The responses of the four main substitution mechanisms of H in olivine to H2O activity at 1050 °C and 3 GPa

The water solubility in olivine CH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left({C}_{{\mathrm{H}}_2\mathrm{O}}\right) $$\end{document} has been investigated at 1050 °C and 3 GPa as a function of water activity aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left({a}_{{\mathrm{H}}_2\mathrm{O}}\right) $$\end{document} at subsolidus conditions in the piston-cylinder apparatus, with aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {a}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} varied using H2O–NaCl fluids. Four sets of experiments were conducted to constrain the effect of aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {a}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} on the four main substitution mechanisms. The experiments were designed to grow olivine in situ and thus achieve global equilibrium (G-type), as opposed to hydroxylating olivine with a pre-existing point-defect structure and impurity content (M-type). Olivine grains from the experiments were analysed with polarised and unpolarised FTIR spectroscopy, and where necessary, the spectra have been deconvoluted to quantify the contribution of each substitution mechanism. Olivine buffered with magnesiowüstite produced absorbance bands at high wavenumbers ranging from 3566 to 3612 cm−1. About 50% of the total absorbance was found parallel to the a-axis, 30% parallel to the b-axis and 20% parallel to the c-axis. The total absorbance and hence water concentration in olivine follows the relationship of CH2O∝aH2O2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{{\mathrm{H}}_2\mathrm{O}}\propto {a_{{\mathrm{H}}_2\mathrm{O}}}^2 $$\end{document}, indicating that the investigated defect must involve four H atoms substituting for one Si atom (labelled as [Si]). Forsterite buffered with enstatite produced an absorbance band exclusively aligned parallel the c-axis at 3160 cm−1. The band position, polarisation and observed CH2O∝aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{{\mathrm{H}}_2\mathrm{O}}\propto {a}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} are consistent with two H substituting for one Mg (labelled as [Mg]). Ti-doped, enstatite-buffered olivine displays absorption bands, and polarisation typical of Ti-clinohumite point defects where two H on the Si-site are charge-balanced by one Ti on a Mg-site (labelled as [Ti]). This is further supported by CH2O∝aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{{\mathrm{H}}_2\mathrm{O}}\propto {a}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} and a 1:1 relationship of molar H2O and TiO2 in these experiments. Sc-doped, enstatite-buffered experiments display a main absorption band at 3355 cm−1 with CH2O∝aH2O0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{{\mathrm{H}}_2\mathrm{O}}\propto {a_{{\mathrm{H}}_2\mathrm{O}}}^{0.5} $$\end{document} and a positive correlation of Sc and H, indicating the coupled substitution of a trivalent cation plus a H for two Mg (labelled as [triv]). Our data demonstrate that extreme care has to be taken when inferences from experiments conducted at aH2O=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {a}_{{\mathrm{H}}_2\mathrm{O}}=1 $$\end{document} are applied to the mantle, where in most cases, a low aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {a}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} persists. In particular, the higher exponent of the [Si] substitution mechanism means that the contribution of this hydrous defect to total water content will decrease more rapidly with decreasing aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {a}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} than the contributions of the other substitution mechanisms. The experiments confirm previous results that the [Mg] mechanism holds an almost negligible amount of water under nearly all T-P-fO2-fH2O conditions that may be anticipated in nature. However, the small amounts of H2O we find in substituting by this mechanism are similar in the experiments on forsterite doped with either Sc or Ti to those in the undoped forsterite at equivalent aH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {a}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} (all buffered by enstatite), confirming the assumption that, thermodynamically, CH2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{{\mathrm{H}}_2\mathrm{O}} $$\end{document} substituting by each mechanism does not depend on the water concentration that substitutes by other mechanisms.


Introduction
Trace concentrations of hydrogen-bearing point defects can change the mechanical properties of olivine and the dominant phase of the Earth's upper mantle, producing a profound effect on mantle rheology (Demouchy et al. 2007; Karato et al. 1986;Mei and Kohlstedt 2000). Such defects also influence transport properties like electrical conductivity (Karato and Wang 2013). Fourier transform infrared spectroscopy (FTIR) shows that the H substitutes by bonding to O 2− anions, producing OH − species according to the generalised reaction O 2− + H 2 O = 2OH − . The H incorporation thus depends on the fugacity of H 2 O, justifying its colloquial designation as "water". Experimental studies on synthetic systems have identified four principal substitution mechanisms, which can be identified from their different O-H stretching modes, using FTIR spectroscopy. Following Kovacs et al. (2010), we use [Si] to denote the substitution mechanism whereby H is charge-balanced by silicon vacancies, [Mg] for H charge-balanced by Mg vacancies, [triv] for H cosubstituting with a trivalent cation, and [Ti] for H cosubstituting with titanium. The thermodynamic equilibria describing these four substitutions are: which give the following equilibrium constants for pure forsterite (that is, in the approximation that a ol Mg 2 SiO 4 is unity): The four substitution mechanisms therefore depend on the activity of silica (a SiO2 ) in different ways, and in the case of the [triv] and [Ti] substitutions, the chemical potentials (effectively, the availability) of the relevant enabling components, R 3+ O 1.5 and TiO 2 , respectively. But the most significant implication is that the way that H is incorporated in olivine may vary with the fugacity of H 2 O, depending on whether the H atoms needed to achieve charge balance are completely associated with the point defect by being bonded to the oxygen atoms surrounding it in specific locations, or are disordered over the lattice by being bonded to oxygen atoms without regard to location. For example, if the four H atoms of the [Si] mechanism are bonded to oxygen atoms surrounding the Si site vacancy to produce local charge balance (that is short-range order), as recently shown by Xue et al. (2017), then the activity of the Mg 2 H 4 O 4 component would be proportional to its mole fraction, such Alternatively, if the H atoms were bonded to four oxygen atoms at random positions in the lattice without short-range order, the configurational entropy of the Mg 2 H 4 O 4 component would be correspondingly greater, with its activity being proportional to its mole fraction to the power of four (or five, if the configurational entropy due to the Si vacancy itself is included), such that C  [triv] mechanism, there is only the one H atom per formula unit of R 3+ HSiO 4 , so if the position where the H bonds to an oxygen is determined by short-range order with respect to where the R 3+ cation is substituting, the activity of the R 3+ HSiO 4 component will again be proportional to its mole fraction, but with the result that C triv ½ H 2 O ∝f H 2 O ð Þ 0:5 . The close association of H substituting by the [triv] mechanism with the R 3+ cation is demonstrated by the correlation of the wavelength of the [triv] infrared absorption with the ionic radius of the R 3+ cation (Berry et al. 2007a). If local charge balance proves to be the case, then even at one specific temperature and pressure, the way that "water" is incorporated into olivine should change with the activity of H 2 O, a H 2 O , defined as f(H 2 O)/f(H 2 O)°, where f(H 2 O)°is the fugacity of pure H 2 O at the T and P of interest. This is an important consideration when laboratory observations are to be extrapolated to olivine in natural environments such as the Earth's mantle. In the laboratory, experiments are typically conducted at high a H 2 O to maximise H 2 O contents, which facilitates measurements, but in the Earth's mantle, a H 2 O is lowered by the presence of other components, and an upper limit to a H 2 O at a given T, P and composition is imposed by partial melting (Green et al. 2010). Whenever amphibole is present, a H 2 O is constrained by amphibole-pyroxene-olivine equilibria and is considerably lower than if a free aqueous fluid phase were present (Lamb and Popp 2009).
