American Mineralogist, Volume 95, pages 1765–1772, 2010
Crystal structure of hydrous wadsleyite with 2.8% H2O and compressibility to 60 GPa
Yu Ye,1,* Joseph R. smYth,2 AnwAR hushuR,3 muRli h. mAnghnAni,3 DAYAnA lonAppAn,3
pRzemYslAw DeRA,4 AnD DAniel J. FRost5
1
Department of Physics, University of Colorado, Boulder, Colorado 80309, U.S.A.
Department of Geological Sciences, University of Colorado, Boulder, Colorado 80309, U.S.A.
3
Hawaii Institute of Geophysics, University of Hawaii, Honolulu, Hawaii 96822, U.S.A.
4
Center for Advanced Radiation Sources, University of Chicago, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A.
5
Bayerisches Geoinstitut, Universität Bayreuth, Bayreuth D95440, Germany
2
AbstRAct
Hydrous wadsleyite (β-Mg2SiO4) with 2.8 wt% water content has been synthesized at 15 GPa and
1250 °C in a multi-anvil press. The unit-cell parameters are: a = 5.6686(8), b = 11.569(1), c = 8.2449(9)
Å, β = 90.14(1)°, and V = 540.7(1) Å3, and the space group is I2/m. The structure was refined in space
groups Imma and I2/m. The room-pressure structure differs from that of anhydrous wadsleyite principally in the increased cation distances around O1, the non-silicate oxygen. The compression of a single
crystal of this wadsleyite was measured up to 61.3(7) GPa at room temperature in a diamond anvil cell
with neon as pressure medium by X-ray diffraction at Sector 13 at the Advanced Photon Source, Argonne
National Laboratory. The experimental pressure range was far beyond the wadsleyite-ringwoodite
phase-transition pressure at 525 km depth (17.5 GPa), while a third-order Birch-Murnaghan equation
of state (EoS) [V0 = 542.7(8) Å3, KT0 = 137(5) GPa, K′ = 4.6(3)] still fits the data well. In comparison,
the second-order fit gives V0 = 542.7(8) Å3, KT = 147(2) GPa. The relation between isothermal bulk
modulus of hydrous wadsleyite KT0 and water content CH2O is: KT0 = 171(1)–12(1) CH2O (up to 2.8 wt%
water). The axial-compressibility βc is larger than both βa and βb, consistent with previous studies and
analogous to the largest coefficient of thermal expansion along the c-axis.
Keywords: Compressibility, hydrous wadsleyite, neon, orthorhombic
intRoDuction
Wadsleyite dominates the mineralogy of the upper transition
zone with pyrolite composition (Anderson 2007; Ringwood
1976) (up to 70 vol%). From a depth of 410 to 525 km downward, wadsleyite transforms to ringwoodite. Smyth (1987,
1994) predicted that wadsleyite can contain up to 3.3 wt% H2O,
because O1, the under-bonded non-silicate oxygen, is a likely
site for hydration. Subsequently, Inoue et al. (1995) synthesized
pure-magnesium hydrous wadsleyite with 3.1 wt% H2O. The
huge amount of water potentially incorporated into these silicate
minerals in the mantle implies that the mass of liquid-water
equivalent stored or recycled through the mantle might amount
to several oceans. Such implications are important for the understanding of the evolution of crust and mantle and changes
of ocean levels in the geological past (Drake and Righter 2002;
Bercovici and Karato 2003).
Hydrogen in the wadsleyite structure has significant effects
on the physical properties such as thermal expansion (Ye et al.
2009; Inoue et al. 1995) and compressibility (Holl et al. 2008).
Inoue et al. (1995) studied the thermal expansion of hydrous
wadsleyite (Mg2SiO4) with as much as 2.6 wt% H2O, by powder
X-ray diffraction up to 973 K at ambient pressure. Yusa and
Inoue (1997) reported the compressibility of hydrous wadsleyite
(Mg2SiO4) with 2.5 wt% H2O, by powder X-ray diffraction to 8.5
* E-mail: yey@colorado.edu
0003-004X/10/1112–1765$05.00/DOI: 10.2138/am.2010.3533
GPa. Hazen et al. (2000) and Holl et al. (2008) have also reported
KT0 up to 10 GPa. We have synthesized hydrous wadsleyite, with
about 2.8 wt% H2O, and refined its crystal structure at ambient
conditions to obtain information on the hydration mechanism.
We also measured the unit-cell parameters up to 61.3 GPa by
single-crystal X-ray diffraction in a diamond anvil cell using
neon as pressure medium at Sector 13 of the Advanced Photon
Source (GSECARS).
