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Calibration of the Lutetium-Hafnium Clock

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Science  27 Jul 2001:
Vol. 293, Issue 5530, pp. 683-687
DOI: 10.1126/science.1061372

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Abstract

Well-defined constants of radioactive decay are the cornerstone of geochronology and the use of radiogenic isotopes to constrain the time scales and mechanisms of planetary differentiation. Four new determinations of the lutetium-176 decay constant (λ176Lu) made by calibration against the uranium-lead decay schemes yield a mean value of 1.865 ± 0.015 × 10−11 year−1, in agreement with the two most recent decay-counting experiments. Lutetium-hafnium ages that are based on the previously used λ176Lu of 1.93 × 10−11 to 1.94 × 10−11year−1 are thus ∼4% too young, and the initial hafnium isotope compositions of some of Earth's oldest minerals and rocks become less radiogenic relative to bulk undifferentiated Earth when calculated using the new decay constant. The existence of strongly unradiogenic hafnium in Early Archean and Hadean zircons implies that enriched crustal reservoirs existed on Earth by 4.3 billion years ago and persisted for 200 million years or more. Hence, current models of early terrestrial differentiation need revision.

Estimates of the timing of dynamic processes in Earth and other planets are almost entirely based on radioactive decay systems that have half-lives between 105 and 1012 years. The Lu-Hf system, with a half-life of ∼37 billion years, is both a versatile geochronometer and a powerful tool for studying the processes that control crust-mantle evolution. However, knowledge of the exact value of the decay constant for the β-decay of 176Lu to176Hf is vital to the correct interpretation of Lu-Hf data. The precision and accuracy of both Lu-Hf ages and initial Hf isotope compositions [ɛ Hf(t), (1)] depend directly on λ176Lu. The first widely used Lu decay constant, 1.94 ± 0.07 × 10−11 year−1, was derived from the slope of a Lu-Hf isochron for eucrite meteorites of known age (2, 3). This value, based on age comparison, was used until 1997, when a more precise value [1.93 ± 0.03 × 10−11year−1, (4)] obtained by decay counting was adopted (5). However, all other decay-counting experiments made since 1980 (6–10) yield lower values. The recommended (10) mean of recent decay-counting results, 1.86 ± 0.01 × 10−11year−1 (7, 9, 10), is ∼4% lower than both of the aforementioned decay constants. The accurate application of Lu-Hf systematics requires the reconciliation of decay constants determined from both decay-counting and age-comparison experiments.

Agreement between the two most recent decay-counting results (9, 10) is due to the elimination of several experimental difficulties related to (i) optimizing detector geometry and calibration, (ii) knowing the exact amount of 176Lu in the sample, and (iii) correcting for the effects of gamma-ray attenuation, true-coincidence summing, and internal conversion (10). Age-comparison studies of minerals and rocks (2, 3, 11), in which λ176Lu is calibrated against the relatively well-constrained U decay constants, have been limited by difficulties with measuring Hf isotope compositions and Lu concentrations by thermal ionization mass spectrometry (TIMS). Here, we measured Lu and Hf isotope ratios using multiple-collector inductively coupled plasma mass spectrometry (MC-ICP-MS). This method allows high-precision analyses of small samples (as low as 5 ng of Hf) that were not possible in previous TIMS-based age-comparison studies.

Geologic samples for λ176Lu calibration by age comparison were selected according to the following criteria: (i) They must contain minerals highly enriched in the parent elements for both Lu-Hf and U-Pb dating methods. (ii) They must have cooled rapidly, so that the potential effects of differing closure temperatures (T C) between the Lu-Hf and U-Pb systems or among different minerals are minimized. (iii) The samples should have remained closed systems with respect to Lu-Hf and U-Pb systems since formation. We note, however, that the last criterion does not necessarily have to be met in the strict sense for the U-Pb system. Lead loss or changes in U content, provided they are recent, will not affect 207Pb/206Pb ages. Single, ancient Pb-loss events will produce a discordia whose upper intercept indicates the time of crystallization.

