A gas standard is available to calibrate the mass spectrometer and to determine the acceptance of the full gas chromatographic process. The gas standard consists of a metal-sealed container with a volume of a few liters that is filled with the noble gases argon, krypton, and xenon. Connected to this container is a second, much smaller volume (\(\sim \) 0.2 cm\(^{3}\)) that is separated from the latter by a fully metal sealed valve. This volume is used to extract a constant fraction of the gas standard (standard pipette). The amount of krypton in one standard pipette was calibrated using a sample of commercially available helium containing a well-known admixture of krypton. This calibration defines the amount of krypton in our standard pipette to be 3.9 \(\times 10^{-11}\) cm\(^{3}\) (\(\pm 16.5\,\%\)).
SEM response
The response of the mass spectrometer to the amount of one standard pipette is determined at least once before the measurement of a xenon batch. In the analysis we are interested in the amount of gas initially transferred to the cold finger, that is at time zero (\(\mathrm t _0\)), before other processes (like implanting accelerated ions into the walls of the mass spectrometer’s vacuum tube) start to change its amount. The time-dependence of the count rate of the background and signal are fitted and extrapolated to \(\mathrm t _0\) where the size of the pedestal, as seen in Fig. 4, is a measure of the amount of gas from the respective isotope in the batch.
In standard data taking mode a loop over the isotopes \({}^{36}\mathrm{Ar }\), \({}^{40}\mathrm{Ar }\), \({}^{84}{\mathrm{Kr }}\), \({}^{86}{\mathrm{Kr }}\) and \({}^{132}\mathrm{Xe }\) is recorded. The ratios of \({}^{40}\mathrm{Ar }\)/\({}^{36}\mathrm{Ar }\) and \({}^{84}{\mathrm{Kr }}\)/\({}^{86}{\mathrm{Kr }}\) provide an intrinsic cross-check since they should match the natural abundances (mole fractions). The amount of gas at time zero is determined for \({}^{84}{\mathrm{Kr }}\) and \({}^{86}{\mathrm{Kr }}\) independently (see Sect. 3.3). From both isotopes the amount of natural krypton is computed using the respective relative abundance. Both numbers are combined in the final result. The gas amount of the initial xenon batch is determined in a calibrated volume (\(\mathrm V _{\mathrm{cal}}\)) equipped with a precise capacitive pressure gauge (P2, see Fig. 2).
Krypton acceptance
The standard pipette is used to determine the acceptance of the gas chromatographic process for krypton. The calibrated mixture of krypton and xenon is transferred by cryogenic pumping to the adsorbent trap T2 (immersed in liquid nitrogen) used for the krypton/xenon separation. Then the full chromatographic procedure is performed—identical to the standard procedure for a normal xenon batch—and the spectrometer’s response to the krypton isotopes is compared to its response without the chromatographic separation process. This calibration procedure yields a krypton acceptance of \(\varepsilon _a = (0.97 \pm 0.02)\).
The procedure described above employs microscopic krypton and xenon gas samples on the order of a few 10\(^{-12}\) cm\(^{3}\), while the standard procedure foresees xenon batches of up to several cm\(^{3}\) containing only traces of krypton. When combining 3.9 \(\times \) 10\(^{-11}\) cm\(^{3}\) of \({}^{nat}{\mathrm{Kr }}\) from the standard pipette with approximately 1.2 cm\(^{3}\) of xenon from sample XE100-3 (1.8 ppt intrinsic krypton, see Sect. 4), we measure (3.2 \(\pm \) 0.7) \(\times \) 10\(^{-11}\) cm\(^{3}\)
\({}^{nat}{\mathrm{Kr }}\). Reevaluating the acceptance for krypton \(\varepsilon _a\), we find \(\varepsilon _a = (0.79 \pm 0.18)\) in agreement with above result. The larger uncertainty in this value is dominated by the uncertainty in the intrinsic krypton level of the bulk xenon and the sample standard deviation of a single measurement (see Sect. 3.4). The weighted average of both, \(\varepsilon _a = (0.97 \pm 0.02)\), will be used throughout this work.
