Wadsleyite II: A new high pressure hydrous phase in the peridotite-H2O system

Joseph R. Smytha* and Tatsuhiko Kawamotob

a Department of Geological Sciences, University of Colorado, Boulder, CO 80309 USA b Department of Geology, Arizona State University, Tempe, AZ USA

Abstract

A new hydrous silicate phase with formula Mg1.71Fe0.177Al0.01Si0.965H0.332O4 has been synthesized at 1400°C and 17.5GPa from a hydrous iron-rich mantle peridotite composition. The space group is Imma and unit cell parameters a = 5.6884(4); b = 28.9238(15); and c =

8.2382(6)Å, so that a and c are approximately those of wadsleyite, whereas b is 2.5 times that of wadsleyite. The calculated density of this phase is 3.513g/cm3. In addition to five Mg/Fe octahedra and two silicate tetrahedra, the structure contains one partially occupied Mg/Fe octahedron and one partially occupied silicate tetrahedron. These two partially occupied sites may be the result of decompression of a single Mg/Si octahedron. The synthesis of this phase which has not been previously noted or described indicates that the crystal chemistry of H incorporation into high pressure spinelloid structures is more complex than previously thought.

Whereas the transition zone of the Earth’s mantle may serve as very large reservoir for hydrogen, further work will be required to outline the relative stabilities and physical properties of the various hydrous silicates that may exist there.

Keywords: hydrous, β-Mg2SiO4, wadsleyite, transition zone, mantle ______*Corresponding author: Voice: (303)492-5521; FAX (303)492-2606; E-mail: [email protected]; URL:http://ruby.colorado.edu/~smyth/Home.html Word count (total): 3348; (exclusive of title and references): 2728

1 1. Introduction

One tenth of one percent H2O by weight in the minerals of the transition zone (400-

670km depth) is an amount equal to 800m of liquid water over the surface of the planet. One half of one percent is more water than in all of the oceans. Clearly, the incorporation of even minor amounts of H in mantle phases may have played a central role in the development and evolution of Earth’s hydrosphere. Further, the presence of H in rocks has a major effect on melting temperature, strength, and elastic properties and thus may control melt generation, solid state convection, and seismic velocities. We report here the synthesis and a full three-dimensional crystal structure determination of a new hydrous ferromagnesian silicate spinelloid phase that contains 2.0 to 2.7 wt% H2O. This phase has not been noted or described in previous studies, but occurs abundantly in hydrous experiments on likely multi-component mantle compositions under conditions of temperature and pressure expected in the transition zone.

The stabilities of possible hydrous and anhydrous phases under mantle conditions has been reviewed by Thompson[1]. Numerous hydrous high pressure magnesium silicate phases

. have now been reported and characterized. Phase A (2Mg2SiO4 3Mg(OH)2)[2] is a high-Mg phase synthesized at relatively low temperatures of 800ºC at 7.7GPa. Phase B

(Mg12Si4O19(OH)2)[3] is also a high Mg hydrous silicate that has an anhydrous modification

(Mg14Si5O24)[3], and a super-hydrous modification (Mg10Si3O14(OH)4) [4]. Phase A, phase B, and superhydrous B all have Mg/Si ratios greater than 2.0. Phase E (Mg2.08Si1.16H3.2O6) [5] synthesized at 15GPa and 1000ºC has an Mg/Si ration close to that of forsterite, but has a low

3 density of 2.822 g/cm . Phase F (Mg3.35Si5.51H7.26O18)[6] synthesized at 17GPa and 1000ºC has an

Mg/Si ratio less than 1.0 and also has a low density of 2.826 g/cm3. However, it has recently been shown that these nominally hydrous magnesium silicates may not be stable at temperatures above

800ºC at 8GPa, and above 1350ºC at 15GPa [7].

2 In addition to these hydrous phases, nominally anhydrous phases contain very significant amounts of hydrogen and thus may serve as major sink for protons in the mantle [8]. Among phases stable in the transition zone, nominally anhydrous wadsleyite (β-Mg2SiO4) might serve as a host phase for H, as it contains an oxygen site not bonded to Si with an anomalously shallow electrostatic potential [9,10]. McMillan et al. [11] observed a small amount of hydroxyl in wadsleyite synthesized under nearly anhydrous conditions. Young et al. [12] observed major amounts of hydroxyl in an Fo92 wadsleyite with up to 1.6% of all oxygens protonated.

