Optimization of the double spike technique using peak jump collection by a Monte Carlo method: an example for the determination of Ca isotope ratios

Abstract

Three important factors, including the choice of an appropriate spike isotope pair, the composition of the double spike, and the ratio of the double spike to the sample, have been proven to have a significant effect on the precision of the double spike technique. Moreover, peak jump (i.e., dynamic) collection mode is frequently used, which could lead to more variable parameters such as cup configurations, ratio combinations and integration times in different jump lines. In order to optimize the above conditions under the peak jump mode, a Monte Carlo method that simulates uncertainties from Johnson noise and counting statistics is applied for the prediction of the precisions of measured results using the double spike technique. As an example, this model was used to predict the possibility of cup configurations and ratio combinations of three double spike pairs of ⁴²Ca–⁴⁸Ca, ⁴³Ca–⁴⁸Ca and ⁴⁶Ca–⁴⁸Ca, respectively, in two jump lines. Predicted internal precisions improved by 25%, 20% and 25% by using ⁴²Ca–⁴⁸Ca, ⁴³Ca–⁴⁸Ca and ⁴⁶Ca–⁴⁸Ca double spikes, respectively, under optimized conditions. The theoretically predicted optimum precision was verified by repeatedly measuring two standards of NIST SRM 915a and NIST SRM 915b using the ⁴²Ca–⁴⁸Ca double spike over several months. The observed internal precisions of δ⁴⁴Ca in these two standards are in good agreement with the predicted internal precisions, validating the effectiveness of the proposed Monte Carlo technique. The observed external precisions in two standards are 8–9 times poorer than the internal precisions, probably due to an extra uncertainty source. Nevertheless, the optimal ratio combination yields the best external precision. As demonstrated, the proposed Monte Carlo simulation is an effective method to predict the optimal cup configurations, ratio combinations and integration times for the double spike technique using peak jump collection mode.