Characterization of a new candidate isotopic reference material for natural Pb using primary measurement method

Analytica Chimica Acta 974 (2017) 27e42

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Characterization of a new candidate isotopic reference material for natural Pb using primary measurement method Naoko Nonose a, *, Toshihiro Suzuki a, Ki-Cheol Shin b, Tsutomu Miura a, Akiharu Hioki a a

National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8563, Ibaraki, Japan b Research Institute for Humanity and Nature, 457-4, Motoyama, Kamigamo, Kita-ku, Kyoto, 603-8047 Japan

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Standard solutions of natural lead are characterized by MC ICP-MS as isotope candidate reference material (NMIJ CRM 3681).
Calibration is done by using a 208 Pb-204Pb double spike solution prepared from enriched stable isotopes.
EDTA titrimetry is used as primary measurement method during the characterization of the candidate isotope reference material.
Combined total uncertainties of obtained absolute Pb isotope ratios are about one third or about one eighth compared with those for NIST SRM 981.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 November 2016 Received in revised form 6 April 2017 Accepted 13 April 2017 Available online 26 April 2017

A lead isotopic standard solution with natural abundance has been developed by applying a mixture of a solution of enriched 208Pb and a solution of enriched 204Pb (208Pb-204Pb double spike solution) as bracketing method. The amount-of-substance ratio of 208Pb:204Pb in this solution is accurately measured by applying EDTA titrimetry, which is one of the primary measurement methods, to each enriched Pb isotope solution. Also metal impurities affecting EDTA titration and minor lead isotopes contained in each enriched Pb isotope solution are quantified by ICP-SF-MS. The amount-of-substance ratio of 208 Pb:204Pb in the 208Pb-204Pb double spike solution is 0.961959 ± 0.000056 (combined standard uncertainty; k ¼ 1). Both the measurement of lead isotope ratios in a candidate isotopic standard solution and the correction of mass discrimination in MC-ICP-MS are carried out by coupling of a bracketing method with the 208Pb-204Pb double spike solution and a thallium internal addition method, where thallium solution is added to the standard and the sample. The measured lead isotope ratios and their expanded uncertainties (k ¼ 2) in the candidate isotopic standard solution are 18.0900 ± 0.0046 for 206 Pb:204Pb, 15.6278 ± 0.0036 for 207Pb:204Pb, 38.0626 ± 0.0089 for 208Pb:204Pb, 2.104406 ± 0.00013 for 208 Pb:206Pb, and 0.863888 ± 0.000036 for 207Pb:206Pb. The expanded uncertainties are about one half of the stated uncertainty for NIST SRM 981, for 208Pb:204Pb, 207Pb:204Pb and 206Pb:204Pb, or one eighth, for 208 Pb:206Pb and 207Pb:206Pb, The combined uncertainty consists of the uncertainties due to lead isotope ratio measurements and the remaining time-drift effect of mass discrimination in MC-ICP-MS, which is

Keywords: Certified reference material Chemical metrology SI traceability Lead isotopic standard solution 208 Pb-204Pb double spike solution MC-ICP-MS

* Corresponding author. E-mail address: [email protected] (N. Nonose). http://dx.doi.org/10.1016/j.aca.2017.04.019 0003-2670/© 2017 Elsevier B.V. All rights reserved.

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not removed by the coupled correction method. In the measurement of 208Pb:204Pb, 207Pb:204Pb and 206 Pb:204Pb, the latter contribution is two or three times larger than the former. When the coupling of a bracketing method with the 208Pb-204Pb double spike solution and a thallium internal addition method is applied to the analysis of NIST SRM 981, the measured lead isotope ratios are in good agreement with its certified values. This proves that the developed method is not only consistent with the conventional one by NIST SRM 981 but also enables measurement of the lead isotope ratios with higher precision. © 2017 Elsevier B.V. All rights reserved.

1. Introduction For the last two decades, the importance of the isotope ratio has been increasingly discussed in various research fields such as earth environmentology [1e7], geology [8e10], medical physiology [11e13], and food adulteration and origins [14,15]. In order to estimate the historical variation of isotope ratios in target materials and their provenances, related isotopic certified reference materials (CRMs) whose isotope ratios are precisely measured would be necessary. Such reference materials for isotope ratio measurements are available from some national metrology institutes, such as the National Institute of Standards and Technology (NIST, Gaithersburg, USA) and the Institute for Reference Materials and Measurements (IRMM, Geel, Belgium). However the recent rapid development of instrumental techniques for isotope ratio measurement, especially the appearance of multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS), has made it difficult to discuss the consistency of data on isotope ratios measured by various testing laboratories, not only because the types of related isotopic reference materials are lacking but also because the precision and trueness of their certified values are less satisfactory from viewpoint of traceability to the International System of Units (SI). Recently the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology (CCQM) in the International Bureau of Weights and Measures (BIPM, Paris, France) mentioned an increasing requirement for isotopic reference materials in the next generation [16] and then carried out some international comparisons on isotope ratio measurements [17e19]. Among these comparisons, an interlaboratory study named CCQM-K98 [19] provided a key comparison of the measurements of lead isotope ratios and molar mass both in a pure lead solution and a bronze sample; this was organized by the Federal Institute for Materials Research and Testing (BAM, Berlin, Germany). The results of this comparison have been published [20] and the testing materials are now on sale as lead isotopic CRMs (ERM-AE142, and ERM-EB400) [21]. However, irrespective of the discussion on the SI traceability of isotopic reference material at the CCQM, all participants, including the authors' institute (National Metrology Institute of Japan NMIJ, Tsukuba, Japan), were required to utilize NIST SRM 981 (NIST, Gaithersburg, USA) as a traceability source for the correction of mass discrimination in lead isotope ratio measurement in order to compare the measurement techniques themselves. Although most participants' results on lead isotope ratios in pure lead solution are in good agreement with each other within their expanded uncertainties, the uncertainty component dominating each expanded uncertainty is that due to NIST SRM 981 itself. It is well-known that there are various methods for correction of the mass discrimination effect in MC-ICP-MS, such as a bracketing method with isotopic standards [9,10,22e24], external standard addition [9,24e27], and double or triple spike addition [7,9,28e33]. These methods have been used singly or in

combination with another method [2,33,34]. However the SI traceability of the isotope ratios in the isotopic standards used for these corrections is not clear. For example, certified values of NIST SRM 981 [36] were determined with a mixture of a solution of enriched 208Pb with a solution of enriched 206Pb; each amount of substance of lead was measured by the primary measurement method (gravimetric analysis with precipitation of PbCrO4), but the estimation of impurities in the enriched isotopes was insufficient due to the lack of instrumental sensitivity. In addition, most of double spike methods utilized such certified values of NIST isotopic CRMs for calibration of the double spike solution. Therefore, in order to establish the SI traceability of isotope ratios in isotopic reference materials, NMIJ has designed a unique concept for the precise measurement of isotope ratios, where not the existing NIST SRM 981 but an isotopic standard solution (a mixture of a solution of enriched 204Pb with a solution of enriched 208 Pb, hereafter, 208Pb-204Pb double spike solution), whose 208 Pb:204Pb ratio is accurately measured by primary measurement methods, is utilized for the correction of the mass discrimination effect in MC-ICP-MS. NMIJ then applied the concept to the development of a lead isotopic standard solution (NMIJ CRM 3681a). An existing technique developed for an elemental standard solution series of NMIJ CRMs [37,38] has been applied to the production of the lead isotopic CRM. EDTA titrimetry, which is one of the primary measurement methods [39], is the key technique in the production of the lead isotopic CRM to attain SI traceability. The amount-of-substance ratio of 208Pb:204Pb in the 208Pb-204Pb double spike solution used for the correction of the mass discrimination effect in MC-ICP-MS is accurately measured by EDTA titrimetry with a smaller uncertainty less than 0.006%. Therefore, the uncertainty of the 208Pb:204Pb ratio in the 208Pb-204Pb double spike solution calibrated by EDTA titrimetry can be expected to be smaller than that of NIST SRM 981. The lead isotope ratios in the candidate isotopic standard solution are measured by bracketing method with the 208Pb-204Pb double spike solution by MC-ICP-MS. The uncertainty of lead isotope ratios in the candidate lead isotopic standard solution, measured with the 208Pb-204Pb double spike solution can therefore not only hold the SI traceability but can also be smaller than that in existing natural lead isotopic standards. This new isotopic standard solution may contribute to an interlaboratory comparison on the measurement capability of MC-ICP-MS with respect to lead isotope ratios. The present paper describes the details of the preparation procedure for 208Pb-204Pb double spike solution, whose 208Pb:204Pb ratio is calibrated by EDTA titrimetry with far smaller uncertainty than that attained in the usual titrimetry, and the correction method for the mass discrimination effect in the measurement of lead isotope ratios with the 208Pb-204Pb double spike solution. Also, the uncertainty calculation procedure for the measured lead isotope ratios is mentioned.

