In-situ Raman spectroscopic analysis of dissolved silica structures in Na2CO3 and NaOH solutions at high pressure and temperature

The dissolved silica structures in quartz-saturated 0.50 and 1.50 m [mol kg H2O–1] Na2CO3 and 0.47 m NaOH solutions at up to 750 °C and 1.5 GPa were investigated by in-situ Raman spectroscopy using a Bassett-type hydrothermal diamond anvil cell. The solubility of quartz in the solutions was determined by in-situ observations of the complete dissolution of the grain. The Raman spectra of the quartz-saturated Na2CO3 and NaOH solutions at high pressures and temperatures exhibited the tetrahedral symmetric stretching band of silica monomers. The lower frequency and broader width of the band than those in pure H2O indicated the presence of both neutral and deprotonated monomers. In addition, we newly confirmed the intense bridging oxygen band and the tetrahedral symmetric stretching band of Q1 (silicate center having a single bridging oxygen atom) in the spectra of the Na2CO3 solutions. The integrated intensity ratios of the bridging oxygen band to the monomer band increased with the addition of Na2CO3 and NaOH to fluids, corresponding to an elevation of the measured quartz solubilities. These observations indicate that the formation of silica oligomers in addition to neutral and deprotonated monomers explains the high dissolved silica concentrations in the solutions. The presence of deprotonated monomers under the experimental conditions suggests that deprotonated oligomers exist in the solutions, because the production of the latter more significantly reduces the Gibbs free energy. The anionic silica species and oligomers formed in alkaline silicate fluids may act as effective ligands for certain metal ions or complexes in deep subduction zones.


Introduction
Aqueous fluids facilitate the mass transport of elements for the deep hydrothermal processes involved in metamorphism, metasomatism, and ore formation in the crust and upper mantle of the Earth. Silica is a major constituent of rock-forming minerals and is abundantly dissolved in the deep aqueous fluids. The mobilization of silica by the aqueous fluids has been observed as quartz veins and silica metasomatic zones of exhumed subduction zone rocks (Bebout and Barton 1989;Yardley and Bottrell 1992;Breeding and Ague 2002) and quartz-rich regions in the lower forearc crust with low Poisson's ratios (Audet and Bürgmann 2014;Hyndman et al. 2015). Understanding the efficiency of silica transportation in the deep crust and upper mantle requires detailed knowledge of silica solubility and speciation in aqueous fluids under high pressure (P) and temperature (T) conditions. Because of such importance, a significant number of experimental studies have been conducted on quartz solubility in pure H 2 O (e.g., Anderson and Burnham 1965;Manning 1994), H 2 O-CO 2 (e.g., Newton and Manning 2000;Shmulovich et al. 2001), and H 2 O-NaCl fluids (e.g., Newton and Manning 2000;Shmulovich et al. 2006 and Burnham 1965;Manning 1994), and this increase in the solubility is associated with the polymerization of aqueous silica monomers to form dimers or more polymerized species (e.g., Manning 2002, 2008;Zotov and Keppler 2002;Mysen 2010;Mysen et al. 2013). These experiments were conducted at near-neutral pH conditions, whereas the solubility behavior of quartz in high pH fluids could provide some insights into the nature of alkaline fluids in subducting lithologies such as crustal pelite (Galvez et al. 2015(Galvez et al. , 2016, crustal basalt (Galvez et al. 2016), and sediments (Connolly and Galvez 2018). The enhanced silica solubility in high pH fluids has been confirmed by early and recent studies on supercritical Na 2 CO 3 or NaOH solutions (Friedman 1948;Anderson and Burnham 1967;Schmidt 2014;Aranovich et al. 2020). Aranovich et al. (2020) have systematically investigated quartz solubility in Na 2 CO 3 and NaOH solutions at 500-700 °C and 0.4 and 0.5 GPa using an internally heated pressure vessel and a phase assemblage bracketing method.  8 ] in the solutions. Till date, there is a Raman spectroscopic study on quartz + 1.6 m Na 2 CO 3 solution up to 600 °C and 1.5 GPa by Schmidt (2014). The Raman spectra revealed the presence of neutral monomers Si(OH) 4 and deprotonated monomers Si(OH) 3 O − in the solutions, but lacked evidence of silica oligomers in the spectral region of interest (> ~ 700 cm −1 for the observation of carbon species). On the other hand, a Raman spectroscopy study with SiO 2 -NaOH-H 2 O systems by Mysen (2018) showed the Q 1 -species band under high P-T conditions, but the presence of anionic silica species in the solution is still uncertain. Thus, the information available on the Raman observations is insufficient to understand silica solubility and speciation in Na 2 CO 3 and NaOH solutions under high P-T conditions. In the present study, we report the dissolved silica structures in quartz-saturated 0.50 and 1.50 m Na 2 CO 3 and 0.47 m NaOH solutions up to 750 °C and 1.5 GPa by in-situ Raman spectroscopy in the silicate network vibration frequency range. In addition, we measured the solubility of quartz by in-situ observations of the complete dissolution of the quartz grain, which allowed for comparison with the Raman spectroscopy results. This information provides insights into silicate speciation and fluid-rock interactions for deep geological environments with the presence of alkaline hydrothermal fluids.