We analyzed a ∼100-cm3 gadolinite crystal from a pegmatite at Evje, Norway, a ∼1-cm3 xenotime crystal from a pegmatite at Tvedestrand, Norway, xenotime from a monazite-xenotime gneiss in the Hudson Highlands, New York, USA, and apatite and baddeleyite from a coarsely crystalline carbonatite from the Phalaborwa intrusion, South Africa (12). The Hudson Highlands gneiss probably formed by short-lived metasomatic processes (13), and the other minerals come from rapidly cooled intrusions. Though minerals from all four localities were previously dated by the U-Pb system, additional U-Pb TIMS analyses were made to verify the ages of the samples used in the present study. All U-Pb ages and errors that were used to calculate λ176Lu values contain the propagated uncertainties of the U decay constants (14).

Five fragments of the Evje gadolinite crystal (EVJ) define a U-Pb upper intercept age of 909 ± 14 million years (Ma), and a cluster of four concordant analyses (gd-5, gd-6, gd-7, and gd-8) gives a concordia age of 910.5 ± 1.6 Ma (Fig. 1A). These ages agree with the 901 ± 20 Ma 207Pb/206Pb age for another gadolinite from the Evje-Iveland area (11). Three fragments of the EVJ gadolinite have the most radiogenic Hf yet measured in a natural sample (176Hf/177Hf = 260 to 272, Table 1 and Fig. 1B); 99.9% of the176Hf was produced by 176Lu decay in the gadolinite crystal. The slope of the Lu-Hf isochron is thus insensitive to the assumed initial 176Hf/177Hf [i.e., that of depleted mantle at 910 Ma, ±20 ɛ-units (15)] that is used as a fourth point in the regression. Although the errors on 176Lu/177Hf and176Hf/177Hf for the gadolinites are larger than those normally achieved for less radiogenic minerals (16), these errors are correlated and therefore the slope of the Lu-Hf isochron is relatively well constrained (±0.8%).

Figure 1

U-Pb concordia and Lu-Hf isochron diagrams (A through H). gd, gadolinite; xt, xenotime; ap, apatite; bd, baddeleyite. Open symbols are excluded from the regressions. U-Pb data are available online (47). Uranium decay constants: λ238U = 1.55125 ± 0.00166 × 10−10 year−1, λ235U = 9.8485 ± 0.0134 × 10−10 year−1 [(48); 95% confidence level]. All regressions are model 1 fits (i.e., points weighted according to the inverse square of their errors) except for the Hudson Highlands U-Pb, which is a model 2 fit (i.e., points weighted equally). MSWD statistics of concordia ages (49) are for combined equivalence and concordance. Lu-Hf errors are smaller than the symbols, except for Evje where depicted by error ellipses. λ176Lu = ln(m + 1)/t, where m is the slope of the Lu-Hf isochron and t is the U-Pb age of the sample in years. Uncertainties on λ176Lu values are derived from the 2 SD uncertainties in t and m using σλ = [σm 2(∂λ/∂m)2+ σt 2(∂λ/∂t)2]0.5.

Table 1

Lu-Hf data. The 2 SD external reproducibilities of176Lu/177Hf and176Hf/177Hf are 0.2% and 0.005%, respectively. Errors in parentheses refer to the last significant digits and are the greater of external reproducibility or 2 SE in-run statistics. Hafnium concentrations and176Lu/177Hf take into account the variable atomic weight of Hf (i.e., from 178.5 in zircon to 176 in gadolinite). Reported 176Hf/177Hf values were adjusted for instrumental bias so that 176Hf/177Hf of JMC-475 = 0.282163.

