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The heat capacity, Cp, 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 λ-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 2σ 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, ΔGex, 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, MnFe = 1221 ± 588 J/cation⋅mol are derived giving a maximum of Δ G ex ≈ 0.7 kJ/cation⋅mol at X Mn grt ≈ 0.6 . ΔHex 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. |
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