Calibration of the Lutetium-Hafnium Clock
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The value of ε Hf is the deviation of the 176 Hf/ 177 Hf of a sample in parts per 10 4 from that of the CHUR reference: [( 176 Hf/ 177 Hf) sample /( 176 Hf/ 177 Hf) CHUR – 1] × 10 4 . The initial ε Hf or ε Hf ( t ) is the deviation from CHUR when the sample crystallized at time t : {[( 176 Hf/ 177 Hf) sample – ( 176 Lu/ 177 Hf) sample (e λ t – 1)]/[( 176 Hf/ 177 Hf) CHUR – ( 176 Lu/ 177 Hf) CHUR (e λ t – 1)] – 1} × 10 4 .
M. Tatsumoto D. M. Unruh P. J. Patchett Mem. Natl. Inst. Polar Res. (Tokyo) Special Issue no. 20 Proceedings of the Sixth Symposium on Antarctic Meteorites (December 1981) p. 237.
Sato J., Ohoka Y., Hirose T., Radiochem. Radioanal. Lett. 58, 263 (1983).
Analytical methods: To optimize spike-sample equilibration all samples (except gd-2 gd-3 ap-2 and ap-3 as explained below) were spiked with 205 Pb- 233 U or 180 Hf- 176 Lu before digestion. To minimize error magnification effects on measured 176 Lu/ 177 Hf and 176 Hf/ 177 Hf three different 180 Hf- 176 Lu tracer solutions covering a wide range of Lu/Hf ratios were made. These tracers were intercalibrated against two different mixed Lu-Hf standard solutions prepared from Ames metals at Münster. Tracers for whole-rock and high-Lu/Hf samples were also cross-calibrated against two more Lu-Hf Ames metal solutions from University of California Santa Cruz (UCSC). Optimally spiked calibrations agreed with the previous Münster calibrations to within 0.2% for Lu/Hf ratios and Lu and Hf concentrations. Because the Lu/Hf of gadolinite exceeds the optimal range of our highest Lu/Hf spike gd-2 and gd-3 were split into Hf IC Hf ID and Lu ID aliquots immediately after digestion and the ID aliquots were optimally spiked for Hf and Lu respectively. To obtain both Lu-Hf and U-Pb ages on single apatite fractions digested ap-2 and ap-3 samples were split into a Lu-Hf aliquot and two U-Pb aliquots (“a” and “b”) before spiking. Samples were digested in Savillex vials placed inside Parr Teflon bombs using HF-HNO 3 (zircon baddeleyite and biotite) 6 M HCl (apatite) HF-HCl (gadolinite) or concentrated H 2 SO 4 (xenotime). Xenotime digestion was completed by periodically cooling the sample and adding concentrated HF during the H 2 SO 4 evaporation step. All digested Lu-Hf samples were evaporated with HClO 4 to ensure complete spike-sample equilibration. Uranium and Pb were separated using a HBr anion exchange column and their isotope compositions were analyzed on the VG Sector 54-30 TIMS at Münster. Hafnium was separated from the bulk matrix and Ti using a single ion-exchange column; the Lu+Yb cut from the Hf column was processed through an αHIBA column to remove Yb. Lutetium and Hf were analyzed in static mode on the Micromass Isoprobe at Münster. Admixed Re was used to apply an external mass bias correction to Lu. Values for the in-house Hf isotopic standard (isotope ratios indistinguishable from JMC-475) are: 176 Hf/ 177 Hf = 0.282151 ± 6 (2 SE n = 29) 178 Hf/ 177 Hf = 1.46718 ± 1 179 Hf/ 177 Hf raw = 0.7367 ± 4 and 180 Hf/ 177 Hf = 1.88652 ± 5 (normalized to 179 Hf/ 177 Hf = 0.7325 using the exponential low). All faraday cup efficiencies were set to unity.
Depleted mantle was modeled using present-day ε Hf = +16 and 176 Lu/ 177 Hf = 0.04. Here ε Hf is calculated (1) relative to 176 Hf/ 177 Hf CHUR = 0.282772 (5).
The low but variable Hf blank (∼30 pg ± 30% Hf sample /Hf blank > 1700) accounts for a substantial portion of the 177 Hf in the measured Hf isotopic compositions of the gadolinites. The uncertainty of the blank correction therefore introduces a large uncertainty in the amount of 177 Hf present resulting in large correlated errors in 176 Lu/ 177 Hf and 176 Hf/ 177 Hf. Error correlations are 0.993 0.206 and 0.315 for gd-1 gd-2 and gd-3 respectively.
