²³⁸U/²³⁵U measurement in single-zircon crystals: implications for the Hadean environment, magmatic differentiation and geochronology

Abstract

Owing to the challengingly small amounts of uranium (U) they contain, the isotopic composition (²³⁸U/²³⁵U) of single zircon grains has never been measured. Leveraging methods we designed for analysis of small sample amounts and modern MC-ICPMS instruments, we show that precise (±0.04 to ±0.25‰) single-zircon ²³⁸U/²³⁵U measurements are now possible. We report data for 31 single grains from the Jack Hills conglomerate, and 3 reference zircon localities (FC-1, R33 and Temora). Consistent with the reducing conditions implied by the small Ce anomalies of many Hadean zircon, Jack Hills grains display only small δ²³⁸U variations (from −0.60 to −0.12‰). The distribution is centered on the average chondritic and bulk continental crust value, arguing against the widespread existence of Oklo-type reactors in the early Earth. The subtle δ²³⁸U variations in Jack Hills zircons are more plausibly explained by a small (∼0.10%) mass-dependent equilibrium isotope fractionation between at least one U-bearing accessory mineral and silicate melts, during magmatic differentiation under reducing conditions. In contrast, the large δ²³⁸U difference between pooled titanite and pooled zircon fractions from the Fish Canyon Tuff sample suggests larger isotope effects during igneous fractional crystallization under oxidizing conditions (∼QFM+2), with preferential removal of ²³⁵U from the melt and into zircon, and/or other accessory phases. We estimate that ∼50% of zircon dated by the CA-ID-TIMS method would be amenable to single-grain U isotope measurements, making this method widely applicable to future studies. This would enable (i) improvements in precision and accuracy of U–Pb and Pb–Pb dates, (ii) accurate investigation of U-series disequilibrium contribution to U–Pb discordance, and (iii) accurate re-evaluation of U decay constants.

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1. Introduction

Earth's known rock record only extends to ∼4.05 Ga (ref. 1). As the only older lithic record, detrital zircons are thus key to understanding the development of crustal rocks and surface environments during the Hadean,^2,3 an eon which presumably saw the waning of the extraterrestrial bombardment,^4,5 the emergence of life,^6,7 and the establishment of continents.^2,8 Numerous chemical and isotopic proxies have therefore been investigated in Hadean zircons and their inclusions (review in ref. 3) but owing to the small size of typical zircon crystals (<10–50 μg), and the even smaller size of Hadean grains (∼1 μg), geochemical studies are limited to the main constituents of, and minor/trace elements partitioning strongly into, zircons. While uranium (U) concentrations are routinely measured in zircons for U–Pb geochronology, the U isotopic composition of single-zircon grains has never been measured. Indeed, significant analytical challenges are associated with the analysis of the small amounts of U contained by individual crystals, which are invariably regarded as insufficient to allow for the precise determination of ²³⁸U/²³⁵U ratios.^9–12

Building on and improving upon methodologies we developed to precisely and accurately determine the ²³⁸U/²³⁵U of small samples,¹³ we show that modern Multi-Collector ICPMS instruments provide sufficient precision to resolve U isotopic differences between single zircon grains. We present a detailed description of these analytical methods, and report data for 31 single grains from the Jack Hills conglomerate (Western Australia) and 3 reference zircon localities. Using data obtained on Jack Hills zircons we assess whether natural nuclear reactors were present in the Hadean, the possible causes of fractionation in magmatic settings, and the implications for high-precision U–Pb and Pb–Pb geochronology. Finally, we discuss the current limitations and future improvements that could help make single-zircon ²³⁸U/²³⁵U determinations more accurate, precise, and practical for a variety of applications in geochemistry and geochronology.

2. Motivations

There are several reasons why quantifying the ²³⁸U/²³⁵U of single zircons, and Hadean ones in particular, is important:

(1) Oklo-type natural nuclear reactors may have been more prevalent in the Hadean,¹⁴ when ²³⁵U abundance was above the ∼3% threshold required for self-sustained neutron-induced fission (∼17% at 4 Ga and ∼25% at 4.5 Ga). So far, the Oklo U ore deposit (Gabon), which reached criticality ∼1.78 Ga, is the only known natural reactor. In the reactor zones, neutron-induced ²³⁵U fission led to ²³⁸U/²³⁵U increases that often reached +100 to +475‰ (ref. 15). These isotopic variations are 100× larger than those documented in other geological settings, which only range from −4.1 to +4.8‰ (ref. 16 and 17). It is thus conceivable that if Oklo-type reactors were common in the Hadean, even small amounts of highly anomalous U isotope composition could have contaminated sediments and igneous rocks and potentially be recorded in Hadean zircons.

(2) While stable isotopic variations were originally thought to be confined to low-T settings and light elements, many studies have now documented variations in high-T settings for heavy elements, reflecting both equilibrium and kinetic processes (review in ref. 18). For U, mass-dependent isotope fractionations (∝1/T²) should be small at magmatic temperatures (∼−0.07‰ at 850 °C), but nuclear volume effects¹⁹ (∝1/T) could induce larger U isotopic fractionations (∼+0.61‰ at 850 °C). At this writing, the U isotopic systematics of igneous rocks is still in its infancy (review in ref. 17), but the available data suggests the existence of mineral specific U isotope effects,^9,11,12 which can result in magmatic differentiation trends, as observed in angrite meteorites.²⁰ Based on studies of different isotopic systems, the potential drivers of U isotope fractionation in magmatic settings would be temperature, the nature of the minerals sequestering U, the redox state of the melt, and the extent of crystallization.

(3) Uranium isotopic variations can affect the accuracy and precision of U–Pb and Pb–Pb dates.^9,16,20,21 Establishing a timeline for the dramatic biological/environmental changes that punctuated Earth's history relative to their potential triggers (e.g., asteroid impacts, large igneous province emplacements) requires, however, highly precise and accurate absolute ages.^22–26 These ages are typically obtained using U–Pb and/or Pb–Pb dates of zircons found within ash layers/lavas associated with the events of interest. Based on the limited U isotope variability (∼0.7‰) observed in pooled zircons (i.e., multi-grain dissolutions) of different ages and localities, a recommended ²³⁸U/²³⁵U was established for accessory-phase geochronology.^9,12 This approach assumes that the recommended value encompasses all ²³⁸U/²³⁵U variability in natural zircon, such that age accuracy after uncertainty propagation is not compromised. The central limit theorem, however, predicts that pooled zircons should display less scatter in their ²³⁸U/²³⁵U than single zircon grains (Fig. 1). Therefore, the only robust way to quantify ²³⁸U/²³⁵U variability in natural zircons is via single-grain U isotope analysis, without which sub-permil accuracy and precision in U–Pb and Pb–Pb geochronology is, a priori, not possible.

Fig. 1 (a) Kernel Density Estimator (KDE) of the U isotope composition of n pooled zircons randomly picked from a uniform distribution centered on δ²³⁸U = 0 and of total range, 1‰. KDEs are built using 50 000 randomly generated sets (Monte-Carlo Simulations, MCS) of n zircons, with n between 2 and 1000. (b) Width (95% confidence interval) of the KDE of n pooled zircons predicted by the central limit theorem as a function of the dispersion in the δ²³⁸U distribution from which the grains are randomly picked (lower x-axis, range covered by a uniform distribution; upper x-axis, 2σ of a normal distribution). For n zircons picked within a distribution of variance σ², the variance of the mean δ²³⁸U of the n zircons tends toward . The uncertainty on the recommended ²³⁸U/²³⁵U for use in geochronology (yellow horizontal band) is based on the analysis of hundreds to thousands of pooled zircons^9,12 and could theoretically hide a true δ²³⁸U variability of greater than 10‰ in individual zircons.

3. Samples

To explore ²³⁸U/²³⁵U variability between single zircon grains, we selected 3 reference zircon localities (FC-1, R33 and Temora; ²⁰⁶Pb/²³⁸U ages between 418 and 1095 Ma; ref. 27) and 31 Jack Hills zircon crystals with apparent ²⁰⁷Pb/²⁰⁶Pb dates between ∼3.3 and 4.2 Ga (ref. 28). As all Jack Hills crystals formed before oxidative conditions could solubilize U in water as U^VI (ref. 29), their composition should be purely controlled by magmatic processes and/or U contributions from Oklo-type reactors. Resolvable U isotope variations in such samples would thus imply that systematic investigation of ²³⁸U/²³⁵U ratios could provide further insight into the magmatic history of individual detrital zircons, which otherwise lack geological context.

