New Experimental Constraints for the Evolution and Thermobarometry of Alkali Ultrabasic to Intermediate Igneous Rocks

Abstract

INTRODUCTION

Even though alkali magmas are less common than other magma series they occur in various tectonic environments on modern Earth, such as continental extensional zones (e.g. East African Rift System, Baker, 1987; Hofmann et al., 1997; Macdonald et al., 2001), intraplate settings (e.g. Hawaii, Macdonald & Katsura, 1964; Clague, 1987; Garcia et al., 2017), and subduction-related plate boundaries (e.g. potassic volcanism of Italy, Conticelli & Peccerillo,,1992; Peccerillo & Frezzotti, 2015). Alkali magmas comprise compositions from SiO₂-undersaturated (nepheline-normative) to SiO₂-oversaturated (quartz-normative) (Yoder & Tilley, 1962; Frost & Frost, 2008) and due to their contrasted geochemical fingerprints when compared with the subalkali magma series, they can provide specific and fundamental information on the composition and evolution of the Earth's mantle (Hofmann, 1997, 2014; Pilet, 2015).

Several models based on petrological and geochemical insights have been explored to explain the origin of alkali rocks (e.g. Green, 1973; Foley, 1992; Hirschmann et al., 2003; Pilet et al., 2008; Davis et al., 2011), whereas their differentiation through the crust is less investigated. The evolution of most igneous rocks can be better understood by examining crystal cargoes that record the main steps of magmatic processes at various mantle and/or crustal levels in the plumbing system before their final emplacement into or eruption over the crust (Blundy & Cashman, 2008; Cashman et al., 2017; Ubide & Kamber, 2018). The proper reconstruction of the magmatic history of these rocks in any tectonic scenario needs the knowledge of the textural and chemical properties of the involved phases as well as the physicochemical conditions prevailing during the crystallization of the observed mineral assemblages. Considering that disequilibrium cases are not unusual in most natural systems, textural and chemical analyses allow the identification of crystal populations that are in equilibrium or disequilibrium with the carrier liquid (e.g. Jerram & Martin, 2008). In turn, intensive parameters (pressure–temperature-fugacity of the volatile species-molar fractions of chemical components, P–T–ƒO₂–X_i) of crystallization could be determined solely through experimental approaches (e.g. Blundy & Cashman, 2008).

The available experimental data for alkali ultrabasic to intermediate systems is still relatively limited and poorly constrained in terms of P–T–ƒO_2–X_i conditions. These previous studies include simulations at high pressures starting with basanite compositions and at high and one-atmosphere pressures starting from alkali basalt and trachybasalt compositions (see Table 1). Because basanite is a natural candidate as a parental magma of alkali magma series (e.g. Pilet et al., 2010), it is important to examine the influence of redox conditions on its evolution, which is still rather unexplored. This could contribute to a better understanding of the oxygen fugacity in the mantle in diverse tectonic settings, as this key parameter also influences the mantle solidus and characteristics of the resultant liquids (e.g. Frost & McCammon, 2008; Kelley & Cottrell, 2012; Laubier et al., 2014). In addition, tephrites have less primitive compositions and are often associated with basanites (e.g. Schleicher et al., 1990; Brotzu et al., 2005; Dallai et al., 2011; González-García et al., 2022), but have never been experimentally investigated.

Having stated that we conducted 47 crystallization experiments using natural and doped basanite and tephrite compositions under specified parameters (P, T, and ƒO₂) in order to broaden the experimental knowledge over a wide range of physicochemical conditions. Our experiments better constrain the evolution of alkali melts from ultrabasic to intermediate compositions and their mineral phases close to equilibrium. In this contribution, we present the textural and chemical (major and minor elements) composition of the produced glasses and crystalline phases, emphasizing olivine and titanian clinopyroxene, along the liquid lines of descent (LLDs) of primary basanitic and tephritic magmas. Combining the available data in the literature with our own, we present optimized olivine/melt and clinopyroxene/melt K_D Fe–Mg values to approach the equilibrium between these mafic minerals and alkali melts.

The barometric methods involving Cpx have recently been reevaluated and large errors are reported (Wieser et al., 2023a, 2023b). Hence, improvements, such as better analytical routines and the adoption of machine learning techniques, have been incorporated in recent years (e.g. Petrelli et al., 2020; Chicchi et al., 2023). Another common strategy is to apply specific thermobarometric formulations for a composition range (e.g. Masotta et al., 2013; Neave & Putirka, 2017). In this sense, new barometric and thermometric equations based on clinopyroxene-only compositions and MgO content in the glasses, respectively, are proposed in this experimental investigation, which are better suitable for the studied alkali ultrabasic and derived intermediate compositions than the existing ones.

EXPERIMENTAL AND ANALYTICAL METHODS

Sample preparation, experimental procedures, and in situ quantitative chemical analyses were performed at the laboratories of the GeoAnalítica Multiuser Center at the Institute of Geosciences, University of São Paulo (IGc-USP).

Starting materials

The starting compositions used in the experiments were based on powdered, double-micronized, and doped natural samples of porphyritic fine-grained basanite (SS-C) and tephrite (SS-A) dikes from the Meso-Cenozoic Serra do Mar Alkaline Province, SE Brazil (de Almeida, 1983), collected near the São Sebastião city in the northern coastal area of the São Paulo state. The province is composed predominantly of plutonic complexes made up of evolved (SiO₂-undersaturated and -oversaturated syenite) and minor mafic-ultramafic rocks and dike swarms ranging between ultrabasic/basic and felsic compositions (e.g. Thompson et al., 1998; Brotzu et al., 2005). This province is related to the opening of the South Atlantic Ocean, intruding the Proterozoic metamorphic terrains, and is structurally controlled by the reactivation of the NE–SW fault system.

The basanite has Mg# = 66 [(MgO/(MgO + FeO(t)), molar] and is made up of olivine macrocrysts in a groundmass composed of olivine, clinopyroxene, spinel, and some alkali feldspar, whereas the more evolved tephrite has Mg# = 47 and contains clinopyroxene macrocrysts in a groundmass with clinopyroxene, spinel, and plagioclase. Primary carbonate occurs in the groundmass of both samples. Chemical compositions for these samples are given in Table 2. The basanite sample was doped with an additional 5 wt.% of powdered olivine crystals (Fo [ = 100 × Mg/(Mg + Fe), molar] ≈ 86) extracted from itself to star from a somewhat more magnesian and primitive sample (MgO ≈ 12 rather than ≈ 10 wt.% in the natural sample). The carried-out experiments were also conceived to examine the crystal/melt partition of trace elements in these alkali systems (Salazar-Naranjo and Vlach, in preparation), thus most starting samples were doped with 30 trace elements using standard aqueous solutions from the GeoAnalitica chemical laboratory. The added concentrations were: 100 μg/g for Ni, Cr, V, Co, Zn, Rb, Sr, Ba, Zr, and U; 200 μg/g for Hf, Li, La, Ce, Nd, and Pr; 250 μg/g for Ta; 350 μg/g for Sm, Eu, Gd, Tb, Dy, and Sc; 400 μg/g for Y and 500 μg/g for Ho, Er, Tm, Yb, Lu, and Nb. After doping, samples were dried and further ground under ethanol with an agate mortar for homogenization. A small number of non-doped samples were also tested for comparison purposes.

