Daniel A Coulthard
email: d.a.coulthard@massey.ac.nz

Georg F Zellmer
email: g.f.zellmer@massey.ac.nz

Akihiko Tomiya
email: a.tomiya@aist.go.jp

Sébastien Jégo
email: s_jego@hotmail.com

Raimundo Brahm
email: r.brahm@massey.ac.nz

Petrogenetic implications of chromite-seeded boninite crystallization experiments: Providing a basis for chromite-melt diffusion chronometry in an oxybarometric context

Keywords: Experimental Petrology, Internally Heated Pressure Vessel, Magma Ascent, Timescales, Crystal-Melt Disequilibrium

Boninites are rare high magnesium andesites that often contain trace chromites. These chromites precipitate from primitive boninitic melts and are thought to be carried to the surface in melts that continue to crystallize a significant volume of silicate minerals. Such magmatic differentiation drives primitive chromite out of equilibrium with the residual melt with respect to both divalent and trivalent cation proportions. Diffusion then operates to alter primitive chromite toward a composition in equilibrium with residual melt. To simulate this process, we have performed internally heated pressure vessel experiments, providing insights into the processes of chromite-melt re-equilibration through time. While Fe-Mg exchange at magmatic temperatures equilibrates the tetrahedrally coordinated divalent cations in chromite in less than 6 hours, equilibration of trivalent cations in octahedral coordination with residual melts is slower. Our experimental results show that chromite Al concentrations are ubiquitously lower, and Fe 2+ /Fe 3+ values are ubiquitously higher than modelled equilibrium values, indicating that there was insufficient time for significant Al and Fe 3+ replacement of Cr. Similar observations can be made for natural chromite compositions in the extrusive sequence of the Troodos ophiolite (Cyprus). Based on a simple model of diffusive equilibration, we estimate that microphenocrystic chromites up to 60 μm in diameter take between 60 days and c. 170 years to equilibrate under conditions analogous to the physiochemical state of melt immediately prior to eruption. For the Troodos ophiolite extrusive sequence, this implies that mafic magmas are erupted less than c. 170 years after extraction from the mantle for disequilibrium textures and compositions to be preserved.

INTRODUCTION

Boninites are rare high magnesium andesites that are produced by the melting of highly depleted mantle (harzburgite) under shallow and hydrous conditions [START_REF] Pearce | Identification, classification, and interpretation of boninites from Anthropocene to Eoarchean using Si-Mg-Ti systematics[END_REF]. The paucity of this rock type in the geologic record may be attributed to the exotic nature of these petrogenetic conditions and/or the tendency of boninites to erupt in places with a low preservation potential (e.g. forearc regions, [START_REF] Stern | Subduction zone infancy: Examples from the Eocene Izu-Bonin-Mariana and Jurassic California arcs[END_REF].

Nevertheless, boninites are generated in several tectonic settings including intraoceanic arcs [START_REF] Meijer | Primitive arc volcanism and a boninite series: examples from western Pacific island arcs[END_REF], intracontinental arcs [START_REF] Tatsumi | High-Mg Andesites in the Setouchi Volcanic Belt, Southwestern Japan: Analogy to Archean Magmatism and Continental Crust Formation?[END_REF], back-arc basins [START_REF] Falloon | Petrology and geochemistry of back-arc basin basalts from Lau Basin spreading ridges at 15°, 18° and 19°S[END_REF], and oceanic plateaus [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF]. Additionally, several boninites have been found in ophiolite terranes (e.g. [START_REF] Bédard | Petrogenesis of Boninites from the Betts Cove Ophiolite, Newfoundland, Canada: Identification of Subducted Source Components[END_REF][START_REF] Cameron | Petrology and origin of primitive lavas from the Troodos ophiolite, Cyprus[END_REF][START_REF] Dilek | Island arc tholeiite to boninitic melt evolution of the Cretaceous Kizildag (Turkey) ophiolite: Model for multi-stage early arc-forearc magmatism in Tethyan subduction factories[END_REF][START_REF] Ishikawa | Boninitic volcanism in the Oman ophiolite: Implications for thermal condition during transition from spreading ridge to arc[END_REF][START_REF] Meffre | Geochemical evolution and tectonic significance of boninites and tholeiites from the Koh ophiolite[END_REF], though the tectonic settings of some ophiolites are topics of rigorous debate (cf. [START_REF] Gass | Is the Troodos Massif of Cyprus a Fragment of Mesozoic Ocean Floor?[END_REF][START_REF] Metcalf | Suprasubduction-zone ophiolites: Is there really an ophiolite conundrum?[END_REF][START_REF] Miyashiro | The Troodos ophiolitic complex was probably formed in an island arc[END_REF][START_REF] Moores | Tethyan ophiolites, mantle convection, and tectonic" historical contingency": A resolution of the" ophiolite conundrum[END_REF][START_REF] Pearce | The Troodos ophiolitic complex probably formed in a subduction initiation, slab edge setting[END_REF][START_REF] Regelous | Formation of the Troodos Ophiolite at a triple junction: Evidence from trace elements in volcanic glass[END_REF][START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF][START_REF] Woelki | Petrogenesis of boninitic lavas from the Troodos Ophiolite, and comparison with Izu-Bonin-Mariana forearc crust[END_REF].

A cogenetic relationship between boninitic melt and podiform chromitite deposits found in some ophiolitic mantle sections has been hypothesized [START_REF] Arai | Origin of podiform chromitites[END_REF]Arai andYurimoto, 1994, 1995;[START_REF] Rollinson | The geochemistry of mantle chromitites from the northern part of the Oman ophiolite: inferred parental melt compositions[END_REF][START_REF] Rollinson | Polymineralic inclusions in mantle chromitites from the Oman ophiolite indicate a highly magnesian parental melt[END_REF][START_REF] Zhou | Origin and tectonic environment of podiform chromite deposits[END_REF][START_REF] Zhou | Formation of podiform chromitites by melt/rock interaction in the upper mantle[END_REF]. With regard to podiform chromitite formation, it has been suggested that primitive hydrous melts react with depleted mantle, become silica-enriched via the incongruent melting of orthopyroxene (implying olivine crystallization), and crystallize a large volume of high-Cr# chromite due to change in the number of available melt octahedral sites [START_REF] Edwards | New insights concerning the influence of water during the formation of podiform chromitite[END_REF]. Separately, mechanisms of chromitite formation have been experimentally explored assuming immiscibility between melt-melt or melt-fluid components [START_REF] Ballhaus | Origin of podiform chromite deposits by magma mingling[END_REF][START_REF] Matveev | Role of water in the origin of podiform chromitite deposits[END_REF]. Initial immiscibility has been observed in other experimental studies that focused on the formation of boninitic melts via the same petrogenetic mechanism (i.e. incongruent melting, [START_REF] Fisk | Basalt magma interaction with harzburgite and the formation of highmagnesium andesites[END_REF], and the boninitic composition of melts are preserved in equilibrium experiments that simulate melt-peridotite reactions [START_REF] Mitchell | Experiments on melt-rock reaction in the shallow mantle wedge[END_REF]. It is noteworthy that one experiment (C608) of [START_REF] Mitchell | Experiments on melt-rock reaction in the shallow mantle wedge[END_REF] not only produced boninite melt in equilibrium with a dunite residual mantle mineral assemblage, but that the composition of the residual mineral assemblage overlaps with the most depleted end of the olivine-spinel mantle array in compositional space [START_REF] Arai | Characterization of spinel peridotites by olivine-spinel compositional relationships: Review and interpretation[END_REF]. Ultimately, few studies have explicitly attempted to reconcile the links between boninite magma genesis, chromitite formation, and/or, more generally, chromite crystallization [START_REF] Arai | Origin of podiform chromitites[END_REF]Arai andYurimoto, 1994, 1995;[START_REF] Rollinson | The geochemistry of mantle chromitites from the northern part of the Oman ophiolite: inferred parental melt compositions[END_REF][START_REF] Rollinson | Polymineralic inclusions in mantle chromitites from the Oman ophiolite indicate a highly magnesian parental melt[END_REF][START_REF] Zhou | Formation of podiform chromitites by melt/rock interaction in the upper mantle[END_REF][START_REF] Zhou | Podiform chromitites in the Luobusa ophiolite (Southern Tibet): Implications for melt-rock interaction and chromite segregation in the upper mantle[END_REF].

If boninitic melts are generated during concomitant olivine and chromite precipitation as described above, then the appearance of high-Cr# chromite (and forsteritic olivine) in boninites may be due to their removal from a mantle domain rather than crystallization from extracted melts in the crustal domain, where chromite has not been observed to crystallize under experimental conditions analogous to those that are realistic for primitive melt differentiation (e.g. pressures > 1 bar, [START_REF] Umino | Experimental studies on boninite petrogenesis[END_REF].

It is important to specify the full implications of this model of boninite + chromitite petrogenesis, namely that boninite and chromitite appear to be linked by a cogenetic relationship based on observations of each in ophiolitic assemblages, that the underlying relationship is essentially a reactive transport process that occurs in the shallow subarc mantle, and that information on such processes may be inferred by detailed studies of chromite-melt or chromite-olivine-melt geochemistry; the systematics of which are preserved to different degrees in natural volcanic and plutonic suites (e.g. [START_REF] Kamenetsky | Factors controlling chemistry of magmatic spinel: An empirical study of associated olivine, Cr-spinel and melt inclusions from primitive rocks[END_REF].

Further, if chromites are plucked from the melt-mantle petrogenetic system, then their melt inclusions (e.g. [START_REF] Kamenetsky | Olivine-enriched melt inclusions in chromites from low-Ca boninites, Cape Vogel, Papua New Guinea: evidence for ultramafic primary magma, refractory mantle source and enriched components[END_REF][START_REF] Umino | Did boninite originate from the heterogeneous mantle with recycled ancient slab?[END_REF][START_REF] Umino | Thermal and chemical evolution of the subarc mantle revealed by spinel-hosted melt inclusions in boninite from the Ogasawara (Bonin) Archipelago, Japan[END_REF] may give valuable information regarding the nature of magma genesis in the reactive transport regime.

In the present study, we conducted a series of high-pressure (c. 2 kbar) experiments to create systems wherein high silica boninite crystallized over brief time periods in the presence of stable chromite. The data presented here demonstrate that chromite is little affected by crystallization processes over short timescales unless unrealistically oxidizing conditions are imposed. Silicate mineral assemblages form via equilibrium crystallization in hydrous melts without significantly altering chromite compositions save for Mg-Fe exchange when buffered near the nickel-nickel oxide (NNO) buffer. We propose that the systems represented by these experiments may be regarded as approximations of what occurs in natural chromite-bearing primary melts during their crustal differentiation [START_REF] Scowen | Reequilibration of chromite within Kilauea Iki lava lake, Hawaii[END_REF]. Similar observations on partial chromite-melt equilibration in natural samples from the Troodos ophiolite (Cyprus) allow a coarse quantification of the extraction time for the mafic magmas of the extrusive suite, but more detailed diffusion chronometry on the chemical zonation patterns of natural chromites will be required to provide tight constraints.

MATERIALS AND EXPERIMENTAL METHODS

Crystallization experiments were performed using internally heated pressure vessels (IHPVs) at the Institut des Sciences de la Terre d'Orléans (ISTO), Université d'Orléans, France, as well as at the Geological Survey of Japan (GSJ) in Tsukuba, Japan. Additional sample preparation took place at ISTO and at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) in Yokosuka, Japan.

