Silicate solution, cation properties, and mass transfer by aqueous fluid in the Earth’s interior

The solubility and solution mechanism(s) of silicate components in aqueous fluids in the Earth’s interior are central to our understanding of the roles of aqueous fluids in material transport within the Earth (Fockenberg et al. 2006; Newton and Manning 2009; Burchard et al. 2011). This is particularly so in and near subduction zones where water-rich fluids released from dehydrating slab materials can transport chemical components into source regions of melting and, at the same time, deplete dehydrating slab materials of fluid-soluble components (Mibe et al. 2008; Kawamoto et al. 2012). In this environment, hydrated rocks ranging from amphibolite and peridotite to felsic gneiss compositions are subjected to dehydration and release of silicate-saturated water-rich fluids.

The abundance of components known to affect silicate solubility in aqueous fluid differs significantly among those rock types in the Earth’s interior. It is necessary, therefore, to determine how individual compositional variables affect the silicate solubility and structure of dissolved silicate in aqueous fluids at relevant high-temperature and high-pressure conditions.

Composition and structure of silicate-saturated aqueous fluids at high temperature and pressure have been determined experimentally for pure SiO₂–H₂O systems as well as for some more complex silicate and aluminosilicate compositions (Newton and Manning 2002; Kessel et al. 2005; Mibe et al. 2008, 2011; Mysen 2010). From those experiments, it is evident that silicate solubility in aqueous fluids depends on the presence of other components in addition to SiO₂. In the MgO–SiO₂–H₂O system, for example, the solubility in the aqueous fluid decreases with increasing Mg/Si abundance ratio (Zhang and Frantz 2000). Addition of aluminosilicate components to SiO₂ also enhances the solubility in fluid (Wilke et al. 2012). However, quantitative characterization of how individual components affect silicate solubility and solution mechanisms of other components in aqueous fluids is not well developed.

Determination of fluid composition and structure at temperature and pressure conditions of the deep crust, upper mantle, and beyond is challenging because silicate-saturated fluids commonly do not retain in solution the chemical components and the fluid structure that existed at the high temperature and pressure after temperature quenching from experimental conditions to ambient temperature and pressure. Various methods have been proposed with which to overcome these obstacles. For example, Kessel et al. (2004) described a method whereby fluids were soaked into layers of pore space among diamond particles during experiments. Analysis of these diamond aggregates after termination of an experiment provided the fluid data. Others rely on accurate weighing of crystals from the experimental charges before and after an experiment at high temperature and pressure during which crystalline material equilibrated with fluid (Manning and Boettcher 1994). The weight difference is the weight of the solute.

An alternative, which does not rely on quenching to ambient conditions before analysis, is to conduct structural characterization of fluids in the equilibrium with one or more condensed phases while at the temperatures and pressures of interest. This can be accomplished with the sample contained in an externally heated hydrothermal diamond anvil cell (Bassett et al. 1993). Here, this experimental protocol was employed to assess the influence of alkalis and alkaline earth cations on SiO₂ solubility in aqueous solutions to temperatures and pressures corresponding to the deep crust and upper mantle.

Three different starting materials were used. Those were crystalline quartz + H₂O, crystalline quartz + 0.7 m NaOH aqueous solution, and an SiO₂ + CaO mixture + H₂O (SiO₂:CaO = 9:1 by mol). By using NaOH as the Na⁺-bearing fluid component, it cannot be ruled out that an increased pH compared with pure H₂O could also affect the silicate solubility in the fluid.

The CaO–SiO₂ material was prepared by melting at ambient pressure at 1725 °C followed by crystallization at 1500 °C. At 1725 °C, this system comprises immiscible silicate liquids (Osborn and Muan 1960). In order to form the crystalline SiO₂ component desired to equilibrate with fluid, the crystallization step at 1500 °C was performed. This mixture, consisting of crystalline tridymite + glass (Ca-rich) was used together with H₂O as a starting material. During the experiments, tridymite converted to quartz and glass to wollastonite, as discussed further below.