Experimental methods

The starting material was previously dried at 100°C/24 h before mounting the experimental charges. Low- to high-pressure and one-atmosphere experiments were carried out with a piston-cylinder and a vertical tube furnace, respectively. In both cases, after the charge load, the temperature was increased at 5°C/min until 100°C above the liquidus temperature, evaluated with the rhyolite-MELTS spreadsheet (Gualda & Ghiorso, 2015). Then, this temperature was held for 1 h (melting step) and later the temperature was lowered to 1°C/min until run temperature for 48 h. The run time was chosen following Suzuki et al. (2012) to approach equilibrium. After the running step, the experiments were quenched. The obtained capsules and pellets were mounted in epoxy resin and polished to expose their cores for analytical purposes. Fourteen experiments were carried out under low- to high-pressure and other 33 under one-atmosphere conditions.

Low- to high-pressure experiments

Experiments under low (0.5 GPa) to high (1.0 to 2.0 GPa) pressure were carried out with an end-loaded Bristol-type piston-cylinder (PC) apparatus, using ¾” and ½” assembly cells composed of MgO, graphite, pyrex glass and NaCl, which was wrapped in Pb-foil (e.g.Vlach et al., 2019). This assembly requires a very low friction correction factor (5%) and it is recommended in the conditions of pressure, temperature, and duration of our experimental studies (Condamine et al., 2022). However, under low pressure, temperatures > ca. 1100°C cannot be achieved with original the design of the ¾‘assembly. To overcome this, the ¾’ assembly was slightly modified by combining the crushable MgO, graphite, and pyrex glass from the ½” assembly, with a thicker NaCl sleeve, compatible with the conventional ¾” assembly and the other components (Supplementary Material Fig. S1-1). This arrangement requires great caution to assemble components and conduct experiments to avoid failure.

The starting material was packed into a graphite inner capsule (2.0 mm inner diameter) covered with a graphite lid, which in turn was placed in a 3.0 mm (inner diameter) Pt outer capsule to avoid Fe loss during the experiments (e.g. Médard et al., 2008; Laporte et al., 2014; Armstrong et al., 2015). This arrangement imposes redox conditions close to the CCO (C–CO–CO₂) buffer, which indicates an oxygen fugacity between 1.24 (2.0 GPa) to 1.80 (0.5 GPa) log units below the QFM buffer according to the calculator developed by Michael Anenburg (see https://fo2.rses.anu.edu.au/fo2app/). No H₂O was added to the experimental charge and the water content come from the starting materials, which is around 1.18 and 1.85 wt.% for basanite and tephrite, respectively. The capsules follow the trashcan design, and the base and top lids were welded with a Lampert PUK U3 high-precision welding machine. The temperature of the experiments was set up and monitored using a B-type thermocouple (Pt₉₄Rh₀₆-Pt₇₀Rh₃₀) and a Eurotherm 2404 PID controller. Piston-cylinder pressures were calibrated following Vlach et al. (2019) and McDade et al. (2002) for the low to high ranges, respectively. During experiments, the pressure was applied following the hot-piston-in technique (Johannes et al., 1971); to maintain the desired pressure during run time, minor pumping was occasionally needed. The charges were quenched to room temperature by turning off the power supply, with a quench rate of ≈30°C/s.

One-atmosphere experiments

Anhydrous one-atmospheric pressure simulations were performed in a high-temperature vertical tube furnace GERO HTRV 70-250/18 coupled to a gas mixing system with Aalborg AFC26 mass flow controllers. The ƒO₂ was controlled through appropriate CO-CO₂ mixtures, computed according to Kress et al. (2004). Charges were mounted using the wire-loop technique (Presnall & Brenner, 1974), mixing the starting sample with a polyethylene gel (polyethylene oxide + water). The Pt wire was pre-saturated with Fe (~9 wt%) to minimize iron loss from sample to wire following the electroplating and annealing procedures described by Grove (1981). The samples were mounted on the obtained Pt–Fe alloy, forming pellets, which were suspended in a Pt ‘chandelier’ (e.g. Mallmann & O'Neill, 2009) and loaded into the hot zone of the furnace. Before starting the experimental work, the vertical temperature profile and the hot zone of the furnace (usually ca. 3 cm thick) and the ƒO₂ in the hot zone were calibrated with a B-type thermocouple and a SIRO2 C700+ solid zirconia electrolyte oxygen sensor. The estimated accuracies for ƒO₂ and T are ca. 0.1 log-bar units and better than 1°C, respectively (cf.Mallmann et al., 2014).

The experiments were performed at five oxygen fugacities relative to quartz–fayalite–magnetite buffer (QFM) from reduced to oxidized conditions (QFM-2 to QFM+2) controlled in melting and running steps. After the time run, the products were quenched by mechanical release and fall of the ‘chandelier’ into distilled and deionized H₂O at room temperature.

Analytical methods

Whole-rock analysis

The compositions of the starting natural samples were determined by X-ray Fluorescence (XRF), with a PANalytical AXIOS MAX advanced spectrometer. Fused and powder discs were used for major, minor, and some trace element quantification, respectively. The analytical procedures and resulting errors are described by Mori et al. (1999). Elemental and isotopic carbon compositions were determined on a Delta V advantage gas isotope ratio mass spectrometer coupled to the Elemental Analyzer IsoLink (Thermo EA-IRMS system) at the Geochronology and Isotopic Geochemistry Research Center at IGc-USP.

Electron microscopy

Textural analysis and identification of the phases in experimental products were performed with backscattered electron (BSE) images and energy-dispersive spectroscopy (EDS) qualitative analysis and compositional mapping. These analyses were carried out with a FEI Quanta 650 FEG field emission scanning electron microscope coupled with a Bruker X-flash 6-60 EDS system under 15 kV for the column accelerating voltage at the Technological Characterization Lab Multiuser Center at the Polytechnic School (USP).

In situ quantitative chemical analysis

The major-, minor-, and some trace-element compositions of minerals and glasses were obtained with a JEOL-8530 field emission electron probe micro-analyzer (FE-EPMA), equipped with five wavelength-dispersive spectrometers (WDS). The analytical conditions were 20 kV accelerating voltage, 10 nA beam current, and 10 μm spot size for glasses, whereas for crystalline phases, were 20 kV, 20 nA, and 5 μm. Natural and synthetic standards from the Smithsonian Institute and the Geller™ (McGuire et al., 1992) were used for the analytical setup (see supplementary material Table S1). The PRZ/Armstrong software provided by JEOL was used to correct for matrix effects and conversions to oxide concentrations. The relative errors (%) for a given oxide were estimated using Equation 2 of Wieser et al. (2023a) by taking into account peak and background counts, counting time, and relative concentrations of the standards and samples.

The structural formulae for olivine, spinel, clinopyroxene, plagioclase, and rhönite were calculated based on 4, 4, 6, 32, and 20 oxygens, respectively. Fe²⁺ and Fe³⁺ proportions in clinopyroxene, spinel, and rhönite were estimated by stoichiometry following Droop (1987). The analytical uncertainties on the formulae were computed through propagation of the oxide errors using the MINERAL (MINeral ERror AnaLysis) software in full error propagation mode, assuming that a set of ‘n’ analyses are correlated to each other (Giaramita & Day, 1990; De Angelis & Neill, 2012).

EXPERIMENTAL RESULTS

The experimental conditions and results are summarized in Fig. 1 and detailed in Tables 3 and 4. In the following, a letter and a number within square brackets correspond to the experiment ID as identified in this figure and related tables.

