Two-point normalization for reducing inter-laboratory discrepancies in δ17O, δ18O, and Δ′17O of reference silicates

The δ17O and δ18O values of a number of terrestrial minerals and rocks have been determined using laser fluorination method worldwide. For the comprehensive and congruous interpretation of oxygen isotope data, the δ-values should be normalized by the two-point method (i.e., the VSMOW-SLAP scale) to eliminate inter-laboratory bias. In this study, the δ17O and δ18O values of VSMOW and SLAP were measured to calibrate our laboratory working standard O2 gas. The O2 gas liberated from the water samples was purified using the preparation line normally employed for solid samples, and analyzed by the same mass spectrometer. From the analyses of VSMOW and SLAP, the oxygen isotope compositions of the international silicate standards (UWG2 garnet, NBS28 quartz, and San Carlos olivine) were normalized to the VSMOW-SLAP scale (two-point calibration), and then the Δ′17O values were determined. Using the δ-values obtained in this way, the inter-laboratory discrepancy of the δ17O and δ18O results of the silicate standards could be reduced. The VSMOW-SLAP scaling for δ17O and δ18O analysis of silicates provides the most effective way to obtain accurate and precise data. In reporting the Δ′17O values, it is important to make the choice of the reference fractionation line into account because the Δ′17O value is quite variable owing to the slope and y-intercept of the linear relation of the δ-values. The reference fractionation line obtained from the measurement of the low- and high-δ18O reference silicates would help to compare ∆′17O values. We confirmed that the ∆′17O results of the international silicate standards based on the two-point silicate reference line were consistent with the results from other laboratories.


Introduction
Oxygen isotopic variations of rocks and minerals have been used in many fields of geo-and cosmochemistry. For the oxygen isotopic analysis of silicates, a laser fluorination method with dual-inlet mass spectrometry has been used for three decades, thereby contributing to the studies of terrestrial and extraterrestrial materials (Eiler 2001;Greenwood et al. 2017;Miller et al. 1999;Miller 2002;Sharp 1990;Spicuzza et al. 1998;Spicuzza et al. 2007). The oxygen isotope ratios of unknown samples are reported in delta (δ)notation relative to the primary reference material, i.e., Vienna Standard Mean Ocean Water (VSMOW; Craig 1961). Many laboratories have calibrated their working standard O 2 gas against the VSMOW scale (Greenwood et al. 2018; Kusakabe and Matsuhisa 2008;Levin et al. 2014;Pack et al. 2016;Tanaka and Nakamura 2013). However, owing to different analytical settings, equipment, and calibration methods, discrepancies in the isotopic results of a given sample between laboratories have been noticed. Thus, it is necessary to reduce the potential analytical errors of each laboratory by introducing multiple reference materials. For water analysis, VSMOW and Standard Light Antarctica Precipitation (SLAP) are commonly used because the isotopic difference between VSMOW and SLAP is well established (Barkan and Luz 2005;Jabeen and Kusakabe 1997;Kusakabe and Matsuhisa 2008;Lin et al. 2010;Schoenemann et al. 2013). To achieve high precision and accuracy in the oxygen isotopic analysis of silicates, it is desirable to measure the oxygen isotope ratios of the silicates, VSMOW, and SLAP under the same analytical conditions, and then normalize the analytical results in the VSMOW-SLAP scale. However, some laboratories have indirectly calibrated their working standard O 2 gas using reference silicate standards only to which δ 18 O values relative to VSMOW have been allocated (Ghoshmaulik et al. 2020;Levin et al. 2014;Miller et al. 2020;Young et al. 2014Young et al. , 2016. This indirect calibration induces an inevitable inter-laboratory variability in the δ-values, because no consensus of δvalues for the silicate standards has been attained, and natural mineral samples may be isotopically heterogeneous. Recently, precise δ 17 O values of reference silicates have been reported (Miller et al. 2020;Wostbrock et al. 2020). The linear relationship between δ 17 O and δ 18 O, defined as δ 17 O = 0.52 × δ 18 O, has been known to follow a theoretical mass-dependent fractionation process (Matsuhisa et al. 1978). Since the development of the laser-based high-precision analytical method for three-oxygen isotopes, researchers have become interested in small variations in the δ 17 O values of terrestrial silicates (Miller et al. 2020;Pack et al. 2016;Sharp et al. 2018;Tanaka and Nakamura 2013;Wostbrock et al. 2020). The small deviation of δ 17 O is usually expressed as a vertical offset from the reference fractionation line, or Δ′ 17 O. Thus, it is critical to evaluate how the reference line is obtained, as a small variability of the line arising from analytical systems used by different groups of people can induce a noticeable difference in Δ′ 17 O.
Here, we present δ 17 O and δ 18 O values of VSMOW and SLAP that were determined by the conventional fluorination method that is used for the silicate analysis. Based on the standard water analyses, we normalized the oxygen isotope values of silicates relative to the VSMOW-SLAP scale. We propose that the VSMOW-SLAP normalization can reduce interlaboratory differences in the δ 17 O and δ 18 O values of silicates. In addition, we support that a 2-point silicate reference line determined from low-and highδ 18 O silicates can be used for inter-laboratory comparison of the Δ′ 17 O. Consequently, a systematic evaluation of the oxygen isotope compositions of silicates is necessary for an accurate inter-laboratory comparison.

