Sander M Molendijk
email: sander.molendijk@kuleuven.be

Olivier Namur

Paul R D Mason

Benoît Dubacq

Benoît Smets

David A Neave

Bernard Charlier

Trace element partitioning in silica-undersaturated alkaline magmatic systems

Keywords: Alkaline magmatism, Partition coefficients, Feldspathoids, Nyiragongo

Alkaline magmatism is an important chemical end-member of magmatic activity that typically occurs in response to small volume melting of asthenospheric-and/or lithospheric mantle material in intra-continental settings. Understanding trace element partitioning and phase equilibria during alkaline magmatism can therefore help provide constraints on intra-continental geodynamic settings. However, the partitioning of trace elements between alkaline melts and their dominant equilibrium mineral phases remains poorly constrained. Feldspathoids have particularly received limited attention with regards to their trace element contents, hampering our ability to interpret geochemical trends in alkaline magmatic systems. In this study, we performed a series of 1 atmosphere experiments in a gas-mixing furnace using a variety of highly alkaline (Na2O + K2O = 4.15 -14.97 wt.%) and silica-undersaturated (SiO2 = 36.73 -45.96 wt.%) lava compositions from Nyiragongo, Democratic Republic of Congo, in order to investigate the partitioning behaviour of trace elements in minerals from alkaline magmas. Experimental runs were performed with oxygen fugacity buffered at both QFM (quartz-fayalite-magnetite equilibrium) and QFM+1 and cover a range of geologically-relevant temperatures (1025 -1200 °C). The quenched products of these experiments contained leucite, nepheline, melilite, clinopyroxene, olivine, and rhönite crystals, of which glass-crystal pairs were analysed for rare earth elements, large-ion lithophile elements, and high-field-strength elements. Leucite and nepheline host considerable quantities of large-ion lithophile elements but take up negligible amounts of more highly charged cations. Åkermanitic melilite readily incorporates mono-to trivalent cations with a preference for light over heavy rare earth elements, but incorporates only select divalent cations. Rhönite and clinopyroxene have analogous partitioning behaviours, with a strong preference for heavy over light rare earth elements. Fractionation modelling using the reported partitioning behaviours can reproduce the 2021 eruption products of Nyiragongo, following 48% fractionation from an olivine-melilitic parental melt composition. Crystallization of trace-element poor feldspathoid amplifies pre-existing high LREE/MREE ratios of the parental magma and progressively increase trace element abundances for all but monovalent cations.

Introduction

Modelling of elemental distributions in mineral assemblages is essential to the decryption of whole-rock compositional trends and magmatic processes as a whole (e.g., Sun and Hanson, 1976;Mittlefehldt and Miller, 1983;Keppler, 1996;[START_REF] Taura | Pressure dependence on partition coefficients for trace elements between olivine and the coexisting melts[END_REF]Matzen et al., 2017;Namur and Humphreys, 2018). However, such modelling requires detailed knowledge of partition coefficients, which is not always readily available, especially for silica-undersaturated systems. Here we investigate mineral-melt partitioning for the lavas of the highly alkali-rich, silica-undersaturated Nyiragongo volcano in the Democratic Republic (DR) of Congo. Samples from this magmatic system have been reported as unusually enriched in large-ion lithophile elements (LILE) and light rare earth elements (LREE), although the reason for this remains uncertain [START_REF] Hertogen | Geochemical evolution of the Nyiragongo volcano (Virunga, Western African Rift, Zaire)[END_REF][START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF][START_REF] Chakrabarti | Isotopic and geochemical evidence for a heterogeneous mantle plume origin of the Virunga volcanics, Western rift, East African Rift system[END_REF]. Quantifying the behaviour of trace elements during melting and fractional crystallization is essential for explaining the origin of these enrichments, in particular for discerning between primary enrichment inherited from the source [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF][START_REF] Chakrabarti | Isotopic and geochemical evidence for a heterogeneous mantle plume origin of the Virunga volcanics, Western rift, East African Rift system[END_REF] and secondary enrichment driven by fractionation (e.g., [START_REF] Hertogen | Geochemical evolution of the Nyiragongo volcano (Virunga, Western African Rift, Zaire)[END_REF].

The partitioning behaviour of trace elements between melt and minerals has been studied for decades (e.g., [START_REF] Jensen | Patterns of trace element partitioning[END_REF][START_REF] Hart | Experimental cpx/melt partitioning of 24 trace elements[END_REF][START_REF] Blundy | Partitioning of trace elements between crystals and melts[END_REF][START_REF] Dubacq | Controls on trace element distribution in oxides and silicates[END_REF], either through the use of glass/groundmass-mineral pairs in rapidly quenched rocks [START_REF] Onuma | Trace element partition between two pyroxenes and the host lava[END_REF][START_REF] Onuma | Mineral/groundmass partition coefficients for nepheline, melilite, clinopyroxene and perovskite in melilitenepheline basalt, Nyiragongo, Zaire[END_REF][START_REF] Fujimaki | Partition coefficients of Hf, Zr, and REE between zircon, apatite, and liquid[END_REF][START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF], [START_REF] Hart | Experimental cpx/melt partitioning of 24 trace elements[END_REF][START_REF] Dygert | An experimental study of trace element partitioning between augite and Fe-rich basalts[END_REF], or theoretical methods [START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF][START_REF] Van Westrenen | Atomistic simulation of trace element incorporation into garnets-comparison with experimental garnet-melt partitioning data[END_REF][START_REF] Dubacq | Controls on trace element distribution in oxides and silicates[END_REF]. Extensive literature is therefore available on partitioning behaviour for minerals commonly crystallizing from tholeiitic magmas such as clinopyroxene (e.g., [START_REF] Skulski | High-pressure experimental trace-element partitioning between clinopyroxene and basaltic melts[END_REF][START_REF] Johnson | Experimental determination of partition coefficients for rare earth and high-field-strength elements between clinopyroxene, garnet, and basaltic melt at high pressures[END_REF][START_REF] Green | SIMS determination of trace element partition coefficients between garnet, clinopyroxene and hydrous basaltic liquids at 2-7.5 GPa and 1080-1200[END_REF][START_REF] Hill | Clinopyroxene-melt trace element partitioning and the development of a predictive model for HFSE and Sc[END_REF][START_REF] Bédard | Parameterizations of calcic clinopyroxene -Melt trace element partition coefficients[END_REF][START_REF] Dygert | An experimental study of trace element partitioning between augite and Fe-rich basalts[END_REF][START_REF] Shepherd | Trace element partitioning between clinopyroxene, magnetite, ilmenite and ferrobasaltic to dacitic magmas: an experimental study on the role of oxygen fugacity and melt composition[END_REF], olivine (e.g., [START_REF] Irving | A review of experimental studies of crystal/liquid trace element partitioning[END_REF][START_REF] Beattie | Partition coefficients for olivine-melt and orthopyroxene-melt systems[END_REF][START_REF] Beattie | Olivine-melt and orthopyroxene-melt equilibria[END_REF][START_REF] Taura | Pressure dependence on partition coefficients for trace elements between olivine and the coexisting melts[END_REF][START_REF] Bédard | Partitioning coefficients between olivine and silicate melts[END_REF][START_REF] Evans | The influence of melt composition on the partitioning of REEs, Y, Sc, Zr and Al between forsterite and melt in the system CMAS[END_REF] and plagioclase (e.g., [START_REF] Bédard | Trace element partitioning in plagioclase feldspar[END_REF]Aigner-Torres et al., 2007;[START_REF] Tepley | Trace element partitioning between high-An plagioclase and basaltic to basaltic andesite melt at 1 atmosphere pressure[END_REF][START_REF] Sun | Trace element partitioning between plagioclase and silicate melt: The importance of temperature and plagioclase composition, with implications for terrestrial and lunar magmatism[END_REF][START_REF] Dygert | Experimental determinations of trace element partitioning between plagioclase, pigeonite, olivine, and lunar basaltic melts and an fO2 dependent model for plagioclase-melt Eu partitioning[END_REF], but data remain limited for minerals solely formed from silica-undersaturated magmas (e.g., leucite, melilite, nepheline). Published partition coefficients between feldspathoids and melt are based mainly on phenocryst-matrix observations [START_REF] Onuma | Mineral/groundmass partition coefficients for nepheline, melilite, clinopyroxene and perovskite in melilitenepheline basalt, Nyiragongo, Zaire[END_REF][START_REF] Ewart | Application of proton-microprobe data to trace-element partitioning in volcanic rocks[END_REF][START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF]Arzamastsev et al., 2009;[START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF]. While such studies provide first-order insights, they are frequently influenced by crystal-melt disequilibrium, crystal zoning, incomplete quenching of the matrix and contamination of analyses by mineral or melt inclusions leading to anomalous results (Albarede and Bottinga, 1972;[START_REF] Lee | Extension of lattice strain theory to mineral/mineral rare-earth element partitioning: An approach for assessing disequilibrium and developing internally consistent partition coefficients between olivine, orthopyroxene, clinopyroxene and basaltic melt[END_REF]. Furthermore, the few experimental studies performed with compositions crystallizing such minerals sometimes omitted alkali metals entirely in their starting compositions [START_REF] Nagasawa | Experimental Mineral/Liquid Partition Coefficients of the Rare Earth Elements (REE) Sc and Sr for Perovskite, Spinel and Melilite[END_REF][START_REF] Lundstrom | Trace element partitioning between type B CAI melts and melilite and spinel: Implications for trace element distribution during CAI formation[END_REF][START_REF] Ustunisik | Trace element partitioning between CAI-type melts and grossite, melilite, hibonite, and olivine[END_REF], filtering out any potential effect of these elements on the partitioning behaviour. The frequently reported influence of crystal and melt compositions on trace element partitioning [START_REF] Beckett | Crystal chemical effects on the partitioning of trace elements between mineral and melt: An experimental study of melilite with applications to refractory inclusions from carbonaceous chondrites[END_REF][START_REF] Dubacq | Controls on trace element distribution in oxides and silicates[END_REF][START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF] render coefficients derived from such studies potentially unreliable for application to alkali-rich natural lavas. This hampers geochemical interpretation in active alkali-rich, silica-undersaturated magmatic regions including the circum-Mediterranean region [START_REF] Lustrino | The circum-Mediterranean anorogenic Cenozoic igneous province[END_REF], the West Antarctic rift system [START_REF] Kyle | Petrologic evolution of anorthoclase phonolite lavas at Mount Erebus, Ross island, Antarctica[END_REF][START_REF] Martin | Petrogenesis of Cenozoic, alkalic volcanic lineages at Mount Morning, West Antarctica and their entrained lithospheric mantle xenoliths: Lithospheric versus asthenospheric mantle sources[END_REF], and the East African rift system [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF][START_REF] Klaudius | Peralkaline silicate lavas at Oldoinyo Lengai, Tanzania[END_REF].

In this study, partition coefficients for a variety of minerals common to (per)alkaline magmatic systems were determined under dry conditions at a pressure of 1 bar. Studied minerals include leucite (KAlSi2O6), melilite ((Ca,Na)2(Al,Mg,Fe)(Si,Al)O7), clinopyroxene, olivine, nepheline ( KNa3Al4Si4O16) and rhönite ((Ca,Na)2(Mg,Fe 2+/3+ , Ti)6(Si,Al,Fe 3+ )6O20). The relevance of these partition coefficients was tested for the Nyiragongo volcanic system, allowing for forward modelling of the trace element evolution of alkaline lavas more generally during fractional crystallization.

