Effects of CO₂ on the structure of silicate melts considering the degree of polymerization under pressure

Abstract

Carbon dioxide (CO₂) is a prevalent volatile in Earth’s interior, but its effects on the structural properties of magmas or silicate melts remain insufficiently understood. Previous studies have indicated that the addition of CO₂ can decrease the viscosity of silicate melts, but only if they are fully polymerized. In this study, we explored the effects of CO₂ considering the degree of polymerization on the structure of silicate melts at high pressures of up to ∼ 5 GPa using in situ synchrotron X-ray diffraction (XRD) measurements and classical molecular dynamics (MD) simulations. The first sharp diffraction peak (FSDP) position of the X-ray structural factor S(Q), which shows the periodicity of an intermediate-range structure, was not affected by the addition of CO₂ for partially depolymerized sodium silicate melt (Na₂Si₃O₇). On the other hand, the height of the FSDP for fully polymerized silica melt (SiO₂) slightly decreased, indicating that the Si-O network structure was disordered by the addition of CO₂. This difference in the behavior of the FSDP may be attributed to the type of carbon species.

INTRODUCTION

Carbon dioxide (CO₂) is an important volatile in Earth’s interior. CO₂-bearing (i.e., carbonated) magmas such as kimberlite are known to be generated deep in Earth’s interior (e.g., Keshav et al., 2005). To uncover the migration behavior of carbonated magma in deep Earth, the transport properties of analogs such as silicate melts have been studied, including density and viscosity. Measurements at high pressures have revealed that the addition of CO₂ decreases the density of silicate melts (e.g., Sakamaki et al., 2011). Although measurements of the viscosity are more limited, they indicate that the effect of CO₂ on the viscosity is affected by the degree of polymerization of silicate melts. The degree of polymerization is often expressed in terms of the parameter NBO/T, which is defined as the ratio between the number of nonbridging oxygen (NBO) atoms and the number of tetrahedrally coordinated (i.e., network-forming) cations (T) (Mysen and Richet, 2019). Adding CO₂ has been shown to decrease the viscosity of fully polymerized silicate melts (i.e., NBO/T = 0). For example, Suzuki (2018) reported that adding 0.5 wt% CO₂ reduced the viscosity of molten jadeite (NaAlSi₂O₆, NBO/T = 0) by one to two orders of magnitude. In contrast, Brearley and Montana (1989) reported that adding 2.0 wt% CO₂ had no effect on the viscosity of molten sodium melilite (NaCaAlSi₂O₇), which is partially depolymerized (NBO/T = 0.67) under the assumption that Al is entirely tetrahedrally coordinated. The physical properties of magmas are known to be sensitive to the atomic structure (e.g., Sakamaki, 2018). Thus, understanding the effects of CO₂ on the structures of silicate melts at high pressures and temperatures is important for clarifying the migration behavior of carbonated magmas.

In this study, we conducted in situ X-ray diffraction (XRD) measurements complemented by molecular dynamics (MD) simulations to investigate the effects of CO₂ on the structure of a sodium silicate melt (Na₂Si₃O₇, NBO/T = 0.67) at high pressures. MD simulations were further conducted to investigate the effects of CO₂ on the structures of silicate melts considering the degree of polymerization.

METHODS

Experiment

Dry Na₂Si₃O₇ was prepared in powder form from reagent-grade SiO₂ and Na₂SiO₃, and carbonated Na₂Si₃O₇ (0.5 wt% CO₂) was prepared in powder form by adding Na₂CO₃ as the CO₂ source. The amount of CO₂ was kept below the solubility of Na₂Si₃O₇ melt under the experimental conditions to avoid the liquid immiscibility of the silicate and carbonate melts (Dasgupta et al., 2006; Brooker and Kjarsgaard, 2011). Figure 1 shows a cross section of the high-pressure cell assembly for the experiment. A boron-epoxy cube was used as a pressure-transmitting medium, and the pressure marker was a mixture of MgO and h-BN (3:2 weight ratio). The temperature T was estimated by calibration against the electric power (Supplementary Fig. S1; Supplementary Figs. S1-S6 are available online from https://doi.org/10.2465/jmps.241126L), which was performed in a preliminary experiment using a cell assembly with a W₉₇Re₃-W₇₅Re₂₅ thermocouple (Supplementary Fig. S2). The pressure P was calculated using the third-order Birch-Murnaghan equations of state of MgO (Tange et al., 2009). XRD measurements were conducted in situ using MAX80 (Shimomura, 1984), which is a cubic multi-anvil apparatus installed at the AR-NE5C beamline of the Photon Factory Advanced Ring (PF-AR) in Tsukuba, Japan. Measurements were conducted over a P range of 2-5 GPa, and T was kept at just above the melting point of the silicates. White X-rays in the energy range of 20-140 keV were used as incident X-rays, and scattered X-rays from the melt were detected with a germanium detector. The detailed experimental procedure is summarized in Ohashi et al. (2018).

