Theoretical calibration of the triple oxygen isotope thermometer

The field of isotope geochemistry began with the study of oxygen isotope geothermometry, most notably for carbonates. For traditional oxygen isotope geothermometry only the relationship between one rare isotope, oxygen-18, and the common isotope, oxygen-16, is used because for most terrestrial processes the 17O-16O relationship scales with the 18O-16O relationship and is thought to not grant any new information. However, theoretical analysis predicts a small temperature-dependence of the equilibrium triple oxygen isotope relationship and instrumentation and techniques now allow for high-precision determination of the oxygen isotope composition for all three oxygen isotopes for a variety of sample types. To set the groundwork for triple oxygen isotope geothermometry, here we present new calibrations based on statistical thermodynamics and density functional theory for both the traditional two isotope and the recently introduced triple isotope thermometer for pairs of quartz, calcite, dolomite, fluorapatite, hematite, magnetite and liquid water. The results compare well with previous studies on 18O/16O fractionation where theoretical and experimental data are available. Of the models given here, pairs of quartz, calcite, dolomite and fluorapatite with water, hematite or magnetite show promising temperature sensitivities as triple isotope thermometers with acceptable uncertainties for surface and low-T hydrothermal environments.