Nyiragongo volcano

Nyiragongo is an active volcano in the DR Congo, and one of the eight major volcanoes of the Virunga Volcanic Province (VVP) located in the western branch of the East African Rift system, generally characterized by the presence of a persistent lava lake in its summit crater [START_REF] Tazieff | Première exploration du cratère du volcan Nyiragongo[END_REF][START_REF] Tazieff | Mt. Nyiragongo: renewed activity of the lava lake[END_REF][START_REF] Durieux | Volcano Nyiragongo (D.R.Congo): Evolution of the crater and lava lakes from the discovery to the present[END_REF][START_REF] Barrière | Intra-Crater Eruption Dynamics at Nyiragongo (D.R. Congo), 2002-2021[END_REF]. Nyiragongo is among the most active volcanoes on Earth (Wright et al., 2015) and threatens the city of Goma, which was impacted by flank eruptions in 1977, 2002, and 2021, which drained the lava lake system at that time (e.g., [START_REF] Pottier | Première éruption historique du Nyiragongo et manifestations adventives simultanées du volcan Nyamuragira (chaîne des Virunga-Kivu-Zaïre: Déc 76 -Juin 77[END_REF][START_REF] Komorowski | The January 2002 flank eruption of Nyiragongo volcano (Democratic Republic of Congo): chronology, evidence for a tectonic rift trigger, and impact of lava flows on the city of Goma[END_REF][START_REF] Barrière | Intra-Crater Eruption Dynamics at Nyiragongo (D.R. Congo), 2002-2021[END_REF]. The lava field of Nyiragongo is also characterised by numerous parasitic cones mostly located at the foot of the main edifice or along radial fracture zones, some of which erupted explosively [START_REF] Poppe | Holocene phreatomagmatic eruptions alongside the densely populated northern shoreline of Lake Kivu, East African Rift: timing and hazard implications[END_REF]. The Nyiragongo volcano is known for the unusual, highly alkaline (Na2O + K2O = 6.3 -13.7 wt.%; [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF]) composition of its main crater lavas (e.g., [START_REF] Sahama | Petrology of Mt. Nyiragongo: a review[END_REF][START_REF] Demant | Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire[END_REF][START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF]). The high alkalinity of Nyiragongo's volcanic products is associated with silica-undersaturation (SiO2 = 35.7 -39.0 wt.%; [START_REF] Barette | Spatial variation of volcanic rock geochemistry in the Virunga Volcanic Province: Statistical analysis of an integrated database[END_REF]Fig. 1), generating some of the lowest viscosity lavas on Earth [START_REF] Giordano | Thermo-rheological magma control on the impact of highly fluid lava flows at Mt. Nyiragongo[END_REF][START_REF] Morrison | The rheology of crystallizing basaltic lavas from Nyiragongo and Nyamuragira volcanoes[END_REF]. Magmatism in the VVP started in the Late Miocene and was related to the doming stage of the development of the Kivu rift [START_REF] Pouclet | The Cenozoic volcanism in the Kivu rift: Assessment of the tectonic setting, geochemistry, and geochronology of the volcanic activity in the South-Kivu and Virunga regions[END_REF]. A compositional transition of the erupted material from sodic alkaline-to potassic alkaline lavas occurred in the late Pliocene [START_REF] Pouclet | The Cenozoic volcanism in the Kivu rift: Assessment of the tectonic setting, geochemistry, and geochronology of the volcanic activity in the South-Kivu and Virunga regions[END_REF]. The exact nature of the potassic source is still debated, with primary hypotheses focusing on metasomatic sources of either lithospheric or deep mantle origins [START_REF] Chakrabarti | Isotopic and geochemical evidence for a heterogeneous mantle plume origin of the Virunga volcanics, Western rift, East African Rift system[END_REF][START_REF] Furman | Evolution of the East African rift: Drip magmatism, lithospheric thinning and mafic volcanism[END_REF]. Nyiragongo itself experienced a transition from more explosive, melilite dominated magmatism to more nepheline-dominated lavas [START_REF] Sahama | The Nyiragongo main cone[END_REF], which are thought to have fractionated primarily at shallow levels (< 4 km) [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF]. More olivine-rich compositions are thought to have crystallized in a magmatic reservoir at 10-14 km depth [START_REF] Demant | Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire[END_REF]. The lithologies currently exposed at the main Nyiragongo crater are similar to the composition of the lava lake, and are feldspar-free, leucite-, melilite-, -nepheline-, oxide-, olivine-, and clinopyroxene-bearing foidites, with a markedly high concentration of LILE, high-field-strength elements (HFSE), and REE [START_REF] Hertogen | Geochemical evolution of the Nyiragongo volcano (Virunga, Western African Rift, Zaire)[END_REF][START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF].

The temperature at the surface of the lake has been measured to be approximately between ~500 (lake skin) and 1000 °C [START_REF] Smyth | Thermal insights into the dynamics of Nyiragongo lava lake from ground and satellite measurements[END_REF], whereas crater fountain temperatures are reported to approach 1100°C [START_REF] Sahama | The Nyiragongo main cone[END_REF], which is the estimated liquidus temperature of the lava lake material [START_REF] Tilley | Melting relations of some ulta alkali volcanics[END_REF]. Conversely, the parasitic cones surrounding the volcano erupt olivine-melilite basalts (e.g., [START_REF] Demant | Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire[END_REF][START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF][START_REF] Barette | Spatial variation of volcanic rock geochemistry in the Virunga Volcanic Province: Statistical analysis of an integrated database[END_REF], with a maximum reported alkali content of ~7 wt.%, and a silica content below 41 wt.% [START_REF] Barette | Spatial variation of volcanic rock geochemistry in the Virunga Volcanic Province: Statistical analysis of an integrated database[END_REF]. Olivine, spinel, clinopyroxene, and melilite are the only minerals present in these lithologies [START_REF] Demant | Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire[END_REF][START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF].

Materials and methods

Sampling strategy and starting materials

Nine rock samples from the Nyiragongo volcano were used as starting materials for hightemperature experiments (Table 1; Fig. 1). Samples were collected during an expedition to the safely accessible south flank of the volcano organized in the summer of 2017. Samples for this study were selected to represent the full range of compositions from Nyiragongo. Compositions A, B, C, and N were collected from the main cone and selected for their large proportions of leucite (A), melilite (B), and nepheline (C and N). Compositions D, E, F, G, and H were collected from the parasitic cones surrounding the main edifice (Table 1; Fig. 1) and selected for being rich in clinopyroxene (D) and olivine (E, F, G, and H). Compositions A to D and N will be referred to as the low-Mg group (2.09-6.37 wt.% MgO), whereas compositions E-H will be referred to as the high-Mg group . This grouping reflects which samples were run together during each experiment, due to similarity in MgO and alkali content and, by extension, expected liquidus temperatures (Table 1). Thirty to 50 grams of each sample were finely powdered at KU Leuven, Belgium. The major element composition of the powders was measured on lithium-metaborate fused glass discs at the University of Liège using an ARL PERFORM-X 4200 XRF (Table 1). Samples were dissolved using HF at Utrecht University, Netherlands, after which trace element contents were analysed using a PerkinElmer NexION 2000P ICP-MS (Table 1). Additional details on the XRF and ICP-MS whole-rock analytical methods are included in Supplementary Materials 2.

Experimental techniques

Experiments were performed at one atmosphere in a GERO HTRV 70-250/18 gas-mixing furnace at the University of Liège, Belgium. Natural rock samples were ground to below 1 µm grain size using a Pulverisette planetary micro mill. Powders were subsequently homogenized in a Pulverisette 2 mortar grinder. Experimental runs were performed with oxygen fugacity (fO2) buffered at either QFM (quartz-fayalite-magnetite) or QFM+1. We used 0.2 mm diameter platinum loops annealed with 10-12 wt.% Fe for QFM or 7-9 wt.% Fe for QFM+1, added by electroplating in order to mitigate for iron-loss during experimental runs [START_REF] Grove | Use of FePt alloys to eliminate the iron loss problem in 1 atmosphere gas mixing experiments: Theoretical and practical considerations[END_REF]. Loops were subsequently kept at 1300°C in the furnace flushed with forming gas (95% N2, 5% H2) for 72 hours to facilitate iron diffusion into the platinum. All low-Mg group compositions were found to be super-liquidus at 1180°C, whereas the high-Mg group compositions were only superliquidus above 1500°C. Powdered samples for all subsequent experiments were mounted on the loops and pre-heated in a muffle-furnace to super-liquidus temperatures (1180 °C for low-Mg, 1500 °C for high-Mg group) for 2 minutes to make them homogeneous. Such a short run over the liquidus is not expected to hamper nucleation [START_REF] Pupier | Experimental quantification of plagioclase crystal size distribution during cooling of a basaltic liquid[END_REF]. Samples were placed into the hotspot of the furnace (ΔTgradient <1°C over 5 cm) alongside a calibrated Pt90-Rh10 S-type thermocouple. Oxygen fugacity in the alumina tube was controlled by a mixture of high-purity CO and CO2 gas introduced at the bottom of the furnace. Accuracy was checked with a SIRO2 yttria-stabilized zirconia oxygen sensor.

Samples were initially kept at super-liquidus conditions (same as muffle furnace) for 2 hours, a sufficient time to ensure fO2 equilibration without affecting nucleation [START_REF] Pupier | Experimental quantification of plagioclase crystal size distribution during cooling of a basaltic liquid[END_REF].

After 2 hours, the temperature was dropped with a constant cooling rate of 2-3 °C/h (below that of the near-equilibrium cooling rate of [START_REF] Lofgren | An experimental study of trace-element partitioning between Ti-Al-clinopyroxene and melt: Equilibrium and kinetic effects including sector zoning[END_REF]) in order to ensure formation of large enough crystals for LA-ICP-MS analysis. Once these experiments reached the target temperature, they were left to equilibrate for 2 to 5 days depending on temperature (Table 2).

Two super-liquidus quench experiments (NYA-2 and NYA-21) were also performed in order to evaluate alkali-loss during the pre-melt in the muffle furnace and the 2-hour super-liquidus stage in the gas-mixing furnace. No loss of alkalis was observed in these experiments. Losses observed in the larger set of experiments are listed in Table 2.

Electron microprobe analysis

Electron microprobe analysis (EMPA) of the experimental products was performed at Utrecht University, Netherlands, using a JEOL JXA-8530F Hyperprobe. Operating conditions were 15 kV for all analyses, using a beam current of 15 nA and 8-10 nA for crystals and glasses, respectively. A beam size of 10 m was applied for both crystal and glass measurements in order to limit diffusion of alkali-metals. On-peak counting times of 20 seconds were employed for all elements, with off-peak (background) counting times of 10 seconds. Na and K were measured first in order to minimize the effect of alkali-loss. Primary standardization was performed using Smithsonian VG-2 (Si, Al for glasses; NMNH 111240-52) and in-house diopside (Si, Mg, Ca), corundum (Al), synthetic TiO (Ti), hematite (Fe), synthetic KTiPO5 (P, K), celestine (Sr), jadeite (Na), barite (Ba) and tephroite (Mn). Secondary standardization was performed on Smithsonian VG-2 and A-99 basaltic glasses (NMNH 111240-52 and NMNH 113498-1, respectively), Kakanui augite (NMNH 122142), San Carlos olivine (NMNH 111312-44), ilmenite (NMNH 96189), and microcline (NMNH 143966). Relative errors on major element concentrations (based on secondary standards) were generally <5% for concentrations above 0.1 wt.%. Specifically, relative errors for minerals and glasses were up to 1.1% and 0.2% for SiO2, 3.0% and 0.5% for Al2O3, 7.0% and 0.9% for MgO, 10.4% and 2.8% for TiO2, 3.6% and 1.1 %for FeO, 1.5% and 0.1% for CaO, 7.7% and 3.5% for Na2O, 0.4% and 3.5% for K2O, and 6.1% and 4.2% for MnO at these concentrations. P2O5 was only measured in glasses with a substantially higher error of 30%, attributed to their low concentrations (<0.38 wt.%).

Laser-ablation mass spectrometry

LA-ICP-MS analyses of experiments up to NYA-15 were performed at the ALIPP6 facility (Institut des Sciences de la Terre de Paris; Sorbonne Université, France) using an Analyte G2 UV excimer laser ablation system (wavelength of 193 nm) in parallel with an Agilent 8800 ICP-MS/MS. Data were acquired with 30 s of ablation, preceded and followed by gas background measurements. We used a pulse repetition rate of 8 Hz at an energy density of 2.48 J cm -2 . A beam diameter of 85 m was applied for standards, melts and large crystals; for small crystals (primarily rhönite) the beam diameter was reduced down to a minimum of 25 m. External standardization was performed using glass reference material NIST SRM 612, and performance evaluations were carried out using measurements of standards BIR-1G, BHVO-2G, ATHO-G, and BCR-2G. Mean relative errors of analysis were estimated to be <10% for concentrations of >1 ppm, and <20% for concentrations of <1 ppm. Analyses of experiments NYA-16 to NYA-22 were performed at Utrecht University, Netherlands using a ThermoFisher Scientific Element 2 magnetic sector ICP-MS connected to a Geolas 193 nm excimer laser, with a pulse repetition rate of 8 Hz, energy density of 2.7 J cm -2 , and a beam diameter of 60 m. External standardization was performed using BCR-2G, and an identical set to of standards to those used at ALIPP6 was used for performance evaluation (barring BCR-2G), resulting in relative errors of <15% for transition and post-transition metals (Zn and Pb, primarily), and <10% for other elements. Laser spots were placed at the rims of crystals when crystal size allowed for it, in all other cases the core was partially ablated. All resulting data were filtered to remove the potential influence of inclusions which were easily spotted by the presence of concentration peaks for some elements in measurement spectra. [START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF] have described the relationship between the partition coefficient (𝐷 i ) of a cation with valence n in a given crystallographic site M with radius 𝑟 0(𝑀) 𝑛+ (in meters*10 -10 ) and elastic modulus 𝐸 (𝑀) 𝑛+ (in Pascals*10 9 ; GPa) can be described by the lattice strain model (see also [START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF][START_REF] Blundy | Partitioning of trace elements between crystals and melts[END_REF][START_REF] Wood | Trace Element Partitioning: The Influences of Ionic Radius, Cation Charge, Pressure, and Temperature[END_REF], following the equation:

Fitting approach

𝐷 𝑖 = 𝐷 0(𝑀) 𝑛+ * 𝑒𝑥𝑝 { -4𝜋𝑁 𝐴 𝐸 (𝑀) 𝑛+ [ 1 2 𝑟 0(𝑀) 𝑛+ (𝑟 𝑖 -𝑟 0(𝑀) 𝑛+ ) 2 + 1 3 (𝑟 𝑖 -𝑟 0(𝑀) 𝑛+ ) 3 ] 𝑅𝑇 }
where 𝑁 𝐴 is Avogadro's Number, and 𝐷 0(𝑀) 𝑛+ is the strain-compensated partition coefficient of a cation of valence n and radius 𝑟 0(𝑀) 𝑛+ . This equation has been used to approximate the parameters 𝑟 0(𝑀) 𝑛+, 𝐸 (𝑀) 𝑛+ , and 𝐷 0(𝑀) 𝑛+ through a best-fit approach using measured Nernst partition coefficients, essentially constructing best-fit Onuma diagrams [START_REF] Onuma | Trace element partition between two pyroxenes and the host lava[END_REF] for cations of a given valence in their crystallographic site (e.g., [START_REF] Dalou | DOUBLE FIT: Optimization procedure applied to lattice strain model[END_REF]. However the lattice strain model has been criticized for its erroneous description of the physics behind trace element incorporation into crystals and for mistakes in the derivation of the governing equation [START_REF] Karato | Physical basis of trace element partitioning: A review[END_REF][START_REF] Dubacq | Controls on trace element distribution in oxides and silicates[END_REF]. In particular, elastic parameters retrieved from fitting partition coefficients with the equations of (Blundy andWood, 1994, 2003) have little physical meaning.

