Pressure-induced elongation of hydrogen-oxygen bond in sodium silicate melts

Abstract

Despite their importance in melting processes in the Earth’s interior, the structure and properties of hydrous silicate melts at high pressure remain poorly constrained due to experimental challenges. Here we explore the structures of dry and hydrated (H₂O and D₂O) Na₆Si₈O₁₉ melt at 0-6 GPa and 1000-1300 K and glasses recovered from high pressure and temperatures by in-situ neutron and X-ray diffraction. The structures of the melts at 0-10 GPa and 3000 K are also investigated by ab-initio molecular dynamics simulation. In-situ neutron experiments reveal that the D-O distance increases with compression due to the formation of -O-D-O- bridging species, which is reproduced by the molecular dynamics simulations. The pressure-induced -O-D-O- formation reflects a more rigid incorporation of hydrogen, which acts as a mechanism for the experimentally observed higher solubility of water in silicate melts. Together with shrinking modifier domains, this process dominates the compression behavior of hydrous Na₆Si₈O₁₉ melt, whereas the compression of dry Na₆Si₈O₁₉ at 0-10 GPa and 3000 K is governed largely by bending of the Si-O-Si angle. The molecular dynamics simulations on hydrous Na₆Si₈O₁₉ melts further suggest that the sodium ions are scavenged from its network-modifying role via 2·(^[4]Si-O⁻ + Na⁺) → ^[4]Si-(O-^[5]Si-O)²⁻ + 2·Na⁺ and Si-O⁻ + Na⁺ + Si-OH → Si-(O-H-O-Si)⁻ + Na⁺ with increasing pressure.

INTRODUCTION

According to experiments at high pressure (P) and temperature (T) and geophysical observations such as seismic-wave velocity and magnetotellurics, magma can be present locally in the deep Earth: in the mantle wedge (Lee et al., 2009; Eilon and Abers, 2017), above the subducting slabs (Schmidt and Poli, 1998; Syracuse and Abers, 2006; Schmidt and Poli, 2014), at the lithosphere-asthenosphere boundary (Schmerr, 2012; Naif et al., 2013; Sakamaki et al., 2013), above the 410-km discontinuity (Sakamaki et al., 2006; Tauzin et al., 2010), below the 660-km discontinuity (Schmandt et al., 2014), and above the core-mantle boundary (Williams and Garnero, 1996; Vidale and Hedlin, 1998; Wen and Helmberger, 1998; Dannberg et al., 2021). Due to its faster transport properties and high reactivity, even a small amount of melt can significantly affect the chemical evolution of the Earth by, for example, filtering incompatible elements (Bercovici and Karato, 2003). It is well known that the physico-chemical properties of melts, such as density, viscosity, and compressibility, are sensitive to atomic structures (e.g., Sakamaki, 2018). Despite the importance to explore macroscopic properties and structures of silicate melts at high P and T, they are not well understood because in situ experiments on melts at extreme conditions are difficult, mainly because high temperature is required to melt samples.

A considerable number of experiments aimed at determining high-P structures of silicate melts and glasses have been conducted by, for example, X-ray diffraction (XRD) (e.g., Funamori et al., 2004; Wang et al., 2014; Ohashi et al., 2018; Hisano et al., 2021; Ohashi et al., 2022), neutron diffraction (ND) (e.g., Wilding et al., 2012; Zeidler et al., 2014; Salmon et al., 2019; Ohashi et al., 2022), and nuclear magnetic resonance (NMR) (e.g., Xue et al., 1991; Allwardt et al., 2004; Lee et al., 2004; Allwardt et al., 2005, 2007). Silicate melts and glasses below 10-20 GPa are characterized by fourfold-coordinated SiO₄ and AlO₄ units, and compression is taken up by the rest of the structure (e.g., Wang et al., 2014; Sanloup, 2016; Petitgirard et al., 2019). On the other hand, some studies proposed the densification mechanism related to the pressure-induced formation of TO₅ and/or TO₆ units (T = Si, Al) (e.g., Allwardt et al., 2005, 2007; Zeidler et al., 2014).

Water is the most abundant volatile component of natural magmas (e.g., Jambon, 1994), and estimates on its budget in the Earth’s mantle range from 1/4 to 4 ocean masses (∼ 10²⁰-10²¹ kg) (Hirschmann, 2006, 2018). Water also leads to changes in the physico-chemical properties of silicate melts, such as a decrease in density (Lange, 1994), an increase in their compressibility below 2 GPa (Agee, 2008), and a decrease in viscosity (Dingwell, 1987; Lange, 1994; Whittington et al., 2000; Poe et al., 2006; Bajgain et al., 2019; Langhammer et al., 2021). Such changes in macroscopic properties are closely related to structural modifications caused by the addition of H₂O (Stolper, 1982):

  

\begin{equation} \text{Si-O-Si} + \text{H$_{2}$O} \rightarrow 2{\cdot}\text{Si-O-H} \end{equation} (1).

