
on MgO in a highly non-hydrostatic (KCl) pressure medium,
resulting in K′ = 4.05(4), we further scrutinize other possible
causes of the anomalously low K′ = 3.74(3) obtained for MgO
compressed in helium.
Zha et al. (2000) obtained primary pressures up to 55 GPa with
MgO because their combined high-pressure X-ray diffraction
and Brillouin scattering measurements allowed direct pressure
determination without reference to a secondary calibrant. In the
current study, the observed deviation of K′ from the primary MgO
scale with K′ = 4.03 in helium might be interpreted in several
ways. Either K′ evolves to lower values (through more negative
K″) above 50 GPa by a different compression mechanism, possibly influenced by diffusion of helium into the MgO sample, or
the ruby fluorescence scale of Mao et al. (1986) requires adjustment for helium pressure media above about 50 GPa. The shear
strength of argon, which was used as the pressure-transmitting
medium in the Mao et al. (1986) ruby-gauge calibration, was
recently shown to rise dramatically in the 30–50 GPa pressure
range (Mao et al. 2006). It is also notable that extrapolation
of the Zha et al. (2000) MgO pressures into the 50–100 GPa
pressure range is not without uncertainty, however, because K′
values of about 4 are consistent with ultrasonic (Jackson and
Niesler 1982; Yoneda 1990) and Brillouin scattering studies
(Sinogeikin and Bass 2000) in the 0–20 GPa range, as well as
with shock-wave (Duffy and Ahrens 1995) and first-principles
studies (Karki et al. 1999) in the 50–150 GPa range, we continue
with the underlying assumption that K′ should be ~4 in the BirchMurnaghan formulation over the current experimental pressure
range. Examination of all the F-f data in Figure 3 shows that
at strains <~0.06 (pressures below about 40 GPa), the helium
data are adequately modeled with K′ ~ 4. Only five or six of
the highest points from Speziale et al. (2001) fall into the range
where K′ < 4. The current data, extending to >100 GPa reveal
a clearer trend of decreasing K′ with strain. However, the fact
JACOBSEN ET AL.: EQUATION OF STATE OF MgO AND A RUBY GAUGE FOR HELIUM MEDIA
that our non-hydrostatic compression data in KCl, measured in
the same way, reproduce typical values for the equation of state
of MgO (dotted line in Fig. 3) suggests a closer examination of
the quasi-hydrostatic ruby pressure gauge.
A re-calibration to higher pressures was required in going
from the non-hydrostatic ruby gauge (Mao et al. 1978) to the
so-called quasi-hydrostatic ruby pressure gauge (Mao et al. 1986)
calibrated against the EoS of Cu in an argon medium. Diffraction
peak-broadening, indicative of non-hydrostatic stress, has been
reported in argon media above 1.9 GPa (Angel et al. 2007), in
contrast to at least 50 GPa for helium (Takemura 2001). Furthermore, the strength of argon increases rapidly with pressure
above 20–30 GPa, exhibiting shear strength >2.7 GPa at 55 GPa
(Mao et al. 2006). Because the quasi-hydrostatic ruby pressure
gauge was calibrated from experiments using an argon medium,
the observed differences between MgO and quasi-hydrostatic
ruby pressures documented here could be attributed to dramatic
stiffening of the argon medium in the ruby calibration of Mao
et al. (1986).
Following the formulation of Mao et al. (1978), ruby pressures are calculated from the measured shift (Δλ/λ0) of the R1 ruby
fluorescence line using P (GPa) = A/B {[1 + (Δλ/λ0)]B – 1}. By
fixing A = 1904 GPa, the value of B is 5.0 for the non-hydrostatic
scale (Mao et al. 1978) and 7.665 for the quasi-hydrostatic scale
(Mao et al. 1986), shown in Figure 4 by the dotted and dashed
curves, respectively. Using our single-crystal volume data for
MgO and the primary pressure scale of Zha et al. (2000), we
obtain a revised ruby calibration for helium with A = 1930(6) GPa
and B = 9.44(23) GPa. The corresponding reduced χ2 is 0.08195
and R2 = 0.99986 when the A parameter is allowed to refine. In
1827
keeping with the formulation of Mao et al. (1986), we fixed A
= 1904 GPa and obtained B = 10.32(7) with a χ2 of 0.1077 and
R2 = 0.99982, shown by the solid curve in Figure 4. We present
the current calibration as a secondary pressure gauge for highpressure studies of minerals using helium pressure media in the
lower-mantle pressure range of 23–140 GPa.
