Early Moon formation inferred from Hafnium-Tungsten systematics

Abstract

The date of the Moon-forming impact places an important constraint on Earth’s origin. Lunar age estimates range from about 30 Myr to 200 Myr after solar system formation. Central to this age debate is the greater abundance of ¹⁸²W inferred for the silicate Moon than for the bulk silicate Earth. This compositional difference has been explained as a vestige of less late accretion to the Moon than the Earth, following core formation. Here we present high-precision trace element composition data from inductively coupled plasma mass spectrometry for a wide range of lunar samples. Our measurements show that the Hf/W ratio of the silicate Moon is higher than that of the bulk silicate Earth. By combining these data with experimentally derived partition coefficients, we find that the ¹⁸²W excess in lunar samples can be explained by the decay of now extinct ¹⁸²Hf to ¹⁸²W. ¹⁸²Hf was only extant for the first 60 Myr after solar system formation. We conclude that the Moon formed early, approximately 50 Myr after the solar system, and that the excess ¹⁸²W of the silicate Moon is unrelated to late accretion.

The Moon likely formed in the aftermath of a giant impact between the proto-Earth and an erstwhile planetary body¹. Extreme chemical and isotopic similarities between the Earth and the Moon² have led to a growing consensus that Earth and Moon share a common chemical ancestry. This similarity in chemical signatures implies either that the bulk silicate Earth (BSE) is the major source of Moon-forming impact debris^3–6 or that proto-Earth and the impactor had virtually identical chemical compositions⁶. Beyond chemical constraints on the Moon forming giant impact event, there is an ongoing controversy regarding its exact timing, with some researchers arguing that the Moon formed early (i.e., 30 to 100 Myrs after Solar System formation – SSF)^7–12, whereas others contend the Moon formed up to 200 Myrs after SSF^13–17. Constraining lunar formation requires knowing the crystallization age of the lunar magma ocean (LMO), a product of the Moon’s high-energy impact formation. Central to the lunar age controversy are small excesses in the ¹⁸²W abundance in lunar basalts when compared to the Earth, which average a value of 25 μ¹⁸²W units^18–20. Assuming that the excess ¹⁸²W in lunar samples stems from the in situ decay of short-lived ¹⁸²Hf to ¹⁸²W (8.9 Myrs half-life²¹) would place lunar formation between 30 and 60 Myrs after SSF when sufficient ¹⁸²Hf was still present. However, this interpretation is at odds with the apparent observation that BSE and the silicate Moon have virtually overlapping ratios of Hf (mother) to W (daughter), with Hf/W ratios of 24.9 and 25.8, respectively^22,23. These apparently identical parent to daughter ratios imply that their different μ¹⁸²W cannot be related to the in situ decay of ¹⁸²Hf. Hence, an alternate explanation invoked that Earth and Moon received a disproportionate contribution of late accretion components with a chondritic Hf/W ratio (~1) and lower ¹⁸²W than BSE¹⁹. Because the Moon is less massive than Earth, it would have received a commensurately smaller contribution from late accretion, and has thus retained a higher μ¹⁸²W than BSE^18–20. The Moon therefore constitutes a suitable highly-siderophile element (HSE) poor end-member in such late accretion models and a possible analogue to a proto-Earth that was essentially devoid of late accretion components²⁰. In addition to this view, the apparent decrease in ¹⁸²W values measured in terrestrial rocks over geologic time has been explained by the protracted mixing of late veneer material into the terrestrial mantle that lowered μ¹⁸²W to its present-day value^12,20,24,25. The presence of negative ¹⁸²W anomalies in Archaean samples, however, preclude the origin of ¹⁸²W excess entirely from late accretion²⁶. Often, the ¹⁸²W anomalies that have been found are coupled with ¹⁴²Nd anomalies, which is a decay product of ¹⁴⁶Sm, both lithophile elements^24,26–29, making it likely that ¹⁸²W excesses are the result of early silicate differentiation events.

