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# Mineral-melt vanadium oxybarometry for primitive arc magmas: effect of hydrous melt composition on fO2 estimates

Saskia Erdmann, Michel Pichavant, Fabrice Gaillard

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Saskia Erdmann, Michel Pichavant, Fabrice Gaillard. Mineral-melt vanadium oxybarometry for primitive arc magmas: effect of hydrous melt composition on fO2 estimates. Contributions to Mineralogy and Petrology, 2024, 179 (4), pp.39. 10.1007/s00410-024-02113-4. hal-04687280

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1 Mineral-melt vanadium oxybarometry for primitive arc magmas:

2 *Effect of hydrous melt composition on fO₂ estimates*

3 *Submitted for publication to Contributions to Mineralogy and Petrology*

4

5 Saskia Erdmann*¹, Michel Pichavant¹, Fabrice Gaillard¹

6

7 (1) Université Orléans, CNRS, BRGM, ISTO, UMR 7327, 45071 Orléans, France

8

9 *Corresponding author. Email: saskia.erdmann@cnrs-orleans.fr; ORCID: 0000-0002-1083-9251

10

11

12 Keywords: Vanadium, oxybarometry, temperature, melt H₂O, primitive arc magma, St. Vincent

13

14 AUTHOR CONTRIBUTIONS

15 All authors contributed to the study conception. Samples were provided by Michel Pichavant. Data

16 collection and analysis were performed by Saskia Erdmann. Data interpretation involved all

17 authors. The draft of the manuscript was written by Saskia Erdmann, while Michel Pichavant and

18 Fabrice Gaillard commented on all versions of the manuscript.

19

20 STATEMENTS AND DECLARATIONS

21 The authors have no relevant financial or non-financial interests to disclose

22
23 **ABSTRACT**

24 If primitive arc magmas are primarily oxidized or if they acquire their oxidizing character during
25 crustal evolution remains debated. Mineral-melt V partitioning is extremely redox sensitive and
26 has the potential to resolve this debate, but critical low-temperature, hydrous experimental
27 partitioning data are limited. We present new experimental V partitioning data for olivine-melt,
28 spinel-melt, and clinopyroxene-melt based on the ≤1200 °C, hydrous basalt phase equilibrium
29 experiments of Pichavant et al. (2002) and Pichavant & Macdonald (2007). Combined with
30 published experimental data, we use our olivine-melt V partitioning coefficients to show that –
31 contrary to previous conclusions – hydrous melt composition, i.e. melt H₂O concentration in
32 addition to the concentration of other melt components, affects V partitioning and thus calculated
33 fO₂, systematically overestimating fO₂ for olivine-melt equilibrated at high melt H₂O concentration.

34 False absolute fO₂ values and false oxidation or reduction trends may be inferred. Based on these
35 findings, we have calibrated a set of new olivine-melt oxybarometers applicable to hydrous arc
36 magmas partially crystallized at ~1025-1350 °C. In a case study on a high-Mg basalt from St.
37 Vincent, Lesser Antilles, we show that olivine-melt V oxybarometry records oxidizing near-
38 liquidus conditions (~QFM+1.8) and possibly limited oxidation (~0.3 log units) during intermittent
39 crustal magma storage.

40

41
42 INTRODUCTION

Most arc magmas are more oxidized than mid-ocean ridge magmas, but it remains debated if their more oxidized character derives from oxidized primary melts or if it results from differentiation at crustal level (Canil 2002; Lee et al. 2005; Mallmann & O'Neill 2009; Kelley & Cottrell 2012; Brounce et al. 2014; Laubier et al. 2014; Grocke et al. 2016; Prytulak et al. 2017; Ulmer et al. 2018; Tang et al. 2018, 2019; Bucholz & Kelemen 2019; Wang et al. 2019). Several whole-rock geochemical models (for V/Sc, Eu/Eu*, Zn/Fe) as well as phase equilibrium experiments have been used to suggest that the majority of mantle-derived magmas initially has an oxygen fugacity ($fO_2$) near the quartz-fayalite-magnetite (QFM) buffer, regardless of their geodynamic origin, and that more oxidized conditions are acquired through fractionation, crustal assimilation, or degassing (e.g., Lee et al. 2005; Mallmann & O'Neill 2009; Ulmer et al. 2018; Tang et al. 2018, 2019). Most mineral-melt oxybarometry, experimental and recent whole-rock geochemical modelling studies, in contrast, support the notion that primitive mantle-derived magmas have variable $fO_2$, where primitive arc magmas are generally more oxidized (commonly ~QFM+0.5 to QFM+3.5) than primitive mid-ocean ridge magmas (commonly ~QFM±0.5) (e.g., Carmichael 1991; Pichavant & Macdonald 2007; Kelley & Cottrell 2012; Brounce et al. 2014; Gaillard et al. 2015; Bucholz & Kelemen 2019). Oxidation of primitive arc magmas through fractionation, crustal assimilation, or degassing is not ruled out, but invoked to be superimposed on relatively oxidized primary melts.

Consensus exists in that accurately constraining the $fO_2$ of primary magmas and their possible redox evolution is critical for resolving the debate and for improving our understanding of Earth's redox reservoirs through time. Vanadium partitioning between minerals and melts is known to be extremely redox sensitive, particularly between ~QFM-5 and QFM+5 (Canil 2002; Lee et al. 2005; Mallmann & O'Neill 2009) and thus over a large $fO_2$ range that covers most estimated
terrestrial magma redox conditions (Gaillard et al. 2015; Righter et al. 2020). A number of mineral-
melt V oxybarometers exists for olivine, clinopyroxene, and spinel (Canil & Fedotchouk 2001;
Mallmann & O'Neill 2013; Shishkina et al. 2018; Wang et al. 2019), which are increasingly
applied, given that V compositions can be easily and rapidly acquired by laser ablation inductively
coupled plasma mass spectrometry and for some minerals by electron microprobe. Existing
experimental V mineral-melt partitioning data are, however, biased towards high-temperature,
anhydrous equilibria. To date, few experimental studies – those of Laubier et al. (2014), Shishkina
et al. (2018), and Wang et al. (2019) – have systematically characterized V mineral-melt
partitioning at relatively low temperatures (≤1200 °C) for compositions approaching those of
primitive arc magmas and at anhydrous to hydrous conditions. To add to the limited database, we
have acquired new partitioning data for olivine-melt, clinopyroxene-melt, and spinel-melt for
hydrous, 1050-1200 °C basalt phase equilibrium experiments of Pichavant et al. (2002) and
Pichavant & Macdonald (2007). Using our and published data, we first test the recent V olivine-
melt, clinopyroxene-melt, and spinel-melt oxybarometers of Mallmann & O'Neill (2013),
Shishkina et al. (2018), and Wang et al. (2019) and then derive a new set of olivine-melt V
oxybarometers for arc magmas, which we apply to constrain $\frac{\text{O}_2}$ and its evolution for a primitive,
high-Mg magma from St. Vincent, Lesser Antilles.

82

## METHODS BACKGROUND

Vanadium can occur in valence states $V^0$, $V^{2+}$, $V^{3+}$, $V^{4+}$, or $V^{5+}$ (Sutton et al. 2005; Wood et al. 2008), with $V^{3+}$ and $V^{4+}$ being the dominant species at terrestrial magma redox conditions (Canil 1997; Lee et al. 2005; Mallmann & O'Neill 2009). In olivine, clinopyroxene, and spinel, $V^{3+}$ is significantly more compatible than $V^{4+}$ (e.g., Canil 1997; Righter et al. 2006; Mallmann & O'Neill
2009; Shishkina et al. 2018; Wang et al. 2019), and olivine/clinopyroxene/spinel-melt V partitioning coefficients therefore strongly decrease with increasing oxidation state, while other intensive parameters also have a minor, but nevertheless relevant effect on mineral-melt V partitioning. Olivine-melt V partitioning coefficients are inferred to increase with decreasing temperature, increasing olivine forsterite content, increasing proportions of melt network formers SiO₂ and Al₂O₃ relative to network modifiers CaO, Na₂O, and K₂O, or decreasing anhydrous melt NBO/T (i.e. the ratio of non-bridging oxygen to tetrahedral cations in the melt) (Mallmann & O'Neill 2013; Wang et al. 2019). Pressure and melt H₂O concentration, in contrast, have been inferred to have no significant effect on V olivine-melt partitioning (Canil & Fedortchouck 2001; Shishkina et al. 2018; Wang et al. 2019). Vanadium partitioning coefficients for clinopyroxene-melt and spinel-melt are inferred to also increase with decreasing temperature and to vary with mineral and melt composition, which in turn are controlled by other variables including pressure (Horn et al. 1994; Toplis & Corgne 2002; Wang et al. 2019; Holycross & Cottrell 2022).

The olivine-melt V oxybarometer of Mallmann & O'Neill (2013) has been calibrated for a large fO₂ range (~QFM-4 to QFM+4), but at high temperature (1200-1530 °C) and anhydrous, atmospheric conditions. Effects of temperature, olivine forsterite content, and melt SiO₂, Al₂O₃, CaO, Na₂O, and K₂O in addition to fO₂ on V partitioning are considered in the calibration, which has an estimated uncertainty of ~0.5 log units at 2σ level. The olivine-melt V oxybarometer of Wang et al. (2019) has also been calibrated for a large fO₂ range (~QFM-4 to QFM+4) and at relatively high temperature (1150-1470 °C), yet for anhydrous to hydrous, low- to high-pressure conditions. Effects of temperature and anhydrous NBO/T in addition to fO₂ on V partitioning are considered in the calibration with an apparent uncertainty of ~0.5 log units at 2σ level (cf. their Fig. S5). The olivine-melt V oxybarometer of Shishkina et al (2018) (equation 4) has been
calibrated for primitive arc magmas crystallized at ≤1250 °C and at hydrous to anhydrous, low- to
intermediate-pressure conditions and for a relatively large fO₂ range (~QFM-2 to QFM+3). Effects
of intensive parameters in addition to fO₂ on olivine-melt V partitioning were not ruled out, but
considered insignificant for the calibration range. The uncertainty of the oxybarometer is estimated
to increase with decreasing V partitioning coefficient (given that V concentrations in olivine
decrease and analytical uncertainties thus increase), ranging between ~0.5 and 1.0 log units at 2σ
level. The clinopyroxene-melt and spinel-melt V oxybarometers of Wang et al. (2019) have been
calibrated for the same fO₂ range (~QFM-4 to QFM+4) as their olivine-melt oxybarometer, also at
high temperature (~1150-1350 °C) and at anhydrous to hydrous, low- to high-pressure conditions.
Effects of temperature and tetrahedral Al (for clinopyroxene) or Cr number (for spinel) in addition
to fO₂ on V partitioning are considered in the calibrations, which have apparent uncertainties of
~0.5 log units at 2σ level (cf. their Fig. S5).

123

124 GEOLOGICAL BACKGROUND

125 Primitive high-Mg basaltic magmas (i.e. primary or near-primary mantle-derived melts) erupt in
126 arcs, but they are not commonplace (e.g. Grove et al. 2012), with some exceptions including the
127 southern section of the Lesser Antilles arc. The Lesser Antilles arc is a mature ocean-ocean
128 subduction zones that extends for ~750 km, resulting from the westward subduction of the Atlantic
129 beneath the Caribbean Plate, which has been active since the early Miocene, following earlier
130 subduction systems in the eastern Caribbean (Macdonald et al. 2000; Evain et al. 2013; Allen et al.
131 2019). It comprises the islands of Saba, Statia, St. Kitts, Nevis, Montserrat, Guadeloupe, Dominica,
132 Martinique, St. Lucia, St. Vincent, the Grenadines, and Grenada, which all have active or
133 potentially active volcanic centres. A wide range of magma types have erupted, ranging from low-
K tholeiites over calc-alkaline basalts to alkalic basalts. The primitive, high-Mg basalts have mostly erupted on St. Vincent, the Grenadines and Grenada, which are interpreted as parental magmas of low-Mg, high-Al basalts and other more evolved magmas of the arc (Heath et al. 1998; Macdonald et al. 2000; Pichavant & Macdonald 2007; Melekhova et al. 2015). They provide an opportunity to study the fO₂ and other intensive parameters of mantle-derived magmas that have been largely unaffected by fractionation or contamination at crustal level.

The island of St. Vincent, from which the sample of our study derives, is dominated by Soufriere volcano in the northern part of the island, which is largely composed of calc-alkaline basalts and basaltic andesites (Heath et al., 1998). Its early activity (~0.6 Ma-10 ka) was dominated by the eruption of basaltic and basaltic andesitic lavas, the so-called Pre-Somma lavas. Later activity produced the Yellow Tuff Formation (black scoria to yellow lapilli and tuff; 3600-4500 years bp), the Crater Lava Formation (ponded basaltic and basaltic andesitic lavas), and the Pyroclastic Formation (succession of pyroclastic fall and flow deposits) with at least five major historic eruptions. Sample STV301 of Heath et al. (1998), which we have used, is a high-Mg basalt that derives from the Pre-Somma unit sampled at Black Point (13°15.65′N, 61°07.05′W). High-Mg basalt STV301 and other high-Mg basalts from the southern part of the arc are inferred to represent slightly enriched, near-primary hydrous mantle melts, which have last equilibrated with peridotite at ~1130-1240°C and ~11-17 GPa (Heath et al. 1998; Pichavant et al. 2002; Bouvier et al. 2008; Melekhova et al. 2015). Experimental studies and olivine-spinel oxybarometry have inferred an oxidized redox state with an fO₂ of ~QFM+0.9 to ~QFM+2.6 for the primitive St. Vincent magmas (Heath et al. 1998; Macdonald et al. 2000; Pichavant et al. 2002; Pichavant & Macdonald 2007), which is within the range of fO₂ conditions (~QFM+0.5 to +3.5) typically inferred for arc magmas using petrological methods (e.g., Carmichael 1991; Kelley & Cottrell
2012; Brounce et al. 2014; Gaillard et al. 2015; Bucholz & Kelemen 2019). Melt H₂O concentrations of high-Mg basalts from St. Vincent, including STV301, are inferred to have been ~5 wt% (Pichavant & Macdonald 2007; Bouvier et al. 2008). Melt CO₂ concentrations and thus direct constraints on melt volatile saturation remain unconstrained for the Pre-Somma lavas, but are high (up to >3000 ppm CO₂) for dacitic melt inclusions from basaltic andesites erupted in 1477 and 1902 AD at St. Vincent (Balcone-Boissard et al. 2023). Some originally volatile-undersaturated high-Mg basalts may have fractionated to high-Al basalts and more evolved magma with ~7-8 wt% H₂O (Pichavant & Macdonald 2007; Balcone-Boissard et al. 2023), but most St. Vincent and Lesser Antilles melt inclusion H₂O and K₂O compositions show no or negative correlation (Bouvier et al. 2008; Balcone-Boissard et al. 2023), which indicates degassing-driven crystallization and thus volatile saturation during partial crystallization at crustal level.

