Isotopic fractionation and the quantification of O-17 anomalies in the oxygen three-isotope system - An appraisal and geochemical significance

The oxygen three-isotope plot provides valuable insights to geochemical and cosmochemical processes in which the relationship of O-17/O-16 relative to O-18/O-16 is of interest. It is generally recognized, however, that the usual format of this diagram, illustrating the variation of delta-O-17 with delta-O-18, is based on the approximation of a power law function to linear format. In contrast, the relationship between delta-O-17 and delta-O-18 for entity a measured with respect to reference b is accurately represented by the linear function: 1000ln(1 + delta-O-17/1000) = lambda x 1000ln(1 + delta-O-18/1000) + 1000ln, where k(a,b) is a measure of the offset (if any) of a from the mass-dependent fractionation line, of slope lambda, on which b lies. The respective ordinate and abscissa scales are essentially unchanged from those of the corresponding delta-O-17 versus delta-O-18 plot, yet, unlike the latter, the slope of the fractionation line is invariant to both the magnitude of the delta values and to the isotopic composition of the reference. Application to high precision measurements which encompass a wide range of delta values reveals that slope differences (or indeed similarities) between comparable data sets may be disguised by the limitations of the deltaO-17 versus delta-O-18 diagram, with adverse consequences for the accurate quantification of Delta-O-17 values. This may be addressed by re-defining Delta-O-17, the offset from a reference fractionation line, as 1000k(a,b). In turn, this is very closely approximated by 1000ln, the intercept on the ordinate axis of a 1000ln versus 1000ln plot, for values of 1000k(a,b) not exceeding about 5. The same analysis shows that the fractionation factor alpha(17/16) for a given system is related to the corresponding alpha(18/16) value by: alpha(17/16) = (alpha(18/16)) exp lamba. These findings are equally applicable to the reporting of data from other three-isotope systems, such as magnesium. (Author)