High-precision analysis of ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W by negative thermal ionization mass spectrometry: Per-integration oxide corrections using measured ¹⁸O/¹⁶O

Abstract

Here we describe a new analytical technique for the high-precision measurement of ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W using negative thermal ionization mass spectrometry (N-TIMS). We improve on the recently reported method of Trinquier et al. (2016), which described using Faraday cup collectors coupled with amplifiers utilizing 10¹³ Ω resistors to continuously monitor the ¹⁸O/¹⁶O of WO₃⁻ and make per-integration oxide corrections. In our study, we report and utilize a newly measured oxygen mass fractionation line, as well as average ¹⁷O/¹⁶O and ¹⁸O/¹⁶O, which allow for more accurate per-integration oxide interference corrections. We also report a Faraday cup and amplifier configuration that allows ¹⁸O/¹⁶O to be continuously monitored for WO₃⁻ and ReO₃⁻, both of which are ionized during analyses of W using Re ribbon. The long-term external precision of ¹⁸²W/¹⁸⁴W is 5.7 ppm and 3.7 ppm (2SD) when mass bias corrected using ¹⁸⁶W/¹⁸⁴W and ¹⁸⁶W/¹⁸³W, respectively. For ¹⁸³W/¹⁸⁴W mass bias is corrected using ¹⁸⁶W/¹⁸⁴W, yielding a long-term external precision of 6.6 ppm. An observed, correlated variation in ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W, when mass bias corrected using ¹⁸⁶W/¹⁸⁴W, is most likely the result of Faraday cup degradation over months-long intervals.

1. Introduction

The short-lived ¹⁸²Hf-¹⁸²W isotopic system (t_1/2 = 8.9 Myr; [2] is useful for constraining the timing of early Solar System metal-silicate equilibration (within the first ~50 Ma of Solar System history) because W is moderately siderophile and largely partitions into Fe-rich metal, whereas Hf is lithophile and partitions entirely into silicate. The most widely used application for this system has been dating core formation of planetary bodies. By measuring W isotopic compositions of iron meteorites, model ages can be calculated, assuming chondritic Hf/W (e.g., [3–5]. The Hf-W isotopic system has also been used to date formation or closure ages of silicate-rich rocks by plotting Hf/W vs. ¹⁸²W/¹⁸⁴W, yielding internal isochrons. For example, Hf-W isochrons have been used to date formation or closure ages of bulk chondritic meteorites [6], calcium-aluminum-rich inclusions [7], chondrules, and matrix [8]. The ¹⁸²Hf-¹⁸²W isotopic system has also been used for terrestrial applications. For example, the W isotopic compositions of mantle-derived rocks have been used to investigate mantle evolution (e.g., [9–13]. In some instances, isotopic variations in ¹⁸²W/¹⁸⁴W are <20 ppm.

During the analysis of W by negative thermal ionization mass spectrometry (N-TIMS) when using Re filaments as the ionizing substrate, the different species of ReO₃⁻ and WO₃⁻ that incorporate ¹⁷O and/or ¹⁸O (e.g., ¹⁸²W¹⁶O₂¹⁸O⁻ and ¹⁸⁵Re¹⁶O₂¹⁷O⁻) form isobaric interferences on the signals of some of the primary W¹⁶O₃⁻ beams measured. The oxygen isotopic compositions of ReO₃⁻ and WO₃⁻ must, therefore, be accurately determined for isobaric interference corrections, and the in-run fractionation of oxygen isotopes during analyses must also be monitored.

Ref. [14] reported an N-TIMS method capable of measuring ¹⁸²W/¹⁸⁴W with a long-term (over a period of 9 months) external reproducibility of <5 ppm (2SD). That study used the oxygen isotopic composition of the atmosphere reported by [15] to make a first-order correction for oxide interferences on primary ^xW¹⁶O₃⁻ signals. Then, a second-order correction utilized the coevolution of ¹⁸³W/¹⁸⁴W and ¹⁸²W/¹⁸⁴W to correct for in-run fractionations of oxygen isotopes. Because it used an assumed ¹⁸³W/¹⁸⁴W in the correction process, this method did not allow a corresponding measurement of ¹⁸³W/¹⁸⁴W, which varies among some meteorites (e.g., [7]).