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

2. Experimental 2.1. Preparation of lead isotopic standard solution All the preparation procedures for the lead isotopic standard solutions and the solution of enriched isotopes were carried out in a clean room of class 10,000. The reagents used for sample preparation, including highly purified water, were of ultrapure grade (Kanto Chemicals Co. Inc., Tokyo, Japan). The raw material of the lead isotopic standard solution is high purity metal lead (99.999%) purchased from Sumitomo Metal Mining Co., Ltd (Tokyo, Japan), which is the same as that used for a lead standard solution of NMIJ CRM 3608-a [40]. The container storing the lead isotopic standard solution was a 30 L polypropylene (PP) bottle with a valve (Nalgene® round carboy with spigot, Thermo Fisher Scientific, Waltham, MA, USA). A 110 mL high density polyethylene (PE) bottle with an inner lid (Sanplatec Corp., Osaka, Japan) was used for subdivision of the lead isotopic standard solution stored in the 30 L PP bottle. These bottles were cleaned in advance as follows: they were soaked in 0.1 mol kg1 nitric acid overnight, washed with pure water three times, then completely dried at approximately 40  C. Approximately 27 g of the metal lead was etched for 10 min in 3.3 mol L1 nitric acid at 80  C on a hot plate (AS ONE ceramic hot plate, CHP-2250AN, AS ONE Corporation, Osaka, Japan). These etching conditions enabled gentle cleaning of the surface of the metal lead, which is the same as that used for preparation of lead standard solution in NMIJ. The etched metal was washed with water, dried at 55  C and then being cooled in a silica gel desiccator for more than 30 min. The metal lead was weighed into a 1 L quartz beaker by using an AX205 mass balance (Mettler-Toledo, Greifensee, Switzerland); 500 mL of 6.4 mol L1 nitric acid was added and the metal lead was dissolved slowly on a hot plate at 80  C. Once the lead solution was cool, it was moved into the 30 L PP bottle and then diluted to 27 L with 0.25 mol L1 nitric acid to yield an approximate lead concentration of 1000 mg kg1. The container storing the lead isotopic standard solution had been weighed before use with an MS32001L mass balance (Mettler-Toledo, Greifensee, Switzerland) with an expanded uncertainty of 0.0002% (relative). The stored solution was homogenized by rolling the container for two days, and it was then subdivided into 235 of the 110 mL PE bottles. Each bottle was sealed in an aluminumlaminated plastic bag (SEINICHI Lamizip®, AL-12, Seisannipponsha LTD., Tokyo, Japan) and kept in a refrigerator (NR-1980MF3, NIHON FREEZER Co., LTD., Tokyo, Japan) at ca. 4  C. 2.2. Preparation of solution of enriched enriched 208Pb

29

(5 mL for 204Pb and 10 mL for 208Pb); both enriched isotopes were the dissolved slowly on the a plate. After cooling of the dissolved solutions, the 204Pb and 208Pb solutions were transferred into 250 mL and 500 mL PE bottles with inner lids (Sanplatec Corp.), respectively, and were then diluted to 250 g and 500 g, respectively, with 0.3 mol L1 nitric acid. Approximate amount-of-substance contents of lead in the 204Pb solution and the 208Pb one, measured by EDTA titration, were 196.73 mg kg1 and 193.17 mg kg1, respectively. Each bottle of enriched Pb solution was sealed in an aluminum-laminated plastic bag (SEINICHI Lamizip®, AL-15) and kept in a refrigerator (UKS-3600HC, NIHON FREEZER Co., LTD.) at ca. 4  C. The mass of each solution, including the bottle, was recorded at every use to monitor the evaporation of the solvent. 2.3. Instrumentation The MC-ICP-MS used in the present study was a Neptune (Thermo Fisher Scientific Inc., Bremen, Germany) equipped with nine Faraday cup collectors labeled L4, L3, L2, L1, C1, H1, H2, H3, and H4. Among nine collectors only seven were used in the measurement of Pb isotope ratios, i.e., L3 for 202Hg, L2 for 203Tl, L1 for 204Hg and 204Pb, C1 for 205Tl, H1 for 206Pb, H2 for 207Pb, and H3 for 208Pb. Although Hg was monitored for the correction of isobaric interference with 204Pb, the signal of 202Hg was four orders of magnitude smaller than that of 204Pb in the measurement of sample solutions, so the effect of this interference was negligible as a matter of fact. A double-focusing sector field inductively coupled plasma mass spectrometer (ICP-SF-MS), an Element2 (Thermo Fisher Scientific Inc., Bremen, Germany), was also used for the quantification of metal impurities and minor Pb isotopes contained in the 204Pb and 208 Pb solutions; see details below. EDTA titration of the solutions was carried out using an automatic titration apparatus, AT-420win (Kyoto Electronics Manufacturing Co., LTD, Kyoto, Japan). The details of the titration system are described elsewhere [37,38]. 2.4. Establishment of SI traceability of lead isotope ratios in lead isotopic standard solution In order to establish the traceability of lead isotope ratios in a lead isotopic standard solution to SI, the authors prepared a 208 Pb-204Pb double spike solution whose 208Pb:204Pb amount-ofsubstance ratio is accurately measured by primary measurement methods. The preparation process is as follows:

204

Pb and solution of

A 208Pb-204Pb double spike solution is gravimetrically prepared from a solution of enriched 204Pb (named 204Pb solution) and a solution of enriched 208Pb (named 208Pb solution). Both enriched 204 Pb isotope and enriched 208Pb one in metallic form were purchased from Oak Ridge National Laboratory (ORNL, Oak Ridge, TN, USA). Although the vendor values of the isotopic abundance of 204 Pb and 208Pb are given as 0.9970 and 0.9986 (listed in Table 1), respectively, actual values are measured in the present study. Each enriched isotope solution was prepared as described in the following paragraph. Approximately 50 mg of enriched 204Pb and approximately 100 mg of enriched 208Pb were washed with three times of 5 mL of pure water and 5 mL of ethanol, dried at 55  C, cooled in a silica gel desiccator for more than 30 min. Each enriched isotope was weighed in a 100 mL beaker and 6 mol L1 nitric acid was added

(1) The ratio of the total lead amount-of-substance content in a 204 Pb solution to that in a 208Pb solution is measured by EDTA titrimetry. Although EDTA titrimetry only enables measurement of the lead amount-of-substance content of each enriched isotope solution with a standard uncertainty of 0.05%, the uncertainty of the lead amount-of-substance content “ratio” of both enriched isotope solutions can be minimized to less than one tenth of 0.05%, because some systematic errors common to both measurements can be compensated for. (2) The lead amount-of-substance ratio obtained in (1) is corrected using the amounts of metal impurities, affecting EDTA titrimetry, in both enriched isotope solutions. The metal impurities are quantified by ICP-SF-MS. (3) The Isotopic abundances of minor lead isotopes in each enriched isotope solution are calculated from the mass fractions of 206Pb, 207Pb, and 208Pb in the 204Pb solution and

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Table 1 Isotopic abundances of enriched

204

Pb and enriched

208

Pb. Measured values by ICP-SF-MS

Vendor values

Mass number isotope

Isotopic abundance (mol mol1)

Standard uncertainty (mol mol1)

Isotopic abundance (mol mol1)

Precision (mol mol1)

204

Pb

204 206 207 208

0.997035 0.001709 0.000597 0.000659

0.000034 0.000011 0.000007 0.000008

0.9970 0.0017 0.0006 0.0007

0.0001 0.00005 0.00005 0.0005

208

Pb

204 206 207 208

0.000006 0.000846 0.000394 0.998753

0.000002 0.000003 0.000002 0.000017

<0.0001 0.0010 0.0004 0.9986

0.0000 0.0001 0.0001 0.0001

those of 204Pb, 206Pb, and 207Pb in the 208Pb solution, which are quantified by a standard addition method (ICP-SF-MS) with a 206Pb enriched isotope solution. (4) Both enriched isotope solutions are gravimetrically mixed, and then the amount-of-substance ratio of 208Pb:204Pb in the mixed-enriched isotope solution is calculated using the result of (3). Each procedure from (1) to (4) is discussed in “Results and Discussion”. The above procedures would ensure the traceability of the 208Pb-204Pb double spike solution to SI. The traceability system used in the development of a lead isotopic standard solution is illustrated in Fig. 1.

3. Results and discussion 3.1. Measurement of lead amount-of-substance content ratio of Pb solution to 204Pb solution by EDTA titrimetry

208

Twenty milliliters of each enriched isotope solution were weighed into a 100 mL beaker and then 50 g of water and 10 mL of 9.1% hexamethylenetetramine were added. In the same way, ten samples of the 204Pb solution and 15 samples of the 208Pb solution were prepared. After adjusting the pH of each solution to about 5.3 with sodium hydroxide, 1 mL of 0.01% xylenol orange was added; then the enriched isotope solutions were titrated with 0.0013 mol dm3 EDTA. The 204Pb and 208Pb solutions were titrated alternately, except that three repetitive titrations of the 208Pb

Fig. 1. Traceability system of lead isotopic standard solution, NMIJ CRM 3681-a.