It has been shown that water in silicate melts generally exists in the forms of -O-H hydroxyl, molecular H₂O, and/or transitional -O-H-O- bridging species, with proportions changing with P, T, and composition, including water concentration (Stolper, 1982; Reimers and Watts, 1984; McMillan and Remmele, 1986; Xue and Kanzaki, 2004; Bajgain et al., 2015). Previous ND, Raman spectroscopy, and NMR studies also suggest that H₂O depolymerizes the Si-O-Si network structure (Zotov et al., 1996; Zotov and Keppler, 1998). However, most experiments investigate structures of recovered glassy samples (e.g., Mysen et al., 1980; Mysen and Cody, 2004; Xue and Kanzaki, 2004; Mysen and Cody, 2005; Le Losq et al., 2015; Cody et al., 2020), and in situ structural data of hydrous melts at high P are limited (Yamada et al., 2007, 2008, 2011).

Sodium is a representative network-modifier cation, which significantly decreases the degree of polymerization, viscosity (Urbain et al., 1982; Knoche et al., 1994), and liquidus T (Shahid and Glasser, 1971). Along the Na₂O-SiO₂ join, Na₆Si₈O₁₉ (3Na₂O-8SiO₂: N3S8) has a relatively low liquidus T, and its water solubility (Mysen and Cody, 2004) and NBO/Si (the average number of non-bridging oxygen per Si) at hydrous condition (Mysen and Cody, 2005) were explored by previous spectroscopic experiments. Here we selected hydrous sodium silicate compositions as a model of natural silicate melts. In this work, we performed in situ XRD and ND experiments together with ab initio molecular dynamics (MD) simulations to determine the structure of dry and hydrous Na₆Si₈O₁₉ glasses and melts at high P and T.

METHODS

Sample preparation

The starting glass of dry N3S8 was prepared from a mixture of SiO₂ (Wako Pure Chemical Industries, Ltd., 99.9% pure) and Na₂CO₃ (Wako Pure Chemical Industries, Ltd., 99.8% pure) powder reagents. The mixture was ground with an agate mortar for 1 h, decarbonized at 973 K for 2 h and then melted at 1573 K for 6 h. This temperature (1573 K) is significantly higher than the melting T of crystalline N3S8 (1072 K) at atmospheric P (Williamson and Glasser, 1965). The quenched glass was subsequently ground with an agate mortar to make a chemically homogeneous powder. The NBO/Si ratio of the glass at ambient P is calculated as 0.75 from its chemical composition based on the definition of Mysen et al. (1982). The hydrous samples for X-ray and neutron diffraction measurements were made by reacting the above starting glass sample with water (or deuterated water) in the high pressure cell. Chemical compositions of the samples used in XRD and ND experiments and MD simulations are summarized in Table 1.

Table 1. Sample compositions investigated in the diffraction experiments and MD simulations

State	Condition	X-ray	Neutron	MD
Melt	high-PT	N3S8 N3S8-H9	N3S8-D10	N3S3 N3S3-H8 N3S3-H14
Glass	high-P		N3S8
	Ambient P		N3S3-D9 N3S3-D12

The number after H (D) identifies the (deuterated) water content (wt%) in the sample.

In situ diffraction experiments at high P and T

Structures of anhydrous N3S8 melt and hydrous melt with 9 wt% H₂O (N3S8-H9) were investigated at high P and T by in situ XRD. For hydrous compositions, the starting glasses and distilled water were contained in a single-crystal diamond sleeve and both ends sealed with Pt or Au₇₅Pd₂₅ caps (Yamada et al., 2007, 2008) (Supplementary Fig. S1a; Figs. S1-S7 are available online from https://doi.org/10.2465/jmps.240926a). In the measurements of the dry melt, the starting glasses were put into a graphite cup, which was capped with another graphite cup (Fig. S1b). The starting glass was kept in a vacuum desiccator when not in use. All the parts of the high-P cell were heated at 400 K for more than 8 h before assembling.