Experimental method
After VSMOW was exhausted, the International Atomic Energy Agency (IAEA) has prepared VSMOW2, which is very close to the VSMOW in oxygen isotopic composition (Lin et al. 2010). Another international standard, SLAP2 (Standard Light Antarctic Precipitation 2), was also prepared by the IAEA to replace the SLAP which was also exhausted. The VSMOW2 and SLAP2 are isotopically indistinguishable from VSMOW and SLAP, respectively (Lin et al. 2010). In this work, we used VSMOW and SLAP as synonymous of VSMOW2 and SLAP2, respectively. To report the oxygen isotopic compositions of rocks and minerals relative to VSMOW, a working standard O 2 gas has to be calibrated by direct comparison with O 2 extracted from VSMOW. We decomposed the water by fluorination in a Ni reaction tube (Fig. 1). Two microliters of water sample was introduced into the reaction tube through a septum using a micro-syringe (Hamilton , USA). The water was rapidly condensed in the evacuated Ni reaction tube at liquid nitrogen temperature and then reacted with a sufficient amount of BrF 5 at 200°C for 60 min. The product gases were passed through the purification line and purified using the same procedures as those followed for the silicate samples. The oxygen isotopic analysis of both the silicates and water was carried out at the Korea Polar Research Institute (KOPRI). The detailed analytical methods are described in Kim et al. (2019).