A more recent analytical study [1] reported measurements of both ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W with long-term external reproducibilities of ~10–11 ppm (2SD) and ~17–18 ppm (2SD), respectively. As in [14], they corrected minor oxide interferences assuming the atmospheric composition reported by [15]. They corrected in-run fractionations of oxygen isotopes using per-integration measured ¹⁸⁶W¹⁶O₂¹⁸O/¹⁸⁶W¹⁶O₃ to calculate ¹⁸O/¹⁶O and infer ¹⁷O/¹⁶O, using a terrestrial fractionation slope (e.g., [16] passed through the ¹⁷O/¹⁶O and ¹⁸O/¹⁶O reported by [15].

The methods reported by these two prior studies bear some additional scrutiny. The use of the ¹⁷O/¹⁶O and ¹⁸O/¹⁶O ratios reported by [15] may not be appropriate for measurements of ReO₃⁻ and WO₃⁻ via N-TIMS. Further, [1] measured only the ¹⁸O/¹⁶O of WO₃⁻ for each integration. The oxygen isotopic composition of ReO₃⁻ was assumed to uniformly follow the same evolution trend, which may not be the case. Ref. [1] reported that the method was limited to analyses with Re/W < 0.3, as a systematic bias to higher ¹⁸²W/¹⁸⁴W was observed for analyses with high Re/W. Some sample and standard analyses, especially those with low W abundances, sometimes have Re/W > 0.3.

Here we present a new analytical technique, refining the methods of [14] and [1], for making measurements of ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W to external precisions ~5 ppm, even for analyses with Re/W > 0.3. This analytical technique uses a newly determined average ¹⁷O/¹⁶O and ¹⁸O/¹⁶O, appropriate for measuring ReO₃⁻ and WO₃⁻ by N-TIMS, and a new oxygen mass fractionation line for oxide corrections. Per-integration fractionations of oxygen isotopes are corrected for both ReO₃⁻ and WO₃⁻ by measuring both ¹⁸⁶W¹⁶O₂¹⁸O/¹⁸⁶W¹⁶O₃ and ¹⁸⁷Re¹⁶O₂¹⁸O/¹⁸⁷Re¹⁶O₃.

2. Experimental section

2.1. Filament preparation and loading

A filament loading technique slightly modified from [14] was used. Either 300 ng, 500 ng, or 1000 ng of Alfa Aesar W standard solution were loaded onto single Re filaments, which were outgassed ~48 h in advance. Throughout this study, both thick (0.76 mm × 0.030 mm) and thin (0.51 mm × 0.025 mm) Re filaments were used. After loading W, Re filaments were briefly (~1 s) heated to a dull glow, and then left to sit for at least 24 h before loading activator. To enhance ionization, 1 μL of activator solution containing 5 μg each of La and Gd in 5% Teflon distilled HNO₃ was then added in 2–3 aliquots to the standard and sample deposits, and then dried until a white crust formed.

2.2. Instrumental setup

Analyses were performed on the University of Maryland (UMd) Thermo-Fisher Triton thermal ionization mass spectrometer. Oxide production was enhanced by bleeding oxygen (P_O2 = 1.0 × 10⁻⁷ mbar) into the source can using a Varian leak valve. Similar to the method of [14], all analyses by this study used a multi-static analytical protocol with two lines of acquisition, which allowed Faraday cup biases to be monitored. Each line of acquisition utilized 9 Faraday cups (Table 1). Seven Faraday cups (L4–H2) were electronically connected to amplifiers with 10¹¹ Ω resistors, which were electronically rotated during analyses to mitigate amplifier biases. Faraday cups H3 and H4 were connected to amplifiers with 10¹² Ω resistors to measure the low signals generated by the minor ¹⁸⁶W¹⁶O₂¹⁸O⁻ and ¹⁸⁷Re¹⁶O₂¹⁸O⁻ species, which were used to calculate per-integration oxide corrections. These amplifiers were not rotated during analyses. The center Faraday cup was centered on masses 232 (¹⁸⁴W¹⁶O₃⁻) and 234 (¹⁸⁶W¹⁶O₃⁻) for acquisition lines 1 and 2, respectively.

Table 1.

Faraday cup-amplifier-resistor configuration for measurement of W using N-TIMS utilizing 9 Faraday cups.