The experimental P and T conditions were 1.5-6.0 GPa and 1120-1310 K, respectively. The MA 6-6 assembly (Nishiyama et al., 2008; Kawazoe et al., 2010) was used to compress the sample. The generated P was determined from the lattice parameters of MgO as a pressure marker by using the Birch-Murnaghan (B-M) equation-of-state (EoS) for MgO (Tange et al., 2009). Temperature was estimated from the electronic power applied to the heater based on power-T calibration curve predetermined by experiments using the W3%Re-W25%Re thermocouple of 0.125-mm diameter (Fig. S1c). The in-situ XRD experiments were carried out using a cubic-type multi-anvil apparatus, MAX80 (Shimomura et al., 1984) at the AR-NE5C beamline of the Photon Factory at KEK, Tsukuba, Japan. The diffraction profiles were collected at 9-11 diffraction angles (2θ = 3, 4, 6, 8, 11, 14, 17, 21, 25, 27, and 30°) in energy-dispersive method to extend the accessible Q range. The energy range for data analysis is approximately 10-50 keV. In all high P-T experiments, the starting vitreous sample crystallized upon heating and melting at a higher temperature was judged from the change in the diffraction patterns.

ND experiments were performed at the BL11 beamline (PLANET) in the Material and Life Science Experimental Facility (MLF) of J-PARC, Ibaraki, Japan (Hattori et al., 2015). The ambient pressure measurement of uncompressed N3S8 glass and the glasses obtained by quenching the 9 wt% D₂O-containing melt (N3S8-D9) at 1574 K and 12 wt% D₂O containing melt (N3S8-D12) at 1273 K was conducted using vanadium cans. Supplementary Figure S3 represents a Raman spectrum for N3S8-D12 glass. Three peaks at 1690, 2220, and 2580 cm⁻¹ originate from OD or D₂O species (Zotov and Keppler, 1998). A weak broad peak was, however, observed at ∼ 3500 cm⁻¹, suggesting a slight contamination of H₂O likely due to the high hygroscopicity of sodium silicate glass (e.g., Mysen and Cody, 2004).

In situ high P-T ND experiments were performed for N3S8 melt with 10 wt% of D₂O (N3S8-D10) at 1-5 GPa and 1000-1300 K. The glass samples and deuterated water (FUJIFILM Wako Pure Chemical Corp., 99.8% pure) were enclosed in a capsule made of Au₇₅Pd₂₅ alloy and then the lids were arc welded to seal the sample (Fig. S2a). The amount of deuterated water was determined by weighing the capsule before and after the addition of D₂O. High P and T were generated by the six-axis multi-anvil press ATSUHIME (Sano-Furukawa et al., 2014) installed at the PLANET beamline. P were determined from the B-M EoS for MgO (Tange et al., 2009). T was estimated from the electronic power applied to the heater based on the power-T calibration curve predetermined using assemblies with the W3%Re-W25%Re thermocouple of 0.125-mm diameter (Fig. S2b). Exposure times for the measurement at each PT point were ∼ 20, ∼ 12, and ∼ 20 h for the sample, vanadium, and the empty cell, respectively. The diffraction data were collected by ³He position-sensitive detectors at 2θ ≈ 90° by the time of flight (ToF) method.

Data processing

X-ray total structure factors S^X(Q) were obtained by correcting diffraction intensities using the MCEDX software (Funakoshi, 1997). S^X(Q) were calculated based on the Faber-Ziman formalism as follows:

  

\begin{equation} {S^{\text{X}}(Q) = \frac{I^{\text{coh}}(Q)/N - \left\{\sum_{\alpha}c_{\alpha}[f_{\alpha}(Q)]^{2} - \left[\sum_{\alpha}c_{\alpha}f_{\alpha}(Q) \right]^{2} \right\}}{\left[\sum_{\alpha}c_{\alpha}f_{\alpha}(Q) \right]^{2}}} \end{equation} (2),

where I^coh(Q), N, c_α, and f_α(Q) are the coherent scattering intensity, the number of atoms, the concentrations for species α, and the atomic scattering factors for α, respectively. Since Hajdu (1971) does not include the fitting parameters for the incoherent scattering intensity of hydrogen, we obtained its fitting parameters by using the data of Hubbell et al. (1975): M = 1.0274, K = 21.213, and L = 10.028 (Fig. S4).

Neutron total structure factors S^N(Q) were acquired using the nvaSqHP.py code developed in the PLANET group. In the ND experiments, the scattering intensity of the sample was corrected using the data for compressed vanadium pellets in the same cell assembly and the empty cell assembly with the dimension at high-P conditions. The detailed procedure is described in Hattori et al. (2015, 2019). The Faber-Ziman S^N(Q) were obtained by:

  

\begin{equation} S^{\text{N}}(Q) = \frac{I^{\text{coh}}(Q)/N - \left\{\sum_{\alpha}c_{\alpha}(b_{\alpha}^{\text{coh}})^{2} - \left[\sum_{\alpha}c_{\alpha}b_{\alpha}^{\text{coh}} \right]^{2} \right\}}{\left[\sum_{\alpha}c_{\alpha}b_{\alpha}^{\text{coh}} \right]^{2}} \end{equation} (3).