Anhydrous wadsleyite crystallizes in the orthorhombic space
group Imma. Hydration causes a volume expansion of the unit
cell together with an apparent decrease in symmetry to monoclinic space group I2/m. Smyth et al. (1997) reported an ironbearing wadsleyite with 2.3 wt% H2O and β = 90.4°; Jacobsen
et al. (2005) observed β up to 90.125(3)° for a sample with 1.06
wt% H2O; Holl et al. (2008) described the sample with 1.66 wt%
H2O and β = 90.090(7)°. In this study, the monoclinic structure
was further studied with respect to even higher water content.
expeRimentAl methoDs AnD Results
Synthesis
Crystals of hydrous pure Mg wadsleyite for this study were synthesized at
15 GPa and 1250 °C using a 2 mm welded Pt capsule in an 18 mm sintered MgO
octahedron assembly in the 5000 ton multi-anvil press at Bayerisches Geoinstitut.
Corner truncations on the 54 mm WC cubes were 8 mm and the heating duration
time was 210 min. Starting material was synthetic anhydrous forsterite plus brucite
and silica (quartz) to give a composition with 5.5 wt% H2O. Single crystals up to 250
µm were obtained. No phases other than wadsleyite were noted in the capsule.
1765
1766
YE ET AL.: STRUCTURE AND COMPRESSION OF HYDROUS WADSLEYITE
Unit-cell parameters
A single crystal about 120 × 100 × 70 µm3 in size was selected for structure
and unit-cell refinement. Measurements for unit-cell refinements were carried out
on a Bruker P4 four-circle diffractometer with a dual scintillation point detector
system using an 18 kW rotating Mo-anode X-ray generator operated at 50 kV and
250 mA. MoKα1-MoKα2 mixed characteristic wavelength was used, and a single
crystal of anhydrous forsterite with spherical shape was used to calibrate Kα(mix)
= 0.71063 Å. Kα(mix) was used for cell refinements. The two-theta range was
from 12 to 30°. After centering of all reflections, a least-squares fitting was done
to calculate the cell parameters with uncertainties. Ninety reflections from the
single crystal were centered to refine cell parameters with both a monoclinic and
orthorhombic model. The refined monoclinic cell is a = 5.6686(8), b = 11.569(1),
c = 8.2449(9) Å, β = 90.14(1)°, and V = 540.7(1) Å3; and the orthorhombic cell is
a = 5.662(1), b = 11.577(2), c = 8.242(2) Å, and V = 540.3(2) Å3.
Crystal structure
Intensity data were collected using a Bruker APEX II CCD detector mounted
on a P4 diffractometer. Refinements of atom positions and anisotropic displacement
parameters were done using the program 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).
XtalDraw (Downs et al. 1993) was used to calculate the bond lengths and polyhedral
coordination parameters. To refine the structure, 6308 diffracted intensities (1179
unique) were measured with 2θ up to 88°. The structure was refined in the space
groups Imma (orthorhombic) and I2/m (monoclinic). The orthorhombic structure
refinement converged to Rint = 0.0339 and R1 = 0.0361 for 984 unique reflections
with Fo > 4σ, and 0.0421 for all 1136 unique reflections. The monoclinic structure
refinement converged to Rint = 0.0305; and R1 = 0.0360 for 1634 unique reflections
with Fo > 4σ, and 0.0447 for all 1975 data. The refined atomic positions and site
occupancy factors are listed in Table 1 for both orthorhombic and monoclinic
structure refinements. CIFs are on deposit1. When the space group was changed
from Imma to I2/m, the origin was shifted to (¼, ¼, ¼), and the x coordinates of
Mg2, Si, O1, O2, and O3 were refined, instead of being fixed to 0. The Mg3 site
splits into two non-equivalent sites: Mg3A (¼, 0.121, ¼) and Mg3B (¾, 0.379, ¼).
Correspondingly, O4 also splits into two non-equivalent sites: O4A that is bonded
to Mg3A, and O4B that is bonded to Mg3B. After adding H atoms, we found most
of the cation vacancies on the Mg3 sites. This is consistent with the refinements
of Holl et al. (2008) and Deon et al. (2010). These vacancies accounted for nearly
20% of the Mg3 sites, as indicated in Table 1, whereas nearly full occupancies
were observed on Mg1, Mg2, and Si. All atoms were refined with anisotropic
displacement parameters (Table 2). There were no significant differences between
the two sets of displacement parameters. The bond lengths, polyhedral parameters,
and edge lengths of cation polyhedra are listed in Table 3. Selected bond distances
from this study (for Imma structure refinement) are compared to those for sample
WS3056 with 0.005 wt% H2O from Holl et al. (2008) in Table 4.
High-pressure XRD
High-pressure XRD experiments were conducted at beamline 13-BM-D, at
GSECARS, Advanced Photon Source (APS), Argonne National Laboratory. The
1
Deposit item AM-10-055, CIFs. Deposit items are available two ways: For a
paper copy contact the Business Office of the Mineralogical Society of America
(see inside front cover of recent issue) for price information. For an electronic
copy visit the MSA web site at http://www.minsocam.org, go to the American
Mineralogist Contents, find the table of contents for the specific volume/issue
wanted, and then click on the deposit link there.
TABLE 1.