## SAMPLES, METHODS, NEW DATA

We have investigated the natural STV301 high-Mg basalt in one thin section and selected run products of phase equilibrium experiments of Pichavant et al. (2002) and Pichavant & Macdonald (2007) that have used STV301 as the starting material. The experimental run products of Pichavant et al. (2002) and Pichavant & Macdonald (2007) were all considered for our study, but only phases from a subset of eleven charges were feasible for trace-element analysis by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Eight of the charges were partially crystallized in internally heated pressure vessels (IHPV; experiments of Pichavant & Macdonald 2007), whereas three of the charges were partially crystallized in piston cylinder presses (PC; experiments of Pichavant et al. 2002). The experiments were performed at conditions ranging from ~QFM+0.7 to ~QFM+3.1, ~1050 to ~1200 °C, and ~400 to 1450 MPa, where melt H₂O
concentration varied between ~2.3 and 7.7 wt% (Table 1). Details on the control of the experimental intensive parameters are provided below, in the supplementary text, and in the publications of Pichavant et al. (2002) and Pichavant & Macdonald (2007).

All samples were imaged in backscatter-electron mode using a ZEISS Merlin Compact SEM at the Institut des Sciences de la Terre d'Orléans (ISTO-CNRS-Université d'Orléans-BRGM), France. Phase proportions of the natural sample were determined by point-counting (this study), while phase proportions of the experimental run products have been previously determined by mass balance (Pichavant et al. 2002 and Pichavant & Macdonald 2007). For the experimental samples, we have used the major- and minor-element phase compositions reported by Pichavant et al. (2002) and Pichavant & Macdonald (2007). For the natural sample, we have determined new major- and minor-element compositions for olivine, spinel, clinopyroxene, and matrix using a Cameca SX five electron microprobe in wavelength dispersive mode (details are provided in the supplementary text). The redox-sensitive V concentrations of olivine, spinel, clinopyroxene, and glass/matrix were determined for the natural and the experimental samples using LA-ICP-MS. Temperature-sensitive concentrations of Sc, Y, and Ni were also determined for all phases by LA-ICP-MS. For the experimental samples, the data showed zoning in Sc for some olivine (equilibrated at low-temperature) and contamination problems for Ni and Y for other charges (equilibrated in PCs). Given these problems, we report the experimental Sc, Y, and Ni data only in the supplementary text, figures, and Table S1. For the natural samples, the Sc, Y, and Ni concentrations are reported in the main text, which we use to interpret and to quantify crystallization conditions. The four elements of interest (V, Sc, Y, Ni) as well as Si and Al as internal standards were measured as masses $^{27}$Al, $^{29}$Si, $^{45}$Sc, $^{51}$V, $^{60}$Ni, and $^{89}$Y using a RESOlution SE ArF excimer laser ablation system coupled to an Agilent 8900 QQQ mass spectrometer. Instrument parameters were set to
common conditions, and calibration and acquisition followed established procedures, which are outlined in the supplementary text and in Table S1. Phase compositions were determined by point analyses, while zoning was evaluated by LA-ICP-MS compositional mapping. Raw LA-ICP-MS data were reduced using Glitter (point analyses; version 4.4.4; van Achterbergh et al. 2000) and Iolite (compositional maps; version 4.7.1; Paton et al. 2011; Petrus et al. 2017). Accuracy and precision determined for V, Sc, Y, and Ni concentrations in BCR-2G, BHVO-2G, and BIR-1G reference materials were mostly better than 15 and 5%, respectively (Table S2).

210

211 OXYBAROMETER TEST AND CALIBRATION DATA

Our aim was to test how the recent olivine-melt V oxybarometers of Mallmann & O'Neill (2013), Shishkina et al. (2018) (equation 4), and Wang et al. (2019) as well as the clinopyroxene-melt and spinel-melt V oxybarometers of Wang et al. (2019) perform for primitive, hydrous arc magmas and to improve on them if possible. We have therefore focused on mineral-melt V partitioning coefficients determined for experiments performed at hydrous conditions and low temperatures with starting material compositions approaching those of primitive arc magmas, but we have also integrated relevant anhydrous V partitioning data (Fig. 1). In addition to our new data presented below, we have considered the experimental studies of Laubier et al. (2014), Shishkina et al. (2018), and Wang et al. (2019), for which a close approach to equilibrium was inferred in the original publications (to which the reader is referred for details). However, to consider only the highest quality data, we have selected a subset of the published data (1) from experiments with estimated melt H₂O concentrations of <10 wt% (which can be quenched to a homogeneous glass); and (2) from experiments with ≤±20% Fe loss/gain (which can be assumed to have approached chemical and fO₂ equilibrium), which excluded data from 17 experiments of Wang et al. (2019).
The hydrous partitioning coefficients of Shishkina et al. (2018), Wang et al. (2019), and our new data were supplemented by anhydrous, low-temperature V partitioning data from Laubier et al. (2014) for the same fO₂ range and similar starting material compositions. This selection yielded an anhydrous to hydrous partitioning dataset equilibrated at an fO₂ of ~ΔQFM-2.0 to ~ΔQFM+4.0, at melt H₂O concentrations of 0-9.5 wt%, and at temperatures of 1025-1350 °C but mostly 1025-1200 °C (Fig. 1) with 54 partitioning coefficients for olivine-melt (Table S4), 13 partitioning coefficients for spinel-melt (Table S5) and 11 partitioning coefficients for clinopyroxene-melt (Table S6). Vanadium partitioning data determined at higher temperatures or for compositions that strongly deviate from the composition of primitive arc magmas (e.g., those of Canil & Fedortchouck 2001; Toplis & Corgne 2002; Papike et al. 2013; Mallmann & O'Neill 2009, 2013; Holycross & Cottrell 2022) were not used. The fO₂ conditions of the considered studies were variably expressed in log units or relative to various QFM or NNO buffer calibrations, which we have recalculated relative to the QFM buffer of O'Neill (1987) (Tables S4-S6).

Our focus on hydrous partitioning data for arc-type magma compositions is different from the approach taken by Shishkina et al. (2018) and Wang et al. (2019) for their V oxybarometers for arc magmas, who have integrated limited hydrous olivine-melt V partitioning data (n=12 or n=26) with anhydrous partitioning data (n=47 or n=169) from experiments extending over a larger temperature range and also a larger compositional range than the hydrous equivalents (Fig. 1). We posit that focusing our dataset on hydrous to anhydrous V partitioning data for compositions, temperatures (~1025-1350 °C), and fO₂ conditions (~QFM-2 to QFM+4) relevant to partial crystallization of most primitive arc magmas (Carmichael 1991; Grove et al. 2012; Kelley & Cottrell 2012; Brounce et al. 2014; Gaillard et al. 2015; Bucholz & Kelemen 2019) permits us to
best assess relevant effects of their various intensive parameters on V partitioning and thus on fO₂
estimates.

250

251

## EXPERIMENTAL fO₂ AND MELT H₂O CONSTRAINTS

For atmospheric pressure experiments in gas mixing furnaces (i.e. for the considered experiments of Laubier et al. 2014), control of intensive parameters is relatively straightforward with melt H₂O concentrations of <0.1 wt% and an accuracy of better than ±0.1 log units for fO₂. For high-pressure experiments, fO₂ and melt H₂O concentration are more difficult to maintain and to determine, given that the systems are partly open. Oxygen fugacity may be imposed through pressurizing gas mixtures (commonly Ar-H₂), experimental assemblies, double-capsule buffer techniques, and fluid concentrations (H₂O-CO₂) in individual charges. The fO₂ imposed by gas mixtures may be directly measured by Shaw membrane (experiments of Shishkina et al. (2018)), but is more commonly determined using solid buffer capsules or redox-sensitive run products (experiments of Pichavant et al. (2002), Pichavant & Macdonald (2007), and Wang et al. (2019). For experiments in internally heated pressure vessels (experiments of Pichavant & Macdonald (2007) and Shishkina et al. (2018)) and piston cylinder presses (experiments of Pichavant et al. (2002) and Wang et al. (2019)), experimental fO₂ is typically constrained with accuracies of better than ~±0.3 to 0.5 and ~±0.5 to 1.0 log units, respectively. Melt H₂O concentrations can be constrained by various techniques, but only indirectly, i.e. for the quenched glasses. Water concentrations measured by secondary ion mass spectrometry (some data from Pichavant et al. (2002) and Pichavant & Macdonald (2007)) or Fourier-transform infrared spectroscopy (some data of Shishkina et al. (2019)) are in most cases accurate to within ±0.5 wt%, whereas melt H₂O concentrations inferred on the basis of saturation models are typically within ±0.5-1.0 wt% (some data of Shishkina et al. (2019)). Melt H₂O

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concentrations calculated by difference from electron microprobe totals (some data from Pichavant et al. (2002) and Pichavant & Macdonald (2007) and all data from Wang et al. (2019)) have accuracies of ideally ~±1.0 wt% (Devine et al. 1995) but may overestimate concentrations by up to ~+2 wt% (Hughes et al. 2019) or more (e.g. Holycross & Cottrell (2022), especially for high melt H₂O concentrations. These uncertainties are indicated and considered below; further details are provided in the published experimental studies of Pichavant et al. (2002), Pichavant & Macdonald (2007), Laubier et al. (2014), Shishkina et al. (2018), and Wang et al. (2019).

## 279 STUDY OUTLINE

We first present a textural-compositional characterization of olivine, spinel, clinopyroxene and glass of the STV301 phase equilibrium experiments of Pichavant et al. (2002) and Pichavant & Macdonald (2007). Together with the selected literature data (Tables S3 to S5), we then use our compositions to evaluate (1) the olivine-melt V oxybarometers of Mallmann & O'Neill (2013), Shishkina et al. (2018) (equation 4), and Wang et al. (2019); and (2) the spinel-melt and clinopyroxene-melt V oxybarometers of Wang et al. (2019). Following the evaluation, we formulate a set of new olivine-melt V oxybarometers for hydrous arc magmas partially crystallized at ~1050-1350 °C, which we then apply in a petrographic case study on the natural STV301 basalt from St. Vincent, in combination with all tested oxybarometers and the Sc/Y and Ni thermometers of Mallmann & O'Neill (2013) and Pu et al. (2017). A challenge for applying the mineral-melt V oxybarometers and thermometers to the natural STV301 sample was that a record of melt compositions in the form of glassy melt inclusions or glassy matrix is lacking. Possible crystallized melt inclusions (i.e. inclusions in 2D but not necessarily in 3D) large enough for LA-ICP-MS analysis are also rare, which precluded meaningful characterization, and we have therefore (1)
294 analyzed the crystallized matrix/groundmass of the natural sample and (2) estimated melt compositions as outlined later in the text.

296

297 **RESULTS AND DISCUSSION**

298 **Experimental constraints**

299 **Phase relations and compositions**

300 The STV301 experimental run products – which have been previously characterized by Pichavant et al. (2002) and Pichavant & Macdonald (2007) in regards to their assemblage, textures, and major- and minor-element phase compositions – comprise olivine-spinel-glass, olivine-spinel-clinopyroxene-glass, olivine-spinel-clinopyroxene-plagioclase-glass, or orthopyroxene-clinopyroxene-spinel-glass and quench crystals (Table 1; Fig. S1). Olivine, spinel, clinopyroxene, and glass were successfully analyzed by LA-ICP-MS in 9, 3, 2, and 12 charges, respectively (Table 1; Tables S4-S6). Olivine (~2-17 wt%) forms subhedral to euhedral crystals, which are up to ~100 µm but typically ~10-20 µm in size. Olivine crystals of the ≥1180 °C experiments are unzoned and largely inclusion-free (Fig. S2a-c). Olivine formed at ≤1090 °C, however, becomes partly zoned and has locally abundant small (<1-2 µm) spinel, glass, and/or fluid inclusions especially in crystal cores (Fig. S2d-i). Unzoned inclusion-free olivine cores and unzoned inclusion-free near-rim zones have low V concentrations (~1.7-12.7 ppm), which decrease with increasing /O₂ (Table 1). The inclusion-rich cores, in contrast, yield relatively V-rich compositions, representing mixtures of olivine±spinel±glass inclusion analyses, which we have removed from the dataset. The variation of V in olivine of individual charges is relatively low (mostly ~<15% 2RSDs; Table 1), indicating that inclusions were successfully eliminated from our data set.
Spinel (~1-2 wt%) in the experimental charges forms euhedral to subhedral crystals and inclusions in olivine, which are commonly ≤10 µm in size (Fig. S2a). In all experimental run products, some spinel crystals show core-rim zoning from BSE-bright cores to BSE-dark rims, where zoning is sharp in the low-temperature, low-H₂O experiments and gradational in the high-temperature, high-H₂O experiments. Cores of the zoned crystals were not analyzed, as they are inherited from the starting material (cf. Pichavant et al. (2002) and Pichavant & Macdonald (2007); Fig. S1a). Cores of the unzoned spinel crystals and near-rim zones of the zoned spinel crystals have high V concentrations (~320-1080 ppm) which strongly decrease with increasing experimental *f*O₂ with limited variation in spinel of individual charges (≤25% 2RSDs) (Table 1). The experimental clinopyroxene crystals (~6-25 wt%) are subhedral-euhedral, typically clustered in the experimental charges, and commonly <5-10 µm large (Fig. S2g-i). They show no obvious core-rim zoning in BSE images, but they were too small to assess trace-element zoning by LA-ICP-MS mapping. The crystals have intermediate V (~130-450 ppm), showing limited variation in crystals within individual charges (≤15% 2RSDs), but only few crystals were large enough for analysis (Table 1).