Fig. 1

Summary of the conducted experiments and their respective P, T, and ƒO₂ (relative to the quartz-fayalite-magnetite (QFM) buffer) conditions and products. Starting materials: basanite (a) and tephrite (b). Colored filled objects inside the pie diagrams display the observed phase assemblages. The asterisk denotes experiments performed with undoped starting samples. Letters and numbers below each pie identify the experiment ID, italic numbers above correspond to the equivalent QFM values for the low- to high-pressure experiments constrained by the CCO buffer.

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Fig. 2

Compositional maps of selected experimental products under one- atmosphere pressure obtained through energy dispersive spectrometry (EDS). Basanite (a-c) and tephrite (d-f). The boxes indicate the ID, temperature, and oxygen fugacity in relation to the QFM buffer. Gl = glass, Ol = olivine, Cpx = clinopyroxene, Sp = spinel, Pl = plagioclase, and Rho = rhönite.

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Textural description

Some experimental products, obtained at the highest temperatures, consisted solely of glasses, being representative of the glassing step and guarantying complete melting of the starting charges. Although the experiments were not designed to obtain liquidus temperatures, it was possible to infer that they are somewhat lower than those estimated with the rhyolite-MELTS model for both starting compositions. For example, in the case of the tephrite, experiments [H1], [H2], and [H3] resulted only in glasses, while rhyolite-MELTS predicted the crystallization of clinopyroxene (Cpx) in the amounts of 8.8, 9.18, and 6.98 wt.%, respectively. A similar situation occurred with the [I3] experiment starting from basanite, for which this theoretical model predicted the precipitation of 13.0 of garnet, 12.4 of Cpx, 9.9 of orthopyroxene, and 0.14 wt.% of whitlockite. Given its compositions, the basanite has a higher liquidus temperature and, importantly, a lower crystallization proportion in the investigated temperature range as compared with the tephrite. For instance, under atmospheric pressure at 1050°C, the basanite composition resulted in a higher fraction of remaining melt (~40 wt.%) than the tephrite (~20 wt.%), and at the lowest temperature of 1000°C, the remaining melt for the basanite charge was 35 wt.% (Table 3). This indicates that, compared with tephrite, basanite magmas crystallized under equilibrium conditions could originate significantly higher amounts of evolved melts along their temperature downward pathways.

The obtained crystals and glasses are relatively homogenous. Most crystals are euhedral, with olivine and clinopyroxene having dimensions larger than 40 μm in most cases, while spinel and rhönite are relatively small (<5 μ) (Fig. 3).

Fig. 3

Compositional maps of selected experimental products under low- to high-pressure obtained through energy dispersive spectrometry (EDS). Basanite (a-c) and tephrite (d-f). The boxes indicate the ID, temperature, and pressure. Gl = glass, Ol = olivine, Cpx = clinopyroxene, Sp = spinel, Pl = plagioclase, and Phl = phlogopite.

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Olivine is the liquidus phase of the basanite composition, followed by clinopyroxene, phlogopite (under high-pressure [S2]), or rhönite (under one-atmospheric pressure [ZA1]) (see Fig. 1). Clinopyroxene crystallized relatively early in reduced conditions (QFM-2) when compared with oxidized [D4] at 1100°C. On the other hand, clinopyroxene is the main liquidus phase in the tephrite composition, followed by plagioclase; olivine was formed only under reduced conditions. Spinel was a relatively earlier phase in both cases; it is absent or its amount is very low in the low- to high-pressure and one-atmosphere reduced experiments and increases significantly with ƒO₂ in the one-atmosphere simulations (Table 3).

Phase compositions

Supplementary material Table S2 gives a summary of the chemical compositions expressed as compositional averages and respective errors calculated from up to 12 analyses for each phase. Supplementary material Table S3 shows the completed data set from which Table S2 was built. Rim and core compositions are given in cases where crystal zoning was identified. Our experimental results under high pressures for basanite starting compositions are similar to those previously published by Adam & Green (1994, 2006).

Glass

The variations of glass compositions with temperature give relevant clues to the evolving LLDs. Anhydrous experiments under one-atmosphere pressure result in glasses varying from alkali ultrabasic to intermediate compositions with decreasing temperatures (Fig. 4a). We used the TAS diagram (Le Maitre et al., 2002) to guide the nomenclature of experimental glasses in the following. Basanite-derived glasses are strongly SiO₂-undersaturated (SSU, nepheline-normative>6) with sodic affinity and follow approximately the same K/(K + Na) ratio of the starting composition (Fig. 4b). Its evolutionary compositional trend starts with ultrabasic tephrite (1150°C, Mg# ~ 54), evolving to a basic tephrite (1100°C, Mg# ~ 46), then to a phonotephrite (1050°C, Mg# ~ 39), and finally to a tephriphonolite (1000°C, Mg# ~ 32). Conversely, starting from the ultrabasic tephrite, with potassic affinity, the K/(K + Na) ratios increase as plagioclase crystallizes, as expected. Under reduced conditions (QFM to QFM-2) the glasses are weakly SiO₂-undersaturated (WSU, nepheline-normative<6) starting with alkali basalt (1100°C, Mg# < 37) and ending with phonotephrite (1050°C, Mg# < 30) compositions, whereas under oxidized conditions (QFM + 1 and QFM + 2), the compositional trend is SiO₂-saturated (SS, hypersthene-normative), beginning with trachybasalt (1100°C, Mg# > 37) and ending with trachyandesite (1050°C, Mg# > 30).

Fig. 4

Experimental glass compositions plotted in the TAS diagram (Le Maitre et al., 2002), with the line dividing alkali and subalkali series (Irvine & Baragar, 1971) and in the K₂O/(K₂O + Na₂O) molar. vs. Mg# [= Mg/(Mg + Fe(t)), molar] diagram discriminating the sodic-, sodic-potassic and potassic associations of Debon & Le Fort (1988). (a-b) Experiments run under one-atmosphere pressure. The variation of oxygen fugacity relative to QFM buffer is shown by color bars, while the temperature of each experiment is indicated by symbols. (c-d) Experiments run under low to high pressure. The variation of pressure is shown by the color bar, while the symbols represent the compositions (+ for basanites and x for tephrites). The open star (basanite) and filled star (tephrite) represent the starting compositions.

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Under low- to high-pressure and reduced conditions (CCO), the produced glasses have alkali ultrabasic compositions and are nepheline-normative in both cases; the most important feature is the increase in total alkalis (Fig. 4c), with a minor effect on SiO₂ contents. Overall, they have the same sodic or potassic affinity as the starting material (Fig. 4d).

Olivine

Our textural evidence and the following chemical features indicate that the olivine crystals are newly crystalline phases and that the crystal seeds added to the basanite starting material were completely melted. The olivine in the basanite-derived products is homogeneous and unzoned in experiments under low- to high-pressure with high forsterite content Fo > 84. However, when clinopyroxene is present it shows a thin rim with somewhat lower Fo (Fig. 5a). On the other hand, olivine from experiments under atmospheric pressure and anhydrous conditions shows slight zoning, with cores close to Fo₈₉ and rims spanning from Fo₈₇ to Fo₈₂ (Fig. 5c). As stated above, in tephrite-derived charges, olivine crystallized solely under reduced conditions; it shows no zoning and has the most evolved compositions, with Fo close to 73 at 1100°C and < 60 at 1050°C.