4. Methods

All Teflon labware (i.e., PFA vials and beakers from Savillex) was pre-cleaned 3× with boiling aqua regia (3 : 1 mixture of HCl : HNO₃), followed by boiling Milli-Q water. Glass vials were cleaned with acetone and MQ water. Centrifuge tubes were leached with 50% (vol) HCl overnight and/or rinsed 3× with MQ water.

4.1. Direct zircon dissolution

Zircon dissolution followed a protocol adapted from those used in geochronology studies.^30,31 Single zircon crystals were pipetted into clean Teflon beakers and cleaned by successive leaching in HCl (16 drops of 6.2 M) and HNO₃ (16 drops of 5 M) on a hotplate at ∼90–100 °C for 30–60 min. These steps aimed at removing any iron oxide coatings, secondary alteration products and/or adsorbed U present at the surface of the grains or in small factures within them. After each leaching step, the grains were sonicated in a hot water bath for 10 min, and the acid solution was transferred to a 2 mL plastic vial. The solution recovered was used to check the amount of U released in each step (Table S1†). Each grain was further rinsed with 10 drops of MQ, which were also collected and added to the leachate solution, before complete dry-down of the grains at 130 °C on hotplate. After cleaning, the grains were transferred to Teflon micro-capsules and immersed in 3 drops (∼75 μL) of 28 M HF. The micro-capsules were then placed on a Teflon holder accommodating up to 18 capsules, itself placed inside a high-volume Parr® acid digestion vessel and into an oven at 210 °C for 48 h. After the HF dissolution step, the samples were dried and converted to HCl by addition of 3 drops of 6.2 M HCl and placed back in the Parr vessel and in the oven at 180 °C for 24 h.

4.2. Zircon chemical abrasion followed by dissolution

To assess the effects of thermal annealing and chemical abrasion on ²³⁸U/²³⁵U ratios, six of the Jack Hills samples were treated with the chemical abrasion method,³⁰ which selectively dissolves radiation damaged subdomains that have may have not remained closed systems for U and Pb isotopes (as leachates), and leaves behind crystalline domains more likely to have remained in closed-systems (as residues). After the HCl and HNO₃ cleaning steps, zircons were annealed in quartz vials at 900 °C for 62 h using a Thermolyne benchtop muffle furnace, transferred to Teflon micro-capsules, and chemically abraded with 28 M HF at 210 °C for 7 h 45 min (in a Parr vessel). The abrasion solutions were collected in clean 7 mL Teflon beakers and the grains were rinsed twice with 8 drops of MQ, which was also collected and added to the leachate solution. The undigested part of the zircons (i.e., residues) were again covered with 3 drops (∼75 μL) of concentrated HF and placed back in the Parr vessel and in the oven at 210 °C for 48 h to achieve complete digestion of the residues. After the HF dissolution step, conversion to a chloride matrix was done by adding 3 drops of 6.2 M HCl and placing the Parr vessel at 180 °C for 24 h. The solutions containing the fully digested residue thus obtained were finally transferred to clean 7 mL Teflon beakers.

4.3. Uranium concentration measurements and spiking

After digestion, all sample solutions (from cleaning, direct dissolution, chemical abrasion and residue digestion) were dried down completely and re-dissolved in 3 mL of 3 M HNO₃. A 2% aliquot (60 μL) was spiked with ∼0.65 ng of IRMM-3636 double-spike (50.46% of ²³³U and 49.51% of ²³⁶U; ref. 32), diluted with 0.3 M HNO₃ to a total volume of 750 μL, and measured using a Nu-Plasma II MC-ICPMS (McGee lab) to determine the amount of U in each sample (Table S1†). Enough IRMM-3636 was then added to each sample to obtain a U_spike/U_sample ratio of ∼3–4%: a value recommended by Weyer et al.³³ to minimize spike consumption, abundance sensitivity effect of ²³⁸U onto ²³⁶U, as well as contribution from amplifier noise and counting statistic on ²³³U and ²³⁶U to the measurement uncertainty. To ensure full homogenization of the sample-spike mixture, all samples were completely dried down on hot plate at 150 °C, taken back in 1 mL of concentrated HNO₃, evaporated to near dryness and taken back into 2.5 mL of 3 M HNO₃ + 0.02 M oxalic acid. The dilute oxalic acid was used to solubilize Zr³⁴ and prevent retention of Zr (which makes up ∼50 wt% of the matrix of zircons) during column chemistry.

4.4. Uranium purification for Zr rich samples

Uranium purification was done on U/Teva resin, following a procedure modified from Tissot and Dauphas¹⁶ (Table 1). Given the small mass of U (∼1–50 ng) and the large Zr/U atomic ratio of the samples (∼481 for a zircon assuming typical Zr and U concentrations of, respectively, 48 wt% and 2600 ppm, ref. 35), two main modifications were brought to the procedure: (i) a more extensive column cleaning was done to minimize blank contribution from the column, and (ii) sample loading and matrix rinsing used 3 M HNO₃ + 0.02 M oxalic acid, as oxalic acid solubilizes Zr.³⁴ The procedure was repeated twice to ensure complete matrix removal. The purified U cuts were then evaporated completely at 175 °C, covered with 0.5–1 mL of HNO₃/H₂O₂ (1 : 1) and dried completely to remove residual organics, before being taken back in 2 mL of concentrated HNO₃ and left on the hotplate overnight at 140 °C to ensure full re-dissolution of the sample.

Table 1 Chromatographic extraction protocol of U in zircons on U/Teva resin. Column volume (cv) = 2 mL

Column #1				Column #2
Step	Acid type	Volume	Comment	Acid type	Volume	Comment
Cleaning	0.05 M HCI	40 mL		0.05 M HCI	40 mL
Conditioning	3 M HNO3 + 0.02 M oxalic acid	10 mL		3 M HNO3 + 0.02 M oxalic acid	10 mL
Sample loading	3 M HNO3 + 0.02 M oxalic acid	2.5 mL		3 M HNO3 + 0.02 M oxalic acid	2.5 mL
Matrix rinse	3 M HNO3 + 0.02 M oxalic acid	12 mL	Elution of matrix except U, Th, Np	3 M HNO3 + 0.02 M oxalic acid	6 mL	Elution of remaining Zr
				3 M HNO3	6 mL	Oxalic rinse
Conversion to HCl	10 M HCl	5 mL		10 M HCl	5 mL
Th rinse	5 M HCl	8 mL	Elution of Th	5 M HCl	8 mL	Elution of remaining Th
Elution	0.05 M HCl	15 mL	U is recovered	0.05 M HCl	15 mL	U is recovered

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4.5. Yield, blanks and purity checks

For each sample, a 1.5% solution aliquot (30 μL) was taken post-column chemistry, diluted with 380 μL of 0.3 M HNO₃, and measured by MC-ICPMS to determine U recovery and Zr/U ratio in the purified solution. Yields, calculated as the ratio of U in the sample solution before and after column chemistry, were between 80 and 98%. The Zr/U atomic ratios varied mostly between 0.1 and 1.2, with four samples showing Zr/U between 1.4 and 6.4 (Table S2†). Given the typical zircon Zr/U atomic ratio of ∼481, these values indicate that ∼99–100% of the Zr was removed during sample purification. The procedural blank was 0.005–0.017 ng U (∼0.002 to 0.7% of sample uranium) and is therefore negligible.

4.6. Mass spectrometry

Uranium isotope analyses were performed on two MC-ICPMS instruments: a Nu-Plasma II-ES in the McGee lab (MIT) and a Thermo Finnigan Neptune upgraded to Neptune Plus specifications at the Origins Lab (University of Chicago). The Nu-II was equipped with high-sensitivity dry plasma cones (Ni sampler cones 319–646, Ni skimmer cones 325–294) and sample introduction was done using an Aridus II desolvating nebulizer, yielding a sensitivity of ∼0.75–1.0 V ppb⁻¹ on ²³⁸U for a sample flow rate of 100 μL min⁻¹. The Neptune was equipped with a set of Jet sample cones and X-skimmer cones and the sample introduction was also done using an Aridus II, yielding a sensitivity of ∼1.5–1.7 V ppb⁻¹ on ²³⁸U for a sample flow rate of 100 μL min⁻¹. The measurements were done in low-resolution mode using static cup configurations (Table 2), and typically comprised 50 or 60 cycles of 4.194 s integration time each. Take up time was set to 60 seconds and rinse time between 450 and 550 seconds were used.

