Introduction

Magmatic melts and fluids provide important means of advective heat and chemical transfer from the mantle to the crust and to the surface, namely in subduction zones (e.g. Hawkesworth et al. 1997). Understanding the mechanisms and origins of fluid release from magmas is crucial for deciphering the variability in trace elements within arc magmas associated with subduction zones. To that effect, stable isotope systems, including non-traditional isotopes, have been used to characterize fluid-mediated processes taking place at high-temperature (Cu and N, Busigny et al. 2018; W, Kurzweil et al. 2019). Among the stable isotope inventory, boron (B), an incompatible and lithophile element, is enriched in both melts and fluids. During fluid-rock interaction at metamorphic and igneous temperatures, boron elemental and isotope variations have been used as tracers of fluid-mediated metasomatism during metamorphism (Moran et al. 1992; Smith et al. 1995; Marschall et al. 2006; e.g. Marschall et al. 2017) and are used to differentiate between melting and fluid mobilization (Schmitt et al. 2002; Kaliwoda et al. 2011; Sugden et al. 2020). Furthermore, B isotope data from oceanic basalts have been used to estimate the δ11B of their mantle sources (Chaussidon and Jambon 1994; Marschall et al. 2017; Hartley et al. 2021; Walowski et al. 2021). For example, Chaussidon and Jambon (1994) derived a δ11B of -7 ± 1‰ from analyzed oceanic basalt glasses and find it to be representative of the upper mantle; Marschall et al. (2017) constrained the δ11B of the depleted upper mantle to be identical to that of the primitive mantle, and to the average MORB (δ11B = -7.1 ± 0.9‰). Walowski et al. (2021) found a limited variation in the δ11B of unaltered worldwide ocean island basalts (OIB), and give a range of δ11B from – 12 to – 5‰ for the mantle sources of different OIB. In order to address the potential modification of the B isotope signature of a magma as it departs the mantle source, one must first understand the mechanisms that can change the B isotope composition of a magma. Following stable isotope theory (e.g. Schauble 2004), the high-mass isotope prefers an environment with higher bond strength and thus a lower coordination number compared to the low-mass isotope. Accordingly, the two stable isotopes of boron, 10B and 11B, prefer the tetrahedral [B[IV]O4] and the trigonal [B[III]O3] species, respectively. Indeed, B isotope fractionation is predominantly driven by the coordination of their respective species. Consequently, 10B, preferentially hosted in [BO4] complexes, is enriched in melts in equilibrium with a hydrous fluid, leading to an enrichment of isotopically light B in the silicate melt and isotopically heavy B (enriched in 11B) in the coexisting hydrous fluid, where predominantly [III]-fold coordinated B is present (London et al. 1988; Li et al. 2021).

As with any other stable isotope system, equilibrium fractionation of B isotopes increases with decreasing temperature. Consequently, existing experimental and modeling studies focused on temperatures ≤ 1100 °C (Hervig et al. 2002; Rustad et al. 2010; Kowalski et al. 2012; Maner and London 2018), and B isotope data for magmatic systems at higher temperature are scarce. However, the knowledge of high-temperature B isotope fractionation during melt-fluid interaction is crucial to understand the high-temperature end of the B isotope cycle. Namely, if a basaltic magma experiences fluid-saturation and degassing at higher temperatures, then it is essential to understand to what extent B isotopes may be fractionated by this process. Doing so has bearing on our ability to constrain the B isotope composition of the mantle sources of fresh basaltic lavas, especially those more prone to fluid-saturation, such as, for example, arc lavas. Moreover, there may be a large analytical uncertainty on published data on high-temperature boron isotope fractionation, because the expected boron isotopic variations were close to the analytical resolution in some older studies. For example, three experiments carried out using a basaltic composition at 1100 °C by Hervig et al. (2002) display non-resolved or barely resolvable B isotope fractionation between melt and fluid. Rhyolitic compositions of the same study display a lighter B isotope composition compared to the starting material but were also performed at lower temperatures (800 ± 50 °C). Maner and London (2018) ran further experiments at lower temperatures (850 to 650 °C) to determine melt-fluid boron isotope fractionation between granitic melts and aqueous fluids (Δ11Bmelt−fluid) and recorded (Δ11Bmelt−fluid values ranging from − 3 to −16‰. Yet, their experimental results show a lot of variability of B isotope fractionation at a given temperature.

An extrapolation of the experimental calibration of Hervig et al. (2002) predicts that melt–fluid equilibrium is expected to result in minor but resolvable B isotope fractionation at higher temperatures (i.e. >1000 °C; see Marschall et al. 2017). This extrapolation is in broad agreement with ab-initio models, which predict melt-fluid fractionation in the range of -2 ± 1‰ for igneous temperature above 1100 °C (Sanchez-Valle et al. 2005; Li et al. 2020, 2021). Consequently, in this contribution we investigated experimentally the B isotope fractionation in fluid-saturated MORB compositions at high temperatures. Starting compositions also contained a suite of fluid-mobile and immobile trace elements to potentially combine trace-element distributions with B isotope systematics. To improve the quality of the analytical resolution, we used state-of-the-art methods to analyze boron isotopes in the glasses from these experiments.