Re-calibration of the ruby-pressure gauge for helium-loaded
diamond cells against MgO pressures is pragmatic following
many decades of mineral physics research on this standard material. The combined X-ray diffraction and Brillouin scattering
study of Zha et al. (2000) provides direct pressures because the
equation of state was obtained without reference any prior pressure standard. Further justification of using MgO to re-calibrate
the ruby scale for the effectively quasi-hydrostatic medium,
helium, stems from a range of observations indicating that K′
should be about 4 in the Birch-Murnaghan equation of state over
a wide range of pressures, including ultrasonic interferometry
(Jackson and Niesler 1982; Yoneda 1990), Brillouin scattering
(Sinogeikin and Bass 2000), shock-wave (Duffy and Ahrens
1995) and first-principles studies (Karki et al. 1999). Future
work should include a cross-check of the MgO-based ruby
gauge for helium with metals used in similar studies (Dewaele
et al. 2004; Chijioke et al. 2005; Silvera et al. 2007), as well as
detailed analysis of the possible effects of anisotropic stress fields
in polycrystalline vs. single-crystal experiments in the pressure
range of the lower mantle.
ACKNOWLEDGMENTS
Work performed at GeoSoilEnviroCARS (Sector 13), Advanced Photon
Source (APS), Argonne National Laboratory was supported by the U.S. National
Science Foundation (EAR-0622171) and the Department of Energy (DOE), DEFG02-94ER14466. Use of the Advanced Photon Source was supported by the U.S.
DOE, Office of Science, Office of Basic Energy Sciences, under Contract no. DEAC02-06CH11357. J.F.L. acknowledges support through the auspices of the U.S.
DOE by Lawrence Livermore National Laboratory, DE-AC52-07NA27344, and a
Lawrence Livermore Fellowship. S.D.J. acknowledges support from the Carnegie/
DOE Alliance Center (CDAC) and NSF grant EAR-0721449.
REFERENCES CITED
FIGURE 4. Proposed ruby pressure gauge (solid line) based on the
shifts of the R1 ruby fluorescence line (Δλ/λ0) and the primary MgO
pressure scale of Zha et al. (2000), compared with the non-hydrostatic
ruby gauge (Mao et al. 1978, dotted line) and the helium-medium
calibration from various metals (Dewaele et al. 2004, dash-dotted line).
Calculated pressure differences are plotted inset.
Angel, R.J., Bujak, M., Zhao, J., Gatta, G.D., and Jacobsen, S.D. (2007) Effective
hydrostatic limits of pressure media for high-pressure crystallographic studies.
Journal of Applied Crystallography, 40, 26–32.
Badro, J., Fiquet, G., Guyot, F., Rueff, J.P., Struzhkin, V.V., Vankò, G., and Monaco,
G. (2003) Iron partitioning in Earth’s mantle: Toward a deep lower mantle
discontinuity. Science, 300, 789–791.
Chang, K.J. and Cohen, M.L. (1984) High-pressure behavior of MgO: Structural
and electronic properties. Physical Review B, 30, 4774–4781.
Chen, G., Liebermann, R.C., and Weidner, D.J. (1998) Elasticity of single-crystal
MgO to 8 gigpascals and 1600 Kelvin. Science, 280, 1913–1916.
Chijioke, A.D., Nellis, W.J., Soldatov, A., and Silvera, I.F. (2005) The ruby pressure
standard to 150 GPa. Journal of Applied Physics, 98, 114905.
Dewaele, A. and Loubeyre, P. (2007) Pressurizing conditions in helium-pressuretransmitting medium. High-Pressure Research, 27, 419–429.
Dewaele, A., Loubeyre, P., and Mezouar, M. (2004) Equations of state of six metals
above 94 GPa. Physical Review B, 70, 094112.
Duffy, T.S. and Ahrens, T.J. (1995) Compressional sound velocity, equation of state,
and constitutive response of shock-compressed magnesium oxide. Journal of
Geophysical Research, 100, 529–542.
Duffy, T.S., Hemley, R.J., and Mao, H.K. (1995) Equation of state and shear
strength at multimegabar pressures: Magnesium oxide to 227 GPa. Physical
Review Letters, 74, 1371–1374.
Holland, T.J.B. and Redfern, S.A.T. (1997) Unit cell refinement from powder
diffraction data: The use of regression diagnostics. Mineralogical Magazine,
61, 65–77.
Isaak, D.G., Anderson, O.L., and Goto, T. (1989) Measured elastic moduli of singlecrystal MgO up to 1800 K. Physics and Chemistry of Minerals, 16, 704–713.
