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Two-point normalization for reducing inter-laboratory discrepancies in δ17O, δ18O, and Δ17O 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 Δ17O 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 Δ17O values, it is important to make the choice of the reference fractionation line into account because the Δ17O 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.


Oxygen isotopic variations of rocks and minerals have been used in many fields of geo- and cosmo-chemistry. 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 O2 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 O2 gas using reference silicate standards only to which δ18O values relative to VSMOW have been allocated (Ghoshmaulik et al. 2020; Levin et al. 2014; Miller et al. 2020; Young et al. 2014, 2016). This indirect calibration induces an inevitable inter-laboratory variability in the δ-values, because no consensus of δ-values for the silicate standards has been attained, and natural mineral samples may be isotopically heterogeneous.

Recently, precise δ17O values of reference silicates have been reported (Miller et al. 2020; Wostbrock et al. 2020). The linear relationship between δ17O and δ18O, defined as δ17O = 0.52 × δ18O, 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 δ17O 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 δ17O is usually expressed as a vertical offset from the reference fractionation line, or Δ17O. 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 Δ17O.

Here, we present δ17O and δ18O 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 inter-laboratory differences in the δ17O and δ18O values of silicates. In addition, we support that a 2-point silicate reference line determined from low- and high-δ18O silicates can be used for inter-laboratory comparison of the Δ17O. 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 O2 gas has to be calibrated by direct comparison with O2 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 BrF5 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).

Fig. 1

Schematic diagram of BrF5 introduction and water fluorination line modified from Kim et al. (2019). Two microliters of water was introduced into the vacuum line through a septum-inlet using a micro-syringe and then transferred in a Ni reaction tube with BrF5 at liquid nitrogen temperature. The reaction was run at 200 °C for 1 h.

Results and discussion

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 δxO = (Rxsample/RxVSMOW) − 1, where R = xO/16O, x = 17 or 18. The δ17O and δ18O 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 O2 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 δ17O and δ18O 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 VSMOW-normalized SLAP as δ17O = − 29.148 ± 0.082‰ and δ18O = −54.477 ± 0.154‰ (n = 8) (Fig. 2 b). The disagreement between the measured δ18O 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.

Table 1 Individual standard water data of this study
Fig. 2

Oxygen isotope compositions of a VSMOW and b SLAP. 3σ outliers are not included in the calculations of average and standard deviation. Solid gray lines indicate average values. Dashed gray lines display 1σ, 2σ, and 3σ standard deviations, respectively

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 inter-laboratory 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 17O/16O 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 δ17O 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), 17O-excess values, or Δ17O (i.e., deviations of the δ17O 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(δ17O + 1) vs. ln(δ18O + 1) (Kusakabe and Matsuhisa 2008; Luz and Barkan 2010; Schoenemann et al. 2013; Wostbrock et al. 2020). Therefore, we used a δ17O value of SLAP of − 29.698‰ calculated using \( {\delta}^{18}{\mathrm{O}}_{\mathrm{VSMOW}-\mathrm{SLAP}}^{\mathrm{assigned}} \) = − 55.5‰ and 17Oexcess = 0 (Schoenemann et al. 2013).

We used the following equation to obtain the VSMOW-SLAP normalized δ-values:

\( {\delta}^x{\mathrm{O}}_{\mathrm{sample}/\mathrm{VSMOW}-\mathrm{SLAP}}^{\mathrm{normalized}} \) = \( \exp \left[\ln \left({\delta}^x{\mathrm{O}}_{\mathrm{sample}/\mathrm{VSMOW}}^{\mathrm{measured}}+1\right)\frac{\ln \left({\delta}^x{\mathrm{O}}_{\mathrm{SLAP}/\mathrm{VSMOW}}^{\mathrm{assigned}}+1\right)}{\ln \left({\delta}^x{\mathrm{O}}_{\mathrm{SLAP}/\mathrm{VSMOW}}^{\mathrm{measured}}+1\right)}\right]-1 \) (1)

From the normalized δ17O and δ18O values, we report a Δ17O value which is the deviation of the 17O/16O ratio from the mass-dependent fractionation line defined by a linear function (Miller 2002):

Δ17O = ln(1 + δ17O) − λRL×(1 + δ18O) − γRL (2)

where λRL is the slope of the reference fractionation line in the linearized three-oxygen isotope plot and γRL 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 + δ17O) versus ln(1 + δ18O) 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. (2019) used λRL = 0.528 ± 0.020 and γRL = −0.040 ± 0.015 of the empirical fractionation line based on the data set for UWG2 garnet, NBS28 quartz, San Carlos olivine, basalt glass, and obsidian to calculate the Δ17O values. This empirical reference fractionation line was chosen to compare the Δ17O values determined from the reference lines based on a theoretical mass-dependent fractionation, meteoric waters, and two reference silicates as discussed in section “Δ17O of silicates”.

