A New Statistical Model and a Redefinition of Isotopic Ratio

Abstract

Ultra-microanalysis of isotopes is required to clarify the origin, structure, and history of extremely small samples, for example micrometeorites and aerosols. However, a decrease in the number of measured atoms reveals a serious problem in the concept of isotopic ratio. The first fundamental defect of the isotopic ratio concept is imperfect reversibility of numerator and denominator, leading to two isotopic compositions inconsistent with each other. Secondly, the probability distribution of isotopic ratio is not the same as the binominal distribution, indicating that the mean isotopic ratio is systematically higher than the true isotopic ratio. Since these demerits should be avoided in ultra-microanalysis as much as possible, isotopic abundance or relative isotopic abundance should be used rather than isotopic ratio. The concept of isotopic ratio is, however, widely used in geochemical and cosmochemical fields, making it very difficult to abandon. Therefore, the potential uncertainty of isotopic ratio and the gap between the obtained isotopic ratio and the true one deriving from the number of sampling atoms and the isotopic ratio are vigorously evaluated here. In addition, a confirmation requirement for confirming an anomalous isotopic ratio is provided. The statistical model shown in the present work clearly indicates that the major isotope must be set as the denominator of isotopic ratio, i.e. isotopic ratio must be below 1, to reduce the effects of distorted probability distribution of isotopic ratio. In the precise measurement of isotopes, the potential error and disagreement with the true value must be tested when the number of sampled atoms is extremely few. Serious problems have not been occurred in research up to the present even in the case of NanoSIMS measurements, but this is because a sufficient number of atoms was analyzed and only extremely large isotopic anomalies were investigated. The correction and evaluation methods established in this paper will be required for accurate ultra-microanalysis.