Mass fractionation of Rb and Sr isotopes during laser ablation-multicollector-ICPMS: in situ observation and correction

Abstract

Background

One of the most critical issues concerning in situ mass spectrometry lies in accounting for elements and molecules that overlap target isotopes of analytical interest in a sample. This study traced the instrumental mass fractionation of Rb and Sr isotopes during laser ablation-multicollector-inductively coupled plasma mass spectrometry (LA-MC-ICPMS) to obtain reliable ⁸⁷Sr/⁸⁶Sr ratios for high-Rb/Sr samples.

Findings

In the LA-MC-ICPMS analysis, Kr interferences were corrected using Ar and He gas blanks measured without ablating material. Contributions from doubly charged Er and Yb ions were corrected using the intensities of half masses and isotopic compositions reported in the literature. After Kr correction, the calculated ¹⁶⁶Er²⁺ intensity of NIST SRM 610 approached the measured intensity at mass 83, and the ¹⁷³Yb²⁺/¹⁷¹Yb²⁺ ratio agreed with the recommended value within error ranges. Kr- and REE²⁺-stripped peak intensities were further corrected for Rb interference. Use of the Sr mass bias factor for the calculation of measured ⁸⁷Rb/⁸⁵Rb yielded ⁸⁷Sr/⁸⁶Sr ratios consistent with the recommended and expected values for low-Rb/Sr materials, such as NIST SRM 616, modern shark teeth, and plagioclase collected from Jeju Island, but failed to account for the ⁸⁷Rb interference from high-Rb/Sr materials including NIST SRM 610 and SRM 612. We calculated in situ mass bias factor of Rb from the known ⁸⁷Sr/⁸⁶Sr ratios of the standards and observed a correlation between Rb and Sr mass fractionation, which allowed inference of the Rb bias from the standard run. Reliable ⁸⁷Sr/⁸⁶Sr and ⁸⁵Rb/⁸⁶Sr ratios were obtained for SRM 610 and SRM 612 using the inferred mass bias factor of Rb calculated by the standard bracketing method.

Conclusions

This study revealed that Rb and Sr isotopes behave differently during LA-MC-ICPMS and suggests the potential usefulness of the standard bracketing method for measuring the Rb–Sr isotopic compositions of high-Rb/Sr materials.

Introduction

The natural radioactivity of rubidium was demonstrated in 1906 by Campbell and Wood and came into use in the field of isotope geology when mass spectrometry analysis became available in the 1950s. Rubidium-87, which presently makes up 27.83% of Rb, decays to stable ⁸⁷Sr by emitting a negative beta particle with a decay constant of 1.42 × 10⁻¹¹ year⁻¹ (Steiger and Jäger 1977) that corresponds to a half-life of 48.8 × 10⁹ years. Strontium consists of four naturally occurring stable isotopes (⁸⁴Sr, ⁸⁶Sr, ⁸⁷Sr, and ⁸⁸Sr). Its isotopic composition, generally represented by the ⁸⁷Sr/⁸⁶Sr ratio, varies widely in the geosphere and hydrosphere resulting from contrasting geochemical behavior of Rb and Sr. The Sr isotope signatures of local ecosystems transferred through the food chain have been used extensively to address archeological and forensic questions since the 1980s (Ericson 1985; Aggarwal et al. 2008).

The Rb–Sr isotope data have long been obtained using isotope dilution thermal ionization mass spectrometry (TIMS) or multicollector-inductively coupled plasma mass spectrometry (MC-ICPMS) combined with the separation of Rb and Sr by cation exchange chromatography. Despite the constraint of time-consuming sample preparation, these wet techniques for bulk samples continue to be used widely, particularly when a high level of precision and accuracy is demanded. However, micro-sampling or in situ analysis is inevitably required to extract the time-series information stored in biogenic materials or to retrieve petrogenetic information from a mineral composed of geochemically heterogeneous micro-domains.

The potential of laser ablation (LA)-MC-ICPMS for in situ Sr isotope analysis was realized in the 1990s (Christensen et al. 1995). Although this technique has become a standard methodology for measuring the Sr isotopic composition of Sr-rich minerals (e.g., feldspar, apatite, and clinopyroxene), carbonate and phosphate rocks, and biogenic materials (e.g., teeth and otoliths), considerable debate remains over isobaric interferences and instrumental mass fractionation (IMF) of Rb and Sr isotopes (Ramos et al. 2004; Vroon et al. 2008; Müller and Anczkiewicz 2016; Willmes et al. 2016).

