Accurate and precise measurement of Ce isotope ratios by thermal ionization mass spectrometry (TIMS)

Chemical Geology 476 (2018) 119–129

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Accurate and precise measurement of Ce isotope ratios by thermal ionization mass spectrometry (TIMS)

T

⁎

Michael Willig , Andreas Stracke Westfälische Wilhelms-Universität Münster, Corrensstr. 24, 48149 Münster, Germany

A R T I C L E I N F O

A B S T R A C T

Editor: K. Mezger

The La-Ce isotope system has been rarely applied, mostly due to analytical difficulties. Recent technical refinements of mass spectrometers have overcome some of these technical limitations, but Ce isotope analyses still face considerable analytical challenges. These are mainly related to the low abundance of the minor isotopes 136 Ce and 138Ce relative to the main isotopes 140Ce and 142Ce (136Ce = 0.19%, 138Ce = 0.25%, 140Ce = 88.45%, 142 Ce = 11.11%). Hence simultaneous measurement of ion beams over a large dynamic range is required, resulting in large differences in count statistical uncertainty on the individual ion beams. In addition, the large abundance of 140Ce introduces a tailing effect of the large 140CeO ion beam onto the 136CeO and 138CeO ion beams, which requires adequate correction. Here, we present a chemical purification scheme and high-precision thermal ionization mass spectrometric (TIMS) method for analyzing CeO isotope ratios in silicate samples. The advantages and disadvantages of different mass spectrometric strategies for data acquisition by TIMS were evaluated, including the use of 1010, 1011, and 1012 Ω amplifiers and different strategies for the 140CeO tail correction. An optimization scheme was developed for different on-peak and off-peak collection schemes, in combination with different tail and baseline correction methods. It is shown that, as long as the integration times for the on-peak, off-peak (half-mass), and baseline signals are adequately optimized for the employed collection scheme and tail correction method, different strategies yield Ce isotope ratios with similar precision of 20–40 ppm (2 S.D.). In contrast to previous studies, we have acquired 140CeO by using a 1010 Ω amplifier, and have determined a long-term average 140Ce/142Ce of = 7.94319 ± 2. Using a common 136Ce/142Ce = 0.01688 for mass fractionation correction, the 136Ce/138Ce of the international rock reference materials BCR-1, BCR-2, and BHVO-2 of this study agree well with those recently reported, when all Ce isotope ratios are reported relative to a common 138Ce/136Ce = 1.337366 for the average Ames Ce metal. In addition, Ce isotope ratios for several other widely available international rock reference materials (AGV-2, BE-N, BIR-1, DNC-1, W2A) are presented, and facilitate easy inter-laboratory comparison.

Keywords: Cerium Rare earth element Thermal ionization mass spectrometry Tail correction Count statistics

1. Introduction The 138La-138Ce decay system shares many similarities with the Sm-144Nd decay system, which is widely applied for geochronology and as a radiogenic isotope tracer in the Earth sciences. 138La undergoes branched decay to 138Ba (66%) by electron capture and to 138Ce (34%) by β-decay. The total 138La half-life of ~ 1.03 × 1011 years (Sato and Hirose, 1981) is similar to the half-life of the 147Sm-144Nd decay system (1.06 × 1011 years, Lugmair and Marti, 1978). Lanthanum, Cerium, Samarium, and Neodymium are rare earth elements (REE) with similar chemical behavior, and usually occur in a 3 + oxidation state. Chemical fractionation of the REE3 + during geological processes usually occurs because their ionic radii decrease with increasing atomic weight, leading to more incompatible behavior of 147

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La3 + relative to Ce3 + and Nd3 + relative to Sm3 + during magmatic processes. Under these conditions high La/Ce values are coupled to low Sm/Nd, or vice versa, and an inverse relationship between Ce and Nd isotope ratios develops with time. However, Ce is the only REE that can naturally occur in a 4+ oxidation state. Cerium4 +, which has a significantly smaller ionic radius than Ce3 +, behaves differently under oxidizing conditions compared to the 3+ ions La, Sm, and Nd. This is evidenced by marked irregularities, often called Ce anomalies, in the REE abundance patterns in many geological materials such as seawater (Elderfield and Greaves, 1982), marine sediments (Piper and Graef, 1974), Fe-Mn crusts (Amakawa et al., 1991; Elderfield et al., 1981), and some lunar rocks (Takahashi, 1998). With time, samples that exhibit “Ce anomalies”, i.e., unusual La/Ce for given Sm/Nd, translate into Ce isotope ratios that deviate from the expected inverse relationship with

Corresponding author. E-mail address: [email protected] (M. Willig).

https://doi.org/10.1016/j.chemgeo.2017.11.010 Received 8 September 2017; Received in revised form 7 November 2017; Accepted 8 November 2017 Available online 11 November 2017 0009-2541/ © 2017 Elsevier B.V. All rights reserved.

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M. Willig, A. Stracke

Aside from the variety in Ce isotope measurement protocols and correction schemes for 140CeO tail contribution, previous studies have used different ratios for mass fractionation correction. Most studies have used 136Ce/142Ce = 0.01688 as proposed by Makishima et al. (1987), but some have used 0.0172 (e.g. Shimizu et al., 1984, 1990). Others have used a range of values for 140Ce/142Ce for mass fractionation correction (e.g. Nakamura et al., 1984; Hayashi et al., 2004). Moreover, whenever 140Ce is not determined to improve count statistics (see discussion above), a constant 140Ce/142Ce has to be used to correct for interfering 140Ce18O on 142Ce16O, but previous studies have also used different values for 140Ce/142Ce (e.g. Tazoe et al., 2007a; Willbold, 2007). The use of all these different methodologies has resulted in large inter-laboratory biases (c.f. Willbold, 2007), which severely hampers data comparison. This problem is exacerbated by the use of different reference materials by different authors. Most of the pioneering studies in the 1980s used JMC 304 and BCR-1 as reference materials. JMC 304 is no longer widely available and different batches appear to be isotopically variable (Willbold, 2007). Moreover, BCR-1 is now unavailable. Willbold (2007) introduced an Ames Ce metal solution as a new reference material that has been adopted by the most recent Ce isotope studies (e.g., Bellot et al., 2015; Doucelance et al., 2014). These latter studies have also reported Ce isotope ratios on the widely accessible USGS reference materials BCR-2 and BHVO-2. In the following, a protocol for the determination of accurate and precise Ce isotope ratios in a diverse range of geologic reference materials will be reported that builds and expands on various methodologies reported previously (e.g., Tazoe et al., 2007b; Willbold, 2007). The advantages and disadvantages of different mass spectrometric strategies for data acquisition by TIMS, including the use of 1010, 1011, and 1012 Ω amplifiers, the correction for simultaneous mass fractionation and XCe18O – X + 2Ce16O interferences, and different strategies for the 140CeO tail correction will be discussed, with the aim to make future methodologies directly comparable. We also report new Ce isotopic data on a larger set of widely accessible reference materials, including the first Ce isotope data on BE-N, BIR-1, DNC-1 and W2-A, with the aim to facilitate inter-laboratory comparison.