The aim of the experimental study presented here is to test the relationships between C H 2 O and a H 2 O for the four principal substitution mechanisms. We chose a representative condition of 3.0 GPa and 1050°C for experimental convenience, with a H 2 O varied using H 2 O-NaCl mixtures. Although the [triv] substitution in natural olivines is likely mostly due to Cr 3+ and Fe 3+ (e.g. Tollan et al. 2015), both these elements also occur in olivine in a 2+ valence state, Fe predominantly so, making the determination of the amounts of Fe 3+ or Cr 3+ from analysed Fe or Cr impractical. Yet, to understand the [triv] substitution mechanism, it is desirable to know the concentration of the R 3+ cation in octahedral coordination. For this reason, we sought a redox-insensitive element with a substantial solubility in forsterite, and a large enough ionic radius to substitute into its octahedral sites only-unlike Al, which may also be important in promoting water solubility in olivine (Grant et al. 2007a). There is really only one choice, Sc 3+ .

Preparation of starting materials
For experiments investigating [Ti], [triv] and [Mg] hydrous defects, powdered synthetic Ti-and Sc-doped forsterite was prepared by a process of solution-gelation. Magnesium nitrate was dissolved in water slightly acidified by nitric acid, with Ti and Sc added to produce forsterite containing 2000 ppm of Ti and Sc, respectively, using ammonium bis(oxalato)oxotitanate(IV) hydrate or scandium oxide. Concentrations in this paper are given in ppm by weight, i.e., μg g −1 . Tetra-ethyl orthosilicate was added with ethanol, after which a few drops of ammonia initiated the gelation process, with the mixture then left overnight to allow complete precipitation. The precipitate was dehydrated by heating on a hot plate at low temperatures for 24 h followed by intensive heating, first over a Bunsen burner and then in a box furnace at 600°C. Pure forsterite, produced by the same method (but without the addition of Sc and Ti), was then mixed with the Scand Ti-doped forsterite powders in various ratios to produce the starting compositions for the hydration experiments. Concentrations of Sc and Ti in recovered olivine crystals are given in Table 1. In order to buffer the silica activity, enstatite powder was also produced by sintering synthetic forsterite with SiO 2 in the appropriate stoichiometric proportions. For experiments investigating the [Si] defect, powdered San Carlos olivine was run with synthetic magnesiowüstite (Fe 0.7 Mg 0.3 O) to produce a low a SiO2 , which enhances water substitution by this mechanism.

Piston-cylinder experiments
One challenge of the experiments was to produce crystals of H 2 O-bearing forsterite or olivine large enough for FTIR spectroscopy, but at sufficiently low temperature to avoid melting and excessive dissolution of silica in the fluid, which informed the choice of 1050°C at 3 GPa. The crystals were grown from the starting materials in a piston-cylinder apparatus. Powders of pure or doped forsterite were packed inside Pt capsules, with a layer of enstatite powder to buffer a SiO2 , and oxygen fugacity was controlled by the intrinsic conditions of the assembly (estimated to be approximately equivalent to the fayalite-magnetite-quartz buffer); at which conditions, the only redox-sensitive element, Ti, should be essentially all Ti 4+ (Mallmann and O'Neill 2009). The experiments using San Carlos olivine and magnesiowüstite were loaded into Au capsules, with oxygen fugacity internally buffered using layers of Re and ReO 2 powders (Pownceby and O'Neill 2000) to ensure a constant Fe 2 All the forsterite crystals that were subsequently analysed grew during the experiments, and the finely ground San Carlos olivine completely recrystallised, which is necessary to achieve the equilibrium pointdefect structure (Matveev et al. 2001). That all the crystals characterised in this study grew during their synthesis in equilibrium with the buffering assemblages and fluid phase is in contrast to the experimental approach that hydroxylates pre-existing crystals (e.g. Bai and Kohlstedt 1993;Zhao et al. 2004;Gaetani et al. 2014). In this latter approach, H moves into the crystal by solid-state diffusion, but the pre-existing point-defect structure of the olivine crystal is conserved. This phenomenon was exploited by Bai and Kohlstedt (1993) to study olivine pre-equilibrated at different oxygen fugacities at atmospheric pressure and then hydroxylated at one oxygen fugacity at a given temperature and pressure. In such experiments, the point-defect structure under which the water is incorporated is metastable and distinguishable to that expected at global equilibrium (Matveev et al. 2001). A spectacular example of conserving preexisting point-defect structure is the study of Jollands et al. (2016) on the decoration of Ti 3+ in forsterite to form the [triv] substitution, by hydroxylation under oxidizing conditions. Stabilizing Ti 3+ in forsterite requires highly reducing conditions (Mallmann and O'Neill 2009); accordingly, Jollands et al. (2016) prepared their material using a CO-CO 2 gas mixture with 97% CO at 1500°C and 1 bar. The hydroxylation was then carried out at oxygen fugacities up to twelve orders of magnitude higher, imposed by the Re-ReO 2 and Ag-Ag 2 O buffers at 850°C and 1.5 GPa (Jollands et al. 2016).