Here, b_α^coh is the coherent scattering length for species α. When light elements such as deuterium were used in ND experiments, one should also consider the large recoil (inelastic) effect, resulting in the incoherent scattering cross section varying with Q. In this study this effect is corrected with the Kameda’s method (Kameda, Bull. Chem. Soc. Jpn, 2018, 91, 1586).

The X-ray and neutron total pair distribution functions, g^X(r) and g^N(r), respectively, were derived by Fourier transformation of S^X,N(Q) (Q_MAX = 20 Å⁻¹) based on:

  

\begin{align} &g^{\text{X},\text{N}}(r) \\&\quad= 1 + \frac{1}{2\pi^{2}nr}\int_{Q_{\min}}^{Q_{\max}}Q[S^{\text{X},\text{N}}(Q) - 1]M(Q)\sin(Qr)\text{d}Q \end{align} (4),

where r is interatomic distance, n denotes the number density, and M(Q) is the Lorch modification function introduced to suppress the termination ripples of g(r) (Lorch, 1969). n for the melts under P was estimated from the B-M EoS computed by ab initio MD simulations: n₀ = 0.0530(5) Å⁻³, K₀ = 7.9(6) GPa, (∂K/∂P)₀ = 4.9(1) for dry N3S8 and n₀ = 0.0527(7) Å⁻³, K₀ = 4.3(4) GPa, (∂K/∂P)₀ = 5.5(2) for N3S8-H8. Here n₀, K₀, and (∂K/∂P)₀ are the number density, the isothermal bulk modulus, and its P derivative at zero-P, respectively.

Ab initio molecular dynamics

In our ab initio MD simulations using the Vienna ab initio simulation package, VASP (Kresse and Hafner, 1993, 1994; Kresse and Furthmüller, 1996a, 1996b), we applied periodic boundary conditions with expanded Kohn-Sham wave functions as a plane-wave basis set (E_cut = 450 eV), and calculated electronic states at the Brillouin zone center. We applied the generalized gradient approximation (GGA) (Perdew et al., 1996, 1997) to approximate exchange correlation functional and the projector augmented wave formalism (Blöchl, 1994; Kresse and Joubert, 1999).

MD simulations were conducted in the N-V-T canonical ensemble with constant number of atoms (N) and constant volume (V), and T regulated by a Nosé-Hoover thermostat (Nosé, 1984a, 1984b; Hoover, 1985; Nosé, 1991). Ab initio MD simulations were set up in cubic supercells with 165 atoms (5·Na₆Si₈O₁₉) for dry N3S8, 168 atoms (4·Na₆Si₈O₁₉ + 12·H₂O) for N3S8-H8 (8 wt% H₂O), and 204 atoms (4·Na₆Si₈O₁₉ + 24·H₂O) for N3S8-H14 (14 wt% H₂O) compositions (Table 1). Following previous computational work (e.g., Pan and Galli, 2016), the weight of hydrogen was doubled to that of deuterium to slow down its fast dynamics. Calculations were performed with V in the range 1.04-1.3·V_ref, which results in P computed from the Hellmann-Feynman stress tensor of approximately 0-10 GPa, covering the experimental P range. The reference volume (V_ref = 1661.552 ų) is based on the unit-cell V of Na₆Si₈O₁₉ crystal at ambient conditions (Krüger et al., 2005). Using E_cut = 900 eV, we estimated a Pulay stress of 0.3-0.5 GPa at 3000 K. However, we did not apply a Pulay correction because this is an insignificant value.

The initial configuration was relaxed through MD simulation for t > 5 ps at 3000 K and V_ref, followed by simulations with instantaneous changes in V between 1.04-1.30 V_ref that ran for t ≥ 20 ps at 3000 K. The initial nonstationary portion of the simulated trajectories (by inspecting the energetics) is discarded in the calculation of equilibrium properties. MD time steps were chosen as Δt = 0.5 fs and Δt = 0.25 fs for dry and hydrous compositions, respectively. The system was confirmed to be in the liquid state by checking partial pair distribution functions g_αβ(r) of all atomic α-β pairs, and the mean squared displacement of all atomic species.

