Introduction

The Earth–Moon system has been hypothesized to originate from a giant impact early in the solar system history1,2. New and traditional theories debate whether the Moon-forming giant impact carried sufficiently high energy that vaporized the Mars-sized impactor (Theia) and proto-Earth to homogenize Earth–Moon chemical and isotopic compositions (e.g. ref. 3), or whether it was less energetic and led to incomplete mixing of the impactors (e.g. refs. 1,2,4,5), that can permit chemical and isotopic heterogeneities of the Earth–Moon system.

These hypotheses are testable with geochemical observations. For example, for mass-independent isotopic compositions, the high-energy giant impact scenario (Synestia)3 predicts an Earth–Moon isotopic similarity [recently discovered for ∆17O6, ε50Ti7, and ε54Cr8,9] due to extensive isotope equilibration within the Moon-forming disk in a well-mixed silicate vapor. In contrast, the traditional giant-impact scenarios allow for considerable Earth–Moon isotopic differences considering the distinct mass-independent isotopic compositions of the impactors (Theia and the Proto-Earth), hinted by the documented isotopic variability among present Solar System objects7,10. For mass-dependent isotopic compositions of lithophile elements (e.g., δ26/24Mg, δ44/40Ca, δ56/54Fe), the differentiated impactors’ mantle layers are expected to be isotopically fractionated caused by planetary magmatic differentiation. As a result, the complete isotopic mixing expected in the Synestia hypothesis still requires indistinguishable mass-dependent isotopic compositions of the bulk silicate Earth (BSE) and Moon (BSM)3. However, the traditional giant-impact models can give rise to marked mass-dependent isotopic differences between the BSE and BSM, considering that the BSM formed by sampling a minimal mass fraction (~2%) from the larger, isotopically heterogenous and insufficiently mixed impactors’ silicate mantle.

Recent studies have shown consistent δ26/24Mg and δ56/54Fe values of the BSE and BSM, supporting an isotope equilibration of the Earth–Moon system before the terrestrial and lunar differentiation11,12,13,14,15. Attempts have been made to infer the mass-dependent Ca isotopic compositions (δ44/40Ca) of the BSM, suggested to be similar to the BSE16. However, reliable quantifications remain lacking due to an underrepresented sample pool of analysis (data from lunar meteorites only) and insufficient constraints provided by a preliminary binary mixing model16. The model treats the δ44/40Ca values of the two mixing endmembers (the lunar mantle and crust) as constants without associated uncertainties16, which does not fully account for the complicated lunar isotopic heterogeneity and hence limits the reliability of the conclusions. Since Ca is one of the most refractory major elements, whose mass-dependent isotopic fractionation is not affected by planetary accretion, core formation, or magmatic degassing, the BSM and BSE δ44/40Ca signatures preserve those of their building materials and give direct evidence for the Moon-forming mechanism. Therefore, the BSM δ44/40Ca composition necessitates a more robust quantitative resolution to help clarify the origin of the primordial Earth–Moon system.

Following the Moon-forming giant impact and accretion, the lunar differentiation started with a hypothesized lunar magma ocean (LMO) of molten silicate rock, which continued to solidify as the Moon cooled17,18. δ26/24Mg and δ56/54Fe variations throughout the LMO crystallization have been observed and demonstrated as the result of lunar igneous processes11,15. In comparison, δ44/40Ca evolution during the LMO crystallization awaits new critical investigations called for by recent testing of mineral-melt Ca-isotope fractionation factors, particularly for plagioclase19. Importantly, when multiple stable isotopic systematics are used in conjunction, they may yield higher confidence in the significance of each record and serve as key differentiation indexes to determine the evolution stage of LMO products. The magmatic context provided by stable isotopes can then be paired with the radiometric dating of lunar samples to constrain the relative and absolute timeline of the lunar differentiation.