	L4	L3	L2	L1	C	H1	H2	H3	H4
Line 1	180W16O3	181Ta16Oa	182w16o3	183w16o3	184w16o3	185Re16O3	186w16o3	186w16o218o	187Re16O218O
Line 2	182w16o3	183w16o3	184w16o3	185 Re16 O3	186w16o3	187Re16O3	186w16o218o	190Os16O3
Resistor	1011 Ω	1011 Ω	1011 Ω	1011 Ω	1011 Ω	1011 Ω	1011 Ω	1012 Ω	1012 Ω

With this analytical protocol, all W¹⁶O₃⁻ and Re¹⁶O₃⁻ species were measured, and inter-collector biases were corrected for all major W species (¹⁸²W¹⁶O₃⁻, ¹⁸³W¹⁶O₃⁻, ¹⁸⁴W¹⁶O₃⁻, and ¹⁸⁶W¹⁶O₃⁻). The ¹⁸⁶W¹⁶O₂¹⁸O⁻ and ¹⁸⁷Re¹⁶O₂¹⁸O⁻ species were also measured, from which the ¹⁸O/¹⁶O could be calculated, and the ¹⁷O/¹⁶O could be inferred using an oxygen mass fractionation line. One isotope each of Ta and Os (¹⁸¹Ta and ¹⁹⁰Os) were also monitored so that isobaric interference corrections for these elements could be made. However, these signals were below detection limits (a few μV) for all analyses.

Typically, 600 integrations were measured over 770 min, although some analyses were cut short because of rapidly decreasing signals. A 1260 s baseline was measured at the beginning of each analysis and then re-measured every 100 integrations. Each integration consisted of 33.6 s and 8.4 s of acquisition duration for lines 1 and 2, respectively. The idle times before integrations were 10 s and 4 s for acquisition lines 1 and 2, respectively.

2.3. Data reduction

In the first data reduction step, single estimated values (see Section 3.1) for ¹⁷O/¹⁶O (0.0003913) and ¹⁸O/¹⁶O (0.002096) were used to make first-order oxide interference corrections to all ^xW¹⁶O₃⁻ and ^xRe¹⁶O₃⁻ signals. Relative abundances of trioxide species for each W and Re isotope (e.g., ¹⁸⁴W¹⁷O¹⁶O₂⁻, ¹⁸⁴W¹⁸O¹⁶O₂⁻, ¹⁸⁴W¹⁸O₂¹⁶O⁻, etc.) were calculated following the calculations of [4], using the estimated ¹⁷O/¹⁶O and ¹⁸O/¹⁶O. In the next step, first-order oxide-corrected ¹⁸⁶W¹⁶O₂¹⁸O⁻/¹⁸⁶W¹⁶O₃⁻ and ¹⁸⁷Re¹⁶O₂¹⁸O⁻/¹⁸⁷Re¹⁶O₃⁻ from each integration were used to calculate per-integration ¹⁸O/¹⁶O for WO₃⁻ and ReO₃⁻. A linear trend with a terrestrial fractionation slope (0.0954) that passed through the estimated values for ¹⁷O/¹⁶O (0.0003913) and ¹⁸O/¹⁶O (0.002096) was then used to calculate per-integration ¹⁷O/¹⁶O from each per-integration ¹⁸O/¹⁶O.

Per-integration ¹⁷O/¹⁶O and ¹⁸O/¹⁶O were then used to make line-by-line oxide corrections to all ^xW¹⁶O₃⁻ and ^xRe¹⁶O₃⁻ signals. All isobaric interferences on ^xW¹⁶O₃⁻ and ^xRe¹⁶O₃⁻ for which corrections were made are listed in Table 2. The most signifi-cant isobaric interferences were from ^xW¹⁷O¹⁶O₂⁻, ^xW¹⁸O¹⁶O₂⁻, xRe¹⁷O¹⁶O₂⁻, and ^xRe¹⁸O¹⁶O₂⁻species. No corrections were made for low abundance trioxide species (e.g., ^xW¹⁸O₃⁻) that do not significantly interfere with primary ^xW¹⁶O₃⁻ and ^xRe¹⁶O₃⁻ signals Yin, [17]).

Table 2.

Interferences on primary x¹⁶O₃⁻ species that require corrections. Oxygen isotopic compositions represent total oxygen masses (e.g., ¹⁸⁴W⁵⁰O₃⁻ = ¹⁸⁴W¹⁶O₂¹⁸O⁻ + ¹⁸⁴W¹⁶O¹⁷O₂⁻).

