Equilibrium mass-dependent fractionation relationships for triple oxygen isotopes

Abstract

With a growing interest in small 17O-anomaly, there is a pressing need for the precise ratio, ln 17 α/ln 18 α, for a particular mass-dependent fractionation process (MDFP) (e.g., for an equilibrium isotope exchange reaction). This ratio (also denoted as “ θ”) can be determined experimentally, however, such efforts suffer from the demand of well-defined process or a set of processes in addition to high precision analytical capabilities. Here, we present a theoretical approach from which high-precision ratios for MDFPs can be obtained. This approach will complement and serve as a benchmark for experimental studies. We use oxygen isotope exchanges in equilibrium processes as an example. We propose that the ratio at equilibrium, θ E ≡ ln 17 α/ln 18 α, can be calculated through the equation below: θ a - b E = κ a + ( κ a - κ b ) ln 18 β b ln 18 α a - b where 18 β b is the fractionation factor between a compound “b” and the mono-atomic ideal reference material “O”, 18 α a−b is the fractionation factor between a and b and it equals to 18 β a/ 18 β b and κ is a new concept defined in this study as κ ≡ ln 17 β/ln 18 β. The relationship between θ and κ is similar to that between α and β. The advantages of using κ include the convenience in documenting a large number of θ values for MDFPs and in estimating any θ values using a small data set due to the fact that κ values are similar among O-bearing compounds with similar chemical groups. Frequency scaling factor, anharmonic corrections and clumped isotope effects are found insignificant to the κ value calculation. However, the employment of the rule of geometric mean (RGM) can significantly affect the κ value. There are only small differences in κ values among carbonates and the structural effect is smaller than that of chemical compositions. We provide κ values for most O-bearing compounds, and we argue that κ values for Mg-bearing and S-bearing compounds should be close to their high temperature limitation (i.e., 0.5210 for Mg and 0.5159 for S). We also provide θ values for CO 2(g)–water, quartz–water and calcite–water oxygen isotope exchange reactions at temperature from 0 to 100 °C.