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Effects of hydration on the structure and compressibility of wadsleyite, β-(Mg₂SiO₄)

¹ Department of Geological Sciences, University of Colorado, Boulder, Colorado 80309, U.S.A.
² Department of Earth and Planetary Sciences, Northwestern University, Evanston, Illinois 60208, U.S.A.
³ Bayerisches Geoinstitut, Universität Bayreuth, Bayreuth 95440, Germany

	ABSTRACT

Top Abstract Introduction Experimental methods Results and discussion Acknowledgments References cited

 
A suite of pure magnesian wadsleyite (β-Mg₂SiO₄) samples containing 0.005, 0.38, 1.18, and 1.66 wt% H₂O was studied by single-crystal X-ray diffraction to determine the effects of hydration on cation ordering and crystal symmetry. Separate compressibility experiments were carried out to 9.6 GPa to determine the effects of hydration on isothermal equations of state. Crystal-structure refinements at ambient conditions show cation vacancies order onto the M3 site. The most hydrous sample (1.6 wt% H₂O) displayed monoclinic symmetry with β = 90.090(7)°, whereas the samples with lower content were statistically orthorhombic. The density of wadsleyite decreases with increasing water content at STP according to the empirical relation, = 3.470(2) – 0.046(2) C_H2O g/cm³ (with C_H2O in wt% H₂O). Bulk moduli and pressure derivatives of wadsleyite are K_T0 = 173(5) GPa, K₀' = 4.1(15) for 0.005 wt% H₂O; K_T0 = 161(4) GPa, K₀' = 5.4(11) for 0.38 wt% H₂O; K_T0 = 158(4) GPa, K₀' = 4.2(9) for 1.18 wt% H₂O; and K_T0 = 154(4) GPa, K₀' = 4.9(11) for 1.66 wt% H₂O. Variation of the bulk modulus of wadsleyite with water content is non-linear, which may be attributable to softening of the structure by ordering of vacancies onto two non-equivalent M3 sites (M3a and M3b) and an accompanying dilution of orthorhombic symmetry.

Key Words: Wadsleyite • bulk modulus • equation of state • nominally anhydrous minerals • mantle Transition Zone

	INTRODUCTION

Top Abstract Introduction Experimental methods Results and discussion Acknowledgments References cited

 
Wadsleyite (β-Mg₂SiO₄) is the stable polymorph of olivine in the mantle Transition Zone from 410 to 525 km depth. The olivine-wadsleyite (-β) transition of Mg₂SiO₄ is thought to produce the seismic discontinuity at 410 km (e.g., Ringwood 1975; Jeanloz and Thompson 1983; Bina and Wood 1987). Wadsleyite is a sorosilicate, isostructural with spinelloid III in the Ni-aluminosilicate system (Moore and Smith 1970; Akaogi and Navrotsky 1984). Because of the presence of an underbonded oxygen site (O1) not bonded to Si, Smyth (1987) predicted that wadsleyite could incorporate significant amounts of water as hydroxyl. Further theoretical studies based on crystal-chemical models (Smyth 1994) predicted that up to 3.3 wt% H₂O could be accommodated by fully protonating the non-silicate oxygen. The presence of variable amounts of hydroxyl in laboratory-synthesized wadsleyite samples was confirmed by Raman and infrared spectroscopy (McMillan et al. 1991; Young et al. 1993).

Inoue et al. (1995) synthesized hydrous wadsleyite at 15.5 GPa and 1200 °C containing 3.1 wt% H₂O (determined by secondary ion mass spectrometry, SIMS), close to the theoretical limit of 3.3 wt% H₂O. The water storage capacity of wadsleyite coexisting with hydrous melt decreases above ~1300 °C, but remains as high as ~1 wt% H₂O at 1400 °C and 15 GPa (Demouchy et al. 2005). Because of the unusually high water storage capacity of β-Mg₂SiO₄, knowledge of the elastic properties of hydrous wadsleyite is needed to constrain the potential hydration state of the mantle Transition Zone from geophysical observation (e.g., van der Lee and Wiens 2006).

