reprint - Joseph Smyth - University of Colorado Boulder
Transcript of reprint - Joseph Smyth - University of Colorado Boulder
ORIGINAL PAPER
Crystal structure, Raman and FTIR spectroscopy, and equationsof state of OH-bearing MgSiO3 akimotoite
Yu Ye • Joseph R. Smyth • Steven D. Jacobsen • Wendy R. Panero • David A. Brown •
Tomoo Katsura • Yun-Yuan Chang • Joshua P. Townsend • Przemyslaw Dera •
Sergey Tkachev • Cayman Unterborn • Zhenxian Liu • Celine Goujon
Received: 18 December 2012 / Accepted: 23 July 2013 / Published online: 14 August 2013
� Springer-Verlag Berlin Heidelberg 2013
Abstract MgSiO3 akimotoite is stable relative to majorite-
garnet under low-temperature geotherms within steeply or
rapidly subducting slabs. Two compositions of Mg–akimot-
oite were synthesized under similar conditions: Z674 (con-
taining about 550 ppm wt H2O) was synthesized at 22 GPa
and 1,500 �C and SH1101 (nominally anhydrous) was syn-
thesized at 22 GPa and 1,250 �C. Crystal structures of both
samples differ significantly from previous studies to give
slightly smaller Si sites and larger Mg sites. The bulk thermal
expansion coefficients of Z674 are (153–839 K) of
a1 = 20(3) 9 10-9 K-2 and a0 = 17(2) 9 10-6 K-1, with
an average of a0 = 27.1(6) 9 10-6 K-1. Compressibility at
ambient temperature of Z674 was measured up to 34.6 GPa at
Sector 13 (GSECARS) at Advanced Photon Source Argonne
National Laboratory. The second-order Birch–Murnaghan
equation of state (BM2 EoS) fitting yields:
V0 = 263.7(2) A3, KT0 = 217(3) GPa (K0 fixed at 4). The
anisotropies of axial thermal expansivities and compress-
ibilities are similar: aa = 8.2(3) and ac = 10.68(9)
(10-6 K-1); ba = 11.4(3) and bc = 15.9(3) (10-4 GPa).
Hydration increases both the bulk thermal expansivity and
compressibility, but decreases the anisotropy of structural
expansion and compression. Complementary Raman and
Fourier transform infrared (FTIR) spectroscopy shows mul-
tiple structural hydration sites. Low-temperature and high-
pressure FTIR spectroscopy (15–300 K and 0–28 GPa)
confirms that the multiple sites are structurally unique, with
zero-pressure intrinsic anharmonic mode parameters
between -1.02 9 10-5 and ?1.7 9 10-5 K-1, indicating
both weak hydrogen bonds (O–H���O) and strong OH bonding
due to long O���O distances.
Communicated by T. L. Grove.
Y. Ye (&)
Department of Physics, University of Colorado,
Boulder, CO 80309, USA
e-mail: [email protected]
Present Address:
Y. Ye
School of Earth and Space Exploration, Arizona State
University, Tempe, AZ 85287, USA
J. R. Smyth � D. A. Brown
Department of Geological Sciences, University of Colorado,
Boulder, CO 80309, USA
S. D. Jacobsen � Y.-Y. Chang � J. P. Townsend
Department of Earth and Planetary Sciences, Northwestern
University, Evanston, IL 60208, USA
W. R. Panero � C. Unterborn
School of Earth Sciences, Ohio State University,
Columbus, OH 43210, USA
T. Katsura
Bayerisches Geoinstitut, Universitat Bayreuth,
95440 Bayreuth, Germany
P. Dera � S. Tkachev
Center for Advanced Radiation Sources,
University of Chicago, Argonne National Laboratory,
Argonne, IL 60439, USA
Z. Liu
Geophysical Laboratory, Carnegie Institution of Washington,
Washington, DC 20015, USA
C. Goujon
Institut Neel, CNRS and Universite Joseph Fourier,
BP 166, 38042 Grenoble Cedex 9, France
123
Contrib Mineral Petrol (2013) 166:1375–1388
DOI 10.1007/s00410-013-0933-y
Keywords Akimotoite � Crystal structure � Thermal
expansion � Compressibility � Anisotropy � FTIR
Introduction
Akimotoite (ilmenite-type MgSiO3) is stable at pressures of
18–25 GPa and up to about 2,000 K in the MgSiO3 system,
with wadsleyite plus stishovite stable at lower pressures,
majorite stable at higher temperatures, and silicate perov-
skite stable at higher pressures and temperatures (e.g., Ito
and Matsui 1977; Sawamoto 1987; Kato et al. 1995; Kuroda
et al. 2000; Gasparik 1990). Wang et al. (2004) measured
the P–V–T equation of state of akimotoite and examined the
possible influence of akimotoite–majorite phase transitions
on the seismic structure of the 660-km seismic discontinu-
ity, where akimotoite could be stable along cold subduction
geotherms. The crystal structure of akimotoite (trigonal
system, space group R�3, Z = 6) was determined by Ito and
Matsui (1977) and refined by Horiuchi et al. (1982) with
unit-cell parameters a = 4.7284 A, c = 13.5591 A, and
corresponding density, q0 = 3.810 g/cm3.
Ashida et al. (1988) measured the thermal expansivity of
akimotoite between 300 and 900 K from polycrystalline
X-ray diffraction data, fitting linear coefficients of thermal
expansivity to the lattice parameters, resulting in a volume
expansion coefficient, a0 = 2.44 9 10-5 K-1. Reynard
et al. (1996) studied the compressibility of akimotoite from
powder X-ray diffraction in a diamond anvil cell up to
28 GPa, using H2O as a pressure medium. In that study,
Reynard et al. (1996) fixed KT0 = 212 GPa from previous
Brillouin scattering results (Weidner and Ito 1985) to refine
dK/dP = K0 = 7.5(±1.0) using ruby fluorescence pres-
sures and K0 = 5.6 using pressures determined from the
equation of state of the H2O pressure medium. Wang et al.
(2004) measured the P–V–T equation of state of akimotoite
up to 19 GPa and 1,373 K and refined a volume coefficient
of thermal expansivity, a0 = 2.41(19) 9 10-5 K-1 with
K0 = 5.6 when KT0 was fixed to 210 GPa. First-principals
lattice dynamics calculations found comparable results
with KT0 = 201 GPa, K0 = 4.64, and a0 = 1.88 9
10-5 K-1 at 300 K (Karki and Wentzcovitch 2002), and an
ab initio study of the elastic behavior gives an adiabatic
bulk modulus (KS) of 222 GPa, with K0 = 4.5 (Da Silva
et al. 1999).