The experiments were carried out in an externally heated, hydrothermal diamond anvil cell (HDAC) of the design originally described by Bassett et al. (1993). In the HDAC, the sample was heated with external heaters. These heaters were comprised of Mo wire wrapped around the SiC diamond seats of upper and lower diamonds that were held in place with alumina high-temperature cement. Iridium gaskets (125 μm thick) with a 500-μm sample hole were employed for sample containment. During an experiment, the gaskets shrunk to about 80 μm thickness and the hole to ~ 400 μm diameter.

MicroRaman spectroscopy and optical microscopy were used to characterize the samples while these were in the HDAC at the pressure/temperature of interest. The Raman system is a JASCO model NRS-3100 confocal microRaman spectrometer with a single monochromator and holographic gratings (1200 and 2400 grooves/mm). A long working distance (25 mm), × 50 magnification, 0.42 N.A. objective lens was used in this design, which provided a better than 5 μm spatial resolution for sample examination and spectroscopic characterization. The sampling depth was about 30 μm (Mysen 2015a). The signals were recorded with an Andor™ Model DV401-F1 1024 × 28 pixel Peltier-cooled CCD (charge-coupled detector). Energy resolution was ± 3 cm⁻¹ with 1200 grooves/mm gratings, whereas with 2400 grooves/mm, spectral reproducibility was about 1 cm⁻¹.

Temperatures in the diamond cell were monitored with two K-type thermocouples that touched the diamonds at a ~ 1-mm distance from the sample chamber. A feedback mechanism was utilized for temperature control. Temperature precision was ± 1 °C, whereas the uncertainty, determined against the melting point of NaCl, was 2–3 °C. The gasket hole in the Ir gasket material deformed some during the experiments, which were not, therefore, strictly isochoric. Pressure could not, therefore, be calculated from the PVT data of pure H₂O. Furthermore, silicate components dissolved in the fluid also affect the equation of state of H₂O (Mysen 2010). Instead, the pressure was measured with the one-phonon Raman line from a chip of synthetic carbon-13 diamond placed inside the sample chamber. From this information, the pressure was determined with the calibration of Mysen and Yamashita (2010). An internal standard of Ne emission lines was employed to optimize the energy resolution. With this standard together with 2400 grooves/mm gratings, a frequency uncertainty of ± 0.1 cm⁻¹ was obtained. This uncertainty translates to a pressure precision of ± 40 MPa. However, the overall pressure uncertainty is approximately ± 110 MPa when taking into considerations the uncertainties in the pressure calibration by Mysen and Yamashita (2010).

Several series of measurements at different temperatures and pressures were carried out with the three different starting materials such that for each of the three starting compositions, the sample was first taken to the highest planned temperature and pressure and left there for an hour before spectroscopic measurements. The sample was then cooled at 1 °C/s in 50–75 °C intervals to the next temperature and pressure condition where the spectra were recorded after about 60-minute dwell time. With this sample configuration, the 60-minute dwell time is sufficient to reach equilibrium (Mysen 2015b).

Quartz and aqueous fluid were present in all experiments (Table 1). Additionally, in the system SiO₂–CaO–H₂O, wollastonite coexists with quartz and fluid (Fig. 1). The quartz and wollastonite, identified from their Raman spectra, grew from the starting materials during the initial hour at the highest temperature and pressure. The high-temperature spectra typically are broader and less well resolved compared with the spectra recorded at ambient temperature and pressure (Fig. 2).