This study traced the IMF of Rb and Sr isotopes during laser ablation-multicollector-inductively coupled plasma mass spectrometry (LA-MC-ICPMS) and proposed an adequate procedure for correcting Rb interference on ⁸⁷Sr using synthesized standards and natural samples. The in situ data obtained in this study indicate the feasibility of the LA-MC-ICPMS technique for measuring the Rb–Sr isotopic composition of high-Rb/Sr materials.

Materials

This study used glass standard reference materials (SRMs) provided by the National Institute of Standards and Technology of the USA (NIST), modern shark teeth, and plagioclase crystals separated from a Quaternary basalt on Jeju Island, Korea.

NIST SRMs 610, 612, and 616 were selected for Rb–Sr isotopic analyses in this study. Their base glass was fused from a mixture of quartz sand, alumina, soda ash, and calcium carbonate (72 wt% SiO₂, 2 wt% Al₂O₃, 14 wt% Na₂O, and 12 wt% CaO) (Kane 1998). These SRMs contain many trace elements with concentrations that are relatively uniform and sufficiently high for chemical and isotopic calibration (ca. 400 μg/g for SRM 610, ca. 40 μg/g for SRM 612, ≤ 40 μg/g for SRM 616). Their chemical and Sr-Nd-Pb isotopic compositions have been measured in many laboratories to evaluate micro-homogeneity in glass samples and constrain best reference values (e.g., Pearce et al. 1997; Rocholl et al. 1997; Woodhead and Hergt 2001; Jochum et al. 2011). Overall means of Sr concentrations are 515.5 μg/g, 78.4 μg/g, and 41.72 μg/g for SRM 610, SRM 612, and SRM 616, respectively (Jochum et al. 2011).

The teeth of two shark species, the bull shark (Carcharhinus leucas) and spot-tail shark (Carcharhinus sorrah), were purchased during the Denver Gem and Mineral Show in 2018. The enameloid (external tooth layer) of the shark teeth consists typically of fluoroapatite (Ca₅(PO₄)₃F) (Kemp and Park 1974) with stoichiometric concentrations of ca. 40 wt% Ca and ca. 18 wt% P. Such teeth are expected to have the Sr isotopic composition of modern seawater (⁸⁷Sr/⁸⁶Sr = 0.70918 ± 0.00001; Faure and Mensing 2005).

Plagioclase crystals were extracted from a Quaternary basalt outcrop on Hwasun Beach, Jeju Island, Korea (33° 14′ 10.21″ N, 126° 20′ 18.10″ E). The length of the plagioclase phenocrysts was approximately 1 cm.

Methods

Solution and laser ablation-assisted Rb–Sr isotopic analyses, including sample preparation and mass spectrometry, were performed at the Korea Basic Science Institute Ochang Center. The instrument operating parameters of (LA)-MC-ICPMS are summarized in Table 1.

Table 1 (LA)-MC-ICPMS instrument operating parameters

Solution ICPMS

Solution ICPMS was carried out for the shark teeth and Jeju plagioclase. Fragments (~ 40 mg) of tooth enameloid were digested overnight in 8 mL of 8 M HNO₃ at 160 °C, then dried and stored in 10 mL of 2 M HNO₃. The sample solutions were diluted 20,000 times with 2% HNO₃. The concentrations of Rb and Sr in the teeth were measured using an X-series quadrupole ICPMS (Thermo Fisher Scientific). Plagioclase crystals (~ 10 mg) were digested overnight in 3 mL of mixed acid (HF:HNO₃:HClO₄ = 10:3:1) at 160 °C and then dried and redissolved in 2.5 N HCl. Chemical separation of Sr was performed twice using ion-exchange chromatography with Eichrom Sr-spec resin (100–150 μm) for the shark teeth and Bio-Rad AG50W-X8 resin (200–400 mesh) for the Jeju plagioclase. Sample digestion and Sr separation were conducted in a clean room equipped with laminar flow benches. The total Sr in the procedural blank was less than 200 pg.