Starting materials

Table 1 provides major element data for the starting materials as well as the bulk composition of the mixture used for the experiments. Analyses of the starting materials are given alongside sample data in the supplemental Tables S1 andS2. A fragment of high-Si boninite taken via dredging from the Mariana forearc (sample YK0612 974-R6, [START_REF] Reagan | Fore-arc basalts and subduction initiation in the Izu-Bonin-Mariana system[END_REF] was chosen as a suitable starting material based on observed chromite phenocrysts and microphenocrysts in thin section, which indicated chromite stability. The fragment was powdered and fluxed to form glass, which was analysed during our routine spectrometric analysis (BO-G, Table S1) and re-powdered for sample loading. Chromite seeds sourced from the mantle section of the Troodos Ophiolite were added to glass powders with the intent of fostering further growth of chromite from boninitic melts. These seeds are unzoned and are homogeneous (avg. Mg# = 62, Cr/[Al+Cr+Fe 3+ ] = 70). Two sample mixtures were made by mixing powdered glass with one size fraction of chromite (either >160 μm or < 32 μm in size), and each starting mixture contained 2% added chromite (by mass). The size of the seeds added to powdered glass were initially varied in order to test if seed size affects the resultant modal mineralogy of the sample.

Nominally pure platinum capsules were used as sample containers. Sample mixtures were first loaded and then hydrated with heavy water ( 2 H 2 O) using a microsyringe before the capsules were welded shut. Each capsule contained c. 1 wt% 2 H 2 O prior to welding (Table 2).

2 H 2 O was used instead of 1 H 2 O to allow future analysis of water using secondary ion mass spectrometry, with this substitution enabling easy distinction between added water and background hydrogen. The quality of the welds was checked by immersing each capsule in hot oil. All capsules were adequately sealed (poor welds emit a bubble stream, indicating an inadequate seal).

NiO+NiPd redox sensors added to each experiment allowed for the hydrogen fugacity (fH 2 ) imposed by the IHPV pressure medium to be evaluated, as redox sensors accurately reflect the oxygen fugacity (fO 2 ) imposed by the gas buffer [START_REF] Pownceby | Thermodynamic data from redox reactions at high temperatures. III. Activity-composition relations in Ni-Pd alloys from EMF measurements at 850-1250 K, and calibration of the NiO+Ni-Pd assemblage as a redox sensor[END_REF][START_REF] Taylor | The calibration and application of accurate redox sensors[END_REF]. These sensors were made by packing two pellets into inert ZrO 2 powder within a platinum capsule so that the pellets are not in contact with the capsule wall. One pellet was made of 50% NiO and 50% Ni x Pd 1-x and the other was made of 50% NiO and 50% Ni y Pd 1-y , with x = 0.5 and y = 0.85. Deionized water was added until the capsule interior became visibly saturated. Then the capsule was welded shut. Welds were checked in the same way for the sensors as they were for the sample capsules.

Experimental design

The IHPVs used at ISTO and GSJ both employed molybdenum furnaces to perform the high temperature experiments described here. Since the same amount of water was initialized in each sample, by varying the temperature of the experiments between 1200, 1150, and 1100℃, variable degrees of crystallinity are achieved in each sample. This determines the concentration of water in residual melts, as the crystallization of nominally anhydrous mafic minerals enriches the melt volume in incompatible volatile elements. The experiments were performed under isobaric conditions, which means the final variable to consider is the fO 2 of the system. Target oxygen fugacities were c. 1-3 log units above the NNO buffer, which are analogous to magmas generated in subduction zone settings [START_REF] Brandon | Constraints on the origin of the oxidation state of mantle overlying subduction zones: An example from Simcoe, Washington, USA[END_REF][START_REF] Evans | Oxidation state of subarc mantle[END_REF][START_REF] Kelley | Water and the Oxidation State of Subduction Zone Magmas[END_REF][START_REF] Parkinson | The redox state of subduction zones: insights from arc-peridotites[END_REF]. The oxidation states were either left unbuffered or buffered by pressurizing the IHPV with an Ar-H 2 gas mixture (pH 2 added , Table 2). Pt capsules are permeable to hydrogen, which diffuses through the capsule wall to bond with oxygen in the melt so that reduction of the sample volume occurs [START_REF] Chou | Diffusion of hydrogen through platinum membranes at high pressures and temperatures[END_REF][START_REF] Shaw | Hydrogen-Water Vapor Mixtures: Control of Hydrothermal Atmospheres by Hydrogen Osmosis[END_REF]. Since the volume of the pressure medium is much greater than the volume of the sample capsule, the pressure medium is effectively an infinite reservoir with respect to hydrogen. Thus, the effective concentration of hydrogen available to each capsule during a given experiment, fH 2 , may be considered constant. Unbuffered experiments cause the redox state of melts to approach a condition known as the intrinsic fO 2 of the IHPV. The intrinsic fO 2 of IHPV systems is highly oxidizing (NNO+2 to NNO+4, [START_REF] Scaillet | Improvements of the Shaw membrane technique for measurement and control of fH2 at high temperatures and pressures[END_REF][START_REF] Taylor | The calibration and application of accurate redox sensors[END_REF], see further discussion in Supplemental Text 1).

The experiments described here each lasted less than 6 hours. The utility of short-period experiments is multifaceted. From a volcanological perspective, fast ascending magmas are extracted from their crustal domains and extruded onto the surface in as little as tens of minutes [START_REF] Lloyd | An Assessment of Clinopyroxene as a Recorder of Magmatic Water and Magma Ascent Rate[END_REF] when melts are hot (>1000℃) and volatile rich. Short timescales of the order of hours to days have also been inferred for volatile poor arc magmas [START_REF] Lormand | Slow ascent of unusually hot intermediate magmas triggering Strombolian to sub-Plinian eruptions[END_REF]. In a rapidly ascending melt, a variety of concomitant processes may alter the physiochemical state of the melt volume, including syn-eruptive mixing (e.g. [START_REF] Tomiya | Short time scales of magma-mixing processes prior to the 2011 eruption of Shinmoedake volcano, Kirishima volcanic group, Japan[END_REF][START_REF] Wolf | Syneruptive mixing, degassing, and crystallization at Redoubt Volcano, eruption of December, 1989 to May 1990[END_REF], crystallization (e.g. [START_REF] Blundy | Rapid decompression-driven crystallization recorded by melt inclusions from Mount St. Helens volcano[END_REF][START_REF] Cashman | Degassing and crystallization of ascending andesite and dacite[END_REF], and whole-rock contamination (e.g. [START_REF] Mattioli | Rapid ascent and contamination of magmas through the thick crust of the CVZ (Andes, Ollagüe region): Evidence from a nearly aphyric high-K andesite with skeletal olivines[END_REF]. Such processes, along with subtleties such as the inclusion of antecrystic minerals, produce disequilibrium mineral assemblages that provide valuable insight into the latest stages of magmatism [START_REF] Couch | Mineral disequilibrium in lavas explained by convective self-mixing in open magma chambers[END_REF][START_REF] Spina | Role of syn-eruptive plagioclase disequilibrium crystallization in basaltic magma ascent dynamics[END_REF][START_REF] Ubide | Antecrysts and their effect on rock compositions: The Cretaceous lamprophyre suite in the Catalonian Coastal Ranges (NE Spain)[END_REF][START_REF] Zellmer | Inferring the Effects of Compositional Boundary Layers on Crystal Nucleation, Growth Textures, and Mineral Chemistry in Natural Volcanic Tephras through Submicron-Resolution Imaging[END_REF][START_REF] Zellmer | Crystal uptake into aphyric arc melts: insights from two-pyroxene pseudo-decompression paths, plagioclase hygrometry, and measurement of hydrogen in olivines from mafic volcanics of SW Japan[END_REF]. Thus, for natural magmatic systems, brief durations on the order of hours represent an end member in an ascent period context, and disequilibrium characteristics may be useful if properly placed into a petrogenetic context. Given boninite petrogenesis occurs at relatively shallow depths and generates hot and hydrous melts, sometimes in extensional settings [START_REF] Reagan | Subduction initiation and ophiolite crust: new insights from IODP drilling[END_REF], rapid ascent rates cannot be precluded. Furthermore, since it is possible that chromites preserved in boninite matrices may have been generated within the source regions of the melts, knowledge of how these minerals react to changes in the physiochemical states of the melts (i.e. experimental observation) is needed in order to assess and contextualize natural sample materials. These considerations provide an incentive to perform experiments on brief timescales and to analyse disequilibrium features.

ANALYTICAL METHODS

Analytical facilities at Victoria University of Wellington, Hokkaido University, Massey

University, and The University of Iowa were utilized to gather the data presented here.

Following removal of the sample holder from the IHPV, each capsule was weighed to assess for mass loss during the experiment. The capsules were then mounted in epoxy and ground to expose their interiors. Ni-Pd alloys recovered from each sensor capsule was separated from powdered ZrO 2 and mounted in epoxy. These sample materials were then polished for imaging and microprobe analysis, using SiC lapwheels and diamond grit paste.

Electron microbeam techniques

Samples produced at ISTO were imaged using an FEI Quanta 200 Environmental scanning electron microscope (SEM) at the Manawatu Microscopy and Imaging Centre (Massey University). This SEM was also used to perform semi-quantitative analyses of calcic silicate minerals using an attached EDAX energy dispersive spectroscope (EDS). Samples produced at GSJ were imaged at the Creative Research Institute of Hokkaido University using a JEOL JSM-7000F Field Emission SEM. An attached XMAX 150 EDS was used here to analyse the capsule Pt walls in contact with sample melts in order to detect iron loss after each experiment (Supplemental Text 2, Table S3). Quantification of Fe in Pt was achieved by calibrating signal intensity to pure Co.

Electron probe microanalysis (EPMA) occurred at multiple laboratories: at Victoria University of Wellington and The University of Iowa, JEOL JXA-8230 Superprobes were used. Additional chromite analyses were performed at Hokkaido University on a JEOL JXA-8800R. Glass analyses were performed using Na-migration mitigation techniques. In addition to using diffuse beam conditions (spot sizes of 5-10 μm), two Na acquisitions are totalled. If analyses return low concentrations (determined using secondary standards), then sodium loss may be corrected by either: removing the second acquisition (if Na is lost), removing either point (if either indicates loss), or back-calculating time-resolved intensity to correct for Na loss. No analyses reported here experienced significant sodium migration as indicated by multiple analyses of both sample and standard materials.

Secondary standards provided by the Smithsonian Institution Department of Mineral Sciences and/or the Max Planck Institute for Chemistry were included in all glass and mineral analyses. Ni-Pd sensor compositions were quantified using metal standards by Astimex.

Repeat analyses of secondary standards provided a basis to assess the accuracy of data gathered during EPMA (Tables S1-S2, and S4). The accuracies associated with glass analyses have been determined to be within 1% for SiO 2 , Al 2 O 3 , MgO, and CaO, 5% for TiO 2 , FeO, and K 2 O, 10% for Na 2 O, and 20% for MnO. For analyses of silicate minerals, SiO 2 , MgO, CaO, and Na 2 O are accurate to within 1%, while FeO, Cr 2 O 3 , MnO, and Al 2 O 3 are better than 2%. Chromite standardization was achieved using several mineral and oxide standards.

Replicate standard analyses demonstrated that all major elements given are accurate to within 5%, while MnO is accurate to within 40%. Secondary standard compositions are taken from [START_REF] Jarosewich | Reference Samples for Electron Microprobe Analysis*[END_REF]; [START_REF] Jochum | MPI-DING reference glasses for in situ microanalysis: New reference values for element concentrations and isotope ratios[END_REF][START_REF] Jochum | Chemical Characterisation of the USGS Reference Glasses GSA-1G, GSC-1G, GSD-1G, GSE-1G, BCR-2G, BHVO-2G and BIR-1G Using EPMA, ID-TIMS[END_REF].