Nevertheless, the lattice strain model was used in this study for its practical applications and due to the complexity of currently available alternatives limited to description of partitioning between melts or between crystals (e.g., [START_REF] Wagner | Trace element partitioning between silicate melts -A molecular dynamics approach[END_REF][START_REF] Figowy | Partitioning of chromium between garnet and clinopyroxene: First-principle modelling versus metamorphic assemblages[END_REF]. The fitting procedure was based on a Monte-Carlo approach using 1 million randomly generated parameters within a given range (0.1 to 50 for 𝐷 0(𝑀) 𝑛+ , 0 to 2500 GPa for 𝐸 (𝑀) 𝑛+ ). Lattice sites for specific elements were determined based on evaluation of D-value trends with cation size in relation to the nearest known major element cation sites. Effective ionic radii were derived from [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF] and [START_REF] Jia | Radii and Effective Ionic Radii of the Rare Earth Ions[END_REF] and the 𝑟 0(𝑀) 𝑛+, range was set per valence and site, limited by the largest and smallest cations in consideration. Because both sites in leucite only have data on one side of their strain parabola, r0 of this mineral was set to a fixed 1.9 Å for the W-site, and 0.39 Å for the Tsite, corresponding to the ideal size of the W-site [START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF] and size of tetrahedrally coordinated Al 3+ , respectively. For each simulation, the quality of the fit was estimated using a chi-squared ( 2 ) test, after which the best fit was stored. This procedure was repeated 100 times using D values falling within the 1σ range for each element. The mean parameter values among the 100 best fit simulations were reported with an error defined as the 1σ value of the remaining best ranked simulations for each parameter.

In order to compare experimental results with natural glass-crystal pairs, we also applied our model to literature data. When no temperature was reported, a temperature of 1000 °C was applied, in accordance with the approximate Nyiragongo lava lake temperature [START_REF] Sahama | The Nyiragongo main cone[END_REF].

Results

Crystallinity and equilibrium of run products

Fifty-five run products were characterised for major elements and were used to constrain phase equilibria. Out of those, only thirty-six were characterized for trace element partitioning. This is because: (1) eight products were not measured because they were run at super-liquidus conditions (Table 2; Figs 3; 4); (2) five experimental products showed insufficient crystal size for laser ablation analysis, and four experimental products showed textural evidence for disequilibrium (e.g., unavoidable significant core-rim zoning, evidence for multi-stage growth, dendritic crystal forms), or abundance of inclusions in crystals (Table 2). Produced glasses were clear and homogeneous, with pools of sufficient size for laser ablation analysis. For most experiments, crystals were distributed homogeneously. However, clustering was observed at sample edges and around the Pt wire. Mass-balance calculations indicate minimal Fe-loss (< 0.5 wt.%) to the Pt wire. No significant correlation between equilibration temperatures and alkaliloss was observed within the low-Mg group, but a 5-10 % difference was frequently observed between the calculated-(based on mass-balance) and initial alkali contents, as measured in the glasses of super-liquidus runs (Table 2). Experimental products varied in crystallinity between 2% and 80%, increasing steadily with decreasing equilibration temperature and the MgO content of the residual melt (Table 1; Fig. 3;4).

Zoning features

Among the experimental run products, clinopyroxene and melilite show signs of zoning in the form of core-rim-and sector-zoning, respectively. Clinopyroxene core-rim zoning formed < 10 µm rims that showed a consistent trend from a Mg-rich core to Fe-rich rims (Fig. 2f). This transition was accompanied by a slight decrease in Al 3+ which replaces Si 4+ , interpreted as a result of the continuous evolution of the melt during slow crystallization. Such features are not uncommon in experimentally derived clinopyroxene (e.g., [START_REF] Dygert | An experimental study of trace element partitioning between augite and Fe-rich basalts[END_REF][START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF].Because the rims were too small for pure LA-ICP-MS measurement, we will refrain from further discussing divalent cation partitioning for clinopyroxene. Whereas trivalent and tetravalent cations were also moderately affected by these features, their concentrations varied within uncertainty limits of the LA-ICP-MS (when measured with a 20 µm spot) , and will therefore be considered as equilibrated.

Melilite sector zoning was a consistent feature in our experimental products, similar to previously published literature (e.g., [START_REF] Lundstrom | Trace element partitioning between type B CAI melts and melilite and spinel: Implications for trace element distribution during CAI formation[END_REF]. Zoned crystals are divided into Alrich and Al-poor domains (Fig. 2e). The Al-rich domains are poor in Mg 2+ , Na + , and Si 4+ , indicating that this Al 3+ is introduced in both tetrahedral sites replacing Si 4+ as well as Mg 2+ , presumably through the following substitution mechanisms:

(1) 2 𝐶𝑎𝑁𝑎𝐴𝑙𝑆𝑖 2 𝑂 7 (𝑁𝑎 -å𝑘𝑒𝑟𝑚𝑎𝑛𝑖𝑡𝑒) + 𝐴𝑙 2 𝑂 3

(𝑙𝑖𝑞) + 2 𝐶𝑎𝑂 (𝑙𝑖𝑞) = 2 𝐶𝑎 2 𝐴𝑙[𝐴𝑙𝑆𝑖]𝑂 7 (𝑔𝑒ℎ𝑙𝑒𝑛𝑖𝑡𝑒) + 2 𝑆𝑖𝑂 2 (𝑙𝑖𝑞) + 𝑁𝑎 2 𝑂 (𝑙𝑖𝑞) (2) 𝐶𝑎 2 𝑀𝑔𝑆𝑖 2 𝑂 7 (å𝑘𝑒𝑟𝑚𝑎𝑛𝑖𝑡𝑒) + 𝐴𝑙 2 𝑂 3 (𝑙𝑖𝑞) = 𝐶𝑎 2 𝐴𝑙[𝑆𝑖𝐴𝑙]𝑂 7 (𝑔𝑒ℎ𝑙𝑒𝑛𝑖𝑡𝑒) + 𝑆𝑖𝑂 2 (𝑙𝑖𝑞) +
𝑀𝑔𝑂 (𝑙𝑖𝑞) .

Such features have been previously reported in clinopyroxene, wherein the faster growing sections are less efficient in rejecting incompatible elements [START_REF] Lofgren | An experimental study of trace-element partitioning between Ti-Al-clinopyroxene and melt: Equilibrium and kinetic effects including sector zoning[END_REF][START_REF] Welsch | Clinopyroxene in postshield Haleakala ankaramite: 2. Texture, compositional zoning and supersaturation in the magma[END_REF]. For this reason, the Al-enriched sections are filtered out in our results. Due to a general agreement of partitioning data with previously published work (see section 5.1.2), we included the low-Al zone data.

Phase equilibria and glass compositions

Run products from experiments at QFM+1 crystallized various combinations of leucite, nepheline, melilite, clinopyroxene, spinel-structured oxides, rhönite, and Ca-phosphate minerals.

Run products from experiments at QFM also included olivine (Table 2). Some samples which failed to produce crystalline Ca-phosphates instead showed spherical Ca-phosphate inclusions in late-crystallizing minerals. Crystals with such inclusions were excluded from trace element analysis, but their observation can help to explain phosphorous deficiencies in mass-balance calculations.

The five compositions of the low-Mg group (Fig. 3) developed differently with temperature, which resulted in differences in mineral assemblages. However, an overall trend of increasing melt Na2O with differentiation was observed (Fig. 3e), coupled with decreasing FeO (Fig. 3b).

Iron speciation in the glass was calculated using the approach of [START_REF] Putirka | Rates and styles of planetary cooling on Earth, Moon, Mars, and Vesta, using new models for oxygen fugacity, ferric-ferrous ratios, olivine-liquid Fe-Mg exchange, and mantle potential temperature[END_REF] for use in the calculation of Fe 2+ -Mg exchange KD values. Experiments on the high-Mg compositions were performed at only two temperatures, limiting discussion of major element trends, especially since these runs only contained olivine and melilite as crystalline products. Detailed compositional information on a per-experiment basis is provided in Supplementary Material 2. temperature (Fig. 3d). In the final temperature interval from 1050 °C to 1025 °C, rhönite and Cabearing phosphates crystallized for all remaining compositions. Although having relatively similar liquidus temperatures, composition B was over 75% crystallized at this point, whereas composition C was still 75% melt, reflecting their contrasting chemistries and therefore crystallization paths.

Compositions

Compositions E, F, G, and H:

Between the liquidus (~1250-1500 °C; Table 1) and 1200°C, the high-Mg group compositions only crystallized olivine, which generated an increase in all oxidecomponents other than MgO, FeO (which remained approximately stable), and the alkali oxides, the latter being related to alkali loss as opposed to crystallization (Fig. 4; Table 2). These trends were stronger for composition F, corresponding to its higher Mg# ([Mg/(Mg + Fe 2+ )]*100) and liquidus.

Major element compositions of the minerals

Major element compositions of crystals are summarized below. A complete overview of representative compositions per experiment is provided in Supplementary Material 1, and a more extensive discussion is listed in Supplementary Materials 2.

Leucite

Leucite was homogeneous between experiments, following the empirical formula of K0.92Na0.08AlSi2O6, similar to the average formula of K0.94Na0.06AlSi2O6 recorded by [START_REF] Platz | Nyiragongo Volcano, DR Congo: Mineral Chemistry and Petrology[END_REF]. Na substitution for K + (0.06-0.12 p.f.u.; 0.91-1.69 wt.% Na2O) in our compositions correlated with the Na + -concentration in the surrounding melt. Trace amounts of Fe 3+ (assumed trivalent based on site filling approach; < 0.03 p.f.u.; < 1.01 wt.% FeO) and Ca 2+ (< 0.01 p.f.u.; < 0.22 wt.% CaO) were also found.

Melilite

Melilite compositions were primarily Mg-rich alumoåkermanite [(Ca, Na)2(Al, Mg, Fe 2+ )Si2O7] [START_REF] Wiedenmann | Alumoåkermanite, (Ca,Na)2(Al,Mg,Fe2+)(Si2O7 ), a new mineral from the active carbonatite-nephelinite-phonolite volcano Oldoinyo Lengai, northern Tanzania[END_REF], including up to 10 mol% gehlenite (Ca2Al2SiO7), and with increasing Na with differentiation from 0.22 Na p.f.u. (2.6 wt.% Na2O) at 1100 °C, to 0.31 Na p.f.u. (3.6 wt.% Na2O) at 1025 °C, with an outlier at 0.37 (4.2 wt.% Na2O)(Fig. S2, in Supplementary Materials 2). The incorporation of Na + can be explained by coupled exchange with Al 3+ for Ca 2+

and Mg 2+ , causing a trend towards Na-åkermanite (CaNaAlSi2O7). All these compositions overlap with the compositional ranges reported by [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF] and [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] (see Figure S2).

Nepheline

The compositions of nepheline used for trace element analysis (experiment 22N) followed the empirical formula [0.3K0.70]Na2.7Ca0.29(Mg,Mn,Sr)0.01 [Fe 3+ 0.1Al3.95Si3.95]O16 based on a fixed 16 oxygen basis, reflecting a partially filled A site and minor Fe 3+ in the T-site. High Ca-nepheline were also reported by [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF], who indicated up to 2.2 wt.% CaO.

Additional nepheline measurements from other experiments ranged in K-incorporation between 0.28 and 0.64, correlating negatively with the Na content of the melt.

Clinopyroxene

Clinopyroxene crystals were depleted in SiO2 (37-45 wt.%, 1.43-1.68 p.f.u.), which was compensated by IV Al 3+ -and Fe 3+ -enrichments (0.28-0.57 and 0.11-0.31 p.f.u., as calculated by the approach of [START_REF] Lindsley | Pyroxene thermometry[END_REF]). The M1 and M2 sites are, in order of descending concentration per formula unit, filled with Ca 2+ (0.90-0.96), Mg 2+ (0.46-0.69), Fe 2+/3+ (0.23-0.39), Ti 4+ (0.06-0.20), VI Al 3+ (≤ 0.12), Na + (0.03-0.07), and Mn 2+ (≤ 0.01), corresponding to Ca-, Mg-, and Alrich diopside. These are diopside crystals richer in the CaTiAl2O6 and CaFe 3+ AlSiO6 components than is traditionally reported in natural samples (Fig. S3a, in Supplementary Materials 2), but similar compositions have been previously reported by [START_REF] Gee | Experimental petrology of melilite nephelinites[END_REF].