The incorporation of water as hydroxyl into wadsleyite and other nominally anhydrous minerals (NAMs) generally requires divalent cation vacancies, which can strongly influence physical properties such as elasticity (e.g., Jacobsen 2006) and rheology (e.g., Karato 2006). Water affects melting and phase relations (e.g., Inoue 1994; Hirschmann 2006; Komabayashi 2006), the depth and pressure interval of phase transitions (e.g., Wood 1995; Smyth and Frost 2002; Chen et al. 2002; Frost and Dolej 2007), electrical conductivity (e.g., Karato 1990; Huang et al. 2005), strain rates and viscosity (e.g., Hirth and Kohlstedt 1996; Mei and Kohlstedt 2000), and shear strength (e.g., Jung and Karato 2001; Kavner 2003).

Because the mass of liquid-water equivalent that may be stored or recycled through the solid mantle could amount to several oceans, the incorporation of water into mantle minerals has implications for understanding the crust-mantle evolution and regulation of ocean levels (Drake and Righter 2002; Bercovici and Karato 2003). Hydrogen has an indefinite atomic radius resulting in geochemical properties that are strongly pressure and temperature dependent. Smyth et al. (2006) and Mosenfelder et al. (2006) showed that the solubility of OH in olivine increases with pressure and temperature, reaching a maximum of about one weight percent H₂O at 12 GPa and 1250 °C, suggesting that hydrogen is more geochemically compatible at conditions near the 410 km discontinuity. Therefore, H may be exchanged between the upper mantle and Transition Zone without severe limitations imposed by dehydration melting, maintaining a deep water cycle between the Transition Zone and the surface (e.g., Smyth and Jacobsen 2006). Hydrogen is probably the least well-constrained compositional variable in current geochemical models of the mantle.

Published compressibility studies of hydrous wadsleyite are limited to one composition with 2.5 wt% H₂O (SIMS) using powder X-ray diffraction to 8.5 GPa (Yusa and Inoue 1997), who reported an isothermal bulk modulus (K_T0) as 155(2) GPa, with pressure derivative (K') fixed at 4.3; significantly lower than K_T0 = 170–173 GPa, determined in studies of anhydrous wadsleyite by Zha et al. (1997), Li et al. (1998), Hazen et al. (2000), and the current study. Smyth et al. (1997) described a hydrous (2.3 wt% H₂O) iron-bearing (Fo₉₅) wadsleyite with monoclinic I2/m symmetry, but did not report its equation of state. Smyth et al. (1997) attributed the dilution of symmetry from orthorhombic to monoclinic in hydrous Fe-bearing wadsleyite as resulting from possible ordering of cations and vacancies within two non-equivalent M3 sites. Kudoh and Inoue (1999) reported monoclinic pure-Mg wadsleyite with 2.5 wt% H₂O and suggested that monoclinic symmetry resulted from stacking arrangement of Mg-vacant structural modules. The data of Jacobsen et al. (2005) show a trend of increasing β-angle with water content up to 90.125(3)° at 1.06 wt% H₂O, however, Kohn et al. (2002) report orthorhombic symmetry in iron-free wadsleyite with ~1.5 wt% H₂O.

We have undertaken a systematic study of iron-free hydrous wadsleyites with varying water contents to determine the effects of incorporated hydrogen on their structures and elastic properties. Samples in this study were synthesized at 14 GPa and 1300 °C using starting materials with consistent cation ratios so that the only major compositional variable was H. Variation in observed properties can therefore be reasonably attributed to differences in water content alone. Unit-cell parameters from well-characterized single-crystal samples were collected to precisely determined volumes of hydration and to identify deviation from orthorhombic symmetry. Crystal structure refinements were performed to observe systematic changes in the structure with water content and determine the degree of vacancy ordering. Single-crystal static compression experiments were performed to determine axial and bulk compression, and to relate trends in these values to the observed structural changes. The ultimate goal is to develop a systematic understanding of the relationships between composition, structure, and elastic properties of hydrous wadsleyite, which can be applied to interpreting seismic observations of the Earth’s mantle.