To ensure analyses of pyroxene were of high quality, raw EPMA data were normalized prior to formulae recalculation using the methods described by [START_REF] Putirka | Thermometers and Barometers for Volcanic Systems[END_REF]. Analyses that returned cation totals much greater than or less than 4 (on an O = 6 basis) were discarded. In a similar manner, raw chromite analyses were recalculated to cation proportions per 4 oxygens. Recalculation of ferric iron proportions used the equation of [START_REF] Droop | A general equation for estimating Fe 3+ concentrations in ferromagnesian silicates and oxides from microprobe analyses, using stoichiometric criteria[END_REF]. No other multivalent cations (e.g. Mn, Cr) were considered.

Determination of phase proportions

In order to provide high-precision phase proportion data, a computationally inexpensive machine learning tool enabled the analysis of backscattered electron (BSE) images and produced segmented images that we interpreted in terms of phase proportions using Adobe Photoshop. Segmented images are images that have been petrographically interpreted using a machine learning algorithm and are color-coded based on which phase each pixel represents (Supplemental Text 3). The machine learning tool used is called Trainable Weka Segmentation, and was developed by [START_REF] Arganda-Carreras | Trainable Weka Segmentation: a machine learning tool for microscopy pixel classification[END_REF]. The algorithm requires limited user input (5-8 user-defined groups of pixels) to "train" the computer-generated classifier, which segments as many mineral phases as the user defines This tool produced the segmented images used to infer the phase proportions given in Table 2. The tool is provided as a plugin on the Fiji Is Just ImageJ (FIJI) platform [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. A minimum of 5 training sessions were conducted for each analysis, and the data derived from each segmented image were averaged to produce the given proportions with the calculated standard deviation providing the precision of each phase classification. Images representative of the sample textures were used for segmentation. See Supplemental Text 3 for more information and an example of a segmented image.

Determination of oxygen fugacities from the solid sensors

Fugacity calculations were performed following the methodology of [START_REF] Scaillet | Experimental crystallization of leucogranite magmas[END_REF].

Sensor compositions, XNi (Ni/[Ni+Pd] calculated using cation proportion), were determined following EPMA. Further discussion of fugacity, including the calculation methodology, is provided in the Supplemental Text 1.

RESULTS

Weighing the capsules after quench indicated that no mass was lost during any experiment.

Table 2 gives information on each sample including the mixture used, initial water concentration, experimental conditions, resultant phase proportions inferred for each sample, sensor compositions, and fO 2 data.

The capsule interiors of every sample except for Bon1200Ub were analysed via EDS in order to assess the degree of iron loss from the melt to the Pt of the capsule wall. Line analyses from the sample-wall contact into the capsule wall yielded no detectable iron c. 30 μm from the interface. Integrating concentration profiles demonstrates that iron loss in unbuffered experiments is limited to 10% or lower (of bulk sample Fe), while buffered experiments lost 20-35% Fe over experiment durations (Supplemental Text 2, Table S3). However, we will demonstrate that none of our discussion topics have been significantly affected by iron loss.

Petrographic observations

Euhedral-subhedral orthopyroxene (opx) is abundant and is the only silicate phase present at 1200℃ and 1150℃ (Figure 1A). In BSE images, these crystals often have bright caps that form at the apices of euhedral crystal forms (Figure 1B). At 1100℃, a petrographically distinct trace silicate phase was observed along with abundant opx in Bon1100U (Figure 1C).

Semi-quantitative EDS analyses of this phase demonstrate that this silicate is rich in Ca, Mg, and Fe. If it is a pyroxene, it is likely augite (c. Wo 31 En 57 Fs 12 ). Chromite is stable in all boninitic samples, and BSE images of moderate-sized grains show that chromite mantles have become brighter than cores (Figure 1D), indicating that diffusive equilibration was interrupted by quenching in large grains. In general, all chromites appear as anhedral grains with sharp-subrounded corners. These are not indications of chromite growth, suggesting that all observed chromites are the original seeds added to each experiment. Likewise, there is no evidence of dissolution, which indicates that chromite was a stable phase for the full duration of each experiment. This implies that our experiments only produced pyroxene crystallization in the presence of stable chromite.

A small number of micro-vesicles occur in all boninitic samples (e.g. Figure 1A). The vesicles are spherical and show no indication of clustering. They appear randomly distributed within the sample volume. No vapour films were observed along any of the capsule walls.

Redox sensors and calculation of imposed fO 2

Average XNi values were calculated for each sensor and used to infer sensor fO 2 for each experiment. For water undersaturated sample melts, aH 2 O must be modelled in order to accurately calculate fO 2 . To this end, the activity model of [START_REF] Burnham | The importance of volatile constituents[END_REF] was used in conjunction with major element data and inferred melt water concentrations (Supplemental Text 1) to model aH 2 O. The uncertainties reported here for fO 2 are similar to those reported elsewhere for the solid sensor technique [START_REF] Jégo | Controls on gold solubility in arc magmas: An experimental study at 1000 C and 4 kbar[END_REF][START_REF] Scaillet | Experimental crystallization of leucogranite magmas[END_REF]. The solubility model of [START_REF] Zhang | Silicate melt properties and volcanic eruptions[END_REF] was used to calculate maximum water concentrations in residual melts under the experimental conditions, which correspond to c. 5.3-5.4 wt%.

According to these model constraints, boninitic melts did not reach saturation (Table 2), and the ubiquitous presence of micro-vesicles (Figure 1A) is therefore not due to water saturation (exsolution) but likely due to the inclusion of atmospheric gas in the sample capsules during preparation.

Complexities associated with quench crystallization were observed in samples Bon1200Ua

Bon1200Ub, Bon1200Ba and Bon1200Bb and are discussed later. A principal effect of quench crystallization is to raise aH 2 O in residual melts. Thus, for these high-T samples, the reported fO 2 data are considered maxima.

Compositional Data

Representative compositional data are given in Table 3. Full sample datasets for each phase, including secondary standard analyses, data compiled from the literature, and model data, are given in Tables S1-S2 andS4. Literature data cited for comparison are provided in Table S5.

Glass compositions

Residual melts formed andesitic glasses, the compositions of which are given with other experimental products in Table 3. These glasses are depleted in FeO, MnO, MgO, and Cr 2 O 3 relative to both the initial boninite glass as well as the bulk composition of the system (Table 1). SiO 2 , CaO, Al 2 O 3 , Na 2 O, K 2 O, and TiO 2 are enriched in residual melt during every experiment, which is consistent with extensive opx crystallization.

The two experiments conducted at high temperature (Bon1200U and Bon1200B) returned four samples with glasses containing low MgO concentrations relative to those from experiments conducted at 1150℃. This is counterintuitive, because the crystallization of opx at higher temperature should produce a lower proportion of minerals relative to lower temperatures, and overall depletion of MgO and FeO relative to the initial glass composition should be smaller. Additionally, glass compositions inferred for sample Bon1200Ua indicate a high degree of heterogeneity beyond the limit of analytical uncertainty, consistent with inefficient quenching producing local melt heterogeneity. These data, along with relatively high melt K 2 O concentrations and the presence of abundant rim formation on opx grains within these samples (Figure 1B) indicate that a significant degree of quench crystallization has occurred in the high temperature experiments. These observations are absent from all experiments conducted at 1150-1100℃, which suggests that quenching was efficient in these latter experiments and that no quench crystallization occurred.

Pyroxene compositions

Opx formed under every temperature and redox condition imposed by the IHPV. In order to confirm the identity of low-Ca pyroxenes as opx and not pigeonite, we calculated calcium molar fractions for an opx-clinopyroxene (cpx) dividing line using equation 38 of [START_REF] Beattie | Partition coefficients for olivine-melt and orthopyroxene-melt systems[END_REF] with the experimental temperatures imposed within the IHPV as the single independent variable. All pyroxene data presented here fall below these model values, which confirms their identity as opx. Opx compositions are graphically illustrated in Figure 2.

Plotted alongside these data are data taken from other experiments conducted using boninitic bulk compositions [START_REF] Tatsumi | Melting experiments on a high-magnesian andesite[END_REF][START_REF] Umino | Experimental studies on boninite petrogenesis[END_REF]) and natural opx compositions sourced from boninitic rocks (Mariana trench, [START_REF] Bloomer | Petrology and geochemistry of boninite series volcanic rocks from the Mariana trench[END_REF]Troodos ophiolite, Cameron, 1985;and Chichijima, Umino, 1986;[START_REF] Yajima | High-Ca and low-Ca boninites from Chichijima, Bonin (Ogasawara) archipelago[END_REF].

Opx Mg# (molar Mg/[Mg+Fe Total ]) positively correlates with temperature, and under buffered redox conditions is lower than in unbuffered products (Figure 2). Differences in MgO and FeO concentrations observed in samples processed at 1200℃ but different fO 2 are on the order of 1-2 wt% for each element. Thus, lower Mg# is associated both with lower temperature as well as lower fO 2 . Minor oxide components in opx include CaO, Na 2 O, Cr 2 O 3 , MnO, TiO 2 , and Al 2 O 3 . The concentrations of each of these oxides are < 5 wt%, with variation of some concentrations correlating with changes in the intensive parameters of the IHPV. Higher cation proportions of Ca, Al, and Mn are observed in samples synthesized under lower temperatures (Figure 2). Cr 2 O 3 , Na 2 O and TiO 2 concentrations are extremely low in all pyroxenes, and potential variations in these oxides due to changes in temperature or redox condition are imperceptible when considering the detection limits for these elements.

The effects of imposing variable redox conditions on the melt-opx partitioning of Ca, Al, and Mn cannot be discerned for a given temperature interval because, with regard to these elements, the mean core compositions for all opx synthesized at a given temperature are not observed to significantly change between high and low fO 2 .

When natural and other experimental opx compositions are compared to the experimentally synthesized opx presented here, the majority of natural and experimental opx compositions are similar to opx synthesized at 1200℃ and under buffered fO 2 conditions in terms of their Mg#. Mn proportions broadly overlap with products of high temperature crystallization, while Al and Ca cation proportions from the literature are, respectively, somewhat lower and higher than our experimental products.

Chromite compositions

Initial seed chromite fragments were analysed by EPMA in order to determine if the chromitite pod could be considered homogeneous. Representative data are given in Table 1 with other starting material compositions. A single analysis revealed minimal enrichment of FeO and TiO 2 (Table S2). Because the level of enrichment is low and rarely observed, we consider the seed chromite to be homogeneous.

Experimental chromite compositions are chromium-rich, typically with 70 < Cr# < 81 (Cr# = molar Cr/[Cr+Al], Table 3), and compositional data are illustrated in Figure 3. Priority was given to small seed chromites (c. 10-15 μm in diameter) that were able to be analysed without significant Si-contamination of the analysis volume from adjacent glass. This was because the initial goal of adding seed chromite was to foster mineral growth from the boninitic liquid. Since this likely did not occur, then the next best action was to analyse material that most likely equilibrated with residual melts by the end of each experiment. Two samples seeded with large chromite fragments (Bon1200Ua and Bon1200Ba) were observed to also contain several small anhedral chromite fragments distributed among the opx crystals (possibly chromite powder contamination from the sieving process). Several of these were analysed in Bon1200Ua, but no analyses of chromite in Bon1200Ba were determined to be free of glass contamination based on high observed concentrations of Si, Ca, and, in some cases, Na. These data were rejected.