Glasses (~51-96 wt%) of the experimental run products are largely homogeneous in BSE imaging mode, but commonly comprise quench crystals, especially those of the H₂O-rich experimental charges (Fig. S2a,d,g). Glasses around quench crystals (Fig. S2a-f) and pyroxene (Fig. S1b,c,d,f,j, S2g) show <5-10 µm wide, BSE-dark boundary layers, which were too narrow for quantitative analysis (Fig. S2d-i). Glasses away from boundary layers have high V (~250-370 ppm), where concentrations primarily vary with phase assemblage and proportions and *f*O₂ (Table 1). They are relatively homogeneous in V (<20% and mostly <3% 2RSDs), where pairs of the homogeneous glass and inclusion-free, near-rim mineral compositions yield V partitioning coefficients for olivine-glass (~0.006-0.041), spinel-glass (~1.1-3.3), and clinopyroxene-glass
339 (~0.3-1.8) that compare to partition coefficients previously determined in other studies, and
340 particularly to those of other low-temperature experiments (Fig. 2a-c; Table 1).

341

342 *Approach to equilibrium for mineral-melt V partitioning*

343 Pichavant et al. (2002) and Pichavant & Macdonald (2007) have inferred a close approach to total
344 equilibrium for most of their STV301 experimental assemblages using established tests (i.e.,
345 experimental duration, textural evidence, homogeneous major- and minor-element phase
346 compositions in individual charges as well as systematic compositional variation between charges,
347 mineral-melt major-element partitioning coefficients in agreement with literature values, and low
348 residuals in mass balance calculations), but highlighted partial disequilibrium for spinel and
349 clinopyroxene. For our study, it is most important to identify partial equilibrium, i.e. equilibrium
350 between the V compositions of selected mineral-glass compositional pairs.

351 (1) Homogenous textures and the lack of zoning in minerals and glasses of most charges is
352 consistent with an approach towards equilibrium. Glass boundary layers around
353 clinopyroxene (<5-10 µm wide), however, indicate partial disequilibrium. Clinopyroxene
354 appears unzoned in BSE images, but crystals were too small to investigate trace-element
355 zoning. The presence of core-rim zoning of spinel in all experiments and core-rim zoning
356 of olivine in ≤1155 °C experiments also records partial disequilibrium. The cores of the
357 zoned spinel crystals are inherited from the starting material (Fig. S1a), which have failed
358 to dissolve completely during preparation of the starting glasses and during the experiments,
359 as reported by Pichavant et al. (2002) and Pichavant & Macdonald (2007). The cores of the
360 zoned olivine crystals (Fig. S2g-i), in contrast, have formed during the experiments, which
361 are interpreted to reflect fast crystallization relative to diffusion and incomplete subsequent
362 equilibration. The presence of compositionally distinct cores of spinel and ±olivine had a
363 limited effect on phase compositions (e.g. some elements were preferentially retained in the
364 crystal cores), but it had no effect on our calculated partition coefficients and calculated
365 intensive parameters, as long as the unzoned near-rim mineral and main melt compositions
366 were in equilibrium.

367 (2) Unzoned olivine and unzoned spinel core and rim compositions and glass compositions of
368 individual charges show low V variation (<20% and mostly <3% 2RSDs) and calculated V
369 partition coefficients that are within the range of published values (Fig. 2a,b; Table 1),
370 which decrease with increasing fO2 as expected (e.g., compared to data of Laubier et al.
371 2014; Shishkina et al. 2018; Wang et al. 2019), suggesting that they reflect equilibrium
372 partitioning. The calculated clinopyroxene-melt V partition coefficients also broadly
373 compare to published low-temperature data (Fig. 2c), falling between the partitioning
374 coefficients of Laubier et al. (2014) and Wang et al. (2019) and those of Toplis & Corgne
375 (2002) and Holycross & Cottrell 2022, and they decrease with increasing fO2 as expected.
376 The presence of melt (now glass) boundary layers around clinopyroxene crystals
377 nevertheless indicates partial disequilibrium, but V compositions may not have been
378 significantly affected with partitioning coefficients close to unity (~0.3 and ~1.5) and thus
379 limited if any V enrichment or depletion in the melt boundary layers. Further below, we
380 therefore continue to assess if our clinopyroxene-melt V partitioning coefficients
381 approached equilibrium, evaluating them against inferred equilibrium partitioning data of
382 Laubier et al. (2014) and Wang et al. (2019).

383

384
385 *Vanadium oxybarometry tests*

386 The focus of our study was on olivine-melt V oxybarometers, but we have also considered spinel-
387 melt and clinopyroxene-melt V oxybarometers, which may extend the range of applications. We
388 have tested overall performance of the calibrations and evaluated bias for calculated compared to
389 experimental fO₂ relative to experimental temperature, pressure, as well as mineral and melt
390 composition. Melt composition was considered through melt H₂O concentration and NBO/T
391 composition (i.e. the ratio of non-bridging oxygen to tetrahedral cations). Melt NBO/T is a first-
392 order approximation of melt polymerization, which was calculated as NBO/T=(2XO-4Xₜ)/Xₜ (cf.
393 Mysen et al. 1982), where X are the atomic proportions of oxygen (O) and tetrahedrally coordinated
394 cations (T=Si⁴⁺, Tᵢ⁴⁺, and P⁵⁺, plus Al³⁺ and Fe³⁺ charge balanced by excess alkalis, with Fe³⁺
395 calculated using the equation of Kress & Carmichael (1991)). In addition to anhydrous NBO/T
396 (commonly used, calculated from anhydrous glass compositions), we have calculated hydrous
397 NBO/T (calculated from hydrous glass compositions considering molecular H₂O concentrations
398 and formation of T-OH bonds, e.g. following Di Muro et al. 2006). Accounting for analytical
399 uncertainties in determining melt composition and especially melt H₂O concentration, we assign
400 uncertainties of 0.1 and 0.2, respectively, to the calculated anhydrous and hydrous NBO/T values.
401 We highlight that the structure of multi-component hydrous melts cannot yet be fully quantified
402 (e.g., Behrens 2020), and that the hydrous NBO/T values may not give a true image of melt
403 structure, but that they permit quantitative comparison of variably hydrous melts, accounting for
404 the fact that hydrous melt component are known to significantly affect melt polymerization.
405

To test the olivine-melt oxybarometers of Mallmann & O'Neill (2013), Shishkina et al. (2018) (equation 4), and Wang et al. (2019) for primitive arc magmas, we have used the selected hydrous to anhydrous experimental V partitioning data equilibrated at conditions (~ΔQFM-2.0 to
408 $\Delta$QFM+4.0, ~1025 to 1350 °C, <10 wt% melt H₂O, 0 to 2000 MPa) that match those typical for
409 partial crystallization within the crust and upper mantle (Table S4). The starting materials of the
410 considered experimental studies were natural high-Mg basalts (our data and the data of Shishkina
411 et al. 2018), natural high-Mg basaltic andesite and mid-ocean ridge basalt (Laubier et al. 2014),
412 and synthetic high-Mg basalt mixed with peridotite (Wang et al. 2019). None of the test data were
413 part of the Mallmann & O'Neill (2013) calibration. However, the data of Laubier et al. (2014) and
414 Shishkina et al. (2018) were part of the Shishkina et al. (2018) calibration, and the data of Laubier
415 et al. (2014) and Wang et al. (2019) were part of the Wang et al. (2019) calibrations. Using some
416 of the oxybarometer calibration data enabled us to test the oxybarometers for the full range of
417 hydrous to anhydrous V partitioning data relevant for arc magmas, permitting direct comparison of
418 the different calibrations. The Shishkina et al. (2018) V oxybarometer is the simplest of the
419 evaluated calibrations in that it considers only the effect of fO₂ on olivine-melt partitioning, thus
420 showing most directly the possible effect of other intensive parameters on V partitioning and
421 oxybarometric estimates.

422 For the test data, the three olivine-melt oxybarometers calculate fO₂ values that are close to
423 the experimental fO₂ values considering uncertainties (Fig. 3a-c). The calculated and experimental
424 fO₂ values are (1) mostly within ±0.8 and 0.7 log units (2SDs) of each other for the Wang et al.
425 (2019) and Mallmann & O'Neill (2013) calibrations (Fig. 3a,b); and (2) mostly within ±0.4 log
426 units (2 SDs) of each other for the Shishkina et al. (2018) calibration, which was specifically
427 derived for hydrous, low-temperature equilibration (Fig. 3c). However, calculated compared to
428 experimental fO₂ values (expressed as $\Delta$QFM (Calc-Exp) show systematic bias as a function of
429 various intensive parameters for all three calibrations (Figs 3d-l). Most of the data show concurring
430 trends, but the data of Wang et al. (2019) deviate from the correlation trends in some instances,
which we describe below. Test data outside the temperature calibration ranges (i.e. data equilibrated at <1200 °C for MO2013, data equilibrated at <1150 °C for W2019, and data equilibrated at >1250 °C for S2018) or the two high-temperature (1350 °C) data, in contrast, do not systematically deviate from correlation trends (Fig. 3). Using the Mallmann & O'Neill (2013) calibration, ΔQFM (Calc-Exp) shows negative correlation with temperature (Fig. 3d; R²=0.65) and no correlation with pressure (Fig. S3a, R²=0.06). ΔQFM (Calc-Exp) also shows no correlation with olivine forsterite content (Fig. S3b), with anhydrous or hydrous NBO/T (Fig. 3g,j), or melt H₂O concentration (Fig. S3c) for the entire test data. However, significant positive correlation is observed with hydrous NBO/T (Fig. 3j) or melt H₂O concentration (Fig. S3c) without the Wang et al. (2019) data, which show a subparallel, but offset trend. Using the Wang et al. (2019) calibration, ΔQFM (Calc-Exp) shows negative correlation with temperature (Fig. 3e; R²=0.35) and no correlation with pressure (Fig. S3d; R²=0.10). ΔQFM (Calc-Exp) and olivine forsterite content (Fig. S3e) or anhydrous NBO/T (Fig. 3h; R²=0.08) are uncorrelated, whereas ΔQFM (Calc-Exp) and hydrous NBO/T or melt H₂O concentration are positively correlated (Fig. 3k and S3f). As for the Mallmann & O'Neill (2013) calibration, the data of Wang et al. (2019) deviate from the hydrous NBO/T and melt H₂O concentration correlation trends, but less significantly. Using the Shishkina et al. (2018) calibration, ΔQFM (Calc-Exp) shows no correlation with temperature (Fig. 3f; R²=0.03), but a weak positive correlation with pressure (Fig. S3g; R²=0.47). ΔQFM (Calc-Exp) and olivine forsterite content (Fig. S3h) or anhydrous NBO/T (Fig. 3i) are uncorrelated, whereas ΔQFM (Calc-Exp) and hydrous NBO/T (Fig. 3i; R²=0.58) or melt H₂O concentration (Fig. S3i; R²=0.49) are positively correlated. As for the other two calibrations, the Wang et al. (2019) data slightly deviate from the hydrous NBO/T and melt H₂O concentration correlation trends (Fig. 3l). That the Wang et al. (2019) data tend to fall off the NBO/T and H₂O concentration correlation trends likely reflects (1) that their
melt H₂O concentrations are slightly overestimated (causing the limited offset visible in Fig. 3l), and (2) variable performance of the three calibrations for their relatively Na- and K-rich melt compositions (e.g. Figs 3j and k versus l).

The bias in ΔQFM (Calc-Exp) as a function of the various tested intensive parameters (typically ≤0.5-1.0 log units) may appear minor, but is important as it is on the order of the characteristic difference in fO₂ inferred for most arc (~QFM+0.5 to +3.5) compared to mid-ocean-ridge magmas (~QFM±0.5). The bias may moreover result in misinterpretation of the redox evolution of individual magma systems, such that false oxidation or reduction trends are calculated. Some of the observed correlations between fO₂ bias and various intensive parameters may be spurious (e.g. weak correlation with pressure may reflect co-correlation with hydrous NBO/T). However, temperature, pressure, and anhydrous as well as hydrous melt compositions are all known to affect mineral-melt element partitioning to some degree (Blundy & Wood 2003), and most of the parameters – i.e., temperature, olivine composition, and anhydrous NBO/T or anhydrous SiO₂-Al₂O₃-Na₂O-K₂O melt compositions – have been inferred to have a significant effect on olivine-melt V partitioning. An effect of melt H₂O concentration or hydrous NBO/T on olivine-melt V partitioning and thus calculated fO₂ values (Fig. 3j-l), which appears to be relevant for all three considered calibrations, in contrast, was ruled out by Shishkina et al. (2018) and Wang et al. (2019).

