Titanium in phengite: a geobarometer for high temperature eclogites

Abstract

Phengite chemistry has been investigated in experiments on a natural SiO₂–TiO₂-saturated greywacke and a natural SiO₂–TiO₂–Al₂SiO₅-saturated pelite, at 1.5–8.0 GPa and 800–1,050°C. High Ti-contents (0.3–3.7 wt %), Ti-enrichment with temperature, and a strong inverse correlation of Ti-content with pressure are the important features of both experimental series. The changes in composition with pressure result from the Tschermak substitution (Si + R²⁺ = Al^IV + Al^VI) coupled with the substitution: Al^VI + Si = Ti + Al^IV. The latter exchange is best described using the end-member Ti-phengite (KMgTi[Si₃Al]O₁₀(OH)₂, TiP). In the rutile-quartz/coesite saturated experiments, the aluminoceladonite component increases with pressure while the muscovite, paragonite and Ti-phengite components decrease. A thermodynamic model combining data obtained in this and previous experimental studies are derived to use the equilibrium MgCel + Rt = TiP + Cs/Qz as a thermobarometer in felsic and basic rocks. Phengite, rutile and quartz/coesite are common phases in HT-(U)HP metamorphic rocks, and are often preserved from regression by entrapment in zircon or garnet, thus providing an opportunity to determine the T–P conditions of crystallization of these rocks. Two applications on natural examples (Sulu belt and Kokchetav massif) are presented and discussed. This study demonstrates that Ti is a significant constituent of phengites that could have significant effects on phase relationships and melting rates with decreasing P or increasing T in the continental crust.

Appendices

Appendix 1

Expression of the minimized function

$$ \begin{aligned} \left( {\int\limits_{{T_{\rm ref} }}^{{T_{2} }} {Cp_{\text{TiP}} {\text{d}}T} - T_{2} \left( {\int\limits_{{T_{\rm ref} }}^{{T_{2} }} {{\frac{{Cp_{\text{TiP}} }}{T}}{\text{d}}T} } \right)} \right) + & G_{{T_{2} ,P_{2} }}^{{{\text{Qz/Cs}}^\circ }} - G_{{T_{2} ,P_{2} }}^{{{\text{MgCel}}^\circ }} - G_{{T_{2} ,P_{2} }}^{{{\text{Rt}}^\circ }} + {\text{RT}}_{2} \ln {\frac{{a_{{_{\text{TiP}} }}^{id} }}{{a_{{_{\text{MgCel}} }}^{id} }}} - \left[ {\Upphi_{\text{Ms}} \cdot W_{{{\text{Ms}} - {\text{MgCel}}}}^{*} + \Upphi_{\text{Pa}} \cdot W_{{{\text{Pa}} - {\text{MgCel}}}}^{ *} + \Upphi_{\text{Prl}} \cdot W_{{{\text{Prl}} - {\text{MgCel}}}}^{*} } \right] \\ = & - \left[ {\Updelta H_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} - T_{2} \cdot {\text{S}}_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} + V_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} \cdot F_{{_{{T_{ 2} ,P_{ 2} }}^{\text{TiP}} }} } \right] \\ & - \left[ {\Upphi_{\text{Ms}}\cdot W_{{{\text{Ms}} - {\text{TiP}}}}^{*} + \Upphi_{\text{Pa}} \cdot W_{{{\text{Pa}} - {\text{TiP}}}}^{*} + \Upphi_{\text{Prl}} \cdot W_{{{\text{Prl}} - {\text{TiP}}}}^{*} + \left( {\Upphi_{\text{MgCel}} + \Upphi_{\text{FeCel}} - \Upphi_{\text{TiP}} } \right) \cdot W_{{{\text{MgCel}} - {\text{TiP}}}}^{*} } \right] \\ \end{aligned} $$

with

$$ V_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} \cdot F_{{_{{T_{2} ,P_{2} }}^{\text{TiP}} }} = \int\limits_{{P_{\text{ref}} }}^{{P_{2} }} {V_{\text{TiP}} {\text{d}}P} $$

