Network polymerization and cation coordination environments in boron-bearing rhyolitic melts: Insights from 17O, 11B, and 27Al solid-state NMR of sodium aluminoborosilicate glasses with varying boron content

Journal Pre-proofs Network polymerization and cation coordination environments in boron-bearing rhyolitic melts: Insights from 17O, 11B, and 27Al solid-state NMR of sodium aluminoborosilicate glasses with varying boron content A Chim Lee, Sung Keun Lee PII: DOI: Reference:

S0016-7037(19)30653-2 https://doi.org/10.1016/j.gca.2019.10.010 GCA 11478

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Geochimica et Cosmochimica Acta

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Please cite this article as: Chim Lee, A., Keun Lee, S., Network polymerization and cation coordination environments in boron-bearing rhyolitic melts: Insights from 17O, 11B, and 27Al solid-state NMR of sodium aluminoborosilicate glasses with varying boron content, Geochimica et Cosmochimica Acta (2019), doi: https:// doi.org/10.1016/j.gca.2019.10.010

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Network polymerization and cation coordination environments in boron-bearing rhyolitic melts: Insights from 17O, 11B, and 27Al solidstate NMR of sodium aluminoborosilicate glasses with varying boron content

A Chim Lee1; Sung Keun Lee1,* 1School

of Earth & Environmental Sciences

Seoul National University Seoul 08826, Korea

* Lee, Sung Keun Professor E-mail: [email protected] Web: http://hosting03.snu.ac.kr/~sungklee ABSTRACT Despite the geochemical implications for the dissolution behaviors of nuclear waste glasses and the properties of boron-bearing rhyolitic melts, a detailed atomic-level understanding of the overall effect of boron content on the structural characteristics of boron-bearing silicate glasses remains elusive. Herein, we explore the effects of B/Al and Si/B ratios on the local configurations around cations and the degree of network polymerization of Na2O-Al2O3-B2O3-SiO2 glasses in nepheline (NaAlSiO4) - malinkoite (NaBSiO4) and albite (NaAlSi3O8) - reedmergnerite (NaBSi3O8) joins using multi-nuclear magnetic resonance (NMR). The 11B NMR results confirmed an increase in the B coordination numbers from 3 ([3]B) to 4 ([4]B) as B/Al and Si/B ratios increase. The 27Al NMR spectra show that the Al is mainly four coordinated, except in NaAl0.25B0.75SiO4 glasses, with a minor amount of [5]Al species, revealing a more prominent control of Si over that of B on the Al coordination environments. The 17O NMR spectra resolve distinct bridging (BO, Si-OAl, Al-O-Al, Si-O-Si, B-O-B, and Si-O-B) and non-bridging oxygens (NBO, Na-O-Si). In

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contrast, the absence of B-O-Al species confirmed the separation between B and Al and prevalent melt depolymerization exclusively in silicate-networks. The fractions of B-O-B and Na-NBO increase as B/Al ratio increases, accounting for a drastic enhancement in the dissolution rate of glasses. A dramatic increase also indicates an enhanced connectivity of relatively weaker bonds such as B-O-B and Na-O-Si as composition reached a certain boron content. This is linked to a decrease in the melt viscosity with increasing B2O3 component. Based on the measured fractions of [3,4]B in 11B NMR spectra with varying composition, the trend of the evolution of boron isotope composition in sodium aluminoborosilicate melts was estimated, confirming the preferential enrichment of 10B into rhyolitic melts with increasing boron content. The decreased fraction of [3]B species with increasing Si/B may partly explain the reduction in δ11B in boron-bearing volcanic rocks at deeper depths in the subduction zone. The results suggest that composition-induced changes in the atomic structures should be constrained to precisely interpret the melt viscosity, boron isotope composition of arc volcanic lavas, and the dissolution rates of nuclear waste glasses. Keywords: Structure of boron-bearing aluminosilicate glasses/Solid-state NMR/Dissolution behaviors/Boron isotope composition 1. INTRODUCTION Boron is an incompatible element that is effectively partitioned into silicate melts, and thereby gets enriched in highly evolved pegmatitic and rhyolitic melts (Simmons et al., 2016; Stilling et al., 2006). Therefore, highly fractionated granites can contain up to ~1 wt% B2O3, although boron is among the trace elements (Pichavant and Manning, 1984). Pegmatites often contain 213-287 ppm of B, whereas the average boron concentrations in the upper continental crust, mid-ocean ridge basalts, and the Earth’s primitive mantle are estimated to be ~17 ppm, ~1.8 ppm, and ~0.19 ppm, respectively (Marschall et al., 2017; Rudnick and Gao, 2014). The boron concentration and its isotope composition (i.e., 10B and 11B)

of volcanic rocks and glasses have been the useful geochemical tracers of subduction

zone processes involving melting or crustal rocks, fluid-rock interactions, and dehydration in OH-bearing minerals (e.g., De Hoog and Savov, 2018; Harvey et al., 2014a; Maner and London, 2018; Marschall et al., 2017; Palmer, 2017; Palmer and Swihart, 1996; Peacock and Hervig, 1999, and references therein). In addition to its utility as a geochemical tracer in a subduction zone, a small amount of boron affects the density, diffusivity, and viscosity of magmatic melts, thus controlling 2

igneous and volcanic processes (Bartels et al., 2013; Chakraborty et al., 1993; Dingwell et al., 1992; Shaw and Sturchio, 1992; Sowerby and Keppler, 2002). For example, an addition of 5 wt% B2O3 lowers the viscosity of anhydrous haplogranitic (Na2O-K2O-B2O3-Al2O3-SiO2) liquids by more than 4 orders of magnitude at ~750 °C (Dingwell et al., 1992). Because the addition of boron significantly lowers the melting temperature of the oxide glasses, B2O3 is one of the essential constituents of diverse technologically important glasses (8~15 wt% B2O3) and nuclear waste glasses (Bunker et al., 1986; Plodinec, 2000; Youngman et al., 1995; Youngman and Zwanziger, 1995). In particular, the latter consists of four major oxide components (e.g., Na2O, B2O3, Al2O3, and SiO2) (Deshkar et al., 2018; El-Alaily et al., 2017; Ellison and Navrotsky, 1989; Li et al., 2003; Marcial et al., 2016; Pierce et al., 2010; Plodinec, 2000). The chemical durability of Na2O-B2O3-Al2O3-SiO2 glasses, which are model nuclear waste glasses in aqueous solution depends on the B/Al ratio; the dissolution rate of NaAlSiO4-NaBSiO4 glasses increases from ~10-9.1 mol/m2s [NaAl0.8B0.2SiO4 glasses, B/(B+Al) = 0.2] to ~10-6.1 mol/m2s [NaAl0.2B0.8SiO4 glasses, B/(B+Al) = 0.8] (Pierce et al., 2010). Furthermore, the boron isotope composition of silicate melts has also been reported to change with varying composition (including that of fluid contents) (e.g., Hervig et al., 2002; Maner and London, 2018; Tonarini et al., 2003, and references therein). Changes in the transport and kinetic properties and the boron isotope composition of boron-bearing silicate melts and glasses indicate the changes in the atomic configurations around boron, other constituent cations, and oxygen with varying melt and glass composition. The changes in the coordination number of diverse cations in boron-bearing complex silicate liquids and glasses are indeed key to the detailed understanding of the properties of glasses and magmatic melts (e.g., Geisinger et al., 1988; Geisler et al., 2015; Hopf et al., 2016; Majérus et al., 2003; Marcial et al., 2019; Mysen and Richet, 2018; Pierce et al., 2010; Richet, 1984; Shelby, 2007; Wu et al., 2009, and references therein). In particular, the local configurations of framework units significantly affect the transport properties of melts and phase relations involving these melts (Lee and Stebbins, 2002; Navrotsky et al., 1982; Richet et al., 1997). In aluminoborosilicate glasses and melts, both B3+ and Al3+ are known to play a role as network formers. However, the atomic configurations around these cations are expected to be largely different, as inferred from the difference in the dissolution of glasses and the melt viscosity with varying B-Al substitution (Marcial et al., 2019; Pierce et al., 2010). For example, B can occupy trigonal and tetrahedral sites (i.e., [3]B and [4]B), whereas Al can occupy tetrahedral, pentahedral, and octahedral sites (i.e., [4]Al, [5]Al, and [6]Al) with respect to the changes in thermodynamic variables, such as temperature, pressure, and composition 3

(e.g., Allwardt et al., 2005; Angeli et al., 2010; Bista et al., 2016; Bista et al., 2017; Dell et al., 1983; Du and Stebbins, 2003b; Du and Stebbins, 2005b; Kelsey et al., 2009; Kroeker and Stebbins, 2001; Lee, 2011; Lee et al., 2004; Lee et al., 2011; Neuville et al., 2004, 2006; Park and Lee, 2012, 2018; Stebbins et al., 2000; Toplis and Dingwell, 2004; Toplis et al., 2000; Xiao, 1981; Yarger et al., 1995, and references therein). Furthermore, a decrease in the polymerization of melt network tends to reduce the rigidity of the melts, leading to an overall decrease in the viscosity of silicate melts. The softening of melt is accompanying with an increase in the fraction of non-bridging oxygen (NBO), with which the extent of network polymerization can be quantified. Here, bridging oxygens (BO) are coordinated by two network formers, whereas NBO links a network former, T (e.g., T = Si, Al, and B), to a non-network former, M (e.g., M = Na and Ca), forming T-O-M bonds (e.g., Na-O-Si) (Mysen and Richet, 2018; Shelby, 2007). Therefore, the estimated decreases in the reduction in the viscosity of pegmatitic and granitic magmas with increasing boron content suggest an increase in the NBO population (Giordano and Dingwell, 2003). The local oxygen configuration and network polymerization also affect the dissolution behavior of nuclear waste glasses because the reactivity of both BO and NBO species are most likely different. Specifically, the abrupt increases in the selective leaching of B and Na from NaAlSiO4-NaBSiO4 glasses with increasing boron content (or B/Al ratio) have been attributed to the changes in boron-topology (i.e., boroxol ring in which [3]B is connected to BOs, producing trigonal ring, and non-ring structures); however, the structural environments around oxygens can provide an additional insight into the dissolution behavior (Pierce et al., 2010). This is partly because the B-O-B linkage is suggested to be more susceptible to hydrolysis compared to the Si-O-(Si,B) linkages (Lee et al., 2001; Marschall et al., 2017). Furthermore, the presence of a high-energy cluster in the glasses (e.g., B-O-Al) may influence the overall glass-leaching behavior. The formation of nano-metersized domains with a particular enrichment of a single type of framework cation may also affect the bulk reactivity. As NBO may also reduce the chemical durability of glasses during hydrolysis, it has been suggested that NBO fraction of silicate glasses may impart a more prominent reactivity (Bunker, 1994). The effect of NBO fraction on the dissolution behaviors of basaltic glasses in contact with aqueous fluids has been proposed (Park and Lee, 2012). This may account for the chemical composition of groundwater that is buffered by the basalts in volcanic islands (Hurwitz et al., 2003; Park and Lee, 2012). Previous experimental analyses to reveal the structures (i.e., coordination environments around B, Al, and oxygens) of boron-bearing oxide glasses are briefly 4