Table 2 Cup configurations for U isotopic measurements by MC-ICPMS in low resolution mode

Isotope	^232Th	^233U	^234U	^235U	^236U	^238U
Neptune Plus (U. of Chicago)
Cup	L2	L1	Axial	H1	H2	H3
Resistor (Ω)	10^11	10^11	SEM	10^11	10^11	10^11
Nu-Plasma II-ES (MIT)
Cup	L4	L3	L2	L1	Axial	H2
Resistor (Ω)	10^11	10^11	10^11	10^11	10^11	10^11

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Due to the large dynamic range of the U system (²³⁸U/²³⁵U ∼137.8), measurements at low concentration are counting statistics limited. To achieve high-precision on small samples loads, the volume of solution was adjusted to obtain a signal of at least 10 V on ²³⁸U (and ∼77 mV on ²³⁵U). Following this protocol, measurements were done at U concentrations between 6.5 and 12 ppb, sometimes in as little as 0.25 mL of solution. Signal intensities were thus between 10 and 20 V for ²³⁸U, 165 and 275 mV for ²³⁶U and ²³³U, 77 and 145 mV for ²³⁵U, 0.6 to 1.2 mV for ²³⁴U (when measured on the Nu-II) and ∼31 000 and 60 000 cps for ²³⁴U (when measured on the axial secondary electron multiplier (SEM) on the Neptune). Estimation of the Neptune “cps-to-volt” conversion factor was done once a week by measuring the ²³⁶U/²³⁸U in a CRM-112a solution spiked with the IRMM-3636 U double-spike using two different cup configurations: first with both ²³⁶U and ²³⁸U on Faraday cups, then with ²³⁶U on the axial SEM and ²³⁸U on a Faraday cup (for more details, see Table S4 in ref. 16). Thorium-232 was monitored during each analysis and the signal was found to be always below 10 mV. Given the extremely low rate of hydride formation relevant to the measurements (∼7 × 10⁻⁷; ref. 16), the residual amount of Th in the sample has virtually no effect on the U isotope analysis. This is clearly demonstrated by replicate analyses of the BCR-2 standard (Fig. 2a and Table S3†), where ²³²Th signals varied between 0.04 and 2.9 mV, with no impact on either the accuracy or the precision of the U isotope data obtained. Baseline measurements and amplifier gain calibrations were done at least daily.

Fig. 2 Accuracy tests. (a) δ²³⁸U values for geostandard BCR-2 measured during each analytical session (letters a to d refer to sample replicates, see Table S3†). Each data point was acquired using a similar number of solution analyses as the one used for zircons (n between 1 and 8). Every measurement is within error of the recommended average value (orange band) of −0.27 ± 0.05‰ (95% CI). (b) δ²³⁸U values measured on Zr-doped CRM-112a solutions vs. Zr/U (atomic) ratios of the doped solutions. All solutions give δ²³⁸U values within uncertainty of 0‰, indicating the absence of resolvable matrix effect.

4.7. Instrumental mass bias correction and data reduction

Isotope mass fractionation introduced during chemical separation and mass spectrometry was corrected for using the ²³³U–²³⁶U IRMM-3636 double-spike and the data reduction methodology described in details in Tissot and Dauphas.¹⁶ In brief, the raw signals are corrected for: (i) on peak zero, (ii) ²³⁸U tail contribution onto ²³⁶U, ²³⁵U, and ²³⁴U signals (respectively, 0.6 × 10⁻⁶, 0.25 × 10⁻⁶, and 0.1 × 10⁻⁶ of the ²³⁸U signal intensity), (iii) hydride formation, and (iv) the decay of the spike isotopes (²³³U and ²³⁶U) between the time of spike calibration and sample analysis. The cup configuration and the set of cones used can result in systematic offsets of up to 0.20‰ in the final ²³⁸U/²³⁵U measured.¹⁶ To account for this, every sample was bracketed by measurements of the CRM-112a standard spiked with IRMM-3636 at the same level as the samples. For sample limited analyses, only 18 to 42 cycles could be obtained and the bracketing standard measurements used to calculate the uncertainty were truncated to match the number of cycles measured on the sample.

5. Results

5.1 Notations

U isotope compositions are reported as δ²³⁸U values relative to the U standard CRM-112a (also named SRM960 or NBL112-a; CRM-145 for the solution form):

δ²³⁸U = [(²³⁸U/²³⁵U)_sample/(²³⁸U/²³⁵U)_CRM-112a − 1] × 10³. (1)

All absolute ratios, including literature data, are calculated assuming ²³⁸U/²³⁵U = 137.837 ± 0.015 for CRM-112a (ref. 36). This value results from an inter-laboratory calibration effort in which different instruments (i.e., MC-ICPMS and TIMS), reference materials (i.e., IRMM-3636, IRMM-072/15, in-house spikes calibrated against IRMM-074/10 or IRMM-184) and instrumental fractionation correction methods were used. This value is therefore preferred over the often used value of 137.829 ± 0.022 from ref. 9, which was obtained using a single instrument and spike. Uncertainties are reported as “2SE external reproducibility” and calculated as , where 2 × σ_standard is the 2 S.D. daily external reproducibility of repeat measurements of CRM-112a bracketed by itself (measured at the same concentration as the sample), and n is the number of repeat analyses of the same sample solution (typically n = 2–4).

5.2 Data accuracy and precision

Given the analytical challenges posed by the analysis of the low U loads of single zircons (1–50 ng of U), a comprehensive series of precision and accuracy tests were performed (additional details in ESI†).

(i) Accuracy test. Four replicates of the Columbia River basalt (BCR-2) were processed and measured with the zircon samples. For each replicate, the average δ²³⁸U obtained are both reproducible (−0.23 ± 0.06‰, −0.27 ± 0.05‰, −0.27 ± 0.04‰ and −0.26 ± 0.04‰) and indistinguishable from the average value of −0.27 ± 0.05‰ (95% CI), based on data from 11 studies (see ESI† in ref. 16). Furthermore, the δ²³⁸U values measured during each daily session, with a similar number of solution analyses as the one used for zircons (n between 1 and 8), are all within uncertainty of the average value (Fig. 2a).

(ii) Zr doping test. To test whether the residual Zr present in the purified U fractions could result in systematic bias of the ²³⁸U/²³⁵U analyses, spiked aliquots of CRM-112a were doped with Zr and measured as “unknown” samples. The δ²³⁸U obtained on Zr-doped CRM-112a solutions are indistinguishable from 0‰ (Fig. 2b), indicating that the presence of Zr at the levels tested does not affect the U isotope measurements.

(iii) Matrix effects. As the IRMM-3636 double-spike consists almost entirely of ²³³U and ²³⁶U, the presence of matrix effects can be investigated by checking the agreement between the δ²³⁸U_DS+SSB values, obtained from the double-spike data reduction, and the δ²³⁸U_SSB values, obtained from the raw ²³⁸U/²³⁵U (striped of the spike ²³⁵U and ²³⁸U contribution and corrected only for on peak zero, hydride formation and tailing of ²³⁸U onto lighter isotopes) bracketed by standard measurements (SSB).^16,37 For all but one sample (Fig. 3) there is a very good agreement between these values (δ²³⁸U_DS − δ²³⁸U_SSB is −0.04‰ on average), indicating that matrix effect did not affect the measurements (except possibly RSES72-18.10 residue).

Fig. 3 δ ²³⁸U values obtained with the double-spike data reduction method (DS + SSB, x-axis) plotted against the raw values measured, striped of the minor ²³⁵U and ²³⁸U spike contribution (SSB, y-axis). All values are standard bracketed (SSB). The agreement of the two sets of values indicates that no resolvable matrix effects affected the measurements (for more details see ref. 16). Grey circles: geostandards; white circles: zircons.

(iv) Reference zircons. Perhaps the most telling evidence of the reliability of our dataset is the excellent agreement of our reference zircon data with that of Hiess et al.⁹ and Livermore et al.¹² Samples FC-1, R33 and Temora were measured both here and in at least one of these previous studies, and yield identical δ²³⁸U values (Fig. 4a). In the present work, analyses were performed with only 7–17 ng of U, while the data from Livermore et al.¹² and Hiess et al.⁹ used 400–801 and 6000–23 000 ng of U from pooled zircons, respectively (Fig. 4b).

