Error magnification factors in the isotopic analysis of oxygen as O 2 + : possibility of determining true isotopic abundance ratios

The simultaneous determination of the 17 O/ 16 O abundance ratio (Y) and 18 O/ 16 O ratio (Z) as $\hbox{\bf O}_{\bf2}^{+}$ is carried out by solving a set of equations:$$\hbox{\bf f}_{\bf i}\hbox{\bf(Y, Z) = R}_{\bf i}\hbox{\bf,} \ \hbox{\bf (i = 1, 2)}$$where R i 's are the measured abundance ratios of chosen pairs (say, j and k) of isotopic $\hbox{\bf O}_{\bf 2}^{+}$ ions. The measured ratios (R j and R k ) are always subject to some errors (δ j and δ k ), and hence the corresponding results of analysis (solutions: Y and Z) will inevitably be at errors (δ Y and δ Z ). Recently, we have shown that the errors δ Y and δ Z are always expected to be different from those of the experimental errors δ j and δ k , and are correlated as:$$|{\delta}_{\bf E}| = \hbox{\bf[REMF]}_{\bf jk}^{\bf E} \hbox{\bf (}|{\delta}_{\bf j}| + |{\delta}_{\bf k}|\hbox{\bf ),} \ \hbox{\bf(E = Y, Z)}$$where the parameter $\hbox{\bf[REMF]}_{\bf jk}^{\bf E}$ is referred to as the relative error magnification factor of analysis. This work investigates the parameters $\hbox{\bf[REMF]}_{\bf jk}^{\bf Y}$ and $\hbox{\bf[REMF]}_{\bf jk}^{\bf Z}$ (the error magnification factors in determining the oxygen isotopic ratios, Y and Z simultaneously, as $\hbox{\bf O}_{\bf 2}^{+}$ ), which control, for any given values of δ j and δ k , the achievable accuracy of the desired results (determined values of Y and Z). The variations of the REMFs as a function of the choice of isotopic molecular pairs j and k, and/or some other parameters, are evaluated and presented. The studies predict that although, depending on different possible parameters of analysis, the REMFs can have any values between 0 and (almost) ∞, it should not be at all difficult in case of a real analysis to pre‐select the analytical conditions so that the REMFs take roughly the desired values (i.e. ≤1). It is shown further that, compared to some other molecular species of oxygen such as the $\hbox{\bf CO}_{\bf 2}^{+}$ ions which are more commonly used than the $\hbox{\bf O}_{\bf2}^{+}$ ions themselves as the monitor species for the isotopic analysis of oxygen, the $\hbox{\bf O}_{\bf 2}^{+}$ ions have better properties as the required monitors ions (i.e. $\{\hbox{\bf [REMF]}_{{\bf O}_{2}^{+}}^{\bf E}\} < \{\hbox{\bf [REMF]}_{{\bf CO}_{\bf 2}^{+}}^{\bf E}\}$ ). Also, choice of the $\hbox{\bf O}_{\bf 2}^{+}$ ions as the monitors (j and k) is expected to yield results close to the true isotopic composition of the analyte oxygen, i.e. it is predicted to be possible in practice to achieve both $\hbox{\bf [REMF]}_{{\bf O}_{\bf 2}^{+}}^{\rm Y}$ and $\hbox{\bf [REMF]}_{{\bf O}_{\bf2}^{+}}^{\bf Z}$ substantially less than unity. Copyright © 2001 John Wiley & Sons, Ltd.