Non-ideal mixing in the phlogopite-annite binary: constraints from experimental data on Mg−Fe partitioning and a reformulation of the biotite-garnet geothermometer

Abstract

The existing experimental data [Ferry and Spear 1978; Perchuk and Lavrent'eva 1983] on Mg−Fe partitioning between garnet and biotite are disparate. The underlying assumption of ideal Mg−Fe exchange between the minerals has been examined on the basis of recently available thermochemical data. Using the updated mixing parameters for the pyrope-almandine asymmetric regular solution as inputs [Ganguly and Saxena 1984; Hackler and Wood 1984], thermodynamic analysis points to non-ideal mixing in the phlogopite-annite binary in the temperature range of 550°C–950°C. The non-ideality can be approximated by a temperature-independent, one constant Margules parameter. The retrieved values for enthalpy of mixing for Mg−Fe biotites and the standard state enthalpy and entropy changes of the exchange reaction were combined with existing thermochemical data on grossular-pyrope and grossular-almandine binaries to obtain geothermometric expressions for Mg−Fe fractionation between biotite and garnet. [T in K]

$$\begin{gathered} {\text{T(HW) = [20286 + 0}}{\text{.0193P - \{ 2080(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{)}}^{\text{2}} {\text{ - 6350(X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)}}^{\text{2}} \hfill \\ {\text{ - 13807(X}}_{{\text{Ca}}}^{{\text{Gt}}} {\text{)(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{) + 8540(X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{)(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{)}} \hfill \\ {\text{ + 4215(X}}_{{\text{Ca}}}^{{\text{Gt}}} {\text{)(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)\} + 4441}}{{{\text{(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} \mathord{\left/ {\vphantom {{{\text{(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} {{\text{[13}}{\text{.138}}}}} \right. \kern-\nulldelimiterspace} {{\text{[13}}{\text{.138}}}} \hfill \\ {\text{ + 8}}{\text{.3143 InK}}_{\text{D}} {\text{ + 6}}{\text{.276(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} )] \hfill \\ {\text{T(GS) = [13538 + 0}}{\text{.0193P - \{ 837(X}}_{{\text{Mg}}}^{{\text{Gt}}} )^{\text{2}} {\text{ - 10460(X}}_{{\text{Fe}}}^{{\text{Gt}}} )^2 \hfill \\ {\text{ - 13807(X}}_{{\text{Ca}}}^{{\text{Gt}}} )(1{\text{ - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{) + 19246(X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} ){\text{(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} ) \hfill \\ {\text{ }}{{{\text{ + 5649(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{\} + 7972(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} \mathord{\left/ {\vphantom {{{\text{ + 5649(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{\} + 7972(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} {{\text{[6}}{\text{.778}}}}} \right. \kern-\nulldelimiterspace} {{\text{[6}}{\text{.778}}}} \hfill \\ {\text{ + 8}}{\text{.3143InK}}_{\text{D}} {\text{ + 6}}{\text{.276(X}}_{{\text{Ca}}}^{{\text{Gt}}} )(1{\text{ - X}}_{{\text{Mn}}}^{{\text{Gt}}} )] \hfill \\ \end{gathered} $$

The reformulated geothermometer is an improvement over existing biotite-garnet geothermometers because it reconciles the experimental data sets on Fe−Mg partitioning between the two phases and is based on updated activity-composition relationship in Fe−Mg−Ca garnet solid solutions.