Any accurate interpretation of lunar ¹⁸²W data relies on an accurate knowledge of the Hf/W ratio value in lunar mantle reservoirs and by inference of the silicate Moon. Unfortunately, lunar Hf-W systematics are poorly constrained, as data of sufficient precision are scarce. This also extends to other highly incompatible elements (e.g., HFSE, U and Th) that are commonly used as proxies for W behaviour during dry terrestrial mantle melting²³. In previous lunar studies³³, W was treated as a perfectly incompatible element (i.e., having a similar behaviour as U or Th) during lunar differentiation. This treatment might be incorrect, as lunar mantle melting occurs under more reducing conditions than in the terrestrial mantle, implying that W may behave less incompatibly than elements like U and Th^30–32. In fact, previous observations show that ratios of W with U or Th appear to be variable in lunar samples, which suggests that W behaves differently to highly incompatible elements like U or Th during lunar magmatism³³, in agreement with recent experimental studies^30–32.

Apollo sample results

To provide robust constraints on the Hf/W ratio value of the silicate Moon, we performed high-precision concentration measurements of W, Th, U, and other high field strength elements (HFSE) by isotope-dilution on a representative sample suite covering most relevant lithological units on the lunar nearside. Our samples include low- and high-Ti basalts, ferroan-anorthosites (FAN), and KREEP-rich rocks. As shown in Figure 1, these groups of samples are compositionally distinct, as expected from radiogenic isotope evidence and geochemical modelling³⁴. Low-Ti mare basalts display a narrow range in U/W and Hf/W ratios between 1.5 and 2.5 and between 30 and 50, respectively. In contrast, high-Ti basalts have Hf/W ratio as high as 150, and slightly more fractionated U/W, with values between 0.5 and 2.2. Finally, the KREEP-rich rocks and FAN samples exhibit the lowest Hf/W range of the studied sample suite, between ca. 5 (FAN) and 23 (KREEP-rich), while their U/W shows the largest range amongst all samples, with values approaching zero for FAN and as high as 3.5 for the KREEP-rich rocks.

Figure 1.

New U/W vs. Hf/W data measured in lunar samples compared to crystallization and melting models for the LMO³⁴. Errors are less than symbol sizes. Measured lunar highland breccia compositions straddle mixing lines between a KREEP-enriched end-member³⁰ and FAN compositions as determined in this study. Contamination with W-rich meteoritic components produces virtually identical trajectories and raises absolute W content. The high-Ti mare basalt source mineral assemblage is defined by a mixture of LMO cumulates matching Apollo 17 mare basalt Hf and Nd isotope systematics¹²,²⁷,³⁰–³²,³⁴. Note the overall excess of Hf/W in lunar basalts compared to recent BSE estimates²³.

Lunar source modelling

Several key observations can be derived from our high precision W-U-Th-HFSE data. For example, when combined, the FAN and KREEP-rich rocks form a clear linear array in Hf/W ratio vs. U/W space (Fig. 1). This array can directly be linked to early lunar crust formation, i.e., likely the result of mixing between a FAN end-member that has an exceedingly low Hf/W and U/W, and a KREEP-like component having elevated U/W and a Hf/W of around 20 (i.e., lower than both bulk silicate Moon and Earth’s mantle). Interestingly, our results for these KREEP-rich samples corroborate previously modelled U/W and Hf/W values for KREEP using a fO₂-sensitive set of partition coefficients³⁰, which predicted that KREEP has an elevated U/W and a lower Hf/W ratio value than the bulk silicate Moon depending on fO₂. Our data thus show that the LMO crystallization model³⁵, as well as the mineral/melt partitioning data^24,25 used here, are sufficiently robust for mass balancing these elements.