Strontium isotopic compositions of the shark teeth and Jeju plagioclase were measured with a Neptune MC-ICPMS and a Nu Plasma II MC-ICPMS instrument, respectively. Strontium isotope data were acquired in static mode (n = 20). The IMF was exponentially normalized to ⁸⁶Sr/⁸⁸Sr = 0.1194. Isobaric interferences from Kr and Rb were negligible. Replicate analyses of NBS 987 with the Neptune and Nu Plasma II MC-ICPMS instruments yielded average ⁸⁷Sr/⁸⁶Sr ratios of 0.710283 ± 0.000007 [2 standard errors (SE), n = 6] and 0.710259 ± 0.000012 (2 SE, n = 18), respectively. Errors of isotopic ratios in this study denote 2 SE unless otherwise stated. ⁸⁷Sr/⁸⁶Sr data were corrected for interlaboratory bias by adjusting them to the recommended NBS987 value (0.710248; Thirlwall 1991).

Laser ablation MC-ICPMS

Fragments of the shark teeth were sonicated in distilled water for 15 min and then dried in an oven at 60 °C. The NIST SRMs were washed with ethanol. The dried teeth and SRMs were mounted in epoxy and ground to expose the sample surface. Plagioclase phenocrysts in polished thin sections (0.1 mm thickness) were used for LA-MC-ICPMS analysis.

The Rb–Sr isotopic measurements were performed with a Nu Plasma II MC-ICPMS connected to an NWR193-nm ArF excimer laser ablation system. The LA-MC-ICPMS measurements consisted of five analytical sessions. SRM 610 was analyzed in all sessions but SRM 612 and SRM 616 were analyzed in session 1 only. The shark teeth were analyzed in sessions 1–4, and the Jeju plagioclase was measured in session 4. The ThO⁺/Th⁺ (248/232) ratio was measured using path ablation mode before the beginning of each analytical session. Three Faraday detectors (L1, H3, and H5) were placed at half mass positions to correct the isobaric interferences from doubly charged rare earth elements (REEs). The laser beam was focused to a spot diameter of ~ 150 μm (sessions 1, 3, 4, 5) or ~ 100 μm (session 2), and the intensities of mass 88 for SRM 610 ranged from ca. 5 to 1 V. Raw data (ca. 80–40% in the middle of the total 150 cycles) were processed using an Excel spreadsheet or Iolite 2.5 within Igor Pro 6.3.5.5 software (Paton et al. 2011).

Results and discussion

Solution ICPMS

The Sr concentrations of the shark teeth were ~ 1600 μg/g, whereas the Rb concentrations were beneath the detection limit (0.1 μg/g). The enameloid of bull shark and spot-tail shark teeth yielded ⁸⁷Sr/⁸⁶Sr ratios of 0.709205 ± 0.000035 and 0.709170 ± 0.000025, respectively. These results were highly consistent with the value of modern seawater (⁸⁷Sr/⁸⁶Sr = 0.70918 ± 0.00001; Faure and Mensing 2005). Triplicate analyses for the Jeju plagioclase yielded average ⁸⁷Sr/⁸⁶Sr ratios of 0.704151 ± 0.000026, 0.704139 ± 0.000024, and 0.704187 ± 0.000024.

Laser ablation MC-ICPMS

Isobaric interferences on Sr isotopes may arise from Ca dimers and Ca argides, Fe dioxides, Ga and Zn oxides, doubly charged REEs and Hf, and singly charged Kr and Rb (Ramos et al. 2004; Vroon et al. 2008). Among them, critical interferences from Kr, doubly charged Er and Yb ions, and Rb are discussed below. The other molecular species have only a limited impact on Sr isotope ratios (Ramos et al. 2004).

Gas blank and REE²⁺ interference

Kr is usually included in Ar and He gas. The signals of Kr isotopes were monitored for 300 s without ablating material before the beginning of each analytical session. The observed ⁸⁴Kr intensities were 0.26 mV (session 1), 1.60 mV (session 2), 0.08 mV (session 3), 0.004 mV (session 4), and 5.4 mV (session 5). The fluctuation of Kr signal might be related to the change of ArF and liquid Ar gas. Kr blanks were subtracted from peak intensities at masses 83, 84, and 86.