Hydrothermal diamond anvil cell experiment
The experiments were performed using a Bassett-type hydrothermal diamond anvil cell (HDAC-V; Anderson et al. 2010). The cell utilized low-fluorescence-grade natural diamond anvils with a culet diameter of 800 μm. Gaskets with an initial thickness of 125 μm and an initial hole diameter of 400 μm, with pure water in the hole, were preheated to approximately 600-700 °C to avoid substantial deformation of the gasket at elevated P-T. An Ar + 2% H 2 mixture was introduced into the gas chamber during the experiments to prevent oxidation of the molybdenum heating wires and anvils at high T. The temperature was measured using K-type thermocouples, with each junction close to the upper and lower anvils. The temperature of the sample chamber was calibrated by direct observation of the melting of Sn (231.9 °C) and NaCl (800.7 °C), and the disappearance of the Raman 355 cm −1 band from the α-quartz at the α-β transition (574 °C) at ambient pressure. The pressure was calculated from the Raman frequency shift of the ~ 464 cm −1 quartz peak (Schmidt and Ziemann 2000) at T < 560 °C, and the ~ 1008 cm −1 zircon peak at T > 560 °C (Schmidt et al. 2013). The positions of the Raman peaks were normalized to the simultaneously obtained neon emission lines. The estimated pressure uncertainties of the reproducibility and random error for the quartz and zircon sensors are approximately 25 and 50 MPa, respectively (Schmidt and Ziemann 2000;Schmidt et al. 2013). For one experiment with a quartzundersaturated system, the pressure was approximated from the isochore corresponding to the liquid-vapor homogenization temperature obtained during heating, based on the equation of state (EoS) of H 2 O (Wagner and Pruβ 2002).
The present study included three series of experiments: (1) quartz + pure H 2 O, (2) quartz + 0.50 and 1.50 m Na 2 CO 3 , and (3) quartz + 0.47 m NaOH. Sodium carbonate and sodium hydroxide (FUJIFILM Wako Pure Chemical Co. Japan) and deionized distilled water were used to prepare the solutions. The NaOH concentration was titrated with oxalic acid solution. Natural quartz (Minas Gerais, Brazil) and natural zircon (Mud Tank, Australia) were used as the starting crystals and the pressure sensors. After loading the quartz and zircon, the sample chamber was filled with the applicable solution and promptly sealed (within several seconds) to avoid concentration changes due to evaporation. It should be noted that the volume of air bubbles in the sample chamber was not controlled by the evaporation process under ambient conditions. We measured the volume of the quartz pieces to determine the solubility under the P-T conditions in which quartz was completely dissolved (Fig. 1). The surface areas of doubly polished sections of quartz were calculated based on the optical microscopic images. As the quartz pieces were not perfectly rectangular parallelepipeds, because the polished section of the quartz were manually broken, as shown in Fig. 1a, e, the surface areas were segmented into transparent parts and rim parts with weak transparency, using the Trainable Weka Segmentation (TWS) plugin of the Fiji ImageJ software (Schindelin et al. 2012;Arganda-Carreras et al. 2017 the quartz piece, resulting in the solubility ranges shown in Table 1. To measure the quartz piece thickness, the other face of the fractured surface of each broken starting piece was imaged by tilting it at 20° or 25° in a field emission scanning electron microscope (FE-SEM; JEOL JSM-7001F). The fluid mass calculation was based on the method of Audétat and Keppler (2005), and the bubble volume was calculated using optical microscopic images obtained below liquid-vapor homogenization temperatures. The densities of the studied fluids at a given T and vapor-saturated P were calculated from the EoS of H 2 O (Wagner and Pruβ 2002) or a model with empirical coefficients for complex aqueous solutions (Laliberté 2009). We considered that the density of the Na 2 CO 3 and NaOH solution is within the model value plus or minus twice the average standard deviation of the solution density residual (experimental-calculated density; 0.73 and 1.50 kg m −3 for Na 2 CO 3 and NaOH solution, respectively ;Laliberté 2009). This creates uncertainty in the lower and upper limits of the solubility values (Table 1). For the experiments with Na 2 CO 3 and NaOH solution, we considered the air bubble volume during the sample loading to attain liquid-vapor homogenization at a temperature that does not significantly exceed ~ 100 and ~ 120 °C, as per the data used in Laliberté (2009). The solubility of quartz determined in the present study is shown in units of molality m (moles of solute per kg of H 2 O, not of aqueous salt solution). The sample chamber was heated at 30-40 °C min −1 . The Raman spectra of the fluids were acquired at 50 or 100 °C increments after holding the sample at each temperature for a few minutes. Before the quartz dissolution was completed, the heating rate was reduced to ~ 15 °C min −1 . Previous time-dependent measurements indicated that quartz and H 2 O in a sample chamber with a similar hole size attained equilibrium within a few minutes at 600 °C (Zotov and Keppler 2002).