Our new results for lunar mare basalts have the best potential to constrain the Hf/W ratio of the silicate Moon. In defining which lunar mantle reservoirs of LMO cumulates were involved in the genesis of mare basalts, radiogenic Hf-Nd isotope data are the most powerful proxies to constrain their source mineral assemblages³⁴. These source mineral assemblages allow us to model the geochemical relation between basalt and mantle compositions for trace elements of interest. For example, Hf-Nd isotope data can clearly identify late-crystallizing mare basalt sources comprising Ti-rich oxide phases and clinopyroxene, a characteristic that is absent from low-Ti mare basalt source regions³⁴. Even at the low fO₂ of the lunar mantle, such oxide phases and clinopyroxene preferentially incorporate Hf over W and U^31,36. Moreover, the mantle source of the Apollo 17 high-Ti mare basalts is the most likely lunar mantle source to contain residual metal during partial melting, owing to its reduced nature^30,31. Residual metal in lunar mantle sources would undoubtedly retain W and not Hf, and thus generate higher Hf/W ratio in co-existing mare basalts. When modelling high-Ti mare basalts with small fractions of residual metal, the high-Ti samples that exhibit the highest Hf/W ratio in our sample suite are perfectly reproduced (see melting curves shown in red in Figure 1). The extreme Hf/W ratio displayed by Apollo 17 high-Ti mare basalts, and their co-variation with U/W (Figure 1), therefore directly reflect the combined effects of residual Ti-rich oxides, pyroxene, and metal in the mantle sources of Apollo 17 high-Ti basalts. An unfortunate consequence of this feature is that any inferred U-W-Hf pattern strongly depends on the degree of partial melting that is not well constrained for Apollo 17 basalts. Thus, Apollo 17 high-Ti mare basalts cannot be reliably used to infer the Hf/W ratio of the bulk silicate Moon, as done previously¹⁸.

In contrast to the sample types above, the sources of low-Ti mare basalts are straightforward to model, as these are not overprinted by KREEP components and are essentially devoid of both Ti-rich oxides and metal³⁴ that may fractionate W from U, Th, or HFSE. . Moreover, low-Ti basalts are thought to result from higher-degrees of partial melting compared to high-Ti basalts^37–40, and the U/W and Hf/W ratio measured in these basalts should be virtually identical to those in their respective sources. Interestingly, there are clearly resolvable differences between the different groups of low-Ti basalt samples (Figure 1). This heterogeneity in Hf/W ratio and U/W values in distinct low-Ti mantle sources is in perfect agreement with the isotopic heterogeneity documented by previously published Hf-Nd isotope data³⁴. Moreover, these variations in Hf/W ratio and U/W observed in our lunar samples are consistent with previous experimental studies that predict that W is less incompatible than Hf during LMO crystallization and partial melting of lunar mantle cumulates^30,31.

The mafic cumulates that constitute the mantle sources of low-Ti basalts are expected to preferentially retain W over Hf and U during LMO crystallization at reducing conditions (crystal/silicate melt partitioning values shown in supplementary materials). Therefore, the LMO cumulates, and by inference, the measured Hf/W ratio of low-Ti lunar mantle sources (30.2 to 48.7) record minimum estimates of the Hf/W ratio in the bulk LMO as well as of the silicate Moon. Altogether, our data therefore show that the Hf/W ratio of the silicate Moon must lie between 30 and 50, clearly higher than the value estimated for the BSE (25.8 ± 2.6)²³. As the addition of late veneer material would lower the lunar Hf/W ratio, the minimum estimate of the Hf/W ratio remains a robust one, being still resolvably higher than the Hf/W ratio of the BSE. In summary, low-Ti mare basalts allow the most reliable Hf/W ratio estimates in the lunar mantle, and the Hf/W ratio of the lunar mantle can be clearly shown to be resolvably higher than that of Earth’s mantle.