There is unnecessary controversy in the literature on the interpretation of experimental results on the incorporation of water in olivine due to the failure to distinguish clearly between the two types of experiments, those aimed at achieving global equilibrium under the conditions at which the water is incorporated and those aimed at hydroxylating existing point-defect structures and compositions, including the minor-element concentrations that determine the amounts of water associated with the [triv] substitution mechanisms. We suggest that to reduce the confusion, all experiments should be labelled "G-type" if global equilibrium is the target and "M-type" if a metastable equilibrium is sought. The experiments reported here are G-type. The interpretation of M-type experiments is likely to be the more difficult by far, because the metastable substitutions depend on the rates of diffusion of the point-defects and/or elements that enable them; in contrast, the global equilibrium that is the aim of a G-type experiment is independent of transport phenomena, by definition. The interpretation of M-type experiments may therefore be aided by H diffusion studies (e.g. Mackwell and Kohlstedt 1990;Demouchy and Mackwell 2006;Padron-Navarta et al. 2014). One potential problem is if the experimental products fall in the no man's land between the two types.

Fourier transform infrared spectroscopy
The forsterite and olivine crystals were analysed by FTIR spectroscopy, using a Bruker Tensor 27 infrared spectrometer with a liquid nitrogen-cooled mercury cadmium telluride detector coupled to a Bruker Hyperion infrared microscope. The analysis chamber was continuously purged with dry air in order to minimise interference of the intrinsic forsterite absorbance band by atmospheric background. Individual crystals were placed on a 100 μm Cu wire grid and measured in transmission mode with polarised and unpolarised light. For polarised measurements, crystal orientation was deduced through comparison of the silicate overtone region (~1200-2200 cm −1 ) with reference spectra for each principal orientation (Lemaire et al. 2004). Background analyses were taken at regular intervals, and both sample and background measurements were the average of 64 individual scans at a resolution of 4 cm −1 . After analysis, the acquired spectra were processed using the Bruker OPUS © software package. Any residual atmospheric contamination was minimised by application of the atmospheric compensation tool, followed by baseline correction using the "concave rubber band" software tool using 64 baseline points and four iterations. Occasionally, a further baseline correction was applied in order to remove broad absorbance bands due to fluid inclusions.

Quantification of data
The areas beneath the major absorbance bands from each experiment were calculated using the integration function of the OPUS software package, and the resulting absorbance value was normalised to a thickness of 1 cm. Crystal thickness was determined by exploiting the relationship with absorbance in the silica overtone region (1625-2150 cm −1 ), whereby thickness (in microns) is calculated by dividing the integrated absorbance of the overtones (between 1625 and 2150 cm −1 ) by the appropriate coefficient. For unpolarised measurements, the coefficient of Shen et al. (2014) was used (0.553). For polarised measurements, coefficients specific for each principal axis were determined by conducting unpolarised and polarised measurements on the same crystal and comparing the respective overtone absorbances. By doing this for multiple crystals, we established coefficients of 0.75, 0.50 and 0.56 for a, b and c-axes, respectively, which were then used in all subsequent thickness calculations for polarised data. Water contents for polarised measurements were calculated by summing the normalised absorbance of each major band along each of the three principal axes and dividing by the integral absorption coefficient. For each experiment design, only the absorbance due to the principal bands is reported (see Table 2 for the integration ranges used), guided by previous experimental and theoretical studies that have reported the association of different defects with specific band positions (e.g., Lemaire et al. 2004;Berry et al. 2005;Walker et al. 2007;Kovacs et al. 2010;Umemoto et al. 2011;Ingrin et al. 2013). Any additional less intense bands at distinctly different wavenumbers were not included in calculations of water, with the exception of bands attributed to Mg vacancies, which are reported separately. The reported uncertainty in the water contents is the standard deviation from measurements of many individual crystals, and is a measure of precision rather than accuracy, as it does not include systematic or semi-systematic uncertainties due to additional factors such as errors in published absorption coefficients, thickness calibrations and baseline corrections, which are likely to be significant, but are difficult to quantify. For the unpolarised absorbances, the measurements from at least 12 crystals from each experiment were averaged, divided by the same integral absorbance coefficient and then multiplied by three, following the method of Kovacs et al. (2008). Uncertainty in water contents following this method is dependent on the degree of polarisation of the defects, the absolute water contents and any unintentional bias in orientation due to crystal shape. Based on this and the comparison with Fig. 1 of Kovacs et al. (2008), an uncertainty of 10% was applied to all unpolarised data.

Spectral deconvolution
When appropriate, complex spectra were deconvoluted in order to isolate the absorbance of individual, overlapping bands. We used a similar method to that of Tollan et al. (2015): bands were fit to a Gaussian function by linear least squares regression, with the optimum halfwidth for each band held constant between spectra such that only band height was allowed to vary. The starting point for each model was the band positions from Tifree [Mg] experiments. The positions of any additional bands were deduced through the regression procedure.