Analysis of standard waters and VSMOW-SLAP normalization
Oxygen isotope ratios are conventionally reported as relative deviations from the standard water VSMOW in the delta notation δ 16 O, x = 17 or 18. The δ 17 O and δ 18 O values of VSMOW are zero by definition. In order to report oxygen isotopic ratios of a sample in δ-notation, the measured raw δ-values need to be converted to the VSMOW scale. Normalization is achieved by direct determination of the δ-value of the working standard O 2 gas against that of VSMOW (Kusakabe and Matsuhisa 2008;Pack et al. 2016;Tanaka and Nakamura 2013). The results of the international standard waters are summarized in Table 1. The δ 17 O and δ 18 O values of VSMOW are zero by definition and the standard deviations were ± 0.030‰ and ± 0.056‰, respectively (n = 11) (Fig. 2 a). We obtained the oxygen isotopic composition of VSMOWnormalized SLAP as δ 17 O = − 29.148 ± 0.082‰ and δ 18 O = −54.477 ± 0.154‰ (n = 8) (Fig. 2 b). The disagreement between the measured δ 18 O value and the accepted value of − 55.5‰ strongly suggests the necessity of normalization of oxygen isotope data (Coplen 1988;Gonfiantini 1978). The difference between the measured and allocated values of SLAP is likely due to unknown isotopic fractionation during analytical operation and the system we used.
To ensure the accuracy of the isotopic results mainly for water samples, it is recommended to perform a 2-point normalization using VSMOW and SLAP (Coplen 1988;Gonfiantini 1978). By introducing the VSMOW-SLAP normalization, isotopic variations of a given sample that may arise from interlaboratory differences in experimental settings and the use of different mass spectrometers can be minimized. There is, however, a problem when applying the normalization, as a consensus has not been attained for the 17 O /16 O ratio of SLAP (Barkan and Luz 2005;Jabeen and Kusakabe 1997;Kusakabe and Matsuhisa 2008;Schoenemann et al. 2013;Wostbrock et al. 2020). Although published δ 17 O values of SLAP relative to VSMOW range from − 28.58 to − 29.74‰ (Jabeen and Kusakabe 1997;Kusakabe and Matsuhisa 2008;Pack et al. 2016;Wostbrock et al. 2020), 17 Oexcess values, or Δ 17 O (i.e., deviations of the δ 17 O value from the global meteoric water line), for the published SLAP were close to zero (Schoenemann et al. 2013). The oxygen isotope data of meteoric water indicate that the global meteoric waters define a linear line with a slope (λ) of 0.528 in the plot of ln(δ 17 O + 1) vs. ln(δ 18 O + 1) (Kusakabe and Matsuhisa 2008;Luz and Barkan 2010;Schoenemann et al. 2013;Wostbrock et al. 2020 (Miller 2002): where λ RL is the slope of the reference fractionation line in the linearized three-oxygen isotope plot and γ RL is a y-axis offset of the line. The theoretical slope of mass-dependent fractionation line under thermodynamic equilibrium is 0.5305 (Matsuhisa et al. 1978;Wiechert et al. 2004). According to the oxygen isotope data of terrestrial rocks and minerals, the slope of the ln(1 + δ 17 O) versus ln(1 + δ 18 O) plot (i.e., the empirical fractionation line) is slightly smaller (λ = 0.524 to 0.528) than the theoretical value of 0.5305 (Ahn et al. 2012;Greenwood et al. 2018;Kusakabe and Matsuhisa 2008;Miller 2002;Miller et al. 2020;Spicuzza et al. 2007;Tanaka and Nakamura 2013). In our previous work, Kim et al.   supplementary Table S1. The UWG2 garnet, NBS28 quartz, and San Carlos olivine have been widely used in laser fluorination oxygen isotope laboratories and can be used for inter-laboratory comparison. The recommended δ 18 O values of UWG2 garnet and NBS28 quartz are 5.80 and 9.57‰ respectively (Hut 1987;Valley et al. 1995); however, no consensus has been reached yet on the San Carlos olivine. The δ 18 O values of the San Carlos olivine vary widely compared to other natural mineral standards owing to its isotopic heterogeneity (Miller et al. 2020;Starkey et al. 2016). Compilation of oxygen isotope data for the international silicate samples, i.e., UWG2 garnet, NBS28 quartz, and San Carlos olivine, over the last two decades shows a fairly wide variation in δ 18 O values. They range from 5.40 to 6.04‰ for UWG2 garnet, 8.69 to 9.75‰ for Table 1 Individual standard water data of this study NBS28 quartz, and 4.64 to 5.58‰ for San Carlos olivine as compiled in Table 3. The inter-laboratory reproducibilities which refer to the standard deviations of the compiled δ 18 O values relative to VSMOW are 0.17‰ for UWG2 garnet, 0.30‰ for NBS28 quartz, and 0.21‰ for San Carlos olivine (Fig. 3 a-c). The ranges and reproducibilities of δ 17 O for the international silicates are approximately one half of the δ 18 O results because the oxygen isotopes normally follow mass-dependent rules (Fig. 4 a- (Greenwood et al. 2018). Unlike the standard water (i.e., VSMOW) which is strictly homogeneous by its own nature, an isotopic heterogeneity of the natural mineral samples could cause analytical variability. In particular, the δ 17 O values of silicate standards are still in poor agreement.
We have compiled the published oxygen isotope data of UWG2 garnet, NBS28 quartz, and San Carlos olivine on the VSMOW-SLAP scale (Table 3). In some cases, the measured δ 18 O values of SLAP were so close to the value recommended by the IAEA that the VSMOW-SLAP normalization was not applied to the published    Fig. 5 a-c). The large variations may have arisen from the choice of different λ RL and γ RL . The literature values were obtained by assigning the slope and y-intercept of the linear equation based on the calculation of equilibrium oxygen isotope fractionation (Pack and Herwartz 2014;Wiechert et al. 2004), the measurements of arbitral silicate samples (Ahn et al. 2012;Kim et al. 2019;Kusakabe and Matsuhisa 2008;Miller 2002;Miller et al. 2020;Starkey et al. 2016;Tanaka and Nakamura 2013), and standard waters Sharp et al. 2016;Wostbrock et al. 2020;Young et al. 2014).
Recently, Miller et al. (2020) proposed an alternative The different sets of λ RL and γ RL values may induce a misleading for the inter-laboratory comparison of Δ′ 17 O. Therefore, we recalculated Δ′ 17 O values for the international silicate standards using four reference lines as follows: (i) λ RL = 0.5305 and γ RL = 0 for the equilibrium fractionation line; (ii) λ RL = 0.528 and γ RL = 0 for the VSMOW-SLAP line; (iii) λ RL = 0.5278 and γ RL = −

Conclusions
We determined the oxygen isotopic compositions of international standard waters (VSMOW and SLAP) and reference silicates (UWG2 garnet, NBS28 quartz, and San Carlos olivine) by fluorination using the same preparation line and mass spectrometer. According to the resulting oxygen isotope data of the above international reference silicates, we conclude that high precision δ 17 O and δ 18 O determination of silicates requires a 2-point calibration or VSMOW-SLAP scaling recommended by the IAEA for the analysis of water isotopes. Using this calibration, we can avoid instrumental bias and systematic differences between laboratories.