To resolve the BSM δ44/40Ca composition and trace the progression of the LMO crystallization, we performed high-precision Ca-isotope measurements for 13 lunar rocks and minerals (Supplementary Table 1) returned from the Apollo missions. These measurements include the first Ca-isotope analyses for lunar olivine and ferroan anorthosite (FAN) samples considered as primary floatation cumulates from the LMO.

Results and discussion

Ca-isotope composition of the Moon and implications for the Moon’s high-energy giant-impact origin

Our δ44/40Ca measurements (relative to standard SRM915a) for lunar basalts show consistency with recently reported values analyzed using a collision-cell MC-ICP-MS method20 (δ44/40Ca = ~0.8–0.9‰) (Fig. 1a). In particular, our analyses for three lunar basalts (15555, 70215, 74275) yielded indistinguishable values (Supplementary Table 1) for the same ones measured by Klaver et al.20, demonstrating the inter-lab reproducibility and accuracy of the analyses. Some earlier δ44/40Ca measurements for the lunar basalts reported systematically heavier Ca-isotope compositions (δ44/40Ca = ~0.9–1.0‰)21,22 or a larger spread (δ44/40Ca = 0.76–1.10‰) with large analytical uncertainties (>0.05‰ overall)23, indicating an ongoing inter-lab difference that requires more efforts to address. Combining our lunar basalt measurements and data from Klaver et al.20 yields distinct average δ44/40Ca values for low-Ti basalts [0.868 ± 0.007‰, two standard errors (2SEs)] and high-Ti basalts (0.824 ± 0.007‰), a significant difference that traces mass-dependent isotopic fractionation during lunar igneous processes (Fig. 1a).

Fig. 1: Ca-isotope composition of the Moon.
figure 1

a δ44/40Ca values of lunar basalts, highland feldspathic rocks, minerals, and the estimated Bulk Silicate Moon (BSM). Closed/open symbols show data analyzed in this study/reported from the literature [lunar basalts from ref. 20, highland feldspathic meteorites (open diamonds) from refs. 16,24]. The colored horizontal lines and shaded bands represent the means and two standard errors (2SE) of individual groups. The presented BSM values (0.879 ± 0.047‰) (95% confidence intervals) are the results of the inversion of the LMO using the preferred experimental deep-LMO model26 (Fig. 1b). See Supplementary Table 1 for details of data. b and c Monte Carlo simulations to back-calculate the BSM values with the deep26 and shallow27 LMO models (Supplementary Note 1). The enclosed initial δ44/40Ca values (at 0% LMO crystallization), tied with individual δ44/40Ca evolution curves of the LMO (purple line), define the plausible range of BSM δ44/40Ca that could reproduce the floatation cumulates (grey line) consistent with observations. The green line and band show the mean and two standard deviations of the highland rocks. The vertical grey lines delineate the individual crystallization stages of each model. The histograms display the estimated BSM values obtained from the two models, where the horizontal lines and bands plot the mean δ44/40Ca values and 2SEs of the BSM (this study) and BSE34.

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Our results for the three FAN samples and the plagioclase in 76535 (a lunar troctolite) exhibit lighter Ca-isotope compositions (δ44/40Ca = ~0.7–0.8‰, averaging at 0.756 ± 0.036‰) that agree with previously reported data for lunar meteorites (feldspathic breccias)16, 24 (Fig. 1), further affirming the overall lighter δ44/40Ca value of the lunar highland. The average of these available values gives δ44/40Ca = 0.763 ± 0.012‰ (Fig. 1a) for the mean of the lunar FANs and feldspathic breccias. In addition, the analyzed olivine mineral separate from 12012, a low-Ti basalt, is substantially heavier in Ca isotopes (δ44/40Ca = 1.09 ± 0.03‰) (Fig. 1a). This result supports the heavy Ca-isotope enrichment of lunar olivine, which, furthermore, infers that the lighter Ca isotopes of lunar basalts and highlands are likely balanced by the heavier Ca isotopes in the lunar mantle, in line with some previous predictions25.