Compositions taken from the literature on boninite-hosted chromites sourced from the Mariana trench wall [START_REF] Bloomer | Petrology and geochemistry of boninite series volcanic rocks from the Mariana trench[END_REF], the Troodos ophiolite [START_REF] Bailey | Ultramafic and related lavas from the Margi area, Troodos ophiolite[END_REF][START_REF] Cameron | Petrology and origin of primitive lavas from the Troodos ophiolite, Cyprus[END_REF][START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF][START_REF] Macleod | The tectonic evolution of the Eastern Limassol Forest Complex, Cyprus[END_REF][START_REF] Thy | Crystallization Orders and Phase Chemistry of Glassy Lavas from the Pillow Sequences, Troodos Ophiolite, Cyprus[END_REF], Guam [START_REF] Reagan | Geology and geochemistry of early arc-volcanic rocks from Guam[END_REF], and Chichijima [START_REF] Umino | Magma mixing in boninite sequence of Chichijima, Bonin Islands[END_REF] are provided for comparison. Note that the chromites from [START_REF] Thy | Crystallization Orders and Phase Chemistry of Glassy Lavas from the Pillow Sequences, Troodos Ophiolite, Cyprus[END_REF] are olivine-hosted mineral inclusions.

In terms of trivalent cation proportions (i.e. Fe 3+ , Al, and Cr), fO 2 buffered experiments produced chromites with compositions that did not significantly change from the initial seed composition (Figure 3A). Chromium is efficiently oxidized above NNO in iron-bearing melts [START_REF] Hanson | The systematics of Cr 3+ and Cr 2+ partitioning between olivine and liquid in the presence of spinel[END_REF]. Thus, all Cr in chromite is Cr 3+ . However, some of these chromites have bright mantles that clearly indicate Fe enrichment (e.g. Figure 1D). Under intrinsic fO 2 conditions corresponding to c. 3.2-4.0 log units above the NNO buffer and at temperatures of 1200-1150℃ (red and yellow diamonds on Fig. 3), significant amounts of Fe 3+ were added to chromite, resulting in an enrichment of total FeO with concentrations > 20 wt%. For these samples, their trend on Figure 3A illustrates significant Fe 3+ -Al exchange between chromite and melt, as the trend of core compositions runs sub-parallel to lines of equal Cr proportion (which caused the observed increase in Cr# for these chromites). Because this trend is linear and the samples do not cluster, it is likely that the Fe 3+ -Al exchange reaction failed to reach equilibrium. It is noteworthy that chromite grains in sample Bon1100U appear to have lost very little Al during the experiments, as Al 2 O 3 concentrations are ≤ 1 wt% different from concentrations in the seed chromite, consistent with the observed invariance of their inferred Fe 3+ contents. TiO 2 was consistently low in all chromites, reaching a maximum value of 0.14 wt% under the lowest temperature setting (Bon1100U).

NiO concentrations were nearly constant throughout the dataset at c. 0.11 wt%.

The literature data lie on a separate trend on Figure 3A that is sub-parallel to lines of constant Fe 3+ proportion. Of these data, chromite inclusions in olivine from the Kythreotis locality (Troodos, [START_REF] Thy | Crystallization Orders and Phase Chemistry of Glassy Lavas from the Pillow Sequences, Troodos Ophiolite, Cyprus[END_REF] and matrix chromite from Guam appear to be the most aluminous, while sample material from the Mariana Trench and Chichijima plot together near the extreme Cr end of the ternary diagram along with other Troodos chromites.

In fact, chromite compositions from Troodos boninites and tholeiites span a wide range on this diagram, plotting between the Kythreotis samples and the highly chromian composition observed for the Kapilio locality [START_REF] Cameron | Petrology and origin of primitive lavas from the Troodos ophiolite, Cyprus[END_REF]. The similarity between some of the chromites observed in Troodos boninites/tholeiites and the seed chromites from the plutonic chromitite is noted, as it was by [START_REF] Cameron | Petrology and origin of primitive lavas from the Troodos ophiolite, Cyprus[END_REF].

In Figure 3B, Mg# (chromite Mg# = Mg/[Mg+Fe 2+ ] using molar proportions) is plotted against Fe 3+ /[Fe 3+ +Cr+Al] (also calculated using molar proportions) in order to visualize the effects of iron enrichment in a compositional space that is more representative of the spinel (sensu lato, hereafter s.l.) solid solution. Again, it is evident that buffered experiments (squares) have the same Fe 3+ proportion as seed chromite. However, it is apparent that some Mg-Fe 2+ exchange has occurred at 1150℃, which represents the rim formation reaction observed in BSE images (yellow square). Thus, in fO 2 buffered experiments conducted at 1150℃, Fe 2+ has been added to chromite and Mg has been lost to the melt. For a given temperature, Mg# appears to decrease with Fe 3+ incorporation. This is observed for samples recovered from experiments Bon1200U and Bon1150U, which plot to higher Fe 3+ relative to products of buffered experiments. Interestingly, natural chromite compositions observed in the Troodos ophiolite span a slightly greater range of Mg# than the experimental products.

Included in these data are additional olivine-hosted chromite inclusion data from [START_REF] Sobolev | Petrology of ultramafic lavas and associated rocks of the Troodos massif, Cyprus[END_REF] and [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF].

DISCUSSION

Assessment of divalent cation distribution and equilibrium state between chromiteopx-melt

Because the experiments described here did not produce any discernible chromite growth, instead of discussing chromite crystallization, the following sections discuss the state and kinetics of chromite equilibration. The physiochemical states imposed upon the boninite system are analogous to a shallow-mid crust setting, and thus these experiments are ideally suited to study the effects of chemical disequilibrium on compositional change as a function of temperature and fO 2 over brief timescales in this setting.

Based on textural evidence, it is apparent that large seed chromites in the samples presented here failed to reach chemical equilibrium with their residual melts (Figure 1D). Since opx crystallization is the process that altered the major element composition of melts during each experiment, it is also the process that determines the extent to which chromite would have to interact with residual melt in order to reach an equilibrium state under the conditions imposed within the IHPV. Thus, it is important to qualify the relationship between opx and residual melt so that chromite-melt relationships can be confidently explored.

In order to test for opx-melt equilibrium, the methodology of [START_REF] Putirka | Thermometers and Barometers for Volcanic Systems[END_REF] was used.

Specifically, for a given sample, melt cation fractions were calculated (X d liq , Table S1) for each glass analysis. From these values, X Si liq was used to calculate model equilibrium Fe-Mg exchange coefficients (K D , Table 4, Figure 4A) using the following relationship given by [START_REF] Putirka | Thermometers and Barometers for Volcanic Systems[END_REF]: Equation 1K D (Fe -Mg) 𝑜𝑝𝑥 -𝑙𝑖𝑞 = 0.4805 -0.3733𝑋 𝑙𝑖𝑞

Si

An uncertainty (1σ) of ± 0.06 was attributed to these modelled K D values, which is an order of magnitude higher than the 1σ associated with the distribution of modelled K D values given in Table 4 and is illustrated as areas on Figure 4A. Observed K D calculations employed molar proportions for opx core analyses and average molar proportions for glass compositions.

Average K D values (including 2σ error bars) for samples Bon1150U and Bon1150B plot completely within their model areas, indicating that the opx sampled in these charges were in equilibrium with their respective residual melts at the time of quenching. K D values calculated for three opx cores in sample Bon1100U produce an average K D that is positioned just outside of the model area. However, since the lower error bar stretches into the uncertainty envelope as illustrated, it is reasonable to say that these crystals also equilibrated with their residual melt. There are two negative effects of quench crystallization that impacted K D calculations and prevented us from determining whether opx in samples processed at 1200℃ were able to reach equilibrium or not. The first is the effect of raising X Si liq , which occurred as quench crystals removed Mg, Fe, and Ca from residual melts. This lowers model K D values (Equation 1). The other effect is the removal of Mg and Fe from the melt phase, which precluded realistic K D values from being observed (Figure 4A). Since opxmelt K D s indicate an equilibrium condition for experiments conducted at 1150-1100℃, none of the iron loss observed in these samples had an observable effect on the equilibrium partitioning of Fe-Mg between opx and melt. This indicates that our equilibration considerations are not significantly affected by this process.

In order to assess for chromite-opx equilibrium, the model of [START_REF] Liermann | Fe 2+ -Mg fractionation between orthopyroxene and spinel: experimental calibration in the system FeO-MgO-Al 2 O 3 -Cr 2 O 3 -SiO 2 , and applications[END_REF] was applied. This model was calibrated at higher pressures than imposed in our experiments.

However, because changes between partial molar volumes (of end-member compositions at the standard state) associated with the Fe 2+ -Mg exchange reaction between chromite and opx appear to exhibit ideal mixing behaviour and because both Fe 2+ and Mg endmembers exhibit similar and predictable pressure dependencies, Liermann and Ganguly (2003) assumed a pressure normalization scheme (their equation 5) to process their K D values and formulate a thermometer for opx-chromite pairs that may be applied under a wide range of pressure conditions. We have rearranged this thermometer (their equation 8) to predict chromite-opx K D (Fe 2+ -Mg, Table 4) at 2 kbar (0.2 GPa): As illustrated on Figure 4B, the Fe 2+ -Mg subcomposition of chromite (given as Mg# in Figure 3B) in several samples has equilibrated with the opx-melt subsystem over the brief timescale of these experiments. The relatively large seed shown in Figure 1D has a rim that is c. 8-10 μm wide. Because our analyses prioritized small chromites that were c. 10-15 μm in diameter, we consider it likely that EPMA sampled chromite that completely equilibrated with respect to Fe 2+ -Mg through diffusion.

Equation 2 K D (Fe 2 + -Mg) 𝑐ℎ𝑟𝑚 -𝑜𝑝𝑥 = exp [ AT(K) + B + 122P(GPa) -C𝑋 𝑜𝑝𝑥 Al + D𝑌 𝑐ℎ𝑟𝑚
Thus, since a self-consistent determination of equilibrium has been established using empirical relationships, then the Fe 2+ -Mg data provided here describe the equilibrium condition of the melt + opx + chromite system under high temperature and fO 2 conditions analogous to those in sub-arc crust. Interestingly, significant degrees of iron loss should raise the Mg# of the sample bulk composition even when the ratio of Fe 2+ to Fe 3+ in melt is maintained by hydration (Supplemental Text 2). This effect should be observable in product opx compositions, as higher melt Mg# should result in higher opx Mg#. Since this is not observed (Figure 2, Table 3), then the observed iron loss (in the case of Bon1150B, 20% bulk Fe) does not significantly affect the equilibrium distribution of Fe 2+ -Mg under our experimental conditions.

Assessing chromite-melt equilibrium based on model equilibrium trivalent cation proportions

Since Fe 2+ -Mg has now been accounted for, it is prudent to also examine the equilibrium state of the trivalent cations in chromite. To this end, multiple modelling methods were integrated to predict equilibrium chromite compositions (with respect to trivalent cation proportions).

Our method modelled system compositional data using the alphaMELTS front end [START_REF] Smith | Adiabat_1ph: A new public front-end to the MELTS, pMELTS, and pHMELTS models[END_REF] and the MELTS thermodynamic model [START_REF] Ghiorso | Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures[END_REF] with Rhyolite-MELTS system corrections enabled [START_REF] Gualda | Rhyolite-MELTS: a modified calibration of MELTS optimized for silica-rich, fluid-bearing magmatic systems[END_REF]. Nested modelling utilized SPINMELT-2.0 (Nikolaev et al., 2018a, b), which calculated an alternative stable chromite composition for each intermediate MELTS step. These models are likely to bookend actual trivalent cation proportions in spinel (s.l.) compositional space (see [START_REF] Davis | Experimental investigation of basalt and peridotite oxybarometers: Implications for spinel thermodynamic models and Fe 3+ compatibility during generation of upper mantle melts[END_REF]Nikolaev et al., 2018a, for information and discussion on how individual models behave when predicting chromite compositions). A detailed description of the modelling methodology is included in Supplemental Text 4. SPINMELT-2.0 cannot make sense of MELTS-modelled liquid compositions at NNO+3 because the liquid composition at this condition lies outside of the calibration range for the SPINMELT-2.0 algorithm. Thus, SPINMELT-2.0 data are not available under highly oxidizing conditions.