summarized herein. The two coordination environments of boron ([3]B and [4]B) coexist in boron-bearing silicate and oxide glasses and melts. Their transformation (i.e., [3]B ↔ [4]B) due to a variation in composition of glasses and melts has been extensively studied (e.g., Angeli et al., 2010; Bista et al., 2016; Bista et al., 2017; Cochain et al., 2012; Dell et al., 1983; Du and Stebbins, 2003b; Du and Stebbins, 2005b; Johnson et al., 1982; Kroeker and Stebbins, 2001; Lee et al., 2005; Lenoir et al., 2008; Manara et al., 2009; Shelby, 2007; Smedskjaer et al., 2011; Wright et al., 2014; Wu and Stebbins, 2009; Xiao, 1981; Yun and Bray, 1978; Zheng et al., 2012, and references therein). Particularly, high-resolution solid-state 11B magic angle spinning (MAS) and triple quantum (3Q) MAS nuclear magnetic resonance (NMR) have been used to study boron-bearing oxide glasses due to its ability to resolve the boron coordination environments and topological distinct ring structures involving boron (see S1 for the detailed topological structures of boron in the borosilicate glasses) (e.g., Angeli et al., 2010; Bartels et al., 2013; Bista et al., 2016; Bista et al., 2017; Du and Stebbins, 2003a, b; Hopf et al., 2016; Kapoor et al., 2017; Lee et al., 2001; Lee and Stebbins, 2002; Pierce et al., 2010; Zheng et al., 2012, and references therein). The fraction of non-ring [3]B in B2O3-SiO2 glasses tends to increase as Si/B ratio increases (Lee and Stebbins, 2002). In alkali borate and ternary borosilicate glasses, an increase in the content of [4]B at the expense of [3]B species is observed as alkali content increases (e.g., Dell et al., 1983; Du and Stebbins, 2003a, b, c; Sen et al., 1998; Youngman and Zwanziger, 1996; Yun and Bray, 1978; Shelby, 2007, and references therein). Earlier NMR studies of Na2O-B2O3-Al2O3-SiO2 glasses (e.g., NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8) showed that [4]B fraction increased as the boron content increases (Geisinger et al., 1988; Marcial et al., 2019; Pierce et al., 2010). This progress with 11B NMR may allow us to establish the overall effects of composition including Si/B, B/Al, and Si/Al ratios, on the boron environments in multi-component aluminoborosilicate melts. Earlier 27Al NMR studies of multi-component aluminosilicate glasses confirmed that Al could exhibit diverse coordination states (i.e., [4,5,6]Al) (e.g., Allwardt et al., 2005; Bista et al., 2017; Kelsey et al., 2009; Le Losq et al., 2014; Lee, 2011; Lee et al., 2004; Lee et al., 2011; Neuville et al., 2004, 2006; Park and Lee, 2012, 2018; Stebbins et al., 2000; Toplis and Dingwell, 2004; Toplis et al., 2000; Urbain et al., 1982; Zheng et al., 2012). In particular, the 27Al

3QMAS NMR particularly distinguishes the various Al environments in aluminosilicate

glasses (Bista et al., 2015; Lee, 2011; Malfait and Xue, 2010; Neuville et al., 2008; Park and Lee, 2012, 2018; Xue and Kanzaki, 2007, 2008; Zheng et al., 2012). The average Al coordination number increases with increasing Al content (i.e., Al/metal cation), field strength [charge/(ionic radius)2, that of Na is ~0.96] of non-network-formers, temperature, and 5

pressure, for diverse aluminosilicate glasses (see Park and Lee, 2018 and references therein). As the field strength of Na is relatively low, Al in sodium aluminoborosilicate glasses is mainly four-coordinated (e.g., Bista et al., 2015; Du and Stebbins, 2005b). The effect of composition on local environments around Al in quaternary sodium aluminoborosilicate glasses, particularly the presence of highly coordinated Al species remains to be explored in detail. The potential results enable us to explain the changes in the melt viscosity. 17O

NMR facilitates the direct investigation of the degree of polymerization and the

nature of chemical mixing between the framework cations. 17O 3QMAS NMR measurements of relatively simple binary and ternary boron-bearing mixed-cation borate and borosilicate glasses have resolved distinct BO and NBO environments (Angeli et al., 2001; Dirken et al., 1997; Du and Stebbins, 2003a, b, c; Du and Stebbins, 2005a; Lee et al., 2001; Lee and Stebbins, 2002; Wang and Stebbins, 1999; Zhao et al., 2000). The structural characteristics related to both NBO and BO control the observed changes in the melt viscosity and the anomalous dissolution behaviors of diverse boron-bearing nuclear waste glasses; however, the direct estimation of oxygen-specific information on complex glasses remains to be explored as experimental verification of the extent of network polymerization in multi-component silicate melts is challenging. The aforementioned advances in multi-nuclear solid-state NMR for multi-component boron-bearing silicate glasses provide a prospect for establishing a systematic and predictive model of the structure-composition (including boron isotope composition)-property relationships for geologically-relevant NaAlSiO4 (nepheline)-NaBSiO4 (malinkoite) and NaAlSi3O8 (albite)-NaBSi3O8 (reedmergnerite) glasses and melts. In particular, boron-bearing albite glasses can serve as model rhyolitic melts with a minor boron contents. Therefore, these systems allow the tracing of the nature of felsic melts and determination of the effect of boron content (e.g., B/Al and Si/B ratios) on the structures of multi-component boronbearing silicate melts. Finally, changes in the boron configurations in multi-component silicate glasses yield atomistic origins of the boron isotope composition of mantle melts and fluids: 11B is preferentially fractionated into a trigonal [3]B, while 10B prefers to be associated with a tetrahedral site (i.e., [4]B) (e.g., Kakihana et al., 1977; Palmer et al., 1987; Palmer and Swihart, 1996; Sanchez-Valle et al., 2005, and references therein). While fractionation of stable isotope is much less significant at temperature conditions relevant to igneous processes, the earlier studies of stable isotope fractionations involving H, C, and S also showed that non-negligible degree of fractionation indeed occurs in diverse aluminosilicate melts at high temperature (e.g., Dalou et al., 2015; Dobson et al., 1989; Labidi et al., 2016; Le 6

Losq et al., 2016; Mysen et al., 2009, and references therein). Therefore, composition (e.g., Si/B, B/Al, and Si/Al)- induced changes in the atomic structure of boron in multicomponent silicate melts should be constrained to precisely interpret the boron isotope composition of arc volcanic lavas. In this study, we investigated the structures, including the boron speciation ([3]B and [4]B), Al coordination number, and oxygen configurations of quaternary Na2O-Al2O3-B2O3-SiO2 glasses with varying composition (or B/Al and Si/B ratio), using 11B, 27Al, and 17O solid-state NMR. We herein propose a link between the network connectivity and corresponding properties on the basis of our spectroscopic results. Particularly, a proposed structural model based on the oxygen configurations allow us to explain the dramatic change in dissolution rates in aluminoborosilicate glasses and the melt viscosity. We finally discuss the effect of boron coordination numbers on the boron isotope composition of boron-bearing multi-component rhyolitic melts. 2. EXPERIMENTAL METHODS 2.1. Glass synthesis NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 glasses. Quaternary aluminoborosilicate glasses in a malinkoite (NaBSiO4)- nepheline (NaAlSiO4) and an albite (NaAlSi3O8)– reedmergnerite (NaBSi3O8) pseudo-binary joins with varying fractions of NaBSiO4 and NaBSi3O8 component were synthesized from oxides (Al2O3, B2O3, and SiO2) and carbonate (Na2CO3) agents. The starting Na2CO3, Al2O3, and SiO2 powders were dried at 400 ºC for 48 h in a box furnace. B2O3 glasses were synthesized by fusing boric acid (H3BO3) with a torch. The melting and quenching of B2O3 have been repeated 5 times, followed by grinding into powders. The oxide powders were then mixed and subsequently decarbonated in a Pt crucible at 800 ºC. The glass samples were then melted above the melting temperatures (950 to 1620 ºC) for 30 min and then quenched into glasses. Approximately ~0.1-0.2 wt% of CoO was added. This will decrease the spin-lattice relaxation time (t1), resulting in a decrease in overall NMR collection time. 17O-enriched NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 glasses were synthesized from 17O-enriched SiO2, together with other oxide and carbon reagents. The oxide powder mixtures were fused for 10 min above their respective melting temperatures (950 to 1620 ºC) in an Ar atmosphere. The melts were quenched by dipping the Pt crucible into water. Table 1 shows the nominal and chemical composition for glasses in the NaAlSiO4-NaBSiO4 pseudo-binary system. Table 2 shows the nominal and chemical compositions for glasses in the NaAlSi3O8-NaBSi3O8 pseudo-binary system. The nominal

