Scale Conversion and Uncertainty Calculations in Isotope Delta Measurements

Abstract

Isotope ratio applications are on the increase and a major part of which are delta measurements, because they are easier to perform than the determination of absolute isotope ratios while offering lower measurement uncertainties. Delta measurements use artefact‐based scales and therefore scale conversions are required due to the lack of the scale defining standards. Such scale conversions often form the basis for comparing data being generated in numerous projects and therefore need to be as accurate as possible. In practice, users are tempted to apply linear approximations, which are not sufficiently exact, because delta values are defined by nonlinear relationships. The bias of such approximations often is beyond typical measurement uncertainties and its extent can hardly be predicted. Therefore, exact calculations are advised. Here, the exact equations and the bias of the approximations are presented, and calculations are illustrated by real‐world examples. Measurement uncertainty is indispensable in this context and therefore, its calculation is described as well for determining delta values but also for scale conversions. Approaches for obtaining a single delta measurement and for repeated measurements are presented. For the latter case, a new approach for calculating the measurement uncertainty is presented, which considers covariances between the isotope ratios.