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

solution were performed at the start and at the end of the measurement sequence. The absorption intensity at 580 nm was used for the calculation of an equivalent point [37,38]. When the lead amount-of-substances in 1 kg of the 208Pb solution and 1 kg of the 204Pb solution are designated as C208CI and C204CI, respectively, the apparent lead amount-of-substance content ratio of the 208Pb solution to the 204Pb solution (C208CI:C204CI)apparent is finally obtained as follows: (C208CI:C204CI)apparent ¼ 0.962953 ± 0.000039 Hereinafter, each value following ± means a combined standard uncertainty. The relative standard uncertainty for the ratio is 0.0040%, which was calculated from the combination of the repeatability of the EDTA titration for the 208Pb solution (0.0033%) and that for the 204Pb solution (0.0023%). Here the repeatability is estimated from the standard deviation for the average of the lead amount-of-substance content. 3.2. Correction of apparent amount-of-substance content ratio of 208 Pb solution to 204Pb one (C208CI:C204CI)apparent by metal impurities 208 in Pb and 204Pb solutions Since EDTA forms complexes with many metals, which influence to influence the measurement of lead amount-of-substance, the measured value of (C208CI:C204CI)apparent shown in the previous section should be corrected using the amount of metal impurities contained in the 208Pb and 204Pb solutions. Approximately 2 g of each enriched isotope solution was weighed and then diluted to ca. 10 mg kg1 mass fraction of lead with 0.3 mol dm3 nitric acid. Metal impurities in the diluted solutions were quantified by ICP-SFMS with a calibration method. Thirty-nine elements were quantified, which were selected according to the stability constants of their complexes with EDTA. The calibration standard solutions were prepared from an SPEX multi-element solution. The certified value of each element in the solution is traceable to a corresponding NIST SRM number. As a result, the total amount-of-substance contents of metal impurities in the raw materials are 0.6197 mmol g1 for 204Pb and 0.6932 mmol g1 for 208Pb; the purities of lead in the 204Pb and 208 Pb enriched isotopes are estimated to be 99.9937% and 99.9946% with regard to the mass fraction, respectively. The quantified amounts of metal impurities and their uncertainties are listed in Supplemental Information 1. The dominant metal impurities are mercury (0.19 mmol g1 ± 0.03 mmol g1) for the 204Pb enriched isotope and iron (0.1761 mmol g1 ± 0.0037 mmol g1) and tin (0.1041 mmol g1± 0.0039 mmol g1) for the 208Pb enriched isotope, where each uncertainty is the combined standard uncertainty. The (C208CI:C204CI)apparent value is corrected on the assumption that all the metal impurities detected by ICP-SF-MS consume EDTA. The molar masses of lead in the 204Pb and 208Pb enriched isotopes are assumed to be 204 g mol1 and 208 g mol1, respectively. Since the impurities of lead contained in both enriched isotopes are estimated to be almost 100%, the total lead amount-of-substance contents in the enriched 204Pb and 208Pb isotopes (in solid) are calculated from the reciprocal of each molar mass to be 4902 mmol g1 and 4807 mmol g1, respectively. Strictly speaking, their molar masses would deviate slightly from 204 g mol1 and 208 g mol1 because both the enriched isotopes include trace amounts of minor lead isotopes. However, in discussing the contribution of the metal impurities to the (C208CI:C204CI)apparent value, the effect of the minor lead isotopes on the molar masses can be neglected considering their contents (see details in section 3.3). Therefore, the amount-of-substance content ratios of the impurities in the 204Pb and 208Pb enriched isotopes are calculated as

31

follows: Pb enriched isotope: 0.6197 mmol g1 /(4902 mmol g1)  100 ¼ 0.0126% 204

Pb enriched isotope: 0.6932 mmol g1 /(4807 mmol g1)  100 ¼ 0.0144% 208

Under the conditions of the EDTA titration of lead, almost all metal impurities quantified in the present study are thought to be titrated along with lead judging from the formation constants of the impurity metals and lead. Even if the formation efficiencies of the complexes with EDTA are insufficient for some metal impurities, the effect of such impurities on the correction of the (C208CI:C204CI)apparent value can be neglected not only because the sum of the detected impurities is in small (0.01%) but also because the effects of the impurities on the 204Pb and 208Pb solutions are cancelled out as expressed in the following equations [Eqns. (1) and (2)]. When the following variables are named, true amount-of-substance content of lead in 204Pb enriched isotope: A204CI, total amount-of-substance content of metal impurities in 204Pb enriched isotope: A204CI-imp, true amount-of-substance content of lead in 208Pb enriched isotope: A208CI, total amount-of-substance content of metal impurities in 208Pb enriched isotope: A208CI-imp, the (C208CI:C204CI) apparent value can be replaced by Eqn (1).

ðC208CI : C204CI Þapparent ¼

A208CI þ A208CIimp A204CI þ A204CIimp

A208CI þ 0:0144%  A208CI A204CI þ 0:0126 %  A204CI 1 þ 0:0144% A208CI  ¼ 1 þ 0:0126% A204CI ¼

(1)

Therefore, when the lead amount-of-substance content ratio of the 208Pb solution to the 204Pb solution after correction of metal impurities is defined as (C208CI:C204CI)cor, it corresponds to (A208CI:A204CI);

ðC208CI : C204CI Þcor ¼ ðA208CI : A204CI Þ 1 þ 0:0126%  ðC208CI : C204CI Þapparent 1 þ 0:0144% ¼ 0:999982  0:962953 ¼ 0:962936

¼

(2)

Considering the uncertainty due to the calibration curve and that due to the repeatability of the measurements (n ¼ 2) for each impurity, the combined standard uncertainties for the amount-ofsubstance content of metal impurities in the 204Pb and 208Pb enriched isotopes are calculated to be 12% and 8%, respectively. As a result, the relative standard uncertainty for the coefficient (0.999982) in Eqn (2) is calculated to be:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     0:0144%  0:12 2 0:0126%  0:08 2 ¼ 0:0018% þ 1:000143 1:000125 (3) Thus, the relative standard uncertainty for (C208CI:C204CI)cor can be estimated as a combination of the result in Eqn (3) and the relative standard uncertainty for (C208CI:C204CI)apparent calculated in the previous section (0.0040%):

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N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:0018%Þ2 þ ð0:0040%Þ2 ¼ 0:0044%

(4)

Finally, the corrected lead amount-of-substance content ratio of the 208Pb solution to the 204Pb solution, (C208CI:C204CI)cor, is obtained as follows: (C208CI:C204CI)cor ¼ 0.962936 ± 0.000043

3.3. Measurement of isotopic abundances of 204Pb and 208Pb enriched isotopes by ICP-SF-MS with standard addition method In order to prepare a 208Pb-204Pb double spike solution whose amount-of-substance ratio of 208Pb:204Pb is accurately known, the isotopic abundances of 204Pb, 206Pb, 207Pb and 208Pb in each enriched isotope solution should be accurately measured. For the measurement of isotopic abundances in the 204Pb and 208Pb solutions, the standard addition method with a solution of enriched 206 Pb is used. In this case, an isotope dilution method, which is a primary measurement method, cannot be applied because “unknown” lead isotopic abundances in the 204Pb and 208Pb solutions as well as the mass fraction of lead in the solution of enriched 206Pb should be “known”. Enriched 206Pb in metallic form with an enrichment factor of 99.67% was purchased from ORNL. Approximately 200 mg kg1 of enriched 206Pb solution (named 206Pb solution) was prepared in the same manner as the 204Pb and 208Pb solutions, and then the mass fraction of lead in the 206Pb solution was accurately measured by EDTA titrimetry (200.35 mg kg1) with a combined standard uncertainty of 0.05%. A schematic diagram of the standard addition method for the measurement of lead isotopic abundances is illustrated in Fig. 2.

Regarding the minor lead isotopes contained as impurities in the Pb and 208Pb solutions, the mass fraction of 206Pb impurity in the 204 Pb and 208Pb solutions is quantified by the standard addition method with the 206Pb solution. The mass fractions of other minor lead isotopes, except for 206Pb, in the 204Pb and 208Pb solutions are quantified from the signal ratio of each minor isotope to 206Pb, with ICP-SF-MS. Finally, the isotopic abundances of lead in each enriched isotope solution are evaluated from the mass fractions of lead measured by EDTA titration (196.73 mg kg1 for the 204Pb solution and 193.17 mg kg1 for the 208Pb solution) and the mass fractions of minor lead isotopes. The measured isotopic abundances in the 204 Pb and 208Pb solutions are listed in Table 1 with their standard uncertainties. With these isotopic abundances, the amount-ofsubstance ratio of 208Pb:204Pb in the 208Pb-204Pb double spike solution can be estimated. 204

3.4. Calculation of true spike solution

208

Pb:204Pb ratio in

208

Pb-204Pb double

The lead amount-of-substance content ratio of the 208Pb solution to the 204Pb solution, (C208CI:C204CI)cor, obtained in the previous section includes four lead isotopes. However, the value required for the estimation of mass discrimination in MC-ICP-MS is the isotope ratio of 208Pb:204Pb in the 208Pb-204Pb double spike solution. Since the 208Pb-204Pb double spike solution is prepared gravimetrically from the 204Pb and 208Pb solutions, the amount-of-substance ratio of 208Pb:204Pb in the 208Pb-204Pb double spike solution can be calculated from the mixed masses (10.07862 g for the 204Pb solution and 10.04110 g for the 208Pb solution), lead isotopic abundances in each enriched solution and (C208CI:C204CI)cor. When the isotopic abundances of 204Pb and 208Pb in the 204Pb solution are f204CI(204) and f204CI(208), the isotopic abundances of 204 Pb and 208Pb in the 208Pb solution are f208CI(204) and f208CI(208), and the mixed masses of the enriched isotope solutions are m204CI

Fig. 2. Schematic diagram of standard addition method for quantification of minor lead isotopes in the solution of enriched

204

Pb and the solution of enriched

208

Pb.