Fig. 4 (a) Comparison of δ²³⁸U values obtained on single-zircon grains (circles, this work) and pooled zircons (squares: ref. 9; diamonds: ref. 12) for 3 reference zircon localities. (b) Uncertainty on δ²³⁸U values vs. amount of U measured (in ng). Uncertainties are 2 SE external reproducibility (see Section 5.1). Grey curves show the theoretical lower limit achievable, calculated with eqn (2), assuming measurements on a Neptune MC-ICPMS with 2.5% ion transmission and ²³⁸U measured at 10 V (dashed grey curve) and 20 V (solid grey curve), and with both ²³⁵U and ²³⁸U measured using 10¹¹ Ω resistors (see Methods and ESI†). The black curve shows the absolute precision limit assuming 100% of ion transmission: i.e., all ions in solution reach the detectors of the instrument.

(v) Achievable precision. The precision of our measurements is in excellent agreement with the lower limit theoretically achievable by MC-ICPMS (grey curves, Fig. 4b). The theoretical curves correspond to the quadratic sum of the counting statistics and Johnson noise uncertainties for ²³⁸U/²³⁵U measured with a ²³³U–²³⁶U double spike on Neptune MC-ICPMS, calculated as (see derivation in the ESI†):

where n₈ is the total number of ²³⁸U atoms reaching the detector, R_U is the ²³⁸U/²³⁵U of the sample (which can be taken as the average crustal ratio of 137.797, ref. 16), p is the is ²³⁶U/²³⁸U in the measured solution (sample + spike), μ_j/i is equal to ln(m_j/m_i), with m_i the mass of isotope i, and σ_Ji² is the Johnson noise uncertainty associated with measurement of the isotope i beam.

5.3 Variable ²³⁸U/²³⁵U between single zircon grains

Our dataset shows that single-zircon ²³⁸U/²³⁵U variations exist and can be resolved by high-precision MC-ICPMS measurements (Fig. 5). Individual zircons have δ²³⁸U values between −0.52 ± 0.17‰ (RSES72-2.2) and −0.12 ± 0.06‰ (RSES72-6.1) and chemically abraded samples show similar variations, with leachate values between −0.40 ± 0.07‰ (RSES72-3.6) and −0.17 ± 0.12‰ (RSES72-18.3), and residue values between −0.60 ± 0.22‰ (RSES72-3.6) and −0.10 ± 0.08‰ (RSES72-18.3). Less than 20% of the total sample U is released during the HCl and HNO₃ pre-cleaning steps, indicating a small, yet non-negligible potential contribution from iron oxides, secondary alteration products and adsorbed U (Table S1†), highlighting the need for cleaning or chemically abrading the grains before dissolution for U isotope measurements. For five of the six chemically abraded samples, leachates and residues have indistinguishable δ²³⁸U (within uncertainties), yet, taken at face value, four of these samples show lower δ²³⁸U in the leachates relative to their residue counterpart. For one sample (RSES72-1.2) the leachate (δ²³⁸U = −0.36 ± 0.08‰) is clearly ²³⁵U depleted compared to the residue (δ²³⁸U = −0.12 ± 0.13‰), in agreement with pooled zircons data and the suggestion that aggressive acid attacks may preferentially mobilize ²³⁵U over ²³⁸U (ref. 9 and 12).

Fig. 5 Single-zircon U isotope data revealing resolvable grain-to-grain variations. Vertical grey band shows the chondritic and continental crust value, while the yellow vertical band shows the recommended ²³⁸U/²³⁵U for use in geochronology. Absolute ratios normalized to ²³⁸U/²³⁵U = 137.837 for CRM-112a (ref. 36). The Probability Density Function (PDF, blue curve) and the optimized bandwidth Kernel Density Estimator (KDE, red curve) of the Jack Hills zircons are shown. Leachates (yellow circles) and residues (red circles) from chemical abrasion suggest preferential mobilization of ²³⁵U during strong acid attack. The high MSWD (=3.58) for the Jack Hills zircons indicates that these samples are isotopically heterogeneous. The PDF/KDE of the Jack Hills zircons is not centered on the recommended ²³⁸U/²³⁵U, suggesting that there is variation in the U isotope composition of zircon populations from different localities.

6. Discussion

6.1 No evidence for widespread Oklo-type reactors in the early Earth

Under the right conditions, U-rich deposits formed before ∼1.8 Ga, when natural ²³⁵U abundance was >∼3%, could have reached criticality. This is particularly true in the Hadean, as ²³⁵U abundance was >17%, and the case has been made that a CFF-Xe (CFF = Chemically Fractionated Fission) component, produced by such nuclear reactors, could be present in Earth's atmosphere and explain its Xe isotopic anomalies.³⁸ Yet, in addition to high ²³⁵U abundance, the conditions required for self-sustained neutron-induced ²³⁵U fission are non-trivial to meet: (i) a high enough U concentration (∼>10–20 wt% in the Hadean) in a sediment layer of at least 50–100 cm of thickness,^14,39 (ii) the presence of a neutron flux moderator (e.g., water) and sufficient porosity for water circulation (10–20%), and (iii) no significant amount of neutron absorbing elements (e.g., REEs).⁴⁰ Our single-zircon ²³⁸U/²³⁵U measurements provide a way to directly test for the possible existence of Oklo-type reactors in the early Earth.

The ²³⁸U/²³⁵U of the 31 Jack Hills zircons cover a range of ∼0.50‰, with the lightest and heaviest samples displaying δ²³⁸U values of −0.60 ± 0.22‰ (RSES72-3.6R) and −0.12 ± 0.06‰ (RSES72-6.1), respectively. This distribution is similar to that of younger igneous rocks, which ranges from −0.50 to +0.17‰ (see compilation in ref. 16), and is centered on the chondritic value of −0.31 ± 0.29‰ (2SD, ref. 41). Therefore, our zircon data shows no evidence of ²³⁵U burn-up such as the high δ²³⁸U values of +24 to +475‰ documented in the Oklo reactor zones.¹⁵ Moreover, the range of δ²³⁸U values in Hadean/Archean zircons is ∼10× smaller than the ∼6.2‰ range observed in uraninites (UO₂) and younger U ore deposits (see compilation in ref. 16), whose compositions are primarily controlled by redox processes leading to ²³⁸U enrichments of up to ∼2‰ in the reduced/mineralized phases. In principle, the 0.50‰ spread in ²³⁸U/²³⁵U in early Earth zircons could thus be explained by minor contributions from natural reactor material (<1% of the U in the grains) and/or incorporation of some amount of sediments whose composition were affected by redox processes (∼25% of the U in the grains). Both scenarii are unlikely because Jack Hills zircons formed before oxidative conditions could solubilize U in water as U^VI (ref. 29), therefore precluding redox driven U isotope fractionation in surface environments and preventing oxidative mobilization and accumulation of U in sediments to the wt% levels required for self-sustained neutron-induced ²³⁵U fission. A scenario of weathering-transport-sedimentation and tidal sorting of uraninite has, however, been proposed as a way to produce U-rich sediments capable of reaching criticality.^14,42 Even in this framework, the fact that the range of δ²³⁸U values measured in early Earth zircons is centered on the chondritic value argues against any contribution from sources with high ²³⁸U/²³⁵U (e.g., nuclear reactor material or mineralized ore sediments). As such, our data provides no evidence for the widespread existence of Oklo-type reactors in the Hadean/Archean, at least within the basin sampled by the Jack Hills conglomerate. This casts some doubts on the idea that CFF-Xe could be present in Earth's atmosphere. Analysis of grains from other localities will be necessary to test these hypotheses over a larger geographic scale.

6.2 Potential sources of U isotope variations in single-zircons

As discussed above, the spread in δ²³⁸U values of Jack Hills zircon crystals is unlikely to stem from U incorporation from natural nuclear reactors and/or ²³⁸U enriched sediments (i.e., source effects). Below we consider the potential mechanisms that could lead to U isotope fractionation during magmatic processes, and discuss them in the light of the available data.

