Abstract

General theory for uncertainty propagations of atomic weight measurement results is presented and the impact of correlation of input variables (isotope ratios and correction factors) on the overall atomic weight uncertainty is discussed. Currently all uncertainty propagations use equations that are fitted for uncorrelated isotope ratios and uncorrelated mass bias correction factors. It is shown here that the correlation of isotope ratios is significant in TIMS and multi-collector ICPMS measurements and ignoring these correlations can lead to significant underestimation of the uncertainty of atomic weight measurement results. Atomic weight uncertainties are inconsistent with reported isotope ratio uncertainties in numerous recent reports as a result of improper uncertainty propagation.