Doubly charged Er (¹⁶⁸Er²⁺ and ¹⁷⁰Er²⁺) and Yb (¹⁶⁸Yb²⁺, ¹⁷⁰Yb²⁺, ¹⁷²Yb²⁺, ¹⁷⁴Yb²⁺, and ¹⁷⁶Yb²⁺) ions overlap at masses 84, 85, 86, 87, and 88. Peak intensities at masses 83, 85.5, and 86.5 measured for SRM 610 were in the range of 10–3 mV when the 88 peak intensity was around 5 V (i.e., session 5). We confirmed that the Kr-stripped ¹⁶⁶Er²⁺ intensity at mass 83 corresponded to the value calculated from the intensity at mass 83.5 (¹⁶⁷Er²⁺) and the Er isotopic composition reported in the literature (¹⁶⁶Er, 33.5027%; ¹⁶⁷Er, 22.8691%; Chang et al. 1998). We also confirmed that the ¹⁷³Yb²⁺/¹⁷¹Yb²⁺ ratio measured at masses 86.5 and 85.5 in each analytical session agreed with the recommended value in the literature (1.132338 ± 0.000050; Vervoort et al. 2004) within errors (for example, session 1 ¹⁷³Yb²⁺/¹⁷¹Yb²⁺ = 1.13 ± 0.02). These correspondences indicate that the Kr and REE²⁺ intensities were measured correctly.

The contributions of Er and Yb to Rb and Sr isotopes were calculated from the measured intensities at masses 83.5 (¹⁶⁷Er²⁺) and 86.5 (¹⁷³Yb²⁺) (Eq. (1), “I” denotes a peak intensity) and the isotopic compositions and ratios of Er and Yb (see Table 2). The IMF was not considered in this calculation but was certainly insignificant at the level of REE²⁺ in the samples and standards analyzed in this study.

Table 2 Er and Yb isotopic compositions and ratios reported in the literature

$$ {\displaystyle \begin{array}{l}{}^{84}\mathrm{S}\mathrm{r}={}^{84}\mathrm{t}\mathrm{otal}\hbox{-} {I}_{83.5}\times \frac{0.269784}{0.228691}\kern0.24em \left({}^{168}\mathrm{E}{\mathrm{r}}^{2+}\right)-{I}_{86.5}\times \frac{0.008876}{1.132338}\kern0.24em \left({}^{168}\mathrm{Y}{\mathrm{b}}^{2+}\right)\\ {}{}^{85}\mathrm{R}\mathrm{b}={}^{85}\mathrm{t}\mathrm{otal}\hbox{-} {I}_{83.5}\times \frac{0.149102}{0.228691}\;\left({}^{170}\mathrm{E}{\mathrm{r}}^{2+}\right)-{I}_{86.5}\times \frac{0.212562}{1.132338}\kern0.24em \left({}^{170}\mathrm{Y}{\mathrm{b}}^{2+}\right)\\ {}{}^{86}\mathrm{S}\mathrm{r}={}^{86}\mathrm{t}\mathrm{otal}\hbox{-} {I}_{86.5}\times \frac{1.531736}{1.132338}\kern0.24em \left({}^{172}\mathrm{Y}{\mathrm{b}}^{2+}\right)\\ {}{}^{87}\left(\mathrm{Rb}+\mathrm{Sr}\right)={}^{87}\mathrm{t}\mathrm{otal}\hbox{-} {I}_{86.5}\times \frac{1.531736}{1.132338\times 0.68321}\;\left({}^{174}\mathrm{Y}{\mathrm{b}}^{2+}\right)\\ {}{}^{88}\mathrm{S}\mathrm{r}={}^{88}\mathrm{t}\mathrm{otal}\hbox{-} {I}_{86.5}\times 0.796310\;\left({}^{176}\mathrm{Y}{\mathrm{b}}^{2+}\right)\end{array}} $$

(1)

Rb interference

Rubidium limits the types of samples that can be analyzed for Sr isotopic composition without chemical purification. Rb can be removed by “on-filament chemistry” in TIMS, which is not available in ICPMS. The mass resolution required for the separation of ⁸⁷Rb and ⁸⁷Sr masses (M/ΔM = ca. 296,000) cannot be achieved by a normal TIMS or ICPMS (M/ΔM = ca. 500).

