Practical application of lead triple spiking for correction of instrumental mass discrimination

The external precision of Pb isotope ratio measurements by TIMS is currently limited to ~0.1% due to variations in instrumental mass discrimination. It was shown by Dodson (1963) that the unknown mass discrimination factor could be obtained from a second measurement on an aliquot of a sample to which a double spike has been added. From the three isotope ratios measured on the two runs it is straightforward to solve for the three unknowns the respective fractionation factors of the two runs and the spike/sample ratio. Practical applications of the Pb double spike technique have used a mixed 2~176 tracer in the ratio ~9:1 (e.g. Hamelin et al. , 1985; Woodhead et al., 1995). These studies have demonstrated that a factor of up to -3 improvement in external precision can be obtained compared with good conventional, uncorrected measurements. Further, any systematic errors arising from matrix effects are effectively eliminated using the technique (Woodhead et al., 1995). Slightly more favourable results have been obtained by using a double spike composed of the non-natural isotopes 2~176 (Todt et al., 1996), which has the added advantage that only one mass spectrometric run is required; a disadvantage, ignoring the cost of these spikes, though, is that isobaric interferences on these masses must be continually monitored and corrected for during measurement. A systematic survey of stable isotope tracer compositions, axis combinations and mathematical solutions to this problem was recently undertaken by Galer (1997). From this study, there appears to be an optimal composition to use as a spike to correct samples of common Pb for instrumental mass fractionation. This spike composition (designated here as TS) is unusual in that it is a mixture of three stable isotopes of lead 2~176176 rather than just two, 2~176 used in previous studies. The error magnification factor 7 on the 2~176 ratio (i.e. the bias-corrected error relative to the measured, unspiked internal error) was estimated by Galer (1997) using a realistic error propagation model based upon the ion statistical uncertainties on the two runs and the TS composition. For the optimized TS composition, 7 lies at ~1.2 over a large range in spike/sample ratios, becoming larger than 2.0 only when the spike/sample ratio is less than 0.05 or greater than 3.8. This implies that when preparing the TS-sample mixture, the quantity of Pb in the sample need only be known to within a factor of ~40 either way to avoid an unfavourable 7 > 2. This behaviour is in sharp contrast to that of the 2~176 double spikes that have been used previously, which never have 7 < 2 for any spike/ sample ratio. Such double spikes as these, even in the most favourable cases, require internal precisions on the individual runs a factor of ~2 better to achieve the same final precision as the TS in effect, measurement times (or sample sizes) would need to be a factor of ~4 larger. In order to see how such an optimal triple spike would perform in practise, a tracer of TS composition was prepared and subjected to a number of tests to evaluate its performance. All Pb isotopic measurements were performed in static multi-collection mode on a Finnigan MAT-261. Inter-cup efficiency biases were determined by simplex minimization from measurements of the NBS-982 equal-atom Pb standard. The TS itself was calibrated by joint runs of the triple spike alone and mixtures in varying proportions with the NBS-982 standard the mass bias-corrected TS isotopic composition can then be obtained by solving the equations with the TS as the 'unknown' (cf. Hamelin et al. , 1985). Thus, any isotopic compositions determined using the TS are traceable to the NBS-982 Pb isotopic composition of Todt et al. (1996) which, in turn, was normalized to a 2~176 ratio of 1.00016. The first test of the triple spike was measurement of the NBS-981 common lead standard, whose isotopic composition has recently been redetermined by Todt et al. (1996). Samples of NBS-981 were mixed with TS in a large range of spike/sample ratios and combined with unspiked runs to yield fractionation-corrected ratios for NBS-981. To improve in-run