Computation of the krypton level
The krypton level of a given batch is the ratio of the amount of krypton gas measured by the mass spectrometer and the initial batch size determined by its pressure in the calibrated volume. We can write:
$$\begin{aligned} \frac{{}^{nat}{\mathrm{Kr }}}{{}^{nat}\mathrm{Xe }} = \frac{\left\langle \left( {}^{i}{\mathrm{Kr }} - B_i \right) \cdot f_m(i)^{-1} \right\rangle _i \cdot \varepsilon _a^{-1}}{{}^{nat}\mathrm{Xe }} \, , \end{aligned}$$
(1)
where \(i\) represents the individual isotope, \(f_m(i)\) is the mole fraction of the respective isotope, \(\langle \dots \rangle _i\) denotes the average over the isotopes \(i\) and \(\varepsilon _a\) is the acceptance of the full chromatographic process for krypton. \({}^{i}{\mathrm{Kr }}\) is the amount of gas of the krypton isotope \(i\) as measured with the spectrometer. It is computed from the abundance of the krypton isotope \(i\) in the standard pipette (\(\textit{std}_{i}\)) and from the ratio of the pedestals of the batch (\(s_i^\text {batch}\)) and the standard pipette (\(s^\text {std}_{i}\)):
$$\begin{aligned} {}^{i}{\mathrm{Kr }} = \frac{s_{i}^{\text {batch}}}{s_{i}^{\text {std}}} \cdot \textit{std}_{i}. \end{aligned}$$
(2)
Finally, \(B_i\) is the procedure blank of the full process for the isotope \(i\), as will be explained in Sect. 3.5, and can be written similar to (2) substituting \(s_i^\text {batch}\) by \(s_i^{B}\). \(^{nat}\)Xe can be computed, if the pressure \(p\) and the temperature \(T\) in the calibrated volume \(\text {V}_\text {cal}\) are known.
Uncertainty budget estimation
Systematic effects common to all measurements are the uncertainty of the standard pipette, the uncertainty in determining the initial xenon batch size and the uncertainty of the chromatographic acceptance for krypton (\(\Delta \varepsilon _a\)). Summing them quadratically, we end up with a relative uncertainty of 17.0 % dominated by the uncertainty of the standard pipette.
Statistical fluctuations of the number of ions detected by the SEM, variations in performing the chromatographic separation and variations in the electrical fields of the ion optics due to high voltage drifts individually affect single measurements. The sum of these effects is estimated (for each sample individually) from the fluctuations of the measurement of several batches around their mean. The resulting uncertainty estimator is added quadratically to the aforementioned systematic uncertainties. In those cases where only a single batch was measured, we estimate its uncertainty by averaging the sample standard deviations of all measurements so far done with this setup. We find 13.5 % to be a single measurement’s standard deviation. Combining both uncertainties by summing them quadratically we find the total relative uncertainty of a single batch to be 21.7 %. If more than one single batch is measured, the relative uncertainty decreases being limited to the systematic uncertainty of 17 %.
Sensitivity—procedure blank and detection limit
The sensitivity is limited by the traces of krypton which are collected during the full process and increase the signal in the mass spectrometer. Sources for this type of krypton are potential microscopic leaks allowing external krypton to enter the system, outgassing of the surfaces involved in the measurement and krypton introduced by the helium carrier gas. The amount of these krypton traces is accessed by performing the full procedure, identical to a normal measurement, but without a xenon batch introduced (procedure blank). A value of (1.00 \(\pm \) 0.04) \(\times \) 10\(^{-12}\) cm\(^{3}\) is found averaging several measurements done between the presented xenon samples of Sect. 4. After a recent system upgrade (refurbished high voltage control of ion optics and identification and removal of tiny air leak in the sample preparation part) the current procedure blank was measured to be (0.081 \(\pm \) 0.004) \(\times \) 10\(^{-12}\) cm\(^{3}\). This is a reduction by more than a factor ten with respect to the value mentioned above. The first xenon sample measured at this significantly reduced background level is in excellent agreement with earlier results at the higher background level (see Sect. 4). The systematic uncertainty of the absolute calibration is neglected in the estimate of the uncertainty of the procedure blank. This is justified as measurements are corrected for the procedure blank before being converted from a count rate to an amount of gas using the absolute calibration factor.
The decision threshold (DT) and detection limit (DL) are computed following [17] and result in 0.007 \(\times \) 10\(^{-12}\) cm\(^{3}\) and 0.015 \(\times \) 10\(^{-12}\) cm\(^{3}\) (\({}^{nat}{\mathrm{Kr }}\)), respectively, assuming a 21.7 % uncertainty of the outcome of a single measurement. The maximal size of the xenon batch that can be processed by the gas chromatographic separation determines the performance of the system. Up to now the largest xenon batch was 1.9 cm\(^{3}\) and we find at 95 % confidence level:
$$\begin{aligned} \text {DL} = \frac{({}^{nat}{\mathrm{Kr }})_\text {min}}{({}^{nat}\mathrm{Xe })_\text {max}} = 8\,\hbox {ppq} \end{aligned}$$
(3)
Note that likely larger xenon batches can be processed by the chromatographic process. The upper threshold for acceptable batch sizes was not determined yet. Consequently, the detection limit of currently 8 ppq may still be lowered in the future.