Equilibrium mass-dependent fractionation relationships for triple oxygen isotopes

With a growing interest in small O-17-anomaly, there is a pressing need for the precise ratio, ln(17)alpha/ln(18)alpha, for a particular mass-dependent fractionation process (MDFP) (e.g., for an equilibrium isotope exchange reaction). This ratio (also denoted as "theta") 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, theta(E) ln(17)alpha/ln(18)alpha, can be calculated through the equation below: theta(E)(a-b) = kappa(a) + (kappa(a) - kappa(b))ln(18)beta(b)/ln(18)alpha(a-b) where (18)beta(b) is the fractionation factor between a compound "b" and the mono-atomic ideal reference material "O", (18)alpha(a-b) is the fractionation factor between a and b and it equals to (18)beta(a)/(18)beta(b) and kappa is a new concept defined in this study as kappa ln(17)beta/ln(18)beta. The relationship between theta and kappa is similar to that between alpha and beta. The advantages of using kappa include the convenience in documenting a large number of theta values for MDFPs and in estimating any theta values using a small data set due to the fact that kappa 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 kappa value calculation. However, the employment of the rule of geometric mean (RGM) can significantly affect the kappa value. There are only small differences in kappa values among carbonates and the structural effect is smaller than that of chemical compositions. We provide kappa values for most O-bearing compounds, and we argue that kappa 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 theta values for CO2(g)-water, quartz-water and calcite-water oxygen isotope exchange reactions at temperature from 0 to 100 degrees C. (C) 2011 Elsevier Ltd. All rights reserved.