Introduction

Titanium is a refractory, lithophile and fluid-immobile element (Kessel et al. 2005; Palme and O’Neill 2014). Due to the absence of Ti-bearing phases in Earth’s mantle, Ti behaves as an incompatible element during partial melting, and terrestrial basalts, like mid-ocean ridge and ocean island basalts have TiO2 contents ranging between ca. 1.5 wt.% and 5 wt.% (e.g.,Gale et al. 2013; Prytulak and Elliott 2007). Lunar basalts, however, can be highly enriched in TiO2, reaching levels up to 16 wt.% TiO2 (Marvin and Walker 1978), which is thought to result from the partial melting of Fe–Ti-oxide-rich cumulates in the lunar interior (Ringwood and Kesson, 1976; Beard et al. 1998; Leitzke et al. 2016). In terrestrial settings, Ti is almost exclusively tetravalent, although some recent studies have reported isolated instances of trivalent Ti present in oxide inclusions of carmeltazite (ZrAl2Ti4O11—Griffin et al. 2018) and tistarite (Ti2O3—Griffin et al. 2016), found in terrestrial corundum. Titanium varies between an average IV-fold coordination ([IV]Ti) in pyroxenes to VI-fold coordination ([VI]Ti) in Ti oxides such as ilmenite and armalcolite, whereas in silicate glasses it exhibits an average V-fold coordination (Leitzke et al. 2018). Stable isotope theory predicts that [V]Ti and [IV]Ti form stiffer bonds than [VI]Ti (Schauble 2004), which is expected to lead to the preferential incorporation of lighter Ti–isotopes into VI-fold coordinated Ti oxides. Consistently, lower coordinated Ti in coexisting silicate melts is isotopically heavier (Farges et al. 1996; Millet et al. 2016; Mandl 2019; Kommescher et al. 2020). In contrast to Fe–Ti oxide minerals the fractional crystallization of silicate minerals like pyroxene, olivine or plagioclase causes limited, and so far, unresolvable Ti stable isotopic differences (Johnson et al. 2019), because Ti is broadly incompatible in these minerals so that any potential mass-dependent stable isotope fractionation is beyond our current ability to resolve. Therefore, the fractional crystallization of Ti-bearing oxides is assumed to be the main driving mechanism for the Ti stable isotope fractionation in magmatic samples (Millet et al. 2016; Deng et al. 2019).

The interpretation of Ti stable isotope fractionation in lunar samples is more complex because of the lower oxygen fugacities (fO2) that characterize lunar magmas, which are typically below the Fe–FeO reference redox equilibrium (IW; Myers and Eugster 1983). Such reducing conditions mean that a significant proportion of Ti3+ is present in basaltic melts (10–30 at. % of total Ti, Leitzke et al. 2018; Simon and Sutton 2018). Changes in the redox state of a given element should affect its isotope fractionation during magmatic processes, as it can affect the bonding nature, bonding strength and spatial coordination of that element in various phases (Schauble 2004). In the final stages of lunar magma ocean (LMO) solidification, ilmenite-bearing cumulates (IBC; Warren 1985; Longhi 1992; Shearer et al. 2006; Gross and Joy 2016) that are isotopically light, and an isotopically heavy residual component that is enriched in incompatible elements such as Th, K, REE and P (i.e., KREEP—Warren 1989) crystallized (see Millet et al. 2016; Greber et al. 2017a, b; Kommescher et al. 2020). Later formed lunar mare basalts that are subdivided into low- and high-Ti basalts based on their TiO2 contents (Warren and Taylor 2014), show only small but still resolvable differences in their δ49Ti. Low-Ti basalts have a mean δ49Ti (+ 0.01 ± 0.047 ‰; Millet et al. 2016; Kommescher et al. 2020) that resembles that of the BSE (+ 0.005 ± 0.005 ‰, Millet et al. 2016), and chondritic values (Greber et al. 2017b; Deng et al. 2018), whereas high-Ti basalts show a broader range of δ49Ti (between + 0.009 ‰ and + 0.115 ‰; Millet et al. 2016; Kommescher et al. 2020). The higher average δ49Ti of lunar mare basalts compared to their terrestrial counterparts is thought to be related to the partial melting or the assimilation of IBC during lunar mantle petrogenesis (see Millet et al. 2016). Working from a larger sample set, Kommescher et al. (2020) noted that ilmenite-bearing high- and low-Ti basalts (Apollo 12 and 17) were systematically heavier than non-ilmenite bearing basalts, which was interpreted to be the result of lunar mantle source heterogeneity, both in respect to their mineral modal proportions (Sprung et al. 2013) and the prevalent fO2 (Fonseca et al. 2014) during partial melting of the lunar mantle. Moreover, Kommescher et al. (2020) have pointed out that at least some of the variability in the δ49Ti of lunar mare basalts could result from the fractional crystallization of Fe–Ti oxides, like ilmenite and armalcolite, during magmatic differentiation. At oxygen fugacities relevant for lunar conditions (between one to two orders of magnitude more reduced than the Fe–FeO reference redox equilibrium or IW-1 to IW-2; Wadhwa 2008), high-Ti basalts might be reduced enough for an incorporation of up to 10% Ti3+ relative to their bulk Ti contents (Krawczynski et al. 2009; Leitzke et al. 2018; Simon and Sutton 2018). A decoupling of Ti3+ from Ti4+ could result in redox dependent Ti stable isotopic differences in high-Ti basalts. A similar redox decoupling process is associated, for example, with the high δ56Fe of MORB samples compared to their mantle sources (Dauphas et al. 2014; Poitrasson et al. 2014; Sossi and Moynier 2017). Furthermore, this expectation seems to be supported by recent ab initio modelling by Wang et al. (2020), whose models suggest the presence of Ti3+ could result in significant Ti isotope fractionation during magmatic processes, and extend beyond Fe–Ti oxide-melt equilibria to include equilibria between silicate minerals and silicate melts. Moreover, synthetic clinopyroxene produced from experimental high-Ti silicate melts contains a mixture of IV- and VI-fold coordinated Ti, with an average of 45%, and as much as 82% of [IV]Ti4+ in pyroxene (Leitzke et al. 2018). Ab initio modelling carried out by Leitzke et al. (2018) suggests that such a high proportion of Ti in low (IV-fold) coordination is expected to favour a heavy Ti isotope composition for pyroxene, which could be extrapolated to other silicate phases.

In this study we experimentally assess the extent and magnitude of Ti stable isotope fractionation between silicate melt, armalcolite and orthopyroxene as a function of fO2. We have carried out seven experiments using compositions from the CaO–MgO–Al2O3–SiO2 + TiO2 (CMAS + TiO2) system that serve as analogues for high-Ti basalts. Compositions were chosen to reproduce equilibria between mineral phases found in lunar mare basalts and Ti–rich silicate melts. Oxygen fugacity conditions ranged from air to IW-1, reproducing highly oxidizing to highly reducing conditions of magma genesis and, therefore, terrestrial and lunar redox conditions. The different mineral phases in each experiment were separated and measured for their Ti isotope composition. The results were then fitted to a logistical function relating the Ti3+/(∑Ti) of different phases in our experiments and the Ti isotope fractionation resulting from two phase equilibria (∆49TiA–B), and subsequently compared with ab initio modelling, as well as Ti isotope data from natural lunar sample suites.

