Thermodynamic mixing properties and behavior of grossular–spessartine, (CaxMn1−x)3Al2Si3O12, solid solutions

Abstract

The heat capacity, Cp, for nine synthetic solid-solution members of the grossular(Gr)–spessartine(Sp) binary was measured in the temperature range between 2 and 300K using relaxation calorimetry and from 280 to 764K using DSC methods. All solid-solution garnets exhibit normal heat capacity behavior from 764K down to low temperatures. Below 7K, 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 λ-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 peak(Néel)-temperature decreases from 6.2K in pure Sp to less than 2K in Gr-rich garnets with XMngrt<0.5. The calorimetric entropy, S298, at 298K for all intermediate composition garnets shows a slight positive deviation from ideality, resulting in an excess calorimetric entropy, ΔSex,cal, of approximately 2J/molK. The vibrational and magnetic parts of the total calorimetric entropy, Svib and Smag, respectively, were separated using the single-parameter phonon dispersion model of Komada and Westrum (1997). A symmetric entropy interaction parameter of WS,CaMngrt=3.8±2.0J/cationmolK is calculated for Ca–Mn mixing in the Gr–Sp binary based on garnets with XMngrt⩾0.5. More Gr-rich garnets have impurity phases, complicating their exact Cp behavior and, thus, they were not used in this calculation. Smag behavior was also determined for intermediate garnets where the λ-anomaly is well pronounced and measurable. A thermodynamic analysis of the displaced phase equilibrium experiments of Koziol (1990) and the exchange experiments of Gavrieli et al. (1996) was also made using the calorimetrically derived WS,CaMngrt. The analysis yields a symmetric enthalpy interaction parameter of WH,CaMngrt=3.2±0.3kJ/cationmol, giving a maximum excess enthalpy, ΔHex, of 0.8kJ/cationmol for the Gr–Sp binary. ΔHex calculated from line broadening of IR powder spectra of the same studied Gr–Sp garnets (Rodehorst et al., 2004) agrees within error with that derived from the phase equilibrium and calorimetry results. ΔGex 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.