Like Shishkina et al. (2018) and Wang et al. (2019), we see only a weak correlation between ΔQFM (Calc-Exp) and melt H₂O concentration or hydrous NBO/T if we consider small datasets (e.g. only the data of Shishkina et al. (2018) or our new data). However, if we consider ΔQFM (Calc-Exp) and hydrous NBO/T or melt H₂O content for the to date largest possible high-quality dataset, as we have done above, or if we consider subsets of our data – i.e. compositions from experiments that were performed in the same IHPV run (at the same temperature and different melt
H₂O concentrations; e.g., our experiments 3-1 and 3-2, 4-1 and 4-2 etc.) – then we can see that
ΔQFM (Calc-Exp) generally increases with increasing melt H₂O concentration and hydrous NBO/T
(Fig. 3j-1, S3c,f,i; Table S4) Our conclusion is new for olivine-melt V partitioning, but in agreement
with other studies who have experimentally shown that trace-element partitioning into silicate
minerals is lower in equilibrium with hydrous than in equilibrium with anhydrous melt, which has
been linked to the lower degree of polymerization of the hydrous relative to the anhydrous melts
(Green et al. 2000; Gaetani et al. 2003; McDade et al. 2003).

Spinel-melt and clinopyroxene-melt V oxybarometers for arc magmas have recently been
484 calibrated by Wang et al. (2019), which may provide an independent test relative to olivine
485 oxybarometers and enlarge the application range, but all calibration data are from experiments
486 equilibrated at >1150 °C, and they should thus be used with caution for arc magmas, as most
487 clinopyroxene will have crystallized and most spinel will have equilibrated at lower temperature
488 (e.g., Heath et al. 1998; Pichavant & Macdonald 2007). As for olivine above, we have used the
489 selected hydrous to anhydrous test data, but our new data for clinopyroxene (n=2) and spinel (n=3)
490 are too limited to conclusively assess oxybarometer accuracy or bias related to various intensive
491 parameters. Our clinopyroxene-melt compositions and the selected subset of data from Wang et al.
492 (2019) and data from Laubier et al. (2014), calculate redox state to mostly within ~±1.0 log units
493 of the experimentally constrained conditions (Fig. S4a-c; Table S6). The estimates are thus
494 moderately accurate for the test dataset, but there moreover appears to be bias, overestimating fO₂
495 for Al-rich clinopyroxene and underestimating fO₂ for Al-poor clinopyroxene compositions (Fig.
496 S4b), indicating that the oxybarometer calibration overestimates the effect of clinopyroxene Al
497 concentration, as was previously suspected by Holycross & Cottrell (2022). Our clinopyroxene-
498 melt compositions are interpreted to have been in partial disequilibrium, but their V concentrations
499
seem to have approached equilibrium as much as the other test data, showing similar ΔQFM (Calc-Exp). Our spinel-melt compositions and the selected subset of data from Wang et al. (2019) calculate redox state to mostly within ~±0.8 log units of the experimentally constrained conditions (Fig. S4d-f; Table S5). The estimates are thus reasonably accurate for the test dataset, but there also appears to be bias, overestimating $fO_2$ for spinel crystallized at oxidizing conditions and underestimating $fO_2$ for spinel crystallized at reducing conditions, likely relating to spinel compositional variation in addition to Cr# (Fig. S4e; Table S4). For the small test datasets, which are dominated by data employed in the calibrations, the ΔQFM (Calc-Exp) values show no clear correlation with anhydrous or hydrous NBO/T (Fig. S4c,f; Tables S5 and S6). However, for clinopyroxene, a subset of the data show positive correlation between ΔQFM (Calc-Exp) and hydrous NBO/T, which we would suspect from our findings for olivine and from previous studies (Green et al. 2000; Gaetani et al. 2003; McDade et al. 2003).

## *New olivine V oxybarometer calibrations*

Following, we now calibrate a new set of olivine-melt V oxybarometers with the aim to eliminate the ΔQFM (Calc-Exp) bias of the evaluated olivine-melt V oxybarometers, using the same dataset as for our tests above (Table S3). Step-wise linear regression for all intensive parameters considered (i.e., temperature, pressure, olivine forsterite content, and anhydrous as well as hydrous NBO/T, and melt H₂O concentration) confirmed a significant effect of hydrous NBO/T on V partitioning and thus on ΔQFM (Calc-Exp). Effects from intensive parameters other than $fO_2$ and hydrous NBO/T are not ruled out, but they are insignificant (with regression p-values>0.05) for the
considered calibration range, including temperature, or directly correlated with hydrous NBO/T (e.g. melt H₂O concentration).

In a first step, we use simple linear regression to define an oxybarometer as a function of olivine-melt V partitioning (Table 2):

$$fO_2 (\Delta QFM) = -3.2848 - 2.9893 \times \text{Log}(D_v) (R^2=0.94, 2SD=0.4; \text{Eqn 1}).$$

In a second step, we use multiple linear regression to yield a more complex oxybarometer as a function of olivine-melt V partitioning and hydrous melt NBO/T (Table 2):

$$fO_2 (\Delta QFM) = -2.8438 - 3.1960 \times \text{Log}(D_v) - 0.8781 \times \text{h-NBO/T} (R^2=0.97, 2SD=0.3; \text{Eqn 2}),$$

where $fO_2 (\Delta QFM)$ is the oxygen fugacity relative to the quartz-fayalite-magnetite buffer of O'Neill (1987) in log units, $D_v$ is the olivine-melt V partitioning coefficient and h-NBO/T is the hydrous NBO/T value. The equation 1 oxybarometer shows a relatively high degree of correlation ($R^2=0.94$) and relatively low uncertainty (2SD=0.4 log units), but $\Delta QFM$ (Calc-Exp) bias as a function of hydrous NBO/T (Table S4). The oxybarometer closely compares to the oxybarometer of Shishkina et al. (2018), which can be used for estimating $fO_2$ in cases where melt composition including melt H₂O concentration is weakly constrained. More importantly, we suggest that the equation 1 oxybarometer is used for estimating Fe₂O₃/FeO concentrations needed to calculate melt NBO/T values (instead of assuming Fe₂O₃/FeO as is commonly done). The equation 2 calibration removes the $\Delta QFM$ (Calc-Exp) bias relative to hydrous NBO/T, but also relative to all other considered intensive parameters (e.g., removing spurious correlation for pressure or individual melt components), showing matching correlation trends for all individual test datasets. The equation
shows a high degree of correlation (R²=0.97) and relatively low uncertainty (2SD=0.3 log units)
(Fig. 4). Errors on estimates for unknowns can be calculated as:

$\sigma$ (Eqn 1) = (0.0279 + 0.0116 x (Log(Dv))² + 8.9359 x (σ(Log(Dv)))²)¹/² and

$\sigma$ (Eqn 2) = (0.0159 + 0.0060 x (Log(Dv)))² + 10.2144 x (σ(Log(Dv)))² + 0.0127 x (h-NBO/T)² + 0.7711 x (σ(h-NBO/T))²)¹/², accounting for regression errors as provided in Table 2 and requiring users to estimate σ for their Log(Dv) and hydrous melt NBO/T input values.

We stress (1) that the hydrous calibration dataset on which our olivine-melt oxybarometers are built remains limited, which should be supplemented by more high-quality experimental data in the future, especially for temperatures >1200 °C and hydrous NBO/T >1.2; and (2) that the oxybarometers should only be employed to phase compositions and intensive system parameters that closely match those of the calibration range, as provided in Table S3. We further suggest that our and other available mineral-melt V oxybarometers are best applied in concert and that the results are then interpreted in detail, as we do below in our case study of the natural St. Vincent high-Mg basalts.

## The St. Vincent case study

Primitive high-Mg basalts erupted at Saint Vincent are primary and near-primary mantle-derived melts (Heath et al. 1998; Macdonald et al. 2000; Pichavant & Macdonald 2007; Melekhova et al. 2015). High-Mg basalt sample STV301 comprises olivine (~16 vol%), spinel (~2 vol%), and clinopyroxene (~9 vol%) phenocrysts with rare inherited xenocrystic or antecrystic cores, embedded in a crystallized, plagioclase-, clinopyroxene, olivine, and spinel-bearing matrix (Fig. S5). No glassy melt inclusions or interstitial glass are present, and potential crystallized melt
inclusions are rare (Fig. S5). Small potential crystallized melt inclusions (Fig. S5b) may be true inclusions, whereas larger inclusions may be apparent, which were connected to matrix/groundmass in 3D (Fig. S5a,d,e). The sample was previously petrologically studied by Heath et al. (1998), Pichavant et al. (2002), and Pichavant & Macdonald (2007), who presented major- and minor-element, but no trace-element compositional data.

## Phenocryst textures and compositions

Olivine phenocrysts of high-Mg basalt STV301 are subhedral to euhedral and up to ~2 mm in size. They have locally spinel and potential crystallized melt inclusions and they rarely contain inherited cores (~1 vol%), which are subround and devoid of inclusions (Fig. S5a,b, S6a-f). The olivine phenocrysts show core-rim zoning with weakly zoned core plateau zones and significantly zoned rims, or more complex zoning where inherited cores are present. The phenocryst cores have high Fo (~84-90), low to intermediate CaO (~0.14-0.23 wt%) and MnO (~0.10-0.32 wt%), low V (~3.8-6.3 ppm), intermediate to high Sc (~5.7-8.4 ppm), low Y (≤0.12 ppm), and intermediate to high Ni (~1350-2600 ppm) (Fig. 5; Table S7). Their compositions match those of the experimental crystals, except that the experimental crystals have overall higher CaO concentrations. The phenocryst rims have lower Fo (~70-77) and Ni (~680-1060 ppm), yet higher MnO (~0.41-0.52 wt%), CaO (~0.26-0.35 wt%), V (~8.0-16.1 ppm) and Y (≥0.15 ppm), and overall higher Sc (~7.1-8.6 ppm) than the phenocryst cores and the experimental crystals (Fig. 5; Table S7). The inherited olivine cores have compositions that are distinct from those of the phenocrysts and the experimental crystals with moderately high Fo (~80-86), low CaO (≤0.07 wt%), low to intermediate MnO (0.08-0.32), and low V (~2.1 ppm), Sc (~2.8), Y (~0.06 ppm), and Ni (~1000 ppm) (Fig. 5; Table S7).
Spinel in sample STV301 forms euhedral to skeletal phenocrysts up to ~200 µm in size and small (<10 µm), or subhedral to euhedral inclusions in olivine and clinopyroxene that commonly occur together with crystallized melt (Fig. S5b,d). The spinel phenocrysts and spinel inclusions show gradational core-rim zoning in BSE imaging mode. The spinel inclusions have high to intermediate Mg# (~45-58%), low to intermediate Fe³⁺/R³⁺ (~7-13%) and low to high Fe³⁺/Fe(tot) (~20-36%) (Fig. 6a,b; Table S8). High-Mg# inclusions that were large enough for LA-ICP-MS analysis have low V (~880 ppm), Sc (~5.7 ppm), and Y (≤0.04 ppm), and intermediate to high Ni (~570-1150 ppm) (Fig. 6c-f; Table S8). The cores of spinel phenocrysts have overall lower Mg# (~28-44%) and lower Fe³⁺/R³⁺ and Fe³⁺/Fe(tot) than the spinel inclusions at equivalent Mg# (Fig. 6a,b; Table S8). Compared to the analyzed spinel inclusions, the phenocryst cores have equivalent to higher V (~870-1520 ppm), Sc (~4.7-11.6 ppm), and Y (~0.03-0.09 ppm), yet lower Ni (~390-590 ppm) (Fig. 6c-f; Table S8). Both high-Mg# spinel inclusions and phenocryst cores have compositions that match those of the low-Mg# experimental crystals. Spinel phenocryst rims have low Mg# (~21-34%) and high Fe³⁺/Fe(tot) (~42-49%), Fe³⁺/R³⁺ (~26-49%), V (>2000 ppm) and Sc (~12 ppm) relative to the phenocryst cores with concentrations that significantly also differ from the experimental spinel compositions (Fig. 6; Table S8).

Clinopyroxene phenocrysts are subhedral to euhedral and typically <500 µm in maximum dimension (Fig. S5c,d). Like olivine, the clinopyroxene phenocrysts locally contain inherited cores (~2 vol%), which are anhedral, comprising coarsely crystallized melt inclusions (Fig. S5d). The phenocrysts show sharp sector zoning with superimposed oscillatory zoning or more complex zoning where inherited cores are present (Fig. S6j-e). The sector-zoned phenocrysts have intermediate to high Mg# (~80-86%), low to high TiO₂ and Al₂O₃ (~0.5-1.4 and ~2.9-7.4 wt%) and high CaO (~21.8-23.6 wt%) (Fig. 7a-c; Table S9). They also have low to high V (~210-400 ppm),
609 high Ni (~110-130 ppm) and Sc (~200-250 ppm), and low Y (~9-14 ppm) (Fig. 7d-f; Table S9).
610 Sector zoning is most prominent in Al₂O₃ and V (Fig. 7b, d-f). The phenocrysts have notably higher
611 Mg#, CaO and Sc, comparable V, Y, and Ni and lower Al₂O₃ than the experimental crystals,
612 showing no compositional match. The inherited clinopyroxene cores show complex patchy zoning
613 (Fig. S6j-l) with low Mg# (~73-76%), high TiO₂ (~0.9-1.3 wt%), low Al₂O₃ (~2.9-3.6 wt%) and
614 CaO (~20.2-21.1 wt%), and intermediate V (~360 ppm) concentrations (Fig. 7; Table S9). Their
615 Ni (~30-90 ppm) and Sc (~140-200 ppm) concentrations are low to intermediate, whereas their Y
616 concentration (~16-30 ppm) is intermediate to high. Their compositions are different from the
617 compositions of both the phenocrysts and the experimental crystals.