Raman spectroscopy
Raman analyses were performed using a HORIBA Jobin Yvon LabRAM 300 Laser Raman microspectrometer connected to a 1024 × 256-pixel charge-coupled device (CCD) detector. Unpolarized Raman spectra of the fluids were recorded using a 632.82 nm He-Ne laser with default power and with a confocal hole of 500 μm, a slit width of 100 μm, 1800 lines mm −1 grating, and 2 or 3 accumulations of 240 s in the single spectral window (159.9-1194.8 cm −1 ). The laser power measured at the sample surface with an Olympus SLMPLN 50 × objective lens (numerical aperture 0.35) was approximately 7 mW. The mechanical focus position was consistently at the culet surface of the upper diamond anvil. To compare the relative integrated intensities between the Raman spectra obtained under different P-T conditions, the spectra were corrected for the temperature factor of the Boltzmann distribution and the frequency and scattering factor (Brooker et al. 1988;Schmidt 2009). The spectra were further normalized by the density of the fluid and the factor for intensity decrease due to reflection at the diamond-fluid interface, according to the procedures described by Schmidt (2009) and Steele-MacInnis and Schmidt (2014). The density of supercritical H 2 O fluids (Zhang and Duan 2005) was used for the supercritical Na 2 CO 3 and NaOH solutions because of the lack of the EoS for the solutions at high P-T conditions. The corrected spectra were baseline-corrected using linear or polynomial functions and fitted by the Gaussian-Lorentzian area function using the software package PeakFit v4.12 (HULINKS Inc.). The quartz solubilities determined for 0.50 and 1.50 m Na 2 CO 3 solutions at 558-730 °C and 0.8-1.5 GPa were greater than those for pure H 2 O at similar P-T conditions (Table 1). Even using the lowest estimation, the enhancing effect of the Na 2 CO 3 on quartz solubility in aqueous fluids was confirmed. The quartz solubility increased at greater Na 2 CO 3 concentrations, which is consistent with previous experimental data for up to approximately 4.7 m Na 2 CO 3 solutions obtained at 300-450 °C and an unspecified P (Friedman 1948), and for 0.3-3.5 m Na 2 CO 3 solutions obtained at 500-700 °C, and 0.4 and 0.5 GPa (Aranovich et al. 2020 Table 2 summarizes the results of Raman spectroscopic measurements. Figure 3 shows the unprocessed Raman spectra of the quartz-saturated and -undersaturated 1.50 m Na 2 CO 3 solutions, and Fig. 4 presents those of the quartz-saturated 0.50 m Na 2 CO 3 and 0.47 m NaOH solutions. The spectra, corrected for the frequency and temperature factors (Brooker et al. 1988;Schmidt 2009), were baseline-corrected by polynomial functions using the ~ 450-500 cm −1 , ~ 730 cm −1 , and ~ 900 or ~ 950 cm −1 regions as anchors. We did not include the higher frequency regions, in which the intensity increased due to the strong fluorescence of the diamond. In the spectra of the Na 2 CO 3 solution, a simple linear baseline correction was applied to remove the background in the range of ~ 950-1150 cm −1 to obtain the relative intensities of the vibrational modes of the carbon species. Figure 5 shows the representative baseline-corrected Raman spectra fitted by the Gaussian-Lorentzian area function and the assignment of the vibrations of silicate species. In the following sections, we use the Q n terminology, which represents the tetrahedral silicate center connected to n bridging oxygen atoms.

