Examination of Water Quantification and Incorporation in Transition Zone Minerals: Wadsleyite, Ringwoodite and Phase D Using ERDA (Elastic Recoil Detection Analysis)

Hydrous wadsleyite, ringwoodite, and phase D have been synthesized in the MgO-SiO 2 -H 2 O and MgO-FeO-SiO 2 -H 2 O systems at mantle transition zone conditions (15–21 GPa and 1,100–1,700 ◦ C) to investigate their water incorporation using Elastic Recoil Detection Analysis (ERDA), which is an absolute quantitative method. Wadsleyite and ringwoodite water contents vary from 0.1 to 3.2 wt% H 2 O and for ringwoodite containing up to 1.16 wt% H 2 O we observe that the (Mg + Fe)/Si ratio vs. water content follows the same trend as for wadsleyite, indicating that H is substituting for Mg as for wadsleyite. We also measured, for the ﬁrst time, the water content of phase D and observed that it varies from 6.7 to 11.2 wt% H 2 O, up to twice less than estimated from electron microprobe analysis totals. Using these experiments, we were able to determine the absorptivity coefﬁcient for OH infrared absorption bands in four wadsleyite and ﬁve ringwoodite samples. The average for the two iron-free wadsleyite samples leads to an absorptivity of 69,000 ± 7,000 L/moles H 2 O/cm 2 , in very good agreement with previous determinations. The wadsleyite with 8 mole% Fe displays an absorptivity of 67,000 ± 5,000 L/moles H 2 O/cm 2 . The absorptivity values vary from 118,500 ± 5,000 for Fe-free ringwoodite to ± 135,000 ± 9,000 for Fe-bearing ringwoodite (10% mole Fe). Our results show that absorptivity coefﬁcient for OH infrared absorption of ringwoodite do not drastically change with Fe content and that the frequency-based calibration of Paterson (1982) under-estimates its water determinations by 50%. This is very important to know when comparing data from different studies where different extinction coefﬁcients have been used.


INTRODUCTION
The transition zone of the Earth's mantle, located between 410 and 660 km of depth, is composed for more than 60% of the high-pressure polymorphs of olivine, (Mg, Fe) 2 SiO 4 , namely wadsleyite and ringwoodite. Given the high ability of these minerals to incorporate water, as hydrogenated point defects (Inoue, 1994;Smyth, 1994;Bolfan-Casanova et al., 2000), the transition zone is potentially a major reservoir for water within Earth. The recent discovery of the first terrestrial ringwoodite containing 1.5-2 wt% H 2 O corroborates the idea that such high water contents in transition zone minerals is not only a laboratory case but a plausible scenario in nature (Pearson et al., 2014). Recently, the importance of phase D has grown as this phase is a potential candidate to transport water in subduction slabs to great depths (Shieh et al., 1998;Ghosh and Schmidt, 2014;Pamato et al., 2015;Walter et al., 2015). Also, extended solid solution with Al has also been reported for this phase, which greatly enhances its thermal stability field, with an aluminum-rich end-member [i.e., Al 2 SiO 4 (OH) 2 ] being experimentally observed (Pamato et al., 2015).
Many studies have focused on the determination of physical properties of hydrous wadsleyite and ringwoodite such as elasticity (Chang et al., 2015, and references therein), seismic velocities (Inoue et al., 1998) and electrical conductivity (Huang et al., 2005;Yoshino and Katsura, 2012). Knowledge of the effect of water content on these physical properties is essential for interpreting the geophysical characteristics of the transition zone in terms of its water content. It is therefore essential to develop a reliable method to precisely quantify OH concentrations in high pressure minerals.
Until recently Fourier Transform infrared Spectroscopy (FTIR) was the only spectroscopic technique available to assess the water contents in nominally anhydrous minerals (NAMS) (Libowitzky and Rossman, 1996;Demouchy and Bolfan-Casanova, 2016). Indeed, FTIR is a very sensitive technique that also provides information on the speciation of water (i.e., structurally bound water or water in grain boundaries or melt inclusions). However, there are limitations of this technique when working on polymineralic and small-grain sized experimental samples (<50 µm) such as peridotite equilibrated at high-pressures, since quantitative FTIR is essentially used in absorbance mode. Another limitation is that the absorptivity of the bands must be known to convert absorbance into concentration. Such calibrations of the absorptivity of OH bands have been carried out previously for several mantle minerals (Bell et al., 1995 for pyroxenes and garnet;Withers et al., 2012 for olivine; Deon et al., 2010 for wadsleyite; Thomas et al., 2015 for ringwoodite). Alternatively, the universal frequencybased calibration of Paterson (1982) or Libowitzky and Rossman (1997) is used. Other methods of quantification need also to be calibrated (e.g., secondary ion mass spectrometry) and unfortunately there are only few methods that are absolute and easily accessible. A further disadvantage of FTIR for transition zone phases is that the infrared radiation is often completely absorbed by very hydrous samples, requiring the use of very thin samples (<30 µm) to levels close to the limits of failure.
