Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 1 – theoretical derivation and feasibility study

The development of a new method for the experimental determination of absolute isotopic abundances using a modified isotope dilution mass spectrometry (IDMS) technique is described. The intention and thus main application will be the quantification of molar masses M of highly enriched materials with improved measurement uncertainty (U_rel(M) ≈ 10^?8 with k = 2). In part 1 of the current work, the theoretical foundation of the new method and its mathematical derivation is shown in detail, while part 2 will cover the experiments based on the new method described. Its core idea is the introduction of a virtual element (VE) consisting of all isotopes but the one having the largest or smallest abundance. IDMS is used to determine the mass fraction of this VE in its matrix, namely the element itself. A new set of equations serve to calculate all isotopic abundances (even the large one omitted with the introduction of the VE) merely from the mass fraction of the VE. A comprehensive uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM) was set up in order to discuss and validate the novel concept. The hypothetical input data of the uncertainty budget were estimated to resemble a silicon material highly enriched with respect to ²⁸Si used in the context of the international Avogadro Project. Considering the calculated results, the experimental determination of the molar mass of the above mentioned silicon seems very promising. As far as the authors know, this will be the first time IDMS was applied to determine a molar mass.