Olivine

The forsterite content (𝑋 𝑀𝑔 𝑜𝑙 /(𝑋 𝐹𝑒 𝑜𝑙 + 𝑋 𝑀𝑔 𝑜𝑙 ) of experimentally produced olivine varied between 0.77 and 0.91 (in agreement with the 0.82 to 0.89 range reported by [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF] for pyroxene nephelinites and alkali olivine basalts). The Fe-Mg partitioning between olivine and melt (𝐾 𝐷 𝐹𝑒-𝑀𝑔 𝑜𝑙-𝑙𝑖𝑞 = [(𝑋 𝐹𝑒 𝑜𝑙 𝑋 𝑀𝑔 𝑙𝑖𝑞 )/(𝑋 𝑀𝑔 𝑜𝑙 𝑋 𝐹𝑒2+ 𝑙𝑖𝑞 )]) ranged from 0.21 -0.26 and 0.25 -0.27 for highand low-Mg compositions, respectively.

Spinel-structured Oxides

Oxide compositions were divided into ulvöspinel, magnetite, and (Mg,Mn)(Al,Fe 3+ )2O4 spinel, varying primarily on the basis of melt composition but overlapping with the majority of published data on Nyiragongo volcanic rocks (Fig. S4, in Supplementary Materials 2). The main compositional variation between samples occurred between magnetite-rich crystals in composition A, C, and D (27-55% Fe3O4, 17-36% Fe2TiO4, 21 -42% Mg(Al,Fe 3+ )2O4) and the Mg-spinel-, and ulvospinel-rich crystals in composition B (8 -34% Fe3O4, 22 -46% Fe2TiO4, 29 -53% (Mg,Mn)(Al,Fe 3+ )2O4).

Rhönite

Rhönite crystals were the primary Ti-rich phases produced, especially at low temperature (< 1050 °C). Their composition depended on the melt composition, with the main variability in the Fe, Mg, and Ti-bearing site. A compositional range was therefore observed between Mg-rich rhönite

[(Ca1.8Na0.2)(Mg3.0Fe 2+ 1.2Fe 3+ 0.8Ti1.0)(Si3.4Al2.3Fe 3+ 0.3)O20],
formed in composition B, and

Fe-rich rhönite [(Ca1.8Na0.2)(Mg2.0Fe 2+ 1.4Fe 3+ 1.9Ti0.7)(Si3.0Al2.7Fe 3+ 0.3)O20],
of compositions A, C, D, and N.

Nernst partition coefficients

Crystal/melt partition coefficients are reported for 15 experimental products which produced inclusion-free crystals of sufficient size without disequilibrium features (see section 4.1) . A description of the trace element concentrations in minerals is given in Supplementary Material 2.

Minerals not considered for partition coefficients (oxides, Ca-phosphates) were not analysed for trace elements, and are not discussed further.

Leucite

Leucite readily incorporated significant amounts of the mono-valent LILE Cs + (DCs = 14.2 -25.1) and Rb + (DRb = 7.0 -13.0), both of which are highly compatible, the degree of compatibility increasing with cation size (Fig. 5a). Following this trend, the partition coefficients of divalent Ba 2+ and Sr 2+ also positively correlated with cation size, ranging from incompatible Sr 2+ (DSr = 0.01 -0.05) to compatible Ba 2+ (DBa = 0.78 -2.06). In accordance with their smaller radius, divalent transition metals were found to be incompatible in leucite (Fig. 5a). The compatibility of all divalent cations increases with temperature.

Trivalent cations were highly incompatible in leucite, with the exception of near-compatible Cr 3+

(DCr = 1.02 -2.8). A trend of decreased compatibility with cation size was observed, indicating a slight preference for HREE over LREE (Fig. 5a). In an extension of the trend formed by HREE, Sc 3+ is only weakly incompatible (DSc = 0.07 -0.54).

Tetravalent and pentavalent high field-strength elements (HFSE) are incompatible in leucite (generally D < 0.01) (Fig. 5a). We observe some variation in these elements without a systematic relationship with temperature, especially Th and U, attributed to the extremely low concentrations in the mineral (generally <0.01 ppm) closing in on the LA-ICP-MS detection limit.

Melilite

Monovalent cations were found to be incompatible in melilite, increasing in compatibility from

Rb + (DRb = 0.001 -0.005) to Cs + (DCs = 0.004 -0.07). The same was true for divalent Ba 2+ (DBa = 0.01 -0.05), which was found to be slightly more compatible than Cs + (Fig. 5b). In contrast, divalent Sr 2+ (DSr = 1.2 -2.5) and transition metals were found to be (near) compatible (Fig. 5b).

Trivalent cations were almost mildly incompatible in melilite, with the exception of nearcompatible Cr 3+ (DCr = 0.6 -2.3). Lanthanides were found to decrease in compatibility from Eu 3+ (DEu = 0.22 -0.54) to Lu 3+ (DLu = 0.03 -0.08) (Fig. 5b), whereas the larger REE La 3+ (DLa = 0.18 -0.46) to Sm 3+ (DSm = 0.19 -0.48) all showed similar (moderately incompatible) partitioning behaviour, with compatibility correlating positively with the Na content of melilite.

Highly charged (4+, 5+) cations were incompatible in melilite (Fig. 5b), following a moderate positive correlation with temperature.

Nepheline

Nepheline was only measured by LA-ICP-MS in experimental products of composition N, due to small crystal sizes (< 50 µm in diameter) in other compositions. Mono-and divalent trace element cations were found to all be moderately incompatible (1 > D > 0.03) in nepheline. LILE decreased in compatibility with cation radius, and the mono-valent Rb + (DRb = 0.68) and Cs + (DCs = 0.28) were more compatible than the divalent Ba 2+ (DBa = 0.06). Sr 2+ (DSr = 0.37) is located near the peak of the divalent curve, slightly above DCs but less compatible than Rb + .

Partitioning of trivalent cations in nepheline was characterized by a shallow upward slope from the highly incompatible LREE to HREE range, beyond which Sc 3+ (DSc = 0.20) and Cr 3+ (DCr = 1.14) appeared to be only moderately incompatible.

Tetra-and pentavalent cations were highly incompatible (D < 0.01) in nepheline (Fig. 5c), reflecting the lack of a suitable site for incorporation of these cations.

Clinopyroxene

Trace elements in clinopyroxene of low-Mg compositions could only be measured in composition D. The large monovalent cations Cs + (DCs = 0.002 -0.25) and Rb + (DRb < 0.02) appeared to be highly incompatible (Fig. 6a) in clinopyroxene.

Partition coefficients of lanthanides increase from the largest cation La 3+ (DLa = 0.20 -0.44) up to intermediate Eu 3+ (DEu = 0.76 -2.15), beyond which partitioning decreased together with cation size following a shallow slope (Fig. 6a). Scandium was the most compatible (DSc = 5.38 -49.03) trivalent cation in the clinopyroxene structure, approximately one order of magnitude more compatible than the REE.

Among the HFSE, only Zr 4+ (DZr = 1.51 -2.91), Hf 4+ (DHf = 1.70 -5.46), and (at low temperatures) V 4+ (DV = 0.61 -2.65) showed compatible behaviour (Fig. 6a). Thorium (DTh = 0.05 -0.20), U 4+ (DU < 0.05), and the pentavalent cations were found to be incompatible in clinopyroxene.

Olivine

The scarcity of olivine crystals produced in the experiments and the abundance of inclusions in the crystals resulted in limited trace element data, with less consistent results than for other silicates.

Monovalent cations in olivine were measured at concentrations close to the detection limits, highlighting their incompatibility but the data is insufficient for further discussion. Divalent transition metals were observed to be compatible, increasing from Co 2+ (DCo = 1.64 -5.74) to

Ni 2+ (DNi = 2.40 -31.6), and divalent LILE were highly incompatible (Fig. 6b).

In the range of trivalent cations, Cr 3+ (DCr = 0.36 -5.39) was found to have the highest partition coefficient, and is the only one above unit values, in an upward trend in partition coefficients starting at the highly incompatible La 3+ (DLa < 0.01; Fig. 6b).

Partition coefficients of highly charged (4+, 5+) cations in olivine decrease with radius per valence (Fig. 6b), but remain highly incompatible (< 0.01).

Rhönite

Despite its common occurrence, analysis of rhönite using LA-ICP-MS has proven difficult due to its elongated habit and commonly small crystal size (< 50 µm width). Nevertheless, sizeable crystals from experiments 10A, 19B, and 22A provided consistent trace element patterns for 1050 °C (Fig. 6c) reminiscent of the structurally similar melilite and clinopyroxene.

LILE were found to be incompatible in rhönite, decreasing in compatibility in the order of Sr 2+

(DSr = 0.10 -0.16), Cs + (DCs = 0.03), Rb 2+ (DRb = 0.01 -0.02), and Ba 2+ (DBa < 0.01). Divalent transition metals were instead found to be clearly compatible in rhönite (Fig. 6c).

Sc 3+ (DSc = 4.81 -8.10) and Cr 3+ (DCr = 2.69 -10.2) showed a high compatibility similar to divalent transition metals, plotting just below Ni 2+ (DNi = 9.94 -26.1). Lanthanides instead followed an increasing compatibility trend from La 3+ (DLa = 0.04 -0.06) to Sm 3+ (DSm = 0.15 -0.23), with a plateau of partition coefficients observed for Eu 3+ (DEu = 0.15 -0.22) to Lu 3+ (DLu = 0.19 -0.33).

Rhönite was found to contain abundant HFSE, with a particularly notable preference for the smaller ions Zr 4+ (DZr = 0.64 -0.74), Hf 4+ (DHf = 1.08 -1.15), V 4+ (DV = 1.43 -1.72), Nb 5+ (DNb = 0.19 -0.21), and Ta 5+ (DTa = 0.55 -0.68), for which the partition coefficients were close to unity (Fig. 6c). The larger tetravalent cations Th 4+ (DTh < 0.01) and U 4+ (DU < 0.02) were found to be significantly less compatible, similar to monovalent cations.

Discussion

Lattice strain model

The partitioning behaviour for elements of each valence state in each mineral/melt pair was modelled using a lattice-strain fitting approach (Blundy and Wood 1994; see section 2.5).

Cations were distributed over the available crystallographic sites based on their radius and charge under the relevant fO2 conditions. Fit parameters were then determined for every unique combination of experimental conditions (temperature, fO2, composition) on a mineral-by-mineral basis, a summary of which can be found in Supplementary Material 1. Representative examples are discussed below.

Leucite [W(T)3O6]

Leucite has two crystallographic sites in which substitution is viable: the distorted twelve-fold coordinated W-site occupied by K + , and the tetrahedral site normally occupied by Al 3+ and Si 4+ (Deer et al., 1967;[START_REF] Volfinger | Structural control of the distribution of trace elements between silicates and hydrothermal solutions[END_REF][START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF]. The large (> 1.3 Å) mono-and divalent cations occupy the larger W-site, whereas the more highly charged, smaller cations fall on parabolic curves consistent with partitioning into the T-site, together with Al 3+ (Fig. 7). A notable exception to the distribution of cations per valence are the divalent transition metals, as well as Mg 2+ , which form a scattered distribution in logD-cation radius space (here displayed with 4-fold coordination). This is a consequence of the lack of an energetically favourable site for these small divalent cation site, resulting in disordered distribution over the 4fold site (Fabbrizio et al., 2008 and references therein). Highly compatible monovalent ions in the W-site define a curve which peaks just beyond Cs + (𝑟 𝐶𝑠 𝑋𝐼𝐼 = 1.88 Å). However, the true r0 value for this site cannot be fitted due to a lack of data on the far side of the curve, and it is therefore fixed to 1.9 Å. The 𝐷 0(𝑊) 1+ -value for our experiments varies between 13.3 to 19.1, with an 𝐸 0(𝑊) 1+ parameter fitted to 31.3 to 35.6 GPa. In line with the findings of [START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF], the divalent W-site curve is shown directly under that of monovalent cations (𝐷 0(𝑊) 2+ = 9.6 -15.4), with r0 fixed to 1.9 Å once again. Outliers were observed for QFM experiments at 1100 °C, which plot significantly higher (𝐷 0(𝑊) 2+ = 22.7 -29.8) on account of a lower DCa value which increases the slope of the lattice strain curve. Nevertheless, the 𝐸 0(𝑊) 2+ -value of divalent cations is uniformly limited to the range of 50.9 to 59.8 GPa. Despite REE commonly substituting for Ca 2+ (e.g., pyroxene), which is mainly found in the W-site of leucite, trivalent cations show a pattern of T-site-incorporation (Fig. 7). As before, Onuma diagrams were fixed to peak at Al 3+ (𝑟 𝐴𝑙 𝐼𝑉 = 0.39 Å) considered as the major host of the site. However, the consistently incompatible behaviour of trivalent cations in leucite means that 𝐷 0(𝑇) 3+ remains low (0.24 -1.01).