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and estimated chemical compositions determined using ICP-AES are largely consistent. The glass structures in the current study reflect the local structures of super-cooled melts at the glass transition temperature (i.e., Tg). Because the most of the local configurations in the melts is frozen below Tg, the glass structures studied here are somewhat different from those of the molten liquids above the liquidus. Nonetheless, the previous studies of the temperature (and thus Tg) effect on the structures revealed relatively minor structural changes in tectosilicate glasses (e.g., the [4]B/[3]B ratio) (Sen et al., 1998; Stebbins et al., 2008; Stebbins and Ellsworth, 1996; Wang and Stebbins, 1999). Note that an increase in temperature above Tg promotes the formation of [5]Al in peraluminous silicate glasses (Le Losq et al., 2014). 2.2. NMR spectroscopy 11B

NMR experiments for NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 glasses. 11B MAS

and 3QMAS NMR spectra for NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 glasses were collected at the Larmor frequency of 128.3 MHz using a Varian solid-state NMR 400 MHz (9.4 T) spectrometer. A 3.2 mm Varian double-resonance probe was used with the relaxation delay of 1 s, and a rf pulse lengths of 0.2 μs. The 3QMAS NMR spectra were collected using a pulse sequence comprising a single 4.3 μs hard pulse and two fast amplitude modulated 1.9 μs pulses with alternating phases, followed by a soft echo pulse of ~21 μs. Echo delay time (integer multiple of the rotor period) was 3000 μs. The 11B MAS spectra for NaAlSiO4NaBSiO4, NaAlSi3O8-NaBSi3O8, and NaAl0.9B0.1Si3O8 glasses were collected using a Bruker solid-state NMR 600 MHz system (14.1 T) at the Larmor frequency (192.6 MHz). A 3.2 mm Bruker triple-resonance probe was used with the relaxation delay of 1 s and a rf pulse length of 0.25 μs. 1920 to 6720 scans were averaged to achieve the current signal to noise ratio collected at 14.1 T. The spectra were referenced to liquid boric acid (H3BO3) whose resonance was located at 19.6 ppm. 27Al

and 17O 3QMAS NMR experiment for NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8

glasses. The 27Al and 17O 3QMAS NMR spectra for NaAlSiO4-NaBSiO4 and NaAlSi3O8NaBSi3O8 glasses were collected at the Larmor frequency of 104.2 MHz for 27Al and 54.2 MHz for 17O with a 3.2 mm Varian double-resonance probe. The pulse sequence consisted of a single hard pulse (3-4.5 μs) and two 0.7-1.1 μs pulses followed by 5000-3570 μs echo time and a 15-19.5 μs soft pulse. The spectra were referenced to liquid aluminum chloride (AlCl3) and to external tap water (H2O) whose resonances were located at 0 ppm.

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The 29Si MAS NMR spectra for the multi-component aluminosilicate glasses, including those in the glasses in nepheline-malinkoite join, do not provide clear structural evolution of Si and Al species (Pierce et al., 2010). B-Al-Si disorder can often be indirectly obtained by exploring detailed atomic configurations around oxygen via 17O NMR spectroscopy (e.g., Angeli et al., 2001; Du and Stebbins, 2005a; Stebbins et al., 2001b). 3. RESULTS 3.1. Evolution of boron environments in boron-bearing glasses and melts in the NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 joins: 11B NMR results We investigated the composition-induced changes in boron coordination environments of NaAlSiO4-NaBSiO4 glasses with varying B/(B+Al). To determine the effect of silicon content on the atomic structure of Na-aluminoborosilicate glasses, we also analyzed the boron coordination environments of NaAlSi3O8-NaBSi3O8 glasses with Si/(B+Al) ratio of 3. Fig. 1 shows the 11B MAS and 3QMAS NMR spectra for NaAlSiO4NaBSiO4 (Figs. 1A and 1B) and NaAlSi3O8-NaBSi3O8 (Figs. 1C and 1D) glasses with varying XMa [= B/(B+Al)] and XRd [= B/(B+Al)] values of 0.25, 0.50, 0.75, and 1. The 11B 3QMAS NMR spectra of these glasses (Figs. 1B and 1D) reveal the presence of [3,4]B. Figs. 1A and 1C also show simulated peaks for non-ring [3]B and [4]B, as labeled in Figs. 1A and 1C. See S2 for quantification for boron species in the spectra. The [3]B and [4]B peak positions in the 2D 11B 3QMAS NMR spectra constrain the quadrupolar coupling constant (Cq) and isotropic chemical shift for [3]B and [4]B with which the simulation of 1D 11B MAS NMR spectra was performed. In both joins, the fraction of [3]B decreases and that of [4]B increases with increasing XMa and XRd in the glasses. The trend is in generally consistent with those reported for previous 11B NMR studies (Geisinger et al., 1988; Marcial et al., 2019; Pierce et al., 2010). The slight differences in the [4]B fractions partly stem from the differences in static magnetic fields used in these studies (from 9.4 T to 21.1 T). Therefore, we also collected 11B NMR spectra of both NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 glasses at 14.1 T; they fully resolved the [3]B and [4]B peaks (in Figs. 1A and 1C). The fractions of [4]B from the 11B NMR results at 14.1 T are slightly larger than those from the results at 9.4 T. For a detailed comparison of the fraction of [4]B species in NaAlSiO4-NaBSiO4 glasses estimated from the 11B

MAS NMR spectra at different magnetic fields in earlier studies, see S4. This

composition-induced change in the boron coordination number indicates the potential change in the melt properties and boron isotope composition with varying B/Al ratio in multi-component boron-bearing silicate melts (see Sections 4.2 and 4.3 below). 9

The results from the two joins allow us to explore the effect of Si/(B+Al) on the boron environments for sodium aluminoborosilicate liquids at constant B/(B+Al) ratios (Figs. 1E). The fraction of [4]B is larger for NaAlSi3O8-NaBSi3O8 glasses than for NaAlSiO4NaBSiO4 glasses with the same B/(B+Al) ratio, especially when the B/(B+Al) ratio is low. The peak maxima for [4]B species also shift to a lower frequency from 0 ppm (NaAlSiO4NaBSiO4) to -3 ppm (NaAlSi3O8-NaBSi3O8) with an increase in Si/(B+Al), highlighting strong control of B/Si ratio on the atomic environments in the boron-bearing quaternary silicate glasses (see Figs. 1E and 1F). Whereas topologically distinct [3,4]B species are not fully resolved in the current 11B 2D 3QMAS NMR spectra at 9.4 T (Figs. 1B and 1D), the changes in [3,4]B peak shape and position in 11B MAS NMR spectra at 14.1 T indicate a presence of a multiple [3,4]B species with varying composition (Fig. 1E): the change in the position of [4]B indicates [4]B species with varying B/Si as a next nearest neighbor. Based on the simulation results (Figs. 1A and 1C), the change in the fraction of [4]B with varying B/(B+Al) ratios is shown in Fig. 2. As for the glasses in the NaAlSiO4-NaBSiO4 join, the [4]B fraction increases from ~12% to ~57% as XMa increases from 0.25 to 1. For the glasses in the NaAlSi3O8-NaBSi3O8 join, the [4]B content increases from ~28% to ~65% as XRd increases from 0.25 to 1, which is roughly consistent with the results of an earlier study (Geisinger et al., 1988). The resulting NMR parameters for [3,4]B in the glasses are shown in S2. The difference between the fractions of [4]B in NaAl0.75B0.25SiO4 and NaAl0.75B0.25Si3O8 glasses is approximately 16%, whereas that for NaBSiO4 and NaBSi3O8 glasses is approximately 8%. The fractions of [3,4]B based on the NMR spectra allow the quantification of the effect of the composition [i.e., B/(B+Al) and Si/(B+Al)] on the boron isotope composition (i.e., δ11B) of complex boron-bearing aluminosilicate melts. This may account for the boron isotope composition in arc volcanic rocks wherein more 10B is enriched as the distance from the trench at the subduction zone increases (see Section 4.4 below for the detailed discussion). 3.2. Effect of B/Al ratio on aluminum environment in boron-bearing multi-component aluminosilicate glasses and melts (NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8): 27Al 3QMAS NMR results In order to identify the structural changes in aluminum environments for glasses in both pseudo-binary joins, the aluminum coordination numbers for various B/Al ratios were determined, indirectly revealing the spatial proximity among B, Si, and Al. Fig. 3 presents the isotropic projections of the 27Al 3QMAS NMR spectra for NaAlSiO4-NaBSiO4 (Fig. 3A) and NaAlSi3O8-NaBSi3O8 (Fig. 3B) glasses. These spectra show that [4]Al is dominant in both 10

pseudo-binary joins. As for the NaAlSiO4-NaBSiO4 glasses, the peak maximum of [4]Al shifts from -40 ± 1 (XMa = 0) to -35 ± 1 ppm (XMa = 0.25). This indicates that the population of Al coordination environment, e.g., Q4Al(nSi) species (four-coordinated Al cluster with n number of silicon as the next nearest neighbors without any NBO) with a larger n, increases. This is because of a decrease in the population of Al-O-Al as B replaces Al (see Section 3.3). The peak width (full-width at half-maximum, FWHM) for [4]Al in the isotropic projection decreases from ~13 ppm (XMa = 0) to ~8 ppm (XMa = 0.25). This suggests a slightly narrower variation in Q4Al(nSi) species as the Al-O-Al population tends to decrease with the addition of boron into NaAlSiO4 glasses, thus reducing the complexity of the Q4Al(nSi) distribution (see Section 3.3). In contrast, both the peak maximum (approximately -38 ppm) and the FWHM (~8 ppm) for [4]Al species do not change with XMa from 0.25 to 0.75, indicating that the Q4Al(nSi) content is not significantly affected by a change in B/(B+Al) ratios. Whereas the previous 27Al MAS NMR spectrum for NaAl0.25B0.75SiO4 glasses with XMa = 0.75 could not resolve [4]Al and [5]Al due to the relatively low magnetic field (e.g., 9.4 T, Lee and Lee, 2016), the isotropic projection shows that there exists a minor amount of [5]Al species (~1-2%) at ~18 ppm along the isotropic dimension (Fig. 3A). 27Al 2D 3QMAS NMR spectra and the detailed NMR characteristics [e.g., isotropic chemical shift and Cq values] will be discussed in detail in the ongoing NMR manuscript. The presence of [5]Al, though minor, may play an important role in the transport properties of these liquids (see Section 4.1 for details). Regarding NaAlSi3O8-NaBSi3O8 glasses, the [4]Al peak maximum does not vary with albite content. The changes in FWHM of the [4]Al peak are also minor [~9 ppm (XRd = 0) to ~8 ppm (XRd = 0.75)]. These results indicate that the Al environment in these glasses is rather invariant with respect to changes in B/Al ratio, indirectly indicating a low spatial proximity between B and Al. As will be discussed in the forthcoming 17O NMR results (Section 3.3), the Al-NBO (Na-O-Al) peak is absent and hence Al is fully polymerized (Allwardt et al., 2003). We also compared glasses in both joins with varying Si/(B+Al) ratios at the same B/(B+Al) ratio. Fig. 3C shows the comparison of the isotropic projections of NaAl1-xBxSiO4 [Si/(B+Al) = 1] and NaAl1-xBxSi3O8 [Si/(B+Al) = 3] glasses at constant x = B/(B+Al) = 0.25 and 0.75. The peak maxima for [4]Al in the glasses shift toward a higher frequency from ~-38 ppm to ~-36 ppm as Si/(B+Al) ratio increases from 1 (NaAl1-xBxSiO4) to 3 (NaAl1-xBxSi3O8) with similar FWHM (~8 ppm). The results confirm that the population of the Q4Al(nSi) species with a larger n increases with increasing Si/(B+Al) ratio. The results indicate a more prominent control of Si over B on the Al coordination environments in the glasses. Note that

