Mineral activity-composition relations and petrological calculations involving cation equipartition in multisite minerals: a logical inconsistency

Equipartition is an assumption that preserves the same relative fraction of the cations on each site, originally used just to distribute cations such as Fe and Mg over two or more sites during mineral recalculation. This approximation has been used in almost all thermometry and barometry applications in petrology involving pyroxene, amphibole, chlorite and biotite mica. It has also become the default approach used in deriving activity–composition relations in multisite minerals where details of element partitioning among the sites is unknown and therefore assumed to be random. It is shown that, where a third element, such as Al, resides on just one of the sites, equipartition introduces a serious logical and numerical inconsistency between the enthalpy and entropy of mixing. In particular, application of equipartition is demonstrated to be equivalent to treating the solution as one in which all cations reside on one type of site. For example, in the case of aluminous orthopyroxene the equipartition assumption implies that Fe, Mg and Al are distributed across two identical sites, and that end-members such as Mg-tschermak's pyroxene have enthalpies characterized by a totally disordered distribution of Mg and Al over the M2 and M1 sites. Clearly this is unsupportable, and solid solutions should be treated with appropriate thermodynamics for order–disorder. For phases where element partitioning data are unavailable, we offer a simple alternative strategy, using the ordering of Fe and Mg on M1 and M2 sites in biotite as an example