According to the theory of stable isotope fractionation (review in ref. 43) mass-dependent isotopic effects during equilibrium isotope exchange reactions vary with the temperature of equilibration (∝1/T²), as well as the oxidation state and bonding environment (or speciation) of the element being exchanged. Typically, heavy isotopes concentrate where coordination numbers are low, bond distances short and valence is high (i.e., stiffest bonds). For U, another equilibrium isotope effect exists: a mass-independent but volume-dependent effect called Nuclear Field Shift (NFS), which stems from differences in the electron density at the nucleus of the two isotopes.¹⁹ The NFS scales as 1/T, occurs during isotope exchange reactions between reduced and oxidized U phases, and results in isotope fractionations 3× larger than, and of direction opposite to, the vibrational mass-dependent effect.^19,44 Changes in the bonding environment, coordination number and/or valence of U during incorporation into minerals could thus lead to ²³⁸U/²³⁵U variations during magmatic differentiation. This hypothesis is consistent with the ²³⁸U excesses of 4.8‰ in pooled titanites relative to pooled zircons in the Fish Canyon Tuff sample,⁹ the ∼0.30‰ variability in multi-grain dissolutions of coexisting phases from single samples (i.e., zircons vs. apatite),^9,12 and the ∼0.20‰ variations among angrite meteorites that correlate with independent tracers of magmatic differentiation (e.g., REE patterns, mineral abundances).²⁰ Because individual zircons from single igneous rock samples can form over protracted periods of magmatic fractional crystallization,^45,46 they are thus likely to record changes in δ²³⁸U of the evolving magma, whether or not the fractionation is due to zircon crystallization itself.

We review the available data on U bonding environment and valence in silicate melts and minerals to determine the mechanisms likely to fractionate U isotopes. In silicate melts, three U oxidation states can coexist (U^IV, U^V, U^VI), depending on the melt's oxygen fugacity (fO₂)⁴⁷ and alkalinity (ref. 48 and references therein). Under the conditions relevant to most magmatic settings (∼QFM buffer), including the Jack Hills zircons (i.e., between IW and QFM buffer⁴⁹), U^IV is the dominant species, with U^V representing <10% of the total U below QFM−1 and up to 40% of the total U at QFM+0.2 (ref. 47). Structure (EXAFS) spectroscopy of silicate glasses indicates that U^IV and U^V occur in 6-fold coordination sites, with slightly different mean U–O distances of, respectively, 2.26–2.29 Å and 2.19–2.24 Å. In contrast, U^VI, present only under highly oxidizing conditions (>QFM+4), occurs in uranyl groups with two axial oxygens at ∼1.77–1.85 Å, and four to five equatorial oxygens at ∼2.21–2.25 Å (ref. 48). Due to its large radius (∼0.89 Å) and charge (4+ or more), U is incompatible during magmatic differentiation until minerals capable of accommodating this large cation start crystallizing: e.g., zircon, baddeleyite, titanite, monazite, apatite, biotite, xenotime, allanite.⁴⁸ While only limited mineral spectroscopic data is currently available (review in ref. 50), U seems to be predominantly incorporated as U^IV in large cation sites in the aforementioned minerals. In zircons, U is thought to be hosted in the large Zr site as U^IV (ref. 48 and 51), although some amount of U^V has been observed in some natural zircons.⁵² The coordination of U in zircons is unclear and both 6-fold⁵¹ and 8-fold⁴⁸ have been proposed. In titanite, U^IV is incorporated in the 7-coordinated Ca^II site via coupled substitution of Mg^II into the Ti^IV site.⁵³ Although no spectroscopic data is available, monazite is also likely to uptake U^IV as it incorporates Th,⁵⁴ which is tetravalent only. To our knowledge, there are no data on U bond length or coordination numbers in these phases. Therefore, under the conditions prevailing in most terrestrial magmatic settings (<∼QFM), no redox changes are expected to occur during uptake of U from the magma into accessory minerals, and thus changes in the coordination number of U and/or the U–O bond length are the most likely driver of U isotopic fractionation.

Although U isotopic fractionation factors between accessory minerals and silicate liquids remain unknown, resolvable δ²³⁸U differences between accessory phases from the same sample (e.g., zircon vs. titanite or apatite^9,12) indicate that U incorporation in at least one of these minerals is accompanied by a non-zero isotope fractionation at magmatic temperatures. The magnitude of NFS and vibrational mass-dependent U isotopes effects in magmatic settings can, to first-order, be estimated using the temperature dependent expression from Fujii et al.⁴⁴: ε = 0.69/T − 82/T², where ε is the isotope fractionation factor between U^IV and U^VI during electron exchange, and T is the temperature in K. At the onset of zircon crystallization (∼850 °C, ref. 55), NFS effects would lead to large isotopic fractionation of ∼+0.61‰, whereas mass-dependent vibrational effects would result in opposite and more subdued fractionation of ∼−0.07‰. By the end of magma crystallization (at ∼700 °C), NFS and mass-dependent effects will have increased to, respectively, +0.71‰ and −0.09‰. Distillation effects would result in larger δ²³⁸U variations. In the simplest scenario, assuming that zircon is the only U host phase crystallizing and using the smaller fractionation factors expected at 850 °C, a Rayleigh distillation during fractional crystallization driven by NFS effects would results in a spread of δ²³⁸U values from +0.61‰ to −1.83‰ (at 95% U removal) around the bulk sample value, whereas the same Rayleigh distillation driven by mass-dependent effects would produce variations between −0.07‰ and +0.22‰ around the bulk value (Fig. 6a). In reality, other phases also uptake U, from pyroxenes to late stage forming phases such as titanite, apatite or monazite, all of which can potentially fractionate U isotopes to different degrees depending on the bonding environment and valence of U in their crystal structure. Nonetheless, this simplified scenario is instructive as it reveals that even the small (∼0.07‰) equilibrium mass-dependent U isotope effects expected at 850 °C can explain the entire spread of ²³⁸U/²³⁵U observed in the Jack Hills zircons (Fig. 6a). Without whole-rock and single-zircon data from the same sample, we cannot definitely conclude as to the direction or magnitude of the Δ_zircon-melt fractionation factor under the conditions (e.g., redox, T) relevant to early Earth zircons, and more work will be needed to constrain this value.

Fig. 6 (a) Melt and instantaneous solid (minerals) U isotope composition evolution during a Rayleigh distillation, as a function of the fraction of U removed from the melt. Two pairs of curves are shown illustrating preferential incorporation of ²³⁵U (solid curves) and ²³⁸U (dashed curves) into the crystallizing phase. The absolute magnitude of the Δ_mineral-melt fractionation factor is 0.07‰ (expected value for vibrational mass-dependent fractionation effects at 850 °C, see text for details). This small mass-dependent effect can explain the entire spread of ²³⁸U/²³⁵U values in the Jack Hills zircons (see density distribution curves). (b) Same as (a), with addition of the bulk solid evolution curve, but using a Δ_mineral-melt fractionation factor of −0.61‰ (expected value for NFS effects at 850 °C). The 4.8‰ offset between pooled titanite and pooled zircons in the Fish Canyon Tuff sample (data from ref. 9) suggests a redox change during U incorporation into zircons (and/or other accessory phases) in oxidizing silicate melts.

In contrast, the offset in ²³⁸U/²³⁵U between pooled titanite and pooled zircons observed in Fish Canyon Tuff sample⁹ provides insight into the mechanisms of U isotope fractionation in magmatic settings under oxidizing conditions (∼QFM+2, ref. 56), and suggests preferential incorporation of ²³⁵U in zircons, or some of the other accessory phases crystallizing before titanite (e.g., monazite, apatite). Indeed, the large (4.8‰) ²³⁸U excess in titanite cannot be explained solely by a NFS effect during U incorporation into titanite, which at ∼850 °C can only produce ²³⁸U excesses 0.61‰ above the bulk rock value (which we assume is represented by the pooled zircon value, for lack of bulk rock data). As titanite is a late forming phase,⁵⁷ the large ²³⁸U excess it records implies that one (or several) of the accessory phases crystallizing before titanite preferentially incorporated ²³⁵U, driving the melt composition towards higher δ²³⁸U values during differentiation. Assuming that the Δ_{titanite-melt} is negligible, a 4.8‰ excess in the residual melt would require formation of titanite after more than 99% of U removal into other phases associated with a NFS Δ_solid-melt of −0.61‰ (Fig. 6b), suggesting a redox change during U incorporation into zircons (and/or other accessory phases) in oxidizing silicate melts.