Experimental and analytical approach

Starting materials

Boron backgrounds (reagents)

Monitoring potential B contamination and its mitigation is crucial for precise and accurate B isotope determination, especially since B contamination was traced in various materials that are commonly present during sample preparation, from polishing pastes to laboratory air filters (Shaw et al. 1988; Marschall and Ludwig 2004; Rosner et al. 2005). The boron background of the reagents used in this study (concentrated HNO3, purified using a sub-boiling quartz distill and Millipore ultrapure water) were determined via ICP-MS (single collector, see below). Approximately 50 mL of reagent (MQ and distilled 14 M HNO3) were filled into a 90 mL Savillex beaker and gently evaporated to dryness over a period of 4 days. In addition, an empty 90 mL beaker was placed next to these blank solutions to monitor the fume hood background. After dryness, 2 mL of 0.5 M HNO3 (run solution) was added to each beaker, the beakers were closed and left on the hot plate at 90 °C for 3 days. After cooling, samples were transferred into 5 mL Eppendorf tubes and measured on the Element XR sector field ICP-MS. Concentrations were determined via standard addition and showed B concentration in the solutions and fume hood to be below 1 µg/mL. Compared to the intended B concentration of ∼ 8000 µg/mL of the stock NIST-SRM951a solution even the addition of 1 µg/mL B of a fictive contaminant with an extreme B isotope composition (+ 100‰) would result in a less than 0.02‰ offset from the real value and is thus negligible. The mitigation strategy for B contamination during preparation is described in the next section.

Preparation of NIST-SRM951a isotope reference material and starting glass

A 5.03 g aliquot of reference material NIST-SRM951a (H3BO3) was weighed in a 125 mL PFA bottle (thoroughly precleaned with 1:1 mixtures of MQ and concentrated acids and acid mixtures, specifically HNO3, HNO3 + HF, HCl + HF, HCl, MQ, for 24 h each, in that order) and dissolved in 115 mL 5% HNO3 resulting in a final B concentration of ∼ 7800 µg/mL.

The initial major-element composition of the starting material was aimed to be close to the average N-MORB composition from White and Klein (2014) and the oxide powders were weighed accordingly. In order to better monitor B mobility, the starting material was doped with aliquots of Alfa Aesar trace-element reference solutions containing elements of varying (in)compatibility and fluid mobility (La, Ce, Sm, Y, Rb, Ba, Pb, Th and Lu) aimed at a final concentration of ∼ 100 µg/g each. An aliquot of the prepared NIST-SRM951a solution was added to achieve a B concentration in the MORB powder of ∼ 450 µg/g. This relatively high concentration limits the effect of B contamination during experimental runs and sample preparation. The dried materials were ground to a fine powder in an agate mortar and transferred into a Pt crucible, previously annealed at 900 °C to close micro fissures. The mixture was then molten in a box furnace at 1600 °C, quenched, re-ground in a steel mortar, and further homogenized by grinding it again in a ball mill. The finely-ground materials were then transferred once again into the box furnace. These steps were repeated three times in total to ensure homogenization of the starting materials, the NIST-SRM951a-doped starting material is henceforth called MORB + B. Fifteen pieces of the final glass were embedded in epoxy resin to serve as a reference material during laser ablation (LA) measurements. Additionally, a piece of B-free Herasil SiO2 glass was added to the mount to serve as a sample preparation blank (following Marschall and Ludwig 2004). Major-element homogeneity was verified via microprobe analysis (see below). This mount was used as a reference material during all trace-element and isotope measurements. One large piece of starting material was kept in reserve, while the remaining material (7–8 g) was ground in a steel mortar to a fine powder.

Experimental approach and conditions

Capsules prepared from Au80Pd20 tubing (2.6 mm inner diameter, 3.0 mm outer diameter, 10–20 mm length), were annealed at 950 °C for ten minutes to sinter any micro fissures that may have been present and were subsequently welded shut on the bottom side using a Lampert PUK 3 Professional arc welding device. Afterwards, ultrapure MilliQ water and glass powder were added in varying proportions to the capsules. After each step, the weight of the capsules was recorded. To check for water loss, samples were weighed before and after final welding, as well as before and after each experimental run. Experiments with different water to glass ratios were prepared, where the lowest water content was ∼ 16 wt% and the highest ∼ 82 wt%. We opted to use such large variations in water-to-glass ratio because the sampling and analysis of the fluid after the experiments is notoriously difficult. Thus, by strongly changing the water-to-glass ratio, the isotope fractionation can be determined by analyzing the isotopic composition of the glass only and then calculating that of the fluid via mass balance calculations.

Experiments were performed in a vertically oriented internally heated pressure vessel (IHPV) at Leibniz Universität Hannover (Holloway et al. 1992; Berndt et al. 2002). The vessel was pressurized using Ar gas and temperatures were recorded at both ends of the capsule, using S-type (Pt–Pt90Rh10) thermocouples. The temperature gradient between the thermocouples did not exceed 12 °C (± 5 °C). Total pressure was controlled continuously with a calibrated Burster Type 8270-10 pressure transducer (pressure uncertainty of ± 0.5 MPa). Experimental temperatures and pressures ranged from 1000 to 1250 °C and 150 to 250 MPa, respectively (Supplementary Table S1). All experiments were conducted for 48 h at intrinsic fO2 conditions (∼ΔFMQ + 3.3; Schuessler et al. 2008). Experiments were heated to target temperatures with a heating rate of 30–50 C/min. To avoid temperature overshooting, heating rates were reduced to 10 °C/min in proximity (30–50 °C) of the equilibration temperatures. Temperature fluctuations at run conditions were generally below ± 1 °C.

Samples were quenched by dropping the capsule onto a copper block resulting in a high quench rate of up to 150 °C/s (Berndt et al. 2002), under isobaric conditions. The capsules were then opened and glass aliquots were embedded in epoxy resin and polished for further analysis. In order to gauge the possibility of B contamination during preparation, a piece of ultra-pure herasil® SiO2 glass was embedded into half of the epoxy mounts containing samples (see Marschall and Ludwig 2004).

