Figure 3. A typical QMS spectrum of2H2O m/z 1 to 40. The small inserts
show the logarithmic plots of m/z 0 to 10 (top) and 14 to 24 (bottom).
In analogy to the mixing of enriched 18O water and the
replicate for SLAP, we added the amount of2H2O that was calculated to achieve a
δ2H ≈ 0‰ to SLAP-rep-O.2H2O was weighed in a glass vial on an
analytical balance (approximately 75 mg was weighed), SLAP-rep-O was
weighed on a precision balance (1 L) in a 1 L brown Duran bottle. This
vial was submerged in the 1 L flask with SLAP-rep-O. The resulting
mixture VSMOW-rep-D was stirred for at least 48 hrs. All weights were
corrected for the buoyancy effect.
In this second approach, the product VSMOW-rep-D (δ2H
≈ 0‰, δ18O, still SLAP-like, ≈ -55.5‰) was the basis
of the mixing process with highly enriched 18O water.
The adding of highly enriched 18O water needed to
arrive at δ18O ≈ 0‰ and the mixing of those two fluids
was the same as described before.
Characterization of the isotopic delta values of VSMOW-rep-D was
performed by the LGR-LWIA by direct comparison with SLAP for
δ18O analysis and by direct comparison with VSMOW for
δ2H analysis (on the VSMOW-SLAP scale). Subsequently,
the produced VSMOW-rep-OD was measured by direct comparison with
original VSMOW water, for both isotopes.
For the calculation of the best δ18O value for SLAP
with the help of a validated spreadsheet (Faghihi16,
the 17O and 18O abundances of the
enriched 2H2O water had to be
characterized as well. In analogy to the determination of2H and 17O abundances in enriched18O water, 2H2O was
diluted first with demineralized Groningen tap water (1:7). Carbon
dioxide with a known isotopic signature was equilibrated with this
diluted 2H2O at 25 ºC for 48 hours
(procedure described in Meijer17. CO2was extracted and δ 18O was measured on a dual
inlet IRMS Mass spectrometer (a VG (now Isoprime) SIRA10). IAEA607 with
approximately the same δ 18O signal as the
diluted 2H2O water and some other
local CIO references were identically treated and were used for
normalization. δ 17O was determined via a method
described in Elsig and Leuenberger18. Theδ 13C from the initial equilibration gas is
known, and deduced from the deviation in δ 13C
of the CO2 gas after equilibration and before
equilibration with the known δ 13C,δ 17O could be determined. IAEA607 and the same
local CIO references as for δ 18O analysis, were
used for normalization. The 17O and18O abundances of the2H2O water are presented in the
results section, along with their standard deviations of three
repetitions.
The difference in stable isotopes measurements and the calculated stable
isotope values by the validated spreadsheet
(Faghini16) translates directly into a bestδ 18O value for SLAP with respect to VSMOW. In
addition, the second approach has the beneficial side-effect that
additionally a best δ 2H for SLAP could be
determined. δ 2HVSMOW-rep-D was
initially calculated from the actually added (buoyancy-corrected) weight
and isotopic abundances of the 2H2O
water and the weight and isotopic delta values of SLAP-rep-O (on the
VSMOW-SLAP scale). Subsequentlyδ 2HVSMOW-rep-D was measured
alongside VSMOW. The difference between this measurement and the
calculated value translates directly into a bestδ 2H value for SLAP with respect to VSMOW.
We took care that the differences between the replicates and the genuine
VSMOW and SLAP were small, so the δ18O and δ2H difference between the officially
δ18O and δ 2H values
(VMSOW-SLAP scale) and the ’true’ isotopic difference, or in other
words, possible scale contractions, did not play a role.
2.4 Final uncertainty calculation.
To calculate the combined uncertainty for each single experiment, a
Monte Carlo simulation was performed for the full experimental process.
