The redox dependence of titanium isotope fractionation in synthetic Ti-rich lunar melts

Equilibria between Ti oxides and silicate melt lead to Ti isotope fractionation in terrestrial samples, with isotopically light Ti oxides and isotopically heavy coexisting melt. However, while Ti is mostly tetravalent in terrestrial samples, around 10% of the overall Ti is trivalent at fO2 relevant to lunar magmatism (~ IW-1). The different valences of Ti in lunar samples, could additionally influence Ti stable isotope fractionation during petrogenesis of lunar basalts to an unknown extent. We performed an experimental approach using gas mixing furnaces to investigate the effect of Ti oxide formation at different fO2 on Ti stable isotope fractionation during mare basalt petrogenesis. Two identical bulk compositions were equilibrated simultaneously during each experiment to guarantee comparability. One experiment was investigated with the EPMA to characterize the petrology of experimental run products, whereas the second experiment was crushed, and fabricated phases (i.e., oxides, silicates and glass) were handpicked, separated and digested. An aliquot of each sample was mixed with a Ti double-spike, before Ti was separated from matrix and interfering elements using a modified HFSE chemistry. Our study shows fO2-dependent fractionation within seven samples from air to IW-1, especially ∆49Tiarmalcolite-melt and ∆49Tiarmalcolite-orthopyroxene become more fractionated from oxidized to reduced conditions (− 0.092 ± 0.028-  − 0.200 ± 0.033 ‰ and  − 0.089 ± 0.027- − 0.250 ± 0.049 ‰, respectively), whereas ∆49Tiorthopyroxene-melt shows only a minor fractionation (− 0.002 ± 0.017-0.050 ± 0.025 ‰). The results of this study show that Ti isotope fractionation during mare basalt petrogenesis is expected to be redox dependent and mineral-melt fractionation as commonly determined for terrestrial fO2 may not be directly applied to a lunar setting. This is important for the evaluation of Ti isotope fractionation resulting from lunar magmatism, which takes place under more reducing conditions compared to the more oxidized terrestrial magmatism.


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 TiO 2 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 TiO 2 , reaching levels up to 16 wt.% TiO 2 (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 (ZrAl 2 Ti 4 O 11 - Griffin et al. 2018) and tistarite (Ti 2 O 3 - Griffin et al. 2016), found in terrestrial corundum. Titanium varies between an average IVfold 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 (fO 2 ) 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 Ti 3+ 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 TiO 2 contents (Warren and Taylor 2014), show only small but still resolvable differences in their δ 49 Ti. Low-Ti basalts have a mean δ 49 Ti (+ 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 δ 49 Ti (between + 0.009 ‰ and + 0.115 ‰; Millet et al. 2016;Kommescher et al. 2020). The higher average δ 49 Ti 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 fO 2 (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 δ 49 Ti 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% Ti 3+ relative to their bulk Ti contents (Krawczynski et al. 2009;Leitzke et al. 2018;Simon and Sutton 2018). A decoupling of Ti 3+ from Ti 4+ 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 δ 56 Fe of MORB samples compared to their mantle sources 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 Ti 3+ 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] Ti 4+ 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 fO 2. We have carried out seven experiments using compositions from the CaO-MgO-Al 2 O 3 -SiO 2 + TiO 2 (CMAS + TiO 2 ) 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 Ti 3+ /(∑Ti) of different phases in our experiments and the Ti isotope fractionation resulting from two phase equilibria (∆ 49 Ti A-B ), and subsequently compared with ab initio modelling, as well as Ti isotope data from natural lunar sample suites.

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-Al 2 O 3 -SiO 2 (CMAS) system, to which ca. 20 wt.% TiO 2 were added (following Leitzke et al. 2016). To produce the starting material, dry oxide powders were ground together with acetone in an agate mortar (CaCO 3 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 fO 2 on Ti stable isotope fractionation from potential interactions between Fe and Ti, our starting composition was FeO-free.