Bolfan-Casanova et al. (2002) studied the incorporation
of H2O into akimotoite, finding up to *350 ppm wt H2O
(calibration of Patterson 1982) in samples synthesized at
19–21 GPa and 1,573–1,773 K. Because of its potential
role in transporting H2O into the lower mantle along cold
subduction geotherms, we have undertaken this study to
determine the influence of H2O on the crystal structure,
thermal expansivity, compressibility, and vibrational
properties of OH-akimotoite for comparison with anhy-
drous akimotoite. In this study, we report crystal structure
refinements of two akimotoite samples, one containing
\*50 ppm wt H2O (sample SH1101) and a hydrous
sample (Z674) containing *550 ppm wt H2O. The com-
pressibility of the hydrous sample (Z674) was determined
by single-crystal synchrotron X-ray diffraction up to
35 GPa Thermal expansivity of the hydrous akimotoite
sample (Z674) was determined by single-crystal X-ray
diffraction on a laboratory rotating anode source between
153 and 839 K. The anisotropy of thermal expansivity and
compressibility is discussed. In addition, low-temperature
(10–300 K) synchrotron FTIR spectra for OH-akimotoite
were measured up to 28 GPa to determine the isobaric and
isothermal mode Gruneisen parameters, as well as an
intrinsic anharmonic mode parameter. Finally, we sum-
marize relationships between isothermal bulk moduli and
density for anhydrous and hydrous MgSiO3 and Mg2SiO4
polymorphs.
Experimental methods and results
Sample synthesis
Hydrous akimotoite sample Z674 was synthesized using
the 5,000 ton press at Bayerisches Geoinstitut, Universitat
Bayreuth, Germany. The welded Pt capsule was 2.4 mm
diameter by 6.7 mm in length. The capsule was placed into
a 14-mm sintered MgO octahedron with a stepped LaCrO3
ceramic heater. The anvils were 54-mm WC cubes with
6-mm corner truncations. The starting material was
85 wt% enstatite and 15 wt% forsterite with an additional
15 wt% H2O as liquid water and synthesized at 22 GPa and
1,500 �C for 8 h.
Nominally anhydrous akimotoite sample SH1101 was
synthesized using the 1,500 ton press at Bayerisches
Geoinstitut, Universitat Bayreuth, Germany. The welded Pt
capsule was 1.2 mm diameter by 2.4 mm in length. The
capsule was in a 10-mm sintered MgO octahedron with a
stepped LaCrO3 ceramic heater. The anvils were 28-mm
WC cubes with 4-mm corner truncations. The starting
material was mixed from powders of MgO (periclase),
SiO2 (quartz), and Mg(OH)2 (brucite) to give stoichiome-
tric MgSiO3 with an additional 2 H2O wt% as OH in
brucite and synthesized at 22 GPa and 1,250 �C for 4 h.
Raman and infrared spectroscopy
Raman and Fourier transform infrared (FTIR) spectroscopy
at ambient conditions was used for sample characterization.
Raman spectra of crystals from runs Z674 and SH1101
were obtained using a 250-mW, 458-nm solid-state diode
1376 Contrib Mineral Petrol (2013) 166:1375–1388
123
laser source (Melles Griot 85-BLS-601). A confocal optical
system with an Olympus-BX microscope and 1009
objective was used to collect spectra for 60 s and averaged
over 3 accumulations, with about 10-mW laser power at the
sample. Spectra were collected using an Andor Shamrock
303i spectrograph (0.3 m focal length) with a grating of
1,200 lines per mm and Newton DU-970 electron-multi-
plying CCD camera. Spectra were obtained from 0 to
4,000 cm-1 shift from the laser line at 1.3 cm-1 resolution.
This setup is particularly useful for studies of Raman shifts
in the OH region because excitation with 458 nm positions
Raman shifts from O–H (3,000–3,600 cm-1 shift) at
530–550 nm, where the CCD camera has highest quantum
efficiency. Unpolarized Raman spectra of akimotoite sam-
ples Z674 and SH1101 in the lattice mode region
(0–1,000 cm-1) are shown in Fig. 1. Raman spectra in the
OH region are plotted in Fig. 2, showing three distinct O–H
stretching modes in akimotoite Z674, whereas akimotoite
SH1101 is nominally anhydrous.
FTIR spectra of akimotoite Z674 were collected from
800 to 4,000 cm-1 at 2 cm-1 resolution and 512 scans
using a Bruker Tensor-37 spectrometer equipped with a
Hyperion microscope, 159 objective, a 250-lm pixel size
MCT detector, KBr beam splitter, and a globar light
source. Two different akimotoite crystals of unknown ori-
entation from run Z674 (called crystal-1 and crystal-2 in
Fig. 3) were measured with unpolarized light. Both sam-
ples were about 150–200 lm in size and polished to about
60 lm thickness.
High-pressure, low-temperature FTIR data for sample
Z674 were measured at the U2A synchrotron-IR beamline
of the National Synchrotron Light Source (NSLS). Data
Fig. 1 Unpolarized Raman spectra of akimotoite crystals from runs
Z674 and SH1101 in the lattice mode regionFig. 2 Unpolarized Raman spectra of akimotoite crystals from runs
Z674 and SH1101 in the O–H stretching region. In Z674, three
distinct O–H stretching modes are observed at 3,295, 3,320, and
3,350 cm-1, whereas SH1101 is nominally anhydrous
Fig. 3 Unpolarized FTIR spectra of two crystals from run Z674
Contrib Mineral Petrol (2013) 166:1375–1388 1377
123
Fig. 4 High-pressure, low-temperature FTIR spectra of Z674 in the order of increasing pressure: a zero-pressure, b 5–10 GPa, c 10–14 GPa, and
d 21–26 GPa
1378 Contrib Mineral Petrol (2013) 166:1375–1388
123
were collected on the custom long-working distance
microscope with a beam aperture of *30 lm, using a KBr
beam splitter and an MCT detector. All spectra were col-
lected with 512 or 1,024 scans with 4 cm-1 spectral
resolution.