618

619 *Melt compositions and mineral-melt partitioning coefficients*

620 High-Mg basalt STV301 comprises no glass inclusions or glassy matrix, and only a limited number
621 of large inclusions that may represent crystallized melt (Fig. S5), which could have been connected
622 to the matrix/groundmass in three dimensions, and we have therefore estimated melt compositions
623 (Fig. 8; Table 3). We highlight that it is common for primitive arc magmas such as STV301 that
624 melt inclusions are absent from phenocrysts or that the melt inclusions are in disequilibrium with
625 their phenocryst hosts (e.g., Bouvier et al. 2008, 2022). In our case study, we show that intensive
626 parameters using mineral-melt compositions can nevertheless be estimated for these rocks, if
627 equilibrium melt compositions are rigorously constrained. Following, we estimate melt
628 compositions for early-stage magma storage (estimates E1 to E3), where primitive phenocryst cores
629 formed (olivine+spinel), and late-stage magma storage (estimates E4 to E6), where evolved
630 phenocryst cores formed (olivine+spinel+clinopyroxene). Following Pichavant & Macdonald
631 (2007), we infer early- to late-stage magma storage at depth at ~400 MPa, at volatile saturated
conditions, and in equilibrium with a hydrous melt with ~5 wt% H₂O. Strongly zoned phenocryst rims and matrix crystals – which have equivalent size and compositions (e.g. <Fo80 olivine) – are inferred to have crystallized or re-equilibrated during magma ascent to the surface and subsequent to eruption, for which equilibrium melt compositions could not be estimated.

During early-stage storage crystallization, olivine, spinel and melt ±fluid were the stable phases of the STV301 magma (Pichavant and Macdonald 2007). Following Heath et al. (1998) and Pichavant & Macdonald (2007), we suggest that the most primitive olivine cores (~Fo89, ~4.0-5.6 ppm V, ~5.7-7.4 ppm Sc, ~0.06-0.08 ppm Y, and ~1780-2590 ppm Ni; Fig. 5; Table S7) crystallized at this stage. Spinel inclusions and phenocrysts were present, but have at least partly equilibrated at lower temperature (in Mg-Fe but possibly also in V), with calculated olivine-spinel equilibration temperatures of ≤1130 °C (cf. Heath et al. 1998). Following common practice (e.g., Putirka 2008), we estimate that the early-stage storage melt composition has approached bulk-rock composition (E1), but that it was slightly more evolved owing to minor crystallization of olivine and spinel and the presence of inherited crystal cores in our sample STV301, in agreement with Pichavant & Macdonald (2007), who experimentally showed that the primary STV301 melt was slightly less primitive (lower in MgO) than the STV301 whole rock. Our best estimate for early-stage storage melt composition are the experimental STV301 glass composition 7-2 in equilibrium with ~3 vol% olivine and ~1 wt% spinel (estimate E2) and a melt composition calculated considering crystallization of olivine and spinel and the presence of inherited crystal cores (combined ~6 wt% olivine, ~1 wt% spinel, and ~2 wt% clinopyroxene) (estimate E3) (Tables 3 and S10). The estimated E2 and E3 melt compositions with ~284-291 ppm V, ~42-44 ppm Sc, ~14.1-14.8 ppm Y, and ~180-230 ppm Ni at ~9.8-10.2 wt% MgO (Table 3) closely match, except for their Ni concentrations (Fig. 8). Their compositions fall onto primitive Saint Vincent whole-
rock compositional trends (Fig. 9; Table 3) and they moreover match the MgO concentrations of primitive olivine-hosted melt inclusions of other high-Mg basalts from Saint Vincent (reported by Bouvier et al. 2008, 2010), but they have overall lower V and Y contents. The difference in estimated STV301 melt and measured melt inclusion V and Y compositions likely reflects variable magma/melt compositions and fO₂ for the studied STV301 magma from the Pre-somma unit and for younger high-Mg magmas (likely from the Yellow Tuff formation) sampled by Bouvier et al. (2008, 2010). Alternatively, the difference in V and Y compositions could record formation of V- and Y-rich melt boundary layers around olivine that were enclosed as melt inclusions, in line with olivine-melt inclusion isotopic disequilibrium detected for a large proportion of the inclusions (Bouvier et al. 2022). In combination, our best estimates for the early-stage storage melt composition (estimates E2 and E3) and the primitive olivine phenocryst core compositions (Table 3) calculate Fe(tot)-Mg partitioning coefficients of ~0.23 to 0.24, which are in the range of equilibrium values for moderately oxidizing crystallization conditions (cf. Blundy et al. 2020), thus suggesting that the estimated melt compositions E2 and E3 and primitive olivine phenocryst cores indeed represent or approach equilibrium pairs. The olivine and melt (E2 and E3) compositions further calculate a limited range of V partition coefficients of ~0.014-0.020 and Sc/Y and Ni partition coefficients of ~24-46 and ~7.8-15 (Table 3), which translate into a small variation in calculated fO₂ (≤0.15 log units difference) and a limited to moderate variation in calculated temperatures (<30 °C for Sc/Y versus <75 °C for Ni) (Table 4).

During late-stage storage conditions (prior to magma ascent towards eruption), olivine, clinopyroxene, spinel, and melt ±fluid were the stable phases of the STV301 magma (Pichavant and Macdonald 2007). Following again the interpretation of Heath et al. (1998) and Pichavant & Macdonald (2007), we suggest that the evolved olivine core (~Fo84-86, ~4.2-5.1 ppm V, ~5.8-8.0
678 ppm Sc, ~0.04-0.10 ppm Y, and ~1350-2000 ppm Ni), Mg-rich spinel phenocryst core (Mg#~40-
679 50%, ~870-980 ppm V), and clinopyroxene phenocryst core (Mg#>80%, ~210-400 ppm V, ~200-
680 250 ppm Sc) compositions crystallized or equilibrated at this stage (Tables S5-S7). Following
681 common practice (e.g. Putirka 2008), we have attempted to calculate the late-stage storage melt
682 composition, subtracting phenocryst and inherited core compositions from the STV301 bulk rock
683 composition (estimate E4) (Tables 3 and S11). The estimated E4 melt composition falls along
684 primitive Saint Vincent whole-rock compositional trends (Fig. 8), but is too evolved to have been
685 in equilibrium with ~Fo84-86 olivine, calculating an Fe(tot)-Mg partitioning coefficient of ~0.16
686 (Table 3), reflecting the difficulty to accurately constrain the phenocryst and inherited crystal core
687 cargos and their average compositions. Moderately evolved experimental STV301 glass
688 compositions (averages of experimental glasses 3-1 and 3-2) and the matrix/groundmass
689 composition of the natural STV301 sample (estimates E5 and E6) are taken as alternative
690 constraints (Table 3). The average experimental glass composition was taken to account for partial
691 crystallization (~7.5 wt% olivine, ~0.5 wt% spinel, and ~7.0 wt% clinopyroxene). The composition
692 of the matrix/groundmass was analyzed with a broad, 100 µm beam away from phenocrysts,
693 averaging a total of 20 analyses. Compared to our estimates of the early-stage storage melt, the E5
694 and E6 melt estimates for the late-stage storage melt remain uncertain given the difficulty to
695 precisely estimate the proportion of phenocryst cores that have been present at this stage (especially
696 for complexly zoned clinopyroxene, which may have crystallized during late-stage storage or
697 magma ascent). However, both estimated E5 and E6 compositions fall along Saint Vincent whole-
698 rock compositional trends (Fig. 8) and they moreover match the MgO and characteristic Y
699 concentrations of evolved olivine-hosted melt inclusions of other high-Mg basalts from Saint
700 Vincent (Fig. 8). The calculated Fe(tot)-Mg partitioning coefficients for olivine and estimated melt
701 compositions E5 and E6 are ~0.23-0.25 (Table 3), which are in the range of equilibrium values for
702 moderately oxidizing crystallization conditions (cf. Blundy et al. 2020), moreover suggesting that
703 the E5 and E6 melt and evolved olivine core compositions indeed represent or approach equilibrium
704 pairs (Table 3). The compositions further calculate olivine-melt V, Sc/Y, and Ni partition
705 coefficients of ~0.013-0.018, ~31-59 and ~15-26, and spinel-melt V partitioning coefficients of
706 ~2.8-3.4 (Table 3). The clinopyroxene phenocrysts show complex sector and oscillatory zoning,
707 and they were therefore not used for estimating equilibrium partitioning coefficients or
708 crystallization conditions below. As for the early-stage storage conditions, our best estimates for
709 the late-stage storage melt compositions (E5 and E6) translate into a small variation in calculated
710 $fO_2$ (≤0.15 log units difference) and a limited to moderate variation in calculated temperatures (<70
711 °C for Sc/Y versus <30 °C for Ni) (Table 4).
712

712

713 Temperature and $fO_2$ of the primitive St. Vincent magma during early-stage storage

714 Average temperatures calculated for early-stage storage olivine and inferred equilibrium-melt (E2
715 and E3) compositions are ~1210±30 °C using the Sc/Y olivine-melt thermometer of Mallmann &
716 O'Neill (2013) and ~1240±60 °C using the Ni olivine-melt thermometer of Pu et al. (2017) (Table
717 4). The calculated Ni temperature appears high, but the calculated Sc/Y temperature closely
718 approaches the experimentally constrained near-liquidus temperature of ~1200 °C of Pichavant &
719 Macdonald (2007), which in combination suggest that the three tested olivine-melt V
720 oxybarometers and our new calibration are all applicable to the inferred mineral-melt equilibrium
721 pairs. To estimate the early-stage storage $fO_2$, we then use the minimum and maximum V
722 concentrations of Fo-rich olivine, the various estimated melt compositions, and a temperature
723 estimate of ~1200 °C (Tables 3 and 4). We assume a melt H₂O concentration of ~5 wt% as
724 experimentally constrained by Pichavant & Macdonald (2007) and as has been detected in primitive
olivine-hosted melt inclusions from other St. Vincent high-Mg basalts (Bouvier et al. 2008), which is consistent with the observation that olivine phenocryst core CaO compositions match or most closely approach those crystallized in H₂O-rich experiments (~≥5 wt% H₂O) (Fig. 5a) (cf. Gavrilenko et al. 2016). For these parameters, the various olivine-melt oxybarometers calculate fO₂ values of ~QFM+1.4 to QFM+2.4 and on average ~QFM+1.8 to QFM+2.1 ±0.5-0.9 log units (Fig. 9a; Table 4). The range of estimated melt compositions (E2 and E3) has a limited effect on the inferred fO₂ (~0.15 log units) and Sc/Y temperature (~30 °C) (Table 4), as melt V, Sc, and Y contents show limited variation after crystallization of minor olivine and traces of spinel and can therefore be fairly well constrained (Fig. 8). The inferred Ni temperatures, in contrast, are more variable (~65 °C), reflecting the difficulty to tightly constrain olivine-melt Ni equilibrium pairs. The range of detected trace-element concentrations in Fo-rich olivine (~1.6 ppm, ~1.7 ppm, ~0.02 ppm; Table S7) are significantly larger than the analytical errors (≤0.24 ppm V, ≤0.37 ppm Sc, ≤0.006 ppm; Table S7), thus likely recording true variation in crystallization conditions, which could reflect fO₂ variation by up to 0.3 log units, temperature variation by up to 60 °C, or variation in other intensive parameters between magma parcels and their phenocryst cargo.

The reason that all applied V oxybarometers calculate closely concurring fO₂ values is consistent with equilibration at relatively high temperature (~1200 °C), but we posit that all previous calibrations and our equation 1 oxybarometer nevertheless tend to systematically overestimate fO₂ for the hydrous magma T(cf. Fig. 3). The estimated average fO₂ values of ~QFM+1.8 to QFM+2.1±0.5-0.9 and our best estimate of ~QFM+1.8±0.5 (calculated using our equation 2 calibration) are overall lower than but within the uncertainty of the previous fO₂ estimate of ~QFM+2.1 to +2.6 of Pichavant & Macdonald (2007) (Fig. 9a). We suggest that our new fO₂
estimate is more accurate for early-stage crystallization conditions than the previous estimate, which was based on the composition of small, high-Mg#, high Fe³⁺/Fe(tot) spinel inclusions, which have partially equilibrated in Mg-Fe with their olivine hosts, consistent with olivine-spinel equilibration temperatures of ≤1130 °C (Heath et al. 1998). Our redox estimate of ~QFM+1.8±0.5 for the early-storage, near-liquidus, mantle-derived STV301 melt is within the range of values characteristic for primitive Lesser Antilles magmas, which vary between ~QFM+0.5 to QFM+4.3 and are mostly ~QFM+1.0 to QFM+3.0 (Heath et al. 1998; Pichavant & Macdonald 2007; Stamper et al. 2014). Our estimate is also within the range of values considered characteristic for arc settings constrained using various mineral-melt oxybarometers, phase-equilibrium experiments and recent whole-rock geochemical modelling (~QFM+0.5 to QFM+3.5, e.g., Gaillard et al. 2015; Bucholz & Kelemen 2019). The inferred early-stage storage, near-liquidus fO₂ is, however, significantly higher than fO₂ values (~QFM) inferred for primitive mantle-derived arc magmas using the bulk-rock V/Sc or Ga/Sc models of Lee et al. (2005) or Mallmann & O'Neill (2009).