The FANs are thought to be the primary floatation cumulates crystallizing from the late-stage LMO (~70–100%) (e.g. refs. 26,27), making them valuable candidates to probe the initial isotopic compositions of the LMO. Some recent studies suggested that a part of the lunar anorthositic samples might trace chemical equilibration with a minor amount of KREEP [highly enriched in potassium (K), rare earth elements (REE), and phosphorus (P)] component (<1%) due to lunar partial mantle overturn28,29. Given the relatively low Ca content of the KREEP (~7 wt%)30 compared to the Ca-rich lunar plagioclase (~19 wt%)31, a maximum of 1% involvement of the KREEP would not modify the primary Ca isotopic signature of the plagioclase acquired from the initial LMO crystallization.

We developed a Monte Carlo method that uses two representative LMO crystallization models of experiments26 and thermodynamic phase equilibrium27 to solve for the best-fit initial δ44/40Ca values of the LMO that reproduce the observed range of FANs and feldspathic breccias (Fig. 1b and c) (Supplementary Note 1). These two LMO crystallization models also account for the debated initial LMO depth, hypothesized to range from as shallow as 500 km27,28,32 to as deep as the whole Moon (e.g. refs. 26,29,33). The experimental model26 assumes a deep (~1150 km), nearly whole-Moon, LMO crystallization condition, and the thermodynamic model27 assumes an initial ~500 km shallow LMO. Despite the different assumptions on the LMO depth, both models involve similar fractionating mineral phases, including olivine, orthopyroxene, clinopyroxene, and plagioclase, but with moderately different mass proportions and fractionating orders (Supplementary Tables 2 and 3). To account for the temperature dependence of isotopic fractionation factors, our isotopic models use experimentally determined crystallization temperature sequences obtained for deep26 and shallow27 LMO crystallization scenarios.

The estimated LMO initial δ44/40Ca values have a mean of 0.879 ± 0.047‰ (95% confidence intervals) using the experimental deep-LMO mineralogy sequence26 and 0.916 ± 0.044‰ using the thermodynamic shallow-LMO model27, both overlapping within error with the estimated BSE value of 0.94 ± 0.05‰34 (Fig. 1b and c) (Supplementary Note 1). T-tests for both LMO estimates find that the null hypothesis of the LMO and BSE having the same δ44/40Ca cannot be rejected at a significance level of 0.05 (t-statistic = 1.78 and 0.72, both <1.96). Recently, more geophysical and geochemical evidence has been uncovered that suggests a high-temperature origin of the Moon and an initially fully molten Moon. These inferences come from the simulation of the Moon-forming impact and the Moon’s accretion (>3000–4000 K)3,5, metal-silicate partitioning experiments (>2600–3700 K)35, and the depletion pattern of lunar and terrestrial moderately volatile elements3,36. Therefore, we take the initial LMO δ44/40Ca = 0.879 ± 0.047‰ obtained from the experimental 1150 km-deep LMO model26, whose depth also agrees with evidence from mass-balance calculations of Nd, Sr, and Hf isotopes33. As such, the LMO δ44/40Ca composition (0.879 ± 0.047‰) is equivalent to that of the BSM.

The mass-dependent stable isotopic closeness between the BSM and BSE has also been discovered for δ26/24Mg and δ56/54Fe11,12,13,14,15. These indistinguishable mass-dependent isotopic ratios of the BSM and BSE lend strong support to a high-energy giant-impact condition (Synestia) that adequately homogenized isotopic compositions within the Moon-forming disk3. In comparison, the traditional, lower-energy, giant-impact scenarios1,2,4,5 would predict notable mass-dependent stable isotopic heterogeneities of the Earth–Moon system. This is because in these less energetic impact scenarios, the silicate Moon forms by sampling a minimal mass fraction (~2%) from the incomplete mixture of the massive, isotopically fractionated mantle layers of the impactors (Theia and the Proto-Earth). Due to the inadequate mixing of the impactors’ mantle, this extracted minor silicate fraction (the BSM) would be difficult to average out the stable isotopic variability inherited from the impactors’ mantle and, thereby, is likely isotopically distinct from the bulk silicate mixture (later becoming the BSE).