LA-ICP-MS
The concentrations of Ti and Sc were determined by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The laser ablation system consists of a CompexPro 110F ArF excimer laser (193 nm wavelength) with a custom-built two-volume ablation cell for rapid aerosol extraction and washout. The laser was run with a frequency of 5 Hz in energy constant mode, which ensured a stable fluence at the sample surface of 3 to 4 J/cm 2 . A focused spot with a diameter of 37 μm was used for sample and standard analyses. The cell was connected to an Agilent 7700x ICP-MS, and ablated material was transported to the ICP-MS in a stream of ultra-high purity He and Ar. Analyses were acquired as a time-resolved signal with 20 s of background followed by 40 s of counts on ablated material. NIST 610 and 612 glasses were used as calibration standards, and Si was used as internal standard.

Results and discussion
Each experiment yielded from three to 15 crystals large enough and sufficiently free of fluid inclusions to obtain quantifiable FTIR data. Polarised spectra from the three principal axes were recovered from each experiment, complemented by unpolarised spectra. Water concentrations calculated from both polarised spectra and unpolarised spectra following the method described by ) are in very good agreement for average water concentrations calculated from each experiment, ranging from 50 to 2500 ppm ( Fig. 1), but particularly at lower water concentrations which are within the range typical of natural mantle olivine. This is consistent with the theory of Sambridge et al. (2008), as implemented by Kovacs et al. (2008), and illustrates the viability of using unpolarised data to calculate accurate water concentrations in olivine with a variety of defect populations. The concentration of H 2 O associated with each species of hydrous point defect shows a clear relationship with the activity of water of the experiment (Fig. 2). Distinctly different polarised band positions and shapes can be identified from experiments investigating each of the different defect types.

Low SiO 2 activity experiments: [Si]
Olivines from experiments conducted at low silica activity (buffered by magnesiowüstite) are characterised by complex polarised spectra consisting of four major absorbance bands and six further minor absorbance bands (Fig. 3). Bands are moderately to strongly polarised, with very small FWHM (full width at half maximum). Parallel to E||a, the strongest bands are centred at 3612 cm −1 followed by 3578 cm −1 . The band at 3612 cm −1 shows strong asymmetry, with a prominent shoulder positioned at 3600 cm −1 , whilst the band at 3578 cm −1 shows minor asymmetry with a small shoulder positioned at 3550 cm −1 . Parallel to E||b, the strongest band is centred at 3550 cm −1 , followed by the band at 3578 cm −1 which has similar intensity as in the E||a direction. The band at 3612 cm −1 is also present, but at a much lower intensity than in the E||a direction. Parallel to E||c, only one major band is present, centred at 3566 cm −1 . This single band however is strongly asymmetric, with a double shoulder at 3545 and 3533 cm −1 . The band at 3612 cm −1 is again present, this time at even lower intensities than along either E||a or E||b. None of the other major bands from E||a or E||b are above the limit of detection. Table 2 Calculated water concentrations in each of the three principal crystallographic orientations using polarised FTIR data and also total water calculated from unpolarised FTIR data using the method of Kovacs et al. (2008) Tables 2 and 3 crystals from the same experiment had similar concentrations, with standard deviations of 5-15%.
Water associated to trivalent cations: [triv] As with [Ti] experiments, two series were conducted: one with fixed a H 2 O and another with fixed Sc concentration, and likewise, spectra from both experiment types were consistent with each other. Scandium-doped forsterite have simple spectra which are consistent with the study of Berry et al. (2007a), with one major band with very small FWHM at 3355 cm −1 , which appears strongly in all three directions but most intensely along E||a and a minor band at 3320 cm −1 , found principally along E||c (Fig. 5) . 3) have similar or identical positions with those in other low silica activity (wüstite-or magnesiowüstite-buffered) experimental studies (Aubaud et al. 2007;Lemaire et al. 2004;Padrón-Navarta et al. 2014;Withers and Hirschmann 2008), but also occur in experiments buffered at high silica activity conducted at significantly higher pressures (Smyth et al. 2006), with the highest intensity bands located at high wavenumbers (>3500 cm −1 ). The precise location of the bands is occasionally offset by 1-8 cm −1 : for example, the band at 3550 cm −1 is found at slightly higher wavenumbers in other studies, likely due to differences in the configuration of Fe in M sites adjacent to the hydrated Si vacancy (Blanchard et al. 2017). The general complexity and number of bands is much  (Balan et al. 2011;Umemoto et al. 2011;Walker et al. 2007). These observations are all consistent with hydrogen bonding to oxygen atoms surrounding silicon vacancies in the olivine structure, as denoted in Eq. 1 and supported by other studies investigating hydrous defect configurations (Ingrin et al. 2013;Blanchard et al. 2017).
Forsterite from the [Ti] experiments also displays absorbance at high wavenumbers, with bands at 3572 and 3524 cm −1 being the most intense (Fig. 4). These band positions are unique to [Ti] experiments, and are identical in wavenumber to previous experimental studies of Tidoped olivine/forsterite Kovacs et al. 2010;Padrón-Navarta et al. 2014). They are also the most commonly observed bands in natural upper mantle olivines sampled in spinel peridotite xenoliths, although their contribution to the total absorbance for a given sample varies significantly Denis et al. 2013;Schmädicke et al. 2013). Precise band positions generally vary slightly in the literature, which can be explained in part due to the overlap with the [Si] bands at 3578-3580 and 3566 cm −1 (Padrón-Navarta et al. 2014). As with previous studies using Ti as a dopant, we assign these bands to formation of a titano-clinohumite point defect within the forsterite structure (Eq. 2), with the resultant generation of a silicon vacancy explaining the similar wavenumbers to bands from [Si] experiments.