Fig. 5

Olivine compositional variations observed in basanite run under low- to high- (a-b) and one-atmosphere pressures (c-d). The forsterite component (Fo) in crystal cores (inner circles) and rims (outer circles) are represented in the pressure vs. temperature (a) and oxygen fugacity (ƒO₂) vs. temperature (c) diagrams. Variations of Mn , Ca , and Ti in μg/g vs. the forsterite contents in olivine are shown in (b) and (d) plots.

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In general, Mn, Ca, and Ti contents increase with decreasing Fo content (Fig. 5b and5d), however olivine crystallized under high-pressure experiments shows high Ti (>100 μg/g) and low Ca (<2600 μg/g), whereas those crystalized under atmospheric pressure show both high Ti (>200 μg/g) and Ca (>2000 μg/g). The Ca behavior is consistent with the decrease in Ca content toward high-pressure at a constant temperature (Köhler & Brey, 1990), which is also comparable with compositional trends in olivine phenocrysts of volcanic rocks derived from continental alkali rocks and ocean island basalt reported by Foley et al. (2013).

Clinopyroxene

Clinopyroxene compositions vary between titanian (1.5 ≤ TiO₂ ≤ 5.7, wt.%) and aluminian (5.4 ≤ Al₂O₃ ≤ 13.6, wt.%) augite to diopside (Fig. 6a). The crystals from the basanite-derived products show an expanded compositional trend from Mg-rich augite (Mg# = 89) at 2 GPa to subsilicic ferroan diopside (1.52 ≤ Si ≤1.70 atoms per formula unit (apfu) and 61 ≤ Mg# ≤84) at 1 atm. Conversely, the compositional variations in the case of the tephrite-derived results are restricted to subsilicic ferroan diopside (62 ≤ Mg# ≤76), from 1.68 ≤ Si (apfu) ≤1.71 at high pressure to 1.58 ≤ Si (apfu) ≤1.68 at 1 atm. The clinopyroxene compositions from the ultrabasic basanite under 1-atm experiments have significantly high wollastonite (Wo) contents (up to 0.54). This is a relatively common feature observed in both natural and experimental alkali systems given that the activities of the SiO₂ and CaO in alkali melts are lower and higher, respectively, as compared with tholeiitic melts (Carmichael et al., 1970; Nicholls et al., 1971). This directly affects the composition of the crystallizing clinopyroxenes and as discussed by Nimis (1995), the entry of Al in clinopyroxene of alkali melts generates larger tetrahedral (T) sites with undercharged coordinated oxygens, causing a contraction in the adjacent octahedral M1-site and favoring the entry of Ca in the M2 site.

Fig. 6

Clinopyroxene compositional variations in experimental products. (a): pyroxene classification diagram (Rock, 1990 after Morimoto, 1988) with enlarged areas highlighting the differences between one-atmosphere and low- to high-pressures results. Vectors indicate compositional variations as a function of temperature, pressure, and ƒO₂. The clinopyroxene compositions from previous studies (see references in Table 1) and ours were represented by gray fields: Bas = basanite, Teph = tephrite, AlkB = alkali basalt, and TchB = trachybasalt. (b): Ti vs. Si diagram depicting their negative correlation, also representing the pressure effect. Field of subsilicic Cpx (with Si < 1.75 apfu) following Morimoto (1988). (c): variation of Mg# with ƒO₂, expressed as ΔQFM, in dependence of run temperatures. (d): ^VIAl vs. estimated Fe³⁺ diagram displaying their negative correlation and the effect of ƒO₂. Symbols and color as Fig. 4. Bars show the propagated errors on structural formulae.

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Previous experiments using basanite, alkali basalts, and trachybasalts as starting materials (see references in Table 1) crystallized clinopyroxenes with similar compositions, evolving from Mg-rich augite to ferroan diopside or decreasing enstatite and increasing wollastonite components in the ternary Ca–Mg–Fe clinopyroxene classification diagram (Rock, 1990 after Morimoto, 1988).

As shown in Fig. 6a, the compositions of the clinopyroxenes are sensitive to pressure, temperature, and ƒO₂ conditions to a significant extent. Si and Ti correlate inversely, and the Ti contents decrease with increasing pressure, where Cpx crystallized at 1 atm are Ti richer and Si poorer than those crystallized at 2.0 GPa (Fig. 6b). The influences of oxygen fugacity and temperature on Cpx compositions are evidenced by our one-atmosphere experiments, which show that the Mg# values increase with temperature at constant ƒO₂ and, conversely, decrease with ƒO₂ at a constant temperature (Fig. 6c). For example, in the basanite, at QFM-2, the Mg# values are 84, 79, and 74 for temperatures of 1150°C, 1100°C, and 1050°C, respectively, but at QFM, the Mg# values are 76, 67, and 62 for temperatures of 1100°C, 1050°C, and 1000°C, respectively. As expected, the homovalent substitution of ^VIAl by Fe³⁺ (stoichiometric estimated) is favored by increasing ƒO₂ (see Fig. 6d).

The decreasing Mg# and increasing Fe³⁺ clinopyroxene contents with ƒO₂ cause a correlated effect on its SiO₂ concentrations, which increases as the environment turns more reduced. Taking our 1-atm experiments under QFM + 2 [R1 and Q3] and QFM-2 [U1 and U2] at 1100°C as an example, the SiO₂ abundances in Cpx increase from 39.94 to 42.46 wt.% for basanite and from 40.81 to 44.29 wt.% for tephrite, respectively.

Spinel

The crystallized oxides are of the oxyspinel subgroup (Bosi et al., 2019) and their compositions show a systematic trend of decreasing Cr# [100*Cr/(Cr + Al), molar] and mg# [(100*Mg/(Mg + Fe²⁺), molar] with increasing Ti and estimated Fe³⁺ (Fig. 7). The spinel from basanite runs under one-atmosphere varies from Cr-spinel at 1150°C to Al-magnetite at 1050°C with higher Cr content under reduced conditions when compared to oxidized conditions (Fig. 7b). In the case of the tephrite products, the composition varies from Al–magnetite under oxidizing conditions to ulvöspinel under reduced conditions (Fig. 7c). At high pressure, the oxides are spinel (stricto sensu) with low chromium and iron contents.

Fig. 7

Spinel compositional variations in experimental products. (a): ternary Fe³⁺-Al-Cr diagram (Stevens, 1944); (b): Cr# [= Cr/(Cr + Al), molar] vs. Ti, and (c) mg# [= Mg/(Mg + Fe²⁺), molar] vs. Ti binary diagrams.

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Plagioclase

Plagioclase crystallized sole from the tephrite starting composition, and its compositions correspond to a relatively homogeneous high bytownite (An_76.5) at 1100°C and reduced conditions (QFM-2). At 1050°C, it is high-K labradorite (52.0 ≤ An ≤ 65.5) with relatively lower and higher An and Fe₂O₃ contents, respectively, with An = 65.5 and Fe₂O₃ = 0.78 wt.% under reduced conditions (QFM-2) and An = 52.0 and Fe₂O₃ = 1.11 wt.% under oxidizing conditions (QFM + 2). So, a slightly positive correlation between the contents of the orthoclase and albite molecules and, of course, Fe₂O₃ and oxygen fugacity is observed and illustrated in the supplementary material Figure S1-2.

Rhönite

Rhönite, a high Ti phase with an ideal formula Ca₂(Mg, Fe²⁺, Fe³⁺, Ti)₆(Si, Al)₆O₂₀, is the typical mineral of the rhönite subgroup in the aenigmatite–rhönite mineral group (Kunzmann, 1999). It was formed close to the end of the crystallization sequence of the basanite at 1000°C and QFM, in equilibrium with the tephriphonolite glass. It has Na = 0.409, Ti = 1.052 (apfu), and Mg# = 44 (see supplementary material Table S2–1.6).