Especially, under traditional giant-impact hypotheses, regardless of how much of the Moon’s building materials were derived from Theia or the proto-Earth [a classic question approached extensively with mass-independent isotopic anomalies (e.g. refs. 6,7)], the BSM would nevertheless likely sample and reflect the impactors’ preexisting mass-dependent isotopic heterogeneities because the BSM accretes from such small proportions of either impactor’s mantle. Therefore, the BSM and BSE having the same mass-dependent stable isotopic signatures is a low-probability outcome of the traditional giant-impact models, irrespective of (i) whether the Moon’s materials are sourced primarily from Theia or the proto-Earth or (ii) the two impactors shared identical pre-impact bulk mass-dependent isotopic compositions. We conclude that the observed BSM-BSE similarity in mass-dependent stable isotopes (δ26/24Mg, δ26/24Ca, and δ56/54Fe) is consistent with the Earth-Moon high-energy giant-impact origin3 and not readily explained by the traditional Moon-forming giant-impact models.

Tracing the lunar differentiation with Ca and Mg isotopes

Once we obtain the initial stable isotopic compositions of the LMO, we can model the stable isotopic fractionation during the LMO crystallization and compare the results with lunar samples to understand the evolution of the lunar differentiation. For this purpose, we forward modeled the Ca and Mg isotopic fractionation throughout the LMO solidification (Supplementary Note 3), whose temperature-dependent mineral-melt fractionation factors have been better constrained in recent years11,19,37,38 (Supplementary Note 2). The isotopic evolution was calculated with both cumulate mineral sequences established by the deep-LMO experiments26 and shallow-LMO thermodynamic modeling27 to test the influence of assumed LMO depths (Fig. 2).

Fig. 2: Ca and Mg isotopic evolution of the LMO.
figure 2

a Modeling δ44/40Ca and δ26/24Mg variations throughout the LMO crystallization using a mineral sequence established by experiments assuming a deep-LMO (~1150 km)26. The LMO liquid, sinking cumulates, and flotation cumulates are shown by solid, dotted, and dashed lines, respectively. The model takes a Monte Carlo method that accounts for propagated errors in the BSM composition (initial LMO value) and temperature-dependent fractionation factors (Supplementary Note 3). The lines and envelopes show the means and associated 95% confidence intervals. EC equilibrium crystallization, FC fractional crystallization. b and c Cross-plot of δ44/40Ca and δ26/24Mg showing the comparison between isotopic data and modeling. Mg isotope data are from the literature;11 Ca isotope data are from this study (closed symbols) and the literature20 (open symbols). All error bars on the data are 2SEs. For the modeling curves, b plots the modeled LMO liquid line of descent, and c plots the modeled floatation cumulates. The median and upper- and lower-bound curves reflect the mean and 95% confidence bounds as shown in (a). The percent of LMO crystallization of the modeling curves is color-coded (color bars on the right), with each crystallization stage signified by the grey line segment and adjacent label (i.e., 78%, 86%, and 95%). d–f show the modeled results using a thermodynamic shallow-LMO (500 km) mineral sequence27.

