Recalculation of stable isotope expressions for HCNOS: EasyIsoCalculator

The stable HCNOS isotope compositions can be reported as (a) the isotope ratio of two stable isotopes (R); (b) the isotope delta value (δ); and (c) the atom fraction of the isotopes (x). Recalculations between these different expressions are needed frequently and require the use of the absolute isotope ratio for the zero points of the stable isotope delta scales (R_std). The inconsistent use of R_std values may lead to a discrepancy in recalculated results.

We summarised the recalculation procedures between different expressions of the stable isotope compositions and introduced a user-friendly EasyIsoCalculator that allows the recalculation between the main expressions of isotope compositions. We mathematically and empirically evaluated the possible inconsistencies in reporting of the stable isotope data due to the use of different R_std and different normalisation methods.

The recalculation between δ-values and other expressions of the stable isotope compositions always involves the use of R_std. The choice of R_std will have a significant influence on the recalculated values. The use of different R_std values has a significant influence also on the normalisation of raw values but only when the normalisation is conducted versus the working standard gas value, causing discrepancy, e.g. for δ(¹³C/¹²C) up to ~ 0.3 ‰.

Differences in the selection of R_std value may lead to significant differences among different laboratories. The uncertainty in the calculations originates primarily from the uncertainty in the R_std determination; however, it is lower than the discrepancy arising from the inconsistent use of R_std. Consistent use of the same R_std values is required to eliminate the unnecessary discrepancy if different data sets are recalculated from delta value to other expressions.