Correction Strategies for Isotopic Ratios in Overspiked Samples Using the Double Spike Technique

The double spike (DS) technique is a highly effective approach for measuring the isotope ratios of many elements. However, it is common for some fraction of the prepared samples to be "overspiked." The usual solution for this problem involves repurifying and reanalyzing the samples to ensure data accuracy. Here, we propose a straightforward mathematical scheme to rectify the isotope ratios of overspiked samples, avoiding repetitive, time-consuming operations. The principle behind this scheme is that adding a standard solution with the certified isotope ratio decreases the overspiked ratio to the normal range. The related theoretical equations and a thorough error propagation model are presented. Taking nickel (Ni) isotopes as an example, we demonstrate how to utilize the spike-to-sample ratios of the overspiked sample and the sample-standard mixture, as well as the spike-subtracted isotope ratios of the mixture (δ⁶⁰Ni_mix), to accurately determine the actual sample isotopes. This method's accuracy and precision (2SD) were evaluated by testing Ni, chromium (Cr), and cadmium (Cd) isotope measurements. Precision consistent with traditional DS measurements can be achieved when the fraction of the added standard solution (f_std) is ≤0.60 (60%) in the mixture or when the overspiked multiple is ≤2.5. The added standard solution is recommended to be the same as the standard used to define the delta scale (e.g., δ⁶⁰Ni = 0.000‰) to simplify the calculation procedures. This method expands the application of DS from the normal to the overspiked range and can be extended to isotope analyses of many elements where DS is applicable.