The ~ 600 cm −1 band region
In the ~ 500-700 cm −1 region, we observed an intense broad band in the Raman spectra of quartz-saturated 0.50 and 1.50 m Na 2 CO 3 solutions (Figs. 3a and 4a), as well as in the quartz-undersaturated 1.50 m Na 2 CO 3 solution (Fig. 3b). The observation of this band in the NaOH solution ( Fig. 4b) was consistent with that reported by Mysen (2018). The band was detected above ~ 300-400 °C in the Na 2 CO 3 solution, ~ 500 °C in the NaOH solution, and ~ 600 °C in pure H 2 O. The band showed increased intensities and broadening to a lower frequency of ~ 500 cm −1 with increasing P and T. In some spectra, the band could be separated into at least two components, with a main band at ~ 600 cm −1 and a weaker band at ~ 650 cm −1 in the Na 2 CO 3 solution (Fig. 5). Experimental and ab initio molecular dynamics studies have shown that the band near 600 cm −1 represents the vibrations of bridging oxygen Si-O-Si of weakly polymerized silica species such as dimers and trimers (e.g., Lasaga and Gibbs 1988;Zotov and Keppler 2000;Hunt et al. 2011;Spiekermann et al. 2012a, b). Spiekermann et al. (2012a) showed that the bridging oxygen symmetric stretching appeared as a major band at ~ 620 cm −1 and a shoulder band at ~ 680 cm −1 for dimers, and a major band at ~ 680 cm −1 for linear trimers. The ring trimer displays a band at ~ 500-600 cm −1 from the ring breathing mode, in addition to the prominent bridging oxygen band at ~ 600 cm −1 (Dutta and Shieh 1985;Hunt et al. 2011;Spiekermann et al. 2012b). These frequency ranges can cover the observed band in the 500-700 cm −1 region, which is interpreted as resulting from a dimer ± trimer formation. However, it may be challenging to assign the separated bands to individual oligomeric species, as the Si-O-Si vibrational frequencies may show a significant variability owing to the structural degree of freedom of the Si-O-Si bending angle (Kubicki and Sykes 1993;Hunt et al. 2011).

The ~ 770 cm −1 band region
The Raman spectra of quartz-saturated 0.50 and 1.50 m Na 2 CO 3 and 0.47 m NaOH solutions showed prominent bands at ~ 770 cm −1 (Figs. 3a and 4). The intensities of the band increased with increasing P-T conditions in the quartzsaturated systems and were greater than those observed with pure H 2 O (Fig. 5). This band can be readily assigned to the tetrahedral symmetric Si-O stretching of monomeric silica species (Lasaga and Gibbs 1988;Zotov and Keppler 2000;Spiekermann et al. 2012a, b). Figure 6 shows the frequency and full width at half maximum (FWHM) of the band in the quartz-saturated H 2 O, Na 2 CO 3 , and NaOH solutions as a function of T (and P). The frequency in the Na 2 CO 3 and NaOH solutions was lower than that in H 2 O at similar P-T conditions (Fig. 6a). The FWHM of the band in H 2 O increased with increasing P and T up to ~ 23 cm −1 . In contrast, the FWHM in the Na 2 CO 3 and NaOH solutions exhibited greater values than ~ 25 cm −1 with all experimental conditions (Fig. 6b). The overall trends were similar for the Na 2 CO 3 and NaOH solutions. Hunt et al. (2011) showed that the frequency of the tetrahedral symmetric stretching of deprotonated monomers [Si(OH) 3 O − ] and doubly deprotonated monomers [Si(OH) 2 O 2 2− ] shifted to the lower frequency regions. The second deprotonation requires extremely high pH (> 13) under ambient conditions (Bergna and Roberts 2005); therefore, the observed low frequency and broad FWHM features of the band can be an indication of deprotonated monomers in addition to the presence of neutral monomers [Si(OH) 4 ]. Schmidt (2014) similarly assigned the two separated peaks of the broad band at ~ 770 cm −1 to the tetrahedral symmetric stretching of neutral and deprotonated monomers for quartz + 1.6 m Na 2 CO 3 experiments up to 600 °C and 1.5 GPa. The present study indicated the prevalence of the deprotonated species in 0.50 and 1.50 m Na 2 CO 3 and 0.47 m NaOH solutions equilibrated with quartz up to 750 °C and 1.5 GPa.