For all different sources in the total process, from weighing waters, to18O abundance measurements by QMS, until isotopic
measurements with the LGR-LWIA, the uncertainties were determined or
estimated.
To ascertain the contribution of uncertainties in the weighing process,
a flask was weighed multiple times in order to determine the
reproducibility of weighing. This procedure revealed that the spread in
the weighing of the same flask multiple times, was within 5 times the
uncertainty specified by the manufacturers, and thus multiplied by a
factor of 5. So, for weights measured on the precision balance the
accuracy was estimated at ± 0.05 g and for the analytical balance the
accuracy was estimated at ± 0.05 mg. As a part of the quality control
measures we have adopted in our laboratory, all balances, including the
ones used in this work, are frequently calibrated.
As a cautious estimate, the uncertainties for the QMS18O abundances of the enriched 18O
waters were chosen to be the standard deviations of the repetitional
measurements. In Table 3 this is displayed for every enriched18O water. The 2H and17O abundances are determined via dilution. The
isotopic measurements of the diluted 18O waters were
performed on two different measurement days, and performed nine times
per measurement day. From the weighted average of the total number of
analyses and twice the standard error of the mean, the2H and 17O abundances were deduced
with their 2σ uncertainty.
The isotopic measurements for SLAP, VSMOW and their replicates were
measured on the LGR-LWIA. Per measurement day every replicate was
injected 60 times, and VSMOW and SLAP were injected 90 times. The
difference in δ18O (Δ δ18O) between
the replicate and its “parent” (so SLAP for SLAP-replicate, and VSMOW
for VSMOW-replicate) was averaged per measurement day. The error in the
mean in the parent-replicate Δ δ18O was calculated
(typically better than 0.03‰) and was the basis for the weights for
calculating the weighted average for every Δ δ18O
parent-replicate on multiple (typically 3) measurement days.
For the Monte Carlo simulation, a calculation was programmed in R. All
calculations steps were performed 10,000 times with all the parameters
and their uncertainties (assumed to belong to a normal distribution) as
described above. This Monte Carlo simulation gives the uncertainty for
product VSMOW-rep-O. A quadratic sum from the Monte Carlo uncertainty
and the standard error in the mean of the isotopic measurements for
product VSMOW-rep-O yielded the combined uncertainty per experiment. The
Monte Carlo simulation was performed for the full calculation process
for each experiment. The combined uncertainties per experiment are shown
in the supplementary material, Table 4, and in the graph, Figure 6.
The three main uncertainty components in this combined uncertainty are
the weight and 18O concentration determination of the
enriched 18O water and theδ 18O measurement of SLAP-rep-O.
Despite one extra step in the second approach, the uncertainty in the
final result is the same. In the first approach the Δδ 18O between SLAP-rep-O and SLAP and
VSMOW-rep-O and VSMOW leads to a best δ 18O
value for SLAP with respect to VSMOW. In the second approach Δδ 18O between VSMOW-rep-D and SLAP and
VSMOW-rep-OD and VSMOW leads to a best δ 18O
value for SLAP with respect to VSMOW.
All uncertainty sources are considered to be random errors, only causing
variability in the end result. In addition, there are two sources of
systematic error. The first would be a biased QMS 18O
measurement method. It is unlikely, but still possible, that we
systematically measure an 18O abundance that is too
low. If this would be the case, the final end result
for δ 18O value for SLAP would be more negative.
In the next section, we describe a number of tests we performed to
scrutinize our QMS-based abundance measurements.
The other source of systematic uncertainty is the 18R
value for (V)SMOW and its uncertainty as reported by
Baertschi7: 18R = (2005.20 ± 0.45) x
10-6. Changing this value by one standard deviation up
would lead to a 0.013‰ less negative delta value for SLAP.
As the total number of experiments is rather small (seven), the standard
error in the mean of the averaged results forδ 18O value for SLAP for seven experiments, is
increased by multiplying with a Student’s T-distribution factor.