Laurie Reisberg
email: laurie.reisberg@univ-lorraine.fr

Catherine Zimmermann

Optimization of 186 Os/ 188 Os analyses by N-TIMS using amplifiers equipped with 10 13 Ohm resistors

Keywords: Os isotopes, 186 Os, 10 13 Ohm amplifiers

Analysis of 186 Os/ 188 Os variations in most natural samples is hampered by their low Os concentrations (usually <100 pg/g), requiring Os separation from up to a kilogram of powder to obtain high precision results. Recently developed amplifiers equipped with 10 13 Ohm feedback resistors improve the signal to noise ratio by an order of magnitude, allowing acquisition of high precision data (2SE <50 ppm) from 186 OsO 3 -ion beams of ~40 fA, and thus analysis of less material (~10 to 500g). Factors controling the accuracy and precision of 186 Os/ 188 Os NTIMS analyses, using a mixed array of 10 13 and 10 11 Ohm amplifiers, include isobaric interferences, baseline variability, gain calibration, decay time corrections and oxygen isotope composition variations. Isobaric interferences present the greatest challenges, but these can be largely overcome by using double Pt filaments and periodically monitoring interferences during each analysis. The optimized procedures produce 186 Os/ 188 Os ratios with precisions close to the theoretical limits imposed by counting statistics and Johnson-Nyquist electronic noise for ion beams of 10 to 70 fA. The long term reproducibility (85 ppm; 2σ) approaches theoretically expected values (~50 to 80 ppm). This reproducibility is sufficient to allow 186 Os/ 188 Os analyses of crustal rocks, for which relatively large variations are expected.

Introduction

Osmium has two isotopes of partly radiogenic origin, 187 Os and 186 Os, formed respectively by the radioactive decay of 187 Re and 190 Pt. While studies of 187 Os/ 188 Os variations in geological samples have become commonplace, analyses of 186 Os/ 188 Os remain rare. This is because the range of variation of 186 Os/ 188 Os is quite limited in most common sample types (e.g. <0.000020 in young mantle samples [START_REF] Brandon | 186 Os-187 Os systematics of Hawaiian picrites[END_REF]), both because of the exceedingly long half-life of 190 Pt (4.5 x 10 11 yr; λ = 1.48 x 10 -12 yr -1 ; [START_REF] Walker | Applications of the 190Pt-186Os isotope system to geochemistry and cosmochemistry[END_REF])), about ten times greater than that of 187 Re, and because of the very low isotopic abundance of 190 Pt (0.014%). As a result, high precision analyses are needed to distinguish natural variations of 186 Os abundances. This difficulty is compounded by the extremely low Os contents of most terrestrial samples. For this reason, studies of 186 Os/ 188 Os variations have been mostly limited to materials with relatively high Os concentrations (several hundred ppt to several ppb). Examples include extraterrestrial samples [START_REF] Brandon | Platinum-osmium isotope evolution of the Earth's mantle: Constraints from chondrites and Os-rich alloys[END_REF], mantle peridotites [START_REF] Brandon | 190 Pt-186 Os and 187 Re-187 Os systematics of abyssal peridotites[END_REF][START_REF] Chatterjee | 186Os/188Os variations in upper mantle peridotites: Constraints on the Pt/Os ratio of primitive upper mantle, and implications for late veneer accretion and mantle mixing timescales[END_REF], ultramafic intrusions [START_REF] Day | Ancient high Pt/Os crustal contaminants can explain radiogenic 186Os in some intraplate magmas[END_REF] and Mg-rich volcanic rocks such as komatiites, picrites and certain ocean island basalts [START_REF] Brandon | 186 Os-187 Os systematics of Hawaiian picrites[END_REF][START_REF] Ireland | Os-186-Os-187 systematics of Hawaiian picrites revisited: New insights into Os isotopic variations in ocean island basalts[END_REF][START_REF] Puchtel | Precise Pt-Re-Os isotope systematics of the mantle from 2.7-Ga komatiites[END_REF]. Conventional 186 Os/ 188 Os analysis of crustal samples, which typically contain only tens of ppt of Os, requires Os extraction from hundreds of grams of material to obtain high precision results and thus very few such studies have been undertaken, a notable exception being that of [START_REF] Mcdaniel | Sources of osmium to the modern oceans: new evidence from the 190Pt-186Os system11Associate editor[END_REF].

The development of amplifiers equipped with 10 12 and 10 13 Ohm resistors in their feedback loops (which will be referred to here as 10 13 Ohm amplifiers for brevity), instead of the 10 11 Ohm resistors used traditionally, has opened up the possibility of high precision analyses of smaller quantities of sample material. This is because the signal/noise ratio of the amplifiers, which is the dominant source of uncertainty on small intensity signals, varies with the square root of the amplifier resistance, and so should be reduced by factors of nearly 3.3 and 10 respectively in 10 12 and 10 13 Ohm amplifiers relative to 10 11 Ohm amplifiers. Recently, 10 12 Ohm amplifiers have been used to measure 186 Os/ 188 Os variations on small to moderate signals with considerable success [START_REF] Liu | Rapid, precise and accurate Os isotope ratio measurements of nanogram to sub-nanogram amounts using multiple Faraday collectors and amplifiers equipped with 1012 Ω resistors by N-TIMS[END_REF]. [START_REF] Koornneef | Measurement of small ion beams by thermal ionisation mass spectrometry using new 1013Ohm resistors[END_REF] used 10 13 amplifiers to measure Sr and Nd isotopic variations by thermal ionization mass spectrometry (TIMS) in quantities as low as 10 pg, achieving a reproducibility of 125 ppm on 100 pg loads of Nd. Other TIMS applications for these amplifiers have been developed for Pb isotopes [START_REF] Klaver | Pb isotope analysis of ng size samples by TIMS equipped with a 1013 Ω resistor using a 207Pb-204Pb double spike[END_REF], U/Pb zircon dating [START_REF] Quadt | High-precision zircon U/Pb geochronology by ID-TIMS using new 1013 ohm resistors[END_REF] and U isotopes [START_REF] Trinquier | Precise and accurate uranium isotope analysis by modified total evaporation using 10(13) ohm current amplifiers[END_REF], while MC-ICP-MS applications include Pt isotope analysis [START_REF] Creech | Application of 10(13) omega Amplifiers in Low-Signal Plasma-Source Isotope Ratio Measurements by MC-ICP-MS: A Case Study with Pt Isotopes[END_REF], and in combination with laser ablation, in situ analysis of Pb isotopes [START_REF] Kimura | High-precision in situ analysis of Pb isotopes in glasses using 1013 Ω resistor high gain amplifiers with ultraviolet femtosecond laser ablation multiple Faraday collector inductively coupled plasma mass spectrometry[END_REF]. Recently, [START_REF] Wang | High-Precision Measurement of 187Os/188Os Isotope Ratios of Nanogram to Picogram Amounts of Os in Geological Samples by N-TIMS using Faraday Cups Equipped with 1013 Ω Amplifiers[END_REF] showed that use of 10 13 Ohm amplifiers allows precisions of 2-3‰ to be obtained for 187 Os/ 188 Os measurements of several tens of picograms of Os, demonstrating that these detectors equal or exceed the performance of secondary electron multipliers for these sample sizes. For 186 Os/ 188 Os analyses, precision and accuracy better than a few hundred ppm are often required to obtain geologically useful information. Our goal here is to explore the factors that optimize the precision and reproducibility of 186 Os/ 188 Os ratios obtained from low intensity OsO 3 -ion beams measured with 10 13 Ohm amplifiers.

Advantages and limitations of 10 13 Ohm amplifiers

Use of 10 13 Ohm amplifiers increases the signal intensity in V by a factor of 100 relative to traditional 10 11 Ohm amplifiers. More importantly, it increases the signal to noise ratio by an order of magnitude. The reason for this is evident from the Johnson-Nyquist equation [START_REF] Johnson | Thermal Agitation of Electricity in Conductors[END_REF][START_REF] Nyquist | Thermal Agitation of Electric Charge in Conductors[END_REF], which expresses the magnitude in volts of electronic noise caused by thermal agitation in the resistor:

𝑉 !" = !×! ! ×!×! ! (1)
where k B is the Boltzmann constant (1.38 x 10 -23 J/ o K), R is the resistance in Ohms, T is the amplifier temperature in o K, and t is the integration time in seconds. The improvement obtained through use of 10 13 Ohm rather than 10 11 Ohm resistors is visually evident in Fig. 1, which compares the signal of 186 OsO 3 -(measured with a 10 13 Ohm amplifier) and 187 OsOsO 3 -(measured with a 10 11 Ohm amplifier). -ion beam (measured with a 10 13 Ohm amplifier) with 187 OsO 3 -ion beam (measured with a 10 11 Ohm amplifier) on a DROsS standard, which has comparable isotopic abundances of 187 Os and 186 Os. To facilitate comparison between amplifiers, signal intensities are presented both as ion currents (fA) and as equivalent volts that would be obtained if the signals were measured with 10 11 Ohm amplifiers. Gaps in traces represent times when peaks were switched that were erased for clarity.

In addition to directly decreasing the random variability of measured signals, the higher signal/noise ratio provided by the 10 13 amplifiers improves performance by providing quieter baselines and more reproducible gains for a given calibration current, as will be discussed in detail below.