The [triv] experiments produced forsterite with absorbance dominated by a single intense band at 3355 cm −1 , similar to the Sc-doped experiments of Berry et al. (2007a). This band, along with the minor band at 3320 cm −1 , are unique to the [triv] experiments and are assigned to coupled substitution of Sc 3+ and H + , with the latter providing local charge balance in octahedral site vacancies (Eq. 3). In natural olivines, bands in this wavenumber region occur sporadically, but can occasionally be the dominant defect type, particularly in olivines with very low Ti concentrations (Soustelle et al. 2013;Soustelle et al. 2010;Tollan et al. 2015). The precise position, polarisation and relative intensity of bands from natural olivines differ from those produced in our [triv] experiments, indicating that Sc is not a significant partner, as expected from the much lower concentrations of Sc in natural mantle olivine (typically 2-10 ppm). Ferric iron and Cr 3+ are both much more abundant trivalent cations in natural olivine and are the likely candidates for the 3+ cation partnering H in this substitution mechanism (Tollan et al. 2015;Blanchard et al. 2017).
Two experiments were conducted specifically investigating [Mg] defects, which are generated most strongly under conditions of high silica activity (orthopyroxene/ enstatite-buffered). However, identical bands were produced in all the other enstatite-buffered experiments, but not in the [Si] experiments, which were buffered at low a SiO 2 by magnesiowüstite. The bands associated to the [Mg] defect are located at lower wavenumbers, and display characteristically broad absorbance with large FWHM, but only along E||c. Two bands can be distinguished, one centred at 3160 cm −1 and another at 3220 cm −1 . Both of these bands are present in [Ti] and [Mg] experiments, with the band at 3220 cm −1 more intense. In [triv] experiments however, the band at 3160 cm −1 is more intense. Lemaire et al. (2004), Balan et al. (2011) and Umemoto et al. (2011) suggested that these band positions can be explained by protonation of vacant M1 and M2 sites. However, as pointed out by Blanchard et al. (2017), protonation of the M2 site was never explicitly modelled in these studies, and the variation in band position can be better explained by protonation of an M1 vacancy coupled with Fe 2+ occupying either a neighbouring M1 or M2 site. Preferential ordering of Sc into one of the two kinds of octahedral sites would imply that vacancies concentrated in the other kind, with the H + bonding to an O 2− surrounding the vacancy, to even out the perturbation of charge density. Based on site occupancy arguments in Blanchard et al. (2017), it is perhaps more likely that the greater intensity at 3160 cm −1 in [triv] experiments indicates that Sc is partitioning more favourably onto the larger M2 site, with the vacancy and its compensating H favouring M1, assuming that Sc is behaving similarly to Fe 3+ . Similar or identical bands to these are commonly observed in other experimental studies and also in natural samples (e.g., Aubaud et al. 2007;Férot and Bolfan-Casanova 2012;Gaetani et al. 2014;Grant et al. 2007a, b). Band positions vary much more than bands from other defects, which may be due to the very broad and often low intensity of these bands, Fig. 6 Percentage that the absorbance from each orientation contributes to the total absorbance, for different point-defect types. The absorbance associated with [Mg] defects is only detectable along E||c making it difficult to precisely locate the wavenumber of maximum intensity. In addition, partitioning of a wide range of trace and minor cations onto either or both octahedral sites could result in slightly different O-H bond lengths and an associated wavenumber shift.
Although our experimental strategy aims to emphasise only one of the four types of substitution mechanism in each group of experiments, it is important to recognise that absorption bands corresponding to some of the other substitution mechanisms are a minor feature of most of the spectra (Figs. 3, 4 and 5 (Table 3) is qualitatively consistent with the theoretical calculations of Walker et al. (2007), the actual values of this ratio differ from those calculated by Walker et al. (2007), which predicts a greater decrease as total water content increases (see Fig. 3 of Walker et al. (2007)). Nevertheless, the important observation here is that at lower water activities, hydrated Mg vacancies are favoured over hydrated Si vacancies when all other conditions are kept constant, the reasons for which we address next.

Relationships with water activity, a H2O
Significant controversy prevails regarding the issue of relating measured absorptions to water contents. Several theoretical and experimental studies have demonstrated that the absorption coefficient should vary as a function of the vibrational energy characteristic of the configuration of H in a given defect (e.g., Kovacs et al. 2010;Balan et al. 2011;Ingrin et al. 2014;Blanchard et al. 2017). Hence, there should be a negative correlation between the infrared wavenumber and absorption coefficient. At present, however, whilst computational studies are useful in defining the expected trend, absolute values are not reliable. Experimental studies on the other hand produce more accurate values, but have so far explored a relatively small number of appropriate defects. Amongst the available experimental studies, the value of 28,450 L mol −1 cm −2 from Bell et al. (2003) has been most widely applied. Kovacs et al. (2010) produced an identical value for olivine bearing [Ti] and [triv] defects, although their absorption coefficients for [Si] and [Mg] defects were compromised by the occurrence of a previously unknown defect involving boron which comprised a significant proportion of the water in the "Pakistani" olivine used in their experiments (Ingrin et al. 2014). More notably, Withers et al. (2012) determined a strikingly different value of 45,200 L mol −1 cm −2 for synthetic olivines with most of the absorbance in their infrared spectra occurring at similarly high wavenumbers to the spectra in the study of Bell et al. (2003), albeit with a different defect ([Si] as oppose to [Ti]). This study utilised elastic recoil detection analysis as