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. (2016Leitzke et al. ( , 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 (Pt 70 Rh 30 -Pt 94 Rh 6 ). Quenching of the samples was performed in air, since Pt wire was used for all experiments. Oxygen fugacity was set by different CO-CO 2 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 fO 2 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 shortly before each column chemistry to limit dissociation of H 2 O 2 . 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 HNO 3 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 47 Ti-49 Ti 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 HNO 3 > > 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.% H 2 O 2 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.% H 2 O 2 onto the cation resin AG50W-X8. Therefore, with 1 M HCl-2 vol.% H 2 O 2 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.% H 2 O 2 resulted in a prolonged Ti elution compared to using 1.75 M HCl-2 vol.% H 2 O 2 , 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): 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.% H 2 O 2 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.% H 2 O 2 ) from W and Mo (6 M HNO 3 -0.2 M HF-2 vol.% H 2 O 2 ) 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.% H 2 O 2 , 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 H 2 O 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.% H 2 O 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 HNO 3 -0.2 M HF solution were mixed with one part 30% H 2 O 2 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 HNO 3 -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 47 Ti-49 Ti double spike was used for our analyses. The final concentration of the 49/47 Ti 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 46 Ti and 48 Ti, 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 Fig . 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 H 2 O 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 and , 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 standardsample 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 49 Ti, 48 Ti, 47 Ti signal intensities of 2-3 × 10 -11 A (2-3 V) using 10 11 amplifiers. Background levels in a pure 0.3 M HNO 3 -0.0014 M HF solution were around 1-4 × 10 −15 A (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): 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 δ 49 Ti (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 δ 49 Ti. 95% confidence interval is calculated including the student's t test. All spike:sample ratios from this study are displayed in Supplementary Table 3.

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 TiO 2 content of the melt and is the result of decreased melt polymerization due to the addition of TiO 2 to the melt (Neuville and Mysen 1996;Rai et al. 2019; also seen in Leitzke et al. 2016Leitzke et al. , 2017. 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 Mg 2 Si 2 O 6 , whereas armalcolites are almost pure MgTi 2 O 5 (i.e., Karrooite), comparable to Mg-rich lunar armalcolites described in Haggerty (1973 (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 fO 2 , and both phases are isotopically heavier than the bulk composition (Table 2). Furthermore, the δ 49 Ti of all phases varies with fO 2. Isotopic differences between phases become progressively larger the more reducing conditions become (Fig. 4 a,  ‰ at IW-1), and orthopyroxene (+ 0.033 ± 0.009 ‰ to + 0.247 ± 0.020 ‰ at IW-1) also increase with decreasing fO 2 , which is, at least, partly related to the distribution of Ti in the different phases present in the experiments. However, absolute changes in δ 49 Ti are much larger when orthopyroxene and silicate glass are compared to armalcolite. Therefore, a better measure of the effect that fO 2 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.    (Fig. 4b).
Results show that the ∆ 49 Ti A-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 fO 2 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, ∆ 49 Ti opx-melt also becomes more fractionated at lower fO 2 but to more positive values, reaching a maximum of ca. + 0.04 ‰ at IW-1.

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 δ 49 Ti values. The result was then compared to the δ 49 Ti of our synthetic glass reference material. Mass balance calculations for almost all experiments are within 2 s.d. of the synthetic glass reference material (δ 49 Ti = − 0.010 ± 0.020 ‰; see Supplementary Table 7). The only exception was the experiment at FMQ-0.5, where the bulk δ 49 Ti determined from the mass balance was + 0.040 ‰, which is 0.050 ‰ higher than expected from our synthetic glass reference material. Since δ 49 Ti of orthopyroxene from this experiment is lower than the δ 49 Ti of the glass, it is likely that this orthopyroxene was contaminated by armalcolite driving its apparent δ 49 Ti to lower values and also to erroneous Δ 49 Ti values that are not in line with the redox dependent trends shown in Fig. 4 and Fig. 5. This can be confirmed by the χ 2 values of our thermodynamic fit, where all Δ 49 Ti A-B at FMQ-0.5 associated with orthopyroxene leads to high χ 2 values (> 3) in comparison to other χ 2 values (< 1).