In this study, we synthesized wadsleyite and ringwoodite with different H contents to carefully investigate the H incorporation in these minerals. In the following, we discuss (1) new water content characterization of wadsleyite and ringwoodite crystals determined by FTIR and ERDA; (2) the determination of new absorptivity coefficients of OH in wadsleyite and ringwoodite to compare to those previously published; (3) the incorporation mechanisms that we observe for wadsleyite and ringwoodite compared to previous reports and (4) finally, we present the first quantitative measurements of the water concentration in phase D, a hydrous phase capable to store up to 18 wt% H 2 O, theoretically, much more than serpentine minerals.

Multi-Anvil Synthesis Experiments
The starting materials used to synthesize minerals in this study consisted in mixtures of high purity oxide powders MgO (99.998%) and SiO 2 (99.998%) that were dehydrated in an oven at 1,000-1,100 • C overnight prior to weighing. Iron was incorporated in the mixture as FeO (99.5%), and water was incorporated by adding brucite, Mg(OH) 2 (95%, the rest being adsorbed CO 2 ), and in some experiments by adding additional distilled H 2 O (see Table 1). Four compositions were prepared: two Fe-free Mg 2 SiO 4 and two Fe-bearing (Fo90) compositions containing 5 and 10 wt% H 2 O, respectively. The weighed oxides and hydroxides were ground in ethanol for 1 h, dried under an IR lamp and then stored in a vacuum furnace until loading. The starting materials were embedded in Au 80 Pd 20 capsules and when Fe-bearing mixtures were employed an additional Re inner capsule was used to avoid iron loss. In some experiments, two capsules were loaded together, and these are referred to as a and b.
The high-pressure (HP) and high-temperature (HT) syntheses were performed in a multi-anvil press installed at Laboratoire Magmas et Volcans (LMV), Clermont-Ferrand (France) using Cr-doped MgO octahedral assemblies of 14 mm edge for experiments at 14 GPa and 10 mm edge for those run at higher pressures. We used tungsten carbide cubes with 8 and 4 mm truncations, respectively, and the pressure calibration previously described by Boujibar et al. (2014) was followed. Heating and thermal insulation of the experimental charge were ensured by a LaCrO 3 furnace and a ZrO 2 sleeve, respectively. To protect the samples from La and Cr contamination, MgO sleeves were placed between the furnace and the capsule. Temperature was monitored during the duration of the experiments (30 min to 5 h, see Table 1) with a W 5 Re/W 26 Re thermocouple.

Electron Probe Micro Analysis
After the experiments, the samples were prepared as doubly polished sections cut parallel to the longest dimension of the capsule. The samples were carbon coated for electron probe microanalysis (EPMA). These analyses were performed using a Cameca SX100 installed at LMV, to determine the chemical composition (Mg, Si, and Fe content) of minerals that crystallized in the HP-HT experiments. The standards used in the analyses were wollastonite (for Si), forsterite (for Mg) and fayalite (for Fe) and operating conditions were 15 keV and 15 nA with 20 s Frontiers in Earth Science | www.frontiersin.org 2 June 2018 | Volume 6 | Article 75 counting time (10 s on the peak and 10 s on the background). The results of the analyses are given in Tables 2, 3.