the matrix-independent method of absolute H 2 O concentration determination, as opposed to nuclear reaction analysis which was used by Bell et al. (2003). The reason for the discrepancy between absorption coefficients is currently unclear, but since the absolute determination of water content is of minor significance for this study, we apply the more commonly used value (Bell et al. 2003), 28,450 L mol −1 cm −2 , with the caveat that calculated values may be systematically wrong as a result, something we address further in the discussion. Furthermore, provided that only one substitution mechanism is being considered, use of a different calibration would change C H 2 O proportionately, and the relationship to a H 2 O would not be affected. experiments are 2.5 ± 0.2, 0.6 ± 0.1 and 1.1 ± 0.1, which are close to but consistently higher than the predicted exponents of 2, 0.5 and 1. Such similar values are a strong indication that the substitution stoichiometries given by equilibria 5 to 7 are substantially correct. The data for the [Ti] experiments present the problem that there is substantial overlap of bands associated with [Si] with those that appear in the [Ti] experiments in the wavenumber region 3650-3450 cm −1 . This is confirmed by [Mg] experiments, which were performed under identical conditions but without being doped with Ti. Spectra from these forsterite crystals show absorption bands at 3578 cm −1 along E||a and 3567 cm −1 along E||c, bands which are most prominently observed in experiments conducted at lower silica activity and higher pressure (Lemaire et al. 2004;Mosenfelder et al. 2011). In order to obtain the correct exponent for water associated with Ti, spectra were deconvoluted into 7-8 bands in an effort to isolate the overlapping, defect-specific bands (Fig. 7, Table 4 There is a tendency for the exponents to be somewhat higher than those expected from the stoichiometry of reactions 1 to 4. This is explicable if there is a negative departure from ideal mixing in H 2 O-NaCl fluids. The data can be reconciled to the expected values of the exponents if we describe the H 2 O-NaCl binary at 1050°C and 3 GPa by a regular solution model, such that RT ln γ H 2 O ¼ W H 2 O−NaCl 1−X H 2 O ð Þ 2 , with an interaction parameter W H 2 O−NaCl of~−5 kJ/mol. This is not in agreement with the experimental study of Aranovich and Newton (1996) experiments, then, although the relative differences between exponent terms for different defects would remain the same, the absolute values would differ, casting doubt on our identifications of their stoichiometries. However, we note that our experiments were conducted at a higher temperature and pressure than the range investigated by Aranovich and Newton (1996), which extends only to 900°C and 1.5 GPa. It should also be noted that we have not allowed for other components, such as SiO 2 , dissolving in H 2 O-NaCl fluids, which would lower a H 2 O compared to the simple binary.

Composition and water incorporation
The association between olivine composition and water incorporation remains a subject of debate in the literature, particularly the role of certain trace elements, such as Ti and trivalent species such as Fe 3+ , Al and Cr 3+ . Experimental studies have shown clear evidence for coupled substitution of hydrogen with these species in simple systems Berry et al. 2007a;Faul et al. 2016;Férot and Bolfan-Casanova 2012;Grant et al. 2007a, b;Kovacs et al. 2010), supported by atomistic simulations (Balan et al. 2011;Blanchard et al. 2017;Walker et al. 2007). Furthermore, the FTIR spectra produced by these studies reproduce well the dominant absorbance bands of natural olivine crystals Schmädicke et al. 2013;Tollan et al. 2015). However, there are few studies reporting good correlations between trace element composition and water content in natural olivine crystals, leading some to conclude that such incorporation mechanisms are of limited importance (Gaetani et al. 2014;Withers and Hirschmann 2008).
Our study confirms a clear relationship between water content and the presence of Ti and Sc. Of particular significance are the correlations between Ti concentration, water concentration and water activity in [Ti] experiments at both fixed water activity and fixed bulk Ti concentration ( Figs. 2 and 8). This indicates that Ti and H are being incorporated together as part of the same point defect, and that the formation of this defect is the dominant method of incorporating both Ti and H in the system studied. Note that Ti concentrations overlap the range found in natural mantle olivines (De Hoog et al. 2010). Extrapolating the trend of H 2 O concentration vs. Ti concentration to anhydrous conditions gives a Ti  (Fig. 8), which is close to the maximum solubility of Ti in olivine under anhydrous conditions at the same temperature and pressure, as estimated from the experimental study of Hermann et al. (2005). This illustrates how Ti solubility in olivine is dramatically increased at high water activities. Converting H 2 O and Ti to molar concentrations allows a further opportunity to assess the relationship between these two species (Fig. 9). The stoichiometry of Ti-clinohumite, MgTi(OH) 2 O 2 , requires two moles of OH (or one mole of H 2 O) for every mole of Ti. Taking [Ti] experiments with a constant water activity of 1 but variable Ti concentration in olivine, we find that the trend of the data is very close to the 1:1 line (moles of Ti to moles of H 2 O), consistent with this stoichiometry. Furthermore, this indicates that at water, saturated conditions a H 2 O ¼ 1 ð Þ at 3 GPa and 1050°C, essentially all Ti substitutes by the Ticlinohumite point-defect mechanism, as opposed to tetrahedral Ti as in the Mg 2 TiO 4 substitution (Berry et al. 2007b). The latter substitution becomes more important at higher temperatures and lower pressures ) and with increasing Fe content (O'Neill 1998). Finally, the good agreement between molar concentrations of Ti and H 2 O is a strong indication that the absorption coefficient of Bell et al. (2003) is reliable for this particular defect. The Bell value was determined using olivines with identical spectra to our [Ti] experiments. Likewise, the identical value obtained from [Ti] experiments by Kovacs et al. (2010) is also validated.