Nd isotope ratios. Hence, the La-Ce isotope system is a unique geochemical tool for dating and tracing time-integrated differences in relative light REE abundances in a diverse range of geologic materials. However, there is limited natural variation in radiogenic 138Ce/136, 142 Ce as a result of the restricted natural variation in La/Ce, and the long half-life and low abundance of the parent isotope 138La (138La = 0.09%, 139La = 99.91%). Therefore, Ce isotope ratios require measurement with similar, or better, precision than Nd isotope ratios to resolve the small natural isotopic variations. Owing to a range of analytical challenges, this has proven difficult, and the 138La-138Ce isotope system has received comparatively little attention since its first reported geological applications (Dickin, 1987a; Makishima et al., 1987; Shimizu et al., 1984; Tanaka and Masuda, 1982). Different analytical protocols for measuring Cerium isotope ratios have been reported in the last four decades, and these clearly document the encountered analytical challenges. With the exception of Willbold (2007), who also investigated Ce isotope measurements by multi-collector inductively coupled plasma mass spectrometry (MC-ICPMS), reported methods invariably use thermal ionization mass spectrometry (TIMS) with evaporation and ionization of Ce as CeO+ (Makishima and Nakamura, 1991; Shimizu et al., 1984; Tanaka and Masuda, 1982), and only rarely as Ce+ (e.g., Chang et al., 1995; Xiao et al., 1994). Thermal ionization has the advantage that potentially interfering isobaric BaO+ is minimized, owing to the high first ionization potential of BaO+ compared to CeO+ (Willbold, 2007). On the other hand, this method requires adequate correction of isobaric XCe18O on X + 2Ce16O. For this purpose, either a constant 18O/16O is assumed (e.g., Nakai et al., 1986; Shimizu et al., 1984, 1991) or, 18O/16O is determined during acquisition (e.g., Amakawa et al., 1996; Bellot et al., 2015; Doucelance et al., 2014; Masuda et al., 1988; Tanimizu, 2000; Tanimizu et al., 2004; Willbold, 2007). Especially in case of a fractionating O isotope reservoir during acquisition, an accurate XCe18O – X + 2Ce16O correction is critical for obtaining accurate and precise Ce isotope ratios. Additional analytical challenges arise from the low abundance of 136 Ce and 138Ce relative to the main isotopes 140Ce and 142Ce (136Ce = 0.19%, 138Ce = 0.25%, 140Ce = 88.45%, 142Ce = 11.11%; Chang et al., 1995) and the resulting requirement for measuring ion beams over a large dynamic range. This issue is partly overcome on new generation mass spectrometers with a dynamic range of 50 V on typical 1011 Ω amplifiers (e.g., the Thermo Scientific Triton, cf. Bellot et al., 2015; Doucelance et al., 2014; Willbold, 2007). The low abundances of 136 Ce and the radiogenic isotope 138Ce, relative to the most abundant isotope 140Ce (140Ce/138Ce ca. 354, 140Ce/136Ce ca. 466) or 142Ce (140Ce/142Ce = 7.493, Section 3.1), however, lead to about 20 times larger count statistical uncertainties on 136,138Ce compared to 140Ce. In contrast, the main Nd isotopes, 142Nd and 144Nd, are only about two times more abundant than the radiogenic isotope 143Nd (142Nd = 27.2%, 144Nd = 23.8%, and 144Nd = 12.2%). For the same total ion beam intensity, Ce isotope measurements thus require much longer acquisition times because the relative count statistical uncertainty on the radiogenic isotope is larger for 138Ce than 143Nd. One strategy to improve count statistics for Ce isotope measurements is to avoid collection of the most abundant isotope 140Ce (e.g., Bellot et al., 2015; Doucelance et al., 2014; Hayashi et al., 2004; Nakamura et al., 1984; Shimizu et al., 1989, 1994, 1996; Tanimizu and Tanaka, 2002a, 2002b; Willbold, 2007), which allows measurement of the remaining ion beams of 136CeO, 138CeO, and 142CeO, at up to eight times higher intensity, that is, almost three times better count statistics using the generally employed 1011 Ω amplifiers. In addition to count statistical issues, the large abundance of 140Ce introduces a tailing effect of the large 140CeO ion beam onto the 136CeO and 138CeO ion beams, which requires adequate correction (e.g., Dickin et al., 1987; Willbold, 2007). However, while some authors employ such a correction (Dickin et al., 1987; Dickin, 1987a, 1987b, 1988; Tanaka et al., 1987), others do not (e.g., Hayashi et al., 2004; Nakamura et al., 1984; Tanimizu et al., 2004).

2. Chemical separation and mass spectrometric procedure A detailed step-by-step description of the chromatographic separation of Ce from silicate rocks and the employed mass spectrometric procedure is given in the Supplementary information. The following two sections present a general overview of the employed techniques and highlight where they deviate from those used previously. 2.1. Sample preparation and chemical separation of Ce from silicate rocks All digestions, leaching, and chemical separations were carried out in Class 10,000 clean laboratory at the Institut für Mineralogie at the Westfälische Wilhelms-Universität (WWU) Münster. Sample handling and processing was carried out in Class 100 laminar flow hoods. All reagents were sub-boiling distilled (HCl, HNO3, HF) or commercially acquired ultra-pure grade (H2O2, KBrO3, H3PO4, ascorbic acid, ammonium thiocyanate), with dilutions performed using Millipore Milli-Q deionized water. Resins for ion exchange chemistry were initially washed and sonicated in HCl and H2O, and repeatedly washed with ~0.2 M HCl and H2O in an ultrasonic bath immediately prior to use, and discarded thereafter. For analyses of the silicate rock reference materials, typically 0.05–0.25 g sample powder was digested in concentrated HF and a few drops of concentrated HNO3. The resulting solution was dried down and re-dissolved in 5 ml of concentrated HCl. Boric acid was then added to re-dissolve Ca-Mg fluorides (cf. Koornneef et al., 2010). Another drydown step is followed by adding 5 ml concentrated HNO3, drying down again, and finally re-dissolving in 2 ml 3 M HNO3. This solution was then centrifuged before loading onto the ion exchange columns. 120

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reproducibility of 33 ppm (2 S.D.). Similar to Bellot et al. (2015), we observed that the absolute 138Ce/136Ce shift between shorter-term measurement periods, each being several months long. Between measurement periods from November 2015–March 2016 and March–August 2016 the average Ames metal 138Ce/136Ce differs by 17 ppm and then by 21 ppm between March–August 2016 and August 2016–January 2017 (Fig. 1). Within each measurement period, the reproducibility (2 S.D.) of the Ames 138Ce/136Ce is ca. 20 ppm, thus slightly better than the long-term reproducibility of 33 ppm. The 138Ce/136Ce during the final measurement period (138Ce/136Ce = 1.337366 ± 10) is identical to the ratios reported in Bellot et al. (2015) and Doucelance et al. (2014), but 0.000014 lower than the value reported by Willbold (2007). 138Ce/136Ce and 138Ce/142Ce reported in this study are reported relative to Ames 138Ce/136Ce = 1.337366. The within period and longterm reproducibility in this study compare favorably to the 80 ppm long-term, and 40 ppm within session reproducibility (2 S.D.) reported by Bellot et al. (2015), as well as the 44 ppm (2 S.D.) by Doucelance et al. (2014) and the 23 ppm (2 S.D.) reproducibility reported by Willbold (2007).