There are nevertheless two trade-offs for the improved signal/noise ratio of the 10 13 Ohm amplifiers that must be considered when developing analytical routines. One is that amplifier saturation occurs at much lower signal intensities than for 10 12 or 10 11 Ohm amplifiers. In the Triton, saturation of the 10 13 Ohm amplifiers occurs at ion beam currents of about 1500 fA (0.15 V -here and elsewhere equivalent voltages that would be measured on 10 11 Ohm amplifiers are given for convenience) in negative ion mode, and about 5000 fA (0.5 V) in positive ion mode, values that are two orders of magnitude lower than those leading to saturation of 10 11 Ohm amplifiers. This must be taken into account when choosing which isotopes to measure with the 10 13 Ohm amplifiers. The other limitation is that the time response of the 10 13 Ohm amplifiers is much slower than that of the 10 11 Ohm amplifiers, i.e., the exponential decay time tau (τ) is much longer. As a result the apparent peak shape obtained on a 10 13 Ohm amplifier will be asymmetrical and offset from the peak of another isotope measured simultaneously on a 10 11 Ohm amplifier (Fig. 2). This means that cup alignment, peak centering and focusing should always be done on ion beams measured by10 11 Ohm amplifiers. The slower response of the 10 13 Ohm amplifiers also implies that a much longer delay time (at least 10 sec) is needed before starting baseline or signal measurements. In addition, if signal intensities are changing rapidly a τ correction may have to be applied to account for the different responses of signals measured simultaneously on 10 13 and 10 11 Ohm amplifiers [START_REF] Craig | Negative thermal ion mass spectrometry of osmium, rhenium, and iridium[END_REF][START_REF] Kimura | High-precision in situ analysis of Pb isotopes in glasses using 1013 Ω resistor high gain amplifiers with ultraviolet femtosecond laser ablation multiple Faraday collector inductively coupled plasma mass spectrometry[END_REF]. Because of the limits on current intensity and the long decay time, amplifier rotation or multi-dynamic analyses involving both 10 13 and 10 11 Ohm amplifiers are not possible.

Experimental set-up

The tests described here were performed by negative thermal ionization mass spectrometry (N-TIMS; [START_REF] Craig | Negative thermal ion mass spectrometry of osmium, rhenium, and iridium[END_REF][START_REF] Volkening | Osmium isotope determinations by negative thermal ionization mass spectrometry[END_REF]) at the CRPG laboratory using a Thermo Triton instrument equipped with three 10 13 Ohm and seven 10 11 Ohm amplifiers. Thirty analyses of 5 ng of the DROsS international Os standard were performed during three analytical sessions. Standards were loaded in HBr on Pt filaments outgassed in air for ~20 minutes and 0.2-0.5 µl of a saturated BaOH-NaOH solution were added to enhance formation of negative ions. Double Pt filaments were used for sessions 1 and 2; single filaments were used for session 3. Filaments were heated quite slowly (at 2 to 5 mA/min) until a measurable signal was obtained (usually at about 750 mA for double filaments, with both filaments heated at the same rate, and at about 800 mA for single filaments). Gain calibrations, lasting nearly 3 hours, were done during heating. These consisted of background readings followed by measurement of a 1.2 pA calibration current by each of the 10 13

Ohm and 10 11 Ohm amplifiers. In some cases long baseline measurements (2-3 hours) were also performed during sample heating. is used in the fractionation correction and so affects the precision and accuracy of the calculated 186 Os/ 188 Os value, we chose not to measure this peak with a 10 13 Ohm amplifier because saturation would occur when ion beams of 186 OsO 3 -approached ~60 fA (0.006V), implying a 192 OsO 3 -signal of ~1500 fA (0.15 V). Ideally, mass 240 could be measured using a 10 12 Ohm amplifier, but no amplifiers of this resistance were available on our instrument. We used the third 10 13 Ohm amplifier to measure mass 242, and thus to monitor possible changes in the oxygen isotope composition.

Three different cup configurations were used during the course of the analyses (Table 1). Total analysis times varied between about 3 and 20 hours. Data were acquired in one or several runs, each consisting of ten blocks (in most cases). Each block was composed of ten data collection cycles, each with an integration time of 67 seconds, preceded in most cases by 10 minutes of baseline measurement. The need to measure baselines and data for approximately equal time periods in order to minimize uncertainties was stressed by [START_REF] Chatterjee | High precision Os isotopic measurement using N-TIMS: Quantification of various sources of error in 186Os/188Os measurements[END_REF] for 186 Os analyses with 10 11 Ohm amplifiers. Nevertheless, much of the sample is wasted during pre-block baseline measurements, so we also tested the use of shorter baselines (5 minutes prior to ~20 minutes of data collection) and long baseline (2-3 hours) measurements during heating and after data acquisition, as suggested by [START_REF] Koornneef | Measurement of small ion beams by thermal ionisation mass spectrometry using new 1013Ohm resistors[END_REF] for Nd and Sr isotope measurements with 10 13 Ohm resistors.

Wait times of 50 seconds were applied before both the baseline measurements and the first cycles of each block, to account for the long decay time of the 10 13 Ohm amplifiers. Assuming a tau value of ~0.65 s, [START_REF] Craig | Negative thermal ion mass spectrometry of osmium, rhenium, and iridium[END_REF], a 50 second wait time is considerably longer than that (~9 s) which would be theoretically needed for the signal to decrease to below 1 ppm of its original value when the ion beam is suddenly cut off. However, as can be seen in Fig. 3, which compares the response of a 10 11 Ohm and a 10 13 Ohm amplifier after closing the analyzer valve, the signal actually falls slightly below the baseline value before rising again. This effect was observed on all three 10 13 Ohm amplifiers. As a result, the signal measured 10 to 20 seconds after valve closure would be systematically false by more than 100 ppm. A 50 second wait time was used to be sure to avoid this effect, though a somewhat shorter wait time (30 to 35 sec) would likely have been sufficient. Short interference runs were performed before and after each data collection run. peaks [START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF].

Data treatment

Data were exported using the "time in seconds" option of the Triton data acquisition program (Evaluate module) and opened in an Excel spreadsheet for data reduction. In some cases, discussed below, raw data without baseline and/or gain corrections were exported, and these corrections were made off-line using averaged baseline or gain values prior to further data processing. Data processing was performed in successive steps, as outlined below. In the following, "analysis" refers to the ensemble of data collected from a given filament, while "run" refers to a segment of data acquisition, normally preceded and succeeded by interference measurements.

1) Baseline correction (if necessary). In most cases, baselines were corrected on-line using the baseline values measured before each block. However, in a few cases (indicated as "offset"), long baselines (~ 2 hours) were measured during heating and at the end of the analysis, with much shorter baselines (5 minutes) measured prior to each 3 or 4 block run segment to monitor any possible drift. A weighted average of the baseline readings was then applied to the imported uncorrected data.

2) Gain correction (when gain not included in exported data). To evaluate the possible effect of spurious gain calibration values, data for each run were exported in two forms, one using the gain values obtained during filament heating prior to the analysis, and the other without gain correction.

In the latter case, gain correction was performed off-line, as discussed below, using the average gain values obtained during the 5 preceding and succeeding gain calibrations.

3) Decay time correction. This step is used to correct for the differing response times of the 10 13 and 10 11 Ohm amplifiers. For the 10 13 Ohm amplifiers used to measure the 2. Results of thirty analyses of the DROsS international Os standard. Data have been corrected as detailed in text for gain variations using average values, amplifier decay times, interpolated isobaric interferences, in-run measured oxygen compositions and mass fractionation (except 192 Os/ 188 Os). For analyses 1-26, baselines of 10 minutes were measured prior to each block of ~11 minutes; for analysis 27 baselines of 5 minutes were measured before each two blocks; for analyses 28-30 long baselines of ~2 hours were performed during heating and after data acquisition, with 5 minute baselines before every 3 or 4 block run. Cup configurations (A,B,C) are defined in Table 1. Ratios included in average (detailed in Table footnotes) include those analyzed with 10 minute pre-block backgrounds or with offset backgrounds that were not subject to large interference corrections.

Results

Table 2 lists results for the thirty analyses performed in this study. 186 OsO 3 -beam intensities varied from 5 to 69 fA (0.0005 to 0.0069 V equiv. 10 11 Ohm amplifier), while the number of 186 OsO 3 -ions measured varied from 0.2 to 8.2 x 10 9 , corresponding to useful Os yields of 0.1 to 3.3 %. These calculated yields include only those ions actually used for data acquisition; they do not include ions emitted during focussing, centering, wait times, or background and interference measurements.

They also do not include the ions arriving at the beginning and ends of measurements, when the 186 OsO 3 -beams are considered too small (usually <10fA; 0.001V) for acquisition of useful data.

In Fig. 4 186 Os signals less and greater than 2.5 mV (equiv. on 10 11 Ohm amplifier) are distinguished. The deep red horizontal line and the gray shaded area represent the average and 2σ variation of the "normal" analyses and of analyses with offset baselines (baselines measured primarily during heating and after analysis). B) Expanded view of (A) comparing results of this study with those of previous studies that analyzed the DROsS standard [START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF][START_REF] Liu | Rapid, precise and accurate Os isotope ratio measurements of nanogram to sub-nanogram amounts using multiple Faraday collectors and amplifiers equipped with 1012 Ω resistors by N-TIMS[END_REF][START_REF] Chu | High-Precision Measurement of 186Os/188Os and 187Os/188Os: Isobaric Oxide Corrections with In-Run Measured Oxygen Isotope Ratios[END_REF][START_REF] Chatterjee | High precision Os isotopic measurement using N-TIMS: Quantification of various sources of error in 186Os/188Os measurements[END_REF]. Fig. 5A shows the internal precision of each analysis (1 standard error) as a function of the number of 186 Os ions reaching the collectors. To facilitate comparison with the theoretical curves, the data are divided into samples with average 186 Os beam intensities greater and less than 25 fA (2.5 mV).

