Thermodynamic mixing properties and behavior of almandine-spessartine solid solutions

The heat capacity, C-p, of five solid-solution members of the almandine(Alm)-spessartine(Sps) binary, consisting of three synthetic polycrystalline and two natural single-crystal samples, was measured in the temperature range between 2 and 300 K using relaxation calorimetry and between 282 and 764 K using DSC methods. All garnets exhibit a lambda-type heat-capacity anomaly at low temperatures resulting from a paramagnetic to antiferromagnetic phase transition. The temperature of the magnetic transition in Fe-rich garnets occurs between those of the two end-members (i.e. 9.2 K for almandine and 6.2 K for spessartine), but lies at lower values between 3.5 and 4.5 K for more Sps-rich compositions with X-Mn(grt) > 0.5. The calorimetric entropy at 298 K shows mechanical-mixture behavior for Sps-rich garnets and a slight possible negative deviation from such behavior for Alm-rich compositions. At the 2 sigma level all data are, however, consistent with ideal mixing behavior and the Margules entropy interaction parameter, W-S,FeMn(grt), is zero for the Alm-Sps binary. Thermodynamic analysis of published high P and T phase-equilibrium Fe-Mn exchange experiments between garnet and ilmenite shows that the excess Gibbs free energy of mixing, Delta G(ex), for Fe-Mn in garnet is positive and asymmetric towards spessartine. Margules enthalpy interaction parameters of W-H,FeMn(grt) 4170 +/- 518 J/cation.mol and W-H,W-MnFe 1221 +/- 588 J/cation.mol are derived giving a maximum of Delta G(ex) approximate to 0.7 kJ/cation.mol at X-Mn(grt) approximate to 0.6. Delta H-ex obtained using autocorrelation analysis of published IR spectra of Alm-Sps solid solutions is in reasonable agreement with that derived from phase-equilibrium and calorimetry data. Previous diffraction and spectroscopic results on Alm-Sps garnets and quantum mechanical calculations made on almandine are used to interpret the macroscopic thermodynamic behavior from a microscopic basis. The relevance of the new garnet Fe-Mn mixing model for petrological calculations is demonstrated by incorporating it into the quaternary garnet mixing model of Berman (1990). Thus, better agreement for temperatures calculated using Fe-Mn garnet-ilmenite and Fe-Mg garnet-biotite geothermometry could be achieved. Temperatures calculated for Mn-poor and Mn-rich garnet-bearing assemblages, applying garnet-biotite thermometry, are in better agreement taking Fe-Mn mixing into account. (C) 2013 Elsevier Ltd. All rights reserved.