The ~ 800-900 cm −1 band regions
The Raman spectra of quartz-saturated 0.50 and 1.50 m Na 2 CO 3 and 0.47 m NaOH solutions showed very weak band centered at ~ 830 cm −1 as a shoulder of the 770 cm −1 band (Figs. 3a and 4). This band can be attributed to the tetrahedral Si-O symmetric stretching of Q 1 units, i.e., dimeric silicates or chain silicate species, and the asymmetric stretching of the ethane-like dimer Si 2 O(OH) 6 , which appeared at 793 cm −1 and 783 cm −1 , respectively (Spiekermann et al. 2012a). The previous work by Schmidt (2014)   In the Raman spectra of the quartz-saturated NaOH solution, the ~ 830 cm −1 band showed broadening to the frequency at ~ 950 cm −1 (Fig. 4b). The band at ~ 900 cm −1 was observed in the SiO 2 -H 2 O system (Zotov and Keppler 2002), but hardly detected in the 0.50 and 1.50 m Na 2 CO 3 solutions, possibly because it overlapped with the stretching band of carbon species in the 1.50 m Na 2 CO 3 solution. The ~ 900 cm −1 band has been assigned to Q 2 units, i.e., the cyclic silicate or middle group in silicate chains, in several studies, but using only this explanation could cause overestimation of the degree of polymerization, because there are several potential species that could be responsible for this band. Spiekermann et al. (2012a) showed that the tetrahedral symmetric stretching of Q 2 appears at 888 cm −1 , coupled with 1081 cm −1 . The presence of the broad band at ~ 950-1050 cm −1 in the NaOH solution is not likely to result only from the coupled features of Q 2 , because the bridging oxygen Si-O-Si asymmetric stretching of Q n or the Si-O − stretching of the deprotonated species appears in these regions, as described below. The ~ 900 cm −1 band may include a contribution from the symmetric stretching of the ethane-like dimer Si 2 O(OH) 6 , which shows a band at 870 cm −1 (Spiekermann et al. 2012a). In addition, the tetrahedral asymmetric stretching of Q 0 and Q 1 and the single non-bridging Si-OH stretching of various Q n units (n = 0-3) appear between 915 cm −1 and 936 cm −1 (Spiekermann et al. 2012a).

The ~ 1000 cm −1 band region
The Raman spectra of the quartz-saturated and -undersaturated 1.50 m Na 2 CO 3 solutions showed prominent bands at ~ 1000 cm -1 and ~ 1060 cm −1 (Fig. 3). The ~ 1060 cm −1 bands in the quartz-saturated solution exhibited broader features than those of the quartz-undersaturated solution. These bands diminished to ~ 600-700 °C in the quartz-saturated 0.50 m Na 2 CO 3 solution (Fig. 4a). These bands can be   (Frantz 1998;Rudolph et al. 2008;Schmidt 2014). Figure 7 shows that the relative intensities of the ~ 1000 cm −1 band to the ~ 1060 cm −1 band (A 1000 /A 1060 ) were higher in the quartz-saturated system than in the undersaturated system. At ~ 600 °C, the relative intensities in the quartz-saturated system remained constant or decreased. This is likely attributed to an intensity increase at ~ 1060 cm −1 owing to the contributions from the silicate species vibrations, as described below.
Broad, weak signals were detected in the high-frequency regions at ~ 950-1150 cm −1 in the quartz-saturated NaOH solution spectra (Fig. 4b). The ~ 1060 cm −1 region of the quartz-saturated 1.50 m Na 2 CO 3 solution spectra also indicated the contribution from silicate species. The bands are likely attributed to the bridging oxygen Si-O-Si asymmetric stretching of Q n (n = 1-4) at ~ 1070 cm −1 (Spiekermann et al. 2012a), because of the presence of the bridging oxygen vibrations at ~ 600 cm −1 . In addition, Spiekermann et al. (2012a) showed that the tetrahedral symmetric stretching of Q 2 and Q 3 units displays bands at 1081 cm −1 and 1103 cm −1 , respectively. Moreover, the tetrahedral asymmetric stretching of Q 2 , Q 3 , and Q 4 units exhibits bands centered at 970, 1015, and 1062 cm −1 , respectively. However, we may exclude contributions from the vibrations of Q 4 units, because those species were not detected in aqueous solutions of up to 40 mol% SiO 2 concentrations in Na 2 O⋅2SiO 2 (NS2)-H 2 O and Na 2 O⋅3SiO 2 (NS3)-H 2 O systems at high P-T conditions (Steele-MacInnis and Schmidt 2014). Another possibility is a contribution from the Si-O − stretching of the deprotonated species centered at ~ 1050 cm −1 (Hunt et al. 2011). Although the high-frequency bands were not as prominent as those observed in highly alkaline silicate solutions at ambient T and up to 2.0 GPa (Dutta and Shieh 1985;Gout et al. 2000;Hunt et al. 2011), the bands may include contributions from the deprotonated species, because of the presence of the deprotonated monomer Si(OH) 3 O − .