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Figure 2a and d illustrate the δ44/40Ca and δ26/24Mg variations of the LMO liquid, sinking mantle cumulates (such as olivine, pyroxene, spinel, and ilmenite), and floatation cumulates (plagioclase), which behave overall similarly for the two models. For both models, δ44/40Ca and δ26/24Mg exhibit remarkable fractionation in the LMO liquid and cumulate (~0.2‰ to ~0.9‰) during the late-stage evolution (>70% crystallization) (Fig. 2a and d), enabling the two systematics to estimate the evolution stage of lunar samples. Note that the LMO crystallization models predict an overall decrease in δ44/40Ca during the late-stage magmatic differentiation (>70%) (Fig. 2a and d), in contrast to the typical terrestrial magma systems that produce increasing δ44/40Ca in the late, felsic crystallization stage19, 39. This contrasting behavior is because feldspar (preferentially taking lighter Ca isotopes) is typically the major Ca host of the fractionating phases in the evolved terrestrial magma, while the abundant pigeonite or low-Ca augite (preferentially taking heavier Ca isotopes) chiefly control the late-stage LMO isotopic fractionation and render the residual LMO liquid overall lighter in Ca isotopes.

In Fig. 2b and e, we present the cross-plots of δ44/40Ca versus δ26/24Mg for the modeled LMO isotopic variations as a function of LMO crystallization. Ca and Mg isotope data for mare basalts from this study and the literature11,20, for which δ44/40Ca and δ26/24Mg have been both analyzed, are also shown. Low-degree partial melting of lunar mantle cumulates has been suggested as the origin of mare basalts11,20. At low degrees of partial melting, the isotopic fractionation effect caused by (i) the crystallization of cumulates out of the LMO and (ii) the subsequent cumulates’ partial melting that produced mare basalts should counteract and nearly cancel out each other11. Therefore, the cumulate partial melting hypothesis for the mare basalt petrogenesis would predict the mare basalts’ isotopic compositions approximating the instantaneous LMO compositions from which their mantle sources formed. Consistently for both LMO models, the δ44/40Ca and δ26/24Mg data of the mare basalts fall closely along the modeled LMO liquid line of descent (Fig. 2b and e) in evolved stages (from ~75% to 98% crystallization). The excellent correspondence between the multi-stable-isotope data and the LMO isotopic fractionation model strongly supports the mare basalts formation by partially melting lunar mantle cumulates and constrains these cumulates to have precipitated late in the LMO magmatic differentiation11,20.

Next, we compared the isotopic signatures of lunar feldspathic samples with modeled floatation cumulates to probe their magmatic context (Fig. 2c and f). For both LMO crystallization scenarios, the Ca and Mg isotopic data of the two FAN samples, 60015 and 60025, agree well with the predicted values for primary flotation crusts and indicate a formation near the end of LMO differentiation (>99% solidification). 62236 is not directly comparable with the modeled flotation cumulates because mafic minerals, rather than plagioclase, are the main host of Mg11. The plagioclase composition of 76535, a troctolite sample from the Mg-suite, falls between ~75% and 95% of LMO crystallization considering uncertainties, reflecting a relatively less-evolved plagioclase component compared to those in the FAN samples (Fig. 2c and f). Some existing Sm–Nd geochronologic constraints suggest that 76535 might have formed later than 6002540. This apparent discrepancy that an earlier-stage mineral composition preserved in a later-forming troctolite could be reconciled by 76535 forming as deep cumulates produced by lunar mantle overturns that postdate the LMO crystallization. Such petrogenic processes may have involved either/both (i) mineral precipitation from the partial melts produced by overturned earlier mafic cumulates or/and (ii) hybrid partial melting of the earlier mafic cumulates and later floatation cumulates40. Considering this possibility, only the analyzed FAN samples (60015 and 60025) are taken as credible indicators of the degree of LMO differentiation associated with their formation ages, which are independently defined by available radiometric dating.

While the crystallization age of 60015 remains largely unclear, extensive geochronologic investigations have been performed for 60025 to understand the significance of its age for the Moon’s formation and differentiation. Temporally, 60025 has been variably associated with the formation of (i) young lunar crusts during a rapid LMO crystallization41,42 and (ii) early lunar crusts during a prolonged crustal formation and LMO crystallization43. These competing interpretations stem from two principal sources. First, the discrepant and controversial absolute dates that were obtained using various chronometers41,44. Second, the propagated uncertainties when relating these debated dates with those for other lunar differentiation events to establish relative temporal relationships (such as the formation of KREEP and source regions of lunar basalts)41,42,43. In circumventing the ambiguities led by traditional methodologies that use comparison between debated absolute ages, our stable isotopic evidence provides an independent and critical resolution elucidating that 60025 marks the final solidification of the LMO. As a further profound implication, the formation age of 60025 should be used unambiguously to indicate the termination of the lunar differentiation.