Lunar formation scenarios

Figure 2 illustrates three scenarios that can explain the higher Hf/W in the lunar mantle: A first, traditional scenario (Fig. 2a) explains the different Hf/W ratios by variable proportions of added late veneer. It has been suggested by several studies^18–20 that the Moon received a considerably lower proportion of late veneer than the BSE. The lower μ¹⁸²W and Hf/W ratio of the BSE are then explained by the addition of a higher amount of unradiogenic W through late accretion to the Earth than to the Moon. In a second scenario (Fig. 2b), the Moon forming event could have taken place amidst ongoing terrestrial core formation, when ¹⁸²Hf was still present. If the Moon formed that early, core formation has certainly been taking place at more reducing conditions than during its final stages^40,41. Under such more reducing conditions, the Hf/W ratio of BSE at the time of the giant impact would have been higher than at present, because W would have been more efficiently extracted into the growing core⁴⁰. This model obviates the need for late accretion to explain the lunar excess in μ¹⁸²W, because the Moon preserved a higher Hf/W ratio than the silicate Earth, leading to less radiogenic μ¹⁸²W in the BSE and more radiogenic μ¹⁸²W in the silicate Moon. In the third scenario (Fig. 2c), core formation in the Moon could have scavenged sufficient W into the lunar core to elevate the Hf/W ratio of BSM to its higher present-day value. This process has been invoked previously to explain the depletion of Cr and siderophile elements in the lunar mantle^42,43, with additional losses through evaporation⁴⁴. If the lunar core, and by inference the Moon, formed while ¹⁸²Hf was extant, the silicate Moon would inevitably develop ¹⁸²W higher than the present day terrestrial value. Collectively, the two last scenarios imply that late accretion was either of no consequence to the W budget and isotope composition of the silicate Moon, or that it was contemporaneous to the Moon forming event.

Figure 2.

Scenarios accounting for the higher Hf/W of the BSM. (a) A late veneer of chondritic material (Hf/W ratio~1) lowers BSE Hf/W from ca. 30-50 to 25.6 after ¹⁸²Hf extinction, while the Moon preserves its original Hf/W. (b) The Moon forming event takes place while Earth’s core is still forming and ¹⁸²Hf is extant. Increasingly oxidised conditions later lower BSE Hf/W. (c) Formation of a small lunar core scavenged W from the BSM, increasing its Hf/W. In models (b) and (c), formation of the Moon must have occurred during the lifetime of ¹⁸²Hf, i.e., within 60 Myrs after solar system formation.

A simple strategy to further evaluate the three models described above is to test the simplest hypothesis to explain why the Hf/W ratio of the silicate Moon is higher than that of BSE, i.e., lunar core formation (model III). If lunar core formation will raise the Hf/W ratio of the silicate Moon to values as high as those shown here (i.e., 30-50), then the first two hypotheses are potentially superfluous. While there is plenty of evidence that the Moon has a small core, its exact composition and formation conditions are not well understood. However, the mass of the lunar core is much better constrained. Based on a recent re-evaluation of lunar seismic data^45–47 the lunar core comprises 1-3 % of the total mass of the Moon. The question remains whether such a small core could have scavenged sufficient W to shift the Hf/W ratio of the silicate Moon to values as high as reported here. A simple mass balance⁴⁸ can be made to model the Hf/W ratio of the silicate Moon after lunar core formation. This model assumes that Hf is perfectly lithophile, and that its abundance in the bulk Moon and the BSE are identical. The Hf-W contents of the modelled silicate Moon can be calculated assuming closed-system core formation, over a range of realistic $D_W^{core/mantle}$ (15-100), initial Hf/W ratio of BSE (25.8), and different core mass fractions (1-3 %). We also include a historical, lower estimate for the BSE⁴⁹. The results of the modelling are depicted in Figure 3, showing that that lunar core formation can indeed reproduce the range of Hf/W ratio of the lunar mantle if one assumes $D_W^{core/mantle}$ higher than 60, and a core mass fraction of at least 1.5%, i.e., in line with recent estimates^45–47. A more massive core (3% mass fraction), would permit smaller $D_W^{core/mantle}$ (ca. 30) to reproduce the Hf/W ratio range of 30-50 reported here. It is thus clear from the results of this model that lunar core formation can viably generate the Hf/W ratio of BSM using realistic values of $D_W^{core/mantle}$ and core mass fractions⁴⁸.

