Article pubs.acs.org/ac
Precise Determination of the Lutetium Isotopic Composition in Rocks and Minerals Using Multicollector ICPMS Josh B. Wimpenny,*,† Yuri Amelin,‡ and Qing-Zhu Yin† †
Department of Earth and Planetary Sciences, University of California, One Shields Avenue, Davis, California 95616, United States Research School of Earth Sciences, Australian National University, Canberra, Australia
‡
S Supporting Information *
ABSTRACT: Evidence of 176Hf excess in select meteorites older than 4556Ma was suggested to be caused by excitation of longlived natural radionuclide 176Lu to its short-lived isomer 176mLu, due to an irradiation event during accretion in the early solar system. A result of this process would be a deficit in 176Lu in irradiated samples by between 1‰ and 7‰. Previous measurements of the Lu isotope ratio in rock samples have not been of sufficient precision to resolve such a phenomenon. We present a new analytical technique designed to measure the 176Lu/175Lu isotope ratio in rock samples to a precision of ∼0.1‰ using a multicollector inductively coupled mass spectrometer (MC-ICPMS). To account for mass bias we normalized all unknowns to Ames Lu. To correct for any drift and instability associated with mass bias, all standards and samples are doped with W metal and normalized to the nominal W isotopic composition. Any instability in the mass bias is then corrected by characterizing the relationship between the fractionation factor of Lu and W, which is calculated at the start of every analytical session. After correction for isobaric interferences, in particular 176Yb, we were able to measure 176Lu/175Lu ratios in samples to a precision of ∼0.1‰. However, these terrestrial standards were fractionated from Ames Lu by an average of 1.22 ± 0.09‰. This offset in 176Lu/175Lu is probably caused by isotopic fractionation of Lu during industrial processing of the Ames Lu standard. To allow more straightforward data comparison we propose the use of NIST3130a as a bracketing standard in future studies. Relative to NIST3130a, the terrestrial standards have a final weighted mean δ176Lu value of 0.11 ± 0.09‰. All samples have uncertainties of better than 0.11‰; hence, our technique is fully capable of resolving any differences in δ176Lu of greater than 1‰. et al.11 give a consistent λ176Lu value of 1.865−1.867 × 10−11 year−1. This is supported by Amelin6 who obtained similar λ176Lu values from analyses of phosphates from an ordinary chondrite (Richardton H5) and achondrite (Acapulco), in which these phosphates are younger than 4556Ma. However, studies calculating λ176Lu from older chondrites and achondrites that formed within the first 10 Ma of solar system formation have resulted in λ176Lu values that are ∼4% greater [λ176Lu = 1.92−1.98 × 10−11 year−1].1,12−15 The use of the λ176Lu of 1.867 × 10−11 year−1, established by age comparison of terrestrial rocks, to calculate the ages of these meteorites
T
he Lu−Hf isotopic system has been widely studied throughout different branches of geochemistry for over 30 years.1−3 The β decay of 176Lu to 176Hf (t1/2 ∼ 37 Ga) makes the Lu−Hf system a useful chronometer in studies investigating the ages of terrestrial and extraterrestrial samples,1,2,4−6 while Lu−Hf systematics in minerals such as zircon can be used as a petrogenetic tracer.3,7,8 In order for the Lu−Hf system to have chronological significance it is imperative to have an accurate and precise value for the decay constant of 176Lu (λ176Lu). Up until recently this λ176Lu value has been in dispute; early γ counting methods were inconsistent and imprecise (see discussion, refs 6 and 9), while more modern studies involving comparative analysis of U−Pb and Lu−Hf systematics in terrestrial and meteorite samples were in disagreement. Analyses of terrestrial rocks by Scherer et al.10 and Söderlund © 2013 American Chemical Society
Received: June 18, 2013 Accepted: October 22, 2013 Published: October 22, 2013 11258
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the true isotopic ratio. A conventional way to overcome this mass bias in multi-isotope elements such as Hf and Sr is to use an assumed constant isotope ratio to internally correct the isotope ratio of choice (e.g., 177Hf/179Hf is used to correct the 176 Hf/177Hf ratio). This is not possible in a two-isotope system such as Lu; instead we must externally normalize data to a standard of known isotopic composition (standard−sample bracketing), as is the typical procedure in measuring stable isotope fractionation using MC-ICPMS.23−27 Such a procedure should also overcome any instability in the mass bias (i.e., instrumental drift); however, in practice the instrumental drift may be unstable and nonlinear. In this case there may be significant uncertainty associated with the normalization of data to bracketed standards (Figure 1a). For this reason it can also