Theoretical studies projected that the phase would contain up to 3.3 wt % H2O if the non-silicate oxygen were fully protonated [13,14]. Kudoh et al. [15] reported the structure of a hydrous wadsleyite with 12% of oxygens protonated (3.3 wt %).

Kohlstedt et al. [16] have measured the solubility of H in Fo89 forsterite, wadsleyite and ringwoodite. Kawamoto et al.[7] have measured partition coefficients of H between hydrous ultramafic melts and wadsleyite and ringwoodite and postulated a hydrous transition zone through cooling of a hydrous magma ocean. In order to assess the mechanism of H incorporation into wadsleyite and ringwoodite, we have conducted additional experiments in this system to produce crystals of sufficient grain size for single-crystal X-ray diffraction. However, in the more

Fe-rich of these experiments (Fo < 92), we have identified a new hydrous spinelloid phase related to wadsleyite, but with a very different b-axis repeat and a distinct crystal chemistry. We produced crystals of the new phase up to 200µm in size and have determined its crystal structure from X-ray single crystal diffraction data.

2. Experimental

The starting material for the run was a mixture of Mg-free KLB-1 peridotite gel, brucite and iron wüstite, resulting in an overall H2O content of 12.8 wt. % and 82.2 Mg/(Mg+Fe) atomic ratio. Cylindrical LaCrO3 was used as a heater outside an Au75Pd25 capsule. Two experiments were conducted; one at 17.5 + 1 GPa and 1400ºC for 22h and one at 18 + 1GPa and 1350ºC for

3 13h. The run products are composed of a light brown majorite garnet, a dark green wadsleyite- like phase with a few small (<5µm) inclusions of stishovite, and dendritic-textured quenched partial melt. Grain sizes of the wadsleyite-like phase are up to 200 µm in the first run and up to

100µm in the second.

The major-element compositions of phases were determined by electron microprobe. H concentrations were determined with a secondary ion mass spectrometer (SIMS) at the Center for

Solid State Science, Arizona State17. The ion beam diameter was ~20 µm. Chemical compositions of the wadsleyite-like phase roughly fall between olivine and phase E. Hence, we used the olivine-phase E calibration to quantify the H+ signal in the sample by assuming that olivine is anhydrous and the H2O content of phase E is 7.6 wt %[5]. The chemical compositions of both samples are shown in Table 1. The relation between (Mg+Fe)/Si atomic ratio and H2O concentration of this phase deviate from the theoretical value between the anhydrous and fully hydrated wadsleyite compositions [8] indicating either that vacancies may play a role[18] or that the mechanism of hydration of (Mg,Fe)2SiO4 is different from Mg2SiO4[19] in wadsleyite structures.

A crystal approximately 80 x 80 x 160 µm was separated from a polished mount of the sample synthesized at 17.5GPa. Using a Siemens/MAC Science 18 kW X-ray generator, the orientation was determined by means of a rotation photograph, and the unit cell refined from centering of 16 non-equivalent X-ray reflections in both positive and negative 2θ regions. Non- linear least-squares refinement of the unit cell parameters gave a = 5.6884(4)Å; b =

28.9238(15)Å; and c = 8.2382(6)Å with an orthorhombic, body-centered lattice. An octant of intensity data with 3.5 < 2θ < 30° was measured without the lattice constraint, and no violations of the body centering were observed. An quadrant of intensity data was then measured out to 2θ

= 65° with the I lattice constraint using θ-2θ scans with scan rates variable from 4 to 20º 2θ per minute. With the X-ray generator operating at 50kV and 200mA, this yielded 2731 measured

4 intensities of which 1337 were greater than 4σ above background, and the mean I/σ was 12.6 for all reflections. The data were corrected for Lorentz and polarization effects and for absorption using an analytical absorption correction routine based on the measured shape of the crystal. The space group determined from the observed intensities was Imma, plus possible acentric subgroups, Im2b and I2mb.