The ion exchange chromatographic procedure uses Eichrom TRU resin (Pin et al., 1994; Caro et al., 2006) in a first step to separate the bulk REE. In a second step, Ce is purified on Eichrom Ln columns, using oxidation of Ce3 + to Ce4 + with KBrO3 to separate the trivalent REE from Ce4 + according to the technique reported by Tazoe et al. (2007a, 2007b). The largest methodological adjustment made to this procedure was the deposition of a thin layer of Eichrom pre-filter resin on top of the Eichrom Ln resin. This layer prevented the Ln resin from floating when 10 M HNO3 was introduced to the Ln column. The final result was a cleaner Ce cut. For further details of the ion exchange chemistry see the Supplementary information. 2.2. Mass spectrometric techniques Approximately 1 to 1.5 μg of Ce were loaded on zone refined Re filaments in HCl together with 1 μl 0.5 M H3PO4. The Ce isotope measurements were performed on a Thermo Scientific Triton thermal ionization mass spectrometer (TIMS) using a double Re filament configuration. The distance between the evaporation and ionization filament is critical for the resulting ionization efficiency; shorter distances result in better ion yields. Rhenium double filament assemblies with < 0.5 mm distance between the ionization and evaporation filament were used in this study. A multi-static acquisition routine was employed using collectors L3 to H3, with a 1010 Ω amplifier connected to the center cup for collection of the large 140CeO ion beam, and 1011 Ω amplifiers connected to all other collectors (Table 1). CeO+ beams and monitors for LaO+ and NdO+ were collected for 8.4 s in the first magnet setting. Subsequently, half-mass intensities were measured with 1 s integration time at magnet settings at − 0.5 and + 0.5 amu offset. The idle time after each magnet setting was set to 3 s, amounting to a total cycle time of 19 s. One measurement of ca. 150–300 cycles typically lasted 1 to 1.5 h at typical 142 CeO beam intensities of 20 V. A ten minute long baseline with closed value was performed prior to each measurement. Calculation of Ce isotope ratios from baseline corrected CeO beam intensities involved subtraction of the contribution from the 140CeO tail on the 136CeO and 138CeO signals. This was done by exponential interpolation between the sample average 151.4/140CeO, 153.4/140CeO and 154.4/140CeO half-mass to oxide ratios (for details of the tail correction procedure, see Supplementary information). The interpolated tail contributions were then subtracted on a cycle by cycle basis. An iterative XCe18O – X + 2Ce16O interference and exponential mass fractionation correction using 136Ce/142Ce = 0.01688 (Makishima et al., 1987) was performed off-line. The underlying equations – following the approach presented in Makishima and Masuda (1994) – are given in the Supplementary information. All ratios outside 2.5 × S.D. of the median value were rejected as outliers.

3.2. The Ce isotope composition of silicate rock reference materials The reproducibility of the 138Ce/136Ce and 138Ce/142Ce ratios in the silicate rock reference materials ranges from 20 to 40 ppm (2 S.D.), close to that achieved for the Ames Ce metal. The 138Ce/136Ce and 138 Ce/142Ce ratios are listed in Table 2 and summarized in the following. Within uncertainty, BCR-1 and BCR-2 have identical 138 Ce/136Ce = 1.336915 ± 9 (n = 19) for BCR-1 and 1.336919 ± 8 (n = 20) for BCR-2. These values are in agreement with the BCR-2 value reported by Doucelance et al. (2014; 1.336894 ± 23) and within error of BCR-1 = 1.336890 ± 65 reported by Makishima and Masuda (1994). They differ outside analytical uncertainty from BCR1 = 1.336801 ± 24 reported by Makishima and Nakamura (1991) and BCR-2 = 1.336866 ± 15 given in Bellot et al. (2015). The average of BHVO-2 (n = 26) is 138Ce/136Ce = 1.336778 ± 7, in-between the values reported by Bellot et al. (2015, 138Ce/136Ce =1.336765 +-32) and Doucelance et al. (2014, 138Ce/136Ce = 1.336819 ± 32). The average 138Ce/136Ce of AGV-2 is 1.336844 ± 12 (n = 12) and 1.336801 ± 8 (n = 13) for BE-N. The mean 138Ce/136Ce of W2-A is 1.336947 ± 10 (n = 6), which is identical to 138Ce/136Ce = 1.336946 ± 12 for DNC-1 (n = 6). BIR-1, which contains < 2 μg g− 1 of Ce (Jochum et al., 2015), and has the lowest 138Ce/136Ce (= 1.336750 ± 27, n = 3) of all silicate rock reference materials reported in this study. 4. Discussion 4.1. Establishing a convention for reporting Ce isotope ratios

3. Results

Recent Ce isotopes studies (Willbold, 2007; Tazoe et al., 2007a; Doucelance et al., 2014; Bellot et al., 2015) have all used 136 Ce/142Ce = 0.01688 for mass fractionation correction, as proposed by Makishima et al. (1987). Following this convention, 136 Ce/142Ce = 0.01688 is also used in this study. Similar results are obtained if 136Ce/140Ce is used instead. In contrast, using 140Ce/142Ce for fractionation correction as in some previous studies (Nakamura et al., 1984; Tanimizu and Tanaka, 1999, 2002b; Tanimizu et al., 2004) increases the variance in our Ames measurements by a factor of 2 (Supplementary information). We therefore recommend using the 136 Ce/142Ce ratio for fractionation correction, with the value of 0.01688 as proposed by Makishima et al. (1987) for ease of comparison. For reporting 138Ce/1XXCe isotope ratios, the reference isotope 1XXCe can either be 136Ce, 140Ce, or 142Ce. Following Willbold (2007), we recommend using 136Ce as a reference isotope, because it yields a 138 Ce/136Ce value close to unity, resulting in more legible numbers than the 138Ce/142Ce values with leading zeros. If a common 136Ce/142Ce is

3.1. The Ce isotope composition of the Ames Ce metal reference material Measurements of the Ames Ce metal were performed over a period of 15 months with a long-term average of 1.337332 ± 6 and Table 1 Configuration of faraday collectors, amplifiers, and magnet positions used in this study. Collector

L3

L2

L1

C

H1

H2

H3

Amplifier

1011

1011

1011

1010

1011

1011

1011

Magnet position 1

136

138

LaO 154.9 155.4 154.4

140

142

NdO 158.9 159.4 158.4

142 Ce18O 159.9 160.4 159.4

Magnet position 2 Magnet position 3

CeO 151.9 152.4 151.4

CeO 153.9 154.4 153.4

CeO 155.9 156.4 155.4

CeO 157.9 158.4 157.4

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1.33732

1.33738

Fig. 1. 138Ce/136Ce values obtained from Ames measurements over a 15 months measurement period (upper panel). The lower panel shows the average 154.4 amu half-mass intensity divided by the 140CeO intensity. Dashed lines correspond to dates where the measured half-mass tail and the 138Ce/136Ce changed. The first shift corresponds to 03/2016, the second shift was in 08/2016. Note that the corresponding shifts in 138 Ce/136Ce Ames values scale with the shift of the average measured tail values.