RESULTS AND DISCUSSION

Structure factor

Figure 1 illustrates the obtained S^X(Q) of the dry and hydrous melts at high P and high T. The oscillations in the range above 6 Å⁻¹ are virtually identical, regardless of P or composition. The most pronounced P-induced changes are observed below 4 Å⁻¹. The first sharp diffraction peak (FSDP) and principal peak (PP) in S^X(Q) are observed at 2.0-2.2 and 3 Å⁻¹, respectively. In S^N(Q), the FSDP and PP appear at 1.7-2.2 and 3 Å⁻¹, respectively (Fig. 2). The FSDP in S^X(Q) tends to gain intensity with P, while it diminishes for S^N(Q). Based on the partial S(Q) for silica glass by a previous Reverse Monte Carlo modelling (Kono et al., 2022), this tendency is understood to result from the competing compression behavior of the intensifying first peak in S_SiSi(Q) and decreasing amplitude in S_OO(Q); the former reflects the FSDP for S^X(Q), the latter for S^N(Q) (Kono et al., 2022). The FSDP position (Q₁) in S^X(Q) and S^N(Q) shifts to higher Q with increasing P (Fig. 3), suggesting the shrinkage of SiO₄ networks. The FSDP shift is also observed in our MD simulations (Fig. S5). The observed P dependence of Q₁ do not show an anomalous shift observed in MgO-SiO₂-H₂O melts (Yamada et al., 2007, 2011), likely due to the distinct NBO/Si and the higher cation field strength of the network modifier Na versus Mg (Brown et al., 1995).

Figure 1. X-ray structure factor S^X(Q) for dry N3S8 (a) and hydrous N3S8-H9 (9 wt% H₂O) melts (b) at high pressures and temperatures. The Q range below 0.8 Å⁻¹ was not accessible in the experiments, and the S^X(Q) in this region are extrapolated by fitting Lorentzian or Gaussian functions to the first sharp diffraction peak (FSDP, Q₁).

Figure 2. (a) Neutron structure factor S^N(Q) for N3S8-D10 (10 wt% D₂O) melt at various pressures and temperatures. (b) S^N(Q) for dry N3S8 glass at ambient conditions and for deuterated N3S8 glasses recovered from high pressure and temperature. The Q range below 0.8 Å⁻¹ was not accessible in the experiments, and the S^N(Q) in this region are extrapolated by fitting Lorentzian or Gaussian functions to the first sharp diffraction peak (FSDP, Q₁). PP refers to the principal peak.

Figure 3. Pressure dependence of the first sharp diffraction peak Q₁ for Na₆Si₈O₁₉-H(D)₂O melts and glasses from neutron and X-ray diffraction experiments. Peak positions were determined by decomposing S(Q) into several Lorentzian and Gaussian peaks. Lines serve as a guide to the eye.

In S^N(Q) of N3S8-D10 melt (Fig. 2a), an additional distinct peak appears at 2.6 Å⁻¹, between the FSDP and the PP, which may mainly come from molecular water at 2.3-2.5 Å⁻¹ (Strässle et al., 2006). The asymmetric peak at 3 Å⁻¹ for deuterated glass (Fig. 2b) may similarly be the result of molecular water and the PP, i.e., S_OO(Q). Comparing S^N(Q) for the N3S8-D10 melt and deuterated glasses, their characteristics below 4 Å⁻¹ are similar except for the FSDP position and the intensity ratio. The S^N(Q) pattern at 4-11 Å⁻¹ for the N3S8-D10 melt is markedly different to that of deuterated glasses, which is manifested by the significantly smaller amplitude of S_OO(Q) for the melt which dominates S^N(Q) at large Q (Onodera et al., 2019). A source of this weakening is the thermal vibration and/or a frequent bond exchange of SiO₄ and H₂O/OH species in the liquid state (Karki et al., 2010; Noritake, 2021). Oscillations above 11 Å⁻¹ in S^N(Q) for the N3S8-D10 melt and the deuterated glass are nearly identical.

Figure 2(b) shows S^N(Q) for dry N3S8 glass at ambient conditions and for deuterated N3S8-D9 and N3S8-D12 glasses, which were recovered from 2 GPa/1573 K and 2 GPa/1273 K, respectively. These deuterated glasses may contain high-P structural features, unlike the uncompressed dry N3S8 glass, and it is therefore possible that the difference in S^N(Q) between dry and deuterated glasses includes not only the effect of water, but also the effect of pressure. S^N(Q) for dry and deuterated N3S8 glasses (Fig. 2b) exhibit identical oscillations above 4 Å⁻¹, a Q-range that reflects nearest-neighbor Si-O and O-O correlations. At lower Q, Q₁ in S^N(Q) shifts from 1.7 to 1.9 Å⁻¹ with deuteration (Fig. 3), consistent with previous ND works (Zotov et al., 1996; Urakawa et al., 2020). Since this difference is much larger than the expected pressure effect, this change in Q₁ is reasonably explained by water-induced depolymerization (Eq. 1). A larger Q₁ suggests that the distance between chains/networks formed by SiO₄ tetrahedra shrinks. Depolymerization promotes SiO₄ tetrahedra to break the bridge to adjacent SiO₄. This increases the degree of freedom for the SiO₄ tetrahedra, and they can pack more densely.