These are compared to the theoretical limits of precision imposed by the combination of counting statistics and of Johnson-Nyquist noise. The counting statistic limit in ppm, defined by the equation:

𝑟𝑠𝑑 !" = 10 ! × ! !"# !"# + ! !"# !""
(2) reflects the random variation of ion arrivals and depends uniquely on the total number of ions measured (cts 186 and cts 188, for 186 Os and 188 Os respectively). Equation 3 expresses the limit on precision imposed by the Johnson-Nyquist effect:

𝑟𝑠𝑑 !" = 10 ! × ! !" ! !"# ! ! ! !" ! !"" ! ! (3)
Here, V JN is the J-N noise in V calculated by Eq. 1, V 186 and V 188 are the signal intensities in V of the 186 Os and 188 Os beams, and n is the number of integrations. Unlike the uncertainty related to counting statistics, that due to J-N noise depends on both the total number of ions measured (through n and V JN , which includes the integration time, t; see eq. 1) and on the intensities of the ion beams. Fig. 5B shows separately the uncertainties predicted from counting statistics and from J-N noise for ion beams of three different beam intensities (10, 30 and 50 fA, corresponding to 1, 3 and 5 mV on 10 11 Ohm amplifiers) in the range of the signal sizes of the analyzed standards.

In Fig. 5A the J-N noise is combined with the counting statistic curve to obtain the total theoretical precision limit (rsd tot ) for each of these three beams, using the equation:

𝑟𝑠𝑑 !"! = 𝑟𝑠𝑑 !" ! + 𝑟𝑠𝑑 !"(!) ! + 𝑟𝑠𝑑 !"(!) ! (4)
where rsd CS , rsd JN(S) and rsd JN(B) represent, respectively, the standard deviations related to counting statistics, J-N noise on the signal and J-N noise on the baseline. As the total measurement times for baseline and signal were approximately the same, rsd JN(S) and rsd JN(B) will be about equal. Analyses without large interference corrections have standard errors approaching the theoretical limits. This suggests that sources of in-run uncertainties other than counting statistics and JN noise are quite small. In particular this suggests that in-run uncertainties related to the fractionation correction, which are not considered in eq. 4, are insignificant.

While the analytical precisions are about as good as can be theoretically expected, this may not be true of the reproducibility. As the analyses spanned a wide range of signal intensity and run length, the expected reproducibility is difficult to estimate. To obtain a rough approximation, we consider the median intensity (0.0037 V) and the median number of counts (2 x 10 9 ) of 186 Os in the runs without obvious anomalies (labelled "1" in Table 2). In this case, the 2σ uncertainty calculated from J-N noise and counting statistics would be about 58 ppm. If this approximation is valid, it would suggest that the theoretical reproducibility of the 186 Os/ 188 Os ratio is significantly better than the observed 2σ variation (85 ppm) over the duration of the study, and could indicate that factors other than J-N noise and counting statistics led to minor variations between runs. One of these could potentially be degradation of the Faraday cups over the period of the study.

A) B)

Figure 5. A) Uncertainties (1 rsd) on 186 Os/ 188 Os data as a function of number of 186 OsO 3 -ions measured. Data are compared with noise levels theoretically predicted from the combination of uncertainties from counting statistics and Johnson-Nyquist noise (including effect on both signal and baseline). As the relative J-N uncertainties depend on both the total number of ions measured and the intensity of the signal, curves are shown for three different signal intensities pertinent to our study. B) J-N uncertainties (1 rsd) predicted for 186 Os signal intensities from 1-5 mV (equiv. 10 11 Ohm amplifier) and uncertainties related to counting statistics. The curve for counting statistic uncertainties is very similar to that for J-N noise for 1 mV signals.

In addition to listing results for 186 Os/ 188 O ratios, Table 2 also presents data for 190 Os/ 188 Os and 187 Os/ 188 Os, for which the isotope peak in the numerator was measured with a 10 11 Ohm amplifier.

The average 190 Os/ 188 Os ratio obtained (1.983891 ± 0.000230, 2σ) agrees with results from previous analyses of the DROsS standard [START_REF] Chatterjee | High precision Os isotopic measurement using N-TIMS: Quantification of various sources of error in 186Os/188Os measurements[END_REF][START_REF] Liu | Rapid, precise and accurate Os isotope ratio measurements of nanogram to sub-nanogram amounts using multiple Faraday collectors and amplifiers equipped with 1012 Ω resistors by N-TIMS[END_REF][START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF] , 2008), though the uncertainty is larger than in those studies because of the order of magnitude difference in signal size. The average 187 Os/ 188 Os ratio (0.160977 ± 0.000304) also agrees with literature data, but the uncertainty is quite large. Comparison of the relative uncertainty of this ratio (1887 ppm) with that of the 186 Os/ 188 Os ratio (85 ppm) suggests that this uncertainty is at least two or three times larger than would be expected simply because of the use of a 10 11 rather than a 10 13

Ohm amplifier to measure 187 OsO 3 . We suspect that this points to the presence of minor unidentified molecular interferences that are not removed by the interference correction routine.

Discussion

Each of the factors that potentially affect the precision and reproducibility of the isotopic results are considered below.

Useful yields

The most direct factor controlling the precision of the results is the number of OsO 3 -ions measured.

In these tests, one of our major concerns was avoiding systematic biases, so very conservative choices were made concerning run parameters. Thus it is possible that some improvement in usable yield could be made by decreasing wait times, minimizing the length (but not the frequency) of interference analyses, and limiting the frequency of focusing and centering. Performing long baseline analyses before and after the run also increases the useful yield, but as discussed below, shorter in-run baseline monitoring is still advisable to catch possible systematic drift. Analyses 28 and 30, two of the three analyses run with baselines offset in time in this manner, have among the highest useful yields and correspondingly low 2SE uncertainties. Another factor that likely improved the yield in these cases was that the 10 interference runs and 9 data collection runs comprising each of analyses 28-30 were programmed in an automatic run sequence, thus eliminating possible time lost during user intervention. Nevertheless, further tests are needed to optimize the loading parameters required to assure large stable ion beams, as this is critical to achieving high yields.

In this context, it is interesting to consider the theoretical minimum amount of osmium required to obtain 186 Os/ 188 Os data of a given precision. To obtain a precision (1 rsd) of 25 ppm, Fig. 5A indicates that ~2.4 x 10 9 atoms of 186 Os would have to be measured, assuming that a signal intensity of 50 fA (0.005V) could be maintained. This corresponds to ~2.5 x 10 -13 moles of total Os, or 0.048 ng. Assuming that 5% of the 186 Os atoms loaded on the filament are actually measured by the collector, this means that the minimum amount of Os needed to obtain 25 ppm precision would be ~ 0.96 ng. In contrast, if a precision (1 rsd) of 10 ppm is required, ~1.43 x 10 10 atoms of 186 Os must be measured, corresponding to ~5.6 ng of Os loaded on the filament using the same assumptions.

Conversely, if 3 ng of Os are loaded, it is not possible to obtain better than 14 ppm precision.

Furthermore, an assumption of 5% useful yield is rather optimistic, and exceeds the values obtained in our experiments (Table 2). Also, as discussed above, in-run precision is often less good than reproducibility, which is of more interest. Nevertheless, for a known amount of Os deposited on the filament, this simple calculation provides some insight into the theoretical optimum result that could be hoped for.

Baselines

The analytical baselines of 10 11 and 10 13 Ohm amplifiers are compared in Fig. 6, and short term

(1.05 s baselines measured successively over 2 hours) and long term (mostly 10 minute baselines measured sporadically over 6 weeks) variations for each of the amplifiers are listed in Table 3.

A) B)

Figure 6. Comparison of baselines measured on 10 11 Ohm (amp 3) and 10 13 Ohm (amp 9) amplifiers over short (~20 minute) and long (6 week) periods. To facilitate comparison, the average baseline reading over the period considered has been subtracted. A) Results of 1200 successive 1.05 second baseline readings; B) Results of baseline measurements averaged over long time periods (mostly 10 minutes) during and prior to analyses and during gain calibrations.