Species	180W16O3−	182W16O3−	183W16O3−	184W16 O3−	185Re16O3−	186W16O3−	187Re16O3−	186W16O2180−	187Re16O218O−
Mass	228	230	231	232	233	234	235	236	237
	180Ta48O3−	180W50O3−	180W51O3−	180W52O3−	181Ta52O3−	182W52O3−	183W52O3−	184W52O3−	185Re52O3−
Interfering		180Ta50O3−	180Ta51O3−	180Ta52O3−	182W51O3−	183W51O3−	184W51O3−	185Re51O3−	186W51O3−
Species		181Ta49O3−	181Ta50O3−	181Ta51O3−	183w50O3−	184w50O3−	185Re50O3−	187Re49O3−
			182w49O3−	182W50O3−	184w49O3−	185Re49O3−	186w49O3−
				183w49O3−

Finally, the per-integration oxide-corrected ¹⁸²W¹⁶O₃⁻/¹⁸⁴W¹⁶O₃⁻ were corrected for instrumental mass bias by normalizing to ¹⁸⁶W/¹⁸³W = 0.92767 or ¹⁸⁶W/¹⁸⁴W = 1.98594 [18], using the exponential law [19]. Per-integration oxide corrected ¹⁸³W¹⁶O₃⁻/¹⁸⁴ W¹⁶O₃⁻ were only corrected for mass bias using ¹⁸⁶W/¹⁸⁴W = 1.98594. Mass bias corrections were calculated using molecular masses (e.g., 232 for ¹⁸⁴W¹⁶O₃).

3. Results and discussion

In order to determine the isotopic composition of oxygen associated with Re trioxide formation, we measured the isotopic compositions of Re beams generated by loading activator onto Re filaments with no W. The results of 8 analyses of Re ribbon are summarized in Table 3, and shown in Fig. 1. Using these results, data for 30 analyses of standard solutions (300 ng–1000 ng Alfa Aesar W) are summarized in Table 4, and shown in Figs. 2, 3, and 4. A natural sample (group IVB iron meteorite Skookum) analyzed using this method, and compared to previously published results, is shown in Fig. 8.

Table 3.

Data for 8 analyses of Re ribbon with only activator (5 μg each La and Gd loaded). Errors are 2SD internal precisions and reflect in-run evolution of oxygen isotopic compositions.

Analysis #	18O/16O	2SD (‰)	17O/16O	2SD (‰)
1	0.002085	5.4	0.0003894	6.2
2	0.002090	7.6	0.0003905	7.1
3	0.002100	2.6	0.0003917	3.8
4	0.002110	2.9	0.0003926	3.9
5	0.002125	2.3	0.0003940	4.7
6	0.002098	4.1	0.0003919	3.8
7	0.002088	8.1	0.0003906	9.1
8	0.002074	8.1	0.0003896	5.7
Mean	0.002096	7.7‰	0.0003913	4.1 ‰

Fig. 1.

Measured oxygen isotopic compositions for ReO₃⁻ (this study), RuO₃⁻ [20], and MoO₃⁻ [21]. The oxygen isotopic composition of atmosphere reported by Nier (1950) and a terrestrial fractionation line (dashed-dotted line), which were used by previous studies [14,1] are shown for reference. Linear regressions are shown as dashed (ReO₃⁻), solid (RuO₃⁻), and dotted (MoO₃⁻) lines.

Table 4.

Standards data for 30 analyses of 300 ng–1000 ng of Alfa Aesar W. Errors are 2SE absolute internal precisions. ¹⁸⁵Re/¹⁸⁴W are the average signal intensity ratios for entire analyses.