Table 1. Chemical analysis and unit cell parameters of hydrous wadsleyite II samples from electron microprobe, SIMS, and X-ray single-crystal diffraction. ______Sample 1 Sample 2 ______Oxide Weight % SiO2 40.04(29) 40.01(65) Al2O3 0.41(2) 0.34(3) Cr2O3 0.19(1) 0.22(2) FeO 8.80(23) 10.60(22) MgO 47.57(47) 44.37(40) CaO 0.00(0) 0.00(0) H2O 2.03(6) 2.72(24)

Total 99.04 98.26

Cations per 4 Oxygens Si 0.964 0.970 Al 0.012 0.009 Cr 0.004 0.004 Fe 0.177 0.215 Mg 1.707 1.603 Ca 0.000 0.000 H 0.326 0.440 a (Å) 5.6884(4) 5.6896(12) b (Å) 28.9238(15) 29.104(6) c (Å) 8.2382(6) 8.243(2) Vol (Å3) 1355.4(1) 1360.8(8)

Density (g/cm3) 3.513 3.495 ______

The crystal structure was solved using the strong similarity to the wadsleyite (β-

Mg2SiO4) structure apparent in the unit cell parameters. A model was created in Imma with the wadsleyite atoms arranged around the mirror normal to b in the much larger cell. Oxygens were placed in positions approximating a close-packed array to fill the rest of the cell, and cation

5 positions determined from the difference Fourier. Using the least-squares refinement package

SHELXTL[20], the crystal structure refined to an R of 4.6 for all reflections with intensity greater than 4σ above background.

The occupancies of the M-sites were modeled by Fe alone using the scattering factor for neutral Fe (26 electrons) and also using a mix of both Fe and Mg (neutral atoms). In both cases, the occupancies of each of the M sites, M1 through M5, refined to approximately equal values with somewhat fewer than 10 electrons (Table 2). These values are computed by taking the refined occupancy using the scattering factor for neutral Fe (26 electrons) times 26 and divided by the equipoint fraction for the site. In each case, this number is less than if the site were occupied by pure Mg, so it appears that octahedral site vacancy is significant in all of the M- sites. However, the X-ray refinement results can only give the total number of electrons at a given site, and given the apparent vacancy, it is not possible to uniquely determine the distribution of Fe, Mg, and vacancy at each site. Final position, thermal and occupancy factors are reported in Table 2. Cation-oxygen distances are reported in Table 3. A [101] projection of the structure is presented as Fig. 1.

3. Discussion

The structure is based on cubic-close-packed array of oxygens as are both wadsleyite (β-

Mg2SiO4) and ringwoodite (γ-Mg2SiO4). The structure is very closely related to that of wadsleyite, although it is clearly a new structure. It has the same space group symmetry and essentially the same a- and c-axes as wadsleyite. The b-axis is, however, 2.5 times that of wadsleyite, so the structure is not simply a super-structure of wadsleyite as might result from cation ordering.

6 Fig 1. A [101] projection (b-horizontal) of the crystal structure of hydrous wadsleyite II.

Octahedral sites are M1, M2, M3, M4, M5, and M6. Tetrahedral sites are Si1, Si2, and

Si3.

Comparing the structure with that of wadsleyite, we see that Si1 is completely analogous to Si in wadsleyite. It forms an Si2O7 group with a bridging oxygen, O2. Si2 would form a Si2O7 group with Si3, if Si3 is occupied, however, fewer than half are occupied. Where Si3 is vacant,

Si2 forms an isolated tetrahedron. Among octahedral sites, M1, M2, and M3 are completely analogous to those sites in wadsleyite, except that M1 in this structure is not on a inversion, so there are twice as many per cell. M2 is located on the mirror perpendicular to b, and M3 forms a continuous double band of octahedra parallel to a, as in wadsleyite. M4, M5, and M6 are new sites without direct analogues in wadsleyite. M4 is somewhat similar to M3, in that together with

7 M6 it forms a continuous double band of octahedra parallel to a. M5 is somewhat similar to M2.

M6 is similar to M4, but is less than half occupied.