Using Eq. ( 1), it can be calculated that the Johnson-Nyquist noise associated with 10 11 Ohm resistors should be about 0.04 mV (0.4 fA) for successive baseline readings of 1.05 seconds, which is approximately equal to the variability (1σ) observed for the 10 11 Ohm amplifiers (Table 3). The J-N noise associated with 10 13 Ohm resistors should be about 0.4 mV, equivalent to 0.04 fA (0.004 mV on a 10 11 Ohm amplifier). The observed baseline variability for the 10 13 Ohm amplifiers is Ohm amplifiers, which contrasts with the factor of 10 improvement that might be expected. Similar slightly sub-optimal performance has been found in previous studies of these amplifiers [START_REF] Koornneef | Measurement of small ion beams by thermal ionisation mass spectrometry using new 1013Ohm resistors[END_REF]. This may suggest that a small amount of the noise in the 10 13 Ohm amplifiers is derived from sources other than the feedback resistor. 3. Baseline and gain variations of the three 10 11 and three 10 13 amplifiers used in this study. For the baselines, mV refers to the absolute variation measured on the amplifier (ie, not normalized to the resistance). For the gains, "Std dev. normalized" means the standard deviation of the individual gains on amp x normalized first to the corresponding gains on amp 8 (gain(x)/gain(8)) and then to the average value of gain(x)/gain(8). 3), it appears that one of the 10 13 Ohm amplifiers (amp 10) displays about three times as much variation as the other two 10 13 Ohm amplifiers (amps 8 and 9). This greater variation is not random, but instead reflects medium term drift in amp 10 occurring during many of the runs. As seen in Fig. 7, which shows an expanded view of 10 days of variation of the baselines of each of the 10 13 Ohm amplifiers, the baseline value of amp 10 seems to be reset to a high value during the gain calibration preceding each analysis, and then to gradually decrease during the run. This drift is not always observed, but when it is, it appears to occur at a rate of about -1 x 10 -5 mV (equiv. 10 11 Ohm amplifier) per minute. For the typical case of ~12 minutes between the start of the baseline reading and the start of data acquisition in each block, this translates to an overcorrection of about 1.2 x 10 -4 mV (equiv. 10 11 Ohm amplifier). Amplifier 10 was never assigned to the 186 OsO 3 peak, and in most cases (Table 2) was used to measure the 188 OsO 3 peak, which almost always had an intensity > 10 mV. This means that the effect of this drift was usually less than ~10 ppm, and was always well within the limits of uncertainty. Nevertheless, these observations underscore the importance of carefully tracking possible baseline drift, even when the short term noise of the amplifier appears normal (Table 3). Chatterjee and Lassiter (2015) emphasized that in order to obtain high precision data it is just as important to reduce the uncertainty associated with Johnson-Nyquist noise on the baseline as it is to reduce the J-N uncertainty of the signal itself. For this reason, for most of our analyses baselines and signal were measured for approximately equal amounts of time, with a baseline reading of about 10 minutes preceding each ~10 minutes of signal measurement. As can be seen in Fig. 5A, this procedure produced 186 Os/ 188 Os ratios with precisions close to those theoretically predicted from the combination of uncertainties related to counting statistics and to J-N noise on the signal and on the baseline. Moreover, the average 186 Os/ 188 Os ratio of the DROsS analyses performed in this manner (ie, excluding analyses 27-30) was 0.1199357 ± 0.0000108 (2σ), in agreement with values found in the literature. Nevertheless, long baseline analyses prior to each block are wasteful of sample material, so we explored possible alternative approaches (runs 27-30). In these tests, the slightly questionable amplifier 10 was used only to measure the heavy oxygen composition and thus does not bias the results. In run 27, baselines were measured for only 5 minutes prior to each 20 minute period of signal analysis. As can be seen in Fig. 4 ("short baselines"), the 186 Os/ 188 Os ratio of this analysis plots slightly outside (though within error of) the field defined by the samples with long pre-block backgrounds. In three runs (28-30) long baselines (2-3 hours) were measured during sample heating and after analysis, after the suggestion of [START_REF] Koornneef | Measurement of small ion beams by thermal ionisation mass spectrometry using new 1013Ohm resistors[END_REF], who successfully used this approach for the analysis of small loads of Sr and Nd with 10 13 Ohm amplifiers. In addition, short baselines (5 minutes) were measured prior to each 30 minute segment of data acquisition to monitor any possible drift during the analysis. A weighted average of all of the long and short baseline measurements was then subtracted off-line from the uncorrected data. The 186 Os/ 188 Os ratios of these three analyses agreed with the values obtained by our normal procedure of ten minute baselines preceding each block (Fig. 4), and the precisions were equal to those expected from theoretical considerations. Thus long pre-and post-analysis baseline measurements provide an effective means of avoiding sample waste. Nevertheless, given the systematic in-run drifts in baseline observed on amplifier 10, and the strong possibility that similar drifts may occur on 10 11 Ohm amplifiers, it is advisable to couple pre-and post-analysis baselines with shorter, periodic baselines during data acquisition to monitor any such effects. It is also important to carefully control medium to long term baseline variations.

Gains

Gain calibration is complicated by the need to use a calibration current that can be measured accurately by both 10 11 and 10 13 Ohm amplifiers. For negative ions, a calibration current of 1.2 pA is used. This corresponds to 12 V, which is nearly full scale, on a 10 13 Ohm amplifier. If the gain pulse and the associated baseline are both measured for 10 minutes, the J-N noise on the resistor would lead to an uncertainty of only about 2 ppm. In contrast, the same calibration current would be measured as 0.12 V on a 10 11 Ohm amplifier, and the J-N noise would correspond to an uncertainty of about 20 ppm, which is not completely negligible. This rough calculation is not expected to match the variability obtained in actual gain calibrations performed sporadically over a several week period, but nevertheless shows why this effect should be considered in measurements employing a mixed array of 10 11 and 10 13 Ohm amplifiers. This problem is less severe for positive ions, as the calibration current is 3.3 pA (0.33 V equiv. 10 11 Ohm amplifier). The average gain values obtained over a six week period are listed in 48, 41 and 56 ppm for amps 1, 3 and 4 respectively, Table 3). In contrast, the relative gain variations of the 10 13 Ohm amplifiers are much smaller (12 and 13 ppm). No statistically significant long term drift in the relative gain is observed for either type of amplifier, though all amplifiers show substantial long term absolute gain drift (~750 ppm) over the six week period (Fig. 8).

In all of the tests, both 186 OsO 3 and 188 OsO 3 were measured using 10 13 amplifiers so the direct effect of gain variations on the 186 Os/ 188 Os ratio should be small. However, the 192 OsO 3 peak which is used for the mass fractionation correction is measured on a 10 11 Ohm amplifier. An error of 100 ppm on the gain calibration of this amplifier would lead to an error of about 50 ppm on the mass bias corrected 186 Os/ 188 Os ratio. To judge the effect of random gain variability on the final results, data reduction was performed for each sample using both the gain measured during filament heating before analysis, and the average of the five preceding and five subsequent gain measurements. As shown in 186 Os/ 188 Os caused by the considered factor are shown, in both absolute and relative values (ppm). The effect on the overall variability of the ensemble of measurements is also shown. The analyses indicated as "good" were defined as those for which the calculated interference correction to 186 Os/ 188 Os was less than 0.000100 (24 analyses).

Decay time effects

The long decay time of the 10 13 Ohm amplifiers will lead to biases in measured values for ion beams of varying intensity, with the direction and extent of the bias depending respectively on whether the signal is increasing or decreasing and on the slope of this change. As the decay time of 10 11 Ohm amplifiers is insignificant isotopic ratios obtained with a combination of 10 11 and 10 13

Ohm amplifiers can be systematically inaccurate. This observation is applicable to the 192 Os/ 188 Os ratios used for mass bias correction in our study. Fortunately, as the extent of bias depends uniquely on the slope of the signal change and the value of the decay time, τ, this effect can be corrected for using equation 5, which can be simply derived from the exponential decay equation [START_REF] Craig | Negative thermal ion mass spectrometry of osmium, rhenium, and iridium[END_REF][START_REF] Kimura | High-precision in situ analysis of Pb isotopes in glasses using 1013 Ω resistor high gain amplifiers with ultraviolet femtosecond laser ablation multiple Faraday collector inductively coupled plasma mass spectrometry[END_REF].

𝐼 ! = 𝐼 ! + ! !!! !! !!! ! !!! !! !!! ×𝜏 (5)
Here I m and I t refer respectively to the measured and true signal intensities of a given measurement cycle. As evident from eq. 5, the slope at the time (t) of each measurement is obtained from the preceding and subsequent measurements. This means that the first and last measurement cycles of each block cannot be used. Since in our study blocks were composed of 10 cycles, applying eq. 5

without modification would result in exclusion of 20% of the data, resulting in some loss of precision. To get around this problem, the average slope of each block was used to estimate the corrections for the first and last cycles. This approximation is justified by the fact that signal changes were nearly linear over the duration of each individual block.

As shown in Table 4, applying the decay time correction changes the final calculated 186 Os/ 188 Os ratio by -8 to +72 ppm, with an average change of +19 ppm. However, the overall range of variation of 186 Os/ 188 Os values is essentially unaffected (change of 2 ppm), indicated that this correction has not improved the reproducibility. This is probably because the slopes of the signal changes were similar (slowly decreasing) for most runs, leading to similar decay time corrections, and because application of equation 5 may have added some noise due to small random signal variations between cycles used to calculate the instantaneous slopes. Nevertheless, even though the decay time correction does not improve the reproducibility, it should improve the accuracy of the result as it takes into account the physical behavior of the amplifiers.

Isobaric interferences

The isotope 186 W is a direct isobaric interference on 186 Os. As noted above, the size of this interference is estimated by measuring the mass 231 peak by ion counting before and after each run or run segment, and subtracting for the heavy oxides of PtO 2 [START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF], which are themselves estimated by measuring masses 228 ( 196 PtO 2 ) and 230 ( 198 PtO 2 ). Assuming that no other interfering species are present, this yields the intensity of 183 WO 3 in counts per second (cps), which is multiplied by the natural 186 W/ 183 W ratio and the cps to V conversion factor to obtain the isobaric interference of 186 WO 3 on 186 OsO 3 . Analogous procedures are used to calculate the isobaric interference of 187 ReO 3 on 187 OsO 3 .