Elastic Recoil Detection Analysis (ERDA)
ERDA analyses were performed using the nuclear microprobe of Laboratoire d'Etude des Eléments Légers, CEA, Saclay, (France) following the set up by Khodja et al. (2001). The detailed analytical procedure is described in detail in Raepsaet et al. (2008) and Bureau et al. (2009) and this technique has been successfully used in a number of recent studies to determine H contents in NAMs (Withers et al., 2012;Novella et al., 2014). The measurements were performed through three different sessions. The samples were gold coated in the first session and carbon coated in the following ones. The metal used for coating has no effect on the measurement of the water content, but we found that Au coating induces a low energy tail in the ERDA spectrum that is difficult to fit. A 3 MeV 4 He + beam was produced by a single stage Van de Graaff accelerator and focused on a 3 × 3 µm² or 2 × 2 µm² surface using quadrupole magnetic lenses. The analysis then utilizes three detectors at the same time: an X-ray detector to record particle induced Xray emissions, an annular detector to record Rutherford backscattered (RBS) particles, and an ERDA detector to record H atoms ejected from the sample through elastic collisions with the alpha particles. The samples and standards may be tilted such that the polished surface is oriented either perpendicular to the beam in the standard Rutherford-backscattering analysis geometry, or at a low "grazing" angle of 15 • from the incident beam for the ERDA configuration as the dedicated detector is located at 30 • relative to the incident beam direction. The beam size on the sample surface was 12 × 3 µm 2 in the ERDA configuration, and the beam was scanned over the sample surface to produce compositional maps. Forward scattered incident He particles were prevented from reaching the ERDA detector by placing a 15 µm Al foil in front of the detector. At the beginning of each session, the standards were analyzed in the RBS geometry to determine the RBS solid angle ( RBS ).
Standards such as Al 2 O 3 , FeS 2 , SiO 2 , CaCO 3 , SnBi, Zr, ZrH, and Kapton are used to calibrate the RBS solid angle. Analysis time was 15 min for each standard, except for the Kapton (30 min). The SIMNRA program (Mayer, 1999) was used to model RBS and ERDA energy spectra. The average solid angle, RBS , thus determined was 73.12 ± 9.72 in the first session, 66.4 ± 3.26 in the second session and 59.53 ± 3.09 in the third session. The ERDA solid angle ( ERDA = 16.66 mSr in the first session, 15.59 ± 0.54 mSr in the second session and 8.47 mSr in the third session) was calibrated from a 3,700 s analysis in ERDA configuration of the Kapton standard, but also of ZrH standard in the second session (Wang, 2004). The RBS spectrum allows the quantification of the charge on the sample during the course of the ERDA measurement. The Kapton standard was assumed to be stoichiometric C 22 H 10 O 5 N 2 .
The samples were analyzed in the ERDA configuration with analysis times that varied between 20 and 120 min. An area of the sample was scanned with the beam (Figure 1A). Using the RISMIN software (Daudin et al., 2003), areas can be selected within the analyzed map to avoid cracks, grain boundaries or secondary mineral phases (see Figure 1B). The H contents of the samples were calculated by simulation of the ERDA spectra using the SIMNRA program. Knowing the composition of the sample, the RBS spectra were fitted in order to monitor the charge, a necessary input to calculate the bulk water content from the ERDA spectrum (see Figure 1C). The thickness of the gold coating (8 to 9 nm, corresponding to 48 × 10 15 atom cm −2 ) or of the C coating (∼100 × 10 15 atom.cm −2 ) was determined for each analyzed area from the RBS spectra, and the surface hydrogen was modeled as a single layer of H atoms that varied between 16 × 10 15 and 47 × 10 15 atom.cm −2 . The principal source of uncertainty in H contents is derived from the detector counting statistics. Additional minor sources of uncertainty include contributions from uncertainties in sample tilt angle, RBS solid angle and ERDA energy calibration. Uncertainties  associated with cross sections and stopping powers used by SIMNRA are minor and were not taken into account. "Surface H" and "bulk H" maps were produced by plotting respectively the number of detector events recorded with energies in the high and low energy regions of the ERDA spectrum. Maps of Au and major elements (Fe, Mg, Si, O, and combinations thereof) were produced from the corresponding energy steps in the RBS spectra. The regions of the analyses used for quantification of H excluded the areas of any surface features that result in anomalies in the Au, H and major element compositional maps but also capsule material as shown in Figure 1B.
A typical ERDA energy spectrum is shown in Figure 2. The intense signal at high energy represents H atoms that have been ejected from the surface of the sample and that arrive at the detector with high energy (Figure 2A). The energy of an alpha particle decreases as the sample is penetrated, so particles that originate from within the sample arrive at the detector with correspondingly lower energy, as represented by the lower energy plateau in the ERDA spectrum. Surface pollution of the sample can therefore be easily distinguished from bulk content, and it is through simulation of the low energy plateau in the ERDA spectrum that the H content of the sample itself is calculated. The bulk H signal was calculated using the integration of the signal between 200 and 500 keV. The signal remained stable throughout the duration of the analyses, showing that the signal is not modified by beam exposure (Bureau et al., 2009).