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

and m208CI, the amount-of-substance ratio of 208Pb to 204Pb in the 208 Pb-204Pb double spike solution, here defined as RIM ð208 : 204Þt , is expressed by the following equation.

RIM ð208 : 204Þt ¼

33

as 0.0058%. Hereafter this solution is named “IM solution”, to be used for the correction of the measured isotope ratios of the candidate isotopic standard solution.

f208CI ð208Þ$m208CI $ðC208CI : C204CI Þcor þ f204CI ð208Þ$m204CI f204CI ð204Þ$m204CI þ f208CI ð204Þ$m208CI $ðC208CI : C204CI Þcor

¼ ð0:998753  10:04110  0:962936 þ 0:000659  10:07862Þ=ð0:997035  10:07862 þ 0:000006  10:04110  0 :962936Þ

(5)

¼ 9:663521=10:048795 ¼ 0:961659

On the other hand, the standard uncertainty of RIM ð208 : 204Þt , expressed as uðRIM ð208 : 204Þt Þ, is calculated by differentiating Eqn (5).

  2 ¼ u RIM ð208 : 204Þt

 f204CI þ

þ

(

In the present study, the measurement of lead isotope ratios in the candidate isotopic standard solution and the correction of mass

m208CI $ðC208CI : C204CI Þcor ð204Þ$m204CI þ f208CI ð204Þ$m208CI $ðC208CI : C204CI Þcor

2

$ ðuðf208CI ð208ÞÞÞ2

!2   2 m208CI $m204CI $ðf208CI ð208Þ$f204CI ð204Þ  f204CI ð208Þ$f208CI ð204ÞÞ $ u ðC208CI : C204CI Þcor 2  f204CI ð204Þ$m204CI þ f208CI ð204Þ$m208CI $ðC208CI : C204CI Þcor  !2 m204CI $ f208CI ð208Þ$m208CI $ðC208CI : C204CI Þcor þ f204CI ð208Þ$m204CI $ ðuðf204CI ð204ÞÞÞ2  2 f204CI ð204Þ$m204CI þ f208CI ð204Þ$m208CI $ðC208CI : C204CI Þcor

Here, the standard uncertainties due to (C208CI:C204CI)cor, f204CI(204), and f208CI(208) are u((C208CI:C204CI)cor), u(f204CI(204)) and u(f208CI(208)), respectively. The components of (C208CI:C204CI)cor, f204CI(204), and f208CI(208) are not strictly independent because they are calculated from the standard addition method with the 206 Pb solution. However, these components are treated as independent factors, considering the ICP-SF-MS signal fluctuation for each isotope. On the other hand, the standard uncertainties due to f204CI(208), f208CI(204) and the ratio of m204CI to m208CI are very small; therefore, these do not have to be taken into consideration for the combined standard uncertainty calculation. When the values in Eqn (2) and the masses of both enriched isotope solutions are substituted into Eqn (6), we obtain the following:

  u RIM ð208 : 204Þt ¼

3.5. Correction of measured lead isotope ratio by bracketing method with IM solution coupled with Tl internal addition

10:04110  0:962936 $048795 10

2

(6)

discrimination in MC-ICP-MS are carried out by coupling of a bracketing method with the 208Pb-204Pb double spike solution and a thallium internal addition method. Usually, the correction factor for the mass discrimination of lead disagrees with that of thallium, so it is expressed as a type of exponential function for the correction that of thallium. Although the use of such a function would help to calculate accurate lead isotope ratios, the function itself is seriously affected by a matrix component in the sample, and the operating conditions of ICP, and other factors [27,29,41]. Therefore it appears to be difficult to obtain accurate lead isotope ratios with a single use of the thallium internal addition method. Reuer et al. [2] and Hattori [34] et al. improved both the precision and trueness of lead isotope ratios with a combination of the thallium internal correction method and a bracketing method with existing lead

 ð0:000017Þ2

    10:04110  10:07862  ð0:997035  0:998753  0:000006  0:000659Þ 2 10:07862  9:663521 2 þ  ð0:000043Þ2 þ 10:048795  10:048795 10:048795  10:048795 )0:5  ð0:000034Þ2 ¼ 0:000056

Finally, the relative standard uncertainty for the 208Pb:204Pb isotope ratio in this 208Pb-204Pb double spike solution is estimated

(7)

isotopic standards. In the present study, the authors employ a procedure similar to that developed by Reuer: the correction of the time-drift effect in lead mass discrimination by the thallium

34

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

Fig. 3. Measurement procedure of sample solutions.

Fig. 4. Effect of thallium internal addition on time-drift mass discrimination of lead isotope ratio measurement. (A) Change in measured isotope ratios of lead (208Pb:204Pb) and thallium (205Tl:203Tl) in IM solution plotted against measurement time. (B) Change in 208Pb:204Pb ratio corrected by thallium internal addition with an exponential law.

internal addition method with the exponential law [42], followed by the correction of bias from true isotope ratios by the bracketing method with the “IM solution” mentioned previously. As an

example, the effect of the thallium internal addition method on the time-drift mass discrimination of lead isotope ratio measurement in the IM solution is shown in Fig. 4. Both the observed 208Pb:204Pb and 205Tl:203Tl ratios showed almost the same behavior against measurement time (150 s for 30 repetitive measurements), resulting in the disappearance of the time-drift effect of lead isotope ratio by the thallium internal addition method. From 235 bottles prepared as candidate isotopic standard solutions, 10 bottles [sam(i), i ¼ 1,2…, 10] were randomly selected for the measurement of lead isotope ratios. Usually, the IM solution and each sample bottle would be alternately introduced into MCICP-MS. However, there is a large difference between the 208 Pb:204Pb isotope ratios of the IM solution and the sample bottle, which necessitates much washing time (>5 min) between them. In the present study, therefore, the IM solution is measured before (named IM1) and after (named IM2) measurement of the five sample bottles. The thallium solution used for the internal addition is NIST SRM 997 with a 203Tl:205Tl ratio of 0.418911. In the coupling of a bracketing method with the IM solution and a thallium internal addition solution, the accuracy of the 203Tl:205Tl ratio does not affect the accuracy of the lead isotope ratio measurement; therefore, the value of 0.418911 given as the 203Tl:205Tl ratio of was treated as a “reference value”, Rð203 : 205Þr , in the present study. The true 208Pb:204Pb ratio in the IM solution is defined as RIM ð208 : 204Þt in the previous section. The observed 208Pb:204Pb ratios are RIM1 ð208 : 204Þm for IM1 and RIM2 ð208 : 204Þm for IM2, and the corresponding correction factors are KPb1 for IM1 and KPb2 for IM2. The observed 203Tl:205Tl ratios are RIM1 ð203 : 205Þm for IM1 and RIM2 ð203 : 205Þm for IM2, and the corresponding correction factors are KTl1 and KTl2. The difference between the mass discrimination for lead and that for thallium can be given as a b correction factor (b1 in IM1 and b2 in IM2) in the exponential law [2,27]; then, b1 and b2 are expressed as follows:

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

ln203  ln205 lnKPb1 $ b1 ¼ ln208  ln204 lnKTl1

(8)

ln203  ln205 lnKPb2 $ ln208  ln204 lnKTl2

(9)

b2 ¼

KsamðiÞ ð208 : 204Þ ¼

(10)

KTl1 ¼

Rð203 : 205Þr RIM1 ð203 : 205Þm

(11)

KPb2 ¼

RIM ð208 : 204Þt RIM2 ð208 : 204Þm

(12)

(13)

ð6  iÞ$b1 þ i$b2 6

ði ¼ 1; 2; 3; 4; 5Þ

(14)

ð11  iÞ$b1 þ ði  5Þ$b2 ði ¼ 6; 7; 8; 9; 10Þ ¼ 6

(14a)

When, in the measurement of sam(i), the observed isotope ratio of 203Tl:205Tl is RsamðiÞ ð203 : 205Þm , and the observed and corrected isotope ratios of 208Pb:204Pb are RsamðiÞ ð208 : 204Þm ; and RsamðiÞ ð208 : 204Þcor , respectively, the following equation is valid.

RsamðiÞ ð208:204Þcor RsamðiÞ ð208:204Þm

!