Timeline of the Moon’s formation and differentiation

The resolved lunar differentiation context of 60025 warrants a new calibration of the early lunar chronology. To gain new insights into the lunar differentiation timeline, we synthesized a database of representative chronologic evidence for various evolution stages of the LMO solidification (Fig. 3). The Moon’s formation (whose age approximates the moon-forming giant impact and initial crystallization of the Moon) has been constrained to from ~30 to 60 million years (Myr) after the formation of the solar system by 182Hf–182W systematics for the silicate Moon45,46,47, lunar metals48 and Earth’s mantle49 and Lu–Hf model ages for lunar zircons50. Early lunar differentiation (<50% LMO crystallization) may be best represented by a dunite sample, 72415, the possibly oldest lunar rock sampled from early mantle cumulates [4527 ± 92 million years ago (Ma)]51. Based on its nearly identical Mg isotope signature to the BSM11, it likely reflects early LMO solidification before plagioclase started to saturate and prominently fractionate Mg isotopes (we assign it with a nominal 40% of LMO solidification between 0% and 80%) (Fig. 3).

Fig. 3: Two lunar differentiation models permitted by chronologic evidence.
figure 3

a A short-lived LMO crystallization (<30 Myr) required by the old formation age of 60025 (4510 ± 10 Ma)44. b A long-lived LMO crystallization (~130–150 Myr) necessitated by the proposed young age of 60025 (4383 ± 17 Ma)40. Error bars on the data points represent two standard errors. The solid vertical line indicates the formation age of the solar system corresponding to the age of calcium–aluminum-rich inclusions (CAIs)60. The curves illustrate exponential fittings to the data, whose color signifies which formation age of the Moon (the colored open circles) is used for the fitting. See text and Supplementary Tables 7 and 8 for the chronologic data and references.

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Late-stage lunar differentiation is delineated by the formation of the lunar crust and KREEP sources. These dates include (i) an average 147Sm–143Nd isochron age (4456 ± 40 Ma) quantified by the mafic fractions from four anorthosites thought to reflect the crystallization of early lunar crust52 (>75% LMO solidification); (ii) 147Sm–143Nd and 176Lu–177Hf model ages for the source of KREEP basalts (4368 ± 29 Ma)42 and the oldest lunar zircons (4417 ± 6 Ma)53 considered crystallizing from KREEP-rich magma (>95% LMO solidification); and (iii) distinguished Pb–Pb isochron ages for plagioclase (4510 ± 10 Ma)44 and pyroxene (4359.2 ± 2.4 Ma)41 and Sm–Nd ages for whole rock and mineral (4367 ± 11 Ma and 4319 ± 30/38 Ma)41 for 60025 (>99% LMO solidification) (Fig. 3).

Given the distinct dates proposed for 60025, the age of 60025 plays an essential role in gauging the timespan of the lunar differentiation. We reexamined the previously reported Pb–Pb data from different labs41, 44,54 and identified two well-defined while distinct mineral isochrons for 60025. One is for pyroxene (4359.2 ± 2.4 Ma, n = 4), which was originally explored by Borg et al.41. The other one is for plagioclase that yields an older age (4477.8 ± 35.7 Ma, n = 6) (Supplementary Fig. 5), overlapping within error with the 4510 ± 10 Ma plagioclase age obtained by44. The two mineral isochrons both intersect with the lunar 207Pb/206Pb–204Pb/206Pb growth curve, indicating products of a multi-stage evolution (Supplementary Fig. 5). The presence of two credible and disparate isochron ages underscores the ongoing challenge of affirming 60025’s formation age and emphasizes the various age possibilities of 60025.