Figure 5 illustrates the relationship between MELTS and SPINMELT-2.0 models and the difference between modelled compositions and the synthetic chromites produced in our experiments. Alternative models were created to observe the effect of 30% iron loss on the system (empty symbols, Figure 5). It appears that under highly oxidizing conditions and 1150-1200℃, experimental chromite Fe 3+ /[Fe 3+ +Cr+Al] values approach values that are attained at NNO+2 in the MELTS models. Still, given the distance on the ternary diagram between modelled chromite compositions and our experimental data, none of the experimental chromites are in equilibrium based on observed trivalent cation proportions.

This includes model data that were generated under conditions where iron loss was accounted for. The principal effect of iron loss is to reduce the proportion of iron in equilibrium chromite. The trend to high Fe 3+ concentrations observed for the oxidized samples illustrated in Figures 3A and5 are likely to represent a segment of a diffusion trend in ternary space.

The concept of diffusion in this compositional space is explored below. Since the volume of chromite in the charges is invariant (i.e. no resorption or crystallization has been observed), then the process by which chromite equilibrates can exclusively be attributed to diffusion.

Differences between MELTS and SPINMELT-2.0 output data are surprisingly large but may be attributed to both our modelling strategy (Supplemental Text 4) as well as inherent limitations of the model platforms. Models in the MELTS family tend to overpredict spinel (s.l.) Fe 3+ proportion and underpredict Cr proportion [START_REF] Davis | Experimental investigation of basalt and peridotite oxybarometers: Implications for spinel thermodynamic models and Fe 3+ compatibility during generation of upper mantle melts[END_REF]Nikolaev et al., 2018a), and the creators of SPINMELT-2.0 claim that their model reproduces several petrologically important chemical aspects of chromite chemistry to better than 20% (Cr/Al and Mg/Fe 2+ , Nikolaev et al., 2018a). What MELTS does describe accurately is Fe-Al exchange within the system during melt evolution and thus likely provides a best fit topology in compositional space [START_REF] Davis | Experimental investigation of basalt and peridotite oxybarometers: Implications for spinel thermodynamic models and Fe 3+ compatibility during generation of upper mantle melts[END_REF]. Because of these observations, we reiterate that our modelling method likely bookends equilibrium chromite compositions;

keeping in mind that multiple experiments were performed beyond the calibration range of SPINMELT-2.0.

In the case where Fe 2+ in chromite is in equilibrium with the co-existing melt/silicate mineral assemblage, the interdiffusion of trivalent cations should occur in chromite with Fe 2+ /Fe 3+ higher than that in coexisting melt, as melt Fe 2+ /Fe 3+ should always be higher than spinel Fe 2+ /Fe 3+ [START_REF] Maurel | Étude expérimentale de l'équilibre Fe 2+ -Fe 3+ dans les spinelles chromifères et les liquides silicatés basiques coexistants, à 1 atm[END_REF]. Using equation 7 of [START_REF] Kress | The compressibility of silicate liquids containing Fe 2 O 3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states[END_REF], model melt Fe 2+ /Fe 3+ values were generated (Table S1) using glass compositions and the intensive parameters imposed by the IHPV to show that most if not all experimental chromites must incorporate more Fe 3+ before reaching an equilibrium Fe 2+ /Fe 3+ threshold (Figure 6). That is, in order to reach an equilibrium condition, the observed Fe 2+ /Fe 3+ in chromite must incorporate more Fe 3+ so that their ratio values fall below the grey lines on Figure 6. The exception is sample Bon1200Bb, the chromite Fe 2+ /Fe 3+ values of which are distributed (mostly) beneath the modelled melt Fe 2+ /Fe 3+ value.

The diffusion of major cations within spinel (s.l., e.g. Figure 19 of Van Orman and Crispin, Cr# [START_REF] Suzuki | Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep[END_REF] and fO 2 affects D Fe [START_REF] Vogt | Fe-Mg diffusion in spinel: New experimental data and a point defect model †[END_REF]. As stated by [START_REF] Vogt | Fe-Mg diffusion in spinel: New experimental data and a point defect model †[END_REF] this behaviour is not well constrained under high-T and high-P conditions. Our results corroborate this inference. Since spinel (s.l.) is an isometric mineral, the given diffusivities do not vary with crystallographic orientation, which is convenient for the purpose of textural analysis (Supplemental Text 5).

As demonstrated in Figure 3A, when buffered at NNO+0.4, +1 and +2.5, chromite compositions did not significantly change from the original seed composition with respect to trivalent cation proportion. Only change in Mg# is observed for these chromites (Figure 3B).

Significant Fe 3+ incorporation was only observed in unbuffered samples at T > 1100℃ and occurred at the expense of Al, since trivalent cation proportions for these samples are distributed along lines of equal Cr proportion (Figure 3A). Thus, Al counter-diffusion facilitated Fe 3+ incorporation in chromite under highly oxidizing conditions at 1150-1200℃;

although it is unlikely these minerals completely equilibrated during the experiments (Figure 5).

The Fe-Mg and Fe-Al exchange reactions have also been observed in natural samples that are allowed to equilibrate over decadal timescales [START_REF] Scowen | Reequilibration of chromite within Kilauea Iki lava lake, Hawaii[END_REF]. Importantly, the observations of [START_REF] Scowen | Reequilibration of chromite within Kilauea Iki lava lake, Hawaii[END_REF] confirm the rank of the diffusivities outlined above and establish that even though Cr is the most sluggish element to diffuse, eventually Cr diffusion does occur in natural settings to equilibrate chromite following Fe-Al interdiffusion.

Based on our observations, we hypothesize that Fe 3+ -Al interdiffusion operates principally as a function of fO 2 to equilibrate chromite Fe 2+ /Fe 3+ (after equilibration of chromite Mg#) on a shorter timescale than is required to equilibrate Cr in the system. This scenario of diffusive re-equilibration may be conceptualized within a multi-step chemical reaction (Figure 7). The first step concerns Fe 2+ -Mg exchange between chromite and melt. This is the only reaction observed in samples processed under buffered fO 2 (and in sample Bon1100U), and since the observed changes in chromite composition are more complex under higher fO 2 conditions, we combine this exchange with the observed increase in Fe 3+ in trivalent cation proportion as reaction 1 (Figure 7). Thus, a relatively high Fe 2+ /Mg + Fe 3+ /Al composition is generated as a magnetite component (FeFe 2 O 4 ) is added to the starting chromite composition. This exchange is facilitated by the counter-diffusion and exchange of Mg and Al, and the spinel (sensu stricto, hereafter s.s.) component thus diminishes (see Table S2 for modelled end-member component compositions). With reaction 1, the chromite composition approaches a tie line between Fe(Al,Cr) 2 O 4 and Mg(Fe,Cr) 2 O 4 in the compositional space of the spinel (s.l.) prism (dashed grey line in Figure 7A). Importantly, the chromite compositional trend will not approach the Cr-magnetite solid solution in the prism space but a spinel (s.l.) composition intermediate between Cr-magnetite and the Mg(Fe,Cr) 2 O 4 solid solution, as spinel (s.l.) Mg concentration is only being diluted by reaction 1 (i.e. Mg is rearranged within the chromite matrix with some flux across the crystal-melt boundary). In order to equilibrate Cr proportion, which is expected to decrease under all imposed experimental conditions (Figure 5), compositions should evolve along lines of equal Fe 3+ /Al (dashed grey line in Figure 7B; reaction 2) in the isothermal state as Cr is lost to the melt phase. An added component with higher Fe 2+ /Mg is required because Mg# in chromite was not observed to increase in any experiment (Figure 3B) and because this is necessary for chromite to equilibrate with the silicate mineral assemblage (Figure 4B).

The difference in diffusivities between mineral species provides an interesting constraint on the origin of the polymineralic microlite assemblages described here. In particular, Fe-Mg interdiffusion in opx occurs more slowly (log D = -19.5 at QFM and high T, [START_REF] Klügel | Prolonged reactions between harzburgite xenoliths and silicaundersaturated melt: implications for dissolution and Fe-Mg interdiffusion rates of orthopyroxene[END_REF] than interdiffusion of any of the major cations in chromite. If, in natural samples, it is found that microlitic silicates like opx are in equilibrium with residual melts and matrix chromites are not, then the likely explanation for this observation is that the microlitic silicate formed from the melt it is in (i.e. an equilibrium crystallization process). Crystallization of ferrous phases is one of several oxidizing mechanisms in arc magmatic systems (see [START_REF] Cottrell | Oxygen Fugacity Across Tectonic Settings[END_REF]. This process provides an impetus for diffusive re-equilibration of chromite to begin, and the grounds for oxyspeedometric analysis of the chromite-melt subsystem in a diffusion chronometric context. Chromite crystals sampled from Chichijima [START_REF] Umino | Magma mixing in boninite sequence of Chichijima, Bonin Islands[END_REF], the Troodos ophiolite [START_REF] Bailey | Ultramafic and related lavas from the Margi area, Troodos ophiolite[END_REF], and Guam [START_REF] Reagan | Geology and geochemistry of early arc-volcanic rocks from Guam[END_REF] exhibit chemical zonation consistent with pre-eruptive oxidation, as chromite rim-mantle zone analyses return more ferric compositions than analyses of their cores. Such features are unique to the pre-eruptive regime but may be confused with compositional trends that are attributable to chemical weathering. Thus, it is important to discern here oxidation of chromite that occurs in this scenario and oxidation that occurs post-eruption (i.e. chemical weathering or metamorphism of chromite). In the literature on the zoned chromites described above, there is no mention of textures consistent with porous-chromite oxidation [START_REF] Gervilla | Diffusion pathways of Fe 2+ and Fe 3+ during the formation of ferrian chromite: a µXANES study[END_REF][START_REF] Hodel | Magnetic Properties of Ferritchromite and Cr-Magnetite and Monitoring of Cr-Spinels Alteration in Ultramafic and Mafic Rocks[END_REF]. The volcanic rocks sampled by the studies cited above were observed to be fresh with little to no evidence of alteration, which is not consistent with a weathering environment capable of significantly modifying chromite compositions in either hydrothermal [START_REF] Hodel | Magnetic Properties of Ferritchromite and Cr-Magnetite and Monitoring of Cr-Spinels Alteration in Ultramafic and Mafic Rocks[END_REF] or metamorphic [START_REF] Gervilla | Diffusion pathways of Fe 2+ and Fe 3+ during the formation of ferrian chromite: a µXANES study[END_REF] regimes. Instead, since the chromite FeO and Al 2 O 3 concentrations are observed to increase from core to rim (which is a geochemical signature of magmatic oxidation in our model, i.e. reaction 2 of Figure 7), we maintain that these zonation patterns are of magmatic rather than secondary origin. With this in mind, the next sections assess natural chromite and glass compositions recovered from the extrusive suite of the Troodos ophiolite in a similar manner as our experimental products, and data available from the literature are used to constrain ascent rates for these lavas.

Experimental observations vs. natural processing in the crustal column

Mafic Troodos glass compositions were taken from the literature for the following localities:

the Kalavassos Mine (eastern end of the Limassol Forest Complex), Margi (northern part of the extrusive sequence), and Kapilio (western end of the Limassol Forest Complex). All data were taken from [START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF] with an additional two glass analyses from [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF] for the Kalavassos Mine locality. The studies cited used laser ablation inductively coupled plasma mass spectrometry to quantify minor-trace concentrations of Cr for these samples. Data on mineral compositions for these locations are sparse. However, multiple compositions were found and taken from [START_REF] Cameron | Petrology and origin of primitive lavas from the Troodos ophiolite, Cyprus[END_REF], [START_REF] Bailey | Ultramafic and related lavas from the Margi area, Troodos ophiolite[END_REF], [START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF][START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF][START_REF] Macleod | The tectonic evolution of the Eastern Limassol Forest Complex, Cyprus[END_REF]. Here, we assess these data to determine if the aforementioned minerals and melts were in equilibrium at the time of eruption. Chromite data were found neither for the Akaki River Canyon section nor for the Arakapas Fault Belt though [START_REF] Ohnenstetter | Geochemistry and mineralogy of lavas from the Arakapas Fault Belt, Cyprus: Consequences for magma chamber evolution[END_REF] performed several analyses, no data are provided in the source. Thus, even though these locations have been widely studied, we are currently unable to assess for chromite-melt equilibrium for these parts of the extrusive sequence.