A doubly polished fragment of Z674 was loaded with a
ruby chip in an Ar pressure medium in a symmetric dia-
mond cell with type IIa diamond anvils and compressed to
21 GPa. Cooling of the DAC was done in a CRYO
Industries cryostat model 102-2572-DCA, cooled with
liquid helium using Varian TPS-compact vacuum system
to *10-4 Pa. Temperature stability and accuracy of the
temperature controller is \0.1 K at T [50 K; *0.5 K for
T \20 K. Upon cooling, the pressure in the cell increases
due to thermal contraction. A small ruby sphere was
therefore mounted on the back of one of the diamonds both
to serve as an internal measure of the zero-pressure R1 shift
and to confirm that the cryostat thermocouple temperature
located above the diamond cell accurately reflects the
temperature of the sample itself. High-pressure data were
collected during three cooling cycles at 21–28, 11–16, and
5.5–10 GPa via cooling at *10 K and then collecting
spectra upon warming up to room temperature. The spectra
at pressures and temperatures are shown in Fig. 4a–d,
and the peak positions versus T and P are listed in
‘‘Appendix 1’’.
Structure refinements
Single crystals from runs Z674 and SH1101 were selected for
structure refinement at ambient conditions, measuring
120 9 105 9 85 lm3 for Z674 and 105 9 90 9 80 lm3 for
SH1101. Unit-cell parameters of each crystal were refined on a
Bruker P4 four-circle diffractometer with a dual-scintillation
point detector system, which used 18-kW rotating Mo-anode
X-ray generator operating at 50 kV and 250 mA. MoKa1-Ka2
mixed characteristic wavelength was used with Ka_avg =
0.71080 A, which was calibrated by a single crystal of anhy-
drous forsterite of spherical shape. Least squares fitting was
performed on 42 centered reflections within the following
classes: (104), (015), (213), (113), (021), (024), (107), (205),
(216), (116), (018), (312) and (314). The unit-cell parameters
are as follows: a = 4.7283(6) A, c = 13.560(2) A, V =
262.55(6) A3 for Z674; a = 4.7295(3) A, c = 13.5601(13) A,
V = 262.68(4) A3 for SH1101. For comparison, Ito and Mat-
sui (1977) studied a sample of akimotoite with a =
4.7284(4) A, c = 13.5591(16) A, V = 262.54(4) A3. Inten-
sity data for both single crystals were collected using a Bruker
APEX II CCD detector mounted on a P4 diffractometer up to
70� 2h. Refinement of atom positions and anisotropic dis-
placement parameters were carried out using SHELXL-97
(Sheldrick 1997) in the software package WinGX (Farrugia
1999). We used scattering factors of Mg2? and Si4? reported by
Cromer and Mann (1968), and those of O2- from Tokonami
(1965). The intensity data collection parameters and refined
atomic position coordinates as well as the unit-cell parameters
are listed in Table 1, and the anisotropic displacement
parameters are listed in Table 2.
The same single crystal of Z674 used for structure
refinement was used for thermal expansion studies between
150 and 900 K at ambient pressure. At each temperature
step, the unit-cell parameters were refined following the
same procedure at ambient temperature described above.
Three low-temperature measurements were conducted at
253, 203, and 153 K. Low temperatures were measured
and controlled by a Bruker LT-2A controller, which uses a
low-temperature N2 gas stream. Next, the single crystal
was transferred inside a silica glass capillary for high-
temperature experiments. Eleven high-temperature points
were taken up to 839 K using a Bruker high-temperature
device, which uses a two-prong ceramic-coated Pt wire
radiant heater, with an Omega temperature control unit. Ye
et al. (2009) reported the temperature calibration in detail.
Unit-cell parameters at various temperatures are listed in
‘‘Appendix 2’’.
High-pressure synchrotron X-ray diffraction
High-pressure XRD experiments for sample Z674 were
conducted at beamline 13-BM-D (GSECARS) of the
Advanced Photon Source (APS) at Argonne National
Laboratory. The single crystal used for the high-pressure
experiment measured about 35 9 30 9 20 lm. We used a
symmetric piston-cylinder-type diamond anvil cell (DAC)
with 300 lm culets. The diamond cell was fitted with a
cubic boron nitride (cBN) seat on the downstream side and
a tungsten carbide (WC) seat on the upstream side. We
used a rhenium gasket, pre-indented to an initial thickness
of *40 lm with a 160-lm-diameter hole. The DAC was
loaded with neon as pressure medium using the COM-
PRES/GSECARS gas-loading system (Rivers et al. 2008).
The pressure inside the cell was about 1.4 GPa after gas
loading, and the gasket-hole diameter decreased by about
30 %. Fine gold powder was mounted in the sample
chamber along with sample to serve as the pressure scale
(Dorogokupets and Dewaele 2007).
Throughout the experiment, monochromatic synchro-
tron radiation with wavelength k = 0.33442 A was used to
collect diffraction patterns on a MAR345 image plate. The
single-crystal diffraction data collection at each pressure
took 10–12 min with omega rotation from ±25�. To obtain
the orientation matrix at the initial pressure of 1.38 GPa, an
omega step-scan was performed with 1� steps. In total, 50
images were collected to calculate omega angles for each
reflection and the orientation matrix, as well as to refine
Contrib Mineral Petrol (2013) 166:1375–1388 1379
123
unit-cell parameters. This orientation matrix was used as a
first approximation to index peaks in images collected at
subsequent pressures. For each pressure step, about 30–40
reflection peaks were used to refine the unit-cell parameters
by the software packages of GSE-ADA (Dera 2007a) and
RSV (Dera 2007b). The unit-cell parameters at various
pressures are listed in ‘‘Appendix 3’’.
Discussion
H2O content calibration
From our FTIR and Raman spectra alone, it is not possible
to accurately quantify the H2O content of the akimotoite
samples. Figure 3 shows unpolarized FTIR spectra of two
crystals from run Z674. In agreement with spectra of OH-
bearing akimotoite from Bolfan-Casanova et al. (2002), we
observe three strong bands at 3,300, 3,320, and
3,390 cm-1, and one weak band around 3,260 cm-1. In
addition, we observe three previously unreported OH bands
at 3,250, 3,345, and 3,410 cm-1. Using the general cali-
bration of Libowitzky and Rossman (1997) on the peaks
shown in Fig. 3, we obtain integrated molar absorption
coefficients (eI) of 1.006 9 105 and 0.989 9 105 cm-2 per
mol H2O/L, respectively, corresponding to H2O contents of
440 ppm wt H2O for crystal-1 and 700 ppm wt H2O for
crystal-2, using the calibration from Libowitzky and
Rossman (1997). For the purpose of comparison with
Bolfan-Casanova et al. (2002), we also applied the Patt-
erson (1982) calibration to the spectra in Fig. 3 and
obtained 250 and 400 ppm wt H2O for crystal-1 and
crystal-2, respectively. In this paper, we take the average of
the two crystals using the Libowitzky and Rossman (1997)
calibration and consider the H2O content of Z674 to be
*550 ppm wt H2O, with an estimated uncertainty of about
200 ppm wt H2O. The Raman spectrum of akimotoite
Z674 in the OH region is shown in Fig. 2. We observe
three bands, at 3,295, 3,320, and 3,350 cm-1, respectively.