Standard #	Session ID #	W Abundance	Type	Date	185Re/184W	182W/184WN6/4	2SE	183W/184WN6/4	2SE	182W/184WN6/3	2SE
1	381	1 μg	Thick	Feb 18, 2016	0.126	0.864893	0.000004	0.467148	0.000002	0.864869	0.000003
2	381	300 ng	Thick	Feb 19, 2016	0.196	0.864890	0.000005	0.467146	0.000002	0.864866	0.000004
3	382	1 μg	Thick	Feb 24, 2016	0.115	0.864893	0.000004	0.467149	0.000002	0.864867	0.000003
4	382	1 μg	Thick	Feb 25, 2016	0.125	0.864893	0.000004	0.467147	0.000002	0.864870	0.000003
5	382	1 μg	Thick	Feb 29, 2016	0.052	0.864890	0.000004	0.467146	0.000002	0.864869	0.000003
6	382	1 μg	Thick	March 3, 2016	0.039	0.864893	0.000004	0.467147	0.000002	0.864870	0.000003
Cup Maintenance Performed				April 1st, 2016	Mean 2SD(ppm)	0.864892 4.0		0.467147 4.3		0.864869 3.6
7	385	1 μg	Thin	April 5, 2016	0.048	0.864889	0.000005	0.467144	0.000002	0.864870	0.000004
8	385	1 μg	Thick	April 6, 2016	0.066	0.864889	0.000004	0.467146	0.000002	0.864866	0.000003
9	385	300 ng	Thick	April 7, 2016	0.118	0.864890	0.000004	0.467145	0.000002	0.864867	0.000003
10	386	1 μg	Thick	April 11, 2016	0.162	0.864889	0.000004	0.467145	0.000002	0.864867	0.000003
11	386	1 μg	Thick	April 12, 2016	0.176	0.864889	0.000004	0.467148	0.000002	0.864866	0.000003
12	386	1 μg	Thick	April 13, 2016	0.057	0.864887	0.000004	0.467146	0.000002	0.864866	0.000003
13	386	1 μg	Thick	April 13, 2016	0.088	0.864891	0.000004	0.467146	0.000002	0.864868	0.000003
14	386	500 ng	Thin	April 14, 2016	0.061	0.864892	0.000004	0.467145	0.000002	0.864870	0.000003
15	386	1 μg	Thin	April 18, 2016	0.050	0.864890	0.000004	0.467144	0.000002	0.864870	0.000003
16	386	500 ng	Thin	April 19, 2016	0.096	0.864890	0.000004	0.467145	0.000002	0.864868	0.000003
17	386	1 μg	Thick	April 19, 2016	0.170	0.864891	0.000004	0.467146	0.000002	0.864869	0.000003
18	386	500 ng	Thick	April 20, 2016	0.102	0.864884	0.000004	0.467143	0.000002	0.864865	0.000003
19	386	500 ng	Thick	April 21, 2016	0.164	0.864887	0.000005	0.467146	0.000002	0.864868	0.000004
20	387	1 μg	Thin	April 25, 2016	0.081	0.864893	0.000004	0.467146	0.000002	0.864871	0.000003
21	387	1 μg	Thick	May 1, 2016	0.026	0.864893	0.000004	0.467145	0.000002	0.864872	0.000003
22	387	500 ng	Thick	May 2, 2016	0.312	0.864886	0.000006	0.467143	0.000003	0.864867	0.000004
23	389	500 ng	Thin	May 16, 2016	0.042	0.864885	0.000004	0.467141	0.000002	0.864868	0.000003
24	389	1 μg	Thin	May 17, 2016	0.038	0.864888	0.000004	0.467145	0.000002	0.864868	0.000003
25	389	1 μg	Thick	May 20, 2016	0.022	0.864892	0.000004	0.467147	0.000002	0.864869	0.000003
26	389	1 μg	Thick	May 22, 2016	0.031	0.864886	0.000004	0.467143	0.000002	0.864866	0.000003
27	390	1 μg	Thin	May 26, 2016	0.051	0.864888	0.000003	0.467144	0.000001	0.864868	0.000002
28	390	1 μg	Thin	May 27, 2016	0.031	0.864887	0.000003	0.467143	0.000002	0.864868	0.000002
29	390	1 μg	Thin	May 30, 2016	0.034	0.864888	0.000004	0.467145	0.000002	0.864867	0.000003
30	390	500 ng	Thin	June 2, 2016	0.081	0.864887	0.000004	0.467142	0.000002	0.864868	0.000003
					Mean 2SD (ppm)	0.864889 5.7		0.467145 6.6		0.864868 3.7

Fig. 2.

¹⁸²W/¹⁸⁴W normalized to ¹⁸⁶W/¹⁸⁴W for 30 analyses of 300ng–1000 ng Alfa Aesar W standards. Mean ¹⁸²W/¹⁸⁴W and 2SD for each period shown in legend. Grey dashed lines mark 5 ppm from the mean. Error bars represent 2SE internal precisions.

Fig. 3.

¹⁸²W/¹⁸⁴W normalized to ¹⁸⁶W/¹⁸³W for 30 analyses of 300ng–1000 ng Alfa Aesar W standards. Mean ¹⁸²W/¹⁸⁴W and 2SD for each period shown in legend. Grey dashed lines mark 5 ppm from the mean. Error bars represent 2SE internal precisions.

Fig. 4.

¹⁸³W/¹⁸⁴W normalized to ¹⁸⁶W/¹⁸⁴W for 30 analyses of 300ng–1000 ng Alfa Aesar W standards. Mean ¹⁸³W/¹⁸⁴W and 2SD for each period shown in legend. Grey dashed lines mark 5 ppm from the mean. Error bars represent 2SE internal precisions.

Fig. 8.