Jackson, I. and Niesler, H. (1982) The elasticity of periclase to 3 GPa and some
geophysical implications. In S. Akimoto and M.H. Manghnani, Eds., High
1828
JACOBSEN ET AL.: EQUATION OF STATE OF MgO AND A RUBY GAUGE FOR HELIUM MEDIA
Pressure Research in Geophysics, p. 93–113. Center for Academic Publishing, Tokyo, Japan.
Jacobsen, S.D., Reichmann, H.J., Spetzler, H.A., Mackwell, S.J., Smyth, J.R.,
Angel, R.J., and McCammon, C.A. (2002) Structure and elasticity of (Mg,Fe)
O and a new method of generating shear waves for gigahertz ultrasonic interferometry. Journal of Geophysical Research, 197, 2037.
Karki, B.B., Wentzcovitch, R.M., de Gironcoli, S., and Baroni, S. (1999) Firstprinciples determination of elastic anisotropy and wave velocities of MgO at
lower mantle conditions. Science, 286, 1705–1707.
Lin, J.F., Vankó, G., Jacobsen, S.D., Iota, V., Struzhkin, V.V., Prakapenka, V.B.,
Kuznetsov, A., and Yoo, C.S. (2007) Spin transition zone in Earth’s lower
mantle. Science, 317, 1740–1743.
Mao, H.K., Bell, P.M., Shaner, J., and Steinberg, D. (1978) Specific volume
measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R1 fluorescence pressure gauge from 0.06 to 1 Mbar. Journal of Applied Physics, 49,
3276–3283.
Mao, H.K., Xu, J., and Bell, P.M. (1986) Calibration of the ruby pressure gauge to
800 kbar under quasi-hydrostatic conditions. Journal of Geophysical Research,
91, 4673–4676.
Mao, H.K., Badro, J., Shu, J., Hemley, R.J., and Singh, A.K. (2006) Strength,
anisotropy, and preferred orientation of solid argon at high pressures. Journal
of Physics: Condensed Matter, 18, S963–S968.
Murakami, M., Hirose, K., Kawamura, K., Sata, N., and Ohishi, Y. (2004) Postperovskite transition in MgSiO3. Science, 304, 855–858.
Occelli, F., Loubeyre, P., and Letoullec, R. (2003) Properties of diamond under
hydrostatic pressures up to 140 GPa. Nature Materials, 2, 151–154.
Oganov, A.R. and Ono, S. (2004) Theoretical and experimental evidence for a postperovskite phase of MgSiO3 in Earth’s D″ layer. Nature, 430, 445–448.
Rivers, M., Prakapenka, V.B., Kubo, A., Pullins, C., Holl, C.M., and Jacobsen, S.D.
(2008) The COMPRES/GSECARS gas loading system for diamond anvil cells
at the Advanced Photon Source. High-Pressure Research, 28, in press, DOI:
10.1080/08957950802333593.
Sinogeikin, S.V. and Bass, J.D. (2000). Single-crystal elasticity of pyrope and MgO
to 20 GPa by Brillouin scattering in the diamond cell. Physics of the Earth and
Planetary Interiors, 120, 43–62.
Spetzler, H. (1970) Equation of state of polycrystalline and single crystal MgO to
8 kilobars and 800°K. Journal of Geophysical Research, 75, 2073–2087.
Speziale, S., Zha, C.-S., Duffy, T.S., Hemley, R.J., and Mao, H.K. (2001) Quasihydrostatic compression of magnesium oxide to 52 GPa: Implications for
the pressure-volume-temperature equation of state. Journal of Geophysical
Research, 106, 515–528.
Sun, L., Ruoff, A.L., and Stupian, G. (2005) Convenient pressure gauge for
multimegabar pressures calibrated to 300 GPa. Applied Physics Letters, 86,
014103.
Silvera, I.F., Chijioke, A.D., Nellis, W.J., Soldatov, A., and Tempere, J. (2007)
Calibration of the ruby pressure scale to 150 GPa. Physica Status Solidi,
244, 460–467.
Takemura, K. (2001) Evaluation of the hydrostaticity of a helium-pressure medium with powder X-ray diffraction techniques. Journal of Applied Physics,
89, 662–668.
Yoneda, A. (1990) Pressure derivatives of elastic constants of single crystal MgO
and MgAl2O4. Journal of Physics of the Earth, 38, 19–55.
Zha, C.-S., Mao, H.K., and Hemley, R.J. (2000) Elasticity of MgO and a primary
pressure scale to 55 GPa. Proceedings of the National Academy of Sciences
U.S.A., 97, 13494–13499.
MANUSCRIPT RECEIVED MARCH 26, 2008
MANUSCRIPT ACCEPTED MAY 15, 2008
MANUSCRIPT HANDLED BY BRYAN CHAKOUMAKOS