11

the change in the peak maxima for [4]Al could be resulted from a decrease in the intertetrahedral angle (e.g., Neuville et al., 2004). 3.3. Composition-induced structural changes in oxygen configuration in boron-bearing multi-component aluminosilicate glasses and melts: 17O 3QMAS NMR results Fig. 4 shows the 17O 3QMAS NMR spectra of NaAlSiO4-NaBSiO4 (Fig. 4A) and NaAlSi3O8-NaBSi3O8 (Fig. 4B) glasses for XMa and XRd = 0, 0.50, and 1. The peaks corresponding to BOs that connect Si and B (e.g., Si-O-Si, Si-O-B, B-O-B) and those connecting Si and Al (e.g., Si-O-Al, and Al-O-Al) are resolved in the glasses in both joins. The peak corresponding to Na-O-Si is also partially resolved from Si-O-Al, as labeled. Here, based on the previously reported peak position for each BO and NBO configuration of diverse borosilicate and aluminosilicate glasses, these peaks in 2D 17O 3QMAS NMR spectra are assigned (Du and Stebbins, 2003a, b, c; Lee et al., 2001; Lee and Stebbins, 2002; Stebbins et al., 2001b; Wang and Stebbins, 1998; Wang and Stebbins, 1999). NaAlSiO4-NaBSiO4 join. The spectrum for nepheline glass (NaAlSiO4, XMa = 0) shows a non-negligible amount of Al-O-Al species, demonstrating that the Al avoidance is imperfect (Lee and Stebbins, 2000). Na-O-Si and BOs were observed in malinkoite glass (NaBSiO4, XMa = 1). Fig. 4A confirmed that the fractions of (Si,B)-O-(Si,B) and Na-O-Si apparently increase, whereas those of (Si,Al)-O-Al decrease as XMa [= B/(B+Al)] increases. The B-O-Al peak was not found for any glass in the join, consistent with the suggestions from the 11B and 27Al NMR spectra, which report the B-Al proximity to be low. Note that the spatial proximity between quadrupolar nuclides could be estimated using rotational echo double resonance and double quantum MAS technique (e.g., Bertmer et al., 2000; Edén, 2010; Lee et al., 2009, and references therein). NaAlSi3O8-NaBSi3O8 join. Si-O-Al and Si-O-Si peaks are observed in the NaAlSi3O8 glasses (XRd = 0), while the peak due to Al-O-Al peak is not observed, consistent with the previous NMR results (Xu et al., 1998). Regarding the NaBSi3O8 endmember glasses, the peaks due to Na-O-Si and BOs are fully resolved. The fractions of (Si,B)-O-(Si,B) and NBO increase as XRd [= B/(B+Al)] increases, whereas those of Si-O-Al decrease. Again, the B-O-Al peak was not observed for any glass in the join, implying that the distribution of B and Al was spatially inhomogeneous. Comparing the oxygen configurations of NaAlSi3O8 (with no Al-O-Al) and NaAlSiO4 (with Al-O-Al) glasses, the lack of the Al-O-Al species in the former join may explain the invariant peak maxima of the Q4Al(nSi) species in the isotropic projections of the 12

27Al

3QMAS NMR spectra for NaAlSi3O8-NaBSi3O8 glasses, whereas a relatively larger

change in the peak maximum of [4]Al species was observed for the glasses in the NaAlSiO4NaBSiO4 pseudo-binary join (Fig. 3). The isotropic projections of the 17O 3QMAS NMR spectra of NaAlSiO4-NaBSiO4 glasses with various XMa values are shown in Fig. 5. The figure also shows the simulated BO peaks and Na-O-Si with six Gaussian functions, as labeled. As demonstrated in 2D 17O 3QMAS NMR spectra (Fig. 4A), the fractions of (Si,Al)-O-Al decrease, and those of (Si,B)-O(Si,B) and Na-O-Si increase as XMa increases. The prominent Na-O-Si peak intensity along the join indicates a reduction in melt polymerization with increasing boron content. On the basis of multiple boron coordination numbers (Fig. 1), the B-O-B peak consists of [3]B-O-[3]B, [4]B-O-[3]B,

and [4]B-O-[4]B peaks. Similarly, Si-O-B also corresponds to Si-O-[3,4]B. These

oxygen species with varying coordination numbers of boron (e.g., [3]B-O-[3]B, [3]B-O-[4]B, and [4]B-O-[4]B)

are not well distinguished (due to the peak overlap); however, we found that the

FWHM for B-O-B (~10 ppm) is apparently larger than those of Si-O-B (~9 ppm) and Si-O-Si (~7 ppm) (see Tables S3 and S4 for the detailed parameters). The larger peak width thus indirectly confirms the presence of multiple B-O-B species with varying boron coordination environments. This trend suggests the evolution of the [n]B-O-[n]B peak from [3]B-O-[3]B to [4]BO-[4]B with increasing Si content (and thus Si/B ratio). Fig. 6 shows the isotropic projections of the 2D 17O NMR spectra of NaAlSi3O8-NaBSi3O8 glasses with varying XRd. As shown in the projections of NaAlSiO4-NaBSiO4 glasses in Fig. 5, an increases in the Na-O-Si peak intensity indicates a decrease in melt polymerization as the B/Al ratio increases in the pseudo-binary join. Quantification of NBO and BO fraction. To better quantify the extent of the B-Al-Si disorder and the network polymerization, the estimation of the fractions of BOs and NBO is necessary. Here, the fractions of each BO and NBO were determined using the isotropic projections of the 17O 3QMAS NMR spectra (Figs. 5 and 6). The oxygen clusters with [5]Al (e.g., Si-O-[5]Al) were not taken into consideration as the fraction of [5]Al was minor. The position and width of each peak are well-constrained based on the spectra, as labeled in the projected spectra (in Figs. 5 and 6). It is notable that the peak positions for (Si,B)-O-(Si,B) in the glasses exhibit a slightly positive shift (i.e., toward higher frequency) with Si/(B+Al) at constant B/(B+Al). This systematic shift results from the transformation of boron coordination number from 3 to 4 with increasing Si/B ratio (e.g., Du and Stebbins, 2003a) (see S3). Fig. 7 shows the calibrated populations of BOs and NBO (Na-O-Si) for glasses in the

13

nepheline-malinkoite (Fig. 7A) and albite-reedmergnerite (Fig. 7B) joins with varying B/(B+Al) ratio estimated from the simulation results of the total isotropic projections (Figs. 5 and 6). It is not trivial to distinguish B-O-Al and Si-O-Si in the 17O NMR spectra alone because these two peaks overlap: the B-O-Al peak may be hidden between Si-O-Si and Si-OAl peaks (Du and Stebbins, 2005a). Nevertheless, the lineshapes of Si-O-Si and Si-O-Al peaks are symmetrical, which indicates that the fraction of B-O-Al, if exist, would be minor. The current 27Al and 11B NMR spectra strongly suggest that the proximity between B and Al would be unlikely, while the presence of B-O-Al cannot be fully disregarded. The signal intensity of each peak in the 2D NMR spectra was calibrated taking the Cq values of BOs and NBO into consideration (Lee et al., 2016; Lee and Stebbins, 2000; Wang and Stebbins, 1999). As for the glasses in the NaAlSiO4-NaBSiO4 join, the NBO (Na-O-Si) fraction increases from 0 to ~22% as XMa increases from 0 to 1. The fraction of Al-O-Al decreases from ~27 to 0% as XMa increases from 0 to 0.5. The fraction of Si-O-Al decreases from ~64 to 0% with increasing XMa from 0 to 1. The fraction of Si-O-Si increases from ~9 (XMa = 0) to ~25% (XMa = 1). The fraction of Si-O-B increases from 0 (XMa = 0) to ~38% (XMa = 1). With increasing XMa from 0 to 1, the fraction of B-O-B increases from 0 to ~15%. For the NaAlSi3O8-NaBSi3O8 glasses, the fraction of Na-O-Si increases from 0 to ~13% as XRd increases from 0 to 1 (Fig. 7B). The fraction of Si-O-Al decreases from ~60 to 0% as XRd increases from 0 to 1. The fraction of Si-O-Si also increases from ~40 (XRd = 0) to ~48% (XRd = 1) and the fraction of Si-O-B increases from 0 (XRd = 0) to ~31% (XRd = 1) with increasing XRd. The fraction of B-O-B also increases from 0 (XRd = 0) to ~8% (XRd = 1). The change in NBO fraction with varying B/(B+Al) ratio is also less prominent in the NaAlSi3O8-NaBSi3O8 glasses than in the NaAlSiO4-NaBSiO4 glasses, implying that the degree of polymerization increases with increasing Si content at the same B/Al ratio. These changes affect leaching of boron and sodium from sodium aluminoborosilicate glasses in aqueous solution and control the viscosity of boron-bearing complex silicate melts (see Section 4.3 and 4.4). 4. DISCUSSION 4.1. [5]Al and its implication for the properties of NaAl0.25B0.75SiO4 glasses and melts [5,6]Al

species are known to become prevalent when the Al/metal cation ratio [e.g., Al/(Na+

or Ca2+)] is greater than 1 (i.e., a metaluminous join). The fractions of the highly coordinated Al tend to increase when modifier cations with a relatively high cation field strength, such as Mg2+ and Ca2+, are present (e.g., Eden, 2015; Iftekhar et al., 2011; Jaworski et al., 2012;

