Thermodynamic behaviour of grossular–andradite, Ca₃(Al_x$Fe1-x3+$⁠)₂Si₃O₁₂, garnets: a calorimetric study

The thermodynamic behaviour of three synthetic, Ca₃(Al_0.25$Fe0.753+$⁠)₂Si₃O₁₂, Ca₃(Al_0.50$Fe0.503+$⁠)₂Si₃O₁₂ and Ca₃(Al_0.75$Fe0.253+$⁠)₂Si₃O₁₂ and three grossular-rich natural solid-solution garnets were investigated. Synthetic garnets were crystallized at high P and T in a piston-cylinder device. They were characterized by optical microscope examination and X-ray diffraction. The larger natural crystals of gem-like quality were characterized by optical microscope examination, microprobe analysis and IR spectroscopy. The heat capacity, C_p, behaviour of both types of garnets was measured using relaxation calorimetry between 2 K and 300 K and by Differential Scanning Calorimetry (DSC) between 143 K and 920 K and between 282 K and 764 K in two different labs. The low-temperature C_p results show a magnetic phase transition for all garnets that decreases in magnitude and sharpness with increasing grossular content in the solid solution. The Néel temperature decreases from 11.3 ± 0.1 K for end-member andradite to 3.0 ± 0.1 for the most andradite-poor composition Ca₃(Al_0.75$Fe0.253+$⁠)₂Si₃O₁₂. The vibrational and magnetic, C_vib and C_mag, contributions to the measured C_p at T < 300 K, were separated by applying a single-parameter phonon dispersion model. The results were used to calculate the vibrational entropy, S_vib, and the magnetic entropy, S_mag, at 298.15 K. The sum of both gives the calorimetric entropy, S_cal, at 298.15 K, whereby “calorimetric” means that any configurational entropy contribution is excluded. An analysis of the results shows linear shifts in S_vib and S_mag as a function of composition across the And-Gro binary join indicating ideal thermodynamic mixing behaviour for Ca₃(Al_x$Fe1-x3+$⁠)₂Si₃O₁₂ garnets. There are no measurable calorimetric, vibrational and magnetic excess entropies of mixing and, thus, ΔS_vib,ex ≈ 0 and ΔS_mag,ex ≈ 0 and ΔS_cal,ex ≈ 0. A revised value for the standard enthalpy of formation, ΔH°_f, of andradite from the elements was calculated using the recently published S° calorimetric value of 325.0 ± 2.0 J K⁻¹ mol⁻¹ for andradite and published phase-equilibrium results on three andradite-bearing reactions. The resulting value is ΔH°_f = −5763.3 ± 1.5 kJ mol⁻¹. The effect of using the recent thermodynamic data for andradite is examined and discussed by calculating several reactions relevant to the formation of skarn and by constructing a phase diagram for a calc-pelite containing the assemblage grossular-almandine-andradite garnet, epidote, clinopyroxene, calcite, plagioclase and quartz.