Methods

Experimental protocol and sample preparation

The starting composition of our experiments consisted of dried high purity major element oxide reagents (Alfa Aesar) mixed in the CaO–MgO–Al2O3–SiO2 (CMAS) system, to which ca. 20 wt.% TiO2 were added (following Leitzke et al. 2016). To produce the starting material, dry oxide powders were ground together with acetone in an agate mortar (CaCO3 was previously decarbonated overnight at 900 °C). The mixture was dried, pressed into pellets, sintered at 900 °C and subsequently reground for further homogenization, and its composition is shown in Table 1. To avoid the loss of iron to the Pt wire and to be able to isolate the effect of fO2 on Ti stable isotope fractionation from potential interactions between Fe and Ti, our starting composition was FeO-free.

Table 1 Composition of synthetic starting material used in this study
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Experiments were performed in a 1 atm vertical gas mixing furnace at the University of Cologne (Germany) using the wire loop technique (Donaldson et al. 1975), and adhered closely to the experimental protocol described by Leitzke et al. (2016, 2017). For this purpose, each sample powder was mixed with polyethylene glycol and water to produce a slurry, which was then placed onto a metal loop and suspended inside the furnace at temperatures around 50–100 °C higher than the liquidus of the sample composition (1400 °C). After a minimum-3-h period that ensured complete melting and homogenization, samples were cooled (cooling ramp of 0.04 °C/min) until the experiment reached its nominal target temperature (1260 °C), where it remained another 72 h to ensure chemical equilibrium. This procedure was optimised to ensure that large enough (> 100 µm) crystals of orthopyroxene and armalcolite could grow in each experiment (see Hill et al. 2000; Leitzke et al. 2016). The temperature throughout the experiments was monitored using an external Type B thermocouple (Pt70Rh30–Pt94Rh6). Quenching of the samples was performed in air, since Pt wire was used for all experiments. Oxygen fugacity was set by different CO–CO2 gas mixtures and controlled using Tylan 2900 series mass flow controllers (see Supplementary Table 1). Furthermore, before and after each experiment, oxygen fugacity was monitored using a Y-stabilized zirconia oxygen sensor to verify how robustly the gas mixtures reproduced the desired fO2 of the experiment. Our experiments yielded crystals of armalcolite and orthopyroxene in equilibrium with glass (see Leitzke et al. 2016). For each experiment, two loops with the same composition were suspended in the furnace simultaneously. One of the loops was mounted in epoxy, polished and carbon coated for later EPMA and SEM analyses that aimed to identify the proportions of each mineral phase and major element compositions from the experiments. The second loop was gently crushed, and any minerals and glass contained within were handpicked and separated under reflected and transmitted light using a Zeiss stemi dv4 stereomicroscope with 32-times magnification. The glass was always transparent and showed characteristic conchoidal fracture, and any crystalline inclusions found within were immediately obvious. The orthopyroxenes were always white (iron-free) and showed a clear cleavage, making them easier to identify. The acicular armalcolite was black in all samples except in the experiment carried out in air, where it was colourless. Moreover, we selected only the mineral and glass separates devoid of obvious contaminants (i.e., inclusions and attached phases) for use in the Ti separation chemistry. This was especially important for the recovery of the relatively TiO2-poor orthopyroxene (ca. 1 wt.% TiO2), which if contaminated by armalcolite (ca. 75 wt.%), and to a lesser extent glass (ca. 15 wt.%), would inevitably result in the adulteration of its Ti isotope composition. All phases that were separated with this procedure were subsequently digested, aliquoted, mixed with a Ti double spike and processed via column chemistry to purify Ti for MC–ICP–MS measurements.

Chemical purification of titanium

All acids used in this study (HCl, HF and HNO3 from EmsureV R, Merck) were distilled using Savillex DST-1000 sub-boiling Teflon stills. All diluted acids were prepared with 18.2 MΩ/cm H2O. All PFA vials were fluxed successively in reagent grade 3 M HCl, 5 M HNO3 and 18.2 MΩ/cm H2O at 120 °C for more than 48 h prior to use. The H2O2-bearing solutions for all columns were prepared shortly before each column chemistry to limit dissociation of H2O2. We followed the Ti separation procedure described by Kommescher et al. (2020), who themselves used a five step, heavily modified HFSE purification chemistry previously developed by Münker et al. (2001), Bast et al. (2015) and Tusch et al. (2019). The separation aimed on keeping Ti in solution during the purification procedure, and avoid a complete dry down and, therefore, precipitation of the samples, while maximizing the Ti chemistry yields.

Handpicked mineral and glass fractions recovered from each experiment were weighed and then digested in a 3:1 mixture of 14 M HNO3 and 24 M HF in pre-cleaned Savillex® PFA beakers. In addition to our samples, the Origins Lab Ti reference material (pure Ti metal rod—OL-Ti; Millet and Dauphas 2014; Millet et al. 2016), as well as a procedural blank, were individually processed in identical fashion. Furthermore, since we wanted to investigate the fractionation of Ti isotopes relative to our starting composition, our in-house glass reference material that was produced by fusing the bulk composition until homogeneous, was also processed during column chemistry.

After complete digestion was verified by visual inspection, aliquots were taken to determine the exact Ti concentration of each fraction using an iCap quadrupole ICP–MS. Afterwards, sample aliquots containing up to 30 µg Ti were mixed with a Ti double spike in the ideal sample to spike proportion (sample:spike of 0.49:0.51—Rudge et al. 2009; Kommescher et al. 2020). We used a 47Ti–49Ti double spike (410.9 ± 0.3 µg/g) that was calibrated against the OL-Ti reference material (Kommescher et al. 2020). Samples were equilibrated overnight in a closed PFA beaker and subsequently evaporated at 75 °C on the hotplate. Dried samples were refluxed in 14 M HNO3 >  > 6 M HCl—0.06 M HF to prevent the formation of secondary fluorides from remaining HF. After drying samples at 75 °C, they were refluxed in 6 M HCl—0.06 M HF to convert the sample solution into chloride form and to dissolve nitrate precipitates. Samples were then dried at 75 °C, laced with 1 mL 1.75 M HCl—2 vol.% H2O2 and centrifuged for ten minutes right before column chemistry.

All chromatographic separation resins were cleaned before and after each of the five separation steps. Each initial cleaning step was followed by equilibration with the acid used in the subsequent loading step to ensure that the ionic form of the resin was of the correct speciation relative to the mobile phase with which ion exchange takes place. Since our experimental samples were matrix-poor compared to natural samples, the chemical purification scheme described by Kommescher et al. (2020) had to be modified, as the lack of matrix elements caused an increased absorption of Ti, when samples were loaded in 1 M HCl—2 vol.% H2O2 onto the cation resin AG50W-X8. Therefore, with 1 M HCl—2 vol.% H2O2 from the original elution scheme, no Ti was recovered after the first step. To test the efficiency of the column chemistry, initial yield tests with all three different mineral separates (armalcolite, orthopyroxene and glass), and two different acid strengths, were performed. Prior to separation and at each subsequent step of our yield test, a 10% aliquot was removed and doped with 0.025 µg to serve as an independent reference during subsequent measurements at the Thermo Scientific iCap quadrupole ICP–MS. Absolute and relative yields of all purification steps could thus be calculated. Our results show that by using a higher acid strength, it is possible to quickly elute all Ti. Using 1.5 M HCl—2 vol.% H2O2 resulted in a prolonged Ti elution compared to using 1.75 M HCl—2 vol.% H2O2, which achieved the fastest accumulation of our Ti yield (Fig. 1c, mean relative Ti yields with two different acid strengths on AG50W-X8; dotted lines show elution with 1.75 M HCl). Furthermore, sample loss of up to 50% was noticeable during the first clean-up on AG1-X8 (Fig. 1a, cyan blue bars indicate the relative cumulative yield from each step). The first clean-up step is designed to remove Cr and V, which were purposely not present in our experiments as they were not added to the starting compositions to avoid known isobaric interferences during analysis. Therefore, this step was skipped in our chemistry to maximize the Ti yields. Nevertheless, Cr and V contents were monitored to test for any potential contamination from the furnaces and reagents used in the experiments, and their concentrations were found to be below detection limit. The adapted chemistry was performed as described in the following (see also Table 3):