9 · 10−7 7· 10−7 5 · 10−7

154.4 / 140CeO

1.33726

138

Ce / 136Ce

M. Willig, A. Stracke

0

10

20

30

Measurement number

40

50

used for mass fractionation correction, 138Ce/136Ce can be converted to 138 Ce/142Ce by multiplying with 136Ce/142Ce = 0.01688. 4.2. The value of

140

reagents but found no statistical difference between them: they all had Ce/142Ce within 2 S.E. from their overall mean. The same applies to the 140Ce/142Ce values of reagents reported by Chang et al. (1995). Both the Ames and natural sample 140Ce/142Ce values differ significantly from the JMC 304 value of 7.94710 ± 30 reported by Makishima et al. (1987) and the value 7.9872 reported by Xiao et al. (1994), 140Ce/142Ce = 7.9764 when normalized to 136Ce/142Ce = 0.01688), and 7.958 (using 136Ce/142Ce = 0.0167 for mass fractionation correction) by Chang et al. (1995). A corollary of this range of 140Ce/142Ce is that previous studies that did not measure the large 140CeO beam have used different values for 140 Ce/142Ce during data reduction. For example, Tanaka and Masuda (1982) used 140Ce/142Ce = 7.992 (with 136Ce/142Ce = 0.0172 for mass fractionation correction) whereas Willbold (2007) used 7.958 from Chang et al. (1995), and Tazoe et al. (2007a) used 7.947 from Makishima et al. (1987), although both latter studies used 140

Ce/142Ce

Measurement of the 140Ce16O beam (Section 2.2) in this study allows determination of 140Ce/142Ce values consistent with 136 Ce/142Ce = 0.01688 used for mass fractionation correction. The average 140Ce/142Ce for a total of 207 measurements in silicate rock samples in this study is 7.94319 ± 2 (2 S.E.). The high precision and large number of measurements in this study result in < 6 ppm uncertainty on 140Ce/142Ce. Hence, the average 140 Ce/142Ce = 7.94333 ± 4 (n = 62) of the Ames metal is statistically different from that of the silicate rock samples. The minor difference found may be due to stable isotope fractionation during refinement or purification. In contrast, Xiao et al. (1994) analyzed five different Ce Table 2 Average Ce isotope ratios for reference materials. Sample

Source

n

138

Ce/136Ce

Amesa Ames Ames Ames AGV-2 BCR-1 BCR-1 BCR-1 BCR-2 BCR-2 BCR-2 BE-N BHVO-2 BHVO-2 BHVO-2 BIR-1 DNC-1 W2A

This study Bellot et al. (2015) Doucelance et al. (2014) Willbold (2007) This study This study Makishima and Masuda (1994) Makishima and Nakamura (1991) This study Bellot et al. (2015) Doucelance et al. (2014) This study This study Bellot et al. (2015) Doucelance et al. (2014) This study This study This study

9 7 53 35 12 21 – 6 20 8 3 13 24 10 8 3 6 6

1.337366 1.337358 1.337363 1.337378 1.336844 1.336915 1.336890 1.336801 1.336919 1.336866 1. 336,894 1.336801 1.336778 1.336765 1.336819 1.336750 1.336946 1.336947

± 2 S.E.

138

Ce/142Ce

± 2 S.E.

10 6 8 5 10 9 65 24 8 15 23 7 7 32 32 27 12 10

0.02257474 0.02257460 0.02257468 0.02257494 0.02256592 0.02256712 0.02256520 0.02256520 0.02256719 0.02256630 0.02256678 0.02256520 0.02256482 0.02256460 0.02256550 0.02256435 0.02256766 0.02256767

16 10 14 9 16 16 110 40 14 25 38 12 12 54 54 46 21 16

Measurements are corrected to 136Ce/142Ce = 0.01688 for mass fractionation and corrected for shifts in 138Ce/136Ce Ames values by adding 38 ppm to measurements done before 03/ 2016 and 21 ppm to measurements done between 03/2016 and 08/2016 (see Fig. 1). a Reported Ames values for this study are from the 08/2016 to 01/2017 measurement period. All ratios are reported relative to Ames 138Ce/136Ce = 1.337366.

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M. Willig, A. Stracke 136 Ce/142Ce = 0.01688 for mass fractionation correction. These differences in 140Ce/142Ce introduce significant analytical bias. Compared to using 140Ce/142Ce = 7.94319, as determined for silicate rocks in this study, differences of + 3 ppm result when using 140Ce/142Ce = 7.947 and + 11 ppm for 140Ce/142Ce = 7.958. This difference in 140Ce/142Ce therefore accounts for the slightly higher Ames metal 138Ce/136Ce value reported by Willbold (2007), Section 3.1, Table 2) compared to the value of 138Ce/136Ce = 1.337366 reported in this study. An inappropriate choice of a constant 140Ce/142Ce in data reduction can therefore introduce a ca. 10 ppm bias on 138Ce/136Ce. Note that using the silicate rock 140Ce/142Ce value, reported here as constant for Ames measurements, introduces only sub ppm differences in 138Ce/136Ce (or 138 Ce/142Ce). If consistent values for 140Ce/142Ce are chosen, collecting 140CeO is not essential. When data from the 140CeO beam is ignored, using the constant value for 140Ce/142Ce presented here for data reduction (7.94319 ± 2, with 142Ce/136Ce = 0.01688 for mass fractionation correction) leads to 138Ce/136Ce that differ by < 0.1 ppm relative to the value calculated using the 140CeO beam. Using a constant 140 CeO/142CeO and not measuring 140CeO is therefore a viable strategy to prevent cup degradation.

With 140Ce/142Ce = 7.94319, 138Ce/142Ce = 0.0225654 (chondrite value reported by Bellot et al., 2015), and 136Ce/142Ce = 0.01688, the relative abundances of the four Ce isotopes are: 136Ce = 0.1879%, 138 Ce = 0.2512%, 140Ce = 88.428%, and 142Ce = 11.133%. The atomic mass of Ce is 140.116 using atomic masses from Baum et al. (2009). This is in line with the atomic mass of 140.115 ± 1 amu recently reported by Xiao et al. (1994) and most values reported previously (Table 3).

interpolated tail contribution to 138CeO was 205 ppm, but decreased to 140 ppm after August 2016. Using constant tail/140CeO values during data reduction, the differences in the calculated 138Ce/136Ce disappear. This observation suggests that bias on the 140CeO tail correction can significantly affect both accuracy and long-term reproducibility of Ce isotope measurements. Measured tail/140CeO ratios could vary due to inaccurate baseline measurements, or the inherent uncertainties in measuring ion beam intensities that are only ten to a few hundred micro volts above baseline. Inaccurate baseline measurements would, however, affect 138CeO, 136CeO and half-mass measurements by the same extent. An error in baseline measurements would thus partially cancel out after 140CeO tail subtraction on the 136CeO and 138CeO mass (and fully if tail correction is done linearly between half-mass measurements done by the same collector, see detailed discussion in Section 4.5). An additional problem, however, could be inaccurate mass calibration. A positive +0.1 amu offset during tail measurement, for example, yields roughly 15% higher tail/140CeO ratios for the typical ion beam intensities used in this study, translating to ~20 ppm lower 138 Ce/136Ce. On the Thermo Scientific Triton, such mass calibration issues can result because the instrument software does not, by default, use CeO compounds (in addition to Ce) as valid masses for computing the mass calibration curve. This has the effect that the mass calibration curve is, effectively, not updated (or recalculated) after performing peak-centers on 1XXCeO beams. When the analysis routine switches to a half-mass, the corresponding magnet current is slightly offset, because it effectively uses an inaccurate mass calibration curve, translating to an offset from the actual target mass (Fig. 2). A simple solution is to add the CeO compounds to the “molecules.mls” file in the “Triton\Libraries” directory. This will flag the oxides as valid compounds for computing the mass calibration curve, update the mass calibration curve after peak-centering on 1XXCeO, and provide sufficient stability of the mass calibration in the 1XXCeO mass range.