	EXPERIMENTAL METHODS

Top Abstract Introduction Experimental methods Results and discussion Acknowledgments References cited

 
Synthesis
All three hydrous samples in this study were synthesized using the 1200 ton Sumitomo multi-anvil press at Bayerisches Geoinstitut, Universität Bayreuth, Germany. Starting materials consisted of mixtures of forsterite (Mg₂SiO₄), and brucite (MgOH₂), with additional MgO and SiO₂ added in proportions to produce a slight silica excess and the desired water concentrations. Final water contents for the three starting material batches (unadjusted for silica excess) were 5.0, 2.5, and 1.2 wt%. Starting materials were sealed in welded 2 mm diameter Pt capsules, and loaded in 18 mm sintered-MgO octahedra with a stepped LaCrO₃ heaters. The press used 32 mm WC cubes with 8 mm corner truncations. Synthesis conditions were 14 GPa and 1300 °C to simulate upper Transition Zone conditions; pressure was maintained for 20 h with a nominal 12 h heating cycle. Starting water concentrations and results of synthesis runs are presented in Table 1. Sample SS0401 contained roughly equal quantities of wadsleyite and clinoenstatite + quenched melt; samples SS0402 and SS0403 contained traces (>5%) of clinoenstatite and quenched melt, with melt concentrated at the capsule ends. Water contents in wadsleyite were determined using the b/a axial ratio calibration of Jacobsen et al. (2005). The water content for SS0403 was verified by polarized FTIR spectroscopy using the calibration of Libowitzky and Rossman (1997) and found to be in excellent agreement. The other two samples produced total absorption of IR radiation at the principal O-H stretching frequencies for wadsleyite, therefore only minimum water contents could be determined by FTIR absorption for these samples. Because there is no absolute calibration for water in wadsleyite, uncertainties in water content were estimated at 10% for plotting and fitting purposes. For comparative and normalization purposes, we also performed structure refinements of a nominally anhydrous sample (WS3056) from the study of Jacobsen et al. (2005).

High-pressure XRD
Lattice parameters of the hydrous wadsleyite samples were determined at pressures up to ~10 GPa by single-crystal X-ray diffraction in a diamond anvil cell using at least eight unique reflections and their symmetry equivalents in both positive and negative 2 positions. A modified Merrill-Bassett type diamond anvil cell (Hazen and Finger 1977) with 500 µm culets and hardened steel seats giving a 60° optical aperture was used. The 2 range was approximately ±10–30° for both ruby and wadsleyite centered peaks. Crystals were oriented and polished parallel to (111) to allow well-distributed observations in reciprocal space, and to minimize differences in axial compression due to non-hydrostatic conditions. A methanol- ethanol-water mixture (16:3:1) was used as the pressure medium. Pressure in the cell was determined using the equation of state of quartz (Angel et al. 1997). Ambient condition analysis was performed to check crystal quality and to determine starting unit-cell parameters. The least hydrous samples (WS3056, SS0403) displayed orthorhombic (Imma) symmetry, whereas the most hydrous (SS0401) displayed monoclinic symmetry (I2/m) with β-angles ranging from 90.09(1) to 90.16(1)°. The crystal with β = 90.09(1)° possessed low mosaicity and produced the lowest cell parameter uncertainties, and therefore was selected for high-pressure study in the DAC. Sample SS0402 displayed variable symmetry among different crystals, although deviation from orthorhombic symmetry was only slightly greater than the uncertainty in the measurement.

	RESULTS AND DISCUSSION

Top Abstract Introduction Experimental methods Results and discussion Acknowledgments References cited

 
Lattice parameters
Room-pressure unit-cell parameters were measured both outside of the DAC for comparison to previous studies (Table 2) and inside the DAC before the addition of the pressure-transmitting medium for equation of state fitting. Parameters were refined in the monoclinic cell (I2/m) for SS0401 and in the orthorhombic cell Imma for samples SS0402, SS0403, and WS3056. Cell volumes vs. water content from the current study and from Jacobsen et al. (2005) are plotted together in Figure 1a. A linear regression to the current data set gives