761

### Temperature and fO₂ of the primitive St. Vincent magma during late-stage storage

Average temperatures calculated for the late-stage storage olivine-melt (E4 and E5) compositional pairs are ~1080±30 °C using the Sc/Y olivine-melt thermometer of Mallmann & O'Neill (2013) and ~1130±60 °C using the Ni olivine-melt thermometer of Pu et al. (2017) (Table 4). The calculated Sc/Y temperature agrees with the experimentally constrained late-stage storage temperatures of ~1050-1100 °C of Pichavant & Macdonald (2007), whereas the Ni thermometer appears to overestimate temperature as for the early-stage storage conditions. To estimate the late-stage storage fO₂, we therefore take a temperature of ~1075 °C, which suggests that the mineral-melt pairs equilibrated outside the calibration range of the Mallmann & O'Neill (2013) and Wang
et al. (2019) V oxybarometers. To estimate the late-stage storage of H₂O, we nevertheless employ all tested and our new olivine-melt V oxybarometers and the spinel-melt V oxybarometer of Wang et al. (2019) to assess and discuss the different results. We use the minimum and maximum V concentrations of the evolved olivine phenocryst core compositions (~Fo84-86), Mg-rich spinel phenocryst core compositions (~Mg#40-60) and estimated (E4 and E5) melt compositions (Table 3). As for the early-stage storage conditions, we assume a melt H₂O concentration of ~5 wt% (cf. Pichavant & Macdonald 2007; Bouvier et al. 2008), given that melt inclusions from St. Vincent and Lesser Antilles magmas in general record volatile (H₂O-CO₂) saturation at ≥5 wt% (cf. Balcone-Boissard et al. (2023)) and given that the STV301 olivine/melt Ca contents show no significant increase with decreasing olivine Fo content (Fig. 5a), which would be expected in the case of significant variation of melt H₂O concentration (cf. Gavrilenko et al. 2016). For these parameters, the various olivine-melt and the spinel-melt oxybarometers calculate fO₂ values of ~QFM+1.9 to QFM+3.1 and on average ~QFM+2.1 to QFM+2.9 ±0.5-0.9 log units, which are much more variable (differing by ~0.8 log units) than the fO₂ values calculated for the early-stage storage condition (differing by ~0.3 log units) (Fig. 9a versus 9b; Table 4). Our equation 1 and 2 olivine-melt V oxybarometers calculate the lowest fO₂ values of ~QFM+2.1±0.6 on average, whereas the Wang et al. (2019) spinel-melt and the Mallmann & O'Neill (2013) and Wang et al. (2019) olivine-melt oxybarometers calculate higher fO₂ values of ~QFM+2.6±0.5, ~QFM+2.7±0.5 and ~QFM+2.9±0.5 on average (Fig. 9b, Table 4). The range of estimated late-stage storage melt (E4 and E5) compositions has a slightly higher, but still limited effect on the calculated fO₂ (Δ <0.2 log units) compared to the early-stage storage melt. The reason for this is that the crystallization of several weight percent of clinopyroxene in addition to olivine significantly fractionates melt V and that equilibrium mineral-melt compositions become more difficult to constrain. The range of trace-
element concentrations in Mg#-rich spinel and in Fo-rich olivine phenocryst cores (ΔV ~100 ppm for spinel; ΔV ~0.9 ppm, ΔSc ~1.7 ppm, ΔY ~0.06 ppm for olivine; Table S4) are significantly larger than the analytical errors (≤30 ppm V for spinel; ≤0.18 ppm V, ≤0.29 ppm Sc, and ≤0.01 ppm Y for olivine) and for olivine on the same order as for the primitive phenocryst cores, suggesting that intensive parameters varied to the same degree (e.g. fO₂ by ~0.3 log units or temperature by ~60 °C), which could indicate that smaller magma parcels and their phenocryst cargo were blended just prior to eruption.

We take an average fO₂ of ~QFM+2.1±0.6, calculated using our olivine-melt V oxybarometers, as the best estimate for the late-stage storage fO₂ (Fig. 9b; Table 4). That our and the Shishkina et al. (2018) oxybarometers calculate closely comparable fO₂ for low-temperature equilibration (~QFM+2.1 and ~QFM+2.2) and relatively less oxidized fO₂ values than the Mallmann & O'Neill (2013) and Wang et al. (2019) calibrations was expected (cf. Fig. 3), which highlights that it is critically important to have tight temperature constraints for the crystallization of the redox-sensitive assemblage, and that the Mallmann & O'Neill (2013) and Wang et al. (2019) oxybarometers should not be applied outside their calibration range at below ~1200-1150 °C. That our oxybarometers and the Shishkina (2018) (equation 4) calibration calculate closely matching values reflects the relatively polymerized character of the estimated equilibration melt (h-NBO of ~0.84-0.97; Table 3) with intermediate melt H₂O concentration (~5 wt%) yet otherwise evolved composition (cf. Figs 31, S4f). Our best estimate of ~QFM+2.1±0.6 falls between the previous estimates of Pichavant & Macdonald (2007) (~QFM+2.1 to QFM+2.6 based on their phase equilibrium experiments and spinel compositions) and Heath et al. (1998) (~QFM+1.5 to QFM+1.8 using the Ballhaus et al. (1991) olivine-spinel oxybarometer) (Fig. 10b), which is slightly higher than our fO₂ estimate for early-stage storage (~QFM+1.8) by ~0.3 log units, which may indicate a
limited $f/O_2$ increase during intermittent crustal storage. If the results from the Mallmann & O'Neill (2013) or Wang et al. (2019) oxybarometers would have been considered, then more significant oxidation by ~0.8 log units may have been erroneously inferred. Results from our equation 1 or the Shishkina et al. (2018) oxybarometers, which do not account for melt compositional variation other than in V, in contrast would have suggested no essential oxidation (i.e. by $\le 0.1$ log units).

## 823 Limited oxidation during intermittent crustal storage of the STV301 magma

Our best $f/O_2$ estimates for early-stage to late-stage storage suggest limited oxidation by ~0.3 log units during intermittent crustal magma storage, but such limited redox variation is within the uncertainty of our method (±0.3 log units) and smaller than the estimated individual uncertainties (±0.5-0.6 log units) (Table 4). Considering the extremes of individual uncertainties, V oxybarometry alone cannot rule out limited reduction (by ~0.8 log units, i.e. from QFM+1.8+0.5 to QFM+2.1-0.6) or more significant oxidation (by ~1.4 log units, i.e. from QFM+1.8-0.5 to QFM+2.1+0.6) for the STV301 magma during intermittent crustal storage. However, limited evidence for contamination (i.e. presence of minor amounts of inherited crystal cores) and lack of evidence for degassing during magma storage in combination with crystallization of moderate amounts of olivine (~7.5-10.5 wt%), clinopyroxene (~6.0-8.0 wt%), and spinel (~0.5-2.5 wt%), are in agreement with limited oxidation. Redox variation of primitive magmas largely owing to fractional crystallization of moderate amounts of olivine, clinopyroxene, and spinel (<25 wt%) is typically inferred to be $\le 0.5$ log units as estimated for natural samples (Cottrell & Kelley 2011; Kelley & Cottrell 2012), but may be higher, e.g. ~0.8 log units as shown in fractionation experiments (Ulmer et al. 2018). For single samples like the studied STV301 basalt, such limited redox variation cannot be reliably resolved by V olivine-melt or other mineral-melt oxybarometry.
However, V mineral-melt oxybarometry for a large number of samples from a single magma system, ideally with well-constrained melt compositions and large degrees of fractionation, have the capacity to establish if primitive arc magmas typically experience oxidation by ~0.5, ~1.0, or more log units. To track autoxidation for large degrees of fractional crystallization (>>25 wt%), which has been suggested to be as high as ≥4 log units based on fractionation experiments (Ulmer et al. 2018), V oxybarometers will have to be rigorously calibrated for lower-temperature equilibria for clinopyroxene-melt, spinel-melt, and/or amphibole-melt.

## CONCLUSIONS

Olivine-melt and spinel-melt V oxybarometry have the potential to further improve our understanding of the redox state and redox evolution of Earth's primitive magmas. For robust constraints and to resolve limited $fO_2$ variation, it is however essential that the effects of temperature and anhydrous to hydrous melt polymerization on $fO_2$ estimates are considered. If they are neglected, olivine-melt and spinel-melt compositions may variably over- or under-estimated $fO_2$ by commonly up to ±1 log unit. This has important implications for constraining $fO_2$ for magmas generated at different geodynamic settings and for constraining redox evolution of magmas during partial crystallization. For primitive, high-Mg basaltic STV301 magma erupted at St. Vincent, Lesser Antilles, new olivine-melt V oxybarometry indicates oxidizing near-liquidus conditions (~QFM+1.8±0.5), consistent with the notion that arc magmas are primarily oxidized. During intermittent crustal storage, limited oxidation (by ~0.3 log units) appears to have occurred, in agreement with redox variation largely controlled by <25 wt% fractionation of olivine-clinopyroxene-spinel, but such limited oxidation cannot be reliably resolved by V or other mineral-melt oxybarometry for individual samples (with uncertainties of ≥±0.3-0.9 log units), requiring
863 characterization of a large number of samples to establish representative averages or other
864 characterization methods.

865

866 ACKNOWLEDGEMENTS

867 This work is part of the project "Tracking the differentiation of redox-sensitive elements in fluid-
868 rich to fluid-poor magmas" of Erdmann et al. supported by LabEx VOLTAIRE (ANR-10-LABX-
869 100-01). The analytical facilities at ISTO that were used are also supported by LabEx VOLTAIRE
870 (ANR-10-LABX-100-01) and by EquipEx PLANEX (ANR-11-EQPX-0036). Patricia Benoist and
871 Ida Di Carlo are thanked for their assistance and guidance in SEM imaging and electron microprobe
872 analyses. Fai Tcha and Henrique da Mota of IRAMAT are thanked for their support of ISTO's LA-
873 ICP-MS laboratory. Emmanuel Le Trong kindly helped with regression-related questions. The
874 Laboratoire Magmas et Volcans is thanked for hosting SE for a six-month stay in 2023. We
875 sincerely thank M. Holycross, an anonymous reviewer, and O. Müntener for their insightful and
876 constructive comments on an earlier version of this manuscript.

877

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1041

1042
1043 FIGURE CAPTIONS

1044 **Figure 1:** Conditions of experiments for which V partitioning was quantified for olivine-melt, spinel-melt, or clinopyroxene-melt in this and in previous studies. Dataset used in this study (summarized in Tables S4 to S6) and datasets used by Shishkina et al. (2018) (S2018) and Wang et al. (2019) (W2019) for their V oxybarometers for arc magmas for comparison.

1048 **Figure 2:** Mineral-melt partition coefficients determined for the STV301 experimental charges (Table 1) compared to published experimental data. Redox-sensitive V partition coefficients for (a) olivine-melt, (b) spinel-melt, and (c) clinopyroxene-melt. Ol=olivine, Cpx=clinopyroxene, Spl=spinel, L=melt. Literature data are from Canil (1997) (C1997), Toplis & Corgne (2002) (TC2002), Righter et al. (2006) (R2006), Karner et al. (2008) (K2008), Mallmann & O'Neill (2009, 2013) (MO2009, MO2013), Davis et al. (2013) (D2013), Papike et al. (2013) (P2013), Laubier et al. (2014) (L2014), Shishkina et al. (2018) (S2018), Wang et al. (2019) (W2019), and Holycross & Cottrell (2022) (HC2022). Errors for our partition coefficients are indicated as 2 RSDs, which are commonly smaller than the symbol size. Estimated errors on $\frac{1}{2}O_2$ and temperature are ±0.5 and ±1.0 log units and ±5 and ±25 °C for our internally heated pressure vessel and piston cylinder experiments, respectively.

1059 **Figure 3:** Calculated $\Delta$QFM versus experimentally-constrained $\Delta$QFM (first row, a-c.), experimental temperature (T) versus $\Delta$QFM (Calc-Exp) (second row, d-f.), calculated anhydrous NBO/T versus $\Delta$QFM (Calc-Exp) (third row, g-i), and calculated hydrous NBO/T versus ($\Delta$QFM (Calc-Exp) (fourth row, j-l) for the three tested oxybarometers. Calculated data shown were determined using the oxybarometers of Mallmann & O'Neill (2013) (first column (a,d,g,j), Eqn M2013), Wang et al. (2019) (second column (b,e,h,k,)), Eqn W2019), and Shishkina et al. (2018) (third column (c,f,i,l,)), Eqn S2018). Test data are from Laubier et al. (2014) (n=22), Shishkina et
al. (2018) (n=12), Wang et al. (2019) (n=11), and our study (n=9) Indicated uncertainties are
estimated experimental and calibration uncertainties. All input and calculated data are provided in
Table S4.

**Figure 4:** Calculated versus experimental $fO_2$ for our equation 2 olivine-melt V oxybarometer. (a) Calculated $fO_2$ values show limited deviation from experimental values. (b-f) Calculated compared to experimental $fO_2$ ($\Delta$QFM (Calc-Exp)) values show no systematic bias in relation to crystallization temperature, pressure, olivine forsterite (Fo) content, or anhydrous or hydrous melt NBO/T ($R^2$ is always <0.05). The two V partitioning data from Wang et al. (2019) for olivine-melt equilibrated at 1350 °C do not significantly deviate from all other ($\le$1200 °C) data. Temperature thus does not appear to significantly affect V partitioning for the investigated temperature range between ~1025 and 1350 °C, but a limited effect (as predicted by Mallmann & O'Neill (2013) or Wang et al. (2019)) needs to be further investigated. Indicated uncertainties are – as for Fig. 3 – estimated experimental and calibration uncertainties. All data are reported in Table S4.