R. K. O'Nions
On the basis of mass balance constraints imposed by Pb isotopes zircon and monazite impurities were ruled out as likely sources of scatter in the xenotime data. Instead we interpret the scatter to be due to a small range in xenotime age reflecting two or more episodes of xenotime growth or partial recrystallization that occurred between two closely spaced thermal events. These events are: (i) the ∼1010 Ma intrusion of the neighboring Canada Hill granite and (ii) an event at 983 Ma recorded by zircon overgrowths in the monazite-xenotime gneiss (13). Both events are bracketed by the 997 ± 25 Ma age which we take to be the mean age of the xenotime in the RS-1 sample.
Zircons as well as whole rocks whose Hf isotope budgets are strongly influenced by zircon were excluded from the regression because the zircons contain variable amounts of inherited relatively unradiogenic Hf. This low- ε Hf component is probably hosted in the obvious zircon cores. Two zircons of >800 μm size have ε Hf = −14.5 whereas ten <250 μm grains have ε Hf = −8.3. Excluding the zircons and whole rocks decreases isochron scatter but does not significantly change the slope.
Reischmann T., S. Afr. J. Geol. 98, 1 (1995).
The relationship between an observed experimental decay constant λ′ and the measured quantities of 176 Lu 176 Hf* (radiogenic 176 Hf) and time ( t ) is 176 Hf*/ 176 Lu = (e λ′ t – 1). If an e – -capture branch of 176 Lu decay exists the relationship between the measured quantities and the β decay constant is 176 Hf*/ 176 Lu = (λ β /λ)(e λ t – 1) where λ β is the decay constant for the 176 Hf*-producing β – -decay branch and λ is the total decay constant (λ β + λ e– ) of 176 Lu. Equating the right-hand sides of these expressions and solving for λ′ gives λ′ = ln[(λ β /λ)(e λ t – 1) + 1]/ t. For values of t relevant to physical decay-counting experiments λ′ approaches λ β . Thus counting experiments report λ β directly and this result would not be affected by the existence of a minor e – -capture branch. In contrast for values of t relevant to age-comparison studies (e.g. 4.55 Ga for eucrites) the assumption that all 176 Lu decays to 176 Hf may cause λ′ to overestimate λ β by up to 0.18% for λ e– /λ ratios up to 0.04.
The highly negative initial ε Hf values of these zircons i.e. −3.4 to −7.8 [(31 32) recalculated using λ 176 Lu = 1.865 × 10 −11 year −1 and the CHUR parameters of Blichert-Toft and Albarède (5)] indicate long-term enrichment (lower Lu/Hf relative to CHUR) in the crustal sources of the zircon-bearing rocks. The time at which these source rocks were derived from a CHUR-like mantle is estimated by tracing their Hf isotope evolution curves back in time until they intersect the CHUR evolution curve. Source rocks that had granitoid-like 176 Lu/ 177 Hf ratios of about 0.0093 [the average of data from (43)] must have formed before 4.3 Ga. Amelin et al. (32) note that if the source rocks were more mafic they would have higher 176 Lu/ 177 Hf ratios (e.g. 0.022) which would result in even earlier mantle separation ages. Alternatively using newly proposed CHUR or BSE (bulk silicate Earth) reference parameters (44–46) or assuming that the source rocks were derived from depleted mantle rather than CHUR would also result in even older mantle separation ages (31 32). Thus 4.3 Ga is a firm minimum age for the separation of the enriched source(s) from the mantle.
For crust with f Sm/Nd values of about –0.4 where f Sm/Nd = [( 147 Sm/ 144 Nd) crust /( 147 Sm/ 144 Nd) CHUR ] – 1.
Göpel C., Manhès G., Allègre C. J., Meteoritics 26, 338 (1991).
Supplemental U-Pb data are available at www.sciencemag.org/fcgi/content/full/293/5530/683/DC1
Deutsche Forschungsgemeinschaft funding (grant ZG 3/16) is gratefully acknowledged. We thank R. Schott for the Hudson Highlands sample K. Cameron for providing the UCSC Ames metal Lu-Hf solutions and T. Kleine for productive discussions. Constructive reviews from two anonymous referees are greatly appreciated.