Fig. 1
figure 1

Elution of Ti and matrix elements. To develop a new column chemistry for matrix-poor samples, we performed a column calibration for pure armalcolite, orthopyroxene and glass separates to test the elution of the elements that were used for our experiments. We took a 10% aliquot of each elution step, which was subsequently doped with an internal standard (0.025 µg In) to quantify yields after element concentration measurements at the Thermo Scientific iCap quadrupole ICP-MS. All elution lines for Ti, Mg, Al and Ca displayed here are average elution lines of all three phases. Cyan blue bars indicate the average relative cumulative yield of Ti after each respective column. Bold labels indicate the dilution of the samples with 18.2 MΩ/cm H2O and 24 M HF until present in 0.3 M HCl—1 M HF prior to loading them onto the columns. a Elution of Ti, Mg, Al and Ca in the 5 step chemistry. Due to the low acid strength of the first clean-up down to 50% of Ti is lost after the clean-up steps as indicated by cyan blue bars. b The problem of sample loss was solved by performing the second clean-up only with a higher acid strength, which leads to higher yields in total (cyan blue bars for every respective column). Furthermore, the sample is matrix-free in the end. (c) Elution of Ti, Mg, Al and Ca with 1.5 M (coloured lines) and 1.75 M (dotted coloured lines) HCl during the first step of column chemistry (AG50W-X8). Overall, the higher acid strength of 1.75 M HCl during the first column leads to a faster elution of Ti

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During the first step, the sample matrix was eluted with 6 M HCl and separated from the HFSE (and Mo and W) plus Ti, which was eluted using 1.75 M HCl—2 vol.% H2O2 in a AG50W-X8 (200–400 mesh) cation exchange resin until the remaining drop of acid at the tip of the column was colourless (11 mL 1.75 M HCl during yield tests). The second separation step isolated Ti, Zr and Hf (1 M HCl—2 vol.% H2O2) from W and Mo (6 M HNO3—0.2 M HF—2 vol.% H2O2) through a AG1-X8 (200–400 mesh) anion exchange resin. In a third step, Ti was separated from Zr and Hf in a column filled with Ln Spec resin, by loading and directly eluting Ti with 1 M HCl—2 vol.% H2O2, and subsequently eluting Zr and Hf using 2 M HF. The fourth step of the Kommescher et al. (2020) protocol was skipped as described above; however, a final clean-up was important for the separation from residual matrix elements (Fig. 1b—cyan blue bars indicate the relative cumulative yield from each step). Prior to this last step, samples were diluted with 18.2 MΩ/cm H2O and 24 M HF until present in 0.3 M HCl—1 M HF. Afterwards, the matrix was eluted using 0.3 M HCl—1 M HF, then Ti was eluted using 6 M HCl—0.06 M HF and 3 M HNO3—0.2 M HF—2 vol.% H2O through the AG1-X8 resin to collect all Ti. After the clean-up step, both the matrix and Ti cuts were dried down on a hotplate at 80 °C. Nine parts of a 6 M HNO3—0.2 M HF solution were mixed with one part 30% H2O2 and every sample was laced with 2 mL of this solution to destroy organic components in the samples. After another sample dry down, all samples were taken up into 2 mL of the 0.3 M HNO3—0.014 M HF running solution and transferred into 5 mL ICP–MS vessels. The mean relative Ti yield that resulted from our method was ~ 90% in the yield test (see Supplementary Table 1and Fig. 1b). A Ti chemistry yield of ~ 90% enabled us to measure samples that contain down to 6 µg Ti, four times in 60 cycles at no loss of analytical precision compared to samples with higher Ti contents.

Double spike MC—ICP–MS analysis

A calibrated 47Ti–49Ti double spike was used for our analyses. The final concentration of the 49/47Ti double spike is 410.9 ± 0.3 µg/g. The double spike was calibrated against OL-Ti as described by Kommescher et al. (2020).

Analyses of Ti stable isotope composition were performed on a Thermo Scientific Neptune MC–ICP–MS at the University of Cologne (Germany). Before each measurement session, detector gain and instrument baselines were determined. All measurements were run in high-resolution mode, to account for polyatomic interferences on 46Ti and 48Ti, using a Ni sample cone and a Ni skimmer H-cone. Typical resolving power (determined by 5–95% peak height) during each measurement was in the range of R ~ 10,000. Lens setting and gas flows were tuned daily to maximize intensity and resolving power. Before and after each of the four measurement blocks of 60 cycles (integration time of 8.4 s), a spiked OL-Ti solution was measured. Furthermore, each sample was bracketed by our synthetic reference material Col-Ti that was produced from a pure Ti metal rod from the same batch as that of reference standard OL-Ti (Millet and Dauphas, 2014), and is described in greater detail by Kommescher et al. (2020). This sample-standard bracketing was carried out to estimate the intermediate precision of our measurement, and to exercise further control on polyatomic interferences. Background measurements were performed for on-peak-zero corrections before and after each standard-sample measurement block. For most analyses a ~ 1 µg/mL Ti solution was measured with a PFA nebulizer having an uptake rate of 125 µl/min. This generated 49Ti, 48Ti, 47Ti signal intensities of 2–3 × 10–11 A (2–3 V) using 1011 amplifiers. Background levels in a pure 0.3 M HNO3—0.0014 M HF solution were around 1–4 × 10−15A (1–4 10–4 V). Washout times were typically around 5 min.

Data reduction was performed offline using a modified version of the Compston and Oversby (1969) algorithm, which allows us to estimate precision using counting statistics (Schoenberg et al. 2008; Kurzweil et al. 2018). Titanium isotope ratios are expressed in the δ-notation (in per mil, ‰) relative to OL-Ti following Millet and Dauphas (2014):

$$\delta (^{49} {\text{Ti/}}^{47} {\text{Ti)}}_{{{\text{OL}} - {\text{Ti}}}} \; = \;\left( {\frac{{^{49} {\text{Ti/}}^{47} {\text{Ti}}_{{{\text{sample}}}} }}{{^{49} {\text{Ti/}}^{47} {\text{Ti}}_{{{\text{OL}} - {\text{Ti}}}} }} - 1} \right)\; \times \;1000$$
(1)

Our long-term reproducibility of OL-Ti is better than 0.035 ‰ (2 s.d.) after n = 79 measurements, which corresponds to a 95% confidence interval of 0.004 ‰ on δ49Ti (Fig. 2). The long-term reproducibility of our glass reference material is 0.020 ‰ (2 s.d.) after n = 13 measurements, which corresponds to a 95% confidence interval of 0.006 ‰ on δ49Ti. 95% confidence interval is calculated including the student’s t test. All spike:sample ratios from this study are displayed in Supplementary Table 3.

