Recalculation of data for short‐lived radionuclide systems using less‐biased ratio estimation

Abstract

Abstract– Ratios determined from counting a subset of atoms in a sample are positively biased relative to the true ratio in the sample ( Ogliore et al. 2011 ). The relative magnitude of the bias is approximately equal to the inverse of the counts in the denominator of the ratio. SIMS studies of short‐lived radionuclides are particularly subject to the problem of ratio bias because the abundance of the daughter element is low, resulting in low count rates. In this paper, we discuss how ratio bias propagates through mass‐fractionation corrections into an isochron diagram, thereby affecting the inferred initial ratio of short‐lived radionuclides. The slope of the biased isochron can be either too high or too low, depending on how it is calculated. We then reanalyze a variety of previously published data sets and discuss the extent to which they were affected by ratio bias. New, more accurate, results are presented for each study. In some cases, such as for 53 Mn‐ 53 Cr in pallasite olivines and 60 Fe‐ 60 Ni in chondrite sulfides, the apparent excesses of radiogenic isotopes originally reported disappear completely. Many of the reported initial 60 Fe/ 56 Fe ratios for chondrules from ordinary chondrites are no longer resolved from zero, though not all of them. Data for 10 Be‐ 10 B in CAIs were only slightly affected by bias because of how they were reduced. Most of the data sets were recalculated using the ratio of the total counts, which increases the number of counts in the denominator isotope and reduces the bias. However, if the sum of counts is too low, the ratio may still be biased and a less‐biased estimator, such as Beale’s estimator, must be used. Ratio bias must be considered in designing the measurement protocol and reducing the data. One can still collect data in cycles to permit editing of the data and to monitor and correct for changes in ion‐beam intensity, even if total counts are used to calculate the final ratio. The cycle data also provide a more robust estimate of the uncertainties from temporal variations in the secondary ion signal.