A general algorithm for the ¹⁷O abundance correction to ¹³C/¹²C determinations from CO₂ isotopologue measurements, including CO₂ characterised by 'mass-independent' oxygen isotope distributions

It is widely recognised that a significant limitation to the ultimate precision of carbon stable isotope ratio measurements, as obtained from dual-inlet mass spectrometric measurements of CO₂ isotopologue ion abundances at m/z 44, 45, and 46, is the correction for interference from ¹⁷O-bearing molecular ions. Two long-established, alternative procedures for determining the magnitude of this correction are in widespread use (although only one has IAEA approval); their differences lead to small but potentially significant discrepancies in the magnitude of the resulting correction. Furthermore, neither approach was designed to accommodate oxygen three-isotope distributions which do not conform to terrestrial mass-dependent behaviour. Stratospheric CO₂, for example, contains a strongly 'mass-independent' oxygen isotope composition. A new strategy for determining the ¹⁷O-bearing ion correction is presented, for application where the oxygen three-isotope characteristics of the analyte CO₂ are accurately known (or assigned) in terms of the slope λ of the three-isotope fractionation line and the ordinate axis intercept 10³ ln(1 + k) on a 10³ ln(1 + δ¹⁷O) versus 10³ ln(1 + δ¹⁸O) plot. At the heart of the approach is the relationship between ¹⁷R, which is the ¹⁷O/¹⁶O ratio of the sample CO₂, and other assigned or empirically determined parameters needed for the δ¹³C evaluation:2 ¹⁸ R_ref fenced(frac(¹⁷ R, (1 + k) ¹⁷ R_ref))^{frac(1, λ)} - 3 (¹⁷ R)² + 2 ¹⁷ R ⁴⁵ R - ⁴⁶ R = 0With ⁴⁵R and ⁴⁶R as the respective 45/44 and 46/44 ion abundance ratios of the sample, as obtained by measurement of δ⁴⁵(CO₂) and δ⁴⁶(CO₂) values reported relative to a reference material (usually VPDB-CO₂), and ¹⁷R_ref and ¹⁸R_ref being the respective ¹⁷O/¹⁶O and ¹⁸O/¹⁶O ratios in the same reference material, ¹⁷R can readily be obtained by numerical methods, for given λ and k values. The correction procedure involves no approximations, in principle, and is equally applicable to CO₂ of terrestrial, mass-dependent oxygen isotopic composition, as well as to more 'exotic' sources. Besides isotopic characterisation of stratospheric CO₂, potential applications include high precision δ¹³C measurements of CO₂ derived from the oxidation of tropospheric CO (also characterised by significantly 'mass-independent' oxygen isotopic composition); high precision isotopic monitoring of atmospheric CO₂; the metrology of carbonate isotopic reference materials; and the isotopic characterisation of CO₂ which has been equilibrated with waters artificially 'labelled' with known enrichments of ¹⁷O and ¹⁸O.