The main problem of Rb interference correction arises from the IMF; the lighter and heavier isotopes of an element behave differently during the course of mass spectrometric measurement. Each element has its own mass bias factor. For Sr, the assumed ratio of ⁸⁶Sr/⁸⁸Sr (= 0.1194) is used for the correction of the IMF, but this internal normalization cannot be applied for Rb because this element consists of only two isotopes.

During ICPMS measurement, isotopic fractionation of two elements of similar mass should be similar, albeit not identical (White et al. 2000). Therefore, for measurement of the ⁸⁷Sr/⁸⁶Sr ratio for low-Rb/Sr materials such as biogenic apatite and plagioclase, it has been assumed that Rb and Sr isotopes behave in the same way during LA-ICPMS analysis (Ramos et al. 2004; Vroon et al. 2008; Willmes et al. 2016). After Kr and REE²⁺ interference correction, the measured ⁸⁷Rb/⁸⁵Rb ratios of NIST SRM 616, Jeju plagioclase, and shark teeth were calculated using the IUPAC ⁸⁷Rb/⁸⁵Rb ratio (= 0.3856; Meija et al. 2016) and mass bias factor (β) of Sr calculated exponentially from measured ⁸⁶Sr/⁸⁸Sr and 0.1194. Then, the ⁸⁷Sr peak intensity was calculated by subtracting the ⁸⁷Rb contribution from the intensity of mass 87. As shown in Fig. 1, the average ⁸⁷Sr/⁸⁶Sr (0.7083 ± 0.0003, n = 14) of SRM 616 closely matched that of the certificate (0.7080 ± 0.0002; Wise and Watters 2012), despite its relatively low Sr concentration (41.72 μg/g). The ⁸⁷Sr/⁸⁶Sr ratio (average = 0.70419 ± 0.00003, n = 32) of Jeju plagioclase was consistent with the solution MC-ICPMS result (0.704187–0.704139). These results indicate that β (Sr) can be used for Rb correction for low-Rb/Sr materials.

Fig. 1

⁸⁷Sr/⁸⁶Sr ratios obtained via LA-MC-ICPMS for NIST SRM 616 (a) and Jeju plagioclase (b) assuming equal mass bias factors for Rb and Sr. Vertical error bars denote 2 standard errors. Gray dotted lines represent average LA-MC-ICPMS results. Red dashed lines represent the certified value (a, 0.7080 ± 0.0002; Wise and Watters 2012) and the solution MC-ICPMS result (b, 0.704187–0.704139)

Polyatomic molecules (⁴⁰Ar³¹P¹⁶O or ⁴⁰Ca³¹P¹⁶O) may exert isobaric interference on mass 87 during the ICPMS analysis of phosphate material (Horstwood et al. 2008; Lewis et al. 2014; Müller and Anczkiewicz 2016; Willmes et al. 2016). The ThO⁺/Th⁺ ratio is typically used as an indicator of oxide formation, because ThO⁺ is the strongest oxide product within the plasma (Kent and Ungerer 2005). The ThO⁺/Th⁺ ratio measured in each session varied from 0.77 to 0.16%. The enameloid of the shark teeth yielded average ⁸⁷Sr/⁸⁶Sr ratios of 0.70929 ± 0.00001 (session 1, n = 11), 0.70922 ± 0.00002 (session 2, n = 19), 0.70921 ± 0.00002 (session 3, n = 16), and 0.70922 ± 0.00002 (session 4, n = 21) (Fig. 2). These ratios approached the modern seawater value (0.70918; Faure and Mensing 2005) and solution MC-ICPMS results (0.709205 ± 0.000035, bull shark; 0.709170 ± 0.000025, spot-tail shark). It is noted that the LA-MC-ICPMS ⁸⁷Sr/⁸⁶Sr ratio was highest in session 1, in which ThO⁺/Th⁺ was also highest (0.77%). However, small ⁸⁷Sr/⁸⁶Sr differences require additional studies to verify the reproducibility of this effect. In fact, it has been reported that polyatomic interference is negligible for samples with Sr contents higher than 1900 μg/g (Simonetti et al. 2008). The shark teeth analyzed in this study are sufficiently high in Sr (~ 1600 μg/g).