1 ln208ln204

Rð203:205Þr ¼ RsamðiÞ ð203:205Þm

!bsamðiÞ $

1 ln203ln205

(15) The ratio in parenthesis on left side of Eqn (15) indicates the correction factor for 208Pb:204Pb in the measurement of sam(i); this is defined as KsamðiÞ ð208:204Þ: From Eqn (15), Eqn (16) is obtained. Table 2 Typical operating conditions of MC-ICP-MS. ICP operating condition ICP torch RF Power Plasma Gas Aux. Gas Carrier Gas Spray chamber Nebulizer Mass spectrometer Resolution (m/Dm) Measured mass number

Integration time Repetition

(16) 204

RsamðiÞ ð208 : 204Þcor ¼ KsamðiÞ ð208 : 204Þ$RsamðiÞ ð208 : 204Þm On the other hand, the correction factors of other isotope ratios in sam(i) are calculated from the exponential law using KsamðiÞ ð208 : 204Þ. For example, KsamðiÞ ð207 : 204Þ and the corrected isotope ratio of 207 Pb:204Pb are calculated from the following equations:





In the present study, five bottles of the candidate isotopic standard solution, named sam(i), are measured between the measurement of IM1 and that of IM2. Since the mass discrimination changes linearly with measurement time [34], as shown in Fig. 4, the b value for sam(i), defined as bsam(i), can be calculated from the weighted mean of b1 and b2, considering the time-drift effect.

bsamðiÞ



ln208ln204 ln203ln205

(17)

Rð203 : 205Þr RIM2 ð203 : 205Þm

bsamðiÞ ¼



Finally, the corrected isotope ratio of Pb: Pb in sam(i), RsamðiÞ ð208 : 204Þcor , can be calculated according to the definition of KsamðiÞ ð208 : 204Þ as follows:

RIM ð208 : 204Þt RIM1 ð208 : 204Þm

KTl2 ¼

Rð203 : 205Þr RsamðiÞ ð203 : 205Þm

!bsamðiÞ $

208

Here,

KPb1 ¼

35

Quartz injector (inner diameter of 1.7 mm) 1200 W 15 L min1 0.7 L min1 1.19 L min1 Quartz double pass spray chamber PFA-100 nebulizer (uptake rate of 150 mL min1) 400 Pb 204, 206, 207, 208 Hg 202, 204 Tl 203, 205 4.2 s 30 times

KsamðiÞ ð207 : 204Þ ¼ KsamðiÞ ð208 : 204Þ

ln207ln204 ln208ln204

(18)

RsamðiÞ ð207 : 204Þcor ¼ KsamðiÞ ð207 : 204Þ$RsamðiÞ ð207 : 204Þm (19) 206

204

Other isotope ratios such as Pb: Pb:206Pb are calculated in the same way.

Pb,

208

Pb:

206

P and

207

3.6. Measurement procedure for lead isotope ratios in sample solutions The lead isotope ratios in the candidate isotopic standard solutions [sam(i), i ¼ 1, 2…, 10] are measured by the bracketing method coupled with thallium internal addition [34,35]. The sam(i) solutions including thallium are prepared so that the mass fractions of lead and thallium were about 300 mg kg1. On the other hand, an IM solution containing thallium is prepared to yield the mass fractions of lead and thallium as ca. 150 mg kg1 and ca. 300 mg kg1, respectively. In addition, a NIST SRM 981 solution mixed with thallium (named NIST 981) is also prepared in order to compare the measurement result with its certified value. According to the sequence shown in Fig. 3, the isotope ratios of all prepared solutions are measured by MC-ICP-MS. The typical operating conditions of MC-ICP-MS are shown in Table 2. Although the bracketing method usually utilizes an isotopic standard whose isotope ratio is similar to that of sample, the 208 Pb:204Pb ratio in the IM solution (¼1.0) employed in the present study is significantly different from that in the candidate material (¼38) with natural lead isotopes. Then, in order to validate the bracketing method with the IM solution, the authors prepared another IM solution with a 208Pb:204Pb isotope ratio of 40 and compared the correction factor of mass discrimination in another IM solution with that in the original IM solution. The correction factors in the original IM solution and the other one are 1.00114 ± 0.0004 and 1.00129 ± 0.0027 (standard deviations for 30 repetitive measurements), respectively, showing agreement with each other within their uncertainties. However, since the uncertainty in the latter solution with a 208Pb:204Pb isotope ratio of 40 is about seven times larger than that in the former solution, it appears to be reasonable to use the IM solution with a smaller uncertainty. Before and after introducing each prepared solution including IM1, IM2, and NIST 981, a blank solution (0.3 mol dm3 nitric acid) is introduced for background correction. In order to eliminate the remaining time-drift mass discrimination (described in section

208

Pb:204Pb

36

Table 3 Measurement results of lead isotope ratios for sam (1) to sam(5) in run1. 203

RIM ð208 : 204Þt uðRIM ð208 : 204Þt Þ

0.961659 0.000056

Rð203 : 205Þr

0.418911

IM1

RIM1 ð208 : 204Þm SDmean KPb1 SDmean

0.984441 0.000018 0.976858 0.000060

RIM1 ð203 : 205Þm SDmean KTl1 SDmean

0.4136247 0.0000049 1.0127811 0.0000049

Rsamð1Þ ð208 : 204Þm

38.96060

Rsamð1Þ ð203 : 205Þm

SDmean Ksamð1Þ ð208 : 204Þ

0.00115 0.976682

SDmean

SDmean Rsamð1Þ ð208 : 204Þcor

0.000056 38.05211

SDmean

0.00246

Rsamð2Þ ð208 : 204Þm

sam(2)

sam(4)

sam(5)

IM2

a

Since the

Pb:204Pb

207

Pb:204Pb

208

Pb:206Pb

207

Pb:206Pb

b1 SDmean

0.93082 0.00257

i j

206 204

207 204

208 206

207 206

0.4135847

Rsamð1Þ ðj : kÞm

18.30133

15.90341

2.128840

0.8689756

0.0000037 1.0128791

bsam(1)

0.93090

SDmean Ksamð1Þ ðj : kÞ

0.00051 0.988216

0.00043 0.982418

0.000017 0.988329

0.0000075 0.994133

SDmean

0.0000037

SDmean

0.00218

SDmean Rsamð1Þ ðj : kÞcor

0.000029 18.08566

0.000043 15.62379

0.000028 2.103993

0.000014 0.863877

SDmean

0.00073

0.00080

0.000063

0.000015

38.95931

Rsamð2Þ ð203 : 205Þm

0.4136159

18.30195

15.90345

2.128697

0.8689481

SDmean Ksamð2Þ ð208 : 204Þ

0.00114 0.976816

SDmean

0.0000034 1.0128027

bsam(2)

0.93097

Rsamð2Þ ðj : kÞm SDmean Ksamð2Þ ðj : kÞ

0.00053 0.988284

0.00048 0.982519

0.000015 0.988396

0.0000062 0.994167

SDmean Rsamð2Þ ð208 : 204Þcor

0.000049 38.05607

SDmean

0.0000034

SDmean

0.00189

0.000025 18.08752

0.000037 15.62544

0.000025 2.103961

0.000012 0.863880

SDmean

0.00221

SDmean Rsamð2Þ ðj : kÞcor SDmean

0.00070

0.00076

0.000051

0.000012

Rsamð3Þ ð208 : 204Þm

38.971381

Rsamð3Þ ð203 : 205Þm

0.4135832

Rsamð3Þ ðj : kÞm

18.30658

15.90791

2.128819

0.868973

SDmean Ksamð3Þ ð208 : 204Þ

0.000844 0.976671

SDmean

0.0000024 1.0128829

bsam(3)

0.93105

SDmean Ksamð3Þ ðj : kÞ

0.00036 0.988210

0.00035 0.982410

0.000016 0.988323

0.000007 0.994131

SDmean Rsamð3Þ ð208 : 204Þcor

0.000045 38.06223

SDmean

0.0000024

SDmean

0.00176

0.000023 18.09075

0.000034 15.62809

0.000023 2.103961

0.000011 0.863872

SDmean

0.00193

SDmean Rsamð3Þ ðj : kÞcor SDmean

0.00055

0.00064

0.000051

0.000013

Rsamð4Þ ð208 : 204Þm

38.96602

Rsamð4Þ ð203 : 205Þm

0.4136055

18.30488

15.90621

2.128723

0.8689726

SDmean Ksamð4Þ ð208 : 204Þ

0.00099 0.976677

SDmean

0.0000035 1.0128283

bsam(4)

0.93112

Rsamð4Þ ðj : kÞm SDmean Ksamð4Þ ðj : kÞ

0.00046 0.988259

0.00039 0.982482

0.000019 0.988371

0.0000077 0.994155

SDmean Rsamð4Þ ð208 : 204Þcor

0.000045 38.06071

SDmean

0.0000035

SDmean

0.00182

SDmean Rsamð4Þ ðj : kÞcor

0.000023 18.089960

0.000034 15.627563

0.000022 2.103969

0.000011 0.863881

SDmean

0.00198

SDmean

0.000613

0.000657

0.000051

0.000012

Rsamð5Þ ð208 : 204Þm

38.96547

Rsamð5Þ ð203 : 205Þm

0.4135912

Rsamð5Þ ðj : kÞm

18.30393

15.90545

2.128803

0.8689638

SDmean Ksamð5Þ ð208 : 204Þ

0.00138 0.976703

SDmean

0.0000036 1.0128632

bsam(5)

0.93118

SDmean Ksamð5Þ ðj : kÞ

0.00069 0.988226

0.00062 0.982434

0.000018 0.988339

0.0000058 0.994138

SDmean Rsamð5Þ ð208 : 204Þcor

0.000053 38.05767

SDmean

0.0000036

SDmean

0.00205

0.000027 18.08842

0.000040 15.62605

0.000027 2.103980

0.000014 0.863870

SDmean

0.00247

SDmean Rsamð5Þ ðj : kÞcor SDmean

0.00084

0.00088

0.000060

0.000013

RIM2 ð208 : 204Þm SDmean KPb2 SDmean

0.984471 0.000012 0.976827 0.000058

203

Rð203:205Þr Rsamð1Þ ð203:205Þm

Rð203:205Þr Rsamð2Þ ð203:205Þm

Rð203:205Þr Rsamð3Þ ð203:205Þm

Rð203:205Þr Rsamð4Þ ð203:205Þm

Rð203:205Þr Rsamð5Þ ð203:205Þm

RIM2 ð203 : 205Þm SDmean KTl2 SDmean

0.4136233 0.0000026 1.0127846 0.0000026

Tl:205Tl ratio does not affect the accuracy of the lead isotope ratio measurement, the

b2 SDmean 203

0.93127 0.00240

Tl:205Tl ratio of 0.418911 is treated as “reference value”.