Analytical methods

Major and trace-element analysis

Major-element contents of the experimental glasses were determined using a JEOL JXA-iHP200F field emission electron microprobe hosted at the Leibniz Universität Hannover (LUH). Measurements were performed employing a 15 kV accelerating voltage, 10 nA beam current and 12 μm spot size. Measurement times were 10 s on peak and background positions for all elements. Sodium and potassium were always measured first to mitigate alkali migration during analysis. Well-characterized glass reference materials of basaltic to rhyolitic compositions were used for calibration. Sets of internal basalt glass reference materials were measured to ensure accuracy of the major (and minor) element contents. Calibrations and corrections were done using in-house reference glasses. Water contents of glasses were estimated via the “by-difference approach” (Hughes et al. 2019) by additionally measuring various basaltic glasses with known H2O contents (Shishkina et al. 2010) and establishing a regression line between H2O content and the difference from 100% totals for each analytical session. Since most of our experiments were performed at water-saturated conditions, the expected water concentrations can also be calculated from water solubility data in the pressure range 150–250 MPa (4 to 6 wt.-%, depending on pressure; Shishkina et al. 2010).

fs-LA SC-ICP-MS and MC-ICP-MS

Trace elements of glasses were determined using the Thermo Scientific Element single-collector ICP-MS coupled to the femtosecond (fs) laser ablation system at the LUH. The main advantage of the deep-UV fs-LA method over e.g. nanosecond-LA systems are the negligible thermal effects during ablation (Poitrasson et al. 2003) and the particle distribution of ablated material, which is shifted towards smaller particles (0.01–0.1 μm diameter; Hergenröder et al. 2006). These characteristics result in close to 100% ablation yields, and therefore constant elemental and isotope ratios (Koch et al. 2004; Horn et al. 2006; Hirata and Kon 2008), making this method ideally suited for the precise determination of stable-isotope ratios. Laser ablation was performed by an in-house-built deep UV (196 nm wavelength) fs-laser ablation system based on a low-energy < 100 femtosecond Ti: sapphire seed laser and a high energy Nd: YLF pump laser (Spectra Physics MaiTai and Spectra Physics Empower − 15; Horn and von Blanckenburg 2007). The laser beam is focused onto the sample surface via a modified New Wave (ESL) stage with an optical microscope. Further information on the sample introduction system and ablation chamber used in this study is given in Horn and von Blanckenburg (2007). Reference materials NIST-SRM610 as well as the in-house reference materials (the NIST-SRM951a-doped starting material, MORB + B) were measured before and after sample concentrations were determined. All sample glasses were measured employing a repetition rate of 35 Hz, 65 μm spot size, and an energy density of 2 J/cm2, masses measured were 11B, 29Si (internal standard) 85Rb, 88Sr, 89Y, 137Ba, 139La, 140Ce, 147Sm, 149Sm, 172Yb, 175Lu, 208Pb and 232Th, all in low mass resolution. Data reduction was done offline via the SILLS software packages (Guillong et al. 2008).

Boron isotope measurements were carried out on a Thermo Scientific Neptune Plus MC-ICP-MS, coupled to the same fs-LA system, in low mass resolution mode (m/Δm = 350, defined using the 5–95% intensity window) using a jet-cone–X-cone interface assembly. Low resolution readily achieves enough mass resolving power to identify potential interferences, e.g. 40Ar4+ or 20Ne2+ (le Roux et al. 2004). Instrumental and ablation conditions are given in Table 1. Boron signal intensities of NIST-SRM610, NIST-SRM951a and samples were matched within 10% in signal intensity by adapting the laser repetition rate (∼ 50 Hz for NIST-SRM610 and ∼ 25 Hz for NIST-SRM951a). Signal intensities were high enough to be measured on the Faraday cups and were acquired on the L3 and H3 cups at ∼ 0.150 × 10− 11 A using 1011 Ω amplifiers (= 150 mV on 11B).

Table 1 Ablation and MC-ICP MS parameters during B isotope ratio measurements
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Sequences always started by ∼ 20 alternating measurements of NIST-SRM610 relative to NIST-SRM951a to cleanse any B remaining in the tubing (lowering the background on 11B by approximately 30% from ∼ 9 mV to 6 mV and below), to ensure the absence of significant signal drift and to gauge the accuracy of the method on the specific measurement day. Standard-sample-bracketing was done using the starting material doped with NIST-SRM951a and NIST-SRM610 was used as a secondary reference material for additional quality control. Every sample is bracketed by single measurements of NIST-SRM610 and NIST-SRM951a which allows to accurately monitor signal drift and buffer potential heterogeneities in the refence material, notably NIST-SRM610 (Eggins and Shelley 2002). Acquisition parameters for analysis were set to acquire 160 cycles of 1 s integrations each (see Table 1 for laser and instrument settings). For each measurement spot, the first ∼ 40 cycles of background signal were acquired and subsequently subtracted from the ablated signal offline. Data evaluation was performed offline using a modified spreadsheet macro ‘LamTool’ initially created for different radiogenic isotope systems by Košler (2007). Variations in boron stable-isotope ratios are given relative to the NIST-SRM951a doped glass as δ(11B/10B)NIST951a (in the following referred to as \({{\delta}}^{11}B=\left({{{\delta}}^{11}B}_{sample}/{{{\delta}}^{11}B}_{NIST951a}-1\right)\times1000\)).