and

$$ F_{{_{{T_{2} ,P_{2} }}^{\text{TiP}} }} = {\frac{{\left( {1 + a_{\text{TiP}}^{0} \left( {T_{2} - T_{\text{ref}} } \right) - 20a_{\text{TiP}}^{0} \left( {\sqrt {T_{2} } - \sqrt {T_{\text{ref}} } } \right)} \right)\kappa_{\text{TiP}} \left( {1 - 1.5 \times 10^{ - 4} \left( {T_{2} - T_{\text{ref}} } \right)} \right)}}{3}}\left[ {\left( {1 + {\frac{{4P_{2} }}{{\kappa_{\text{TiP}} \left( {1 - 1.5 \times 10^{ - 4} \left( {T_{2} - T_{\text{ref}} } \right)} \right)}}}} \right)^{{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 4}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$4$}}}} - 1} \right] $$

Right-hand side of the function: known values and left-hand side: unknown parameters $\Updelta H_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} ;\,S_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} ;\,V_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} ;\,W_{{{\text{Ms}} - {\text{TiP}}}} ;\,W_{{{\text{Pa}} - {\text{TiP}}}} ;\,W_{{{\text{Prl}} - {\text{TiP}}}} ;\,W_{{{\text{MgCel}} - {\text{TiP}}}}$ and input data (constraints)

$$ T_{2};\;P_{2};\;F_{{_{{T_{2} ,P_{2} }}^{\rm TiP} }};\;\left( {X_{\rm MgCel} + X_{\rm FeCel} - X_{\rm TiP} } \right);\;X_{\rm Ms};\;X_{\rm Pa} $$

Appendix 2

Molar thermodynamic parameters obtained at Fe³⁺ = 0%:

$$ \Updelta H_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} = - 5{,}863{,}800 \pm 4{,}000\;\left( {\text{J}} \right) $$

$$ S_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} = 322.3 \pm 3.7\;\left( {\text{J/K}} \right) $$

$$ V_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} = 14.700 \pm 0.037\;\left( {{\text{J}}/{\text{bar}}} \right) $$

$$ W_{{{\text{MgCel}} - {\text{TiP}}}} = W_{{{\text{FeCel}} - {\text{TiP}}}} = 12{,}500 \pm 2{,}000 $$

$$ W_{{{\text{Ms}} - {\text{TiP}}}} = 0\;\left( {{\text{J}}/{\text{mol}}} \right) $$

$$ W_{{{\text{Pa}} - {\text{TiP}}}} = 80{,}000 \pm 9{,}000\;\left( {{\text{J}}/{\text{mol}}} \right) $$

$$ W_{{{\text{Prl}} - {\text{TiP}}}} = 40{,}000 \pm 6{,}000\;\left( {{\text{J}}/{\text{mol}}} \right). $$

Molar thermodynamic parameters obtained at Fe³⁺ = 20%:

$$ \Updelta H_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} = - 5{,}862{,}950 \pm 4{,}000\;\left( {\text{J}} \right) $$

$$ S_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} = 323.0 \pm 3.7\;\left( {{\text{J}}/{\text{K}}} \right) $$

$$ V_{{_{{T_{\text{ref}} ,P_{\text{ref}} }}^{\text{TiP}} }} = 14.696 \pm 0.037\;\left( {{\text{J}}/{\text{bar}}} \right) $$

$$ W_{{{\text{MgCel}} - {\text{TiP}}}} = W_{{{\text{FeCel}} - {\text{TiP}}}} = 12{,}000 \pm 2{,}000\;\left( {{\text{J}}/{\text{mol}}} \right) $$

$$ W_{{{\text{Ms}} - {\text{TiP}}}} = 0\;\left( {{\text{J}}/{\text{mol}}} \right) $$

$$ W_{{{\text{Pa}} - {\text{TiP}}}} = 80{,}000 \pm 9{,}000\;\left( {{\text{J}}/{\text{mol}}} \right) $$

$$ W_{{{\text{Prl}} - {\text{TiP}}}} = 40{,}000 \pm 6{,}000\;\left( {{\text{J}}/{\text{mol}}} \right). $$