Discussion
Comparisons with previous solubility data in Na 2 CO 3 solutions Aranovich et al. (2020) determined the quartz solubility in 0.2-3.5 m Na 2 CO 3 solutions at conditions of 500, 600, and 700 °C and 0.4 GPa, and 600 °C and 0.5 GPa, using an internally heated pressure vessel and a phase assemblage bracketing method. Those authors showed a slight increase of quartz solubility in the Na 2 CO 3 solutions with increasing P and T. Figure 2 shows that our measured solubilities in 0.50 m Na 2 CO 3 solutions at 579 °C (0.92 GPa), 635 °C (0.84 GPa), and 695 °C (1.42 GPa), and 1.50 m Na 2 CO 3 solutions at 558 °C (1.20 GPa) and 629 °C (1.41 GPa) overlapped, within errors, with the calculated values from the Aranovich et al. (2020) experiments at 0.4 and 0.5 GPa. This agreement indicates that the pressure dependence of the quartz solubility is negligible at these temperature and compositional ranges. In contrast, our measured solubilities in the 0.50 m Na 2 CO 3 solution at 730 °C (1.52 GPa) and the 1.50 m Na 2 CO 3 solution at 648 °C (1.31 GPa) were higher than the values extrapolated from the lower temperature results. This might suggest that the solubility of quartz becomes more dependent on temperature at higher P as P-T conditions approach the critical curve. Schmidt (2014) reported the silica solubility in 1.6 m Na 2 CO 3 solution at 600 °C and 1.5 GPa based on the in-situ Raman spectroscopic study to be ~ 1 m, which is approximately two times lower than our lowest estimation of the solubility in 1.50 m Na 2 CO 3 at 629 °C and 1.41 GPa (2.22 ± 0.52 m). This discrepancy likely relates to the calculation used by Schmidt (2014) being based on the integrated intensities of the monomeric silica band. In the present study, the in-situ Raman spectroscopy in the frequency regions of silicate newly revealed the strong bridging oxygen band and the tetrahedral symmetric stretching band of the Q 1 unit in the quartz-saturated 1.50 m Na 2 CO 3 solution spectra (Figs. 3 and 5), indicating the presence of silica oligomers in the solution. Therefore, basing the total silica solubility calculation solely on the integrated intensities of the monomeric silica band could lead to underestimation in this system. The present study shows the effect of the alkaline

m Na2CO3
Qz-saturated Qz-undersaturated Fig. 7 The integrated intensity ratios of the ~ 1000 cm −1 band to the ~ 1060 cm −1 band as a function of temperature (and pressure) in the quartz-saturated and -undersaturated systems. The bands are mainly contributed from the C-OH stretching of HCO − 3 and the C-O symmetric stretching of CO 2− 3 , respectively Na 2 CO 3 solution on enhancing silica solubility at high P conditions becomes clearer.

Comparison with thermodynamic modeling
We compared the measured quartz solubilities in 0.50 and 1.50 m Na 2 CO 3 with thermodynamically predicted solubilities at similar P and T conditions based on the equilibration between aqueous silica species, using an equilibrium constant database for aqueous species from the DEW model (Sverjensky et al. 2014;Huang and Sverjensky 2019) and the EQ3NR code (Wolery 1992). In this calculation, we assumed that the oxygen fugacity was near the fayalite-magnetite-quartz (FMQ) buffer, because Schmidt (2014) reported no CH 4 formation in Na 2 CO 3 solutions in equilibrium with quartz using an experimental setup similar to ours. We also confirmed that the calculated solubilities were not significantly changed by carbon speciation under more oxidized conditions than that of the FMQ buffer. It should be noted that carbon species were predicted to be mainly electrically neutral under these conditions, which is not consistent with the observed Raman band. In Fig. 2, we showed the thermodynamically predicted silica solubility curves in 0.5 and 1.5 m Na 2 CO 3 solutions at 1.0 and 1.5 GPa, where the aqueous silica species were Si(OH) 4 , Si(OH) 3 O − , Si 2 O(OH) 6 , and Si 3 O 2 (OH) 8 . These curves were lower than our lowest estimation of quartz solubility. Aranovich et al. (2020) also reported that the quartz solubility in Na 2 CO 3 solutions based only on the above species underestimated the values at lower pressure ranges (0.4 and 0.5 GPa). Our solubility data, together with those of Aranovich et al. (2020), indicated that the available speciation modeling was insufficient to explain the high quartz solubilities and aqueous speciation in the Na 2 CO 3 solution at high P-T conditions.