μ¹⁸³W_N6/4 vs. μ¹⁸²W_N6/4 for the group IVB iron meteorite Skookum. One analysis is from this study, and two analyses were taken from [5]. The error bars for the datum from this study are 2SD, and the error bars for the data from [5] are 2SE (n = 5) of repeated measurements.

3.1. First-order and per-integration oxide corrections

High-precision W analyses at the ~5 ppm level require either second-order [14] or per-integration [1] oxide corrections because of in-run mass-dependent oxygen fractionation. This study utilized per-integration oxide corrections because ¹⁸³W/¹⁸⁴W, which varies nature, can be measured using this method.

Before per-integration oxide corrections could be performed, the signals used to calculate per-integration ¹⁷O/¹⁶O and ¹⁸O/¹⁶O for WO₃⁻ and ReO₃⁻ (¹⁸⁶W¹⁶O₂¹⁸O⁻, ¹⁸⁶W¹⁶O₃⁻, ¹⁸⁷Re¹⁶O₂¹⁸O⁻, and ¹⁸⁷Re¹⁶O₃⁻) had to be first-order oxide-corrected. First-order oxide correction is defined as an oxide correction using a single, assumed value (i.e., an estimated ¹⁷O/¹⁶O and ¹⁸O/¹⁶O). For this estimate, the means of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O calculated from ¹⁸⁷Re¹⁶O₂¹⁷O⁻/¹⁸⁷Re¹⁶O₃⁻ and ¹⁸⁷Re¹⁶O₂¹⁸O⁻/¹⁸⁷Re¹⁶O₃⁻ measured on Re filaments (n = 8) loaded with only 5 μg each of La and Gd were used (Table 3). The means of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O determined by this study were 0.0003913 and 0.002096, respectively (Fig. 1). These values are significantly higher than the values used by previous studies, e.g., ¹⁷O/¹⁶O = 0.0003749 and¹⁸O/¹⁶O = 0.002044 [15,14,1]. Because ¹⁸⁷Re¹⁶O₃⁻ is an isobar with ¹⁸⁶W¹⁶O₂¹⁷O⁻, measured ¹⁸⁶W¹⁶O₂¹⁷O⁻/¹⁸⁶W¹⁶O₃⁻ and ¹⁸⁶W¹⁶O₂¹⁸O⁻/¹⁸⁶W¹⁶O₃⁻ could not be used to make this estimate.

The repeated measurements of ¹⁸⁷Re¹⁶O₂¹⁷O⁻/¹⁸⁷Re¹⁶O₃⁻ and ¹⁸⁷Re¹⁶O₂¹⁸O⁻/¹⁸⁷Re¹⁶O₃⁻ from Re filaments also provides an oxygen mass fractionation line that is consistent with recently reported oxygen mass fractionation lines for OsO₃⁻, RuO₃⁻, and MoO₃⁻ (Fig. 1) measured by N-TIMS [20–23]. These lines are all offset from the oxygen fractionation line used by previous W studies utilizing N-TIMS. The slope of a linear regression through the ReO₃⁻ oxygen mass fractionation line (0.0985 ± 0.0018 2SD) is similar to the slope of the terrestrial fractionation line (0.0954), so the terrestrial fractionation slope was used to infer ¹⁷O/¹⁶O from measured ¹⁸O/¹⁶O.

3.2. External and internal precision

The external precision (n = 6) of 300 ng–1000 ng Alfa Aesar W standards analyzed in February 2016 was 4.0 ppm and 3.6 ppm for¹⁸²W/¹⁸⁴W normalized to ¹⁸⁶W/¹⁸⁴W (¹⁸²W/¹⁸⁴W_N6/4) and ¹⁸⁶W/¹⁸³W (¹⁸²W/¹⁸⁴W_N6/3), respectively (Table 4; Figs. 2 and 3). After Faraday cup maintenance (mechanical removal of deposits on graphite inserts from each Faraday cup, except the center cup) was performed in April 2016, the mean ¹⁸²W/¹⁸⁴W_N6/4 shifted downwards by ~3 ppm (Fig. 2), whereas the ¹⁸²W/¹⁸⁴W_N6/3 only shifted by ~1 ppm (Fig. 3). Faraday cup condition, therefore, appears to have a ~3x larger influence on ¹⁸²W/¹⁸⁴W_N6/4 than ¹⁸²W/¹⁸⁴W_N6/3.