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

sam(3)

206

a

IM

sam(1)

b

Tl:205Tl

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

3.7), four repetitive sequences (run1 to run4) are carried out, where sam(i) solution is introduced in ascending order in run1 and run3, and in descending order in run2 and run4. While typical signals of 204 Pb, 208Pb, and 203Tl in the sam(i) solutions were about 0.2 V, 9 V, and 4.5 V, respectively, the typical signals of 204Pb and 208Pb in the IM solution were about 9 V. The signal level of 204Pb in the sam(i) solutions is about 45 times lower than that in the IM solution. Therefore, the introduction system of MC-ICP-MS should be carefully washed out between the IM solution and a corresponding sample solution until the background 204Pb level is reduced to less than 0.0002 V [41]. Although no desolvation system is connected with the nebulizer in order to avoid the memory effect caused by introduction of a high level of 204Pb in the IM solution [29], a long washout time of 480 s is set among the samples. For each sample solution, 30 repetitive measurements of isotope ratios are carried out. During the repetitive measurements, however, an unexpectedly large pulsing signal of 204Pb arising from the IM solution occasionally appeared; this is probably caused by a memory effect. In the present study, therefore, the data containing pulsing signals are rejected on the basis of statistical considerations.

3.7. Results of lead isotope ratio measurements and their uncertainties According to the measurement sequence shown in Fig. 3, five lead isotope ratios in the sam(i) solutions are measured. In the present study, not only three isotope ratios, 206Pb:204Pb, 207 Pb:204Pb, and 208Pb:204Pb, but also isotope ratios of 208Pb:206Pb and 207Pb:206Pb are also measured in order to compare with the uncertainties of certified values of NIST SRM 981. For example, the measurement results of five samples [sam(1)-sam(5)] in run1 are summarized in Table 3. The standard deviations of corrected lead

37

isotope ratios, each of which is calculated from the average isotope ratio for 30 repetitive measurements, varied in the range from 0.001% to 0.006% as relative values. Considering the uncertainties of the b values calculated from the correction factors of both 208 Pb:204Pb and 203Tl:205Tl, the b values appear to maintain almost constant during this sequence (run1), which means that the timedrift effect of mass discrimination in the lead isotope ratio measurements is effectively cancelled by the thallium internal addition method within this time range. However, the corrected lead isotope ratios, especially 208Pb:204Pb, 207Pb:204Pb, and 206Pb:204Pb, in the sam(1) to sam(5) solutions differ widely beyond their measurement precision. On the other hand, 208Pb:206Pb and 207Pb:206Pb in the five solutions have similar values within their measurement precision. The larger differences of the corrected isotope ratios observed for 208Pb:204Pb, 207Pb:204Pb, and 206Pb:204Pb among five samples are probably because the time-drift effect of the 204Pb signal is not negligible, suggesting difficulty in achieving complete correction of the time-drift effect in isotope ratio measurements even with coupling of the bracketing and thallium addition methods [34]. Therefore, in the present study, both (A) standard uncertainties due to isotope ratio measurement and (B) the remaining time-drift effect of mass discrimination are taken into consideration when calculating the combined standard uncertainties of the corrected lead isotope ratios. The contribution of (A) is estimated by combination of the standard uncertainties for 5 variables (or 4 variables in case of 208 Pb:204Pb) appearing in Eqns (17) and (19). The combined standard uncertainties for 208Pb:204Pb and the other four lead isotope ratios are expressed as Eqns (20) and (21), respectively. The derivation of the uncertainty calculation is described in Supplemental Information 2.

12 0  12  12 0  0  2 u R  u RsamðiÞ ð208 : 204Þcor u RsamðiÞ ð208 : 204Þm samðiÞ ð203 : 205Þm lnK Pb1 @ A ¼@ A þ A $@ RsamðiÞ ð208 : 204Þcor RsamðiÞ ð208 : 204Þm RsamðiÞ ð203 : 205Þm lnKTl1 ( ( ) )  2 6  i2  i 2  1 2 uR ð208 : 204Þ 2 uR ð208 : 204Þ 2 IM IM1 t m þ lnKsamðiÞ ð203 : 205Þ $ þ $ þ $ 6 6 lnKTl1 RIM ð208 : 204Þt RIM1 ð208 : 204Þm

(20)

( ) !2   2 2 6  i2  i 2  u RIM1 ð203 : 205Þm lnKPb1 þ $ ði ¼ 1; 2; 3; 4; 5Þ $ þ lnKsamðiÞ ð203 : 205Þ $ 6 6 RIM1 ð203 : 205Þm ðlnKTl1 Þ2

12 0  12  12 0  0  2 u R  u RsamðiÞ ð208 : 204Þcor u RsamðiÞ ð208 : 204Þm samðiÞ ð203 : 205Þm lnK Pb1 @ A ¼@ A þ A $@ RsamðiÞ ð208 : 204Þcor RsamðiÞ ð208 : 204Þm RsamðiÞ ð203 : 205Þm lnKTl1 ( ( ) )  2 11  i2 i  52  1 2 uR ð208 : 204Þ 2 uR ð208 : 204Þ 2 IM IM1 t m þ lnKsamðiÞ ð203 : 205Þ $ þ $ þ $ 6 6 lnKTl1 RIM ð208 : 204Þt RIM1 ð208 : 204Þm ( ) !2   2 2 11  i2 i  52  u RIM1 ð203 : 205Þm lnKPb1 þ $ ði ¼ 6; 7; 8; 9; 10Þ $ þ lnKsamðiÞ ð203 : 205Þ $ 6 6 RIM1 ð203 : 205Þm ðlnKTl1 Þ2

(20a)

38



uðgi Þ gi

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

2

 ¼

uðpi Þ pi

2

2  12 0  (  2 u R  2 6  i2 ð203 : 205Þm samðiÞ lnK Pb1 26 A @ þc 4 $ þ lnKsamðiÞ ð203 : 205Þ $ 6 RsamðiÞ ð203 : 205Þm lnKTl1

( 2   2 )  2 )  2 (  2 6  i2  u RIM ð208 : 204Þt u RIM1 ð208 : 204Þm i 1 þ $ þ $ þ lnKsamðiÞ ð203 : 205Þ $ 6 lnKTl1 6 RIM ð208 : 204Þt RIM1 ð208 : 204Þm 3 !2   2  2 ) u RIM1 ð203 : 205Þm i lnKPb1 7 þ $ $ 5ði 6 RIM1 ð203 : 205Þm ðlnKTl1 Þ2 ¼ 1; 2; 3; 4; 5Þ (21)



uðgi Þ gi

2

 ¼

uðpi Þ pi

2

2  12 0  (   2 u R ð203 : 205Þm samðiÞ lnK 11  i 2 6 2 Pb1 2 @ A þc 4 $ þ ðlnyi Þ $ 6 RsamðiÞ ð203 : 205Þm lnKTl1

( 2   2 )  )   2 (  u RIM ð208 : 204Þt u RIM1 ð208 : 204Þm i5 2 1 11  i 2 $ þ $ þ ðlnyi Þ2 $ 6 lnKTl1 6 RIM ð208 : 204Þt RIM1 ð208 : 204Þm 3 !2   2  )  u RIM1 ð203 : 205Þm i5 2 lnKPb1 7 þ $ $ 5ði 6 RIM1 ð203 : 205Þm ðlnKTl1 Þ2 

þ

¼ 6; 7; 8; 9; 10Þ

Fig. 5. Corrected lead isotope ratios in 10 candidate isotopic standard solutions. The ratios are normalized to the average for 10 sample bottles.

(21a)

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42 Table 4 Uncertainty budget for

208

39

Pb:204Pb in lead isotopic standard solution.

Components of uncertainty

(1) calculated value of 208Pb:204Pb in IM Combination of (a) to (e) (a)amount of substance of 204Pb (b)amount of substance of 208Pb (c)correction factor for metal impurities (d)isotopic abundance of 204Pb in 204Pb enriched isotope (e)isotopic abundance of 204Pb in 204Pb enriched isotope Pb:204Pb in IM

(A)  (B)

Standard uncertainty (A)

Sensitivity coefficient (B)

Symbol

Relative value

RIM1 ð208 : 204Þt

0.0058%

Symbol sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi n 2  2 o  ðlnyi Þ2 $ 6i ¼ kIM þ 6i $ lnK1 6

Value 0.78769

0.0046%

Tl1

C204CI C208CI f204CI ð204Þ f208CI ð208Þ

0.0023% 0.0033% 0.0019% 0.0034% 0.0017%

0.0018% 0.0026% 0.0015% 0.0027% 0.0013% sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi n 2  2 o  ðlnyi Þ2 $ 6i þ 6i $ lnK1 6 Tl1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2ffi u n 2  2 o u lnKPb1 tðlny Þ2 $ 6i i þ 6 $ 2 i 6

(2)observed

208

RIM1 ð208 : 204Þm

0.0010%

(3)observed

203

RIM1 ð203 : 205Þm

0.0010%

(4)observed

208

RsamðiÞ ð208 : 204Þm

0.0030%

e

1

0.0030%

(5)observed

203

RsamðiÞ ð203 : 205Þm

0.00080%

lnKPb1 lnKTl1

1.84581

0.0015%

Tl:205Tl in IM

0.78769

0.00079%

1.45393

0.0015%

ðlnKTl1 Þ

Pb:204Pb in sample Tl:205Tl in sample

(6) Time-drift effect of mass discrimination

0.010%

Combined standard uncertainty % (combination of (1) to (6)) Combined standard uncertainty (mol mol1) Expanded uncertainty %(k ¼ 2) Expanded uncertainty (k ¼ 2) (mol mol1)

0.012% 0.0044 0.023% 0.0089

Table 5 Uncertainty budget for

207

Pb:204Pb in lead isotopic standard solution.