High quartz solubility associated with the formation of oligomers
The solubility of silica in aqueous solutions rapidly increases at levels of pH > 9 under ambient conditions (Iler 1979). The studied Na 2 CO 3 and NaOH solutions were alkaline, involving the hydrolysis reaction of aqueous carbonate species (CO 3 2− + H 2 O = HCO 3 − + OH − ) or the dissociation of NaOH (NaOH = Na + + OH − ). The present study showed the favorable formation of HCO 3 − in Na 2 CO 3 solutions in the quartz-saturated condition compared to the quartzundersaturated condition (Fig. 7), which can readily be explained by the consumption of OH − through the reaction with quartz. Schmidt (2014) demonstrated that the formation of the deprotonated silica monomers in the solutions (SiO 2 (s) + H 2 O + OH − = SiO(OH) 3 − ) reflected the higher quartz solubility in Na 2 CO 3 solutions than that in pure H 2 O. Our Raman spectroscopic studies confirmed the higher intensities of the monomer bands in the Na 2 CO 3 and NaOH solutions than those in pure H 2 O (Fig. 5), with the presence of deprotonated monomers up to our highest experimental conditions of 750 °C and 1.5 GPa. Together with the results of Schmidt (2014), we have verified that the formation of deprotonated monomers contributed to the high quartz solubility in the Na 2 CO 3 solutions.
Furthermore, the present study newly observed the bridging oxygen band in the Raman spectra of the Na 2 CO 3 solutions, which indicates the formation of silica oligomers (Figs. 3,4,and 5). In particular, the Raman band regions of the tetrahedral symmetric Si-O stretching of structural Q n units indicate that at least dimeric silicates or chain silicate species, including Q 1 units, are present in the solutions (Fig. 5). To quantify the relative concentrations of species in aqueous solutions and melts, the previous studies considered the ratios of the tetrahedral symmetric stretching band of Q n species, which are assumed to have the same Raman scattering cross-sectional area (e.g., Mysen 2010;Mysen et al. 2013;Steele-MacInnis and Schmidt 2014). However, the intensities of the detected tetrahedral symmetric stretching bands of Q 1 units in our Na 2 CO 3 and NaOH solutions were too low to detect differences in the Q 1 /Q 0 ratios between the solutions. Instead, we used the ratio of the intense bridging oxygen Si-O-Si symmetric stretching band to the tetrahedral symmetric stretching band of Q 0 (A 600 /A 770 ) in a similar manner to Hunt et al. (2011). Comparison of the A 600 /A 770 obtained under different P-T conditions requires the assumption that the ratios of the relative Raman scattering cross-sectional factors are independent of P and T. Steele-MacInnis and Schmidt (2014) reported no detectable change in the silicate band intensities with increasing P at constant T and SiO 2 concentrations. Thus, we compared the ratios among spectra of different solutions under similar T conditions. Figure 8a shows the integrated intensity ratios, A 600 /A 770 , in the quartz-saturated Na 2 CO 3 , NaOH, and H 2 O solutions at P = 0.8-1.5 GPa as a function of T. The ratios generally increased in the following order: H 2 O < 0.47 m NaOH < 0.50 m Na 2 CO 3 < 1.50 m Na 2 CO 3 . In addtion, the increase in the ratios corresponded to the elevation of silica solubility determined by the in-situ observations of the complete dissolution of quartz (Fig. 8b). If the ratios were simply proportional to the concentration ratios of oligomeric species to monomers, the increase in silica oligomers in the solutions would account for the observed high quartz solubilities in the Na 2 CO 3 and NaOH solutions. The ratios could also be increased by the formation of silica oligomers with different Raman scattering cross-sectional factors with increasing silica concentration. Therefore, the observed high solubility of quartz in the Na 2 CO 3 and NaOH solutions is assumed to have resulted from the formation of silica oligomers in addition to the neutral and deprotonated monomers.

Silica speciation in alkaline high P-T solutions
Based on our solubility data and Raman observations, the oligomeric silica species contribute to the high quartz solubility in alkaline Na 2 CO 3 and NaOH solutions under high P-T conditions. In particular, the Raman band regions of the tetrahedral symmetric Si-O stretching of structural units Q n indicate that at least dimeric silicates or chain silicate species, including Q 1 units, are present in the solutions. This suggests that the deprotonated dimer, Si 2 O(OH) 5 O − , could be present in quartz-saturated alkaline solutions at high P-T conditions, as proposed by Aranovich et al. (2020). However, we could not infer the presence of the deprotonated dimers from the Si-O − stretching Raman band, which appears at ~ 1050 cm −1 in the alkaline silicate solutions under ambient conditions and up to 2 GPa (e.g., Hunt et al. 2011). On the other hand, our experiments confirmed the presence of deprotonated monomers in the quartz-saturated Na 2 CO 3 and NaOH solutions under all experimental conditions. As the deprotonation of silica dimers and trimers lowers the Gibbs free energy more efficiently than that of the silica monomers in aqueous solutions at room temperature to 450 K (Tossell and Sahai 2000;Mora-Fonz et al. 2007), the deprotonated oligomers could be favorably present in the solutions even at elevated P-T conditions. Other possible stable silica oligomers are ion pairs between sodium cations and deprotonated silica oligomers or sodium-silicate complexes, as observed in alkali-silicate solutions under ambient conditions by NMR spectroscopy (Kinrade and Swaddle 1986;McCormick et al. 1989) and fast atom bombardment mass spectroscopy (FAB-MS; Tanaka and Takahashi 1999). Manning et al. (2010) and Wohlers et al. (2011) demonstrated the presence of polymerized Na-Al-Si complexes in aqueous fluids in equilibrium with albite + paragonite + quartz or jadeite + paragonite + quartz at 350-600 °C and 1-2.25 GPa. Although evidence for oligomers involving alkali metals was not directly inferred from the in-situ Raman spectroscopic studies, the effect of alkali metal cations on aqueous silicate equilibria is indicated by the differences in the Raman spectra and integrated intensity ratios between the quartz-saturated 0.50 m Na 2 CO 3 and 0.47 m NaOH solutions. The equilibria involving such oligomers at elevated P-T conditions will accurately describe silicate solubility in alkaline fluids.