Results

Experimental run products

Experimental run conditions and weighing protocols are given in the supplementary information Table S1. Three capsules showed variations when comparing their weight before experiment and after quenching: One capsule (B21_09) lost water during the experimental runs (based on weights before and after run). While the capsule of B22_14 after experiment indicated weight loss, the capsule weight of B22_15 was higher after the experiment. These two capsules were run together as a package and their combined weight after the experiment was 1.2256 g, which is a difference of less than 2‰ relative to their combined weight before the experiment. Water was released during the opening of both capsules. Thus, conditions were fluid-saturated during the IHPV run and the difference in weight was most likely due to alloying between the two capsules. Except for runs B22_011 and 013 (9.6 mg powder to 11.4 mg H2O and 12.1 mg powder to 23.6 mg H2O; see supplements for details), all samples showed homogenous glass (verified via inspection of the mount under optical microscope and during the major-element measurements). Samples B22_011 and 013 yielded crystals with sizes below 10 μm. Crystal formation in the two samples is likely a consequence of the low experimental temperature (1000 °C). The scanning-electron microscope JEOL JSM-6390 A at the LUH was used to confirm the existence of mineral phases in B_22_011 and B_22_013. In both cases, predominantly clinopyroxene and spinel were identified in a glassy matrix, with sporadic amphibole and plagioclase (see the supplementary information of this manuscript for a more in-depth view).

Major and trace elements in glasses

Except for samples B_22_011 and B_22_013, with small crystals in BSE images and clear shifts in their major-element contents relative to the starting bulk composition, the recalculated anhydrous compositions of the glasses are close to or within 5% to that of the dry starting glass (Supplementary Table S2): Apart from Pb loss, which likely resulted from volatile loss during synthesis of the starting material (vitrification at 1600 °C), the incompatible trace elements show little variability, and only a slight positive covariation among them, e.g. Sr in the glass increases with increasing Th (Table S2). Most trace-element concentrations (and their ratios, e.g. La/Yb, not shown) remain broadly constant with their concentration varying between 5 and 10% relative to the starting material. Boron contents decrease with increasing fluid-melt ratio (i.e. the weight ratio of water to sample) and with decreasing temperature.

Boron isotope composition of experimental MORB melts

Accuracy and intermediate precision of B isotope composition

The initial 18 measurements of NIST-SRM610 relative to our B-doped glass yielded an average of -1.19 ± 0.4‰ (2 s.d.) and 34 randomly placed spots on different pieces of NIST-SRM951a-doped MORB glass yielded a tentative precision of ± 0.6‰, suggesting homogenous distribution of B isotopes in the NIST-SRM951a-doped glass within analytical resolution. Given the reported heterogeneity of the NIST-SRM610, especially for B (Eggins and Shelley 2002), we use both NIST-SRM610 and our (NIST-SRM951a-doped) MORB + Bas bracketing reference materials. Intermediate precision is constrained by 173 measurements of MORB + B (i.e. NIST-SRM951a) and 138 measurements of NIST-SRM610, resulting in an intermediate precision for MORB + B of ± 0.68‰ (2 s.d., 95% c.i. = 0.03‰). The δ11B of the NIST-SRM610 after 138 measurements relative to MORB + B yields an average value of -1.36 ± 1.01‰ (2.s.d, 95% c.i. = ±0.04‰), which is indistinguishable from values reported by Fietzke et al. (2010; NIST-SRM610 = -0.55 ± 1.06‰ (2 s.d.); n = 16) and Kasemann et al. (Kasemann et al. 2001 grey symbols, -0.78 ± 0.70‰,- P TIMS and − 1.31 ± 0.68‰, NTIMS) and with solution studies by le Roux et al. (2004; not shown). Intermediate precision is likely better than the value of ± 0.68‰ based on the reproducibility of MORB + B, which is ± 0.6‰, based off our initial characterization of the MORB + B Fig. 1.

Fig. 1
figure 1

Precision and accuracy of the isotope measurements represented by box-and-whisker plots of MORB + B (NIST SRM951a, blue) and NIST SRM610 (green), averages are shown in the green shaded area. Diamond symbols represent δ11B values for NIST SRM610 by Kasemann et al. (2001; grey, -0.78 ± 0.70‰, P-TIMS and black, -1.31 ± 0.68‰, N-TIMS), circle symbol represents datum by Fietzke et al. (2010; -0.55 ± 1.06‰). Each set of shaded NIST SRM610 and MORB + B (NIST SRM951a) represent a measurement day, ∼ 10–15 h of sequence time. Data were collected over the course of 6 months. Separate blue and green rectangles represented the average values ± 95% c.i. Boxes represent the upper and lower quartiles; whiskers represent the 2 s.d. range

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Boron contamination during sample preparation was monitored via the addition of a piece of ultra-pure herasil SiO2 glass to every second to third mount. Determined B blanks of these glasses are barely higher than the measured background signal (< 6 µg/g), precluding significant B contamination during preparation (see Fig. 2).

Fig. 2
figure 2

Typical B backgrounds of a Herasil SiO2 glass blank and a MORB + B measurement, given are measured and blank-corrected (= absolute) intensities for a Herasil SiO2 glass blank and the prior MORB + B. During ablation on Herasil, the 11B signal increased from 8 mV to 9 mV. Background-corrected 11B intensity of the preceding NIST SRM610 (measured at 125 Hz) yielded 90 mV signal, compared to 1.6 mV on 11B (Herasil). The B concentration of the specific NIST SRM610 (via B/Ca) was 307 µg/g. The B content of Herasil can thus be estimated to be well below 6 µg/g

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Boron isotope analysis of materials with low B contents suffer from an interference from scattered ions (potentially Ca) on the Faraday detectors in Thermo Scientific Neptune instruments, specifically via a ghost peak signal on 10B (Standish et al. 2019; Evans et al. 2021). Such artifacts are likely negligible in our experiments because of the comparatively high B contents of the run-product glasses (100–400 µg/g compared to the 21 µg/g in Standish et al. (2019), which is an approximately 5–20 times higher B concentration). Nevertheless, in order to confirm this, we take advantage of simultaneous determination of B isotope ratios and B/Ca using an OceanInsight high-sensitivity Maya 2000 Pro spectrometer connected to a custom-built injector. See Kaczmarek et al. (2015) and the supplements for further information and method description. No systematic variation of δ11B and B/Ca or 11B/Ca suggests that our B isotope compositions are unaffected by the previously observed artifacts (see Figure S2 a and b).

