Isotopic analysis of a 6Li enriched lithium sample employing the Li2BO2+ ion beam method: verification of the theoretical accuracy

2000

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.

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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+

2000

“…Now, however, we consider the case of determining any single E i at a time by the molecular ion beam method3–17 (MIBM), e.g. either L or Y as $\hbox{Li}_{2}\hbox{BO}_{2}^{+}$ .…”

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confidence: 99%

Error‐systematics of determining simultaneously the isotopic abundance ratios of natural lithium and natural boron as Li ₂ BO ₂ ⁺

2000

Recently, we have shown how the errors delta(j) and delta(k), that occur when measuring the two different isotopic molecular abundance ratios required for analysis, are transformed into the actual errors of elemental isotopic analysis, (deltaEi/Ei)'s. With a view to gain further understanding as to how the errors (deltaEi/Ei)'s are governed, we now evaluate theoretically the effects of selecting different isotopic molecular pairs as the monitor pairs (j and k) for measurements, and of the measurement errors (delta(j) and delta(k)), on the results of analysis (the 6Li/7Li and the 10B/11B abundance ratios), by considering all the constituent elements of Li2BO2+ at their natural isotopic abundances. It is shown that the ratio of measurement errors, delta(j)/delta(k), is a more fundamental parameter than either the individual errors (delta(j) and delta(k)), or their sum, absolute value(delta(j)) + absolute value(delta(k)), in governing deltaEi/Ei. The important implication of this observation is that it reveals the possibility of achieving not only a desired level of accuracy in analysis, but even absolute accuracy (i.e. deltaEi/Ei = 0) by causing mutual cancellation of the effects of individual measurement errors delta(j) and delta(k), through proper regulation of measurement parameters. However, as the measurement errors cannot be pre-set, it is shown how selection of proper monitor pairs (j and k) can help achieve the desired accuracy in analysis. The present work sets guidelines for the more general problem of selecting monitor pairs to avoid larger errors in analysis.

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

2000

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.