Atom
Mg1
Mg2
Mg3
Si
O1
O2
O3
O4
size of the single crystal for the high-pressure measurement was about 45 × 35
× 20 µm3. We used a symmetric piston-cylinder type diamond anvil cell (DAC),
with 300 µm culets. The diamond cell was fitted with cubic boron nitride (cBN)
seat on the downstream side, and hexagonal tungsten carbide (hWC) seat on the
upstream side. A rhenium gasket, pre-indented to initial thickness of 30 µm, with
a 165 µm diameter hole was used for the experiment. The DAC was loaded with
neon as pressure medium using the COMPRES/GSECARS gas-loading system
(Rivers et al. 2008). The pressure inside the cell was about 1.5 GPa after closing,
and the gasket-hole diameter decreased by about 30%. Throughout the experiment,
we used monochromatic synchrotron radiation with wavelength: λ = 0.3344 Å. An
annealed ruby sphere placed in the sample chamber along with the sample served
as the pressure marker.
For the high-pressure measurement, the diffractometer is a simple highprecision 1-axis rotation stage, and the detector was a MAR345 image plate,
working in the low-resolution mode with a pixel size of 0.150 mm. The singlecrystal diffraction data collection involved measuring three separate ω-oscillation
images (“center,” “left,” and “right”) at each pressure point: –13.5 to 15.5° with
5 min for “center” image, –30 to –19° with 2 min for “left” image, and 19 to 30°
with 2 min for “right” image. The gaps in the rotation between these image ranges
were omitted because of strong powder diffraction from hWC (on the upstream
side) caused by the only partially absorbed transmitted X-ray beam. To obtain the
orientation matrix at the initial pressure of 1.55 GPa, an ω step scan was performed
in the range from –13.5 to 15.5°, with the step size of 1° and exposure time of 1
TABLE 2.
Anisotropic displacement parameters
Cation Param.
Imma
I2/m
Anion Param.
Imma
I2/m
Mg1
U11
0.0200(3) 0.0201(3) O1
U11
0.0086(4) 0.0201(3)
U22
0.0081(3) 0.0080(2)
U22
0.0129(5) 0.0080(2)
U33
0.0184(3) 0.0190(3)
U33
0.0122(5) 0.0190(3)
U23
0.0033(2) 0.0035(2)
U23
0
0.0035(2)
U13
0
0.0017(2)
U13
0
0.0017(2)
U12
0
0.0058(2)
U12
0
0.0157(2)
Ueq
0.0155(2) 0.0157(2)
Ueq
0.0112(2) 0.0113(2
Mg2
U11
0.0124(2) 0.0124(2) O2
U11
0.0086(4) 0.0086(3)
U22
0.0063(2) 0.0061(2)
U22
0.0129(5) 0.0130(4)
U33
0.0083(2) 0.0083(2)
U33
0.0122(5) 0.0124(4)
U23
0
0
U23
0
0
U13
0
–0.000(2)
U13
0
0.0002(3)
U12
0
0
U12
0
0
Ueq
0.009(1)
0.009(1)
Ueq
0.0095(2) 0.0096(2)
Mg3A U11
0.0107(2) 0.0110(3) O3
U11
0.0117(3) 0.0116(3)
U22
0.0142(3) 0.0152(4)
U22
0.0113(4) 0.0113(3)
U33
0.0092(3) 0.0099(3)
U33
0.0087(3) 0.0090(3)
U23
0
0
U23
0.0009(2) 0.0010(2)
U13 –0.0008(2) –0.0007(2)
U13
0
0.0000(2)
U12
0
0
U12
0
0.0001(2)
Ueq
0.0114(2) 0.0120(2)
Ueq
0.0106(2) 0.0107(2)
Mg3B
U11
–
0.0106(3) O4A
U11
0.0097(2) 0.0096(2)
U22
–
0.0132(3)
U22
0.0080(3) 0.0082(3)
U33
–
0.0084(3)
U33
0.0101(3) 0.0103(3)
U23
–
0
U23
0.0002(2) 0.0004(2)
U13
–
0.0004(2)
U13
0.0004(2) 0.0004(2)
U12
–
0
U12
0.0003(2) 0.0004(2)
Ueq
–
0.0107(2)
Ueq
0.0093(2) 0.0094(2)
Si
U11
0.0091(1) 0.0092(1) O4B
U11
–
0.0096(2)
U22
0.0076(2) 0.0075(1)
U22
–
0.0079(3)
U33
0.0076(2) 0.0076(1)
U33
–
0.0099(3)
U23 –0.00025(9) –0.00024(7)
U23
–
–0.0003(2)
U13
0
0.00003(8)
U13
–
–0.0004(2)
U12
0
0.00002(7)
U12
–
0.0002(2)
Ueq
0.0081(1) 0.00811(9)
Ueq
–
0.0092(2)
Atomic position coordinates and occupancy factors
x/a
0
0
0.25
Imma
y/b
0
0.25
0.12057(5)
z/c
0
0.97086(8)
0.25
Occupancy
0.984(4)
0.994(4)
0.804(7)
0
0
0
0
0.2602(1)
0.12120(3)
0.25
0.25
0.98671(8)
0.12408(4)
0.61531(4)
0.2260(2)
0.7159(2)
0.2563(1)
0.99517(8)
0.980(4)
1.0
1.0
1.0
1.0
Atom
Mg1
Mg2
Mg3A
Mg3B
Si
O1
O2
O3
O4A
O4B
x/a
0
0.0004(1)
0.25
0.75
0.00003(5)
–0.0000(2)
–0.0004(2)
–0.0002(1)
0.2607(1)
0.7402(1)
I2/m
y/b
0
0.25
0.12052(6)
0.37937(5)
0.12119(2)
0.25
0.25
0.98671(7)
0.12416(6)
0.37597(6)
z/c
0
0.97083(7)
0.25
0.25
0.61532(3)
0.2261(1)
0.7158(1)
0.25640(8)
0.99527(9)
0.99526(9)
Occupancy
0.984(3)
0.992(3)
0.805(4)
0.803(3)
0.978(4)
1.0
1.0
1.0
1.0
1.0
YE ET AL.: STRUCTURE AND COMPRESSION OF HYDROUS WADSLEYITE
TABLE 3.