Fig. 2

⁸⁷Sr/⁸⁶Sr ratios obtained via LA-MC-ICPMS for the shark teeth assuming equal mass bias factors for Rb and Sr. Vertical error bars denote 2 standard errors. The dashed line represents the modern seawater value (⁸⁷Sr/⁸⁶Sr = 0.70918; Faure and Mensing 2005). The ThO⁺/Th⁺ ratios measured before the beginning of each analytical session are marked as thick gray lines

The ⁸⁵Rb/⁸⁶Sr ratios of glass SRMs measured during laser ablation varied inconsistently (Fig. 3), manifesting that the IMF of Rb and Sr isotopes occurred differently. The employment of β (Sr) as β (Rb) yielded widely variable ⁸⁷Sr/⁸⁶Sr ratios for SRM 610 and 612. The averages for SRM 610 (0.7138 ± 0.0011, n = 81) and SRM 612 (0.7116 ± 0.0004, n = 15) deviated substantially from the recommended values.

Fig. 3

Variations of ⁸⁵Rb/⁸⁶Sr ratios measured for SRM 610 during LA-MC-ICPMS sessions. The dashed line represents the recommended ⁸⁵Rb/⁸⁶Sr ratio (= 6.196; Jochum et al. 2011)

We calculated β (Rb) using known ⁸⁷Sr/⁸⁶Sr ratios of standard materials as described in Eq. (2), where “m” and “c” denote the measured and corrected values, respectively, and “M” indicates atomic weight. The ⁸⁷Rb/⁸⁵Rb ratio of 0.3856 was taken from Meija et al. (2016).

$$ {\displaystyle \begin{array}{c}\left(\frac{{}^{87}\mathrm{S}\mathrm{r}}{{}^{86}\mathrm{S}\mathrm{r}}\right)\underset{m}{}=\left(\frac{{}^{87}\mathrm{S}\mathrm{r}}{{}^{86}\mathrm{S}\mathrm{r}}\right)\underset{c}{}\times \left(\frac{M_{86\;\mathrm{strontium}}}{M_{87\mathrm{strontium}}}\right)\overset{\beta }{}\\ {}{}^{87}\mathrm{R}\mathrm{b}\underset{m}{}=\mathrm{Intensity}\underset{87}{}-\left(\frac{{}^{87}\mathrm{S}\mathrm{r}}{{}^{86}\mathrm{S}\mathrm{r}}\right)\underset{m}{}\times {}^{86}\mathrm{S}\mathrm{r}\underset{m}{}\\ {}\beta\;\left(\mathrm{Rb}\right)=\frac{\ln \left[\frac{0.3856}{\left(\frac{{}^{87}\mathrm{R}\mathrm{b}}{{}^{85}\mathrm{R}\mathrm{b}}\right)\underset{m}{}}\right]}{\ln \left(\frac{M_{87\;\mathrm{r}\mathrm{ubidium}}}{M_{85\;\mathrm{r}\mathrm{ubidium}}}\right)}\end{array}} $$

(2)

The calculated β (Rb) and β (Sr) for SRM 610 and SRM 612 in session 1 are plotted in Fig. 4. As shown here, there were weak to moderate correlations between β (Rb) and β (Sr). The correlation coefficient (R²) and the difference between β (Sr) and β (Rb) calculated for each analytical session are summarized graphically in Fig. 5. Spot-by-spot data and regression parameters are listed in Table S1. The R² values of NIST SRM 610 varied significantly from 0.74 to 0.26 (session 1, n = 14), 0.57 to 0.04 (session 2, n = 23), 0.58 to 0.11 (session 3, n = 17), 0.71 to 0.17 (session 4, n = 17), and 0.61 to 0.29 (session 5, n = 10). This was also true for SRM 612 (R² = 0.36–0.02, n = 15). As displayed in Fig. 5, β (Sr) was consistently higher than β (Rb), except for data obtained in session 2.

Fig. 4

Plots of β (Rb) versus β (Sr) calculated from NIST SRM data for analytical session 1 of LA-MC-ICPMS. Data for each analyzed spot are shown in different colors

Fig. 5

R² values and differences between β (Sr) and β (Rb) [Δ_β(Sr−Rb)] calculated from LA-MC-ICPMS data for NIST SRMs

In summary, Rb and Sr isotopes behaved differently during LA-MC-ICPMS but there was a correlation (albeit not strong) between the mass bias factors of these elements.