In most cases, fewer than 5 cps of 183 WO 3 were present, leading to calculated corrections to 186 Os/ 188 Os of less than 0.000006 (3 to 48 ppm with an average of 24 ppm; Table 4). In a few cases, however, the corrections were considerably larger, either because the PtO 2 -corrected mass 231 peak was higher (up to 16 cps, analysis 19) or because the OsO 3 intensity was quite low (e.g., analysis 22). More disturbingly, these corrections do not seem to fully account for the entire budget of interferences isobaric with 186 OsO 3 . As seen in Fig. 4, even after correction the analyses with large calculated interferences (effect on 186 Os/ 188 Os >0.000010) have 186 Os/ 188 Os ratios that plot substantially above the range defined by the analyses with smaller interferences.

Two non-exclusive hypotheses can be proposed to explain why the measured interferences do not seem to adequately account for the interferences present on the 186 OsO 3 peak. One is that molecular interferences other than 186 WO 3 may be present. This possibility has been raised by previous authors, such as [START_REF] Chatterjee | High precision Os isotopic measurement using N-TIMS: Quantification of various sources of error in 186Os/188Os measurements[END_REF] who suggest organic molecules as a possible isobaric contaminant. Interferences on mass 233 that cannot be fully explained by 185 ReO 3 are frequently observed in 187 Os/ 188 Os studies, suggesting that species other than oxides of W, Re, Pt and Os may be present in the mass range of interest. Though there is not a perfect correlation, the fact that the interference corrections yield unsatisfactory results when the mass 231 peak is large suggest that unidentified molecular species in addition to 183 WO 3 sometimes fall on this mass. [START_REF] Yin | 187Os-186Os and 187Os-188Os method of dating: An introduction[END_REF] suggested that certain Ba-bearing species ( 138 Ba 16 OHBr -and 138 Ba 16 O 6 -) isobaric with 186 OsO 3 -may be present in NTIMS analyses. This suggestion is plausible, as the DROsS standard used for our study is dissolved in HBr, and Ba is an integral constituent of the loading solution. In Considering mass 231 to be composed solely of 183 WO 3 would then lead to undercorrection of the interference. Potentially significant molecular interferences are listed in Table 5. A second potential explanation for the poor performance of the interference correction when the measured interferences are large is that the interpolation procedure may not adequately account for the level of interferences present during data collection. This effect could pose problems even if all of the isobarically interfering species are correctly identified. Fig. 11A shows the first run of analysis 26. It is evident that simple linear interpolation between the interferences measured before and after this run is unlikely to provide accurate estimates of the interferences present during each acquisition cycle. A further complication arises from the fact that potential interferences and the OsO 3 signal do not vary synchronously (Fig. 11B). This problem can be partially addressed by interspersing short data collection runs with interference measurements (as was done in the example of analysis 28, shown in Fig. 11B), so that interpolated values more closely approximate the actual interferences present at the time of data acquisition. In contrast, analysis 24 (Fig. 11C) provides an example of an action to avoid. In this analysis, which consisted of a single run, the temperature of the filament was increased between each block to compensate for the rapidly dying signal. It is clear that linear interpolation of the interferences measured before and after this run will not accurately approximate the interferences present at the times of data acquisition, which may explain why the calculated 186 Os/ 188 Os ratio of this analysis is rather high (0.1199465), though within error of the average value. We suggest that if it is necessary to change the filament temperature during a run interference peaks should be measured before and after doing so.

As indicated in Table 4, interferences were considerably larger when analyses were performed using single Pt filaments (session 3) rather than double Pt filaments (sessions 1 and 2). In the double filament configuration the same current was applied to both filaments. Higher filament currents, typically by about 0.05 to 0.1 amps, were required for single filaments relative to double filaments to achieve similar levels of OsO 3 -emission and ionization. This may be because in the double filament configuration, radiative heating from the ionization filament helps to heat the sample loaded on the evaporation filament, allowing emission at lower current levels. We note that the source of the instrument was baked prior to analytical session 3, arguing that the interferences were derived from the filament material rather than from pollution in the source. We tentatively suggest that the lower current levels required in the double filament case may have limited the release of impurities from the filament material. Though further testing is needed, use of a double rather than a single filament configuration seems advisable.

We conclude that there is still room for improvement when addressing the issue of interference corrections on small 186 OsO 3 -signals measured with 10 13 Ohm amplifiers. All of the samples defined as "good" in Table 4 had calculated corrections for 186 WO 3 -on the 186 Os/ 188 Os ratio < 0.0000060, and their average 186 Os/ 188 Os value agrees within uncertainty with those of previous studies. Nevertheless, the fact that unsatisfactory results are obtained for calculated interference corrections on 186 Os/ 188 Os > 0.0000100 implies that there may be smaller effects on analyses with only minor corrections, but that the resulting errors are too small to be recognized at the current uncertainty level. In this case the average 186 Os/ 188 Os ratio obtained in our study could be slightly too high (Fig. 4B). While the precisions of the individual low-interference analyses (indicated as "1" in Table 2) are similar to those expected from J-N noise and counting statistics (Fig. 5A), the overall reproducibility of these analyses (85 ppm) may not be optimal, as discussed above.

Imperfect interference correction is one potential explanation for this somewhat higher than expected variability between analyses. Finally, we stress that the potential issues related to interferences discussed here are a consequence of the measurement of very small signals and do not in any way reflect a flaw in the 10 13 Ohm amplifiers.

Heavy oxide corrections

It has long been recognized that variations in the oxygen isotopic composition in the ion source and/or in the BaOH loading solution could significantly influence the calculated 186 Os/ 188 Os ratio in NTIMS measurements. To address this problem, authors have determined the 18 O and 17 O abundances in their instruments by a variety of methods, including dedicated analyses of large beams of ReO 4 [START_REF] Brandon | Platinum-osmium isotope evolution of the Earth's mantle: Constraints from chondrites and Os-rich alloys[END_REF][START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF], long term monitoring of periodically determined values [START_REF] Ireland | Os-186-Os-187 systematics of Hawaiian picrites revisited: New insights into Os isotopic variations in ocean island basalts[END_REF], pre-and post-run measurements [START_REF] Chatterjee | High precision Os isotopic measurement using N-TIMS: Quantification of various sources of error in 186Os/188Os measurements[END_REF], and in-run cycle by cycle heavy oxide measurements during Os analyses [START_REF] Chu | High-Precision Measurement of 186Os/188Os and 187Os/188Os: Isobaric Oxide Corrections with In-Run Measured Oxygen Isotope Ratios[END_REF][START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF]. These studies have generally concluded that oxygen isotope variations have a small, but not completely negligible, effect on the calculated 186 Os/ 188 Os composition. For all analyses, the effect of the heavy oxide contributions on the 186 Os/ 188 Os ratios was corrected using the measured in-run oxygen isotope composition, and compared with the 186 Os/ 188 Os ratio obtained assuming a fixed oxygen composition. For the latter we used the values ( 18 O/ 16 O =0.20349; 17 O/ 16 Os =0.000380) measured by [START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF] in a Triton mass spectrometer on ReO 4 . We chose to use this oxygen composition, rather than the classical values of [START_REF] Nier | A Redetermination of the Relative Abundances of the Isotopes of Carbon, Nitrogen, Oxygen, Argon, and Potassium[END_REF], because it was measured in the same type of instrument and because it plots closer to the TFL. We found that the 186 Os/ 188 Os ratios obtained using the measured in-run oxygen compositions were 2 to 17 ppm higher (average 7 ppm) than those obtained using the fixed composition (Table 4). This very small but systematic shift would be removed if the average oxygen composition determined on our instrument were used for the fixed composition rather than that of [START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF]. Use of the in-run measurements had essentially no effect (+1 ppm) on the overall variability of the thirty 186 Os/ 188 Os analyses. Thus it appears that variations in oxygen isotope composition have very little influence on the 186 Os/ 188 Os values measured on small signals with 10 13 Ohm amplifiers.

Mass fractionation correction

The pioneering studies of 186 Os/ 188 Os variations (e.g. [START_REF] Brandon | 186 Os-187 Os systematics of Hawaiian picrites[END_REF]) used 189 Os/ 188 Os for mass bias correction as this ratio is less subject to perturbation by errors in oxygen composition than the more commonly used 192 Os/ 188 Os ratio. However, it became clear that uncertainties related to errors in oxygen isotope abundances are small compared to those induced by using a ratio with a small mass difference between numerator and denominator for this purpose. [START_REF] Chatterjee | High precision Os isotopic measurement using N-TIMS: Quantification of various sources of error in 186Os/188Os measurements[END_REF][START_REF] Chu | High-Precision Measurement of 186Os/188Os and 187Os/188Os: Isobaric Oxide Corrections with In-Run Measured Oxygen Isotope Ratios[END_REF][START_REF] Ireland | Os-186-Os-187 systematics of Hawaiian picrites revisited: New insights into Os isotopic variations in ocean island basalts[END_REF][START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF] adopt a normalizing value of 3.083, and assume that mass fractionation follows an exponential law. This facilitates comparison between studies, as contrasting mass bias correction procedures can induce differences in 186 Os/ 188 Os of several tens of ppm (see Chatterjee and[START_REF] Chatterjee | High precision Os isotopic measurement using N-TIMS: Quantification of various sources of error in 186Os/188Os measurements[END_REF][START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF] for more complete discussions of this issue). One small difference concerns the study of [START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF], who added a second mass correction step to account for residual correlations between certain isotopic ratios observed after application of the normal mass fractionation procedure. This second correction lowers the 186 Os/ 188 Os ratio of the DROsS standard by about 20 ppm, likely explaining why the Luguet et al. value plots towards the bottom of the field in Fig. 4B.