4.4. Possible mechanisms affecting the long-term Ce reproducibility

4.5. Correcting for the

4.3. The natural isotopic composition and atomic mass of Ce

Table 3 Ce isotopic abundances and atomic weights. Isotopic abundance [%] 138

140

0.18868 0.18806 0.18795 0.18795 0.18722 0.18697 0.18792

0.24707 0.25192 0.25436 0.25137 0.24311 0.25195 0.25121

88.3862 88.4189 88.4229 88.4260 88.4684 88.4847 88.4283

Ce

Inghram et al., 1947 Umemoto, 1962 Nakamura et al., 1984 Tanaka and Masuda, 1982 Xiao et al., 1994a Chang et al., 1995 This study

Ce

Ce

142

Ce

at. wt. Ce

11.1781 11.1411 11.1348 11.1347 11.0913 11.0764 11.1326

140.1169 140.1161 140.1160 140.1160 140.1154 140.1149 140.1160

CeO tail contribution

In mass spectrometric jargon the term “tail” describes an increased background on the low mass side of an ion beam. This effect results from low energy ions that are produced by collisions of ions with gas molecules or electrostatic repulsion in the ion beam. Low energy ions are more deflected in a given magnetic field than higher energy ions of the same mass, and can thus raise the background on the low mass side of a large ion beam. This effect is investigated on the Thermo Scientific Triton TIMS at WWU using mono-isotopic Pr. There is a significant tail contribution up to four amu away from the main Pr ion beam for beam sizes typical for 140CeO during our measurements (Supplementary Fig. 2). For Ce isotope measurements, the tail of the large 140CeO ion beam consequently interferes with both the 138CeO and 136CeO ion beams. Measurement of accurate 138Ce/136, 142Ce therefore requires adequate subtraction of the 140CeO tail contribution to the 138CeO and 136 CeO ion beams (e.g., Willbold, 2007; Bellot et al., 2015). Different strategies for this tail correction are discussed in the following. The calculated 140CeO tail contribution amounts to roughly 140 ppm of the 138CeO beam intensity. Several different tail correction methods have been tested for our Ames measurements. The results are shown in Table 4. The tail contribution to 138CeO and 136CeO can be estimated by linear interpolation of the background beam at + 0.5 amu and − 0.5 amu offset from each ion beam (Fig. 3). This simple correction overestimates actual tail contributions owing to the curvature of the CeO tail profile (Fig. 3). Since the measured CeO tail intensity scales exponentially with the mass number in the 151.4–154.4 amu mass range, the tail contributions to 138CeO and 136CeO are better approximated with an exponential correction. If any measured half-mass falls below the baseline value (i.e., has a baseline-corrected value < 0) –either due to an inaccurate baseline or to measurement uncertainty on the individual half-mass integration– linear interpolation of the logarithms of half-mass integrations becomes problematic. Such negative

Differences in the Ce isotope ratios during different measurement periods are not unique to this study, but have also been observed by Bellot et al. (2015) and Doucelance et al. (2014). Makishima and Masuda (1994) also report different BCR-1 values compared to an earlier study (Makishima and Nakamura, 1991), despite using identical analytical protocols. Long-term changes in operating conditions of mass spectrometers therefore appear to affect the Ce isotope measurements significantly. In this study, the difference in Ames metal 138Ce/136Ce between measurement periods appears to be related to the 140CeO tail correction applied to 136CeO and 138CeO (see discussion in Section 4.5). The changes in Ames 138Ce/136Ce over time scale with differences in average measured half-mass/140CeO (Fig. 1). Before March 2016, the

136

140

All values are normalized to 136Ce/142Ce = 0.01688. Isotopic abundances in the upper 5 rows are after Xiao et al. (1994), atomic weights calculated using the isotopic masses from Baum et al. (2009). a Isotopic abundances reported by Xiao et al. (1994) add up to ~ 99.99%. The abundances normalized to 100.00% are: 0.18724%, 0.2431%, 88.4772%, and 11.0924%.

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Fig. 2. Schematic explanation of the effect of an inaccurate mass calibration on half-mass measurements. In atomic mass (x-axis) versus mass spectrometer magnet current (y-axis) space, the mass calibration curve relates each atomic mass with a specific magnet current. When the mass calibration curve (solid line) used by the instrument software is offset from the true mass calibration curve (dashed line), a mass offset in half-mass measurements results. In the graph shown above, the magnetic field strength for the 154.4 target mass is determined using an inaccurate (i.e., not updated) mass calibration curve. This magnetic field strength corresponds to a higher mass on the true (i.e., updated) mass calibration curve (dashed line). Thus, inaccurate mass calibration can lead to increased or decreased half-mass values. Note that the horizontal axis is not drawn to scale.

Table 4 Reproducibility of

138

Ce/136Ce for different tail correction methods. 138 Ce/136Ce average Ames (08/ 2016 to 01/2017)

2 S.D. [ppm] overall average

Measurement period Exponential tail Linear tail Tail/154.4 half-mass Constant Tail/140CeO constant

2 S.D. [ppm] for different measurement periods

1

2

3

1.337366 1.337332 1.337366

33 35 35

20 25 25

19 18 20

11 17 17

1.337366

30

34

22

37

Ames 138Ce/136Ce calculated using different methods for correction for the 140CeO tail. The three measurement periods cover the following time spans: (1) November 2015–March 2016, (2) March–August 2016, and (3) August 2016–January 2017. The exponential tail correction produces the most reproducible data within each measurement period. All results were obtained using the same raw data and 136Ce/142Ce = 0.01688 for fractionation correction.

half-mass measurements can partially be avoided by calculating average half-mass/140CeO values for measurements and performing an exponential interpolation on these more precise averages. A more robust method, however, is fitting an exponential equation of the form V = exp(a + b × mass) + c to three or more half-mass measurements (Fig. 3, for details see the Supplementary information). This strategy avoids problems with negative tail measurements and uses more halfmasses for the fit. For the measurement scheme used in this study, the most reproducible results were achieved by fitting V = exp(a + b × mass) + c to ratios of 151.4 amu/140CeO, 153.4 amu/140CeO and 154.4 amu/140CeO that are averaged over the course of one measurement and using this fit to substract for the tail contribution on 136CeO and 138CeO on individual CeO integrations. This procedure results in a reproducibility of 20 ppm within each of the three measurement periods (Fig. 2 and Table 4). Similar reproducibility (but offset values) were achieved by linear tail interpolation between − 0.5 amu and + 0.5 amu, showing that linear tail interpolation is feasible if a correction (of ca. 18 ppm in this study) could be applied to correct for overestimated tail contributions (Fig. 3). Similar external precision is achieved by scaling the tail contribution to the 138CeO and 136CeO beam by the measured intensity on 154.4 amu. Application of a constant for tail/140CeO ratios, however, yields a poor overall reproducibility of ~30 ppm. Such an approach results in a reproducibility similar to methods lacking tail correction, but offset absolute 138Ce/136Ce.

Fig. 3. Upper panel: Schematic illustration of the linear tail fit plotting atomic mass on the horizontal axis and signal intensity on the vertical axis. For peaks to be tail corrected, tail values are measured at − 0.5 and + 0.5 amu and then linearly interpolated. Note that calculated tail contributions to 136CeO and 138CeO (black lines) are larger than the actual tail contributions due to the curvature of the exponential tail (gray curve, c.f. Thirlwall, 2001). Lower panel: Illustration of the exponential tail fit over the 151.4–154.4 amu mass range. Note that both the 136CeO and 138CeO peak are tail-corrected using the same combination of half-masses, as opposed to the linear tail fit shown above.

4.6. Measurement optimization strategies 4.6.1. Optimizing on-peak vs. baseline integration times Recent Ce isotope studies (e.g., Willbold, 2007; Bellot et al., 2015) have used different measurement strategies for measuring baselines and half-masses. This study uses three magnet positions (Table 1). The first is allocated to measuring oxides on 1XXCeO masses, and the two following are shifted by + 0.5 and − 0.5 amu. Bellot et al. (2015) used 124

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Table 5 Three-magnet-position set-up. The measurement set-up used in this study. In this configuration adjacent half-masses. L4

136

CeO and

138

CeO share the same detector (and baseline value) with their respective

L3

L2

L1

C

H1

H2

H3

136

CeO 151.9 152.4 151.4

138

CeO 153.9 154.4 153.4

139

LaO 154.9

140

CeO 155.9

142

CeO 157.9

143

NdO 158.9

142 Ce18O 159.9

L4

L3

L2

L1

C

H1

H2

H3

136

137

138

139

140

142

143

142 Ce18O 159.9

Position 1 Position 2 Position 3

Table 6 Two-magnet-position set-up.