14

Neuville et al., 2004, 2006; Neuville et al., 2008; Pahari et al., 2012; Park and Lee, 2018; Stebbins et al., 2000; Stevensson and Edén, 2013; Toplis et al., 2000, and references therein). The 27Al 3QMAS NMR spectrum of NaAl0.25B0.75SiO4 glasses indicates the presence of a small amount of [5]Al (~1-2 %) (Fig. 3A). It is intriguing that [5]Al is present in NaAl0.25B0.75SiO4 glasses when Al/Na is smaller than 1, and the field strength of Na+ is low (~0.96). While the origin of [5]Al in this glass is not clear, Na+ in the glasses is shared by Si (forming Na-O-Si) and B (forming [4]B). This may have led to a situation where the local environments are similar to those of metaluminous joins, facilitating the formation of [5]Al species. A small amount of [5]Al may account for a further decrease in the viscosity of NaAl0.25B0.75SiO4 melts: as the presence of [5]Al results in an increase in the configurational entropy (Sconf). Though minor, an increase in Sconf contribute to a decrease in the melt viscosity (η), as predicted by the Adam-Gibbs relation [i.e., η ∝ exp(1/Sconf)] (Adam and Gibbs, 1965; Le Losq and Neuville, 2017; Le Losq et al., 2014; Neuville, 2006; Richet, 1984). 4.2. The nature of network polymerization and the extent of inter-mixing among B, Al, and Si in quaternary Na2O-B2O3-Al2O3-SiO2 glasses Composition-induced changes in NBO and variations in the mixing behavior (e.g., chemical order, random mixing, and phase separation) among framework cations account for changes in the configurational entropy, viscosity, and diffusivity in silicate melts (Hess, 1995; Lee, 2011; Lee et al., 2001; Mysen and Richet, 2018; Richet, 1984; Richet and Neuville, 1992; Stebbins et al., 2001a; Stebbins and Xue, 2014). The extent of disorder can also affect the bulk reactivity of glasses during hydrolysis because the reactivity of distinct oxygen clusters may have unique kinetic stability (Phillips et al., 2000). Although earlier studies of boronbearing silicate glasses often assumed presence of B-rich and Si-rich domains in the glasses, previous 17O NMR studies have confirmed that Si and B exhibit a moderate degree of mixing between these two cations between complete phase separation (or cationic segregation) and a random distribution of these units (Du and Stebbins, 2003a; Lee et al., 2001; Wang and Stebbins, 1998). The degree of separation between B and Al is also reflected in the lack of BO-Al linkages, revealing an extensive mixing between Si and Al, a slightly less prominent mixing between Si-B, and finally un-mixing between Al and B. Here, we present the oxygen site-specific structural mechanisms for the network connectivity which are consistent with the current experimental observations based on the 11B, 27Al, and 17O NMR spectra. The following relations in quasi-chemical equations determine the degree of polymerization

15

involving distinct types of BOs in sodium aluminoborosilicate glasses (modified from Lee et al., 2016 and references therein): Al-O-Al + Na-O-Na → 2(Na-O-Al)

(1.1)

Si-O-Al + Na-O-Na → Na-O-Si + Na-O-Al

(1.2)

Si-O-Si + Na-O-Na → 2(Na-O-Si)

(1.3)

Si-O-B + Na-O-Na → Na-O-Si + Na-O-B

(1.4)

B-O-B + Na-O-Na → 2(Na-O-B)

(1.5)

B-O-Al + Na-O-Na → Na-O-B + Na-O-Al

(1.6)

There was no clear evidence for the presence of Na-O-Al, and the fraction of Na-O-B was negligible, whereas the prominent Na-O-Si peak was shown in the 17O NMR spectra (Fig. 4). This confirms that NBO forms preferentially in the silicate network (Du and Stebbins, 2003a, b, c). Furthermore, considering structural details from our multi-nuclear NMR spectra, following oxygen-site specific schemes in quasi-chemical equations can describe the bonding preference during depolymerization of melt network where Na* refers to the chargecompensator (modified from Lee et al., 2016 and references therein): Si-O-Al∙∙∙Na* + Na-O-Al → Al-O-Al∙∙∙Na* + Na-O-Si

(2.1)

Si-O-Si + Na-O-Al → Si-O-Al∙∙∙Na* + Na-O-Si

(2.2)

Si-O-B∙∙∙Na* + Na-O-B → B-O-B∙∙∙Na* + Na-O-Si

(2.3)

Si-O-Si + Na-O-B → Si-O-B∙∙∙Na* + Na-O-Si

(2.4)

The bonding preferences toward the right-hand side of the schemes are revealed, confirming that melt depolymerization is prevalent exclusively in silicate-networks in Naaluminoborosilicate melts and glasses. The mechanisms described in Eqs. 2.1 and 2.3 also show the change of the role of Na from charge-compensator into network-modifier by forming NBO (i.e., Na-O-Si). The change of the role of Na is also supported by 23Na MAS NMR spectra (see S5). We note that the above quasi-chemical relations can be modified in such a way that the role of involved cations are explicitly specified (see Le Losq et al., 2014 and references therein). The current notations used in Eq. 2.1-2.4 may not capture the full details of structural arrangement involving multiple species. Nevertheless, the current simple notations comply well with those used in the 17O NMR studies (e.g., Lee et al., 2016; Lee and Stebbins, 2006; Lee and Stebbins, 2009). The 11B and 27Al NMR results show two distinct B coordination environments and the primary presence of [4]Al with varying B/(B+Al) ratio (Figs. 1 and 3). The following quasi-chemical equations describe the extent of mixing among B, Al, and Si, accounting for 16

the relative population of BOs determined from the 17O NMR spectra (modified from Lee et al., 2016 and references therein): Si-O-Si + Al-O-Al = 2(Si-O-Al)

(3.1)

Si-O-Si + B-O-B = 2(Si-O-B)

(3.2)

Al-O-Al + B-O-B = 2(B-O-Al)

(3.3)

The quasi-chemical equilibrium constants (K) for the schemes in Eqs. (3.1)-(3.3) are: KSi-O-Al = [Si-O-Al]2/([Si-O-Si]· [Al-O-Al])

(3.4)

KSi-O-B = [Si-O-B]2/([Si-O-Si]· [B-O-B])

(3.5)

KB-O-Al = [B-O-Al]2/([B-O-B]· [Al-O-Al])

(3.6)

The estimated values of KSi-O-Al, KSi-O-B, and KB-O-Al based on the 17O NMR results are shown in Table 3. While the noticeable presence of the Si-O-Al peak demonstrates substantial mixing between Si and Al, KSi-O-Al does not change significantly for B/(B+Al) ratios of 0 (NaAlSiO4) and 0.25 (NaAl0.75B0.25SiO4). This indicates that the mixing between Si and Al is not strongly dependent on the addition of boron. A salient Si-O-B peak for the glasses studied here indicates the enhanced mixing between Si and B. KSi-O-B tends to slightly increase with increasing B/(B+Al) ratio (Table 3). The smaller KSi-O-B values for boronbearing albite glasses than for boron-bearing nepheline glasses at B/(B+Al) = 0.50 indicate that the mixing between Si and B is favored as Si/(B+Al) ratio decreases. Finally, the absence of B-O-Al linkages (Fig. 4) confirms that B and Al tend to separate from each other. This phase separation (or cationic segregation) between B and Al promotes the formation of B-OB linkages, which are more susceptible to hydrolysis. This leads to an enhancement in the overall glass reactivity in aqueous solution (see section 4.3 below). Taking into consideration the NMR results and the aforementioned structural mechanisms for network connectivity, Fig. 8 illustrates the schematic structures of Na-aluminosilicate (Fig. 8A) and Naaluminoborosilicate (Fig. 8B) glasses. As these are the schematic descriptions of the structures with a limited number of oxygen clusters, details of the glass structures cannot be fully described. 4.3. Effect of atomic structure and the degree of melt polymerization on dissolution rate and viscosity of sodium aluminoborosilicate glasses and melts. Here, we discuss the atomic and nanoscale origins of the composition-induced changes in the dissolution rate of boron-bearing silicate glasses and the viscosity of multicomponent sodium aluminoborosilicate melts. 17

Atomistic origins of dissolution rate of boron-bearing sodium aluminosilicate glasses with varying B/Al ratios. The atomic structures of glasses in the NaAlSiO4-NaBSiO4 join affect their dissolution behavior in aqueous solutions. Particularly, when high-level radioactive waste, composed of Na2O, B2O3, Al2O3, SiO2, CaO, MgO, and ZrO2 (while Na2O, B2O3, Al2O3, and SiO2 are four main components) is loaded into glasses, nepheline (NaAlSiO4) often crystallizes from the melts by taking up Si and Al from the melts (Aréna et al., 2019; Deshkar et al., 2018; Lee et al., 2006; Marcial et al., 2016; Marcial et al., 2019). This uptake of Al and Si from the melts elevates the boron content in the residual glasses. The glasses with high boron content are known to be more susceptible to hydrolysis and exhibit low chemical durability (Bunker, 1994; Deshkar et al., 2018; Marcial et al., 2016; Pierce et al., 2010). Taking into consideration their applications as nuclear waste glasses, the effect of boron content (or B/Al ratio) on the leaching behavior of boron-bearing silicate glasses was extensively explored (Li et al., 2003; Marcial et al., 2019; Pierce et al., 2010; Plodinec, 2000). It has also been shown that the dissolution rates estimated from the leaching of Si and Al are rather invariant, while the leaching rates of Na and B increase with increasing B/(B+Al) (Pierce et al., 2010): the log-scale dissolution rate estimated from B-leaching drastically increases from ~-8.2 mol/m2s (NaAl0.4B0.6SiO4 glasses, B/(B+Al) = 0.6) to ~-6.1 mol/m2s (NaAl0.2B0.8SiO4 glasses, B/(B+Al) = 0.8) (Pierce et al., 2010). This rather abrupt change in the dissolution rate in NaAlSiO4-NaBSiO4 glasses was attributed to a reduction in the non-ring [3]B fraction, i.e., from 9.8% (NaAl0.4B0.6SiO4 glasses) to 0.1% (NaAl0.2B0.8SiO4 glasses) (Pierce et al., 2010). The distinction between non-ring and boroxol ring is not trivial because the peak position of each species may change with composition. In contrast, as shown in Fig. 4, the oxygen sites are well-resolved. The changes in the dissolution behavior with varying B/Al ratio may thus be accounted for by the observed changes in the oxygen configuration. Hydrolysis and ionexchange reactions may prevail during dissolution of boron-bearing silicate glasses (Bunker, 1994). Firstly, the following quasi-equilibrium reactions for oxygen-site specific hydrolysis may be taken into consideration to account for the dissolution of the glasses where Na* refers to the charge-compensator (modified from Lee et al., 2001; Malfait and Xue, 2010, and references therein): Al-O-Al∙∙∙Na* + H2O → 2(Al-O-H) + Na+