We have adopted the standard mass bias correction procedures, which allow our data to be directly compared with earlier studies. As shown in Fig. 4B, our results agree within uncertainty with previous studies. Fig. 5A shows that the precisions on our analyses can be fully accounted for by J-N noise and counting statistics on the measured 186 Os/ 188 Os ratios. Thus any additional uncertainties introduced by the mass fractionation correction must be quite small. This is not unexpected. The relative J-N noise on the 192 OsO 3 peak should be ~2.5 times smaller than that on the 186 OsO 3 -peak, because 192 Os is about 25 times more abundant than 186 Os, which more than compensates for the fact that 192 OsO 3 -is measured using a 10 11 Ohm amplifier. Furthermore, any relative errors on the measured 192 Os/ 188 Os ratio will result in relative errors a factor of two smaller on the massfractionation corrected 186 Os/ 188 Os ratio. Taken together, this implies that uncertainties related to mass fractionation corrections are insignificant at current precision levels.

Conclusions and recommendations

This study shows that the theoretical limits of precision on 186 Os/ 188 Os ratios can be fully achieved on 186 OsO 3 -ion beams of 10 to 70 fA (0.001 to 0.007 V on a 10 11 Ohm amplifier) measured with 10 13 Ohm amplifiers. The long term reproducibility (2σ) obtained for signals in this range was 85 ppm, which approaches the reproducibility that can be theoretically expected (2σ ~ 50 to 80 ppm)

for the range of counts of 186 OsO 3 -(1 to 3x10 9 ) and the signal intensities that encompass most of our analyses. The precision and reproducibility obtained here is sufficient to allow useful 186 Os/ 188 Os analyses of crustal rocks, which are expected to show much larger variations than mantle samples.

As crustal rocks and sediments typically contain ~10 to 500 pg/g of Os, use of 10 13 Ohm amplifiers would allow 186 Os data to be obtained from 10 to 500g of sample material, rather than the ~kg quantities that are required for analyses using 10 11 Ohm amplifiers. Nevertheless, if sufficient Os (typically tens of ng) is available to obtain large (> ~800 fA or 0.08 V) 186 OsO 3 -signals, use of 10 11

Ohm amplifiers is preferable as these avoid the decay time issues discussed above, and allow the possibility of multidynamic analyses. Similarly, 10 12 Ohm amplifiers may be best adapted to 186 OsO 3 -signals in the range of ~100 to 800 fA. For 186 OsO 3 -ion beams greater than ~150 fA, signals for 188 OsO 3 -, 189 OsO 3 -, 190 OsO 3 -, and 192 OsO 3 -will all approach or exceed the saturation limit for 10 13 Ohm amplifiers (~1500 fA). The essential point is that the amplifier configuration should be chosen to fit the signal intensity.

We suggest here ways of optimizing the various aspects of 186 Os/ 188 Os NTIMS analyses of small samples with 10 13 amplifiers, presented in order of decreasing importance.

Isobaric interferences. In this study, isobaric interferences were the largest single factor leading to inaccurate 186 Os/ 188 Os ratios. This is because the small signals that can be measured with the 10 13

Ohm amplifiers are more sensitive to the presence of minor interferences than the much larger signals typically measured with 10 11 Ohm amplifiers. Correction for these interferences is problematic when the calculated correction on 186 Os/ 188 Os is > 0.000100. This is partly because molecular interferences on mass 234 may include species other than 186 WO 3 . Use of a double, rather than a single, Pt filament configuration seems to largely eliminate these unidentified interferences.

Linear interpolation based solely on interference runs before and after the entire analysis does not adequately quantify potential 186 WO 3 interferences because the interference and the OsO 3 signals do not vary synchronously, and neither species is likely to vary in a linear manner. Instead, it is recommended to measure interferences periodically throughout the analysis, allowing interpolation over shorter time periods, and to avoid heating between blocks.

Baselines. Johnson-Nyquist noise on the baseline is one of the most important sources of uncertainty. To minimize this effect, baselines should be measured for approximately the same amount of time as the signal itself. This can be done during slow heating before the analysis, as well as after data acquisition is terminated, to avoid sample waste and increase the sample yield.

However, if this is done, short baselines should be performed several times during the analysis to monitor potential drift in the amplifiers.

Decay time corrections.

If a mixed array of 10 11 and 10 13 amplifiers is used, it is important to apply a correction for their very different exponential decay times. In this study, this correction led to changes of -8 to +72 ppm in the final 186 Os/ 188 Os values, but did not improve the overall reproducibility. Nevertheless, this correction is based on the physical behavior of the amplifiers, thus its application should lead to final results that are more accurate.

Figure 1 .

 1 Figure 1. Comparison of signals of 186 OsO 3 -ion beam (measured with a 10 13 Ohm amplifier) with 187 OsO 3 -ion beam (measured with a 10 11 Ohm amplifier) on a DROsS standard, which has comparable isotopic abundances of 187 Os and 186 Os. To facilitate comparison between amplifiers, signal intensities are presented both as ion currents (fA) and as equivalent volts that would be obtained if the signals were measured with 10 11 Ohm amplifiers. Gaps in traces represent times when peaks were switched that were erased for clarity.

Figure 2 .

 2 Figure 2. Apparent peak shapes of 188 OsO 3 -measured on central cup using a 10 13 Ohm amplifier (red) and 190 OsO 3 -

Figure 3 .

 3 Figure 3. Comparison of response times of 10 11 (A) and 10 13 (B) Ohm amplifiers after closing analyzer valve. The different color traces represent repeated experiments, with the orange line representing the average. The signal intensity is normalized to the value before closing the valve.

  fA, that is, it is improved by a factor of 5 or 6 relative to what is obtained with the 10 11

Fig.

  Fig. 6B compares longer term baseline variations in typical 10 11 and 10 13 Ohm amplifiers. Most of the points shown were 10 minute baselines measured before each block of data collection, though some points represent baselines measured during gain calibrations or long baselines measured between sample analyses. It is clear that the 10 11 Ohm amplifiers display substantial long term drift not observed with the 10 13 Ohm amplifiers. Nevertheless, when looked at in detail (Table3), it

Figure 8 .

 8 Figure 8. Variation of measured gain of typical 10 11 Ohm (amp 3) and 10 13 Ohm (amp 8) amplifiers over a six week period.

Figure 9 .

 9 Figure9. Variations (in ppm) of gains of 10 11 Ohm amplifiers (amps 1, 3 and 4) and 10 13 Ohm amplifiers (amps and 10) normalized to gain of amp 8 (10 13 Ohm). To facilitate comparison the ratio gain(x)/gain(8) is normalized to the average value over the six week period.

  the scan shown in Fig. 10, masses 222, 223 and 225 are present in the relative abundances of 134 Ba, 135 Ba and 137 Ba, with possible 136 Ba and 138 Ba-bearing species hidden by the large PtO 2 peaks, arguing for the existence of Ba compounds not far from the mass range of interest. If the BaOHBr - and/or BaO 6 -species suggested by Yin et al. are indeed present, 138 Ba bearing molecules on mass 234 would be associated with ~11 times less abundant 135 Ba bearing molecules on mass 231.

Figure 10 .

 10 Figure10. SEM scan in the mass range of 217 to 226. In addition to the two large PtO 2 peaks, three small but nonnegligible peaks are observed, indicating that unidentified molecular ion beams exist close to the range of interest. These peaks have the relative abundances of 134 Ba, 135 Ba, and 137 Ba, suggesting that they may be Ba-bearing species. The search for such peaks closer to mass 234 ( 186 OsO 3 ) is complicated by the presence of PtO 2 , WO 3 and ReO 3 peaks.

Figure 11 .

 11 Figure 11. A) First run of analysis 26. Linear interpolation of interferences (green) measured before and after run would not accurately approximate interference levels during data acquisition. violet: 192 OsO 3 ; red: 190 OsO 3 ; black: 188 OsO 3 ; dark blue: 186 OsO 3 . Interference runs were composed of 3 cycles of SEM measurements of masses 228 ( 196 PtO 2 ); 230 ( 198 PtO 2 ); 231 ( 183 WO 3 ); 232 ( 184 OsO 3 ); 233 ( 185 ReO 3). B) Analysis 28, included nine data acquisition runs each preceded and succeeded by interference runs, programmed in the sequence routine. Signals and interferences do not evolve at the same rates, but interpolation of frequent interference measurements can nevertheless allow for acceptable correction of known interferences. Colors as in (A). C) Evolution of the 186 OsO 3 signal in run 1 of analysis 24. Filament was heated before each 10 cycle block to keep signal at an acceptable level. Interpolation of interferences taken before and after the 15 block run would be unlikely to produce reliable corrections.

Table 1 .