Phlogopite

Phlogopite crystallized only in the basanite products under high pressure (1.5 GPa), and its composition is Ti–Fe-rich phlogopite according to Tischendorf et al. (2007), with Mg# = 0.82, Ti = 0.436 apfu, Fe_tot = 0.419 apfu. F and BaO concentrations are significant, reaching 2.07 and 1.38 wt.%, respectively (see supplementary material Table S2–2.5).

DISCUSSION

Effects of redox conditions on the LLDs

The differentiation of igneous rocks continues to be a subject under discussion in petrology because of the large combination of factors (e.g. temperature, pressure, and chemical composition) and processes (e.g. assimilation, fractional crystallization, and degassing) that are involved and ultimately shape the dynamics and architecture of an igneous system (e.g. Cicconi et al., 2020). The redox conditions of the system under consideration exert a great impact, as they control mineral stabilities, the composition of the precipitating phases, and the evolving liquid compositions along the LLDs (Ghiorso & Carmichael, 1990; Moretti & Neuville, 2021). The main effects of redox conditions over basaltic systems are well known (Osborn, 1959; Hamilton et al., 1964), however, there are limited data for our simulated compositions, and in this respect, our experiments at 1-atm pressure contribute to the discussion.

As described in the previous section, the glasses derived from ultrabasic basanite and tephrite exhibit contrasted patterns of silica saturation, which can be projected from the classical normative basaltic Fo–Ne–Di–Qz tetrahedron of Yoder & Tilley (1962) onto the R1-R2 diagram (De la Roche et al., 1980) presented in Fig. 8a. For the sake of simplicity, we consider reduced (ΔQFM < 0) and oxidized (ΔQFM > 0) conditions hereafter. Also, to supplement our discussion, we included experiments by Thy (1991) and Scoates et al. (2006) that started with alkali basalt and were performed under reduced (QFM) and oxidized (between QFM + 1 to QFM + 2) conditions, respectively. Overall, the LLDs resulting from these three initial compositions have similar behavior, being relatively more SiO₂-undersaturated under reduced environment compared to oxidized ones. These features are depicted in the R1-R2 diagrams, where the starting and the obtained glass compositions of each experiment are plotted as a function of their most distinctive CIPW normative features (Fig. 8a). As observed, the projected points in this diagram depart more to the left of the critical plane of silica saturation as their silica saturation degree decreases for a given R2 value. The LLD pathways are represented in Fig. 8b.

Fig. 8

R1-R2 diagram of De la Roche et al. (1980) for experimental glasses at 1-atm. (a) Plot of all glass compositions depicting their silica saturation based on the CPIW norm. (b) Main evolutionary trends of basanite (this work), tephrite (this work), and alkali basalts (Thy, 1991; Scoates et al., 2006) in dependence on redox state. The arrows derived from each starting material (stars) represent the LLD under reduced and oxidized environments (left and right arrows, respectively). SSU = strongly SiO₂-undersaturated (nepheline-normative >6); WSU = weakly SiO₂-undersaturated (nepheline-normative ≤6); SS = SiO₂-saturated (hypersthene-normative) and SO = SiO₂-saturated (quartz-normative). Critical plane of silica saturation of the Yoder & Tilley (1962) tetrahedron.

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These figures show that under reducing conditions both the strongly undersaturated (SSU) basanite and weakly undersaturated (WSU) tephrite LLDs run roughly parallel to the silica saturation line and the degree of silica saturation decreases as crystallization proceeds. A similar tendency is observed in the results of Thy (1991), corresponding to a saturated (SS) alkali basalt, which shows a higher decrease of silica saturation in the first produced liquids. Conversely, under oxidizing environments, the basanite SSU and tephrite-saturated (SS) LLDs progressively approach the silica saturation line and evolve towards increasing saturation degrees. The starting alkali basalt composition of Scoates et al. (2006) is close to the saturation line and the respective LLD evolves towards silica-oversaturated conditions. These evolutionary trends allow visualizing the effects of oxidation state on the silica saturation of the progressively evolved remaining liquids from the same parental alkali magma and explain the transitions from nepheline- to hypersthene- and hypersthene- to quartz-normative liquid compositions under relatively oxidizing conditions, as observed in several natural occurrences (e.g. Duke, 1974).

These trends reflect well the redox control in the mineral assemblage, particularly spinel, whose crystallization is largely favored under relatively oxidizing conditions. (e.g. Hill & Roeder, 1974). As this phase is almost SiO₂-absent, its crystallization will result in SiO₂-enriched remaining liquids. In our 1-atm products at 1100°C, for example, spinel is found at QFM + 2 [R1 and Q3 experiments] but not at QFM-2 [U1 and U2] for both basanite and tephrite starting compositions, where the amounts of spinel progressively decrease to zero from QFM + 2 to QFM-2 (e.g. 4.5 to 0 for basanite and 4.7 to 0 wt.% for tephrite, see Table 3). Clinopyroxene and olivine exert additional contribution to the saturation degree, and under oxidizing environments, they reinforce the spinel effect, as their SiO₂ contents are somewhat lower than the SiO₂ contents of the liquids from which they precipitate. On the other hand, under reducing conditions, the decrease in the silica saturation degree should mainly be related to the crystallization of relatively SiO₂-rich clinopyroxene.

Fe and mg partition between olivine, clinopyroxene, and alkali melts

Roeder & Emslie (1970) present the first experimental approaches to estimate the exchange coefficient between olivine and Hawaiian, mainly tholeiitic, basalts, and obtained |${K}_{D,{Fe}^{2+}- Mg}^{ol- liq}=0.30\pm 0.03$|⁠. More recently, Matzen et al. (2011) revised this canonical coefficient to 0.340 ± 0.012 for tholeiitic compositions (Na₂O + K₂O ≤ 3 wt.%). The Fe–Mg exchange between minerals and melts is sensitive to the melt composition, particularly the contents in silica and alkalis (Sack et al., 1987; Gee & Sack, 1988), and, therefore, alkali melts (Na₂O + K₂O > 3 wt.%) require particular attention.

A drawback of most experimental data is the absence of quantitative determinations for Fe³⁺ in the glasses, which becomes more problematic as experiments are performed under more oxidizing conditions. We tried to minimize this issue by calculating the Fe³⁺/Fe(t) ratios according to the algorithms proposed by Kress & Carmichael (1991), Borisov et al. (2018), and Hirschmann (2022). These models consider the combined effects of melt composition, temperature, and pressure on the Fe³⁺/Fe(t) ratio in silicate melts, with the exception of Borisov et al. (2018), which was only evaluated at 1 atm. The ratios derived from Hirschmann (2022) Fe³⁺/Fe(t) are somewhat greater than those of Kress & Carmichael (1991), which in turn is slightly higher than Borisov et al. (2018) values and, thus, the Fe²⁺–Mg partitioning estimates will increase in the opposite sense. Combining the available data in the literature with our data for olivine in equilibrium with alkali ultrabasic to intermediate melts, the obtained |${K}_{D,{Fe}^{2+}- Mg}$| show a strong agreement whiting the estimated 2σ deviations, giving 0.291 ± 0.022, 0.282 ± 0.022 and 0.279 ± 0.028, respectively, with a weighted mean of 0.285 ± 0.014 (Fig. 9a). Considering the involved deviations, this mean value approaches better the first estimate presented by Roeder & Emslie (1970) and is significantly lower than the revised value suggested by Matzen et al. (2011) for tholeiitic compositions. Furthermore, it agrees well with the thermodynamic model of Toplis (2005), which quantifies the effects of liquid compositions (silica and alkali content) and predicted values lower than 0.3. In the cases where the Fe³⁺/Fe(t) ratios could not be estimated and/or ƒO₂ is unknown, a value of |${K}_{D, Fe(t)- Mg}=0.26\pm 0.02$| may be taken as a reasonable first approximation.