Bond lengths (Å) and polyhedral parameters (Å) of cation polyhedra
Imma
O3 ×2
O4A ×4
O4B
O4A(1)
O4A(2)
O4B(1)
O4B(2)
O4B(1)
O4B(2)
Avg. bond
Avg. edge
Poly. V (Å3)
O3
O4A
I2/m
Mg1
2.118(1)
2.058(1)
–
3.055(2)
2.848(2)
–
–
2.874(2)
2.947(2)
2.078(1)
2.939(2)
11.898(5)
2.120(1)
2.061(1)
2.057(1)
3.060(2)
2.849(2)
3.051(2)
2.852(2)
2.872(2)
2.951(2)
2.079(2)
2.938(2)
11.916(5)
2.103(1)
2.101(1)
2.081(2)
–
2.813(2)
–
3.097(2)
–
2.945(2)
2.916(2)
2.089(1)
2.947(2)
12.040(5)
2.104(1)
2.102(1)
2.082(2)
2.084(2)
2.818(2)
2.811(2)
3.099(2)
3.100(2)
2.951(2)
2.915(2)
2.090(1)
2.949(2)
12.054(5)
2.071(1)
2.010(2)
2.102(2)
2.859(2)
3.058(2)
2.813(2)
3.041(2)
2.833(2)
3.055(2)
2.927(2)
2.091(2)
2.957(2)
12.1003(6)
2.071(1)
2.100(2)
2.102(2)
2.861(2)
3.056(2)
2.818(2)
3.037(2)
2.838(2)
3.060(2)
2.924(2)
2.091(2)
2.958(2)
12.1103(6)
O1
O3
O1 ×2
O3 ×2
O4B ×2
O1
O3
O4B(1)
O4B(2)
O3
O4B(1)
O4B(2)
Avg. bond
Avg. edge
Poly. V (Å3)
Mg2
O1
O2
O4A ×4
O4B
O4A
O4B
O4A
O4B
O4B(1)
O4B(2)
Avg. bond
Avg. edge
Poly. V (Å3)
O1
O2
O4A
O1 ×2
O3 ×2
O4A ×2
O1
O3
O4A(1)
O4A(2)
O3
O4A(1)
O4A(2)
Avg. bond
Avg. edge
Poly. V (Å3)
O1
O3
TABLE 4.
1767
Imma
I2/m
–
–
–
–
–
–
–
–
–
–
–
–
–
2.071(1)
2.010(2)
2.101(2)
2.862(2)
3.056(2)
2.811(2)
3.045(2)
2.834(2)
3.051(2)
2.929(2)
2.091(2)
2.957(2)
12.1002(6)
1.706(1)
1.637(1)
1.635(1)
–
2.750(1)
2.645(2)
–
2.714(2)
–
2.716(2)
1.653(1)
2.697(2)
2.3088(4)
1.705(1)
1.636(1)
1.637(1)
1.637(1)
2.748(1)
2.647(2)
2.644(2)
2.716(2)
2.713(2)
2.718(2)
1.654(1)
2.698(2)
2.3102(4)
Mg3B
Si
O2
O3
O4A
02
O3
O4A ×2
O4B
O3
O4A
O4B
O4A
O4B
O4B
Avg. bond
Avg. edge
Poly. V (Å3)
Mg3A
Comparison of interatomic distances in wadsleyites with
0.005 and 2.8 wt% H2O
CH2O (wt% H2O)
0.005
2.8 (for space group Imma)
Mg1-O3(2) (Å)
Mg1-O4(4) (Å)
Avg. bond (Å)
Poly. V (Å3)
Mg2-O1(1) (Å)
Mg2-O2(1) (Å)
Mg2-O4(4) (Å)
Avg. bond (Å)
Poly. V (Å3)
Mg3-O1(2) (Å)
Mg3-O3(2) (Å)
Mg3-O4(2) (Å)
Avg. bond (Å)
Poly. V (Å3)
2.112(2)
2.050(1)
2.071(2)
11.756(9)
2.029(4)
2.101(4)
2.092(1)
2.082(2)
11.96(2)
2.018(1)
2.124(2)
2.131(2)
2.091(4)
12.072(5)
2.118(1)
2.058(1)
2.078(1)
11.898(5)
2.103(1)
2.101(1)
2.081(2)
2.089(1)
12.040(5)
2.071(1)
2.010(2)
2.102(2)
2.091(2)
12.1003(6)
min per image. The resulting 29 images were used to calculate ω angles for each
reflection and the orientation matrix, as well as unit-cell parameters. This orientation
matrix was then used as a first approximation to index peaks in images collected
at subsequent pressures.