results in apparent ages that are older than the birth of the solar system.13,14 The current uncertainty in λ176Lu also has consequences for our understanding of crust−mantle evolution. Hf model ages and calculations of initial 176Hf/177Hf ratios help to constrain the source and timing of crustal extraction from the mantle. Initial 176Hf/177Hf ratios are calculated using the present day 176Hf/177Hf and Lu/Hf ratios, and the U−Pb age of the sample, so are dependent on the λ176Lu value. Uncertainty in the λ176Lu causes a corresponding uncertainty in the initial 176 Hf/177Hf ratio so blurs the potential sources of depleted mantle from the enriched crust. This is clearly unacceptable, but as yet there is no consensus to explain why the λ176Lu calculated from terrestrial rocks and early formed meteorites are so different. It is possible that the problem lies with the suite of meteorite samples used during these studies; in particular, bulk chondrites and achondrites may not be cogenetic or may have experienced shock or thermal metamorphism (see discussion, refs 4 and 11). The possibility of 176Lu branch decay to 176Yb has been investigated but ruled out as the cause of the 5% discrepancy.16,17 Possible interlaboratory bias in spike calibration has also been ruled out.10−12,15,18,19 An alternative explanation, and one that has been invoked in recent studies, is that a γ-ray or cosmic ray irradiation event briefly enhanced the decay rate of 176Lu through the production of its short-lived nuclear isomer 176mLu.9,13,14 This mechanism would result in excess production of 176Hf correlated with the Lu/Hf ratio, explaining why Lu−Hf systematics in some meteorite samples give apparent ages that are too old (e.g., SAH9955514). Such a process would result in any irradiated samples having 176 Lu/175Lu ratios that are depleted in 176Lu by ∼1−7‰ relative to 176Lu/175Lu ratios in samples that have not experienced irradiation.13,20 Thus, one way to test the theory of the formation of an excited 176Lu isomer would be to measure the isotopic composition of Lu in meteorites formed within 10 My of solar system formation and compare the isotopic ratio with younger samples (e.g., terrestrial materials). To date, no published studies have been able to measure the 176 Lu/175Lu isotope ratio to sufficient precision in order to address this question. Work by Scherer et al.20 could only achieve a precision for 176Lu/175Lu ratios of 1‰ in terrestrial and meteorite samples using a multicollector inductively coupled mass spectrometer (MC-ICPMS).20 While this study showed that all samples have comparable 176Lu/175Lu ratios within uncertainty, the work was only published as an abstract without full presentation of the data, and the precision attained was not sufficient to fully reject the irradiation mechanism as an explanation for excess 176Hf. The aim of this project is to develop a new technique for measuring Lu isotopes by MCICPMS that could improve the precision of Scherer et al.20 by an order of magnitude (to 0.1‰) sufficient to resolve whether excitation of 176Lu in meteorites older than 4556 Ma could explain the observed excesses in 176Hf.
Figure 1. Schematic showing two methods for correcting the mass bias in a two-isotope system. (a) Standard−sample bracketing assumes a constant mass bias in between bracketing standards. This normalization technique can lead to larger uncertainties in the calculated isotopic composition of an unknown if the mass bias is actually unstable. (b) A sampling routine that utilizes an internally doped element to correct for instability in the mass bias. The relationship between f Lu and f W is established through repeat measurements of a standard throughout the analytical session. Once this is established the measured f W in a sample can be used to calculate the time equivalent f Lu. In this case the uncertainty on a single measurement will be controlled by the uncertainty in the relationship f Lu vs f W (shaded region). Green diamonds represent standards, while red diamonds represents samples.
