Thermodynamic Mixing Properties and Behavior of Grossular-Spessartine, (CaxMn1-x)3Al2Si3O12, Garnet Solid Solutions

Abstract:

The heat capacity, C_p, for nine synthetic solid-solution members of the grossular(Gr)-spessartine(Sp) binary was measured between 2 and 300 K using relaxation calorimetry and from 280 K to 764 K using DSC methods. All solid-solution garnets exhibit normal heat capacity behavior from 764 K down to low temperatures. Below 7 K, a heat-capacity anomaly, originating from a paramagnetic to antiferromagnetic phase transition related to an ordering of the electron spins of the Mn cation, is observed. This lambda-anomaly is sharp and pronounced for Mn-rich solid-solution members and it becomes more flattened and rounded with decreasing Mn concentration in the garnet. The corresponding Néel temperature decreases from 6.2 K in pure Sp to less than 2 K in Gr-rich garnets with X_Mn^grt < 0.5. The calorimetric entropy, S₂₉₈, at 298 K for all intermediate composition garnets shows a slight positive deviation from ideality, resulting in an excess calorimetric entropy, ΔS_ex,cal, of approximately 2 J/mol∙K. The vibrational and magnetic parts of the total calorimetric entropy, S_vib and S_mag, respectively, were separated using a single-parameter phonon dispersion model. A symmetric entropy interaction parameter of W_S,CaMn^grt = 3.8 ± 2.0 J/cation∙mol∙K is calculated for Ca-Mn mixing in the Gr-Sp binary based on garnets with X_Mn^grt ≥ 0.5. More Gr-rich garnets have impurity phases, complicating their exact C_p behavior and, thus, they were not used in this calculation.

A thermodynamic analysis of the published phase equilibrium experiments was also made using the calorimetrically derived W_S,CaMn^grt. The analysis yields a symmetric enthalpy interaction parameter of W_H,CaMn^grt = 3.2 ± 0.3 kJ/cation∙mol, giving a maximum excess enthalpy, ΔH_ex, of 0.8 kJ/cation∙mol for the Gr-Sp binary. ΔH_ex calculated from line broadening of IR powder spectra of the same studied Gr-Sp garnets agrees within error with that derived from the phase equilibrium and calorimetry results. ΔG_ex for Gr-Sp garnets is slightly positive at 500°C and becomes more negative with increasing temperatures. Its absolute values are small though and, thus, Ca-Mn mixing in garnet can be considered nearly ideal at most geologically relevant P-T conditions.