**Figure 5:** Olivine compositions, where forsterite (Fo) content was calculated as $Fo=Mg/(Mg+Fe)*100$. Olivine phenocryst cores have compositions that largely match the compositions of the experimental STV301 olivine, whereas inherited cores and phenocryst rim compositions differ. The STV301 olivine compositions are from this study (round symbols) and the study of Heath et al. (1998) (square symbols). Our STV301 data and their uncertainties are reported in Tables 1 and S7. Shown for comparison are olivine compositions of low-Mg basalts from St. Vincent (LMB) (Heath et al. 1998), Grenada basaltic to andesitic lavas (Stamper et al. 2014), St. Vincent and Grenada cumulates (Tollan et al. 2012; Stamper et al. 2014), and peridotite xenoliths including primary and secondary olivine (Vanucci et al. 2007).
**Figure 6:** Spinel compositions, where spinel Mg# was calculated as Mg/(Mg+Fe²⁺)*100, Fe³⁺ was calculated through charge balance, and R³⁺ was calculated as the sum of Al, Cr, and Fe³⁺. The Mg#-rich spinel phenocryst cores and inclusions are close in composition to the experimental STV301 spinel, but the inclusions have overall higher Mg#, Fe³⁺/Fe(tot), and Fe³⁺/R³⁺. The STV301 spinel compositions are from this study (round symbols) and the study of Heath et al. (1998) (square symbols). Our STV301 data and their uncertainties are reported in Tables 1 and S8. Shown for comparison are spinel compositions of low-Mg basalts from St. Vincent (LMB) (Heath et al. 1998), Grenada basaltic to andesitic lavas (Stamper et al. 2014), St. Vincent and Grenada cumulates (Tollan et al. 2012; Stamper et al. 2014), and peridotite xenoliths (Vanucci et al. 2007).

**Figure 7:** Clinopyroxene compositions, where Mg# was calculated as Mg/(Mg+Fe)*100. Sector-zoned clinopyroxene phenocrysts and inherited cores differ from each other in composition and they also differ from the composition of the experimental STV301 clinopyroxene. The STV301 clinopyroxene compositions are from this study (round symbols) and the study of Heath et al. (1998) (square symbols). Our STV301 data and their uncertainties are reported in Tables 1 and S9. Shown for comparison are clinopyroxene compositions of low-Mg basalts from St. Vincent (LMB) (Heath et al. 1998), Grenada basaltic to andesitic lavas (Stamper et al. 2014), and St. Vincent and Grenada cumulates (Tollan et al. 2012; Stamper et al. 2014) and peridotite xenoliths including primary and secondary clinopyroxene (Vanucci et al. 2007).

**Figure 8:** Estimated early-stage storage (E1 to E3) and late-stage storage (E4 to E6) melt compositions for the STV301 magma (see Table 3 for full compositions and uncertainties). Our best estimates are compositions E2 and E3 for early-stage storage and E5 and E6 for late-stage storage conditions. Shown for comparison are the compositions of olivine-hosted melt inclusion compositions for other high-Mg basalts from St. Vincent (Bouvier et al. 2010, possibly from a
sample of the Yellow Tuff formation), and St. Vincent whole-rock compositions (extracted from the GEOROC database). (b and e) are close-ups of (a and d) as indicated.

**Figure 9:** Calculated average $fO_2$ values for the St. Vincent STV301 magma at early-stage and late-stage storage conditions for the different melt proxies and in comparison to previous estimates (see Table 4 for all calculated values). (a) All calculated $fO_2$ values for early-stage, near-liquidus condition are relatively close to each other, varying between ~QFM+1.8 and ~QFM+2.1 with our best estimate at ~QFM+1.8. (b) Calculated $fO_2$ values for late-stage storage condition vary over a large range, between ~QFM+2.1 and ~QFM+2.9. Indicated uncertainties (±0.5 log units in (a) and ±0.6 log units in (b)) are for our best estimates based on equation 2. All other uncertainties (±0.5-0.9) are given in Table 4. Previous estimates are from Heath et al. (1998) (H1998) and Pichavant & Macdonald (2007) (PM2007), which are based on olivine±spinel composition. Calibrations of Mallmann & O'Neill (2013) (MO2013), Shishkina et al. (2018) (S2018), Wang et al. (2019) (W2019), and our new calibrations (Eqn 1 and 2).
<figure><img src="image_3.png" /></figure>

Test and/or calibration data: This study ◊ S2018 ● W2019

<caption>Figure 1 – Erdmann et al.</caption>
<figure><img src="image_4.png" /><figcaption>Figure 2 - Erdmann et al.</figcaption></figure>
<figure><img src="image_5.png" /></figure>

O1 data: STV301 ● L2014 ● S2018 ● W2019 ●

<caption>Figure 3 – Erdmann et al.</caption>
<figure><img src="image_6.png" /></figure>

Data: STV301 ● L2014 ● S2018 ● W2019 ●

<caption>Figure 4 – Erdmann et al.</caption>
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>Figure 5 – Erdmann et al.</figcaption></figure>
<figure><img src="image_9.png" /></figure>

STV301: ● Inclusions in Ol
● Phenocryst cores
● Phenocryst rims
◆ Experimental
○ LMB — Grenada lavas — St. Vincent-Grenada cumulates ◇ Peridotite XLTHs

Figure 6 - Erdmann et al.
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

STV301: ● Sector-zoned phenocrysts
○ Inherited cores
◆ Experimental

○ LMB — Grenada lavas — St. Vincent-Grenada cumulates
◇ Grenada lavas

<caption>Figure 7 - Erdmann et al.</caption>
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

STV301 early-storage melt: E1 ◆ E2 ● E3 ▲ late-stage storage melt: E4 ▲ E5 ○ E6 ◆

St. Vincent whole-rock compositions ■ Olivine-hosted melt inclusions (Bouvier et al. 2010; Yellow Tuff?) ○

<caption>Figure 8 – Erdmann et al.</caption>
<figure><img src="image_22.png" /></figure>

Calibration: ◆ MO2013 ● S2018 ◆△ W2019 (Ol/Spl) ● Eqn 1 ● Eqn2

○ Our best estimates ⬐ H1998 ☐ PM2007

<caption>Figure 9 - Erdmann et al.</caption>
<table><caption>Table 1: Experimental details, V compositions, and partitioning coefficients of minerals and glasses</caption><thead><tr><th>Charge</th><th>Ref.<br>Exp.</th><th>Temp.<br>Press.</th><th>ΔQFM<br>(log)</th><th>Melt H<sub>2</sub>O<br>(wt%)</th><th>Assemblage</th><th>Phase<br>(n)</th><th>V<br>ppm(2RSD%)</th></tr></thead><tbody><tr><td rowspan="3">4-1</td><td rowspan="3">PM2007<br>IHPV</td><td rowspan="3">1050 °C<br>400 MPa</td><td rowspan="3">1.3</td><td rowspan="3">7.7</td><td rowspan="3">Gl-Ol-Spl-Cpx-Q</td><td>Gl(10)</td><td>353(2.8)</td></tr><tr><td>Ol(5)</td><td>7.31(23.6)</td></tr><tr><td>D-Ol/L</td><td>0.021(25.0)</td></tr><tr><td rowspan="3">4-2</td><td rowspan="3">PM2007<br>IHPV</td><td rowspan="3">1050 °C<br>400 MPa</td><td rowspan="3">1.0</td><td rowspan="3">6.3</td><td rowspan="3">Gl-Ol-Spl-Cpx-Q</td><td>Gl(10)</td><td>297(8.0)</td></tr><tr><td>Ol(5)</td><td>9.0(12.6)</td></tr><tr><td>D-Ol/L</td><td>0.03(12.8)</td></tr><tr><td rowspan="4">4-3</td><td rowspan="4">PM2007<br>IHPV</td><td rowspan="4">1050 °C<br>400 MPa</td><td rowspan="4">1.1</td><td rowspan="4">5.9</td><td rowspan="4">Gl-Ol-Spl-Cpx-Pl-Q</td><td>Gl(3)</td><td>254(18.8)</td></tr><tr><td>Cpx(3)</td><td>451(13.8)</td></tr><tr><td>D-Cpx/L</td><td>1.8(23.4)</td></tr><tr><td>Spl(3)</td><td>1078(15.6)</td></tr><tr><td rowspan="3">3-1</td><td rowspan="3">PM2007<br>IHPV</td><td rowspan="3">1092 °C<br>402 MPa</td><td rowspan="3">1.1</td><td rowspan="3">5.1</td><td rowspan="3">Gl-Ol-Spl-Q</td><td>Ol(3)</td><td>6.7(8.8)</td></tr><tr><td>D-Ol/L</td><td>0.02(8.8)</td></tr><tr><td>D-Spl/L</td><td>3.3(15.6)</td></tr><tr><td rowspan="3">3-2</td><td rowspan="3">PM2007<br>IHPV</td><td rowspan="3">1092 °C<br>402 MPa</td><td rowspan="3">0.7</td><td rowspan="3">4.2</td><td rowspan="3">Gl-Ol-Spl-Cpx-Q</td><td>Gl(10)</td><td>298(11.8)</td></tr><tr><td>Ol(3)</td><td>9.6(10.0)</td></tr><tr><td>D-Ol/L</td><td>0.03(15.4)</td></tr><tr><td rowspan="3">6-1</td><td rowspan="3">PM2007<br>IHPV</td><td rowspan="3">1155 °C<br>415 MPa</td><td rowspan="3">0.8</td><td rowspan="3">4.2</td><td rowspan="3">Gl-Ol-Spl-Q</td><td>Gl(8)</td><td>310(0.6)</td></tr><tr><td>Ol(3)</td><td>12.70(13.2)</td></tr><tr><td>D-Ol/L</td><td>0.041(13.2)</td></tr><tr><td rowspan="3">7-2</td><td rowspan="3">PM2007<br>IHPV</td><td rowspan="3">1198 °C<br>420 MPa</td><td rowspan="3">2.9</td><td rowspan="3">4.7</td><td rowspan="3">Gl-Ol-Spl-Q</td><td>Gl(12)</td><td>284.4(1.4)</td></tr><tr><td>Ol(5)</td><td>1.86(13.8)</td></tr><tr><td>D-Ol/L</td><td>0.007(13.9)</td></tr><tr><td rowspan="5">7-3</td><td rowspan="5">PM2007<br>IHPV</td><td rowspan="5">1198 °C<br>420 MPa</td><td rowspan="5">2.1</td><td rowspan="5">2.3</td><td rowspan="5">Gl-Ol-Spl-Q</td><td>Gl(9)</td><td>295.4(0.6)</td></tr><tr><td>Ol(8)</td><td>5.64(16.0)</td></tr><tr><td>Sp(4)</td><td>553(22.0)</td></tr><tr><td>D-Ol/L</td><td>0.019(16.0)</td></tr><tr><td>D-Spl/L</td><td>1.9(22.0)</td></tr><tr><td rowspan="3">PCW11</td><td rowspan="3">P2002<br>PC</td><td rowspan="3">1160 °C<br>1500 MPa</td><td rowspan="3">3.5</td><td rowspan="3">5.8</td><td rowspan="3">Gl-Cpx-Opx-Spl-Q</td><td>Gl(8)</td><td>369(1.2)</td></tr><tr><td>Cpx(3)</td><td>128(6.0)</td></tr><tr><td>D-Cpx/L</td><td>0.3(6.2)</td></tr><tr><td rowspan="5">PCW12</td><td rowspan="5">P2002<br>PC</td><td rowspan="5">1180 °C<br>1450 MPa</td><td rowspan="5">2.3</td><td rowspan="5">3.7</td><td rowspan="5">Gl-Ol-Spl-Q</td><td>Gl(9)</td><td>286(0.6)</td></tr><tr><td>Ol(3)</td><td>2.74(39.0)</td></tr><tr><td>Sp(3)</td><td>323(6.0)</td></tr><tr><td>D-Ol/L</td><td>0.010(39.0)</td></tr><tr><td>D-Spl/L</td><td>1.1(6.0)</td></tr><tr><td rowspan="3">PCW13</td><td rowspan="3">P2002<br>PC</td><td rowspan="3">1180 °C<br>950 MPa</td><td rowspan="3">3.1</td><td rowspan="3">5.0</td><td rowspan="3">Gl-Ol-Spl-Q</td><td>Gl(7)</td><td>288(1.8)</td></tr><tr><td>Ol(7)</td><td>1.74(13.4)</td></tr><tr><td>D-Ol/L</td><td>0.006(13.6)</td></tr></tbody></table>

Gl=glass, Ol=olivine, Spl=spinel, Cpx=clinopyroxene, Opx=orthopyroxene, Pl=plagioclase, Q=quench crystals, L=liquid, D-Ol/L=olivine-liquid partition coefficient; n=number of averaged analyses. Ref.=reference; Exp.=experiment; Temp.=temperature; Press.=pressure; P2002=Pichavant et al. 2002; PM2007=Pichavant & Macdonald 2007; IHPV=internally heated pressure vessel experiment; PC=piston cyclinder experiment; uncertainties on compositions are given as two relative standard deviations (2RSD%). The reported fO₂ values are expressed relative to the QFM buffer defined by O'Neill (1987) in log bar units.
<table><caption>Table 2: Regression parameters for equation 1 and 2 olivine-melt V oxybarometers</caption><thead><tr><th>Equation 1</th><th>Coeff.</th><th>Error</th><th>Probability</th><th></th><th></th></tr></thead><tbody><tr><td>Constant</td><td>-3.2848</td><td>0.1670</td><td>3.4955E-25</td><td>R<sup>2</sup></td><td>0.94</td></tr><tr><td>Log(D<sub>v</sub>)</td><td>-2.9893</td><td>0.1075</td><td>4.4346E-32</td><td>Observations</td><td>52</td></tr><tr><td></td><td></td><td></td><td></td><td>Regressions</td><td>1</td></tr></tbody></table><table><thead><tr><th>Equation 2</th><th>Coeff</th><th>Error</th><th>Probability</th><th></th><th></th></tr></thead><tbody><tr><td>Constant</td><td>-2.8438</td><td>0.1261</td><td>1.5999E-27</td><td>R<sup>2</sup></td><td>0.97</td></tr><tr><td>Log(D<sub>v</sub>)</td><td>-3.1960</td><td>0.0772</td><td>8.8955E-40</td><td>Observations</td><td>52</td></tr><tr><td>h-NBO/T</td><td>-0.8781</td><td>0.1127</td><td>3.9404E-10</td><td>Regressions</td><td>2</td></tr></tbody></table>