CeO 151.9 151.4

Position 1 Position 2

BaO 152.9 152.4

CeO 153.9 153.4

LaO 154.9 154.4

CeO 155.9

CeO 157.9

NdO 158.9

One of the possible two-magnet-position measurement set-ups. This configuration is similar to the one used by Bellot et al. (2015). In this configuration both 136CeO and 138CeO share the same detector with one of their respective adjacent half-masses.

two magnet positions, one for the 1XXCeO masses, and one shifted by − 0.5 amu, with integration times of 8 s and 4 s punctuated by a 30 s baseline for every 120 s on peak (Table 5). Willbold (2007) used six magnet positions, one for CeO followed by five successive 1 s integrations, each offset by 0.5 amu and inserted a 40 s baseline for every 75 s on peak. Although these recent studies use similar on-peak integration times (8–10 s), there are significant differences between the off-peak integration times. The latter significantly affect the precision of the tail contribution calculated from the off-peak signals. In each of these recent studies, a significant amount of time is also spent on measuring baselines, but the proportion of baseline and half-mass to on-peak measurement time differs. In addition to other factors, the relative integration time of on-peak versus background (i.e., baseline and halfmass measurements) determines measurement precision (e.g., Ludwig, 1997).

integration time), and calculate 138Ce/136Ce values and their uncertainty due to baseline noise. This procedure was repeated using more precise baseline values determined by longer integration times of 2, 4, 8, … 400 s to investigate the relationship between baseline precision and final 138Ce/136Ce uncertainty. As expected, the 138Ce/136Ce uncertainty as a result of baseline measurements scales with 1/sqrt (baseline integration time). Two different methods of tail subtraction were used to evaluate how the data reduction method affects the propagation of baseline uncertainties. The first method calculates tail contributions by two-point linear interpolation between intensities measured at −0.5 and + 0.5 amu from the peak (136CeO, 138CeO, respectively). Although such a linear interpolation does not fully capture the shape of the 140CeO tail and thus introduces a bias (Fig. 3 and discussion above), it is instructive to investigate how this linear tail correction affects measurement precision.

4.6.1.1. Uncertainty from baseline corrections. The effect of baseline uncertainty on the final 138Ce/136Ce values is complicated by the subtraction of the 140CeO tail from the 136CeO and 136CeO signal. If both 13XCeO and its contribution from the 140CeO tail are measured using the same collector, subject to the same baseline values, the baseline subtraction will affect the tail and 13XCeO peaks equally. The baseline term (and its associated uncertainty) then cancels out when subtracting the 140CeO tail contribution from the 13XCeO signal. In short, if on- and off-peak masses and baseline are measured using one common collector, the baseline and tail-corrected 13XCeO intensity is: (peak − baseline) − (tail − baseline) = peak − tail.1 If different collectors (with different associated baseline values) are involved in tail subtraction, the baseline values and associated uncertainties do not cancel. Hence, depending on how many collectors are involved in peak and tail measurements, baseline uncertainties contribute more or less to measurement uncertainty. To quantitatively evaluate uncertainties associated with baseline correction, we take representative signals for peaks and tails and subtract randomly generated baseline values that vary by 7 × 10− 5 V (2 S.D., corresponding to typical noise on 1011 Ω amplifiers for 1 s

peak−tail = (peak−b1) ((tail−0.5amu − b2) + (tail+0.5amu − b3)) − 2

Equation one details linear tail interpolation including background subtraction, where each b represents a baseline value, and subscripts 1–3 refer to different collectors. For b1 = b2 = b3, that is, all peak, tail, and baseline values are determined on the same collector, baseline correction and associated uncertainty cancel. Uncertainty due to baseline subtraction increases if b1, b2 and b3 are different, which is the case if peak, tail, and baseline values are determined on different collectors (cf. Tables 5, 6). The second tested method is the one employed in this study, which is a three-point least-squares exponential interpolation using the following formula: tail = exp(a + b × mass) + c, using masses 151.4, 153.4 and 154.4. Rather than determining an individual tail fit for 136 CeO and 138CeO as done for the linear interpolation, one exponential curve is fitted over the entire 151.4–154.4 amu mass range. If 136CeO, 138 CeO and the three half-masses are measured using the same collector, baselines cancel out during tail correction. Using more collectors increases the extent to which baseline uncertainty propagates to 138 Ce/136Ce uncertainty. Which signals are measured using the same collector depends on the collector configuration and number of magnet positions. Two different approaches are shown in Tables 5 and 6. Employing two magnet positions allows using the same collectors for measuring CeO peaks and their − 0.5 amu half-masses. If three magnet positions are used, any CeO peak and its + 0.5 and − 0.5 amu half-mass

1 This statement is valid when any offset in measured half-mass will directly translate to the same offset in interpolated tail values. This property holds for linear interpolation and the 3 half-mass exponential fit discussed in this paper but not necessarily for all types of tail fitting. For instance linear interpolation of the log of the tail does not satisfy this

(

property: exp

ln(x) + ln(z) 2

) ≠ exp(

ln(x + c) + ln(z + c ) 2

) − c for x ≠ z. Using such tail inter-

polation method, inaccurate baselines can affect measured using the same collector.

(1)

138

Ce/136Ce even if all signals are

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Table 7 Optimized integrations times for different Ce isotope measurement set-ups. Optimal time allocation

Two-magnet-position

Three-magnet-position

Linear tail

Exponential tail

Linear tail

Exponential tail

Time tail Time baseline Time peak

18% 20% 61%

11% 27% 62%

35% 1% 65%

15% 21% 64%

Uncertainty from different sources Tail S.D. 138Ce/136Ce [1 s] Baseline S.D. 138Ce/136Ce uncertainty [1 s] Peak S.D. 138Ce/136Ce uncertainty [1 s]

8.78 × 10− 5 1.09 × 10− 4 2.93 × 10− 4

4.97 × 10− 5 1.47 × 10− 4 2.93 × 10− 4

1.24 × 10− 4 4.81 × 10− 6 2.93 × 10− 4

7.03 × 10− 5 1.06 × 10− 4 2.93 × 10− 4

4.90 × 10− 4 8.16 × 10− 6

4.90 × 10− 4 8.16 × 10− 6

4.25 × 10− 4 7.08 × 10− 6

4.69 × 10− 4 7.81 × 10− 6

12.2

12.2

10.6

11.7

Total optimal error uncertainty/sec (excl. idle) Total S.E. uncertainty 138Ce/136Ce 1 h measurement excl. idle time 2 S.D. [ppm] 138Ce/136Ce 1 h measurement excl. idle time

List of the optimal total percentage of time allocated to baseline, half-mass, and tail measurements excluding idle time for several measurement strategies (columns). Also given are the uncertainty contributions to 138Ce/136Ce associated with 1 s of baseline, half-mass, and on peak measurement time. The on-peak uncertainty constitutes the largest source of uncertainty for any measurement strategy. The amount of uncertainty propagated from half-mass and baseline uncertainty however is strongly dependent on the measurement strategy.