Infrared Spectroscopy
Polarized and unpolarized Fourier Transform infrared spectra were acquired using a Vertex70 Bruker spectrometer coupled to a Hyperion microscope equipped with ×15 objective and condenser at LMV. Beam size in the analyses varied from 30 to 50 µm depending on the size of the crystals and the presence of cracks/inclusions. The spectra were collected through a CaF 2 plate with a resolution of 2 cm −1 and with up to 300 scans. After application of a linear baseline with anchor points outside the OH stretching region, the absorbance was integrated from 3,200 to 3,650 cm −1 for wadsleyite and 2,000 to 3,730 cm −1 for ringwoodite. The absorption coefficient was then quantified using the Beer-Lambert law: where A is the absorbance, ε is the absorption coefficient in L.mol −1 .cm −2 , c is the concentration in moles H 2 O/L and t is the thickness in cm. Density factors required in order to convert water concentrations from ppm weight H 2 O into moles of H 2 O/L were calculated for wadsleyite and ringwoodite using crystallographic data from several sources (see Table 4). Thickness of the samples was accurately measured either using a Mitutoyo micrometer or the microscope of a Renishaw Raman spectrometer, with uncertainties in thickness measurements of the order of 1-3 µm on average.
For orthorhombic wadsleyite, the water quantification was based on the average of ∼10 unpolarized measurements performed on randomly oriented grains within the doubly polished thin sections. The absolute absorbance of the crystal is then equal to three times the average of the unpolarized measurements as demonstrated by Kovacs et al. (2008) and Bali et al. (2008). The error associated with the use of unpolarized radiation was estimated by Sambridge et al. (2008) to be 20% of the absolute absorbance if 10 grains are used. Given that the anisotropy of OH absorption in wadsleyite is less than in olivine (see Jacobsen et al., 2005;Bali et al., 2008;Deon et al., 2010), the error here should be less when applying unpolarized radiation on wadsleyite than on olivine.

Phase Compositions and Water Contents
The composition of wadsleyite and ringwoodite crystals are shown in Figure 3. The Mg/Si or (Mg+Fe)/Si ratios as measured by EPMA are observed to decrease with increasing water content as determined by ERDA, in agreement with the observations of Inoue et al. (1995) using Secondary ion Mass Spectrometry (SIMS). We also observe that determination of water content using EPMA totals overestimates water contents by 1-2 wt% H 2 O compared to quantification based on ERDA. Also, there is more scattering when plotting (Mg+Fe)/Si ratios vs. EPMA weight totals, indicating that using the EPMA totals below 99-101 wt% is less precise for determining water contents than the ERDA method (Figures 3A,B). The trend in (Mg+Fe)/Si ratio vs. water content does not depend on the presence of iron in neither wadsleyite, nor ringwoodite, thus we neglected the ferric iron species when calculating the molar concentration of H (see Table 2). Moreover, we do not observe a change in the infrared OH absorption bands with the incorporation of iron.  Demouchy et al. (2005), reported this experiment as unreliable in terms of water content and Mg/Si, but we believe that its water content, as we measured by ERDA, is correct, even if almost 3 times higher than reported by SIMS.