Similar trends can also be observed for the [triv] experiments, where water activity was held constant and bulk Sc concentration varied. In this case, there is a good positive correlation between Sc concentration and H 2 O concentration; however, when converted to molar concentrations, there is a deviation of approximately one third away from the expected Sc:H 2 O molar ratio, such that there is more water than expected, given the Sc concentration. This deviation is consistent with the results of the study by Berry et al. (2007a), implying that this is not isolated just to Sc but to all R 3+ cations (Fig. 10). We suggest that the simplest explanation for this is that the absorption coefficient used is not appropriate for this particular defect and should be increased by one third from the values reported by Bell et al. (2003) and Kovacs et al. (2010) and close to the value reported by Withers et al. (2012), in order to compensate for the excess water calculated here and by Berry et al. (2007a). This is also consistent with predictions from theoretical calculations for this type of defect (Blanchard et al. 2017), although the absolute value obtained in that study is somewhat unlikely. Since this defect is relatively common in natural olivines and thus a major contributor to mantle water storage (Tollan et al. 2015), an experimental study specifically designed to determine the absorption coefficient for this defect is required.
A further result that contrasts with the [Ti] experiments is that there is no correlation between the very  [triv] experiments conducted at constant water activity but variable in Sc concentration and at fixed bulk Sc concentration. Note that the latter experiments show no correlation between forsterite water concentration and Sc concentration, for reasons discussed in the text. For comparison, we have also plotted data from Berry et al. (2007a), which were similar experiments but at 1400°C and 1.5 GPa and performed with a variety of trivalent cations in addition to Sc (Al, V, Ga, Y, In, Gd, Dy, Tm and Lu). Both sets of data confirm a consistent increase of C H2O with the availability of an R 3+ cation at fixed water activity, but the deviation from the expected stoichiometry for the substitution may indicate that the absorption coefficient used in this study to calculate C H2O is in error; the value obtained by Withers et al. (2012) may be more appropriate (see text for further discussion) high concentrations of Sc and H 2 O concentration in the series at variable water activity, suggesting that another charge-balancing mechanism for Sc is operating in addition to the hydrous defect proposed here. Under anhydrous conditions, considerable Sc in olivine can be charge-balanced by an octahedral site vacancy (Spandler and O'Neill 2010) or, alternatively, Na + could be incorporated from the salt-water solution and charge-balance Sc instead of H + . The latter would be increasingly important at lower water activities, where the NaCl/H 2 O ratio of the fluid increases substantially. But Grant and Wood (2010) found little evidence for coupled substitution of Na and Sc, so this reaction seems unlikely. It is possible that other charge-balancing species (such as Li) were present as contaminants in the salt; this would require further work to demonstrate.
Comparisons with other studies Matveev et al. (2001) conducted experiments on natural olivines from Mount Porndon (initially Fo 90-91 ) at a range of water activities, controlled by diluting H 2 O with CO 2 at 1300°C and 2 GPa. Although their experiments were designed to be M-type, the olivine partially recrystallised to some extent in all runs, and FTIR spectra were reported only for the recrystallised material, using the marked change in Fo content (to~Fo 96-97 ) as a discriminant. Their results are therefore for G-type experiments, which explain why they were able to obtain completely different FTIR spectra in orthopyroxenebuffered experiments from magnesiowüstite-buffered experiments, as in this study. They found a factor of 1.3 decrease in water concentration in olivine over the range in X H 2 O from 1.0 to 0.3, in four orthopyroxene-buffered experiments. Inspection of their spectra shows that the [triv] defect dominates the total absorbance, and we can therefore directly compare their results to ours for this defect, but with the caveat that the trivalent cations associated with the [triv] substitution in the natural olivines are likely Fe 3+ or/and Cr 3+ (cf. Tollan et al. 2015) rather than Sc. Considerable Fe 3+ in their olivines is expected given the relatively high oxygen fugacities of their experiments, achieved using the Re-ReO 2 buffer. The exponent for this defect derived from their data (following the same data-fitting procedure as for this study) is 0.58 ± 0.21, which is identical within uncertainty to the exponent calculated for the [triv] substitution in this study, supporting our hypothesis that the configurational entropy of the [triv] substitution is independent of the identity of the trivalent cation. The [triv] substitution was absent in the spectra from their magnesiowüstite-buffered experiments, although these were conducted at the same oxygen fugacity (Re-ReO 2 ); this observation confirms the role of high a SiO 2 in promoting this substitution, according to reaction (3). Their attribution of the [Si] substitution mechanism to the FTIR spectra of natural olivines published by Miller et al. (1987) was a mistake due to confusing the [Si] substitution in their experiments with the [Ti] substitution in the natural crystals. In the experiments, the Ti in the starting crystals of Mount Porndon olivine, which is low anyway (~20 ppm in an example analysed by Eggins et al. 1998), would have been lost during recrystallisation, while the infrared fingerprint of the [Ti] substitution was only recognised later . Gaetani et al. (2014) performed what they assumed were M-type experiments on San Carlos olivine, but with re-equilibration of fO 2 -sensitive defects. Only the orthopyroxene-buffered condition was investigated.