Components of uncertainty

(1) calculated value of 208Pb:204Pb in IM Combination of (a) to (e) (a)amount of substance of 204Pb (b)amount of substance of 208Pb (c)correction factor for metal impurities (d)isotopic abundance of 204Pb in 204Pb enriched isotope (e)isotopic abundance of 204Pb in 204Pb enriched isotope Pb:204Pb in IM

Standard uncertainty (A)

Relative value Symbol

RIM1 ð208 : 204Þt

0.0058%

C204CI C208CI f204CI ð204Þ f208CI ð208Þ

0.0023% 0.0033% 0.0019% 0.0034% 0.0017%

(2)observed

208

RIM1 ð208 : 204Þm

0.0010%

(3)observed

203

RIM1 ð203 : 205Þm

0.0010%

Tl:205Tl in IM

(A)  (B)

Sensitivity coefficient (B)

Symbol

Value

C$kIM C ¼ ðln207  ln204Þ=ðln208  ln204Þ

0.59220 0.0035% 0.0014% 0.0019% 0.0011% 0.0020% 0.00099%

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n 2  2 o  c2 $ðlnyi Þ2 $ 6i þ 6i $ lnK1 6 Tl1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 u n  2   2 o u lnKPb1 tc2 $ðlny Þ2 $ 6i i þ $ 2 i 6 6

0.59220 0.00059% 1.09308 0.0011%

ðlnKTl1 Þ

(4)observed

207

pi ¼ RsamðiÞ ð207 : 204Þm

0.0027%

e

1

(5)observed

203

Pb:204Pb in sample

RsamðiÞ ð203 : 205Þm

0.00080%

Pb1 c$lnK lnK

1.38770 0.0011%

Tl:205Tl in sample

0.0027%

Tl1

(6) Time-drift effect of mass discrimination

0.011%

Combined standard uncertainty % (combination of (1) to (6)) Combined standard uncertainty (mol mol1) Expanded uncertainty %(k ¼ 2) Expanded uncertainty (k ¼ 2) (mol mol1)

0.012% 0.0018 0.023% 0.0036

Table 6 Corrected lead isotope ratios and corresponding expanded uncertainties of lead isotopic standard solution (mol mol1). 206

Pb:204Pb

207

Pb:204Pb

208

Pb:204Pb

208

Pb:206Pb

207

Pb:206Pb

Corrected isotope ratio (A) Standard uncertainty due to isotope ratio measurement Relative %

18.0900 0.00069 0.0038%

15.6278 0.00073 0.0047%

38.0626 0.0022 0.0059%

2.10406 0.000056 0.0027%

0.863888 0.000013 0.0015%

(B) Time-drift effect of mass discrimination Relative %

0.00222 0.012%

0.00166 0.011%

0.0038 0.010%

0.000035 0.0017%

0.000012 0.0014%

Combined standard uncertainty (combination of (1) and (2)) Expanded uncertainty (k ¼ 2) Expanded uncertainty (k ¼ 2) Relative %

0.0023

0.0018

0.0044

0.000066

0.000018

0.0046 0.026%

0.0036 0.023%

0.0089 0.023%

0.00013 0.0063%

0.000036 0.0041

40

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

Table 7 Comparison of measurement result of NIST SRM 981 with their certified values. 206

Pb:204Pb

SDmean

207

Pb:204Pb

SDmean

208

Pb:204Pb

SDmean

208

Pb:206Pb

SDmean

207

Pb:206Pb

SDmean

run1 run2 run3 run4

16.9315 16.9284 16.9359 16.9348

0.0007 0.0006 0.0006 0.0006

15.4912 15.4894 15.4963 15.4951

0.0008 0.0007 0.0008 0.0008

36.7084 36.7069 36.7236 36.7199

0.0023 0.0021 0.0024 0.0023

2.16805 2.16836 2.16838 2.16831

0.00006 0.00005 0.00013 0.00007

0.91494 0.91500 0.91500 0.91498

0.00002 0.00001 0.00006 0.00002

Average for 4 runs SD RSD % Combined standard uncertainty Expanded uncertainty (k ¼ 2)

16.9327 0.0034 0.020 0.0035 0.0069

0.0006

15.4930 0.0032 0.021 0.0033 0.0066

0.0008

36.7147 0.0083 0.023 0.0086 0.0172

0.0023

2.16828 0.00015 0.0064 0.00017 0.00034

0.00008

0.91498 0.00003 0.0032 0.00004 0.00008

0.00003

NIST certified value Expanded uncertainty (k ¼ 2) Reported valueRef9 2SDmeanb

16.9371a 0.0106a 16.9412 0.0003

a

15.4913a 0.0112a 15.4988 0.0006

36.7213a 0.0267a 36.7233 0.0013

These values are not certified; therefore, those are estimated from the certified values of 2 standard deviation for the average of 13 institutes obtained by poly-spike study.

b

Here,KsamðiÞ ð203 : 205Þ Tl:205Tl in sam(i);

:

correction

factor

for

observed

203

KPb1 : correction factor for observed 208Pb:204Pb in IM1. [see Eqn (10)]; KTl1 : correction factor for observed 203Tl:205Tl in IM1. [see Eqn (11)]; gi , ðgi Þ : corrected lead isotope ratio except 208Pb:204Pb and its standard uncertainty in the sample; pi , ðpi Þ : observed lead isotope ratio except 208Pb:204Pb and its standard uncertainty in sam(i); c: constant depending on measured isotopes; (ln207-ln204)/ (ln208-ln204) for 207Pb:204Pb, (ln206-ln204)/(ln208-ln204) for 206 Pb:204Pb, (ln208-ln206)/(ln208-ln204) for 208Pb:206Pb, and (ln207-ln206)/(ln208-ln204) for 207Pb:206Pb. It should be noted that Eqns (20) and (21) do not include the uncertainty due to the 203Tl:205Tl ratio used as the internal addition; uðRð203 : 205Þr Þ. This is because thallium is only used for correction of the time-drift effect of lead mass discrimination and because the trueness of the corrected lead isotope ratios is dependent only on the accuracy of the 208Pb:204Pb ratio in the IM solution used for the bracketing method. On the other hand, the contribution of (B) the time-drift effect of mass discrimination is estimated from the standard deviation of the corrected isotope ratios for 10 samples [sam(1)-sam(10)]. Fig. 5 shows the variation in the corrected isotope ratios for 10 samples from run1 to run4, although some of the data are omitted because of statistical and/or sample handling problems. The vertical axis shows the corrected lead isotope ratio normalized to the average for all corrected ratios. A remarkable time-drift of mass discrimination is observed for the ratio of 204Pb to the other three lead isotopes, particularly in the latter part of run4. Considering the total measurement time for one run sequence (approximately 7 h), it appears to be difficult to correct the long time-drift of mass discrimination for the isotope ratio measurement including 204Pb. This is probably due to (1) a long washing time between the IM solution and the sample and (2) measurement of the IM solution every five sample bottles. As an example, the uncertainty budgets for 208Pb:204Pb and 207 Pb:204Pb are summarized in Table 4 and Table 5, respectively, where the uncertainty component of (6), the time-drift effect of mass discrimination, is similar to the contribution of (B). Although the sensitivity coefficient for each uncertainty source is, strictly speaking, dependent on the measurement order of samples (i ¼ 1, 2,

208

Pb:206Pb,

2.1681 0.0008 2.16770 0.00008 207

Pb:206Pb and

204

0.91464 0.00033 0.914861 0.00003

Pb:206Pb.