Fig. 9

Fe⁺²/Mg and Fe(t)/Mg molar ratios in olivine (a) and clinopyroxene (b) vs. alkali glasses, respectively. The |${K}_{D,{Fe}^{2+}- Mg}$| values in Fig. 9a were derived from the used models to estimate Fe³⁺/Fe(t) in melts: Hirschmann (2022); B18: Borisov et al. (2018); KC91: Kress & Carmichael (1991). The plotted Fe⁺²/Mg ratios in glass were computed with the H21 model. Open symbols: data compiled from the literature: S80: Shimizu (1980); T91: Thy (1991); AG94: Adam & Green (1994); G00: Green et al. (2000); WT01: Wood & Trigila (2001); AG06: Adam & Green (2006); S06: Scoates et al. (2006); MS21: Ma & Shaw (2021); B21: Bonechi et al. (2021). Filled symbols: this study. The enveloped area in (b) highlights results from experiments under oxidized conditions.

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The accurate computation of the exchange coefficients for the equilibrium between Ca-rich clinopyroxene and melts is somewhat more problematic because, as the melts, they may contain significant Fe³⁺ contents (Rudra et al., 2021). Overall they show a relatively wide variation range; Putirka (2008) compiled more than 1200 experimental results and suggested a general |${K}_{D, Fe- Mg}=0.28\pm 0.08$|⁠, while |${K}_{D,{Fe}^{2+}- Mg}$|= 0.26 and |${K}_{D, Fe(t)- Mg}=0.23$|were determined for mid-ocean-ridge basalts (Grove & Bryan, 1983; Sisson & Grove, 1993). For the alkali compositions studied herein and the available data from the literature, the best value is |${K}_{D, Fe(t)- Mg}=0.24\pm 0.02$|(R² = 0.966 and n = 102, Fig. 9b) that is almost equivalent to |${K}_{D,{Fe}^{2+}- Mg}$| = 0.250 ± 0.012, 0.247 ± 0.012 and 0.230 ± 0.020 obtained using the models of Hirschmann (2022), Kress & Carmichael (1991), and Borisov et al. (2018) for the glasses, respectively, and the stoichiometric Fe²⁺/Fe³⁺ partition in the clinopyroxene, which result in a weighted mean |${K}_{D,{Fe}^{2+}- Mg}$| of 0.245 ± 0.008 (2σ). However, considering solely oxidizing conditions (ΔQFM ≥1), a higher values of 0.37 ± 0.03 (R² = 0.97 and n = 9) is obtained for |${K}_{D, Fe(t)- Mg}$| (cf. Fig. 9b), due to the decreasing MgO contents in clinopyroxene.

The case of ^IVTi in titanian clinopyroxenes

Common Ca-rich clinopyroxenes present relatively small contents of Ti, but titanian diopside and augite, the characteristic phases in alkali ultrabasic to intermediate rocks, may have more than 3 wt.% TiO₂ (e.g. Deer et al., 2013 and suplementary material Table S2). Ti is usually allocated in the octahedral-coordinated M1 site by the coupled substitutions |${Si}_T^{+4}+{Al}_{M1}^{+3}\leftrightarrow {Al}_T^{+3}+{Ti}_{M1}^{+4}$| (1) or |$2{Si}_T^{+4}+{Mg}_{M1}^{+2}\leftrightarrow 2{Al}_T^{+3}+{Ti}_{M1}^{+4}$| (2). However, Ti (ionic radii = 42 pm) may also substitute for Si (26 pm) without charge imbalance (⁠|${Ti}_T^{+4}\leftrightarrow {Si}_T^{+4}$|⁠) in the tetrahedral sites, which is in better agreement with the lattice strain model (Blundy & Wood, 1994) although it is slightly larger than Al⁺³ (39 pm), as substitutions (1) and (2) are heterovalent. Barth (1931) suggested this type of substitution, later reinforced by the experiments synthetizing clinopyroxene in the system CaO-MgO-SiO₂-TiO₂ (Sepp & Kunzmann, 2001), which also shows that this substitution is favored at lower pressure, as previously noted by Thy (1991) and Adam & Green (1994). From the chemical standpoint, it is not possible to properly discriminate the entry of Ti according to heterovalent (1) or to homovalent substitution in the tetrahedral sites because both will result in a close 1:1 negative correlation between Ti and Si. On the other hand, the observed Ti increase with decreasing pressure in the previous and our results (Fig. 10a) strongly suggest that the CaMgTi₂O₆ (Ti-diposide) component in clinopyroxene may be responsible for this behavior. In this case, some important implications emerge: 1) the CaMgTi₂O₆ molecule can be used as a barometric proxy, 2) less Al needs to be allocated in the tetrahedral site and consequently more octahedral Al will be available, which turns the activity of jadeite (NaAlSi₂O₆) component more dependent on |${Na}_{M2}^{+}$| rather than |${Al}_{M1}^{+3}$| contents, and, importantly, 3) this may explain why the available barometers significantly underestimated the pressure computed from titanian clinopyroxenes equilibrated with alkali compositions, as discussed in the next section.

Fig. 10

Ti content variations of clinopyroxene in experiments from previous and this works. (a) Ti vs. Si diagram supporting their correlated variation with pressure. Stars represent titanaugite compositions from Deer et al. (1978). (b) TiO₂ concentrations vs. pressure (GPa) within the 1400–1000°C temperature range. Data sources as Fig. 9.

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A new clinopyroxene-only composition barometer

Clinopyroxene is a common rock-forming mineral in igneous rocks and its composition and equilibrium with melts have been broadly used to reconstruct crystallization conditions in a single chamber or along discrete steps in the evolution of a plumbing magmatic system (e.g. Jerram & Martin, 2008; Larrea et al., 2013; da Silva et al., 2020).

Barometers based on clinopyroxene-melt exchange reactions and clinopyroxene compositions have been improved significantly over the last decades. There are three types of calibrations. The first is based on the exchange of the jadeite (NaAlSi₂O₆) molecule between clinopyroxene and liquid according to the formulations of Putirka et al. (1996), Putirka (2008) and Neave & Putirka (2017), the latter specifically for tholeiitic basalts. The second type is a barometer based on the Al-exchange between these phases (Putirka, 2008). Lastly, Putirka (2008) and Wang et al. (2021) proposed two additional calibrations based on clinopyroxene compositions that have the advantage of not requiring information on coexisting phases. Except for the calibrations of Neave & Putirka (2017) and Wang et al. (2021), which have estimated errors of ±0.14 and ± 0.16 GPa, respectively, the other formulations have larger errors (ca. ± 0.3–0.5 GPa) and thus are best suitable for high pressures.