Pressure calibration
Ruby R1 fluorescence line is widely used as pressure scale for high-pressure
experiments in diamond anvil cells, with λ0 = 694.24 nm for ambient pressure at
298 K (Silvera et al. 2007). Mao et al. (1986) calibrated the relationship between
pressure and wavelength shift (∆λ) as in Equation 1 for “quasi-hydrostatic” argon
to 80 GPa:
PAr = (A/B){[1 + (∆λ/λ)]B – 1} (GPa)
(1)
where A = 1904 GPa and B = 7.665.
According to Dewaele et al. (2008), neon is a good quasi-hydrostatic pressure
medium up to at least 80 GPa at room temperature, and the equation of state was
reported in the pressure range up to 208 GPa, in which the crystal structure remained
face-center-cubic. The diffraction patterns at 6, 12, 29, and 61 GPa are shown in
Figures 1a–1d, created with software package GSE-ADA (Dera 2007a). Neon reflections were identified as short streaks, compared with the sharp reflection spots from
the single crystal of hydrous wadsleyite and diamond. For each step above 12 GPa,
neon reflections of (111), (200), and (220) could be observed on the 2D diffraction
patterns, as indicated in Figures 1a–1d. Hence, for each step above 12 GPa, 6 to 8
reflection “streaks” from the diffraction patterns were used to calculate the pressure
with statistical uncertainties, using the PVT equations of states from Fei et al. (2007)
and Dorogokupets and Dewaele (2007). The pressure values read from the spectrometer and calculated from neon diffraction patterns are listed in Table 5.
In the following discussion and calculation, we have used the pressure values
from neon diffraction patterns for the steps above 12 GPa. For the measurements
below 12 GPa, the pressure values were derived from a spectrometer program that
measured R1 peak-shift and calibrated pressures on the basis of Equation 1, and we
assume that the given values are of sufficient accuracy in the lower pressure range.
Generally, the pressure values from neon diffraction patterns were slightly smaller
than those from the ruby spectra. As pressure increased, the ruby moved to the edge
of the gasket hole that may have caused the ruby to record slightly higher values
than the crystal, due to the non-hydrostatic pressure from the edge of the gasket
hole. In this study, we did not calibrate the ruby pressure scale in our neon pressure
medium, because the uncertainties for pressures derived from neon diffraction
patterns are larger than those from MgO volumes (Jacobsen et al. 2008), but still
good enough to derive a reasonable value of KT0 as discussed below.
1768
YE ET AL.: STRUCTURE AND COMPRESSION OF HYDROUS WADSLEYITE
FiguRe 1. (a–d) The single-crystal diffraction patterns of “left,” “center,” and “right” images at the pressures of 6, 12, 29, and 61 GPa,
respectively. The diffraction patterns from hydrous wadsleyite, which are used to calculate the unit-cell parameters, are marked with squares, and
most of the unmarked strong relection spots are from diamond. The neon relection streaks appeared at 12 GPa, and became more apparent at 29
and 61 GPa. In b, the streaks on the inner rings are (111) streaks, the ones on the outer rings are (220). (200) streaks appeared in c and d between
the rings for (111) and (220), although not as strong as (111) and (220) streaks.
YE ET AL.: STRUCTURE AND COMPRESSION OF HYDROUS WADSLEYITE
TABLE 5.