SPINMELT-2.0 was used to model equilibrium chromite compositions in a similar way as in the experimental scenario discussed above. Physiochemical variables were set to approximate eruption conditions with pressure set to 0.5 kbar, which corresponds to a water depth of 5000 meters (inferred eruption condition, [START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF], and the fO 2 of the system was set to QFM+0.25 (c. NNO-0.5), QFM+0.75 (c. NNO), and QFM+1.25 (c. NNO+0.5). This range compares well with the natural range of fO 2 for the Troodos magmas; crystallization of olivine + chromite occurred at fugacities slightly above QFM+0.25 [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF];

and glasses recovered from a Troodos "upper pillow lava" [START_REF] Rautenschlein | Isotopic and trace element composition of volcanic glasses from the Akaki Canyon, Cyprus: implications for the origin of the Troodos ophiolite[END_REF] have Fe 2+ /Fe 3+ (recalculated to molar ratios) that return fO 2 values ≥ QFM+1.35 (NNO+0.6) using a pressure of 0.5 kbar, a temperature of 1130℃ (upper limit of eruption temperature given by [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF], a rearranged equation 7 from [START_REF] Kress | The compressibility of silicate liquids containing Fe 2 O 3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states[END_REF], and the fugacity conversions of [START_REF] Frost | Introduction to oxygen fugacity and its petrologic importance[END_REF], providing a reasonable estimate for the upper limit for our fugacity setting.

SPINMELT-2.0 output was treated in a similar way as the experimental data (Supplemental Text 4). When fO 2 is provided, melt Fe 2+ /Fe 3+ is calculated internally and used to model chromite composition. Since temperature is not provided to the program, it must be predicted by the algorithm to provide a chromite composition estimate for each input melt composition.

For these lavas, liquid temperatures have been inferred to vary between c. 1030-1130℃ [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF]. These temperatures are consistent with temperatures inferred from viscosity models [START_REF] Schouten | Melt viscosity, temperature and transport processes, Troodos ophiolite, Cyprus[END_REF] generated for lavas on the North side of the extrusive sequence and with independent thermometry (inferred to provide a quantification of closure temperature) performed by [START_REF] Dare | Tectonic discrimination of peridotites using fO 2 -Cr# and Ga-Ti-Fe III systematics in chrome-spinel[END_REF] for the Kalavassos Mine locality.

SPINMELT-2.0 output was observed to lie within 25℃ of this temperature range for a majority of the glass samples (Table S6) for each fO 2 condition. Thus, we inferred that our models faithfully replicated equilibrium conditions for chromite-melt at the time of eruption.

Figure 8 illustrates the relationships between modelled and observed chromite compositions of the Troodos (cf. Figure 5). Sample glass recovered from the Kalavassos Mine produced one major cluster for each fO 2 condition and one Al-rich glass sample displaced modelled chromite compositions to higher Al and lower Cr. All glass samples were determined to be "tholeiitic" by [START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF]. All of the matrix chromite compositions observed for this locality are similar to olivine-hosted chromite inclusions observed in these same lavas [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF]. A single natural chromite composition is displaced to higher Al compared with the others. However, according to our models, all of these chromite compositions are too Cr-rich and require Fe 3+ +Al incorporation to be in equilibrium with residual melts. [START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF] determined that the glass samples recovered from the Kapilio locality range from boninitic to tholeiitic in composition. The chromite data from this locality include the most chromian spinel (s.l.) analysis from the Troodos sample suite [START_REF] Cameron | Petrology and origin of primitive lavas from the Troodos ophiolite, Cyprus[END_REF] and three relatively simple (number of elements reported = 4) analyses of chromite given by [START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF]. These compositions are also far from the modelled chromite compositions. As with the samples from the Kalavassos Mine, Fe 3+ +Al incorporation is required for re-equilibration. If a tie line is drawn through the natural samples from the Cr apex, it would intersect the model array at the point where the data generated at QFM+0.75 touches the data generated at QFM+1.25.

Finally, chromites taken from the Margi locality exhibit a compositional trend that is similar to that observed in the data from the Kapilio suite. Glasses taken from this locality produced a high-Al and low-Al trend, which reflects a modest separation of the glass data into more and less differentiated populations, respectively. Chromite core analyses given by [START_REF] Bailey | Ultramafic and related lavas from the Margi area, Troodos ophiolite[END_REF] lie in roughly the same area as those of the Kalavassos Mine. However, rim analyses reported in this study are displaced to higher Fe 3+ concentrations with a single analysis reaching the Fe 3+ proportion inferred for chromite in equilibrium with melt at QFM+0.75. However, for this mineral rim, Cr-Al interdiffusion must also occur to reach the Al concentration inferred to represent an equilibrium composition. Thus, we conclude that the chromites observed in the Troodos extrusive suite were not in equilibrium with their residual melt compositions at the time of eruption, but in multiple localities these minerals were likely in a state of active equilibration (via diffusion) at the time they were erupted.

Regarding Fe 2+ , slowly cooled chromites lose Mg to coexisting ferromagnesian silicates [START_REF] Ozawa | Olivine-spinel geospeedometry: Analysis of diffusion-controlled Mg-Fe2+ exchange[END_REF], while rapidly quenched mineral pairs preserve high-temperature compositions (e.g. [START_REF] Scowen | Reequilibration of chromite within Kilauea Iki lava lake, Hawaii[END_REF]. Since the glasses sampled from the Troodos rapidly quenched upon eruption (e.g. [START_REF] Robinson | Volcanic glass compositions of the Troodos ophiolite, Cyprus[END_REF], chromite Mg# may have been preserved. By focusing on a single locality where glass, opx, and chromite data exist, we may treat natural samples in the same way as the experimental products above and test for system Fe 2+ -Mg equilibrium. To this end, we refocus on the Kapilio locality. Glass data from this site [START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF] were processed to predict K D (Fe-Mg) opx-liq values using equation 1.

Mineral data from this locality are from [START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF]. In total, two opx and three chromite compositions were used (their sample AM-4, Table 5). Unfortunately, there is no way of determining if these materials come from the same outcrops as the glass, which is why all glass data were used in modelling. Based on model physiochemical constraints outlined above, the opx sampled by [START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF] is in equilibrium with residual melts (within 1σ of the mean model K D (Fe-Mg) opx-liq value). Using a median Y Cr chrm for the matrix chromites (0.70), model K D (Fe-Mg) chrm-opx values (calculated using equation 2) are observed to vary between c. 4.68-4.96 at 1130℃ and 0.5 kbar and 5.41-5.86 at 1030℃ and 0.5 kbar (Table 5). Varying Y Cr chrm by 0.1 (the actual variation observed among the sample chromites) causes these model K D values to vary by ±0.07 (c. ±3%), which is roughly one half of the magnitude of the uncertainty associated with the model parameters. Observed K D (Fe-Mg) chrm-opx values are found to vary between 4.8 and 7.3 depending on which chromite-opx pair is used. Two of the three chromite grains are seen to be in equilibrium with at least one of the opx grains based on these K D models. One other chromite grain in this sample returned high observed K D values for both opx grains, reflecting low MgO concentrations. This chromite also has a low total EPMA composition (94.79) compared to the other analyses (c. 98). Regardless, it is remarkable, given the dearth of mineral data available for the Troodos extrusive sequence, that any equilibrium condition could be established at all. These findings further the point that more mineral data should be gathered from the Troodos ophiolite and other natural chromite-bearing rocks to assess for mineralmineral/mineral-melt equilibrium.

The effects of natural quench crystallization and syn-eruptive microlite growth on modelling equilibrium chromite composition also needs to be considered. Depending on the Fe-Mg ratio of the minerals that crystallize, Fe 2+ may be enriched or depleted in the residual melt. Using equilibrium exchange coefficients (e.g. [START_REF] Putirka | Thermometers and Barometers for Volcanic Systems[END_REF], the crystallization of ferromagnesian silicates like olivine and opx are expected to enrich melts in FeO relative to MgO, and the differentiation of melt by these minerals should modestly enrich Fe 3+ over Fe 2+ [START_REF] Birner | Peridotites and basalts reveal broad congruence between two independent records of mantle fO 2 despite local redox heterogeneity[END_REF][START_REF] Kelley | The influence of magmatic differentiation on the oxidation state of Fe in a basaltic arc magma[END_REF][START_REF] O'neill | The oxidation state of iron in Mid-Ocean Ridge Basaltic (MORB) glasses: Implications for their petrogenesis and oxygen fugacities[END_REF][START_REF] Shorttle | Fe-XANES analyses of Reykjanes Ridge basalts: Implications for oceanic crust's role in the solid Earth oxygen cycle[END_REF]. Melt Al 2 O 3 is expected to increase with the equilibrium crystallization of ferromagnesian silicates. Based on observations of the experimental products made at 1200℃, melt Al 2 O 3 concentrations were not significantly affected by quench crystallization (Table 3). Although this effect will depend on the volume of crystallization produced during quenching, which was not constrained, we do not expect minor degrees of quench crystallization to significantly affect melt Al 2 O 3 unless an aluminous phase crystallizes. In some relatively differentiated Troodos lavas, plagioclase feldspar is observed [START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF][START_REF] Schmincke | Troodos extrusive series of Cyprus: A comparison with oceanic crust[END_REF].

Feldspar crystallization is expected to reduce melt Al 2 O 3 and thus modelled chromite Al 2 O 3 concentrations, which would cause observed chromite compositions to appear closer to equilibrium. Instead, we propose that (i) the higher chromite Al concentrations predicted by our modelling (Figure 8) reflect Al 2 O 3 enrichment in the magmas (and thus the absence of plagioclase in glasses sampled by [START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF] that comprise the Troodos extrusive sequence, which is consistent with the predominate silicate mineral assemblages observed therein; namely olivine, olivine+cpx, or olivine+opx+cpx [START_REF] Flower | Petrogenesis of a tholeiite-boninite sequence from Ayios Mamas, Troodos ophiolite: evidence for splitting of a volcanic arc?[END_REF][START_REF] Malpas | Petrology of the Upper Pillow Lava suite, Troodos ophiolite, Cyprus[END_REF][START_REF] Schmincke | Troodos extrusive series of Cyprus: A comparison with oceanic crust[END_REF], and that (ii) quench crystallization does not significantly affect these data. Since the most primitive glasses sampled by [START_REF] Woelki | Petrogenesis of boninitic lavas from the Troodos Ophiolite, and comparison with Izu-Bonin-Mariana forearc crust[END_REF] were observed to classify as boninite liquids, we infer that the most Cr-rich equilibrium chromite compositions in our models (Figure 8), which correspond to these relatively primitive melt compositions, represent chromite compositions that genuinely reflect the equilibrium composition of chromite in melts unaffected by quench/syn-eruptive crystallization.

Estimation of maximum/minimum ascent time through diffusion modelling

Since stable chromite was driven into chemical disequilibrium during magmatic differentiation, remained in a state of disequilibrium with respect to trivalent cation proportions at the time of eruption, and equilibrated with co-existing silicate minerals with respect to Fe-Mg exchange (divalent cation proportion), magma ascent time may be estimated on the basis of disequilibrium/equilibrium between chromite and the equilibrium condition defined by the physiochemical state of the residual melts. Here, the maximum ascent time was modelled based on the lowest interdiffusivity for the chromite compositional system (D Cr-Al ), and minimum ascent time was modelled based on the highest interdiffusivity (D Fe-Mg ).