We evaluated the applicability of all these six calibrations for our and the compiled experimental data for clinopyroxene and coexisting alkali ultrabasic to intermediate melts. All calculations were done using the measured experimental temperatures when required and the reported H₂O content when available. The results are summarized in Fig. 11. The parameters used to assess the performance of each barometer are based on the linear regression of the calculated and experimental pressures, with the slope, intercept, coefficient of determination (R²), and root-mean-square error (RMSE) evaluated. The best-fitted lines result in underestimated values for high pressures in all cases, particularly above 1 GPa, and the slopes relating experimental and calculated pressures vary between 0.40 in the worst and 0.77 in the better cases, with 0.515 ≤ R² ≤ 0.921. Furthermore, practically all barometers give overestimated values at low-pressure, with intercepts ranging from 0.31 to 0.84 GPa, with the exception of Wang et al. (2021), who had a value of 0.07 GPa. In conclusion, the best results were obtained by using the models of Putirka (2008) and Wang et al. (2021), based on jadeite exchange and clinopyroxene compositions, respectively, and the calibration of Wang et al. (2021) works better in the lowest pressure range. Wieser et al. (2023b) got comparable results by assessing the performance of barometers in arc magmas (subalkali-type), showing that they result in significant errors (up to 0.4 GPa) and among them, the Cpx-only type barometers are somewhat better. In addition, as observed by these authors, the RMSEs reported for each barometer are significantly lower than those estimated from our and the available data for alkali systems, for example, 0.14 vs 0.39 GPa in the case of Neave & Putirka (2017) or 0.17 vs 0.31 GPa in the case of Wang et al. (2021).

Fig. 11

Comparison between experimental and calculated pressures for alkali ultrabasic to intermediate systems for the available barometers based on jadeite exchange between clinopyroxene and liquid (a-c), clinopyroxene-only composition (d-e), and aluminum exchange between clinopyroxene and liquid (f). The barometer references are indicated in each graph. Full lines represent the best fit for the used barometer calibration. Dashed lines are the 1:1 correlation between observed and calculated pressures. The total data set (n = 97) includes our experiments (n = 31) and the available literature (n = 66). R² = determination coefficient and RMSE = root-mean-square error.

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These relatively poor results encouraged the search for an alternative and improved approach for alkali melts, given that they crystallize clinopyroxenes with relatively high Ti and Al and low Si contents, and such compositions were not considered in the above calibrations. Masotta et al. (2013) calibrated a barometer and a thermometer specifically for alkali-evolved SiO₂-undersaturated and -oversaturated magmas (mainly phonolites and trachytes) and herein we present a calibration for alkali ultrabasic to intermediate compositions, applicable for pressures from 1 atm to 4 GPa, temperatures from 1000° to 1400°C, and oxygen fugacity between QFM − 2 and QFM + 2. Our calibration closely follows the main recommendations of Wieser et al. (2023a) to improve barometry tools. In this sense, Na was measured in a TAPH large crystal analyzer with a counting time of 10 s on the peak, which resulted in relative errors ranging from 0.99 to 6.94%, with 80% of analyses having an error of less than 5% relative. We also present up to 12 quantitative spot analyses for each phase, and the analytical errors of the clinopyroxene compositions were propagated on the structural formulae using Giaramita & Day's (1990) complete propagation approach. Finally, we give a full report of the obtained analytical data in the supplementary material to allow easier access to the results of our experimental and analytical procedures.

Starting from the structural formulae computed for 6O in our compositional database for clinopyroxenes (supplementary material Table S2) and the corresponding experimental pressures, we searched for correlations between relevant molar fractions or combined molar fractions and pressure. The final relationship is based on multiple linear regression analysis considering multiple independent variables.

The best correlation was obtained for the combined fractions of Na, Ti/(Ti + Al(t)), and Si (apfu). These parameters account for the well-known increase of the jadeite component with pressure, herein computed from the Na fraction, and also consider the combined effects of the Ti-diopside component in clinopyroxene (NaAlSi₂O₆ ↔ CaMgTi₂O₆) and of the Mg-augite to ferroan diopside solid solution (cf. Figs. 10 and 6a).

This new barometer was tested with the available dataset of clinopyroxene compositions in alkali ultrabasic to intermediate compositions (n = 66) by comparing calculated and experimental pressures in Fig. 12 (see references therein). Both the whole- and test-data fit the 1:1 relationship substantially better than the prior barometers, with slopes close to 1, intercept close to zero, and R² around 0.914. Wieser et al. (2023b) evaluated the performance of available clinopyroxene barometers and observed that the RSME values originally reported in the original calibrations are significantly lower (or optimistic) when compared with the RMSEs obtained using independent data sets. In our case, the application of the proposed barometer results in an RSME value of 0.19 GPa considering solely the available independent data set (n = 66). The performance of our barometer for alkali ultrabasic to intermediate alkali systems is just reasonable, allowing the secure identification of ca. 15 km depth differences along transcrustal magmatic systems at the applied confidence level.

Fig. 12

Performance of the barometer based on clinopyroxene-only composition proposed in this work for ultrabasic to intermediate alkali liquids, evaluated by comparing observed vs. calculated pressures. The dashed line is the 1:1 correlation between observed and calculated pressures while the full line is the linear regression. Note the better adjustment than the previous barometers shown in Fig. 11. Data sources and symbols as Fig. 11.

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Fig. 13

Comparative performance of glass thermometers in the alkali ultrabasic to intermediate compositional range. (a) Experimental temperatures vs. MgO-in-melt diagram and the resulting temperatures (full line) calculated with Equation 13 of Putirka (2008). (b) Experimental vs. calculated temperature using equation 16 according to Putirka (2008). (c) Experimental temperatures vs. MgO-in-melt (wt.%) for the available and our data. The best formulation applicable for anhydrous compositions at 1-atm pressure and the influence of pressure (arrow up) and H₂O contents (arrow down) on the measured temperatures are indicated. (d) Comparison between the calculated vs. experimental temperatures considering our equation for low-H₂O (< 3 wt.%) crystallization environments. Gray areas in (a), (b), and (d) represented the error envelopes of each model. Data sources as Fig. 9.

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A drawback of the clinopyroxene-only barometers results from those chemical variations not depending solely on crystallization pressure. Although the herein synthetized clinopyroxenes do not show significant compositional zoning, when dealing with natural rocks, particularly alkali ultrabasic to intermediate types, strong sector zoning may develop in response to the degree of undercooling of the host magmas. This zoning pattern is characterized by significant relative enrichments of Al, Ti, and Fe and depletions of Si and Mg in the prism sectors {100, 110, and 010} relative to the hourglass sector {−111}, while the Na and Ca contents remain almost constant (Strong, 1969; Nakamura, 1973; Downes, 1974; Ubide et al., 2019). Thus, pressures calculated on sector-zoned crystals based mainly on Na content or according to formulations that somehow compensate for these chemical effects should result in better estimates. Ubide et al. (2019) studied and mapped in detail the sector zoning observed in clinopyroxenes from recent Mt. Etna alkali magmatism and we here explore their results to evaluate the performance of our barometer in these critical cases. Starting from the average clinopyroxene compositions given by them, our barometer gives 0.52 GPa and 0.29 GPa for inherited corroded crystal cores and crystal rims, while values of 0.44, 0.42, and 0.40 GPa were estimated for the {−111}, {010}, and {110} sectors, respectively. Looking at the range of results and the associated errors, the computed pressures in different sectors compare reasonably well and, overall, the obtained values for these crystal areas agree with the interpretations for the magmatic evolution of the host rocks, as presented by the authors.

