Unbiased isotope equilibrium factors from partial isotope exchange experiments in 3-exchange site systems

Two methods are available in order to evaluate the equilibrium isotope fractionation factors between exchange sites or phases from partial isotope exchange experiments. The first one developed by Northrop and Clayton (1966) is designed for isotope exchanges between two exchange sites (hereafter, the N&C method), the second one from Zheng et al. (1994) is a refinement of the first one to account for a third isotope exchanging site (hereafter, the Z method).In this paper, we use a simple model of isotope kinetic exchange for a 3-exchange site system (such as hydroxysilicates where oxygen occurs as OH and non-OH groups like in muscovite, chlorite, serpentine, or water or calcite) to explore the behavior of the N&C and Z methods. We show that these two methods lead to significant biases that cannot be detected with the usual graphical tests proposed by the authors.Our model shows that biases originate because isotopes are fractionated between all these exchanging sites. Actually, we point out that the variable mobility (or exchangeability) of isotopes in and between the exchange sites only controls the amplitude of the bias, but is not essential to the production of this bias as previously suggested. Setting a priori two of the three exchange sites at isotopic equilibrium remove the bias and thus is required for future partial exchange experiments to produce accurate and unbiased extrapolated equilibrium fractionation factors.Our modeling applied to published partial oxygen isotope exchange experiments for 3-exchange site systems (the muscovite-calcite (Chacko et al., 1996), the chlorite-water (Cole and Ripley, 1998) and the serpentine-water (Saccocia et al., 2009)) shows that the extrapolated equilibrium fractionation factors (reported as 1000 ln(α)) using either the N&C or the Z methods lead to bias that may reach several δ per mil in a few cases. These problematic cases, may be because experiments were conducted at low temperature and did not reach high exchange percentages (<50%) such as the chlorite-water and the serpentine-water experiments.