The signal-to-noise ratio (SNR) for the OH band at
3,350 cm-1 was calculated using SNR = S/ry, where S is
the average signal peak height above the background and
ry is the standard deviation of the peak height (McCreery
2005). For the spectrum, we obtain SNR *20. Because
sample Z674 contains about 550 ppm wt H2O (from FTIR
above), the SNR suggests that sample SH1101 contains
less than *30 ppm wt H2O, based upon the lack of
observed Raman modes in the 3,300–3,400 cm-1 region.
Therefore, we conclude from Raman spectroscopy that
akimotoite SH1101 is nominally anhydrous.
FTIR at high-P and low-T
Low-temperature vibrational spectra at 10-4 Pa and over
three different high-pressure ranges at 21–28, 11–16, and
5.5–10 GPa were collected from 15 to 300 K. We observe
three OH bands throughout the measurements, with 300 K
frequencies of about 3,300, 3,320, and 3,388 cm-1. These
OH bands shift to higher frequencies upon decreasing tem-
perature, with average shifts of -0.0039, -0.0049 and
-0.046 (cm K)-1in the range of 15–300 K (Fig. 5). We
Table 1 Intensity data collection parameters and refined atomic position coordinates for akimotoite samples Z674 and SH1101
Z674 SH1101 Z674 SH1101
a (A) 4.7283(6) 4.7295(3) R1 for I [ 4r (%): 2.96 3.58
c (A) 13.560(2) 13.560(1) Rint (%): 1.98 1.85
Vol. (A3) 262.55(6) 262.68(4)
No. total refl.: 925 1,092 Mga z: 0.36001(6) 0.35999(8)
No. unique total: 254 270 Sia Z: 0.15777(4) 0.15768(6)
No. unique
I [ 4r:
235 O x: 0.3222(2) 0.3222(3)
GooF: 0.819 0.930 y: 0.0370(2) 0.0367(3)
z: 0.24008(6) 0.24011(8)
a: x = y = 0 for Mg and Si coordinates
Table 2 Anisotropic displacement parameters (A2) for Z674 and
SH1101
Z674 SH1101 Z674 SH1101
Mga U11: 0.0067(4) 0.0092(5) O U11: 0.0050(5) 0.0072(6)
U33: 0.0083(4) 0.0068(6) U22: 0.0053(5) 0.0077(6)
U12: 0.0034(2) 0.0046(2) U33: 0.0066(5) 0.0067(6)
Ueq: 0.0073(3) 0.0084(4) U23: 0.0008(3) 0.0008(4)
Sia U11: 0.0053(3) 0.0077(4) U13: 0.0001(3) 0.0000(4)
U33: 0.0068(4) 0.0057(4) U12: 0.0020(3) 0.0032(4)
U12: 0.0026(2) 0.0039(2) Ueq: 0.0059(3) 0.0074(4)
Ueq: 0.0058(3) 0.0071(3)
a U22 = U11; U23 = U13 = 0 for Mg and Si
1380 Contrib Mineral Petrol (2013) 166:1375–1388
123
observed a significant sharpening of 3,389 cm-1 band from
21 cm-1 (300 K) to 12 cm-1 (15 K) FWHM at ambient
pressure (Fig. 4a), with less than 10 % narrowing of the
other two bands. The sharp 3,700 cm-1 peaks in Fig. 4a
suggest micro-inclusions of brucite inside the hydrous
akimotoite sample, which were also observed in Raman
spectra and reported by Bolfan-Casanova et al. (2002). Peaks
between 2,800 and 3,000 cm-1 may be due to the diamond.
Upon decompression from high-pressure, we find steep
room temperature frequency shifts with pressure (dm/dP) of
-10, -8.2, and -11.4 (cm GPa-1) (Fig. 6). The three
bands become very broad and overlap at 21–25.5 GPa at all
temperatures (Fig. 4d). However, upon cooling from 300 to
10 K at pressures from 10.8 to 13.6, the three OH bands
can be resolved except at 10 K. (Fig. 4c). Upon cooling at
5.4–7.5 GPa, the three OH bands become more clearly
resolved, but still overlap (Fig. 4b).
The sample pressure increased upon cooling due to
thermal contraction of the diamond cell, and thus, the
measured frequency shifts are therefore a consequence of
both changing temperature and pressure. Assuming that the
pressure dependence is independent of temperature, we
determine larger temperature dependence of the frequency
increases with increasing pressure.
The frequency shifts for the 3,300, 3,320, and 3,388 cm-1
bands are -0.21(1) (cm K)-1, -0.19(1) (cm K)-1, and
-0.206(4) (cm K)-1 at 5.5 GPa, respectively, while
-0.16(3), -0.12(2), and -0.17(5) (cm K)-1 at 10–13 GPa,
respectively. Due to overlapping bands at higher pressure, it
is more difficult to resolve the temperature dependence.
With both pressure and temperature dependence of the
OH vibrational modes in akimotoite, along with thermal
expansion and bulk modulus measurements on the same
sample, it is then possible to calculate the isobaric and
isothermal mode Gruneisen parameters as in Eqs. (1, 2),
respectively,
ci;P ¼1
ao ln mi
oT
� �P
ð1Þ
Fig. 5 Variation in vibrational frequencies with temperature at room
pressure for the three OH bands of Z674
Fig. 6 Variation in vibrational frequencies with pressure and
temperature for the three OH bands in OH-akimotoite sample Z674
Contrib Mineral Petrol (2013) 166:1375–1388 1381
123
ci;T ¼ KT
o ln mi
oP
� �T
ð2Þ
The intrinsic anharmonic mode parameter, ai, can therefore
be derived from these values,
ai ¼ a ci;T � ci;P
� �¼ aKT
o ln mi
oP
� �T
� o ln mi
oT
� �P
¼ o ln mi
oT
� �V
ð3Þ
Given the volume thermal expansion coefficient
a0_V = 14.8(9) 9 10-6 K-1 (153–300 K) and isothermal
bulk modulus KT = 217(3) GPa (BM2 EoS), we reported
the isobaric and isothermal mode Gruneisen parameters
(Eqs. 1, 2), as well as the intrinsic anharmonic mode
parameter for the samples Z674 (*550 ppm wt H2O)
(Eq. 3) in Table 3.