be beneficial to dope the sample with an external element with a fixed isotopic composition that can be used to correct an unstable mass bias (Figure 1b). This method has been successfully employed for the laser ablation analyses of Pb isotopes, using Tl to correct for mass bias effects,26,28−31 and using Zn to correct for isotopic analyses of Cu.32 However, care must be taken when using this approach because the mass fractionation factors between two different elements will not be the same.29,30,33,34 This relationship must be carefully characterized in order to use an externally added element to correct for mass bias effects. Five elementsEr, Yb, Hf, W, and Rehave isotopes with masses close to those of 175Lu and 176Lu, and similarly high ionization efficiency in ICPMS,35 and can be potentially used
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ANALYTICAL BACKGROUND Lutetium has two isotopes 175Lu (97.41%) and 176Lu (2.59%) with a terrestrial average isotopic composition of 176Lu/175Lu = 0.02656 ± 0.00002.21 Any isotopic analyses of Lu must be able to account for mass bias effects caused by Coulombic repulsion of positively charged ions in the interface and ion optics region of the mass spectrometer.22 This process discriminates against light isotopes meaning that a measured isotopic ratio will always be relatively enriched in the heavy isotope compared to 11259
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for mass fractionation correction in MC-ICPMS measurements. Two of these elements are lanthanides and are chemically close to Lu, so their ionization behavior is also expected to be similar. Natural Er contains two interference-free isotopes 166Er and 167 Er. The ratio of these isotopes has been used for normalization in Lu isotope dilution analysis.33 However, determination of the mass bias from the isotopic ratio with 1 amu mass difference, with subsequent extrapolation over a 9 amu mass difference, would result in an uncertainty of the mass bias that is unacceptably large for this study. Natural Yb has also been utilized for mass bias correction when measuring the Lu concentrations by isotope dilution with 176Lu spike (e.g., refs 4 and 36); this was not desirable for the purpose of the current study where the low natural abundance of 176Lu has to be precisely determined. To reduce the effects of the isobaric interference of 176Yb (12.7% natural abundance) on 176Lu (2.59%), the chemical separation of Lu involved the removal of almost all Yb from the samples and the pure Lu standards used as bracketing standards such as Ames metal contain no Yb. Otherwise, 176Yb interference would seriously compromise the accuracy of Lu isotopic composition. The addition of double 171 Yb−174Yb spike was considered at the early stage of this project; however, the content of 176Yb in the available Yb spikes was too high and isobaric correction on 176Lu is still significant. Normalization to Hf would, obviously, suffer from a similar problem. On the other hand, normalization to an element that has no common isobars with Lu, such as Re or W, eliminates this problem. In this study W and Re were chosen as the internal calibration elements for Lu as both are similar in mass to Lu and so can be analyzed in the same static collector array. Both of these elements were used successfully for normalization in analyses of Lu by isotope dilution.10,37
capacity. This can be a problem for Ti-rich samples such as basalts and many achondrite meteorites. Ti is then washed out as a peroxide complex with a dilute nitric acid−citric acid− hydrogen peroxide mixture. This Ti washout is slow and requires large volume of the eluent, which can lead to increased blanks for the elements that are eluted after Ti. In our procedure, removal of Fe (Supporting Information Table S1) before the Ln-Spec separation (Supporting Information Table S2) allows us to load the sample in a HNO3−H2O2 mixture so that Ti is bound in a peroxide complex and is not absorbed by the resin. This allows using smaller columns and process larger samples because Ti no longer takes up resin capacity, substantially speeds up the separation, and reduces blanks. Completeness of Ti removal is monitored by the color of the resin in HNO3−H2O2 medium: orange-brown if Ti is present, white if Ti is absent. In all separations with this procedure 4−5 mL of HNO3−H2O2 was enough to completely remove Ti, compared to 20 mL or more in the original procedure34 where Ti is initially absorbed by the resin. The HNO3−H2O2 solutions were found to be stable for at least 1 week, but needed replacement, or addition of concentrated H2O2, if stored at room temperature for several months. Quantitative separation of Lu from Yb requires columns with sufficiently high resolution and finding a compromise between efficiency of separation and elution time. After trying various column lengths, resin bead sizes (50−100 and 100−150 μm), and HCl eluent concentrations between 3 and 4 M, we found the conditions listed in Supporting Information Table S3 a reasonable compromise (Figure 2). Because of slow elution, the separation takes 2 days. Two passes through these columns reduce the Yb/Lu ratio by 104−105, with total Lu yield of >90%.