Figure 3.

The effect of lunar core formation on the Hf/W ratio of the silicate Moon. The models assume different metal–silicate partition coefficients for W ($D_W^{core/mantle}$ between 15–100), and different lunar core mass fractions (1.5–3%). The initial Hf/W of the Bulk Moon is the same as that of the Bulk Silicate Earth. The lunar Hf/W ratio value is reached with $D_W^{core/mantle}$ values between 30 and 60, and core mass fractions between 1 to 3% of the mass of the Moon. The two estimates of the BSE Hf/W encompass a historical value (ref. ⁴⁹) and a revised value based on high precision measurements of Ta and W (ref. ²³)

Implications for dating lunar formation

While the presence of a lunar core helps settle the ¹⁸²W excess, there remains evidence from other radiometric dating systems for a young Moon. Evidence from direct measurements such as zircons and FAN ages can provide a younger age, but may be long offset from the parent body age^13–15,24. Amongst these, our suggested age concurs with the oldest age found via U-Pb, at 4.51 Ga⁷. Other methods, such as Sm-Nd model ages, have indicated a young age for lunar crust formation, varying from 4.35 to 4.45 Ga based on lunar basalts¹⁵ and KREEP^13,17. However, the age implied by these samples is for lunar crust formation, rather than for lunar formation. Importantly, the Sm-Nd model ages can represent post-formation mantle processes which may have reset the different isotope systems.

In conclusion, we prefer a simple model for the lunar Hf-W patterns, wherein the difference in Hf/W ratio between the silicate Moon and the silicate Earth is the result of lunar core formation. Figure 4 illustrates variations of lunar ¹⁸²W systematics as a function of Hf/W ratio and age. The range of Hf/W ratio measured in our study, combined with recent estimates for the lunar μ¹⁸²W requires lunar differentiation to have occurred between 40.5 and ca. 60 Myrs after SSF. We can thus unambiguously relate the ¹⁸²W excess in lunar samples to in-situ decay of ¹⁸²Hf to ¹⁸²W. The combination of a robust set of experimental partitioning data with high precision HFSE analysis is thus in favour of an “old Moon,” while simultaneously diminishing the role of late accretion in creating the μ¹⁸²W signature of the Moon. In addition to helping settle the ongoing strife between “old” and “new” Moon scenarios, this method can also be used to unravel formation timescales of other planetary bodies, being of key importance to future sample return missions.

Figure 4.

Tungsten isotope composition (μ¹⁸²W) of the silicate Moon as a function of the lunar Hf/W ratio and formation age. Low-Ti mare basalts proxy for the range of the BSM Hf/W. The intersection with the mean reported BSM pre-exposure μ¹⁸²W provides the age interval at which the Moon must have formed to explain its μ¹⁸²W difference to Earth by in-situ decay of ¹⁸²Hf. The aggregated μ¹⁸²W is from ref. 18. The starting age of the curves (37 Myrs) is taken from ref. 23, as core formation ages from protracted core formation or incomplete equilibration models yield a younger age than this.

Methods

1. Sample selection

Samples were provided by the Curation and Analysis Planning Team for Extraterrestrial Materials (CAPTEM), and selected to represent the major lithological units of the Moon as sampled by the NASA Apollo missions. Characterizing their chemical composition, our particular focus lay on the quantification of any inherent U/W, Th/W, and Hf/W variability as inferred from the few previous studies available. Some sample duplicity with previous studies allows for an additional quality assessment. In total, lunar samples from Apollo 11 (3), Apollo 12 (6), Apollo 14 (3), Apollo 15 (6), Apollo 16 (4), and Apollo 17 (4) were analyzed. Of these, 7 were Apollo 11 or Apollo 17 high-Ti mare basalts and soils, 14 were low-Ti mare basalts from Apollo 12 and 15, 2 Apollo 16 ferroan-anorthosites (FAN), as well as 7 KREEP-rich samples including a meteorite and KREEP-rich breccias and KREEP-basalts from the Apollo 14, 16, and 17 missions.