Table 3. Selected cation -oxygen distances and coordination polyhedron parameters hydrous wadsleyite II.

M1 M2 M3 Pt.Sym. m Pt.Sym. mm2Pt.Sym.2 O3a 2.129(7) O1 2.128(11) O1(x2) 2.019(3) O3b 2.096(7) O2 2.081(11) O3a(x2) 2.106(7) O4(2x) 2.059(13) O4(x4) 2.032(11) O4(x2) 2.116(7) O5(2x) 2.062(13) Mean 2.078 Mean 2.080 Mean 2.080 Poly Vol 11.90 Poly.Vol. 11.43 Poly.Vol. 11.91 O.Q.E. 1.0033 O.Q.E. 1.0098 O.Q.E. 1.0063 A.V. 10.68 A.V. 32.97 A.V. 20.58

M4 M5 M6 Pt.Sym. 2 Pt.Sym. m Pt.Sym. 2 O3b(x2) 2.067(9) O3c 2.023(10) O3c(x2) 2.084(8) O3d(x2) 2.038(7) O3d 2.130(12) O3d(x2) 2.121 (8) O5(x2) 2.099(3) O5(x2) 2.095(12) O6(x2) 2.061(8) O6(x2) 2.063(17) Mean 2.068 Mean 2.078 Mean 2.089 Poly Vol 11.77 Poly.Vol. 11.91 Poly.Vol. 12.08 O.Q.E. 1.0016 O.Q.E. 1.0037 O.Q.E. 1.0042 A.V. 4.74 A.V. 12.33 A.V. 14.02

Si1 Si2 Si3 Pt.Sym. m Pt.Sym. m Pt.Sym. m O2 1.662(5) O3a 1.624(9) O3c 1.976 (15) O3b 1.705(11) O3c 1.698(10) O3d 1.791(11) O4(x2) 1.677(10) O5(x2) 1.657(7) O6(x2) 1.680(20) Mean 1.680 Mean 1.660 Mean 1.781 Poly.Vol. 2.413 Poly.Vol. 2.339 Poly.Vol. 2.868 T.Q.E. 1.0063 T.Q.E. 1.0015 T.Q.E. 1.0130 A.V. 22.02 A.V. 6.39 A.V. 29.035 ______

The disorder apparent in the M6 and Si3 positions is worthy of discussion. By sharing faces, these sites are so close to one another that it is unlikely that adjacent Si3 and Mg6 could both be occupied. Further, if fully occupied, adjacent Si3 tetrahedra would share an edge with each other (unknown among ordered stoichiometric silicates). Also, the site is very distorted with abnormally long Si-O bond lengths. The total occupancy of Mg6 and Si3 equals that of a fully

8 occupied M6 site (8g position) in Imma. The structure co-exists with majorite garnet and stishovite which both contain octahedral silica. It appears possible, therefore, that what we observe in this uncompressed structure is the result of decompression of a fully occupied Mg/Si octahedron at the M6 position. Si3 would then represent Si that has moved into adjacent unoccupied tetrahedral voids in the close-packed oxygen array on decompression. If this is true, the structure might be expected to show a relatively low bulk modulus at pressures below those of its stability field, and it might be possible to return the Si to octahedral coordination by the application of pressure. Within its pressure stability field, however, the close-packed oxygen in the structure should give it a bulk modulus comparable to those of periclase (160GPa) and wadsleyite (162GPa) [22], or possibly higher if the octahedral Si hypothesis is correct.

The two crystals studied have formulas, Mg1.71Fe0.177Al0.01Si0.965O4H0.334, and Mg1.60Fe0.215

Al0.01Si0.970O4H0.440, based on electron microprobe together with H from SIMS, for a formula weights of 143.26g and 143.16g respectively. The Z is 20 for this formula with 80 oxygens per cell. This gives densities of 3.511 and 3.495g/cm3. In order to compare the density of this structure with those of other reported hydrous magnesium silicates, we have estimated the density of the Fe-free composition. Using the slope of the density as a function of Fe/(Fe+Mg) for anhydrous wadsleyite from Finger et al.[21] of 0.0134, we extrapolated the density of this phase back to the Fe-free composition and obtain estimated densities of 3.383 and 3.337g/cm3.