Glass thermometer: Liquidus temperature

The whole data exhibits a very reasonable correlation (R² = 0.819) as well as the RMSE value and most of the previous experimental data under low water contents plot within the defined error envelope (gray area in Fig. 13d). Given the scarcity of experiments starting from compositions with high water contents (≥ 3 wt.%), the use of this equation is not recommended as the results are overestimated when compared with the few available experimental temperatures.

As expected, the liquidus temperatures for the more primitive (≥ 8 wt.% MgO) compositions are higher for alkali melts as compared with tholeiitic ones (e.g. Falloon et al., 2007), as computed from Equations 3 to 5. For example, both alkali and tholeiitic compositions with 10 wt.% of MgO result in liquidus temperatures of 1257 and 1215°C using Equations 7 and 3, respectively.

We compared this optimized thermometer with the thermometer based on the Al-exchange between olivine and spinel (Wan et al., 2008; Coogan et al., 2014), which have been widely used to estimate temperatures of mantle-derived melts. As olivine and spinel are the first phases to crystallize from such primitive melts, the registered temperatures should approach liquidus temperatures. The calculated thermometry data from volcanic samples from six different localities were used for comparison: Buku Volcanic Complex and Dabbahu Rift Zone from East African Rift (Wong et al., 2022), Laacher See hybrids and Rothenberg from Eifel Volcanic Fields (Sundermeyer et al., 2020), Borgarhraun from Northern Volcanic Zone Island (Matthews et al., 2016, 2021) and Androy massif from Madagascar (Coogan et al., 2014). The whole-rock geochemistry of each sample was obtained from the literature (see references in Fig. 14) and it was used to calculate the temperature using Equation 7. Both thermometers show a similar performance with an almost 1:1 correlation considering the involved errors, the unique exception being the Rothember sample, which resulted in a distinct higher MgO-in-melt temperature (Fig. 14). The error associated with the MgO-in-melt method is significantly lower (≤ ca. 0.5% relative) and thus, Equation 7 is much appropriated to estimate liquidus temperatures for alkali ultrabasic to intermediate melts.

Fig. 14

Comparison between the temperatures calculated using the olivine-spinel Al exchange thermometer (Coogan et al., 2014) and MgO-in-melt (1-atm, anhydrous) optimized in this work for alkali volcanic rocks. Thermometry data from: the Buku Volcanic Complex (BVC) and Dabbahu Rift Zone (DRZ), East African Rift (Wong et al., 2022); Laacher See hybrids (LSH) and Rothenberg (R), Eifel Volcanic Fields (Sundermeyer et al., 2020); Borgarhraun (B), Northern Volcanic Zone Island (Matthews et al., 2016); Androy massif (AM), Madagascar (Coogan et al., 2014). Whole-rock compositions to calculate MgO-in-melt temperature are from Tadesse et al. (2019) to BVC, Ferguson (2011) to DRZ, Wörner & Schmincke (1984) to LSH, Bednarz & Schmincke (1990) to R, Maclennan et al. (2003) to B, and Mahoney et al. (2008) to AM.

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SUMMARY AND CONCLUDING REMARKS

Experimental simulations on the crystallization of basanitic and tephritic charges under one-atmosphere pressure at reducing to oxidizing conditions (−2 ≤ ΔQFM ≤2) and under low- to high-pressure at reducing conditions (−1.80 ≤ ΔQFM ≤ −1.24) provided new constraints for the evolution of the alkali ultrabasic to intermediate magmas and their mineral assemblage, as well as geothermobarometry calculations. The main findings of this investigation can be summarized as follows:

• The ultrabasic basanitic and tephritic initial compositions evolve along a sodic and a sodic-potassic/potassic liquid lines of descent, respectively, under 1-atm and temperatures between 1150–1000°C. Under low- to high-pressures and reduced conditions, the main evolution trend is marked by the increase in the total alkalis with minor variations in SiO₂ contents, and about constant K/(K + Na) ratios.

• The ƒO₂ effect on melt evolution is nicely shown by our one-atmosphere experiments and is somewhat more critical for tephrite compositions in terms of SiO₂ saturation. The glasses derived from the ultrabasic basanite charges are strongly SiO₂-undersaturated, while those from the ultrabasic tephritic change from weakly SiO₂-undersaturated to SiO₂-saturated under increasing redox conditions. Importantly, the basanite charges result in lower crystallization proportion and thus in higher amounts of remaining melts than the tephrite for the same temperature, indicating that basanite parental magmas can generate large amounts of evolved sodic melts during equilibrium crystallization.

• The available barometers based on the equilibrium clinopyroxene-melt or clinopyroxene-only composition and calibrated for predominantly subalkali compositions result in underestimated pressures of crystallization over 1 GPa and overestimated below 1 GPa for alkali ultrabasic to intermediate melts. In part, it is due to the contrasted compositions of clinopyroxene in these systems, given by their high Ti and Al contents and Si deficiency. The entry of Ti in tetrahedral sites, substituting for Si, rather than in octahedral sites, will increase of octahedral-coordinate Al in the clinopyroxene structure and influence the jadeite molecule content calculation. In this sense, the new proposed barometer is relatively simple and based on the Na, Ti, Al(t), and Si clinopyroxene molar proportions. It presents significantly better performances for alkali ultrabasic to intermediate compositions crystallized under varying ƒO₂ conditions, with a reasonable estimated 1σ error (± 0.16 GPa), similar to or better than the available ones.

• The obtained data allow evaluation of the available MgO-in-melt thermometers and propose an optimized formulation for relatively anhydrous melt compositions, with almost insignificant errors (± 5°C). This formulation agrees very well with independent thermometric estimates for volcanic rocks based on the partition of Al between olivine and spinel. The main effects of pressure and H₂O contents in the melts at such temperatures were also evaluated and a second approximate formulation was derived considering the pressure effect for a relatively low-H₂O crystallization environment (< 3 wt.%), with an estimated error of ±20°C. However, more data is needed to constrain better the proposed thermometer, particularly for H₂O-rich systems.

• As a final remark, also stated by Wieser et al. (2023a), even for the strong experimental and analytical efforts carried out in the last decades, the available barometers do not allow identify pressure differences lower than ca. 0.2–0.4 GPa, or > ca. 15 km differences in depth. Thus, significant experimental and analytical improvements are still needed to resolve and quantify P–T paths during the evolution of magmatic plumbing systems along the Earth’s crust with the desirable accuracy.

Funding

The São Paulo Research Foundation (FAPESP) funded this research, with grants to AFSN (Doctorate Fellowship 2018/16755–4) and to V. Janasi (Project 2019/22084–8).

Data availability statement

The complete datasets used in this article are accessible in the Supplementary Material Tables S1, Tables S2, Tables S3, and Tables S4. Some additional illustrations are included in the Supplementary Material Figures S1-1.

Supplementary Data

Supplementary data are available at Journal of Petrology online.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

The authors would like to thank the São Paulo Research Foundation (FAPESP, Project Proc. 2019/22084-8) for funding this research and the staff of the GeoAnalítica and Technological Characterization Lab Multiuser Centers at the University of São Paulo, particularly Artur Takashi Onoe, Marcos Mansueto, and Liz Zanchetta. AFSN also thanks FAPESP for a doctorate fellowship (Proc. 2018/16755-4) and Bernard Wood for his insightful feedback during a short academic visit to the University of Oxford. Finally, we are grateful to Andreas Audétat (Editor) and the three reviewers: anonymous, Tong Hou, and Hilary Downes for their constructive remarks and ideas that greatly improved the quality of this manuscript.

References