NONIDEAL MIXING IN THE PHLOGOPITE-ANNITE BINARY - CONSTRAINTS FROM EXPERIMENTAL-DATA ON MG-FE PARTITIONING AND A REFORMULATION OF THE BIOTITE GARNET GEOTHERMOMETER

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-degrees-C-950-degrees-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] T(HW) = [20286 + 0.0193P - {2080(X(Mg)Gt)2 - 6350(X(Fe)Gt)2 - 13807(X(Ca)Gt)(1 - X(Mn)Gt) + 8540(X(Fe)Gt)(X(Mg)Gt)(1 - X(Mn)Gt) + 4215(X(Ca)Gt)(X(Mg)Gt - X(Fe)Gt)} + 4441(2X(Mg)Bt - 1)]/[13.138 + 8.3143 InK(D) + 6.276(X(Ca)Gt)(1 - X(mn)Gt)] T(GS) = [13538 + 0.0193 P - {837(X(Mg)Gt)2 - 10460(X(Fe)Gt)2 - 13807(X(Ca)Gt)(1 - X(Mn)Gt) + 19246(X(Fe)Gt)(X(Mg)Gt)(1 - X)Mn)Gt) + 5649(X(Ca)Gt)(X(Mg)Gt - X(Fe)Gt)} + 7972(2X(Mg)Bt - 1)]/[6.778 + 8.3143 InK(D) + 6.276(X(Ca)Gt)(1 - X(Mn)Gt)] 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.