This would make it substantially more dense than phase A (2.959 g/cm3), phase E (2.822 g/cm3), phase F (2.826 g/cm3), and superhydrous phase B (3.214 g/cm3), and roughly similar to phase B

(3.368 g/cm3) and hydrous wadsleyite (3.31 g/cm3).

The two samples show that, like wadsleyite, the structure can accommodate variable amounts of H. It is unknown if the structure would occur in an anhydrous system. This study also shows that the incorporation of H into Mg-Fe silicates results in an unexpectedly complex crystal chemistry. This phase, with 18 atoms in the asymmetric unit (compared to 8 for wadsleyite) is

9 surprisingly complex. It is a spinelloid, in that it has a cubic-close-packed oxygen array with Si in tetrahedral voids and Mg and Fe in octahedral voids. It is not clear why this structure should be preferred over that of ordinary hydrous wadsleyite with its 11Å b-axis whose composition it overlaps. One possible explanation is that it contains octahedral Si at pressure and so increases its density relative to hydrous wadsleyite and phase B.

It is also interesting that the structure has not been seen before despite numerous experiments in the MgO-SiO2-H2O system. Perhaps it appeared but was assumed to either wadsleyite or ringwoodite. Our calculated X-ray powder diffraction patterns for wadsleyite I and

II are nearly identical, differing only in a few minor peaks. Perhaps wadsleyite II requires, or is stabilized by, the presence of Fe, so that it might not occur in Fe-free systems. Alternatively, the phase might be completely metastable, as intermediate spinelloid structures have been noted in studies of the wadsleyite-olivine transition [23]. However, the duration of this synthesis experiment was long (22h) relative to previous studies. The crystals are of very high quality with narrow diffraction peaks and no streaking parallel to b*. Also, the structure is based on the same cubic-close-packed oxygen array as wadsleyite and ringwoodite, so that epitaxial growth of either of these phases would likely have occurred if they represented a thermodynamically more stable configuration. Also, we have seen it in two different experiments and have five separate crystals from the first experiment that are identical within error.

We therefore assume that it represents a new stable phase in the system MgO-FeO-SiO2-

H2O. It has appeared in experiments at pressures and temperatures somewhat greater than those of hydrous wadsleyite and so may be a significant hydrous component of the transition zone. The discovery of a new phase in this system points out the importance of working in multicomponent systems and careful examination of run products. It also leaves us with some important questions and opportunities. In particular, measurement of the elastic properties of this phase and of hydrous wadsleyite may allow us to constrain the amount of H actually present in the transition

10 zone. Further, our structure determination suggests that the phase may incorporate variable amounts of octahedral silica, which is expected to increase with pressure and may stabilize this phase relative to hydrous ringwoodite. Clearly, further synthesis experiments with careful examination of run products will be required to work out the complex stability relations we now expect among hydrous phases in the transition zone.

ACKNOWLEDGMENTS

We thank A. Haeril, R.M. Hazen, T. Inoue, K. Leinenweber, R. Pacalo, and two anonymous referees for discussion and constructive reviews; R. Hervig and J. Holloway for help with analysis and synthesis; and Y. Kudoh and T. Inoue for making works in press available to us. This work was supported by the U.S. National Science Foundation and the Japan Society for

Promotion of Science.

References

[1] A.B. Thompson, Water in the Earth’s upper mantle. Nature 358, 295-302, 1992.

[2] H. Horiuchi, N. Morimoto, K. Yamamoto, and S. Akimoto, Crystal structure of 2Mg2SiO4

. 3Mg(OH)2, a new high pressure structure type. Am. Mineral. 64, 593-598, 1979.

[3] L.W. Finger, R.M. Hazen, and C.T. Prewitt, Crystal structures of Mg12Si4O19(OH)2 (phase B) and

Mg14Si5O24 (phase AnhB). Am. Mineral. 76, 1-7, 1991.