(4.1)

Si-O-Al∙∙∙Na* + H2O → Si-O-H + Al-O-H + Na+

(4.2)

Si-O-Si + H2O → 2(Si-O-H)

(4.3)

Si-O-B∙∙∙Na* + H2O → Si-O-H + B-O-H + Na+

(4.4)

18

B-O-B∙∙∙Na* + H2O → 2(B-O-H) + Na+

(4.5)

B-O-Al∙∙∙Na* + H2O → (B-O-H) + Al-O-H + Na+

(4.6)

Note that Na is dominantly a charge compensator in presence of Al (e.g., Angeli et al., 2000; Angeli et al., 2006; Lee, 2010; Lee and Stebbins, 2003; Stebbins et al., 2013, and references therein). Because B-O-Al species were not observed in the glasses studied here, the schemes shown in Eqs (4.1)-(4.5) would be useful to describe the hydrolysis involving the BOs. With regard to the leaching of boron from the glasses [i.e., as dissolution rates are often estimated from dissolution of boron (Marcial et al., 2019; Pierce et al., 2010)], the schemes in Eqs. (4.4) and (4.5) control the overall reactivity of the glasses in contact with aqueous solution; earlier quantum chemical calculations of oxygen-specific hydrolysis reactions showed that [3]B-O[3]B

was more susceptible to hydrolysis than Si-O-Si (Lee et al., 2001). An earlier study on

both reacted and pristine sodium aluminoborosilicate glasses (14Na2O-4B2O3-17Al2O3-65SiO2) in an aqueous solution showed that the B-O-B and Na-O-Si peaks disappeared after leaching (Angeli et al., 2001). Furthermore, the Al-O-Al species are likely to be more prone to hydrolysis than the Si-O-Al species (Malfait and Xue, 2010). The ion-exchange reaction is expressed as T-O-M + H2O → T-O-H + M+ + OH-, where T is the network-forming cation and M is the network modifying cation. Therefore, the following quasi-equilibrium reactions for NBO species could be taken into consideration (modified from Bunker, 1994, and references therein): Al-O-Na + H2O → Al-O-H + Na+ + OH-

(5.1)

Si-O-Na + H2O → Si-O-H + Na+ + OH-

(5.2)

B-O-Na + H2O → B-O-H + Na+ + OH-

(5.3).

Because Na-O-Al and Na-O-B species were not observed in the current NMR spectra, the ion-exchange reaction involving Na-O-Si species (Scheme in Eq. 5.2) may have played a dominant role during dissolution. With increasing fraction of Na-O-Si [at higher B/(B+Al)], the leaching of Na is reported to increase (Pierce et al., 2010), suggesting a preferential interaction between Na-NBO and H2O. The relationship between the fractions of oxygen sites vs. the reactivity of glasses can be established based on the above oxygen site-specific reaction schemes. As B/Al ratio increases, the fraction of B-O-B also increases with B/Al ratio from 0% [B/(B+Al) = 0] to 16% [B/(B+Al) = 1]. As the B-O-B linkage is more susceptible to hydrolysis (Scheme in Eq. 4.5), Fig. 9A presents the relationship between the B-O-B fraction (from Fig. 5 and 7A) and the estimated dissolution rate (estimated from the leaching of boron in aqueous solution) for 19

NaAlSiO4-NaBSiO4 glasses. Furthermore, Fig. 9A shows an abrupt increase in the leaching rate of boron, particularly for boron-rich glasses, although the fraction of B-O-B increases linearly with B/(B+Al) ratio. Therefore, a dramatic increase in the dissolution rates indicates a certain threshold boron content, above which the B-O-B bonds are spatially well-connected. Preferential hydrolysis of B-O-B species and proximity among B-O-B clusters may account for the abrupt increase in the overall dissolution rates in NaAlSiO4-NaBSiO4 glasses with higher B/(B+Al) ratios (≥ 0.60). The observed increase in the overall dissolution rate with increasing B/(B+Al) ratio can also be partially explained by an increase in the population of Na-O-Si species (Angeli et al., 2001) (Scheme in Eq. 5.2). Fig. 9B also exhibits the positive correlation between the population of Na-O-Si and the leaching rate of Na, suggesting that an increase in the Na-NBO content contributes to an overall increase in the dissolution rate. Therefore, the overall dissolution rate of sodium aluminoborosilicate glasses, estimated from the B- and Na-leaching rates, may have been significantly promoted through an enhanced connectivity of relatively weaker bonds such as B-O-B and Na-O-Si as composition reached a certain boron content. Finally, a decrease in the Al-O-Al fraction in NaAlSiO4-NaBSiO4 glasses with increasing B/(B+Al) ratio could explain the slight decrease in the Al-leaching rate from glasses for B/(B+Al) range from 0 to 0.25. Whereas the experimental dissolution rates for the glasses in the NaAlSi3O8-NaBSi3O8 join are not available, because an increase in the B-O-B fraction is less prominent in the NaAlSi3O8-NaBSi3O8 join (compared with that in the NaAlSiO4-NaBSiO4 join), an expected increase in the dissolution rate would be less significant. Atomistic origins of viscosity of boron-bearing sodium aluminosilicate glasses and melts with varying B/Al ratio. The melt viscosity heavily depends on the composition of melts (e.g., Giordano and Dingwell, 2003; Hess, 1995; Mysen and Richet, 2018; Stebbins et al., 1995, and references therein). The addition of boron into silicate melts significantly reduces the melt viscosity; the estimated viscosity of haplogranitic (Na2O-K2O-Al2O3-SiO2) melts decreases from ~1012.5 Pa·s (K2O: 4.2 wt%, Na2O: 4.6 wt%, Al2O3: 12.1 wt%, SiO2: 79.0 wt%) to ~1010 Pa·s (K2O: 4.0 wt%, Na2O: 4.2 wt%, Al2O3: 11.6 wt%, SiO2: 71.1 wt%, B2O3: 8.9 wt%) as the content of B2O3 increases from 0 to 9 wt% at 750 °C (Dingwell et al., 1992). The reduction in the viscosity of the boron-bearing silicate melts can be explained by an increase in the NBO fraction as B replaces Al; the NBO fraction increases from 0 (XMa = 0) to ~15% (XMa = 0.25) (Fig. 7A). For NaAlSi3O8-NaBSi3O8 glasses (Fig. 7B), although the experimental melt viscosity data are not available, a decrease in the degree of polymerization due to an

20

increase in the Na-O-Si fraction indicates that the melt viscosity is also likely to decrease with increasing boron content. As the albite (NaAlSi3O8) melts can be regarded as a simplified model granitic liquids, the current insights from NaAlSi3O8-NaBSi3O8 glasses and melts would be useful for inferring the boron-induced changes in the properties of rhyolitic melts where the addition of a small amount of boron is expected to decrease the melt viscosity. 4.4. Boron coordination environment in boron-bearing rhyolitic melts and its effect on boron isotope composition in multi-component silicate melts. Melting of crustal and mantle rocks and their interactions with coexisting fluids are accompanied by a moderate degree of boron isotope fractionation, as suggested from their manifested mass difference (e.g., White, 2013 and references therein). For example, the decomposition of boron-bearing hydrous clay minerals, layer silicates, amphiboles, and/or OH-bearing cyclosilicates during subduction often releases fluids enriched in boron (e.g., Harvey et al., 2014a; Klemme et al., 2011; Kowalski et al., 2013; Meyer et al., 2008; Palmer et al., 1992; Peacock and Hervig, 1999; Williams et al., 2001; Wunder et al., 2005, and references therein). The boron coordination numbers for these fluids were often assumed to be 3 and those for boron-bearing silicate minerals and melts to be 4 (e.g., Hervig et al., 2002; Kowalski et al., 2013; Maner and London, 2018; Sanchez-Valle et al., 2005; Schmidt et al., 2005, and references therein). Taking the preferential partitioning of 11B into triply-coordinated B (whereas 10B is selectively enriched in borate structures with four-coordinated B, [4]B) (e.g., Kakihana et al., 1977; Palmer et al., 1987; Palmer and Swihart, 1996; Schauble, 2004; White, 2013, and references therein), the released fluids are enriched in 11B, while 10B is partitioned into remaining silicates. Therefore, the variations in isotope composition have been used to trace fluid-induced igneous processes occurring during subduction (e.g., Hervig et al., 2002; Maner and London, 2018; Palmer, 2017; Palmer and Swihart, 1996; Peacock and Hervig, 1999; Tonarini et al., 2003, and references therein). Indeed, while stable isotope fractionation factors become less significant at higher temperature, the pioneering experimental study of fluid-felsic glasses interaction at high temperature (~1100 °C) reported that the difference in δ11B between silicate melts and fluid (i.e., ∆11Bsilicate melt-fluid) can be up to ~-3‰ and thus boron in silicate melts has a lighter isotope composition than that in fluids (Hervig et al., 2002). This also confirms a significant change in boron isotope compositions in melts and fluids even at the magmatic temperature (Hervig et al., 2002; Maner and London, 2018).