EXPERIMENTAL SECTION Lu Sample Purification. Samples were dissolved in HF/ HNO3 on a hot plate at 110 °C and converted to a soluble chloride form by evaporation with concentrated HNO3 three times, and once with 6 M HCl. After dissolution in the second portion of 6 M HCl on a hot plate in closed vials overnight, and checking for the possible presence of colloidal material (which was not observed), the samples were ready for chemical separation. Preparation of Lu for isotopic analysis involved four steps using three types of columns (Supporting Information Tables S1−S3): (1) separation of Fe and U from most other elements including Lu using anion-exchange columns, (2) separation of heavy REE from iron-free bulk sample using columns with 0.5 mL of Eichrom Ln-Spec resin, and (3 and 4) separation of Lu from Yb using a longer columns containing finer-grained LnSpec. The last stage was repeated twice to ensure sufficiently low residual content of Yb in the Lu fraction. The second stage of Lu preparation, separation of the Lu-rich heavy REE fraction, was modified from the procedure of Münker et al.38 that uses a single Ln-Spec column, but involves an important change that eliminates an important deficiency of the original version. The efficiency of the original Münker et al.38 procedure is compromised by the presence in the rocks of two abundant elements that are absorbed by the Ln-Spec resin in 2−3 M HCl or HNO3: Fe3+ and Ti4+. In the original version, absorption of Fe is prevented by reducing it to Fe2+ with ascorbic acid, while titanium is retained by the resin during sample loading and matrix washout, and takes up the column
Figure 2. Separation of Lu from Yb using long Ln-Spec columns (see Supporting Information Table S3 for details).
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Lu Isotopic Analyses. Isotopic measurements were made using an MC-ICPMS (Thermo Scientific Neptune Plus) at UC Davis. Samples were introduced in solution mode using an ESI Apex IR which partially desolvates the sample resulting in a 3fold increase in sensitivity over the standard introduction system. All samples were normalized to pure Lu metal obtained from the Department of Energy Ames Laboratory (subsequently referred to as Ames Lu) in order to account for mass bias effects, and samples and standards were analyzed at a concentration of ∼10 ppb. All Lu standards and samples were also doped with ca. 10 ppb Re metal (99.99%) and ca. 20 ppb W metal (99.95%) to be used as internal calibration elements to 11260
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Table 1. Isotopic Composition of Lu in Terrestrial Standards, Normalized to Ames Lu and NIST3130aa corrected using n
δ Lu Ames
Ames Lu Ames Lu (processed) NIST 3130a Specpure Lu BHVO-2 BIR-1 BCR-2 av weighted mean
51 5 13 14 9 7 6
184
W/182W
2σ
δ Lu NIST3130a
0.00 0.05
0.08 0.10
1.12 1.24 1.17 1.18 1.28 1.20 1.22
0.08 0.11 0.09 0.07 0.05 0.12 0.08
176
corrected using 2σ
δ Lu Ames
−1.12 −1.07
0.08 0.10
0.00 0.11 0.05 0.06 0.16 0.09 0.11
0.08 0.11 0.09 0.07 0.05 0.10 0.09
176
187
Re/185Re
2σ
δ Lu NIST3130a
0.00 −0.40
0.10 0.52
1.13 1.22 1.15 1.17 1.28 1.19 1.21
0.11 0.12 0.14 0.13 0.08 0.12 0.09
176
standard−sample bracketing 2σ
δ176Lu Ames
2σ
δ176Lu NIST3130a
2σ
−1.13 −1.53
0.10 0.52
N/A 0.07
N/A 0.06
N/A −1.09
N/A 0.06
0.00 0.09 0.01 0.03 0.15 0.07 0.10
0.11 0.12 0.14 0.13 0.08 0.12 0.10
1.17 1.20 1.17 1.21 1.32 1.22 1.22
0.22 0.14 0.12 0.07 0.10 0.13 0.08
0.00 0.03 0.00 0.04 0.15 0.06 0.06
0.22 0.14 0.12 0.07 0.10 0.13 0.10
176
a n = number of analyses. Weighted means take the uncertainty of each point into account and were calculated using Isoplot 4.1544 which uses an identical calculation to that described in ref 45.
correct for drift in the mass bias. Lu and Yb intensities in the pure Re and W solutions were indistinguishable from background levels. Typical background intensities were 0.85, relative to a published value of 0.79631 (ref 36).