Pair distribution function

Figures 4 and 5 display the obtained pair distribution functions g^X(r) and g^N(r). The observed peaks in g(r) can be assigned to the following atomic pair correlations: D-O at ∼ 1.0 Å, Si-O at ∼ 1.6 Å, Na-O at ∼ 2.3 Å, O-O at ∼ 2.65 Å, and Si-Si at ∼ 3.1 Å. Due to the different X-ray and neutron weighting factors, the Si-Si correlation can be observed only in g^X(r), while g^N(r) shows D-O (only for deuterated compositions) and intense O-O correlations.

Figure 4. X-ray pair distribution function g^X(r) for dry N3S8 (a) and hydrous N3S8-H9 (9 wt% H₂O) melts (b) at high pressure and temperature. Labels in (a) indicate the association of the respective peaks to ion pairs.

Figure 5. (a) Neutron pair distribution function g^N(r) for hydrous N3S8-D10 (10 wt% D₂O) melt at various pressures and temperatures. (b) g^N(r) for dry N3S8 glass at ambient and for deuterated N3S8 glasses quenched from melts at high pressure and temperature. Labels in (a) indicate the association of the respective peaks to ion pairs.

The P dependence of mean interatomic distances (r_αβ) for D-O (r_DO), Si-O (r_SiO), O-O (r_OO), and Si-Si (r_SiSi) pairs are illustrated in Figure 6. The distance between D and O, r_DO, monotonically increases with P (Fig. 6a) due to the increase in D-O coordination number, i.e., the formation of -O-D-O- bridges at the expense of -O-D deuteroxyls with constant molecular D₂O, consistent with our ab initio MD results (Fig. 7). The -O-D-O- bridges which are formed on compression, as indicated by the increase of r_DO, can hold hydrogen more rigidly in the melt structure than -O-D and D₂O species, and a larger number of -O-D-O- bridges contributes to an increase in solubility and ideality of mixing in the silicate-water system (Karki et al., 2010, 2021), supporting the general notion that water solubility in silicate melts increases with P (e.g., Mysen and Cody, 2004).

Figure 6. Pressure dependence of interatomic distances r_DO (a), r_SiO (b), r_OO (c), and r_SiSi (d) for dry and hydrous Na₆Si₈O₁₉ melts and glasses inferred from the pair distribution functions. In (d), Si-Si and Na-Si distances and their distribution for Na₆Si₈O₁₉ crystal (Krüger et al., 2005) are included.

Figure 7. Pressure dependence of the populations of hydrogen speciation, for N3S8-H8 (8 wt% H₂O) (a) and N3S8-H14 (14 wt% H₂O) (b) from molecular dynamics simulations at 3000 K.

The distance between Si and O, r_SiO, for the dry and hydrous N3S8 melts generally increase with compression, likely due to a gradual decrease in the Si-O-Si angle and weakening of the Si-O bond (Ross and Meagher, 1984; Noritake and Kawamura, 2015; Noritake, 2019) (Fig. 6b), and r_SiO values from g^X(r) are virtually independent of water content, showing that SiO₄ tetrahedra are not modified by H₂O content. Effective r_SiO from g^N(r) for deuterated compositions are larger than the dry glass due to the influence of D-D correlations at ∼ 1.6 Å (Soper and Ricci, 2000; Karki et al., 2010) which also accounts for the difference of ∼ 0.01 Å in r_SiO for the hydrous melts between XRD and ND experiments.

At ambient P, the deuterated glasses have larger r_OO than dry glass likely due to the effect of O···D-O repulsion forces (Zotov et al., 1996). With compression, r_OO for the N3S8-D10 melt shows a monotonic decrease, approaching r_OO for the dry N3S8 glass at ambient conditions (Fig. 6c). Since r_OO of deuterated glasses at ambient P fall on the trend of N3S8-D10 melt at high P, the larger r_OO for N3S8-D10 melt can be attributed primarily to deuteration rather than the effects of T or state of matter, i.e., vitrification.