δ17O and δ18O values of the international silicate standards on the VSMOW-SLAP scale

We measured the δ17O and δ18O values of the silicate minerals using the laser fluorination system (Kim et al., 2019). Table 2 shows the results normalized by the VSMOW-SLAP scale. Details of individual sample weight, oxygen yield, and δ-values relative to working standard O2 gas are available in 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 δ18O 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 δ18O 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).

Table 2 δ17O and δ18O values of the waters and silicates measured in this study

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 δ18O values. They range from 5.40 to 6.04‰ for UWG2 garnet, 8.69 to 9.75‰ for 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 δ18O 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 δ17O for the international silicates are approximately one half of the δ18O results because the oxygen isotopes normally follow mass-dependent rules (Fig. 4 a–c). Variability of δ17O and δ18O values likely arises from an analytical problem that is specific to experimental procedures for water and silicate analyses at each laboratory, as well as the way in which the working standard O2 gas was calibrated against VSMOW. Several laboratories performed the calibration using the international silicate standards, such as UWG2 garnet (Levin et al., 2014; Miller et al., 2020), NBS28 quartz (Ghoshmaulik et al. 2020), and San Carlos olivine (Young et al., 2014, 2016) (Levin et al. 2014; Miller et al. 2020; Wostbrock et al. 2020; Young et al. 2016), or in some cases, atmospheric O2 (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 δ17O values of silicate standards are still in poor agreement.

Table 3 Literature data of δ17O and δ18O for the international silicate standards and normalization methods
Fig. 3

Comparison of published δ18O values relative to VSMOW (ac) and VSMOW-SLAP (ef) for international silicate standards

Fig. 4

Comparison of published δ17O values relative to VSMOW (ac) and VSMOW-SLAP (ef) for international silicate standards

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 δ18O values of SLAP were so close to the value recommended by the IAEA that the VSMOW-SLAP normalization was not applied to the published data (Pack and Herwartz 2014; Tanaka and Nakamura 2013; Wostbrock et al. 2020). In other words, their δ-values were regarded as already normalized to the VSMOW-SLAP scale. Nevertheless, if we apply the VSMOW-SLAP normalization to their published δ17O and δ18O values of international silicate standards, the reproducibility of the reported values improved: 0.07 and 0.12‰ for UWG2 garnet, 0.07 and 0.20‰ for NBS28 quartz, and 0.09 and 0.15‰ for San Carlos olivine (Fig. 3 e, f and Fig. 4 e, f). The improved statistical indicator of the VSMOW-SLAP normalized values supports that the normalization can avoid the isotopic shrinking or stretching induced by analytical procedures and systems, leading to the correct isotopic ratios of natural rocks and minerals. For water analysis, this practice has provided good agreement with the δ17O and δ18O values of the Greenland Ice Sheet Precipitation (GISP) (Schoenemann et al. 2013). Consequently, the reporting of the δ-values normalized on the VSMOW-SLAP scale of silicates is required in order to make a valid comparison of the oxygen isotope data produced in different laboratories.

Δ17O of silicates

In oxygen isotope geochemistry, only δ18O values are determined because δ17O values are simply derived from the mass-dependent fractionation law, which has a slope of ~ 0.52 in a δ17O vs. δ18O diagram (Matsuhisa et al. 1978). Δ17O, defined in Eq. 2, can display a vertical deviation of the δ17O value from the reference fractionation line. Recently, it has been recognized that hydrothermally altered minerals and sediments have negative Δ17O values, which can be explained by water-rock interaction over a wide temperature range (Pack and Herwartz 2014; Sharp et al. 2018). This suggests that the precise determination of the Δ17O values of silicates may be used to establish new geochemical tracer. Published Δ17O values of the international reference silicates ranged from − 0.102 to 0.049‰ in UWG2 garnet, − 0.104 to 0.332‰ in NBS28 quartz, and − 0.103 to 0.12‰ in San Carlos olivine (Table 4, Fig. 5 a–c). The large variations may have arisen from the choice of different λRL and γRL. 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 (Pack et al. 2016; Sharp et al. 2016; Wostbrock et al. 2020; Young et al. 2014). Recently, Miller et al. (2020) proposed an alternative reference line using the low-δ18O of KRS (Khitostorv Rock Standard, − 25.20‰) and high-δ18O SKFS (Stevns Klint Flint Standard, 33.93‰) to report Δ17O values of UWG2 garnet, NBS28 quartz, and San Carlos olivine. The advantage of Δ17O values calculated from the KRS-SKFS 2-point reference line is that the Δ17OKRS-SKFS can be reported without the careful calibration of the working standard O2. Therefore, the measurements of KRS and SKFS may be useful for reporting a comparable Δ17O for oxygen isotope studies of silicates.