SiO2–H2O			SiO2–NaOH–H2O			SiO2–CaO–H2O
Temp (°C)a	Press (MPa)b	Phases	Temp (°C)	Press (MPa)	Phases	Temp (°C)	Press (MPa)	Phases
25	0.1	Qtz + fluid	25	0.1	Qtz + fluid	25	0.1	Qtz + Wo + fluid
550	391	Qtz + fluid	550	583	Qtz + fluid	575	396	Qtz + Wo + fluid
625	542	Qtz + fluid	625	638	Qtz + fluid	625	468	Qtz + Wo + fluid
700	696	Qtz + fluid	700	851	Qtz + fluid	675	498	Qtz + Wo + fluid
775	956	Qtz + fluid	775	1012	Qtz + fluid	725	709	Qtz + Wo + fluid
800	725	Qtz + fluid	800	1134	Qtz + fluid	775	952	Qtz + Wo + fluid
						825	933	Qtz + Wo + fluid

^aTemperature uncertainty, 2–3 °C

^bPressure uncertainty, ± 110 MPa

The spectra of silicates and fluid at high temperature and pressure show Raman signals in a high-frequency region centered between 3500 and 3600 cm⁻¹ and a low-frequency region between 300 and 1200 cm⁻¹. The high-frequency region comprises that of the fundamental O–H vibrations in OH groups, whether in molecular H₂O or as OH groups that form bonding with metal cations (Ratcliffe and Irish 1982; Walrafen et al. 1986). The low-frequency region, between about 300 and 1200 cm⁻¹, includes the Raman bands assigned to vibrations in Si–O, Al–O, and metal oxide components (Brawer and White 1975; McMillan et al. 1992).

The high-frequency region comprises a single slightly asymmetric band. The asymmetry is less pronounced in the spectra from fluid in SiO₂–CaO–H₂O than for the other two compositions (Fig. 3). The low-frequency region characteristically has a strong and sharp band between 770 and 800 cm⁻¹ (Fig. 4). In the SiO₂–CaO–H₂O fluid spectra, this is the only Raman band in this frequency region (Fig. 4c), whereas for SiO₂–H₂O and SiO₂–NaOH–H₂O fluids, there is a Raman intensity on both the low- and high-frequency side of 770–800 cm⁻¹ peak (Fig. 4a, b). These latter intensities are strongest in the spectra of SiO₂–NaOH–H₂O fluids (Fig. 4b). The intensity of all bands grows with the increasing temperature and pressure.

The 770–800 cm⁻¹ band is assigned to Si–O⁻ stretch vibrations in isolated SiO₄ tetrahedra (Q⁰ species) with one or more of the nonbridging oxygens forming bonds with H⁺ (Zotov and Keppler 2002; Mibe et al. 2008). This is the same vibration as that gives rise to a ~ 850 cm⁻¹ Raman band in anhydrous silicate melts and glasses (see review of Raman band assignments in such systems by Mysen and Richet 2005). The lower frequency of the Si–O⁻ stretch vibration in hydrous melts is because of the much smaller radius of H⁺ bonded to nonbridging oxygens in the structure compared with alkali metals and alkaline earths. Raman intensity at a higher frequency, as observed in the spectra of SiO₂–H₂O and SiO₂–NaOH–H₂O fluid, is assigned to Si–O⁻ vibrations in silicate species more polymerized than isolated SiO₄ groups. Most likely, these are species with one bridging oxygen (Q¹ species) (Mysen et al. 2013). Bending vibrations of such a bridge give rise to the intensity centered near 600 cm⁻¹.

It follows, therefore, that for fluids in equilibrium with quartz in the system SiO₂–NaOH–H₂O, the silicate polymerization with Q⁰ and Q¹ species is similar to that in SiO₂–H₂O fluid spectra at higher pressures (Mysen et al. 2013). It also resembles the aqueous fluids in the equilibrium with alkali aluminosilicate melt under similar temperature and pressure conditions (Mysen 2010).

The Raman spectra indicate that the silicate concentration and speciation in the fluid at given temperature and pressure is dependent on the nature of the crystalline materials in the equilibrium with the fluid.

Solubility

Silicate solubility in the aqueous fluids might be estimated by combining silica solubility in the fluid in the system SiO₂–H₂O (Manning 2004) with the intensity of relevant Raman bands in order to generate a calibration curve from the intensity of Raman bands in spectra of fluid. This calibration curve then may be used to compute an approximate solubility of SiO₂ in the fluids from the other two series of experiments (SiO₂–NaOH–H₂O and SiO₂–CaO–H₂O).