2. Sample Preparation

To obtain high precision data, we measured all elements of interest by isotope dilution and added several isotope tracers to ca. 100 mg (250 mg for anorthosites) of each sample prior to digestion. The mixed isotope tracers included ²²⁹Th-²³³U-²³⁶U and ¹⁸³W-¹⁸⁰Ta-¹⁸⁰Hf-¹⁷⁶Lu-⁹⁴Zr mixed solutions. Samples were digested in 3 ml of double distilled HF and 3 ml of distilled HNO₃ for 24 hours at 120 °C. Prior to drydown, 0.5 ml of perchloric acid were added to ensure sample-spike equilibrium for Th. Samples were re-dissolved with concentrated HNO₃ and trace HF to ensure re-dissolution of HFSE. These sample solutions were subsequently dried down again, and re-dissolved in 6 ml 6 M HCl- 0.06 M HF to ensure full sample-spike equilibrium for HFSE. These samples were then aliquoted, with 10% of the solution being used for conventional trace element analysis, 20% for W isotope dilution measurements, and 70% for high field strength and U-Th element analysis. For a first batch of samples, an additional aliquot of 10% for U-Th was taken. The anorthosite samples were aliquoted with 85% to a combined HFSE, W, and U-Th aliquot, and 15% for trace element analysis.

The trace element aliquot was dried down, dissolved in concentrated HNO₃, and then dried down again. This residue was subsequently dissolved in 1 ml concentrated HNO₃, with 4 ml MQ H₂O added, and then diluted with MQ H₂O to 50 ml. Conventional trace elements on these aliquots were performed at the Quadrupole ICP-MS laboratory at the Institut für Geowissenschaften at CAU zu Kiel using the procedure of ref. 50.

Our protocol for separating individual HFSE and U-Th cuts from lunar samples is a modified protocol based on refs ^22,51,52. During the protocol, individual cuts containing a matrix, HRRE, Zr-Nb, Ta, Hf and U-Th were separated from the HFSE aliquot. Tungsten was separated from the W isotope dilution step via a separate set of anion exchange resin microcolumns (after ref. 52, Table 4).

In our HFSE protocol, the sample aliquots were dissolved in 3N HCl and loaded onto a Ln Spec resin column. Matrix and LREE were eluted in 3M HCl. An HREE fraction containing most Lu was eluted with 6N HCl, followed by elution of an HFSE cut containing Ti-Zr-Nb-Hf-Ta-U-Th in 2N HF. A quantitative Zr/Nb aliquot was taken from this fraction (see ref. 51). The remaining HFSE cut was loaded onto a Bio-Rad column containing AG 1 x8 100-200 mesh resin. The U-Th fraction was collected in 2N HF, and a Ti-Zr-Hf fraction was collected in 6N HNO₃/0.2N HF. A clean Ta fraction was subsequently collected in 6N HNO₃/0.2N HF/1%H₂O₂. The Ti-Zr-Hf fraction was dried down overnight and loaded onto the stage I Ln Spec resin column in 3 N HCl. After cleanup in 6N HCl and MQ H₂O, Ti was eluted using a 1N HNO₃ 2% - H₂O₂ mixture (ref. ⁵³), and some Zr in 6N HCl -0.06N HF. Hafnium was finally eluted in 2N HF.

Separation of U-Th was performed in two ways, following a modified protocol of (54). For the first batch of samples, a full aliquot was used, whereas for the other batches the U-Th fraction from the 2N HF elution step above was taken. After drydown, the U and Th bearing cuts were dissolved in 1.5N HNO₃, before being loaded onto columns containing TRU-Spec resin (200-400 mesh). Modifying the chemistry of (54), all major elements were initially eluted in 1.5N HNO₃. After removal of rare earth elements in HC3N HCl, Th was subsequently eluted in 0.2N HCl. Finally, U was eluted in 0.1N HCl/0.3N HF.