The peak at ∼ 3.1 Å in g^X(r) mainly stems from the Si-Si correlations, based on a comparison with the Si-Si and Na-Si distances of N3S8 crystal (Krüger et al., 2005). r_SiSi decreases with compression as the Si-O-Si angle decreases, with lower sensitivity to P for depolymerized N3S8-H10 melt (Fig. 6d) because the compression mechanism of depolymerized melts is characterized by the shrinkage of modifier domains and O-H-O formation rather than bending of the Si-O-Si angle (Wang et al., 2014). The large fluctuation of the data for N3S8-H9 melt is probably caused by weakening Si-Si correlations due to depolymerization, which makes it more difficult to separate O-O, Si-Si, and Na-Si peaks.

The pressure dependence of interatomic distances and coordination number for N3S8, N3S8-H8, and N3S8-H14 from MD simulations at 3000 K is shown in Figure S6. Among the interatomic correlations, especially r_NaO, r_NaNa, r_NaSi, and CN_OO depend on water content. This implies that water significantly modifies the interplays between NaO_X and NaO_X/SiO₄. By contrast, the correlations between SiO₄ do not seem to be influenced by water (r_SiSi in Fig. S6).

Chemical speciation

To elucidate the P dependence of chemical speciation, the molar fractions of Si-O-Si, Si-O + Na, Si-O-H, and Na-O-H complexes at 0-10 GPa and 3000 K are computed (Fig. 8). With increasing water content, the relative abundance of Si-O-Si speciation decreases, while that of Si-O + Na and Si-O-H increase as Na₂O is dissociated into Na⁺ and O²⁻ with depolymerizing the Si-O-Si bridge:

  

\begin{equation} \text{Si-O-Si} + \text{Na$_{2}$O} \rightarrow 2{\cdot}(\text{Si-O}^{-} + \text{Na}^{+}) \end{equation} (5),

with Na₂O fully dissociated in N3S8-H14. Both N3S8-H8 and N3S8-H14 do not show Na-O-H complexes at 0-10 GPa, suggesting that the reaction:

  

\begin{equation} \text{Si-O}^{-} + \text{Na}^{+} + \text{Si-O-H} \rightarrow \text{Si-O-Si} + \text{Na-O-H} \end{equation} (6)

does not take place. This is consistent with previous NMR results (Xue and Kanzaki, 2004) observing a marginal amount of Na-O-H in hydrous sodium silicate glasses.

Figure 8. Pressure dependence of cation-oxygen-cation speciation in molar fractions for dry N3S8 (a), hydrous N3S8-H8 (8 wt% H₂O) (b), and N3S8-H14 (14 wt% H₂O) (c) from molecular dynamics simulations at 3000 K. Black dashed and red dash-dotted lines, respectively, indicate the molar fraction of Si-O-Si and Si-O + Na complexes when all Na₂O contents are dissociated to cut off Si-O-Si bridge without H₂O.

The population of Si-O-Si in dry N3S8 increases with P while the population of Si-O + Na remains constant, suggesting that polymerization is mainly caused by ring closure, which scavenges the Na cation from its network-modifying role by the following mechanism:

  

\begin{equation} 2{\cdot}({}^{[4]}\text{Si-O}^{-} + \text{Na}^{+}) \rightarrow {}^{[4]}\text{Si-(O-${}^{[5]}$Si-O)}^{2-} + 2{\cdot}\text{Na}^{+} \end{equation} (7),

with one O shared by a four-fold and five-fold coordinated Si; charge balance for Na⁺ is maintained by a negatively charged O in the SiO₅ polyhedron. As shown in Figure S6, CN_SiO linearly increases with compression. This behavior suggests that SiO₄ tetrahedra monotonically shrink with pressure, and O atoms of neighboring SiO₄ are pushed closer together, also leading to an increase in the abundance of SiO₅ (Fig. S7).

N3S8-H8 also shows an increase in Si-O-Si population with compression. However, the relative abundance of the Si-O + Na complex decreases while the Si-O-H population remains constant, suggesting that Na⁺ is scavenged from its network modifying role. With increasing P, H⁺ cations act as network modifiers more dominantly in N3S8-H8, with SiO₄ polymerization (Fig. 8) and the -O-H-O- bridging species increasing (Fig. 7). In N3S8-H14, the abundance of Si-O-Si (polymerization) and Si-O-H complexes remains constant for 0-10 GPa, with the abundance of Si-O + Na decreasing less significantly than in N3S8-H8 with compression, as Si-O-H-O-Si formation prevents Na-NBO bonding without Si-O-Si formation. The P evolution of speciation in the hydrous compositions suggests that H₂O molecules do not modify Si-O-Si bonds to form Si-O-H, rather they scavenge Na⁺ from its network-modifying role by polymerization of tetrahedra via reaction (7) and the formation of Si-O-H-O-Si bridging complexes via:

  

\begin{equation} \text{Si-O}^{-} + \text{Na}^{+} + \text{Si-O-H} \rightarrow \text{Si-(O-H-O-Si)}^{-} + \text{Na}^{+} \end{equation} (8);

here charge compensation for Na⁺ is obtained by the negative charge of H in the Si-O-H-O-Si complex as a transitional state (Karki et al., 2010). Reactions (7) and (8) become more significant at higher water content due to the formation of Si-O + Na, i.e., the Na₂O dissociation at hydrous condition (Fig. 8).