Figure 1. Schematic illustration for the high-P cell assemblies used in XRD measurements.

We derived two different functions to analyze the structure of the silicate melts. The total structure factor S(Q) was determined by correcting diffraction profiles using the MCEDX code (Funakoshi, 1997), and it is defined as

  

\begin{equation} S(Q) = \frac{I^{\text{coh}}(Q)/N - \left[\sum_{i}\{c_{i}f_{i}(Q)\}^{2} - \left\{\sum_{i}c_{i}f_{i}(Q)\right\}^{2}\right]}{\left\{\sum_{i}c_{i}f_{i}(Q)\right\}^{2}} \end{equation} (1),

where N, I^coh(Q), c_i, and f_i(Q) are the number of atoms in the scattering system, coherent scattering intensity, the concentration of atoms i, and atomic scattering factor, respectively. The reduced pair distribution function G(r) was used to analyze the local structure and short-range order of the silicate melts, and it is derived as

  

\begin{equation} G(r) = \frac{2}{\pi}\int_{Q_{\min}}^{Q_{\max}}Q\{S(Q) - 1\}M(Q)\sin(Qr)\mathrm{d}Q \end{equation} (2),

where r is the atomic distance. M(Q) is the Lorch modification function, which was introduced to suppress the termination ripples of G(r) (Lorch, 1969).

Simulation

Classical MD simulations of dry and carbonated (0.5 and 5.0 wt% CO₂) Na₂Si₃O₇ and SiO₂ melts were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator code (Thompson et al., 2022). The Na₂Si₃O₇ melt was partially depolymerized (NBO/T = 0.67), whereas the SiO₂ melt was fully polymerized (NBO/T = 0). Table 1 gives the specifications of the simulated systems, where each contained approximately 30000 particles. We employed the empirical force field developed by Guillot and Sator (2011), which can be used to treat the chemical reaction of CO₂ + O²⁻ ↔ CO₃²⁻, in which CO₂ molecules react with O²⁻ in a silicate melt to form CO₃²⁻ and vice versa. P was kept at 2 or 5 GPa, and T was kept at 2000 K. Ewald summations were applied to evaluate long-range Coulombic interactions. Periodic boundary conditions were imposed in the simulations, and the time step was 1 fs. The simulation was started with atoms assigned random configurations and velocities. We first ran calculations for 50 ps at 2 or 5 GPa and at 3000 K. Then, the systems were cooled to 2000 K for 10 ps and relaxed for 50 ps. All simulations were carried out in the NPT (isothermal isobaric) ensemble.

Table 1. Number of atoms i (N_i) of each species in the simulated systems of silicate melts

	Na2Si3O7	Na2Si3O7 + 0.5 wt% CO2	Na2Si3O7 + 5.0 wt% CO2	SiO2	SiO2 + 0.5 wt% CO2	SiO2 + 5.0 wt% CO2
NSi	7500	7449	7017	10000	9932	9361
NNa	5000	4966	4678
NO	17500	17517	17661	20000	20000	20000
NC		68	644		68	639
Ntot	30000	30000	30000	30000	30000	30000

The three-dimensional structure was analyzed to obtain Qⁿ species (Stebbins, 1995; Mysen and Richet, 2019), carbon species, and ring statistics. The primitive (Si-O)_n ring size distributions for melts were calculated using the SOVA package (Shiga et al., 2023).