3, 4, 5), it is given as the average value of 5 samples in the tables. Among five uncertainty components related to isotope ratio measurements [(1) to (5)] listed in the tables, the uncertainty due to the true value of 208Pb:204Pb in the IM solution (1) and the repeatability of the target isotope ratio measurement in the sample (4) are dominant. The results of the lead isotope ratio measurements in the candidate lead isotopic standard solutions are summarized in Table 6, in which (A) standard uncertainties due to isotope ratio measurement and (B) the time-drift effect of mass discrimination are compared. While the time-drift effect of mass discrimination for 208Pb:206Pb and 207Pb:206Pb showed almost the same values as the standard uncertainties due to the isotope ratio measurement, those for 208Pb:204Pb, 207Pb:204Pb, and 206Pb:204Pb are about two or three times larger than the standard uncertainties due to the isotope ratio measurement. Finally, the expanded uncertainties for 208 Pb:204Pb, 207Pb:204Pb and 206Pb:204Pb are dominated by the time-drift effect of mass discriminations arising from the variation in the 204Pb signal. However, the expanded standard uncertainties of the lead isotope ratios in the candidate isotopic standard solution developed in the present study are found to be one half to one eighth of the stated uncertainty in NIST SRM 981. 3.8. Measurement of NIST SRM 981 by the developed method and international comparison study of lead standard solution Lead isotope ratios of NIST SRM 981 were measured by the developed method in the present study and were then compared with their certified values. As is shown in Fig. 3, the IM solution is measured before and after two repetitive measurements of NIST 981 solutions mixed with thallium; this process is then repeated four times (from run1 to run4). The obtained isotope ratios for each run are listed in Table 7 in comparison with the certified values of NIST SRM 981 [36] and lead isotope ratios reported Taylor et al. [9]. Each combined standard uncertainty in the authors' result is calculated from a combination of a standard uncertainty due to the isotope ratio measurement and a standard deviation for four runs. While our measured isotope ratios for NIST SRM 981 agree well with the certified values within their measurement uncertainties, quite large differences are observed between the authors' measured isotope ratios and Taylor's reported values, which are obtained by double or triple spiking methods (poly-spike study), except for 208Pb:204Pb. However, the uncertainties of the values reported in Ref. [9] appear to be underestimated in terms of the traceability to SI because they only included the standard deviation

N. Nonose et al. / Analytica Chimica Acta 974 (2017) 27e42

for an average of 13 reported values [25]. As for the lead isotope ratio measurement, an international comparison of CCQM-K98, “Pb isotope amount ratios in bronze and pure solution” was carried out [19], in which lead isotope ratios of 206 Pb:204Pb, 207Pb:204Pb, 208Pb:204Pb, and 208Pb:206Pb were reported. We NMIJ employed a combination of a bracketing method with NIST SRM 981 and a thallium addition method for the correction of the time-drift effect of lead mass discrimination, whose concept is similar to that of the method developed in the present study, although all the uncertainties of lead isotope ratios in NIST SRM 981 are larger than those in the IM solution. The authors' results are all in good agreement with the reference values of the CCQM comparison, which proves that the combination of the bracketing method with the isotopic standard and the thallium internal addition method would be efficient [19,20] in the discussion on the comparability of lead isotope ratio measurement. Since the traceability source employed in the international comparison is not the IM solution with the combined standard uncertainty of 0.0058% for 208Pb:204Pb but NIST SRM 981, whose expanded uncertainties of lead isotope ratios are in the range 0.02%e0.04%, the uncertainties of the lead isotope ratios in NMIJ's result for the international comparison includes the contribution from the NIST SRM. NMIJ's reported uncertainties for 206Pb:204Pb, 207Pb:204Pb, 208 Pb:204Pb, and 208Pb:206Pb are 0.025%, 0.034%, 0.042%, and 0.021%, respectively, as relative, being almost dominated by the uncertainties of the certified values in NIST SRM 981. Some of the other participants of CCQM-K98 also reported the same tendencies. The use of IM solution with about one order of magnitude smaller uncertainty for 208Pb:204Pb than that of NIST SRM 981 would enable observation of the time-drift effect of the mass discrimination, which is probably caused by measurement-time fluctuation of the 204Pb signal. Finally, the authors mention the characteristics of lead isotope ratios of NMIJ's developed isotopic standard solution. The lead isotope ratios of the isotopic standard solution developed in this study (Table 6) have large biases from those of NIST SRM 981 (Table 7). Also, the lead isotope ratios of this isotopic standard solution deviated greatly from the distribution range of those referred to by the IUPAC [43]. It is well-known that lead isotopic abundances in geological materials depend on both the age and the location of the mine in which the uranium is produced. According to archeological references [44e47], the lead isotope ratios of this isotopic standard solution are quite close to the distribution of lead isotopes in archeological remains in Japan and East Asia. 4. Conclusion In order to contribute to international traceability of the isotope ratio measurements, NMIJ has developed an NMIJ CRM of a lead isotopic standard solution with natural isotopic abundances. The lead isotope ratio measurements of the candidate CRM are carried out by a bracketing method with a 208Pb-204Pb double spike (IM solution) whose 208Pb:204Pb ratio is precisely measured by EDTA titrimetry and gravimetrical preparation with a relative standard uncertainty of 0.0058%. The amount-of-substance ratio of 208 Pb:204Pb obtained by titrimetry is corrected with both metal impurities that form complexes with ETDA and minor lead isotopes contained in each raw material of the enriched isotopes. The contribution of such corrections to the amount-of-substance ratio of 208Pb:204Pb is, however, so negligibly small that the standard uncertainty of the amount-of-substance ratio of 208Pb:204Pb is governed by the standard deviation for repetitive measurements in EDTA titrimetry, which is far smaller than the standard uncertainty of 208Pb:204Pb in NIST SRM 981 (0.036%). In addition, a thallium solution is added to all measured sample solutions, including the

41

IM solution used for correction of the time-drift effect on the mass discrimination in MC-ICP-MS. As a result, the combined standard uncertainties of the developed lead isotopic standard solution are about one third for 208Pb:204Pb, 207Pb:204Pb, and 206Pb:204Pb or about one eighth for 208Pb:206Pb and 207Pb:206Pb compared with those in NIST SRM 981; the combined standard uncertainties of 208 Pb:204Pb, 207Pb:204Pb and 206Pb:204Pb are governed by the remaining time-drift effect of mass discrimination, which is not removed even by using the coupling method of bracketing with thallium addition. In order to reduce this mass discrimination effect, which is probably caused by the fluctuation of small signals of 204 Pb, and to achieve long term reproducibility (less than 0.01%) for 208 Pb:204Pb, 207Pb:204Pb, and 206Pb:204Pb over several hours, further discussion would be required on the washing conditions and the acceptable lead ratio of the IM solution. The lead isotope ratios of NIST SRM 981 measured by the developed method in the present study disagree with Taylor's reported values obtained by the latest poly-spike study with respect to their uncertainties. However, the developed method employed not existing isotopic reference materials but an IM solution characterized by using primary measurement methods; in addition, all related uncertainties are estimated. The traceability of the measured lead isotope ratios to SI is clearly established. Therefore, the disagreement between Taylor's reported values and the authors' results with respect to their uncertainties appears to be due to underestimation of the uncertainties of the former. The NMIJ CRM of the lead isotopic standard solution will be useful for discussing the comparability of lead isotope ratio measurements because the lead isotope ratios of this solution not only hold combined standard uncertainties smaller than those in NIST SRM 981 but also are traceable to SI. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.aca.2017.04.019. References [1] J. McManus, T.F. Naegler, C. Siebert, C.G. Wheat, D.E. Hammond, Geochemistry, Oceanic molybdenum isotope fractionation: diagenesis and hydrothermal ridge-flank alteration, Geophys. Geosyst. 3 (2002) 1e9. [2] M.K. Reuer, E.A. Boyle, B.C. Grant, Lead isotope analysis of marine carbonates and seawater by multiple collector ICP-MS, Chem. Geol. 200 (2003) 137e153. [3] D. Jouvin, D.J. Weiss, T.F.M. Mason, M.N. Bravin, P. Louvat, F. Zhao, F. Ferec, P. Hinsinger, M.F. Benedetti, Stable isotopes of Cu and Zn in higher plants: evidence for Cu reduction at the root surface and two conceptual models for isotopic fractionation processes, Environ. Sci. Technol. 46 (2012) 2652e2660. [4] S. Takano, M. Tanimizu, T. Hirata, Y. Sohrin, Isotopic constraints on biogeochemical cycling of copper in the ocean, Nat. Commun. 5 (2014) 5663. DOI: 10.1038, ncomms6663. [5] K. Yamaoka, E. Hong, T. Ishikawa, T. Gamo, H. Kawahata, Boron isotope geochemistry of vent fluids from arc/back-arc seafloor hydrothermal systems in the western Pacific, Chem. Geol. 392 (2015) 9e18. [6] M. Allan, N. Fagel, M. Van Rampelbergh, J. Baldini, J. Riotte, H. Cheng, R.L. Edwards, D. Gillikin, Y. Quinif, S. Verheyden, Lead concentrations and isotope ratios in speleothems as proxies for atmospheric metal pollution since the industrial revolution, Chem. Geol. 401 (2015) 140e150. [7] E.K. Skierszkan, M. Amini, D. Weis, A practical guide for the design and implementation of the double-spike technique for precise determination of molybdenum isotope compositions of environmental samples, Anal. Bioanal. Chem. 407 (2015) 1925e1935. [8] V. Renson, J. Coenaerts, K. Nys, N. Mattielli, F. Vanhaecke, N. Fagel, P. Claeys, Lead isotopic analysis for the identification of late bronze age pottery from Hala Sultan Tekke (Cus), Archaeometry 53 (2011) 37e57. [9] R.N. Taylor, O. Ishizuka, A. Michalik, J.A. Milton, I.W. Croudace, Evaluating the precision of Pb isotope measurement by mass spectrometry, J. Anal. At. Spectrom. 30 (2015) 198e213. [10] A. Bazzano, K. Latruwe, M. Grotti, F. Vanhaecke, Lead isotopic analysis of Antarctic snow using multi-collector ICP-mass spectrometry, J. Anal. At. Spectrom. 30 (2015) 1322e1328. [11] Y. Anoshkina, M. Costas-Rodriguez, F. Vanhaecke, High-precision Fe isotopic analysis of whole blood for biomedical purposes without prior isolation of the

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