Boron isotope composition of experimental MORB melts

Initial tests with low fluid-melt ratios (∼ 0.2, henceforth ff/m) yielded δ11B for the silicate glass that did not differ significantly from the bulk starting compositions (experiments B_21_06 to B_21_09). Increasing ff/m to values above 0.4 resulted in more negative δ11B for the glass, with δ11B as low as -1.5‰, as more B partitioned into the fluid. Experiments with varying P and T were all done with ff/m close to 0.5, 1 and 2 (Fig. 3a-c). Experiments performed at different pressures resulted in δ11B values for the glass of approximately − 1 ± 0.5‰, regardless of dissolved water content (Fig. 3a). The highest-T experiments were performed at 1250 °C. The water-bearing experiment B_22_005 yielded a δ11B of -0.7‰ (fluid/melt of 1.8), the dry experiment is identical within uncertainty to MORB + B. Decreasing temperature leads to a higher degree of isotope fractionation, resulting in a glass composition down to δ11B of approximately − 2‰ (Fig. 3b). Similarly, increasing the amount of water, increases the degree of B isotope fractionation (Fig. 3c).

Fig. 3
figure 3

Boron isotope composition of of each experiment result (glass fraction). Data is ordered by experimental campaigns: (a) temperature, (b) pressure and (c) ff/m. Uncertainties given are the 95% c.i. of at least 5 spots for every sample. Intermediate precision (see 3.3.1.) is likely better then ± 0.68‰. Different colors or symbols represent different P and T conditions

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Table 2 Experimental run conditions and B isotope composition of synthetic MORB glass. Water loss during experiment was determined by the weight difference of the capsule before and after the experimental run. The number of individual measurements (i.e. spots) of the glass is given by n. Boron concentration determined via (fs-LA) SC-ICP-MS. fO2 at intrinsic conditions of the IHPV, ∼ ΔFMQ + 3.3
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Discussion

Pressure and temperature effects on the B isotope composition of synthetic melts

A first order observation from our dataset is that irrespective of pressure and temperature, fluid saturation leads to melt-fluid B-isotope fractionation on the order of ∼ 1‰. Water solubility in silicate melts is known to increase with pressure (Shishkina et al. 2010), however, changing pressure did not result in a systematic variation of the δ11B of the glass (Fig. 4a). This result is unsurprising as it has been shown that B coordination in silicate melt only begins to change at pressures above 500 MPa leading to potential changes in melt-fluid boron fractionation factors. This is largely thought to be the result of the stabilization of [B(OH)4]− complexes relative to [B(OH)3]0 in hydrous fluid with increasing pressure (Schmidt et al. 2005). In our experiments, which were carried out between 150 and 200 MPa, B coordination in silicate melt is not expected to change, which is consistent with the lack of correlation between pressure and the δ11B from the glasses recovered in our experiments. Therefore, the amount of water dissolved in MORB (Fig. 4b) is likely clustered too closely to produce resolvable differences in the δ11B of the basaltic glass.

Fig. 4
figure 4

Boron isotope composition (a) and dissolved water content (b) vs. experimental run pressure. Data broadly overlaps with the calibration curve of Shishkina et al. (2010). The uncertainty of the water content is assumed to be ± 1 wt.-%, even if the statistical, propagated uncertainty is likely overestimated

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It follows that the amount of water dissolved in the MORB glass does not affect the B isotope composition in the observed pressure range under H2O-saturated conditions.

Decreasing temperature results in larger B isotope fractionation, well in agreement with other experimental data and modeling (e.g. Kowalski and Wunder 2018; Maner and London 2018; Li et al. 2020; Li et al. 2021). Our data reveal two major findings: first, inasmuch as temperature dependence is concerned, our dataset is slightly offset to higher Δ11Bmelt−fluid compared to Hervig et al. (2002). Maner and London (2018) report similar Δ11Bmelt−fluid as calculated here at similar temperatures, albeit with a large variability (up to -4‰ at a given temperature), and for rhyolitic compositions. Secondly, our data clearly show that significant melt-fluid B isotope fractionation is expected at magmatic temperatures (1250 and 1200 °C, Fig. 5), in the range of -0.5 to -1‰, relative to the bulk isotope composition of the experiment. Our results confirm the evolution that was expected from the extrapolation of the Hervig et al. (2002) dataset to higher magmatic temperatures as previously proposed by Marschall et al. (2017).

Fig. 5
figure 5

Degree of boron isotope fractionation vs. 106/T2. Given that the experiments in e.g. Hervig et al. (2002) were doped with NIST-SRM951a as well, our data can directly be compared through the relationship 1000 ln a ≈ Δ11Bmelt-fluid. Uncertainty for our data is smaller than the symbols in most cases. See the next section for the calculation if Δ11Bmelt-fluid. Colored areas and fine red lines represent the 95% c.i. of the regression lines

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We determined three regressions to express Δ11Bmelt−fluid as a function of temperature, first exclusively based on our data, second exclusively based on Hervig et al. (2002) data and third by combining the data sets of the two studies\(\::\)

$${\Delta}^{11}{B}_{melt-fluid}=3.5213-11.0206\frac{{10}^{6}}{{T}^{2}};{R}^{2}=0.550,$$
(1a)

this study,

$${\Delta}^{11}{B}_{melt-fluid}=2.039-9.040\frac{{10}^{6}}{{T}^{2}}{;R}^{2}=0.914$$
(1b)

Hervig et al. (2002) and

$${\Delta}^{11}{B}_{melt-fluid}=2.913-9.693\frac{{10}^{6}}{{T}^{2}};{R}^{2}=0.910$$
(1c)

both studies.