The negative intrinsic anharmonic mode parameters for
the 3,300.6 and 3,320.2 cm-1 vibrational modes indicate
relatively weak bonding in the OH���O in the akimotoite
structure, comparable to the external XO6 and Mg trans-
lational modes in akimotoite (Okada et al. 2008). The
positive intrinsic anharmonic mode parameter for
3,387.5 cm-1 is comparable to the values for internal
vibrational modes in akimotoite, indicative of strong bonds
through long O–O distances, consistent with the higher
vibrational frequency.
Crystal structures
The crystal structure of akimotoite (space group R 3) has a
distorted hexagonal close packing (HCP) of oxygen anions
with Mg2? and Si4? cations occupying octahedral sites
(Horiuchi et al. 1982). The MgO6 and SiO6 octahedra form
alternating layers along the c axis, and the cations are
completely ordered if each layer contains only Mg or only
Si, so that the closest pairs of cations in the face-sharing
octahedra are always Mg–Si. The bond lengths and poly-
hedral volumes of cation polyhedral for the current akim-
otoite samples of Z674 and SH1101 are calculated using
the software package XTALDRAW (Downs et al. 1993)
and listed in Table 4, compared with those from Horiuchi
et al. (1982). The Mg–O, Si–O bond lengths and octahedral
volumes of the current samples are identical with each
other, in spite of the different H2O contents, indicating that
such small water contents have no significant impact on the
crystal structures.
Although the unit-cell volumes of the two samples are
identical within error to each other and to the previous
results of Horiuchi et al. (1982), the oxygen position
parameters differ significantly from those of the previous
study giving the current samples a slightly larger Mg and
slightly smaller Si octahedron. The\Mg–O[and\Si–O[lengths of akimotoite from Horiuchi et al. (1982) are
0.4(1) % smaller and 1.0(1) % larger, respectively, than
those of the current samples, indicating that the sample from
Horiuchi et al. (1982) might not be completely ordered.
Since Mg2? cation has a larger radius than Si4?, even a
small portion of Mg and Si sites exchange could reduce the
measured Mg–O lengths, while increase the measured Si–O
lengths without changing the structure of R 3. This would be
consistent with a more complete ordering of the cation in
the current samples. The durations of the heating cycles for
the current samples were 8 and 4 h, respectively, whereas
that of the sample studied by Horiuchi et al. (1982) was only
20 min, at the experimental conditions of 22 GPa and
1,550 �C, which were similar to those of the current sam-
ples. On the other hand, both the samples of Z674 and
SH1101 share nearly identical internal structures, indicating
that small water contents of *500 ppm wt have no sig-
nificant impact on the crystal structure of akimotoite.
Table 3 Isobaric and isothermal mode Gruneisen parameters and intrinsic anharmonic mode parameter for hydrous MgSiO3 akimotoite samples
of Z674 and Bolfan-Casanova et al. (2002)
Frequency at ambient
condition (cm-1)
Z674 Bolfan-Casanova
et al. (2002)
ci,Pa ci,T
b ai (10-5 K-1) ci,pc
3,300.6 -0.12(2) -0.45(12) -1.02(12) -0.32
3,320.2 -0.06(3) -0.37(10) -0.96(10) -0.42
3,387.5 -1.1(2) -0.55(11) 1.7(2) -0.41
a At 0 GPa, b up to 11 GPa, c up to 10 GPa
Table 4 Bond lengths (A) and polyhedral volumes (A3) of cation
polyhedral for akimotoite
Z674 SH1101 Horiuchi et al. (1982)
Mg O 9 3: 2.175(1) 2.175(1) 2.163(2)
O 9 3: 1.994(1) 1.993(1) 1.990(2)
\Mg–O[: 2.084(1) 2.084(1) 2.076(2)
Poly. Vol.: 11.35(1) 11.35(1) 11.24(2)
Si O 93: 1.825(1) 1.827(1) 1.830(2)
O 93: 1.760(1) 1.761(1) 1.768(2)
\Si–O[: 1.793(1) 1.794(1) 1.799(2)
Poly. Vol.: 7.51(1) 7.52(1) 7.59(1)
1382 Contrib Mineral Petrol (2013) 166:1375–1388
123
Thermal expansion
Temperature variation in the lattice parameters and unit-
cell volume for sample Z674 (*550 ppm wt H2O) nor-
malized to 300 K are plotted in Fig. 7, compared with
those of anhydrous MgSiO3 akimotoite from Ashida et al.
(1988). The fitted curves indicate that the slope of a versus
T for Z674 is slightly larger than reported by Ashida et al.
(1988), whereas the slope of c versus T for Z674 is slightly
smaller. The linear temperature-dependent expansion
coefficients a1 and a0, as well as average thermal expansion
coefficient (a0) for Z674, are summarized in Table 5,
compared with Ashida et al. (1988). a0(V) for sample Z674
is 29.0(2) 9 10-6 K-1 (300–839 K), 19 % larger than
previous results from Ashida et al. (1988), and a0(c) is
*30 % larger than a0(a) for sample Z674, while *50 %
larger for Ashida et al. (1988). Hence, according to these
two samples of akimotoite, hydration slightly increases
bulk thermal expansivity and decreases the anisotropy of
axial thermal expansivities.
The c/a ratio versus temperature for sample Z674 is
plotted in Fig. 8. The c/a ratio thus increases with tem-
perature because of larger thermal expansion in c direction.
Conversely, the positive slope becomes smaller with tem-
perature because a1(a) is significantly larger than a1(c)
for the temperature-dependent coefficients. Here, we fit the
c/a ratio as a second-order polynomial function of T as in
Eq. (4):
c=a ¼ 2:8625 8ð Þ þ 2:0 3ð Þ � 10�5 � T � 1:3 3ð Þ� 10�8 � T2 ð4Þ
It is important to notice that the change in unit-cell
parameters for Z674 is not significant after heating to
839 K, compared with the uncertainties of a, c, V. There
are no obvious differences of unit-cell parameters and
internal structures between anhydrous and hydrous
(550 ppm wt H2O) akimotoite samples, as discussed in the
previous part of crystal structures. Hence, X-ray is not an
efficient method to determine whether dehydration hap-
pened or not in this study.