Based on chromite-melt behaviour modelled above and observed in the mafic lavas of the extrusive suite of the Troodos ophiolite, we estimated the maximum and minimum ascent times by calculating the time (t) it would take to equilibrate a hypothetical groundmass chromite microphenocryst [30-60 μm diameter with a composition similar to those of primitive chromite microphenocryst cores and mineral inclusions from the Kalavassos Mine locality (Figure 8, [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF][START_REF] Sobolev | Petrology of ultramafic lavas and associated rocks of the Troodos massif, Cyprus[END_REF]] with residual melt under the inferred eruptive conditions using the following relationship from [START_REF] Crank | The Mathematics of Diffusion[END_REF]:

Equation 3 τ = Dt/a 2
where a is the crystal radius, t is time, τ is non-dimensional time, and D is the interdiffusion coefficient.

D Cr-Al , the interdiffusivity coefficient of Cr-Al in chromite, is positively correlated with both temperature and Cr# [START_REF] Suzuki | Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep[END_REF]. For this reason, we calculated D Cr-Al for chromite with Cr# = 80 at 1030℃ and 1130℃ by extrapolating the relationships illustrated in Figures 5

and 10 of [START_REF] Suzuki | Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep[END_REF] to low temperatures. In detail, we reproduced the Arrhenius plot of [START_REF] Suzuki | Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep[END_REF] for chromite with Cr# = 80 and fit linear equations to their diffusivity data to predict logD Cr-Al as a function of temperature (Supplemental Text 5). The following equation was recovered: Equation 4logD Cr -Al = -2.4199 ( 10 4 T(K) ) +2.3902 Using this equation, we estimate logD Cr-Al (cm 2 /s) to be -16.2 at 1030℃ and -14.9 at 1130℃ (Table 6).

We elected to use self-diffusion coefficients from [START_REF] Liermann | Diffusion kinetics of Fe 2+ and Mg in aluminous spinel: experimental determination and applications[END_REF] to estimate logD Fe-Mg at the same conditions as logD Cr-Al . We also reproduced their Arrhenius plots for both Fe and Mg self-diffusion (Supplemental Text 5) and then used their equation 4 to calculate an interdiffusivity coefficient, logD Fe-Mg . For this calculation, we used the following linear equations recovered from their Arrhenius plots: Equation 5logD Fe = -1.0322 ( 10 4 T(K) ) -4.7506 Equation 6

logD Mg = -1.0545 ( 10 4 T(K) ) -4.7125

Using these equations and equation 4 of [START_REF] Liermann | Diffusion kinetics of Fe 2+ and Mg in aluminous spinel: experimental determination and applications[END_REF], logD Fe-Mg was calculated to be -12.7 at 1030℃ and -12.2 at 1130℃ (Table 6).

With these D values, we calculated maximum ascent time using the simple equation for diffusion in a sphere (equation 3) by assuming τ = 0.04 (i.e. insignificant change in core composition) and minimum ascent time by assuming τ = 0.4 (i.e. complete re-equilibration, Table 6). At 1030℃, in order to preserve a matrix chromite core whose Cr# = 80, a maximum of c. 170 years can pass before the core of the chromite begins to to equilibrate , which means that the mafic lavas of the Troodos ophiolite, once extracted from their mantle source, crystallized their silicate cargo and erupted in less than c. 170 years. If T is raised to 1130℃, the maximum amount of time is reduced to 8 years. Since the interdiffusivity coefficient is positively correlated with Cr#, if chromite has a lower Cr# than 80, then maximum ascent time increases. In fact, when Cr# approaches 0, D Cr-Al approaches values two orders of magnitude lower than when Cr# = 80 [START_REF] Suzuki | Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep[END_REF]. Maximum ascent times would increase accordingly. However, because the chromites of the Troodos presented here are highly chromian, we expect our maximum ascent times to be within reason. We calculated minimum ascent time (for the same hypothetical chromite grain) at 1030℃ to be c. 220 days.

At 1130℃ this value is lowered to 60 days. These back-of-the-envelope calculations demonstrate that it will be possible to constrain the ascent rate of boninitic magmas through study of diffusion profiles in matrix chromite crystals that they carry, and this should be done systematically in future research.

Overall, the melt temperature data cited as independent observations for the Troodos extrusive suite are corroborative, but it is important to discuss these data because temperature exerts strong control over diffusion. The three methods of temperature estimation are based on geochemical modelling [START_REF] Dare | Tectonic discrimination of peridotites using fO 2 -Cr# and Ga-Ti-Fe III systematics in chrome-spinel[END_REF][START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF][START_REF] Schouten | Melt viscosity, temperature and transport processes, Troodos ophiolite, Cyprus[END_REF]. [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF] used olivine-melt compositional data and the equilibrium relationships given by [START_REF] Ford | Olivine-liquid equilibria: temperature, pressure and composition dependence of the crystal/liquid cation partition coefficients for Mg, Fe 2+ , Ca and Mn[END_REF] and [START_REF] Almeev | The effect of H 2 O on olivine crystallization in MORB: Experimental calibration at 200 MPa[END_REF] to quantify minimum crystallization temperatures, which they interpreted as eruption temperatures. [START_REF] Schouten | Melt viscosity, temperature and transport processes, Troodos ophiolite, Cyprus[END_REF] used the geothermometer of [START_REF] Sisson | Temperatures and H 2 O contents of low-MgO highalumina basalts[END_REF] to estimate temperature for their viscosity models. Finally, [START_REF] Dare | Tectonic discrimination of peridotites using fO 2 -Cr# and Ga-Ti-Fe III systematics in chrome-spinel[END_REF] calculated temperature using the olivine-spinel thermometer of [START_REF] Ballhaus | High pressure experimental calibration of the olivine-orthopyroxene-spinel oxygen geobarometer: implications for the oxidation state of the upper mantle[END_REF] and inferred this temperature as a closure temperature for chromite. Taken together, since the present discussion is focused on the kinetics of chromite-melt re-equilibration at pre-eruptive conditions, the estimates of [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF] represent our preferred liquid temperatures because they are most likely to constrain melt temperatures prior to significant syn-eruptive crystallization of microlitic pyroxene. Granted, when significant pyroxene crystallization occurs, melt water concentrations assumed by [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF] for Troodos glasses (c. 3 wt%) represent maxima and their temperatures minima following the liquidus depression relationships given by [START_REF] Almeev | The effect of H 2 O on olivine crystallization in MORB: Experimental calibration at 200 MPa[END_REF]. [START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF] quantified water concentrations in boninite glasses to be 1.7-2.7 wt%, which is slightly below the value provided by [START_REF] Golowin | The role and conditions of second-stage mantle melting in the generation of low-Ti tholeiites and boninites: the case of the Manihiki Plateau and the Troodos ophiolite[END_REF]. This means our models may use temperatures that are slightly underestimated. The consequence of this is that our model ascent rates may be minima under high-temperature conditions and that ascent times for the Troodos extrusive sequence may be higher than modelled here. The likelihood of lower liquid temperatures are low due to the high closure temperature of 1100℃ inferred by [START_REF] Dare | Tectonic discrimination of peridotites using fO 2 -Cr# and Ga-Ti-Fe III systematics in chrome-spinel[END_REF].

Additional complexity is added when considering the effect of changing Cr# during oxidation. Since logD Cr-Al becomes lower as chromite loses Cr [START_REF] Suzuki | Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep[END_REF], since we elected to regress data provided for the highest Cr# chromites in the study of [START_REF] Suzuki | Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep[END_REF] in order to estimate maximum ascent rate, and since natural chromites have slightly less Cr (Table S5), our maximum ascent times may be underestimated. This is an additional knowledge gap that should be addressed with future experimental work.

Because primitive compositional characteristics of the oxide mineral cargo are retained in several chromite crystals in the matrices of lavas of the Troodos ophiolite extrusive sequence and because, in some cases, mineral textures relating to diffusive equilibration seem to be preserved, we propose that chromites in such boninitic-tholeiitic lavas are products of either (i) crystallization from primary magmas or the incongruent melting reaction that is known to produce olivine + chromite in the shallow sub-arc mantle, or (ii) crystallization in complex fluid-melt or melt-melt mixtures in the same part of the magmatic system. In either case, chromite is likely precipitated prior to extensive pyroxene crystallization, as melt fractionation by pyroxene tends to compromise chromite stability in some igneous systems (e.g. layered mafic intrusions or ocean island basalts, [START_REF] Irvine | Chromian spinel as a petrogenetic indicator. Part 2. Petrologic applications[END_REF][START_REF] Roeder | Chromite; from the fiery rain of chondrules to the Kilauea Iki lava lake[END_REF]. Such

behaviour appears to be absent in boninites and tholeiites associated with ophiolitic terranes such as the Troodos or the forearc regions of intra-oceanic arc systems (e.g. [START_REF] Whattam | Mineral compositions and thermobarometry of basalts and boninites recovered during IODP Expedition 352 to the Bonin forearc[END_REF]. In these rocks, matrix chromite appears with stable pyroxene minerals as euhedralsubhedral mineral grains with no signs of resorption or breakdown. Thus, chromite is most likely a primitive component of the boninite-tholeiite petrogenetic system that perseveres through differentiation in arc systems and likely records compositional traits that reflect the full range of physiochemical states these magmas undergo prior to eruption (Figure 9).

In our petrogenetic model, synthesized in Figure 9, chromite forms in equilibrium with primitive boninitic melt prior to the growth of many silicate minerals (Figure 9B) and has a primitive composition characterized by high Mg# and Y Cr (Stage 1). Once silicate minerals nucleate (Figure 9C), chromite Mg# will immediately begin to re-equilibrate, as this parameter is highly sensitive to the presence of ferromagnesian silicates (Stage 2). As these silicates grow, melt oxidation occurs, and Fe 3+ -Al exchange begins (Stage 3, Figure 9D).

Finally, Cr exchange begins to occur with Fe 3+ and Al (such that chromite Fe 3+ /Al remains constant, Figure 7B) and the volume of chromite at the edge of the grain reaches an equilibrium state with melt prior to eruption (Stage 4). If this chromite grain is entrained in an ascending melt that is quenched upon eruption, then the differential diffusivities of the major trivalent cations in chromite can be interpreted in a chronometric context (Figure 9E). Careful analysis of chromite should include a quantification of Fe-speciation (see EPMA methodology of [START_REF] Davis | Experimental investigation of basalt and peridotite oxybarometers: Implications for spinel thermodynamic models and Fe 3+ compatibility during generation of upper mantle melts[END_REF]) so that precise thermometry and fugacity information can be inferred from natural samples.

CONCLUSIONS

1) The experiments presented here enabled us to infer the kinetic behaviour of chromite in boninitic melt. Pyroxene is a ubiquitous component of the experimentally synthesized boninites, and residual melts are andesitic in composition. Matrix glasses preserved in natural boninites [START_REF] Coulthard | Magma Source Evolution Following Subduction Initiation: Evidence From the Element Concentrations, Stable Isotope Ratios, and Water Contents of Volcanic Glasses From the Bonin Forearc (IODP Expedition 352)[END_REF][START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF] demonstrate that olivine ± pyroxene crystallization commonly generates residual melts that are basaltic andesitic to andesitic in composition, similar to the products of these crystallization experiments.