(i.e., tail correction) is also dependent on the number of magnet positions (hence number of collectors involved) and the method used for tail correction. For any given total half-mass measurement time, fewer magnet positions allow longer measurement time for each specific halfmass leading to lower uncertainty on half-mass measurements. Using linear interpolation between −0.5 and + 0.5 amu, the tail contribution on 136CeO and 138CeO are calculated independently, that is, half-masses used to correct for tailing on 136CeO are not used for the 138CeO tail correction and vice versa. Hence, the uncertainties of the tail contributions on 136CeO and 138CeO are independent. In contrast, for an (exponential) interpolation of the 140CeO tail over the 151.4 to 154.4 amu range the tail contributions on 136CeO and 138CeO are correlated, which de-amplifies the uncertainty on 138Ce/136Ce. For example, if the measured 153.4 amu signal is slightly too high, calculated tail contributions on both 136CeO and 138CeO will also be too high. Subtracting the calculated tail contribution from both the numerator and denominator of 138Ce/136Ce results in a final error on 138Ce/136Ce due to tail correction that is lower that on 138Ce and 136Ce alone. Consistent with the logic above, the uncertainty on 138Ce/136Ce propagated from uncertainty on 1 s half-mass measurements using the exponential fit over the 151.4–154.4 amu mass range results in lower uncertainties on 138Ce/136Ce than the linear tail interpolation. For example, a three-magnet-position setup with a 1 s half-mass measurement time (0.5 s each half-mass line) translates to a 1.4 × 10− 4 (100 ppm) 2 S.D. uncertainty on 138Ce/136Ce values compared to 2.5 × 10− 4 (185 ppm) uncertainty for a linear tail interpolation. Using a twomagnet-position method (as done in Bellot et al., 2015) all half-masses can be measured at the same time, which improves uncertainty on the half-mass measurements by a factor of 2 for both tail interpolation methods. In general, optimized methods using more magnet positions have higher uncertainty derived from half-mass measurements but less from baseline uncertainty.

signals are measured with the same collector. When 140CeO tail contributions to 136CeO and 138CeO are determined by two-point linear interpolation in the three-magnet-position setup, uncertainties in baseline signals on 136CeO and 138CeO cancel out for reasons discussed above. Baseline uncertainties on 140CeO, 142CeO, and 142Ce18O collectors do not cancel out, because no tail subtraction is performed on these masses. These baseline uncertainties produce a combined ca. 10− 5 V (7 ppm, 2 S.D.) uncertainly on 138Ce/136Ce for a one second baseline integration time. Optimum baseline measurement time is short in this setup: a minute-long baseline measurement already reduces the associated 138Ce/136Ce uncertainty to sub-ppm levels. If linear tail interpolation is employed using the two-magnet-position setup, more than one collector is required to determine the 136CeO and 138CeO peak and associated − 0.5 and + 0.5 amu half-mass intensities. As discussed above, baseline uncertainties do not cancel out fully in this case. Using a 1 s integration time for the baseline results in a ca. 2.1 × 10− 4 (160 ppm) 2 S.D. uncertainty on 138Ce/136Ce. In a static (one-magnet-position) measurement where baseline values for every measurement parameter are uncorrelated, the baseline uncertainty gives rise to a 3.6 × 10− 4 (270 ppm, 2 S.D.) uncertainty on 138 Ce/136Ce for a 1 s baseline. Exponential fitting of 140CeO tails following the formula tail = exp (a + b × mass) + c requires at least three different half-masses, in this study 151.4, 153.4 and 154.4 amu (Fig. 3). Owing to the use of multiple collectors, baseline uncertainties partially cancel out. For a threemagnet-position measurement, a 1 s baseline correction results in 2.1 × 10− 4 (160 ppm, 2 S.D.) uncertainty where two-magnet-position and 2 S.D. uncertainties due to baseline are calculated to be 3 × 10− 4 (220 ppm) and 3.1 × 10− 4 (230 ppm) for a single-magnet-position measurement. For the 10 min baseline performed in this study uncertainties due to baseline correction reduce to < 7 ppm (2 S.D.).

4.6.1.2. Effect of uncertainty on half-mass measurements. We evaluate the effect of half-mass measurement uncertainty in a similar way to evaluating propagation of baseline uncertainties. Representative signals for peaks and tails were modified by adding randomly generated noise on half-mass measurements varying by 7 × 10− 5 V (2 S.D., corresponding to 1011 Ω amplifiers and 1 s integration time), and calculating 138Ce/136Ce values. The spread in the calculated 138 Ce/136Ce represents the uncertainty propagated from half-mass uncertainty alone. The uncertainty on 138Ce/136Ce due to half-mass measurements

4.6.1.3. Optimized measuring schemes and words of caution. For any fixed time allocated to baseline and half-mass measurement, different measurement strategies result in different uncertainties propagated from half-mass and baseline uncertainties (Table 7). Fewer magnet positions and using one 140CeO tail fit over the 151.4–154.4 amu domain decrease 138Ce/136Ce uncertainty contributed by the halfmass measurements. On the other hand, minimizing the number of collectors used for any 13XCeO peak and corresponding half-mass measurements reduces the contribution of baseline uncertainty. If 126

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23% respectively. Such improvements on tail signal/noise allows for ca. 40% less time to be allocated to tail measurements, while retaining the same precision. Testing the effect of measuring the 142Ce18O beam with a 1012 Ω amplifier is more complicated, because the 142Ce18O/140Ce16O changes during the course of the measurement due to mass fractionation of Ce and changing 18O/16O. The approach taken is to predict the 142 Ce18O/142Ce16O by interpolation from the value for the integration immediately before and after. The average discrepancy between predicted 142Ce18O/142Ce16O and measured 142Ce18O/142Ce16O is used as a measure for noise on the 142Ce18O signal. By this measure, the use of 1012 Ω amplifiers leads to a 20% reduction in noise on the 142Ce18O signal compared to use of a 1011 Ω amplifier. However, this 20% reduction in noise on 142Ce18O only leads to sub ppm improvements on the final uncertainty on 138Ce/136Ce. The use of 1012 amplifiers to measure the 142Ce18O signal is therefore an ineffective way to improve measurement precision. Half-masses and baseline measurements (for 136CeO and 138CeO) are more critical for optimizing measurement precision. However, count statistical uncertainty on the on-peak 1XXCeO signals remains the largest source of internal uncertainty on 138Ce/136Ce (see discussion above). A reduction of off-peak measurement uncertainty will thus only lead to modest (ca. 15%) improvements of the internal measurement uncertainty.

