TitaniQ under pressure: the effect of pressure and temperature on the solubility of Ti in quartz

Abstract

Quartz and rutile were synthesized from silica-saturated aqueous fluids between 5 and 20 kbar and from 700 to 940°C in a piston-cylinder apparatus to explore the potential pressure effect on Ti solubility in quartz. A systematic decrease in Ti-in-quartz solubility occurs between 5 and 20 kbar. Titanium K-edge X-ray absorption near-edge structure (XANES) measurements demonstrate that Ti⁴⁺ substitutes for Si⁴⁺ on fourfold tetrahedral sites in quartz at all conditions studied. Molecular dynamic simulations support XANES measurements and demonstrate that Ti incorporation onto fourfold sites is favored over interstitial solubility mechanisms. To account for the P–T dependence of Ti-in-quartz solubility, a least-squares method was used to fit Ti concentrations in quartz from all experiments to the simple expression

$$ RT\ln X_{{{\text{TiO}}_{ 2} }}^{\text{quartz}} = - 60952 + 1.520 \cdot T(K) - 1741 \cdot P(kbar) + RT\ln a_{{{\text{TiO}}_{ 2} }} $$

where R is the gas constant 8.3145 J/K, T is temperature in Kelvin, $X_{{{\text{TiO}}_{ 2} }}^{\text{quartz}}$ is the mole fraction of TiO₂ in quartz and $a_{{{\text{TiO}}_{ 2} }}$ is the activity of TiO₂ in the system. The P–T dependencies of Ti-in-quartz solubility can be used as a thermobarometer when used in combination with another thermobarometer in a coexisting mineral, an independent P or T estimate of quartz crystallization, or well-constrained phase equilibria. If temperature can be constrained within ±25°C, pressure can be constrained to approximately ±1.2 kbar. Alternatively, if pressure can be constrained to within ±1 kbar, then temperature can be constrained to approximately ±20°C.

Appendix

The equation to convert Ti (ppm) to mole fraction TiO₂ in quartz ($X_{{{\text{TiO}}_{ 2} }}^{\text{quartz}}$) is

$$ X_{{{\text{TiO}}_{ 2} }}^{\text{quartz}} = {\frac{{{\frac{\text{Ti(ppm)}}{1E4 \times 0.599 \times 79.87}}}}{{{\frac{\text{Ti(ppm)}}{1E4 \times 0.599 \times 79.87}} + \left[ {\left( {100 - {\frac{\text{Ti(ppm)}}{1E4 \times 0.599 \times 79.87}}} \right) \times {\frac{1}{60.09}}} \right]}}}. $$

The equation to convert Zr (ppm) to mole fraction ZrO₂ in rutile ($X_{{{\text{ZrO}}_{ 2} }}^{\text{rutile}}$) is

$$ X_{{{\text{ZrO}}_{ 2} }}^{\text{rutile}} = {\frac{{{\frac{\text{Zr(ppm)}}{1E4 \times 0.74 \times 123.22}}}}{{{\frac{\text{Zr(ppm)}}{1E4 \times 0.74 \times 123.22}} + \left[ {\left( {100 - {\frac{\text{Zr(ppm)}}{1E4 \times 0.74 \times 123.22}}} \right) \times {\frac{1}{79.87}}} \right]}}}. $$

The equation to convert Zr (ppm) to mole fraction ZrO₂ in sphene ($X_{{{\text{ZrO}}_{ 2} }}^{\text{sphene}}$) is

$$ X_{{{\text{ZrO}}_{ 2} }}^{\text{sphene}} = {\frac{{{\frac{\text{Zr(ppm)}}{1E4 \times 0.74 \times 123.22}}}}{{{\frac{\text{Zr(ppm)}}{1E4 \times 0.74 \times 123.22}} + \left[ {\left( {100 - {\frac{\text{Zr(ppm)}}{1E4 \times 0.74 \times 123.22}}} \right) \times {\frac{1}{196.03}}} \right]}}}. $$