Fig. 2
figure 2

Long-term reproducibility of glass reference material (top) and OL-Ti (below) over several months. Blue areas indicate the long-term 95% confidence interval. Colours of OL-Ti indicate different measurement sessions, whereas the large coloured dots represent the mean of the respective session. The large white dots are the overall means of the respective standard. OL-Ti was measured over several months from December 2019 to March 2020, whereas the more valuable synthetic glass reference material was measured only in the sessions, where synthetic samples were measured. Errors are stated as 95% confidence interval

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Results

Experimental run products

All experiments yielded glass, orthopyroxene and armalcolite (Fig. 3). Mineral phases had crystal sizes exceeding hundreds of µm in length. The large crystal size can directly be related to the high bulk TiO2 content of the melt and is the result of decreased melt polymerization due to the addition of TiO2 to the melt (Neuville and Mysen 1996; Rai et al. 2019; also seen in Leitzke et al. 2016, 2017 for identical compositions).

Fig. 3
figure 3

Backscatter electron (BSE) images of typical run products. a T5-20 composition overview of a complete experimental run. b T5-20 composition with large armalcolite crystals. c T5-20 composition in a close-up with acicular armalcolite crystals

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Armalcolite typically shows acicular crystal habits, whereas orthopyroxene is predominantly prismatic (Fig. 3; see Leitzke et al. 2016). Minerals showed no compositional zonation, indicating equilibrium. Orthopyroxenes consist of pure enstatite Mg2Si2O6, whereas armalcolites are almost pure MgTi2O5 (i.e., Karrooite), comparable to Mg-rich lunar armalcolites described in Haggerty (1973). Nevertheless, EPMA measurements showed that cation deficiencies in armalcolite increased with decreasing fO2 of the experiments (see Supplementary Table 4), which can be explained by a small amount of Ti3+ present in the M2 site (Stanin and Taylor 1980) and was already described for a similar composition by Leitzke et al. (2016).

Ti stable isotope composition of experimental run products

Our results show that armalcolite has lighter Ti isotope compositions relative to the bulk composition of the experiment, and to the other coexistent phases (glass and orthopyroxene). Glass is isotopically lighter than orthopyroxene at low fO2, and both phases are isotopically heavier than the bulk composition (Table 2). Furthermore, the δ49Ti of all phases varies with fO2. Isotopic differences between phases become progressively larger the more reducing conditions become (Fig. 4 a, Table 2). The δ49Ti of armalcolite becomes gradually higher with decreasing fO2, increasing from − 0.056 ± 0.019 ‰ in air to − 0.003 ± 0.029 ‰ at IW-1, predominantly overlapping (within error) with the δ49Ti of the bulk composition (− 0.010 ± 0.006 ‰). This overlap is related to armalcolite having most of the bulk Ti content of the experiment, which means its δ49Ti is always close to that of the bulk composition of the experiment. Conversely, the δ49Ti of glass (+ 0.035 ± 0.009 ‰ at air to + 0.197 ± 0.005 ‰ at IW-1), and orthopyroxene (+ 0.033 ± 0.009 ‰ to + 0.247 ± 0.020 ‰ at IW-1) also increase with decreasing fO2, which is, at least, partly related to the distribution of Ti in the different phases present in the experiments. However, absolute changes in δ49Ti are much larger when orthopyroxene and silicate glass are compared to armalcolite. Therefore, a better measure of the effect that fO2 has on Ti isotope fractionation is to look at mineral–mineral and mineral-melt Ti isotope fractionation, as this parameter is independent of any Ti mass balance effect.

Table 2 δ49Ti isotope composition and 95% c.i. in ‰ of all synthetic phases at 1260 °C from this study
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Fig. 4
figure 4

Overview of δ49Ti and Δ49Ti compared to the fO2. a Titanium isotope composition of experimental run products (given as δ49Ti in ‰) as a function of fO2 relative to Fe-FeO equilibrium (ΔIW). b Isotope fractionation (Δ49Ti) of orthopyroxene(opx)-melt, armalcolite(arm)-melt and armalcolite-orthopyroxene equilibria are shown relative to ΔIW

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The Ti stable isotope fractionation (∆49TiA–B = δ49TiA − δ49TiB) expressed in each phase is a function of the lever rule, enabling us to isolate what effect fO2 has on the fractionation of Ti isotopes between different phases in equilibrium (Fig. 4b).

Results show that the ∆49TiA-B for equilibria between armalcolite and other phases in the experiments (i.e., opx and melt) becomes more fractionated to lower values, at increasingly lower fO2 reaching − 0.2 to− 0.25 ‰ for armalcolite-melt and armalcolite-opx equilibria, respectively, from a starting value of ~ − 0.1 ‰ in experiments carried out in air (see Table 3 and Supplementary Table 5). Interestingly, ∆49Tiopx-melt also becomes more fractionated at lower fO2 but to more positive values, reaching a maximum of ca. + 0.04 ‰ at IW-1.

Table 3 α-values, Δ49Ti isotope composition and 95% c.i. in ‰ of all synthetic phases at 1260 °C from this study
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Mass balance of experimental run products and their Ti isotope composition

In all experiments, where both loops were recovered, we have carried out mass balances as a check for possible contamination during production of the different phase separates. First of all, we determined the modal abundance of each phase from SEM images of each experiment using ImageJ, and weighted them based on the density of each phases. Afterwards, we have determined the fraction of Ti present in each phase and multiplied it with the respective δ49Ti values. The result was then compared to the δ49Ti of our synthetic glass reference material. Mass balance calculations for almost all experiments are within 2 s.d. of the synthetic glass reference material (δ49Ti =  − 0.010 ± 0.020 ‰; see Supplementary Table 7). The only exception was the experiment at FMQ-0.5, where the bulk δ49Ti determined from the mass balance was + 0.040 ‰, which is 0.050 ‰ higher than expected from our synthetic glass reference material. Since δ49Ti of orthopyroxene from this experiment is lower than the δ49Ti of the glass, it is likely that this orthopyroxene was contaminated by armalcolite driving its apparent δ49Ti to lower values and also to erroneous Δ49Ti values that are not in line with the redox dependent trends shown in Fig. 4 and Fig. 5. This can be confirmed by the χ2 values of our thermodynamic fit, where all Δ49TiA-B at FMQ-0.5 associated with orthopyroxene leads to high χ2 values (> 3) in comparison to other χ2 values (< 1).

Fig. 5
figure 5

Overview of Δ49TiA–B compared to the absolute fO2 and ΔIW. Isotope fractionation (Δ49TiA–B) of orthopyroxene (opx)-melt, armalcolite (arm)-melt and armalcolite-orthopyroxene equilibria is shown relative to log fO2 and ΔIW. The thermodynamical fits represented by the blue line were calculated with Eq. 4 and the constants from Table 4 and show a clear redox-dependency of all equilibria

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As shown by the mass balance carried out on the FMQ-0.5 experiments, even slight variations resulting from either contamination during processing of the mineral separates, or from flawed estimates of mineral modal abundances in the experiments, have a large and obvious effect on the mass balance and Δ49Ti values. This indicates that all other experiments that are within 2 s.d. from our synthetic glass reference material have worked well and our general experimental setup is successful. Furthermore, since our mass balance varies within 2 s.d. of our synthetic glass reference material to positive and negative values, Ti-poor phases like orthopyroxene, and to a lesser extent glass, are most likely uncontaminated with isotopically light armalcolite as this would result in clear shifts in their Ti isotope composition to lighter values.