As in previous studies in Mg 2 SiO 4 +H 2 O system, we observe that at low temperature in the olivine-water system, phase D [MgSi 2 O 4 (OH) 2 ] coexists with brucite + superhydrous phase B, and as temperature increases, superhydrous phase B + melt (Frost and Fei, 1998;Ohtani et al., 2000;Ganskow and Langenhorst, 2014). Phase D and superhydrous phase B grow as an intimate mixture in the Mg 2 SiO 4 -water system (Frost, 1999), and only phase D could be analyzed using ERDA because large crystals grew at the interface with the silicate melt. The analysis totals vary between 83 and 88 wt%, indicating large variations in water content [the composition MgSi 2 O 4 (OH) 2 corresponds to a theoretical water content of 18 wt% H 2 O, hence a theoretical weight total of 82%]. In this study, phase D displays a variable composition with Mg/Si ratio between 0.56 and 0.65, within the range reported in the literature (0.55 and 0.77, see Frost and Fei, 1998;Ohtani et al., 2000;

Infrared Spectra and Bands Assignment
The averages of nine to twelve unpolarized infrared spectra of wadsleyites are shown in Figure 4 (see also Supplementary Figure 1) as measured on four different samples. We identified up to nine OH absorption bands: three weak bands at 3,692, 3,260, and 3,472 + 3,428 cm −1 , three strong bands at 3,400-3,350, ∼3,320 and 3,300 cm −1 , and two bands at 3,613 and 3,580 cm −1 , and a very weak band around 3,000 cm −1 observed in H-poor wadsleyite. Compared to the spectra reported by Jacobsen et al. (2005), those in this study display an additional band at 3,400 cm −1 , which was observed in the study of Kohn et al. (2002). The bands at 3,613 and 3,580 cm −1 , and also the two weak bands at 3,428 and 3,472 cm −1 , seem to appear at high water contents (here above 800 ppm wt H 2 O). The spectra of ringwoodite are shown in Figure 5, where the average of four to six unpolarized spectra recorded on different grains is shown. The spectra display the typical very broad band at 3,117 cm −1 , accompanied of weaker satellite bands at 3,687 + 3,733 cm −1 and 2,538 + 2,441 cm −1 . A shoulder of the main band located at 3,210 cm −1 is detected in some samples and a very weak feature at 3,550 cm −1 is observed in some iron-bearing samples. Sometimes a band at 2,666 cm −1 is observed as well as a feature at 2,364 cm −1 . The samples are homogeneous, judging from the similarity of the spectra (ringwoodite is cubic, hence no pleochroism should be observed for the absorption bands of structural OH).
Interpretation of spectroscopic data is not always straightforward in terms of site occupancy. For example, Smyth et al. (2003) noticed that the frequency of the main OH band at ∼3,117 cm −1 in the infrared spectrum of ringwoodite would correlate with a distance of 2.7 Å, rather in the range of O-O distances found for the tetrahedral edge (2.71 Å) than for the octahedral edges (2.86-2.31 Å). But it is not easy to use the distance-frequency (i.e., d O−O vs. ν OH ) correlation (see Libowitzky, 1999) as it is influenced by the angle made by the O-H and H. . . O bonds. More recently, Ganskow et al. (2010) and Mrosko et al. (2013) assigned the main band at 3,117 cm −1 to H coupled to Mg vacancies because they observed that this band shifts to higher wavenumbers when iron content of the ringwoodite increases. This observation is in agreement with the expansion of the octahedron upon the incorporation of larger iron cations and with the positive correlation between O. . . O interatomic distances and OH frequencies (Libowitzky, 1999). Mrosko et al. (2013) assigned the 3,700 cm −1 band to H in the tetrahedron, in agreement with Blanchard et al. (2009), based on the fact that this band shifts to lower wavenumbers when iron content increases. This would imply that the tetrahedron shrinks upon iron incorporation, which is not the case (see Hazen et al., 1990;Smyth et al., 2014), or that the O-H. . . O bond angle varies. They also observed a band at 3,420 cm −1 which is attributed to H coupled to Mg substituted to Si in tetrahedral sites. Concerning the group of bands at ∼2,500 cm −1 its assignment to OH stretches remains controversial. Hofmeister and Mao (2001) interpreted this band as a combination of overtones of Si-O related vibrations, however we insist on the fact that their sample contained water (as can be seen on their spectra) and also on the fact that this band is extremely weak in H-poor samples as observed by Bolfan-Casanova et al. (2000). If indeed, due to an OH stretch, the frequency of the bands at ∼2,500 cm −1 corresponds to 2.6 Å, in agreement  Table 4).