The long-term external precision (n = 24; over a period of 3 months after Faraday cup maintenance) of 300 ng–1000 ng Alfa Aesar W standards analyzed from April-June 2016 was 5.7 ppm and 3.7 ppm for¹⁸²W/¹⁸⁴W_N6/4 and ¹⁸²W/¹⁸⁴W_N6/3, respectively (Table 4; Figs. 2 and 3), which is 2–3 x more precise for ¹⁸²W/¹⁸⁴W_N6/4 and ¹⁸²W/¹⁸⁴W_N6/3 than the most recently reported method for measuring W via N-TIMS [1]. These improvements in precision are likely the result of the more accurate oxide corrections for both WO₃⁻ and ReO₃⁻. Consistent with prior studies [14,1], the long-term external precision of ¹⁸²W/¹⁸⁴W is better when normalizing to ¹⁸⁶W/¹⁸³W than ¹⁸⁶W/¹⁸⁴W because of the closer proximity of the normalizing isotopes (¹⁸³W vs. ¹⁸⁴W). However, normalization to ¹⁸⁶W/¹⁸³W is only appropriate for samples with ¹⁸³W/¹⁸⁴W identical to terrestrial standards, as ¹⁸³W varies among some meteorites. The long-term external precision of ¹⁸²W/¹⁸⁴W_N6/4 and ¹⁸²W/¹⁸⁴W_N6/3 were 5.2 ppm and 2.6 ppm, respectively, for thin ribbon (n = 11). For thick ribbon (n = 13), the ¹⁸²W/¹⁸⁴W_N6/4 and ¹⁸²W/¹⁸⁴W_N6/3 were 6.2 and 4.3 ppm, respectively.

The external precision of ¹⁸³W/¹⁸⁴W_N6/4 for February 2016 was 4.3 ppm (Table 4; Fig. 4). ¹⁸³W/¹⁸⁴W_N6/4 is also sensitive to Faraday cup condition and shifted by ~5 ppm after cup maintenance was performed in April 2016. The long-term external precision (n = 24) of 300 ng–1000 ng Alfa Aesar W standards analyzed from April-June 2016 was 6.6 ppm for¹⁸³W/¹⁸⁴W_N6/4 (Table 4; Fig. 4). The long-term external precision of ¹⁸³W/¹⁸⁴W_N6/4 was 6.0 ppm for thin filaments (n = 11), and 6.5 ppm for thick filaments (n = 13).

The internal precisions of interspersed 300 ng, 500 ng, and 1000 ng Alfa Aesar W standards were similar (~4–5 ppm 2 standard error of the mean (SE) for ¹⁸²W/¹⁸⁴W_N6/4) when the same signal intensity (~1 V on ¹⁸⁴W) was achieved for 600 integrations (Fig. 5). However, only 1000 ng W standards measured on thin Re ribbon achieved much greater than ~1 V on ¹⁸⁴W, and correspondingly better internal precision (~3 ppm 2SE for ¹⁸²W/¹⁸⁴W_N6/4). The best internal precisions (average 2SE of 3.6 ppm) for ¹⁸²W/¹⁸⁴W were achieved by using ¹⁸⁶W/¹⁸³W for mass bias corrections. By contrast, the average of internal precisions of ¹⁸²W/¹⁸⁴W mass bias corrected using ¹⁸⁶W/¹⁸⁴W was 4.7 ppm 2SE. For ¹⁸³W/¹⁸⁴W mass bias corrected using ¹⁸⁶W/¹⁸⁴W, the average internal precision was 4.2 ppm 2SE.

Fig. 5.

Average ¹⁸⁴W signal (volts) during analyses vs. the internal precision (2SE) for ¹⁸²W/¹⁸⁴W (normalized to ¹⁸⁶W/¹⁸⁴W) of 26 analyses of 300ng–1000 ng Alfa Aesar W standards that were measured for 600 integrations. Analyses of both thick and thin filaments are included. Analyses that were measured for fewer than 600 integrations are not included.

3.3. Measurements with high Re signals

Ref. [1] reported correlations between Re/W signals, ¹⁸²W/¹⁸⁴W, and oxygen isotopic compositions. Because that study used the oxygen isotopic composition of atmosphere reported by [15] to calculate ¹⁷O/¹⁶O from measured ¹⁸O/¹⁶O, corrections for species incorporating ¹⁷O were too low, as the [15] isotopic composition deviates negatively in ¹⁷O/¹⁶O from the oxygen isotopic compositions measured during N-TIMS analyses and reported here (Fig. 1). Thus, the interference corrections for ¹⁸⁷Re¹⁷O¹⁶O₂ on ¹⁸⁶W¹⁸O¹⁶O₂ (which [1] used to determine ¹⁸O/¹⁶O and then calculate ¹⁷O/¹⁶O) were too low. In this study, the use of more accurate ¹⁷O/¹⁶O removes this bias, and a correlation between Re/W signals and ¹⁸²W/¹⁸⁴W is not observed (Fig. 6).

