Heat capacities and entropies of mixing of pyrope-grossular (Mg (sub 3) Al (sub 2) Si (sub 3) O (sub 12) -Ca (sub 3) Al (sub 2) Si (sub 3) O (sub 12) ) garnet solid solutions; a low-temperature calorimetric and a thermodynamic investigation

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 C (sub P) measurements indicate positive excess heat capacities (Delta C (sub P) (super xs) ) for all solid-solution compositions at temperatures <50 K with a maximum value of 2.31+ or -0.18 J/(mol.K) for the composition Py (sub 50) Gr (sub 50) at about 35 K. Pyrope-rich garnets (i.e., Py (sub 90) Gr (sub 10) and Py (sub 75) Gr (sub 25) ) have no or slightly positive Delta C (sub P) (super xs) at higher temperatures, whereas grossular-rich garnets (i.e., Py (sub 10) Gr (sub 90) and Py (sub 25) Gr (sub 75) ) show negative Delta C (sub P) (super xs) values in the temperature range between 50 and 150 K. At T>150 K, Delta C (sub P) (super xs) values scatter around zero for all compositions and the experimental error is too large to permit a clear determination of whether Delta C (sub P) (super xs) is different from zero within 2sigma uncertainty. Excess entropies (Delta S (super xs) ) at 298.15 K, calculated from the C (sub P) 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 Delta S (super 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 degrees C at X (sub Gr) = 0.35 compared to previous thermodynamic models (T (sub crit) <600 degrees 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 (sub P) data. Published IR and Raman spectra are consistent with the occurrence of positive Delta C (sub P) (super xs) values at low temperatures.