The silicate contents of fluid in equilibrium with quartz in the SiO₂–H₂O system were calculated with the algorithm of Manning (1994) in which the temperature and the density of pure H₂O are variables. For the density of the fluid, the calculations by Withers, using the formulism of Pitzer and Sterner (1994), were employed [URL: https://www.esci.umn.edu/people/researchers/withe012/fugacity.htm]. Those SiO₂ solubilities (Table 2) were then used to create a calibration curve based on the 770 + 850 cm⁻¹ integrated Raman intensities from the fluid spectra (see Fig. 4). The data points defining the solubility relations were fitted to the function (Fig. 5):

SiO2–H2O
Temp (°C)	Press (MPa)	Density (g/cm3)	fH2O (MPa)	SiO2 solubility, mSiO2 (kg/mol)a
800	728	0.794	852	0.0304
775	956	0.876	1440	0.0273
700	696	0.831	668	0.0082
625	542	0.813	364	0.0022
550	391	0.789	178	0.0004
SiO2–NaOH–H2O
Temp (°C)	Press (MPa)	Density (g/cm3)	fH2O (MPa)	SiO2 solubility, mSiO2 (kg/mol)b
800	1135	0.911	1978	0.0238
775	1012	0.891	1642	0.0448
700	851	0.88	999	0.0288
550	583	0.871	328	0.0092
SiO2–CaO–H2O
Temp (°C)	Press (MPa)	Density (g/cm3)	fH2O (MPa)	SiO2 solubility, mSiO2 (kg/mol)b
575	396	0.775	198	4.86525E−08
625	468	0.779	291	1.43231E−07
675	498	0.764	362	1.38469E−05
725	709	0.824	723	9.61047E−05
775	953	0.875	1430	0.000369701
825	933	0.849	1444	0.000506355

^aCalculations using the formalism from Manning (1994)

^bSee text for calculations

$$ \log\ {m}_{\mathrm{SiO}2}\left(\mathrm{mol}/\mathrm{kg}\right)=1.6-2.0\bullet {\mathrm{Int}}^{-0.32}\left(\mathrm{cts}/\mathrm{s}\right), $$

(1)

where “Int” is the integrated intensity of the 770 + 850 cm⁻¹ Raman bands in counts per second, and m_SiO2 is silica molality.

The SiO₂ solubility in the SiO₂–NaOH–H₂O and SiO₂–CaO–H₂O fluids was then derived from the calibration curve in Fig. 6 and the integrated Raman intensities at 770 + 850 cm⁻¹ from the SiO₂–NaOH–H₂O and CaO–SiO₂–H₂O fluid spectra. In doing this, it was assumed that the different cations, H⁺, Na⁺, and Ca²⁺, in the aqueous solutions had no effect on the Raman intensities and that possible temperature and pressure effects in the pressure range under study on Raman intensity can be ignored.

With the above caveats in mind, the SiO₂ solubility in SiO₂–CaO–H₂O fluids from the calibration curve in Fig. 6 is an order of magnitude, or more, lower than in the SiO₂–NaOH–H₂O and SiO₂–H₂O fluids in the f_H2O (H₂O fugacity) range defined by the temperature and pressure conditions of these experiments (Fig. 6; Table 2). The solubility difference does, however, decrease with increasing fugacity of H₂O.

The significant solubility depression resulting from 10 mol% CaO to SiO₂ appears similar to that from MgO in the system MgO–SiO₂–H₂O (Zhang and Frantz 2000). This effect contrasts with adding NaOH where, despite the dilution of SiO₂ concentration, the SiO₂ solubility in aqueous fluids is similar to that in the simpler SiO₂–H₂O system. The solubility is, however, more sensitive to f_H2O in the SiO₂–NaOH–H₂O system so that at high H₂O fugacity, the SiO₂ solubility in the SiO₂–NaOH–H₂O system exceeds that in SiO₂–H₂O fluids (Fig. 6). The temperature/pressure coordinates of the solubility cross-over (750–800 °C at ~ 900 MPa), from linear extrapolation of the curves in Fig. 6, occur at the conditions just below the second critical point in the SiO₂–H₂O system at 1080 °C and 970 MPa (Kennedy et al. 1962). In contrast, linear extrapolation of the SiO₂–CaO–H₂O line leads to a cross-over at an f_H2O corresponding to ~ 1300 MPa pressure at 800 °C. These pressure and temperature conditions are inside the supercritical region of the SiO₂–H₂O system, which means that conditions of greater silica solubility in SiO₂–CaO–H₂O fluids than in SiO₂–H₂O and SiO₂–NaOH–H₂O cannot be realized.