Isothermal compressibility
Variations in the unit-cell volumes with pressure for
akimotoite samples of Z674, Wang et al. (2004) and
Reynard et al. (1996) are plotted in Fig. 9, with second-
order Birch–Murnaghan equation of state (BM2 EoS) fit-
ting for each data set. The BM2 fitting results are listed in
Table 6, compared with the theoretical values from Karki
and Wentzcovitch (2002) and Da Silva et al. (1999). For
sample Z674, the calculated V0 from BM2 is 263.7(2) A3,
0.4 % larger than the value measured in our laboratory,
which can be attributed to the systematic difference
between two experimental set ups in Sector 13, APS, and
our laboratory (Ye et al. 2010, 2012). For BM2 EoS fit-
tings, the KT value from Reynard et al. (1996) is signifi-
cantly larger than that from this study, and Reynard et al.
(1996) adopted pure H2O as the pressure-transmitting
medium, which transforms to the ice-VII polymorph above
2.3 GPa. The KT value from Wang et al. (2004) is slightly
larger than the current value, which is consistent with the
previous conclusion that the bulk thermal expansion coef-
ficient of this study is slightly larger than that from Wang
et al. (2004). The variation in densities with pressure (up to
20 GPa) for samples of Z674, Wang et al. (2004) and
Reynard et al. (1996) is shown in Fig. 10. For this pressure
range up to 20 GPa, linear regressions are adopted to
demonstrate how densities decrease as functions of pres-
sure (to the first order of approximation), with slopes of
0.0157(1) g/(cm3 GPa) (R2 = 0.9993) for sample Z674,
0.0150(2) g/(cm3 GPa) (R2 = 0.9993) for Wang et al.
(2004), and 0.0152(3) g/(cm3 GPa) (R2 = 0.9993) for
Reynard et al. (1996). The slope for sample Z674 is larger
than those of anhydrous samples from Wang et al. (2004)
and Reynard et al. (1996). This is also consistent with the
current sample being slightly more compressible than the
anhydrous ones presumably due to Mg2? vacancies asso-
ciated with the *550 ppm wt H2O content of the sample.
In addition, third-order BM EoS fitting for sample Z674
gives V0 = 263.4(2) A3, KT0 = 235(9) GPa, K0 = 2.7(6).
K0 is significantly smaller than 4. The results of sample
Z674 for both third-order and second-order B-M EOS fit-
tings are plotted in Fig. 11 with confidence ellipsoids for
68.3, 90, and 95.4 % (Angel 2000), and the point for sec-
ond-order fitting is on the ellipsoid for 90 %.
The a and c axes versus pressure are plotted in Fig. 12,
and the axial compressibilities are summarized in Table 6.
100 200 300 400 500 600 700 800 9000.996
0.998
1.000
1.002
1.004
1.006
1.008
1.010
1.012
1.014
1.016
1.018a/a
0
c/c0
V/V0
2nd-order polynomial fits for Z674 linear fits for Ashida et al. (1988)
X/X
0
T (K)
Fig. 7 Fractional unit-cell parameters versus temperature for sample
Z674 (solid symbols 153–839 K) and Ashida et al. (1988) (open
symbols 298–820 K). The two sets of unit-cell parameters at
temperatures are normalized to room temperature
Contrib Mineral Petrol (2013) 166:1375–1388 1383
123
The results from Reynard et al. (1996) and Wang et al.
(2004) are consistent with each other, while the axial
compressibilities of the current sample are 11(3) % larger
in a direction and 11(2) % smaller in c direction, compared
with those of Wang et al. (2004). On the other hand, all
three studies are consistent in having the c axis more
compressible than the a axis: bc/ba ratios are 1.39(5),
1.73(9), and 1.82(4) for this study, Wang et al. (2004) and
Reynard et al. (1996) respectively. The anisotropy of axial
compressibilities is consistent with the anisotropy of axial
thermal expansion, discussed above. Further, this is con-
sistent with the conclusion that longitudinal moduli
C33 \ C11 from elasticity studies of akimotoite (Li et al.
2009; Weidner and Ito 1985) and the observation that
P-wave anisotropies of akimotoite single crystal have
minimum value in the c direction by the crystallographic
preferred orientation studies of Shiraishi et al. (2008) and
Zhang et al. (2005). The c/a ratios versus pressure are
plotted in Fig. 13. For this study, the c/a ratio is linearly
fitted as in Eq. (5):
c=a ¼ 2:8700 9ð Þ � 0:0017 1ð Þ � P GPað Þ ð5Þ
The linear regression slopes for c/a versus P are
-0.0019(3) for Wang et al. (2004) and -0.0026(1) for
Reynard et al. (1996), both of which are larger in absolute
values compared with that of the current study, because of
the larger bc/ba ratios. Hence, hydration decreases the
anisotropy of axial compressibilities, as well as axial
thermal expansivities discussed above.
There are several previous studies reporting isothermal
compressibilities of MgSiO3 polymorphs (Hugh-Jones and
Angel 1994 for orthoenstatite; Hazen et al. 1994 for maj-
orite; Wang et al. 2004 for akimotoite; Ross and Hazen
1990 for perovskite, etc.), as well as Mg2SiO4 polymorphs
(e.g., Couvy et al. 2010 for forsterite; Holl et al. 2008 for
wadsleyite; Ye et al. 2012 for ringwoodite, etc.). In addi-
tion, the H2O contents can be up to *3 wt% in wadsleyite
(e.g., Inoue et al. 1995) and ringwoodite (e.g., Ye et al.
2012). Hydration has a significant effect on decreasing the
bulk moduli and densities of these materials (Holl et al.