Boron partitioning, isotope fractionation, and the influence of fluid-melt ratio

Our data reveal a systematic decrease in δ11B with increasing ff/m (Fig. 6a), which is coupled to the decrease of δ11B with decreasing B concentration in the melt (Fig. 6b). Considering that B was only present in the starting glasses but not in the added water, a simple mass balance calculation involving B concentration and sample mass shows that a decrease of B in the silicate melt is expected with increasing ff/m, if some boron is incorporated into the fluid. Such a mass-balance calculation can also be used to estimate the partitioning of B between melt and fluid in natural systems.

Fig. 6
figure 6

Boron isotope composition of synthetic MORBs versus the mass ratio of fluid to dry glass powder (melt) in the experiments (a) and boron concentration in the glass (b). The starting material is fluid free and is shown in Figure a) as a reference

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Following the approach of earlier studies (Hervig et al. 2002; Maner and London 2018), we can use mass-balance calculations based on the known melt and fluid masses in the experimental charges and the trace-element concentration in glasses, specifically that of boron, to determine the B fluid/melt partition coefficient (\({D}_{B}^{fluid/melt}\)). This can be achieved via the following mass-balance relations:

$${\left[B\right]}_{bulk}={\left[B\right]}_{melt}\cdot{f}_{sample}+{\left[B\right]}_{fluid}\cdot\left(1-{f}_{sample}\right)$$
(2)

where \({f}_{sample}={m}_{sample}/\left({m}_{sample}+{m}_{fluid}\right)\), and

$${D}_{B}^{fluid/melt}={\left[B\right]}_{fluid}/{\left[B\right]}_{melt}$$
(3)

In a similar fashion, the B isotope fractionation between melt and fluid (Δ11Bmelt−fluid) can be estimated according to:

$${\delta ^{11}}{B_{bulk}} = {{\left( \matrix{{\delta ^{11}}{B_{melt}} \cdot {\left[ B \right]_{melt}} \cdot {f_{sample}} \hfill \cr + {\delta ^{11}}{B_{fluid}} \cdot {\left[ B \right]_{fluid}} \cdot \left( {1 - {f_{sample}}} \right) \hfill \cr} \right)} \over {{{\left[ B \right]}_{bulk}}}}$$
(4)
$${{\Delta}^{11}B}_{melt-fluid}={{\delta}^{11}B}_{melt}-{{\delta}^{11}B}_{fluid}$$
(5)

The low water contents in the first set of experiments appear to preclude enough B mobilization so that B concentrations in glasses were within the analytical uncertainty of the starting material (see, for example, sample B_21_06). Mass-balance calculations include here a large propagated uncertainty into the modeled B concentration of the fluid and hence yield inaccurate modeled B concentration (see Fig. 7). Apart from that, B is shown to be consistently fluid mobile, and all experiments have \(\:{D}_{B}^{fluid/melt}\) above unity with an average value of 2.3 ± 2.0 (2 s.d., 95% c.i. = 0.6; n = 13 experiments). An exception is sample B_21_09, which experienced water loss during the run.

This partition behavior differs from data obtained for basaltic melts by Hervig et al. (2002), who found B to be preferentially enriched in the melt in their experiments, with \(\:{D}_{B}^{fluid/melt}\) only exceeding unity for rhyolitic compositions.

The degree of isotope fractionation (Δ11Bmelt−fluid) between melt and fluid is on average − 1.7 ± 0.9‰ (2 s.d., 95% c.i. = 0.3; 13 experiments, see Fig. 7). The findings of our study align closely with the projections made by Hervig et al. (2002). Despite the considerable uncertainties associated with their high-temperature experiments (conducted at 1100 °C), the temperature calibration of Hervig et al. (2002) anticipated a Δ11Bmelt−fluid of up to -3‰ at 1100 °C. Our independently calculated Δ11Bmelt−fluid for the same temperature is -2.2 ± 0.5‰, falling well within the range of uncertainty indicated by Hervig et al.‘s predictions. The observed variation might stem from the use of distinct analytical methods in our investigation (specifically, LA-fs-MC-ICP-MS) as opposed to the approach employed by Hervig et al. (2002; secondary ionization mass spectrometry – SIMS, using a small-radius instrument, Cameca ims6f). This methodological improvement over the past two decades could perhaps explain the systematic offset in the calculated Δ11Bmelt−fluid values derived from the two datasets. However, based on the current data we are not able to further evaluate this apparent offset.

Fig. 7
figure 7

Boron isotope composition of experimental melts and modeled fluids using Eqs. 2 and 3 and data from Table 2. Open symbols are the calculated fluid compositions (Table S3), with the same shape and color corresponding to the measured experiments (filled symbols)

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Our data demonstrate that resolvable B isotope fractionation is present over all conditions studied (150 to 250 MPa, 1000 to 1250 °C, ff/m between 0.6 and 8). For experiments with ff/m between 1 and 2, the modelled Δ11Bmelt−fluid closely match the calculated values using the equations the previous section. The Δ11Bmelt−fluid determined here are consistent with spectroscopic data from Sanchez-Valle et al. (2005), which yielded a range for Δ11Bmelt−fluid between + 3.0 to + 2.1‰ from 1000 °C to 1250 °C (Sanchez-Valle et al. 2005), as well as an independent estimate of + 2 ± 1‰ as a function of the B[III]/B[IV] for igneous temperature above 1100 °C (Li et al. 2020, 2021). This supports the notion that the subsequently lower B[III]/B[IV] and associated change in average B–O bond length is the driving factor of B isotope fractionation (Kowalski et al. 2012). Most importantly, however, this degree of fractionation needs to be considered when assessing the δ11B of mantle sources of degassed, water-rich basaltic magmas.