At this writing, the available δ²³⁸U data from different phases within a single sample is too limited to allow systematic trends to be identified. For instance, Hiess et al.⁹ reported δ²³⁸U values 0.23 ± 0.06‰ lower in apatite than zircon of the Mud Tank carbonatite, whereas Livermore et al.¹² reported values up to 0.30‰ higher in apatite than in zircons in leucogabbro and orthogneiss from Labrador. These differences could be explained in at least two ways: (1) by different crystallization times of apatite from a magma of evolving U isotope composition; or (2) by different U coordination environment in carbonatite and silicate melts, leading to opposite equilibrium fractionation in these phases during fractional crystallization. Single-grain U isotope analysis will allow investigations of these questions through quantification of mineral-melt fractionation factors, and the extent of δ²³⁸U variability within a mineral type for any given sample.

6.3 A shift in global zircon ²³⁸U/²³⁵U after the Paleo-archean?

Multi-grain zircon dissolution data,^9,12 which include samples spanning Earth's post-Eo-Archean history, are not centered on the chondritic (−0.31 ± 0.29‰, ref. 41) or bulk continental crust value (−0.29 ± 0.03‰, ref. 16), but are displaced toward higher δ²³⁸U values by ∼0.20‰ (Fig. 5). In contrast, the Jack Hills zircons δ²³⁸U distribution is indistinguishable from that of chondrites and the bulk continental crust. Taken at face value, this suggests an increase in ²³⁸U/²³⁵U in (some) zircon populations sometime after the Eo- to Paleo-archean transition. Such increase in ²³⁸U/²³⁵U could be the result of either (1) the influence of source materials with higher δ²³⁸U in younger rocks, or (2) a change in mantle redox conditions sometime after the Eo-Archean, allowing the expression of a stronger zircon-melt U isotope fractionation than those observed in older zircons. More work on Hadean/Archean zircons will be necessary to confirm the statistical significance of the δ²³⁸U offset relative to younger zircons.

6.4 Practical relevance of single grain analyses for U–Pb and Pb–Pb geochronology

Owing to analytical advances, sources of uncertainty that were once dominant (e.g., procedural blank, instrumental mass fractionation, Pb-isotope counting statistics) no longer represent a major impediment for high precision U–Pb and Pb–Pb geochronology. State-of-the-art measurements^58,59 using CA-ID-TIMS (chemical abrasion-isotope dilution-thermal ionization mass spectrometry^10,30) can now attain single-zircon U–Pb date precisions on the order of 0.2‰. Although laboratory blank Pb isotope composition and U-series disequilibrium remain a main limitation for high-precision ²⁰⁶Pb/²³⁸U dating of Phanerozoic zircons,⁶⁰ the accuracy with which geological events in the Proterozoic and earlier rock/mineral record can be determined is now significantly limited by how precisely and accurately the sample ²³⁸U/²³⁵U is known. Single-zircon ²³⁸U/²³⁵U measurements have been theoretically recognized as a way to refine U–Pb and Pb–Pb geochronology, but the small U mass harvested from individual zircons has led to claims that only limited, if any, improvements could be gained from such measurements.^10–12 Here, we consider these claims in the light of our data.

For single-zircon ²³⁸U/²³⁵U analyses, uncertainties vary as a function of the amount of U measured (Fig. 4b) and are often limited by counting statistics. Nevertheless, the ± 0.25‰ external reproducibility uncertainty (2SE) obtained here on U loads of only 2 ng is still 25% smaller than the ± 0.33‰ uncertainty associated with the ‘recommended ²³⁸U/²³⁵U value’ that is widely used for U–Pb geochronology⁹ (grey band, Fig. 4b). Moreover, by measuring ²³⁵U on a 10¹² Ω instead of a 10¹¹ Ω amplifier, precision better than 0.30‰ can theoretically be achieved for U loads as low as 0.4–0.5 ng (see Section 6.6). To determine if these U-mass limits are an impediment for application of single-zircon ²³⁸U/²³⁵U analysis to high-precision geochronology, literature data from 2515 individual zircon crystals dated by CA-ID-TIMS at the MIT and Princeton University labs were compiled (Fig. 7). The compilation includes grains covering Earth's history and shows that the typical U mass recovered from chemically abraded zircons ranges from 0.01 to 10 ng. Contrary to the prevailing notion that chemical abrasion results in insufficient amounts of U for precise ²³⁸U/²³⁵U determination in routine U–Pb geochronology analyses,^9–12 the data reveal that 48% of the zircons in those studies yielded more than 0.4 ng of U, and 24% yield more than 1 ng of U. Therefore, virtually every other zircon dated by the CA-ID-TIMS method would be amenable to single-grain U isotope measurements.

Fig. 7 Histograms and associated survival functions of post chemical abrasion U mass (in ng) recovered from 2515 individual zircon crystals analyzed in recent high-precision geochronology studies (data from ref. 23, 24, 35, 66, 67 and 70–94). (a) All data, (b), data shown by geological time periods. For each panel, the % of grains with more than 0.4 ng of U is shown on the survival function. The decrease in U content with increasing age is an artifact due to the chemical abrasion treatment. Indeed, radiation damages on the crystal lattice are more extensive in older zircons, resulting in greater proportion of the grain being leached away during the chemical abrasion step.

6.5 Implications for U–Pb and Pb–Pb geochronology

Below we show how single-grain U isotope measurements would yield more accurate, and in many instances more precise, high-precision Pb–Pb and U–Pb dates than those calculated using a ‘recommended’ ²³⁸U/²³⁵U ratio.^9,12 To the exception of the section discussing chemically abraded zircons, the general chronological considerations below directly apply to all U–Pb geochronology, including other U-rich accessory phases such as baddeleyite,⁶¹ or titanite.^62,63

6.5.1 In a single grain. The typical accuracy and precision improvements brought by single-zircon ²³⁸U/²³⁵U measurements are best shown as age offsets resulting from the difference between the measured and assumed ²³⁸U/²³⁵U (Fig. 8). Although U–Pb dates should theoretically be independent of the ²³⁸U/²³⁵U ratio, they are also affected because ID-TIMS analyses are most commonly made using ²³³U–²³⁵U mixed spikes (e.g., ET-535 and ET-2535; ref. 10), which require knowledge of the sample ²³⁸U/²³⁵U to correct for U mass fractionation during sample preparation and analysis.^64,65 Moreover, due to the low thermal ionization efficiency of U metal, isotopic measurements by ID-TIMS are typically made as oxides.¹⁰ This requires that uncertainties in the effective isotopic composition of oxygen be taken into account. While some methods exist to minimize the contribution of U-oxide correction uncertainties,^10,59 direct measurement of single-zircon ²³⁸U/²³⁵U by MC-ICPMS removes this source of uncertainty altogether.

Fig. 8 Age corrections for the (a) ²⁰⁷Pb–²⁰⁶Pb, (b) ²⁰⁷Pb–²³⁵U and (c) ²⁰⁶Pb–²³⁸U ages of the zircons measured in this work (blue = bulk grain, red = chemical abrasion residue) stemming from the difference between the recommended ²³⁸U/²³⁵U from ref. 9 and the ratio measured in each grain. Lines of equal ΔU values (ΔU = [²³⁸U/²³⁵U_sample/²³⁸U/²³⁵U_Hiess − 1] × 1000, in ‰) are shown and were calculated using eqn (A.3), (A.4), and (A.5).

To further illustrate the impact that single-zircon ²³⁸U/²³⁵U analysis can have on high-precision Pb–Pb and U–Pb age determinations, we use data from two geologically important samples: a 1.09 Ga Midcontinent Rift zircon⁶⁶ and a 3.97 Ga lunar zircon.⁶⁷ While Midcontinent Rift zircon dates have been used to constrain the rates of plate motions in the past, lunar zircons provide the most direct constraint on the age of the Moon. Substituting the median ²³⁸U/²³⁵U uncertainty of our measurements (i.e., ± 0.10‰) in place of the ± 0.33‰ uncertainty of the recommended value from Hiess et al.,⁹ we estimate that, in addition to an increase in accuracy, ²⁰⁷Pb–²⁰⁶Pb dates would become 23 to 54% more precise (Fig. 9 and S1†). Provided laboratory blank and instrumental Pb mass fractionation are not the main sources of uncertainty, removal of the U-oxide correction uncertainty through MC-ICP-MS ²³⁸U/²³⁵U measurement could improve the typical precision of ²⁰⁶Pb–²³⁸U and ²⁰⁷Pb–²³⁵U dates by 6 to 22% (Fig. 9 and S1†).