1769
X-ray diffraction data for hydrous wadsleyite in neon pressure medium
Pspect†
Pneon*
a
b
c
V
(GPa)
(GPa)
(Å)
(Å)
(Å)
(Å3)
1.6(1)
–
5.656(6)
11.540(7)
8.221(4)
536.6(7)
2.9(2)
–
5.638(6)
11.516(7)
8.186(4)
531.5(7)
6.0(2)
–
5.612(7)
11.443(7)
8.131(4)
522.2(7)
12.1(2)
11.8(2)
5.544(8)
11.319(8)
8.032(5)
504.1(8)
14.6(2)
14.8(4)
5.522(8)
11.282(9)
7.985(5)
497.4(9)
17.5(4)
17.1(2)
5.51(1)
11.23(1)
7.940(7)
491(1)
20.2(3)
19.6(2)
5.50(1)
11.18(1)
7.904(7)
486(1)
23.0(4)
22.5(4)
5.46(1)
11.16(1)
7.865(7)
480(1)
25.7(6)
25.0(5)
5.439(7)
11.096(8)
7.852(5)
473.9(7)
29.5(4)
28.9(5)
5.413(8)
11.050(8)
7.804(5)
466.8(9)
32.7(3)
31.7(7)
5.391(8)
11.012(9)
7.775(5)
461.5(8)
36.4(5)
35.5(5)
5.379(7)
10.967(7)
7.734(5)
456.2(7)
40.5(2)
39.6(5)
5.351(9)
10.940(9)
7.703(6)
451.0(9)
45.6(4)
45.0(4)
5.32(1)
10.89(1)
7.639(8)
443(1)
51.7(2)
50.8(4)
5.28(1)
10.82(1)
7.600(7)
434(1)
55.6(3)
55.1(5)
5.26(1)
10.78(1)
7.563(6)
429(1)
61.2(2)
61.3(7)
5.24(1)
10.73(1)
7.515(7)
422(1)
Note: The pressure values used for further calculations are marked bold.
* Pneon values were determined from the equation of state of neon (Fei et al. 2007;
Dorogokupets and Dewaele 2007).
† Pspect values were read from spectrometer, using the ruby fluorescence line
calibrated by Mao et al. (1986). The uncertainty was determined by the difference
between the values read before and after each measurement.
For each pressure, more than 50 reflections were used to refine the unit-cell
parameters by the software packages of GSE-ADA (Dera 2007a) and RSV (Dera
2007b). The cell parameters, listed in Table 5, were calculated as orthorhombic unit
cell. Because of the large uncertainties, we were unable to resolve a β-angle different
from 90°. The program EoSFit (Angel 2001) was used to fit the pressure-volume
data to the second- and third-order Birch-Murnaghan equations of state (B-M EOS).
Volume vs. pressure are plotted in Figure 2, Birch normalized pressure (FE) vs.
Euler finite strain (fE) are plotted in Figure 3, and a, b, and c axes compressions
are plotted in Figures 4a–4c.
Discussion
in Figure 1 in Holl et al. (2008). For an increase of 1 wt% of
H2O, the a and c axes decrease by 0.20 and 0.05%, respectively;
while the b axis and V increase by 0.40 and 0.16%, respectively.
If we assume that vacancies only occur at Mg3 sites in the orthorhombic structure of hydrous wadsleyite (Deon et al. 2010), the
density of the current sample should be 3.344(1) g/cm3, which
is also consistent with Figure 2 in Holl et al. (2008).
Crystal structure
Water content and unit cell
Jacobsen et al. (2005) determined a relation between unit cell
and water content for waddsleyite as:
b/a = 2.008(1) + 1.25(3) × 10–6 CH2O (ppm wt.).
FiguRe 2. Plot of volume vs. pressure data with the itting curve
for the third-order B-M EOS. The calculated V0, K0, and K′ are listed.
The horizontal and vertical error bars represent pressure and volume
uncertainties, respectively, if they are larger than the symbol sizes. The
zero-pressure volume from our lab is marked as an open square symbol.
(2)
The water contents of samples WZ304, WH833, and WZ292
in that study were derived by the average of two values derived
by the calibrations of Paterson (1982) and Libowitzky and
Rossman (1997), respectively. However, Deon et al. (2010)
published a new absorption coefficient for hydrous wadsleyite,
which would give water contents about 20 wt% higher than those
from Libowitzky and Rossman (1997). Calibration of the water
contents of minerals from FTIR spectra is still an open problem
with no absolute values yet, and each mineral seems to require its
own calibration. Since Equation 2 is relatively well established
and has been used in several studies, we use it here to calculate
the water content of our sample for consistency with previous
studies. We estimate an uncertainty of as much as 20% to cover
any possible discrepancy caused by different calibration methods.
The b/a ratio is 2.041 (2.63 wt% H2O) for monoclinic structure,
while 2.445 (2.92 wt% H2O) for orthorhombic structure. Hence,
we assume the water content to be the average of 2.8 wt% H2O,
with an uncertainty of 0.5 wt%.