We now discuss the plausible lunar differentiation scenarios permitted by the absolute dating for 60025. If the old 4510 ± 10 Ma Pb–Pb age44 for pristine plagioclases in 60025 represents the sample’s formation age, it requires an old Moon’s formation predating ca. 4510 Ma and a rapid LMO solidification within the subsequent about <30 Myr (short-lived LMO model, Fig. 3a). Such a comparatively short duration has been explained by the LMO solidifying under a relatively high-conductivity anorthosite lid55. This scenario also agrees with the closeness of the mean age of dunite 72417 (4527 Ma)51 and the Pb–Pb plagioclase age of 60025 (4510 Ma). Moreover, this model could reconcile with some of the older KREEP model age estimates averaging at 4456 ± 65 Ma41 but would argue against the younger estimates [such as 4368 ± 29 Ma by Gaffney and Borg42 and ca. 4270–4190 Ma by Maurice et al.43]. The 4510 ± 10 Ma age of 60025 thereby places an upper bound on the completion of the lunar differentiation.

If the young Pb–Pb isochron age for pyroxene and Sm–Nd isochron ages for 60025 are valid [averaging at 4383 ± 17 Ma at the solidus temperature of 6002556], this would suggest a prolonged lunar differentiation that lasted ~130–150 Myr based on the variously estimated timing of the giant impact (long-lived LMO model) (Fig. 3b). A slushy LMO, lacking efficient crystal-liquid separation, has been used to argue for this long timescale57. Moreover, the implied upper limit of ~150 Myr does not conflict with the modeled protracted LMO solidification taking up to ~200 Myr43 involving mantle heat-piping and an anorthosite crust with a lower thermal conductivity than that of Elkins-Tanton et al.55. However, our results would necessitate the LMO solidification to complete by ca. 4387 Ma, disputing the models placing the end of the lunar differentiation between ca. 4270 and 4190 Ma43. Furthermore, differing from some prior suggestions that favor the younger (4368 ± 29 Ma) and preclude the older (4456 ± 65 Ma) KREEP model ages (e.g. ref. 41), we find the young age of 60025 (4383 ± 17 Ma) compatible with both the proposed KREEP ages because 60025 likely documents the last solids of the LMO. Using these compatible age sets, we performed weighted-least-squares exponential fittings (Fig. 3b), which agree with an initial rapid crystallization of the LMO followed by slower cooling and prolonged solidification once the anorthosite crust formed43,55,57. In this model, the 4383 ± 17 Ma age of 60025 puts a lower bound on the cessation of the LMO crystallization.

Accounting for both the proposed old and young formation ages of 60025, our new isotopic evidence requires the LMO to have fully crystallized by either 4510 or 4387 Ma, with the total solidification timescales from <30 to ~130–150 Myr, respectively. A clearer distinction between a short-lived and long-lived LMO calls for better absolute chronology on the early LMO products to pair with stable isotopic constraints. We also conclude that the important magmatic differentiation context provided by the novel tool of multi-stable isotope systematics warrants more extensive applications in planetary problems in combination with traditional major and trace element methods.