Bracketing calibration

The correlation between the mass bias factors of Rb and Sr led us to apply the standard bracketing method (Albarède and Beard 2004) to measure ⁸⁷Sr/⁸⁶Sr and ⁸⁵Rb/⁸⁶Sr ratios. First, β (Rb) was interpolated from the β (Rb)–β (Sr) correlation observed before and after each measurement. Then, measured ⁸⁷Rb/⁸⁵Rb was exponentially derived from the interpolated β (Rb) and IUPAC ⁸⁷Rb/⁸⁵Rb (= 0.3856, Meija et al. 2016), and the ⁸⁷Rb contribution was subtracted from the intensity of mass 87. Finally, the ⁸⁷Sr/⁸⁶Sr ratio was calculated from the Rb-corrected ⁸⁷Sr/⁸⁶Sr and β (Sr). The corrected ⁸⁷Sr/⁸⁶Sr ratios of the NIST SRMs are shown in Fig. 6. The mean of all ⁸⁷Sr/⁸⁶Sr ratios for SRM 610 (0.70986 ± 0.00017, n = 71) was consistent with the recommended value (0.709699 ± 0.000018; Woodhead and Hergt 2001) within an acceptable error range. The ⁸⁵Rb/⁸⁶Sr ratios calculated using this bracketing protocol ranged from 6.479 to 5.739, with an average of 6.186 ± 0.027 (n = 71), which coincides with the recommended value (6.196; Jochum et al. 2011). Average values of SRM 612 were 0.70899 ± 0.00038 for ⁸⁷Sr/⁸⁶Sr and 3.001 ± 0.035 for ⁸⁵Rb/⁸⁶Sr (n = 13), which also agree with the recommended values (⁸⁷Sr/⁸⁶Sr = 0.709063 ± 0.000020, Woodhead and Hergt 2001; ⁸⁵Rb/⁸⁶Sr = 3.005, Jochum et al. 2011). These results suggest the possibility that LA-MC-ICPMS can yield reliable Rb–Sr isotope results for high-Rb/Sr materials using the correlation between β (Rb) and β (Sr). It is noted that the analytical strategy proposed in this study is different from the bracketing method described in previous Sr isotopic works (McCulloch et al. 2005; Jackson and Hart 2006), where the measured ⁸⁵Rb/⁸⁷Rb of bracketing standard was externally used to correct the mass bias of Rb in samples.

Fig. 6

⁸⁷Sr/⁸⁶Sr and ⁸⁵Rb/⁸⁶Sr ratios determined with the standard bracketing method. Vertical error bars denote 2 standard errors. Total average ratios are marked as gray dotted lines. Red dashed lines represent recommended values of ⁸⁷Sr/⁸⁶Sr (Woodhead and Hergt 2001) and ⁸⁵Rb/⁸⁶Sr (Jochum et al. 2011)

Conclusions

• (1) After the Kr and REE²⁺ correction, the ⁸⁷Sr/⁸⁶Sr ratios of low-Rb/Sr materials (NIST SRM 616, Jeju plagioclase, and shark teeth) were measured accurately by assuming that Rb and Sr isotopes behave in the same way during LA-MC-ICPMS. During measurements of the shark teeth, polyatomic isobaric interference on mass 87 was seemingly insignificant.

• (2) Use of the Sr mass bias factor for the correction of Rb interference yielded highly variable and inaccurate ⁸⁷Sr/⁸⁶Sr ratios for high-Rb/Sr materials such as NIST SRM 610 and SRM 612. The mass bias factor of Rb was calculated from the recommended ⁸⁷Sr/⁸⁶Sr ratios of these SRMs. There were weak to moderate correlations between the mass bias factors of Rb and Sr. Reliable ⁸⁷Sr/⁸⁶Sr and ⁸⁵Rb/⁸⁶Sr results were obtained using the interpolated mass bias factor of Rb calculated by the standard bracketing method.

• (3) This study showed that the Rb–Sr isotopic composition of high-Rb/Sr materials can be measured accurately using LA-MC-ICPMS by monitoring the IMF of Rb and Sr isotopes and applying the standard bracketing method.