characterized during any future analytical session or analyses performed using a different mass spectrometer. Instrumental blanks were monitored every three samples, and the average of the bracketing blanks was subtracted from each sample. On a daily basis the instrument was tuned for maximum sensitivity, the peak shape and peak alignments were optimized, and detector gains were calibrated. Each analysis involved 50 8 s integrations, preceded by an off-peak baseline measurement to account for detector noise. Testing was performed to decide whether 183W/182W, 184 W/182W, or 187Re/185Re should be used to internally normalize the 176Lu/175Lu ratio. Repeat analyses of the doped 11261
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calculate the value of f Lu, as illustrated in Figure 1b. The f Lu does not equal the f W (i.e., the slope f Lu/W ≠ 1), which means that Lu and W exhibit different fractionation behavior during the analyses. This is probably a result of different physical properties of these elements during ionization and extraction into the mass spectrometer. This difference in fractionation behavior has been observed previously in studies of Os and Ir, Cu and Zn, and Lu and Er, among others.32−34 Typically, the f Lu ≈ 0.6f W; however, this value was not a constant and ranged between 0.59 and 0.73 during different analytical sessions (Figure 4). Hence, to avoid introducing errors into our analyses the fractionation factor ratio was calculated on a daily basis. The isotopic composition of each unknown was calculated as a parts-per-thousand (‰) difference from Ames Lu using the measured Lu and W fractionation factors in each sample ( f Lu sample, f W sample), where f Lu sample and f W sample were calculated as below:
Ames Lu standard in multiple analytical sessions consistently showed that when plotted versus 176Lu/175Lu the 184W/182W ratio produced a regression line with the least scatter, and so would provide the least uncertainty to the final Lu isotope ratio. For example, the analytical session of the 11th of January yielded regression lines with an R2 of 0.87, 0.85, and 0.83 when plotting 176Lu/175Lu versus 184W/182W, 183W/182W, and 187 Re/185Re, respectively. Thus, all final Lu isotope data discussed in this study are calculated using the 184W/182W ratio to internally normalize any drift in the mass bias (Figure 4), and the following methodology reflects this. However, in
⎡ (184 W/182 W) ⎤ fW = ln⎢ 184 182 m ⎥ ⎣ ( W/ W)t ⎦
(2)
⎡ (184 W/182 W) ⎤ W sample ⎥ fW sample = ln⎢ 184 182 ⎢⎣ ( W/ W)W metal(t) ⎥⎦
(4)
fLu Ames = fLu/W fW sample
(5)
The final δ176Lu value of the sample is then the difference between the measured f Lu sample and the calculated f Lu Ames, where these values are time equivalent. Thus, we will have accounted for both mass bias and mass bias instability.
Table 1 we also present Lu isotope data normalized using the 187 Re/185Re ratio and calculated by sample−standard bracketing to provide a comparison. Repeat measurements of the Ames Lu standard (doped with W and Re) were made at the start of and throughout each analytical session in order to characterize the relationship between the fractionation factor of 176Lu/175Lu (f Lu) and 184 W/182W ( f W). The logarithm of the mass fractionation factors ( f) for Lu and W were calculated as the following:
(1)
(3)
Because all of the standards and samples are doped with the same W metal solution, and we are normalizing all of our samples to Ames Lu, then by using the measured f Lu/W and f W sample values, we can calculate what the f Lu Ames would be at the time of sample measurement.
Figure 4. Relationship between f Lu and f w during different analytical sessions. The fractionation factor of Lu was always characterized using Ames Lu. The equation of the regression line was used to correct for instrumental drift during that analytical session.
⎡ (176 Lu/175Lu) ⎤ m ⎥ fLu = ln⎢ 176 ⎣ ( Lu/175Lu)t ⎦
⎡ (176 Lu/175Lu) ⎤ Lu sample ⎥ fLu sample = ln⎢ 176 ⎢⎣ ( Lu/175Lu)Lu Ames(t) ⎥⎦
δ176 Lu = (fLu sample − fLu Ames ) × 1000
(6)
By definition, if we treat Ames Lu as an unknown it should have a δ176Lu value of 0‰. After 51 repeat measurements over five analytical sessions we obtain a δ176Lu value for Ames Lu of 0.00 ± 0.08‰. We measured five terrestrial samples and compared their Lu composition to that of Ames metal as the Lu reference standard. These are two additional pure Lu standards, NIST 3130 and Alfa Aesar “Specpure’” Lu solution, and three USGS basalt standards that were processed through column chemistry: BCR-2, BHVO-2, and BIR-1a.