Given the low concentrations of the elements of interest in anorthosites, we performed a different separation protocol for these samples. Ca. 70% of the 85% HFSE aliquots of anorthosites were loaded on anion exchange resin in 1N HCl/0.5N HF solution. The eluted matrix cut and an additional fraction rinsed in 0.5N HCl/0.5NHF contained most of the Rb-Sr, Sm-Nd and U-Th. A fraction containing Ti/Zr/Hf was collected in 6NHCl/0.06NHF, from which Hf was further purified using Ln Spec resin (see above). A W fraction was subsequently eluted in 6N HNO₃/0.2N HF, followed by Ta elution in 6 N HNO₃ / 0.2N HF / 1% H₂O₂. After drydown, the Ta cut was loaded on the same anion resin column again for cleanup, and the Ta was again eluted in 6N HNO₃/0.2N HF / 1% H₂O₂ after cleanup in 6N HNO₃/0.2N HF. The remaining 15% of the anorthosite HFSE aliquots were loaded on Ln Spec resin in 3N HCl. Two fractions containing HREE and Zr/Nb werde eluted from the column in 6N HCl and 2N HF as described above. The advantage of this approach is that a larger W fraction is collected, thus avoiding low sample-to-blank ratios during W ID measurements.

3. Analytical protocols

All isotope dilution measurement were performed using the Neptune MC-ICP-MS at Cologne. Detailed descriptions of the analytical protocols for HFSE measurements, analytical uncertainties and further references are given in (22). For ²²⁹Th/²³²Th measurements, we used an SEM ion counter equipped with an RPQ system on mass ²²⁹Th. The Th cuts were doped with the NBL CRM 112A U standard for mass bias correction, and the ion counter was calibrated with concentration-matched IRM-035 and IRM 036 standards for ion counter yield corrections. For U measurements, mass bias was corrected using the measured ²³³U/²³⁶U of the spiked U cuts and the certified ²³³U/²³⁶U from (55) for the doped IRM-3636 double spike that was used for preparation of the mixed U-Th tracer. Our external precision and accuracy for elemental ratios determined by isotope dilution involving U and Th typically is better than ±1% for both U/W and Th/W (2σ r.s.d.). Typical blanks during the course of the measurements were below 50 pg for W, 66 pg for U, 32 pg for Th, and 30 pg for Hf. These blanks proved negligible, with total blank-uncertainty-including propagated errors of less than ±1%.

4. Results (and modeling constraints)

Measured HFSE and HFSE/U-Th ratios are distinct for different sample groups and mineralogy, with only small variations in U/W and Hf/W between samples from the same lithology. High-Ti basalts are particularly heterogeneous, with samples from the three measured localities showing distinct Hf/W and U/W values. Apollo 17 High-Ti breccias both have similar values, with Hf/W ranging from 31 to 35, at a constant U/W of 1.9. This is distinct from Apollo 17 high-Ti mare basalts, where U/W correlates positively with Hf/W. The Apollo 11 high-Ti mare basalts both have Hf/W of 42 and U/W of 2.2. Unique amongst all samples are the Apollo 17 high-Ti mare basalts, which bear exceptionally high Hf/W ratios, between 120 and 150. Likewise, the low-Ti basalts plot as particularly distinctive groups according to mission site. The Apollo 12 ilmenite basalts have similar U/W to the Apollo 12 olivine and pigeonite basalts, of 2.07 and 2.25, respectively. However, they are distinct in their Hf/W, with both pigeonite-bearing basalts near 30 and ilmenite-basalts of 43-48. The Apollo 15 quartz-normative and olivine-normative low-Ti basalts have different U/W, ranging from an average of 2.45 in the former to 1.75 in the latter. The Hf/W of the two low-Ti basalt groups also vary from 45 (quartz-normative) to 30 (olivine normative). Whereas the olivine-normative low-Ti basalts of both Apollo 15 and Apollo 12 have identical Hf/W, their U/W differ significantly, from amongst the lowest values (1.63) measured to the highest (2.53). The KREEP-rich samples have a very narrow range in Hf/W of ca. 20. The U/W of KREEP samples has the largest spread, with most samples ranging from 1.63 to 2.51, and minimum and maximum values of 0.54 and 3.38, respectively.