Modelling B isotope fractionation of water-rich basaltic melts during degassing

Using our experimental dataset, we model B mobilization and associated isotope fractionation as a function of temperature and fraction of degassing water. We consider only those experiments where the temperature changed and the ff/m was set between 0.4 and 2, to avoid extreme ff/m and large uncertainties associated with [B]fluid. In a first step, we calibrate \(\:{D}_{B}^{fluid/melt}\) as a function of temperature, or more precisely, the reciprocal temperature, with a linear (Eq. 6a) and an polynomial model (Eq. 6b). Equation parameters (see below) are adjusted iteratively to solve for the best fit to the data via minimizing the deviation of observed vs. predicted values (Fig. 8a).

$$\begin{aligned}{logD}_{B}^{fluid/melt}&=2.466\left(1000/T\right)-1.537;{X}^{2}\\ &=0.9988;{R}^{2}=0.581\end{aligned}$$
(6a)
$$\begin{aligned}{logD}_{B}^{fluid/melt}=&\,{3.188\left(1000/T\right)}^{2}-2.059\left(1000/T\right)\\ &+0.063;{X}^{2}=0.9984;{R}^{2}=0.667\end{aligned}$$
(6b)
Fig. 8
figure 8

Calibration of \(\:{\:D}_{B}^{fluid/melt}\)as a function of 1000/T in K (a) and B distribution and isotope fractionation during degassing (b). Green fields and yellow dotted lines in (a) represent 95% c.i. of the regressions. Colored lines in (b) represent the calculated B isotope evolution during degassing at different conditions, see text for details. The inset in (b) shows the δ11B evolution as a function of H2O content

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This iterative approach allows the calculation of \(\:{D}_{B}^{fluid/melt}\)at any given temperature. Using the calibration from Fig. 5, both\(\:{\:D}_{B}^{fluid/melt}\) and Δ11Bmelt−fluid can be calculated for the same temperature. In a second step, we set the initial conditions for the assumed water-rich (10 wt% H2O) basalt (average MORB according to Marschall et al. (2017): [B] = 1.19 µg/g and δ11B = -7.1‰, respectively). Using these parameters, we calculated the B evolution of the basaltic melt and a degassing hydrous fluid using the partitioning data derived from the polynomial model. At 1250 °C, the \(\:{\:D}_{B}^{fluid/melt}\) and Δ11Bmelt−fluid are constrained to 1.22 and − 1.229‰ (corresponding to an α of 1.0012), respectively. Water is now removed from the basalt in steps of 0.1 wt% and B concentration in the melt is modeled by a Rayleigh equation, resulting in a decrease of B concentration in the silicate melt and its increase in the fluid. These concentrations are then used to model the evolution of δ11B assuming Rayleigh fractionation, which is calculated using the above equations and the given parameters (Fig. 8b).

At 1250 °C, the final modelled δ11B of the silicate melt and the fluid after degassing (i.e. water extraction) are − 7.7 and − 6.4‰, respectively. This difference would approach analytical resolution and is consistent with predictions from ab-initio modeling, i.e. fractionation at high T is small, as observed in our 1250 °C experiment. These calculations were repeated for a temperature range between 1200 and 1100 °C (50 °C steps, Table S4), and they show that B isotope fractionation increases with decreasing temperature, as expected (Fig. 8b). Finally, we repeated the same calculations using the lowest δ11B reported for OIB by Waloswski et al. (Walowski et al. 2019, δ11B = −10.5‰, Table S5). Consistently, this result means that the lower the temperature, the larger the difference in δ11B. Our modelled data is a close match to variations observed in Marschall et al. (2017), albeit those samples had low H2O contents. Nevertheless,, B isotope studies in (volcanic) samples with high water contents, e.g. subduction zone related magmas, need to consider the effects of B isotope fractionation during degassing.

Boron coordination and melt depolymerization

Boron isotope fractionation is a function of the B[III]/B[IV] ratio and by extension a function of the average B–O bond strength in melt and fluid. In contrast to the significant boron concentrations in the hydrous fluid (27.5–42.1 wt.-% H3BO3) studied by Schmidt et al. (2005) using spectroscopy, our investigation focuses on comparatively low B concentrations (400 µg/g and below). Consequently, the exploration of B coordination through Raman spectroscopy is prone to high uncertainties. Furthermore, the absence of information on the Raman scattering cross sections of the B species precludes the determination of relative proportions, such as B[III]/B[IV] ratios, as highlighted by Schmidt et al. (2005). The amount of tetrahedrally coordinated B (N4-parameter) is based on nuclear magnetic resonance (NMR) studies and on empirical models in boro-silicate melts (Yun and Bray 1978; Dell et al. 1983; Smedskjaer et al. 2011) and may not be applicable for aluminosilicate melts, such as the ones investigated in this study. Consequently, an alternative approach to assess the role of B[III]/B[IV] is required and may be provided via melt-depolymerization models. These models empirically quantify the number of non-bridging oxygens (NBO) relative to the tetrahedrally coordinated units (T; Mills 1993). Among the tetrahedrally coordinated network formers such as Si4+ and Al3+, B3+ also occurs as trigonally coordinated B3+ plus a bridging oxygen (Schmidt et al. 2005; Wu and Stebbins 2013). If the B[III]/B[IV] changes as a function of B removal, (London et al. 1988; since B[III] is more fluid mobile, Li et al. 2021), then melt-depolymerization models may give insight into B coordination, albeit indirect and qualitative. We thus calculated melt depolymerization parameters, specifically the NBO/T parameters following Mills (1993; Table S6) using the anhydrous compositions (all the while the hydrous compositions yield slightly different NBO and T values, the ratios remain the same). One shortcoming of NBO/T is however that it assumes formal oxidization states to be equal to charge, whereas in a polymerized melt the charge is more likely to be a fractional charge (Moretti 2009). Moreover, in a chemically complex melt the capability of shifting fractional electronic charges from the ligands to the central cation is a function of the melt structure, which in turn affects the polarization state of the ligand itself (Moretti 2009). Optical basicity (Λ), a parameter used in an expanded melt-depolymerization model, better accounts for charge balance by considering these fractional charges (Mills 1993; Duffy 1996; Moretti 2009):