Infrared Extinction Coefficients for OH Bands in Wadsleyite and Ringwoodite
The extinction coefficient or molar absorptivity can be recalculated from Beer-Lambert law, knowing the absorbance, the concentration of water (independently determined by ERDA in this study) and the thickness. Concerning wadsleyite, knowing the water content of the sample and the average of unpolarized absorbance, multiplied by three (see Kovacs et al., 2008), yields the molar absorptivity or extinction coefficient. We measured four different wadsleyite samples, with water contents ranging from 800 to 4,200 ppm wt (Table 4, Figure 6) and we observe no effect of water content on the absorptivity. The average for the two iron free samples leads to an absorptivity of 69,000 ± 7,000 L/moles H 2 O/cm 2 , in excellent agreement with the value of 73,000 ± 7,000 L/moles H 2 O/cm 2 determined by Deon et al. (2010). The absorptivity for the samples containing 8 to 10 mole% Fe is 67,000 ± 5,000 and 75,000 ± 15,000 L/moles H 2 O/cm 2 , respectively, very similar to values for the Mg end-member and virtually the same when considering uncertainties. The molar absorptivity of ringwoodite was calculated separately from the FTIR analysis performed on 5 different samples ( Table 4). The absorptivity values vary from 118,000 ± 4,000 for sample #362 (with no Fe) to 139,000 ± 9,000 for #224 (with 10% mole Fe). The error bar on each absorptivity value is calculated from the standard deviation determined from measurements on different grains of the same sample, and amounts to approximately 6%. We do not observe an effect of iron content on the absorptivity coefficient unlike what Koch-Muller and Rhede (2010) observed for ringwoodites containing between 40 and 100 mole% Fe. For example, the sample containing 3% FeO here displays an absorptivity of 131,000 ± 6,000 L/moles H 2 O/cm 2 , similar to that of the samples containing 10% FeO: 135,000 ± 9,000 L/moles H 2 O/cm 2 (see Figure 6). Based on the data presented here we propose an absorptivity of 118,000 ± 5,000 for Fe-free ringwoodite and 135,000 ± 9,000 for Fe-bearing (Fo90) ringwoodite. Our value of ε for Fe-free ringwoodite is 15% higher than that extrapolated by Koch-Muller and Rhede (2010) and 10% higher than the more recent value determined using proton-proton scattering from Thomas et al. (2015). Indeed, Thomas et al. (2015) did not take into account the infrared feature at 2,500 cm −1 , which we did. We also tested calculating ε without taking into account this band in the integration of the absorbance and differences correspond to a maximum of 11%, thus explaining the 10% difference between the ε value from Thomas et al. (2015) and from the current study.
If we calculate the water content of the ringwoodites using the absorptivity coefficient of Paterson (1982), we find that the water contents are about approximately 50% lower than the water contents determined by ERDA ([H 2 O] Paterson /[H 2 O] ERDA ∼ 0.55 ± 0.02). This ratio between water contents determined using Paterson (1982) and those measured using ERDA can also be estimated graphically on Figure 7 for any wavenumber.
FIGURE 6 | Absorptivity coefficient (ε) measurement for wadsleyite and ringwoodite of this study as a function of the iron content, and compared to previous determinations. KMR stands for Koch-Muller and Rhede (2010) and T. for Thomas et al. (2015). Note that the value of KMR for iron-free ringwoodite is interpolated from values measured on samples with different iron contents (not shown). Within the error bar, we do not observe an effect of iron on the value of ε.

Incorporation of Water in Wadsleyite and Ringwoodite
In this study we observe the same decrease in (Mg+Fe)/Si atomic ratio as a function of water content (measured by ERDA) for wadsleyite and ringwoodite. This trend compares well with those established by Inoue et al. (1995), Kawamoto et al. (1996), andDemouchy et al. (2005) for wadsleyite, that used SIMS to measure water contents. However, the behavior reported by Ohtani et al. (2000) for ringwoodite (using SIMS as well), indicates that more H substitutes for Si sites in this phase than in its lower pressure polymorph (see Figure 3C).
The trend first observed by Inoue et al. (1995) and also observed in this study is consistent with two H atoms substituting for one octahedral Mg in wadsleyite, (2H) x Me in Kröger-Vink notation (Kröger and Vink, 1956). This is in agreement with the predictions of Smyth (1994) based on electrostatic considerations that shed light on the under-bonded character of the O1 oxygen of wadsleyite (the only one not bonded to a silicon atom) and that makes it the best candidate for protonation. This H incorporation mechanism was in fact later confirmed by X-ray single crystal diffraction (Kudoh et al., 1996(Kudoh et al., , 2000Smyth and Kawamoto, 1997;Ye et al., 2012), and more recently by neutron powder diffraction (Sano-Furukawa et al., 2011), showing vacancies mainly in the M3 octahedral site of wadsleyite. Also, most infrared features in wadsleyite have been assigned to hydrogen in Mg vacancies by Jacobsen et al. (2005) and Deon et al. (2010), except for the band around 3,000 cm −1 that was assigned to H replacing Si, based on its pleochroism and frequency (see also Kohn et al., 2002).
