Heat capacities and entropies of mixing of pyrope-grossular (Mg₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂) garnet solid solutions: A low-temperature calorimetric and a thermodynamic investigation

Abstract

The low-temperature heat capacities for a series of synthetic garnets along the pyrope-grossular (Py-Gr) join were measured with the heat capacity option of the Physical Properties Measurement System (PPMS) produced by Quantum Design. The measurements were performed between 5 and 300 K on milligram-sized polycrystalline garnets that have been well characterized in previous studies. The CP measurements indicate positive excess heat capacities (ΔC_P^xs) for all solid-solution compositions at temperatures <50 K with a maximum value of 2.31 ± 0.18 J/(mol·K) for the composition Py₅₀Gr₅₀ at about 35 K. Pyrope-rich garnets (i.e., Py₉₀Gr₁₀ and Py₇₅Gr₂₅) have no or slightly positive ΔC_P^xs at higher temperatures, whereas grossular-rich garnets (i.e., Py₁₀Gr₉₀ and Py₂₅Gr₇₅) show negative ΔC_P^xs values in the temperature range between 50 and 150 K. At T > 150 K, ΔC_P^xs values scatter around zero for all compositions and the experimental error is too large to permit a clear determination of whether ΔCP xs is different from zero within 2σ uncertainty. Excess entropies (ΔS^xs) at 298.15 K, calculated from the CP data of the various solid-solution members, are asymmetric in nature with the largest positive deviations in pyrope-rich compositions. An asymmetric Margules mixing model was found to be inappropriate for modeling the ΔS^xs-X data and, thus, a two-parameter Redlich-Kister model was used to describe the excess entropy-composition relationships. Using this macroscopic mixing model for the excess entropy, a T-X diagram for Py-Gr garnets was calculated using different published values for the excess enthalpies of mixing. The effect of short range Ca-Mg order in the solid solution also was considered in the calculations. The calculations give a solvus for the pyrope-grossular join with a higher critical temperature in the range 850-1330 °C at XGr = 0.35 compared to previous thermodynamic models (T_crit < 600 °C) that use symmetric mixing models to describe the excess entropy. Unmixing of garnets in nature, as documented from occurrences in ultramafic diatremes may, therefore, have occurred at higher temperatures than previously thought. The atomistic and lattice-dynamic properties of Py-Gr garnets are reviewed and compared to the macroscopic C_P data. Published IR and Raman spectra are consistent with the occurrence of positive ΔC_P^xs values at low temperatures.