New thermodynamic models and revised calibrations for the Ti-in-zircon and Zr-in-rutile thermometers

Abstract

The models recognize that ZrSiO₄, ZrTiO₄,  and TiSiO₄, but not ZrO₂ or TiO₂, are independently variable phase components in zircon. Accordingly, the equilibrium controlling the Zr content of rutile coexisting with zircon is ZrSiO₄ = ZrO₂ (in rutile) +  SiO₂. The equilibrium controlling the Ti content of zircon is either ZrSiO₄ + TiO₂ = ZrTiO₄ + SiO₂ or TiO₂ + SiO₂ = TiSiO₄, depending whether Ti substitutes for Si or Zr. The Zr content of rutile thus depends on the activity of SiO₂ $(a_{\text{SiO}_{2}})$ as well as T, and the Ti content of zircon depends on $a_{\text{SiO}_{2}}$ and $a_{\text{TiO}_{2}}$ as well as T. New and published experimental data confirm the predicted increase in the Zr content of rutile with decreasing $a_{\text{SiO}_{2}},$ and unequivocally demonstrate that the Ti content of zircon increases with decreasing $a_{\text{SiO}_{2}}$. The substitution of Ti in zircon therefore is primarily for Si. Assuming a constant effect of P, unit $a_{\text{ZrSiO}_{4}},$ and that $a_{\text{ZrO}_{2}}$ and $a_{\text{ZrTiO}_{4}}$ are proportional to ppm Zr in rutile and ppm Ti in zircon, [log(ppm Zr-in-rutile) + log$a_{\text{SiO}_{2}}$] = A₁ + B₁/T(K) and  [log(ppm Ti-in-zircon) + log$a_{\text{SiO}_{2}}$ − log$a_{\text{TiO}_{2}}$] = A₂ + B₂/T, where the A and B are constants. The constants were derived from published and new data from experiments with $a_{\text{SiO}_{2}}$ buffered by either quartz or zircon + zirconia, from experiments with $a_{\text{SiO}_{2}}$ defined by the Zr content of rutile, and from well-characterized natural samples. Results are A₁ = 7.420 ± 0.105;  B₁ = −4,530 ± 111;  A₂ = 5.711 ± 0.072;  B₂ = −4,800 ± 86 with activity referenced to α-quartz and rutile at P and T of interest. The zircon thermometer may now be applied to rocks without quartz and/or rutile, and the rutile thermometer applied to rocks without quartz, provided that $a_{\text{SiO}_{2}}$ and $a_{\text{TiO}_{2}}$ are estimated. Maximum uncertainties introduced to zircon and rutile thermometry by unconstrained $a_{\text{SiO}_{2}}$ and $a_{\text{TiO}_{2}}$ can be quantitatively assessed and are ≈60 to 70°C at 750°C. A preliminary assessment of the dependence of the two thermometers on P predicts that an uncertainty of ±1 GPa introduces an additional uncertainty at 750°C of ≈50°C for the Ti-in-zircon thermometer and of ≈70 to 80°C for the Zr-in-rutile thermometer.