From the electrostatic point of view, ringwoodite was not expected to be a fully hydrated structure since there is no nonsilicate bonding oxygen in the structure, as there is in wadsleyite (see Smyth, 1994). Using single crystal X-ray diffraction, Kudoh et al. (2000) observed that, in Mg 1.89 Si 0.98 H 0.30 O 4 ringwoodite containing 2 wt% H 2 O (as determined by SIMS analyses), the vacancies are mainly located at the Mg site. Still, they realized that the Mg/Si ratio of this ringwoodite was higher (1.95) than that of wadsleyite containing the same water content (1.8); this led them to suggest the coupled substitution 3Mg = 6H and Si = MgH 2 in hydrous ringwoodite, resulting into Mg 2 Si = 8H. This Mg-Si disorder could be responsible for the very large width of the band centered at 3,120 cm −1 as observed in the IR spectrum of hydrous ringwoodite. On the other hand, Smyth et al. (2003) observed a systematic increase of the size of the octahedral site with H incorporation together with cation occupancy deficiency in this site, whereas the tetrahedral site is nearly full in a series of ringwoodites containing from 0.2 to 1.1 wt% H 2 O. Using first principle calculations (Blanchard et al., 2009) interpreted the major absorption band at ∼3,100 cm −1 as H located on the O-O edge shared between two octahedra, while the higher frequency band at 3,675 cm −1 is attributed to a tetrahedral edge.
More recently, Purevjav et al. (2014) published the first neutron powder diffraction data on ringwoodite with 2.4 wt% D 2 O (as determined from the unit cell expansion using the systematics reported in previous reports) and a Mg/Si of 1.93. They concluded to a partial occupancy of the tetrahedral site by Frontiers in Earth Science | www.frontiersin.org FIGURE 7 | Change in absorptivity coefficient (ε) of the OH band in the infrared as a function of the mean frequency of vibration of the OH (i.e., the latter being represented by the most intense absorption band in the spectrum of the phase of interest). Our value of ε for ringwoodite and wadsleyite agree well with those of Koch-Muller and Rhede (2010) and Deon et al. (2010). We confirm that the experimentally determined ε are lower than the trend of Paterson (1982) but also Libowitzky and Rossman (1997) for wadsleyite and ringwoodite in the latter case.
D. It is suggested that the substitution of silicon by H occurs at elevated water contents (see also Ye et al., 2012). It could be that there is a change in the incorporation mechanism of water in ringwoodite at high water contents. However, at least up to 1.16 wt% H 2 O, we observe a trend of Mg/Si in agreement with substitution in the octahedral site, while Ohtani et al. (2000) observe the Mg 2 Si = 8H substitution active at 1.5 wt% H 2 O. Thus, ringwoodite crystals with higher water contents need to be investigated in order to verify the change in incorporation mechanism.

Incorporation of Water in Phase D
Phase D is of particular interest because it has been proposed as a water carrier down to the lower mantle (Shieh et al., 1998;Ghosh and Schmidt, 2014;Walter et al., 2015). Its wide stability field can be explained by its extended compositional range with large variations in its EPMA weight totals associated to variations of the Mg/Si ratio (see Figure 8, 0.55 and 0.77, see Frost and Fei, 1998;Ohtani et al., 2000;Ganskow and Langenhorst, 2014;Ghosh and Schmidt, 2014). Extended solid solution with Al has also been reported, with an aluminum-rich endmember such as Al 2 SiO 4 (OH) 2 being experimentally observed (Pamato et al., 2015). The water content of phase D as determined by ERDA in this study varies from 6.7 to 11.2 wt% H 2 O, much lower than the water content recalculated from the EPMA weight totals as explained earlier. These low water contents compared to the expected 18 wt% H 2 O of the theoretical end-member MgSi 2 O 4 (OH) 2 can be explained by the high temperatures of synthesis of phase D. In this study we observe that the atomic ratio decreases with increasing water content, in disagreement with previous studies reporting that the Mg/Si ratio negatively correlates with the analyzed totals (see Frost and Fei, 1998, Figure  8 of this study) or the water contents as measured by SIMS by (Ohtani, 1997). Still our compositional range is too limited to conclude, in comparison to previous studies that indeed investigated lower temperatures, as low as 800 • C, compared to 1,100-1,400 • C here. The compositional range, as proposed by previous authors, arises probably from two incorporation mechanisms (Yang et al., 1997;Frost and Fei, 1998), see Figure 8: The compositions shown in Figure 8 indicate the Si 4+ = 2H + + Mg 2+ mechanism as being the dominant one. However as shown in Figures 3A,B, the use of EPMA totals to determine water contents in hydrous phases is unreliable. For example, analyses for ringwoodite samples 271 and sample 238 yield very different analysis totals of 97.6 and 100.4 wt%, respectively, implying rather different water contents. However, their similar (Mg+Fe)/Si ratios of 1.96 and 1.95 indicate similar water contents, as confirmed by ERDA with 0.43 and 0.44 wt% H 2 O, respectively. FIGURE 8 | Electron probe micro analyses showing the (Mg+Fe)/Si ratio in phase D as a function of analysis totals from this study compared to previous reports. Our results agree with those obtained at high temperatures by Frost and Fei (1998).

