The statistical mechanical basis of the triple isotope fractionation relationship

Abstract

Multiple stable isotope relationships have found a growing variety of uses in geochemistry and cosmochemistry. Approximations to the statistical-mechanical models for predicting isotope effects have led to the notion that mass fractionation laws are 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 this study, we demonstrate generically that the mass fractionation exponent, θ, can take any value for small fractionations and that these deviations are measurable. In addition, we characterise and advocate the use of the 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 haematite-water system.