Theory and Utility of the Three Isotope Fractionation Relationship

The field of isotope geochemistry began with the study of oxygen isotope geothermometry, most famously for carbonates. Traditionally oxygen isotope studies are only concerned with the relationship between one rare isotope, oxygen-18, and the common isotope, oxygen-16. In these cases, the abundance of the third stable isotope, oxygen-17 is ignored because for almost all terrestrial processes the 17O-16O relationship roughly scales with the 18O-16O relationship through a fractionation processes and is thought to not provide any new information. However, the discovery of large “mass independent” isotope effects for ozone chemistry has driven a multitude of uses for triple isotope relationships. Triple stable isotope relationships have found uses including, but not limited to, in geochemistry to determine ancient atmospheric pCO2, atmospheric chemistry to understand the details of ozone cycling, and biochemistry to study enzymatic pathways. These uses rely on a component of “mass-independent” isotope fractionation, previously described by deviation from a “canonical” range of mass-fractionation exponent values. However, recent advances in analytical techniques and precision have allowed for the measurement of small mass dependent variations in three isotope composition that hold information not present in the two isotope composition. The purpose of this work is to re-investigate the generic theoretical boundaries of mass-dependent variations in three isotope composition through fractionation processes and to demonstrate the utility of mass-dependent isotope fractionation. In the first study presented here, the boundaries and behaviors of mass-dependent isotope fractionation are investigated from a theoretical perspective. Previous approximations to the statistical-mechanical models for predicting isotope effects have led to the notion that mass fractionation laws are constant, and later, constrained to a “canonical” range of possible values. Despite previous work indicating that these mass fractionation exponents can be highly variable, the concept of a constant relationship remains common. In the first study presented here, it is demonstrated generically that the mass fractionation exponent, θ, can take any value for small fractionations, that these deviations are measurable and that the half-reaction mass fractionation exponent, κ, is bounded by upper and lower limits to a close approximation. In addition, we characterize and advocate the use of ∆∆‡M or “change/difference in cap-delta” as a necessary and more reliable descriptor of multiple isotope fractionation relationships. Deviations from the “canonical” range are demonstrated by experimental data in the geochemically relevant hematite-water system. The results of this work are valid for any element where nuclear volume effects are not significant. In the second