CONCLUSION
Hydrous wadsleyite and ringwoodite have been synthesized in the MgO-SiO 2 -H 2 O and MgO-FeO-SiO 2 -H 2 O systems at pressures from 15 to 22 GPa and temperatures from 1,100 to 1,700 • C. Their water contents have been measured using Elastic Recoil Detection Analysis (ERDA) and vary from 0.02 to 3.1 wt% H 2 O. For ringwoodite samples, containing up to 1.16 wt% H 2 O, we observe that the (Mg+Fe)/Si ratio vs. water content follows the same trend as for wadsleyite, indicating that hydrogen is substituting for magnesium. Our measurements agree with the trends of (Mg+Fe)/Si vs. water observed for wadsleyite using SIMS but not for ringwoodite. At least at water contents below 1.2 wt% H 2 O.
We also measured, for the first time, quantitative water contents of phase D and observed that it varies from 6.7 to 11.2 wt% H 2 O (up to twice less than estimated from EPMA totals) and that the Mg/Si atomic ratio decreases with increasing water content, in disagreement with earlier data, but as we explained above our compositional field is very narrow compared to previous reports.
Using the samples from this study, we were able to determine the absorptivity coefficient for OH infrared absorption bands in four wadsleyite samples and five ringwoodite samples. The average for the two iron-free wadsleyite samples leads to an absorptivity of 69,000 ± 7,000 L/moles H 2 O/cm 2 , in very good agreement with that determined by Deon et al. (2010). The wadsleyite with 8 mole% Fe, displays an absorptivity of 67,000 ± 5,000 L/moles H 2 O/cm 2 . The absorptivity values vary from 118,000 ± 5,000 for ringwoodite without Fe to 135,000 ± 9,000 for Fe-bearing ringwoodite (10% mole Fe). Our values of ε for ringwoodite and wadsleyite agree well with those of Koch-Muller and Rhede (2010) and Deon et al. (2010). We thus confirm that the experimentally determined ε are lower than the trend reported in the calibration of Paterson (1982), but also lower than the trend reported in the calibration of Libowitzky and Rossman (1997) in the case of ringwoodite and wadsleyite. We find that the calibration of Paterson (1982) under-estimates the water contents by 50%. This should be taken into account when studying the effect of water on the elasticity of wadsleyite and ringwoodite.

AUTHOR CONTRIBUTIONS
NB-C is responsible for project design, funding, and wrote the manuscript. NB-C and DN are responsible for performing the multi-anvil experiments, ERDA, EPMA, and Raman measurements and data treatment. FS is responsible for the FTIR and Raman measurements on ringwoodite as well as assessing the extinction coefficients. HB, CR, and HK are responsible for the operation of the nuclear probe and standardization. SD brought two samples that were previously analyzed by SIMS.
high-pressure lab. Jean-Luc Devidal and Jean-Marc Hénot are thanked for their help in EPMA and SEM analyses, respectively. We also acknowledge the LEEL's staff for their assistance during the nuclear microprobe analysis. This work was conducted in the framework of the ANR Jeune Chercheuse HYDEEP Hydrogen in the Deep Earth awarded to NB-C (ANR 11 JS56 01501). This work benefitted from Labex Clervolc grants to DN and FS. This is ClerVolc contribution n • 303.