The unit-cell parameters for current sample are consistent
with the relationships of unit-cell parameters vs. water content
Selected interatomic distances from Imma structure refinements for the two samples are compared in Table 4. Relative to
anhydrous wadsleyite, the Mg-O distances around O1 expand,
whereas those around the other O atoms contract. In anhydrous
wadsleyite, the O1 position is bonded only to five Mg atoms (four
Mg3 and one Mg2) and thus is strongly under-bonded (Smyth
1987). Protonation of O1 relieves this imbalance, lengthens the
bonds around O1, and permits the longer bonds around the other
O atoms to contract. For the samples from Holl et al. (2008)
and this study, the O1-O1, O1-O4, and O3-O3 edge lengths
on M3 and O4-O4 edge length shared by M1 and M2 show a
systematic decrease as water content increases. By extending the
water content to 2.8 wt%, it further supports the claim by Smyth
(1987) that O1, the non-silicate oxygen, is a preferred site for
H in the structure, since H+ cations have an effect of mitigating
the repulsion between neighboring O2– anions. The Mg1 and
Si polyhedra from this study are about 0.4 and 0.3% larger,
respectively, than those of SS0401, while the volumes of Mg2,
Mg3A, and Mg3B polyhedra do not differ much. On the other
hand, Deon et al. (2010) suggested that most protonation occurs
along O1-O4 and O3-O4 edges of a vacant Mg3 octahedron, and
the protonation is random with either two O1, two O3, or one
O1 and one O3 in the vacant Mg3 octahedron. Slight splits for
some reflection spots were observed on the diffraction patterns
when intensity data were collected on the CCD detector, which
supports the signs of strain due to polysynthetic twinning in the
1770
YE ET AL.: STRUCTURE AND COMPRESSION OF HYDROUS WADSLEYITE
FiguRe 3. Birch normalized pressure (FE) vs. Euler inite strain (fE).
The linear regressions gives the bulk modulus as y-intercept, and the
positive slope shows that K′ is larger than 4.
orthorhombic structure, noted by Holl et al. (2008).
In the structure refinement, several atoms are seen to deviate
significantly from their equivalent positions in the orthorhombic
structure. This split can be explained by the slight deviation of
Mg2-O1 direction from the original direction, which had been
perpendicular to the a-b plane. This could be induced by the protonation, since O1 is a preferable site for H atoms. In the O1 site
tetrahedron, the observed distance from Mg2 to Mg3A and Mg3B
are 3.087(2) and 3.093(2) Å, and the angles of Mg2-O1-Mg3A
and Mg2-O1-Mg3B are 95.33(8) and 95.61(8)°, respectively.
These differences are small but significant. Nevertheless, these
distances and angles are identical for each Mg3 position in the
orthorhombic structure. Hence, the Mg3A sites [(¼, 0.12, ¼) and
(¼, 0.38, ¼)] were split from the Mg3B sites [(–¼, 0.12, ¼) and
(–¼, 0.38, ¼)] along the direction of a axis, by the symmetry
change, causing β to deviate slightly from 90°. We therefore
refined the x coordinates in Table 1, to determine the splitting
of the atom positions in the monoclinic structure.
Compression to 61.3 GPa
In a pyrolite composition model (Ringwood 1976; Anderson
2007), wadsleyite transforms to ringwoodite at about 525 km
where T = 1790 K and P = 17.5 GPa. At 525 km depth, the
density increases from 3.70 to 3.77 g/cm3, and the adiabatic bulk
modulus KS increases from 231.9 to 249.5 GPa, whereas the bulk
sound velocity VΦ = (KS/ρ)1/2 increases from 7.91 to 8.13 km/s
(Yu et al. 2008). For better understanding of the compression
mechanism of hydrous wadsleyite, we have investigated the
room-temperature stability of hydrous wadsleyite up to 61.3
GPa, which is about three times higher than the pressure of the
wadsleyite-ringwoodite phase transition at temperatures around
1800 K (Inoue et al. 2006; Kuroda et al. 2000; Suzuki et al. 2000).
At room temperature, no phase change was observed because
the kinetic energy is not high enough to overcome the barrier
for the phase transition.
The calculated ambient condition unit-cell parameters from
the third-order Birch-Murnaghan EoS are: a = 5.675(6), b =
11.592(8), c = 8.258(5) Å, and V = 542.7(8) Å3. These values are
FiguRe 4. (a–c) The a-, b-, and c-axes compressions with itting curves
for third-order B-M EOS. The horizontal (pressure) and vertical (axes
length) error bars are represented if they are larger than the symbol sizes.
The zero-pressure axial lengths are marked as open square symbols.
larger than the ones measured in our lab, as indicated in Figures 2
and 4. This can be attributed to a systematic difference between
the equipment in our lab and that at APS. However, the derived
ambient condition b/a ratio is 2.043(3), which is in good agreement with the ratio value measured in our lab.
The best-fit parameters (V0, KT0, and K′) from Birch-Murnaghan (B-M) EoS for the present study are listed in Table 6
together with other reported wadsleyite samples, and the ambient isothermal bulk modulus (KT0) vs. water content is plotted
in Figure 5 for the third-order B-M EOS. As can be seen, KT0
decreases as water content increases. The linear fitting gives the
relation as (R2 = 0.9498):
KT0 (GPa) = 171(1) – 12(1) CH2O (wt%).
(3)
YE ET AL.: STRUCTURE AND COMPRESSION OF HYDROUS WADSLEYITE
TABLE 6.
H2O
wt%
0
0
0
0.005
FiguRe 5. Plot of ambient KT0 vs. water content with linear itting.