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 Δ 49 Ti values. This indicates that all other

Ti isotope composition of mineral separates
Terrestrial magmatic samples show a large range of δ 49 Ti between − 0.05-+ 2.32 ‰. These values are positively correlated with the SiO 2 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 δ 49 Ti values, from 0.005 to 1.914 ‰, positively correlated with SiO 2 and negatively correlated with MgO sample content. The same study did not report any dependence of δ 49 Ti on either MgO or SiO 2 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. 2018Deng et al. , 2019Johnson 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 δ 49 Ti of low-Ti basalts (+ 0.01 ± 0.047 ‰; Millet et al. 2016;Kommescher et al. 2020) broadly resembles that of the BSE (δ 49 Ti = + 0.005 ± 0.005 ‰, Millet et al. 2016), whereas high-Ti basalts show a wider range of δ 49 Ti (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 (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 δ 49 Ti than coexisting melt in agreement with previous studies (Johnson et al. 2019;He et al. 2020). We note, however, that while the δ 49 Ti values of armalcolite, and to a lesser extent glass, are likely less vulnerable to contamination during handpicking because of their higher TiO 2 contents (ca. 80 wt.% and 15 wt.% TiO 2 , respectively), the δ 49 Ti of orthopyroxene is highly susceptible to crosscontamination because of its low TiO 2 content (ca. 1 wt.%). This is the most likely explanation for some of the lower than expected δ 49 Ti values for orthopyroxene in our dataset (i.e., at FMQ-0.5), as even a slight contamination by armalcolite will shift the δ 49 Ti to lower values. Nevertheless, since orthopyroxene contains only ~ 1 wt.% TiO 2 , 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 Δ 49 Ti A-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 fO 2 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 Ti 3+ is known to be stable in addition to Ti 4+ (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;Sutton 2017, 2018;Leitzke et al. 2018). High-pressure experiments showed that armalcolites near metal saturation (~ IW) can incorporate a significant M 3+ 2 TiO 5 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 M 3+ 2 TiO 5 component in a solid solution. Stanin and Taylor (1980) conducted dynamic crystallization experiments and detected increasing Ti 3+ contents in armalcolite (< 1-15% of the total Ti fraction) with decreasing fO 2 (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 fO 2 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 IVand 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.% Ti 3+ ) at fO 2 relevant to lunar magmatism (Leitzke et al. 2018). These results are consistent with recent XANES measurements carried out by 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 (MgTi 2 O 5 ). The largest fractionation factor (β) was observed for the incorporation of Ti 4+ into the tetrahedral Si site of clinopyroxene, whereas the lowest β value was predicted for both the incorporation of Ti 3+ 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% Ti 3+ relative to total Ti in VI-fold coordination, while on average a little less than half (45%) of its Ti 4+ 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 δ 49 Ti values relative to armalcolite at fO 2 relevant to lunar magmatism (i.e., a positive Δ 49 Ti opx-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 (Δ 49 Ti opx-arm ~ + 0.3 ‰) is very close to what was determined for our experiments carried out IW-1 (Δ 49 Ti opx-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 Ti 3+ 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 fO 2 to favour VI-fold coordination. This may account for the slightly higher Δ 49 Ti opx-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 Δ 49 Ti opx-melt and fO 2 is reminiscent of a similar relationship seen between the partitioning of Ti between pyroxene and melt and fO 2 (Mallmann and O'Neill 2009). In that case the D Ti Opx/melt was shown to increase with decreasing fO 2 due to an increasing proportion of Ti 3+ . It should be noted, however, that ab initio modelling indicates the substitution of Ti 3+ in VI-fold coordination in orthopyroxene , which should result in lighter Ti isotope compositions in orthopyroxene due to the longer Ti 3+ -O bond lengths and lower force constants compared to Ti 4+ -O bonds. This expectation is not confirmed by our experimental results, as Δ 49 Ti arm-opx are larger at lower fO 2 , 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 Ti 4+ 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 Ti 4+ is perhaps pushed from VI-fold into IVfold coordination, because Ti 3+ 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 fO 2 .