$$\:{\Lambda\:}=\frac{\sum\:{x}_{1}{n}_{1}{{\Lambda\:}}_{element\:1}+{x}_{2}{n}_{2}{{\Lambda\:}}_{element\:2}+\dots\:}{\sum\:{x}_{1}{n}_{1}+{x}_{2}{n}_{2}+\dots\:}$$
(7)

where x is the mole fraction of the major element, n the number of oxygens in the respective.

Both calculated parameters show a steady increase with decreasing B isotope composition, from approximately 0.65 to 0.90 (NBO/T) and 0.54 to 0.59 (Λ, see Table S6 and Fig. 9a-b). Additionally, B/Th and B/Ce are given relative to Λ to monitor the mobilization of B over fluid immobile elements, one highly incompatible (Th) and another of similar incompatibility (Ce) to B. Up to 75% of B is removed from the melt at the most extreme ff/m (up to 8) as illustrated by a steady decrease in B/Th and B/Ce vs. optical basicity from ∼ 5 down to almost unity (Fig. 9c and d). This decrease is consistent with the fluid-induced mobilization of B. Since the degree of B isotope fractionation is intrinsically linked to the B[III]/B[IV] (and by extension the associated change in B–O bond lengths i.e. melt structure), the observed correlation of optical basicity with δ11B implies a variation in B[III]/B[IV]. Assuming that there is no re-arrangement of melt structure and especially B coordination in our experiments, the remaining melt contains more BO4 after extraction of 3-fold coordinated B into the degassed fluid (London et al. 1988; Li et al. 2021), leading to lower B[III]/B[IV] in the silicate melt. Presumably, the lower B[III]/B[IV] of the silicate melt should lead to a larger fraction of longer B–O bonds relative to the shorter bonds, which would drive δ11B to higher values in the co-existing fluid. This qualitative interpretation is consistent with the modelled B isotope fractionation by Kowalski et al. (2012), wherein the heavier δ11B is found in our (modelled) fluid and lighter δ11B in the remaining (measured) melt.

Fig. 9
figure 9

Boron isotope composition vs. optical basicity (a), NBO/T (b) B/Th and B/Ce vs. optical basicity (c) and (d). The y-axis in a and b is the same, as well as the x-axis in a, c and d. The legend gives run conditions as well as an overview over the ff/m (fluid / melt)

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While the accurate determination of B coordination is beyond the scope of this study (e.g. using XANES, Fleet and Muthupari 1999; or nuclear magnetic resonance, Smedskjaer et al. 2011) the correlation between the δ11B values measured in our experiments and melt depolymerization parameters like Λ provide valuables insight into B coordination in the silicate glasses.

These calculated melt-depolymerization parameters indeed show a consistent decrease with B mobilization as exemplified by B/Ce and B/Th. Boron mobilization coupled with the observed decrease in boron-isotope composition and increasing degree of polymerization indicates a steady mobilization of B[III] compared to B[IV], which leads to a putative decrease in B[III]/B[IV].

Conclusions

Increased precision and accuracy of in-situ methods enabled us to quantify the high-temperature B isotope fractionation between basaltic melt and hydrous fluids that was implied in earlier studies (e.g., Hervig et al. 2002). We observe preferential partitioning of boron into the hydrous fluid coexisting with basaltic melt with a \(\:{D}_{B}^{fluid/melt}\) between 1 and 5 irrespective of temperature, pressure and ff/m. Pressure and the associated variation in dissolved water do not affect the degree of B isotope fractionation within analytical resolution. Rather, the experiments consistently yielded a δ11B relative to the starting material of approximately − 1‰, regardless of ff/m and water content. Boron isotope fractionation (between melt and fluid) increases with decreasing temperature (consistent with the results of Hervig et al. 2002; Maner and London 2018) and with increasing ff/m. Yet, even at 1250 °C, the presence of free water leads to a decrease of δ11B in the melt of -0.5 to -1‰, and of up to -2‰ at 1200 °C compared to the starting material. Further mass balance considerations yield an average Δ11Bmelt−fluid of -1.7 ± 0.9‰ over a range of conditions and a more generalized \(\:{\varDelta\:}^{11}{B}_{melt-fluid}=2.913-9.693\frac{{10}^{6}}{{T}^{2}}\) (this study and Hervig et al. 2002). This degree of fractionation is consistent with predictions from modelling studies (Sanchez-Valle et al. 2005; Konrad-Schmolke and Halama 2014; Li et al. 2020, 2021). Most importantly, our observed B isotope fractionation data and the associated Rayleigh distillation modelling implies that simply equating the B isotopic compositions of degassed basaltic magmas with their mantle sources is incorrect and instead, the effects of B isotope fractionation during degassing need to be considered. This is particularly true for samples derived from magmas with higher water content, e.g. in subduction zone related magmas. Specifically, such high fluid-melt ratios potentially occur during the decompression of H2O-rich arc basalts from lower-crustal/mantle regions in superhydrous arc settings. Such magmas already contain a lot of H2O and during (rapid)decompression and the decrease of saturation levels, quite high proportions of fluid will be released (Goltz et al. 2020; Müntener et al. 2021). However, the fluid has to stay in contact with the melt and cannot be allowed to escape the system.