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The current experimental results of aluminoborosilicate glasses quenched from melts at high temperature can provide an additional insight into the variations in the isotope composition of volcanic rocks. As shown in Figs. 1 and 2, the boron coordination environment in Na-aluminoborosilicate glasses depends on small changes in melt composition as boron can indeed occupy both trigonal ([3]B) and tetrahedral ([4]B) sites. Fig. 10 also shows the 11B MAS NMR spectrum of boron-bearing albite composition glasses (NaAl0.9B0.1Si3O8, 1.3 wt% B2O3, Table 3), which are structural model system for natural boron-bearing rhyolitic melts. The spectrum reveals that the fractions of [3]B and [4]B are ~75% and ~25%, respectively. This suggests that [3]B is also likely to be dominant in natural rhyolitic melts (Schmidt et al., 2004), although [4]B has been assumed to be dominant in silicate melts in contact with fluids formed by dehydration during subduction. Fig. 11A also shows the trend of the estimated and expected fractions of [4]B species in the sodium aluminoborosilicate glasses with varying B/(B+Al) and Si/(B+Al) ratios. Because only limited experimental data (in both binary joins) were available, the data between the experimental data from the current study were interpolated. Therefore, Fig. 11A provides a semi-quantitative information of the boron coordination environments. Nevertheless, it is clear that the [4]B fraction tends to increase with increasing B/(B+Al) and Si/(B+Al) ratios. Considering the selective enrichment of 11B in [3]B (e.g., Kakihana et al., 1977; Palmer et al., 1987; Palmer and Swihart, 1996; Sanchez-Valle et al., 2005, and references therein), the trend in boron isotope composition in silicate melts can be predicted based on the coordination number of boron in silicate magma in contact with fluids and mineral phases: δ11Bmelt = X[3]B· δ11,[3]B + X[4]B· δ11,[4]B

(6)

where X[4]B + X[3]B = 1 and α = (11,[3]B/11,[4]B)/(10,[3]B/10,[4]B) = (δ11,[3]B/1000 + 1)/(δ11,[4]B/1000 + 1). While it is expected to be larger than 1 (i.e., δ11,[3]B is larger than δ11,[4]B), the exact value of the fractionation factor (α) remains to be confirmed. Based on the scheme 6 above and the results shown in Fig. 11A, the 2D contour plot of δ11B values for oxide melts is presented in Fig. 11B where the increase in the [4]B fraction with increasing Si/(B+Al) could result in the reduction of δ11B of the boron-bearing silicate glasses. The experimental results here suggest that the changes in the atomic structure of boron (i.e., coordination number) in silicate melts and glasses need to be fully understood to better account for the boron isotope composition of crustal materials. B2O3 content in the rhyolitic glass (up to ~1 wt%) is much smaller than those of SiO2 and Al2O3. Therefore, the composition range of the typical volcanic glasses is somewhat different from those shown in Fig. 11. Note that the current discussion is 22

designed to demonstrate the effect of boron on the melt properties, including its boron dissolution rate. In order to manifest the effect of boron content, therefore, a substantially larger amount of boron was added in the aluminosilicate glasses. Nevertheless, the observed trends in the [3]B fraction (and thus the expected changes in the properties with boron content) would prevail in the natural glasses and melts as shown in the 11B MAS NMR spectrum for the model rhyolitic glass with ~1 wt% of B2O3 (Fig. 10). The proposed relations may explain the systematic reduction in δ11B in boronbearing silicate glasses at deeper depths in the subduction zone. Because the loss of fluid from the slab during subduction is expected to decrease the 11B/10B ratio in the subducting slab, increasing the dehydration depth during subduction causes a decrease in the 11B/10B ratio in the fluids released from the slab at depth. A systematic decrease in δ11B in volcanic rocks from island arc has thus been interpreted to be due to the progressive dehydration within the slab (e.g., Ishikawa and Nakamura, 1994; Marschall et al., 2007; Peacock and Hervig, 1999; Rosner et al., 2003, and references therein). In addition to the effect of dehydration-induced changes in the isotope composition, the current experimental results imply an additional contribution of melt structures to the overall variations in the isotope composition of remaining silicate melts. In particular, the Si/B ratio in volcanic rocks often tends to increase as the distance from the trench increases and provides insights into the formation depth of partial melts (e.g., Ishikawa and Nakamura, 1994; Ishikawa and Tera, 1997; Ishikawa et al., 2001; Leeman et al., 2004; Rosner et al., 2003; Tonarini et al., 2011; Wunder et al., 2005, and references therein). While the actual composition of the boronbearing felsic melts certainly deviates from the glasses studied here, the structural changes in the boron coordination numbers in sodium aluminoborosilicate glasses and melts with varying Si/B ratio provide useful constraints on the boron isotope composition of the silicate melts with varying distance from the trench: the [4]B population in the silicate melts and glasses increased with increasing Si/(B+Al) ratios (Figs. 2 and 11A). Therefore, 10B is expected to be enriched in those melts with a larger Si/B ratio, which in part accounts for the observed boron isotope composition of the volcanic rocks near island arc. Therefore, future model of boron isotope composition may need to take such distinct coordination environments into consideration. Finally, it was observed that the [4]B fraction tends to increase with pressure in diverse boron-bearing oxide glasses and multi-component aluminoborosilicate glasses (e.g., Bista et al., 2017; Brazhkin et al., 2008; Carini et al., 2011; Du et al., 2004; Lee et al., 2005; Lee et al., 2007; Lee et al., 2018; Svenson et al., 2016; Zeidler et al., 2014, and references therein). While the present results bring new insights into boron 23

isotope behavior dependent on melt composition, the effect of pressure on the structures (particularly boron speciation and network connectivity) needs to be constrained to better understand the isotope composition of silicate glasses and melts. 5. CONCLUSION We explored the changes in the detailed atomic structures in two important classes of boron-bearing quaternary aluminosilicate glasses (e.g., NaAlSiO4-NaBSiO4 and NaAlSi3O8NaBSi3O8). The 11B NMR spectra exhibit a systematic increase in the fraction of [4]B in boronbearing nepheline and albite melts with increasing B/Al and Si/B ratios, allowing us to establish the overall effects of Si/B and B/Al on the boron coordination environments in the complex aluminoborosilicate melts. While [4]Al is dominant for all the aluminoborosilicate glasses studied here, a small amount of [5]Al is observed in NaAl0.75B0.25SiO4 melts. This may have increased the configurational entropy and reduced the melt viscosity. The [4]Al environments are mainly controlled by Si/B ratios rather than B/Al ratios, indicating the low spatial proximity between B and Al. This is also confirmed by the absence of the B-O-Al species in the 17O 3QMAS NMR spectra. The 17O NMR results show that B-O-B and Na-O-Si species increase as B/Al ratio increases, and those species have promoted the overall dissolution of aluminoborosilicate glasses in an aqueous solution. The results indicate that an increase in the NBO fraction due to an addition of boron into the felsic melts tends to decrease the melt viscosity. Based on a systematic change in boron coordination environments with B/Al and Si/B, the composition-induced changes in the 11B composition in the melts were discussed. Particularly, 10B is expected to be enriched in those melts with a larger Si/B ratio, which in part accounts for the observed boron isotope composition of the volcanic rocks near island arc. The current study highlights the atomistic control of the boron coordination number and the detailed degree of network disorder over the boron isotope composition, melt viscosity, and dissolution rates of multi-component boron-bearing aluminosilicate glasses and melts.

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34

Table 1. Nominal compositions (weight %) and ICP analyses of NaAlSiO4-NaBSiO4 glasses (Top: non-enriched, Bottom: 17O-enriched). XMa is the mole fraction of the malinkoite component. Composition (non-enriched) XMa

wt% (ICP analysis)

Na2O

Al2O3

B2O3

SiO2

Na2O

Al2O3

B2O3

0

21.8

35.9

0

42.3

39.4

60.2

0.4

0.25

22.5

27.7

6.3

43.5

41.2

47.3

11.6

0.50

23.1

19.0

13.0

44.9

42.7

32.9

24.4

0.75

23.9

9.8

20.1

46.2

45.3

17.4

37.3

1

24.6

0

27.7

47.7

46.5

0

53.2

Composition (17O-enriched) XMa

wt% (nominal composition)

wt% (nominal composition)

wt% (ICP analysis)

Na2O

Al2O3

B2O3

SiO2

Na2O

Al2O3

B2O3

0

21.6

35.6

0

42.8

39.1

60.8

0.2

0.25

22.3

27.5

6.3

44.0

40.8

47.1

12.0

0.50

22.9

18.9

12.9

45.3

42.9

32.9

24.2

0.75

23.6

9.7

19.9

46.7

44.1

17.5

38.4

1

24.4

0

27.4

48.2

46.3

0.4

53.3

a Because

SiO2 is removed by reacting with HCl solution, the current ICP analysis results

report those of Na2O, Al2O3, and B2O3.

35

Table 2. Nominal compositions (weight %) and ICP analyses of NaAlSi3O8-NaBSi3O8 glasses (Top: non-enriched, Bottom: 17O-enriched). XRd is the mole fraction of the reedmergnerite component. Composition (non-enriched) XRd

wt% (ICP analysis)

Na2O

Al2O3

B2O3

SiO2

Na2O

Al2O3

B2O3

0

11.8

19.4

0

68.7

38.7

61.3

0

0.10

11.9

17.6

1.3

69.2

39.5

56.7

3.9

0.25

12.0

14.8

3.4

69.8

40.4

48.6

11.1

0.50

12.2

10.0

6.9

70.9

42.6

34.9

22.5

0.75

12.4

5.1

10.4

72.1

45.9

17.6

36.6

1

12.6

0

14.2

73.3

49.8

0

50.2

Composition (17O-enriched) XRd

wt% (nominal composition)

wt% (nominal composition)

wt% (ICP analysis)

Na2O

Al2O3

B2O3

SiO2

Na2O

Al2O3

B2O3

0

11.7

19.2

0

69.2

39.8

60.2

0

0.25

11.9

14.8

3.4

69.9

41.7

49.0

9.3

0.50

12.1

10.0

6.9

71.0

43.2

36.0

20.8

0.75

12.3

5.1

10.5

72.1

42.6

18.8

38.6

1

12.4

0

13.9

73.6

49.4

0.1

50.5

a Because

SiO2 is removed by reacting with HCl solution, the current ICP analysis results

report those of Na2O, Al2O3, and B2O3.