Discussion

Ti isotope composition of mineral separates

Terrestrial magmatic samples show a large range of δ49Ti between − 0.05-  + 2.32 ‰. These values are positively correlated with the SiO2 content of the rock (Millet et al. 2016; Deng et al. 2019; Hoare et al. 2020), which was interpreted to be the result of Ti oxide crystallization controlling the Ti budget with increasing magmatic differentiation. In a recent study, Zhao et al. (2020) analysed 60 magmatic samples from different tectonic settings and discovered that those saturated with a Fe–Ti oxide phase show a large range of δ49Ti values, from 0.005 to 1.914 ‰, positively correlated with SiO2 and negatively correlated with MgO sample content. The same study did not report any dependence of δ49Ti on either MgO or SiO2 content for rocks that did not have an Fe–Ti oxide phase, which corroborates and expands upon the interpretation and dataset of former studies (see Millet et al. 2016; Greber et al. 2017a, b; Deng et al. 2018, 2019; Johnson et al. 2019; Kommescher et al. 2020). Fractional crystallization of Ti oxides was also shown to be a key factor for Ti stable isotope fractionation present in lunar basalts (Millet et al. 2016; Kommescher et al. 2020). Since the δ49Ti of low-Ti basalts (+ 0.01 ± 0.047 ‰; Millet et al. 2016; Kommescher et al. 2020) broadly resembles that of the BSE (δ49Ti =  + 0.005 ± 0.005 ‰, Millet et al. 2016), whereas high-Ti basalts show a wider range of δ49Ti (between + 0.009 and + 0.115 ‰; Millet et al. 2016; Kommescher et al. 2020), this difference between the different types of mare basalt suites has been interpreted to be the result of the fractional crystallization of ilmenite/armalcolite, as well as the partial melting of an IBC-component (Kommescher et al. 2020). However, most of these studies used whole rock bulk samples for their analyses. So far only a few studies investigated mineral separates (Johnson et al. 2019; Mandl 2019; He et al. 2020), which is, however, fundamental to understand mechanisms of Ti stable isotope fractionation during magmatic processes. Johnson et al. (2019) measured the Ti isotope compositions of mineral separates and the corresponding bulk rock from Kilauea Iki lava lake. Titanium oxides from that study (mostly ilmenite) display slightly lighter to overlapping δ49Ti (between − 0.03 ± 0.02 ‰ and + 0.06 ± 0.03 ‰) compared to the whole rock (between 0.00 ± 0.04 ‰ and + 0.05 ± 0.03 ‰). Silicate mineral separates from the same samples showed higher δ49Ti (between + 0.07 ± 0.03 ‰ and + 0.28 ± 0.02 ‰) compared to the bulk rock. He et al. (2020) recently measured the Ti isotope compositions of mineral separates from the Qinghu monzonite. Ilmenite (δ49Ti =  + 0.121 ± 0.038 ‰) and titanite (δ49Ti =  + 0.146 ± 0.008‰) showed a lighter Ti isotope composition compared to the whole rock (δ49Ti =  + 0.309 ± 0.020 ‰), whereas silicates like K-feldspar and plagioclase were isotopically heavier (δ49Ti =  + 0.529 ± 0.042 ‰; + 0.613 ± 0.064 ‰). Only one study so far examined the Ti isotope fractionation of mineral separates from lunar basalt samples (Mandl 2019). Since all of their samples contained ilmenite, a clear Ti stable isotope fractionation between mineral separates and the host rock was observed (e.g., sample 12005 low-Ti ilmenite basalt: δ49Ti =  − 0.008 ± 0.011 ‰ and ilmenite: δ49Ti =  − 0.022 ± 0.007 ‰; recalculated to OL-Ti from Mandl 2019). Likewise, our experimental armalcolites are isotopically lighter than coexisting melt and orthopyroxene, which is in line with previous results from natural samples (Millet et al. 2016; Johnson et al. 2019; Mandl 2019; He et al. 2020; Kommescher et al. 2020), unsurprisingly confirming the key role that Ti oxides play in determining the Ti stable isotope composition of magmatic samples during their differentiation and petrogenesis. Furthermore, orthopyroxene is the only silicate in our samples that systematically shows higher δ49Ti than coexisting melt in agreement with previous studies (Johnson et al. 2019; He et al. 2020). We note, however, that while the δ49Ti values of armalcolite, and to a lesser extent glass, are likely less vulnerable to contamination during handpicking because of their higher TiO2 contents (ca. 80 wt.% and 15 wt.% TiO2, respectively), the δ49Ti of orthopyroxene is highly susceptible to cross-contamination because of its low TiO2 content (ca. 1 wt.%). This is the most likely explanation for some of the lower than expected δ49Ti values for orthopyroxene in our dataset (i.e., at FMQ-0.5), as even a slight contamination by armalcolite will shift the δ49Ti to lower values. Nevertheless, since orthopyroxene contains only ~ 1 wt.% TiO2, it is expected to have only a negligible effect on the Ti stable isotope fractionation in natural magmatic systems.

How do redox conditions affect the Ti isotope fractionation Δ49TiA–B between two phases in equilibrium?

In most studies dealing with Ti stable isotope fractionation in magmatic systems, Ti has been exclusively tetravalent, and the influence of fO2 on the high-temperature stable isotope fractionation of Ti has not been considered beyond its role on the stability of Ti-bearing oxide phases (Millet et al. 2016; Deng et al. 2019; Johnson et al. 2019; He et al. 2020; Kommescher et al. 2020). Nevertheless, the role of oxygen fugacity and of varying redox conditions on Ti stable isotope fractionation needs to be addressed, especially when considering the more reducing conditions operating during lunar basalt petrogenesis (e.g., Kommescher et al. 2020), where Ti3+ is known to be stable in addition to Ti4+ (Simon and Sutton 2018; Leitzke et al. 2018).

There are several studies dealing with the oxidation state of Ti in pyroxenes, Ti oxides and glasses in lunar environments (Lindsley et al. 1974; Kesson and Lindsley 1975; Stanin and Taylor 1980; Simon et al. 2014; Simon and Sutton 2017, 2018; Leitzke et al. 2018). High-pressure experiments showed that armalcolites near metal saturation (~ IW) can incorporate a significant M3+2TiO5 component (Lindsley et al. 1974; Kesson and Lindsley 1975), and thus a significant amount of a trivalent cation. This was supported by Wechsler et al. (1977) who indicated that most lunar armalcolites contained between 4 and 11 mol % of a M3+2TiO5 component in a solid solution. Stanin and Taylor (1980) conducted dynamic crystallization experiments and detected increasing Ti3+ contents in armalcolite (< 1–15% of the total Ti fraction) with decreasing fO2 (up to IW-1.2). A more recent study by Leitzke et al. (2018) performed experiments in a gas mixing furnace using the same starting composition as in our study. The Ti valence and its spatial coordination number were determined in their experimental run products via K-edge XANES spectroscopy (Leitzke et al. 2018). Armalcolites produced in the experiments by Leitzke et al. (2018) showed a strong fO2 related trend of Ti valence in armalcolite from ~ 4 (air) to ~ 3.7 (IW-1.7) with a constant VI-fold coordination number. Pyroxenes, in particular, showed that they can contain a mixture between IV- and VI-fold coordinated Ti, with as much as 82% (45% on average) in the IV-fold site, and have an average Ti valence of 3.75 (or ca. 25 mol.% Ti3+) at fO2 relevant to lunar magmatism (Leitzke et al. 2018). These results are consistent with recent XANES measurements carried out by Simon and Sutton (2017, 2018) in natural lunar minerals.