The data are from Table 6 by the third-order B-M EOS [(0, 172) is from
Hazen et al. (2000), (2.8, 137) is from the current study, and other data
are from Holl et al. (2008)]. The errors for KT0 and water content are
shown as vertical and horizontal error bars, respectively.
Isothermal bulk moduli KT were generally derived from
measuring high-pressure unit-cell volumes in diamond anvil
cells by X-ray diffraction, while adiabatic moduli KS were determined by elasticity measurements. The relationship between
KS and KT is
KT = KS/(1 + αγT)
(4)
where α is thermal expansion coefficient (Inoue et al. 2004; Ye
et al. 2009), γ is Grüneisen parameter (Chopelas 1991), and T is
temperature in Kelvin.
Mean isothermal axial compressibility values of βa, βb, and
βc from this and previous studies are listed in Table 7. For the
sample in the current study, the mean axial compressibility values
calculated in the pressure range up to 14.8 GPa are larger than
those in pressure range up to 6.13 GPa, because the isothermal
axial β values will decrease when pressure increases. Nevertheless, the general trend shown in Table 7 indicates that βa, βb,
and βc all increase with increasing water content. Based on a
single-crystal study, Ye et al. (2009) also reported that hydrous
wadsleyite has larger αa, αb, and αc than anhydrous one. Protonating the non-silicate O1 site will decrease bond strength around
the vacant octahedron, resulting in a larger compressibility and
thermal expansion (Ye et al. 2009). On the other hand, for each
sample in Table 6, βc is generally about 30 to 40% greater than
βa and βb, and Zha et al. (1997) and Mao (2008a) reported that
the longitudinal modulus C33 is smaller than C11 and C22 for their
wadsleyite samples. In addition, Suzuki et al. (1980), Inoue et
al. (2004), and Ye et al. (2009) each reported that the thermal
expansion along the c-axis was greater than those parallel to a
and b for anhydrous and hydrous samples. Evidence from compressibility and thermal expansion indicate that wadsleyite has
the most flexibility in c-axis.
1771
Parameters for B-M equation of state, listed in the order of
increasing water content
KT0
K′
Reference
(GPa)
172(3)
6.3(7)
Hazen et al. (2000)
170(2)*
4.3(2)
Zha et al. (1997)
172(2)*
4.2(1)
Li et al. (1998)†
538.2(1)
173(5)
4(1)
Holl et al. (2008)
538.2(1)
174(1)
4.0
0.38
9.01
539.2(1)
161(4)
5(1)
Holl et al. (2008)
539.1(2)
165(1)
4.0
Mao et al. (2008b)
0.84
12
160.3(7)* 4.1(1)
1.18
8.56
539.8(1)
158(4)
4.2(9)
Holl et al. (2008)
539.8(1)
159.2(8)
4.0
1.66
9.58
540.6(2)
154(4)
5(1)
Holl et al. (2008)
540.6(1)
160(1)
4
2.5
8.5
155(2)
4.3
Yusa and Inoue (1997)
2.8
61.3
542.6(8)
137(5)
4.5(3)
This study
541.6(6)
147(2)
4.0
Note: V0 values are given if they were refined in the references, and some of K′ are
listed without uncertainties if they were fixed, instead of being refined.
* Adiabatic bulk modulus.
† The sample is assumed to be anhydrous because no water content was reported, the formula is (Mg0.88Fe0.12)2SiO4.
TABLE 7.
H2O
wt%
0
0.005
0.38
1.18
1.64
2.5
2.8
2.8
Pmax
(GPa)
10.12
14.2
9.6
7.3
V0
(Å3)
539.26(9)
Mean isothermal axial compressibilities of wadsleyite for
some of the samples listed in Table 6, which were measured
by static compression
βa
(10–3 GPa–1)
1.45(2)
1.55(4)
1.66(4)
1.64(5)
1.48(9)
1.67(3)
1.86(5)
1.32(5)
βb
(10–3 GPa–1)
1.46(3)
1.57(3)
1.60(3)
1.78(3)
1.85(11)
1.87(3)
1.83(8)
1.26(5)
βc
(10–3 GPa–1)
2.00(4)
2.22(2)
2.21(3)
2.30(3)
2.21(3)
2.32(4)
2.23(7)
1.52(6)
Reference
Hazen et al. (2000)
Holl et al. (2008)
Holl et al. (2008)
Holl et al. (2008)
Holl et al. (2008)
Yusa and Inoue (1997)
This study (to 14.8 GPa)
This study (to 61.3 GPa)
AcknowleDgments
This work was supported by U.S. National Science Foundation grant EAR 0711165 (to J.R.S.) and EAR 05-38884 (to M.H.M.). Use of the IMCA-CAT beamline
13-BM-D at Advanced Photon Source was supported by the U.S. Department of
Energy, Office of Science, Office of Basic Energy Sciences, under contract no.
W-31-109-Eng-38.
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Manuscript received February 17, 2010
Manuscript accepted July 2, 2010
Manuscript handled by lars ehM