Implications for element transfer in deep subduction zones
The present study suggests that alkaline fluids can dissolve a significant amount of silica compared to pure H 2 O at elevated P-T conditions, which is explained by the formation of neutral and deprotonated monomers and the subsequent formation of oligomers. The presence of deprotonated monomers under all experimental conditions suggested the presence of deprotonated and other possible oligomers such as ion pairs between sodium cations and anionic deprotonated silica oligomers. The presence of anionic silica species in alkaline fluids enhances the attractive electrostatic force between opposite ions, which acts as an effective ligand for certain metal ions or complexes. For example, the interaction energies of gold complexes with silica species depend on the pH conditions (Mohammadnejad et al. 2017). Additional examples are Zr and Ti, which are representatives of nominally insoluble high field strength elements. Only SiO 2 components in aqueous fluids did not significantly enhance the solubility of Ti and Zr (Antignano and Manning 2008;Bernini et al. 2013), while the addition of NS2 or NS3 glass or albite components to pure H 2 O enhanced the solubility  Fig. 8 a The integrated intensity ratios of the oligomeric silica species band area to the monomer band area (A 600 /A 770 ) as a function of temperature (and pressure) and b as a function of solubility of quartz determined by in-situ observations. Molal concentrations of silica in H 2 O at the experimental P and T were calculated based on the DEW model (Sverjensky et al. 2014;Huang and Sverjensky 2019) of Ti and Zr by producing alkaline silicate-rich fluids similar to our experimental system (Antignano and Manning 2008;Manning et al. 2008;Wilke et al. 2012;Louvel et al. 2013). Based on X-ray absorption spectroscopy, Louvel et al. (2013) found that Zr dissolved by forming alkali-zirconosilicate clusters via octahedral coordination with oxygen and Si(Na) second neighbors. The anionic silica species and subsequently formed silica oligomers in alkaline fluids are thus assumed to affect the solubility of these metals by forming complexes.

Conclusions
1. The solubilities of quartz in 0.50 and 1.50 m Na 2 CO 3 solutions at 558-730 °C and 0.84-1.52 GPa indicated the enhancing effect of Na 2 CO 3 on quartz solubility at elevated P-T conditions. The present study, together with Aranovich et al. (2020), showed that the conventional aqueous silica species [Si(OH) 4 , Si(OH) 3 O − , Si 2 O(OH) 6 , and Si 3 O 2 (OH) 8 ] alone were insufficient to describe the observed high solubility. 2. The Raman spectra of the quartz-saturated Na 2 CO 3 and NaOH solutions exhibited tetrahedral symmetric stretching bands under the experimental conditions. The low frequency and broad FWHM of the bands were interpreted to be due to the deprotonated monomer Si(OH) 3 O − in addition to the neutral monomer Si(OH) 4 . 3. We newly confirmed the intense bridging oxygen band and the tetrahedral symmetric stretching band of Q 1 units, suggesting the formation of silica oligomers in the solutions. The integrated intensity ratios of the bridging oxygen band area to the monomer band area increased in the following order: H 2 O < 0.47 m NaOH < 0.50 m Na 2 CO 3 < 1.50 m Na 2 CO 3 . The increase in the ratios corresponded to the elevation of quartz solubilities, suggesting that oligomers contributed to the high solubility. 4. Considering the presence of deprotonated monomers under all experimental conditions, we assumed that energetically favorable oligomer deprotonation occurred in the solutions. Sodium-silicate complexes or ion pairs between sodium cations and deprotonated silica oligomers were also possible, although these were not confirmed by in-situ Raman spectroscopic studies. The anionic silica species or oligomers formed in alkaline silicate fluids may act as effective ligands for certain metal ions or complexes in deep subduction zones.