2008; Jacobsen and Smyth 2006; Ye et al. 2012, etc.). Here,
the isothermal bulk moduli KT values for MgSiO3 poly-
morphs, as well as anhydrous and hydrous Mg2SiO4 poly-
morphs, are plotted against density q in Fig. 14, with linear
regressions for MgSiO3 and Mg2SiO4 polymorphs, respec-
tively. All KT values are derived by second-order B-M EoS
fitting with K0 fixed at 4, for better investigation of
Table 5 Volume and axial thermal expansion coefficients for akimotoite Z674 (153–839 K), compared with those from Ashida et al. (1988)
(298–820 K)
a = a1 9 T ? a0 Ashida et al. (1988)
a1 (10-9 K-2) a0 (10-6 K-1) R2 a0 (10-6 K-1) R2 a0 (10-6 K-1) R2
V 20(3) 17(2) 0.9980 27.1(6) 0.9929 24.4(9) 0.9342
a 10(1) 3.4(8) 0.9957 8.2(3) 0.9831 7.1(6) 0.8970
c 1(1) 10.1(5) 0.9991 10.68(9) 0.9990 10.0(7) 0.8963
2.864
2.865
2.866
2.867
2.868
2.869
2.870
2.871
2.872
c / a
T (K)100 200 300 400 500 600 700 800 900
Fig. 8 Variation in the c/a axial with temperature for OH-akimotoite
sample Z674 with second-order polynomial regression
0 5 10 15 20 25 30 35230
235
240
245
250
255
260
265 Z674 Wang et al. (2004) T0150 Wang et al. (2004) T0133 Reynard et al. (1996) Fitting for Z674 Fitting for Wang et al. (2004) Fitting for Reynard et al. (1996)
V(Å
3 )
P (GPa)
Fig. 9 Unit-cell volumes versus pressure with the fitting curves with
BM2 EoS fitting
1384 Contrib Mineral Petrol (2013) 166:1375–1388
123
relationship between KT and q. There are some discrepan-
cies among the compressibility studies for perovskite, and
the results from Ross and Hazen (1990), Yagi et al. (1982)
are significantly lower than the linear fitting trend. The
linear regression for MgSiO3 and Mg2SiO4 polymorphs is
expressed in Eqs. (6) and (7), respectively:
MgSiO3 : KT GPað Þ ¼ 162 5ð Þ � q g=cm3� �
� 401 11ð ÞR2 ¼ 0:9901� �
ð6Þ
Mg2SiO4 : KT GPað Þ ¼ 170 7ð Þ � q g=cm3� �
� 421 18ð ÞR2 ¼ 0:9813� �
ð7Þ
According to Fig. 14, hydration decreases both densities
and bulk moduli for wadsleyite and ringwoodite, but still
obeys the linear relationship (Eq. 7). This is consistent with
the conclusion from Mookherjee and Stixrude (2009) that
hydrous Mg2SiO4 polymorphs tend to obey Birch’s law
nearly as well as anhydrous ones, which establishes the
compressional wave velocity Vp is linearly dependent of
the density.
In summary, our experiments support the following:
1. Both hydrous (Z674) and anhydrous (SH1101)
MgSiO3 akimotoite samples were synthesized under
multi-anvil pressure, simulating the high-pressure and
temperature conditions of the lower transition zone.
The FTIR and Raman spectra at ambient condition
indicate the water contents are *550 ppm wt for
sample Z674 and \50 ppm wt for SH1101.
2. High-pressure low-temperature FTIR experiments
were conducted for sample Z674 to derive the isobaric
and isothermal mode Gruneisen parameters
(0–11 GPa, 10–300 K) as well as the intrinsic anhar-
monic mode parameters at 3,300, 3,321, and
3,389 cm-1.
3. Single-crystal X-ray diffraction studies demonstrate
that both the samples Z674 and SH1101 share nearly
identical unit-cell parameters and internal structure,
implying such small water contents have no significant
effect on the akimotoite crystal structure. Both the
current samples have larger \Mg–O[ while smaller
\Si–O[ than Horiuchi et al. (1982), meaning the
Table 6 Isothermal bulk moduli and axial compressibilities (10-4 GPa) for akimotoite
KT (GPa) K0 V0 (A3)a ba bc Pmax (GPa)
Z674 217(3) 4 263.7(2) 11.4(3) 15.9(3) 34.6
Wang et al. (2004) 221(4) 4 264.1(3) 10.3(4) 17.8(6) 17.0
Reynard et al. (1996) 227(7) 4 262.0(3) 10.0(2) 18.2(2) 25.2
Karki and Wentzcovitch (2002)b 201 4.64
Da Silva et al. (1999)c 222 4.5
a Volume values are derived from BM2 EoS fittingsb Calculated from first-principals lattice dynamicsc Adiabatic bulk modulus calculated from ab initio study of the elastic behavior
0 5 10 15 20
3.80
3.85
3.90
3.95
4.00
4.05
4.10 Wang et al. (2004) T0150 Wang et al. (2004) T0133 Reynard et al. (1996) This study
(g/c
m3 )
P (GPa)
ρ
Fig. 10 Variation in density with pressure for OH-akimotoite sample
Z674 (solid squares) compared with other studies
Fig. 11 Confidence ellipsoid plots for K0 versus KT0 from B-M EOS
fittings, with error bars for the point from third-order Birch–
Murnaghan equation of state fitting
Contrib Mineral Petrol (2013) 166:1375–1388 1385
123
current structures are more ordered, due to longer
reaction time during synthetic process.
4. The hydrous sample Z674 has a larger thermal
expansivity and compressibility than the anhydrous
ones (Wang et al. 2004; Ashida et al. 1988; Reynard
et al. 1996), indicating that hydration could soften
MgSiO3 akimotoite, as it softens Mg2SiO4 polymorphs
(e.g., Holl et al. 2008; Ye et al. 2009, 2010, 2012).
5. In akimotoite structure, the c direction has larger
thermal expansivity and compressibility than the
a direction, causing c/a ratio increasing with increased
temperature while decreasing with increased pressure.
On the other hand, hydration would decrease the
anisotropies of axial thermal expansivity and
compressibility.
Acknowledgments This work was supported by US National Sci-
ence Foundation Grants EAR 11-13369 to JRS, EAR-0748707
(CAREER) to SDJ, and EAR-0955647 (CAREER) to WRP. We also
acknowledge the support from Carnegie/DOE Alliance Center
(CDAC) and the David and Lucile Packard Foundation. Synthesis was
carried out at Bayerisches Geoinstitut (BGI), through support of the
BGI Visitors Program. Neal Blair is acknowledged for access to the
FTIR microscope at Northwestern University. GeoSoilEnviroCARS
was supported by the NSF (EAR-0622171), the Department of Energy
(DOE) DE-FG02-94ER14466, and the State of Illinois. Use of the
Advanced Photon Source was supported by the DOE Office of Sci-
ence, Office of Basic Energy Sciences, Under Contract No. DE-
AC02-06CH11357. The use of the U2A beamline at the National
Synchrotron Light Source beamline was supported by COMPRES,
through the NSF Cooperative Agreement EAR 06-49658 and by the
DOE, Office of Science, Office of Basic Energy Sciences, under
Contract No. DE-AC02-98CH10886.
Appendix 1
See Table 7.