Silicate speciation in fluid

The approximate concentration of the silicate species in fluid (Qⁿ species) can be obtained from the integrated intensities of the 770 and 850 cm⁻¹ bands of the Raman spectra of fluid. The concentrations thus obtained depend, however, on the assumption that the relative intensities of these two Raman bands are equal to the mol fraction of the species. Given the similar Si–O⁻ force constants for Si–O⁻ stretch vibrations in Q⁰ and Q¹ in hydrous melts (Cody et al. 2005), the equivalence of relative intensities of the 770 and 850 cm⁻¹ bands and the mol fraction of Q⁰ and Q¹ species seems a reasonable assumption.

In the SiO₂–H₂O and SiO₂–NaOH–H₂O systems, silica-saturated fluids contain both Q¹ and Q⁰ species, whereas in the SiO₂–CaO–H₂O system, only Q⁰ species were detected in the temperature and pressure range. For the SiO₂–H₂O and SiO₂–NaOH–H₂O fluids, the Q⁰ abundance decreases with increasing temperature and pressure although this decrease is more pronounced in the SiO₂–NaOH–H₂O system. This decrease is coupled with increasing Q¹ abundance. The rate of change of the abundance ratio, X_Q1/X_Q0, with temperature and pressure is considerably faster in the SiO₂–NaOH–H₂O system and, in fact, can be expressed as linear functions of SiO₂ molality, m_SiO2 (Fig. 7). Qualitatively, this behavior resembles that for SiO₂–H₂O and SiO₂–MgO–H₂O fluids at pressures above 2 GPa (Mysen et al. 2013). This behavior also is qualitatively similar to that of increased silicate polymerization with increasing total SiO₂ concentration in silicate melts (Buckermann et al. 1992). The difference in silicate species abundance between SiO₂–H₂O and SiO₂–NaOH–H₂O fluids probably occurs because steric hindrance associated with nonbridging oxygen (NBO) bonding to H⁺ is greater than Na⁺–NBO bonding given the much smaller ionic radius of H⁺. Protons will, therefore, favor nonbridging oxygen in Q⁰ species, whereas Na⁺ will form bonding with nonbridging oxygen in Q¹ species. Hence, the more rapid increase in X_Q1/X_Q0 in the SiO₂–NaOH–H₂O systems than in SiO₂–H₂O.

Thermodynamic considerations

When Q⁰ and Q¹ species are present in the fluid, the equilibrium is:

$$ {2\mathrm{Q}}^0\iff {\mathrm{Q}}^1, $$

(2)

with the equilibrium constant:

$$ {K}_{(2)}={X}_{\mathrm{Q}1}/{\left({X}_{\mathrm{Q}0}\right)}^2, $$

(3)

where X_Q1 and X_Q0 are mol fractions of Q¹ and Q⁰, respectively. This equilibrium applies to the SiO₂–H₂O and SiO₂–NaOH–H₂O fluids in the temperature and pressure range discussed here. We note that it differs from that of SiO₂–H₂O at higher pressures (1.8–5.2 GPa) where the silica concentration is sufficiently high to stabilize even more polymerized Q² species as well (Mysen et al. 2013).