 1 Cup

	Os peak	186 OsO 3	187 OsO 3	188 OsO 3	190 OsO 3	192 OsO 3	192 Os 16 O 2	18 O
	Mass	234	235	236	238	240	242
	Amplifier type (Ohm)	10 13	10 11	10 13	10 11	10 11	10 13
	Configuration A
	Cup	L2	L1	C	H1	H2	H3
	Amplifier #	8	1	9	3	4	10
	Configuration B
	Cup	L3	L2	L1	C	H1	H2
	Amplifier #	8	1	10	3	4	9
	Configuration C
	Cup	L3	L2	L1	C	H1	H2
	Amplifier #	8	1	9	3	4	10

and amplifier configurations used during study. Amplifiers 1 -4 have 10 11 Ohm resistors; amplifiers 8 -10 have 10 13 Ohm resistors.

Heavy oxygen correction. The interference-corrected data were then corrected for heavy oxides of OsO 3 masses by two alternative methods to allow the importance of this effect to be evaluated

	signals a decay time (τ) of 0.65 seconds, in agreement with the τ values obtained by Craig et al. 6)
	(2017), was determined by fitting an exponential curve to the signal measured after closing the
	analyzer valve. While small differences in the exact value of τ for different 10 13 Ohm amplifiers can
	have a substantial effect on isotopic ratios obtained for rapidly varying signals, such as those
	measured during laser ablation experiments (Kimura et al., 2016), these are not a concern for the
	much more stable signals considered here. In contrast, coupling measurement of 188 OsO 3	-with a
	10 13 Ohm amplifier with the use of a 10 11 Ohm amplifier for the 192 OsO 3	-peak can significantly
	bias the measured 192 Os/ 188 Os ratio and thus the mass fractionation correction if the different
	response times are not taken into account.
	4) Isobaric interference correction. Potential isobaric interferences were estimated by
	interpolation based on ion counting measurements of masses 228 ( 196 PtO 2 ), 230 ( 198 PtO 2 ), 231
	( 183 WO 3 ), 232 ( 184 OsO 3 and 184 WO 3 ) and 233 ( 185 ReO 3 ) performed before and after each data
	collection run. As a check on the ion counting results, mass 232 was also measured on the central
	Faraday cup, but as this cup was usually linked to a 10 11 Ohm amplifier the Faraday data obtained
	for this very small peak were highly imprecise. After correction for heavy oxides, the 183 WO 3 and
	185 ReO 3 signals and the natural isotopic compositions of W and Re were used to estimate count rates
	of 186 WO 3 and 187 ReO 3 . A conversion factor of 6250 cps/fA (62500 cps/mV) was assumed to
	calculate the corrections to apply to masses 234 and 235 to obtain, respectively, intensities of
	186 OsO 3 and 187 OsO 3 . As most analyses were composed of several runs, interferences were usually
	measured several times during data acquisition.
	5) for each analysis. In one, the oxygen isotope composition ( 18 O/ 16 O = 0.0020349; 17 O/ 16 O =
	0.0003835) measured in a Triton mass spectrometer by Luguet et al. (2008) was assumed. In the
	other, the mass 242/240 ratio measured during each cycle was used to determine the 18 O/ 16 O ratio.
	In order to do this, it is first necessary to remove oxide interferences from the lighter Os isotopes
	that are isobaric with masses 240 and 242 (for example, 190 Os 16 O 2	18 O on mass 240). This correction
	requires using an assumed oxygen composition. While we used the Luguet et al. (2008) values for
	this second order correction, use of the Nier (1950) composition would have a negligible effect on
	the final result. Based on the calculated 18 O/ 16 O ratio, mass dependent fractionation was assumed to
	calculate the corresponding 17 O/ 16 O ratio, and the resulting values were used to correct the OsO 3
	data.
			186 OsO 3	-and 188 OsO 3	-

Mass fractionation correction. The

  heavy-oxygen corrected Os isotope ratios ( 186 Os/ 188 Os, 187 Os/ 188 Os, 190 Os/ 188 Os) obtained by both methods were then corrected for mass fractionation in the instrument. An exponential law and a "true" 192 Os/ 188 Os value of 3.083 were assumed.

	7) Data combination. If the analysis was composed of several runs these were combined to obtain
	the final isotope ratios and corresponding uncertainties. For analyses 28-30 a sequence of 9 short
	runs was programmed, with interference runs interspersed between them.

Run Cup Set- up Notes Filament type 186 Os (mV 10 11 Ω amp) Total counts 186 Os (10 9 ) Useful yield % 186 Os/ 188 Os 190 Os/ 188 Os 187 Os/ 188 Os 192 Os/ 188 Os measured 18 O/ 16 O

	Session 1
	1	A	Double	1.39	2.05	0.8	0.1199359	1.983820	0.160988	3.077093	0.0020155
							0.0000089	0.000014	0.000014	0.000014	0.0000139
	2	A	Double	1.80	2.28	0.9	0.1199352	1.983720	0.160961	3.079254	0.0020225
							0.0000090	0.000054	0.000045	0.000482	0.0000025
	3	A	Double	3.96	4.15	1.6	0.1199273	1.983793	0.160948	3.088402	0.0020157
							0.0000054	0.000035	0.000030	0.000703	0.0000006
	4	A	Double	1.11	1.06	0.4	0.1199376	1.983752	0.160880	3.089792	0.0020161
							0.0000121	0.000084	0.000063	0.000698	0.0000011
	5	A	Double	4.14	2.98	1.2	0.1199287	1.983877	0.160920	3.082185	0.0020109
							0.0000060	0.000035	0.000026	0.000493	0.0000005
	Session 2
	6	B	Double	2.80	2.97	1.2	0.1199358	1.983879	0.160931	3.086256	0.0020232
							0.0000064	0.000037	0.000028	0.000265	0.0000005
	7	B	Double	4.03	1.57	0.6	0.1199425	1.983843	0.160930	3.084415	0.0020240
							0.0000063	0.000036	0.000037	0.000386	0.0000006
	8	B	Double	4.38	1.78	0.7	0.1199286	1.983871	0.160954	3.086742	0.0020156
							0.0000070	0.000050	0.000030	0.000398	0.0000005
	9	B	Double	5.92	7.06	2.8	0.1199330	1.983841	0.160958	3.085727	0.0020195
							0.0000036	0.000019	0.000013	0.000551	0.0000003
	10	B	Double	6.79	2.76	1.1	0.1199447	1.983815	0.160993	3.087846	0.0020208
							0.0000051	0.000030	0.000021	0.000344	0.0000005
	11	B	Double	5.86	2.33	0.9	0.1199321	1.983811	0.160924	3.087537	0.0020206
							0.0000052	0.000031	0.000022	0.000289	0.0000006
	12	B	Double	3.44	1.35	0.5	0.1199313	1.983831	0.160989	3.083691	0.0020287
							0.0000089	0.000047	0.000042	0.000481	0.0000008
	13	B	Double	1.95	0.93	0.4	0.1199435	1.983849	0.161637	3.082619	0.0020287
							0.0000139	0.000075	0.000133	0.000770	0.0000016
	14	B	Double	3.52	1.40	0.6	0.1199441	1.983923	0.160919	3.085349	0.0020188
							0.0000088	0.000048	0.000042	0.000698	0.0000008
	15	B	Double	3.78	1.52	0.6	0.1199408	1.983965	0.160962	3.091081	0.0020226
							0.0000064	0.000047	0.000032	0.000268	0.0000006
	Session 3
	16	B	Single	3.66	4.33	1.7	0.1199717	1.984009	0.160924	3.090872	0.0020137
							0.0000045	0.000027	0.000021	0.000585	0.0000004
	17	B	Single	6.90	8.21	3.3	0.1199324	1.984062	0.160961	3.093264	0.0020061
							0.0000039	0.000030	0.000015	0.000396	0.0000004
	18	B	Single	3.10	1.23	0.5	0.1199371	1.984021	0.160865	3.092825	0.0020189
							0.0000106	0.000052	0.000044	0.000615	0.0000008
	19	B	Single	3.37	1.34	0.5	0.1199661	1.984123	0.160892	3.081798	0.0020166
							0.0000115	0.000055	0.000038	0.000616	0.0000009
	20	B	Single	4.07	1.65	0.7	0.1199337	1.983804	0.160933	3.089131	0.0020219
							0.0000087	0.000039	0.000032	0.000364	0.0000006

Table 2 .