Methods

Sample preparation and description

All sample preparations were performed in a clean room at Harvard University. About 10–100 mg (whole rocks) and 2–10 mg (separated minerals) of well-mixed powdered samples were dissolved in a mixture of HF–HCl–HNO3. A CEM MARS 6 microwave digestion system and MARS Xpress high-pressure reaction vessels with a three-step procedure were used for sample dissolution; first step: 0.5 ml HF + 2 ml HNO3 + 1 ml HCl; second step: 0.5 ml HNO3 + 1.5 ml HCl + 1 ml H2O; third step: 3–4 ml HNO3; Power 400 W; Temperature 200 °C; 15 min ramping + 45 min holding + 30 min cooling. Dissolved samples from each step were dried with heat lamps in ultrapure N2 and dissolved in adequate amounts of 2.5 N HCl after the third step to form a 10 μg/μl Ca solution. To correct the isotopic fractionation produced by chemical separation and instrumental analysis, a double spike technique was used by adding a certain amount of 43Ca–48Ca double spike solution to each sample solution before column chemistry58. Calcium was purified by ion-exchange chromatography using a cation exchange resin (Bio-Rad AG50W-X12 [200–400 mesh]) in 2.5 N HCl media following a previously established procedure58. Each sample was processed through the column chemistry twice to ensure that the final Ca solution was free of other elements. About 5.0 μg Ca from the purified solution was loaded as Ca(NO3)2 onto one of the side filaments of a zone-refined Re triple filament assembly58.

The set of lunar samples analyzed for Ca isotopes in this study is the same as in Sedaghatpour and Jacobsen11 for Mg isotopic analysis, from which detailed descriptions of the samples are provided (Supplementary Information: Lunar samples description).

Ca-isotope measurement

Calcium isotopic ratios were measured using a GV Isoprobe-T thermal ionization mass spectrometry (TIMS) at Harvard University. All Ca isotopes were measured in a two-sequence method reported earlier by our group35. In the first sequence, the peaks for 40Ca to 44Ca were collected. In this step,41K was also measured to monitor possible isobaric interference of 40K. Furthermore, a mass range from 39 to 49 was scanned to ensure there were no 47Ti, 49Ti, or double-charged Sr species (84Sr2+ and 88Sr2+) to interfere with Ca isotope measurements. Each analysis includes 20 blocks, 10 cycles each with a 6-s integration time for each sequence, followed by a 1-s waiting time, resulting in a total analytical time of ~120 min (including the 25-min heating routine). Isotope data are reported as part per thousand deviations from spiked measurements of NIST SRM915a standard with δ-notation (Supplementary Table 1):

$${\delta}^{44/i}{{{{{{\rm{Ca}}}}}}}({\textperthousand })=[({\;\!}^{44}{{{{{{\rm{Ca}}}}}}}/{\;\!}^{i}{{{{{{\rm{Ca}}}}}}})_{{{{{\rm{sample}}}}}}/({\;\!}^{44}{{{{{{\rm{Ca}}}}}}}/{\;\!}^{i}{{{{{{\rm{Ca}}}}}}})_{{{{{{\rm{SRM}}}}}}915{{{{{\rm{a}}}}}}}-1] \times 1000$$
(1)

where i is the Ca isotope mass 40 or 42. Sample analysis was done multiple times for each sample, with the averages and external reproducibility (two standard errors, 2SE) of δ44/40Ca and δ44/42Ca reported in Supplementary Table 1. Combined spiked and unspiked measurements of NIST SRM915a yield 40Ca/44Ca = 47.1562 and 42Ca/44Ca = 0.3121794, which are used to calculate the δ-values. Standards measured relative to these values are BHVO-2 with δ44/40Ca = 0.85 ± 0.03‰ and IAPSO seawater with δ44/40Ca = 1.83 ± 0.03‰.

In Supplementary Fig. 1, we plot all measured lunar samples in a three-Ca-isotope diagram of 44Ca/42Ca versus 44Ca/40Ca. Most data plot closely along the expected lines of mass-dependent relationships44 within uncertainty (Supplementary Table 1). To more firmly ascertain the δ44/40Ca values of the samples, we also calculate δ44/40Ca from the measured δ44/42Ca according to mass-dependent relationships (δ44/40Ca ≈ 2.0483*δ44/42Ca)59. These calculated δ44/40Ca values from δ44/42Ca were then weight-averaged with the directly measured δ44/40Ca to obtain the mean δ44/40Ca values and propagated uncertainties (Supplementary Table 1), taken as the best estimate in this study.