[4] R.E.G. Pacalo and J.B. Parise, Crystal structure of superhydrous B, a hydrous magnesium silicate

synthesized at 1400ºC and 20GPa. Am. Mineral. 77, 681-684, 1992.

[5] Y. Kudoh, L.W. Finger, R.M. Hazen, C.T. Prewitt, M. Kanzaki, and D.R. Veblen, Phase E: A high

pressure hydrous silicate with unique crystal chemistry. Phys. Chem. Minerals 19, 357-360, 1993.

[6] Y. Kudoh, T. Nagase, S. Sasaki, M. Tanaka, and M. Kanzaki, Phase F, a new hydrous magnesium

silicate synthesized at 1000ºC and 17 GPa: Crystal structure and estimated bulk modulus. Phys.

Chem. Minerals 22, 295-299, 1995.

11 [7] T. Kawamoto, R.L. Hervig, and J.R. Holloway, Experimental Evidence for a hydrous transition zone

in the early Earth’s mantle. Earth Planet. Sci. Lett. 142, 587-592, 1996.

[8] D.R. Bell and G.R. Rossman, Water in Earth’s mantle: The role of nominally anhydrous minerals.

Science 255, 1391-1396, 1992.

[9] J.R. Smyth, β−Mg2SiO4: A potential host for water in the mantle? Am. Mineral., 72, 1051-1055,

1987.

[10] J.W. Downs, Possible sites for protonation in β-Mg2SiO4 from experimentally derived electrostatic

potential. Am. Mineral. 74, 1124-1129, 1989.

[11] P.F. McMillan, M. Akaogi, R.K. Sato, B. Poe, and J. Foley, Hydroxyl groups in β-Mg2SiO4. Am.

Mineral. 76, 354-360, 1991.

[12] T.E. Young, H.W. Green II, A.M. Hofmeister, and D. Walker, Infrared spectroscopic investigation

of hydroxyl in β-(Mg,Fe)2SiO4 and coexisting olivine: Implications for mantle evolution and

dynamics. Phys. Chem. Minerals 19, 409-422, 1993.

[13] J.R. Smyth, A crystallographic model for hydrous wadsleyite: An ocean in the Earth’s interior? Am.

Mineral. 79, 1021-1024, 1994.

[14] K. Wright, and C.R.A. Catlow, Calculations on the energetics of water dissolution in wadsleyite.

Phys. Chem. Minerals 23, 38-41, 1996.

[15] Y. Kudoh T. Inoue, and H. Arashi, Structure and crystal chemistry of hydrous wadsleyite Mg1.75

SiH0.5O4: Possible hydrous magnesium silicate in the mantle transition zone. Phys. Chem. Minerals,

23, 1996 (in press).

[16] D.L. Kohlstedt, H. Keppler, and D.C. Rubie, The solubility of water in α, β and γ phases of

(Mg,Fe)2SiO4. Contributions to Mineralogy and Petrology 123, 345-357, 1996.

[17] P.D. Ihinger, R.L. Hervig, and P.F. McMillan, Analytical methods for volatiles in glasses. M.S.A.

Reviews in Mineralogy 30, 67-121, 1994.

[18] T. Inoue, H. Yurimoto, and Y. Kudoh, Hydrous modified spinel, Mg1.75SiH0.5O4: a new water

reservoir in the mantle transition region. Geophys. Res. Lett. 22, 117-120, 1995.

[19] T. Gasparik, The role of volatiles in the transition zone. J. Geophys. Res. 98, 4287-4299, 1993.

12 [20] G. Sheldrick, SHELXTL-PC Release 4.1 Siemens Analytical X-ray Instruments, Inc., Madison WI,

296pp 1990.

[21] L.W. Finger, R.M. Hazen, J. Zhang, J. Ko, and A. Navrotsky, The effect of Fe on the crystal structure

of wadsleyite β-(Mg1-xFex)2SiO4, 0.00 < x < 0.40. Phys. Chem. Minerals 19, 361-368, 1993.