measurement time is optimally partitioned between half-mass, peak and baseline integration times, the combined predicted 138Ce/136Ce uncertainty for any given amount of total measurement time is similar for all the methods discussed above. However, the proportion of time that should be spend on baselines and tails between the different measurement strategies discussed above differs significantly. For any given method for tail correction, therefore, measurement times on halfmass, peak, and baseline must be chosen accordingly. Table 7 summarizes the calculated optimum proportions of baseline, halfmass and peak measurement times for each setup discussed above. For example, Bellot et al. (2015) employ a two-magnet-position approach combined with an exponential tail fit. Their half-mass to peak time ratio of 0.5 is only slightly higher than the < 0.2 optimum calculated here. Also, their baseline to peak time ratio of 0.25 is only slightly less than the optimum ~0.4 (Table 7). Therefore, by small adjustments of the chosen half-mass, peak, and baseline integration times, a modest improvement of internal precision of roughly 5% would be expected. For the method employed by Willbold (2007), all half-mass positions and the 138CeO peak are measured with the same collector (using six magnet positions). This has the advantage that baseline uncertainty on tail-corrected 138CeO cancels out. However, the 136CeO is also tailcorrected but not measured on the same collector as the half-masses. Thus, baseline uncertainty propagates onto tail-corrected 136CeO. Because the 136CeO signal is smaller than the 138CeO signal, the proportional effect of baseline noise on 136CeO is larger than on 138CeO and uncertainty in baseline measurements significantly affects uncertainty on 138Ce/136Ce. Although the six-magnet-position setup facilitates sufficient total measurement time on each half-mass, the total acquisition time could be shortened significantly by using fewer magnet positions. It should be noted that the estimated optimum integration time allocation for half-mass, peak, and baseline measurements for any given method only considers count statistical uncertainties, but does not take into account any potential other sources of uncertainty or errors. These could be due to signal drift, changes in tail shape, or the effects of inaccurate mass calibration. Idle time, which can be considerable when using short integration times (but can be reduced by decreasing the frequency of magnet jumps) is also not taken into consideration. Nevertheless, this exercise illustrates the importance of optimizing the integration times on half-mass, peak, and baseline measurements (cf. Ludwig, 1997). This exploration of measurement optimization also reveals that there is a trade-off between uncertainty contribution from baseline and tail corrections that is inherent to the Ce isotopic system. Understanding how different integration times for on-peak, baseline, and half-mass measurement for different measurement methods influence the overall measurement uncertainty is therefore crucial for finding the most precise method that is also least prone to systematic measurement bias for any given element.

5. Renormalizing literature data Great care must be taken when comparing previous Ce isotope ratios that are corrected for mass fractionation with different values for 136 Ce/142Ce and also apply an in-situ 18O correction. In this case, a change in the 136Ce/142Ce value will alter both the calculated 18O/16O and the extent of mass fractionation (see Supplementary information). Hence, a simple renormalization of the data using different ratios for 136 Ce/142Ce (e.g., 0.0172 versus 0.01688, Nakamura et al., 1984, Makishima and Masuda, 1994) neglects the change in calculated 18 O/16O inherent in calculating the extent of mass fractionation. An example is shown using a rock sample analysis, calculated using 136 Ce/142Ce = 0.0172 for mass fractionation correction and recalculating to 136Ce/142Ce = 0.01688 afterwards. The resulting renormalization bias is roughly 35 ppm (Supplementary information), which is significant compared to measurement precision. Care must thus be taken when normalizing literature data generated using in-situ 18 O data, because the calculated 18O/16O and 136Ce/142Ce are dependent variables during data reduction. 6. Conclusions Ce isotope analyses face considerable analytical challenges, which are mainly related to the low abundance of the minor isotopes 136Ce and 138Ce relative to the main isotopes 140Ce and 142Ce (136Ce = 0.19%, 138Ce = 0.25%, 140Ce = 88.43%, 142Ce = 11.13%). Hence, simultaneous measurement of ion beams over a large dynamic range is required, resulting in large differences in count statistical uncertainty on the individual ion beams. In addition, the large abundance of 140Ce introduces a tailing effect of the large 140CeO ion beam onto the 136CeO and 138CeO ion beams, which requires adequate correction (e.g., Dickin et al., 1987; Willbold, 2007). Although all of the most recent Ce isotope studies measure Ce as the oxide species (CeO+) to suppress interfering isobaric BaO+, and have used the same type of thermal ionization mass spectrometer (Thermo Scientific Triton; Willbold, 2007; Doucelance et al., 2014; Bellot et al., 2015), they have used different collector configurations and number of magnet positions for measuring on-peak and half-mass signals. The latter are determined for correction for the contribution of the 140CeO tail onto the 136CeO and 138CeO ion beams. Evaluation of these different strategies shows that, as long as the integration times for the on-peak, half-mass, and baseline signals are adequately optimized for the

4.6.2. Use of 1012 Ω amplifiers To evaluate whether it is advantageous to use 1012 Ω amplifiers on the low intensity peaks 136CeO, 138CeO, and 142Ce18O mass, the Ce Ames standard has been measured repeatedly, with and without the use of 1012 Ω amplifiers. The 1012 Ω amplifier achieves ca. 3 times better signal to noise ratio for ion beams < ~2 × 10− 13 A than the 1011 Ω amplifier (Koornneef et al., 2013). The smallest signals measured in the CeO routine are in order of increasing signal strength: (1) baselines (~ 0 A), (2) half-masses between 151.4 and 144.4 (10− 16 to 10− 15 A, or 10− 5 to 10− 4 V on a 1011 Ω amplifier), and (3) the 142Ce18O signal (~ 4 × 10− 13 A, or 0.04 V on a 1011 Ω amplifier). On the Thermo Scientific Triton at WWU Münster, the baseline noise on 1012 Ω amplifiers is ca. 44% lower than on the 1011 Ω amplifiers (ca. 4 × 10− 5 V versus 7 × 10− 5 V for 1 s integration times), allowing ca. 65% less measurement time to be spend on baselines retaining the same precision. Using 1012 Ω amplifiers, the noise on halfmasses 151.4, 153.4, and 154.4 signals are reduced by 32%, 27% and 127

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employed tail correction method, the different strategies can yield Ce isotope ratios with similar precision for a given measurement time. The half-mass and baseline measurements can be further improved by using 1012 Ω amplifiers on the low-intensity ion beams. The overall greatest source of uncertainty remains the count statistical uncertainty on the 136CeO and 138CeO beams, which can be minimized by measuring at high intensity. The latter can be achieved by avoiding collection of the most abundant isotope 140Ce, as done by several recently reported methods (Willbold, 2007; Doucelance et al., 2014; Bellot et al., 2015). This allows measurement of the remaining ion beams of 136CeO, 138CeO, and 142CeO, at up to eight times higher intensity, that is, almost three times better count statistics using the generally employed 1011 Ω amplifiers. Using this approach, however, requires assuming a constant ratio of 140Ce over another isotope, usually 142Ce (e.g., Tanaka and Masuda, 1982; Tazoe et al., 2007a, 2007b) for the simultaneous correction for mass fractionation and isobaric XCe18O – X + 2Ce16O interferences. It is shown here that, as long as the chosen 140Ce/142Ce value is internally consistent with the 136 Ce/142Ce value used for fractionation correction, using a constant 140 Ce/142Ce is indeed a viable strategy for avoiding cup degradation caused by measuring the 140CeO beam. In this study, we have acquired 140 CeO by using a 1010 Ω amplifiers, and have determined along-term average 140Ce/142Ce of = 7.94319 ± 2 in the silicate samples measured in this study. We recommend this value in conjunction with 136 Ce/142Ce = 0.01688 (Makishima et al., 1987) for mass fractionation correction for future Ce isotope studies to assure easy inter-laboratory comparison. Overall, it has been shown that Ce isotope ratios can be determined by TIMS with a reproducibility of 20–40 ppm (2 S.D.) using a common 136 Ce/142Ce = 0.01688 (Makishima et al., 1987) for mass fractionation correction. Furthermore, the 136Ce/138Ce of the international rock reference materials BCR-1, BCR-2, and BHVO-2 of this study agree well with those recently reported (Doucelance et al., 2014; Bellot et al., 2015), when all Ce isotope ratios are reported relative to a common 138 Ce/136Ce = 1.337366 of the average Ames Ce metal. In addition, Ce isotope ratios for several other widely available international rock reference materials (AGV-2, BE-N, BIR-1, DNC-1, W2A) are presented, and facilitate easy inter-laboratory comparison.

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