Table 4 Literature data of ΔЭ17O and recalculated Δ'17O relative to different assigned reference lines
Fig. 5

Comparison of published Δ'17O (ac) and recalculated Δ'17O using four different λRL and γRL (df). Gray symbol: λRL = 0.5305 and γRL = 0, light blue symbol: λRL = 0.528 and γRL = 0, orange symbol: λRL = 0.5278 and γRL = −0.040, light green: λRL = 0.5273 and γRL = −0.099 as mentioned in the text. The Δ'17O values change significantly according to the different set of λRL and γRL

The different sets of λRL and γRL values may induce a misleading for the inter-laboratory comparison of Δ17O. Therefore, we recalculated Δ17O values for the international silicate standards using four reference lines as follows: (i) λRL = 0.5305 and γRL = 0 for the equilibrium fractionation line; (ii) λRL = 0.528 and γRL = 0 for the VSMOW-SLAP line; (iii) λRL = 0.5278 and γRL = − 0.040 for the terrestrial silicate line measured in this study; (iv) λRL = 0.5273 and γRL = −0.099 for the 2-point silicate reference line defined by the KRS and SKF measurements. The re-calculated Δ17O values indicate that the choice of λRL and γRL shows wide variation in Δ17O (Fig. 5 d–f). Although the reason for the Δ17O discrepancy is still uncertain, the different reference lines may interrupt a comparative study in a small Δ17O deviation of silicate. Each laboratory has calibrated its own reference O2 gas in their own way as mentioned above. The oxygen isotopic ratios of these materials do not follow the theoretical mass-dependent fractionation line exactly. In other words, their 17O/16O ratios are fractionated, leading to a Δ17O shift from the fractionation line by physicochemical processes such as evaporation, precipitation, and diffusion (Luz and Barkan 2010). The 17O/16O ratio of atmospheric O2 also shows a variation at a given 18O/16O ratio relative to the water reference line due to photosynthesis, respiration, and photodissociation (Young et al. 2014). In silicates, hydrothermal alteration of the rocks and minerals produces a negative variation in Δ17O relative to the water reference line (Pack and Herwartz 2014; Sharp et al. 2018). Therefore, the different materials used to calibrate the working standard O2 gas may lead to noticeable variability in the inter-laboratory comparison of Δ′17O. A reference line produced from the same materials and methods should be used for inter-laboratory comparison of Δ17O of silicates. Miller et al. (2020) suggested the use of the KRS and SKFS to define a 2-point silicate reference line and showed a superb agreement in Δ′17O between the Open University and Georg-August-Universität Göttingen data based on the low- and high-δ18O silicates reference line. In order to verify the 2-point silicate reference line, we measured the oxygen isotope compositions of two newly proposed silicate standards (KRS and SKFS) that are vastly different in δ-values and calculated Δ17O values of international silicate standards. They are Δ17O = 0.045 ± 0.011‰ for UWG2 garnet, 0.062 ± 0.009‰ for NBS28 quartz, and 0.060 ± 0.011‰ for San Carlos olivine. These values are in excellent agreement with the reported Δ17O values at Georg-August-Universität Göttingen: 0.049 ± 0.008‰ for UWG2 garnet, 0.060 ± 0.004‰ for NBS28 quartz, and 0.056 ± 0.009‰ for San Carlos olivine (Miller et al. 2020). Here we emphasize that Δ17O values should be evaluated by the identical reference fractionation line, that is the KRS-SKFS fractionation line. This approach can provide Δ17O results that are comparable with those calculated from the working standard O2 calibrated by VSMOW-SLAP fluorination.


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 δ17O and δ18O 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. The small variation in Δ17O with respect to the reference fractionation line is nowadays an important tool for investigating geological processes. We have confirmed that the Δ17O values of natural silicates calculated from 2-point reference line defined by low and high δ18O silicates were consistent with the Δ17O values reported in other laboratories. Consequently, the VSMOW-SLAP normalization and two-point silicate reference line can provide reliable data for δ17O, δ18O, and Δ17O.

Availability of data and materials

Research data have been provided in the manuscript and supporting information files.



Vienna Standard Mean Ocean Water


Standard Light Antarctic Precipitation


International Atomic Energy Agency


Korea Polar Research Institute


University of Wisconsin Garnet


National Bureau Standards


Greenland Ice Sheet Precipitation


Khitostorv Rock Standard


Stevns Klint Flint Standard


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The authors thank Dr. M.F. Miller for providing the KFS and SKFS samples. We would also like thank to anonymous reviewers for insightful comments. This research was supported by “PE20200” projects of the Korea Polar Research Institute (KOPRI).


This study was funded by the Korea Polar Research Institute (Institutional Program: PE20200).

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NKK and MK performed the measurements on waters and silicates and NKK wrote the draft of the manuscript. NKK, CP, and MK revised the manuscript critically. All authors read and approved the final version of the manuscript.

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Correspondence to Nak Kyu Kim.

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Kim, N.K., Park, C. & Kusakabe, M. Two-point normalization for reducing inter-laboratory discrepancies in δ17O, δ18O, and Δ17O of reference silicates. J Anal Sci Technol 11, 51 (2020).

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  • Oxygen three isotope
  • Silicates
  • VSMOW-SLAP scaling
  • Inter-laboratory comparison
  • Δ17O