Error-systematics of determining elemental isotopic abundance ratios by the molecular ion beam method: a case study for the simultaneous isotopic analysis of lithium and boron as Li2BO2+

The simultaneous isotopic analysis of lithium and boron by the Li2BO2+ ion beam method involves measurements of two different molecular abundance ratios (say, Rj+/-delta(j) and Rk+/-delta(k)), and subsequently extensive calculations to arrive at the analyte isotopic ratios (say, L and Y). It is not presently known how the measurement errors (delta(j) and delta(k)) are transformed into the errors of analysis (deltaL and deltaY). This work addresses this question from fundamental considerations. In the literature, the calculations are sometimes simplified using Ri formulae based on Li2B16O2+ ions and then applying correction factors for the actual Li2BO2+ ions, but this procedure is not generally applicable. We show how equations based on true Li2BO2+ ions (with full isotopic variations of all the constituent elements) can be solved, and illustrate the procedure with several examples. These studies show that accuracy of analysis depends not only on the accuracies of measurements, delta(j) and delta(k), but also on the particular isotopic Li2BO2+ ion-pairs (j and k) used as the monitor pairs. Moreover, this dependence is shown to be different for the different isotopic ratios (L and Y) to be determined simultaneously. Therefore, proper selection of monitor molecular pairs is a requirement for avoiding larger (propagated) errors in the analysis. Similar arguments would, in fact, apply to any arbitrarily chosen case of determining two or an even greater number of isotopic abundance ratios (Ei's) by the molecular ion beam method, irrespective of whether the different analyte ratios, Ei's, relate to a single multi-isotopic element, or different elements.