36

Table 3. The calibrated fraction (%) of oxygen configurations of NaAlSiO4-NaBSiO4 (top) and NaAlSi3O8-NaBSi3O8 (bottom) glasses with varying XMa and XRd, respectively. KSi-O-Al, KSi-O-B, and KB-O-Al are also shown. Composition

XMa 0

0.25

0.50

0.75

1

Al-O-Al

27 ± 3

11 ± 3

0

0

-

Si-O-Al

64 ± 3

50 ± 5

43 ± 5

20 ± 5

-

Si-O-Si

9±3

13 ± 3

18 ± 3

21 ± 3

25 ± 3

Si-O-B

-

7±3

14 ± 3

24 ± 3

38 ± 3

B-O-B

-

4±3

7±3

14 ± 3

15 ± 3

Na-O-Si

0

15 ± 5

18 ± 5

21 ± 5

22 ± 5

KSi-O-Al

16.3

18.1

-

-

-

KSi-O-B

-

1.1

1.6

2.0

4.0

KB-O-Al

-

0

0

0

-

Composition

XRd 0

0.25

0.50

0.75

1

Al-O-Al

0

0

0

0

-

Si-O-Al

60 ± 3

45 ± 5

30 ± 3

14 ± 3

-

Si-O-Si

40 ± 3

39 ± 3

43 ± 3

45 ± 3

48 ± 3

Si-O-B

-

9±3

13 ± 3

22 ± 3

31 ± 3

B-O-B

-

3±3

4±3

6±3

8±3

Na-O-Si

0

4±5

10 ± 5

13 ± 5

13 ± 5

KSi-O-Al

-

-

-

-

-

KSi-O-B

-

0.7

1.0

1.9

2.3

KB-O-Al

-

0

0

0

-

37

Figure captions Fig. 1. (A) 11B MAS NMR spectra [collected at 9.4 T (left) and 14.1 T (right)] for NaAlSiO4NaBSiO4 glasses with varying XMa = 0.25, 0.50, 0.75, and 1 with simulated peaks corresponding to [3]B and [4]B, as labeled. (B) 11B 3QMAS NMR spectra for NaAlSiO4NaBSiO4 glasses with various XMa. Contour lines in the spectrum for glasses with XMa = 0.25 are drawn in 5% intervals from relative intensities of 13~93% with lines added at 5% and 10%. Contour lines for the spectra with XMa = 0.50, 0.75, and 1 are drawn in 5% intervals from relative intensities of 8~93% with lines added at 2.5% and 5%. (C) 11B MAS NMR spectra [collected at 9.4 T (left) and 14.1 T (right)] for NaAlSi3O8-NaBSi3O8 glasses with varying XRd = 0.25, 0.50, 0.75, and 1 as labeled. (D) 11B 3QMAS NMR spectra for NaAlSi3O8-NaBSi3O8 glasses with varying XRd. Contour lines in the spectrum for glasses with XRd = 0.25 are drawn in 5% intervals from relative intensities of 8~98% with line added at 5%. Contour lines for the spectra with XRd = 0.50, 0.75, and 1 are drawn in 5% intervals from relative intensities of 8~93% with lines added at 2.5% and 5%. (E) 11B MAS NMR spectra collected at 14.1 T for NaAl1-xBxSiO4 and NaAl1-xBxSi3O8 glasses with varying x [= B/(B+Al)] = 0.50 and 0.75. Note that the thick black lines in the 11B MAS NMR spectra collected at 9.4 T refer to the experimental data. The thin black lines refer to the total simulation results. Fig. 2. The fraction of [4]B species in NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 glasses with varying B/(B+Al) ratios from 11B MAS NMR spectra collected at 14.1 T, as labeled. The red squares refer to the fraction of [4]B species in NaAlSiO4-NaBSiO4 glasses estimated from 11B MAS NMR spectra collected at 14.1 T. The blue circles refer to the fraction of [4]B species in the NaAlSi3O8-NaBSi3O8 glasses estimated from 11B MAS NMR spectra collected at 14.1 T. The error bars were estimated from the uncertainty in sample composition, the contribution of spinning side bands, phasing parameters in the NMR spectra, and NMR processing conditions. Fig. 3. (A) Total isotropic projections of the 27Al 3QMAS NMR spectra for NaAlSiO4NaBSiO4 glasses with varying XMa [= NaBSiO4/(NaBSiO4+NaAlSiO4)]. Regarding NaAl0.25B0.75SiO4 glasses, the isotropic projection is also shown (scaled by a factor 15) to better resolve [5]Al. (B) Total isotropic projections of the 27Al 3QMAS NMR spectra for NaAlSi3O8-NaBSi3O8 glasses with varying XRd [= NaBSi3O8/(NaBSi3O8+NaAlSi3O8)], as labeled. (C) Total isotropic projections of the 27Al 3QMAS NMR spectra for NaAl1-xBxSiO4 (in black lines) and NaAl1-xBxSi3O8 (in blue lines) glasses compared with varying B/(B+Al)

38

and Si/(B+Al) ratios. The dashed lines show the positive shift of peak position of [4]Al species with increasing Si/(B+Al) ratio from 1 to 3 at the same B/(B+Al) ratio. Fig. 4. 17O 3QMAS NMR spectra for NaAlSiO4-NaBSiO4 and NaAlSi3O8-NaBSi3O8 glasses at 9.4 T with varying XMa [= NaBSiO4/(NaBSiO4+NaAlSiO4)] and XRd [= NaBSi3O8/(NaBSi3O8+NaAlSi3O8)], as labeled. Contour lines in the spectrum for glasses with XMa = 0 are drawn in 5% intervals from relative intensities of 13~88% with lines added at 1%, 3%, 5%, and 9%. Contour lines for the spectra from glasses with XMa = 0.50 and 1 are drawn in 5% intervals from relative intensities of 8~88% with lines added at 2%, 4%, and 6%. Contour lines for the spectra with XRd = 0 are drawn in 5% intervals from relative intensities of 7~97% with lines added at 2.5%. Contour lines for the spectra with XRd = 0.50 and 1 are drawn in 5% intervals from relative intensities of 2~97%. Fig. 5. Total isotropic projections of 17O 3QMAS NMR spectra for NaAlSiO4-NaBSiO4 glasses with varying XMa [= NaBSiO4/(NaBSiO4+NaAlSiO4)] with simulated peaks corresponding to distinct oxygen configurations, as labeled. The detailed simulation parameters are shown in Table S3. Fig. 6. Total isotropic projections of 17O 3QMAS NMR spectra for NaAlSi3O8-NaBSi3O8 glasses with varying XRd [= NaBSi3O8/(NaBSi3O8+NaAlSi3O8)] with simulated peaks corresponding to oxygen configurations, as labeled. The detailed simulation parameters are shown in Table S4. Fig. 7. (A) Variation of Na-O-Si and BOs fractions in boron-bearing nepheline glasses with varying boron content (XMa). (B) Variation of Na-O-Si and BOs fractions in boron-bearing albite glasses with varying boron content (XRd). The fractions were obtained from the simulation results of the total isotropic projections from 17O 3QMAS NMR spectra collected at 9.4 T. The red squares refer to the population of Na-O-Si. Violet and brown circles refer to those of Al-O-Al and Si-O-Al, respectively. Black circles refer to the population of Si-O-Si. Gray and blue circles refer to the population of Si-O-B and B-O-B, respectively. The uncertainty in chemical composition was estimated based on the difference between nominal composition and the composition from ICP analyses in Tables 1 and 2. The uncertainty in peak area (intensity) of 17O NMR spectra was estimated by changing the NMR processing conditions and phasing parameters. Fig. 8. A schematic atomic structure of boron-free (A) and boron-bearing (B) sodium aluminosilicate glasses. Na* refers to the charge-balancing Na. NBO refers to the nonbridging oxygen in Na-O-Si. 39

Fig. 9. (A) The dissolution rate of boron in NaAlSiO4-NaBSiO4 glasses with varying B-O-B fraction and B/(B+Al) ratio. (B) The dissolution rate of sodium in NaAlSiO4-NaBSiO4 glasses with varying Na-O-Si and B/(B+Al) ratio. The pale blue shadows show a threshold boron content, above which the B-O-B bonds are spatially well-connected resulting in the drastic increase in the dissolution rate of B and Na in NaAlSiO4-NaBSiO4 glasses. Note that the fractions of the B-O-B and Na-O-Si were estimated from the trend lines obtained from Fig. 7A. The measured dissolution rates of boron and sodium were taken from a previous study (Pierce et al., 2010). Fig. 10. 11B MAS NMR spectra for 1.33 wt% B2O3 of NaAl0.9B0.1Si3O8 glasses collected at 14.1 T. Fig. 11. (A) Interpolated proportion of [4]B in Na-aluminoborosilicate glasses with B/(B+Al) and Si/(B+Al) ratios. Here, [4]B populations between the experimental data points were estimated from the interpolated fractions in Fig. 2. (B) The proposed trend of δ11Bmelt of sodium aluminoborosilicate glasses and melts with varying B/(B+Al) and Si/(B+Al) ratios based on Eq. 6. (C) δ11B values in various geological reservoirs (Boschi et al., 2008; Chaussidon and Albarède, 1992; Foster et al., 2010; Harvey et al., 2014b; Ishikawa and Nakamura, 1993; Marschall et al., 2017; Smith et al., 1995; Spivack and Edmond, 1987; Tonarini et al., 2011).

40

Fig. 1AB

41

Fig. 1CD

42

Fig. 1E

43

Fig. 2

44

Fig. 3

45

Fig. 4 46

Fig. 5

47

Fig. 6

48

Fig. 7

49

Fig. 8

50

Fig. 9

51

Fig. 10

52

Fig. 11

53