THEORETICAL CALIBRATION OF THE QUARTZ-WATER TRIPLE OXYGEN ISOTOPE THERMOMETER

Of the three stable isotopes of oxygen (¹⁶O, ¹⁷O, and ¹⁸O), only two (¹⁸O and ¹⁶O) have been widely used for isotope geothermometry. Ratios of ¹⁸O to ¹⁶O can be used to determine mineral formation temperatures provided two preconditions are met, namely, (1) growth occurred at equilibrium and (2) the isotopic composition of the source fluid is known. However, verifying these preconditions continues to be a challenge in the rock record. For most terrestrial processes (i.e. mass-dependent processes) the ¹⁷O-¹⁶O relationship scales with the ¹⁸O-¹⁶O relationship and is thought to grant little new information. However, theory predicts a small temperature-dependence of the equilibrium triple oxygen isotope composition that offers an independent constraint on mineral growth conditions. New advances in analytical precision have, for the first time, made these small variations useful. For example, if both the ¹⁸O/¹⁶O ratios and triple-isotope variations imply the same set of possible formation temperatures, then the mineral likely grew at equilibrium. Here, we present new theoretical triple-isotope geothermometer calibrations for the quartz-H₂O_(liq.) system based on statistical thermodynamics and density functional theory. The new theoretical results compare well with previous experimental results for ¹⁸O/¹⁶O and ¹⁷O/¹⁶O equilibrium fractionation where data is available. In addition, we report new isotopic analyses of the ~3.5Ga Buck Reef Chert which has previously been determined to be pristine and marine in origin. The measured oxygen isotope composition of the cherts are found to be incompatible with a seawater which has a modern-like oxygen isotope composition. Our results indicate that the seawater in which those cherts formed had a δ’¹⁸O value less than ‒9.8‰±0.3‰ and was cooler than 68±2°C. These values are consistent with previous results from coupled ¹⁸O/¹⁶O and D/H analyses of cherts in the same formation as well as previous modeling of seawater oxygen isotope compositions.