0 5 10 15 20 25 30 350.940
0.945
0.950
0.955
0.960
0.965
0.970
0.975
0.980
0.985
0.990
0.995
1.000
1.005
Z674 (dark: a axis; gray: c axis) run T0150 Wang et al. (2004) run T0133 Wang et al. (2004) Reynard et al. (1996) fitting line for current data fitting line for Reynard et al. (1996)
c/c0
X /
X0
P (GPa)
a/a0
Fig. 12 Variation in the normalized lattice parameters with pressure
for OH-akimotoite sample Z674, with a0 = 4.726(2) A,
c0 = 13.567(3) A
0 5 10 15 20 25 30 35
2.80
2.81
2.82
2.83
2.84
2.85
2.86
2.87
2.88
c/a
P (GPa)
Z674run T0150 Wang et al. (2004)run T0133 Wang et al. (2004) Reynard et al. (1996) fitting line for Z674
fitting line for Reynard et. (1996)
Fig. 13 Variation in axial c/a ratio with pressure for akimotoite
3.2 3.4 3.6 3.8 4.0 4.2
80
100
120
140
160
180
200
220
240
260
280
300
320forstertite wadsleyiteringwooditeperovskite akimotoitemajoriteHigh-P clinoenstatiteLow-P clinoenstatiteorthoenstatite
KT
0 (G
Pa)
(g/cm3ρ )
MgSiO3
Mg2SiO
4
Fig. 14 Isothermal bulk modulus KT (K0 fixed at 4) versus density qfor MgSiO3 and Mg2SiO4 polymorphs, with linear regressions (dash
lines), respectively. (enstatite: Hugh-Jones and Angel 1994; low-
P and high-P clinoenstatite: Jacobsen et al. 2010; majorite: Hazen
et al. 1994; akimotoite: this study, Wang et al. 2004; Reynard et al.
1996; perovskite: Ross and Hazen 1990; Yagi et al. 1982; Knittle and
Jeanloz 1987; Mao et al. 1989; forsterite: Couvy et al. 2010;
wadsleyite: Holl et al. 2008; Yusa and Inoue 1997; Ye et al. 2010;
ringwoodite: Hazen 1993; Yusa et al. 2000; Ye et al. 2012)
1386 Contrib Mineral Petrol (2013) 166:1375–1388
123
Appendix 2
See Table 8.
Appendix 3
See Table 9.
References
Angel RJ (2000) Equations of state. In: Hazen RM, Downs RT (eds)
High-pressure and high-temperature crystal chemistry, MSA.
Rev Mineral Geochem 41:35–60
Ashida T, Kume S, Ito E, Navrotsky A (1988) MgSiO3 ilmenite: heat
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Table 7 OH frequencies (cm-1) for akimotoite Z674 at pressures
and temperatures
P (GPa) T (K) OH frequencies (cm-1)
Cooling cycle 1
21.3 300 3259.1
250
23.9 200 3,220.5 3,264.9 3,301.5
25.7 150 3,257.2
27 100 3,237.9 3,266.8
27.8 50 3,226.3 3,264.9
28.2 15 3,228.2 3,264.9
Cooling cycle 2
10.8 300 3,226.3 3,261 3,297.7
12.5 250 3,226.3 3,263 3,295.7
13.8 200 3,230.2 3,268.7 3,307.3
14.7 150 3,234 3,266.8 3,318.9
15.7 100 3,247.5 3,274.5
16.2 50 3,226.3 3,264.9
16.3 15 3,236 3,266.8 3,313.1
Cooling cycle 3
5.44 300 3,245.6 3,276.5 3,326.6
7.2 250 3,237.9 3,274.5 3,317
8.1 200 3,239.8 3,274.5 3,317
8.8 150 3,237.9 3,278.4 3,318.9
9.6 100 3,245.6 3,286.1 3,322.7
10.2 50 3,251.4 3,290 3,324.7
10.2 15 3,257.2 3,291.9 3,330.5
Cooling cycle 4 (different sample fragments)
0 300 3,300.6 3,320.2 3,387.5
0 250 3,300.9 3,320.5 3,390.2
0 200 3,301.1 3,320.3 3,393
0 150 3,301.5 3,320.5 3,396.5
0 100 3,300.6 3,320.65 3,399.4
0 50 3,302.3 3,321.84 3,400
0 15 3,301.6 3,321.4 3,399.4
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153(2) 4.7264(5) 13.542(2) 261.96(5)
203(2) 4.7269(5) 13.546(2) 262.12(5)
253(2) 4.7276(6) 13.552(2) 262.31(6)
300(2) 4.7283(5) 13.560(2) 262.54(6)
349(3) 4.7306(6) 13.568(2) 262.94(6)
395(3) 4.7320(5) 13.575(2) 263.26(5)
Table 9 Unit-cell parameters of akimotoite Z674 as functions of
pressure
P (GPa) a (A) c (A) V (A3)
1.38(2) 4.722(4) 13.559(5) 261.9(3)
2.02(4) 4.717(3) 13.535(4) 260.8(3)
2.81(9) 4.719(2) 13.502(3) 260.4(2)
3.92(9) 4.712(3) 13.474(3) 259.1(2)
5.77(6) 4.694(4) 13.467(5) 257.0(3)
9.01(6) 4.686(3) 13.373(4) 254.3(2)
11.54(8) 4.672(3) 13.321(4) 251.8(2)
13.91(7) 4.656(5) 13.257(6) 248.8(4)
16.00(7) 4.647(4) 13.208(6) 247.1(3)
18.54(5) 4.639(5) 13.156(6) 245.2(4)
20.53(8) 4.633(3) 13.121(4) 243.9(2)
21.84(8) 4.616(3) 13.099(4) 241.7(2)
26.62(5) 4.601(4) 13.001(5) 238.3(3)
29.40(9) 4.590(5) 12.963(6) 236.5(4)
30.88(7) 4.581(5) 12.942(7) 235.2(4)
34.46(7) 4.576(3) 12.839(4) 232.9(2)
Table 8 continued
T (K) a (A) c (A) V (A3)
440(4) 4.7338(7) 13.581(3) 263.56(7)
483(4) 4.7355(7) 13.586(3) 263.86(7)
537(4) 4.7379(8) 13.594(3) 264.27(7)
586(4) 4.7405(6) 13.603(2) 264.73(6)
632(5) 4.7426(6) 13.607(2) 265.05(6)
681(5) 4.7443(6) 13.617(2) 265.42(6)
736(5) 4.7464(6) 13.625(2) 265.83(6)
782(5) 4.7485(5) 13.631(2) 266.18(5)
839(5) 4.7519(5) 13.639(2) 266.71(5)
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