Computational study of the effect of pressure on the Ti-in-zircon geothermometer

Understanding how Ti partitions between the Si and Zr sites in zircon is crucial for developing the Ti-in-zircon geothermometer. Energies calculated using quantum-mechanical methods (VASP, CASTEP, Dmol³, Crystal) were used to compare the relative favorability of substitution into each site at pressures ranging from 0 to 10 GPa. The results of these quantum-mechanical calculations were used in Monte-Carlo calculations to derive the excess enthalpy of mixing (ΔH_excess), entropy of mixing (ΔS_excess), and free energy of mixing (ΔG_excess) for the binaries ZrSiO₄–ZrTiO₄ and ZrSiO₄–TiSiO₄ (assuming that all compositions have zircon structure) at temperatures ranging from 333 K to 3000 K, and estimates are made of the maximum amount of Ti that may be incorporated into each site as a function of temperature and pressure. The results are considered in thermodynamic reference to other oxides, such as SiO₂, ZrO₂, and TiO₂, that are involved in substitution reactions. At pressures below about 3.5 GPa, substitution into the Si site is more thermodynamically favorable and thus dominates, whereas at higher pressures, substitution into the Zr site becomes more important in zircon. The latter result suggests that the reaction TiO_2(rutile) + ZrSiO_4(zircon) → TiSiO_4(zircon) + ZrO_{2(baddeleyite)} becomes predominant for the substitution of Ti-in-zircon for ultra-high pressure assemblages. The molar volume of the theoretical zirconstructured compound ZrTiO₄ was calculated using quantum mechanics (VASP, CASTEP, Dmol³) and determined to be 44.21 ± 0.45 cm³/mol. The resulting ΔV for the reaction ZrSiO_4(zircon) + TiO_2(rutile) = ZrTiO_4(zircon) + SiO_2(quartz) is doubled. The Clapeyron slope (dP/dT) of the reaction is halved, and the pressure correction to the Ti-in-zircon thermometer is twice as large as a previous estimate.