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The Tvedestrand xenotime (TVS) comes from a pegmatite that intruded into a regionally cooling terrane (the Bamble sector of southern Norway) whose temperature at the time of intrusion is constrained by hornblende 40Ar/39Ar ages [(17) and references therein] to be ≤600°C. TheT C for U-Pb in xenotime is similar to that of monazite [(13, 18); i.e., ∼725°C (19)] or higher [≥800°C (20)], and thus the U-Pb age for sample TVS is taken to be the crystallization age. Three xenotime fragments define a U-Pb chord that has an upper intercept at 1094 ± 11 Ma (Fig. 1C). The minor apparent Pb loss in these fragments was assumed to have occurred during heating associated with magmatism in the Permian Oslo Rift; allanite and zircon from the Bamble sector exhibit similar Permian Pb-loss patterns (17, 21). The lower intercept was therefore anchored at 280 ± 50 Ma. Removing this constraint results in an identical xenotime age of 1094 +76/−17 Ma. Though less radiogenic than the EVJ gadolinite, two TVS xenotime fragments have sufficiently elevated 176Lu/177Hf and176Hf/177Hf ratios, and they lie on an isochron that uses a range of possible initial176Hf/177Hf ratios [i.e., depleted mantle at 1094 Ma, ±20 ɛ-units (15)] as a third point (Fig. 1D).

Three U-Pb analyses of single xenotime grains from the Hudson Highlands gneiss (RS-1) are plotted in Fig. 1E together with previously published (13) xenotime analyses from the same outcrop. Aleinikoff and Grauch (13) excluded one of four analyses from their discordia regression and report a xenotime age of 986.5 ± 1.5 Ma. However, the scatter in the combined data sets precludes any objective elimination of points, and combining the data sets yields an upper intercept age of 997 ± 25 Ma. The mean square of weighted deviates (MSWD) is 60, indicating geologic scatter that we interpret to be a small variability in xenotime age (22). The slope of the Lu-Hf isochron is constrained by two xenotime fractions and the biotite fraction (Fig. 1F). Zircons and whole rocks were excluded from the regression because the zircons contain an inherited Hf component (23).

The Phalaborwa carbonatite (PHB) contains abundant baddeleyite needles and prismatic, greenish-gray apatite crystals. Two types of apatite were picked: large (10 mm long by 5 mm diameter) turbid crystals and small (<4 mm long by <1 mm diameter) clear crystals. Three U-Pb analyses of baddeleyite (bd-1, bd-3, and bd-4) yield a concordia age of 2059.9 ± 3.4 Ma (Fig. 1G). The large apatites are slightly discordant (+1% and –8%) and lie on or near a chord between the baddeleyite age and 0 Ma. The smaller apatites, which are more discordant (+5 to +18%) and lie substantially below the discordia, were not used for Lu-Hf analyses. Both the concordia age and the baddeleyite-apatite upper intercept age (2059.6 ± 6.6 Ma) agree well with published ages for the Phalaborwa carbonatite [2058 to 2061 Ma (24–26)]. A Lu-Hf isochron is defined by the two large apatites and a baddeleyite fraction (Fig. 1H). The 176Hf/177Hf ratio of the baddeleyite has been confirmed by an unspiked replicate analysis (Table 1).

The λ176Lu values determined from the four independent age comparisons are shown in Fig. 1. There is remarkable agreement among these results compared to the scatter among some of the physical counting experiments of the past two decades [e.g., (4,7, 8, 10)], suggesting that the U-Pb ages and Lu-Hf slopes reflect the true crystallization ages of the minerals. Our unweighted mean results (with 2 SD uncertainties) are: λ176Lu(β) = 1.865 ± 0.015 × 10−11 year−1 and t½ 176Lu(β) = 3.717 ± 0.030 × 1010 year. This decay constant agrees with those from the two most recent decay-counting experiments [i.e., λ176Lu(β) = 1.86 ± 0.02 × 10−11 year−1, and 1.88 ± 0.01 × 10−11 year−1 (9,10)]. Weighting our individual determinations by inverse variance gives a mean λ176Lu of 1.858 ± 0.004 × 10−11 year−1 with a MSWD of 0.59. This mean is strongly influenced by the Phalaborwa carbonatite, which has the smallest amount of geologic scatter of the samples. The other three samples, however, yield systematically higher λ176Lu values, and we therefore recommend the unweighted mean as the result of this study.