D<sub>v</sub> is the V partitioning coefficient for olivine-melt; h-NBO/T is the hydrous NBO/T, calculated as outlines in the text. Coeff.=Coefficients of the regression. Uncertainties can be calculated as
<table><caption>Table 3: Estimated range of possible melt compositions and calculated mineral-melt partitioning coefficients for the STV301 magma during intermittent crustal storage</caption><thead><tr><th rowspan="2">Estimate</th><th colspan="3">Early-stage storage<sup>a</sup></th><th colspan="3">Late-stage storage<sup>b</sup></th></tr><tr><th>E1<br>Bulk rock</th><th>E2*<br>Exp. glass</th><th>E3*<br>Calc. melt</th><th>E4<br>Calc. melt</th><th>E5*<br>Exp. glass</th><th>E6*<br>Matrix</th></tr></thead><tbody><tr><td>SiO<sub>2</sub></td><td>45.0(0.8)</td><td>45.9(0.4)</td><td>45.8(0.9)</td><td>48.0(1.7)</td><td>47.0(0.5)</td><td>45.5(1.4)</td></tr><tr><td>TiO<sub>2</sub></td><td>1.1(0.6)</td><td>1.0(0.1)</td><td>1.1(0.6)</td><td>1.3(0.2)</td><td>1.2(0.1)</td><td>0.7(0.3)</td></tr><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>14.7(0.4)</td><td>15.0(0.4)</td><td>15.7(0.6)</td><td>18.8(1.8)</td><td>17.4(0.2)</td><td>20.6(4.3)</td></tr><tr><td>Fe<sub>2</sub>O<sub>3</sub><sup>d</sup></td><td>3.0(0.2)</td><td>3.1(0.2)</td><td>2.9(0.3)</td><td>2.7(0.5)</td><td>2.9(0.1)</td><td>2.7(1.8)</td></tr><tr><td>FeO<sup>d</sup></td><td>6.3(0.4)</td><td>6.4(0.3)</td><td>6.0(0.5)</td><td>4.9(0.9)</td><td>5.6(0.2)</td><td>5.0(3.2)</td></tr><tr><td>MnO</td><td>0.2(0.1)</td><td>0.1(0.1)</td><td>0.2(0.1)</td><td>0.2(0.1)</td><td>0.2(0.1)</td><td>0.1(0.1)</td></tr><tr><td>MgO</td><td>11.5(0.2)</td><td>10.2(0.6)</td><td>9.3(0.7)</td><td>3.8(2.9)</td><td>6.4(0.2)</td><td>5.3(2.0)</td></tr><tr><td>CaO</td><td>10.5(0.2)</td><td>11.0(0.4)</td><td>11.1(0.3)</td><td>11.7(0.6)</td><td>11.3(0.2)</td><td>11.7(1.8)</td></tr><tr><td>Na<sub>2</sub>O</td><td>2.2(0.1)</td><td>2.2(0.2)</td><td>2.3(0.1)</td><td>3.0(0.4)</td><td>2.5(0.1)</td><td>2.8(0.5)</td></tr><tr><td>K<sub>2</sub>O</td><td>0.5(0.1)</td><td>0.5(0.1)</td><td>0.5(0.1)</td><td>0.7(0.2)</td><td>0.6(0.1)</td><td>0.6(0.1)</td></tr><tr><td>H<sub>2</sub>O<sup>c</sup></td><td>5.0(1.0)</td><td>5.0(1.0)</td><td>5.0(1.0)</td><td>5.0(1.0)</td><td>5.0(1.0)</td><td>5.0(1.0)</td></tr><tr><td>V</td><td>284(3)</td><td>284(4)</td><td>291(5)</td><td>285(7)</td><td>315(19)</td><td>283(92)</td></tr><tr><td>Sc</td><td>42.0(0.9)</td><td>44.0(1.0)</td><td>41.5(1.0)</td><td>31.1(4.1)</td><td>40.9(2.5)</td><td>39.8(17.8)</td></tr><tr><td>Y</td><td>14.4(0.3)</td><td>14.1(0.4)</td><td>14.8(0.7)</td><td>17.8(1.7)</td><td>16.0(1.7)</td><td>17.1(2.5)</td></tr><tr><td>Ni</td><td>340(5.0)</td><td>177(2.3)</td><td>228(29)</td><td>87(99)</td><td>89(14)</td><td>77(39)</td></tr><tr><td>NBO/T</td><td>0.81</td><td>0.74</td><td>0.70</td><td>0.37</td><td>0.50</td><td>0.40</td></tr><tr><td>h-NBO/T</td><td>1.32</td><td>1.24</td><td>1.20</td><td>0.82</td><td>0.97</td><td>0.86</td></tr><tr><td>K<sub>D</sub>OI/L(FeT-Mg)</td><td>0.27</td><td>0.24</td><td>0.23</td><td>0.16</td><td>0.25</td><td>0.23</td></tr><tr><td>K<sub>D</sub>OI/L(V)</td><td>0.014-0.020</td><td>0.014-0.020</td><td>0.014-0.019</td><td>0.015-0.018</td><td>0.013-0.016</td><td>0.015-0.018</td></tr><tr><td>K<sub>D</sub>OI/L(Sc/Y)</td><td>26-44</td><td>24-41</td><td>27-46</td><td>45-79</td><td>31-54</td><td>34-59</td></tr><tr><td>K<sub>D</sub>OI/L(Ni)</td><td>5.2-7.6</td><td>10-15</td><td>7.8-11</td><td>16-23</td><td>15-22</td><td>18-26</td></tr><tr><td>K<sub>D</sub>Spl/L(V)</td><td>-</td><td>-</td><td>-</td><td>2.9-3.3</td><td>2.8-3.1</td><td>3.1-3.4</td></tr></tbody></table>

Concentrations nomalized to 100 wt% for major and minor oxide components including H₂O and in ppm for trace elements V, Sc, Y, and Ni with estimated uncertainties (2std) in parentheses. a=Estimated early-stage storage melt compositions (E1 to E3) and calculated partitioning coefficients for primitive olivine phenocrysts cores (~Fo89, ~4.0-5.6 ppm V, ~5.7-7.4 ppm Sc, ~0.06-0.08 ppm Y, ~1780-2590 ppm Ni). b=Estimated late-stage storage melt compositions (E4 to E6) and calculated partitioning coefficients for evolved olivine phenocryst cores (~Fo84-86, ~4.2-5.1 ppm V, ~5.8-8.0 ppm Sc, ~0.04-0.10 ppm Y, ~1350-2000 ppm N) and spinel cores (>Mg#40, ~870-970 ppm V). c=estimated following Pichavant & Macdonald (2007). d=estimated using the formulation of Kress & Carmichael (1991) with fO₂ constrained using our equation 1 oxybarometer. (E1) Bulk-rock sample, which was analyzed as a glass fused from STV301 rock powder, which was the experimental starting material for the STV301 experiments. Oxide concentrations are from PM2007. (E2) Experimental glass composition 7-2. Oxide concentrations are from PM2007. (E3) Bulk-rock composition minus xenocryst and primitive phenocryst core compositions. (E4) Bulk-rock composition minus xenocryst and primitive to evolved phenocryst core compositions. (E5) Average of glass compositions 3-1 and 3-2. Oxide concentrations are from PM2007. (E6) Coarsely crystallized matrix composition. Indicated uncertainties for E1, E2, E4, and E5 are analytical uncertainties; indicated uncertainties for E3 and E6 are analytical uncertainties for bulk-rock composition plus and an estimated arbitrary uncertainty of ±20% on mineral proportions used for calculating residual melt composition. PM2007=Pichavant & Macdonald (2007). * Our best estimates. Additional details on the calculated melt compositions are provided in Tables S10 and S11.
<table><caption>Table 4: Calculated temperature (T) in °C and oxygen fugacity (fO₂) relative to ΔQFM in log units for the STV301 magma</caption><thead><tr><th>Calibration</th><th></th><th>Early-stage storage</th><th>Late-stage storage</th><th></th><th></th></tr></thead><tbody><tr><td rowspan="3">T_Ol/L_Sc/Y_MO2013</td><td>Av</td><td>E1 1207</td><td>E2* 1220</td><td>E3* 1194</td><td>**Av±σ(2sd) 1209±30</td><td>E4 1059</td><td>E5* 1044</td><td>E6* 1112</td><td>**Av±σ(2sd) 1078±30</td></tr><tr><td>Max</td><td>1262</td><td>1276</td><td>1248</td><td></td><td>1104</td><td>1090</td><td>1161</td><td></td></tr><tr><td>Min</td><td>1151</td><td>1163</td><td>1139</td><td></td><td>1013</td><td>998</td><td>1063</td><td></td></tr><tr><td rowspan="3">T_Ol/L_Ni_P2017</td><td>Av</td><td>1365</td><td>1207</td><td>1277</td><td>1242±60</td><td>1163</td><td>1144</td><td>1117</td><td>1130±60</td></tr><tr><td>Max</td><td>1418</td><td>1250</td><td>1325</td><td></td><td>1206</td><td>1186</td><td>1157</td><td></td></tr><tr><td>Min</td><td>1312</td><td>1164</td><td>1229</td><td></td><td>1120</td><td>1102</td><td>1076</td><td></td></tr><tr><td rowspan="3">fO₂_Ol/L_V_MO2013</td><td>Av</td><td>1.73</td><td>1.83</td><td>1.93</td><td>1.9±0.5</td><td>2.70</td><td>2.68</td><td>2.64</td><td>2.7±0.5</td></tr><tr><td>Max</td><td>2.02</td><td>2.12</td><td>2.19</td><td></td><td>2.88</td><td>2.86</td><td>2.81</td><td></td></tr><tr><td>Min</td><td>1.43</td><td>1.53</td><td>1.66</td><td></td><td>2.52</td><td>2.50</td><td>2.46</td><td></td></tr><tr><td rowspan="3">fO₂_Ol/L_V_W2019</td><td>Av</td><td>1.93</td><td>1.99</td><td>2.13</td><td>2.1±0.5</td><td>2.87</td><td>2.90</td><td>2.86</td><td>2.9±0.5</td></tr><tr><td>Max</td><td>2.21</td><td>2.27</td><td>2.41</td><td></td><td>3.03</td><td>3.06</td><td>3.02</td><td></td></tr><tr><td>Min</td><td>1.64</td><td>1.70</td><td>1.85</td><td></td><td>2.71</td><td>2.74</td><td>2.69</td><td></td></tr><tr><td rowspan="3">fO₂_Ol/L_V_S2018</td><td>Av</td><td>2.12</td><td>2.12</td><td>2.16</td><td>2.1±0.9</td><td>2.15</td><td>2.29</td><td>2.14</td><td>2.2±0.9</td></tr><tr><td>Max</td><td>2.34</td><td>2.34</td><td>2.38</td><td></td><td>2.28</td><td>2.42</td><td>2.27</td><td></td></tr><tr><td>Min</td><td>1.89</td><td>1.89</td><td>1.93</td><td></td><td>2.02</td><td>2.16</td><td>2.01</td><td></td></tr><tr><td rowspan="3">fO₂_Ol/L_V_Eqn1</td><td>Av</td><td>2.03</td><td>2.03</td><td>2.06</td><td>2.1±0.5</td><td>2.07</td><td>2.20</td><td>2.06</td><td>2.1±0.6</td></tr><tr><td>Max</td><td>2.25</td><td>2.25</td><td>2.28</td><td></td><td>2.19</td><td>2.32</td><td>2.18</td><td></td></tr><tr><td>Min</td><td>1.81</td><td>1.81</td><td>1.84</td><td></td><td>1.94</td><td>2.07</td><td>1.93</td><td></td></tr><tr><td rowspan="3">fO₂_Ol/L_V_Eqn2</td><td>Av</td><td>1.68</td><td>1.75</td><td>1.82</td><td>1.8±0.5</td><td>2.16</td><td>2.17</td><td>2.11</td><td>2.1±0.6</td></tr><tr><td>Max</td><td>1.91</td><td>1.98</td><td>2.05</td><td></td><td>2.29</td><td>2.30</td><td>2.24</td><td></td></tr><tr><td>Min</td><td>1.45</td><td>1.52</td><td>1.59</td><td></td><td>2.02</td><td>2.03</td><td>1.98</td><td></td></tr><tr><td rowspan="3">fO₂_Spl/L_V_W2019</td><td>Av</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>2.78</td><td>2.59</td><td>2.53</td><td>2.6±0.5</td></tr><tr><td>Max</td><td>-</td><td>-</td><td>-</td><td></td><td>3.01</td><td>2.82</td><td>2.76</td><td></td></tr><tr><td>Min</td><td>-</td><td>-</td><td>-</td><td></td><td>2.54</td><td>2.35</td><td>2.29</td><td></td></tr></tbody></table>

Temperatures were calculated using the Sc/Y thermometer of Mallmann & O'Neill (MO2013) and the Ni thermometer of Pu et al. (2017) (P2107). The fO₂ values were calculated using the oxybarometers of Mallmann & O'Neill (2013) (MO2013), Wang et al. (2019) (W2019), Shishkina et al. (2018) (S2018), and our new equation 1 and equation 2 oxybarometers. * Our best estimates; ** average for the best estimates E2 and E3 or E5 and E6, respectively. Reported uncertainties (σ at 2SD level) are inferred standard errors for M2013, W2019, and P2017, and calculated for S2018 and our calibrations. For Eqn 1 and 2, we have assumed errors of 0.001 (E1 to E3) and 0.002 (E4 to E5) on K₀Ol/L(V) and errors of 0.1 (E1 to E3) and 0.2 (E4 to E5) on estimated hydrous melt NBO/T, following from the range of compositions presented in Table 3. L=liquid, Ol=olivine, Spl=spinel.