2) The fact that these same natural glasses are enriched in Fe 3+ upon eruption [START_REF] Brounce | The oxidation states of iron and volatile compositions of Expedition 352 glasses[END_REF][START_REF] Rautenschlein | Isotopic and trace element composition of volcanic glasses from the Akaki Canyon, Cyprus: implications for the origin of the Troodos ophiolite[END_REF] suggests that primitive boninitic melts (i) crystallize chromite under less oxidizing conditions than those characteristic of the pre-eruptive crustal column and within what are likely complex melt-fluid/melt-melt mixtures present in the sub-arc or back-arc mantle, (ii) crystallize olivine/pyroxene phenocrysts under magmatic conditions without significant chromite crystallization in the crust, and (iii) entrain most of their chromite crystal cargo prior to microlitic growth during ascent and eruption, to produce natural boninites and derived andesiticbasaltic andesitic glasses. 3) If chromite, including microlitic matrix chromite, were to crystallize from these residual liquids, then they would incorporate more Fe 3+ and Al than observed, as shown by the natural samples taken from the extrusive sequence of the Troodos Ophiolite. Thus, most chromites are products of primitive melt crystallization in the crustal domain or of the incongruent melting of orthopyroxene in the mantle domain.

When entrained in an evolving magma, melt oxidation perturbs the equilibrium chromite composition to higher Fe 3+ . If sufficiently oxidizing conditions are achieved, Fe 3+ replaces Al efficiently such that Fe 2+ /Fe 3+ + Fe 3+ /Al chromite-melt equilibrium is approached. The disequilibrium textures and compositions preserved in some phenocrystic-microphenocrystic chromites should be examined closely to ascertain ascent rates using Fe 3+ diffusivity. 4) In chromite, Cr-Al/Fe 3+ equilibrium is achieved over much longer timescales. If considered the limiting factor of chromite-melt equilibration, natural microphenocrystic chromite observed in the extrusive suite of the Troodos ophiolite would equilibrate with residual melts in less than c. 170 years. Diffusion may be much more rapid, and future work on the diffusive equilibration of both experimental and natural chromites should provide tighter constraints.

  equation utilizes opx Al molar proportion (X Al opx ), chromite Cr/[Cr+Al+Fe 3+ ](Y Cr chrm ), and constants derived for Al-Fe 3+ system correction using the charge balance method: A = -0.351±0.102, B = 1217±120, C = 1863, and D = 2345±188 (Table4of[START_REF] Liermann | Fe 2+ -Mg fractionation between orthopyroxene and spinel: experimental calibration in the system FeO-MgO-Al 2 O 3 -Cr 2 O 3 -SiO 2 , and applications[END_REF]. Uncertainties associated with the model K D s were calculated to be ±0.157 (i.e. better than ±7%, 2σ relative) based on propagating the uncertainties provided for coefficients A, B, and D. Assuming the compositional parameter for opx does not significantly change, and since Cr proportions for the synthetic chromites are not observed to change significantly between any of the samples (Figure3A), this equation predicts the equilibrium state of chromite-opx with regard to Fe 2+ -Mg exchange for each experimental condition at the time of quenching (Figure4B, observed K D values were calculated using molar proportions with chromite X FeO multiplied by molar Fe 2+ /ΣFe inferred from stoichiometry).

  2010) are ranked by order of decreasing diffusivity (log D, m 2 /s) at 1100℃ (10 4 /K = c. 7.3): Mg-Al (extrapolated, c. -13.5), Fe (self-diffusion, c. -16), Mg (self-diffusion, c. -16.5), and Cr-Al (below x-axis, see below). Thus, D Cr-Al is likely the limiting factor in chromite-melt diffusive equilibration, though uncertainties associated with D Cr-Al are reportedly large at high

Figure 1 :

 1 Figure 1: A) BSE image of Bon1150U. This image is representative of the "general" texture

Figure 2 :

 2 Figure 2: Cation proportion (O = 6) vs Mg# (calculated using Fe total ) for opx core analyses.

Figure 3 :

 3 Figure 3: Chromite compositional data. A) A portion of a conventional ternary diagram

Table 1 : Starting material compositions

 1 Composition from Reagan et al. (2010, XRF Analysis) **All analyses of starting materials are provided in the supplemental TablesS1 and S2***Converted from ppm Cr to wt% Cr 2 O 3 -= not quantified

		High-Si Boninite	Troodos Chromitite	Boninite Glass	Normalized Mixture Composition
		*YK0612 974-R6	**Chromite Seed	**BO-G	BO-G with 2 wt% added Chromite
	SiO 2	56.74	0.05	57.92	55.51
	TiO 2	0.17	0.05	0.04	0.17
	Cr 2 O 3	***0.19	53.81	0.19	1.26
	Al 2 O 3	10.66	15.11	10.69	10.73
	FeO	8.75	15.34	8.38	8.87
	MnO	0.23	0.24	0.16	0.23
	MgO	15.04	14.01	14.62	15.01
	CaO	5.54	-	6.16	5.42
	Na 2 O	2.01	-	1.86	1.97
	K 2 O	0.82	-	0.46	0.80
	P 2 O 5	0.03	-	0.08	0.03
	Total	100.18	98.72	100.48	100.00
	*

Table 2 : Sample identification and characterization, experiment descriptions, and preliminary results

 2 Capsule ID IHPV Lab Initial CompositionExperimental Conditions Seed Size (μm) wt% D 2 O (1σ) T (℃) P (kbar) pH 2 added (bars) Duration (hrs) Names: U = intrinsic fO 2 , B = buffered fO 2 , a and b designate a difference in the seed size of the chromite added 1348

	Bon1200Ua	ISTO	x < 32	1.136 (0.142)	1200	2.13	0.0	4.0
	Bon1200Ub	ISTO	160 < x < 250	1.395 (0.155)	1200	2.13	0.0	4.0
	Bon1200Ba	ISTO	x < 32	0.916 (0.153)	1200	2.12	1.9	1.4
	Bon1200Bb	ISTO	160 < x < 250	0.763 (0.191)	1200	2.12	1.9	1.4
	Bon1150U	ISTO	x < 32	0.770 (0.128)	1150	2.16	0.0	4.2
	Bon1150B	ISTO	x < 32	0.705 (0.141)	1150	2.14	1.4	3.2
	Bon1100U	GSJ	x < 32	1.280 (0.142)	1100	2.00	0.0	5.1

Table 2

 2

	(continued)
	Capsule ID	Product Phase Proportions (1σ)	Activity Model	Oxygen Fugacity
		Orthopyroxene Chromite	Glass	Final wt% 2 H 2 O (1σ) aH 2 O (1σ) Sensor X Ni (1σ) log fO 2 (bars) ΔNNO (1σ)
	Bon1200Ua	0.49 (0.01)	0.02 (0.01) 0.49 (0.02)	2.32 (0.30)	0.34 (0.07) 0.020 (0.004)	-3.69	3.81 (0.17)
	Bon1200Ub	0.50 (0.03)	0.02 (0.00) 0.48 (0.03)	2.91 (0.37)	0.48 (0.08) 0.020 (0.004)	-3.39	4.11 (0.17)
	Bon1200Ba	0.59 (0.07)	0.01 (0.00) 0.40 (0.07)	2.29 (0.55)	0.31 (0.11) 0.256 (0.003)	-6.77	0.73 (0.26)
	Bon1200Bb	0.55 (0.01)	0.01 (0.01) 0.44 (0.01)	1.73 (0.44)	0.22 (0.08) 0.256 (0.003)	-7.07	0.43 (0.27)
	Bon1150U	0.40 (0.08)	0.02 (0.00) 0.58 (0.08)	1.33 (0.29)	0.17 (0.07) 0.020 (0.004)	-4.88	3.21 (0.29)
	Bon1150B	0.60 (0.06)	0.02 (0.00) 0.38 (0.05)	1.86 (0.44)	0.26 (0.09) 0.194 (0.003)	-7.09	1.00 (0.26)
	Bon1100U	0.45 (0.05)	0.01 (0.01) 0.54 (0.05)	2.37 (0.34)	0.32 (0.07) 0.069 (0.009)	-6.21	2.52 (0.16)

Table 5 : Assessment of Fe-Mg equilibrium between opx, chromite, and melt in Kapilio lavas

 5 * Compiled from all avalable analyses of Kapilio glass from[START_REF] Woelki | Enrichment of H 2 O and fluidsoluble trace elements in the Troodos Ophiolite: Evidence for a near-trench origin[END_REF]

	Opx data (norm.)	SiO 2	Al 2 O 3	FeO	MnO	MgO	CaO	Moles MgO	Moles FeO	X Al opx
	*AM-4 opx-a	55.38	2.71	9.01	0.00	32.43	0.47	0.805	0.125	0.112
	*AM-4 opx-b	56.14	1.65	8.15	0.00	32.63	1.43	0.810	0.113	0.068
	Chromite data	Cr 2 O 3 Al 2 O 3	FeO	MgO	Total				Average Y Cr chrm
	*AM-4 chrm-a	51.65	9.82	23.73	9.59	94.79		0.238	0.244	0.70
	*AM-4 chrm-b	52.71	9.98	23.43	11.60	97.72		0.288	0.216
	*AM-4 chrm-c	53.80 10.18	23.46	11.25	98.69		0.279	0.228
	Glass data and model K D	**Average Model K D (Fe-Mg) opx-liq (1σ)		**Average melt molar MgO (1σ)	**Average melt molar FeO (1σ)
				0.292 (0.004)				0.232 (0.024)		0.108 (0.004)
	Modelled K D (Fe-Mg) chrm-opx opx-a opx-b	***(1σ)
	1030℃ (0.5 kbar)	4.676 4.955	0.157
	1130℃ (0.5 kbar)	5.408 5.755	^* Taken from Flower and Levine (1987)
	Observed K D Values	K D (Fe-Mg)	****(1σ)	Equilibrium?		*** Same model uncertainty as in previous table
	opx-a and average melt	0.334	0.041	yes			**** Calculated using error propagation methods applied to average melt composition
	opx-b and average melt	0.300	^yes			^ = Same as above
	chrm-a and opx-a	6.587	-	no			-= Cannot be calculated using available data
	chrm-a and opx-b	7.324	-	no
	chrm-b and opx-a	4.827	-	yes (1030℃)
	chrm-b and opx-b	5.367	-	yes (mod T)
	chrm-c and opx-a	5.238	-	yes (mod T)
	chrm-c and opx-b	5.824	-	yes (opx-b 1130℃)

*

ACKNOWLEDGEMENTS

Thanks go to Mark K. Reagan for providing the natural samples for these experiments, to Michel Pichavant for providing a wealth of insight into interpreting experimental oxygen fugacity data, to Keith Putirka for useful dialogue on opx-melt equilibrium uncertainties, to Fred Davis for insight on chromite equilibria as well as modelling methods, and finally to

Alexandre Corgne and an anonymous reviewer for their constructive criticism of this manuscript. This research was funded by the Royal Society of New Zealand through the Marsden Fund (grant MAU1704 to GFZ). equilibrate chromite Mg#, Fe 2+ /Fe 3+ , and Fe 3+ /Al, with Cr equilibration following, then reequilibration is a process that may be approximated by reactions 1 and 2 in a multi-step fashion. A) Reaction 1 displaces chromite compositions to higher Fe 2+ /Mg and Fe 3+ /Al as the spinel (s.s.) component in chromite decreases. In ternary space, this reaction causes a shift to higher Fe 3+ concentrations along lines of equal Cr proportion (B). Reaction 2 proceeds along lines of equal Fe 3+ /Al (dashed grey line in B) as Cr is lost to the melt phase. Reaction 2 proceeds in a direction perpendicular to the page (up) in A. [START_REF] Droop | A general equation for estimating Fe 3+ concentrations in ferromagnesian silicates and oxides from microprobe analyses, using stoichiometric criteria[END_REF] for chromite or the model of [START_REF] Kress | The compressibility of silicate liquids containing Fe 2 O 3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states[END_REF] for glass bdl = below detection limit, -= not analyzed/calculated 57 1352

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: