Understanding the relationship between plutonic and volcanic rocks has vexed Earth scientists for decades. Active debate about whether granites and rhyolites reflect similar magmatic processes and timescales rages; the relationship of alkalic volcanics to associated plutonics such as syenites is even less understood, given their lower occurrence. However, alkalic ring complexes of syenites surrounding carbonatites are ubiquitously observed, providing an important spatial connection that may bear on the volcanic-plutonic connection. A prominent ring complex in North America is Magnet Cove (Arkansas) where syenites surround a core of ijolites and carbonatites.

Earth’s upper crust is a major thermal boundary layer with loss of heat ultimately controlling the extent of differentiation that magmas undergo. Magma bodies are often compositionally zoned with cooler mush existing above relatively hotter magma. Yet the fact that no large, km-scale blobs of mostly melt are seismically observed anywhere on Earth raises fundamental questions about how much liquid exists during magma differentiation. Indeed, standard models of differentiation become particularly problematic when geochronology is considered. For instance, using multiple chronometers on the same rocks, Davis et al. (2012) showed that granitic plutons undergo nearly instantaneous cooling with unresolvable age differences between U-Pb zircon closure (∼800°C) to Ar-Ar in hornblende closure (∼560°C) indicating that if traditional magma differentiation at >700°C actually operates, it must be extremely rapid. However, the same rocks record being held above 330°C (biotite Ar-Ar age) for up to 12 Myrs, possibly allowing low temperature differentiation (if it exists) to occur for extended durations. Several recent observations suggest that silicic magmatic systems exist in cold storage for considerable durations (Rubin et al., 2017; Ackerson et al., 2017; Ackerson et al., 2018).

The lack of visible magma bodies by seismology is curiously contradicted by newer electrical conductivity observations. For instance, extremely low electrical resistance is observed in the Cascades between Mounts Ranier, Adams and St. Helens, interpreted by Hill et al. (2009) to reflect >30% melt. Notably, this same area is very melt-poor based on seismic tomography (Lees, 1992). Combined seismology/conductivity studies may thus provide important insight into how differentiation in Earth’s upper crust occurs. Such a study around ODL could be particularly useful since electrical conductivity of dry sodium carbonatite melt is >100x that of silicate melt (Gaillard et al., 2008) and water would likely increase this conductivity further. Carbonate-melt/fluids decrease dihedral angles thus increasing connectivity of fluid (Hunter and McKenzie, 1989). Low dihedral angles also mean the liquid fully wets crystal faces, which produces even greater mismatch between observed seismic velocities and electrical conductivities if hydrous carbonate liquids did indeed exist.

Ol Doinyo Lengai is situated in the East Africa Rift in northern Tanzania. Although known for its quiescent release of natrocarbonatite at ∼450°C (Dawson, 1962), ODL is actually a young stratovolcano dominantly made of nephelinites with minor phonolite generation. Cyclical volcanic activity consisting of quiescent natrocarbonatite lava effusion punctuated by explosive silicate eruptions characterizes this volcano. Explosive silicate eruptions occurred in 1933, 1965, 1983 and 2008 (Dawson et al., 1995) leading to a general cycle periodicity of ∼30 years. ODL natrocarbonatite lavas are characterized by very high alkali contents and alkali/alumina ratios (e.g. >30 wt% Na₂O (Na+K)/Al>300, extreme peralkalinity; Dawson et al., 1995). Natrocarbonatite lavas also contain high contents of barium, strontium, sulfur, chlorine, phosphorous and fluorine. The nephelinite tephras are highly porphyritic containing voluminous scoriaceous lapilli with nepheline, wollastonite, combeite, Ti-andradite, apatite and clinopyroxene phenocrysts. Reynes et al. (2020) show that andradites with 11 wt% TiO₂ (like those at ODL) have >1,000 ppm water contents, perhaps providing further evidence for the water-rich nature of ODL magmas.

The most recent eruption cycle involved natrocarbonatite lava flows from 1983 through 2007 ending with explosive eruptions in 2007–2008. Early eruptions produced tephras of dominantly nephelinite composition but with many having significant carbonatite component mixed in. During early 2008 (Jan-April), a compositionally zoned set of nephelinite tephras having little natrocarbonatite component was explosively erupted (Kervyn et al., 2010). The final tephra erupted from this sequence was carbonatite-rich nephelinite (ODL-1, last erupted tephra in Figure 2). The compositional zoning of this eruption shows the unusual nature of differentiation at ODL. Like most zoned magma systems, the coolest magma erupted first, followed by less differentiated, hotter magmas as shown by MgO increasing stratigraphically up (Figure 2 ). However, in behavior generally unique to ODL, the most differentiated, first-out magma was lower in silica than the later erupted hotter magmas. This unusual feature of ODL may provide insight into the possible processes producing compositional zoning in Earth’s upper crustal systems.

The origin of carbonatites, igneous rocks that have occurred throughout Earth history, remains enigmatic and debated (Woolley and Church, 2005; Kamenetesky et al., 2021). Notably, ODL erupts natrocarbonatite while calcio- and magnesio-carbonatites, often occurring as intrusive stocks, dikes or sills, make up the majority of carbonatites in the ancient record (Jones et al., 2013). Previous experimental work has focused on assessing whether ODL natrocarbonatites form by liquid immiscibility reactions (Freestone and Hamilton, 1980; Kjarsgaard et al., 1995). While experiments have shown that two immiscible melts can form, the conjugate melt to natrocarbonatite is phonolite rather than the nephelinites that are currently co-erupted. Furthermore, the experimental conditions producing two immiscible melts are significantly higher in temperature than the eruption temperatures of ODL natrocarbonatite which are measured as 450–500°C. Previous studies have questioned the melt immiscibility interpretation based on both the phase equilibria and mismatches in trace element partitioning between immiscible melts (Nielsen and Veksler, 2002).

The finding that ODL magmas are H₂O-rich (de Moor et al., 2013) fundamentally changes the relevant phase relationships. For instance, Koster van Groos (1990) showed that a single-phase Na₂CO₃ + H₂O liquid, regardless of proportion, exists at upper crustal pressure and temperatures (400°C and 0.1 GPa), similar to those of the ODL natrocarbonatite. Furthermore, the major control on carbonate-silicate melt immiscibility depends on relative differences in structure of the two melts (Jones et al., 2013). In this light, it is not surprising that typical silicate melts and carbonatite melts remain immiscible over a wide range of P-T conditions, given differences in polymerization and viscosity and the ionic character of hydrous carbonatites. However, we note that the low temperature hydrous Na silicate liquids from Lundstrom (2020) are also unpolymerized and ionic meaning that these liquids are much more likely to be miscible with hydrous Na₂CO₃. Furthermore, based on molecular dynamics modeling, H₂O—carbonate interactions in alkalic melts are predicted to play a crucial role in stabilizing both volatile species into a single liquid, impacting both melt miscibility and degassing behaviors (Pan and Galli, 2016).

While Schairer and Bowen (1947, 1956) mapped out the Na₂O-Al₂O₃-SiO₂ system under dry conditions (Figure 1B), exploration of the peralkaline portion of this system with addition of H₂O has been minimal. In addition, examination of the silica undersaturated (nepheline-albite saturated) portion of this ternary with H₂O is nonexistent. Water bearing experiments along the nepheline-albite binary show that the eutectic drops by 234°C under water saturated conditions relative to dry conditions (Edgar, 1964). By adding a peralkaline hydrous melt, we seek to determine albite-nepheline saturated melt compositions along the cotectic valley which should continue down temperature away from the eutectic. Note that melt compositions in the silica undersaturated system will be more Al₂O₃ rich than those in the quartz saturated system. Notably work by Mysen et al. (2000) shows that increasing Al₂O₃ leads to greatly decreasing H₂O solubility. Thus, one might suspect lower H₂O solubility in these albite-nepheline saturated melts relative to the quartz albite saturated liquids of Lundstrom (2020) which had up to 37 wt% H₂O.

The first set of experiments built off the results of Lundstrom (2020) by equilibrating a hydrous sodium disilicate starting material (Na₂Si₂O₅ having 33 wt% H₂O) with albite and natural nepheline crystals inside silver capsules (99.999% Ag) in cold seal vessels at 0.1 GPa. The nepheline starting material (like most natural nepheline) contains significant K₂O (∼25% kalsilite). The experiments involved sealing powder mixtures (lying within the region bounded by Ab-Ne-DS; Figure 1B) at variable temperature from 3 to 21 days durations (lower temperature =longer durations).

A second set of experiments similarly reacted the hydrous sodium disilicate starting material with the natural nepheline, albite and microcline (Or₉₅ amazonite from Pikes Peak, CO)+/-Na₂CO₃ at 0.1 GPa. Into one run at 630°C (5 days), two capsules were loaded—one contained just the hydrous Na₂Si₂O₅ powder (plus minerals) while the other contained hydrous Na₂Si₂O₅ with ∼9 wt% Na₂CO₃. This direct comparison using two capsules was also performed at 350°C (19 days). Finally, the desire to understand a K-free system led to one experiment in which synthetic nepheline was combined with albite, hydrous Na disilicate and Na₂CO₃, run at 0.1 GPa and 434°C in a gold capsule for 13 days.

All experiments were rapidly quenched by dropping the bomb into water producing a quench to glass. All capsules were re-weighed after each run with experiments having mass changes outside of the 0.0002 g precision of the balance discarded. Capsules were then mounted in cold set epoxy, polished with oil and immediately loaded into the SEM for analysis to avoid problems of hydration of alkali rich glass exposed to air (Lundstrom, 2020).

Three piston cylinder (Rockland Research) experiments of 1, 2, and 5 weeks duration were conducted in the experimental petrology lab at UIUC at 0.5 GPa pressure. The 2 and 5 weeks experiments both involved packing a 5% Na₂CO₃—93% ODL nephelinite powder mixture with 2% H₂O added by pipette (by mass) into a sealed 18 mm long Au-Pd₁₀ capsule that sat in the imposed 1,000–350°C thermal gradient of the piston cylinder vessel. The 1 week experiment involved adding 6% BaCO₃ and 1% UO₂CO₃ in a layer near the capsule bottom (instead of the Na₂CO₃) along with 91% nephelinite powder with 2% H₂O added by pipette into a sealed Au-Pd₁₀ capsule. The thermocouple arrangement of the piston cylinder dictates the hot end being above the cold end in the experiment, opposite to likely gradients in the Earth. However, an experiment of Lesher and Walker (1988) showed that when the cold end did occur above the hot end, the exact same thermal migration process took place—e.g., the material differentiated down temperature.

All experiments were characterized using multiple techniques including SEM-EDS, X-ray tomography, LA-ICPMS and SIMS. Details of analytical protocols and observations from each thermal gradient experiment are given in the appendix.

Supplementary Table S1 presents observed phases and melt compositions within the isothermal crystallization experiments. All low temperature (<500°C) runs in the first set of Ne-Ab bearing experiments (run from 819 to 330°C) were failures (not reported) due to the fact that they fell apart during grinding and polishing—all of these experiments, even those above 500°C that we report on, show vapor bubble indicating H₂O saturation (also consistent with observation of fluid emanating upon breaching the capsule).

The microcline bearing experiments, which compared two capsules run simultaneously (one with Na₂CO₃ and one without), allowed a clear picture of the impact of CO₂ on formation of melt and thus water solubility. This comparison results in a fundamental observation, that the presence of Na₂CO₃ changes the solubility of H₂O in the melt. Indeed, the 350°C carbonate bearing experiment produced a quench glass that shows no obvious vapor bubbles (Figure 3). The corresponding Na₂CO₃-free capsule at 350°C was puffed out (an indication of vapor saturation) and completely fell apart when opened and polished (perhaps indicating lack of melt?), making it unanalyzable. In the 630°C experiments, the carbonate-free experiment produced large vapor bubbles (like the early non-carbonate bearing H₂O-only experiments), unambiguously documenting vapor saturation. In contrast, the carbonate bearing 630°C experiment may or may not have been vapor saturated based on small amounts of porosity seen in the mount. However, clearly a much smaller volume of vapor existed in this experiment compared to the carbonate-free one. Imaging of the two carbonate-bearing experiments show that Na₂CO₃ crystals tend to disperse along the silicate grain boundaries, perhaps indicating the carbonate fluid’s role in facilitating wetting of silicate crystals. Unfortunately, there were other complications in these experiments limiting their usefulness including the observation that nephelines develop large rims of a nepheline-albite solid solution (composition approximately 27 wt% Na₂O, 23 wt% Al₂O₃ and 50 wt% SiO₂). Therefore, we do not report melt compositions for the microcline bearing experiments. Finally, the sole experiment using a synthetic Na-only nepheline and Na₂CO₃ produced a nepheline-albite-melt assemblage with little evidence for a vapor phase present confirming the carbonate-H₂O effect found in the microcline experiments.

Melt compositions in the nepheline-albite experiments closely follow the phase boundaries of the dry system (Schairer and Bowen, 1947; Figure 1B). Melt compositions at higher temperature are relatively Al₂O₃ rich and become progressively more Na₂O rich down temperature while silica remains constant at ∼57.5 wt%. The glass in the Na₂CO₃-saturated K-free experiment contains 17 wt% CO₂. However, considerable uncertainty exists in this composition due to difficulties of quantitation of the low energy carbon x-ray.

Water contents of the glasses are difficult to quantify but can be estimated based on observed phase proportions. For instance, 11.7 wt% H₂O was added to the K-free nepheline capsule and assuming water only enters the ∼40% modal volume of the glass phase, we estimate the dissolved water content of the liquid to be ∼29 wt% H₂O.

In each of the 15–20 mm long capsules (ODL-1wk, ODL-2wk and ODL-5wk), we observe systematic changes in mineralogy and geochemistry as a function of position (thus temperature). Because there are essentially no visible melt pools in any of the colder, lower ¾ portions of these experiments, the only way to present compositional data is to provide bulk compositions, modal determinations and some mineral compositions—analyses of melt compositions are not possible.

Because ODL-5wk and ODL-2wk involve identical starting materials, the mineralogical changes serve to illustrate the temporal evolution of the thermal migration process. For instance, ODL-2wk quenched to a transitional nepheline+melt partially molten area near its top whereas ODL-5wk has a sharp transition between 100% melt at its top and an almost entirely crystalline lower portion. In ODL-5wk, melilite forms the liquidus phase. The shift in liquidus phase from nepheline to melilite is reproduced by IRIDIUM models (see appendix SFig. 4). Most of the observations and discussion that follow focus on experiment ODL5-wk although collectively, the three experiments contribute to understanding the thermal gradient differentiation process.

ODL-5wk evolves to a crystal-free silicate melt in the hot, upper 25% of the capsule which abruptly shifts to a melt-poor mineralogically-layered crystal aggregate in its lower 75% (Figures 4A,B; Supplementary Table S2). Peaks in different mineral modes testify to the thorough dissolution-and-reprecipitation-based reaction process occurring as a function of temperature. As predicted by IRIDIUM, melilite occurs at highest temperature, then garnet, then clinopyroxene and finally wollastonite representing the prominent layering produced by the thermal migration process (nepheline is found throughout with little variation in its mode). A striking observation is the sharpness of layering indicated by apatite (Figure 4C) at ∼400°C where a jump to 5% higher apatite mode is defined by a single line of the mineral across the capsule.

Bulk compositions of major elements in ODL-5wk follow smooth trends that reflect these changing mineral modes and the elemental contents of the phases ( Supplementary Table S2; Figure 5 ). MgO, Al₂O₃, and even SiO₂ all decrease down temperature. Melilite compositions change in Ca#, consistent with decreasing temperature (and IRIDIUM prediction) while nepheline composition remains invariant (Supplementary Tables S3–6). Volatile element contents (SIMS spots of ∼15 μm diameter) of the hot 100% melt area are homogeneous and indicate ∼4 wt% CO₂ and 3 wt% H₂O. However, within the crystal-rich lower portion, these spot analyses produce highly heterogeneous CO₂ contents, reflecting randomly encountering carbonate solids along the silicate grain boundaries. F, Cl, and SO₄ analyses also vary widely, consistent with observed fluorite, halite and potassium aluminum sulfate existing at the cold end of ODL-5wk. An x-ray phase map (Figure 6) shows the interstitial material between broken silicate grains; a qualitative analysis gives 46.7 wt% Na₂O, 5.0 wt% SiO₂, 5.1 wt% S, 5.7 wt% K₂O and 37.3 wt% CaO excluding C from the analysis. Using 7 KV for C/Si analysis of this same region, we obtain ∼13 wt% for CO₂. While this is only a rough composition, the finding of only these peaks (and O) is consistent with a carbonate (silicate) liquid with Na, Ca and K being the major cation components (similar to observed natrocarbonatite at ODL). Finally, the complete redistribution of U and Ba in ODL-1wk observed via x-ray tomography and SEM mapping illustrates the rapid transport process occurring leading to deposition of carbonates along the silicate phase boundaries (Supplementary Figure S6; see movie of tomography of experiment in Supplementary Material). The addition of Ba to this experiment also stabilized alkali feldspar relative to ODL-5wk and ODL-2wk.

Finally, the distribution of trace elements within ODL-5wk is very regular and clearly controlled by the major phases existing at a given location in the experiment. This is well illustrated by the distribution of each REE as a function of position (Figure 7). For instance, HREE concentrate in the location where the garnet mode peaks, reflecting their high garnet-melt partition coefficient (^gt/meltD_HREE) with a systematic decrease in concentration going from MREE to LREE. Correspondingly, the LREE become enriched in the bottom portion of ODL-5wk, where carbonates and apatite become most prevalent.

The isothermal crystallization experiments show that a melt co-exists with nepheline + albite down temperature with melts becoming more peralkaline, following compositional behavior seen in the dry system (Schairer and Bowen, 1947). Addition of Na₂CO₃ appears to increase water solubility allowing a carbonate-hydrous silicate liquid to co-exist with nepheline and feldspar at 330°C.

Excepting the microcline-bearing experiments, we argue that melt compositions reported in the nepheline-feldspar crystallization experiments (Supplementary Table S1) represent a close approach to chemical equilibrium, producing changes in alumina, silica and alkali concentrations with temperature following expectation based on the dry system. The duration of experiments was similar to those of Lundstrom (2020) in which variation of starting material mixtures and time series experiments argued for attainment of equilibrium. The correspondence to the dry albite-nepheline phase boundary of Schairer and Bowen (1947) suggests consistency with previous equilibrium experiments. The high concentration of CO₂ in the peralkaline silicate liquid reflects solubility of Na₂CO₃ into these liquids as Na₂CO₃ is residual in the solid assemblage. H₂O and Na₂CO₃ appears to have mutual effects on each other’s solubility suggesting a complicated structure to the liquid.

Assessing equilibrium in thermal gradient experiments must be done with the acknowledgement that compositions of phases in these experiments can only reflect transient changes occurring as components move through melt and shift the proportions of the major phases. As such, the extent to which these experiments reached the full expected redistribution of components is unknown and frankly irrelevant. However, assessments of local equilibrium can be made. In the ODL-5wk thermal gradient experiment, the systematic change in Ca# of melilite (consistent with thermodynamic prediction) and the systematic partitioning of trace elements into observed phases both argue for a relatively close approach to mineral-melt equilibrium. Close examination shows a remarkably consistent change in concentration for each REE as a function of temperature ( Figure 7 ). Indeed, each area produces a smooth REE pattern consistent with expected patterns based on the mineralogy at that location. That this occurs within 5 weeks attests to extremely fast transport of elements through the liquid and, likely, a dissolution-reprecipitation dominated process for equilibrating minerals with liquid. This argument for equilibrium partitioning is further evidenced by examination of the concentration patterns with position of chemically similar element pairs (Zr-Hf or Nb-Ta; Supplementary Appendix Figure). While the shorter thermal gradient experiments may have had less time to reach equilibrium, the fact that the time series behavior, in which component migration leads to changes in liquidus phase, is consistent with thermodynamic control of the process.

Interpretation of vapor saturation in both isothermal crystallization and thermal gradient experiments is somewhat tricky. If we observe bubbles in the glass or a fluid upon opening a capsule, we have unambiguous evidence for vapor phase saturation. However, the lack of bubbles trapped in glass could be indication of the inability of low viscosity liquids to trap any vapor phase. We acknowledge this possibility but argue that lack of observation of water escaping during polishing likely argues for vapor undersaturation in the lower temperature carbonate bearing experiments. Clearly future work determining vapor saturation in mixed alkali-silicate-Na₂CO₃-H₂O systems (both silica saturated and undersaturated) is needed.

Within the thermal migration experiments, we also interpret the melt as being vapor undersaturated (in the 0.5 GPa experiments). Based on measured H₂O and CO₂ in the glass of ODL-5wk, retention of mass including volatiles within the capsule appears to have occurred, arguing for closed system behavior. While CO₂ solubility is known to strongly correlate with pressure and alkalinity (Lowenstern, 2001; Moussallam et al., 2016), the measured CO₂ concentrations in the silicate glass at the high temperature end of ODL-5wk (∼4 wt% CO₂) far exceed predicted CO₂ solubility in typical silicate melts. Furthermore, previous work shows that a single-phase 80%H₂O-20%Na₂CO₃ liquid can exist at 400°C and 0.2 GPa (Koster van Groos, 1990) and our nepheline-albite experiment at 434°C produced a hydrous silicate liquid with 17 wt% CO₂. Thus, we interpret that a carbonate-water-silicate liquid occurs at the low temperature end of ODL-5wk. The presence of a H₂O-Na₂CO₃ liquid at the cold end is also consistent with molecular dynamics simulations that indicate H₂O-CO₃-alkali fluids (rather than dissolved CO₂) dominate at upper crustal pressures (Pan and Galli, 2016).

At the outset, we emphasize that while thermal gradient experiments can be highly illustrative of processes of differentiation in an imposed temperature gradient, we do not advocate that Earth’s magma chambers necessarily represent an analogous process of a statically held magma body in an imposed gradient over longer spatial and temporal scales—a more dynamic process clearly must exist to overcome diffusion length scale limitations. Further, differentiation is likely to involve some combination of mechanical and chemical processes. The main take home messages from these experiments should be: 1) that significant chemical differentiation of partially molten material will occur over cm scales on week time scales; 2) a fully connected compositionally changing melt can exist from 1,000 down to 350°C in a range of compositional systems. The demonstration that a plane of continuously changing silicate-carbonate liquids in equilibrium with nepheline in the phase equilibrium experiments provides a reason for the liquid continuum inferred in the nephelinite thermal migration experiments. The observation of systematic mineral layering and redistribution of elements in these experiments attests to the reactive and pervasive nature of the hydrous carbonate liquid which rapidly transports components by diffusion.

The observed capsule evolution from a partially-molten-everywhere initial condition to a nearly complete melt-crystal segregation is consistent with predicted thermal migration experiment behavior (Lesher and Walker, 1988). Furthermore, using IRIDIUM (Boudreau, 2003), which combines mineral-melt equilibrium calculations with diffusive transport equations, the observed time evolution from ODL-2wk to ODL-5wk is reproduced (Supplementary Figure S4). This occurs despite the fact that the program does not include carbonate as a component in the melt and cannot calculate equilibria involving a melt below 600°C.

The systematic changes in mineral composition and mode with position (temperature) document that a continuous interconnected liquid must exist in the thermal migration experiments. The fact that no interface between two distinct (immiscible) liquids could be observed in any of these experiments argues for a continuum of liquid compositions from carbonate bearing nephelinite at high temperature (1,000°C) to a hydrous, alkalic carbonate (-silicate?) liquid at 350°C. Unfortunately, we must acknowledge that these experiments do not allow quantitative analyses of the interstitial liquid leaving compositions poorly known. However, the observed porosity (<3%) of plucked material along grain boundaries—which represents the maximum amount of liquid that could have existed—is clearly very small in each experiment. Indeed, most of ODL-5wk can be described as a “virtually melt (liquid)-free” crystal aggregate.

We infer that carbonate ion is a major constituent of the liquid everywhere and especially at lower temperatures based on the observation of increasing carbonate solids along silicate phase grain boundaries at the cold end of ODL-5wk. The x-ray tomograph (supplementary material movie) of ODL-1wk reveals rapid redistribution of U carbonates throughout the capsule. Effectively, the carbonate minerals track the path of the liquid existing within these experiments. In addition, vertically aligned streaks of carbonates are observed running through nepheline grains, probably tracing the dissolution-reprecipitation pathway of the liquid directly through this mineral.

The un-Earth-like temperature gradients in thermal migration experiments may lead some to dismiss their relevance. However, comparison of the few studies to date presenting wet (H₂O bearing) thermal migration experiments with Earth’s differentiation trends shows notable similarity in behavior on a TAS (total alkalis vs. silica) diagram ( Figure 8 ). For instance, a study presenting an andesite plus 4 wt% H₂O experiment placed in a 950 to 350°C temperature offset produced a compositional trend of sub-samples that reproduces a calc-alkaline differentiation trend (Huang et al., 2009; also see AFM plot in Lundstrom, 2016). Likewise, a study of phonolite plus water with an 800–1,050°C temperature offset reproduces typical alkalic differentiation trends (Masotta et al., 2011). Here, ODL-5wk shows that thermal migration involving a hydrous nephelinite + Na₂CO₃ starting material produces an anti-correlated trend of subsamples in total alkalis against silica. Clearly, this is a unique compositional trend distinct from both calc-alkaline and alkalic trends with down temperature differentiation producing lower silica content materials.

Notably, the compositional evolution in ODL-5wk provides an intriguing parallel to the compositional zoning observed in the 2008 ODL eruption. On the TAS diagram, the 2008 eruption illustrates an endmember behavior whereby the down temperature differentiation trend leads toward increasing alkali contents, lower MgO and decreasing silica. Sub-samples of ODL-5wk mimic this trend with samples from the low temperature end having lower silica, lower MgO and higher alkali contents. Note that erupted ODL nephelinites are crystal-rich (like the bottom of the experiment), consistent with formation as a zoned crystal-rich mush that was then erupted. In other words, the differentiation trend on a TAS diagram reflects compositional changes of the whole crystal mush, not the evolution of the liquid alone.

It is well accepted that magma differentiation in natural samples conforms closely to the expectations of a process controlled by mineral-melt equilibrium. A hundred years of experimental petrology producing high quality phase equilibrium and partition coefficient data have built this as a foundation. Thus, there is agreement that the major and trace element trends of differentiation in Earth’s magmatic systems follow predictions of mineral-melt equilibrium. However, how differentiation controlled by mineral-melt equilibrium actually works remains an open question. Despite sound arguments against crystal settling in mafic systems (Campbell, 1978; McBirney and Noyes, 1979), fractional crystallization involving mechanical separation of phases (as typically viewed) remains the paradigm for upper crustal differentiation of mafic magmas. The basis of support for this conclusion has been the ability to quantitatively model major and trace element changes by mass balance box models (e.g., Gast, 1968). However, such models do not uniquely support a mechanical separation process—if diffusive transport timescales can keep up with vertical sill accumulation rates, a close approach to equilibrium phase behavior including trace element partitioning will occur. If so, a match between Gastian model and observation is simply not unique as the same mass balance-based box model would apply to this coupled diffusion-advection case. In summary, it is reasonable to ask if the diversity of igneous rocks, dominated by differentiation in the upper crust of the Earth, could reflect thermal migration processes and not fractional crystallization/crystal settling. While questions about transport scaling must always be considered, the notable similarity between trends of these experiments and the compositional trends observed for Earth’s magmatic systems should give food for thought, given the observed paucity of large blobs of magma anywhere in Earth’s upper crust.

Igneous differentiation is most often attributed to mechanical separation of minerals from melt by fractional crystallization or partial melting. However, given the rapid diffusion of components observed in the thermal migration experiments, a thermal gradient-based differentiation process tied to sill emplacement may also be a viable mechanism for forming ODL’s zoned magma body. The formation of hydrous carbonate-silicate liquid within a mineral mush leads to our suggested model (Figure 9) explaining three key features of ODL: 1) production of a nephelinite magma, “reversely” zoned in silica; 2) natrocarbonatite effusion; and 3) recurrence of eruption cycles.

We suggest ODL operates by continuous arrival and ponding of a CO₂-bearing nephelinitic melt to the upper crust, forming a sill complex which builds top down as arriving magmas pond beneath a permeability barrier in the volcanic pile. Such a scenario is consistent with high precision dating of many intrusions including granitic plutons which unambiguously build top down as sill complexes (Leuthold et al., 2012). When a sill emplaces, heat is preferentially lost out its upper contact. Younger sills underplate previous ones, heating the bottom of that sill, resulting in relatively strong thermal gradients. A constant rate of vertical sill accumulation balanced by steady vertical heat loss results in a moving thermal gradient zone where differentiation can occur building a compositionally zoned mush (Lundstrom, 2009). As a strawman example, imagine emplacement of sills approximately circular in shape in map view (∼5 km in radius surrounding the volcano conduit). If the sills vertically accumulate at ∼5 cm/yr for 30 years, the zoned mush (sill complex) would have a volume of ∼5 x 10⁷ m³, approximately the volume of tephra erupted in 2008 (Kervyn et al., 2010). Vertical accumulation rates or sill complex aspect ratios could differ from this strawman but still give similar results. Regardless, simple heat flow calculations indicate that such thin sills in the upper crust will cool to <500°C quickly (Annen et al., 2006). Yet the arrival of new sills maintains the high temperature end of the gradient, providing an imposed thermal gradient on the differentiating mush.

Compositional differentiation would thus follow trends dictated by mineral-melt equilibrium as long as the Peclet number (the relative length scales of vertical accumulation of sills vs. mass diffusion: LV/D) is ∼1. Given 5 cm of sill accumulation in a year and a diffusivity of 10^–5 cm²/s, thermal gradient differentiation will operate over a ∼0.6 m effective length scale, thus satisfying the Peclet requirement. Thus, we suggest this top-down sill complex builds a nephelinite mush with its cooler top having lower SiO₂ and MgO and its hotter bottom having the opposite.

The finding that a hydrous carbonate liquid forms at the cold end of thermal migration experiments explains the second feature of this model. Adding a twist to the top-down sill differentiation model of Lundstrom (2009), we suggest this low viscosity liquid will be buoyant relative to the minerals in the mush. Viscosities are likely <10^–3 Pas based on measurements of Na₂CO₃ (Dobson et al., 1996; Stagno et al., 2018) and hydrous Na-silicates (Yang et al., 2008). Thus, this liquid will form and percolate up through the mush and eventually ooze out the surface, erupted as natrocarbonatite. During its final ascent through the crust, it will degas H₂O at near surface pressure, emanating as the dry natrocarbonatite lava at ∼450–500°C as observed. Such a model presents a significant advance on both the fluid condensate (Nielsen and Veksler, 2002) and liquid immiscibility (Freestone and Hamilton, 1980; ChurchJones, 1995; Kjarsgaard et al., 1995; Mitchell, 2009) models for natrocarbonatite formation by producing a carbonate liquid without invoking formation of a second liquid/vapor phase. Our experiments document a plausible liquid at ∼400°C, similar to natrocarbonatite eruption temperatures; in contrast, the liquid immiscibility model requires hundreds of degrees of further cooling and differentiation, despite no evidence for it. Indeed, given our experiments which show no sharp carbonate-silicate melt immiscibility boundary anywhere, it can be questioned whether immiscibility would occur in the realistic scenario of a crustal thermal gradient. Finally, a similar upflow of hydrous low temperature silicate liquids up through mush zones has recently been proposed as a major process occurring in granitic plutons (Lundstrom et al., 2022)—an implication of upward advection of these water-rich liquids is that they will rapidly remove heat from magma systems, strongly influencing isotherms and shortening the thickness of the thermal gradient differentiation zone. If hydrous alkalic liquids commonly flow up through and above sill complexes, it would have profound impact on models of differentiation on Earth.

The third feature of this model is that it may explain the cyclical eruption behavior of ODL. We posit that H₂O will build up in the liquid layer at the base of the sill complex over the 30 years repose interval of ODL. H₂O vapor saturation in this liquid ultimately causes the explosive silicate eruption. As the experiment illustrates, H₂O concentrations must increase in the melt-rich layer at the base of the sill complex as it builds down because the mush consists of anhydrous minerals. We can use the observed H₂O behavior in ODL-5wk to constrain the partitioning of H₂O between melt and mush: the experiment starts with 2 wt% H₂O homogeneously distributed and evolves to a melt in the upper 25% of the capsule having 3 wt% H₂O. If so, H₂O in the area of arriving melt at the base of the sill complex would reach ∼9.6 wt% H₂O in ∼30 years (assuming ODL nephelinites start with 2 wt% H₂O). This concentration is similar to H₂O measured in nepheline melt inclusions in the 2008 eruption (de Moor et al., 2013). We suggest that when H₂O vapor saturation occurs, the chamber undergoes expansion and carapace cracking, causing depressurization, devolatilization and finally catastrophic eruption of zoned silicate mush (Gregg et al., 2012). Thus, this model provides a plausible mechanism for eruption triggering over a fixed but short timescale, with repose interval between eruptions directly tied to the amount of magma added.

This model explains several important geochemical features of ODL. First, large fractionations of very short-lived parent-daughter pairs within the U-series decay chain occur. For instance (²²⁸Ra)/(²³²Th) are >5 in a 1988 natrocarbonatite (Pyle et al., 1991) indicating Ra-Th fractionation <10 years before eruption. If this fractionation reflects two immiscible melts separating, full separation must occur in 10 years (or possibly even less)—while this may be possible, the strict timing does raise questions to this model. In contrast, using our upflow model, Th-Ra fractionation could literally occur just prior to emanation from the ground through simple partitioning or even sorption like processes. Second, experiments measuring trace element partitioning between two immiscible melts poorly match trace element patterns of ODL natrocarbonatite (Nielsen and Veksler, 2002). Although a pure carbonatite melt cannot be analyzed in these experiments, we can compare bulk element concentrations between the bottom of the capsule (dominated by hydrous carbonate melt) and the nephelinite material at higher temperature (averaging ablation transects). This relative comparison shows strong enrichments in LREE, Th, U, W and Mo of the carbonate material relative to the nephelinite material. The trace element pattern made by comparison of the two parts of the experiment provides qualitative reproduction of the pattern of ODL natrocarbonatite compared to nephelinite (Figure 10). In detail, both clinopyroxene and garnet are still present and thus included in the bulk concentrations of the carbonate-rich sample (at bottom of experiment). This probably greatly increases Ti, Zr, Hf, Ta and Th concentrations in the experimental “carbonatite”, perhaps accounting for the relative mismatch of these elements. Notably, the shape of the REE patterns for the two bottom-most samples of the ODL-5wk (Figure 7) matches those of ODL natrocarbonatite with relatively flat MREE to HREE slopes but steep slopes on the LREE. Thus, a model of natrocarbonatite melt percolating up through nephelinite mush likely could produce trace element patterns similar to those observed in ODL natrocarbonatites.

Alkali ring-complexes involving ubiquitous alkali metasomatism surround carbonatite dikes (feeder zones) throughout the world. Magnet Cove, Arkansas, provides an excellent example reflecting an alkalic ring of syenites of ∼5 km radius around an intrusive core of spar calcite (Erickson and Blade, 1963; Flohr and Ross, 1990). While the calcitic core is interpreted to reflect crystallization of calcium carbonate magma, precipitation of calcite from an ODL-like sodium carbonatite liquid is equally plausible. Indeed, recent work on an ancient calcio-carbonatite from Canada found that calcite crystals contain abundant Na₂CO₃ fluid inclusions (Chen and KamenetskySimonetti, 2013). This raises the possibility that some calcio-carbonatites found around the world could reflect calcite crystallization from ODL-like hydrous natrocarbonatite liquids. The sodic nature of natrocarbonatite provides a ready explanation for the extensive alkali metasomatism that ubiquitously occurs around carbonatite complexes such as Magnet Cove.

Magnet Cove consists of a calcite core surrounded by concentric layers of ijolite (nepheline, clinopyroxene, melilite garnet) and various syenites (pseudoleucite, sphene; Erickson and Blade, 1963). The Magnet Cove ijolite is very similar compositionally to ODL nephelinites having 41 wt% SiO₂ and 3 wt% MgO. Outward from the calcite/ijolite core, the syenites become progressively more differentiated with MgO reaching values as low as 0.2 wt%. Other indexes of differentiation such as FeO, CaO, TiO₂ and P₂O₅ also systematically decrease away from the core of the complex (Flohr and Ross, 1990). Thus, the ring sequence follows down temperature evolution consistent with the outermost portions being cooled by contact with ambient crust. A final connection between experiment and syenite formation is the compositional similarity between glass inclusions in Tenerife syenites (Wolff and Toney, 1993) and the liquids determined here in equilibrium with albite and nepheline.

We have provided two lines of evidence supporting our inference that a continuum of liquid compositions co-exists in equilibrium with nepheline as temperature decreases, changing from a hydrous alkali silicate melt with dissolved carbonate to a hydrous carbonate-silicate liquid at lower temperature. First, the systematic compositional change and mineralogical layering from 1,000 to 350°C in thermal migration experiments could not occur unless a fully connected liquid existed. Second, liquid compositions in isothermal crystallization experiments evolve down temperature in a manner consistent with previous work (Schairer and Bowen, 1947) and only show existence of liquid (glass) at <500°C when carbonate was added to the system. While there is a bit of disconnect between the feldspar saturated simple system experiments and the more complicated nephelinite thermal migration runs where feldspar was usually not present (it was present in ODL-1wk due to Ba addition), inferring a hydrous-carbonate-silicate continuum is not an over-interpretation.

The miscibility between carbonate and silicate might be fully expected based both on melt polymerization and compositional changes with temperature. For instance, as temperature decreases and less aluminum is incorporated into the melt, it is expected that water solubility into the melt will increase (Mysen et al., 2000). The solubility of Na₂CO₃ into a hydrous Na silicate liquid might also be expected based on the completely depolymerized structure of both liquids. For instance, spectroscopic studies have found silica dimers to be the most common structure in hydrous Na silicate liquids (Svensson et al., 1986). Finally, with the demonstrated existence of a continuum of liquids existing from 1,000 down to 350°C in the thermal gradient experiments, the known small wetting angles of carbonate fluids (WatsonBrenan, 1987; Hunter and McKenzie, 1989) explains the profound observation that a large amount of differentiation occurs with virtually no observable liquid present. Lastly, the silicate to carbonate melt continuum also would have profound implications for mobilization of REE and critical mineral deposits.

Production of carbonatite as a down temperature differentiation product of basalt is consistent with previous conclusions (FischerBurnard et al., 2012) that ODL natrocarbonatite does not form from a strongly CO₂ enriched source but instead reflects derivation from typical alkali basalt. For instance, if the ODL parent magma had a CO₂/Nb of 100 (FischerBurnard et al., 2012) and 250 ppm Nb (typical East Africa Rift alkali basalt), it would not be vapor saturated upon arrival in the upper crust. In other words, a fairly typical enriched mantle alkalic basalt can account for the CO₂ forming the natrocarbonatites. What appears to be unusual about ODL is its Na₂O content and this appears to control how the volcano releases its CO₂.

Volcanic outputs of CO₂ gas represent a significant atmospheric input that play a major role in Earth’s carbon cycle over 10⁴–10⁵ year timescales with rifts playing a major role in release of CO₂ sequestered in the continental lithosphere (Brantley and Koepenick, 1995; Brune et al., 2017). Yet why certain volcanoes output more CO₂ remains nebulous. For instance, while the ODL system is obviously extremely rich in oxidized carbon, its CO₂ degassing flux is much smaller than another alkalic volcano on the western East Africa Rift, Nyiragongo (Burton et al., 2013; Foley and Fischer, 2017).

Comparison of bulk compositions of erupted nephelinites from ODL and Nyiragongo show that ODL nephelinites have upwards of 11 wt% Na₂O (along with ∼2 wt% CO₂) while nephelinites at Nyiragongo are much less sodic (∼5 wt%; Andersen et al., 2012; Sawyer et al., 2008). We suggest the Nyiragongo system is unlikely to form the hydrous Na-carbonate-silicate liquid that ODL forms (due to its lower Na₂O), thus a CO₂ vapor forms and outgases. Water contents for Nyiragongo are unknown but may also play an important role in stabilization of these liquids. Thus, ODL, with much greater total CO₂ content, ironically results in less delivery of CO₂ to the atmosphere because of its more alkalic nature.