[22] R.M. Hazen, J. Zhang, and J. Ko, Effects of Fe/Mg on the compressibility of synthetic wadsleyite: β-

(Mg1-xFex)2SiO4 (x < 0.25). Phys. Chem. Minerals 17, 416-419, 1990.

[23] B. Reynard, F. Takir, F. Guyot, G.D. Gwanmesia, R.C. Lieberman, and P. Gillet, High temperature

Raman spectroscopic and X-ray diffraction study of β-Mg2SiO4: Insights into its high temperature

thermodynamic properties and the β− to α-phase transformation and kinetics. Am. Mineral. 81, 585-

594, 1996.

13 Table 2. Final position, occupancy, and thermal parameters for hydrous wadsleyite II.

Atom x/a y/b z/c occ.* U11 U22 U33 U12 U13 U23 Ueq ______

Mg1 0.0 0.1491(3) 0.0023(4) 11.9(4) 0.022(2) 0.014(2) 0.034(2) 0.0 0.0 0.0027(8)` 0.0233(14) Mg2 0.0 0.25 0.9643(9) 10.5(3) 0.015(2) 0.008(2) 0.013(2) 0.0 0.0 0.0 0.0122(16) Mg3 0.25 0.20107(12) 0.25 11.3(3) 0.0117(17) 0.0153(17) 0.0062(14) 0.0 -0.0020(9) 0.0 0.0110(9) Mg4 0.25 0.10273(15) 0.75 9.3(2) 0.0128(19) 0.0088(18) 0.0176(19) 0.0 0.0027(10)0.0 0.0130(11) Mg5 0.0 0.0493(2) 0.0149(5) 10.1(4) 0.014(3) 0.010(2) 0.0103(17) 0.0 0.0 0.0022(11) 0.0116(14) Mg6 0.25 0.0021(2) 0.25 3.6(1) 0.017(7) 0.024(6) 0.033(6) 0.0 0.001(4) 0.0 0.025(3)

Si1 0.0 0.19959(9) 0.6148(3) 0.452(6) 0.0039(13) 0.0046(12) 0.0054(11) 0.0 0.0 0.0009(11) 0.0046(7) Si2 0.0 0.10256(12) 0.3792(3) 0.409(5) 0.0082(12) 0.0038(12) 0.0089(10) 0.0 0.0 -0.0003(14) 0.0069(6) Si3 0.0 0.99571(18) 0.3809(8) 0.235(7) 0.009(3) 0.015(2) 0.015(2) 0.0 0.0 0.001(2) 0.0127(16)

O1 0.0 0.25 0.2226(9) 0.25 0.010(4) 0.011(3) 0.000(2) 0.0 0.0 0.0 0.0070(20) O2 0.0 0.25 0.7117(9) 0.25 0.003(3) 0.006(3) 0.000(2) 0.0 0.0 0.0 0.0029(17) O3a 0.0 0.1474(3) 0.2607(6) 0.5 0.000(2) 0.015(3) 0.009(2) 0.0 0.0 -0.006(2) 0.0080(15) O3b 0.0 0.1546(3) 0.7485(7) 0.5 0.012(3) 0.007(3) 0.009(2) 0.0 0.0 0.000(2) 0.0091(16) O3c 0.0 0.0547(3) 0.2598(13) 0.5 0.041(7) 0.028(4) 0.044(5) 0.0 0.0 -0.019(4) 0.038(3) O3d 0.0 0.0523(4) 0.7565(14) 0.5 0.016(5) 0.044(5) 0.075(7) 0.0 0.0 0.013(5) 0.045(3) O4 0.250(2) 0.2005(3) 0.9931(6) 1.0 0.030(7) 0.037(6) 0.052(4) -0.014(5) -0.006(2) 0.000(2) 0.040(3) O5 0.2627(12) 0.1000(4) 0.0045(3) 1.0 0.010(3) 0.010(2) 0.0082(19) -0.006(4) 0.0008(9) 0.0011(15) 0.0094(14) O6 0.2613(19) 0.0 0.0 0.5 0.000(4) 0.000(3) 0.001(2) 0.0 0.0 -0.0020(13) 0.000(2)

*reported as numbers of electrons for M1 - M6

14