Nevertheless, our results confirm that changing fO 2 leads to the development of isotopically resolvable differences of δ 49 Ti 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 fO 2 clearly impacts on the value of Δ 49 Ti A-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 Δ 49 Ti A-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 fO 2 : and, where x is the valence of the reduced Ti redox species, z the number of electrons exchanged between both sides of reaction (2), Δ 49 Ti x+z A-B and Δ 49 Ti x A-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., Ti 3+ and Ti 4+ -the number of electrons exchanged (z) is one, and Eq. (3) can be simplified to: From Eq. (4) it is clear that Δ 49 Ti A-B will depend on fO 2, Δ 49 Ti 4+ A-B , which is known from the most oxidized experiments carried out in air, where all Ti is tetravalent, and Δ 49 Ti 3+ A-B , which represents a case, where all Ti is trivalent, and K'. The Δ 49 Ti A-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 (2) TiO x∕2 + z∕4O 2 = TiO (x+z)∕2 (3) Neill 2007Neill , 2009Leitzke et al. 2017) to fO 2 , the results of which are shown in Table 4 and Fig. 5. 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 (Ti 3+ 2 O 3 ) 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 Δ 49 Ti A-B has a clear dependence on fO 2 , 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 fO 2 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 fO 2 , 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 (fO 2 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 Δ 49 Ti A-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 fO 2 . Millet et al. (2016) parameterized the temperature dependence of Δ 49 Ti oxides-melt for their Agung volcanic samples with a range in SiO 2 from 54-65 wt.%, and obtained: A similar temperature dependence of Δ 49 Ti oxides-melt was determined by Deng et al. (2019) who obtained Δ 49 Ti oxides-melt ~ − 0.1 ‰ at ~ 1500 K and ~ − 0.5 ‰ at ~ 1150 K, on a sample set of Hekla lavas with a wider SiO 2 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 δ 49 Ti and 1/T 2 . Johnson  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 Δ 49 Ti arm-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 (Δ 49 Ti arm-melt of − 0.2‰) compared to ilmenite (Δ 49 Ti ilmenite-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 δ 49 Ti 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 Δ 49 Ti A-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, δ 49 Ti 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, δ 49 Ti of the melt becomes more and more positive until the presence of ilmenite (~ 95% fractional crystallization), where this trend is further accelerated. The high δ 49 Ti 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 Δ 49 Ti arm-melt and Δ 49 Ti opx-melt values at IW-1 (− 0.2 and + 0.05 ‰, respectively) and the Δ 49 Ti for ilmenite (− 0.356‰) from Mandl (2019). The expected relationship between δ 49 Ti 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 Fig. 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 δ 49 Ti of low-Ti basalts are reproduced by 60-75% fractional crystallization of Ti-oxides with previous mineral separate Ti stable isotope measurements (Johnson et al. 2019;Mandl 2019;He et al. 2020). Δ 49 Ti A-B shows increasing fractionation with decreasing fO 2 (~ IW-1). The relationship between Δ 49 Ti A-B and fO 2 appears to be directly related to the increasing abundance of Ti 3+ 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 Δ 49 Ti A-B shows a smaller extent of redox-dependent fractionation, which is possibly due to the fact that orthopyroxene contains only minor amounts of TiO 2 (~ 1 wt.%). Nevertheless, the Δ 49 Ti opx-melt is reminiscent of the redox-dependent D Ti Opx/melt by Mallmann and O'Neill (2009). The fractionation Δ 49 Ti A-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.