Leitzke et al. (2018) also carried out ab initio modelling based on density-functional theory (DFT) of mass dependent Ti equilibrium isotope fractionation. They assumed different oxidation states of Ti (3+/4+) and coordination environments (IV-/VI-fold coordination) for clinopyroxene and the Mg-rich endmember of the armalcolite–karrooite solid solution series (MgTi2O5). The largest fractionation factor (β) was observed for the incorporation of Ti4+ into the tetrahedral Si site of clinopyroxene, whereas the lowest β value was predicted for both the incorporation of Ti3+ into the octahedral Mg site of clinopyroxene, and Ti in armalcolite (see Fig. 7 in Leitzke et al. 2018). More recently, Wang et al. (2020) reached similar conclusions with their own DFT ab initio modelling. Judging from the XANES data reported by Leitzke et al. (2018), pyroxene in our experiments should contain fewer than 25% Ti3+ relative to total Ti in VI-fold coordination, while on average a little less than half (45%) of its Ti4+ is expected to be present in IV-fold coordination at ca. IW-1. Based on the ab initio modelling by Leitzke et al. (2018), the pyroxene in our experiments is then expected to show higher δ49Ti values relative to armalcolite at fO2 relevant to lunar magmatism (i.e., a positive Δ49Tiopx-arm). This expectation, is reflected by our own dataset, where the Ti isotope fractionation for armacolite–orthopyroxene equilibria predicted by the Leitzke et al. model (Δ49Tiopx-arm ~  + 0.3 ‰) is very close to what was determined for our experiments carried out IW-1 (Δ49Tiopx-arm ~  + 0.25‰).

There are, however, apparent inconsistencies between our dataset and the ab initio modelling by Leitzke et al. (2018) and later by Wang et al. (2020). For example, both Leitzke et al. (2018) and Wang et al. (2020) have argued that Ti3+ in orthopyroxene substitutes into the VI-fold M1 site of this mineral, so it is possible that the spatial coordination of Ti changed slightly in orthopyroxene at lower fO2 to favour VI-fold coordination. This may account for the slightly higher Δ49Tiopx-melt seen in our more reduced experiments compared to those carried out in air, where all Ti is tetravalent. Indeed, the sigmoidal relationship shown between Δ49Tiopx-melt and fO2 is reminiscent of a similar relationship seen between the partitioning of Ti between pyroxene and melt and fO2 (Mallmann and O’Neill 2009). In that case the DTiOpx/melt was shown to increase with decreasing fO2 due to an increasing proportion of Ti3+. It should be noted, however, that ab initio modelling indicates the substitution of Ti3+ in VI-fold coordination in orthopyroxene (Wang et al. 2020), which should result in lighter Ti isotope compositions in orthopyroxene due to the longer Ti3+–O bond lengths and lower force constants compared to Ti4+–O bonds. This expectation is not confirmed by our experimental results, as Δ49Tiarm-opx are larger at lower fO2, possibly because the modelling of Wang et al. (2020) did not consider the presence of multiple simultaneous equilibria as we did in our experiments. Furthermore, Leitzke et al. (2018) did not determine how Ti4+ is distributed between the tetrahedral and octahedral sites in pyroxene under more oxidizing conditions, so a direct comparison with experiments carried out at IW-1 is not possible. Given the limited constraints, at present, we can only speculate that under more reducing conditions Ti4+ is perhaps pushed from VI-fold into IV-fold coordination, because Ti3+ is exclusively sited in the octahedral Mg site in VI-fold coordination. The net effect of this process could presumably lead to a higher overall proportion of Ti–O bonds in IV-fold coordination relative to VI-fold coordination and hence to overall higher β values at lower fO2.

Nevertheless, our results confirm that changing fO2 leads to the development of isotopically resolvable differences of δ49Ti between armalcolite, orthopyroxene and melt, which is probably due to their different coordination environments in conjunction with the oxidation state of Ti in the different phases.

However, given that our results show that fO2 clearly impacts on the value of Δ49TiA-B, it is necessary to consider the effect of this parameter for more reducing environments like those associated with lunar magmatism. We, therefore, fitted our Δ49TiA–B data for the different phase equilibria (i.e., armalcolite-melt, orthopyroxene-melt and armalcolite–orthopyroxene) obtained at 1533 K to a logistical function based on the redox change of Ti as a function of fO2:

$${\text{TiO}}_{x/2} \; + \;z/4{\text{O}}_{2} \; = {\text{TiO}}_{(x + z)/2} \;$$
(2)

and,

$$\Delta^{49}\sum {\text{Ti}}_{{{\text{A}} - {\text{B}}}} = \frac{{\Delta^{49} {\text{Ti}}_{{{\text{A}} - {\text{B}}}}^{{\left( {x + z} \right)}} + \Delta^{49} {\text{Ti}}_{{{\text{A}} - {\text{B}}}}^{x} \; \times \;K^{^{\prime} - 1} \; \times \;{\text{e}}^{{\log f{\text{O}}_{2}^{{ - \frac{z}{4}}} }} }}{{1 + K^{^{\prime} - 1} \; \times \;{\text{e}}^{{\log f{\text{O}}_{2}^{{ - \frac{z}{4}}} }} }}$$
(3)

where x is the valence of the reduced Ti redox species, z the number of electrons exchanged between both sides of reaction (2), Δ49Tix+zA–B and Δ49TixA–B are the Ti isotope fractionation of fictive oxidized and reduced end-members, and K the equilibrium constant related to reaction (2). Because we know the oxidation state of Ti in both sides of reaction (2)—i.e., Ti3+ and Ti4+—the number of electrons exchanged (z) is one, and Eq. (3) can be simplified to:

$$\Delta^{49}\sum {\text{Ti}}_{{{\text{A}} - {\text{B}}}} = \frac{{\Delta^{49} {\text{Ti}}_{{{\text{A}} - {\text{B}}}}^{4 + } + \Delta^{49} {\text{Ti}}_{{{\text{A}} - {\text{B}}}}^{3 + } \; \times \;K^{^{\prime} - 1} \; \times \;{\text{e}}^{{{\log fO_{2}{ - \frac{1}{4}}} }} }}{{1 + K^{^{\prime} - 1} \; \times \;{\text{e}}^{{{\log fO_{2}{ - \frac{1}{4}}} }} }}$$
(4)

From Eq. (4) it is clear that Δ49TiA–B will depend on fO2, Δ49Ti4+A–B, which is known from the most oxidized experiments carried out in air, where all Ti is tetravalent, and Δ49Ti3+A–B, which represents a case, where all Ti is trivalent, and K’. The Δ49TiA–B values for the different phase equilibria were fitted to Eq. (4) using least squares regression likewise to what was commonly done to relate the partitioning of redox-sensitive elements like Re, V or Mo (Mallmann and O’Neill 2007, 2009; Leitzke et al. 2017) to fO2, the results of which are shown in Table 4 and Fig. 5.