This curve has a higher fitted E0 parameter (𝐸 0(𝑇) 3+ = 98 -173 𝐺𝑃𝑎 ) than the W-site, highly influenced by 𝐷 𝑆𝑐 𝐿𝑒𝑢𝑐𝑖𝑡𝑒 . No Onuma curves are constructed for tetravalent cations.

The same best-fit lattice strain approach applied to previous studies [START_REF] Francalanci | Partition coefficients for minerals in potassiumalkaline rocks: Data from Roman province (Central Italy)[END_REF][START_REF] Ewart | Application of proton-microprobe data to trace-element partitioning in volcanic rocks[END_REF]Wood and Trigila, 2001;[START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF][START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF][START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] reveals mostly similar results. Curves constructed from the data of [START_REF] Francalanci | Partition coefficients for minerals in potassiumalkaline rocks: Data from Roman province (Central Italy)[END_REF] were excluded due to anomalously low 𝐷 𝐶𝑠 𝐿𝑒𝑢𝑐𝑖𝑡𝑒 (below 𝐷 𝑅𝑏 𝐿𝑒𝑢𝑐𝑖𝑡𝑒 values hampering fitting). The other studies show monovalent partitioning curves in agreement with the present study, except for slight variations in 𝐷 0(𝑊) 1+ (Fig. 7). In particular, partition coefficients from [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] are high (𝐷 0(𝑊) 1+ = 21.3 -26.8) compared to both natural and experimental studies from other alkaline systems (Wood and Trigila, 2001;[START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF][START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF], which provide 𝐷 0(𝑊) 1+ values between 7.1 and 13.0. This discrepancy reflects significantly higher DRb (11.0 -11.1) and DCs (23.0 -24.6) values in the former study, which may be explained through the higher W K/ W Na ratio in their leucite crystals leading to an, on average, larger site (a feature which cannot be evaluated here due to the lack of high-r constraints). A similar pattern is found for divalent cations, with the 𝐷 0(𝑊) 1+ values of Wood and Trigila (2001), Foley and[START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF][START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF] being significantly lower than those of [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] and our own (Fig. 7). However, this can be explained by an elevated DCa value in the latter studies, causing curve flattening despite comparable DBa and DSr values, and also explaining the difficulty fitting Ca reported by [START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF]. Despite a lack of complete sets of trivalent leucite partition coefficients, data of [START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF], [START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF], and Minissale et al. ( 2019) agree largely with our data. Measurements of tetravalent cations in leucite are limited to one sample from Minissale et al. (2002)'s , falling within error of our results.

Melilite [X2T1(T2)2O7]

Substitution in melilite is possible in the eight-fold coordinated X-site which hosts Ca 2+ and Na + , the four-fold coordinated T1-site, which is occupied by Mg 2+ , Fe 2+ , Fe 3+ , and Al 3+ [START_REF] Smyth | Thermal insights into the dynamics of Nyiragongo lava lake from ground and satellite measurements[END_REF][START_REF] Bindi | Five-dimensional structure refinement of natural melilite[END_REF], and the similarly coordinated T2-site which hosts Si 4+ and/or Al 3+ . The inclusion of monovalent cations is only observed in the X-site forming a curve that peaks at radius slightly larger than Na + (𝑟 𝑁𝑎 𝑉𝐼𝐼𝐼 = 1.18 Å, 𝑟 A variety of authors have previously studied trace element partitioning into the melilite structure, some focusing on their presence in calcium-aluminium inclusions (CAIs) in chondritic meteorites (e.g., [START_REF] Beckett | Crystal chemical effects on the partitioning of trace elements between mineral and melt: An experimental study of melilite with applications to refractory inclusions from carbonaceous chondrites[END_REF][START_REF] Lundstrom | Trace element partitioning between type B CAI melts and melilite and spinel: Implications for trace element distribution during CAI formation[END_REF][START_REF] Ustunisik | Trace element partitioning between CAI-type melts and grossite, melilite, hibonite, and olivine[END_REF], others carrying out measurements over natural or experimental igneous melilite (e.g [START_REF] Nagasawa | Experimental Mineral/Liquid Partition Coefficients of the Rare Earth Elements (REE) Sc and Sr for Perovskite, Spinel and Melilite[END_REF][START_REF] Onuma | Mineral/groundmass partition coefficients for nepheline, melilite, clinopyroxene and perovskite in melilitenepheline basalt, Nyiragongo, Zaire[END_REF][START_REF] Kuehner | Determination of trace element mineral/liquid partition coefficients in melilite and diopside by ion and electron microprobe techniques[END_REF]Arzamastsev et al. 2009;[START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF].

Application of the fitting approach to the available divalent data reveals an overall agreement with ours, especially with the data from natural samples of [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] (Fig. 8). X-site occupancy parameters for divalent cations are comparable between studies, except for 𝐷 0(𝑋) 2+ , which is noticeably lower (1.59 -1.92) for the gehlenite-rich experimental products of [START_REF] Lundstrom | Trace element partitioning between type B CAI melts and melilite and spinel: Implications for trace element distribution during CAI formation[END_REF] and [START_REF] Ustunisik | Trace element partitioning between CAI-type melts and grossite, melilite, hibonite, and olivine[END_REF]. This is somewhat unexpected given that gehlenite requires a fully divalent X-site, and the feature is therefore attributed to the melt composition, given that both studies are performed on CAI melts as opposed to terrestrial ones.

A similar pattern is observed for trivalent cation incorporation, wherein 𝐷 0(𝑋) 3+ is significantly depressed (0.04 -0.08) in the samples of [START_REF] Beckett | Crystal chemical effects on the partitioning of trace elements between mineral and melt: An experimental study of melilite with applications to refractory inclusions from carbonaceous chondrites[END_REF], [START_REF] Kuehner | Determination of trace element mineral/liquid partition coefficients in melilite and diopside by ion and electron microprobe techniques[END_REF] Which indeed explains the high 𝐷 0(𝑋) 3+ values reported by [START_REF] Ustunisik | Trace element partitioning between CAI-type melts and grossite, melilite, hibonite, and olivine[END_REF], but fails to explain the variations between åkermanite-rich compositions, since it does not take sodium into account, which may greatly affect the X-site of melilite by allowing coupled substitution with Na. Instead, we observed that a combination of XNa (increasing 𝐸 0(𝑋) 3+ ), Al T (decreasing 𝐸 0(𝑋) 3+ ), and temperature (decreasing 𝐷 0(𝑋) 3+ ) most adequately explains the differences between studies.

The 𝐸 0(𝑋) 3+ values reported by [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] are anomalously high for their crystal compositions, but this can be explained through large discrepancies in the heaviest HREE (Tm, Yb, and Lu; all reported at 0.1 ppm, likely close to the detection limit) which artificially flatten the strain curve.

Tetravalent substitution into the T-sites is consistent between our data and those of Minissale et al. (2019) in terms of site radius and high fitted elastic modulus (𝐸 0(𝑇) 4+ = 1572 -2218 𝐺𝑃𝑎), but has a variable 𝐷 0(𝑇) 4+ (0.22 -1.03) on account of frequently being controlled by at most three cations.

Nepheline [AB3(T1-4)8O16]

Aside from its four tetrahedral sites, nepheline comprises an eight-fold coordinated B-site primarily occupied by Na + and a nine-fold coordinated A-site occupied by K + , both of which may be subject to trace element substitution [START_REF] Smyth | Thermal insights into the dynamics of Nyiragongo lava lake from ground and satellite measurements[END_REF][START_REF] Tait | The crystal chemistry of Nepheline[END_REF]Antao and Nicholls, 2018). [START_REF] Dollase | The crystal chemistry of silica-rich, alkali-deficient nepheline[END_REF] described the A-site as only including either a vacancy or charge balancing K + (or Rb + , Cs + ) ion. Since we report partition coefficients from experiment 22N only, lattice parameters are given as single values with associated error based on the fitting approach. As was the case for leucite, a lack of data for one side of the parabola complicates establishing the monovalent partitioning curve for nepheline. The obtained monovalent Onuma diagram forms a near-flat curve, with an elastic modulus (𝐸 0(𝐴) 1+ ) of 10 ± 4

GPa. The site's 𝑟 0(𝐴 𝐵

⁄ ) 1+

is larger than Na + (𝑟 𝑁𝑎 𝑉𝐼𝐼𝐼 = 1.18 Å), at 1.21 ± 0.01 Å. Divalent cation incorporation is considered to occur primarily in the B-site. Lattice strain parabola indicate a similar optimal site radius to monovalent incorporation, at 1.23 ± 0.01 Å. The fitted elastic modulus for divalent cations is significantly higher, at 88 ± 13 GPa. Whereas lanthanides may substitute in the same site as Ca 2+ , their distribution in the Onuma diagram suggests an unrealistically low 𝑟 0(𝐵) 3+ when using 8-fold coordination (Fig. 9). Instead, T-site incorporation appears likely, but the scarcity of the data prohibited constructing partitioning curves.

Monovalent data from samples of [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] Trivalent cations in nepheline have not been thoroughly reported. [START_REF] Larsen | Distribution of REE and other trace elements between phenocrysts and peralkaline undersaturated magmas, exemplified by rocks from the Gardar igneous province, south Greenland[END_REF] and Minissale et al. (2019) provide the only available complete data-sets of REE partition coefficients, the former of which reports phenocryst/whole-rock coefficients, and the latter phenocryst/glass partitioning.

The data of [START_REF] Larsen | Distribution of REE and other trace elements between phenocrysts and peralkaline undersaturated magmas, exemplified by rocks from the Gardar igneous province, south Greenland[END_REF] is thoroughly clustered around D 3+ = 10 -2 and lacks Sc 3+ , and the data of [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] provides an image similar to that of our study, but with significantly higher partition coefficients for MREE to HREE (e.g., DYb = 0.14 vs our 6 -7*10 -3 ). However, it is noteworthy that the nepheline REE data of [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] are scarce, and their HREE data are close to detection limits.

Clinopyroxene [M2M1(T)2O6]

Trace element substitution in clinopyroxene is well-documented to occur in the VI-coordinated M1 and VIII-coordinated M2 sites, (e.g., [START_REF] Wood | A predictive model for rare earth element partitioning between clinopyroxene and anhydrous silicate melt[END_REF][START_REF] Lundstrom | Crystal chemical control of clinopyroxene-melt partitioning in the Di-Ab-An system: Implications for elemental fractionations in the depleted mantle[END_REF][START_REF] Neumann | Evidence for Fractional Crystallization of Periodically Refilled Magma Chambers in Tenerife, Canary Islands[END_REF]Wood and Trigila, 2001;[START_REF] Hill | Erratum to: Clinopyroxene-melt trace element partitioning and the development of a predictive model for HFSE and Sc[END_REF][START_REF] Mollo | Trace element partitioning between clinopyroxene and trachy-phonolitic melts: A case study from the Campanian Ignimbrite (Campi Flegrei, Italy)[END_REF][START_REF] Bonechi | High pressure trace element partitioning between clinopyroxene and alkali basaltic melts[END_REF], the latter of which potentially incorporates the full range of REE. Monovalent cation partitioning data in this study are insufficient to construct meaningful Onuma curves, and are therefore excluded. Similarly, divalent partition coefficients are excluded for equilibrium reasons (see Section 4.2). Among trivalent cations Cr 3+ and Sc 3+ partition into the smaller M1 site, whereas the REE 3+ + Y 3+ partition into M2, for which the ideal site radius is close to that of Gd 3+ = 4.74 -15.17), whereas the M2-site curve is left out due to only being pinned by Th 4+ and U 4+ . The investigation of clinopyroxene in alkaline systems has recently received significant attention (e.g., [START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF][START_REF] Baudouin | Trace element partitioning between clinopyroxene and alkaline magmas : parametrization and role of M1 site on HREE enrichment in clinopyroxenes[END_REF][START_REF] Bonechi | High pressure trace element partitioning between clinopyroxene and alkali basaltic melts[END_REF], allowing for more thorough comparison between studies. Nevertheless, the high degree of M1-site incorporation of HREE reported by the first two of these authors was not reproduced with our samples, which lack a significant aegirine component. Meaningful M1-site trivalent strain curves can be constructed for the data of [START_REF] Larsen | Distribution of REE and other trace elements between phenocrysts and peralkaline undersaturated magmas, exemplified by rocks from the Gardar igneous province, south Greenland[END_REF], Wood and Trigila (2001), [START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF] decreasing electrostatic penalty at high aegirine contents (due to VI Fe 3+ ), coinciding with a decreasing radius of the M1-site [START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF][START_REF] Baudouin | Trace element partitioning between clinopyroxene and alkaline magmas : parametrization and role of M1 site on HREE enrichment in clinopyroxenes[END_REF]. Trivalent cation occupancy into the M2-site may consequently be negatively correlated with that of the M1-site since it performs a charge-compensating role. Nevertheless, data from the experiments of Beard et al. ( 2019) still produce significantly elevated M2-site partitioning curves for trivalent cations (Fig. 10). The same can be said for the data of Wood and Trigila (2001). Those of the remaining natural studies more often present comparative enrichment of REE in the melt compared to the crystal. Despite being compositionally unusual, our M2-partitioning data is in line with previous observations of a link between increased D-values and tetrahedral aluminium (e.g., [START_REF] Hill | The effect of Ca-Tschermaks component on trace element partitioning between clinopyroxene and silicate melt[END_REF]Wood and Trigila, 2001;[START_REF] Sun | Distribution of REE between clinopyroxene and basaltic melt along a mantle adiabat: Effects of major element composition, water, and temperature[END_REF], but needs to be adjusted for silicaundersaturated cpx-components (CaTiAl2O6 and CaFe 3+ AlSiO6), since these leave no room for additional trivalent substitution. The tetravalent partitioning curves constructed from data of Arzamastsev et al. ( 2009), Ambrosio and Azzone (2018), and [START_REF] Baudouin | Trace element partitioning between clinopyroxene and alkaline magmas : parametrization and role of M1 site on HREE enrichment in clinopyroxenes[END_REF] are comparable to ours, despite our high Ca2Al2SiO6 component which would be expected to increase the DHFSE [START_REF] Mollo | Trace element partitioning between clinopyroxene and trachy-phonolitic melts: A case study from the Campanian Ignimbrite (Campi Flegrei, Italy)[END_REF][START_REF] Ma | An experimental study of trace element partitioning between peridotite minerals and alkaline basaltic melts at 1250°C and 1 GPa: crystal and melt composition impacts on partition coefficients[END_REF].

Olivine [(M1,M2)2TO4]

The structure of olivine is composed of a single tetrahedral site occupied by Si 4+ , and two independent six-fold coordinated octahedral sites M1 and M2, of which the latter is slightly larger (Della [START_REF] Giusta | Precision estimates of interatomic distances using site occupancies, ionization potentials and polarizability in Pbnm silicate olivines[END_REF]Zanetti et al., 2004). Larger cations (Ca 2+ , Mn 2+ ) tend to preferentially occupy the M2 site, whereas smaller cations such as transition metals (Ni 2+ , Co 2+ , Zn 2+ ) are more commonly observed to prefer the M1 site. Nevertheless, the similarity in site radius between M1 and M2 allows for interpretation as if these were a single M-site (Zanetti et al., 2004). Divalent partitioning curves suffer from a lack of constraints at low ionic radii and strong dependence on major elements (Fig. 11), on account of which lattice strain parabolas were not built for this valence. Trivalent cations were typically below detection limits in our olivine crystals, but when measured display a parabolic pattern peaking at radii smaller than Sc 3+ (0.59 -0.61 Å; 𝑟 𝑆𝑐 𝑉𝐼 = 0.745 Å). On account of Al being distributed among tetrahedral and octahedral sites, the trivalent curve is ill-constrained at low radii, leading to a low fitted elastic modulus (𝐸 0(𝑀) 3+ = 167 -172 GPa). However, the expected peak of said curve is in general agreement with the work of [START_REF] Sun | The importance of crystal chemistry on REE partitioning between mantle minerals (garnet, clinopyroxene, orthopyroxene, and olivine) and basaltic melts[END_REF]. Tetravalent curves in Onuma diagrams peak at a higher radius (0.59 to 0.64 Å), with a significantly higher fitted elastic modulus (𝐸 0(𝑀) 4+ = 922 -2136 𝐺𝑃𝑎).

Identical treatment of data from chemically similar systems [START_REF] Larsen | Distribution of REE and other trace elements between phenocrysts and peralkaline undersaturated magmas, exemplified by rocks from the Gardar igneous province, south Greenland[END_REF][START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF][START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] yields comparable patterns. Trivalent partitioning data on olivine from alkaline systems remain scarce, in part due to the low uptake of REE in the olivine crystal.

Those studies which report sufficient partitioning values to construct complete strain parameters [START_REF] Larsen | Distribution of REE and other trace elements between phenocrysts and peralkaline undersaturated magmas, exemplified by rocks from the Gardar igneous province, south Greenland[END_REF][START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF]) peak near our lower bound estimates (𝑟 0(𝑀) 3+ = 0.58 -0.59 Å), also with a comparable 𝐷 0(𝑀) 3+ (0.19 -0.42) in general agreement with olivine from tholeiitic systems (Zanetti et al., 2004;[START_REF] Evans | The influence of melt composition on the partitioning of REEs, Y, Sc, Zr and Al between forsterite and melt in the system CMAS[END_REF][START_REF] Sun | The importance of crystal chemistry on REE partitioning between mantle minerals (garnet, clinopyroxene, orthopyroxene, and olivine) and basaltic melts[END_REF]Dygert et al., partitioning has been discussed briefly for experiments by [START_REF] Lofgren | An experimental study of trace-element partitioning between Ti-Al-clinopyroxene and melt: Equilibrium and kinetic effects including sector zoning[END_REF], and more thoroughly for natural samples by [START_REF] Kogarko | Trace element partitioning between rhönite and silicate melt in Cape Verde volcanics[END_REF]. The most notable difference between these studies is found with regards to lanthanides, for which [START_REF] Lofgren | An experimental study of trace-element partitioning between Ti-Al-clinopyroxene and melt: Equilibrium and kinetic effects including sector zoning[END_REF] reports significantly more incompatible behaviour (𝐷 0(𝑋) 3+ = 0.05) compared to the 𝐷 0(𝑋) 3+ of 0.58 for the samples of [START_REF] Kogarko | Trace element partitioning between rhönite and silicate melt in Cape Verde volcanics[END_REF] (Fig. 12). An additional distinction is that whereas the samples of [START_REF] Lofgren | An experimental study of trace-element partitioning between Ti-Al-clinopyroxene and melt: Equilibrium and kinetic effects including sector zoning[END_REF] display HREE partitioning into the Y-site similar to our experimental products, all HREE in the natural samples of [START_REF] Kogarko | Trace element partitioning between rhönite and silicate melt in Cape Verde volcanics[END_REF] are incorporated into the Xsite. This feature is explained through a lack of Fe 3+ in the compositions of the latter study, causing the electrostatic penalty of introducing REE to be higher, similar to what is observed for clinopyroxene [START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF][START_REF] Baudouin | Trace element partitioning between clinopyroxene and alkaline magmas : parametrization and role of M1 site on HREE enrichment in clinopyroxenes[END_REF]. Divalent partitioning into the X-site is determined by few elements (Sr 2+ and Ba 2+ ), which results in both studies being within error of each other. Nevertheless, the data of [START_REF] Kogarko | Trace element partitioning between rhönite and silicate melt in Cape Verde volcanics[END_REF] is also elevated for this valence, and thus our data corresponds better with that of [START_REF] Lofgren | An experimental study of trace-element partitioning between Ti-Al-clinopyroxene and melt: Equilibrium and kinetic effects including sector zoning[END_REF]. Tetravalent cation incorporation is also elevated in these studies, with DTi stretching between 6.25 [START_REF] Kogarko | Trace element partitioning between rhönite and silicate melt in Cape Verde volcanics[END_REF] and 10.68 [START_REF] Lofgren | An experimental study of trace-element partitioning between Ti-Al-clinopyroxene and melt: Equilibrium and kinetic effects including sector zoning[END_REF], in contrast to our reported range of 3.42 to 5.22.

Insufficient data exists to properly discuss trends for this phase.

Recommended partition coefficients

For use in highly silica-undersaturated, feldspathoid bearing systems we recommend a selection of partition coefficients listed in Table 3. These partition coefficients are the mean values reported for each phase at their approximate liquidus temperature in silica-undersaturated (~SiO2 < 42 wt.%), alkali-rich (~Na2O + K2O > 6 wt.%) systems. Though they may well be applicable to more primitive systems as well as to silica-saturated systems, these coefficients should perform best for compositions and conditions similar to those studied here. We believe that for the case of silica-undersaturated, alkali-rich, terrestrial volcanic systems, our values take precedent over those previously reported on account of (a) being derived under controlled conditions instead of from natural samples, (b) our run products having a clear compositional overlap with those of natural lavas, and (c) our use of natural starting compositions which are both silica-undersaturated and alkali-rich, instead of one or the other. We also supply a more complete range of D-values for a number of phases (3+ in leucite, nepheline), which had so far been left unreported. Caution is advised when applying partition coefficients for elements of particularly low abundance in our starting compositions (e.g., transition metals in low-Mg compositions) to systems more enriched in such elements. Such elements are more subject to detection limits and rounding errors, and may behave differently at higher abundance. Similarly, partition coefficients in hydrous systems may vary substantially from those observed in anhydrous experiments. For more detailed trace element modelling covering a range of temperatures, we supply our complete dataset in Supplementary Materials 1.

Geological application

The experimentally derived partition coefficients were used to model the behaviour of trace elements during fractionation processes at Nyiragongo volcano. Specifically, using our newly established partition coefficients, we determined the degree of fractional crystallization necessary to reach the composition of the most recent eruptions [START_REF] Minissale | The geochemistry of recent Nyamulagira and Nyiragongo potassic lavas, Virunga Volcanic Province, and implications on the enrichment processes in the mantle lithosphere of the Tanzania-Congo craton[END_REF] of Nyiragongo. Nyiragongo's eruption products are dominated by olivine, clinopyroxene, melilite, nepheline, leucite, oxides, and apatite. Partition coefficients have been measured for the first five of these minerals. For oxides and apatite, partition coefficients are available from [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF], allowing modelling of all major phases in the system. In order to adequately model the Nyiragongo volcanic system we require a primitive, parental melt composition. Previously Platz et al. ( 2004) used an olivine melilite composition retrieved from the Rutoke parasitic cone from [START_REF] Denaeyer | Les laves du fossé tectonique de l'Afrique Centrale (Kivu, Rwanda, Toro-Ankole): I. Supplément au recueil d'analyses de 1965 II. Magmatologie[END_REF]. However, no trace element data is available for this sample, and we have therefore selected the compositionally similar sample LV1 of [START_REF] Minissale | The geochemistry of recent Nyamulagira and Nyiragongo potassic lavas, Virunga Volcanic Province, and implications on the enrichment processes in the mantle lithosphere of the Tanzania-Congo craton[END_REF] shown in bold). These elements were therefore linearly adjusted to lie directly between their neighbours in terms of MgO (86 ppm Rb, 1457 ppm Ba). A two-step fractionation model was applied, to account for the contrasting mineral assemblages between samples of the parasitic cones and those of the main crater complex (e.g., [START_REF] Demant | Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire[END_REF][START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF][START_REF] Minissale | The geochemistry of recent Nyamulagira and Nyiragongo potassic lavas, Virunga Volcanic Province, and implications on the enrichment processes in the mantle lithosphere of the Tanzania-Congo craton[END_REF]. The partition coefficients listed in section 5.3 were used, selecting values for 'primitive' compositions (Table 3) for the first fractionation step where possible (only olivine), and the 'evolved' values for the second step. Divalent cation partition coefficients for clinopyroxene and all D-values for oxides and apatite were derived from the work of [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF].

Trace elements were modelled using the step-wise Rayleigh fractionation equation:

𝐶 𝑙 = 𝐶 0 * 𝐹 (𝐷-1)
wherein 𝐶 𝑙 is the concentration in the liquid after fractionation, 𝐶 0 is the concentration in the parental liquid, 𝐹 is the fraction of melt over crystallizing material, and 𝐷 is the bulk partition coefficient of the considered element. The total crystallized fraction was recalculated after each step. Major elements were concurrently modelled using the following equation:

𝐶 𝑙 = (𝐶 0 -0.01 * 𝐶 𝑓 )/𝐹 wherein 𝐶 𝑙 , 𝐶 0 , and 𝐶 𝑓 are the bulk concentrations of a given oxide in the fractionated liquid, starting liquid, and fractionating crystal assemblage, respectively. For the initial fractionation step we used an adjusted fractionating assemblage based on the one used by [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF] consisting of 60% olivine, 15% melilite, and 25% clinopyroxene, consistent with the mineralogical diversity of the Rushayo chain [START_REF] Demant | Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire[END_REF]. Calculating fractionation for this assemblage to the point of 21% crystallization results in a composition comparable to evolved pyroxene nephelinites described by [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF], which marks the point at which the fractionating assemblage is changed in the model (Fig. 13). In order to constrain the second fractionation assemblage, we performed a using a least-squares fit Monte-Carlo simulation with varying mineral modes (only including locally minerals found in the natural lavas and using both major and trace element concentrations). This meant that the fractionation model was run for 10.000 arbitrarily determined mineral modes, after each of which the mismatch of the resulting composition with the (average of the) [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] glass compositions (in % of both major and trace elements) was calculated. Only the assemblage with the smallest mismatch was kept and is reported below. The 2016 glasses were chosen over the newly reported 2021 lavas [START_REF] Minissale | The geochemistry of recent Nyamulagira and Nyiragongo potassic lavas, Virunga Volcanic Province, and implications on the enrichment processes in the mantle lithosphere of the Tanzania-Congo craton[END_REF] in order to filter out potential influence of crystal accumulation on compositional data. Indeed, significant differences in trace element compositions reported by various authors for identical eruptive events were found (Fig. 13; 14), likely due to a combination of analytical uncertainties and variable inclusion of phenocrysts in analysed powders. Therefore, the glasses of [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF] which were analysed by point-instead of bulk-analysis were deemed most trustworthy.

