Physical model for multi-point normalization of dual-inlet isotope ratio mass spectrometry data

A simple model is presented for multi-point normalization of dual-inlet isotope ratio mass spectrometry (DI-IRMS) data. The model incorporates the scale contraction coefficient and the normalized working reference gas isotope delta value as its two physical parameters. The model allows the full use of isotope measurement data and outputs the normalized sample isotope delta value along with the mentioned parameters. The model reduces to the expected linear behavior on application to a natural range CO₂ isotopic composition sample, under typically observed scale contraction levels. Next, DI-IRMS measurements of the NIST CO₂ gas isotopic reference materials (RMs) 8562, 8563, and 8564 are used to construct a three-point linear calibration, spanning 40‰ for the [Formula: see text] and 20‰ for the [Formula: see text] raw data. Accuracy of the regression at the 0.009‰ level for [Formula: see text] and 0.01‰ for [Formula: see text] is observed for the three NIST RMs. The model derived scale contraction term is found to be a more accurate measure of cross-contamination in contrast to its end of day measurements by the enriched sample method. The constructed multi-point normalization model is next used to assign [Formula: see text] and [Formula: see text] isotope delta values on the Vienna PeeDee Belmnite-CO₂ (VPDB-CO₂) scale, for pure CO₂ gas samples in the natural isotopic range. A Monte Carlo analysis of the uncertainty, including estimates for the normalization step, is provided to assist future multi-point normalization with more than three reference points.