A thermodynamic model for di-trioctahedral chlorite from experimental and natural data in the system MgO–FeO–Al₂O₃–SiO₂–H₂O: applications to P–T sections and geothermometry

Abstract

We present a new thermodynamic activity-composition model for di-trioctahedral chlorite in the system FeO–MgO–Al₂O₃–SiO₂–H₂O that is based on the Holland–Powell internally consistent thermodynamic data set. The model is formulated in terms of four linearly independent end-members, which are amesite, clinochlore, daphnite and sudoite. These account for the most important crystal-chemical substitutions in chlorite, the Fe–Mg, Tschermak and di-trioctahedral substitution. The ideal part of end-member activities is modeled with a mixing-on-site formalism, and non-ideality is described by a macroscopic symmetric (regular) formalism. The symmetric interaction parameters were calibrated using a set of 271 published chlorite analyses for which robust independent temperature estimates are available. In addition, adjustment of the standard state thermodynamic properties of sudoite was required to accurately reproduce experimental brackets involving sudoite. This new model was tested by calculating representative P–T sections for metasediments at low temperatures (<400 °C), in particular sudoite and chlorite bearing metapelites from Crete. Comparison between the calculated mineral assemblages and field data shows that the new model is able to predict the coexistence of chlorite and sudoite at low metamorphic temperatures. The predicted lower limit of the chloritoid stability field is also in better agreement with petrological observations. For practical applications to metamorphic and hydrothermal environments, two new semi-empirical chlorite geothermometers named Chl(1) and Chl(2) were calibrated based on the chlorite + quartz + water equilibrium (2 clinochlore + 3 sudoite = 4 amesite + 4 H₂O + 7 quartz). The Chl(1) thermometer requires knowledge of the (Fe³⁺/ΣFe) ratio in chlorite and predicts correct temperatures for a range of redox conditions. The Chl(2) geothermometer which assumes that all iron in chlorite is ferrous has been applied to partially recrystallized detrital chlorite from the Zone houillère in the French Western Alps.

Appendix: From structural formulae to composition variables

The calculation is based on a structural formula of chlorite (normalized on the basis of 14 oxygen atoms) where the concentrations of Si, Ti, Al, Fe²⁺, Fe³⁺, Mg, Na, Ca and K are known in atoms per formula unit (p.f.u.). From the structural formula, the composition variables x, y and z (Eqs. 6, 7 and 8, respectively) can be derived using the following approach: (1)

$$\begin{aligned} X^{\text{Fe}} & = {\text{Fe}}^{2 + } /\left( {{\text{Fe}}^{2 + } + {\text{Mg}}} \right) \\ x & = X^{\text{Fe}} \\ \end{aligned}$$

(2)

$$\begin{aligned} {\text{Al}}_{\text{IV}} & = 4{-}\left( {{\text{Si}} + {\text{Ti}}} \right) \\ {\text{Al}}_{\text{VI}} & = {\text{Al}}_{\text{total}} {-}{\text{Al}}_{\text{IV}} \\ R1 & = {\text{Na}} + {\text{K}}; \\ \square & = 1/2\;\left( {{\text{Al}}_{\text{VI}} {-}{\text{Al}}_{\text{IV}} + {\text{Fe}}^{3 + } {-}R1} \right) \\ z & = \square \\ \end{aligned}$$

(3)

$$\begin{aligned} {\text{Al}}^{\text{M4}} & = 1{-}{\text{Fe}}^{3 + } \\ {\text{Al}}^{\text{M23}} & = 2\square^{\text{M1}} \\ {\text{Al}}^{\text{M1}} & = {\text{Al}}_{\text{VI}} {-}\left( {{\text{Al}}^{\text{M23}} + {\text{Al}}^{\text{M4}} } \right) \\ y & = {\text{Al}}^{\text{M1}} \\ \end{aligned}$$