RESULTS AND DISCUSSION

Figure 2 shows the total structure factors S(Q) and reduced pair distribution functions G(r) for dry and carbonated (0.5 wt% CO₂) Na₂Si₃O₇ melts at high pressures, obtained by XRD measurements. Figure 3 shows S(Q) for dry and carbonated (5.0 wt% CO₂) Na₂Si₃O₇ and SiO₂ melts at high pressures, obtained by MD simulations. In previous studies, the first sharp diffraction peak (FSDP) of S(Q) for silicate melts has been assigned to a succession of SiO₄ polyhedra with corner-sharing oxygen atoms manifested by the periodicity given by 2π/Q_FSDP (Price, 1996; Onodera et al., 2019a). For the Na₂Si₃O₇ melt, the overall features of S(Q) and the FSDP obtained by XRD measurements (Fig. 2a) and MD simulations (Fig. 3a) changed negligibly with the addition of CO₂. Neither did the overall features of G(r) change significantly (Fig. 2b). Note that as carbon capsules were used as sample containers, there is some concern as to whether CO₂ is fully retained during the XRD experiments. The MD simulations confirmed that S(Q) remained the same for both melts with the addition of only 0.5 wt% CO₂ (Supplementary Fig. S3). However, a different behavior was observed when 5.0 wt% CO₂ was added to the SiO₂ melt, which resulted in a slight decrease in the height of the FSDP (Fig. 3b), indicating that the Si-O network structure became disordered.

Figure 2. Total structure factors S(Q) and reduced pair distribution functions G(r) for dry and carbonated (0.5 wt% CO₂) Na₂Si₃O₇ melts at high pressures obtained by XRD measurements. Successive curves are displaced upward by 1 (left) and 5 (right) for clarity, respectively.

Figure 3. Total structure factors S(Q) for dry and carbonated (5.0 wt% CO₂) melts at high pressures obtained by MD simulations: (a) Na₂Si₃O₇ and (b) SiO₂. Successive curves are displaced upward by 1 for clarity.

Slight pressure-dependent changes are observed in S(Q) and real-space function, which are discussed in detail in Supplementary Document (see Supplementary Figs. S4 and S5).

It is also revealed that the degree of polymerization of these melts changed negligibly with the addition of CO₂. Figure 4 shows the distributions of Qⁿ species for dry and carbonated (5.0 wt% CO₂) Na₂Si₃O₇ and SiO₂ melts obtained by MD simulations. The distributions of Qⁿ species for these melts are almost identical between CO₂-free and CO₂-bearing conditions, indicating that the degree of polymerization of these melts is almost unchanged. This result is consistent with that reported by Morizet et al. (2015), who used first-principles MD simulations of basaltic melts containing CO₂, and showed that CO₂ may have a limited effect on the degree of polymerization of basaltic melt. Therefore, a slight decrease in the height of the FSDP observed in CO₂-bearing SiO₂ melts (Fig. 3b) may not be caused by a change in the degree of polymerization of the melt structure.

Figure 4. Distributions of Qⁿ species for dry and carbonated (5.0 wt% CO₂) melts obtained by MD simulations at 5 GPa and 2000 K: (a) Na₂Si₃O₇ and (b) SiO₂.

The MD simulations confirmed the formation of two types of carbon species: molecular CO₂ and carbonate ions (CO₃²⁻). The pressure dependence of CO₂/(CO₂ + CO₃²⁻) for CO₂-bearing melts is summarized in Supplementary Figure S6. In our MD simulation, three types of carbonate ions was found: free carbonate ions that were not connected to Si (CO₃²⁻, Fig. 5a), nonbridging carbonate ions connected to one Si atom (Si-CO₃²⁻, Fig. 5b), and network carbonate ions connected to two Si atoms (Si-CO₃²⁻-Si, Fig. 5c). We recognized two structural types of network carbonate ions that connect to two Si atoms (Fig. 5c), but it was difficult to qualify their fraction using our program code. The charge neutrality of nonbridging and network carbonate ions in SiO₂ melt should be carefully considered. In general, these carbonate ions are considered to interact with network modifier cations such as Na⁺ and Ca⁺ (Guillot and Sator, 2011; Ni and Keppler, 2013). Although SiO₂ melt does not have such network modifier cations, a considerable amount of carbonate ions exists, probably owing to a structure in the melt where a local charge compensation is not maintained. Indeed, we find the presence of Q³ in addition to Q⁴ (Fig. 4b) which is the signature of a structure in which a charge compensation is not maintained locally. Figure 6 shows the fractions of carbon species in the Na₂Si₃O₇ and SiO₂ melts at 5 GPa, obtained by MD simulations. Previous investigations of carbonated quenched glasses by infrared (IR) spectroscopy (Mysen, 1976; Fine and Stolper, 1986) have revealed that carbonate ion is dominant in depolymerized (basic and ultrabasic) melts, but the depolymerized melt in our study (i.e., Na₂Si₃O₇) contained approximately 20% molecular CO₂ at 5 GPa (Fig. 6a). This discrepancy may be because the previous studies using IR spectroscopy underestimated the abundance of CO₂ species of the glasses because the following reaction occurs upon quenching: CO₂ + O²⁻ → CO₃²⁻ (Morizet et al., 2001; Guillot and Sator, 2011; Konschak and Keppler, 2014; Vuilleumier et al., 2015).