View larger version (10K): [in this window] [in a new window]   FIGURE 1. Unit-cell volumes vs. water content for Fo100 hydrous wadsleyite (a). Solid symbols represent the current study, open symbols are data from Jacobsen et al. (2005). Estimated 10% uncertainty in water contents is shown. The data from Jacobsen et al. (2005) were collected on different instruments than in the current study, so direct comparison of absolute volumes is not warranted. Alternatively, all data were normalized against the near-anhydrous value for each set and plotted in b to directly compare the relative volumetric and axial expansions. Triangles = SS0401, SS0402, and SS0403 from current study; squares = data from Jacobsen et al. (2005); circles = samples BT1 and BT4 from Kohn et al. (2002).

where C_H2O is the water content in wt% H₂O determined from b/a axial ratios (Jacobsen et al. 2005). The volume increase of 0.17% per wt% H₂O in wadsleyite is similar to that in olivine, reported as 0.18% per wt% H₂O (Smyth et al. 2006). For an idealized structure with exactly one-quarter of M3 sites vacant and 3.3 wt% H₂O, V = 541.76 ų and = 3310 kg/m³. In comparison to thermal expansion, hydrating wadsleyite to 1 wt% H₂O has approximately the same effect on volume as a temperature increase of 550 °C, using the thermal expansion coefficient determined by Inoue et al. (2004). However, the variation of volume with water content in the current study is offset from values determined by Jacobsen et al. (2005). Figure 1a illustrates the problem of comparing absolute volumes measured using different instruments and experimental procedures. A preferable method compares lattice parameters normalized to anhydrous values (Fig. 1b), which allows us to combine the current sample suite with those from Jacobsen et al. (2005) into a merged data set. Variation of density with water content was calculated for the entire suite of samples in this manner, resulting in a best-fit to the merged data (Fig. 2):

View larger version (9K): [in this window] [in a new window]   FIGURE 2. Density vs. water content for Fo100 hydrous wadsleyite. Solid symbols represent the current study, open symbols are data from Jacobsen et al. (2005). Estimated 10% uncertainty in water contents is shown. The best-fit line is shown for the merged data sets.

where C_H2O is water content in wt% H₂O.

Smyth et al. (1997) observed monoclinic symmetry with β angles up to 90.397(9)° in iron-bearing (Fo₉₄) hydrous wadsleyite with 2.25 wt% H₂O. Violation of orthorhombic symmetry was attributed to ordering of H and Mg onto non-equivalent M3 sites normally related by a mirror plane perpendicular to the a-axis in the nominal structure. Vacancies in the M3 sites are introduced by substitution of H (which is thought to reside along the O-O edges and not in the M sites themselves) and trivalent (Fe³⁺) cations for Mg (in the case of Fe-bearing wadsleyite). In iron- free wadsleyite, monoclinic symmetry was confirmed by Kudoh and Inoue (1999). If monoclinic symmetry is due to vacancy ordering onto two non-equivalent M3 sites upon quenching, the two sites would have differing compressibilities, and increasing pressure would increase the β angle. Therefore, β angles were refined for SS0401 at high pressure in the diamond cell to track changes in the β angle with increasing pressure, however, no systematic variation was observed. Also, as discussed below, the crystals show signs of strain due to polysynthetic twinning on the orthorhombic cell which further limits the precision of β-angle measurement.

Structure refinements
Refined atomic positions, cation site occupancy factors, and displacement parameters are presented in Tables 3 and 4. Selected interatomic distances and polyhedral parameters are presented in Table 5. Refined parameters for WS3056 are in agreement with Hazen et al. (2000) for anhydrous wadsleyite. Constraining occupancy factors to unity (Table 3) did not alter the refinement statistics or position parameters significantly. Refinements with oxygen modeled entirely as O^2– resulted in lower R_f values than for those in which oxygen was modeled as a mixture of O^2– and O^1– ions. These refinements resulted in occupancy factors in better agreement with measured water contents; therefore, results presented here are based on refinements using only O^2– scattering factors for oxygen. Additionally, it was assumed that no Si occupied octahedral sites. Using these assumptions, all three samples show full occupancy of the M1 and M2 sites. Nearly all vacancies were ordered onto the M3 site, with vacancy occurring on 13.6%, 11.0%, and 3.9% of available M3 sites for SS0401, SS0402, and SS0403, respectively. The tetrahedral site is fully occupied within statistical uncertainties for all compositions studied. From these results, hydration of wadsleyite appears to be almost entirely accomplished by vacancy on the M3 site, with disorder onto other sites unimportant over this range of water contents. Sample SS0401 was refined in I2/m, with the M3 site split into two non-equivalent sites (M3a and M3b) at (, 0.123, ) and (, 0.377, ). Occupancy was slightly higher on M3a than on M3b, supporting the proposal by Smyth et al. (1997) that the break in orthorhombic symmetry is due to preference for one site of the nonequivalent M3 pair.