The molar fractions of Si-O-Si, Si-O + Na, Si-O-H, and Na-O-H complexes and their pressure dependence are largely different from the corresponding complexes for Mg in hydrous Mg₂SiO₄ melt (Yuan et al., 2020), for which Si-O-Mg > Mg-O-H > Si-O-Si > Si-O-H (6 wt% H₂O) and Si-O-Mg > Mg-O-H > Si-O-H > Si-O-Si (17 wt% H₂O), showing marginal increases in the relative abundance with increasing pressure. The Mg-O-H complex is abundant while Na-O-H is not present because of the higher field strength of Mg²⁺ compared to Na⁺, as proposed by NMR experiments combined with ab initio static simulations (Xue and Kanzaki, 2004). In addition, in contrast to the slight increase in the population of Si-O-Mg on compression, Si-O + Na decreases its abundance. The difference can be understood by the structural difference in sodium and magnesium silicate melts at intermediate length scale: The Na domain structure is characterized by diffusive channels (Greaves, 1985; Meyer et al., 2004), while Mg domains are ordered densely-packed structure (Gaskell et al., 1991; Kohara et al., 2011). Therefore, Si-O + Na is easily replaced by Si-O-H due to the diffusive nature of Na (Kargl et al., 2006), while Mg-O bonds are strong and long-lasting (Karki et al., 2010; Ni and de Koker, 2011).

CONCLUSION

Using in situ X-ray/neutron diffraction experiments and ab initio molecular dynamics simulations, we investigated the structural evolution of dry and hydrous Na₆Si₈O₁₉ (N3S8) melts under P of up to 10 GPa. In the neutron diffraction data, we observed an increase in the interatomic distance of deuterium and oxygen, r_DO, upon compression due to the formation of O-D-O bridges. The compression in dry N3S8 melt was taken up by the bending of Si-O-Si angle as evidenced by the decrease in r_SiSi with P, while O-H-O formation and the shrinkage of modifier domains (Wang et al., 2014) are dominant for N3S8-H9 (9 wt% H₂O) melt. Further, our molecular dynamics results suggested that in hydrous melts compression changes the structural role of Na⁺ from network modifier to a charge balancing cation via the reactions exeressed by 2·(^[4]Si-O⁻ + Na⁺) → ^[4]Si-(O-^[5]Si-O)²⁻ + 2·Na⁺ and Si-O⁻ + Na⁺ + Si-OH → Si-(O-H-O-Si)⁻ + Na⁺, which are promoted by the dissociation of Na₂O into Na⁺ and O²⁻ induced by H₂O. The latter reaction increases the H-O coordination number, probably leading to the increase in water solubility with P.

ACKNOWLEDGMENTS

The supports of Yuki Shibazaki in carrying out our experiments at KEK are highly appreciated. Acknowledgments are also expressed to Asami Sano-Furukawa, Shin-ichi Machida, and Jun Abe for their experimental and analytical helps during beamtimes at J-PARC. The support for ab initio simulations by Jie Yao (University of Adelaide) and Florian Trybel (Linköping University) are also appreciated. The XRD experiments were conducted at AR-NE5C beamline with the approval of the KEK (Proposal Nos. 2017G580, 2019G567, and 2021G512). The ND experiments were carried out at BL11 beamline (PLANET) at the MLF of the J-PARC under user programs (Proposal Nos. 2018A0016, 2018B0026, 2019A0003, 2020B0138, and 2021B0048).

This work was realized with support of JSPS KAKENHI (grant Nos. JP20J22919 to TO; grant Nos. JP17H04860, JP17K18797, JP21K18641, and JP22H01317 to TS). TO was supported by the International Joint Graduate Program in Earth and Environmental Science (GP-EES), Tohoku University and the JSPS Japanese-German Graduate Externship.

SUPPLEMENTARY MATERIALS

Supplementary Figures S1-S7 are available online from https://doi.org/10.2465/jmps.240926a.

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