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RESULTS AND DISCUSSION Lu isotopic measurements are presented in Table 1 for the three different normalization methods: internal mass bias correction using 184W/182W or 187Re/185Re and standard− sample bracketing. The three methods give very similar final δ176Lu values; however, the precision using the 184W/182W ratio is up to a factor of 2 better than the other methods. Therefore, in the following section all δ176Lu data is calculated using the 184 W/182W ratio to correct for mass bias effects. All processed and unprocessed samples have δ176Lu values that range between 1.12‰ and 1.28‰, with analytical precision better than 0.11‰. On average, these terrestrial standards are fractionated relative to Ames Lu by 1.22 ± 0.09‰. With the exception of Ames metal, the terrestrial
where m and t denote measured and true isotope ratios, and Ames Lu and W metal were used to calculate f Lu and f W, respectively. Ames Lu was assumed to have a true 176Lu/175Lu ratio of 0.02656 ± 0.00002,21 and the true 184W/182W ratio of 99.95% W metal was assumed to be 1.156364 ± 0.000004.39 When plotting all of the standard data from a single analytical session in x−y space the data form a linear array, with the slope of the line corresponding to the fractionation factor ratio f Lu/W as illustrated in Figures 1b and 4. By characterizing the relationship between f Lu and f W we can both correct for mass bias and reduce the effects of mass bias instability during sample measurement. The relationship f Lu/W follows a linear trend (Figures 1b and 4) which means that once this relationship is established we can measure f W in order to 11262
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materials in this study have a constant δ176Lu value to within ∼0.1‰. This suggests that terrestrial materials have a relatively homogeneous Lu isotopic composition although a more detailed characterization of δ176Lu in terrestrial materials would be required to confirm this. The offset between the δ176Lu value of Ames Lu and the other terrestrial standards implies that its Lu isotope ratio is atypical, and as such Ames Lu may not be the most suitable normalization standard. The reason that it is highly fractionated relative to other terrestrial materials is unclear; it is not due to our chemical purification of Lu as processed and unprocessed Ames Lu have the same δ176Lu values within error (Table 1). While some kind of terrestrial heterogeneity could be responsible we see no evidence for it in the other standards; our limited data set contains two endmember values (0 and 1.22‰), but no samples show any evidence of mixing between the two. Far more likely is that the production of the pure Lu metal at Ames will have caused isotopic fractionation during its production. Preparation of high-purity rare earth elements at the Ames laboratory involves reaction of the metal oxide with HF to form a fluoride, followed by calcium reduction of the metal fluoride to form pure metal.40 Subsequently, any volatiles and nonvolatiles are removed by vacuum casting and distillation, respectively. Refining processes such as these have been shown to cause isotopic fractionation; for example, the refining of ZnS and PbS ores to Zn and Cd metal is known to fractionate δ66/64Zn and δ114/110Cd, with the metal being isotopically heavy by up to 0.5‰ relative to the starting ore.41 Similarly, study of Zn isotopes and the stable isotopes of Sr show that terrestrial samples are consistently offset from the chosen pure metal standard, in both cases with the processed standard being isotopically light relative to the natural samples.42,43 The magnitude of such a fractionation will depend on the recovery yield of pure metal; if near 100% yield is achieved then little or no isotopic fractionation can occur. If fractionation of Lu occurred during refining and this favored 175 Lu in the recovered metal (i.e., the refined metal is isotopically lighter than the starting ore), together with incomplete recovery, then this could explain why Ames metal is relatively enriched in 175Lu relative to the other terrestrial standards. In this case either of the pure Lu standards NIST 3130a or Specpure Lu would be more suitable for bracketing purposes. However, of the two we would recommend the use of NIST 3130a; the Alfa Aesar standard is primarily used as a standard for concentration, and there is no guarantee that the source of the Lu standard will remain the same over time. NIST3130a is likely to be more strictly controlled, and lot numbers and certificates of analyses are readily available from NIST. Normalization to NIST 3130a does not provide any advantage over Ames Lu in terms of accuracy or precision but will be more convenient when discussing future results if we consider that terrestrial materials will have δ176LuNIST3130a values of ∼0. For this reason we have recalculated our results as δ176LuNIST3130a, where this is equal to the difference between the δ176Lu of the sample and the δ176Lu of NIST3130a (1.12‰). In this case the terrestrial standards have a weighted mean δ176LuNIST3130a value of 0.11 ± 0.09‰ relative to NIST3130a (Table 1, Figure 5). Our data hint that small isotopic heterogeneities on the scale of
