NEW THERMODYNAMIC ANALYSIS AND CALIBRATION OF THE TI-IN-ZIRCON AND ZR-IN-RUTILE GEOTHERMOMETERS

This new analysis recognizes that ZrSiO₄, ZrTiO₄, and TiSiO₄, but not ZrO₂ or TiO₂, are independently variable phase components in zircon (Zrn). Accordingly, the equilibrium controlling the Zr content of rutile (Rt) coexisting with Zrn is (1) ZrSiO₄ = ZrO₂ (Rt) + SiO₂; the equilibrium controlling the Ti content of Zrn is either (2) ZrSiO₄ + TiO₂ = ZrTiO₄ + SiO₂ or (3) TiO₂ + SiO₂ = TiSiO₄, depending on whether Ti substitutes for Si or Zr. The Zr content of Rt thus depends on the activity of SiO₂ (a_SiO2) as well as T; the Ti content of Zrn depends on a_SiO2 and a_TiO2 as well as T. The prediction from Eq. (1) that the Zr content of Rt should increase with decreasing a_SiO2 is confirmed by the lower Zr content of Rt saturated with quartz (Qtz) in Run QTi13 of [1], 1697±56 ppm, than that of Rt in Qtz-undersaturated Run 87a at the same P and T, 2411±176 ppm. A new experiment with Zrn + Rt + baddeleyite (Bd) at 1.0 GPa, 1050°C, and log(a_SiO2) = -0.538 crystallized Zrn with 368±28 ppm Ti compared to 108±23 ppm in Zrn in Qtz-saturated Run 66 of [1] at the same P and T. Results quantitatively confirm both the dependence of Ti in Zrn on a_SiO2 and the substitution of Ti for Si in Zrn specified by Eq. (2). Following [1] in neglecting the effect of P and assuming a_ZrTiO4 and a_ZrO2 are proportional to ppm Ti in Zrn and ppm Zr in Rt, log(ppm Zr in Rt) + log(a_SiO2) = A₁ + B₁/T(K) and log(ppm Ti in Zrn) + log(a_SiO2) - log(a_TiO2) = A₂ + B₂/T, where A and B are constants. The constants were derived from those experiments from [1] and 5 new experiments with a_SiO2 buffered by either Qtz or Zrn + Bd and from data for natural samples in [1] except the Labait harzburgite. Results are A₁ = 7.283; B₁ = -4405; A₂ = 5.564; B₂ = -4659 with activity referenced to α-Qtz and Rt. Data for almost all runs with unbuffered a_SiO2 in [1] are consistent with these best-fit values for A and B. T may now be calculated for rocks without Qtz and/or Rt provided that a_SiO2 and a_TiO2 are estimated. Thermometry of out-of-context Zrns must consider reduced a_SiO2 as well as reduced a_TiO2. For example, for Zrn with Ti content corresponding to 750°C in Qtz- and Rt-saturated rocks, T = 687°C if a_SiO2 = 0.5 and T = 822°C if a_TiO2 = 0.5 (the latter a plausible minimum for Zrn-saturated granitoid melts [1]). Because the effects of reduced a_SiO2 and a_TiO2 compensate, T = 750°C if a_SiO2 = a_TiO2 = 0.5.

[1] Watson et al. (2006) Contrib. Mineral. Petrol., v. 151, p. 413-433.