Axial compression
Table 6 lists unit-cell parameters for hydrous wadsleyite at pressures up to 9.6 GPa. Linear compressibilities were obtained by calculating linear fits to axial strain vs. pressure. Compressibilities parallel to crystallographic axes (β_a, β_b, β_c) are 0.00147(8), 0.00183(11), and 0.00218(3) GPa^–1, respectively, for SS0401; 0.00163(6), 0.00178(3), and 0.00228(3) GPa^–1 for SS0402; and 0.00163(6), 0.00159(2), and 0.00220(3) GPa^–1, respectively for SS0403. Compression is strongly anisotropic with the c-axis approximately 40% more compressible than the a- and b-axes for SS0403 (~0.4 wt% H₂O), consistent with previous compression studies of anhydrous wadsleyite (Hazen et al. 1990, 2000) and predictive models (Kiefer et al. 2001). With the incorporation of axial compression data from Hazen et al. (2000) and Yusa and Inoue (1997) for near-anhydrous and 2.5 wt% H₂O samples, respectively, all axes show increasing compressibility with increasing water content (Fig. 3), although the compressibility increase may be lesser at higher water contents. For the most hydrous sample studied (SS0401, ~1.6 wt% H₂O), the c-axis is nearly 50% more compressible than the a-axis, but only 20% more compressible than the b-axis. A possible explanation of the increase in b-axis compressibility is the expansion of the axis with hydration, shown in Figure 1b, due to lengthening of the shared O1-O3 edges of M3 corresponding to the H-bonds. Mitigation of O-O repulsion by these hydrogen bonds may facilitate compression in the preferred overall H-bond direction in the crystal. The a- and c-axes reach limits to compressibility at lower water concentrations,

View larger version (11K): [in this window] [in a new window]   FIGURE 3. Linear compressibility parallel to crystallographic axes for wadsleyite. Squares = a-axis; triangles = b-axis, circles = c-axis. Solid symbols represent the current study; open symbols near 0 wt% are data from Hazen et al. (2000); open symbols at 2.5 wt% are from Yusa and Inoue (1997). Best-fit lines were added to aid in comparing slopes of the data.

View larger version (10K): [in this window] [in a new window]   FIGURE 4. Bulk modulus of wadsleyite vs. water content, and comparison with other Mg-silicate series. The dashed line represents the trend of the grossular-hydrogarnet series. Wadsleyite appears to have a non-linear relation of bulk modulus to water content, whereas ringwoodite and the forsterite-hydroxylchondrodite series were shown to have linear relations. References: hydrous wadsleyite = this study; anhydrous wadsleyite = Hazen et al. (2000); ringwoodite = Smyth et al. (2004); forsterite = Downs et al. (1992); OH-clinohumite and OH-chondrodite = Ross and Crichton (2001); grossular-hydrogarnet = Wang and Ji (1997), O’Neill et al. (1993), Lager et al. (2002).

View larger version (13K): [in this window] [in a new window]   FIGURE 5. Plots of Birch normalized pressure (FE) vs. Euler finite strain (fE) for hydrous wadsleyites. Bulk moduli from y-intercepts of linear regressions are 160(3), 153(3), and 149(3) GPa for samples with 0.38, 1.18, and 1.66 wt% H2O, respectively. Positive slopes of the linear regressions indicate K' > 4.

View larger version (13K): [in this window] [in a new window]   FIGURE 6. Bulk sound speed plots for anhydrous and hydrous wadsleyite (solid black curves), and a hypothetical curve representing possible behavior of hydrous wadsleyite at Transition Zone pressures (gray). Curves are extrapolated from zero-pressure Birch-Murnaghan equation of state parameters; data points represent pressures at which volume data were collected. The dashed curve represents a refit of the hydrous data with K' = 4.0, consistent with the anhydrous value. The gray curve is calculated from the fitted K0 and K', with K'' selected so that bulk sound speeds for the hydrous composition remain lower than the speeds for the anhydrous composition through the pressure stability range of wadsleyite in the Transition Zone. The vertical line represents the approximate pressure at the 410 km seismic discontinuity.