 2 Continued on next page.

	Run	Cup Set-up	Notes	Filament type	186 Os (mV 10 11 Ω amp)	Total counts 186 Os (10 9 )	Useful yield %

186 Os/ 188 Os 190 Os/ 188 Os 187 Os/ 188 Os 192 Os/ 188 Os

											measured	18 O/ 16 O
	21	B	1	Single	2.97	2.36	0.9	0.1199335	1.983853	0.160904	3.090736	0.0020147
								0.0000075	0.000044	0.000038	0.000668	0.0000007
	22	B	2	Single	0.47	0.19	0.1	0.1199487	1.983829	0.160922	3.092929	0.0020148
								0.0000419	0.000281	0.000253	0.000764	0.0000063
	23	B	2	Single	1.34	0.54	0.2	0.1199660	1.983822	0.160865	3.088025	0.0020201
								0.0000195	0.000097	0.000086	0.000758	0.0000020
	24	B	3	Single	1.23	0.74	0.3	0.1199465	1.983938	0.160882	3.093110	0.0020249
								0.0000177	0.000089	0.000099	0.000414	0.0000015
	25	B	2	Single	1.31	1.31	0.5	0.1199948	1.984089	0.160917	3.093004	0.0020264
								0.0000145	0.000085	0.000067	0.000468	0.0000016
	26	B	2	Single	2.21	5.70	2.3	0.1199965	1.983958	0.160945	3.094710	0.0020106
								0.0000056	0.000030	0.000025	0.000329	0.0000005
	27	C	4	Single	3.19	3.57	1.4	0.1199472	1.984092	0.161132	3.089300	0.0020136
								0.0000065	0.000064	0.000017	0.000667	0.0000003
	28	C	1, 5	Single	5.64	5.46	2.2	0.1199400	1.984123	0.160966	3.087470	0.0020130
								0.0000038	0.000022	0.000015	0.000651	0.0000004
	29	C	1, 5	Single	2.29	1.94	0.8	0.1199373	1.983999	0.160947	3.085441	0.0020110
								0.0000077	0.000054	0.000038	0.000760	0.0000008
	30	C	1, 5	Single	5.61	7.97	3.2	0.1199393	1.984144	0.161020	3.087543	0.0020065
								0.0000033	0.000020	0.000012	0.000365	0.0000005
	Average ("1" runs)		3.88	2.95	1.1	0.1199361	1.983891	0.160977	3.086564	0.0020180
	2 Std. deviations		3.37	4.43	1.7	0.0000102	0.000230	0.000304	0.008059	0.0000123
	2 S.D. (ppm)						85	116	1887	2611	6105
	1:

Included in average -No obvious anomalies 2: Excluded from average -Interference correction on 186 Os/ 188 Os > 0.0000100 3: Excluded from average -Signal dying rapidly so heated between each block 4: Excluded from average -Short baselines 5: Included in average -Offset backgrounds Table

  the 186 Os/188 Os ratios obtained after all data corrections are shown as a function of the number of measured 186 Os ions. Analyses run under standard conditions for which no obvious[START_REF] Chu | High-Precision Measurement of 186Os/188Os and 187Os/188Os: Isobaric Oxide Corrections with In-Run Measured Oxygen Isotope Ratios[END_REF][START_REF] Liu | Rapid, precise and accurate Os isotope ratio measurements of nanogram to sub-nanogram amounts using multiple Faraday collectors and amplifiers equipped with 1012 Ω resistors by N-TIMS[END_REF][START_REF] Luguet | 184Os/188Os and 186Os/188Os measurements by negative thermal ionisation mass spectrometry (NTIMS): Effects of interfering element and mass fractionation corrections on data accuracy and precision[END_REF]. The half-filled violet circle represents an analysis done with short baselines, while the half-filled green square denotes a filament that was substantially heated (filament current increased by 5 to 10 mA) before each block. The open symbols represent analyses requiring unusually large interference corrections. It is clear that even after interference correction, these latter samples often have 186 Os/ 188 Os ratios exceeding the normal range.

	anomalies were observed ("normal", filled symbols), together with analyses with "offset" baselines (half-black symbols), have an average 186 Os/ 188 Os ratio of 0.1199361 ± 0.0000102 (2σ; 85 ppm), in agreement with previously published high precision analyses of the DROsS standard (Chatterjee and Lassiter, 2015; A)
	B)

Figure 4. A) 186 Os/ 188 Os ratios as a function of number of 186 OsO 3 -ions measured, after all data corrections. Analyses with

Table 3

 3

	, and plots of the gain

shown in Fig.

8

. As the relative variations are of much more interest than the absolute variations, in Fig.

9

all of the gains have been normalized to that of amplifier 8, the 10 13 Ohm amplifier used to measure

186

OsO 3 in all cases. This plot shows that individual gain calibration values (normalized to amp 8) of the 10 11 Ohm amplifiers can vary by as much as 100 ppm (relative standard deviations of

  Table 4, the use of averaged rather than individual gains improves the overall reproducibility of the 186 Os/ 188 Os ratio by about 12 ppm. Thus using averaged gain values can lead to a small, but non-negligible improvement in reproducibility, and can eliminate outlier values caused by spurious individual calibrations.

Table 4 .

 4 Effects of various factors on final calculated 186 Os/ 188 Os ratios. The range and the average value of the change in

		Change in 186 Os/ 188 Os (Range)	Change in 186 Os/ 188 Os (Average)	Range of change ppm	Average change ppm	Effect on overall variability (ppm change in 2σ of all analyses)
	Gain averaging	-0.0000065 to 0.0000065	-0.0000001	-54 to 54	-1	-12
	Decay time correction	-0.0000010 to 0.0000087	0.0000023	-8 to 72	19	+2
	Individual vs. fixed O2 correction	0.0000002 to 0.0000020	0.0000008	2 to 17	7	+1
	Interferences (all runs)	0.0000003 to 0.0000639	0.0000092	3 to 533	77
	Interferences (good only -see caption)	0.0000003 to 0.0000058	0.0000029	3 to 48	24
	Interferences (single filaments)	0.0000024 to 0.0000639	0.0000151	20 to 533	126
	Interferences (double filaments)	0.0000003 to 0.0000045	0.0000015	3 to 38	13

Table 5 .

 5 Potential molecular isobaric interferences on the masses of interest discussed in the text. Minor interferences involving higher order terms are ignored. A more complete table of possible interferences including masses up to 246 can be found inLuguet et al. (2007).

					Ba 16 OH 81 Br
					138
					Ba 16 OH 81 Br
					137
				Pt 18 O 2	Ba 16 OH 81 Br	Ba 16 Br OH 79	Ba 16 O 6
				198	136	138	138
					Ba 16 OH 81 Br	Ba 16 Br OH 79	Ba 16 O 6
					135	137	137
					Br	Br
			Pt 18 O 2 Pt 16 O 18 O	Ba 16 OH 81	Ba 16 OH 79	Ba 16 O 6
			196	198	134	136	136
						Br
		Pt 18 O 2	Pt 16 O 17 O		Ba 16 OH 79	Ba 16 O 6
		195		198		135	135
	Pt 18 O 2	Pt 16 O 18 O	Pt 16 O 2		Ba 16 Br OH 79	Ba 16 O 6
	194		196	198		134	134
		Pt 16 O 18 O	Pt 16 O 17 O
		195	196
	Pt 16 O 18 O	Pt 16 O O 17	Pt 16 O 2
		195	196

  To evaluate the extent to which this effect might influence the much smaller signals measured with the 10 13 Ohm amplifiers we used one of these amplifiers to measure mass 242, which is essentially composed of 192 Os 16 O 2 18 O -, simultaneously with the measurement of the main OsO 3 -peaks. After subtracting calculated expected abundances of rare OsO 3 isotopologues containing two or three heavy oxygen atoms from masses 240 and 242, the mass(242)/mass(240) ratio was used to calculate the 18 O/ 16 O ratio in the ion source. The oxygen terrestrial fractionation line (TFL) was then used to determine the corresponding 17 O/ 16 Os ratio, assuming that the TFL passes through the composition of Vienna Standard Mean Ocean Water (VSMOW). The 18 O/ 16 O ratios obtained from the analyses Figure 12. 18 O/ 16 O ratios measured in-run on the CRPG Triton mass spectrometer. The 17 O/ 16 Os compositions are estimated from the measured 18 O/ 16 Os ratios by assuming that all analyses should plot on the Terrestrial Fractionation Line (TFL) passing through the VSMOW value. Literature values are shown for comparison.

	are shown in Table 2, and yield an average value of 0.0020179 ±0.0000119 (2σ), which
	corresponds to a 17 O/ 16 O value of 0.0003812 ±0.0000012. These results are compared to values
	obtained in other laboratories in Fig. 12. The in-run 2SE uncertainties on the measured 18 O/ 16 O
	ratios of each analysis are nearly all much smaller than the range of the mean values of all analyses,
	suggesting that there is very limited oxygen isotope fractionation during analyses, but more
	substantial fractionation between analyses.

  Gain corrections. The gain calibration card used for detector arrays including both 10 13 and 10 11 Ohm amplifiers employs a 1.2 pA (120 mV) calibration current in negative ion mode, which is very far from full range of the 10 11 Ohm amplifiers. As a result, the individual gain calibration values obtained for the 10 11 Ohm amplifiers can vary by as much as 100 ppm from the average values. As the 192 Os peak used for the fractionation correction was measured on a 10 11 Ohm amplifier, this occasionally led to spurious values. This problem can be alleviated by using the average gain factors obtained in the days preceding and following the measurement. Gain calibrations were normally performed during slow sample heating before each analysis. Using time-averaged gain values rather than individual readings improved the overall reproducibility of the 186 Os/ 188 Os by about 12 ppm, which is small but not completely negligible. Variations in oxygen isotope composition had very little effect (several ppm) on the186 Os/ 188 Os ratio in these measurements. It is quite simple to perform in-run oxygen composition determinations by measuring mass 242 ( 192 Os 16 O 2 18 O) with a 10 13 Ohm amplifier to obtain 18 O/ 16 O, and calculating 17 O/ 16 O from the terrestrial fractionation line. However, adequate results can also be obtained if the average oxygen isotope composition in the instrument is determined in separate measurements.

	Oxide corrections.

Acknowledgements

We thank Christiane Parmentier for technical assistance, Larry Shengold for helpful and animated discussions and Gareth Davies for an informal review. We also thank two anonymous reviewers for their constructive comments. This project was funded by the French ANR project INTOCC.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.