Figure 5. Characterization of carbonate ions in the silicate melts (snapshots) under high pressure. For clarity, only bonds between atoms are shown. (a) Free carbonate ion, (b) Nonbridging carbonate ion, and (c) Network carbonate ions.

Figure 6. Fractions of carbon species in carbonated (5.0 wt% CO₂) melts at 5 GPa and 2000 K: (a) Na₂Si₃O₇ and (b) SiO₂.

The behaviors of FSDP upon the addition of CO₂ can be explained by the carbon species in the melts. For Na₂Si₃O₇ melt, molecular CO₂ and nonbridging carbonate ions predominantly exist (Fig. 6a). Previous results suggest that molecular CO₂ is only loosely associated with the melt structure (Ni and Keppler, 2013), and nonbridging carbonate ions are mainly formed by displacement from NBO atoms (Guillot and Sator, 2011). A similar behavior is observed in the FSDP of S(Q) where carbonate ions do not greatly change the intermediate-range structure of melt (Figs. 2a and 3a). On the other hand, SiO₂ melt has molecular CO₂ and carbonate ions as nonbridging and network carbonate ions (Fig. 5b). The Si-O network of the SiO₂ melt has a relatively ordered structure in which SiO₄ tetrahedra are almost fully bonded via bridging oxygen atoms. However, the inclusion of nonbridging and network carbonate ions disrupts the order of this network, which causes the reduction in the correlation length estimated by the FSDP full width at half maximum (FWHM) (Onodera et al., 2019a) associated with the height decrease of the FSDP (Fig. 3b).

To obtain deep insight into the intermediate-range structure, the (Si-O)_n ring size distribution between dry and CO₂-bearing melts is compared. The primitive (Si-O)_n ring size distributions for dry and carbonated (5.0 wt% CO₂) Na₂Si₃O₇ and SiO₂ melts are plotted in Figure 7. It is found that there is little difference between dry and carbonated melts for Na₂Si₃O₇ melt, but a distinct difference was observed for SiO₂ melt. As can be seen in Figure 7b, the large (Si-O)_n rings are transformed into smaller (Si-O)_n rings by nonbridging and network carbonate ions; this is associated with bond interchange under high P-T conditions. This behavior is different from that caused by alkali ions (network modifier cations) in silicate glass at ambient pressure (Onodera et al., 2019b).

Figure 7. Primitive ring size statistics for dry and carbonated (5.0 wt% CO₂) (a) Na₂Si₃O₇ and (b) SiO₂ melts at high pressures obtained by MD simulations.

Our results suggest that the addition of CO₂ changes the network structure of the fully polymerized SiO₂ melt (NBO/T = 0) to some extent, whereas it negligibly changes the network structure of the depolymerized Na₂Si₃O₇ melt (NBO/T = 0.67). This behavior can be explained by the structural effect of carbonate species on the network structure of melts.

ACKNOWLEDGMENTS

We thank K. Obata for assistance with the experimental preparations. This research was performed with the support of JSPS KAKENHI Grant Numbers JP20H05878, JP20H05881, JP21K18641, and JP23K22588. Synchrotron experiments were conducted at the AR-NE5C beamline with the approval of the High Energy Accelerator Research Organization (KEK) (Proposal Nos. 2021G512 and 2023G519), and the calculations in this study were performed using the Numerical Materials Simulator at the National Institute for Materials Science (NIMS).

SUPPLEMENTARY MATERIALS

Supplementary Document and Figures S1-S6 are available online from https://doi.org/10.2465/jmps.241126L.

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