Fig. 9 Contribution of the different sources of uncertainty to the high-precision ²⁰⁶U–²³⁸Pb age of a 1.09 Ga Midcontinent rift zircon⁶⁶ (sample BBC-SBA1, fraction z1) and the ²⁰⁷Pb–²⁰⁶Pb age of a 3.97 Ga lunar zircon⁶⁷ (sample 14 304, fraction z20). ²⁰⁶U–²³⁸Pb and ²⁰⁷Pb–²⁰⁶Pb dates are typically reported for events younger and older, respectively, than ∼1.5 Ga. For each sample the published errors calculated using the recommended ²³⁸U/²³⁵U from ref. 9 are compared to the errors that would be achieved if a single-zircon U isotope measurement with precision of ±0.10‰ had been performed instead. Details of error contribution on all Pb–Pb and U–Pb ages are shown in ESI Fig. S1.†

6.5.2 In a grain population. To achieve higher precision and provide stronger temporal constraints, geochronological studies typically report the weighted mean age of ∼15–20 zircon grains coming from the same sample. Since it is assumed that grains of similar apparent age formed at the same time, it is common practice to reject “outlier” grains based on their ages alone, so as to achieve a weighted mean with near unit MSWD. This practice implicitly assumes that all grains have the same ²³⁸U/²³⁵U. A Monte-Carlo analysis (ESI†) exploring the effect of U isotope variability on the accuracy of the weighted mean of 20 co-genetic zircon grains reveals statistically significant effects on both ²⁰⁷Pb–²⁰⁶Pb and ²⁰⁷Pb–²³⁵U ages as soon as individual grain age precisions better than 0.05 to 0.10% are achieved (Fig. 10). This implies that at such high precision, and in the absence of single-zircon U isotope data, rejecting grains based solely on their apparent ages to achieve a unit MSWD does not ensure that the rejected grains are true outliers. In such scenarii, single-zircon ²³⁸U/²³⁵U analyses will allow to better assess whether grains belong to the same population, and to calculate more meaningful and accurate weighted mean ages. Given that decay constants errors almost completely cancel out when considering age intervals,²⁰ the improvements in precision and accuracy achievable through single-zircon ²³⁸U/²³⁵U measurements will provide unprecedented resolution power for establishing the timescales of short-lived events and processes.

Fig. 10 (a, top-panel) Example of KDE of the U-corrected MSWD of the weighted mean age calculated for 500 Ma zircons (20 grains), for relative precision on the age measurement of individual grains between 2 and 0.01% (see legend bottom panel). The Monte-Carlo analysis used 50 000 simulations (MCS) and δ²³⁸U values were randomly picked within a uniform distribution of width 1‰, centered on the ‘recommended’ value from ref. 9. For simplicity, and to be conservative, age uncertainties are kept constant before and after age correction: i.e., only the improvement in accuracy is evaluated. (a, bottom-panel) Median shift in MSWD of the weighted mean ²⁰⁷Pb/²⁰⁶Pb age of 20 zircon grains resulting from U-based age corrections. Grey areas denote statistically insignificant shifts (horizontal band), and ages for which ²⁰⁶Pb–²³⁸U ages are preferred to ²⁰⁷Pb–²⁰⁶Pb ages (which are too imprecise, vertical band). (b and c) Same as bottom-panel a, but for ²⁰⁷Pb–²³⁵U and ²⁰⁶Pb–²³⁸U ages, respectively.

6.5.3 ²⁰⁶Pb–²³⁸U ages. Although ²³⁸U/²³⁵U variations predominantly impact the accuracy of ²⁰⁷Pb–²³⁵U and ²⁰⁷Pb–²⁰⁶Pb dates over ²⁰⁶Pb–²³⁸U dates (Fig. 8, 10, and ESI†), the existence of extremely fractionated δ²³⁸U values in some zircons (e.g., Table Cape pooled zircon; ²³⁸U excess of 3.4‰; ref. 9) means that even ²⁰⁶Pb–²³⁸U dates will be affected in some rare occasions. For a 250 Ma old zircon, a difference of 3.4‰ between the assumed and actual ²³⁸U/²³⁵U would translate into an age offset of ∼15.4 kyr. This offset is similar in magnitude to the extent by which the end-Permian extinction is currently resolved from being an instantaneous event (60 ± 48 kyr; ref. 23). Thus, examination of the rock record at sub-permil age precision, even in Phanerozoic samples,^23,68 will benefit from concomitant measurement of U isotopes for as long as ²³⁵U-based spikes are utilized.

6.5.4 Concordance and half-lives. Uranium isotopic analyses will also prove useful in assessing U–Pb dates concordance. For CA-ID-TIMS U–Pb dates, small degrees of discordance are mainly interpreted as the result of disequilibrium incorporation of intermediate daughter products in a sample,^45,68 and/or systematic errors in the U decay constants.^27,31 Disequilibrium effects are only significant for the longest-lived nuclides, ²³⁰Th (t_1/2 = 75.4 ky) and ²³¹Pa (t_1/2 = 32.76 ky), and affect, respectively, ²⁰⁶Pb–²³⁸U and ²⁰⁷Pb–²³⁵U dates. Given the strong sensitivity of ²⁰⁷Pb–²³⁵U dates to U isotope variations, single-zircon ²³⁸U/²³⁵U measurements will (i) help resolve the contributions of intermediate daughter disequilibrium to the discordance of U–Pb dates observed in some samples^45,68 (Fig. 11), and (ii) allow a proper re-evaluation of the accuracy of U decay constants, for which revisions have only been proposed based on non-U-corrected U–Pb ages^27,31 or U–Pb ages calculated using pooled zircon data.⁹ This latter key advantage will enable a finer-scale calibration of other radio-chronometers (e.g., Ar–Ar) against the Pb clock.

Fig. 11 Concordia diagram, with error envelope due to the uncertainty in U half-lives (grey), showing the effect of a difference between actual and assumed ²³⁸U/²³⁵U of the sample. Lines of equal ΔU values are 1‰ apart and were calculated using eqn (A.1) and (A.2). Also shown are the data for five zircons from the Midcontinent rift sample BBC-SBA166 (blue).⁶⁶ Excess of ²³¹Pa and U isotope variations both result in horizontal displacement of the data in a concordia diagram (green), and as such, disequilibrium of intermediate decay products can only be properly assessed if single-zircon U isotope measurements are performed. Half-lives and their uncertainties from ref. 95.

6.6 Current limitations and future improvements

Some zircons will be either too small, too radiation damaged, or too U-poor to yield sufficient U amounts for high-precision single-zircon U analysis. Taking a fiducial amount of U of 0.4 ng (see below), we estimate (Fig. 7) that ∼50% of zircons will contain too little U to allow direct ²³⁸U/²³⁵U measurement with current methodologies. The precision achieved in this study is at the theoretical level of MC-ICPMS counting statistics (Fig. 4b) but only ∼2.5% of the atoms in the solution make it to the detector. A recent study showed that up to 5% efficiency for U was achievable using cavity source TIMS.⁶⁹ There is thus ample room for improvement as the transmission of mass spectrometers continues to improve (black curve on Fig. 4b shows absolute precision limit: 100% ion transmission). In cases where U contents remain too low, measurement of small pooled fractions of co-genetic zircons (e.g., 2 to 5 grains) is the only way to obtain useful estimates approaching the true sample ²³⁸U/²³⁵U variability, for high-precision Pb–Pb and U–Pb chronology.

The method presented here is by no means fully optimized and significant improvements would help make single-zircon U isotope measurements more routine. In particular, exploration of the parameter space relevant to measurement precision using eqn (2) reveals that using higher spiking ratios and amplifiers equipped with 10¹² and/or 10¹³ Ω resistors could significantly improve measurement precision for small U loads (<2 ng U, Fig. 12).