The existence of a minor (≤4%) decay branch of 176Lu to176Yb by electron capture has been debated (27,28). If it does exist, it can only contribute a maximum bias of 0.18% between counting experiment and age-comparison results (29). This potential bias is greatest when the oldest samples (e.g., 4.55 Ga eucrites) are used in the age comparisons. The mean age of the samples in this study is 1.3 Ga. Correcting our results for e-capture decay would lower our λ176Lu(β) by ≤0.05%. When e-capture is neglected in both our λ176Lu determination and in Lu-Hf age calculations, this bias cancels out for ∼1.3 Ga ages, whereas Lu-Hf ages would be ≤0.13% too old for 4.56 Ga samples, and ≤0.5% too young for samples younger than 1.3 Ga. These shifts are minor relative to the present uncertainty of the decay constant, and we have therefore neglected any e-capture when calculating our λ176Lu(β) values.

A value of 1.865 ± 0.015 × 10−11year−1 for λ176Lu(β) requires the correction of Lu-Hf ages and many of the initial Hf isotope ratios that have been used to document the paired processes of crust formation and mantle depletion in the early Earth. Most published Lu-Hf ages are ∼4% too young and therefore conclusions drawn from the comparison of Lu-Hf ages with those of other isotope systems (e.g., Sm-Nd, Rb-Sr, U-Pb) may need modification. More importantly, initial Hf isotope compositions reported for some of Earth's oldest minerals and rocks need to be recalculated. Most published initialɛ Hf values for early Archean zircons and evolved, low-Lu/Hf rocks shift downward by 2 to 4 ɛ-units when using the new λ176Lu. For example, the reportedɛ Hf(t) of 0 to +4.6 for a set of early Archean gneisses and zircons from West Greenland (30) drops to –2.8 to +1.7 when recalculated with the new decay constant. For these low-Lu/Hf samples, most of this change is caused by the shift in the position of the chondritic uniform reservoir (CHUR) evolution curve projected back through time, rather than the shift in the initial Hf isotope composition of the sample itself. In contrast, theɛ Hf(t) of rocks that have near-chondritic Lu/Hf will not change substantially, and rocks having super-chondritic Lu/Hf will shift to higherɛ Hf(t) values. This adjustment ofɛ Hf(t) values has significant implications for inferences regarding differentiation processes in the early silicate Earth and on other planetary bodies. Models based on Hf isotopes have to be revised for: (i) the ages of Earth's first enriched reservoirs, (ii) the minimum residence time of these reservoirs, and (iii) the early depletion history of Earth's mantle.

Amelin et al. (31) have noted that if a λ176Lu of ∼1.86 × 10−11year−1 is correct, then some of Earth's oldest zircons [Jack Hills (32)] would indicate the existence of enriched reservoirs that had ɛ Hf = −3.7 to −8.0 at 4.1 to 4.0 Ga. To produce such highly unradiogenic Hf compositions by that time, the enriched reservoir(s) (e.g., early crust) must have separated from the mantle source at or before 4.3 Ga and then survived until the zircons crystallized some 200 to 450 million years later (31–33). These initial Hf isotope ratios, recalculated with the new 176Lu decay constant, therefore imply the existence of a differentiated silicate crust on Earth at or before 4.3 Ga. Such early crust formation in Hadean time (>4.0 Ga) is corroborated by the recently reported 4.3 to 4.4 Ga crystallization ages of the oldest preserved terrestrial zircons (34, 35). Short-lived isotope systems such as146Sm-142Nd and92Nb-92Zr [e.g. (36–40)] provide no compelling evidence for large-scale mantle depletion or crust formation on Earth before 4.51 Ga. In contrast to 92Zr, which could develop anomalies in crustal reservoirs only until ∼4.51 Ga, resolvable 142Nd anomalies may have been generated in crust as late as 4.3 Ga (38,40, 41). Hadean detrital minerals, which may have preserved these anomalies, have not yet been analyzed for 142Nd. The available short-lived nuclide data on terrestrial rocks, together with the reevaluated Lu-Hf zircon data, suggest that Earth's first persistent crust formed between 60 and 260 million years after the condensation of the oldest solid matter in the solar system [4.566 Ga (42)].

  • * To whom correspondence should be addressed. E-mail: escherer{at}nwz.uni-muenster.de

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