5. Lunar Magma Ocean fractionation and partial melting modelling

The Lunar Magma Ocean (LMO^56–58) crystallization model utilized in this study is based on the cumulate crystallization sequence of (35). We have previously shown³⁰ that the results of this and other LMO crystallization models (e.g., refs ^59,60) are in good agreement. The same starting composition used in (30) after (22) was chosen to evaluate the general HFSE-W-U-Th systematics of a crystalizing LMO. For W, an additional mass balance between the estimate of its content in the bulk silicate Moon after core formation was done following (43), considering different core mass fractions (1-3% of the total mass of the Moon). The LMO crystallization model is divided into four main steps: (i) equilibrium crystallization of olivine and orthopyroxene (until 78% solidification), (ii) fractional crystallization of plagioclase, olivine, and pigeonite (until 86% solidification), (iii) fractional crystallization of clinopyroxene, plagioclase, and pigeonite (until 95% solidification), and (iv) crystallization of pigeonite, plagioclase, clinopyroxene, and ilmenite (until 99.5% solidification). The remaining 0.5% after LMO crystallization is a liquid residue strongly enriched in incompatible trace elements and called urKREEP, which reflects its characteristic enrichments in K, REE, and P^61,62. The LMO crystallization model assumes that various amounts of trapped instantaneous residual liquid (TIRL, i.e. coexisting melt at the time of crystallization) are part of lunar mantle cumulates in order to take into account major element variation observed in lunar mare basalts³⁵. The model also considers that at the moment plagioclase appears on the liquidus, 98% of the crystallizing plagioclase floated to the uppermost portion of the LMO to form the lunar crust with only 2% being entrained in the cumulates, in order to account for the Al content of lunar basaltic samples³⁵. Following LMO crystallization, the layered lunar mantle underwent a density driven mantle overturn which mixed the different cumulate layers, producing new hybrid mantle domains that served as the source for partial melts that crystallized to form the lunar mare basalts⁶³. To understand the implications of these processes for the trace element inventory of mare basalts thus involved aggregate modal fractional melting models of hybrid lunar mantle domains. The mixing proportions of different primary LMO cumulates in the hybridized lunar mantle sources, their mineral assemblages, as well as the amount of trapped instantaneous residual liquid (TIRL) were constrained from the Lu–Hf and Sm–Nd isotope patterns of lunar basalts³⁴. We have also assumed that a small proportion of residual metal may be required at the lunar mantle source to reproduce the values observed for high-Ti basalts, which is in agreement with the extremely reduced nature of the lunar mantle and the depletion in Ni observed for lunar olivine^64,65. A lunar magma ocean equilibrated at ca. IW −1 was assumed throughout the entire modelling, in agreement with the current estimates of oxygen fugacity for the lunar mantle^65,66. Trace element crystal/silicate melt partition coefficients for different pyroxenes, plagioclase, and olivine (see supplemental materials) were selected taking into account the variation of TiO₂ exhibited by lunar mare basalts and the changing composition of the LMO during crystallization (see ref. 32) as well as the effect of fO₂ on the partitioning behaviour of W (see ref. 30,31). Ilmenite/silicate melt trace element partition coefficients are an average of the high-Ti experiments listed in (36). Liquid metal/silicate melt W partition coefficients are from Righter et al. (2010) and (43), which cover a wide range of values (15-100).