Table 4 Fitting parameters derived from Δ49TiA–B (in ‰) of experimental samples
Full size table

It should be pointed out, however, since we know that around IW-1.7 the mean Ti valence is 3.69 (Leitzke et al. 2018), our reduced experiment at IW-1 does not represent the real end member, where only trivalent Ti would be present. Therefore, our more reduced experiments are located at the slope of the fitted curve and not at the plateau on the more reduced end of the plot (Fig. 5). The reduced plateau at around IW-12 is supported by the known stability of tistarite (Ti3+2O3) with very reducing conditions near IW-13 (Barin 1995). However, the more oxidized plateau is well defined by our oxidized experiments carried out in air that contain only tetravalent Ti (Leitzke et al. 2018). Our data indicates that the Δ49TiA–B has a clear dependence on fO2, namely larger Ti isotope fractionation at more reducing conditions. This isotope fractionation is probably connected to the change in oxidation state and spatial coordination (see Young et al. 2015; Sossi and O'Neill 2017) with decreasing fO2 described by Leitzke et al. (2018). However, Leitzke et al. did not identify a significant shift in the spatial coordination of Ti in armalcolite, orthopyroxene and silicate melt as a function of fO2, whereas the oxidation state of Ti in armalcolite, and to a lesser extent pyroxene, shows a clear redox dependence (Mallmann and O’Neill 2009; Leitzke et al. 2018). The oxidation state of Ti (fO2 dependent) thus appears to have a larger effect on Ti stable isotope fractionation than the coordination environment in the case of armalcolite, although we are hesitant to extent this conclusion to other phases, namely those we have not investigated in our study.

Potential implications for the behaviour of stable Ti isotopes during lunar magmatism

Several studies have investigated Δ49TiA–B in association with mineral-melt equilibria focussing on the effects of temperature and melt compositions, yet have not taken into account the influence of fO2. Millet et al. (2016) parameterized the temperature dependence of Δ49Tioxides-melt for their Agung volcanic samples with a range in SiO2 from 54–65 wt.%, and obtained:

$$\Delta^{49} {\text{Ti}}_{{\text{oxides-melt}}} \;(\permille)\; = \; - 0.23\; \times \;10^{6} /{\text{T}}^{2}$$
(5)

A similar temperature dependence of Δ49Tioxides-melt was determined by Deng et al. (2019) who obtained Δ49Tioxides-melt ~  − 0.1 ‰ at ~ 1500 K and ~  − 0.5 ‰ at ~ 1150 K, on a sample set of Hekla lavas with a wider SiO2 range from 46–72 wt.%. They were also the first to notice that their fractionation factors were not only controlled by temperature since there was no linear correlation between δ49Ti and 1/T2. Johnson et al. (2019) derived a new parameterization that incorporated Δ49Tioxides-melt data from Deng et al. (2019) to account for the effect of SiO2 combined with temperature:

$$\begin{aligned} \Delta ^{{49}} {\text{Ti}}_{{{\text{melt-oxide}}}} \;(\permille)\; & = \;[ - 0.5\;( \pm \;0.1)\; + \;0.017\; \\ & \quad ( \pm \;0.002)\;({\text{SiO}}_{2} )] \times \;10^{6} /{\text{T}}^{2} \\ \end{aligned}$$
(6)

More recently, Hoare et al. (2020) argued that while temperature certainly affects Ti stable isotope fractionation, its effect is relatively minor when compared to different oxide-melt equilibria. Specifically, Hoare et al. (2020), pointed out that the δ49Ti of natural magmatic samples varies (1) non-linearly with temperature for a given magmatic suite, and (2) its range is larger than expected from the temperature dependence alone. Instead, most of the variability seen in δ49Ti seems to depend on melt composition, namely the slope of the relationship between FeO/TiO2 and the SiO2 content of a magmatic sequence [d(FeO/TiO2)/dSiO2], and the stoichiometry of any Ti-bearing oxides that crystallize throughout magmatic differentiation. Hoare et al. (2020) obtained the following relationship between the bulk solid-melt Ti isotope fractionation (αsolid–melt) and d(FeO/TiO2)/dSiO2 for − 0.75 < d(FeO/TiO2)/dSiO2 <  + 1.6:

$$\begin{aligned} \alpha _{{({\text{solid-melt}})}} & = - 3.1 \times 10^{{ - 4}} ( \pm 5\; \times \;10^{{ - 5}} )\; \\ & \quad \times \;\frac{{d\left( {\frac{{{\text{FeO}}}}{{{\text{TiO}}_{2} }}} \right)}}{{d{\text{SiO}}_{2} }}\; + \;0.99976\;( \pm 3\; \times \;10^{{ - 5}} ) \\ \end{aligned}$$
(7)

From Eq. (7), because lunar mare basalts have high d(FeO/TiO2)/dSiO2 melts, the fractional crystallization of Fe–Ti oxide phases like ilmenite and armalcolite is expected to produce significant Ti stable isotope fractionation, which is also observed in lunar (Millet et al. 2016; Kommescher et al. 2020) and terrestrial (Zhao et al. 2020) samples and supported by our experimental results. This is exemplified by the heavier Ti isotope composition of KREEP-rich lunar samples (δ49Ti ~  + 0.3 ‰) when compared to primitive high-MgO mare basalts (δ49Ti ~  + 0 ‰) (Millet et al. 2016; Greber et al. 2017a, b; Kommescher et al. 2020). Our isotopically light armalcolites confirm this behaviour especially since the armalcolite related fractionation is higher at lunar fO2 (i.e., IW-1) when compared to more oxidizing conditions. The observed change in δ49Ti as a function of fO2 is also expected for the crystallization of other Ti oxides, namely ilmenite (Millet et al. 2016; Kommescher et al. 2020).

Natural lunar basalts are sub-divided into high- and low-Ti basalts and are considered to have different origins. Low-Ti basalts are thought to result from the partial melting of mafic lunar mantle cumulates without the direct involvement of Ti-rich phases like ilmenite, which leads to overall average δ49Ti close to that of the bulk silicate Earth (BSE—Millet et al. 2016). On the other hand, high-Ti basalt petrogenesis has been linked to the partial melting of a mixture of lunar mantle cumulates, including the IBC (Longhi 1992; Sprung et al. 2013), which accounts for their higher δ49Ti values (Millet et al. 2016; Kommescher et al. 2020).

To model the behaviour of δ49Ti during mare basalt petrogenesis and fractional crystallization, we have combined trace element and Ti isotope data from natural lunar samples (Hf and Ta: Thiemens et al. 2019; δ49Ti: Kommescher et al. 2020) with experimental partitioning data for the trace elements sensitive to Fe–Ti oxide crystallization (i.e., Ti, Ta and Hf—van Kan Parker et al. 2011; Leitzke et al. 2016), and the experimentally determined Δ49TiA–B from this study (see Supplementary tables 8, 9 for model parameters). For armalcolite and clinopyroxene we have used our experimentally determined Δ49Tiarm-melt and Δ49Tiopx-melt values at IW-1 (− 0.2 and + 0.05 ‰, respectively), where we use our orthopyroxene data as an approximation for clinopyroxene. Titanium isotope fractionation data from ilmenite was taken from Mandl (2019) using the difference between their measured δ49Tiilmenite and δ49Tibulk as a proxy for Δ49Tiilmenite-melt (− 0.356‰). Mineral-melt partition coefficients for Ti, Ta and Hf were taken from Leitzke et al. (2016) and van Westrenen et al. (2000).