Fig. 12 Theoretical limit on δ²³⁸U values uncertainty (2 SE external) achievable on Neptune MC-ICPMS plotted as a function of the sample spiking level (bottom x-axis, U_Spike/U_Sample; top x-axis, parameter p from eqn (2), which relates the number of ions of ²³⁶U and ²³⁸U as: n₆ = p n₈). The various curves represent different amounts of total U measured (in ng). Uncertainties are calculated using eqn (2), assuming ²³⁸U is measured at 10 V with a 10¹¹ Ω resistor, and each cycle of 4.192 s consumed 0.072 ng of U. Left, center and right panels assume that ²³⁵U is measured using, respectively, a 10¹¹, 10¹² or 10¹³ Ω resistor, with the top, center and bottom row assume that the spike isotopes (²³³U and ²³⁶U) are measured using, respectively, 10¹¹, 10¹² or 10¹³ Ω resistors, respectively. For small U loads, optimal precision can be achieved using U_Spike/U_Sample ratio of ∼8–10% (where uncertainties plateau) and by measuring ²³⁵U in a 10¹² or 10¹³ Ω resistor.

6.6.1. Increasing spiking ratio. Regardless of the amplifier setup and for sample loads as low as 0.4 ng of U, uncertainties plateau beyond a spiking level, U_Sp/U_Smp, of ∼8–10% (Fig. 12). This spiking ratio is higher than the value of 3% used in the present work, and should supersede it for future work on low U amounts. Increasing the spiking level will increase the spike contribution to the ²³⁵U and ²³⁸U budget, but even at U_Sp/U_Smp = 10% these contributions remain minimal (0.3‰ and 0.01‰, respectively). As long as the sample and bracketing standards have similar spiking levels, no systematic bias will be introduced and measurement uncertainties on the ²³⁸U/²³⁵U will thus be efficiently minimized. The same is not true for ²³⁴U where the spike contribution would reach ∼349‰ for U_Sp/U_Smp = 10%, which would require propagation of the error of the spike ²³⁴U abundance onto the final uncertainty of the ²³⁴U/²³⁸U reported.

6.6.2. Use of high ohmic amplifiers. For a given amount of U analyzed, the achievable uncertainties are lowered by measuring ²³⁵U, and to a much lesser extent ²³³U + ²³⁶U on 10¹² and/or 10¹³ Ω resistors (Fig. 12). Using a U_Sp/U_Smp of 10%, optimal precisions achievable with modern instrumentation are shown in Fig. 13 as a function of (i) the total U measured (assuming a 10 V signal on ²³⁸U), and (ii) the resistance linked to the amplifier used to measure ²³⁵U. As can be seen on Fig. 13, measurement precisions improve by more than 0.1‰ on δ²³⁸U values for low U amount analyses (below 1 ng of U) when using a 10¹² to 10¹³ Ω resistor to measure ²³⁵U. At such high spiking levels, changing the resistance linked to the amplifier used to measure ²³³U and ²³⁶U from 10¹¹ to 10¹³ Ω has virtually no impact on the results. Uncertainties on the order of ±0.30‰ can still be achieved using only 0.4–0.5 ng of U, implying that single-zircon ²³⁸U/²³⁵U measurement can provide higher precision and accuracy than the currently recommended ²³⁸U/²³⁵U ratio from ref. 9, even for grains with such low U sample loads.

Fig. 13 Theoretical limit on δ²³⁸U values uncertainty (2 SE external) achievable on Neptune MC-ICPMS plotted as a function of the amount of U measured (in ng). Uncertainties are calculated using eqn (2) assuming a U_Sp/U_Smp of 10%, that ²³⁸U is measured at 10 V with a 10¹¹ Ω resistor, and that each cycle of 4.192 s consumed 0.072 ng of U. The three black curves show the theoretical lower limit achievable when ²³⁵U is measured using a 10¹¹, 10¹² or 10¹³ Ω resistor (see legend). The spike isotopes can be measured with 10¹¹, 10¹² or 10¹³ Ω resistors without any significant impact on the results given the high spiking level. Even for U sample loads as low as 0.4–0.5 ng, a precision of 0.30‰ is achievable, comparable to the ± 0.33‰ of the recommended ²³⁸U/²³⁵U value from ref. 9.

6.6.3 Micro-column chemistry. The U purification protocol used here, developed for large sample masses with complex matrices,¹⁶ results in blanks of up to ∼0.02 ng, which would be significant for high-precision U–Pb and Pb–Pb dating of loads ∼0.4 ng U. Purifying U using the 50 μL AG1-X8 columns typically used in U–Pb geochronology (e.g., ref. 31) would decrease elution volumes, and consequently blanks, by a factor > 250 (from 85 mL to 300 μL), thus streamlining integration of single-zircon ²³⁸U/²³⁵U measurement into geochronological work.

7. Concluding remarks

As the exact origin of U isotope variations in zircons is unknown, future investigations using extended X-ray absorption fine structure (EXAFS) and/or synchrotron spectroscopy will be needed to address the cruel lack of data on the bonding environment (bond length, coordination number) and valence state of U in minerals. Future works trying to understand the causes of these variations in greater detail could explore potential correlations between ²³⁸U/²³⁵U ratios and other geochemical and isotopic tracers of magmatic and/or source rock nature and evolution, such as Th/U ratios, oxygen isotopes, initial ¹⁷⁶Hf/¹⁷⁷Hf ratios, or Ti-thermometry. Through such investigations, which are beyond the scope of this study, single-zircon ²³⁸U/²³⁵U analysis has the potential of becoming a new tool to probe processes of crustal formation and differentiation, potentially tied to sediment burial or changes in the oxygenation state of the atmosphere-ocean system.

Funding

This work was supported by an NSF grant (EAR1824002) and Crosby Postdoctoral Fellowships (MIT) to FT and MI, a Chamberlin Postdoctoral Fellowship (University of Chicago) to PB, grants from NSF (PG EAR1444951 and CSEDI EAR1502591) and NASA (LARS NNX17AE86G, EW NNX17AE87G, and SSW NNX15AJ25G) to ND, an MIT Ferry Fund award and NSF award (EAR1439559) to DM, and a NASA (EW 80NSSC17K0773) grant to TG.

Author contributions

FT, PB, MI and ND initiated the study; FT, PB and MI designed the research; TMH provided the Jack Hills zircons; FT and MI performed the research. FT performed the measurements on ND's and DM's instruments and analyzed the data (including modeling). FT, MI and PB interpreted the data. FT wrote the manuscript with contributions from all co-authors.

Data and materials availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the ESI.† Additional data related to this paper may be requested from the authors.

Appendix A: shift in concordia space and age corrections

For a given sample, unrecognized U isotope variations will lead to erroneous age calculations^9,16 and shifts in a concordia diagram (Fig. 11), which were quantified using the following analytical formulae (see derivations in the ESI†). Let's consider ΔU, the difference between the actual and assumed U isotope composition of the sample, and defined as: ΔU = (²³⁸U/²³⁵U_actual/²³⁸U/²³⁵U_assumed −1) × 1000).

Parameters specific to the spike used for the U–Pb measurement will influence the magnitude of these age and concordia offsets. Here we take the example of U–Pb measurements made with the EARTHTIME ET535 tracer (a mixed ²⁰⁵Pb–²³³U–²³⁵U tracer). For a given shift in U isotope composition, the corresponding shifts in the ratio of radiogenic Pb isotope to parent U isotope, ²⁰⁶Pb*/²³⁸U and ²⁰⁷Pb*/²³⁵U, are respectively noted ΔR68 and ΔR75, and calculated as:

andwhere λ_i is the half-life of isotope i, R85m is the ²³⁸U/²³⁵U measured in the sample + spike mix, R_U is the assumed ²³⁸U/²³⁵U of the sample, and t8 and t5 are the uncorrected ²⁰⁶Pb/²³⁸U and ²⁰⁷Pb–²³⁵U ages of the sample, respectively (i.e., calculated using the assumed ²³⁸U/²³⁵U).

Similarly, for a given shift in U isotope composition, the corresponding offsets in ²⁰⁷Pb/²⁰⁶Pb, ²⁰⁶Pb/²³⁸U and ²⁰⁷Pb/²³⁵U dates, are respectively noted Δt, Δt8 and Δt5, and calculated as (see derivations in ESI†):

Conflicts of interest

Authors declare no competing interests.

Acknowledgements

We thank Melanie Barboni for providing the lunar zircon data and Blair Schoene and Jahan Ramezani for compiling some of the data in Fig. 7. Comments on an earlier version of the manuscript by A. Bauer, M. Barboni, C. Y. Chen, M. Collinet, N. Greber, J. Ramezani and D. Trail are greatly appreciated.

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Footnote

† Electronic supplementary information (ESI) available: Additional notes on Materials and methods, supplementary text, Fig. S1–S11, Tables S1–S5. See DOI: 10.1039/c9ja00205g

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