The best results were obtained using an assemblage of 20% clinopyroxene, 27% melilite, 19% nepheline, < 1% leucite, 2% olivine, 25% oxides, and 7% apatite, most likely representing a combination of pyroxene-nephelinite and melilitite lithologies [START_REF] Demant | Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire[END_REF]. By

continuing fractionation using this assemblage, the 2016 glass composition was reached when approximately 48% of the starting melt had crystalized (Fig. 13; 14). The resulting composition adequately matches the 2016 glass compositions in both major and trace element composition, and has a slightly higher concentration of feldspathoid-incompatible trace elements (e.g.

MREE 3+

) than the 2021 eruptive material (Fig. 13c,d;14b). Comparison with the 2002 eruptive material suffers from disagreement between authors, with data from [START_REF] Chakrabarti | Isotopic and geochemical evidence for a heterogeneous mantle plume origin of the Virunga volcanics, Western rift, East African Rift system[END_REF] reporting significantly higher trace element contents for a select group of elements (e.g. Ba 2+ , Yb 3+ , Nb 3+ ; Fig. 13b,d,f). Nevertheless, the remaining dataset and those of other authors [START_REF] Platz | Nyiragongo Volcano, DR Congo: Mineral Chemistry and Petrology[END_REF][START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF], match our calculated composition within a few percent fractionation. Remaining significant compositional disagreements are for divalent cations, especially transition metals. This is attributed to a combination of low (near zero) concentrations as well as to the lack of well-established partition coefficients for these elements in a variety of phases (also in part due to low concentrations, as well as zoning features).

Leucite is notably missing from our modelled fractionation assemblage despite being a major constituent of the main cone lithologies (e.g., [START_REF] Sahama | The Nyiragongo main cone[END_REF][START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF]. As a result, the most LILE-rich compositions in the reported datasets cannot be adequately explained through simple fractionation (Fig. 13a). Instead we argue that, in line with the interpretations of [START_REF] Platz | Low-pressure fractionation of the Nyiragongo volcanic rocks, Virunga Province, D.R. Congo[END_REF], the majority of leucite crystallization appears limited to the lava-lake system, which leads to accumulation features through floatation [START_REF] Sahama | The Nyiragongo main cone[END_REF], and explains the remaining leucite-rich samples. Simple addition of leucite to our modelled 48% fractionated composition confirms this (Fig. 13).

Rhönite has not been reported for the Nyiragongo volcanic system and has not been included in the modelling. However, rhönite may be important in more shallow fractionating alkali systems such as Cape Verde and the Kaiserstuhl volcanic complex (e.g., [START_REF] Cameron | Rhönite from Big Bend National Park, Texas[END_REF][START_REF] Kyle | Occurrences of Rhönite in Alkalic Lavas of the McMurdo Volcanic Group, Antarctica, and Dunedin Volcano' New Zealand[END_REF][START_REF] Grapes | Fe2+-dominant rhonite in undersaturated alkaline basaltic rocks, Kaiserstuhl volcanic complex, Upper Rhine Graben, SW Germany[END_REF][START_REF] Mata | The 2014-15 eruption and the short-term geochemical evolution of the Fogo volcano (Cape Verde): Evidence for smallscale mantle heterogeneity[END_REF] where it mimics Na-rich clinopyroxene partitioning behaviour in terms of REE 3+ [START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF][START_REF] Baudouin | Trace element partitioning between clinopyroxene and alkaline magmas : parametrization and role of M1 site on HREE enrichment in clinopyroxenes[END_REF], and forms a major sink of HFSE 4+ .

Conclusions

We performed 1 atmosphere gas mixing furnace experiments using alkali-rich, silicaundersaturated whole-rock compositions from the Nyiragongo volcano to determine partition coefficients for phases common in alkali-rich magmatic systems. Experiments were carried out between 1025 °C and 1200 °C with oxygen fugacity buffered to QFM and QFM+1 in order to investigate the partitioning of trace elements in alkaline magmatic systems.

-Partition coefficients for trace elements of mono-to pentavalent charges were determined for leucite, melilite, nepheline, clinopyroxene, olivine, and rhönite at geologically relevant temperatures. In particular, we present partition coefficients for trivalent to pentavalent cations in the leucite and nepheline structures.

-The lattice strain model [START_REF] Wood | A predictive model for rare earth element partitioning between clinopyroxene and anhydrous silicate melt[END_REF] was used to calculate Onuma diagram parameters in order to allow for extrapolation of trace element partition coefficients.

-A set of trace element partition coefficients applicable for alkali-rich silicaundersaturated settings is proposed (Table 3).

-Fractional crystallization modelling of the Nyiragongo volcanic products using the reported partition coefficients explains progressive enrichment of light over heavy rare earth elements. Our results indicate that 48% crystallization from an olivine melilite basalt composition parental melt reproduces the composition of recent eruptions.

-Our experiments provide insight into phase equilibria for feldspathoid dominated magmatic systems at various fractionation stages under anhydrous, low-pressure conditions.

7 Acknowledgements

1233

MELTS liquidus estimates are reported for QFM conditions using Rhyolite-MELTS 1.0.2 [START_REF] Gualda | Rhyolite-MELTS: A modified calibration of MELTS optimized for silica-rich, fluid-bearing magmatic systems[END_REF]. of Nyiragongo, Mikeno and Nyamuragira [START_REF] Barette | Spatial variation of volcanic rock geochemistry in the Virunga Volcanic Province: Statistical analysis of an integrated database[END_REF], Pico do Fogo [START_REF] Hildner | Barometry of lavas from the 1951 eruption of Fogo, Cape Verde Islands: Implications for historic and prehistoric magma plumbing systems[END_REF][START_REF] Eisele | Pleistocene to Holocene offshore tephrostratigraphy of highly explosive eruptions from the southwestern Cape Verde Archipelago[END_REF], the Eifel [START_REF] Jung | Petrogenesis of Tertiary Mafic Alkaline Magmas in the Hocheifel, Germany[END_REF][START_REF] Tomlinson | Chemical zoning and open system processes in the Laacher See magmatic system[END_REF], Etna [START_REF] Viccaro | Continuous magma recharge at Mt. Etna during the 2011-2013 period controls the style of volcanic activity and compositions of erupted lavas[END_REF], Terceira [START_REF] Mungall | Petrogenesis of basalt-comendite and basalt-pantellerite suites, Terceira, Azores, and some implications for the origin of ocean-island rhyolites[END_REF][START_REF] Regenauer-Lieb | Melt instabilities in an intraplate lithosphere and implications for volcanism in the Harrat Ash-Shaam volcanic field (NW Arabia)[END_REF], Mount Morning [START_REF] Martin | Petrogenesis of Cenozoic, alkalic volcanic lineages at Mount Morning, West Antarctica and their entrained lithospheric mantle xenoliths: Lithospheric versus asthenospheric mantle sources[END_REF], and Mount Erebus [START_REF] Caldwell | Mineralogy and Geochemistry of Ejecta erupted from Mount Erebus, Antarctica, Between 1972 and 1986[END_REF][START_REF] Iverson | Eruptive history and magmatic stability of Erebus volcano, Antarctica: Insights from englacial tephra[END_REF]. Note that experiments above 1100 °C were performed with High-Mg starting compositions.

Fig. 7 Representative best-fit lattice strain curves for mono-to tetravalent ions in the leucite structure for a single set of conditions (listed top left). Ionic radii are for twelve-fold (1+, 2+) and four-fold (3+, 4+) coordination taken from [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. Four-fold radii are in a large part acquired extrapolation, see section 2.5. D0 values are unit-less, E0 values are in GPa, and r0 values are listed in Å. Open symbols were not considered for the fitting approach. Shaded areas and/or lines represent literature data, whereas full opacity lines are from this study. This also applies for further figures. Abbreviations for sources of literature curves are as follows: Fab08: [START_REF] Fabbrizio | Experimental determination of radium partitioning between leucite and phonolite melt and 226Ra-disequilibrium crystallization ages of leucite[END_REF], FJ04: [START_REF] Foley | Trace element partitioning in lamproitic magmas-the Gaussberg olivine leucitite[END_REF]), Min19: [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF], WT01: (Wood and Trigila, 2001).

Fig. 8 Representative best-fit Onuma curves for mono-to tetravalent ions in the melilite structure for a single set of conditions (listed top left). Ionic radii are for four-(T1-site) and eight-fold (Xsite) coordination taken from [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. Select four-fold radii are acquired through extrapolation following the approach by [START_REF] Jia | Radii and Effective Ionic Radii of the Rare Earth Ions[END_REF], see section 2.5. Abbreviations for sources of literature curves are as follows: Arz09: (Arzamastsev et al., 2009), Beck90 [START_REF] Beckett | Crystal chemical effects on the partitioning of trace elements between mineral and melt: An experimental study of melilite with applications to refractory inclusions from carbonaceous chondrites[END_REF], Kue89: [START_REF] Kuehner | Determination of trace element mineral/liquid partition coefficients in melilite and diopside by ion and electron microprobe techniques[END_REF], Lun06: [START_REF] Lundstrom | Trace element partitioning between type B CAI melts and melilite and spinel: Implications for trace element distribution during CAI formation[END_REF], Min19: [START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF], Nag80: [START_REF] Nagasawa | Experimental Mineral/Liquid Partition Coefficients of the Rare Earth Elements (REE) Sc and Sr for Perovskite, Spinel and Melilite[END_REF], Onu81: [START_REF] Onuma | Mineral/groundmass partition coefficients for nepheline, melilite, clinopyroxene and perovskite in melilitenepheline basalt, Nyiragongo, Zaire[END_REF], Ust19: [START_REF] Ustunisik | Trace element partitioning between CAI-type melts and grossite, melilite, hibonite, and olivine[END_REF]. Fraction Crystallized (%)

  A, B, C, D, and N: Descending in temperature from 1180 °C, all low-Mg compositions started by crystallizing oxides, as evidenced by a continuous decrease in FeO and MgO (Fig. 3b). The next crystallizing phase on the liquidus varied depending on composition, between leucite (Comp A, C, D), nepheline (Comp N), or melilite (Comp B). For compositions A, B, and C, these phases were observed to crystallize above 1100 °C (Figs. 3d; 3f), whereas for compositions D and N, feldspathoids started crystallizing between 1100 °C and 1075 °C (Figs. 3e; 3f). Experiments on composition B at QFM conditions formed olivine in this temperature interval. Descending further from 1075 °C to 1050 °C, clinopyroxene and (minor) nepheline crystallized from all compositions, with rhönite appearing in samples of compositions A, D, and N. Leucite stopped being the dominant crystallizing phase for compositions A and C at this temperature (Fig. 3f), and clinopyroxene formation dominated composition D samples below this

  23 -1.27 Å; Fig. 8). Despite Na + being a major component in the alumoåkermanite structure, partition coefficients for monovalent cations into this site are moderately low (𝐷 0(𝑋) 1+ = 0.53 -0.71). The site has a moderate fitted elastic modulus (𝐸 0(𝑋) 1+ = 77 -107 𝐺𝑃𝑎). Divalent cations are distributed over the X-and T1-sites depending on size; with the T1 site incorporating Mg 2+ and the transition metals, and the X-site incorporating the larger alkaline earth metals. T1-site incorporation of transition metals (𝐷 0(𝑇1) 2+ = 1.11 -3.09) peaks near Ni ( 𝑟 0Å), but is subject to uncertainty resulting from the lack of smaller cations. Divalent cation incorporation into the X site represents the highest lying curve for melilite (𝐷 0(𝑋) 2+ = 4.07 -4.95), peaked by Ca 2+ (𝑟 𝐶𝑎 𝑉𝐼𝐼𝐼 = 1.12 Å; 𝑟 0(𝑀) 2+ = 1.07 -1.14 Å), followed by decreasingly compatible Sr 2+ and Ba 2+ . The X-site also hosts the trivalent lanthanide group, with a peak in D values between Pr 3+ and Nd 3+ (𝐷 0(𝑋) 3+ = 0.28 -0.48; 𝑟 0(𝑋) 3+ = 1.11 -1.12 Å). Slightly elevated Al 3+ concentrations, replacing divalent cations in the T1-sites in the Al-rich domains of zoned crystals promote the incorporation these elements through coupled substitution, but the corresponding concentration changes are of lower magnitude than inter-crystal variability combined with errors on LA-ICP-MS measurements. Trivalent cations in the T-sites are limited to Al 3+ , Cr 3+ , and Sc 3+ . Tetravalent cation incorporation in melilite is scarce, with Th 4+ and U 4+ partitioning into the X-site, and Ti 4+ , Hf 4+ , and Zr 4+ preferring the T-sites. The associated partitioning curves for the latter have a low 𝐷 0(𝑇) 4+ (0.04 -0.09), high elastic moduli (𝐸 0(𝑇) 4+ = 1172 -1900 𝐺𝑃𝑎), and consistent 𝑟 0(𝑇) 4+ of 0.46 to 0.47 Å.

(

  05 -1.06 Å). Lu 3+ and Yb 3+ are observed to diverge slightly from this curve, indicating minor incorporation into the M1-site. No M1-site parabola for this valence could be constructed on account of Cr 3+ and Sc 3+ being the only contributing cations. Trivalent M2-site Onuma curve E0-values decrease with temperature (287 -331 GPa between 1025 and 1075 °C). M1-site tetravalent trace element incorporation is dictated by V 4+ , Ti 4+ , Hf 4+ , and Zr 4+ , which form a tight curve (𝑟 0

  ,Arzamastsev et al. (2009), Ambrosio and Azzone (2018),[START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF],[START_REF] Minissale | The petrology and geochemistry of Nyiragongo lavas of 2002, 2016, 1977 and 2017 AD, and the trace element partitioning between melilitite glass and melilite, nepheline, leucite, clinopyroxene, apatite, olivine and Fe-Ti oxides: a unique scenario[END_REF][START_REF] Baudouin | Trace element partitioning between clinopyroxene and alkaline magmas : parametrization and role of M1 site on HREE enrichment in clinopyroxenes[END_REF], among which the data of Ambrosio and Azzone (2018) are in best agreement with our data (Fig.10). The samples of[START_REF] Beard | Clinopyroxene/melt trace element partitioning in sodic alkaline magmas[END_REF] and[START_REF] Baudouin | Trace element partitioning between clinopyroxene and alkaline magmas : parametrization and role of M1 site on HREE enrichment in clinopyroxenes[END_REF] display unusually high degrees of REE incorporation into the M1-site, a feature attributed to a

Fig. 1

 1 Fig. 1 Total Alkali-Silica (TAS) diagram including the starting compositions used for all

Fig. 2

 2 Fig. 2 Representative comparison between rate-cooled (a, c) and isothermal (b, d) experimental

Fig. 3 Fig. 4

 34 Fig. 3 Evolution of melt composition with equilibrium temperature for the low-Mg compositions

Fig. 5 Fig. 6

 56 Fig. 5 Crystal-glass partition coefficients for (a) leucite, (b) melilite, and (c) nepheline. One

Fig. 9

 9 Fig.9Representative best-fit Onuma curves for mono-to tetravalent ions in the nepheline

Fig. 10

 10 Fig. 10Representative best-fit lattice strain curves for di-to tetravalent ions in the clinopyroxene

Fig. 11

 11 Fig. 11 Representative best-fit Onuma curves for di-to tetravalent ions in the olivine structure

Fig. 12

 12 Fig. 12Representative best-fit Onuma curves for di-to tetravalent ions in the rhönite structure

Fig. 13

 13 Fig. 13 Binary trace elements (ppm) vs MgO (wt.%) diagrams comparing modelled

Figure 1

 1 Figure 1 Click here to access/download;Figure;Figure 1.eps

  Figure 2

Figure 4

 4 Figure 4 Click here to access/download;Figure;Figure 4.eps

  Figure 5 Click here to access/download;Figure;Figure 5.eps

Figure 7

 7 Figure 7 Click here to access/download;Figure;Figure 7.eps

Figure 9

 9 Figure 9 Click here to access/download;Figure;Figure 9.eps

  Figure 10 Click here to access/download;Figure;Figure 10.eps

  Figure 11 Click here to access/download;Figure;Figure 11.eps

  Figure 12 Click here to access/download;Figure;Figure 12.eps

Figure 14

 14 Figure 14 Click here to access/download;Figure;Figure 14.eps

  , and[START_REF] Lundstrom | Trace element partitioning between type B CAI melts and melilite and spinel: Implications for trace element distribution during CAI formation[END_REF]. Conversely, REE partitioning in the gehlenite-rich samples ofUstunisik Kuehner et al., 1989). Previous work by[START_REF] Beckett | Crystal chemical effects on the partitioning of trace elements between mineral and melt: An experimental study of melilite with applications to refractory inclusions from carbonaceous chondrites[END_REF] linked the individual partitioning of LREE in melilite with the Xgeh/XAk ratio, following the reaction:

	2𝐶𝑎 2 𝐴𝑙 2 𝑆𝑖𝑂 7 (𝑔𝑒ℎ𝑙𝑒𝑛𝑖𝑡𝑒) + 𝑅𝐸𝐸 2 𝑂 3 (𝑙𝑖𝑞) + 2𝐹𝑒𝑂/𝑀𝑔𝑂 (𝑙𝑖𝑞)
	= 2𝐶𝑎𝑅𝐸𝐸(𝐹𝑒, 𝑀𝑔)𝐴𝑙𝑆𝑖𝑂 7 + 2𝐶𝑎𝑂 (𝑙𝑖𝑞) + 𝐴𝑙 2 𝑂 3 (𝑙𝑖𝑞)

et al. (2019) appears elevated (𝐷 0(𝑋) 3+ = 1.26), with a significantly smaller fitted elastic modulus (𝐸 0(𝑋) 3+ = 81 𝐺𝑃𝑎), which is better in line with current views on melilite REE-incorporation (

  (MgO = 10.35 wt.%) was thus selected. This sample has Rb and Ba concentrations which appear anomalously low for their MgO compared to the rest of the dataset (41, 21, and 116 ppm Rb and 836, 789, and 1862 ppm Ba corresponding to 17.51, 10.35, and 5.65 wt.% MgO samples; LV1

  Wood B. J. and Trigila R., 2001. Experimental determination of aluminous clinopyroxene-melt partition coefficients for potassic liquids, with application to the evolution of the Roman province potassic magmas.Chem. Geol. 172,[213][214][215][216][217][218][219][220][221][222][223] Table1Major element oxide and trace element compositions of starting materials for the gas-mixing furnace experiments.

	P2O5	1.35	1.97	0.75		1.83	0.81	1.46	1.05	1.03	0.75
	LOI	0.63	0.00	1.29		-0.22	1.28	-0.23	-0.30	0.50	0.32
				101.3
	Total	101.05	100.24	7	99.96 102.44 98.97 100.52 100.56 99.30
	ppm
	Wright R., Blackett M. and Hill-Butler C., 2015. Some observations regarding the thermal flux Sc 2.4 12.7 1.6 5.6 2.1 23.6 27 28.5	34.5
	V	186	384	49.2		318	117	392	236	405	338.7
	from Earth's erupting volcanoes for the period of 2000 to 2014. Geophys. Res. Lett. 42, Cr b.d.l. 16.4 b.d.l. b.d.l. b.d.l. 388 1227 177	188.7
	Co	30.6	36.1	18.6		42.4	19.3	55.9	74.2	51.8	48.1
	282-289. Ni	21.0	47.4	2.5		25.0	11.1	189.7 701.7	144.5	105.6
	Cu Zanetti A., Tiepolo M., Oberti R. and Vannucci R., 2004. Trace-element partitioning in olivine: 96.5 65.0 13.4 156.1 37.6 100.4 67.5 68.5 Zn 82.6 91.1 98.4 107.9 77.8 82.8 64.9 84.9	69.3 81.5
	Modelling of a complete data set from a synthetic hydrous basanite melt. Lithos 75, 39-54. Rb 294.6 83.7 254.7 112.2 166.5 81.0 43.4 73.7	66.0
	Sr	2243	3380	2753		2619	3099	2200	1649	1346 1253.7
	Y	27.9	41.2	29.0		35.4	24.3	28.3	22.8	26.9	24.8
	Zr	245	345	275		329	229	267	181	280	248.0
	Nb	144.6	226.3	231.1 152.5	185.3	114.5	80.8	95.9	79.6
	Mo 10 Tables Cs	4.2 4.9	1.5 0.70	4.4 2.8		3.2 1.3	5.6 1.7	2.7 0.73	3.0 0.44	2.4 0.74	2.0 0.7
	Ba	2478	2480	3047		2155	2899	1230	832	1334 1414.1
	La	180	281	208		170	199	119	97	102	87.3
	Grouping Ce	331	Low-Mg group 518 366	332	347	240	High-Mg group 187 207	184.5
	Sample name Pr	A 33	B 50	C 34		D 35	N 33	E 27	F 20	G 23	H 19.6
	Nd	Glom-113	174	112		Py-133	110	102	75	88	77.8
	Lithology Sm Eu Gd MELTS liquidus Tb	eropor-phyritic Leu-citite 16 4.4 11 1.3	Melilitite 25 6.8 18 2.0	Leu-citite 15 4.3 10 1.2	rox-ene-Neph-elinite 20 5.5 15 1.7	Nephe-linite 15 4.3 11 1.2	Oli-vine-Meli-lite 16 4.4 12 1.3	Oli-vine-Meli-lite 12 3.2 8.9 1.0	Oli-vine-Meli-lite 14 3.9 11 1.3	Oli-12.5 vine-3.5 Meli-9.8 lite 1.2
	(°C) Dy	1236 6.4	1475 9.8	1233 6.1		1182 8.6	1198 5.9	1221 6.3	1558 5.0	1201 6.4	1184 6.2
	wt.% Ho	1.1	1.7	1.1		1.5	1.1	1.0	0.84	1.1	1.1
	SiO2 Er TiO2 Tm Yb	42.50 3.0 2.18 0.38 2.4	36.73 4.5 2.85 0.56 3.4	45.96 39.43 3.2 3.9 1.43 3.25 0.44 0.48 2.9 3.0	43.48 3.0 1.53 0.39 2.5	38.31 38.78 2.7 2.2 3.14 1.86 0.32 0.27 1.9 1.6	39.63 2.8 3.53 0.34 2.1	2.8 41.06 0.4 3.39 2.2
	Al2O3 Lu	19.23 0.35	12.78 0.50	20.66 15.06 0.42 0.42	23.41 0.37	10.47 0.28	8.07 0.23	11.47 0.30	12.25 0.3
	Fe2O3 Hf	10.57 3.7	12.47 5.9	9.18 4.0	13.86 6.1	7.95 4.0	12.75 11.43 5.6 4	13.83 7.4	13.05 7.1
	MnO Ta	0.21 45	0.29 54	0.22 26		0.27 16	0.18 24	0.22 4	0.20 10	0.22 12	0.20 12.9
	MgO W	2.91 3.0	6.37 1.3	2.09 2.9		4.94 1.7	2.30 1.9	10.73 21.63 1.4 1.5	10.00 1.4	8.61 1.5
	CaO Pb	8.03 1.7	17.39 5.8	6.02 5.2	12.58 4.2	6.53 5.4	16.08 13.65 2.7 3.8	15.28 2.6	15.06 1.8
	Na2O Th	5.87 18	5.04 28	6.82 24		4.41 14	8.50 29	2.99 9.6	2.36 7.6	2.56 8.7	2.25 8.1
	K2O U	7.56 6.3	4.35 15	6.95 10		4.55 5.2	6.48 16	3.06 4.0	1.79 2.8	2.50 3.7	2.35 2.3

Table 2

 2 List of experiments analysed by EMPA and LA-ICPMS. A full table including experiments analysed by EMPA but

	rejected for LA-ICMPS are listed in Supplementary Material 1. Numbers in brackets for run products, including glass (Gl), are
	volume percentages. Sodium and potassium losses are in percentage relative to the glass compositions from super-liquidus
	experimental runs 2 and 21, with the exception of composition N, for which XRF data was used.

Table 3

 3

Recommended partition coefficients for main minerals in primitive and evolved systems as indicated by low and high whole-rock MgO. One standard deviation values are listed in brackets following the recommended coefficient. Zero values for standard deviations indicate that only a single measurement was used to constrain the recommended value. See Supplementary Material 1 for a more detailed overview.

  Cs Rb Ba Sr Co Zn Ni La Ce Pr Nd Sm Eu Gd Tb Dy Y Ho Er Tm Yb Lu Sc Cr Th U Zr Hf V Nb Ta Rb Ba Sr Co Zn Ni La Ce Pr Nd Sm Eu Gd Tb Dy Y Ho Er Tm Yb Lu Sc Cr Th U Zr Hf V Nb Ta

	1+	2+	Leucite	3+	4+	5+
	D Leucite/Glass
	1+	2+		3+	4+	5+
	D Melilite/Glass
	1+	2+		3+	4+	5+
	D Nepheline/Glass

Cs

Cs Rb Ba Sr Co Zn Ni La Ce Pr Nd Sm Eu Gd Tb Dy Y Ho Er Tm Yb Lu Sc Cr Th U Zr Hf V Nb Ta

Appendix A. Supplementary Material

The authors would like to thank Benoît Caron and Helen de Waard for their help with LA-ICP-MS analyses. We are additionally grateful to Tilly Bouten and Eric Hellebrand of the Microprobe facility in Utrecht for their assistance. We would like to express our gratitude towards Nicolas Delmelle and Jacqueline Vander Auwera for their assistance with XRF analysis. David A. Neave acknowledges support from NERC (NE/T011106/1). Olivier Namur and Sander M. Molendijk acknowledge support from the FWO through an Odysseus grant to Olivier Namur.

Bernard Charlier is a Research Associate of the Belgian Fund for Scientific Research -FNRS.

We thank three anonymous reviewers and the handling editor who helped greatly improve this work. We thank the Goma Volcano Observatory (OVG) and the Congolese Institute for Nature Conservation (ICCN) for the provided assistance and necessary authorizations during fieldwork.

Supplementary material associated with this manuscript can be found in the online version. This includes an overview of all performed experimental runs, including those rejected for analysis, an overview of all major and trace element data, and an summary of calculated Onuma diagram parameters for both our own data and those of previous literature. In addition, we supply an extended discussion on whole-rock geochemical methods, melt compositional evolution and the trace element compositions of crystallized phases.

Aigner-Torres M., Blundy J., Ulmer P. and Pettke T., 2007. Laser Ablation ICPMS study of trace element partitioning between plagioclase and basaltic melts: An experimental