Thermodynamics of the amphiboles: Fe-Mg cummingtonite solid solution

A thermodynamic solution model for the ferromagnesian amphiboles is developed. The model accounts explicitly for intersite nonconvergent cation ordering of Fe²⁺ and Mg between octahedral M1, M2, M3, and M4 sites and intrasite interaction energies arising from size-mismatch of unlike cations. The model is formulated with 15 parameters: two standard-state contributions, three ordering energies involving the exchange of Fe²⁺ and Mg between the four crystallographically distinct sites, six reciprocal terms that describe the noncoplanarity of the Gibbs energy of mechanical mixing in composition-ordering space, and four regular-solution type parameters involving Fe²⁺-Mg interaction on each site. The model may be readily collapsed to approximations that distinguish cation ordering over only three sites (M13, M2, and M4) or two sites (M123 and M4), or that assume the absence of ordering (i.e., a macroscopic model), in which case the number of parameters decreases to 10, 6, and 3, respectively. The proposed model is calibrated for the ferromagnesian monoclinic amphiboles, under the assumptions of energetic equivalency of the M1 and M3 sites and the absence of excess volume or excess vibrational entropy, using the X-ray site occupancy data of Hirschmann et al. (1994) and the phase equilibrium data of Fonarev and Korolkov (1980). Reference-state thermodynamic quantities for magnesio-cummingtonite [Mg₇Si₈O₂₂(OH)₂] and grunerite [Fe₇Si₈O₂₂(OH)₂] are derived from previously published results. The calibrated model is internally consistent with the database of Berman (1988) and the work of Sack and Ghiorso (1989) on ferromagnesian orthopyroxene. Gibbs energy of mixing, enthalpy of mixing, and activity-composition relation plots are constructed from the calibration.