Monoclinic symmetry in wadsleyite has been observed in various studies for hydrous compositions, but the monoclinic angle and presumably the degree of ordering is variable between samples with similar water contents. In the current study, sample SS0401 was monoclinic with β angle at ambient conditions ranging from 90.09° to 90.16° for a hydrous iron-free composition with ~1.6 wt% H₂O. Sample SS0402 (~1.2 wt% H₂O) contained some crystals with orthorhombic and some with monoclinic symmetry. All crystals of sample SS0403 (~0.4 wt% H₂O) examined were statistically orthorhombic. Smyth et al. (1997) described an iron-bearing wadsleyite with 2.3 wt% H₂O and a maximum β-angle of 90.4°. Jacobsen et al. (2005) observed orthorhombic symmetry in samples with 0.32 wt% H₂O and below, increasing to β = 90.055(3)° for the sample with 0.6 wt% H₂O, and up to 90.125(3)° in the sample with 1.06 wt% H₂O. Kohn et al. (2002) report iron-free wadsleyites with orthorhombic symmetry at water contents up to ~1.5 wt%.

If hydrous wadsleyite is orthorhombic at mantle P-T conditions, it is likely that differences in quenching rates are partially responsible for the inconsistency in reported β angles. It is unclear if the hydrous samples were monoclinic or orthorhombic at synthesis conditions; however, the presence of strain consistent with fine polysynthetic twinning suggests that they were orthorhombic and that ordering of the vacancies occurred on quench. It may be possible to resolve this question by examination of crystals quenched at different rates.

Sample SS0402 contained wadsleyite crystals with a maximum diameter of ~300 µm. Unit-cell dimensions at ambient conditions were measured for several crystals to characterize symmetry. Roughly half of the crystals were statistically orthorhombic, and half were statistically monoclinic with β angles ranging to approximately 90.1°. To identify possible internal strain, directional scans in reciprocal space were performed on both orthorhombic and monoclinic crystals from SS0402. A representative scan set is shown in Figure 7. Significant relative peak broadening was observed in the c* direction of the orthorhombic sample and in the b* direction of the monoclinic crystal. Strain in the orthorhombic structure may be related to polysynthetic twinning normal to (0 0 1), whereas strain in the monoclinic structure may be primarily due to distortion of the edge-sharing M3 quartets. Data collection using the CCD area detector revealed no significant peaks inconsistent with either Imma or I2/m indicative of possible polytypism. No relative broadening was observed in the a* direction, but possible peak splitting in the monoclinic sample was observed, perhaps related to violation of the mirror plane normal to a*.

View larger version (5K): [in this window] [in a new window]   FIGURE 7. Omega scans of the (2 4 4) diffraction peak for two separate wadsleyite crystals from sample SS0402. Black = orthorhombic crystal; gray = monoclinic crystal. Width of scan field is approximately 1.5°. Broadening in the monoclinic sample is interpreted to result from polysynthetic twinning.

	ACKNOWLEDGMENTS

Top Abstract Introduction Experimental methods Results and discussion Acknowledgments References cited

 
This study was supported by U.S. National Science Foundation grant EAR 03-37611 to J.R.S., the Bayerisches Geoinstitut Visitors Program, and the Alexander von Humboldt Foundation. Thorough reviews by W. Crichton and J. Burt significantly improved the manuscript. C.M.H. is supported in part by NSF EAR-0721449 to S.D.J.

	Footnotes

 
^* Present address: Department of Earth and Planetary Sciences, Northwestern University, Evanston, Illinois 60208, U.S.A. E-mail: chrish{at}earth.northwestern.edu

MANUSCRIPT HANDLED BY GEORGE LAGER

MANUSCRIPT RECEIVED February 21, 2007; MANUSCRIPT ACCEPTED October 12, 2007

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