Error-systematics of determining simultaneously the6Li /7Li and the10B/11B abundance ratios as Li2BO2+: considerations for analyte elements of varying isotopic abundance patterns

Abstract

In the Li2BO2+ ion beam method of isotopic analysis of elements, the (two) analyte isotopic abundance ratios (E i's) are determined by solving a set of (two) simultaneous equations: f i(E i's) = R i ± δ i, (i = 1, 2) where the R i's are the measured isotopic molecular abundance ratios. We have shown recently that, in the process of solution of these equations, the experimental errors (δ i's) are transformed into the actual errors of analysis, δE's, through some multiplication factors (MFs). For a given isotopic abundance distribution (IAD) of the Li2BO2+ ions, the MFs are shown to depend on the combination of two molecular pairs (CTMPS) used as the monitor pairs for measurements, thereby indicating the requirement of careful selection of monitor pairs for avoiding large (propagated) errors in analysis. In this work, we study how the requirements for a correct analysis vary with the IADs of the elements to be analyzed. The results not only lay great emphasis on the need for proper selection, but also show that no CTMPS can be identified as the universal monitor pairs irrespective of molecular IAD. These observations are, moreover, independent of the actual isotopic abundances of the monitor ions and/or the achievable measurement accuracy (δ i). It is noted further that, depending on the IADs of the analyte elements and hence the specific IAD of the Li2BO2+ ions, it may also happen that none of the different possible CTMPS really fits the criteria as the recommended monitor pairs, and then one has to ensure that the measurements are not only accurate but as perfect as possible (δ i's → 0) so as to achieve a reasonable accuracy in analysis. These findings are explained in terms of variations of MFs as a function of molecular IAD, and elaborated using experimental data. A comparative discussion on the determination of both 6Li/7Li and 10B/11B abundance ratios together, and that of either of them, as Li2BO2+, is also presented with a view to highlighting different possible aspects of the involvement of computation steps in analysis. The important implication of the present investigation is that it sets guidelines for the general problem of accurately analyzing unknown samples, irrespective of their sources of origin. Copyright © 2000 John Wiley & Sons, Ltd.