Fig. 6.

Mean ¹⁸⁵Re/¹⁸⁴W (for each measurement) vs. ¹⁸²W/¹⁸⁴W (normalized to ¹⁸⁶W/¹⁸³W) for 30 analyses of 300ng–1000 ng Alfa Aesar W standards. Grey dashed lines mark 5 ppm from the mean. Error bars represent 2SE internal precisions.

3.4. Correlation of mass bias corrected ratios

Within the standards data reported by this study, a correlation exists between ¹⁸²W/¹⁸⁴W_N6/4 and ¹⁸³W/¹⁸⁴W_N6/4 (Fig. 7). A linear regression through the 30 measured standards using ISO-PLOT [24] has a slope of 1.41 ± 0.53 (2σ) and a mean square weighted deviation (MSWD) of 0.5. Ref. [1] also observed a correlated drift in ¹⁸²W/¹⁸⁴W_N6/4 and ¹⁸³W/¹⁸⁴W_N6/4 over a 9 month period. Among other possibilities, they stated that this could be the result of Faraday cup degradation over time. Because of the correlated, pronounced shift in ¹⁸²W/¹⁸⁴W_N6/4 and ¹⁸³W/¹⁸⁴W_N6/4 after cup maintenance, we conclude that the most likely cause of the correlated shift is Faraday cup degradation.

Fig. 7.

¹⁸³W/¹⁸⁴W_N6/4 vs. ¹⁸²W/¹⁸⁴W_N6/4 for 30 analyses of 300ng–1000 ng Alfa Aesar W standards. Error bars represent 2SE internal precisions.

3.5. Measurement of natural samples

The measurement of natural samples with previously reported ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W provides a means to assess the accuracy of this analytical method. Ref. [5] reported that the ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W of group IVB iron meteorite Skookum, measured using a multi collector-inductively coupled plasma mass spectrometer (MC-ICP-MS), were well resolved from terrestrial standards (Fig. 8). Isotopic deviations of samples from standards here are described in μ units, where μ^xW is the isotopic deviation in parts per million of ^xW/¹⁸⁴W from a terrestrial standard. The μ¹⁸²W_6/4 (−334.8 ± 5.7 2SD) and μ¹⁸³W_6/4 (12.7 ± 6.6 2SD) of Skookum reported here is identical, within uncertainty, to one of two W isotopic compositions for the sample (μ¹⁸²W_6/4 = −330 ± 4 2SE, and μ¹⁸³W_6/4 = 13 ± 4 2SE) reported by [5]. Further, the precision reported here is for a single measurement and is defined as the 2SD long-term external precision of standards analyzed during this study. By contrast, the precision reported by [5] represents the 2SE (n = 5) of repeated measurements. Thus, the datum reported here illustrates the accuracy and precision of single measurements using this new analytical method.

4. Conclusions

We have refined recently reported N-TIMS techniques [14,1] to measure WO₃⁻ and determine ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W to high-precision. Most significantly, this technique makes more accurate first-order and per-integration oxide corrections to primary ^xWO₃⁻ signals by (i) utilizing updated values for ¹⁷O/¹⁶O and ¹⁸O/¹⁶O for first-order corrections, (ii) measuring ¹⁸O/¹⁶O for both WO₃⁻ and ReO₃⁻, and (iii) using a new oxide mass fractionation line to calculate per-integration ¹⁷O/¹⁶O from measured ¹⁸O/¹⁶O. The long-term external precisions for ¹⁸²W/¹⁸⁴W_N6/4, ¹⁸²W/¹⁸⁴W_N6/3, and ¹⁸³W/¹⁸⁴W_N6/4 are 5.7 ppm, 3.7 ppm, and 6.6 ppm, respectively. This level of precision is ~2–3 x better for single measurements than the most recently reported N-TIMS method for measuring both ¹⁸²W/¹⁸⁴W and ¹⁸³W/¹⁸⁴W [1]. We have demonstrated that this method is capable of producing accurate and precise data for natural samples by using this method to measure a group IVB iron meteorite, and comparing the datum to previously reported data for this sample [5].