Here, the component Fe 2+ H 2 SiO 4 represents essentially the same substitution mechanism in ferromagnesian olivines that we refer to as [Mg] in forsterite (Eq. 2). This reaction suggests that reduction of the Fe 3+ [triv] substitution would increase the [Mg] substitution in M-type experiments, but as the olivines used by Gaetani et al. (2014) differed in composition, and the partitioning of C Total H 2 O amongst the three different substitution mechanisms was not reported, this hypothesis cannot yet be tested. Yang et al. (2014) also used different ratios of H 2 O and CO 2 , finding a difference of a factor of 2 between values of C H 2 O in olivines from experiments with pure H 2 O and those with H 2 O-CO 2 , but changing X CO2 from 0.22-0.50 apparently had no effect on the water solubility. This observation disagrees with those of Matveev et al. (2001) and Gaetani et al. (2014). Otsuka and Karato (2011) where ΔV solids is the change in partial molar volume of the solid components. For the example of the [Si] mechanism (reaction 1), ΔV solids is given by: Here, V olivine Mg 2 H 4 O 4 is the partial molar volume of the Mg 2 H 4 O 4 component in the olivine, and V SiO 2 is the effective molar volume of the system, as determined by the coexisting phases. The standard states are the conventional ones of the pure components at the P, T of interest for the solid phases, and pure H 2 O as an ideal gas at T and 1 bar. The value of V olivine Mg 2 H 4 O 4 (298,1) may be calculated from the data in Smyth et al. (2006) as 45.2 cm 3 /mol, by recalculating the H 2 O contents of hydrous forsterites given in Table 2  In contrast, the differential effect of the change in f(H 2 O)°with pressure comes simply from the stoichiometry of the reaction: increasing pressure will favour the [Si] substitution, because C H 2 O ∝f H 2 O ð Þ 2 . That the [Si] mechanism is indeed the dominant mechanism in experiments with a H 2 O~1 at P >> 3 GPa, even at high a SiO 2 (buffered by orthopyroxene) is evident from several experimental studies (Kohlstedt et al. 1996;Mosenfelder et al. 2006;Withers and Hirschmann 2008). However, decreasing a H 2 O at any pressure and temperature will decrease the proportion of [Si] relative to [Mg], [Ti] and especially [triv]. Higher temperatures should favour the mechanisms with higher configurational entropy, if differences in vibrational entropies are of subsidiary importance (Walker et al. 2007). With this assumption, the relative amounts of water associated with the different defects should increase with increasing temperature in the reverse order from the effect of pressure at a H 2 O~1 : [triv] > [Mg]~[Ti] > [Si] (Eqs. 1, 2, 3 and 4), other variables remaining constant.
We reiterate the point made by Ingrin et al. (2013), who emphasised that water incorporation into olivine cannot be described by a single solubility law. The existence of the four main solubility mechanisms with their different controlling stoichiometries mandates that the relationship between C H 2 O and the intensive thermodynamic variables of temperature, pressure, fH 2 O and compositional variables requires four separate terms, one for each mechanism. Quantifying water substitution in olivine must also allow for the availability of Ti and the trivalent cations, particularly Fe 3+ , whose concentration is sensitive to fO 2 . Varying a SiO 2 also affects substitution mechanisms in different ways. Obviously, increasing a SiO 2 increases Mg vacancies but decreases Si vacancies and vice versa, but increasing a SiO 2 should also promote the [triv] substitution but decrease [Ti] (Eqs. 3 and 4). The values of a SiO 2 as buffered at low or high values by magnesiowüstite or pyroxene, respectively, also both change with P and T. The effect of the major element compositional variable Mg/Fe 2+ on each mechanism also requires systematic study.
The fact that there are three ways by which increasing pressure at constant given a H 2 O and relative a SiO 2 changes C X ½ H 2 O for each of the four substitution mechanisms means that it is difficult to deduce the nature of the substitution mechanism from the change of C X ½ H 2 O with pressure; it would be even more difficult to deduce how water dissolves in olivine with the change of C Total H 2 O with pressure. Interactions between the four defect mechanisms should also be taken into account in the interpretation of the water contents of natural olivines and their FTIR spectra. The speciation of water in olivine observed in simple-system experiments may not be preserved in natural olivines because of rearrangements on cooling and/or decompression. Where this occurs without mass transfer of components into or out of the olivine by diffusion, such rearrangements may be rapid. To give one example, it is possible that water may transfer from the [triv] mechanism to the [Ti] mechanism according to the reaction: where all components are in olivine. The R 3+ 4/3 SiO 4 component is the anhydrous substitution of R 3+ into olivine, charge-balanced by octahedral site vacancies (Evans et al. 2008), while the Mg 2 TiO 4 component is the anhydrous substitution of Ti for Si in olivine studied by Hermann et al. (2005). Therefore, the observation that [Ti] is the dominant mechanism for water incorporation in olivine from San Carlos xenoliths  may reflect internal re-equilibration during cooling to some extent as yet unknown. Loss of water from olivine, which has often been inferred from both phenocryst olivines in magmas during eruption, or from olivines in xenoliths during their exhumation (e.g. Tollan et al. 2015 and references therein), may also affect speciation. Water loss changes a SiO 2 (inter alia), hence the pointdefect structure of the olivine, in different ways according to the different substitution mechanisms (Eqs. 1, 2, 3 and 4). The effects of this are further complicated by the different rates of diffusion of H associated with the different substitution mechanisms .

Conclusions
This study presents the results of G-type experiments at one condition of temperature and pressure, namely 1050°C and 3 GPa, which confirm the identities of the four main substitution mechanisms by which water is likely to be incorporated into mainstream mantle olivines. The results demonstrate the role that a H 2 O plays in determining which mechanisms are significant at the experimental condition, but from the stoichiometries of the substitution mechanisms, the same principle should apply at other pressures and temperatures. Evaluating water solubilities is not straightforward because it depends on the mechanisms by which water is incorporated (the type of hydrous defect), which in turn is dictated by other factors, most notably composition and silica activity. The consequence of this is that under otherwise identical conditions, higher water activities will favour hydrated silicon vacancies ([Si]) over other defects. Conversely, at low water activities, the ratio of hydrated silicon vacancies to other hydrous defects will be much lower. This has profound impacts for our understanding of water storage in the mantle and interpretation of measurements of natural olivine from different mantle domains. For example, the absence of the infrared absorption bands associated with the [Si] mechanism does not necessarily indicate high silica activity but could be due to low water activities, as expected in most mantle environments (Bali et al. 2008;Lamb and Popp 2009). This is highlighted by our observation that the [Si] substitution features prominently in enstatitebuffered experiments at high pressures and high a H2O , even dominating total absorbance (Smyth et al. 2006). In order to understand the role of water in the mantle, careful consideration needs to be given to several factors that have hitherto been underappreciated, including the limitations on a H 2 O and the role of minor components, especially Ti and the more abundant R 3+ cations, Fe 3+ and Cr 3+ .