The silicate speciation in the SiO₂–CaO–H₂O fluids is simpler than in the other two systems as the only species throughout the temperature and pressure is Q⁰ only (Fig. 4). Under such circumstances, the equilibrium constant equals concentration in the fluid, m_SiO2:

$$ K={m}_{\mathrm{SiO}2}. $$

(4)

From the temperature dependence of the equilibrium constants, the enthalpy change of the reactions follows from:

$$ \ln\ K=-\Delta H/ RT+\Delta S/R, $$

(5)

where ∆H and ∆S are the enthalpy and entropy changes, T is absolute temperature, and R is the gas constant. It is assumed in using this equation that there is no pressure effect on the equilibria in the pressure range of these experimental results (Table 1). This conclusion is substantiated by the SiO₂–H₂O and SiO₂–MgO–H₂O fluid data of Mysen et al. (2013) who did not detect a pressure dependence in the same pressure range as the present experiments.

A linear fit to ln K versus 1/T yields significantly different ∆H values for the equilibria among the Qⁿ species in the fluid (Fig. 8). For the SiO₂–CaO–H₂O system (Fig. 8a), equilibrium (4) describes the situation. It is more sensitive to temperature (∆H = 322 ± 4 kJ/mol) than equilibrium (2), which describes the speciation variations in the SiO₂–H₂O (22 ± 12 kJ/mol) and SiO₂–NaOH–H₂O systems (51 ± 17 kJ/mol; see Fig. 8).

Silicate speciation in silica-saturated aqueous fluids suggested from thermodynamic modeling indicates that species more polymerized than Si (OH)₄ type exist in aqueous fluids under pressure/temperature conditions relevant to upper mantle processes (Newton and Manning 2003). This suggestion is consistent with the structural observations reported here and elsewhere (Zotov and Keppler 2002; Mysen et al. 2013). We also note, however, that when NaOH instead of CaO is the third component added to SiO₂–H₂O, the silicate solubility is higher, and both Q⁰ and Q¹ species occur in the SiO₂–NaOH–H₂O fluids at lower pressures than in the alkaline earth systems. We note, though, that in these experiments Na⁺ was added as an NaOH + H₂O solution. We cannot rule out a contribution to the silicate solubility from the alkaline nature of the fluid such as, for example:

where, therefore, pH would be a contributing factor to the silicate solubility.

Furthermore, as the silicate concentration in aqueous fluids increases and silicate species becomes more polymerized with pressure and temperature, the types and abundance Qⁿ species more closely resemble those in hydrous silicate melts (Zotov and Keppler 1998; Cody et al. 2005; Mysen 2010). This structural evolution may lead to complete miscibility between silicate and aqueous fluid. It is likely that complete miscibility between fluid and melt occurs at lower pressure in alkali silicate systems than in those of alkaline earth silicate systems because of the greater silicate solubility in alkali silicate fluids. This conclusion accords with experimental observations that show complete miscibility near 1–1.5 GPa in alkali silicate and aluminosilicate systems, whereas pressure exceeds 3 GPa before reaching miscibility in alkaline earth systems (Bureau and Keppler 1999; Stalder et al. 2001; Mibe et al. 2007).

Experimental data indicate that solubility of geochemically important minor and trace elements in aqueous fluids can be significantly affected by other silicate components (Manning 2007; Mysen 2012a, b). This happens because the stability and concentration of minor and trace element complexes (oxy complexes) in fluids depend on the electronic properties of cations available for this purpose in the fluid (Mysen 2012b, 2015b). This means that when considering partitioning of such elements between minerals and aqueous fluids in the upper mantle and deep crust, pressure-dependent partition coefficients likely reflect changing silicate-cation interaction in the fluid as a function of silicate solubility and speciation.

Qualitatively, this behavior also means that for fluids in equilibrium with mafic and ultramafic mineral assemblages where alkaline earths are dominating cations, the silicate solubility in fluid is less and silicate polymerization is less extensive than in fluids in the equilibrium in felsic systems such as typical gneiss compositions, for example, where alkali metals are more important. Moreover, because the fluid composition in equilibrium with such different crystalline rocks differs, minor and trace element complexing in those different fluids also differs, which leads to different fluid-melt-crystal partition coefficients as a function of rock type (mineral assemblage) with which aqueous fluids equilibrated.