The results of these models are shown in Fig. 6, where δ49Ti is plotted against a proxy for ilmenite, the Ta/Hf ratio, which is fractionated by both partial melting in the presence of ilmenite and armalcolite, or by their crystallization (Klemme et al. 2006; van Kan Parker et al. 2011; Leitzke et al. 2016). From the model results shown in Fig. 6, it is apparent that fractional crystallization forms a quasi-vertical array, where Ta/Hf slightly decreases while δ49Ti increases. Conversely, partial melting of a lunar mantle source containing variable proportions an Fe–Ti oxide and orthopyroxene, forms arrays, where both δ49Ti and Ta/Hf increase with increasing degree of melting.

Fig. 6
figure 6

Modelling results of this study compared to natural lunar data (Figure symbols are identical to Kommescher et al. 2020). The high-Ti basalts can be reproduced best by partial melting of a source that contains 10% olivine + opaques, of which 25% is ilmenite, whereas the rest is armalcolite (purple line). The turquoise lines represent the partial melting of a source that either contains pure armalcolite or pure ilmenite. The δ49Ti of low-Ti basalts are reproduced by 60–75% fractional crystallization of Ti-oxides

Full size image

The Apollo 11 and 17 high-Ti ilmenite basalts are thought to have originated from 250 km depth (Delano and Lindsley 1982). A parent magma similar to Apollo 17 sample 70017 is assumed for Apollo 11 and 17 high-Ti ilmenite basalts based on their high MgO/FeO and K/Rb ratios (Shi et al. 1975). Apollo 17 sample 75035 was reproduced by partial melting of a mantle source with 90% clinopyroxene and 10% olivine + ilmenite, whereas the samples 74255 and 74275 are thought to have originated from a mantle with 70% clinopyroxene and 30% olivine + ilmenite (Shi et al. 1975). To evaluate how δ49Timelt changes during partial melting, we carried out aggregate partial melting models assuming different bulk Ti fractionation factors using both our experimental Ti isotope data for armalcolite and orthopyroxene, and the natural ilmenite Ti isotope data from Mandl (2019). Following Kommescher et al. (2020) a lunar mantle source with 90% clinopyroxene and 10% olivine + ilmenite was assumed, as it is shown to reproduce the bulk of high-Ti mare basalt suites. In addition of modelling a source with just 10% ilmenite, we have also varied the ratio of ilmenite to armalcolite using the isotope fractionation data for both phases. Of course, armalcolite is not known to be stable at the higher pressures of mare basalt petrogenesis (6 to 15 kbar—Rai et al. 2019), and phases like ilmenite, rutile and ülvospinel likely dominate the IBC oxide assemblage under these conditions (Friel et al. 1977; Semytkivska 2010). However, we thought that using Δ49Tiarm-melt from our experiment at IW-1 is likely a good proxy for a more realistic IBC oxide assemblage containing a mixture of ilmenite and other oxide phases with less Ti, as it seems to have a slightly heavier Ti isotope composition (Δ49Tiarm-melt of − 0.2‰) compared to ilmenite (Δ49Tiilmenite-melt of − 0.356‰). The models show that ~ 10% of partial melting of a lunar mantle source, where the ratio between armalcolite and ilmenite is 3:1 is able to reproduce the δ49Ti and Ta/Hf values of high-Ti ilmenite basalt samples 74255 and 74275. Taken at face value, the results of the fractional melting models indicate that the sources of these high-Ti basalts are unlikely to contain pure ilmenite in their oxide assemblage, and rather must contain a more complex oxide assemblage with higher overall Δ49TiA–B compared to a source with just ilmenite. These results highlight the potential of our experimental data in further discerning the nature of lunar mantle sources. However, it must be pointed out, that more Ti isotope data for a wider range of phase equilibria are required to robustly model the Ti isotope composition of lunar melts, and that the results of the current models should only be taken as rough estimates.

The low-Ti basalts are best represented by fractional crystallization of Ti-oxides after aggregate partial melting of a lunar mantle source with a composition close to the most primitive mare basalt sample in the sample suite low-Ti olivine basalt 12004 (as described in Kommescher et al. 2020). This liquid composition is produced from an assemblage that represents a late stage cumulate of the lunar magma ocean (90% percent solidification with 20% clinopyroxene, 48% plagioclase and 32% pigeonite by Charlier et al. 2018) and subsequently used to model fractional crystallization of an ilmenite-bearing assemblage. Fractional crystallization was modelled with modal abundances derived for the low-Ti olivine basalt 12004 at 50 MPa from Rhyolite MELTS for Excel (Gualda and Ghiorso 2015). We found that up until 50% fractional crystallization, δ49Ti of the melt becomes slightly negative until the first Ti-oxide (armalcolite) shows up at around 50% fractional crystallization. With the onset of Ti-oxide crystallization, δ49Ti of the melt becomes more and more positive until the presence of ilmenite (~ 95% fractional crystallization), where this trend is further accelerated. The high δ49Ti values of Apollo 12 low-Ti ilmenite basalts 12022, 12051, 12063 and 12054 could be reproduced between 60 and 75% fractional crystallization with our experimentally determined Δ49Tiarm-melt and Δ49Tiopx-melt values at IW-1 (− 0.2 and + 0.05 ‰, respectively) and the Δ49Ti for ilmenite (− 0.356‰) from Mandl (2019). The expected relationship between δ49Ti and Ta/Hf as a function of the degree of fractional crystallization is in broad agreement with natural observations.

Concluding remarks

Experimentally synthesized armalcolites have an isotopically light composition, whereas corresponding orthopyroxenes and glasses show an isotopically heavier composition. Our experimental results are, therefore, consistent with interpretations from previous whole rock Ti stable isotope measurements (Millet et al. 2016; Kommescher et al. 2020) as well as with previous mineral separate Ti stable isotope measurements (Johnson et al. 2019; Mandl 2019; He et al. 2020). Δ49TiA–B shows increasing fractionation with decreasing fO2 (~ IW-1). The relationship between Δ49TiA–B and fO2 appears to be directly related to the increasing abundance of Ti3+ at more reducing conditions, consistent with earlier studies that suggest a clear redox-dependency in armalcolite and pyroxene (see Leitzke et al. 2018). However, orthopyroxene-related Δ49TiA–B shows a smaller extent of redox-dependent fractionation, which is possibly due to the fact that orthopyroxene contains only minor amounts of TiO2 (~ 1 wt.%). Nevertheless, the Δ49Tiopx-melt is reminiscent of the redox-dependent DTiOpx/melt by Mallmann and O’Neill (2009). The fractionation Δ49TiA–B determined in this study will be useful for modelling approaches of the lunar magma ocean, however, for future Ti isotope investigations, other Ti-bearing minerals (e.g., ulvöspinel, ilmenite and silicate minerals like clinopyroxene) should be targeted, especially since first order modelling results from Zhao et al. (2020) suggest that the magnetite–ulvöspinel solid solution influences the Ti isotope composition of a given system to an even larger degree than ilmenite and rutile. Titanium K-edge XANES measurements of pyroxenes synthetized at reducing conditions (IW-1.8) showed an average Ti valence of 3.75 and a mixture of IV- and VI-fold coordination numbers (Leitzke et al. 2018). Especially in high-Ti basalts, where a large fractionation of Ti isotopes has been identified (Kommescher et al. 2020), Ti in pyroxenes is more often octahedrally coordinated than in low-Ti basalts (Simon and Sutton 2018). Therefore, it would be interesting to further analyse clinopyroxenes from Ti-rich melt compositions, since they incorporate up to twice the amount of Ti when compared to orthopyroxene, and could potentially incorporate larger proportions of Ti in IV-fold coordination, which may lead to larger Ti isotope fractionation.