Normalization of measured stable isotopic compositions to isotope reference scales--a review

In stable isotope ratio mass spectrometry (IRMS), the stable isotopic composition of samples is measured relative to the isotopic composition of a working gas. This measured isotopic composition must be converted and reported on the respective international stable isotope reference scale for the accurate interlaboratory comparison of results. This data conversion procedure, commonly called normalization, is the first set of calculations done by the users. In this paper, we present a discussion and mathematical formulation of several existing routinely used normalization procedures. These conversion procedures include: single-point anchoring (versus working gas and certified reference standard), modified single-point normalization, linear shift between the measured and the true isotopic composition of two certified reference standards, two-point and multi-point linear normalization methods. Mathematically, the modified single-point, two-point, and multi-point normalization methods are essentially the same. By utilizing laboratory analytical data, the accuracy of the various normalization methods (given by the difference between the true and the normalized isotopic composition) has been compared. Our computations suggest that single-point anchoring produces normalization errors that exceed the maximum total uncertainties (e.g. 0.1 per thousand for delta(13)C) often reported in the literature, and, therefore, that it must not be used for routinely anchoring stable isotope measurement results to the appropriate international scales. However, any normalization method using two or more certified reference standards produces a smaller normalization error provided that the isotopic composition of the standards brackets the isotopic composition of unknown samples.